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Values of Dirichlet L-functions at positive integers
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Numbers
$q$
$n$
$s$ 
$L(s,\chi)$
1
1
2:
1.644934066848226436472415166646025189218949901206798437735558229370007470403200873833628900619758705 + i * 0
comment: $\chi=1$, the trivial character: $L(s,1)=\zeta(s)$; $\zeta(2)=\pi^2/6$
equals: $\zeta(2)$
1
1
3:
1.202056903159594285399738161511449990764986292340498881792271555341838205786313090186455873609335258 + i * 0
comment: $\chi=1$, the trivial character: $L(s,1)=\zeta(s)$; $\zeta(3)$ is Apéry's constant
equals: $\zeta(3)$
3
2
1:
0.6045997880780726168646927525473852440946887493642468585232949784627077270421179612280416627373533896 + i * 0
equals: $\kappa_{-3}$
comment: $\chi=\left(\frac{-3}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{3\sqrt{3}}$
3
2
2:
0.7813024128964862968671874296240923563651343365452854202221000629668869846516182180928695708322098610 + i * 0
comment: $\chi=\left(\frac{-3}{\cdot}\right)$, odd
3
2
3:
0.8840238117500798567430579168710118077479461861176589347825874147491156670333231870163596364689553606 + i * 0
comment: $\chi=\left(\frac{-3}{\cdot}\right)$, odd; $L(3,\chi)=\frac{4\pi^3}{81\sqrt{3}}$
4
3
1:
0.7853981633974483096156608458198757210492923498437764552437361480769541015715522496570087063355292670 + i * 0
equals: $\kappa_{-4}$
comment: $\chi=\left(\frac{-4}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{4}$
4
3
2:
0.9159655941772190150546035149323841107741493742816721342664981196217630197762547694793565129261151062 + i * 0
comment: $\chi=\left(\frac{-4}{\cdot}\right)$, odd; $L(2,\chi)=G$, Catalan's constant
4
3
3:
0.9689461462593693804836348458469186000695402676839096154420168157439498411708033136739594072688401935 + i * 0
comment: $\chi=\left(\frac{-4}{\cdot}\right)$, odd; $L(3,\chi)=\frac{\pi^3}{32}$
5
2
1:
0.8648062659772099672311820658586233370382855569022839962132095739893327093411871296480402330159296621 + i * 0.2041530661383851461940023066482593028631653683642405897934536823902884403378877835797636449267669995
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=\frac{-3 + i}{5}$; $L(1,\chi)=\frac{\pi}{5}\left(\cot\frac{\pi}{5}+i\cot\frac{2\pi}{5}\right)$
5
2
2:
0.9587161227168831553919364293311785264159715307582960686724044479103954560598657095160051881214868845 + i * 0.1455658767850895904617045118119864537208051468890990138342266111925591477167064448634376460632286923
comment: $\chi$ of order $4$, odd
5
2
3:
0.9881916816240571937974695504152548525212407906586590782063499890018874828384309172587897645450388907 + i * 0.08910518834573959516382505339268229125210873564650226195554394466072483028332869287784249125669181611
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=\frac{12 - 6i}{5}$
5
3
1:
0.8648062659772099672311820658586233370382855569022839962132095739893327093411871296480402330159296621 + i * -0.2041530661383851461940023066482593028631653683642405897934536823902884403378877835797636449267669995
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=\frac{-3 - i}{5}$; $L(1,\chi)=\frac{\pi}{5}\left(\cot\frac{\pi}{5}-i\cot\frac{2\pi}{5}\right)$
5
3
2:
0.9587161227168831553919364293311785264159715307582960686724044479103954560598657095160051881214868845 + i * -0.1455658767850895904617045118119864537208051468890990138342266111925591477167064448634376460632286923
comment: $\chi$ of order $4$, odd
5
3
3:
0.9881916816240571937974695504152548525212407906586590782063499890018874828384309172587897645450388907 + i * -0.08910518834573959516382505339268229125210873564650226195554394466072483028332869287784249125669181611
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=\frac{12 + 6i}{5}$
5
4
1:
0.4304089409640040388894332329506054254245706825402896547570061039925612154611319613614902646972199554 + i * 0
equals: $\kappa_{5}$
comment: $\chi=\left(\frac{5}{\cdot}\right)$, even
5
4
2:
0.7062114032597409699310031757625640276602464718529468639421174021656776044383830076833745664105736044 + i * 0
comment: $\chi=\left(\frac{5}{\cdot}\right)$, even; $L(2,\chi)=\frac{4\pi^2}{25\sqrt{5}}$
5
4
3:
0.8548247666485430102356900835381376971383964649370052827307024993811238334126894281284209567187097874 + i * 0
comment: $\chi=\left(\frac{5}{\cdot}\right)$, even
7
2
1:
0.5377473805049041590659855539089882237539970005956541944557264437184502725541631358349468000375547280 + i * -0.1052975456307955586657977861125521741179323985473165515287080849095995906801199363272015839959009684
comment: $\chi$ of order $3$, even
7
2
2:
0.7992187436382862900891712952962168433325882911511189169129006078737567404883009170770244560689566909 + i * -0.1018472971194699401517354066759910170678244402375468754403633834811784257118893625447997504533345001
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=\frac{12 + 4\zeta_{3}}{7}$
7
2
3:
0.9124052208551546979186854041977896407597870267943094054909884117425605912230056932279262317109458047 + i * -0.06976362901709455799415333135521407886901102521939305093683286811165577592695251570067066350805186509
comment: $\chi$ of order $3$, even
7
3
1:
0.8042057293867806445360268023666598036217605342382118554333791474004493637537859976655480068491103626 + i * 0.3986666988188730901265280839094487432557319086589083359595970964464702887780559253886676257802838936
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=\frac{-6 + 4\zeta_{6}}{7}$
7
3
2:
0.9022470253012568614963623353077000995839122292625043305176308979285541679883957274255235371457413538 + i * 0.2325489812778949953298520414711347431396988741239204934546963217312706057006490793468454138908943983
comment: $\chi$ of order $6$, odd
7
3
3:
0.9490006574408565025765230736411776779286683661733928952574057686820808904451328248230648034515363787 + i * 0.1209345410055784494766555591459100133145577425344777295094338815165705273283446273523836756915376729
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=6 - 6\zeta_{6}$
7
4
1:
0.5377473805049041590659855539089882237539970005956541944557264437184502725541631358349468000375547280 + i * 0.1052975456307955586657977861125521741179323985473165515287080849095995906801199363272015839959009684
comment: $\chi$ of order $3$, even
7
4
2:
0.7992187436382862900891712952962168433325882911511189169129006078737567404883009170770244560689566909 + i * 0.1018472971194699401517354066759910170678244402375468754403633834811784257118893625447997504533345001
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=\frac{8 - 4\zeta_{3}}{7}$
7
4
3:
0.9124052208551546979186854041977896407597870267943094054909884117425605912230056932279262317109458047 + i * 0.06976362901709455799415333135521407886901102521939305093683286811165577592695251570067066350805186509
comment: $\chi$ of order $3$, even
7
5
1:
0.8042057293867806445360268023666598036217605342382118554333791474004493637537859976655480068491103626 + i * -0.3986666988188730901265280839094487432557319086589083359595970964464702887780559253886676257802838936
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=\frac{-2 - 4\zeta_{6}}{7}$
7
5
2:
0.9022470253012568614963623353077000995839122292625043305176308979285541679883957274255235371457413538 + i * -0.2325489812778949953298520414711347431396988741239204934546963217312706057006490793468454138908943983
comment: $\chi$ of order $6$, odd
7
5
3:
0.9490006574408565025765230736411776779286683661733928952574057686820808904451328248230648034515363787 + i * -0.1209345410055784494766555591459100133145577425344777295094338815165705273283446273523836756915376729
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=6\zeta_{6}$
7
6
1:
1.187410411723725948784625297949363029992334686165035757515202385858458890934071575482089999880522849 + i * 0
equals: $\kappa_{-7}$
comment: $\chi=\left(\frac{-7}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{\sqrt{7}}$
7
6
2:
1.151925470544491047101692397320549964797821404686566914083968636166124163454591547556677519062972125 + i * 0
comment: $\chi=\left(\frac{-7}{\cdot}\right)$, odd
7
6
3:
1.093343069429533571976579815007700234780192584832383646350230943243281069032362174340462292161044686 + i * 0
comment: $\chi=\left(\frac{-7}{\cdot}\right)$, odd; $L(3,\chi)=\frac{32\pi^3}{343\sqrt{7}}$
8
3
1:
1.110720734539591561753970247515173424653655422343922555771348901739108698274868477643831733691191309 + i * 0
equals: $\kappa_{-8}$
comment: $\chi=\left(\frac{-8}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{\sqrt{8}}$
8
3
2:
1.064734171043503370392827451461668889483099151774485124419874508063990171758643763666534250524453661 + i * 0
comment: $\chi=\left(\frac{-8}{\cdot}\right)$, odd
8
3
3:
1.027722585936858567879256618002255767210100318536997465331084755185257772468584968035107312600267742 + i * 0
comment: $\chi=\left(\frac{-8}{\cdot}\right)$, odd; $L(3,\chi)=\frac{3\pi^3}{32\sqrt{8}}$
8
5
1:
0.6232252401402305133940200802505680026506953123465672528987147760961700045470141804676690732356266281 + i * 0
equals: $\kappa_{8}$
comment: $\chi=\left(\frac{8}{\cdot}\right)$, even
8
5
2:
0.8723580249548599417696951170211756612399832838685052957691870834399884703541346518334251671638514296 + i * 0
comment: $\chi=\left(\frac{8}{\cdot}\right)$, even; $L(2,\chi)=\frac{\pi^2}{4\sqrt{8}}$
8
5
3:
0.9583804545630945620516694028615778188248953179397753407575045070470756974842979364782526997775137298 + i * 0
comment: $\chi=\left(\frac{8}{\cdot}\right)$, even
9
2
1:
1.136275918771377728679468583789272497482927996780805380894164349974525313035288483602065737192404879 + i * 0.4135706123462626771331269175697160776580850803955416103716183384163395355392375387092734777108554223
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=\frac{-4 + 2\zeta_{6}}{3}$
9
2
2:
1.099240737729187192074775942304666082693574831337946974294953859256939474612515537228035330254668130 + i * 0.2245063353368379665606996873638313601836403427507306609953947351623586462269502938932223229843431929
comment: $\chi$ of order $6$, odd
9
2
3:
1.056444495359249782902771432694724862286736876422862303140983257935152035322826247730994795894883220 + i * 0.1129407665111272913358083493510074913934212863715026589386913297906069817484709945218248704567420806
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=14 - 10\zeta_{6}$
9
4
1:
0.5894898173762609042578946555850289413301737198995939648225562304057914076149474461493215642828925979 + i * 0.1730977885063472899437610442623229838945225260003533552117853143647498316745352886176496340687750533
comment: $\chi$ of order $3$, even
9
4
2:
0.8313555571860201262728120067716752244520983858832075334995892877163340608179462951925811351820725581 + i * 0.1465904152938145198517409130592519071591652554567159470506611884482157371617306503497487786604081787
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=\frac{4 - 4\zeta_{3}}{3}$
9
4
3:
0.9265043945679737268855629813210480071301160071280214022764455699996594808693146135430172574015094737 + i * 0.09048467928895974683351272231483601266444775135674972837014883967842808680754787631801473004727012665
comment: $\chi$ of order $3$, even
9
5
1:
1.136275918771377728679468583789272497482927996780805380894164349974525313035288483602065737192404879 + i * -0.4135706123462626771331269175697160776580850803955416103716183384163395355392375387092734777108554223
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=\frac{-2 - 2\zeta_{6}}{3}$
9
5
2:
1.099240737729187192074775942304666082693574831337946974294953859256939474612515537228035330254668130 + i * -0.2245063353368379665606996873638313601836403427507306609953947351623586462269502938932223229843431929
comment: $\chi$ of order $6$, odd
9
5
3:
1.056444495359249782902771432694724862286736876422862303140983257935152035322826247730994795894883220 + i * -0.1129407665111272913358083493510074913934212863715026589386913297906069817484709945218248704567420806
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=4 + 10\zeta_{6}$
9
7
1:
0.5894898173762609042578946555850289413301737198995939648225562304057914076149474461493215642828925979 + i * -0.1730977885063472899437610442623229838945225260003533552117853143647498316745352886176496340687750533
comment: $\chi$ of order $3$, even
9
7
2:
0.8313555571860201262728120067716752244520983858832075334995892877163340608179462951925811351820725581 + i * -0.1465904152938145198517409130592519071591652554567159470506611884482157371617306503497487786604081787
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=\frac{8 + 4\zeta_{3}}{3}$
9
7
3:
0.9265043945679737268855629813210480071301160071280214022764455699996594808693146135430172574015094737 + i * -0.09048467928895974683351272231483601266444775135674972837014883967842808680754787631801473004727012665
comment: $\chi$ of order $3$, even
11
2
1:
1.415747663426981506281930765466415384688813632919226711010651229919861020003262418231022831930122930 + i * 0.1740328837199926974855235554517685345182673809821300046365230764956927554356378868643278774386967420
comment: $\chi$ of order $10$, odd; $B_{1,\bar\chi}=\frac{-16 + 8\zeta_{10} - 12\zeta_{10}^{2} + 10\zeta_{10}^{3}}{11}$
11
2
2:
1.226098585061606423910019835064639492218117853154747920786425625319778545545995515770983647026120814 + i * 0.09794327555369501394097411130959497326271012469243014709428363098411861438795919133945849296972086911
comment: $\chi$ of order $10$, odd
11
2
3:
1.112003125629970407627613787073627803082446578996328900675195967461770655841323902135642577907987387 + i * 0.05351953374912626513736120163760186428914262286986715209505537449097109114917439068667991211839618376
comment: $\chi$ of order $10$, odd; $B_{3,\bar\chi}=\frac{216 - 156\zeta_{10} + 246\zeta_{10}^{2} - 210\zeta_{10}^{3}}{11}$
11
3
1:
0.7250693190175078244375447578535220920408443990664627657980523346884472798148734117122213835725399754 + i * -0.1998680382283386338794634586907782344133050712512115390978210433514496181828438364642283683459320608
comment: $\chi$ of order $5$, even
11
3
2:
0.9443115800575722477061633431214443938129867410088824362259859972689056019260665209289149479812492080 + i * -0.1602243320474826918365181023547362007010257580496378605265851006682570915332516109247718482290230354
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=\frac{40 + 24\zeta_{5} + 4\zeta_{5}^{2} + 12\zeta_{5}^{3}}{11}$
11
3
3:
0.9976416722651488631352589260806498379731717021947787946563666731326483145680518468412351617193185390 + i * -0.09626536408815421043574063325934752361804478702325892962127616053797457166041898260388425561966849030
comment: $\chi$ of order $5$, even
11
4
1:
0.7250693190175078244375447578535220920408443990664627657980523346884472798148734117122213835725399754 + i * 0.1998680382283386338794634586907782344133050712512115390978210433514496181828438364642283683459320608
comment: $\chi$ of order $5$, even
11
4
2:
0.9443115800575722477061633431214443938129867410088824362259859972689056019260665209289149479812492080 + i * 0.1602243320474826918365181023547362007010257580496378605265851006682570915332516109247718482290230354
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=\frac{16 - 24\zeta_{5} - 12\zeta_{5}^{2} - 20\zeta_{5}^{3}}{11}$
11
4
3:
0.9976416722651488631352589260806498379731717021947787946563666731326483145680518468412351617193185390 + i * 0.09626536408815421043574063325934752361804478702325892962127616053797457166041898260388425561966849030
comment: $\chi$ of order $5$, even
11
5
1:
0.5805311136890726388264455316628209198560998930755964697910568180209602962710266558433978332761888679 + i * 0.2129383511836631666507311628154543866653188836568833929520617709340816444497176770105330962981125658
comment: $\chi$ of order $5$, even
11
5
2:
0.8091145011157223538864395760426929530521546904365064886116587515070032993454561324628090413686572529 + i * 0.1571585304712366343198558401473264298501960155513218555680582769848728543738522117238224988184925520
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=\frac{28 - 8\zeta_{5} - 12\zeta_{5}^{2} + 12\zeta_{5}^{3}}{11}$
11
5
3:
0.9064941497181457490698895236542400281006145406368177442309415112522786872231981466167263207698951488 + i * 0.08643394617385632924894074325592189980695271949808015926136295002407137979570500056783449822223293238
comment: $\chi$ of order $5$, even
11
6
1:
1.415747663426981506281930765466415384688813632919226711010651229919861020003262418231022831930122930 + i * -0.1740328837199926974855235554517685345182673809821300046365230764956927554356378868643278774386967420
comment: $\chi$ of order $10$, odd; $B_{1,\bar\chi}=\frac{-8 - 8\zeta_{10} - 2\zeta_{10}^{2} + 4\zeta_{10}^{3}}{11}$
11
6
2:
1.226098585061606423910019835064639492218117853154747920786425625319778545545995515770983647026120814 + i * -0.09794327555369501394097411130959497326271012469243014709428363098411861438795919133945849296972086911
comment: $\chi$ of order $10$, odd
11
6
3:
1.112003125629970407627613787073627803082446578996328900675195967461770655841323902135642577907987387 + i * -0.05351953374912626513736120163760186428914262286986715209505537449097109114917439068667991211839618376
comment: $\chi$ of order $10$, odd; $B_{3,\bar\chi}=\frac{60 + 156\zeta_{10} + 54\zeta_{10}^{2} - 90\zeta_{10}^{3}}{11}$
11
7
1:
0.5422944263230440743489744920882666612836058586057517428337813467564537830690313045694786853325164238 + i * -0.5305008734666658120314404899983612968079205595720561956995774359125623477467137744443782376048837220
comment: $\chi$ of order $10$, odd; $B_{1,\bar\chi}=\frac{-4 - 2\zeta_{10} + 4\zeta_{10}^{2} - 12\zeta_{10}^{3}}{11}$
11
7
2:
0.8099702912341097786033931087222376618700613909947531939587018079614494423789521017640297353613112718 + i * -0.2748683812569493376978081223447484063669565956588410014634530906865055441673826016358689211372968007
comment: $\chi$ of order $10$, odd
11
7
3:
0.9232847091405262527511758290228031087600239679101625448966662170445837999800567827139151572659767938 + i * -0.1344118161498801398525938697451974561194501230192161861117910487308340839363419771558500568508870092
comment: $\chi$ of order $10$, odd; $B_{3,\bar\chi}=\frac{-30 + 36\zeta_{10} - 90\zeta_{10}^{2} + 246\zeta_{10}^{3}}{11}$
11
8
1:
0.5422944263230440743489744920882666612836058586057517428337813467564537830690313045694786853325164238 + i * 0.5305008734666658120314404899983612968079205595720561956995774359125623477467137744443782376048837220
comment: $\chi$ of order $10$, odd; $B_{1,\bar\chi}=\frac{-6 + 2\zeta_{10} + 10\zeta_{10}^{2} - 2\zeta_{10}^{3}}{11}$
11
8
2:
0.8099702912341097786033931087222376618700613909947531939587018079614494423789521017640297353613112718 + i * 0.2748683812569493376978081223447484063669565956588410014634530906865055441673826016358689211372968007
comment: $\chi$ of order $10$, odd
11
8
3:
0.9232847091405262527511758290228031087600239679101625448966662170445837999800567827139151572659767938 + i * 0.1344118161498801398525938697451974561194501230192161861117910487308340839363419771558500568508870092
comment: $\chi$ of order $10$, odd; $B_{3,\bar\chi}=\frac{6 - 36\zeta_{10} - 210\zeta_{10}^{2} + 54\zeta_{10}^{3}}{11}$
11
9
1:
0.5805311136890726388264455316628209198560998930755964697910568180209602962710266558433978332761888679 + i * -0.2129383511836631666507311628154543866653188836568833929520617709340816444497176770105330962981125658
comment: $\chi$ of order $5$, even
11
9
2:
0.8091145011157223538864395760426929530521546904365064886116587515070032993454561324628090413686572529 + i * -0.1571585304712366343198558401473264298501960155513218555680582769848728543738522117238224988184925520
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=\frac{36 + 8\zeta_{5} + 20\zeta_{5}^{2} - 4\zeta_{5}^{3}}{11}$
11
9
3:
0.9064941497181457490698895236542400281006145406368177442309415112522786872231981466167263207698951488 + i * -0.08643394617385632924894074325592189980695271949808015926136295002407137979570500056783449822223293238
comment: $\chi$ of order $5$, even
11
10
1:
0.9472258250994829364296343818169740666199880726617575060010800816767267330182590945148907202816771720 + i * 0
equals: $\kappa_{-11}$
comment: $\chi=\left(\frac{-11}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{\sqrt{11}}$
11
10
2:
0.9095391053238837015320859390586052692591856791824288975949313317735045883182516365260861518593109658 + i * 0
comment: $\chi=\left(\frac{-11}{\cdot}\right)$, odd
11
10
3:
0.9271481823696551249916271393598117731322913063525639152918236287473159388156308827587934260544242778 + i * 0
comment: $\chi=\left(\frac{-11}{\cdot}\right)$, odd; $L(3,\chi)=\frac{12\pi^3}{121\sqrt{11}}$
12
11
1:
0.7603459963009463475310942548804058242016277309471764270205706702600551226549107530284583647984873467 + i * 0
equals: $\kappa_{12}$
comment: $\chi=\left(\frac{12}{\cdot}\right)$, even
12
11
2:
0.9497031262940093952634984917457415158736519509096929448809176543683051955687928817260068032848353502 + i * 0
comment: $\chi=\left(\frac{12}{\cdot}\right)$, even; $L(2,\chi)=\frac{\pi^2}{3\sqrt{12}}$
12
11
3:
0.9900400194381599497918167768633040508568850676572361455536607003423520533671811677856022318535150635 + i * 0
comment: $\chi=\left(\frac{12}{\cdot}\right)$, even
13
2
1:
1.300817583412818563388677987165413471861507659555460627266020119617100472675894196115682919362761042 + i * 0.5339369191833621237936482585665960526646229646326988660198716008954398028442192598161328990922500523
comment: $\chi$ of order $12$, odd; $B_{1,\bar\chi}=\frac{-16 - 8\zeta_{12} + 12\zeta_{12}^{2} + 6\zeta_{12}^{3}}{13}$
13
2
2:
1.177734267637530603396625457253126509706619306683026516394485863756429160367938372345981019361743100 + i * 0.2361597903438248821439519852786552546864002454947121743319671521187133034583246717338936973988390873
comment: $\chi$ of order $12$, odd
13
2
3:
1.095168843565102468495013360012257920890009381513926190154724787053068704978956245533882405993673409 + i * 0.1008317969668706922521584112516940957824832097211651679552069040643637613615909985954609658257815692
comment: $\chi$ of order $12$, odd; $B_{3,\bar\chi}=24 + 12\zeta_{12} - 30\zeta_{12}^{2} - 6\zeta_{12}^{3}$
13
3
1:
0.5663299165427518957226651972801277076814201347089190876724302790669554219618699530622661843260866495 + i * 0.3150964447655262223512581413020643257718115532546669196454987836676982580332041738235589163937256442
comment: $\chi$ of order $3$, even
13
3
2:
0.8121434926455224842929416005500674191184504204677546056694493333303428109792720862230122407967882506 + i * 0.2232040770846173337732504389709349166884881102470156597146852040677035453748848251979005266937533082
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=-4\zeta_{3}$
13
3
3:
0.9164490831094432462064682676701334921289980994177786740725925325987589635496436073754324183415377377 + i * 0.1207106903241591235792946991991032026522823345296402612175513541139105129490097423026805497160622493
comment: $\chi$ of order $3$, even
13
4
1:
0.8231273762391330898120649155580381049601046898860396647847372557472037034505062048727618592685401187 + i * 0.1859280777963253944408840269010427250124954279181736376434364884152857599864668149159012921785119055
comment: $\chi$ of order $6$, even
13
4
2:
1.008216079823012879634499077982498649530280981327432908689750440453734095027174401899967462076020174 + i * 0.1425184235922118229191814253260590147494352457764446784771307705687999836501791038059643593931728971
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=\frac{72 - 28\zeta_{6}}{13}$
13
4
3:
1.029926885441876468169707595361332454874240523222660334935899373998547598184955963777220111071304076 + i * 0.08421325565302656149088225957417066323141288555471416188614538431342453379437173328925884512472049443
comment: $\chi$ of order $6$, even
13
5
1:
1.086429434114656679047564360367514172097037580752372835327044761927455426157156658174759330908598450 + i * -0.5814393878814690507969526240113440619049957566256923781886923553560899564611734662267650493026388159
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=-1 - i$
13
5
2:
1.049590362381417471904605237808205342674565550143426506286257964543744061354746834134426292424341300 + i * -0.2787023897766063867459001179687011713440208647734423389594750165036372075465524591601118647600070294
comment: $\chi$ of order $4$, odd
13
5
3:
1.021612864357409786875595667279757463652140331215022067137783680092624211632984083829734181788532993 + i * -0.1323708954153657707083207871620164167318679389355150933332731509879542505265235269566843437593726980
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=\frac{162 + 360i}{13}$
13
6
1:
0.5541243135162595856416800997136011945567993629275652833197807271519733466029032002971697843353222111 + i * -0.2274472859040164501837180958169971811638863632740140415819992547699090963130614892234475713505418660
comment: $\chi$ of order $12$, odd; $B_{1,\bar\chi}=\frac{-4 + 8\zeta_{12} - 12\zeta_{12}^{2} - 2\zeta_{12}^{3}}{13}$
13
6
2:
0.7660421338076222288902445571759048329730705166116660876202925156255131654330467973042569209409693986 + i * -0.03400940750026205350901745993054346319167227528267909018185620277719005790337242323762393814498992907
comment: $\chi$ of order $12$, odd
13
6
3:
0.8825233766370867729973463689597779747269545005864451890630826042383494218197958951883946666263322230 + i * 0.01317252810194530072026962706552613176965464113891531633088698599752653347940637025737171312004815547
comment: $\chi$ of order $12$, odd; $B_{3,\bar\chi}=-6 - 12\zeta_{12} + 30\zeta_{12}^{2} + 6\zeta_{12}^{3}$
13
7
1:
1.300817583412818563388677987165413471861507659555460627266020119617100472675894196115682919362761042 + i * -0.5339369191833621237936482585665960526646229646326988660198716008954398028442192598161328990922500523
comment: $\chi$ of order $12$, odd; $B_{1,\bar\chi}=\frac{-4 - 8\zeta_{12} - 12\zeta_{12}^{2} + 2\zeta_{12}^{3}}{13}$
13
7
2:
1.177734267637530603396625457253126509706619306683026516394485863756429160367938372345981019361743100 + i * -0.2361597903438248821439519852786552546864002454947121743319671521187133034583246717338936973988390873
comment: $\chi$ of order $12$, odd
13
7
3:
1.095168843565102468495013360012257920890009381513926190154724787053068704978956245533882405993673409 + i * -0.1008317969668706922521584112516940957824832097211651679552069040643637613615909985954609658257815692
comment: $\chi$ of order $12$, odd; $B_{3,\bar\chi}=-6 + 12\zeta_{12} + 30\zeta_{12}^{2} - 6\zeta_{12}^{3}$
13
8
1:
1.086429434114656679047564360367514172097037580752372835327044761927455426157156658174759330908598450 + i * 0.5814393878814690507969526240113440619049957566256923781886923553560899564611734662267650493026388159
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=-1 + i$
13
8
2:
1.049590362381417471904605237808205342674565550143426506286257964543744061354746834134426292424341300 + i * 0.2787023897766063867459001179687011713440208647734423389594750165036372075465524591601118647600070294
comment: $\chi$ of order $4$, odd
13
8
3:
1.021612864357409786875595667279757463652140331215022067137783680092624211632984083829734181788532993 + i * 0.1323708954153657707083207871620164167318679389355150933332731509879542505265235269566843437593726980
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=\frac{162 - 360i}{13}$
13
9
1:
0.5663299165427518957226651972801277076814201347089190876724302790669554219618699530622661843260866495 + i * -0.3150964447655262223512581413020643257718115532546669196454987836676982580332041738235589163937256442
comment: $\chi$ of order $3$, even
13
9
2:
0.8121434926455224842929416005500674191184504204677546056694493333303428109792720862230122407967882506 + i * -0.2232040770846173337732504389709349166884881102470156597146852040677035453748848251979005266937533082
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=4 + 4\zeta_{3}$
13
9
3:
0.9164490831094432462064682676701334921289980994177786740725925325987589635496436073754324183415377377 + i * -0.1207106903241591235792946991991032026522823345296402612175513541139105129490097423026805497160622493
comment: $\chi$ of order $3$, even
13
10
1:
0.8231273762391330898120649155580381049601046898860396647847372557472037034505062048727618592685401187 + i * -0.1859280777963253944408840269010427250124954279181736376434364884152857599864668149159012921785119055
comment: $\chi$ of order $6$, even
13
10
2:
1.008216079823012879634499077982498649530280981327432908689750440453734095027174401899967462076020174 + i * -0.1425184235922118229191814253260590147494352457764446784771307705687999836501791038059643593931728971
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=\frac{44 + 28\zeta_{6}}{13}$
13
10
3:
1.029926885441876468169707595361332454874240523222660334935899373998547598184955963777220111071304076 + i * -0.08421325565302656149088225957417066323141288555471416188614538431342453379437173328925884512472049443
comment: $\chi$ of order $6$, even
13
11
1:
0.5541243135162595856416800997136011945567993629275652833197807271519733466029032002971697843353222111 + i * 0.2274472859040164501837180958169971811638863632740140415819992547699090963130614892234475713505418660
comment: $\chi$ of order $12$, odd; $B_{1,\bar\chi}=\frac{-16 + 8\zeta_{12} + 12\zeta_{12}^{2} - 6\zeta_{12}^{3}}{13}$
13
11
2:
0.7660421338076222288902445571759048329730705166116660876202925156255131654330467973042569209409693986 + i * 0.03400940750026205350901745993054346319167227528267909018185620277719005790337242323762393814498992907
comment: $\chi$ of order $12$, odd
13
11
3:
0.8825233766370867729973463689597779747269545005864451890630826042383494218197958951883946666263322230 + i * -0.01317252810194530072026962706552613176965464113891531633088698599752653347940637025737171312004815547
comment: $\chi$ of order $12$, odd; $B_{3,\bar\chi}=24 - 12\zeta_{12} - 30\zeta_{12}^{2} + 6\zeta_{12}^{3}$
13
12
1:
0.6627353910718455897136965154768502617589474430137896226806516351046752231616931308479474581031511892 + i * 0
equals: $\kappa_{13}$
comment: $\chi=\left(\frac{13}{\cdot}\right)$, even
13
12
2:
0.8422571535307157189703844904162417019560170873606619045386034991728435854345704371711162588134284466 + i * 0
comment: $\chi=\left(\frac{13}{\cdot}\right)$, even; $L(2,\chi)=\frac{4\pi^2}{13\sqrt{13}}$
13
12
3:
0.9125079249256948580358484938645480317953745104545038163164485810913552008483344914140497895428558408 + i * 0
comment: $\chi=\left(\frac{13}{\cdot}\right)$, even
15
2
1:
0.7385666321629636268939183511642408411804347513123713270212456681381741147210274037509698200791830199 + i * -0.3168026445884791474347438856962515786235469676599699084598696998077449569346682110938661799442864483
comment: $\chi$ of order $4$, even
15
2
2:
0.9353234166396618373889480405658734684756581866845547694726199652103848422832909411471851708830483493 + i * -0.2207999072743181143632395711826459152189998127427647894271367964108039871596661795964040673615007966
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=4 + 4i$
15
2
3:
0.9840773240638181746284138064565950120992624152372370375732522706180074508048669508097603812978163234 + i * -0.1206660842002058758906376271291557797082911963290183696702878181868306913659744396034580641243575865
comment: $\chi$ of order $4$, even
15
8
1:
0.7385666321629636268939183511642408411804347513123713270212456681381741147210274037509698200791830199 + i * 0.3168026445884791474347438856962515786235469676599699084598696998077449569346682110938661799442864483
comment: $\chi$ of order $4$, even
15
8
2:
0.9353234166396618373889480405658734684756581866845547694726199652103848422832909411471851708830483493 + i * 0.2207999072743181143632395711826459152189998127427647894271367964108039871596661795964040673615007966
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=4 - 4i$
15
8
3:
0.9840773240638181746284138064565950120992624152372370375732522706180074508048669508097603812978163234 + i * 0.1206660842002058758906376271291557797082911963290183696702878181868306913659744396034580641243575865
comment: $\chi$ of order $4$, even
15
14
1:
1.622311470389444758781184308119175619982003625269461867120402245079614344366397470921835576774872864 + i * 0
equals: $\kappa_{-15}$
comment: $\chi=\left(\frac{-15}{\cdot}\right)$, odd; $L(1,\chi)=\frac{2\pi}{\sqrt{15}}$
15
14
2:
1.296618596633237733240236594378533682777371129159731529610532965465167614882246553948242368795224967 + i * 0
comment: $\chi=\left(\frac{-15}{\cdot}\right)$, odd
15
14
3:
1.138600705997753791112996484968748262262604502271349723087491701244874588276278352423851619792294776 + i * 0
comment: $\chi=\left(\frac{-15}{\cdot}\right)$, odd; $L(3,\chi)=\frac{32\pi^3}{225\sqrt{15}}$
16
3
1:
1.026172152977030888871467780872831974979621588195816119622549646668685031755632713418915336562048511 + i * -0.4250544230926846181573761562042291622879462387036991530599819365068143038192349444645002542921028168
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=-1 - i$
16
3
2:
1.007286437116433621803201800490117161856466729304580102306757404556595002137472866708933736446641868 + i * -0.1403444560709706362237921487264550709224103338075767310105638668857798746481525414626432369918918331
comment: $\chi$ of order $4$, odd
16
3
3:
1.001465009294563645990155106738104588837811609182994126619531027545994773761189239121961663293828240 + i * -0.04402075206444418752303266837715597246804306443129904784545210003842897816725976700600208277136848552
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=21 + 45i$
16
5
1:
0.8231312585740451584499694036915367795815756070517714708815629541318604610061037974871881352053274026 + i * -0.1227420153243526082320294273651569406066211042608664675703087151398775171118667522300687550074727560
comment: $\chi$ of order $4$, even
16
5
2:
0.9728722058982436487852957441828243005909287148281810609656472858481410400882787941088842441916715027 + i * -0.06913989889792627465263900286580713404065070504516429312580719510601628743700998950294268199648886722
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=6 + 2i$
16
5
3:
0.9961077217004656459327222070604678632364497984091720374867139469899705871207548344028965503659118937 + i * -0.02877140784999309963004926098308527397822576235626456979417901536443158533056662530305652303747116763
comment: $\chi$ of order $4$, even
16
11
1:
1.026172152977030888871467780872831974979621588195816119622549646668685031755632713418915336562048511 + i * 0.4250544230926846181573761562042291622879462387036991530599819365068143038192349444645002542921028168
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=-1 + i$
16
11
2:
1.007286437116433621803201800490117161856466729304580102306757404556595002137472866708933736446641868 + i * 0.1403444560709706362237921487264550709224103338075767310105638668857798746481525414626432369918918331
comment: $\chi$ of order $4$, odd
16
11
3:
1.001465009294563645990155106738104588837811609182994126619531027545994773761189239121961663293828240 + i * 0.04402075206444418752303266837715597246804306443129904784545210003842897816725976700600208277136848552
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=21 - 45i$
16
13
1:
0.8231312585740451584499694036915367795815756070517714708815629541318604610061037974871881352053274026 + i * 0.1227420153243526082320294273651569406066211042608664675703087151398775171118667522300687550074727560
comment: $\chi$ of order $4$, even
16
13
2:
0.9728722058982436487852957441828243005909287148281810609656472858481410400882787941088842441916715027 + i * 0.06913989889792627465263900286580713404065070504516429312580719510601628743700998950294268199648886722
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=6 - 2i$
16
13
3:
0.9961077217004656459327222070604678632364497984091720374867139469899705871207548344028965503659118937 + i * 0.02877140784999309963004926098308527397822576235626456979417901536443158533056662530305652303747116763
comment: $\chi$ of order $4$, even
17
2
1:
0.8412819557439870327901724798748078353392031694722337345631897405113371675907246517201517936343507051 + i * 0.2607920837855770460097690936472357252839531610813378094565551335498793994881898776260485463828563290
comment: $\chi$ of order $8$, even
17
2
2:
0.9894673233908740931568318206848346209739497403215898298422752583549244563028845775354854841830729546 + i * 0.1820725264857122366355080497885353379558101030929748072001780163341406399144614596973055611010343373
comment: $\chi$ of order $8$, even; $B_{2,\bar\chi}=\frac{72 + 36\zeta_{8} - 84\zeta_{8}^{2} - 8\zeta_{8}^{3}}{17}$
17
2
3:
1.005661426985112206089449633694359836914295656861656242781154575676569925251641299217810778683857499 + i * 0.1026725855955349319168656618355133375775719478035350797066258767096414507344717291381368788502594998
comment: $\chi$ of order $8$, even
17
3
1:
1.601018356193224854762619092080671531928377826546415012029573160443971879488296818319464494613271817 + i * -0.3927743947173973965158183698052216998026366554418179090986464219499557525553432120301073687365760725
comment: $\chi$ of order $16$, odd
17
3
2:
1.273250223247200539550883158864394715840038248100963076781482276633855270247589035894643234216692883 + i * -0.1808599649270197285927331630837685245352049755030077360482109028273295697334328118101795977340765400
comment: $\chi$ of order $16$, odd
17
3
3:
1.121774091216046092276027116739513503653432476729728401750169300356674449994754334401871226837607180 + i * -0.08624881716557772868053355339998865581114233661793509641625000668845864983320032067311619225417804934
comment: $\chi$ of order $16$, odd
17
4
1:
0.5927817455486307226033236210953806298394615663487956439442067174753308940757122614902495382741154053 + i * -0.1936151527175592313753059473784454116924240005887604417494829522176014186234395226496591685012209726
comment: $\chi$ of order $4$, even
17
4
2:
0.7905606152421442226835353950430582626906340335408440948285919885270493362708036747582570939791733540 + i * -0.09732245912806679515121065164111572284034985847453810743782758570720614072253483219016608901525264985
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=4 + 4i$
17
4
3:
0.8877542584777883348867950164092240491056913796611290777866026929642327685222636699967444291338650175 + i * -0.03673027001193041413674690296657472027466137701186701718130978129196903496835478805268564260337952779
comment: $\chi$ of order $4$, even
17
5
1:
0.3364536872641760495544905950259125051034853044721034326669967634635948774159613447905711722620665980 + i * 0.3041433867077192760080772140840014313184685464346843424274019499722961577227477859333865468156578666
comment: $\chi$ of order $16$, odd
17
5
2:
0.7352164757317380051160840622866621265843192430068132593215666079584849177353820678309046493688798471 + i * 0.1916495427677161294534288760586201581688843418251676217162489508278777030073270168540828805370522588
comment: $\chi$ of order $16$, odd
17
5
3:
0.8877819547350305165421876848673097919701313415576144036351939148969693518589667740356657225596139056 + i * 0.1016728297385482817708662760952658754312208401993337925769942162769198610018709788020185888617920285
comment: $\chi$ of order $16$, odd
17
6
1:
1.601018356193224854762619092080671531928377826546415012029573160443971879488296818319464494613271817 + i * 0.3927743947173973965158183698052216998026366554418179090986464219499557525553432120301073687365760725
comment: $\chi$ of order $16$, odd
17
6
2:
1.273250223247200539550883158864394715840038248100963076781482276633855270247589035894643234216692883 + i * 0.1808599649270197285927331630837685245352049755030077360482109028273295697334328118101795977340765400
comment: $\chi$ of order $16$, odd
17
6
3:
1.121774091216046092276027116739513503653432476729728401750169300356674449994754334401871226837607180 + i * 0.08624881716557772868053355339998865581114233661793509641625000668845864983320032067311619225417804934
comment: $\chi$ of order $16$, odd
17
7
1:
0.3364536872641760495544905950259125051034853044721034326669967634635948774159613447905711722620665980 + i * -0.3041433867077192760080772140840014313184685464346843424274019499722961577227477859333865468156578666
comment: $\chi$ of order $16$, odd
17
7
2:
0.7352164757317380051160840622866621265843192430068132593215666079584849177353820678309046493688798471 + i * -0.1916495427677161294534288760586201581688843418251676217162489508278777030073270168540828805370522588
comment: $\chi$ of order $16$, odd
17
7
3:
0.8877819547350305165421876848673097919701313415576144036351939148969693518589667740356657225596139056 + i * -0.1016728297385482817708662760952658754312208401993337925769942162769198610018709788020185888617920285
comment: $\chi$ of order $16$, odd
17
8
1:
0.6432504208356161019010742993744467249966405898128269257214895096947604216987005064741472535153783334 + i * -0.4152647231508630219884679606298983191303269742614103458841613230321738534937219309281255776312841940
comment: $\chi$ of order $8$, even
17
8
2:
0.8829673979592085031639035771399235459646102385377077822098764226864734665536811909396162565716518106 + i * -0.2724422571559408515396541712729895662575586996596819120993880638043756476125328652479212417806798872
comment: $\chi$ of order $8$, even; $B_{2,\bar\chi}=\frac{72 - 8\zeta_{8} + 84\zeta_{8}^{2} + 36\zeta_{8}^{3}}{17}$
17
8
3:
0.9627838159586018111010944291608630769957107700063484977778481936944589870401644996690685140336907129 + i * -0.1413908833517294582021241417651219169900915631648061477985931933158134459381527951488951038523834506
comment: $\chi$ of order $8$, even
17
9
1:
0.8412819557439870327901724798748078353392031694722337345631897405113371675907246517201517936343507051 + i * -0.2607920837855770460097690936472357252839531610813378094565551335498793994881898776260485463828563290
comment: $\chi$ of order $8$, even
17
9
2:
0.9894673233908740931568318206848346209739497403215898298422752583549244563028845775354854841830729546 + i * -0.1820725264857122366355080497885353379558101030929748072001780163341406399144614596973055611010343373
comment: $\chi$ of order $8$, even; $B_{2,\bar\chi}=\frac{72 + 8\zeta_{8} + 84\zeta_{8}^{2} - 36\zeta_{8}^{3}}{17}$
17
9
3:
1.005661426985112206089449633694359836914295656861656242781154575676569925251641299217810778683857499 + i * -0.1026725855955349319168656618355133375775719478035350797066258767096414507344717291381368788502594998
comment: $\chi$ of order $8$, even
17
10
1:
0.9903324006169564367054085628776885455021283640185136263318696146157109689596982401540707302920783905 + i * 0.01074511378850215333356596542532984209878379951056820669880933572274392608579048336329241742240157568
comment: $\chi$ of order $16$, odd
17
10
2:
0.9169729837118594462190000802519163251601333474953971790714413735616766086988784372895409697992470635 + i * -0.04758703132331565192290135486486737919727617759184519863692500324145386570272239856298893638652716329
comment: $\chi$ of order $16$, odd
17
10
3:
0.9363480238477992173982843935154045621121542806951019657670039056003242223810186428498137046438470055 + i * -0.04520185023259361196982649174605546043110790044866116627457242762154797909759045564265542362352255702
comment: $\chi$ of order $16$, odd
17
11
1:
1.026557040981183135964992859733802111392536649693387003658784783442032028222180646270425289703797758 + i * 0.7114857552746037445568038343209529680093290813393287169310069235449312515100042807371205393642787145
comment: $\chi$ of order $16$, odd
17
11
2:
1.070622131241017491930907004902099790461350078047570417316523523697929128669134817420766192739102468 + i * 0.2910918547939498148545311646999485790717077325261547703011592179457247173076294593056028004674722176
comment: $\chi$ of order $16$, odd
17
11
3:
1.053781525359896242377480402756391881103274368844748415212170710231607709048121934244023756709996867 + i * 0.1216387120913534422515090026910639012451334064566498705132492795474963762856265819282933646503041350
comment: $\chi$ of order $16$, odd
17
12
1:
0.9903324006169564367054085628776885455021283640185136263318696146157109689596982401540707302920783905 + i * -0.01074511378850215333356596542532984209878379951056820669880933572274392608579048336329241742240157568
comment: $\chi$ of order $16$, odd
17
12
2:
0.9169729837118594462190000802519163251601333474953971790714413735616766086988784372895409697992470635 + i * 0.04758703132331565192290135486486737919727617759184519863692500324145386570272239856298893638652716329
comment: $\chi$ of order $16$, odd
17
12
3:
0.9363480238477992173982843935154045621121542806951019657670039056003242223810186428498137046438470055 + i * 0.04520185023259361196982649174605546043110790044866116627457242762154797909759045564265542362352255702
comment: $\chi$ of order $16$, odd
17
13
1:
0.5927817455486307226033236210953806298394615663487956439442067174753308940757122614902495382741154053 + i * 0.1936151527175592313753059473784454116924240005887604417494829522176014186234395226496591685012209726
comment: $\chi$ of order $4$, even
17
13
2:
0.7905606152421442226835353950430582626906340335408440948285919885270493362708036747582570939791733540 + i * 0.09732245912806679515121065164111572284034985847453810743782758570720614072253483219016608901525264985
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=4 - 4i$
17
13
3:
0.8877542584777883348867950164092240491056913796611290777866026929642327685222636699967444291338650175 + i * 0.03673027001193041413674690296657472027466137701186701718130978129196903496835478805268564260337952779
comment: $\chi$ of order $4$, even
17
14
1:
1.026557040981183135964992859733802111392536649693387003658784783442032028222180646270425289703797758 + i * -0.7114857552746037445568038343209529680093290813393287169310069235449312515100042807371205393642787145
comment: $\chi$ of order $16$, odd
17
14
2:
1.070622131241017491930907004902099790461350078047570417316523523697929128669134817420766192739102468 + i * -0.2910918547939498148545311646999485790717077325261547703011592179457247173076294593056028004674722176
comment: $\chi$ of order $16$, odd
17
14
3:
1.053781525359896242377480402756391881103274368844748415212170710231607709048121934244023756709996867 + i * -0.1216387120913534422515090026910639012451334064566498705132492795474963762856265819282933646503041350
comment: $\chi$ of order $16$, odd
17
15
1:
0.6432504208356161019010742993744467249966405898128269257214895096947604216987005064741472535153783334 + i * 0.4152647231508630219884679606298983191303269742614103458841613230321738534937219309281255776312841940
comment: $\chi$ of order $8$, even
17
15
2:
0.8829673979592085031639035771399235459646102385377077822098764226864734665536811909396162565716518106 + i * 0.2724422571559408515396541712729895662575586996596819120993880638043756476125328652479212417806798872
comment: $\chi$ of order $8$, even; $B_{2,\bar\chi}=\frac{72 - 36\zeta_{8} - 84\zeta_{8}^{2} + 8\zeta_{8}^{3}}{17}$
17
15
3:
0.9627838159586018111010944291608630769957107700063484977778481936944589870401644996690685140336907129 + i * 0.1413908833517294582021241417651219169900915631648061477985931933158134459381527951488951038523834506
comment: $\chi$ of order $8$, even
17
16
1:
1.016084833842840752194671412616704865527117348072465546895466506423184457990092433415884153439894246 + i * 0
equals: $\kappa_{17}$
comment: $\chi=\left(\frac{17}{\cdot}\right)$, even
17
16
2:
1.126461492837435458265892887412826388927717078316468244567236068193256234138549832820477637791655551 + i * 0
comment: $\chi=\left(\frac{17}{\cdot}\right)$, even; $L(2,\chi)=\frac{8\pi^2}{17\sqrt{17}}$
17
16
3:
1.089774163235281299225584911772953627007072718812586746983743688463496126848701806600872075607456447 + i * 0
comment: $\chi=\left(\frac{17}{\cdot}\right)$, even
19
2
1:
1.660301634053727002663142013381698363421941022958281638135594288554882984799167709893351441594232910 + i * -0.1000769021410507717896230931004604199380834636972795113546657368496050934229732317657080812398726310
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-20 - 10\zeta_{18} - 24\zeta_{18}^{2} + 8\zeta_{18}^{3} + 4\zeta_{18}^{4} + 2\zeta_{18}^{5}}{19}$
19
2
2:
1.285570830215873904216052841863063654664025501673088773018235774057769096519312126015637196080752469 + i * -0.009837016806008897008629813714164326222280134729223458884715386571935190600364399633303343856498751371
comment: $\chi$ of order $18$, odd
19
2
3:
1.128398045975378402535657373495290178889493670824224386992451234579415200388852242578086698026633804 + i * 0.01043788444013892843172163426728460774357353813766614493881621101215957103839907250167098015196806488
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=30 + 30\zeta_{18} + 60\zeta_{18}^{2} - 36\zeta_{18}^{3} - 6\zeta_{18}^{4} + 6\zeta_{18}^{5}$
19
3
1:
0.4003261943713131020479700181245300355201927037956530078290407260631558519118150096401038599714810519 + i * -0.1023120427925468149724282560282310927637774510729218607966363556195400867623196683209610745621617738
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-20 + 4\zeta_{18} + 22\zeta_{18}^{2} + 8\zeta_{18}^{3} + 6\zeta_{18}^{4} - 24\zeta_{18}^{5}}{19}$
19
3
2:
0.7976241605863742804748168208307242301166422673078452123371570111343596513845628234162465367987432934 + i * -0.1357109223196513937950036613365602306203132494164070478676282533517507385926690219043765297118882028
comment: $\chi$ of order $18$, odd
19
3
3:
0.9310429195090484265710725363010220019835952930390400289517797714400164998274525224092942875670219369 + i * -0.09122044632067278551135706046352362900669533430091188174799936946096659008223629714402645294347360741
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=30 - 6\zeta_{18} - 66\zeta_{18}^{2} - 36\zeta_{18}^{3} - 24\zeta_{18}^{4} + 60\zeta_{18}^{5}$
19
4
1:
0.9346598879236698696706556835092500587527219717443080224107800151784677252757566761603990532702178930 + i * 0.3179639679248922479598403583556424479613603136787334165678599864982642667218563021665918835700106793
comment: $\chi$ of order $9$, even
19
4
2:
1.069337323395953546991699305416378411178253242357897807346842745168949250372537468249207781358982578 + i * 0.1955179333185552367517850097924634883733641840303982514242148308824367371043613316081004652489952610
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{140 - 60\zeta_{9} - 72\zeta_{9}^{2} + 8\zeta_{9}^{3} - 36\zeta_{9}^{4} - 28\zeta_{9}^{5}}{19}$
19
4
3:
1.059269571534832410224316597812063551983256458936553591057030010596125208263171352666668986871946453 + i * 0.09676864981065079030209399625020352713838266631547723242615181988043869125854180651855626992081523114
comment: $\chi$ of order $9$, even
19
5
1:
0.9346598879236698696706556835092500587527219717443080224107800151784677252757566761603990532702178930 + i * -0.3179639679248922479598403583556424479613603136787334165678599864982642667218563021665918835700106793
comment: $\chi$ of order $9$, even
19
5
2:
1.069337323395953546991699305416378411178253242357897807346842745168949250372537468249207781358982578 + i * -0.1955179333185552367517850097924634883733641840303982514242148308824367371043613316081004652489952610
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{132 + 72\zeta_{9} + 60\zeta_{9}^{2} - 8\zeta_{9}^{3} + 44\zeta_{9}^{4} + 24\zeta_{9}^{5}}{19}$
19
5
3:
1.059269571534832410224316597812063551983256458936553591057030010596125208263171352666668986871946453 + i * -0.09676864981065079030209399625020352713838266631547723242615181988043869125854180651855626992081523114
comment: $\chi$ of order $9$, even
19
6
1:
0.9148777962022762220715608428119757962809802952688614806247297501081272174287348814684360780559774707 + i * -0.2743962000131312170844062982318720034845389472808489920656846345136820519571174210832327353922569785
comment: $\chi$ of order $9$, even
19
6
2:
1.034902939242754601341269677105501826939751323870616983208122364484059183100081120677430199358721822 + i * -0.1863117758923493190144251090479084101843084244626199704176438931170646401354534994764949737637051491
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{140 + 24\zeta_{9} + 28\zeta_{9}^{2} + 8\zeta_{9}^{3} + 60\zeta_{9}^{4} - 44\zeta_{9}^{5}}{19}$
19
6
3:
1.028923484238557625339348911534637074446270982529366559361084517834687006804000596628924874865813505 + i * -0.1035740669287917535196799152587929474201159450361603070589552901157903812171638027346048693344540474
comment: $\chi$ of order $9$, even
19
7
1:
0.4992035152928479177227903985197203004560757263477553619525672343941901326336194550266026389088532162 + i * 0.4022141313761837794741632374531846639175714117944929742910707985740244564385402714727938881782219175
comment: $\chi$ of order $3$, even
19
7
2:
0.7860953108997776941031420413644937521628215168972715562946826774611471627959618648377666119496144909 + i * 0.2524543087754220645960933967436976549987922043541595758497580809431449101352955477626866204042557844
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=-4 - 8\zeta_{3}$
19
7
3:
0.9092619952994870845158678244428376808477574215291136966215847577657068581720272914588500788679153522 + i * 0.1277686395193641659277573311156400104320804803583326123560694785713436862609129095366989238843578268
comment: $\chi$ of order $3$, even
19
8
1:
1.171924367921643277281586155788322338194046247870360115532788379920957627270767530914718749653749895 + i * 0.8392882274477430589880055292299847592605131904140982605975522218735628172748697939545510278928471922
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2 + 2\zeta_{6}$
19
8
2:
1.124043779631022128883898251702887038667603443061332524840396036596271812183876398896830587928087276 + i * 0.3517064886101509216125722312117766601125666040276233242700843153191243761767457067760198552121111484
comment: $\chi$ of order $6$, odd
19
8
3:
1.068144768420300935067774284747477887803606142261940013472544636113553747710043957449374010836582942 + i * 0.1507494638704560152327364592519208916647347262459094980423848123209354587445270837233473560783156480
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=\frac{966 - 1800\zeta_{6}}{19}$
19
9
1:
0.6806203626588661763006859164273795115513256378354097378573153242222774163800342149134219759982731539 + i * -0.07154573942671784539033884476708951169496785887858586040101386839821942312283665410030202806674554966
comment: $\chi$ of order $9$, even
19
9
2:
0.8307103449968350380156243971227078295685997475638170852932653718019946686677350554009793585183344206 + i * -0.01831779715024491850945461836395898437649801413685897392746952891623843598689084397009799775784585678
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{140 + 36\zeta_{9} + 44\zeta_{9}^{2} + 8\zeta_{9}^{3} - 24\zeta_{9}^{4} + 72\zeta_{9}^{5}}{19}$
19
9
3:
0.9032041630173602393770534314968903800398888833033860365444136758073138088677624580003870762570960169 + i * 0.004746202757889447326131991778553782252320702185102832627797812349622052556610955247191417651733688279
comment: $\chi$ of order $9$, even
19
10
1:
1.660301634053727002663142013381698363421941022958281638135594288554882984799167709893351441594232910 + i * 0.1000769021410507717896230931004604199380834636972795113546657368496050934229732317657080812398726310
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-12 - 24\zeta_{18} - 10\zeta_{18}^{2} - 8\zeta_{18}^{3} + 22\zeta_{18}^{4} + 6\zeta_{18}^{5}}{19}$
19
10
2:
1.285570830215873904216052841863063654664025501673088773018235774057769096519312126015637196080752469 + i * 0.009837016806008897008629813714164326222280134729223458884715386571935190600364399633303343856498751371
comment: $\chi$ of order $18$, odd
19
10
3:
1.128398045975378402535657373495290178889493670824224386992451234579415200388852242578086698026633804 + i * -0.01043788444013892843172163426728460774357353813766614493881621101215957103839907250167098015196806488
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-6 + 60\zeta_{18} + 30\zeta_{18}^{2} + 36\zeta_{18}^{3} - 66\zeta_{18}^{4} - 24\zeta_{18}^{5}$
19
11
1:
0.4992035152928479177227903985197203004560757263477553619525672343941901326336194550266026389088532162 + i * -0.4022141313761837794741632374531846639175714117944929742910707985740244564385402714727938881782219175
comment: $\chi$ of order $3$, even
19
11
2:
0.7860953108997776941031420413644937521628215168972715562946826774611471627959618648377666119496144909 + i * -0.2524543087754220645960933967436976549987922043541595758497580809431449101352955477626866204042557844
comment: $\chi$ of order $3$, even; $B_{2,\bar\chi}=4 + 8\zeta_{3}$
19
11
3:
0.9092619952994870845158678244428376808477574215291136966215847577657068581720272914588500788679153522 + i * -0.1277686395193641659277573311156400104320804803583326123560694785713436862609129095366989238843578268
comment: $\chi$ of order $3$, even
19
12
1:
1.171924367921643277281586155788322338194046247870360115532788379920957627270767530914718749653749895 + i * -0.8392882274477430589880055292299847592605131904140982605975522218735628172748697939545510278928471922
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2\zeta_{6}$
19
12
2:
1.124043779631022128883898251702887038667603443061332524840396036596271812183876398896830587928087276 + i * -0.3517064886101509216125722312117766601125666040276233242700843153191243761767457067760198552121111484
comment: $\chi$ of order $6$, odd
19
12
3:
1.068144768420300935067774284747477887803606142261940013472544636113553747710043957449374010836582942 + i * -0.1507494638704560152327364592519208916647347262459094980423848123209354587445270837233473560783156480
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=\frac{-834 + 1800\zeta_{6}}{19}$
19
13
1:
0.4003261943713131020479700181245300355201927037956530078290407260631558519118150096401038599714810519 + i * 0.1023120427925468149724282560282310927637774510729218607966363556195400867623196683209610745621617738
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-12 + 22\zeta_{18} + 4\zeta_{18}^{2} - 8\zeta_{18}^{3} + 2\zeta_{18}^{4} - 10\zeta_{18}^{5}}{19}$
19
13
2:
0.7976241605863742804748168208307242301166422673078452123371570111343596513845628234162465367987432934 + i * 0.1357109223196513937950036613365602306203132494164070478676282533517507385926690219043765297118882028
comment: $\chi$ of order $18$, odd
19
13
3:
0.9310429195090484265710725363010220019835952930390400289517797714400164998274525224092942875670219369 + i * 0.09122044632067278551135706046352362900669533430091188174799936946096659008223629714402645294347360741
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-6 - 66\zeta_{18} - 6\zeta_{18}^{2} + 36\zeta_{18}^{3} + 6\zeta_{18}^{4} + 30\zeta_{18}^{5}$
19
14
1:
0.8659980343507915895287097639711355027714068208856450788408777861410669673029963665079777979846859292 + i * 0.4996074426993470175328844477237355532881736074364307337188844097572945172981127943359293753032891744
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-20 + 6\zeta_{18} + 2\zeta_{18}^{2} + 8\zeta_{18}^{3} - 10\zeta_{18}^{4} + 22\zeta_{18}^{5}}{19}$
19
14
2:
0.9051659103209370358786833999527672819812094509916761070288862625181043211892155792246695370697061348 + i * 0.2021857306522132955072712662558592536073918808006505409932055836461689691818633204223231083336650436
comment: $\chi$ of order $18$, odd
19
14
3:
0.9386888759619142628556443498678918499556119854111912466954461654553328957717941554093595004027256034 + i * 0.09009034337780310068977961239623229708450884170235662297471400755292651597146622169481789847139384554
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=30 - 24\zeta_{18} + 6\zeta_{18}^{2} - 36\zeta_{18}^{3} + 30\zeta_{18}^{4} - 66\zeta_{18}^{5}$
19
15
1:
0.8659980343507915895287097639711355027714068208856450788408777861410669673029963665079777979846859292 + i * -0.4996074426993470175328844477237355532881736074364307337188844097572945172981127943359293753032891744
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-12 + 2\zeta_{18} + 6\zeta_{18}^{2} - 8\zeta_{18}^{3} - 24\zeta_{18}^{4} + 4\zeta_{18}^{5}}{19}$
19
15
2:
0.9051659103209370358786833999527672819812094509916761070288862625181043211892155792246695370697061348 + i * -0.2021857306522132955072712662558592536073918808006505409932055836461689691818633204223231083336650436
comment: $\chi$ of order $18$, odd
19
15
3:
0.9386888759619142628556443498678918499556119854111912466954461654553328957717941554093595004027256034 + i * -0.09009034337780310068977961239623229708450884170235662297471400755292651597146622169481789847139384554
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-6 + 6\zeta_{18} - 24\zeta_{18}^{2} + 36\zeta_{18}^{3} + 60\zeta_{18}^{4} - 6\zeta_{18}^{5}$
19
16
1:
0.9148777962022762220715608428119757962809802952688614806247297501081272174287348814684360780559774707 + i * 0.2743962000131312170844062982318720034845389472808489920656846345136820519571174210832327353922569785
comment: $\chi$ of order $9$, even
19
16
2:
1.034902939242754601341269677105501826939751323870616983208122364484059183100081120677430199358721822 + i * 0.1863117758923493190144251090479084101843084244626199704176438931170646401354534994764949737637051491
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{132 - 28\zeta_{9} - 24\zeta_{9}^{2} - 8\zeta_{9}^{3} - 72\zeta_{9}^{4} + 36\zeta_{9}^{5}}{19}$
19
16
3:
1.028923484238557625339348911534637074446270982529366559361084517834687006804000596628924874865813505 + i * 0.1035740669287917535196799152587929474201159450361603070589552901157903812171638027346048693344540474
comment: $\chi$ of order $9$, even
19
17
1:
0.6806203626588661763006859164273795115513256378354097378573153242222774163800342149134219759982731539 + i * 0.07154573942671784539033884476708951169496785887858586040101386839821942312283665410030202806674554966
comment: $\chi$ of order $9$, even
19
17
2:
0.8307103449968350380156243971227078295685997475638170852932653718019946686677350554009793585183344206 + i * 0.01831779715024491850945461836395898437649801413685897392746952891623843598689084397009799775784585678
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{132 - 44\zeta_{9} - 36\zeta_{9}^{2} - 8\zeta_{9}^{3} + 28\zeta_{9}^{4} - 60\zeta_{9}^{5}}{19}$
19
17
3:
0.9032041630173602393770534314968903800398888833033860365444136758073138088677624580003870762570960169 + i * -0.004746202757889447326131991778553782252320702185102832627797812349622052556610955247191417651733688279
comment: $\chi$ of order $9$, even
19
18
1:
0.7207307841456679453905980583723501538266288309205605877012859815947338210842627846935177873703854488 + i * 0
equals: $\kappa_{-19}$
comment: $\chi=\left(\frac{-19}{\cdot}\right)$, odd; $L(1,\chi)=\frac{\pi}{\sqrt{19}}$
19
18
2:
0.7688512743992464896880839155603387794496251230203445814891576027406540517644410936364280896586398706 + i * 0
comment: $\chi=\left(\frac{-19}{\cdot}\right)$, odd
19
18
3:
0.8669983923684360969493489078245374854772960154700510352760817377313048119273278353601893187260872578 + i * 0
comment: $\chi=\left(\frac{-19}{\cdot}\right)$, odd; $L(3,\chi)=\frac{44\pi^3}{361\sqrt{19}}$
20
3
1:
0.8595478356027176901335843798312781908134469576112549376755770562358453803487853811021490528179038895 + i * -0.1767421806314802125532797103547685219882078028368892792134509587560745537226379826695916919031589653
comment: $\chi$ of order $4$, even
20
3
2:
0.9829724428297573530902302426517033700835305661373366445925349254998993708391601534044705932141887729 + i * -0.08863456987724250476826887816448348239052595384790077759005788620610178712150984614591831466208466160
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=8 + 4i$
20
3
3:
0.9980772256851182972970657793697452505054411304934999373525660530094813075776676406518232261489178039 + i * -0.03389532474861161944946512858325067521212586591290601372215369212226854425024162333670914145336835034
comment: $\chi$ of order $4$, even
20
7
1:
0.8595478356027176901335843798312781908134469576112549376755770562358453803487853811021490528179038895 + i * 0.1767421806314802125532797103547685219882078028368892792134509587560745537226379826695916919031589653
comment: $\chi$ of order $4$, even
20
7
2:
0.9829724428297573530902302426517033700835305661373366445925349254998993708391601534044705932141887729 + i * 0.08863456987724250476826887816448348239052595384790077759005788620610178712150984614591831466208466160
comment: $\chi$ of order $4$, even; $B_{2,\bar\chi}=8 - 4i$
20
7
3:
0.9980772256851182972970657793697452505054411304934999373525660530094813075776676406518232261489178039 + i * 0.03389532474861161944946512858325067521212586591290601372215369212226854425024162333670914145336835034
comment: $\chi$ of order $4$, even
20
19
1:
1.404962946208145278631274928640978959893301837413440483997944205238428376123837641020828483073153448 + i * 0
equals: $\kappa_{-20}$
comment: $\chi=\left(\frac{-20}{\cdot}\right)$, odd; $L(1,\chi)=\frac{2\pi}{\sqrt{20}}$
20
19
2:
1.128043324740947072848331707869738421799450103349934403194123784071705779428816212949246003723612597 + i * 0
comment: $\chi=\left(\frac{-20}{\cdot}\right)$, odd
20
19
3:
1.039982135794753683931004957112589563495662493477295390293935321123916415613195664425177384164240083 + i * 0
comment: $\chi=\left(\frac{-20}{\cdot}\right)$, odd; $L(3,\chi)=\frac{3\pi^3}{20\sqrt{20}}$
21
2
1:
1.141608742077595292990071163543167891207049862792224982939389018394996090966717421028992607382415724 + i * 0.7593774607127571344299187206114825569703311127640346275425444078138471104971112523292273088692158292
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2 + 2\zeta_{6}$
21
2
2:
1.101299759098218422510864795918781518412620833289738128270441198583763524244402250943843643345812774 + i * 0.3015359241255544510718451005777873709274079847227490472210739879447146070188941817276068004223732853
comment: $\chi$ of order $6$, odd
21
2
3:
1.056951693134228691504689415394908517660051584379810385923131576664593300221538796121931489717966893 + i * 0.1285685432627706419400782429292624612465237895533904580232770849817367673545731282350943032354180306
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=66 - 120\zeta_{6}$
21
5
1:
0.9424309741578794620789462722706733151229945888377099387977012938272181495237973582054872067720538060 + i * 0.3602888690240446376745383930518178947102209621797968832229017861713108269221541288167216070269886468
comment: $\chi$ of order $6$, even
21
5
2:
1.062266100410912951907408660389751308868818622488845314701595507007360677785639826680690251384339022 + i * 0.2227770763634460112167661902842457482363278424023877586783426058365770424472122332203823417821710203
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=12 - 8\zeta_{6}$
21
5
3:
1.049175949622437943381570422325898314076817305480687514644638740045248004430159344509081275178540778 + i * 0.1134680487822504185355553703013806953598415163556723025190690379874725950035946430976805506001556959
comment: $\chi$ of order $6$, even
21
11
1:
1.141608742077595292990071163543167891207049862792224982939389018394996090966717421028992607382415724 + i * -0.7593774607127571344299187206114825569703311127640346275425444078138471104971112523292273088692158292
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2\zeta_{6}$
21
11
2:
1.101299759098218422510864795918781518412620833289738128270441198583763524244402250943843643345812774 + i * -0.3015359241255544510718451005777873709274079847227490472210739879447146070188941817276068004223732853
comment: $\chi$ of order $6$, odd
21
11
3:
1.056951693134228691504689415394908517660051584379810385923131576664593300221538796121931489717966893 + i * -0.1285685432627706419400782429292624612465237895533904580232770849817367673545731282350943032354180306
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=-54 + 120\zeta_{6}$
21
17
1:
0.9424309741578794620789462722706733151229945888377099387977012938272181495237973582054872067720538060 + i * -0.3602888690240446376745383930518178947102209621797968832229017861713108269221541288167216070269886468
comment: $\chi$ of order $6$, even
21
17
2:
1.062266100410912951907408660389751308868818622488845314701595507007360677785639826680690251384339022 + i * -0.2227770763634460112167661902842457482363278424023877586783426058365770424472122332203823417821710203
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=4 + 8\zeta_{6}$
21
17
3:
1.049175949622437943381570422325898314076817305480687514644638740045248004430159344509081275178540778 + i * -0.1134680487822504185355553703013806953598415163556723025190690379874725950035946430976805506001556959
comment: $\chi$ of order $6$, even
21
20
1:
0.6838072478309644333954367325330239675766316778131110446612101315181827630519440031346307188525576254 + i * 0
equals: $\kappa_{21}$
comment: $\chi=\left(\frac{21}{\cdot}\right)$, even
21
20
2:
0.8204663809026990415324992505201508944793653717383754675174205779608168096268639249838662921689277496 + i * 0
comment: $\chi=\left(\frac{21}{\cdot}\right)$, even; $L(2,\chi)=\frac{8\pi^2}{21\sqrt{21}}$
21
20
3:
0.8949346306641878397343586265527183115725567440491152096508508043730632637011181186700321285973672565 + i * 0
comment: $\chi=\left(\frac{21}{\cdot}\right)$, even
23
2
1:
0.7656286297963001013807203150518763426433280272802726569568376086951770528906410953595930116487552885 + i * 0.4719765327749424771132783133304476065500295424879828250437716587236426906953355369668160370552497965
comment: $\chi$ of order $11$, even
23
2
2:
0.9672215919560759313358715144215020204656568607238599033655279587875999220316394262223088152887410747 + i * 0.2739402349683996213900262112494531974427421698693630810964537582542423384662211796522773522688613070
comment: $\chi$ of order $11$, even
23
2
3:
1.009007441778512538812037507492039472322622047117032008780500282362112297660047000752568179401612848 + i * 0.1325257664596752464866413058565647115928438982506685392227659362896604930133141758028608938260463212
comment: $\chi$ of order $11$, even
23
3
1:
0.5201889752370527999184847107723028219631212972607019421609769480363622627465145081917755702662687594 + i * -0.1855913550444719104712333616680517274870329832472379701293742583564590730122497598423005685356567923
comment: $\chi$ of order $11$, even
23
3
2:
0.7474164567192259098440271167422845155678204899507555381662962726776048425002884538610504469391808831 + i * -0.05578764038974010331029986836897280049222907804132924931479340012566466218480172392779689676045009128
comment: $\chi$ of order $11$, even
23
3
3:
0.8708231708478553730913290695440495507863945807554120140788143283532822531680899166354519679824598700 + i * -0.005372442545480192612554169559994177981553549076567046958762640714245991175828961067393946983678725744
comment: $\chi$ of order $11$, even
23
4
1:
0.8044174782041349179817418885159712037049163771679421671545592393403805211466803445920335165057954513 + i * 0.1800159172769768227760433210355503863189240086006231560989628975954318131989666056034618085177351961
comment: $\chi$ of order $11$, even
23
4
2:
0.9128002441469700327156202143089374657419830739808552602087583104396016993838457659002159969676410813 + i * 0.1208466794849723201844598243075508580336211078836104515897066302147769886941072118789382294286887644
comment: $\chi$ of order $11$, even
23
4
3:
0.9472416328708303556218706377169437260692568315016650088410404558642404737059154240423152918676153567 + i * 0.07019226694364667564490239457531104116742722379027235295734658179382998318519210632994141192382530603
comment: $\chi$ of order $11$, even
23
5
1:
1.683741036566251573066086825459527235043686655040233858063872058832226815238017031169775031038039131 + i * 0.1252447533953622127731147227361774041257329331486836593657316436686476643979236802557578757985539845
comment: $\chi$ of order $22$, odd
23
5
2:
1.269538322469295336125159185324613705821250603354996619972418410177828404438749531105697426367000803 + i * 0.07385322921654813482351247340189746310343317789184314706720487530871041844338835557163401209850173546
comment: $\chi$ of order $22$, odd
23
5
3:
1.116440987819207387569503722366754315500684476271512805473891704137634673401940569706000920586072787 + i * 0.04367028719675955136736591968192669717326029736602666220020931408505187426484180251364148794352525482
comment: $\chi$ of order $22$, odd
23
6
1:
0.8044174782041349179817418885159712037049163771679421671545592393403805211466803445920335165057954513 + i * -0.1800159172769768227760433210355503863189240086006231560989628975954318131989666056034618085177351961
comment: $\chi$ of order $11$, even
23
6
2:
0.9128002441469700327156202143089374657419830739808552602087583104396016993838457659002159969676410813 + i * -0.1208466794849723201844598243075508580336211078836104515897066302147769886941072118789382294286887644
comment: $\chi$ of order $11$, even
23
6
3:
0.9472416328708303556218706377169437260692568315016650088410404558642404737059154240423152918676153567 + i * -0.07019226694364667564490239457531104116742722379027235295734658179382998318519210632994141192382530603
comment: $\chi$ of order $11$, even
23
7
1:
0.7210110963832219570294446926514447315251382197314357644102695173055904862873997728595113514518559746 + i * -0.8129020667043820478116608626720524057151653340067110898429158342667327776804166413203170003772919821
comment: $\chi$ of order $22$, odd
23
7
2:
0.9341814945564959670558394421684898429595954160463767694543324686260960895116414022765089507414853408 + i * -0.3547132171816651454092670109634582841655164500011438985222058983374065120556870729993514487942346105
comment: $\chi$ of order $22$, odd
23
7
3:
0.9808509332689295194878871580400674354295231543248951200163269067883139379072967628816462536974599904 + i * -0.1583921500552341815686820921985321686691120458853368397905876810421689717108643779329660843764130802
comment: $\chi$ of order $22$, odd
23
8
1:
0.5201889752370527999184847107723028219631212972607019421609769480363622627465145081917755702662687594 + i * 0.1855913550444719104712333616680517274870329832472379701293742583564590730122497598423005685356567923
comment: $\chi$ of order $11$, even
23
8
2:
0.7474164567192259098440271167422845155678204899507555381662962726776048425002884538610504469391808831 + i * 0.05578764038974010331029986836897280049222907804132924931479340012566466218480172392779689676045009128
comment: $\chi$ of order $11$, even
23
8
3:
0.8708231708478553730913290695440495507863945807554120140788143283532822531680899166354519679824598700 + i * 0.005372442545480192612554169559994177981553549076567046958762640714245991175828961067393946983678725744
comment: $\chi$ of order $11$, even
23
9
1:
1.130623330821761971737173092550150997868942352487129522063754435502135073427090899619811953175036242 + i * -0.08441276772510103830419003141464033592029883358133836600513008560178921775072504398417764199163468935
comment: $\chi$ of order $11$, even
23
9
2:
1.164597403512054421229304542405110919434629729734711494300880135388617527211304692818547926142816748 + i * -0.06574514992255617121542672500557739217504972145816319742980462937314586718866627091987164773642889374
comment: $\chi$ of order $11$, even
23
9
3:
1.096933914730913819871680353195166734763648605731050398727966409208654840793159445047576270514916119 + i * -0.04179168603595921032060052300047904669435950116025159148282645603158030064371021757611259429443029578
comment: $\chi$ of order $11$, even
23
10
1:
0.7210110963832219570294446926514447315251382197314357644102695173055904862873997728595113514518559746 + i * 0.8129020667043820478116608626720524057151653340067110898429158342667327776804166413203170003772919821
comment: $\chi$ of order $22$, odd
23
10
2:
0.9341814945564959670558394421684898429595954160463767694543324686260960895116414022765089507414853408 + i * 0.3547132171816651454092670109634582841655164500011438985222058983374065120556870729993514487942346105
comment: $\chi$ of order $22$, odd
23
10
3:
0.9808509332689295194878871580400674354295231543248951200163269067883139379072967628816462536974599904 + i * 0.1583921500552341815686820921985321686691120458853368397905876810421689717108643779329660843764130802
comment: $\chi$ of order $22$, odd
23
11
1:
0.5095007080346868795615116214819377659799487855327410822984338001455294225656162090709717657883273026 + i * -0.5442675104246678834471632670491246269643352466588109990746978122243560340687334700859556929751680312
comment: $\chi$ of order $22$, odd
23
11
2:
0.9072325105559465401686793246949581344474108422986730080747435000508987670548926195561101899055053919 + i * -0.2707696281622047074577508583119083697068078751620839297973026321692619770847253040776009026968307970
comment: $\chi$ of order $22$, odd
23
11
3:
0.9963581939240777553135741997972658102009089875622566083931575101249333360208876519295273999471864877 + i * -0.1294430437818897333106236903204408637204853024916980073120899475657988787374142619118141518751658746
comment: $\chi$ of order $22$, odd
23
12
1:
0.7656286297963001013807203150518763426433280272802726569568376086951770528906410953595930116487552885 + i * -0.4719765327749424771132783133304476065500295424879828250437716587236426906953355369668160370552497965
comment: $\chi$ of order $11$, even
23
12
2:
0.9672215919560759313358715144215020204656568607238599033655279587875999220316394262223088152887410747 + i * -0.2739402349683996213900262112494531974427421698693630810964537582542423384662211796522773522688613070
comment: $\chi$ of order $11$, even
23
12
3:
1.009007441778512538812037507492039472322622047117032008780500282362112297660047000752568179401612848 + i * -0.1325257664596752464866413058565647115928438982506685392227659362896604930133141758028608938260463212
comment: $\chi$ of order $11$, even
23
13
1:
0.7124830147946480639586508741292489746077814843394303532031025344662597485603808007577763662511716384 + i * 0.4910059593361894977176810749885750019506579997535322122081911332084787005876825606768929964386040732
comment: $\chi$ of order $11$, even
23
13
2:
0.9213847174427959354788987054755108056113991263536543333980686353082174008241126445186456616426588658 + i * 0.2959843330336535630655197482393723959757509710685926896718065373854530238869387093512786724386675870
comment: $\chi$ of order $11$, even
23
13
3:
0.9761122298103638769091948486322569254546828303504779179558508965916838164150699221830117173235907750 + i * 0.1472910387247373998172451984396812842466586154997007160420955988204436228739768993504326063802349497
comment: $\chi$ of order $11$, even
23
14
1:
1.683741036566251573066086825459527235043686655040233858063872058832226815238017031169775031038039131 + i * -0.1252447533953622127731147227361774041257329331486836593657316436686476643979236802557578757985539845
comment: $\chi$ of order $22$, odd
23
14
2:
1.269538322469295336125159185324613705821250603354996619972418410177828404438749531105697426367000803 + i * -0.07385322921654813482351247340189746310343317789184314706720487530871041844338835557163401209850173546
comment: $\chi$ of order $22$, odd
23
14
3:
1.116440987819207387569503722366754315500684476271512805473891704137634673401940569706000920586072787 + i * -0.04367028719675955136736591968192669717326029736602666220020931408505187426484180251364148794352525482
comment: $\chi$ of order $22$, odd
23
15
1:
0.5441219459676419460350496246857662797311207430525690650362431142032999682369691273815597723331038462 + i * -0.1794606337847326643623126939874228405765307603435708300623534983554950486172747666644028455120259411
comment: $\chi$ of order $22$, odd
23
15
2:
0.7499275942657719791038239058367975568636852243956745853857122387875734758289203597887448846739436736 + i * -0.03370451543459869130841455648846509843043081828119236631578608589722021088117157222405882429788122727
comment: $\chi$ of order $22$, odd
23
15
3:
0.8713830365450402788240628773752591446482494225207966083841815963883372232377664863476525722871500332 + i * -0.01334372712893294758566736138500838339014805814786459311552144253002610714429045101889788408704591395
comment: $\chi$ of order $22$, odd
23
16
1:
0.7124830147946480639586508741292489746077814843394303532031025344662597485603808007577763662511716384 + i * -0.4910059593361894977176810749885750019506579997535322122081911332084787005876825606768929964386040732
comment: $\chi$ of order $11$, even
23
16
2:
0.9213847174427959354788987054755108056113991263536543333980686353082174008241126445186456616426588658 + i * -0.2959843330336535630655197482393723959757509710685926896718065373854530238869387093512786724386675870
comment: $\chi$ of order $11$, even
23
16
3:
0.9761122298103638769091948486322569254546828303504779179558508965916838164150699221830117173235907750 + i * -0.1472910387247373998172451984396812842466586154997007160420955988204436228739768993504326063802349497
comment: $\chi$ of order $11$, even
23
17
1:
1.024776888119099266246456870627455843897355281642458804345989852681540653124869881552178376199019425 + i * 0.06836387700757800415666813478058897320783677231388469907630126394488850684470381050644406376347391945
comment: $\chi$ of order $22$, odd
23
17
2:
0.9353309948380348457265031842640096027199957153382275138976848072329617639586618605980677533560021215 + i * -0.05595510929883418988009384695111263308103736662362816015198073486146021874346764414361324973297838089
comment: $\chi$ of order $22$, odd
23
17
3:
0.9481990067152063548163002668391409856689831646602918479640815123017139226438816992269172816880743326 + i * -0.05584670284630558456835648727571267340608196716434578355432091858974829416004453924620609617164958930
comment: $\chi$ of order $22$, odd
23
18
1:
1.130623330821761971737173092550150997868942352487129522063754435502135073427090899619811953175036242 + i * 0.08441276772510103830419003141464033592029883358133836600513008560178921775072504398417764199163468935
comment: $\chi$ of order $11$, even
23
18
2:
1.164597403512054421229304542405110919434629729734711494300880135388617527211304692818547926142816748 + i * 0.06574514992255617121542672500557739217504972145816319742980462937314586718866627091987164773642889374
comment: $\chi$ of order $11$, even
23
18
3:
1.096933914730913819871680353195166734763648605731050398727966409208654840793159445047576270514916119 + i * 0.04179168603595921032060052300047904669435950116025159148282645603158030064371021757611259429443029578
comment: $\chi$ of order $11$, even
23
19
1:
1.024776888119099266246456870627455843897355281642458804345989852681540653124869881552178376199019425 + i * -0.06836387700757800415666813478058897320783677231388469907630126394488850684470381050644406376347391945
comment: $\chi$ of order $22$, odd
23
19
2:
0.9353309948380348457265031842640096027199957153382275138976848072329617639586618605980677533560021215 + i * 0.05595510929883418988009384695111263308103736662362816015198073486146021874346764414361324973297838089
comment: $\chi$ of order $22$, odd
23
19
3:
0.9481990067152063548163002668391409856689831646602918479640815123017139226438816992269172816880743326 + i * 0.05584670284630558456835648727571267340608196716434578355432091858974829416004453924620609617164958930
comment: $\chi$ of order $22$, odd
23
20
1:
0.5441219459676419460350496246857662797311207430525690650362431142032999682369691273815597723331038462 + i * 0.1794606337847326643623126939874228405765307603435708300623534983554950486172747666644028455120259411
comment: $\chi$ of order $22$, odd
23
20
2:
0.7499275942657719791038239058367975568636852243956745853857122387875734758289203597887448846739436736 + i * 0.03370451543459869130841455648846509843043081828119236631578608589722021088117157222405882429788122727
comment: $\chi$ of order $22$, odd
23
20
3:
0.8713830365450402788240628773752591446482494225207966083841815963883372232377664863476525722871500332 + i * 0.01334372712893294758566736138500838339014805814786459311552144253002610714429045101889788408704591395
comment: $\chi$ of order $22$, odd
23
21
1:
0.5095007080346868795615116214819377659799487855327410822984338001455294225656162090709717657883273026 + i * 0.5442675104246678834471632670491246269643352466588109990746978122243560340687334700859556929751680312
comment: $\chi$ of order $22$, odd
23
21
2:
0.9072325105559465401686793246949581344474108422986730080747435000508987670548926195561101899055053919 + i * 0.2707696281622047074577508583119083697068078751620839297973026321692619770847253040776009026968307970
comment: $\chi$ of order $22$, odd
23
21
3:
0.9963581939240777553135741997972658102009089875622566083931575101249333360208876519295273999471864877 + i * 0.1294430437818897333106236903204408637204853024916980073120899475657988787374142619118141518751658746
comment: $\chi$ of order $22$, odd
23
22
1:
1.965202054107859165902767005122336415129675978665620359073438303765018594895942447270005424629926352 + i * 0
equals: $\kappa_{-23}$
comment: $\chi=\left(\frac{-23}{\cdot}\right)$, odd; $L(1,\chi)=\frac{3\pi}{\sqrt{23}}$
23
22
2:
1.403216904595041267826775983736615953164103862184474879748876721663389017976524819848998304401242065 + i * 0
comment: $\chi=\left(\frac{-23}{\cdot}\right)$, odd
23
22
3:
1.173278901610753856711859134483347506574098488789771478322724362818709049876121619175315517103548969 + i * 0
comment: $\chi=\left(\frac{-23}{\cdot}\right)$, odd; $L(3,\chi)=\frac{96\pi^3}{529\sqrt{23}}$
24
5
1:
1.282549830161864095544036359671006411467260667564092323101389606756398823513022101033286919052394441 + i * 0
equals: $\kappa_{-24}$
comment: $\chi=\left(\frac{-24}{\cdot}\right)$, odd; $L(1,\chi)=\frac{2\pi}{\sqrt{24}}$
24
5
2:
1.057806613211504429466442468366796150091955934794855282941474394637494328112125771890809407597324516 + i * 0
comment: $\chi=\left(\frac{-24}{\cdot}\right)$, odd
24
5
3:
1.010902664280502416411682504567429702973994310086063148120560137282530608012594431562646583561835307 + i * 0
comment: $\chi=\left(\frac{-24}{\cdot}\right)$, odd; $L(3,\chi)=\frac{23\pi^3}{144\sqrt{24}}$
24
11
1:
0.9358813101035701104869091592664068516533568855377713480466697048389909387585423200153352723177516328 + i * 0
equals: $\kappa_{24}$
comment: $\chi=\left(\frac{24}{\cdot}\right)$, even
24
11
2:
1.007312281074837315291628436796198608736773884377182864287186102815338648468509639558772700240199171 + i * 0
comment: $\chi=\left(\frac{24}{\cdot}\right)$, even; $L(2,\chi)=\frac{\pi^2}{2\sqrt{24}}$
24
11
3:
1.003941623150056320717685549326414864337288937242674756375964218068309123360480567811568990365267869 + i * 0
comment: $\chi=\left(\frac{24}{\cdot}\right)$, even
25
2
1:
1.378802374828595942906863497237975307799165569067590954640688857815374603996897692664120343200015255 + i * 0.7129109418539022878648255822472061889802178732136556777591988135620708440548159470660968140948866329
comment: $\chi$ of order $20$, odd
25
2
2:
1.205527846009152346974905162631228512360303064104340812810339471611238190126015853869557889622921187 + i * 0.2342435355680545845543093962000944320467495360257081907806278196711348499338401729558171478830730694
comment: $\chi$ of order $20$, odd
25
2
3:
1.106716135149797216579439836971370556470255379504318134143663342804889338922856461351006766082882864 + i * 0.08310554956513594837513026030335508228705965053960302286469275775373529054771417538549740030241898132
comment: $\chi$ of order $20$, odd
25
3
1:
0.4848512120138758373938491708822529379557156670932297505578893539149708140679606933061013451891588015 + i * 0.02760602250833656993466381097698425775309390452711794293374529120543958228540573963772277906172607045
comment: $\chi$ of order $20$, odd
25
3
2:
0.7544874821177058537157073563982067693700877639661005885360532446988245843769976041579478844302772564 + i * 0.1328290203097043254557979107573198770368695127923946154011628578124928239720374180494648675667286291
comment: $\chi$ of order $20$, odd
25
3
3:
0.8903018884423295046317726194399868097193830557861273088739063868348326552221298056481772836988753542 + i * 0.09042931857497247165184128995657088064456005869502903349725890876339846094040617533028664576676168754
comment: $\chi$ of order $20$, odd
25
4
1:
1.137110429478126768715044726627339214436567408276420237688909140460872625442501756645051669121258709 + i * 0.1227687919323519134040171022172987192624838107974429907290263859879319273138477023880727255675547731
comment: $\chi$ of order $10$, even
25
4
2:
1.157815225222047390691729264332367633148873717818848963244198156853325055851490516238316438340277400 + i * 0.08538233343808962695222924337340910626231768190190262748584051968603416425901739522842449115543251624
comment: $\chi$ of order $10$, even; $B_{2,\bar\chi}=\frac{84 - 48\zeta_{10} + 52\zeta_{10}^{2} - 36\zeta_{10}^{3}}{5}$
25
4
3:
1.091043730746121007341939796977230787109844318901399267697299146921864771514626132036633472481517327 + i * 0.05037336267040775105716196933977081803019375762638968209497544288314716607422202274639829533681490529
comment: $\chi$ of order $10$, even
25
6
1:
0.7399223180240800295444540297759823514490147796879485227828567851459427595523952746503330821580552967 + i * -0.04332015061986801960514145890220732076715703192665468072660569161264836595448099862963318498753816213
comment: $\chi$ of order $5$, even
25
6
2:
0.8579346804837281688559088986639473873897152238371839223204907380305526400297008077491246409016683746 + i * 0.01662460838188885538114189690337215325162770576046768426099662977808545067690964671277215361062146499
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=8 + 8\zeta_{5} - 4\zeta_{5}^{2} + 4\zeta_{5}^{3}$
25
6
3:
0.9174252297609743325634394689813837219881312706726269436401127525710343088699311115350893423952310912 + i * 0.02892843181314242689611465735194513089734017842550374554123615400921461276444049684985569620226281419
comment: $\chi$ of order $5$, even
25
8
1:
1.502935290729904693509721364101902096867675100492804870443175631751667260260311133942664043474284683 + i * 0.8146263744546676844900920408536827215791324092126003315928901293939706123716309318189498171208240173
comment: $\chi$ of order $20$, odd
25
8
2:
1.231856024689580790005799467314331048851547622589852394815009418033786093680003054859133777204052286 + i * 0.3124749844461988589378813593656458368839588284216600750028286514720574661744470074301708324855401391
comment: $\chi$ of order $20$, odd
25
8
3:
1.104050190778592666972874606190598680330630773206602365564892850122051992181963861567002177246885981 + i * 0.1303922250872818239067703021326780398102647126099748132523910966532634837980894070559774132705884433
comment: $\chi$ of order $20$, odd
25
9
1:
0.7706990758162022165718781846735419633423087047477993998368520470542733771334676412365343365910530039 + i * -0.4515038146971815330869242199535820710906101879354807788261159745394821490243808363283378102290291133
comment: $\chi$ of order $10$, even
25
9
2:
0.9357835987655698516354852465464797206843836314793188331213575478845025602971861416813512776296932639 + i * -0.2658227411168407433785512432121383414006976077886583005791796897445702972803098750364720898398842634
comment: $\chi$ of order $10$, even; $B_{2,\bar\chi}=\frac{32 + 16\zeta_{10} - 4\zeta_{10}^{2} + 52\zeta_{10}^{3}}{5}$
25
9
3:
0.9740676767636747589307491483017211017768848639075963673741036815016374739151462424444870232351186354 + i * -0.1325986737501038605739548172285641615675986391852839267013530790511331079441295747904847801158691263
comment: $\chi$ of order $10$, even
25
11
1:
0.6893399648956523997797579112993984396369273522377365874055983282667209106008696669055327479515964463 + i * -0.5231126992844592369449603856721627904195244162740064244316124222603349615613472495736087373061080280
comment: $\chi$ of order $5$, even
25
11
2:
0.9321947181189841489100743881833034967787847414714443197958468077485761392923769584996130270102339372 + i * -0.3006362763380597091931869706163067520319459391063336782199792469856680443453174941653112522787314575
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=12 + 8\zeta_{5} + 12\zeta_{5}^{2} + 4\zeta_{5}^{3}$
25
11
3:
0.9946064675948782302165260890179856645497210555838622234325995720258920397025148214612938590919565164 + i * -0.1445328925945533940199100485642934716089449290709939474842199497494808352031953153947621117467247417
comment: $\chi$ of order $5$, even
25
12
1:
0.7422581621697787683672077225699817177807785424882336994883508380661915008009827283031573200553518163 + i * 0.4449586825683291788075775931917935177179782617471666894501324994324517187560209000796198988356647470
comment: $\chi$ of order $20$, odd
25
12
2:
0.8478696344410160860986522662366231821015270952745882141779642180237549131528887524046981312995001367 + i * 0.1551223967673757887997952634525373902636745672380618706040002043777811578036854008620632356807357057
comment: $\chi$ of order $20$, odd
25
12
3:
0.9106565634915008491240205638615588010728691122808600973059938218394732303803247319254619518087321833 + i * 0.06243652325275120167934650182811418731983650654875568470862503305965968037793735794021134934818443605
comment: $\chi$ of order $20$, odd
25
13
1:
1.378802374828595942906863497237975307799165569067590954640688857815374603996897692664120343200015255 + i * -0.7129109418539022878648255822472061889802178732136556777591988135620708440548159470660968140948866329
comment: $\chi$ of order $20$, odd
25
13
2:
1.205527846009152346974905162631228512360303064104340812810339471611238190126015853869557889622921187 + i * -0.2342435355680545845543093962000944320467495360257081907806278196711348499338401729558171478830730694
comment: $\chi$ of order $20$, odd
25
13
3:
1.106716135149797216579439836971370556470255379504318134143663342804889338922856461351006766082882864 + i * -0.08310554956513594837513026030335508228705965053960302286469275775373529054771417538549740030241898132
comment: $\chi$ of order $20$, odd
25
14
1:
0.7706990758162022165718781846735419633423087047477993998368520470542733771334676412365343365910530039 + i * 0.4515038146971815330869242199535820710906101879354807788261159745394821490243808363283378102290291133
comment: $\chi$ of order $10$, even
25
14
2:
0.9357835987655698516354852465464797206843836314793188331213575478845025602971861416813512776296932639 + i * 0.2658227411168407433785512432121383414006976077886583005791796897445702972803098750364720898398842634
comment: $\chi$ of order $10$, even; $B_{2,\bar\chi}=\frac{48 - 16\zeta_{10} - 36\zeta_{10}^{2} - 12\zeta_{10}^{3}}{5}$
25
14
3:
0.9740676767636747589307491483017211017768848639075963673741036815016374739151462424444870232351186354 + i * 0.1325986737501038605739548172285641615675986391852839267013530790511331079441295747904847801158691263
comment: $\chi$ of order $10$, even
25
16
1:
0.6893399648956523997797579112993984396369273522377365874055983282667209106008696669055327479515964463 + i * 0.5231126992844592369449603856721627904195244162740064244316124222603349615613472495736087373061080280
comment: $\chi$ of order $5$, even
25
16
2:
0.9321947181189841489100743881833034967787847414714443197958468077485761392923769584996130270102339372 + i * 0.3006362763380597091931869706163067520319459391063336782199792469856680443453174941653112522787314575
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=4 - 8\zeta_{5} - 4\zeta_{5}^{2} + 4\zeta_{5}^{3}$
25
16
3:
0.9946064675948782302165260890179856645497210555838622234325995720258920397025148214612938590919565164 + i * 0.1445328925945533940199100485642934716089449290709939474842199497494808352031953153947621117467247417
comment: $\chi$ of order $5$, even
25
17
1:
0.4848512120138758373938491708822529379557156670932297505578893539149708140679606933061013451891588015 + i * -0.02760602250833656993466381097698425775309390452711794293374529120543958228540573963772277906172607045
comment: $\chi$ of order $20$, odd
25
17
2:
0.7544874821177058537157073563982067693700877639661005885360532446988245843769976041579478844302772564 + i * -0.1328290203097043254557979107573198770368695127923946154011628578124928239720374180494648675667286291
comment: $\chi$ of order $20$, odd
25
17
3:
0.8903018884423295046317726194399868097193830557861273088739063868348326552221298056481772836988753542 + i * -0.09042931857497247165184128995657088064456005869502903349725890876339846094040617533028664576676168754
comment: $\chi$ of order $20$, odd
25
19
1:
1.137110429478126768715044726627339214436567408276420237688909140460872625442501756645051669121258709 + i * -0.1227687919323519134040171022172987192624838107974429907290263859879319273138477023880727255675547731
comment: $\chi$ of order $10$, even
25
19
2:
1.157815225222047390691729264332367633148873717818848963244198156853325055851490516238316438340277400 + i * -0.08538233343808962695222924337340910626231768190190262748584051968603416425901739522842449115543251624
comment: $\chi$ of order $10$, even; $B_{2,\bar\chi}=\frac{36 + 48\zeta_{10} - 12\zeta_{10}^{2} - 4\zeta_{10}^{3}}{5}$
25
19
3:
1.091043730746121007341939796977230787109844318901399267697299146921864771514626132036633472481517327 + i * -0.05037336267040775105716196933977081803019375762638968209497544288314716607422202274639829533681490529
comment: $\chi$ of order $10$, even
25
21
1:
0.7399223180240800295444540297759823514490147796879485227828567851459427595523952746503330821580552967 + i * 0.04332015061986801960514145890220732076715703192665468072660569161264836595448099862963318498753816213
comment: $\chi$ of order $5$, even
25
21
2:
0.8579346804837281688559088986639473873897152238371839223204907380305526400297008077491246409016683746 + i * -0.01662460838188885538114189690337215325162770576046768426099662977808545067690964671277215361062146499
comment: $\chi$ of order $5$, even; $B_{2,\bar\chi}=-8\zeta_{5} - 4\zeta_{5}^{2} - 12\zeta_{5}^{3}$
25
21
3:
0.9174252297609743325634394689813837219881312706726269436401127525710343088699311115350893423952310912 + i * -0.02892843181314242689611465735194513089734017842550374554123615400921461276444049684985569620226281419
comment: $\chi$ of order $5$, even
25
22
1:
1.502935290729904693509721364101902096867675100492804870443175631751667260260311133942664043474284683 + i * -0.8146263744546676844900920408536827215791324092126003315928901293939706123716309318189498171208240173
comment: $\chi$ of order $20$, odd
25
22
2:
1.231856024689580790005799467314331048851547622589852394815009418033786093680003054859133777204052286 + i * -0.3124749844461988589378813593656458368839588284216600750028286514720574661744470074301708324855401391
comment: $\chi$ of order $20$, odd
25
22
3:
1.104050190778592666972874606190598680330630773206602365564892850122051992181963861567002177246885981 + i * -0.1303922250872818239067703021326780398102647126099748132523910966532634837980894070559774132705884433
comment: $\chi$ of order $20$, odd
25
23
1:
0.7422581621697787683672077225699817177807785424882336994883508380661915008009827283031573200553518163 + i * -0.4449586825683291788075775931917935177179782617471666894501324994324517187560209000796198988356647470
comment: $\chi$ of order $20$, odd
25
23
2:
0.8478696344410160860986522662366231821015270952745882141779642180237549131528887524046981312995001367 + i * -0.1551223967673757887997952634525373902636745672380618706040002043777811578036854008620632356807357057
comment: $\chi$ of order $20$, odd
25
23
3:
0.9106565634915008491240205638615588010728691122808600973059938218394732303803247319254619518087321833 + i * -0.06243652325275120167934650182811418731983650654875568470862503305965968037793735794021134934818443605
comment: $\chi$ of order $20$, odd
27
2
1:
1.693468257439594863001517558992703572079429976340464449437358426439281740691219922936684294113118365 + i * 0.5069911147078847843958277748444444658531720058977206651951899901419461294114034337159550114807794204
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-4 - 2\zeta_{18} - 4\zeta_{18}^{2} + 2\zeta_{18}^{3} + 4\zeta_{18}^{4} + 2\zeta_{18}^{5}}{3}$
27
2
2:
1.290397357359104318073556851829263233135494507575290681206531318558577307349892811686667699793600154 + i * 0.1643549479312102716424738789959139883513715878772450656429163570140234460596872885360547878438642296
comment: $\chi$ of order $18$, odd
27
2
3:
1.130462423279179076835027334729635587999227471386774372225935574837680527245105348721767116045950523 + i * 0.06056151842435440796490272841322840222506160359834955635225290715771937099154864784247457109174052572
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=86 + 58\zeta_{18} + 110\zeta_{18}^{2} - 106\zeta_{18}^{3} - 134\zeta_{18}^{4} - 10\zeta_{18}^{5}$
27
4
1:
1.115760427452665524582547038153409460624374328791498488248004354211680476688344449426353342101597343 + i * 0.3412711769185109705670235325242660513881108550291900044985961241718408976725293370799085132506034949
comment: $\chi$ of order $9$, even
27
4
2:
1.151508774123342403026740551226549959778739208578287080271212941993331397992840258576570868494516986 + i * 0.1899186423186134375062016337467312181756665464658937264597052102417073040096797985678345507284860325
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{28 - 20\zeta_{9} - 20\zeta_{9}^{2} - 4\zeta_{9}^{3} - 4\zeta_{9}^{4} - 28\zeta_{9}^{5}}{3}$
27
4
3:
1.089581970483172560082474831140798836566200639679318137835234161767608886489360563511441015766697695 + i * 0.09070309944790490531081560861875661487254477465888712446290329640788620400494029197747024274005785596
comment: $\chi$ of order $9$, even
27
5
1:
0.4465541098793417324565500290496198043549679288457711801616508720474153131325026420182017983559023577 + i * 0.4213020739903156484389681066544179872422742232055318647252015741560432416352048224293389800131118421
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-2 + 2\zeta_{18} + 4\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}}{3}$
27
5
2:
0.8515349946205237225497554515682924463157677588319658101798911279811745003770265186683932223814613797 + i * 0.2363237585144476135640263633349940604160626350962473244215148672512515417058472782586857914346007327
comment: $\chi$ of order $18$, odd
27
5
3:
0.9550674867048917074074770032021664539906256119030400533675854477764827127402694989778158772941126685 + i * 0.1212934263900449846286008839107601413158112201485241845925779313703732894478175819116851990265275615
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-20 - 100\zeta_{18} - 134\zeta_{18}^{2} + 106\zeta_{18}^{3} - 10\zeta_{18}^{4} + 58\zeta_{18}^{5}$
27
7
1:
1.115760427452665524582547038153409460624374328791498488248004354211680476688344449426353342101597343 + i * -0.3412711769185109705670235325242660513881108550291900044985961241718408976725293370799085132506034949
comment: $\chi$ of order $9$, even
27
7
2:
1.151508774123342403026740551226549959778739208578287080271212941993331397992840258576570868494516986 + i * -0.1899186423186134375062016337467312181756665464658937264597052102417073040096797985678345507284860325
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{32 + 20\zeta_{9} + 20\zeta_{9}^{2} + 4\zeta_{9}^{3} - 8\zeta_{9}^{4} + 16\zeta_{9}^{5}}{3}$
27
7
3:
1.089581970483172560082474831140798836566200639679318137835234161767608886489360563511441015766697695 + i * -0.09070309944790490531081560861875661487254477465888712446290329640788620400494029197747024274005785596
comment: $\chi$ of order $9$, even
27
11
1:
0.4465541098793417324565500290496198043549679288457711801616508720474153131325026420182017983559023577 + i * -0.4213020739903156484389681066544179872422742232055318647252015741560432416352048224293389800131118421
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-4 + 4\zeta_{18} + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 4\zeta_{18}^{5}}{3}$
27
11
2:
0.8515349946205237225497554515682924463157677588319658101798911279811745003770265186683932223814613797 + i * -0.2363237585144476135640263633349940604160626350962473244215148672512515417058472782586857914346007327
comment: $\chi$ of order $18$, odd
27
11
3:
0.9550674867048917074074770032021664539906256119030400533675854477764827127402694989778158772941126685 + i * -0.1212934263900449846286008839107601413158112201485241845925779313703732894478175819116851990265275615
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=86 - 134\zeta_{18} - 100\zeta_{18}^{2} - 106\zeta_{18}^{3} + 76\zeta_{18}^{4} + 110\zeta_{18}^{5}$
27
13
1:
0.6708527834997067177762363504238727126764368218085076697565152224116284697052568637190570735880627795 + i * 0.1803680129252321836474438055593717548640720102907750537070208269383444547694945803874208468407996039
comment: $\chi$ of order $9$, even
27
13
2:
0.8154394354061857665278611702047965613349424201613460563534559025655335097281893613768342895234872056 + i * 0.08960571682523145794116610759069781528228216049369834623918075528771860110029483361397863353802833807
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{28 + 4\zeta_{9} - 8\zeta_{9}^{2} - 4\zeta_{9}^{3} - 16\zeta_{9}^{4} + 20\zeta_{9}^{5}}{3}$
27
13
3:
0.8960721559663816893011654320217475975816557840627880813242172411175898142676800356656738735167920664 + i * 0.04213108148936475279460678645422293863752758713320322690876895490188708067733226566814431085684581361
comment: $\chi$ of order $9$, even
27
14
1:
1.693468257439594863001517558992703572079429976340464449437358426439281740691219922936684294113118365 + i * -0.5069911147078847843958277748444444658531720058977206651951899901419461294114034337159550114807794204
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-2 - 4\zeta_{18} - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}}{3}$
27
14
2:
1.290397357359104318073556851829263233135494507575290681206531318558577307349892811686667699793600154 + i * -0.1643549479312102716424738789959139883513715878772450656429163570140234460596872885360547878438642296
comment: $\chi$ of order $18$, odd
27
14
3:
1.130462423279179076835027334729635587999227471386774372225935574837680527245105348721767116045950523 + i * -0.06056151842435440796490272841322840222506160359834955635225290715771937099154864784247457109174052572
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-20 + 110\zeta_{18} + 58\zeta_{18}^{2} + 106\zeta_{18}^{3} - 100\zeta_{18}^{4} + 76\zeta_{18}^{5}$
27
16
1:
0.8427329235067230567866848539885032459222741831620914688650610479901145222386767169970264281329519871 + i * 0.4707643909480144245363490106681759392126140770401018549200501360912357912345898727828558913234727603
comment: $\chi$ of order $9$, even
27
16
2:
0.9909773598908120868236659390012534489298249887015948671557301465064050846719083968218029526118760739 + i * 0.2665742936175943290585958819135047917810366235337328801971398673757958081027945742871201134015625773
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{32 - 28\zeta_{9} - 16\zeta_{9}^{2} + 4\zeta_{9}^{3} - 20\zeta_{9}^{4} + 4\zeta_{9}^{5}}{3}$
27
16
3:
1.009626893154537185234691368097600584376013978900979987223466937642877881954899876550685469333198330 + i * 0.1305019036835240057442717378222915963168990961245227445500460497395299553460759584393672207921034111
comment: $\chi$ of order $9$, even
27
20
1:
0.9010756389803662948413654087752211005944093611322063102630911668907037599747408520697118916890202866 + i * 0.2697643375574582437315561961000159729327556120238371489878701849874509683435453333691509203881777032
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-4 - 2\zeta_{18} + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}}{3}$
27
20
2:
0.8670738223608907541309151210226263784549363465616308152259752191013873267476974313386893290712520597 + i * 0.1243718040326454339718452372109889654505854755889197108695926855674622432910387200707705772550561918
comment: $\chi$ of order $18$, odd
27
20
3:
0.9159584640565150246999160273292842611473141448664056984642652053671822463249426736006916559988946996 + i * 0.06756143677337148806417163632153234713386469840789758576721649826583253134099631548487172501143321355
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=86 + 76\zeta_{18} - 10\zeta_{18}^{2} - 106\zeta_{18}^{3} + 58\zeta_{18}^{4} - 100\zeta_{18}^{5}$
27
22
1:
0.8427329235067230567866848539885032459222741831620914688650610479901145222386767169970264281329519871 + i * -0.4707643909480144245363490106681759392126140770401018549200501360912357912345898727828558913234727603
comment: $\chi$ of order $9$, even
27
22
2:
0.9909773598908120868236659390012534489298249887015948671557301465064050846719083968218029526118760739 + i * -0.2665742936175943290585958819135047917810366235337328801971398673757958081027945742871201134015625773
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{28 + 16\zeta_{9} + 28\zeta_{9}^{2} - 4\zeta_{9}^{3} + 20\zeta_{9}^{4} + 8\zeta_{9}^{5}}{3}$
27
22
3:
1.009626893154537185234691368097600584376013978900979987223466937642877881954899876550685469333198330 + i * -0.1305019036835240057442717378222915963168990961245227445500460497395299553460759584393672207921034111
comment: $\chi$ of order $9$, even
27
23
1:
0.9010756389803662948413654087752211005944093611322063102630911668907037599747408520697118916890202866 + i * -0.2697643375574582437315561961000159729327556120238371489878701849874509683435453333691509203881777032
comment: $\chi$ of order $18$, odd; $B_{1,\bar\chi}=\frac{-2 + 2\zeta_{18} - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 4\zeta_{18}^{4} + 4\zeta_{18}^{5}}{3}$
27
23
2:
0.8670738223608907541309151210226263784549363465616308152259752191013873267476974313386893290712520597 + i * -0.1243718040326454339718452372109889654505854755889197108695926855674622432910387200707705772550561918
comment: $\chi$ of order $18$, odd
27
23
3:
0.9159584640565150246999160273292842611473141448664056984642652053671822463249426736006916559988946996 + i * -0.06756143677337148806417163632153234713386469840789758576721649826583253134099631548487172501143321355
comment: $\chi$ of order $18$, odd; $B_{3,\bar\chi}=-20 - 10\zeta_{18} + 76\zeta_{18}^{2} + 106\zeta_{18}^{3} + 110\zeta_{18}^{4} - 134\zeta_{18}^{5}$
27
25
1:
0.6708527834997067177762363504238727126764368218085076697565152224116284697052568637190570735880627795 + i * -0.1803680129252321836474438055593717548640720102907750537070208269383444547694945803874208468407996039
comment: $\chi$ of order $9$, even
27
25
2:
0.8154394354061857665278611702047965613349424201613460563534559025655335097281893613768342895234872056 + i * -0.08960571682523145794116610759069781528228216049369834623918075528771860110029483361397863353802833807
comment: $\chi$ of order $9$, even; $B_{2,\bar\chi}=\frac{32 + 8\zeta_{9} - 4\zeta_{9}^{2} + 4\zeta_{9}^{3} + 28\zeta_{9}^{4} - 20\zeta_{9}^{5}}{3}$
27
25
3:
0.8960721559663816893011654320217475975816557840627880813242172411175898142676800356656738735167920664 + i * -0.04213108148936475279460678645422293863752758713320322690876895490188708067733226566814431085684581361
comment: $\chi$ of order $9$, even
28
3
1:
0.8272499164049314558331680411552352177252556204381471252338084947812609923568458600079373724009271050 + i * -0.2685074801340814142652917542540307343837432462104955226943470332019009129656963715276059144734511753
comment: $\chi$ of order $6$, even
28
3
2:
0.9542788262522103118606737323442667582787257192152640739345970177577227561099080144385801748935834893 + i * -0.1110151281483997291285113058014606976215890320200068543482079475781118515510580413649934481258767931
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=4 + 12\zeta_{6}$
28
3
3:
0.9845266558405222987639960250086385756288465412619023516139116626795992491203914294098891728662529016 + i * -0.03700604124625547778521890170097212433284594366441487265356096734990217649477425807704533585198052940
comment: $\chi$ of order $6$, even
28
11
1:
1.063864181445365119648246331075625711862569371661856266282094996520561272783031705715201164535842053 + i * 0.5273864705389128736174618232435213603330738250134940978059863586405626827435837037540041568219144077
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2 + 2\zeta_{6}$
28
11
2:
1.034663779168900183757015146246514700032719446279551043162694959825334132354994684418449879065964680 + i * 0.1422678584371903780630376213501867507781411455291157229016468013364998639270059971596558986963365857
comment: $\chi$ of order $6$, odd
28
11
3:
1.014340306949921305675264029839835091445704392716478680460329393898979928524277565398477014548329918 + i * 0.04047660899406678417434863139635111169289775808337919380042575341115261385029791397944367609867989770
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=138 - 234\zeta_{6}$
28
19
1:
0.8272499164049314558331680411552352177252556204381471252338084947812609923568458600079373724009271050 + i * 0.2685074801340814142652917542540307343837432462104955226943470332019009129656963715276059144734511753
comment: $\chi$ of order $6$, even
28
19
2:
0.9542788262522103118606737323442667582787257192152640739345970177577227561099080144385801748935834893 + i * 0.1110151281483997291285113058014606976215890320200068543482079475781118515510580413649934481258767931
comment: $\chi$ of order $6$, even; $B_{2,\bar\chi}=16 - 12\zeta_{6}$
28
19
3:
0.9845266558405222987639960250086385756288465412619023516139116626795992491203914294098891728662529016 + i * 0.03700604124625547778521890170097212433284594366441487265356096734990217649477425807704533585198052940
comment: $\chi$ of order $6$, even
28
23
1:
1.063864181445365119648246331075625711862569371661856266282094996520561272783031705715201164535842053 + i * -0.5273864705389128736174618232435213603330738250134940978059863586405626827435837037540041568219144077
comment: $\chi$ of order $6$, odd; $B_{1,\bar\chi}=-2\zeta_{6}$
28
23
2:
1.034663779168900183757015146246514700032719446279551043162694959825334132354994684418449879065964680 + i * -0.1422678584371903780630376213501867507781411455291157229016468013364998639270059971596558986963365857
comment: $\chi$ of order $6$, odd
28
23
3:
1.014340306949921305675264029839835091445704392716478680460329393898979928524277565398477014548329918 + i * -0.04047660899406678417434863139635111169289775808337919380042575341115261385029791397944367609867989770
comment: $\chi$ of order $6$, odd; $B_{3,\bar\chi}=-96 + 234\zeta_{6}$
28
27
1:
1.046454884756166976644578641789551720493642740851725040469475434022158632347258214245213772198257743 + i * 0
equals: $\kappa_{28}$
comment: $\chi=\left(\frac{28}{\cdot}\right)$, even
28
27
2:
1.065817093219225468172008621250038071217468707343639076639549878521200632945334008195223736731140961 + i * 0
comment: $\chi=\left(\frac{28}{\cdot}\right)$, even; $L(2,\chi)=\frac{4\pi^2}{7\sqrt{28}}$
28
27
3:
1.028909459254884479025463765860450912245894086534101929785673775540541580717867005559395259142429122 + i * 0
comment: $\chi=\left(\frac{28}{\cdot}\right)$, even
29
2
1:
1.863111678567218778892754383702752699991743288611521209394111338665142634958509034944247678336757202 + i * 0.5674444185641066731077142781148342952534987909444177174567313155651521430764811429364369448662775286
comment: $\chi$ of order $28$, odd
29
2
2:
1.354170325043969720591979009680201385543614883860989557701825754423831590692851268331671212243101502 + i * 0.1865090318791123480728232187957219329879789231005798289994975237888904409574157438684955110831200706
comment: $\chi$ of order $28$, odd
29
2
3:
1.153468356778784972142889065953701012189237110319969348765101752612657960456568615443610842036654204 + i * 0.06707718491087106275849618612666474294134230534328527323796510194129885781534599022552403962532785752
comment: $\chi$ of order $28$, odd
29
3
1:
1.607775250316088033204129300475528047762210321986229978911982878565448318596045403392267199045750097 + i * 0.5051594150687983231500417528601130489918633383363606659383381180811329667638328091614962503964376819
comment: $\chi$ of order $28$, odd
29
3
2:
1.216380570168147390509779340416237503553927440878382105688066720810834400406197097918743316701797444 + i * 0.2127613001244286796177022653336351186767975453333163177944911796049980618548216604668233971478047062
comment: $\chi$ of order $28$, odd
29
3
3:
1.085068875770112390393408597633059868435884426387312915112260792650967282389973257151685160955504291 + i * 0.1021461084779834880494615216553336478148866781138614498322384821814035048645801528607358387345802387
comment: $\chi$ of order $28$, odd
29
4
1:
1.077049267312924022848219886832710117743240692998563879280614579680127764242452520549708868662049300 + i * 0.4215966082980289319405755070155309410715268741023557723638737283058939570671969916229831612223110517
comment: $\chi$ of order $14$, even
29
4
2:
1.138894282118110489442667660922011122056326208214368396850122284254147984656866786568967729509775777 + i * 0.2121905483861771359903624187888701250241547451062617843534760888081796939660753476376355890480397162
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{484 - 276\zeta_{14} - 20\zeta_{14}^{2} - 112\zeta_{14}^{3} + 108\zeta_{14}^{4} - 312\zeta_{14}^{5}}{29}$
29
4
3:
1.089019771301555188578365191856885870078502796880193265164625888738110369581920554752029440172482949 + i * 0.09088372993423973613964435162678427378065522482557018418213978877906594467653191688155793548956541364
comment: $\chi$ of order $14$, even
29
5
1:
0.9788579405933912737367549299318992756538418629400599964505336696677352273501862949978746295958730665 + i * -0.5013789824495794884372457959879603591986397372517573520424344258131161569784357492221248952553207293
comment: $\chi$ of order $14$, even
29
5
2:
1.065497721901258973254196354647638514896218036513529703628284239716211012327956488199180994300276758 + i * -0.2846437435025228339697433797116420995319399733581682094125502413337233374543476971089350039755024926
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{172 + 332\zeta_{14} - 204\zeta_{14}^{2} + 312\zeta_{14}^{3} - 36\zeta_{14}^{4} + 200\zeta_{14}^{5}}{29}$
29
5
3:
1.041524322181716708753837799851903974325548010541611423915484144709368861626084830130075671128995127 + i * -0.1388486298343264230281613006805956573986405148158382729359477283666828074448858718823817604855522840
comment: $\chi$ of order $14$, even
29
6
1:
0.9788579405933912737367549299318992756538418629400599964505336696677352273501862949978746295958730665 + i * 0.5013789824495794884372457959879603591986397372517573520424344258131161569784357492221248952553207293
comment: $\chi$ of order $14$, even
29
6
2:
1.065497721901258973254196354647638514896218036513529703628284239716211012327956488199180994300276758 + i * 0.2846437435025228339697433797116420995319399733581682094125502413337233374543476971089350039755024926
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{504 - 332\zeta_{14} + 132\zeta_{14}^{2} - 296\zeta_{14}^{3} + 20\zeta_{14}^{4} - 128\zeta_{14}^{5}}{29}$
29
6
3:
1.041524322181716708753837799851903974325548010541611423915484144709368861626084830130075671128995127 + i * 0.1388486298343264230281613006805956573986405148158382729359477283666828074448858718823817604855522840
comment: $\chi$ of order $14$, even
29
7
1:
0.6528919956690995062953543814021631118323047056578747050046222954626201227724046053869008002743693343 + i * 0.3316007111437381129631141885005830877781166183999323017072414203069713320644133162408212989009039398
comment: $\chi$ of order $7$, even
29
7
2:
0.8326062007273920626009872190087976833799259003974352095684627841335334501384855802497602335505417826 + i * 0.1673215775194738740249674850647372965650238819511883066546693271683891697965021297203276513768685015
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=-4\zeta_{7} - 12\zeta_{7}^{2} - 8\zeta_{7}^{3} + 4\zeta_{7}^{4} - 8\zeta_{7}^{5}$
29
7
3:
0.9104045050594959398569988992381529364382218165342420805353887128548597959732804268091547077220478168 + i * 0.07552569722388780345037717751772941989634535997451068826302481468638706524578373274781029220383394895
comment: $\chi$ of order $7$, even
29
8
1:
0.8558977307700744832286860225070560738442494151544364501087185949817025115423593645926161030258002197 + i * 0.6589800951225375128421575083809983593510908074819893539212145910170636885459350116245240594541722623
comment: $\chi$ of order $28$, odd
29
8
2:
1.050803823515235006305229314700413557424036454328568413399430733794687081754510863212961019451908739 + i * 0.2288579614597406990744009764836791178799568162073526766307346898654389199015927910252690017306171202
comment: $\chi$ of order $28$, odd
29
8
3:
1.056026957046021121721769219836182933464013317494769251138825085455843468297265057114544805946062279 + i * 0.09175056292927379147445148436557956869010214218824028191155544292286907586374084151308479270228729008
comment: $\chi$ of order $28$, odd
29
9
1:
0.7883965330630419235358867828544800169515407463831183816892869533068224530788045175651780264796286353 + i * -0.02553417020540173813731892465157138249173856387790159576104863292914999165672352587621134519866077312
comment: $\chi$ of order $14$, even
29
9
2:
0.8859033552082932808978190355518527357878675684119894160771273076141787467685056587293239505812238018 + i * 0.04227164810669320345595153376070173419607788044300932360082677432221381535366587275743916184242527154
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{376 - 4\zeta_{14} - 108\zeta_{14}^{2} + 128\zeta_{14}^{3} + 204\zeta_{14}^{4} - 168\zeta_{14}^{5}}{29}$
29
9
3:
0.9339325224397388103076485617073594214503724242101298318599622242067298416961841681670921894167621940 + i * 0.04735861974612536264798957582525259461482153968595688071035435620976665331380387269982191192299225632
comment: $\chi$ of order $14$, even
29
10
1:
1.607775250316088033204129300475528047762210321986229978911982878565448318596045403392267199045750097 + i * -0.5051594150687983231500417528601130489918633383363606659383381180811329667638328091614962503964376819
comment: $\chi$ of order $28$, odd
29
10
2:
1.216380570168147390509779340416237503553927440878382105688066720810834400406197097918743316701797444 + i * -0.2127613001244286796177022653336351186767975453333163177944911796049980618548216604668233971478047062
comment: $\chi$ of order $28$, odd
29
10
3:
1.085068875770112390393408597633059868435884426387312915112260792650967282389973257151685160955504291 + i * -0.1021461084779834880494615216553336478148866781138614498322384821814035048645801528607358387345802387
comment: $\chi$ of order $28$, odd
29
11
1:
0.8558977307700744832286860225070560738442494151544364501087185949817025115423593645926161030258002197 + i * -0.6589800951225375128421575083809983593510908074819893539212145910170636885459350116245240594541722623
comment: $\chi$ of order $28$, odd
29
11
2:
1.050803823515235006305229314700413557424036454328568413399430733794687081754510863212961019451908739 + i * -0.2288579614597406990744009764836791178799568162073526766307346898654389199015927910252690017306171202
comment: $\chi$ of order $28$, odd
29
11
3:
1.056026957046021121721769219836182933464013317494769251138825085455843468297265057114544805946062279 + i * -0.09175056292927379147445148436557956869010214218824028191155544292286907586374084151308479270228729008
comment: $\chi$ of order $28$, odd
29
12
1:
0.4625314657412357731791844001331171737097293931706122770695103811320242462760615183839487578847182508 + i * 0.6831742205969025894989686484738718749791263586963704123618725560860629643073277818209371196113690861
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=1 + i$
29
12
2:
0.8791889734492851371248078567350973058776955894761753575871791541469142098657582952664190926362390207 + i * 0.3412097500381734210321693658223671740782154709974139537831344330939312198731166295307031459866133580
comment: $\chi$ of order $4$, odd
29
12
3:
0.9732544222042515494973353051615624501949031984639600413313579280699273664987240106552916493676564031 + i * 0.1595433518998214344702302903196370467214539572150697840640713949571377571213754714020627419990006814
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=-216 + 6i$
29
13
1:
0.7883965330630419235358867828544800169515407463831183816892869533068224530788045175651780264796286353 + i * 0.02553417020540173813731892465157138249173856387790159576104863292914999165672352587621134519866077312
comment: $\chi$ of order $14$, even
29
13
2:
0.8859033552082932808978190355518527357878675684119894160771273076141787467685056587293239505812238018 + i * -0.04227164810669320345595153376070173419607788044300932360082677432221381535366587275743916184242527154
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{372 + 4\zeta_{14} + 164\zeta_{14}^{2} - 200\zeta_{14}^{3} - 132\zeta_{14}^{4} + 112\zeta_{14}^{5}}{29}$
29
13
3:
0.9339325224397388103076485617073594214503724242101298318599622242067298416961841681670921894167621940 + i * -0.04735861974612536264798957582525259461482153968595688071035435620976665331380387269982191192299225632
comment: $\chi$ of order $14$, even
29
14
1:
0.3747250616311040126376087490452590141744320167749053269524873341395931560570871305357745242134839398 + i * 0.2511309087038515192240157339746486189828070322530919034517905614409182717399651531981768464518958226
comment: $\chi$ of order $28$, odd
29
14
2:
0.7363156471994181940958767492687024121255871229237239378379492706302923525992161908404700947196757074 + i * 0.1282042467801825864018997717478571853704925302594536224748325177285108001891297053018072476136479499
comment: $\chi$ of order $28$, odd
29
14
3:
0.8732187872674919657197087511386336923072808545465328229488111220405560134277037619211312875774065295 + i * 0.05605330051730899918496873587007074653132843345750436884178109694967786414769069582730702679396826440
comment: $\chi$ of order $28$, odd
29
15
1:
1.863111678567218778892754383702752699991743288611521209394111338665142634958509034944247678336757202 + i * -0.5674444185641066731077142781148342952534987909444177174567313155651521430764811429364369448662775286
comment: $\chi$ of order $28$, odd
29
15
2:
1.354170325043969720591979009680201385543614883860989557701825754423831590692851268331671212243101502 + i * -0.1865090318791123480728232187957219329879789231005798289994975237888904409574157438684955110831200706
comment: $\chi$ of order $28$, odd
29
15
3:
1.153468356778784972142889065953701012189237110319969348765101752612657960456568615443610842036654204 + i * -0.06707718491087106275849618612666474294134230534328527323796510194129885781534599022552403962532785752
comment: $\chi$ of order $28$, odd
29
16
1:
1.107935304826313615593883320736263047921692986909504709103218353362815476748611833655199794969213160 + i * 0.2465575357161472914858490701942789334492058563333131989105933820169196735125165105264742738467427542
comment: $\chi$ of order $7$, even
29
16
2:
1.123703826331220002407217217161567753421769532805309292921968748339545208803638577455138151959875483 + i * 0.1470175403707752671029061687708530819570845298258607252342214909207452301297562256081230351807244395
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=-4 - 12\zeta_{7} - 4\zeta_{7}^{2} - 16\zeta_{7}^{3} - 12\zeta_{7}^{4} - 8\zeta_{7}^{5}$
29
16
3:
1.069867617898473831242866039469436734432231685241627164565033959224548703783277715354682094400670064 + i * 0.07804486704090951528413102992879936444363073705605589194033432057909578358005237415647285319201628084
comment: $\chi$ of order $7$, even
29
17
1:
0.4625314657412357731791844001331171737097293931706122770695103811320242462760615183839487578847182508 + i * -0.6831742205969025894989686484738718749791263586963704123618725560860629643073277818209371196113690861
comment: $\chi$ of order $4$, odd; $B_{1,\bar\chi}=1 - i$
29
17
2:
0.8791889734492851371248078567350973058776955894761753575871791541469142098657582952664190926362390207 + i * -0.3412097500381734210321693658223671740782154709974139537831344330939312198731166295307031459866133580
comment: $\chi$ of order $4$, odd
29
17
3:
0.9732544222042515494973353051615624501949031984639600413313579280699273664987240106552916493676564031 + i * -0.1595433518998214344702302903196370467214539572150697840640713949571377571213754714020627419990006814
comment: $\chi$ of order $4$, odd; $B_{3,\bar\chi}=-216 - 6i$
29
18
1:
0.9517205724422937824108322212343615198789924683437908809511595645340122824501913083180074044904312365 + i * -0.1276036800316451376776815820561981831494141337284844477009802737928811137518356971580336884819149353
comment: $\chi$ of order $28$, odd
29
18
2:
0.9084610115959780971619100713437147160900351526829521148709527766130218905554435599487992031735873756 + i * 0.04524921843225337460839572533920517581450600367765746110059228834890667570342986472773283619746038699
comment: $\chi$ of order $28$, odd
29
18
3:
0.9366738010034072845074838050480718293099681306111416760076492862469288797684752708834672151848149456 + i * 0.04963051819057596969834996655633487972062423127144014994461479278602684281612084668194243701740799808
comment: $\chi$ of order $28$, odd
29
19
1:
0.8568338239227482057272451545378552191938926632321629780088618598172240421602352683326054884434261429 + i * 0.1013611466735976045600400800316137626580762590295167974864630510128426498690176424219711518733373936
comment: $\chi$ of order $28$, odd
29
19
2:
0.8532967813600544418554882756313862906139704863333650269325471052276596859817424601461451142824935484 + i * 0.1134275970803916036641054733345907293382117867442814785461402385962581081906933379031812339414288909
comment: $\chi$ of order $28$, odd
29
19
3:
0.9222242890076805391317634849587203163554268998399797860617580851963764237373601837363563784956332869 + i * 0.07830918118603776539675768387565041284944798335903238161425626053563037486989697391117889398589722948
comment: $\chi$ of order $28$, odd
29
20
1:
1.107935304826313615593883320736263047921692986909504709103218353362815476748611833655199794969213160 + i * -0.2465575357161472914858490701942789334492058563333131989105933820169196735125165105264742738467427542
comment: $\chi$ of order $7$, even
29
20
2:
1.123703826331220002407217217161567753421769532805309292921968748339545208803638577455138151959875483 + i * -0.1470175403707752671029061687708530819570845298258607252342214909207452301297562256081230351807244395
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=8 + 12\zeta_{7} + 4\zeta_{7}^{2} - 4\zeta_{7}^{4} + 8\zeta_{7}^{5}$
29
20
3:
1.069867617898473831242866039469436734432231685241627164565033959224548703783277715354682094400670064 + i * -0.07804486704090951528413102992879936444363073705605589194033432057909578358005237415647285319201628084
comment: $\chi$ of order $7$, even
29
21
1:
0.9517205724422937824108322212343615198789924683437908809511595645340122824501913083180074044904312365 + i * 0.1276036800316451376776815820561981831494141337284844477009802737928811137518356971580336884819149353
comment: $\chi$ of order $28$, odd
29
21
2:
0.9084610115959780971619100713437147160900351526829521148709527766130218905554435599487992031735873756 + i * -0.04524921843225337460839572533920517581450600367765746110059228834890667570342986472773283619746038699
comment: $\chi$ of order $28$, odd
29
21
3:
0.9366738010034072845074838050480718293099681306111416760076492862469288797684752708834672151848149456 + i * -0.04963051819057596969834996655633487972062423127144014994461479278602684281612084668194243701740799808
comment: $\chi$ of order $28$, odd
29
22
1:
1.077049267312924022848219886832710117743240692998563879280614579680127764242452520549708868662049300 + i * -0.4215966082980289319405755070155309410715268741023557723638737283058939570671969916229831612223110517
comment: $\chi$ of order $14$, even
29
22
2:
1.138894282118110489442667660922011122056326208214368396850122284254147984656866786568967729509775777 + i * -0.2121905483861771359903624187888701250241547451062617843534760888081796939660753476376355890480397162
comment: $\chi$ of order $14$, even; $B_{2,\bar\chi}=\frac{208 + 276\zeta_{14} + 36\zeta_{14}^{2} + 168\zeta_{14}^{3} - 164\zeta_{14}^{4} + 296\zeta_{14}^{5}}{29}$
29
22
3:
1.089019771301555188578365191856885870078502796880193265164625888738110369581920554752029440172482949 + i * -0.09088372993423973613964435162678427378065522482557018418213978877906594467653191688155793548956541364
comment: $\chi$ of order $14$, even
29
23
1:
0.4060286231942714205573887035718001942908100162218712018480351881155686578936383286173968559271867184 + i * -0.4387473455931068696822658632308689511387991310417234420759459305632222478033968864530483214006972151
comment: $\chi$ of order $7$, even
29
23
2:
0.7801654149504513918165223866390114970130906035563263695509861969948309799871779240694727275779940795 + i * -0.2640833973627735506160341475082074584325067976890502601384385230947314514209488037350667134432024482
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=8 - 4\zeta_{7} + 12\zeta_{7}^{2} + 8\zeta_{7}^{3} + 4\zeta_{7}^{4}$
29
23
3:
0.9219298703489266269827674822885797527743866423107285661687933985217416340280912546620003780830568089 + i * -0.1331461490688349600146373678664926415469594932067495451034671582796829324526995885113736027971395034
comment: $\chi$ of order $7$, even
29
24
1:
0.4060286231942714205573887035718001942908100162218712018480351881155686578936383286173968559271867184 + i * 0.4387473455931068696822658632308689511387991310417234420759459305632222478033968864530483214006972151
comment: $\chi$ of order $7$, even
29
24
2:
0.7801654149504513918165223866390114970130906035563263695509861969948309799871779240694727275779940795 + i * 0.2640833973627735506160341475082074584325067976890502601384385230947314514209488037350667134432024482
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=12 + 4\zeta_{7} + 4\zeta_{7}^{2} + 8\zeta_{7}^{3} + 12\zeta_{7}^{4} + 16\zeta_{7}^{5}$
29
24
3:
0.9219298703489266269827674822885797527743866423107285661687933985217416340280912546620003780830568089 + i * 0.1331461490688349600146373678664926415469594932067495451034671582796829324526995885113736027971395034
comment: $\chi$ of order $7$, even
29
25
1:
0.6528919956690995062953543814021631118323047056578747050046222954626201227724046053869008002743693343 + i * -0.3316007111437381129631141885005830877781166183999323017072414203069713320644133162408212989009039398
comment: $\chi$ of order $7$, even
29
25
2:
0.8326062007273920626009872190087976833799259003974352095684627841335334501384855802497602335505417826 + i * -0.1673215775194738740249674850647372965650238819511883066546693271683891697965021297203276513768685015
comment: $\chi$ of order $7$, even; $B_{2,\bar\chi}=4 + 4\zeta_{7} - 4\zeta_{7}^{2} + 8\zeta_{7}^{3} - 4\zeta_{7}^{4} - 8\zeta_{7}^{5}$
29
25
3:
0.9104045050594959398569988992381529364382218165342420805353887128548597959732804268091547077220478168 + i * -0.07552569722388780345037717751772941989634535997451068826302481468638706524578373274781029220383394895
comment: $\chi$ of order $7$, even
29
26
1:
0.8568338239227482057272451545378552191938926632321629780088618598172240421602352683326054884434261429 + i * -0.1013611466735976045600400800316137626580762590295167974864630510128426498690176424219711518733373936
comment: $\chi$ of order $28$, odd
29
26
2:
0.8532967813600544418554882756313862906139704863333650269325471052276596859817424601461451142824935484 + i * -0.1134275970803916036641054733345907293382117867442814785461402385962581081906933379031812339414288909
comment: $\chi$ of order $28$, odd
29
26
3:
0.9222242890076805391317634849587203163554268998399797860617580851963764237373601837363563784956332869 + i * -0.07830918118603776539675768387565041284944798335903238161425626053563037486989697391117889398589722948
comment: $\chi$ of order $28$, odd
29
27
1:
0.3747250616311040126376087490452590141744320167749053269524873341395931560570871305357745242134839398 + i * -0.2511309087038515192240157339746486189828070322530919034517905614409182717399651531981768464518958226
comment: $\chi$ of order $28$, odd
29
27
2:
0.7363156471994181940958767492687024121255871229237239378379492706302923525992161908404700947196757074 + i * -0.1282042467801825864018997717478571853704925302594536224748325177285108001891297053018072476136479499
comment: $\chi$ of order $28$, odd
29
27
3:
0.8732187872674919657197087511386336923072808545465328229488111220405560134277037619211312875774065295 + i * -0.05605330051730899918496873587007074653132843345750436884178109694967786414769069582730702679396826440
comment: $\chi$ of order $28$, odd
29
28
1:
0.6117662895623068698258128340458616710179192358179643741847055063750198423554003478202328381995953697 + i * 0
equals: $\kappa_{29}$
comment: $\chi=\left(\frac{29}{\cdot}\right)$, even
29
28
2:
0.7583749766623480819283600644913412843977129204188543315135428462769403486866995052527695134548860878 + i * 0
comment: $\chi=\left(\frac{29}{\cdot}\right)$, even; $L(2,\chi)=\frac{12\pi^2}{29\sqrt{29}}$
29
28
3:
0.8660237146696257008519319951860173420344249746800306974160276948318521875317686795643612337088283193 + i * 0
comment: $\chi=\left(\frac{29}{\cdot}\right)$, even
Definition
The value $L(s,\chi)=\sum_{m=1}^{\infty}\chi(m)\,m^{-s}$ [3] of the Dirichlet $L$-function of a primitive Dirichlet character $\chi$ of conductor $q$ at a positive integer $s$, listed for every primitive character, each indexed by its Conrey label $(q,n)$ [7], $\chi=\chi_q(n,\cdot)$.
Parameters
$q$
—   conductor of $\chi$ ($q\geq 1$, $q\not\equiv 2\pmod 4$)
$n$
—   Conrey index of $\chi$ ($1\leq n\leq\max(q-1,1)$, $\gcd(n,q)=1$, and $\chi_q(n,\cdot)$ primitive)
$s$
—   argument of $L$ ($s\geq 1$, and $s\geq 2$ when $q=1$)
Formulas
(1)
$L(s,\chi)=q^{-s}\sum_{a=1}^{q}\chi(a)\,\zeta(s,a/q)$ for $s\geq 2$, with $\zeta(s,x)=\sum_{m=0}^{\infty}(m+x)^{-s}$ the Hurwitz zeta function; and for $\chi\neq 1$, $L(1,\chi)=-\frac{1}{q}\sum_{a=1}^{q}\chi(a)\,\psi(a/q)$ with $\psi$ the digamma function, the poles of $\zeta(s,a/q)$ at $s=1$ cancelling because $\sum_a\chi(a)=0$.
(2)
$L(s,\chi)=\prod_{p}\left(1-\chi(p)\,p^{-s}\right)^{-1}$ over the primes, for $s\geq 2$; for $s=1$ and $\chi\neq 1$ the Dirichlet series converges conditionally and the product converges to the same value [2].
(3)
$L(s,\bar\chi)=\overline{L(s,\chi)}$ for real $s$, since $\bar\chi(m)= \overline{\chi(m)}$; in Conrey's labels, the entry $(q,n',s)$ is the conjugate of $(q,n,s)$ when $nn'\equiv 1\pmod q$.
(4)
For a character $\chi$ modulo $m$ induced by the primitive character $\chi^*$ of conductor $q\mid m$: $L(s,\chi)=L(s,\chi^*)\prod_{p\mid m}\left(1-\chi^*(p)\,p^{-s}\right)$.
(5)
For primitive $\chi$ of conductor $q$ with $\chi(-1)=(-1)^s$: $L(s,\chi)=(-1)^{s-1}\,\frac{\tau(\chi)}{2}\left(\frac{2\pi i}{q}\right)^{s} \frac{B_{s,\bar\chi}}{s!}$, with $\tau(\chi)=\sum_{a=1}^{q}\chi(a)e^{2\pi ia/q}$ the Gauss sum and $B_{k,\chi}$ the generalized Bernoulli numbers, $\sum_{a=1}^{q}\chi(a)\frac{te^{at}}{e^{qt}-1} =\sum_{k\geq 0}B_{k,\chi}\frac{t^k}{k!}$ [1]. It is the functional equation (9) at $s$ together with $L(1-s,\bar\chi)=-B_{s,\bar\chi}/s$.
(6)
For the real character $\chi=\left(\frac{D}{\cdot}\right)$ of conductor $q=|D|$ with $\chi(-1)=(-1)^s$, where $\tau(\chi)=i^{\mathfrak a}\sqrt{q}$ and $B_{s,\chi}$ is rational: $L(s,\chi)=(-1)^{s-1+(\mathfrak a+s)/2}\,\frac{2^{s-1}B_{s,\chi}}{s!\,q^{s-1/2}}\,\pi^s$. At $s=1$ and $D<0$ this is Dirichlet's class number formula $L(1,\chi)=\frac{2\pi h}{w\sqrt{q}}$, $h$ the class number and $w$ the number of roots of unity of $\mathbb{Q}(\sqrt{D})$.
(7)
For odd primitive $\chi$: $L(1,\chi)=\frac{\pi}{2q}\sum_{a=1}^{q-1}\chi(a)\cot\frac{\pi a}{q}$, from (1) and $\psi(1-x)-\psi(x)=\pi\cot\pi x$.
(8)
For even primitive $\chi\neq 1$: $L(1,\chi)=-\frac{\tau(\chi)}{q}\sum_{a=1}^{q-1}\bar\chi(a)\log\left|1-e^{2\pi ia/q}\right|=-\frac{\tau(\chi)}{q}\sum_{a=1}^{q-1}\bar\chi(a)\log\left(2\sin\frac{\pi a}{q}\right)$ [1].
(9)
With $\mathfrak a=0$ for even $\chi$ and $\mathfrak a=1$ for odd $\chi$, $\Lambda(s,\chi)=(q/\pi)^{s/2}\,\Gamma\!\left(\frac{s+\mathfrak a}{2}\right)L(s,\chi)$ satisfies $\Lambda(s,\chi)=\varepsilon(\chi)\,\Lambda(1-s,\bar\chi)$ with the root number $\varepsilon(\chi)=\tau(\chi)/(i^{\mathfrak a}\sqrt{q})$ [2].
Comments
(10)
The Conrey label $(q,n)$ [7] names the character $\chi_q(n,\cdot)$ with $\chi_q(n,m)=\prod_{p^e\parallel q}\chi_{p^e}(n,m)$, where for an odd prime power $p^e$, with $g$ the least positive integer generating $(\mathbb{Z}/p^k\mathbb{Z})^\times$ for every $k\geq 1$, $\chi_{p^e}(g^a,g^b)=e^{2\pi i ab/\varphi(p^e)}$; for $2^e$ with $e\geq 2$ and the units written as $(-1)^a5^b$, $\chi_{2^e}\big((-1)^a5^b,(-1)^{a'}5^{b'}\big)=e^{2\pi i(aa'/2+bb'/2^{e-2})}$; and $\chi_q(n,m)=0$ when $\gcd(m,q)>1$. So the trivial character is $\chi_q(1,\cdot)$, $\chi_q(n,\cdot)\chi_q(n',\cdot)=\chi_q(nn',\cdot)$, and $\overline{\chi_q(n,\cdot)}=\chi_q(n',\cdot)$ with $nn'\equiv 1\pmod q$. The zeros of $L(s,\chi)$, the generalized Bernoulli numbers $B_{k,\chi}$ and the Gauss sums $\tau(\chi)$ on this site, and the characters in the LMFDB [5], are indexed the same way; the LMFDB's page for the $L$-function of $\chi_q(n,\cdot)$, among its $L$-functions of degree one [6], is reached from its page for the character.
(11)
Only primitive characters are listed, and for $q=1$ only $s\geq 2$, since $L(s,1)=\zeta(s)$, the Riemann zeta function, has its pole at $s=1$. No primitive character has conductor $q\equiv 2\pmod 4$, because the only character modulo $2$ is trivial. The $L$-function of an imprimitive character is that of the primitive character inducing it with finitely many Euler factors removed, by (4).
(12)
Write $\mathfrak a=0$ if $\chi$ is even, $\chi(-1)=1$, and $\mathfrak a=1$ if $\chi$ is odd. When $s\equiv\mathfrak a\pmod 2$, the value is an algebraic multiple of $\pi^s$, given by (5) in terms of the Gauss sum $\tau(\chi)$ and the generalized Bernoulli number $B_{s,\bar\chi}$; for a real character it is then a rational multiple of $\pi^s/\sqrt{q}$, (6). When $s\not\equiv\mathfrak a\pmod 2$ no such expression is known: $L(1,\chi)$ for even $\chi$ is a combination of logarithms of cyclotomic units, (8), and $L(2,\chi_4(3,\cdot))=G$ is Catalan's constant, for which not even irrationality is known.
(13)
For a real character, $\chi=\left(\frac{D}{\cdot}\right)$ is the Kronecker symbol of the fundamental discriminant $D=\chi(-1)\,q$, and every value $L(s,\chi)$ is real; the imaginary part is written as an exact $0$. At $s=1$ the value is $\kappa_D$, the residue of the Dedekind zeta function of $\mathbb{Q}(\sqrt{D})$, and is the entry $D$ of the residues of Dedekind zeta functions of quadratic fields, which gives its closed form by the class number formula.
(14)
The values of a character and of its complex conjugate $\bar\chi= \chi_q(n',\cdot)$ are complex conjugates, (3), so a value with a nonzero imaginary part is listed twice, once with each sign; $\chi\neq\bar\chi$ exactly when $\chi$ is not real.
(15)
For $q>1$, each entry's comment gives the parity of $\chi$ and, for a nonreal character, its order; for a real character it gives the Kronecker symbol $\left(\frac{D}{\cdot}\right)$ in place of the order and, when $s\equiv\mathfrak a\pmod 2$, the value as a rational multiple of $\pi^s/\sqrt{q}$; for a nonreal character of order $d$ with $s\equiv\mathfrak a\pmod 2$ and $\varphi(d)\leq 6$, the exact $B_{s,\bar\chi}\in\mathbb{Q}(\zeta_d)$, $\zeta_d=e^{2\pi i/d}$, from which (5) and the Gauss sum give the value. The two entries with $q=1$ name $\zeta(2)$ and $\zeta(3)$.
(16)
For the quartic characters modulo $5$, (7) gives $L(1,\chi_5(2,\cdot))=\frac{\pi}{5}\left(\cot\frac{\pi}{5}+i\cot\frac{2\pi}{5}\right)$ and its conjugate for $\chi_5(3,\cdot)$; the real part $\frac{\pi}{5}\cot\frac{\pi}{5}=0.8648062659\ldots$ is the isoperimetric quotient $4\pi A/P^2$ of the regular pentagon, [8].
Programs
(P1)
Sage
chi = [c for c in DirichletGroup(7) if c.conrey_number() == 2][0]   # chi_7(2, .)
CBF = ComplexBallField(400)
sum(CBF(chi(a)) * CBF(2).zeta(CBF(a/7)) for a in range(1, 7)) / 7^2            # L(2, chi) = 0.79921874... - 0.10184729...i
-sum(CBF(chi(a)) * CBF(RealBallField(400)(a/7).psi()) for a in range(1, 7)) / 7  # L(1, chi) = 0.53774738... - 0.10529754...i
(P2)
PARI/GP
L = lfuncreate([znstar(7, 1), 2]); lfun(L, 2)      \\ L(2, chi_7(2, .)); the 2 in the label is the Conrey index
References
[1]
L. C. Washington, Introduction to Cyclotomic Fields, second edition, Graduate Texts in Mathematics 83, Springer, 1997, Theorems 4.2 and 4.9.
[2]
H. Davenport, Multiplicative Number Theory, third edition, Graduate Texts in Mathematics 74, Springer, 2000, Chapters 4, 6 and 9.
Links
Similar tables
Residues of Dedekind zeta functions of quadratic fields —   holds every entry here with $\chi$ real and $s=1$, as $\kappa_D=L(1,\chi_D)$, indexed by $D$
Generalized Bernoulli numbers —   $B_{s,\bar\chi}$ under the same labels, the Bernoulli factor of the closed form (5) when $\chi(-1)=(-1)^s$; $L(1-k,\chi)=-B_{k,\chi}/k$ gives the values at $s\leq 0$
Gauss sums of primitive Dirichlet characters —   $\tau(\chi)$ under the same labels, the Gauss-sum factor of the closed form (5) when $\chi(-1)=(-1)^s$
Zeros of Dirichlet L-series —   zeros of the same $L(s,\chi)$ under the same labels
Values of the Riemann zeta function at rational numbers —   holds the entries $q=1$, $L(s,1)=\zeta(s)$
Values of the Hurwitz zeta function at pairs of rational numbers —   $\zeta(s,a/q)$, of which every entry with $s\geq 2$ is the combination $q^{-s}\sum_a\chi(a)\zeta(s,a/q)$
Rational multiples of pi —   holds $L(1,\chi_4(3,\cdot))=\pi/4$ as its entry $a=1/4$
Data properties
Entries are of type: complex number
How well the digits are known: proven
Table is complete: no (every primitive character of conductor $q\leq 30$ at $s=1,2,3$ is here, 503 entries)
How they were obtained:

Each value is a complex ball at $397$ bits: the sum (1) with arb's Hurwitz zeta function at $s=2,3$ and arb's digamma function at $s=1$, the character value $\chi(a)=e^{2\pi ir}$ being arb's exponential of a ball containing the exact rational $r$, which is computed from Conrey's definition of the label by discrete logarithms.

more

A hundred digits are written; the widest ball, at $(29,27,1)$, supports $117$. Before any entry is returned the generator requires, for every character of every modulus in range, that the hand-built character agree with Sage's character of the same Conrey number at every argument and in primitivity; and for the entry, that the ball overlap a second enclosure computed from Sage's exact character values by a hand-written Euler-Maclaurin summation of each $\zeta(s,a/q)$ or $\psi(a/q)$, whose remainder is bounded by the first omitted term; that (5), with Sage's exact Gauss sum and exact $B_{s,\bar\chi}$ enclosed in balls, (7) and (8) hold where they apply; and, for a real character, that the imaginary part contain $0$ and the value contain the rational multiple of $\pi^s/\sqrt{q}$ of (6). Outside the generator, every one of the $501$ entries with $q>1$ agrees with PARI's lfun at $120$ digits, the character handed to PARI as its Conrey label; the $19$ real characters at $s=1$ reproduce the stored digits of the residues $\kappa_D$; $\zeta(2)$, $\zeta(3)$ and $\pi/4$ reproduce their stored digits; for $q\leq 11$ the closed form assembled from the stored digits of the Gauss sums and of the generalized Bernoulli numbers on this site reproduces every entry of matching parity; $L(2,\chi_4(3,\cdot))$ contains arb's Catalan constant, $L(3,\chi_4(3,\cdot))$ contains $\pi^3/32$, and the real part of $L(1,\chi_5(2,\cdot))$ contains the $300$ digits of OEIS A381152. Controls that must fail did: a value against PARI's value for the conjugate character, $\kappa_{-3}$ against $\kappa_{-4}$, the closed form with $B_{1,\bar\chi}$ in place of $B_{2,\bar\chi}$, and the constants shifted by $10^{-90}$.



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