Gauss sums of primitive Dirichlet characters

$q$

$n$

$\tau(\chi_q(n,\cdot))$

1

1:

1

equals: One
comment: $\chi=1$, the trivial character: $\tau(1)=1$

3

2:

0 + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576

comment: $\chi=\left(\frac{-3}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{3}$
equals: $i\sqrt{3}$

4

3:

0 + i * 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

comment: $\chi=\left(\frac{-4}{\cdot}\right)$, odd: $\tau(\chi)=2i$
equals: $2i$

5

2:

-1.175570504584946258337411909278145537195304875286291982144544961514556948324703915017008099725482672 + i * 1.902113032590307144232878666758764286811397268251500444894611288860306340170387003437585621941622763

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 30x^4 + 625$

5

3:

1.175570504584946258337411909278145537195304875286291982144544961514556948324703915017008099725482672 + i * 1.902113032590307144232878666758764286811397268251500444894611288860306340170387003437585621941622763

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 30x^4 + 625$

5

4:

2.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275 + i * 0

comment: $\chi=\left(\frac{5}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{5}$
equals: $\sqrt{5}$

7

2:

2.370469405576200591575014652012719431896824192689206316096648317290560957369461853727827521979756115 + i * -1.175106291884787002617705689834330505880381342264232633682944973876955467337466541553438448070598490

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 7x^3 + 343$

7

3:

-2.440133358345537678987988371076050317831644295726459168193395957427673998583782617378339949233694000 + i * 1.022618791871794130874525703202543037841873964584837496757737644534740783286667511222407577435701141

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 497x^6 + 117649$

7

4:

2.370469405576200591575014652012719431896824192689206316096648317290560957369461853727827521979756115 + i * 1.175106291884787002617705689834330505880381342264232633682944973876955467337466541553438448070598490

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 7x^3 + 343$

7

5:

2.440133358345537678987988371076050317831644295726459168193395957427673998583782617378339949233694000 + i * 1.022618791871794130874525703202543037841873964584837496757737644534740783286667511222407577435701141

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 497x^6 + 117649$

7

6:

0 + i * 2.645751311064590590501615753639260425710259183082450180368334459201068823230283627760392886474543611

comment: $\chi=\left(\frac{-7}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{7}$

8

3:

0 + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145

comment: $\chi=\left(\frac{-8}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{8}$

8

5:

2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145 + i * 0

comment: $\chi=\left(\frac{8}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{8}$

9

2:

-2.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480 + i * 1.928362829059617978967930229721790298722679652617045370974931764013338508722875919131464683152783055

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)=3\zeta_{18}^{7}$, $\tau(\chi)$ a root of $x^6 - 27x^3 + 729$

9

4:

2.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480 + i * 1.928362829059617978967930229721790298722679652617045370974931764013338508722875919131464683152783055

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)=3\zeta_{9}$, $\tau(\chi)$ a root of $x^6 + 27x^3 + 729$

9

5:

2.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480 + i * 1.928362829059617978967930229721790298722679652617045370974931764013338508722875919131464683152783055

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)=3\zeta_{9}$, $\tau(\chi)$ a root of $x^6 + 27x^3 + 729$

9

7:

2.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480 + i * -1.928362829059617978967930229721790298722679652617045370974931764013338508722875919131464683152783055

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)=3\zeta_{9}^{8}$, $\tau(\chi)$ a root of $x^6 + 27x^3 + 729$

11

2:

-0.9553018779843698435274415934490394335235503080009052153059074171084305872130745422832068521314577824 + i * 3.176066485752389937154763761685318473651996577443476655642024917514980262800178438050941402208392484

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

11

3:

2.636105564324835211009476712824911217573788057464825777744349186661656708147798671726115861584516668 + i * -2.012696562757447074396693080942412321526613359428353618749879763404971723031049108299552439054898833

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

11

4:

2.636105564324835211009476712824911217573788057464825777744349186661656708147798671726115861584516668 + i * 2.012696562757447074396693080942412321526613359428353618749879763404971723031049108299552439054898833

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

11

5:

2.070162099831070633299581531771927369992674434637863715468901401746598826360412694489316751764410640 + i * 2.591221503542877815049754795339975998026271209851329162262051344298502181253392744759530001567975421

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

11

6:

0.9553018779843698435274415934490394335235503080009052153059074171084305872130745422832068521314577824 + i * 3.176066485752389937154763761685318473651996577443476655642024917514980262800178438050941402208392484

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

11

7:

2.541278024715501424500240946015393687375483420178428421026262370938635198399915006190009812454516043 + i * -2.131174793652101951174050358427203338456687810747584253992616544011310720650279091133149649537965821

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

11

8:

-2.541278024715501424500240946015393687375483420178428421026262370938635198399915006190009812454516043 + i * -2.131174793652101951174050358427203338456687810747584253992616544011310720650279091133149649537965821

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

11

9:

2.070162099831070633299581531771927369992674434637863715468901401746598826360412694489316751764410640 + i * -2.591221503542877815049754795339975998026271209851329162262051344298502181253392744759530001567975421

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

11

10:

0 + i * 3.316624790355399849114932736670686683927088545589353597058682146116484642609043846708843399128290651

comment: $\chi=\left(\frac{-11}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{11}$

12

11:

3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151 + i * 0

comment: $\chi=\left(\frac{12}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{12}$

13

2:

-3.074972058995239211504215848740700709729502094979841711621966528865689640837829820260259955773871933 + i * 1.882696692619015332561992721072039235922551627808851707182733758274629104468111331942397138956147774

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

13

3:

0.9108358324463263917972347669412424842771404785151263031983177087382775490378731093198136517472946719 + i * 3.488606897650093168915985637234943479623924884712387338679869026867119862964244175827541831518182437

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 65x^3 + 2197$

13

4:

3.099124683740938337045407731414102814230201732647460001260878615508684319017988843281170594722944811 + i * 1.842668226954496801450559513872052811619376003697366742327046682728267599508348053550305141913952252

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 4381x^6 + 4826809$

13

5:

3.450844376844018728210313284732720330766009645739972014725897545898386951971901676744535133430822184 + i * 1.044831606912815430033964769575588455701788057448407924057283950873409234811014560456578894586248588

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 130x^4 + 28561$

13

6:

3.602863631595991697554615520008578056112077091504506825980786961261659966775236166329040139774556381 + i * -0.1391892672692194886598654798489990262779244932624457695158695990480320548497880065769680776615926084

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

13

7:

3.074972058995239211504215848740700709729502094979841711621966528865689640837829820260259955773871933 + i * 1.882696692619015332561992721072039235922551627808851707182733758274629104468111331942397138956147774

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

13

8:

-3.450844376844018728210313284732720330766009645739972014725897545898386951971901676744535133430822184 + i * 1.044831606912815430033964769575588455701788057448407924057283950873409234811014560456578894586248588

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 130x^4 + 28561$

13

9:

0.9108358324463263917972347669412424842771404785151263031983177087382775490378731093198136517472946719 + i * -3.488606897650093168915985637234943479623924884712387338679869026867119862964244175827541831518182437

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 65x^3 + 2197$

13

10:

3.099124683740938337045407731414102814230201732647460001260878615508684319017988843281170594722944811 + i * -1.842668226954496801450559513872052811619376003697366742327046682728267599508348053550305141913952252

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 4381x^6 + 4826809$

13

11:

-3.602863631595991697554615520008578056112077091504506825980786961261659966775236166329040139774556381 + i * -0.1391892672692194886598654798489990262779244932624457695158695990480320548497880065769680776615926084

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

13

12:

3.605551275463989293119221267470495946251296573845246212710453056227166948293010445204619082018490718 + i * 0

comment: $\chi=\left(\frac{13}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{13}$

15

2:

2.036147841820508733803923453575630594042932657704135318108550529555199065591622637019928799383808842 + i * -3.294556414185327703509680157112760012118642055644945569405262031857126869661478038291826897629751409

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 270x^4 + 50625$

15

8:

2.036147841820508733803923453575630594042932657704135318108550529555199065591622637019928799383808842 + i * 3.294556414185327703509680157112760012118642055644945569405262031857126869661478038291826897629751409

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 270x^4 + 50625$

15

14:

0 + i * 3.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673518

comment: $\chi=\left(\frac{-15}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{15}$

16

3:

3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384 + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=4\zeta_{16}$, $\tau(\chi)$ a root of $x^8 + 65536$

16

5:

3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384 + i * -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=4\zeta_{16}^{15}$, $\tau(\chi)$ a root of $x^8 + 65536$

16

11:

-3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384 + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=4\zeta_{16}^{7}$, $\tau(\chi)$ a root of $x^8 + 65536$

16

13:

3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384 + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=4\zeta_{16}$, $\tau(\chi)$ a root of $x^8 + 65536$

17

2:

3.047929408358189043874427415149720705609607392514201133749446062460952808076658769412888863203335865 + i * 2.776711422108048248408056397095729151944826196211011351073768323263761057826310988858091106010671481

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

17

3:

2.325224300372918556026350123475097095845316137920397358689347679863121673128893831137205409611931485 + i * 3.404898229456391758701501679793081974890700833732495856554843369956563671012952419779467647231986572

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

4:

2.537409542661800924340363067917240953928820634116950828560253380579217309194755018244759612002493392 + i * -3.249854275626651890340223383757732207784900029338498333690951816308385194734482477480592845846330783

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 510x^4 + 83521$

17

5:

0.9325909986699080644551338553120791056252071161002190435090095971177402318867936048895291211916722196 + i * -4.016251240796554492208485556474088886656704260649468401413169552290958544004493751161912283002050274

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

6:

-2.325224300372918556026350123475097095845316137920397358689347679863121673128893831137205409611931485 + i * 3.404898229456391758701501679793081974890700833732495856554843369956563671012952419779467647231986572

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

7:

-0.9325909986699080644551338553120791056252071161002190435090095971177402318867936048895291211916722196 + i * -4.016251240796554492208485556474088886656704260649468401413169552290958544004493751161912283002050274

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

8:

0.3128860714060261934594317235185069179886745842429732464777838652966410821169314005730174021922674026 + i * -4.111216645510195328417876221815658135489735782883911045544338756335761626565698529128556996427011094

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

17

9:

3.047929408358189043874427415149720705609607392514201133749446062460952808076658769412888863203335865 + i * -2.776711422108048248408056397095729151944826196211011351073768323263761057826310988858091106010671481

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

17

10:

-0.6251245538455434650031960967689965191517173221489460838890712853975844868279250850098739504056297400 + i * 4.075440993583321435386612668431875314936400958650743207765335097899960233388264098172025910453207467

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

11:

-4.082933557471906089484849355687681550599556364760831100887795568091210883499214743263778916686870428 + i * -0.5741546527459351119219120222812670933743864592053503311820924690684034794046675410964775684395878614

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

12:

0.6251245538455434650031960967689965191517173221489460838890712853975844868279250850098739504056297400 + i * 4.075440993583321435386612668431875314936400958650743207765335097899960233388264098172025910453207467

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

13:

2.537409542661800924340363067917240953928820634116950828560253380579217309194755018244759612002493392 + i * 3.249854275626651890340223383757732207784900029338498333690951816308385194734482477480592845846330783

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 510x^4 + 83521$

17

14:

4.082933557471906089484849355687681550599556364760831100887795568091210883499214743263778916686870428 + i * -0.5741546527459351119219120222812670933743864592053503311820924690684034794046675410964775684395878614

comment: $\chi$ of order $16$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=128$

17

15:

0.3128860714060261934594317235185069179886745842429732464777838652966410821169314005730174021922674026 + i * 4.111216645510195328417876221815658135489735782883911045544338756335761626565698529128556996427011094

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

17

16:

4.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684297 + i * 0

comment: $\chi=\left(\frac{17}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{17}$

19

2:

0.8561529586993510663673897196005237130137426437864090226682908194008168820096475259987730538477859788 + i * 4.273991356017270569698459138278557577682041346457689869703350467052557656558443830376707531617176071

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

3:

-2.799666187742926153363078432535284530687094832052876659172851781155282559424193159149380941250347887 + i * -3.340938376745220748105701175561869323806489996505789123198965613547776775278868363604870543143821726

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

4:

2.929820885283875052031017008491552799515761980867278866336854522325940710943772453563463874016883128 + i * 3.227406014147338522396989577542925113764821255512869361787096145669699373977922560798096896857128455

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

5:

2.929820885283875052031017008491552799515761980867278866336854522325940710943772453563463874016883128 + i * -3.227406014147338522396989577542925113764821255512869361787096145669699373977922560798096896857128455

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

6:

3.296272443510166972872642822884794616982975018580236475530989736886978548256850482808375970915158635 + i * -2.852119909498111035322879351803188307219210306148105054649995823109962879292714919432036475033421267

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

7:

-1.332814243394786401400020075277575923398793241611629100401372662736477864262245381308298754467665498 + i * 4.150133274077349804812658277939111691646807953044548455177933311684264187728327791104928186314398932

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 133x^3 + 6859$

19

8:

-4.338030160332437651663014814817815456218100678531944276865933395021543011925243552846717961424305397 + i * -0.4260215112481120728672087647721152310909840287474112966301585868939068778168729849923867085125576458

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 11419x^6 + 47045881$

19

9:

4.119076089906456487673351672465702257314363238130445072771847909072896326456755320266017436660967485 + i * -1.425907488430065574424183122238720080976860483918160923928871218331217498591813238594389263364762325

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

10:

-0.8561529586993510663673897196005237130137426437864090226682908194008168820096475259987730538477859788 + i * 4.273991356017270569698459138278557577682041346457689869703350467052557656558443830376707531617176071

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

11:

-1.332814243394786401400020075277575923398793241611629100401372662736477864262245381308298754467665498 + i * -4.150133274077349804812658277939111691646807953044548455177933311684264187728327791104928186314398932

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 133x^3 + 6859$

19

12:

4.338030160332437651663014814817815456218100678531944276865933395021543011925243552846717961424305397 + i * -0.4260215112481120728672087647721152310909840287474112966301585868939068778168729849923867085125576458

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 11419x^6 + 47045881$

19

13:

2.799666187742926153363078432535284530687094832052876659172851781155282559424193159149380941250347887 + i * -3.340938376745220748105701175561869323806489996505789123198965613547776775278868363604870543143821726

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

14:

-4.352515551254310661077101197191208214282436952004121443738108458823764650210530670188158531306496784 + i * 0.2358142830478768618241142590449024890667886870529248123392238666743666790166398291796200693838353727

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

15:

4.352515551254310661077101197191208214282436952004121443738108458823764650210530670188158531306496784 + i * 0.2358142830478768618241142590449024890667886870529248123392238666743666790166398291796200693838353727

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

19

16:

3.296272443510166972872642822884794616982975018580236475530989736886978548256850482808375970915158635 + i * 2.852119909498111035322879351803188307219210306148105054649995823109962879292714919432036475033421267

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

17:

4.119076089906456487673351672465702257314363238130445072771847909072896326456755320266017436660967485 + i * 1.425907488430065574424183122238720080976860483918160923928871218331217498591813238594389263364762325

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

19

18:

0 + i * 4.358898943540673552236981983859615659137003925232444936890344138159557328203158085656159155851944527

comment: $\chi=\left(\frac{-19}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{19}$

20

3:

3.804226065180614288465757333517528573622794536503000889789222577720612680340774006875171243883245527 + i * -2.351141009169892516674823818556291074390609750572583964289089923029113896649407830034016199450965344

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 480x^4 + 160000$

20

7:

3.804226065180614288465757333517528573622794536503000889789222577720612680340774006875171243883245527 + i * 2.351141009169892516674823818556291074390609750572583964289089923029113896649407830034016199450965344

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 480x^4 + 160000$

20

19:

0 + i * 4.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550

comment: $\chi=\left(\frac{-20}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{20}$

21

2:

-4.573376009283457970283321610535054585394581679084777766257335586888858218653281750231911886135293361 + i * -0.2902272862956068733060339864677116289926393951139449872391379244707731039684856708954104026330135582

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 189x^3 + 9261$

21

5:

2.774586185369981180707273032250411475746239643403721766791737844282867983651169276834484504809257737 + i * 3.647145664756763787552638578567249514526975739488442216275546784731884949861404589664956085996341253

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 13419x^6 + 85766121$

21

11:

4.573376009283457970283321610535054585394581679084777766257335586888858218653281750231911886135293361 + i * -0.2902272862956068733060339864677116289926393951139449872391379244707731039684856708954104026330135582

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 189x^3 + 9261$

21

17:

2.774586185369981180707273032250411475746239643403721766791737844282867983651169276834484504809257737 + i * -3.647145664756763787552638578567249514526975739488442216275546784731884949861404589664956085996341253

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 13419x^6 + 85766121$

21

20:

4.582575694955840006588047193728008488984456576767971902607242123906868425547770886604361559493445033 + i * 0

comment: $\chi=\left(\frac{21}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{21}$

23

2:

0.4898319656114067528139677908789425930041688521624909621328024330777461959049542772903351648388812017 + i * 4.770750951943023574575882118343440050461910921226989702167467686704750496284802870156118094501123621

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

3:

1.830514688420521169934369831808456420133888075834433724572206536342530941021265471280104429664884862 + i * -4.432743617160451374289103325308203671287269345038200673709637441010621941327454700605431138244180621

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

4:

4.098211212957684478179472435695741858908126821541389967225596615362728581442459125359493948244737610 + i * 2.490916468689366653330232728041828037028514771640190970246555001577621404354784985166971385305913197

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

5:

-0.7650723318352006302471258992818563045643357590668877033947492240376684883021236551423885882111799310 + i * 4.734412775314405203835645048863297319525946473121943047755302336005171164841667976676673766928727684

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

6:

4.098211212957684478179472435695741858908126821541389967225596615362728581442459125359493948244737610 + i * -2.490916468689366653330232728041828037028514771640190970246555001577621404354784985166971385305913197

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

7:

3.049018860150666147578680704598791272672628010225613199794235353173684998844615188633404844090126669 + i * -3.701821712406681066647494531946903318328749261185948139406554636198438440785803577323970288554595551

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

8:

1.830514688420521169934369831808456420133888075834433724572206536342530941021265471280104429664884862 + i * 4.432743617160451374289103325308203671287269345038200673709637441010621941327454700605431138244180621

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

9:

4.730008795625146952800266840428360673486856609163777928906768352382753293949349369997830445529780132 + i * -0.7918439197902240663411049982653555767901563233097012175376197846137918180785582824192426445560432427

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

10:

-3.049018860150666147578680704598791272672628010225613199794235353173684998844615188633404844090126669 + i * -3.701821712406681066647494531946903318328749261185948139406554636198438440785803577323970288554595551

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

11:

0.3141110438465625430192235845134775003432285889318529919719929530865676343674499454465535018687355968 + i * -4.785533852365232497308947643956906716230307335554597525590899701877469335627172739878658834073239175

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

12:

0.4898319656114067528139677908789425930041688521624909621328024330777461959049542772903351648388812017 + i * -4.770750951943023574575882118343440050461910921226989702167467686704750496284802870156118094501123621

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

13:

-0.05647650178896710856061732770587475262783731989528175191245476480100617516400453999385496407617823975 + i * 4.795498973490212394186455921492894197574778710480256645450824924388194018369308776151142684696415254

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

14:

0.7650723318352006302471258992818563045643357590668877033947492240376684883021236551423885882111799310 + i * 4.734412775314405203835645048863297319525946473121943047755302336005171164841667976676673766928727684

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

15:

4.795381096768059106098129969696128534397243011319289394520258306422991721561536706647064155488061420 + i * -0.06572774725765783784157467678613008316004552237824668670187218239945353492548853043712091099531376137

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

16:

-0.05647650178896710856061732770587475262783731989528175191245476480100617516400453999385496407617823975 + i * -4.795498973490212394186455921492894197574778710480256645450824924388194018369308776151142684696415254

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

17:

-1.934140306193108460140672575566980552267827708315340487566479075368482672090473626920148450377164780 + i * 4.388519257786073410862266520373571739422846357823479658817880901008683970624922378819159602483481058

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

18:

4.730008795625146952800266840428360673486856609163777928906768352382753293949349369997830445529780132 + i * 0.7918439197902240663411049982653555767901563233097012175376197846137918180785582824192426445560432427

comment: $\chi$ of order $11$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=110$

23

19:

1.934140306193108460140672575566980552267827708315340487566479075368482672090473626920148450377164780 + i * 4.388519257786073410862266520373571739422846357823479658817880901008683970624922378819159602483481058

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

20:

-4.795381096768059106098129969696128534397243011319289394520258306422991721561536706647064155488061420 + i * -0.06572774725765783784157467678613008316004552237824668670187218239945353492548853043712091099531376137

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

21:

-0.3141110438465625430192235845134775003432285889318529919719929530865676343674499454465535018687355968 + i * -4.785533852365232497308947643956906716230307335554597525590899701877469335627172739878658834073239175

comment: $\chi$ of order $22$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=220$

23

22:

0 + i * 4.795831523312719541597438064162693919996707041904129346485309114448257235907464082492191446436918861

comment: $\chi=\left(\frac{-23}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{23}$

24

5:

0 + i * 4.898979485566356196394568149411782783931894961313340256865385134501920754914630053079718866209280470

comment: $\chi=\left(\frac{-24}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{24}$

24

11:

4.898979485566356196394568149411782783931894961313340256865385134501920754914630053079718866209280470 + i * 0

comment: $\chi=\left(\frac{24}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{24}$

25

2:

-4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048 + i * 0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$, $\tau(\chi)=5\zeta_{100}^{47}$

25

3:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}$

25

4:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}$

25

6:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * -1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}^{24}$

25

8:

-4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{50}^{23}$

25

9:

0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014 + i * -4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{50}^{39}$

25

11:

-0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014 + i * -4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}^{18}$

25

12:

-4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048 + i * -0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$, $\tau(\chi)=5\zeta_{100}^{53}$

25

13:

4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048 + i * 0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$, $\tau(\chi)=5\zeta_{100}^{3}$

25

14:

0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014 + i * 4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{50}^{11}$

25

16:

-0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014 + i * 4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}^{7}$

25

17:

-4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{50}^{23}$

25

19:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * -1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}^{24}$

25

21:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}$

25

22:

4.842915805643155597450841877323679069180062013769438753075424571394790231913641967013035533537556018 + i * 1.243449435824273941211418730032239842087837032221096351181127421642155001111548850445876153349028288

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$, $\tau(\chi)=5\zeta_{25}$

25

23:

4.911436253643443405428208714326342081942364433175069388547272680705099423977732560297036179428433048 + i * -0.9369065729286231527127536722364573466931307588382093312972261003119336388767058257857053160383584014

comment: $\chi$ of order $20$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$, $\tau(\chi)=5\zeta_{100}^{97}$

27

2:

-3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{41}$

27

4:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{13}$

27

5:

1.198315215472929997878974479351140137983223669684462666148894367061199124825663720446473706897713088 + i * -5.056089461665612711273653553861710438175032439199443860314070750331312790658527212893076923490571075

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{85}$

27

7:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * -3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{95}$

27

11:

-1.198315215472929997878974479351140137983223669684462666148894367061199124825663720446473706897713088 + i * -5.056089461665612711273653553861710438175032439199443860314070750331312790658527212893076923490571075

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{77}$

27

13:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{13}$

27

14:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{13}$

27

16:

1.198315215472929997878974479351140137983223669684462666148894367061199124825663720446473706897713088 + i * 5.056089461665612711273653553861710438175032439199443860314070750331312790658527212893076923490571075

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{23}$

27

20:

-3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{41}$

27

22:

1.198315215472929997878974479351140137983223669684462666148894367061199124825663720446473706897713088 + i * -5.056089461665612711273653553861710438175032439199443860314070750331312790658527212893076923490571075

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{85}$

27

23:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * 3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $18$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{13}$

27

25:

3.779544309872742275808496037855561571165289966136145577367406230194355213322855966890510455450504988 + i * -3.565816149173787158662719348749081180146799492355904528454041317833899224888917850093080102935597801

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=18$, $\tau(\chi)=\sqrt{27}\,\zeta_{108}^{95}$

28

3:

3.203816162026351051607174344324326877686455620637534445520142991324806766576139134440281862249877940 + i * -4.211361062642188354537407419803378319834097896098393139190108141144960027032791915844390787316260527

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 31808x^6 + 481890304$

28

11:

-5.280879740130361757082890732272745281506804159284820509210055744449368077286837508004574597548421076 + i * 0.3351256037378864257334153869807685567981334125872697318719220953845273921712839144474863156484377381

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 40768x^6 + 481890304$

28

19:

3.203816162026351051607174344324326877686455620637534445520142991324806766576139134440281862249877940 + i * 4.211361062642188354537407419803378319834097896098393139190108141144960027032791915844390787316260527

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 31808x^6 + 481890304$

28

23:

5.280879740130361757082890732272745281506804159284820509210055744449368077286837508004574597548421076 + i * 0.3351256037378864257334153869807685567981334125872697318719220953845273921712839144474863156484377381

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 40768x^6 + 481890304$

28

27:

5.291502622129181181003231507278520851420518366164900360736668918402137646460567255520785772949087221 + i * 0

comment: $\chi=\left(\frac{28}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{28}$

29

2:

-3.875404238508721604326158872488495208514584564658202670351974834445596615588196622086093383084466552 + i * 3.739149901802364974690794339362168852902387166518371106381733504793092547528121520339300892449331042

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

3:

-3.760702705444883436742947582441432210312619792221876013397913536204794605787863479075478956386996235 + i * 3.854492853963999021447269225023399192546581240893613551918512521533794739260872567811892241168791975

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

4:

2.958101685414206425308207827417359713544753061900410126159178475002851668744450170258731172819761403 + i * 4.499959379677735638298195736289442104891859717421435427857717043476635299967481295702051595245067240

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

5:

1.923871613967428165773654081387444886874109894991476410368542624125367829557517867428586916178675830 + i * -5.029783098004362559350156809805434068468628825202999924659337001840666558751309569985822533210078567

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

6:

1.923871613967428165773654081387444886874109894991476410368542624125367829557517867428586916178675830 + i * 5.029783098004362559350156809805434068468628825202999924659337001840666558751309569985822533210078567

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

7:

1.218675872302557371441192918068345667969082373271357349565783130376062894525656465599692687533971802 + i * 5.245457951243875987740878202237224989606367793541093380435067954668237379618593719439741801545094467

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

8:

-4.102350622190853915935267619418772965217867282355791417752320846118550166472033822378204208110512863 + i * -3.488655811714637141507982783090227310352367042313326543351578933005920924918049242863093760005898597

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

9:

5.259788420194844887411914448907695206218249037108647887015901730960207713146005465621796199762918552 + i * -1.155260046389650677315739629900638813844565958401000327241858783339210499408257084516475832808139715

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

10:

3.760702705444883436742947582441432210312619792221876013397913536204794605787863479075478956386996235 + i * 3.854492853963999021447269225023399192546581240893613551918512521533794739260872567811892241168791975

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

11:

4.102350622190853915935267619418772965217867282355791417752320846118550166472033822378204208110512863 + i * -3.488655811714637141507982783090227310352367042313326543351578933005920924918049242863093760005898597

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

12:

1.018375167688087297203192525695582632303110449268395008913483685277285428854238453916525541539788079 + i * -5.287996975967011658719005288458239136380679531044655936151906991541553679515318804071635116769427046

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 1218x^4 + 707281$

29

13:

5.259788420194844887411914448907695206218249037108647887015901730960207713146005465621796199762918552 + i * 1.155260046389650677315739629900638813844565958401000327241858783339210499408257084516475832808139715

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

14:

1.399122243532459661262379033094105519957031755442591204201548146631738670246369236290543314991864230 + i * -5.200236239600341141368212108114524511240486511273095543778171630679678461149557041883882093175048645

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

15:

3.875404238508721604326158872488495208514584564658202670351974834445596615588196622086093383084466552 + i * 3.739149901802364974690794339362168852902387166518371106381733504793092547528121520339300892449331042

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

16:

4.606829782761047509865972888209602512075904905323138987837704651423610617977110111917065184382952460 + i * 2.788748707335567696306814558265796508790535488597295512556131480224221340617590802001234953693866629

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

17:

-1.018375167688087297203192525695582632303110449268395008913483685277285428854238453916525541539788079 + i * -5.287996975967011658719005288458239136380679531044655936151906991541553679515318804071635116769427046

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 1218x^4 + 707281$

29

18:

3.571661861447575566580258475969225885350519021185531277515185351957092667361493498015153316468403873 + i * 4.030289263499685765037560215952252676777817425014860915050264281435279047367011753113566964599087914

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

19:

-0.4930828931123500282832201488741305761207600069314328059631273085625465280428674138204126443931886270 + i * 5.362543170970277120966925078474230788915983062487990478070800221469474255970887528110931308484132952

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

20:

4.606829782761047509865972888209602512075904905323138987837704651423610617977110111917065184382952460 + i * -2.788748707335567696306814558265796508790535488597295512556131480224221340617590802001234953693866629

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

21:

-3.571661861447575566580258475969225885350519021185531277515185351957092667361493498015153316468403873 + i * 4.030289263499685765037560215952252676777817425014860915050264281435279047367011753113566964599087914

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

22:

2.958101685414206425308207827417359713544753061900410126159178475002851668744450170258731172819761403 + i * -4.499959379677735638298195736289442104891859717421435427857717043476635299967481295702051595245067240

comment: $\chi$ of order $14$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

29

23:

-4.487161998266122810511105929470525839643916404019813300287024205336821773439313422959134297304450022 + i * -2.977478329277372871955412302899023524877374032213378008414250088273914707190573597446902273475328640

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

24:

-4.487161998266122810511105929470525839643916404019813300287024205336821773439313422959134297304450022 + i * 2.977478329277372871955412302899023524877374032213378008414250088273914707190573597446902273475328640

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

25:

1.218675872302557371441192918068345667969082373271357349565783130376062894525656465599692687533971802 + i * -5.245457951243875987740878202237224989606367793541093380435067954668237379618593719439741801545094467

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

29

26:

0.4930828931123500282832201488741305761207600069314328059631273085625465280428674138204126443931886270 + i * 5.362543170970277120966925078474230788915983062487990478070800221469474255970887528110931308484132952

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

27:

-1.399122243532459661262379033094105519957031755442591204201548146631738670246369236290543314991864230 + i * -5.200236239600341141368212108114524511240486511273095543778171630679678461149557041883882093175048645

comment: $\chi$ of order $28$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=336$

29

28:

5.385164807134504031250710491540329556295120161644788837680388670016645962827658692876633781679835484 + i * 0

comment: $\chi=\left(\frac{29}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{29}$

31

2:

4.552416669473279118809518850810427093650585467000731890481180719407921283451344285953930908151428094 + i * 3.205542460723585071329278448498552010982394226291126297185254633359806310449009117817417537258408550

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

31

3:

5.535531384911800324622872038149268060041588560186530245968854804228191346743109223985619317992891133 + i * -0.5982409937946796348628956150194498836789117471192882821819653001556728067034031442243013142032026410

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

4:

5.226579352648107065417247110214661388455542058956010012619788431481063033584258063319185284209063861 + i * -1.919080058380184951993603231995710410219506814824766623451067473561321403671729756078618133415283002

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

31

5:

5.125808539153411496797868757617443828842039301630307241141472464322066859367797415437350547829277201 + i * -2.173956489891637541106020208472309005927115693952089887731564731494594909791509439057692993216865539

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 124x^3 + 29791$

31

6:

4.002786042464823955702490422034103041713148265809327873137177104744589347001290015304010860048467755 + i * 3.870103861429146781346995715466020831088329096569965644874543962719968498178219108806249783780094702

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 6014x^6 + 887503681$

31

7:

5.567750626415898090396194925411992105929862946688281621060011203439735497140850838658797746495228213 + i * 0.01236778255688615815142995336004099463138511493960126060074688792572435686787878270485875687423471443

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

8:

5.226579352648107065417247110214661388455542058956010012619788431481063033584258063319185284209063861 + i * 1.919080058380184951993603231995710410219506814824766623451067473561321403671729756078618133415283002

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

31

9:

5.567750626415898090396194925411992105929862946688281621060011203439735497140850838658797746495228213 + i * -0.01236778255688615815142995336004099463138511493960126060074688792572435686787878270485875687423471443

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

10:

-2.780438667131383504267689558287964135756182015948834535166315005152629351072415702363841951445582521 + i * 4.823811855609695683774478639441162588254276238877192343771557874173296280626517902659090074682442501

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

11:

0.4712401443163695780837816152745403091202313315953933161107611667786702221812437397662630748149666310 + i * -5.547786290619411303283043275134453479556767001014336575509672714425443244389150304603099119350451768

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

12:

5.515372427566480738115002997304638076202149670943826188340443230478647451088304411446550349408054390 + i * -0.7620150820288435628535739726434187484265063114269731339204912743518861302729860512079475157409495527

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

13:

-5.515372427566480738115002997304638076202149670943826188340443230478647451088304411446550349408054390 + i * -0.7620150820288435628535739726434187484265063114269731339204912743518861302729860512079475157409495527

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

14:

-3.365161917190767116732163199626879069521341733228861227625329666884345990049261661891015057206281041 + i * -4.435728268400687395569416713127095783421358555367972172713827023365846727415688610064453761871920734

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

15:

1.841420091325686267113591311394550058377756976173677050387630073909942353812771018950671253587402496 + i * -5.254443076793400875260802260770279579956890462380310007756629735280495247770497814162034533509951017

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

31

16:

4.552416669473279118809518850810427093650585467000731890481180719407921283451344285953930908151428094 + i * -3.205542460723585071329278448498552010982394226291126297185254633359806310449009117817417537258408550

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

31

17:

-0.4712401443163695780837816152745403091202313315953933161107611667786702221812437397662630748149666310 + i * -5.547786290619411303283043275134453479556767001014336575509672714425443244389150304603099119350451768

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

18:

0.8659945154188722586491197560368796527708291131151944248936870450014484282588081323043514279799383978 + i * -5.500004863567343484597121652109276387051316748610915266170925588905822798252117066029368207925042431

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

19:

0.8659945154188722586491197560368796527708291131151944248936870450014484282588081323043514279799383978 + i * 5.500004863567343484597121652109276387051316748610915266170925588905822798252117066029368207925042431

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

20:

-3.365161917190767116732163199626879069521341733228861227625329666884345990049261661891015057206281041 + i * 4.435728268400687395569416713127095783421358555367972172713827023365846727415688610064453761871920734

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

21:

-5.535531384911800324622872038149268060041588560186530245968854804228191346743109223985619317992891133 + i * -0.5982409937946796348628956150194498836789117471192882821819653001556728067034031442243013142032026410

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

22:

-0.8881968359595689398344162657802288556446074831299773863719092413936277819795748532813958940343366683 + i * 5.496463079162036050893166007314043269849329746929265779667770677733307397952789368438286809859192935

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

23:

4.670109433912551688057010721680569658056244697612772754733716448468425751286923619525485116552384345 + i * 3.031514122560042770083352276413465058244166611261245856207867176725301675583762582953802721406702962

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

31

24:

0.8881968359595689398344162657802288556446074831299773863719092413936277819795748532813958940343366683 + i * 5.496463079162036050893166007314043269849329746929265779667770677733307397952789368438286809859192935

comment: $\chi$ of order $30$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=240$

31

25:

5.125808539153411496797868757617443828842039301630307241141472464322066859367797415437350547829277201 + i * 2.173956489891637541106020208472309005927115693952089887731564731494594909791509439057692993216865539

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 124x^3 + 29791$

31

26:

-4.002786042464823955702490422034103041713148265809327873137177104744589347001290015304010860048467755 + i * 3.870103861429146781346995715466020831088329096569965644874543962719968498178219108806249783780094702

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 6014x^6 + 887503681$

31

27:

-4.670109433912551688057010721680569658056244697612772754733716448468425751286923619525485116552384345 + i * 3.031514122560042770083352276413465058244166611261245856207867176725301675583762582953802721406702962

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

31

28:

-2.780438667131383504267689558287964135756182015948834535166315005152629351072415702363841951445582521 + i * -4.823811855609695683774478639441162588254276238877192343771557874173296280626517902659090074682442501

comment: $\chi$ of order $15$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=120$

31

29:

-1.841420091325686267113591311394550058377756976173677050387630073909942353812771018950671253587402496 + i * -5.254443076793400875260802260770279579956890462380310007756629735280495247770497814162034533509951017

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

31

30:

0 + i * 5.567764362830021922119471298918549520476393377570414303968432585603589839254236292927218396184926678

comment: $\chi=\left(\frac{-31}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{31}$

32

3:

-4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580 + i * -3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{19}$

32

5:

3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526 + i * 4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{5}$

32

11:

4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580 + i * -3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{29}$

32

13:

3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526 + i * -4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{27}$

32

19:

-3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526 + i * 4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{11}$

32

21:

4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580 + i * -3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{29}$

32

27:

3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526 + i * 4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{5}$

32

29:

4.703502409677434867897868418445045111606501394581163611029672712160279329342118576561561180349564580 + i * 3.142779833548408725111589470628867184184968452565525148993655996202172779054721934758958706476841526

comment: $\chi$ of order $8$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=16$, $\tau(\chi)=\sqrt{32}\,\zeta_{32}^{3}$

33

2:

3.273583985855009787620860501137620050040058619441183114477290601771414772654334564537757539260815664 + i * -4.720555887557484164513861340977111754598801344263280281922411310068876919430968169714233041280161733

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

5:

4.797040520139616957926835921271781827378999784333480585313027611876821162372354669532058380691823475 + i * 3.160443362589912509041852609107232527402591328438938694068175059152461711494770151138394639542461056

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

8:

0.3991179937766175661559528286689071348415364151319640412772546684417815521927494482195603771549172430 + i * -5.730681009011383444701111118603768617338627639022925342247387826773274427205992096420944592500813487

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

14:

5.504058571666434571231439201892059609633690592749244133387348486748234096670808117871806936997442967 + i * 1.644791549001042299239597427005348353910589204504634333322135647199376007317527013038613667776821225

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

17:

3.273583985855009787620860501137620050040058619441183114477290601771414772654334564537757539260815664 + i * 4.720555887557484164513861340977111754598801344263280281922411310068876919430968169714233041280161733

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

20:

-4.797040520139616957926835921271781827378999784333480585313027611876821162372354669532058380691823475 + i * 3.160443362589912509041852609107232527402591328438938694068175059152461711494770151138394639542461056

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

26:

-5.504058571666434571231439201892059609633690592749244133387348486748234096670808117871806936997442967 + i * 1.644791549001042299239597427005348353910589204504634333322135647199376007317527013038613667776821225

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

29:

0.3991179937766175661559528286689071348415364151319640412772546684417815521927494482195603771549172430 + i * 5.730681009011383444701111118603768617338627639022925342247387826773274427205992096420944592500813487

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

33

32:

5.744562646538028659850611468218929318220264457982792367699877470565900721457404627027125365596788122 + i * 0

comment: $\chi=\left(\frac{33}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{33}$

35

2:

2.467574426604034853854433896759148074185186987750747629248364919480679819041055827028814561747852235 + i * 5.376902123822765718622929566658131154181769585750763391311797494455167913008773840876211131317321601

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

3:

2.449149299184269227156469457032823586117095181712949619297925644001988558958110493699918729343616837 + i * 5.385319647922971981581160330437633787038667423457661399098421705939786603613855854128565952806043502

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

4:

4.925848913972617729711220829047696631524741924687084754591984708765604492372241774936592613875615716 + i * -3.276585490524363299376932788770729920109355588409389236799069298715190547692374664738003245585311261

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 79625x^6 + 1838265625$

35

9:

4.925848913972617729711220829047696631524741924687084754591984708765604492372241774936592613875615716 + i * 3.276585490524363299376932788770729920109355588409389236799069298715190547692374664738003245585311261

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 79625x^6 + 1838265625$

35

12:

2.449149299184269227156469457032823586117095181712949619297925644001988558958110493699918729343616837 + i * -5.385319647922971981581160330437633787038667423457661399098421705939786603613855854128565952806043502

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

13:

-3.110267203754483866928176307877435944030429374079696273505717455232833220988853513611194018313460807 + i * -5.032518049768849456722631850957995508673963189519056769241739825702507496088931973259440139691213660

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1470x^4 + 1500625$

35

17:

3.721483461324000547895225356788581213410734745075219567328954080116459650279318700163323769343055015 + i * -4.598973890672998386793195923539401906847915975633678573300886178428743318363937370317951722081219927

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

18:

-2.467574426604034853854433896759148074185186987750747629248364919480679819041055827028814561747852235 + i * 5.376902123822765718622929566658131154181769585750763391311797494455167913008773840876211131317321601

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

19:

-0.7478592564936343873219733667438794343274150880299445428780072877023403787998400261685548529400305847 + i * -5.868620496545741742931509314336957660260008795602250278898016934754233019001327211787031184253902829

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 62125x^6 + 1838265625$

35

23:

-5.912780294377615704676387824491387644308318708999132706332592399700739144659337115828582916156397153 + i * -0.1975580684754641177205708977512861731001240106555270078985668434512605008189370121743967981873386524

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

24:

0.7478592564936343873219733667438794343274150880299445428780072877023403787998400261685548529400305847 + i * -5.868620496545741742931509314336957660260008795602250278898016934754233019001327211787031184253902829

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 62125x^6 + 1838265625$

35

27:

-3.110267203754483866928176307877435944030429374079696273505717455232833220988853513611194018313460807 + i * 5.032518049768849456722631850957995508673963189519056769241739825702507496088931973259440139691213660

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1470x^4 + 1500625$

35

32:

5.912780294377615704676387824491387644308318708999132706332592399700739144659337115828582916156397153 + i * -0.1975580684754641177205708977512861731001240106555270078985668434512605008189370121743967981873386524

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

33:

3.721483461324000547895225356788581213410734745075219567328954080116459650279318700163323769343055015 + i * 4.598973890672998386793195923539401906847915975633678573300886178428743318363937370317951722081219927

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

35

34:

0 + i * 5.916079783099616042567328291561617048415501230794340322879719669142822459105653036765752527183109178

comment: $\chi=\left(\frac{-35}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{35}$

36

7:

-5.908846518073248356200458147537138082023859510319054512740154514134965599658217435648070460336719395 + i * 1.041889066001582093110299760615888776002254063104416323417448268792394932834088412529099678944397444

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=6\zeta_{36}^{17}$, $\tau(\chi)$ a root of $x^{12} - 46656x^6 + 2176782336$

36

11:

5.908846518073248356200458147537138082023859510319054512740154514134965599658217435648070460336719395 + i * -1.041889066001582093110299760615888776002254063104416323417448268792394932834088412529099678944397444

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=6\zeta_{36}^{35}$, $\tau(\chi)$ a root of $x^{12} - 46656x^6 + 2176782336$

36

23:

5.908846518073248356200458147537138082023859510319054512740154514134965599658217435648070460336719395 + i * 1.041889066001582093110299760615888776002254063104416323417448268792394932834088412529099678944397444

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=6\zeta_{36}$, $\tau(\chi)$ a root of $x^{12} - 46656x^6 + 2176782336$

36

31:

5.908846518073248356200458147537138082023859510319054512740154514134965599658217435648070460336719395 + i * 1.041889066001582093110299760615888776002254063104416323417448268792394932834088412529099678944397444

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=6\zeta_{36}$, $\tau(\chi)$ a root of $x^{12} - 46656x^6 + 2176782336$

37

2:

5.223505065773082120385976169205972483378360916606999484792807379939627716619201256446501491321315638 + i * 3.116888645403128454761600720334309296553360961187554864611014030876765075173468922253983199069732489

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

3:

-4.049367035034275107756345992158328026284263862922679802098757857830139244608790264034021187462438162 + i * -4.539011634219251898486267823101800641866780607249524169603473623688816990882956255673234515244547992

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

4:

3.458013897225698242663704625210969485252091736189931981051191626924302997402154833559851802444730346 + i * 5.004212214384391799444395571431795098537891300058211411072406402820302128123727638930037511382050737

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

5:

-5.942862663109936751531649894310895594040436381469512869990372340719318944649944591116065727919207070 + i * 1.297067217770100918161189655267389996711338238498216976937298417239892019450819167943222337314807370

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

6:

-3.931744998706158481008576599084240283631244690286860356839201938564053879717244747796222190957720926 + i * 4.641269359253900256711579576978698201969364863247802251418633550352579914116041022802464927604748931

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 2590x^4 + 1874161$

37

7:

5.586328900244307973697813585101610485342268951683800598342831245097132246892271405082534825568520748 + i * -2.406850518477460538281603671624453895288278057662765199942651992769058096684578970783457401795913631

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

8:

-5.761751474243332746718528347989442534506191568028135383740321023419662957503953983400456966282277560 + i * 1.949928190743131366092165220409090532699490336675188831864376985614337995860700178419485157669668914

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

37

9:

1.875021774175258817976895974503314892395603014223218366969846119308701067608621661481190760188595884 + i * 5.786561444102072673020639263248306604261538195797832905645155868638578686477321625454516110173001527

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

10:

2.236417336768138642223481980186338055908773078695839895552736958125644079724004699777274593156313356 + i * 5.656716140642281331723076734030570140417651992563547409553865670176469396239731818547773812140068287

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 407x^3 + 50653$

37

11:

-1.383146685971572477102503026699190395855818745479626109420073237188324938100447349758008194124123942 + i * -5.923420063197093256792555641912855723025388374641469898687399504185494735978819445087446069623427905

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 19573x^6 + 2565726409$

37

12:

4.391540733956755916664558213120548092294334028327404837457177196459974363588634150290837693508709630 + i * -4.208844257275215161265891544035765241340933227709454147793057288968535791720738124227340475412095246

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

13:

-3.208411932587452934265570484046568896696749622959558332409659358205374172676344495548980406826859013 + i * 5.167793810789130678131683801375402166178180672497234249856608710860171845556794193213938473669084232

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

14:

5.761751474243332746718528347989442534506191568028135383740321023419662957503953983400456966282277560 + i * 1.949928190743131366092165220409090532699490336675188831864376985614337995860700178419485157669668914

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

37

15:

5.942862663109936751531649894310895594040436381469512869990372340719318944649944591116065727919207070 + i * 1.297067217770100918161189655267389996711338238498216976937298417239892019450819167943222337314807370

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

16:

5.586328900244307973697813585101610485342268951683800598342831245097132246892271405082534825568520748 + i * 2.406850518477460538281603671624453895288278057662765199942651992769058096684578970783457401795913631

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

17:

-4.565586728929195113660969703362541471274837039534888006694163782104047406610290272147659053081912707 + i * -4.019380278180407783475482825893216998162079567966342354992931917181384204776314903561472818767142483

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

18:

-6.063760587154141640560558690466565528747272905391356801641898070656855872997718459406512796707970094 + i * 0.4804243350165137308070530018396615230031016777825737112098511327128599773920124413122213178496104634

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

19:

-5.223505065773082120385976169205972483378360916606999484792807379939627716619201256446501491321315638 + i * 3.116888645403128454761600720334309296553360961187554864611014030876765075173468922253983199069732489

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

20:

3.208411932587452934265570484046568896696749622959558332409659358205374172676344495548980406826859013 + i * 5.167793810789130678131683801375402166178180672497234249856608710860171845556794193213938473669084232

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

21:

3.084896199745330467898417809705636112539300019826820942285755339089725714407931103769193435809620468 + i * -5.242462726314495995475021859402234718348572986611434166605266419145414359853801513713374670473803875

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

22:

4.371954370266629646620526647312282624606441310508375082722675227890076683278545623048237902429846887 + i * -4.229186090054032820118546104347028670439262025379141695363770087825272631646432184007689254922513351

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

23:

2.870623426728783462424145299003076853367548288141426849645816057182342298454161194896015115735954781 + i * -5.362790424948181467396603049044555135820449423997892233202860839303000352775997607516397602354079135

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

37

24:

4.565586728929195113660969703362541471274837039534888006694163782104047406610290272147659053081912707 + i * -4.019380278180407783475482825893216998162079567966342354992931917181384204776314903561472818767142483

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

25:

-4.049367035034275107756345992158328026284263862922679802098757857830139244608790264034021187462438162 + i * 4.539011634219251898486267823101800641866780607249524169603473623688816990882956255673234515244547992

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

26:

2.236417336768138642223481980186338055908773078695839895552736958125644079724004699777274593156313356 + i * -5.656716140642281331723076734030570140417651992563547409553865670176469396239731818547773812140068287

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 407x^3 + 50653$

37

27:

-1.383146685971572477102503026699190395855818745479626109420073237188324938100447349758008194124123942 + i * 5.923420063197093256792555641912855723025388374641469898687399504185494735978819445087446069623427905

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} + 19573x^6 + 2565726409$

37

28:

3.458013897225698242663704625210969485252091736189931981051191626924302997402154833559851802444730346 + i * -5.004212214384391799444395571431795098537891300058211411072406402820302128123727638930037511382050737

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

29:

-2.870623426728783462424145299003076853367548288141426849645816057182342298454161194896015115735954781 + i * -5.362790424948181467396603049044555135820449423997892233202860839303000352775997607516397602354079135

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

37

30:

3.084896199745330467898417809705636112539300019826820942285755339089725714407931103769193435809620468 + i * 5.242462726314495995475021859402234718348572986611434166605266419145414359853801513713374670473803875

comment: $\chi$ of order $18$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=108$

37

31:

3.931744998706158481008576599084240283631244690286860356839201938564053879717244747796222190957720926 + i * 4.641269359253900256711579576978698201969364863247802251418633550352579914116041022802464927604748931

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 2590x^4 + 1874161$

37

32:

-4.371954370266629646620526647312282624606441310508375082722675227890076683278545623048237902429846887 + i * -4.229186090054032820118546104347028670439262025379141695363770087825272631646432184007689254922513351

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

33:

1.875021774175258817976895974503314892395603014223218366969846119308701067608621661481190760188595884 + i * -5.786561444102072673020639263248306604261538195797832905645155868638578686477321625454516110173001527

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

34:

4.391540733956755916664558213120548092294334028327404837457177196459974363588634150290837693508709630 + i * 4.208844257275215161265891544035765241340933227709454147793057288968535791720738124227340475412095246

comment: $\chi$ of order $9$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=54$

37

35:

6.063760587154141640560558690466565528747272905391356801641898070656855872997718459406512796707970094 + i * 0.4804243350165137308070530018396615230031016777825737112098511327128599773920124413122213178496104634

comment: $\chi$ of order $36$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=432$

37

36:

6.082762530298219688999684245202067062084970094786411186419153046486332725318910239803066427957848663 + i * 0

comment: $\chi=\left(\frac{37}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{37}$

39

2:

6.242921251921868741926100210841760171533142266155273803512588720526291012765140186976624083831154982 + i * -0.1610411199113042648241633366124029436606769693707461828253468106210912951330489358356003845904117748

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

39

5:

-1.809701428526829720964875853955186050997092124900847177615229972952231815481174445761410657333709663 + i * 5.977037789707201760803219289562204403104618901420511304348433825825684935681355630971503477475487217

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 1170x^4 + 2313441$

39

8:

-1.809701428526829720964875853955186050997092124900847177615229972952231815481174445761410657333709663 + i * -5.977037789707201760803219289562204403104618901420511304348433825825684935681355630971503477475487217

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 1170x^4 + 2313441$

39

11:

5.283754006004701588709108626206065904751320749894468097635290351390834089772562434136819211726888377 + i * 3.328955332237016947692581222768895354376315575196933455727184063592289687987488537365294124766302447

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

39

17:

6.244484520900431231093237980174269914135284199247923401664246176274629090236886149712315841000802324 + i * 0.08008163481667835817214699700415378948274192242558686907360970435477658307792639061070748899881714157

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 118287x^6 + 3518743761$

39

20:

6.242921251921868741926100210841760171533142266155273803512588720526291012765140186976624083831154982 + i * 0.1610411199113042648241633366124029436606769693707461828253468106210912951330489358356003845904117748

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

39

23:

-6.244484520900431231093237980174269914135284199247923401664246176274629090236886149712315841000802324 + i * 0.08008163481667835817214699700415378948274192242558686907360970435477658307792639061070748899881714157

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 118287x^6 + 3518743761$

39

29:

1.654968448513110175785390972798938136144380656528142419631516268014851228136880157203536142391558165 + i * -6.021717316050804870527820161625102668575413972935415879613949578613347741005600595138073167150617747

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 351x^3 + 59319$

39

32:

5.283754006004701588709108626206065904751320749894468097635290351390834089772562434136819211726888377 + i * -3.328955332237016947692581222768895354376315575196933455727184063592289687987488537365294124766302447

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

39

35:

-1.654968448513110175785390972798938136144380656528142419631516268014851228136880157203536142391558165 + i * -6.021717316050804870527820161625102668575413972935415879613949578613347741005600595138073167150617747

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 - 351x^3 + 59319$

39

38:

0 + i * 6.244997998398398205846893120939794461072959977991656308452971930609611200583514500633336112221340587

comment: $\chi=\left(\frac{-39}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{39}$

40

3:

3.325015502219627428719739712905081473778027878016878579357053822321256570656356625501068661292152361 + i * 5.379988095711658615680471751085990047014264888340441209563353161378076233231950612529648087827233100

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1920x^4 + 2560000$

40

13:

5.379988095711658615680471751085990047014264888340441209563353161378076233231950612529648087827233100 + i * -3.325015502219627428719739712905081473778027878016878579357053822321256570656356625501068661292152361

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1920x^4 + 2560000$

40

19:

0 + i * 6.324555320336758663997787088865437067439110278650433653715009705585188877278476442688496216758600590

comment: $\chi=\left(\frac{-40}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{40}$

40

27:

3.325015502219627428719739712905081473778027878016878579357053822321256570656356625501068661292152361 + i * -5.379988095711658615680471751085990047014264888340441209563353161378076233231950612529648087827233100

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1920x^4 + 2560000$

40

29:

6.324555320336758663997787088865437067439110278650433653715009705585188877278476442688496216758600590 + i * 0

comment: $\chi=\left(\frac{40}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{40}$

40

37:

-5.379988095711658615680471751085990047014264888340441209563353161378076233231950612529648087827233100 + i * -3.325015502219627428719739712905081473778027878016878579357053822321256570656356625501068661292152361

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 + 1920x^4 + 2560000$

41

2:

1.904681140948217370229137212520406674797316038689224457186668301354479016198190890084270967980828721 + i * -6.113279786768817349129432880184698136112192839245601980084175530942740564826217081471565598443986336

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

3:

-6.385064883671733505423375937426645956283317463043434599714031769276015820395557931783799291190036449 + i * 0.4805688621852983496960973810984878268881722188472489639560245971619490424959680925598320016755225226

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

41

4:

-5.420003557907024019070851256222254941627888678316053651932628466215147375228658296555577853409707178 + i * -3.409334455912942685326386348131475185698623368210735299872701026522766852061921843594712570444434686

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

41

5:

-4.196921453809886673539595725120814175045342886016446779627303161299529026387542677275262677030371271 + i * 4.835891883670509365018844371880234854368348793364541496342740549706964477287638318534788771005620477

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

6:

5.241978842368065899738074884475876870745497822575781672528708435731605945134718952307914801401891575 + i * 3.677180688539190035825136181919462987196367311310503156659162206162217699367639963092853852989680444

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

7:

-5.241978842368065899738074884475876870745497822575781672528708435731605945134718952307914801401891575 + i * 3.677180688539190035825136181919462987196367311310503156659162206162217699367639963092853852989680444

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

8:

5.997065111509468400427916055717294611705047293479663907357033468878028927320047787803524820388289552 + i * -2.243927371444077585703813617433488105634216420467710755449156491008732349151618018063032918800168569

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

9:

-2.119478569464168534502413122777687533466720385099958512586759073185357099765493508541775498975975192 + i * 6.042169361544090458417432447042396084082232035774388162384756589994181003498352222874385962547081214

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 738x^4 + 2825761$

41

10:

1.784314468041394677472200267932970288059655951363280410498085238867402426467366807380446454702878505 + i * 6.149489562487130096533474654102983051946855617472953130099348068670393365955357533044798426490807131

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

41

11:

1.731206361939698536309424790410670569849558433888413358060663024637046858814424718166462505544123673 + i * 6.164651209304506427272040588678490206599391251459621570212775903967135306409672755732394115992390660

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

12:

-3.393608256127735457755157366969374219733552778828015965973148891641319968147575565032034001269305789 + i * 5.429863994976455232645237439552968988536848081035152937247877879423613295489047664193382525376331411

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

13:

-6.310721856607017585196545708289710224413881137118600113680375925172776196739946728955705903937646428 + i * -1.083877137198897179450148070267479303115325310426906291426698097397627347990421985114013594474261034

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

14:

6.385064883671733505423375937426645956283317463043434599714031769276015820395557931783799291190036449 + i * 0.4805688621852983496960973810984878268881722188472489639560245971619490424959680925598320016755225226

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

41

15:

-1.731206361939698536309424790410670569849558433888413358060663024637046858814424718166462505544123673 + i * 6.164651209304506427272040588678490206599391251459621570212775903967135306409672755732394115992390660

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

16:

6.372033231482862099756777638890178316625342420515693804834870762300786453476658102685852140763234344 + i * -0.6302320976260047225853319360117173926140148922697808209437622442536778269232180000757346710681600192

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

41

17:

-0.5235336810367241464094693518458698446050021894564617716159327667013700477656481879338765581763320815 + i * -6.381685708715224529777520059204544926537552397910271602347114417328182720013028775906170308608148451

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

18:

6.372033231482862099756777638890178316625342420515693804834870762300786453476658102685852140763234344 + i * 0.6302320976260047225853319360117173926140148922697808209437622442536778269232180000757346710681600192

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

41

19:

6.310721856607017585196545708289710224413881137118600113680375925172776196739946728955705903937646428 + i * -1.083877137198897179450148070267479303115325310426906291426698097397627347990421985114013594474261034

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

20:

6.393546916973171013573647994315678944927036118696762126651736465053748164644457976299092314691046635 + i * 0.3500825909165719681519316051748586082198777779659139590612905105795902644273320377731598495080384561

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

21:

1.904681140948217370229137212520406674797316038689224457186668301354479016198190890084270967980828721 + i * 6.113279786768817349129432880184698136112192839245601980084175530942740564826217081471565598443986336

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

22:

6.233738805488832316342847873739240580546064145951813022664625308363085168555577885036915732076247445 + i * -1.463044942899112042076882267370271828049585945731659017536675403599296966320296236176926595722982211

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

23:

6.348809069116511848908059654085028347208877433436878239886328257182709076270404589501389729188646038 + i * -0.8322399917715624130613441488171165609459128262073176870173611164678827513775186757879093454232251794

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

41

24:

3.393608256127735457755157366969374219733552778828015965973148891641319968147575565032034001269305789 + i * 5.429863994976455232645237439552968988536848081035152937247877879423613295489047664193382525376331411

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

25:

6.348809069116511848908059654085028347208877433436878239886328257182709076270404589501389729188646038 + i * 0.8322399917715624130613441488171165609459128262073176870173611164678827513775186757879093454232251794

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

41

26:

-4.799511917554389942950603934861599552612609575953314590730644906847122200169121543948869416486569281 + i * -4.238476772763227357188568348365541311060068634850382562531808716601927530090074990120600042990471047

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

27:

2.566979185676147605024748650523984964845965904448286269652564957895782785105079524319379760284246990 + i * 5.866056414688271826249849284001974164742890322439200209104606385763362600199577211404108741946522416

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

41

28:

-6.233738805488832316342847873739240580546064145951813022664625308363085168555577885036915732076247445 + i * -1.463044942899112042076882267370271828049585945731659017536675403599296966320296236176926595722982211

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

29:

0.5235336810367241464094693518458698446050021894564617716159327667013700477656481879338765581763320815 + i * -6.381685708715224529777520059204544926537552397910271602347114417328182720013028775906170308608148451

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

30:

4.799511917554389942950603934861599552612609575953314590730644906847122200169121543948869416486569281 + i * -4.238476772763227357188568348365541311060068634850382562531808716601927530090074990120600042990471047

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

31:

-5.420003557907024019070851256222254941627888678316053651932628466215147375228658296555577853409707178 + i * 3.409334455912942685326386348131475185698623368210735299872701026522766852061921843594712570444434686

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

41

32:

-2.119478569464168534502413122777687533466720385099958512586759073185357099765493508541775498975975192 + i * -6.042169361544090458417432447042396084082232035774388162384756589994181003498352222874385962547081214

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)$ a root of $x^8 - 738x^4 + 2825761$

41

33:

-4.196921453809886673539595725120814175045342886016446779627303161299529026387542677275262677030371271 + i * -4.835891883670509365018844371880234854368348793364541496342740549706964477287638318534788771005620477

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

34:

3.443673469471620990257534346693497947314793294261906994146680365527470829850717880441992037630184897 + i * -5.398250923739770792429645994253759774868713468503332509116340350609383641233333818171620041980612560

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

35:

-3.443673469471620990257534346693497947314793294261906994146680365527470829850717880441992037630184897 + i * -5.398250923739770792429645994253759774868713468503332509116340350609383641233333818171620041980612560

comment: $\chi$ of order $40$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=640$

41

36:

5.997065111509468400427916055717294611705047293479663907357033468878028927320047787803524820388289552 + i * 2.243927371444077585703813617433488105634216420467710755449156491008732349151618018063032918800168569

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

37:

1.784314468041394677472200267932970288059655951363280410498085238867402426467366807380446454702878505 + i * -6.149489562487130096533474654102983051946855617472953130099348068670393365955357533044798426490807131

comment: $\chi$ of order $5$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=20$

41

38:

-2.566979185676147605024748650523984964845965904448286269652564957895782785105079524319379760284246990 + i * 5.866056414688271826249849284001974164742890322439200209104606385763362600199577211404108741946522416

comment: $\chi$ of order $8$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=32$

41

39:

6.393546916973171013573647994315678944927036118696762126651736465053748164644457976299092314691046635 + i * -0.3500825909165719681519316051748586082198777779659139590612905105795902644273320377731598495080384561

comment: $\chi$ of order $20$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=160$

41

40:

6.403124237432848686488217674621813264520420132621018885529272626668182758196876074289354302249869963 + i * 0

comment: $\chi=\left(\frac{41}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{41}$

43

2:

-3.302655547658774340966512538252770019320671163979280783643512293257509519550247574560119690248685793 + i * -5.665021300358783410718036212897076735862323142673986340729401632219398953200987191577010357645633654

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

3:

6.325992712583278959583006316250013565012359524827737595525127051501346000573301419181898803939235682 + i * -1.726793618341013026831042741189986909989926938546061510972380865772525267243535152393365799053089597

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

4:

6.482325633191789668641367080071685140242774942593003419284972414386109061662392618392687867816812561 + i * 0.9896738782369994131289114344780604864380476211759002554473861239826481888492417454505545001751141252

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

5:

1.457062544764120003939858911763278083931761064910663072424655968780737582627688863860986740646995210 + i * 6.393509892120720476839276741991854000198356774625952465270517498857905583568957220887470361186653389

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

6:

4.832354013265117169742910219282041141185935217408087458585338651585831605271707544540604134101765292 + i * -4.432646465767433137383769507665918751744895478147416667612720249623029991668088977026285986111916294

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 344x^3 + 79507$

43

7:

6.533074418876609803338550612267338038252160772965778825186440085573464418434033829477371452972891319 + i * 0.5647465249295891981879884743646461790678491133728813495325645908766167292228082252629801111860810911

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 138202x^6 + 6321363049$

43

8:

-4.226220308182726846182122617919296305114149473687711152303118179114713503267435610929378040253016646 + i * 5.013886906054413321828951953358894160726748073391869007738614865861418233133823250235317745942167700

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

9:

0.4521424872734200009192503414315067388362783986896055993713912875467422851333285852568246120222276694 + i * 6.541832095919476075811562156732991352455048015484667787435538158341265482135111010972894676068967366

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

10:

0.7770594832408628649684797526465911905413095975535074145271931135616079119066253844712001040649530199 + i * 6.511234795298464981034391677131976319798159664404944868224659215153160555129262689422228853482116063

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

11:

6.482325633191789668641367080071685140242774942593003419284972414386109061662392618392687867816812561 + i * -0.9896738782369994131289114344780604864380476211759002554473861239826481888492417454505545001751141252

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

12:

1.046630152117543381683104161404051431481712737431743783140313738379291437444958131024679180582433536 + i * 6.473373565976121542211522875374857846028079304934151473892959986290976180630539037245599148436894843

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

13:

0.7770594832408628649684797526465911905413095975535074145271931135616079119066253844712001040649530199 + i * -6.511234795298464981034391677131976319798159664404944868224659215153160555129262689422228853482116063

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

14:

0.1765652817972580455663731414683009428955895287629645945280594259138332628255454679250904681874688370 + i * -6.555060999049807076987661751895867094864001815483575791819035006822507273090829855862885085161049562

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

15:

-6.389756574664535941126451878987028259737108235701117131818415649828702987655550585117935412577748043 + i * 1.473435073741404028280744723285215633655791282690850187938955933836856936109866960700364449799628988

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

16:

3.915621138636623671980000909420758039238451009886102411420726823199866758942480056616425070726438113 + i * 5.260029572033034753219965286630532005043050593486399379483766774214828753757435853009295330833598289

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

17:

4.845972102075695622339471226709552950183428479675157091676300512292070046784476288702470282723215460 + i * -4.417754450612218425519128580820183164333147089513374045049858409874330058291404734529633375242008594

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

18:

-1.046630152117543381683104161404051431481712737431743783140313738379291437444958131024679180582433536 + i * 6.473373565976121542211522875374857846028079304934151473892959986290976180630539037245599148436894843

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

19:

6.138441440673206102723025514689779344039743613830246096675688907439942903339452336642643004067879487 + i * -2.306412079275048785252071250943551503833831531243552630732510291496242340632407033162984123268874597

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

20:

5.567456759907910250784014228550264922260592636882166760712816825094122550655916520295262472321306806 + i * -3.464595968732243646289123096849634091054828411916694883583984855924468823381825278830781505057776880

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

21:

5.151750339025108962622566748817025444131446022536134400749326735333882510865768417961609553589826727 + i * 4.057027045060788705019611364064936848422441100074207786874496337347191327202754591571038773436796829

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

22:

3.302655547658774340966512538252770019320671163979280783643512293257509519550247574560119690248685793 + i * -5.665021300358783410718036212897076735862323142673986340729401632219398953200987191577010357645633654

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

23:

-6.389756574664535941126451878987028259737108235701117131818415649828702987655550585117935412577748043 + i * -1.473435073741404028280744723285215633655791282690850187938955933836856936109866960700364449799628988

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

24:

0.4521424872734200009192503414315067388362783986896055993713912875467422851333285852568246120222276694 + i * -6.541832095919476075811562156732991352455048015484667787435538158341265482135111010972894676068967366

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

25:

1.032176825735974087985457284498603527211797715384882354988777099218064680913552341841005701724862436 + i * 6.475693862468608744077203266547391024636790222214600131373921284418932911416457411644231352084423776

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

26:

-1.457062544764120003939858911763278083931761064910663072424655968780737582627688863860986740646995210 + i * 6.393509892120720476839276741991854000198356774625952465270517498857905583568957220887470361186653389

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

27:

4.226220308182726846182122617919296305114149473687711152303118179114713503267435610929378040253016646 + i * 5.013886906054413321828951953358894160726748073391869007738614865861418233133823250235317745942167700

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

28:

-5.567456759907910250784014228550264922260592636882166760712816825094122550655916520295262472321306806 + i * -3.464595968732243646289123096849634091054828411916694883583984855924468823381825278830781505057776880

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

29:

-6.325992712583278959583006316250013565012359524827737595525127051501346000573301419181898803939235682 + i * -1.726793618341013026831042741189986909989926938546061510972380865772525267243535152393365799053089597

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

30:

-5.666108297569389829274031347510488072391043569862733893103525011519642879680520452786804021678578239 + i * -3.300790323576356905053493597930351493831165675136813949389430871180184885033260966796624794588140566

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

31:

1.032176825735974087985457284498603527211797715384882354988777099218064680913552341841005701724862436 + i * -6.475693862468608744077203266547391024636790222214600131373921284418932911416457411644231352084423776

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

32:

-6.176309441770842320932295176626523611161463155824126100525820603170477455254714211359265174376509538 + i * -2.202998338513296770709900394633021226648343180473467579524216806235060664511821758957552395602016447

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

33:

5.666108297569389829274031347510488072391043569862733893103525011519642879680520452786804021678578239 + i * -3.300790323576356905053493597930351493831165675136813949389430871180184885033260966796624794588140566

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

34:

-6.138441440673206102723025514689779344039743613830246096675688907439942903339452336642643004067879487 + i * -2.306412079275048785252071250943551503833831531243552630732510291496242340632407033162984123268874597

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=504$

43

35:

3.915621138636623671980000909420758039238451009886102411420726823199866758942480056616425070726438113 + i * -5.260029572033034753219965286630532005043050593486399379483766774214828753757435853009295330833598289

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

36:

4.832354013265117169742910219282041141185935217408087458585338651585831605271707544540604134101765292 + i * 4.432646465767433137383769507665918751744895478147416667612720249623029991668088977026285986111916294

comment: $\chi$ of order $3$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=6$, $\tau(\chi)$ a root of $x^6 + 344x^3 + 79507$

43

37:

-6.533074418876609803338550612267338038252160772965778825186440085573464418434033829477371452972891319 + i * 0.5647465249295891981879884743646461790678491133728813495325645908766167292228082252629801111860810911

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)$ a root of $x^{12} - 138202x^6 + 6321363049$

43

38:

4.845972102075695622339471226709552950183428479675157091676300512292070046784476288702470282723215460 + i * 4.417754450612218425519128580820183164333147089513374045049858409874330058291404734529633375242008594

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

39:

6.176309441770842320932295176626523611161463155824126100525820603170477455254714211359265174376509538 + i * -2.202998338513296770709900394633021226648343180473467579524216806235060664511821758957552395602016447

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$

43

40:

0.1765652817972580455663731414683009428955895287629645945280594259138332628255454679250904681874688370 + i * 6.555060999049807076987661751895867094864001815483575791819035006822507273090829855862885085161049562

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=252$

43

41:

5.151750339025108962622566748817025444131446022536134400749326735333882510865768417961609553589826727 + i * -4.057027045060788705019611364064936848422441100074207786874496337347191327202754591571038773436796829

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$

43

42:

0 + i * 6.557438524302000652344109997636001627926966319883789769865460105585659853488575639355805290969678548

comment: $\chi=\left(\frac{-43}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{43}$

44

3:

0.1576834991891041147383025000690941537448243652663207813784332186406597274006599595626309799825555286 + i * 6.631375114867464636478508726024812130346718488975102068927214135715920351740163161434926823124033565

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

7:

6.435764741901582141188802385837780985383408035708396982165240652712678799026469222642355773876193421 + i * 1.606527991320556421082624257248057019460443696761386914968120202571109385764674398680322726662407113

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

15:

-0.1576834991891041147383025000690941537448243652663207813784332186406597274006599595626309799825555286 + i * 6.631375114867464636478508726024812130346718488975102068927214135715920351740163161434926823124033565

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

19:

6.435764741901582141188802385837780985383408035708396982165240652712678799026469222642355773876193421 + i * -1.606527991320556421082624257248057019460443696761386914968120202571109385764674398680322726662407113

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

27:

-2.336219348094091366266371969783032321177998990642471238677311817909931114721632112740384164375843599 + i * -6.208226732134613232040582039861115442436204877715258784746386270125865455731426122417101951887307375

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

31:

2.336219348094091366266371969783032321177998990642471238677311817909931114721632112740384164375843599 + i * -6.208226732134613232040582039861115442436204877715258784746386270125865455731426122417101951887307375

comment: $\chi$ of order $10$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

35:

0.1458248865523453334571852552587202044546971381894162991622316504070602156180279166932242253790819639 + i * 6.631646485033863414548831748402915452474288547297469381133419488338934512533663817345947715472193416

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

39:

0.1458248865523453334571852552587202044546971381894162991622316504070602156180279166932242253790819639 + i * -6.631646485033863414548831748402915452474288547297469381133419488338934512533663817345947715472193416

comment: $\chi$ of order $10$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=40$

44

43:

6.633249580710799698229865473341373367854177091178707194117364292232969285218087693417686798256581302 + i * 0

comment: $\chi=\left(\frac{44}{\cdot}\right)$, even: $\tau(\chi)=\sqrt{44}$

45

2:

6.232054012322000889725506814801007811034358940801993100145465389485855940758050993455466741441026013 + i * 2.482237455905709674885470770564718881078439360778669861930755783786591045835070710355244719078371436

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

4:

1.164867388296651284864770922482732627006446002168273779385802531579788675931585446409031457007556978 + i * -6.606291241512361498531982782942260468086791883668121365996846671521680247079264314897351231236709336

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=\sqrt{45}\,\zeta_{9}^{7}$, $\tau(\chi)$ a root of $x^{12} + 91125x^6 + 8303765625$

45

7:

6.232054012322000889725506814801007811034358940801993100145465389485855940758050993455466741441026013 + i * 2.482237455905709674885470770564718881078439360778669861930755783786591045835070710355244719078371436

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

13:

-6.232054012322000889725506814801007811034358940801993100145465389485855940758050993455466741441026013 + i * 2.482237455905709674885470770564718881078439360778669861930755783786591045835070710355244719078371436

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

14:

-1.164867388296651284864770922482732627006446002168273779385802531579788675931585446409031457007556978 + i * 6.606291241512361498531982782942260468086791883668121365996846671521680247079264314897351231236709336

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=\sqrt{45}\,\zeta_{18}^{5}$, $\tau(\chi)$ a root of $x^{12} + 91125x^6 + 8303765625$

45

22:

-5.007239957280982652970170551162413060973399613808579283254025744542502662479445226279075042139407394 + i * -4.464028226860661665967264520125147002682202312804437452337285962023191104674826989211701453778379961

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

23:

6.232054012322000889725506814801007811034358940801993100145465389485855940758050993455466741441026013 + i * -2.482237455905709674885470770564718881078439360778669861930755783786591045835070710355244719078371436

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

29:

1.164867388296651284864770922482732627006446002168273779385802531579788675931585446409031457007556978 + i * 6.606291241512361498531982782942260468086791883668121365996846671521680247079264314897351231236709336

comment: $\chi$ of order $6$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=\sqrt{45}\,\zeta_{9}^{2}$, $\tau(\chi)$ a root of $x^{12} + 91125x^6 + 8303765625$

45

32:

5.007239957280982652970170551162413060973399613808579283254025744542502662479445226279075042139407394 + i * 4.464028226860661665967264520125147002682202312804437452337285962023191104674826989211701453778379961

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

34:

1.164867388296651284864770922482732627006446002168273779385802531579788675931585446409031457007556978 + i * 6.606291241512361498531982782942260468086791883668121365996846671521680247079264314897351231236709336

comment: $\chi$ of order $6$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=12$, $\tau(\chi)=\sqrt{45}\,\zeta_{9}^{2}$, $\tau(\chi)$ a root of $x^{12} + 91125x^6 + 8303765625$

45

38:

5.007239957280982652970170551162413060973399613808579283254025744542502662479445226279075042139407394 + i * -4.464028226860661665967264520125147002682202312804437452337285962023191104674826989211701453778379961

comment: $\chi$ of order $12$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

45

43:

5.007239957280982652970170551162413060973399613808579283254025744542502662479445226279075042139407394 + i * -4.464028226860661665967264520125147002682202312804437452337285962023191104674826989211701453778379961

comment: $\chi$ of order $12$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=48$

47

2:

6.848688428294738395090178341720038126954932838728940459509223403493480550368311159366641210197830926 + i * -0.3089770414476550463662790193106306649274614800716927321461758495492403984077432992119422415144833939

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

3:

-4.442633879413871719535150116648490105173112348366303295954362969609088264739556061514103478397945554 + i * -5.221398683636794681618599038330178107038527219385937133039050497355836064985858611805921695111583415

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

4:

6.855264517948910248321460361268333081527052780916614963649856490894057495199406196144847197313938098 + i * 0.07313268045610799180340985722084341140001355734914325561903501738203742185796814673086733504394223650

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

5:

-6.625000671774959077049802662703728846047665246777138816771742518493885056961757853586818550009715946 + i * 1.763339473550496160245437245081613204346030755636636920518357178219978221869797290821856653813567646

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

6:

-1.487449354895147293438644951372718652717932708337423160831632209466067598489362644140299349860353066 + i * -6.692345957631151195810784483325737138519865061366401349433751549595549905063583619902769426491906351

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

7:

4.116213852864953373663830968224167341671640990010490902955861573865220690877547602935298333983268512 + i * -5.482406726747173395930493896397159762773634064000785652139484660852359543044467100467029113083837281

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

8:

-1.487449354895147293438644951372718652717932708337423160831632209466067598489362644140299349860353066 + i * 6.692345957631151195810784483325737138519865061366401349433751549595549905063583619902769426491906351

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

9:

3.622109920350496477756781360642716113640217135460081728937273205345564092222241661721293142155079439 + i * -5.820680348971116629072644145524937811834573381050224045169532439151064535117094246771766994256762383

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

10:

4.795300578490033633197356574834249188207164273487673655548462054381843034591358476415397883878425091 + i * -4.899499195013011611663123234123500646360423156693283579604661678861819079635284450541583130694329964

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

11:

4.487718016513303041201093902233297802538629624817932915971015836397845630175050204195540337101483320 + i * 5.182700744231901446281080409143745161804164597432859366905651019570267250141945424013985033170969270

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

12:

6.855264517948910248321460361268333081527052780916614963649856490894057495199406196144847197313938098 + i * -0.07313268045610799180340985722084341140001355734914325561903501738203742185796814673086733504394223650

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

13:

6.855614370606043975581632940906780309721402992303823932831483208483671734343582544479709645186429051 + i * -0.02348619892395369996191943234321312702587126494567652041574282503865078047007809726821132497453388105

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

14:

1.185597148070620584510599781907149851590349427975730529844129903586387423721952424542563532608325078 + i * -6.752359543336448473365164154397617355299479171272949569097329755460146117445147806878496292180604826

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

15:

1.404492971106937519032230564845093442470212297948539159332338562307091708899054121277895716069300968 + i * -6.710245859438475684335011959486355638900189372331611772479082545112060736260616518434561946421702426

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

16:

-4.442633879413871719535150116648490105173112348366303295954362969609088264739556061514103478397945554 + i * 5.221398683636794681618599038330178107038527219385937133039050497355836064985858611805921695111583415

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

17:

1.403841248809529960287939700877867833630131860537377821939847034950791393284162745103718796978774353 + i * 6.710382235621224237196580372776444996903451034832096043258223770702659169402404478691902806350306645

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

18:

5.220718330668350680260965154750335930060786208749603590740736205057571746033644742239151361455333082 + i * 4.443433369796768968418133901510955360592512183462989022729030482263121617319110543755617524083081365

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

19:

6.625000671774959077049802662703728846047665246777138816771742518493885056961757853586818550009715946 + i * 1.763339473550496160245437245081613204346030755636636920518357178219978221869797290821856653813567646

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

20:

3.919030148586836122783175305492545360847459296591179437928787597079414887728329294557220404172466642 + i * 5.625051350384940368700994782807837094366676325767114493439168993524349543453482952230294187172010768

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

21:

3.622109920350496477756781360642716113640217135460081728937273205345564092222241661721293142155079439 + i * 5.820680348971116629072644145524937811834573381050224045169532439151064535117094246771766994256762383

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

22:

-1.404492971106937519032230564845093442470212297948539159332338562307091708899054121277895716069300968 + i * -6.710245859438475684335011959486355638900189372331611772479082545112060736260616518434561946421702426

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

23:

-3.230150110052786046189388964919683117431064349075890222004624729245492829179713275182121098330159553 + i * 6.046993489869653745416053341534805218848610886628696198172715406074704052047300141612814568925681773

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

24:

6.848688428294738395090178341720038126954932838728940459509223403493480550368311159366641210197830926 + i * 0.3089770414476550463662790193106306649274614800716927321461758495492403984077432992119422415144833939

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

25:

-0.2031365467395775609806161491300171314464801805031468175167810597573030805143786841058643925799333679 + i * -6.852644419738902476199942652167209364563675826984441050945783609304609857299732170637376766731740164

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

26:

-6.852041977008538976447858615770867181654940542794081340257831773416214346286663140980187020483328322 + i * -0.2225325713528530206770016098770235873371478452975083573721571808814226730584465051500115837774898593

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

27:

4.116213852864953373663830968224167341671640990010490902955861573865220690877547602935298333983268512 + i * 5.482406726747173395930493896397159762773634064000785652139484660852359543044467100467029113083837281

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

28:

0.1755685616009391289398218080810757271099828704866091235251267622603237671860310722028732325712108625 + i * 6.853406137110026638086693793245567481299259719796035256024684092000053461852596395289995369441588157

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

29:

-6.855614370606043975581632940906780309721402992303823932831483208483671734343582544479709645186429051 + i * -0.02348619892395369996191943234321312702587126494567652041574282503865078047007809726821132497453388105

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

30:

-4.487718016513303041201093902233297802538629624817932915971015836397845630175050204195540337101483320 + i * 5.182700744231901446281080409143745161804164597432859366905651019570267250141945424013985033170969270

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

31:

-2.061938099581074983521944681006007226553645159070788915738566031926927790969314325732097635807381406 + i * -6.538226921229943431158106786771069980869201964051646917473185096688561954297898388227607868119049934

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

32:

-0.2031365467395775609806161491300171314464801805031468175167810597573030805143786841058643925799333679 + i * 6.852644419738902476199942652167209364563675826984441050945783609304609857299732170637376766731740164

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

33:

-4.795300578490033633197356574834249188207164273487673655548462054381843034591358476415397883878425091 + i * -4.899499195013011611663123234123500646360423156693283579604661678861819079635284450541583130694329964

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

34:

5.220718330668350680260965154750335930060786208749603590740736205057571746033644742239151361455333082 + i * -4.443433369796768968418133901510955360592512183462989022729030482263121617319110543755617524083081365

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

35:

6.318719565217465172019629933774754914257762010103414294959853562460050379172003250847940460698497666 + i * 2.659658447270627999849037933902004058074937865463416847864076850130904576331351594802419935914923698

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

36:

1.403841248809529960287939700877867833630131860537377821939847034950791393284162745103718796978774353 + i * -6.710382235621224237196580372776444996903451034832096043258223770702659169402404478691902806350306645

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

37:

1.185597148070620584510599781907149851590349427975730529844129903586387423721952424542563532608325078 + i * 6.752359543336448473365164154397617355299479171272949569097329755460146117445147806878496292180604826

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

38:

6.852041977008538976447858615770867181654940542794081340257831773416214346286663140980187020483328322 + i * -0.2225325713528530206770016098770235873371478452975083573721571808814226730584465051500115837774898593

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

39:

6.038510849671184740799833167245929063396438135129443504660358517643209299896296294112235637940604014 + i * -3.245980085952990950749352526587999339618941382710695728144773405875074034273187355958061532684789615

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

40:

-3.919030148586836122783175305492545360847459296591179437928787597079414887728329294557220404172466642 + i * 5.625051350384940368700994782807837094366676325767114493439168993524349543453482952230294187172010768

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

41:

-6.038510849671184740799833167245929063396438135129443504660358517643209299896296294112235637940604014 + i * -3.245980085952990950749352526587999339618941382710695728144773405875074034273187355958061532684789615

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

42:

0.1755685616009391289398218080810757271099828704866091235251267622603237671860310722028732325712108625 + i * -6.853406137110026638086693793245567481299259719796035256024684092000053461852596395289995369441588157

comment: $\chi$ of order $23$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=506$

47

43:

-6.318719565217465172019629933774754914257762010103414294959853562460050379172003250847940460698497666 + i * 2.659658447270627999849037933902004058074937865463416847864076850130904576331351594802419935914923698

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

44:

2.061938099581074983521944681006007226553645159070788915738566031926927790969314325732097635807381406 + i * -6.538226921229943431158106786771069980869201964051646917473185096688561954297898388227607868119049934

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

45:

3.230150110052786046189388964919683117431064349075890222004624729245492829179713275182121098330159553 + i * 6.046993489869653745416053341534805218848610886628696198172715406074704052047300141612814568925681773

comment: $\chi$ of order $46$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=1012$

47

46:

0 + i * 6.855654600401044124935871449084848960460643461001326275485108185678517115136816999227325148500066837

comment: $\chi=\left(\frac{-47}{\cdot}\right)$, odd: $\tau(\chi)=i\sqrt{47}$

48

5:

6.400825161530124202242620279306907503176527945642310005934994285721192411400301485158068326257084990 + i * -2.651308592284734292125482934423241065739740864960711929335455338441077428165820397945436787463041401

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=\sqrt{48}\,\zeta_{16}^{15}$, $\tau(\chi)$ a root of $x^8 + 5308416$

48

11:

6.400825161530124202242620279306907503176527945642310005934994285721192411400301485158068326257084990 + i * -2.651308592284734292125482934423241065739740864960711929335455338441077428165820397945436787463041401

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=\sqrt{48}\,\zeta_{16}^{15}$, $\tau(\chi)$ a root of $x^8 + 5308416$

48

29:

-6.400825161530124202242620279306907503176527945642310005934994285721192411400301485158068326257084990 + i * -2.651308592284734292125482934423241065739740864960711929335455338441077428165820397945436787463041401

comment: $\chi$ of order $4$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=\sqrt{48}\,\zeta_{16}^{9}$, $\tau(\chi)$ a root of $x^8 + 5308416$

48

35:

6.400825161530124202242620279306907503176527945642310005934994285721192411400301485158068326257084990 + i * 2.651308592284734292125482934423241065739740864960711929335455338441077428165820397945436787463041401

comment: $\chi$ of order $4$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=8$, $\tau(\chi)=\sqrt{48}\,\zeta_{16}$, $\tau(\chi)$ a root of $x^8 + 5308416$

49

2:

6.594736658828733677285987980788072118232106641892173386041525799712245816853921580343812026784954262 + i * 2.347221421319350159760049794273813579801903038338530807372932635110917095079827804757426600859941258

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{8}$

49

3:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

4:

-2.134643743394590659818870807585357933931050200960180362835471467784752400987689277855941328427100522 + i * 6.666580539435965517073688211061414234861840833985844547252142444838008236857822618267118206376226503

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{44}$

49

5:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

6:

-6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{98}^{47}$

49

8:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

9:

-1.264614950244792629444108524736704790726044358696925343992830995860345721990990194189858980978372075 + i * 6.884820188473868971146023567518179392107712534317711203599504038202050996364734841508238902020568840

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{41}$

49

10:

-6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{98}^{47}$

49

11:

-1.264614950244792629444108524736704790726044358696925343992830995860345721990990194189858980978372075 + i * -6.884820188473868971146023567518179392107712534317711203599504038202050996364734841508238902020568840

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{106}$

49

12:

-2.134643743394590659818870807585357933931050200960180362835471467784752400987689277855941328427100522 + i * -6.666580539435965517073688211061414234861840833985844547252142444838008236857822618267118206376226503

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{103}$

49

13:

5.330121708583941047841879456051367327506062283195248042048694803851900094862931386153953045806582187 + i * -4.537598767154518811385973773244365812305809495979180396226571403091133901284907036750812301160627582

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{98}^{87}$

49

15:

-5.330121708583941047841879456051367327506062283195248042048694803851900094862931386153953045806582187 + i * -4.537598767154518811385973773244365812305809495979180396226571403091133901284907036750812301160627582

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{30}$

49

16:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * -0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{48}$

49

17:

6.840749975223808176423800039047318454850712175548357033705317152537600934264132091796214380342920247 + i * 1.484634559908756744956069578340866581455959723990959915174907629652210383208213610923621190055917894

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{5}$

49

20:

-4.706106231829217516604929231461960520919661974588176670869845684752848533276442813940273051915819725 + i * 5.181945979527208772117618632720547653405881109994884632077234815185797853649609007343497016320308609

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{18}$

49

22:

-4.706106231829217516604929231461960520919661974588176670869845684752848533276442813940273051915819725 + i * -5.181945979527208772117618632720547653405881109994884632077234815185797853649609007343497016320308609

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{31}$

49

23:

6.840749975223808176423800039047318454850712175548357033705317152537600934264132091796214380342920247 + i * -1.484634559908756744956069578340866581455959723990959915174907629652210383208213610923621190055917894

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{142}$

49

24:

6.594736658828733677285987980788072118232106641892173386041525799712245816853921580343812026784954262 + i * -2.347221421319350159760049794273813579801903038338530807372932635110917095079827804757426600859941258

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{139}$

49

25:

6.594736658828733677285987980788072118232106641892173386041525799712245816853921580343812026784954262 + i * -2.347221421319350159760049794273813579801903038338530807372932635110917095079827804757426600859941258

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{139}$

49

26:

-6.840749975223808176423800039047318454850712175548357033705317152537600934264132091796214380342920247 + i * 1.484634559908756744956069578340866581455959723990959915174907629652210383208213610923621190055917894

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{294}^{137}$

49

27:

4.706106231829217516604929231461960520919661974588176670869845684752848533276442813940273051915819725 + i * 5.181945979527208772117618632720547653405881109994884632077234815185797853649609007343497016320308609

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{98}^{13}$

49

29:

-4.706106231829217516604929231461960520919661974588176670869845684752848533276442813940273051915819725 + i * 5.181945979527208772117618632720547653405881109994884632077234815185797853649609007343497016320308609

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{18}$

49

32:

6.840749975223808176423800039047318454850712175548357033705317152537600934264132091796214380342920247 + i * 1.484634559908756744956069578340866581455959723990959915174907629652210383208213610923621190055917894

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{5}$

49

33:

-6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{98}^{47}$

49

34:

-5.330121708583941047841879456051367327506062283195248042048694803851900094862931386153953045806582187 + i * -4.537598767154518811385973773244365812305809495979180396226571403091133901284907036750812301160627582

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{30}$

49

36:

-5.330121708583941047841879456051367327506062283195248042048694803851900094862931386153953045806582187 + i * 4.537598767154518811385973773244365812305809495979180396226571403091133901284907036750812301160627582

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{19}$

49

37:

-2.134643743394590659818870807585357933931050200960180362835471467784752400987689277855941328427100522 + i * -6.666580539435965517073688211061414234861840833985844547252142444838008236857822618267118206376226503

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{103}$

49

38:

1.264614950244792629444108524736704790726044358696925343992830995860345721990990194189858980978372075 + i * 6.884820188473868971146023567518179392107712534317711203599504038202050996364734841508238902020568840

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{294}^{65}$

49

39:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * -0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{48}$

49

40:

-1.264614950244792629444108524736704790726044358696925343992830995860345721990990194189858980978372075 + i * 6.884820188473868971146023567518179392107712534317711203599504038202050996364734841508238902020568840

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{147}^{41}$

49

41:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $14$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

43:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * -0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $7$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}^{48}$

49

44:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

45:

2.134643743394590659818870807585357933931050200960180362835471467784752400987689277855941328427100522 + i * -6.666580539435965517073688211061414234861840833985844547252142444838008236857822618267118206376226503

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{294}^{235}$

49

46:

6.942530096762722762702099440531494496133002936080938867117136603699577254620214800249093262460829637 + i * 0.8951401317915420741339390556172556876785917473325822801565360009270350293190834477835889380767454669

comment: $\chi$ of order $21$, even; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=42$, $\tau(\chi)=7\zeta_{49}$

49

47:

-6.594736658828733677285987980788072118232106641892173386041525799712245816853921580343812026784954262 + i * -2.347221421319350159760049794273813579801903038338530807372932635110917095079827804757426600859941258

comment: $\chi$ of order $42$, odd; $[\mathbb{Q}(\tau(\chi)):\mathbb{Q}]=84$, $\tau(\chi)=7\zeta_{294}^{163}$