NumberDB$^\beta$ Advanced search Tags Tables Help Login
Feynman periods of the primitive log-divergent non-$\phi^4$ graphs
edit · history · discussion · files · short url · transcendental period physics
Numbers
$\ell$
$k$ 
$P^{\mathrm{non}\text{-}\phi^4}_{\ell,k}$
5
1:
70.58444941673459787878582848948577317199044923956670944920981956001210348221490147422678782396959268
comment: The wheel with 5 spokes has period $\binom{8}{4}\zeta(7)$.
6
1:
252.5061149921727180332988978465678392423726745515119666502463472092658334543451165354990534200467357
comment: The wheel with 6 spokes has period $\binom{10}{5}\zeta(9)$.
6
2:
168.3374099947818120221992652310452261615817830343413111001642314728438889695634110236660356133644905
equals: T464#6,1
6
3:
188.3560031089205572985892928477125200268339616506251255760641973010846391996146637316457674843363412
7
1:
375.1706292654425570835850387266689443816838571595063460187806357373857224019911872886379041102569889
7
2:
201.5558663943134731789971483635800867902518838815686378758194445333132692336827301714916091729289885
7
3:
430.0876677546674146844605342756047417351377306989782982819346705322506719065245869240792355431276705
7
4:
430.0876677546674146844605342756047417351377306989782982819346705322506719065245869240792355431276705
equals: T466#7,3
7
5:
647.3215877855996052030386546339006108402265365797529542408490131231606570188271557159731576572422504
7
6:
294.0353141852964238424980465745848549988891621270650576783364730744721065151666263135955366474079997
equals: T464#7,4
7
7:
576.9707937352820619320986063724142178230499742855944086255499883864257799689729256950346542911365992
7
8:
381.8937882626172512969342779479756648681471550514158507811553460683540818950752606344186602915968402
7
9:
339.6840127944230433158538131859747770828317795625349233313197207940175423787295285207377606633084049
7
10:
277.2336662823174577843019671205441275531034611969024374846381608328197360699784793682945873725879687
7
11:
650.6809919495574601405886767624942795194303462000488973530863035295544818252119044610580811903069256
7
12:
430.0876677546674146844605342756047417351377306989782982819346705322506719065245869240792355431276705
equals: T466#7,3
7
13:
509.0791480626301311847283137123872258664580274765542068193038083405974424684289197756351544189718349
7
14:
400.8998290993212283079735470485049403698356966377864378702017490682204859438877743233126841049403200
7
15:
651.7017600927965715557343610748876073152664176423239678767430277727299553369077063756817663423437396
7
16:
339.2851835019248694325274594135849074304105143121163540536351059233789532403738527871417701516266845
7
17:
634.2896009440595889047291440463948547547302770701231210576484890808907989831034899282601719503893135
7
18:
254.7630095958172824868903598894810828121238346719011924984897905955131567840471463905533204974813036
equals: T464#7,5
7
19:
400.8998290993212283079735470485049403698356966377864378702017490682204859438877743233126841049403200
equals: T466#7,14
7
20:
375.1706292654425570835850387266689443816838571595063460187806357373857224019911872886379041102569889
equals: T466#7,1
7
21:
924.4566302702063852522409090544582212969923466405847622180866869564499512535551087851948629537700220
comment: The wheel with 7 spokes has period $\binom{12}{6}\zeta(11)$.
7
22:
676.0512758703888327460359004875653586559606797316607504855919937968504461042197193017184660491249980
7
23:
591.3655215278706605577130401764747744171522504693468899343301932884686300892369510819679196918879212
7
24:
380.8878295341900847984585830831078412702630570893434483879072982479418073341519268734440951804095206
equals: T464#7,2
7
25:
527.7450517669760781880817243095484153944325728868963235207046209578394531988766050710124691973809891
equals: T464#7,1
7
26:
432.6268698917316272406261260662123217773505825823031624723829006209615059612381385907219287308177048
7
27:
646.9950571868690282405863204527387400854305079030720304786514991747909488666791928571371798115830733
7
28:
336.0670721108467360236940229108821051345490437057062089387806496422942362998827550174096090983607144
equals: T464#7,3
7
29:
453.1351321562660846040485935874058248214068021783455054266391650325231008081155877088605294914308888
7
30:
555.2380817442612508377146386222296826304124500239312466062912512265844807540489896888018300188650325
7
31:
363.7412832425724652193485478782773705647627085022424728873825599597408803915899511804397546256677989
7
32:
500.7206423049227797158309589665163069803488146275230062346499722644314303258620548220786869080131163
7
33:
407.6516396879873211798396098101954151560357958420964818555816386404292352486643365559185988879231514
7
34:
482.0906397449762061042438196829477618348119913167893787232332576559731995889760014586253755857673320
7
35:
375.1706292654425570835850387266689443816838571595063460187806357373857224019911872886379041102569889
equals: T466#7,1
7
36:
400.8998290993212283079735470485049403698356966377864378702017490682204859438877743233126841049403200
equals: T466#7,14
7
37:
339.6840127944230433158538131859747770828317795625349233313197207940175423787295285207377606633084049
equals: T466#7,9
7
38:
453.1351321562660846040485935874058248214068021783455054266391650325231008081155877088605294914308888
equals: T466#7,29
7
39:
380.8878295341900847984585830831078412702630570893434483879072982479418073341519268734440951804095206
equals: T464#7,2
7
40:
527.7450517669760781880817243095484153944325728868963235207046209578394531988766050710124691973809891
equals: T464#7,1
7
41:
509.0791480626301311847283137123872258664580274765542068193038083405974424684289197756351544189718349
equals: T466#7,13
7
42:
591.3655215278706605577130401764747744171522504693468899343301932884686300892369510819679196918879212
equals: T466#7,23
7
43:
453.1351321562660846040485935874058248214068021783455054266391650325231008081155877088605294914308888
equals: T466#7,29
7
44:
555.2380817442612508377146386222296826304124500239312466062912512265844807540489896888018300188650325
equals: T466#7,30
7
45:
432.6268698917316272406261260662123217773505825823031624723829006209615059612381385907219287308177048
equals: T466#7,26
7
46:
456.9614273502147996615875654057206520305285531584185740970585566224305716776210953639683070801674746
7
47:
531.0112616651732795717239488329810019766984643921459644217578236724938264965211244549690760274242175
7
48:
381.8937882626172512969342779479756648681471550514158507811553460683540818950752606344186602915968402
equals: T466#7,8
7
49:
576.9707937352820619320986063724142178230499742855944086255499883864257799689729256950346542911365992
equals: T466#7,7
7
50:
430.0876677546674146844605342756047417351377306989782982819346705322506719065245869240792355431276705
equals: T466#7,3
8
1:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
8
2:
671.5917295042062026498373217139861979146304197802184478717872197443342527585398574166682743948746319
8
3:
538.1196540874985014228738131052773038513907479867691423233352335036105502907697898171508840383174424
8
4:
495.7678147198370373127577832400107888674975775616810880221960321816500810041750370663335106444316366
8
5:
1136.832742125413130012352074845986815190568571767005234645782080392483880288111453892054966043648522
8
6:
2256.574934610598092169468534079536397619595011945276532818688511887898139437230582250508290570294582
8
7:
633.4389145496823178678219700957963039453785996197679838312899327078674105086378127067211423128229185
equals: T464#8,16
8
8:
845.1469082337330415623729059546426008025344301832910851022975637019782188438686223372486638381525410
8
9:
470.7201255349266341730116527622521722939816239536112680414903904332287281945892074669657903302813201
equals: T464#8,32
8
10:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
12:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
8
13:
602.6148119078387054304770068552020768619463874798215394908904879333165736918519498491074521937799353
8
14:
552.6194823804015197363743579523954866635809034772188992433272405933398756324535345119612304678786302
8
15:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
16:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
8
17:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
8
18:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
8
19:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
equals: T466#8,17
8
20:
2406.042913917238911943483085673822914193120874197871125475929563299267373979272954524709744336041608
8
21:
1449.069060951466619569520208863569952524288268193071174126054557295530368986024909753494415178885276
8
22:
2038.970945421437465326497352018924683268671547653339772697742113866519905463051545681187567928961528
8
23:
986.3992589356793239475990741963234897552243935702398716112406972200101707407562760031836985105328962
8
24:
2108.244279041234941326575871799882443847961487855302522944244992583311320615879068982871299153726416
8
25:
1116.439052619464214503828958852273832680151787695567641563427203592122122063843465355363809449319561
8
26:
1939.940129926454113858668478761593018850308994296606148738867581080578082928918312502927076728534681
8
27:
1179.916317261161335672936439602126901291999975716822030506038066062002919028479285261949614504002054
8
28:
1203.001359292986395363517503875572677835161796270243080193931507912756805365740082676507093209581697
8
29:
735.7641034682980549642713858006820306576874821086949067028760493025807628282160405507049179739600302
equals: T464#8,10
8
30:
968.6603751135589419720734519201520224342551534664816653562063069965202159641979132225951544685275265
8
31:
905.6604198517519964561805546391239504984691100594456308480007676266636665114040246045435849486736663
8
32:
1231.272767272023738964789641636571809643830327997713712474762161704049397521720279963987273486421066
8
33:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
34:
502.2788895464048459736340326441166461172560048955446152620173714345513919482055415398207385074165342
8
35:
807.3025258383869022776798951978526317168689715975869293063035025147864575181569821255477922292279526
8
36:
1013.205952342823707178008440309632321813180488579822812574771316154654380908980559490786222408284827
8
38:
460.0885382469178784340499342388281161611020551401644375902796027026761853387372443853020919470483634
equals: T464#8,31
8
39:
554.5878455612546357160220903461855813032205966103006214476921145277574817760211495364097374795287139
comment: This period contains alternating multiple polylogarithms [1], equation (5.6).
8
40:
929.2687956150515299321313158091905982617750112562078916814143409594718579600440731338660068152372845
8
41:
1401.137294673766762610249250909148254282868726811256449970462691065289078580508996868498920101599994
8
42:
696.9381688369515638424740149213751061675252587979681596174493381817063796294039088740637994557217850
8
43:
576.3664616454976112205069923199163523968895515233050080727608591939378243923962826273496365517156027
8
44:
862.7381942985126557112751982082841177792692405550710385000949775945933518284935602355033124832932494
8
45:
478.5525013099909297327592234296286678060513690211501561863600469027514947609417881070251126560425627
8
46:
1583.753523364130408317697460608046267541544281018082551491700749709324000609844939286436487485304465
8
47:
1821.160311698109237968636638362957310164306834943092557286893331091211627904328309613950041811394885
8
48:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
8
49:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
8
50:
2451.707447349569464981588017664493710625622014874206900194776550731303617666818706318215253094173181
8
51:
1185.607142261197104604970707234655833429198086365304615968258838320511356380578984749311279478991624
8
52:
2378.641850609255447009211244655485089644253240034904968510862996388621793775490001110385577697968332
8
53:
946.4467073443551968411308999965848545450075187424761448873855202636359051523696636932982508680462973
8
54:
2179.718984483210260500278252791730802498375360304893927150803233435727291148662172944393830721385638
8
55:
1329.666999034721115634542714080116427157072935602956995658117735530624121204378609885308382142819333
8
56:
2205.833823372125970992823438572243061259574111877418435826590951127873157848241474396631569131111351
8
57:
822.0785259191753569143677360375413587929631982854594302607577700203218580414789239151744034068833720
8
58:
1018.257343511443788863243492109340620578701138089981581015284004258283507949266509041735510030126391
8
59:
916.3115984256698105823455710572686706189664852276881973250930733001786009094638375646676035243929982
8
60:
1273.947113118339244534730402290734394061322005203628369018840495325851074992060978574151141809970868
8
61:
1058.151501686164260806778943645382778914432718805796494295509150869094776429226677585140220048068393
8
62:
797.8671706742264173738303903468699938211837860063419727398546454254844431623523588228462998954556106
8
63:
688.8983612960199708142608425087004241645878076060838230346406528073870470840754183872818805470518271
equals: T464#8,12
8
64:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
65:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
66:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
67:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
8
68:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
69:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
70:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
71:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
72:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
73:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
74:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
75:
914.3956983154534439297774845148243147346505307177584807744778977272250990630304162089693817279738675
8
76:
2580.709225613400084305312286672429588933939771487617183568251834417555183407908859651790877645536724
8
77:
1067.865703319497876835439875819492220893650664323611568076813877796013789979914475220232218937391755
8
78:
853.4809791830308182194777016274166368202089167517975379291674963226168785951190417678625393273394100
8
79:
643.1303998104103352087219562884790616944851855679204056089163082258611374644083699076048622084447584
8
80:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
81:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
82:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
83:
688.8983612960199708142608425087004241645878076060838230346406528073870470840754183872818805470518271
equals: T464#8,12
8
84:
508.9214815406819395034286822411094621513355565263623465744271858858116086060717204782728675403132945
8
85:
822.0785259191753569143677360375413587929631982854594302607577700203218580414789239151744034068833720
equals: T466#8,57
8
86:
797.8671706742264173738303903468699938211837860063419727398546454254844431623523588228462998954556106
equals: T466#8,62
8
87:
1018.257343511443788863243492109340620578701138089981581015284004258283507949266509041735510030126391
equals: T466#8,58
8
88:
520.4708335026517395481584622768998757335538410584358575487579636956792220592495597972067614886427971
8
89:
916.3115984256698105823455710572686706189664852276881973250930733001786009094638375646676035243929982
equals: T466#8,59
8
90:
1273.947113118339244534730402290734394061322005203628369018840495325851074992060978574151141809970868
equals: T466#8,60
8
91:
508.9214815406819395034286822411094621513355565263623465744271858858116086060717204782728675403132945
equals: T466#8,84
8
92:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
93:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
94:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
95:
643.1303998104103352087219562884790616944851855679204056089163082258611374644083699076048622084447584
equals: T466#8,79
8
96:
853.4809791830308182194777016274166368202089167517975379291674963226168785951190417678625393273394100
equals: T466#8,78
8
97:
1067.865703319497876835439875819492220893650664323611568076813877796013789979914475220232218937391755
equals: T466#8,77
8
98:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
99:
515.7262754487112300878787391490005455223335890551731625376295220644308476506977847007336930316808908
8
100:
538.1196540874985014228738131052773038513907479867691423233352335036105502907697898171508840383174424
equals: T466#8,3
8
117:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
8
122:
807.0489160151473504216848839309015057981181643332467748493988584722693810658168067228131291452130207
8
123:
1561.251026769613438367056720182367685081246638534065562648320534525808230488237201940588984327429727
8
125:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
equals: T466#8,17
8
126:
1600.816537173410804001992199896202681899327907352524091073498256479367075714420877666925098022778752
8
127:
805.3473885075099739727415538185746087726949567579216701644803181268229282378132785018514020962671983
equals: T464#8,11
8
128:
805.3473885075099739727415538185746087726949567579216701644803181268229282378132785018514020962671983
equals: T464#8,11
8
129:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
130:
1561.251026769613438367056720182367685081246638534065562648320534525808230488237201940588984327429727
equals: T466#8,123
8
131:
554.5878455612546357160220903461855813032205966103006214476921145277574817760211495364097374795287139
equals: T466#8,39
8
132:
807.0489160151473504216848839309015057981181643332467748493988584722693810658168067228131291452130207
equals: T466#8,122
8
133:
968.6603751135589419720734519201520224342551534664816653562063069965202159641979132225951544685275265
equals: T466#8,30
8
134:
1203.001359292986395363517503875572677835161796270243080193931507912756805365740082676507093209581697
equals: T466#8,28
8
135:
1231.272767272023738964789641636571809643830327997713712474762161704049397521720279963987273486421066
equals: T466#8,32
8
136:
598.6176907501957880831491838922227405778251308263097466704485970130748131212354747562848479177079046
equals: T464#8,19
8
137:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
138:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
139:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
140:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
141:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
142:
735.7641034682980549642713858006820306576874821086949067028760493025807628282160405507049179739600302
equals: T464#8,10
8
143:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
144:
1939.940129926454113858668478761593018850308994296606148738867581080578082928918312502927076728534681
equals: T466#8,26
8
145:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
146:
1116.439052619464214503828958852273832680151787695567641563427203592122122063843465355363809449319561
equals: T466#8,25
8
147:
905.6604198517519964561805546391239504984691100594456308480007676266636665114040246045435849486736663
equals: T466#8,31
8
148:
2038.970945421437465326497352018924683268671547653339772697742113866519905463051545681187567928961528
equals: T466#8,22
8
149:
1449.069060951466619569520208863569952524288268193071174126054557295530368986024909753494415178885276
equals: T466#8,21
8
150:
710.7157803563025775063376095762954813972550448272572791458114586116873244392239586004899158226690186
8
151:
762.3349722637514670391549898649757224134007025321300231042062812453578998309978285239716522457094455
8
152:
968.6603751135589419720734519201520224342551534664816653562063069965202159641979132225951544685275265
equals: T466#8,30
8
153:
1203.001359292986395363517503875572677835161796270243080193931507912756805365740082676507093209581697
equals: T466#8,28
8
154:
2073.416073623159570183643683586880448816781374189046073948949899906029494354744282412248074290066330
8
155:
1688.031143734923996035527702121716225017874430662283349229039645800507421960223322264912573917625356
8
156:
696.9381688369515638424740149213751061675252587979681596174493381817063796294039088740637994557217850
equals: T466#8,42
8
157:
1401.137294673766762610249250909148254282868726811256449970462691065289078580508996868498920101599994
equals: T466#8,41
8
158:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
159:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
160:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
161:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
162:
3432.421152208889374751652302958458582091392163433389788509163569002917566480025328077847794287616241
comment: The wheel with 8 spokes has period $\binom{14}{7}\zeta(13)$.
8
163:
2161.085097271124661653015234515792517133977379633009813369594519147840506392790092673878527568139700
8
164:
2111.954799761488180342529032235223992287239546005689686925461656134894835013860754210823444651024821
8
165:
2484.707121178464528624833599631198950482149876374368743847377152191161790592556865194733041610265742
8
166:
1105.107697390380571481750718398180520990357606630164969906863691080393088885859715568466805242627290
equals: T464#8,3
8
167:
1716.210576104444687375826151479229291045696081716694894254581784501458783240012664038923897143808121
equals: T464#8,1
8
168:
1112.321944173278141504558752425419428474647611831130850767594427801115730067061359491577181467111152
8
169:
1968.267805846567380204142289198422210509686451228060689430102948622241150967903613560797864662397313
8
170:
1526.176745107776094160320235015307442519029468412658029809343137170212740707019936668836466214786134
8
171:
2347.470918164993733402757359994974169138514148296994223662318146176001759362971296527791181786494640
8
172:
1371.862083169939829661146235794665806984548769956042991109870428872179620362820902272898457674815827
8
173:
1804.609257401702446420030049257989248541282805233750586380522068370528563521873912236440483765263650
8
174:
1307.145690768442796304844239767070180728788135105283305223607350315117226540951751341328118715734618
8
175:
1891.959416355773124361704335007138834259432724371657267373908511927684201634874661773941002776631781
8
176:
1657.861273863056368176888955402827800041250631091602238526682065396201082766552244153259265592067354
8
177:
1968.860940450572137948954091499657396062233411361017993408461302203236440980671540332585544356946205
8
178:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
8
179:
1406.931639001077614186952329476183829222995157926022336783522701139567508593763444022134420532184992
8
180:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
181:
847.6461156397111251207670837670689902453735503393825637271084556248374782788666005729678024107691507
equals: T464#8,7
8
182:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
8
183:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
8
184:
1508.235108680625828260869140619089826452277853327648982017518914869003732359330646410606374168847374
8
185:
904.2808243578157996899656671139994051607494437202343474230631730723491404179423009925618140377085746
equals: T464#8,6
8
186:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
191:
925.8787141322678972254903647171329947640274253066307522973841863229459825154085163049075234169965863
8
192:
1488.617416964677986943298376856121772186001285035317145456855800347055507089065943413178990550390315
8
193:
1112.321944173278141504558752425419428474647611831130850767594427801115730067061359491577181467111152
equals: T466#8,168
8
194:
1984.860739736791815354422279086766230392163843389360196561436630967858760987540892255880608167254925
8
203:
863.8855479687435999129536989695703587240993182284536157943590559178843101990523077981790911759347813
8
212:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
219:
903.1361963474187183710477456877743701325308039279228625593098803168753353504267064402557233452917999
8
229:
1179.916317261161335672936439602126901291999975716822030506038066062002919028479285261949614504002054
equals: T466#8,27
8
230:
1657.861273863056368176888955402827800041250631091602238526682065396201082766552244153259265592067354
equals: T466#8,176
8
231:
1105.107697390380571481750718398180520990357606630164969906863691080393088885859715568466805242627290
equals: T464#8,3
8
232:
1716.210576104444687375826151479229291045696081716694894254581784501458783240012664038923897143808121
equals: T464#8,1
8
233:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
234:
742.9770903664300002188614578326673385751282088052628089324441266088040245398648843715976386693655588
equals: T464#8,13
8
235:
986.3992589356793239475990741963234897552243935702398716112406972200101707407562760031836985105328962
equals: T466#8,23
8
236:
1307.145690768442796304844239767070180728788135105283305223607350315117226540951751341328118715734618
equals: T466#8,174
8
237:
1891.959416355773124361704335007138834259432724371657267373908511927684201634874661773941002776631781
equals: T466#8,175
8
238:
2108.244279041234941326575871799882443847961487855302522944244992583311320615879068982871299153726416
equals: T466#8,24
8
239:
749.8186229956812217736182060128660712173130131258009834868211701392831566066139841555241716217257988
equals: T464#8,14
8
240:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
241:
805.3473885075099739727415538185746087726949567579216701644803181268229282378132785018514020962671983
equals: T464#8,11
8
242:
1483.853205610634561524682386383597860573228672216121724034359066752485581525408470396798645330744654
8
243:
905.6604198517519964561805546391239504984691100594456308480007676266636665114040246045435849486736663
equals: T466#8,31
8
244:
965.3407046855803511145044765578812432932730644964648420005079698142783955890394144603918859856301333
8
245:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
246:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
247:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
248:
977.7681942720455433915677759831495839210795503214461745144144180489506115515887953871275348243148137
8
249:
1095.961460726639817506644903521201252306664303617905807310382178969863780832455368559207594498243901
8
250:
1489.532737036169772438284412952334795667359918735837107708599008212842368340349193254401095395042887
8
251:
1783.694844800847770391550297740298030841695531834529799563859811845723586969478138820355020308459506
8
252:
968.6603751135589419720734519201520224342551534664816653562063069965202159641979132225951544685275265
equals: T466#8,30
8
253:
1203.001359292986395363517503875572677835161796270243080193931507912756805365740082676507093209581697
equals: T466#8,28
8
254:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
equals: T466#8,117
8
255:
1231.272767272023738964789641636571809643830327997713712474762161704049397521720279963987273486421066
equals: T466#8,32
8
256:
904.2808243578157996899656671139994051607494437202343474230631730723491404179423009925618140377085746
equals: T464#8,6
8
257:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
258:
863.8855479687435999129536989695703587240993182284536157943590559178843101990523077981790911759347813
equals: T466#8,203
8
259:
1508.235108680625828260869140619089826452277853327648982017518914869003732359330646410606374168847374
equals: T466#8,184
8
260:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
equals: T466#8,178
8
261:
735.7641034682980549642713858006820306576874821086949067028760493025807628282160405507049179739600302
equals: T464#8,10
8
262:
968.6603751135589419720734519201520224342551534664816653562063069965202159641979132225951544685275265
equals: T466#8,30
8
263:
905.6604198517519964561805546391239504984691100594456308480007676266636665114040246045435849486736663
equals: T466#8,31
8
264:
847.6461156397111251207670837670689902453735503393825637271084556248374782788666005729678024107691507
equals: T464#8,7
8
265:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
266:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
267:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
268:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
equals: T466#8,17
8
269:
735.7641034682980549642713858006820306576874821086949067028760493025807628282160405507049179739600302
equals: T464#8,10
8
270:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
271:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
272:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
273:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
274:
1526.176745107776094160320235015307442519029468412658029809343137170212740707019936668836466214786134
equals: T466#8,170
8
275:
1673.879699181906599650351527304030262287259880976352186003136600307463714644563425270320588001390050
8
276:
1976.171025346595400368305899518840559215312038268337603332726117063522820753197241271915460821474794
8
277:
1371.862083169939829661146235794665806984548769956042991109870428872179620362820902272898457674815827
equals: T466#8,172
8
278:
1804.609257401702446420030049257989248541282805233750586380522068370528563521873912236440483765263650
equals: T466#8,173
8
279:
1657.861273863056368176888955402827800041250631091602238526682065396201082766552244153259265592067354
equals: T466#8,176
8
280:
1968.860940450572137948954091499657396062233411361017993408461302203236440980671540332585544356946205
equals: T466#8,177
8
281:
805.3473885075099739727415538185746087726949567579216701644803181268229282378132785018514020962671983
equals: T464#8,11
8
282:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
283:
749.8186229956812217736182060128660712173130131258009834868211701392831566066139841555241716217257988
equals: T464#8,14
8
284:
1112.321944173278141504558752425419428474647611831130850767594427801115730067061359491577181467111152
equals: T466#8,168
8
285:
1547.692421011306656293277923353860219654778056521140301675826124784936377948983057922766888875483593
8
286:
1968.267805846567380204142289198422210509686451228060689430102948622241150967903613560797864662397313
equals: T466#8,169
8
287:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
288:
1095.961460726639817506644903521201252306664303617905807310382178969863780832455368559207594498243901
equals: T466#8,249
8
289:
977.7681942720455433915677759831495839210795503214461745144144180489506115515887953871275348243148137
equals: T466#8,248
8
290:
1783.694844800847770391550297740298030841695531834529799563859811845723586969478138820355020308459506
equals: T466#8,251
8
291:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
292:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
293:
1483.853205610634561524682386383597860573228672216121724034359066752485581525408470396798645330744654
equals: T466#8,242
8
294:
965.3407046855803511145044765578812432932730644964648420005079698142783955890394144603918859856301333
equals: T466#8,244
8
295:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
equals: T466#8,117
8
296:
904.2808243578157996899656671139994051607494437202343474230631730723491404179423009925618140377085746
equals: T464#8,6
8
297:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
298:
1116.439052619464214503828958852273832680151787695567641563427203592122122063843465355363809449319561
equals: T466#8,25
8
299:
1939.940129926454113858668478761593018850308994296606148738867581080578082928918312502927076728534681
equals: T466#8,26
8
300:
1136.832742125413130012352074845986815190568571767005234645782080392483880288111453892054966043648522
equals: T466#8,5
8
301:
2256.574934610598092169468534079536397619595011945276532818688511887898139437230582250508290570294582
equals: T466#8,6
8
302:
845.1469082337330415623729059546426008025344301832910851022975637019782188438686223372486638381525410
equals: T466#8,8
8
303:
696.9381688369515638424740149213751061675252587979681596174493381817063796294039088740637994557217850
equals: T466#8,42
8
304:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
305:
710.7157803563025775063376095762954813972550448272572791458114586116873244392239586004899158226690186
equals: T466#8,150
8
306:
1203.001359292986395363517503875572677835161796270243080193931507912756805365740082676507093209581697
equals: T466#8,28
8
307:
762.3349722637514670391549898649757224134007025321300231042062812453578998309978285239716522457094455
equals: T466#8,151
8
308:
1688.031143734923996035527702121716225017874430662283349229039645800507421960223322264912573917625356
equals: T466#8,155
8
309:
2073.416073623159570183643683586880448816781374189046073948949899906029494354744282412248074290066330
equals: T466#8,154
8
310:
845.1469082337330415623729059546426008025344301832910851022975637019782188438686223372486638381525410
equals: T466#8,8
8
311:
633.4389145496823178678219700957963039453785996197679838312899327078674105086378127067211423128229185
equals: T464#8,16
8
312:
845.1469082337330415623729059546426008025344301832910851022975637019782188438686223372486638381525410
equals: T466#8,8
8
313:
929.2687956150515299321313158091905982617750112562078916814143409594718579600440731338660068152372845
equals: T466#8,40
8
319:
1105.107697390380571481750718398180520990357606630164969906863691080393088885859715568466805242627290
equals: T464#8,3
8
324:
986.3992589356793239475990741963234897552243935702398716112406972200101707407562760031836985105328962
equals: T466#8,23
8
326:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
327:
1939.940129926454113858668478761593018850308994296606148738867581080578082928918312502927076728534681
equals: T466#8,26
8
328:
1116.439052619464214503828958852273832680151787695567641563427203592122122063843465355363809449319561
equals: T466#8,25
8
329:
1110.775269681505092680842499107047731632318454011272395012366913524295843397361378151888591842605262
8
333:
1359.443029320723507510152344544449463324053294473190403201972393033105498132767927705926675202280860
8
334:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
equals: T466#8,178
8
336:
873.9514034849341957627198002639135936478493944569775055556217936298365780270488027479816001771348838
8
338:
905.6604198517519964561805546391239504984691100594456308480007676266636665114040246045435849486736663
equals: T466#8,31
8
339:
1483.853205610634561524682386383597860573228672216121724034359066752485581525408470396798645330744654
equals: T466#8,242
8
340:
965.3407046855803511145044765578812432932730644964648420005079698142783955890394144603918859856301333
equals: T466#8,244
8
347:
2552.672730528475982938787453304873086178882322565048427363834882755809625857193485953870465214183286
8
348:
1140.779261261061391896687460248243673969509388822148837411335560581065284428297118742379632148173278
8
349:
2452.172471518926025926463573419352213689019804502518217587627385588440689861758397509389780111615815
8
350:
670.3825055069387064936556564359558546454142023774490507709275190217411347607303474766686664675264022
8
351:
1090.128618872126322179296802973660194243517926934911032407880108013545802901807518785719751439345927
8
352:
753.3077570130507311552821791434438193489436634176491583383308771904761860902296125869812727085661165
8
353:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
354:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
355:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
356:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
357:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
358:
753.3077570130507311552821791434438193489436634176491583383308771904761860902296125869812727085661165
equals: T466#8,352
8
359:
1090.128618872126322179296802973660194243517926934911032407880108013545802901807518785719751439345927
equals: T466#8,351
8
360:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
361:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
362:
670.3825055069387064936556564359558546454142023774490507709275190217411347607303474766686664675264022
equals: T466#8,350
8
363:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
364:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
365:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
366:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
367:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
368:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
369:
1219.079638248789957592785850502048039982287959554086624115120322935533120546039053189153508714408910
8
370:
1892.695968903909480977552175675258460713781201780528346613107706290720869961556305184804413540799135
8
371:
1475.617090180964695888274921632480537088460104261461510721997179737491290870186303365708068790963908
8
372:
1405.314771211597662933143680621549395669444388318717782811966750058259294205383865225766505682160236
8
375:
1489.532737036169772438284412952334795667359918735837107708599008212842368340349193254401095395042887
equals: T466#8,250
8
376:
742.9770903664300002188614578326673385751282088052628089324441266088040245398648843715976386693655588
equals: T464#8,13
8
377:
1354.269966084205687256538167449512279400553244605515648815989571238252697516899253640828847310321310
8
381:
801.5942687047178159189005041235099068142194688133672276009466172401542890225264971080706927331979490
8
382:
923.0790596240495604027577138292691624497199985825058798285117234885433373231776355301070407891839216
8
383:
906.9829228397003090274755626915117723945280906698215006691062941705246697179801357225233044925250987
8
384:
1860.255507101132751833882164505508113185582254304426150037909325051184096852985667536221116451177206
8
386:
859.2101919938945445257537724522274123702374741098410407817754035205929860286395253768687343452301667
8
387:
1428.603203773160314217970908232317944694748613202536949440428796728754103323214165047951478653242028
8
389:
1087.517950948632060796416486319092353266413212035237677477568715620252171962284057105717325696021028
8
393:
873.9514034849341957627198002639135936478493944569775055556217936298365780270488027479816001771348838
equals: T466#8,336
8
394:
976.2689247909036611172725858586330039260462435596123915195647357472270276848716656093128260053688245
8
396:
1028.995478167517234462698467776537222459020458601323700070205568640245244852615808091942763899696041
8
397:
1657.861273863056368176888955402827800041250631091602238526682065396201082766552244153259265592067354
equals: T466#8,176
8
398:
1968.860940450572137948954091499657396062233411361017993408461302203236440980671540332585544356946205
equals: T466#8,177
8
399:
1547.692421011306656293277923353860219654778056521140301675826124784936377948983057922766888875483593
equals: T466#8,285
8
400:
1984.860739736791815354422279086766230392163843389360196561436630967858760987540892255880608167254925
equals: T466#8,194
8
401:
1354.269966084205687256538167449512279400553244605515648815989571238252697516899253640828847310321310
equals: T466#8,377
8
402:
742.9770903664300002188614578326673385751282088052628089324441266088040245398648843715976386693655588
equals: T464#8,13
8
403:
863.8855479687435999129536989695703587240993182284536157943590559178843101990523077981790911759347813
equals: T466#8,203
8
404:
1110.775269681505092680842499107047731632318454011272395012366913524295843397361378151888591842605262
equals: T466#8,329
8
405:
976.2689247909036611172725858586330039260462435596123915195647357472270276848716656093128260053688245
equals: T466#8,394
8
406:
1962.488266671808648391701743115580280667193006381311889045732934774186577966383202269982051739892707
8
407:
965.3407046855803511145044765578812432932730644964648420005079698142783955890394144603918859856301333
equals: T466#8,244
8
408:
1483.853205610634561524682386383597860573228672216121724034359066752485581525408470396798645330744654
equals: T466#8,242
8
409:
641.7233582974217226531476315556340108583909248665495260338280841884983438913861462810457600701220101
equals: T464#8,18
8
410:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
411:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
412:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
413:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
414:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
415:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
416:
1087.361379495173070519717739456320844096479318653175597363602164489997502758345666309657483099495893
8
417:
1603.198923916493505649102674397207220206305824498280022033534052578863384819416336933933795343896954
8
418:
906.9829228397003090274755626915117723945280906698215006691062941705246697179801357225233044925250987
equals: T466#8,383
8
419:
1028.995478167517234462698467776537222459020458601323700070205568640245244852615808091942763899696041
equals: T466#8,396
8
420:
801.5942687047178159189005041235099068142194688133672276009466172401542890225264971080706927331979490
equals: T466#8,381
8
421:
1860.255507101132751833882164505508113185582254304426150037909325051184096852985667536221116451177206
equals: T466#8,384
8
422:
1428.603203773160314217970908232317944694748613202536949440428796728754103323214165047951478653242028
equals: T466#8,387
8
423:
976.2689247909036611172725858586330039260462435596123915195647357472270276848716656093128260053688245
equals: T466#8,394
8
424:
1354.269966084205687256538167449512279400553244605515648815989571238252697516899253640828847310321310
equals: T466#8,377
8
425:
863.8855479687435999129536989695703587240993182284536157943590559178843101990523077981790911759347813
equals: T466#8,203
8
426:
1962.488266671808648391701743115580280667193006381311889045732934774186577966383202269982051739892707
equals: T466#8,406
8
427:
1508.235108680625828260869140619089826452277853327648982017518914869003732359330646410606374168847374
equals: T466#8,184
8
428:
859.2101919938945445257537724522274123702374741098410407817754035205929860286395253768687343452301667
equals: T466#8,386
8
429:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
430:
652.1316118393033451206397031717885157298263669280843612993999227779736414414159874651303784037167452
8
431:
903.1361963474187183710477456877743701325308039279228625593098803168753353504267064402557233452917999
equals: T466#8,219
8
432:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
equals: T466#8,117
8
433:
868.9797935260465499936378825181425790060191716697055880822427730731687311884519358707260622533680146
8
434:
1478.712914246010047793762787869806255322159365814076367150835134403087107862013992204210301510501245
8
435:
1781.440435282846172064645339068418172766505390194592437386460143452774757033396048343613873816374245
8
436:
873.9514034849341957627198002639135936478493944569775055556217936298365780270488027479816001771348838
equals: T466#8,336
8
437:
1359.443029320723507510152344544449463324053294473190403201972393033105498132767927705926675202280860
equals: T466#8,333
8
438:
1110.775269681505092680842499107047731632318454011272395012366913524295843397361378151888591842605262
equals: T466#8,329
8
439:
1595.493459679953486986609663351103430664503006753005311100423791303270240081647960211113199052493760
8
440:
916.3115984256698105823455710572686706189664852276881973250930733001786009094638375646676035243929982
equals: T466#8,59
8
441:
1273.947113118339244534730402290734394061322005203628369018840495325851074992060978574151141809970868
equals: T466#8,60
8
442:
1058.151501686164260806778943645382778914432718805796494295509150869094776429226677585140220048068393
equals: T466#8,61
8
443:
641.3466996208366990680369537053461304570227885162204770580325857947593268016544605111353658231972142
equals: T464#8,20
8
444:
1087.517950948632060796416486319092353266413212035237677477568715620252171962284057105717325696021028
equals: T466#8,389
8
445:
923.0790596240495604027577138292691624497199985825058798285117234885433373231776355301070407891839216
equals: T466#8,382
8
446:
749.8186229956812217736182060128660712173130131258009834868211701392831566066139841555241716217257988
equals: T464#8,14
8
447:
1483.853205610634561524682386383597860573228672216121724034359066752485581525408470396798645330744654
equals: T466#8,242
8
448:
1110.775269681505092680842499107047731632318454011272395012366913524295843397361378151888591842605262
equals: T466#8,329
8
449:
844.5125186033249391551602012080025663235677568424293073378251400712683200219181261845747194468507093
equals: T464#8,5
8
450:
1104.245691354858540334433017812761395783501738976604268270982760543709772667548120537453197111725318
8
451:
553.2737946123595615783838778346382293655804335760081532437544517696097756320517417490654862183827582
equals: T464#8,29
8
452:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
equals: T466#8,117
8
453:
1329.666999034721115634542714080116427157072935602956995658117735530624121204378609885308382142819333
equals: T466#8,55
8
454:
2205.833823372125970992823438572243061259574111877418435826590951127873157848241474396631569131111351
equals: T466#8,56
8
455:
688.8983612960199708142608425087004241645878076060838230346406528073870470840754183872818805470518271
equals: T464#8,12
8
456:
946.4467073443551968411308999965848545450075187424761448873855202636359051523696636932982508680462973
equals: T466#8,53
8
457:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
458:
797.8671706742264173738303903468699938211837860063419727398546454254844431623523588228462998954556106
equals: T466#8,62
8
459:
1018.257343511443788863243492109340620578701138089981581015284004258283507949266509041735510030126391
equals: T466#8,58
8
460:
2179.718984483210260500278252791730802498375360304893927150803233435727291148662172944393830721385638
equals: T466#8,54
8
461:
776.8486857392782841029611043421226400736413051864938089297248721191409523074981265462149749808323431
equals: T466#8,16
8
462:
1282.984114164895403195942415431776019540579065336772391093271566220222281273187940116482551309729867
equals: T466#8,12
8
463:
1307.145690768442796304844239767070180728788135105283305223607350315117226540951751341328118715734618
equals: T466#8,174
8
464:
1891.959416355773124361704335007138834259432724371657267373908511927684201634874661773941002776631781
equals: T466#8,175
8
465:
1821.160311698109237968636638362957310164306834943092557286893331091211627904328309613950041811394885
equals: T466#8,47
8
466:
2161.085097271124661653015234515792517133977379633009813369594519147840506392790092673878527568139700
equals: T466#8,163
8
467:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
468:
904.2808243578157996899656671139994051607494437202343474230631730723491404179423009925618140377085746
equals: T464#8,6
8
469:
1371.862083169939829661146235794665806984548769956042991109870428872179620362820902272898457674815827
equals: T466#8,172
8
470:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
471:
1112.321944173278141504558752425419428474647611831130850767594427801115730067061359491577181467111152
equals: T466#8,168
8
472:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
473:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
474:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
475:
1968.267805846567380204142289198422210509686451228060689430102948622241150967903613560797864662397313
equals: T466#8,169
8
476:
847.6461156397111251207670837670689902453735503393825637271084556248374782788666005729678024107691507
equals: T464#8,7
8
477:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
478:
1804.609257401702446420030049257989248541282805233750586380522068370528563521873912236440483765263650
equals: T466#8,173
8
479:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
480:
1105.107697390380571481750718398180520990357606630164969906863691080393088885859715568466805242627290
equals: T464#8,3
8
481:
1716.210576104444687375826151479229291045696081716694894254581784501458783240012664038923897143808121
equals: T464#8,1
8
482:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
483:
1508.235108680625828260869140619089826452277853327648982017518914869003732359330646410606374168847374
equals: T466#8,184
8
484:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
485:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
486:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
487:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
equals: T466#8,178
8
488:
1406.931639001077614186952329476183829222995157926022336783522701139567508593763444022134420532184992
equals: T466#8,179
8
489:
1508.235108680625828260869140619089826452277853327648982017518914869003732359330646410606374168847374
equals: T466#8,184
8
490:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
491:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
492:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
493:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
equals: T466#8,178
8
494:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
495:
953.7855112432990314291860452783239512800607898948718291957814718033685296500554062256620684925197927
equals: T466#8,67
8
496:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
497:
1701.150007449006111557533437359337092495165173796728575543396982885580962584866766357878123145403320
8
498:
1846.938041215365204719341208270194768210466703442897833377756457675224817754149137121620701964848927
8
500:
652.1316118393033451206397031717885157298263669280843612993999227779736414414159874651303784037167452
equals: T466#8,430
8
501:
868.9797935260465499936378825181425790060191716697055880822427730731687311884519358707260622533680146
equals: T466#8,433
8
502:
1104.245691354858540334433017812761395783501738976604268270982760543709772667548120537453197111725318
equals: T466#8,450
8
503:
1781.440435282846172064645339068418172766505390194592437386460143452774757033396048343613873816374245
equals: T466#8,435
8
504:
1478.712914246010047793762787869806255322159365814076367150835134403087107862013992204210301510501245
equals: T466#8,434
8
505:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
equals: T466#8,17
8
506:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
507:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
508:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
509:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
510:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
521:
977.7681942720455433915677759831495839210795503214461745144144180489506115515887953871275348243148137
equals: T466#8,248
8
522:
1783.694844800847770391550297740298030841695531834529799563859811845723586969478138820355020308459506
equals: T466#8,251
8
523:
1215.849711048769794600034576870100475176440727670813742208575164366043289618337014989357091844369657
equals: T466#8,183
8
524:
1489.532737036169772438284412952334795667359918735837107708599008212842368340349193254401095395042887
equals: T466#8,250
8
525:
1095.961460726639817506644903521201252306664303617905807310382178969863780832455368559207594498243901
equals: T466#8,249
8
526:
1093.654894720872771560743233352549034577687262693651999612119255303183839615257737913813825648666808
equals: T466#8,182
8
532:
904.2808243578157996899656671139994051607494437202343474230631730723491404179423009925618140377085746
equals: T464#8,6
8
533:
1145.592929599713130090219511911411448267325484966987091830717829045881549251298166500046596199840045
equals: T464#8,2
8
534:
1716.210576104444687375826151479229291045696081716694894254581784501458783240012664038923897143808121
equals: T464#8,1
8
535:
822.0785259191753569143677360375413587929631982854594302607577700203218580414789239151744034068833720
equals: T466#8,57
8
536:
1112.321944173278141504558752425419428474647611831130850767594427801115730067061359491577181467111152
equals: T466#8,168
8
537:
1488.617416964677986943298376856121772186001285035317145456855800347055507089065943413178990550390315
equals: T466#8,192
8
538:
1371.862083169939829661146235794665806984548769956042991109870428872179620362820902272898457674815827
equals: T466#8,172
8
539:
925.8787141322678972254903647171329947640274253066307522973841863229459825154085163049075234169965863
equals: T466#8,191
8
540:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
541:
1371.862083169939829661146235794665806984548769956042991109870428872179620362820902272898457674815827
equals: T466#8,172
8
542:
1804.609257401702446420030049257989248541282805233750586380522068370528563521873912236440483765263650
equals: T466#8,173
8
543:
1358.487802731767750977771964914536686872128975437781286370646656490304446962128363917650966672829767
equals: T466#8,49
8
544:
966.8308019861797060577711510960472003418160280528182909657418457194083989634621674211698586767987366
equals: T464#8,4
8
546:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
548:
976.2689247909036611172725858586330039260462435596123915195647357472270276848716656093128260053688245
equals: T466#8,394
8
549:
1237.300350480363593755655119327936039760164868217890527773592079406448342405848591720538021274927852
equals: T466#8,178
8
550:
1354.269966084205687256538167449512279400553244605515648815989571238252697516899253640828847310321310
equals: T466#8,377
8
554:
1307.145690768442796304844239767070180728788135105283305223607350315117226540951751341328118715734618
equals: T466#8,174
8
555:
1891.959416355773124361704335007138834259432724371657267373908511927684201634874661773941002776631781
equals: T466#8,175
8
556:
1463.819493634507066445887682764339735122407902601328611752300719350927745796662877582698836146086494
equals: T466#8,17
8
558:
2111.954799761488180342529032235223992287239546005689686925461656134894835013860754210823444651024821
equals: T466#8,164
8
559:
921.3429757385047453565802223557702597517229761084626491741354101906222027768862975594269273117126243
equals: T466#8,117
8
560:
1561.251026769613438367056720182367685081246638534065562648320534525808230488237201940588984327429727
equals: T466#8,123
8
561:
807.0489160151473504216848839309015057981181643332467748493988584722693810658168067228131291452130207
equals: T466#8,122
8
568:
1307.145690768442796304844239767070180728788135105283305223607350315117226540951751341328118715734618
equals: T466#8,174
8
569:
1600.816537173410804001992199896202681899327907352524091073498256479367075714420877666925098022778752
equals: T466#8,126
8
570:
986.3992589356793239475990741963234897552243935702398716112406972200101707407562760031836985105328962
equals: T466#8,23
8
571:
1078.775437273096981311271367385246898891716206003256175451102289664223840380888984120014441060416532
equals: T466#8,1
8
572:
1152.757851237174314826136550176917541408896223298546281754936816488855599814872016096375333465043114
equals: T466#8,18
8
573:
1214.106874465406158645757758908638206776204556628728371524595554060807751936218873075966694540929923
equals: T466#8,48
8
574:
1105.107697390380571481750718398180520990357606630164969906863691080393088885859715568466805242627290
equals: T464#8,3
8
575:
1716.210576104444687375826151479229291045696081716694894254581784501458783240012664038923897143808121
equals: T464#8,1
Definition
For a connected primitive log-divergent graph $G$ with at least one vertex of degree greater than four, its Feynman period is $P(G)=\int_{(0,\infty)^{N_G-1}}\left.\Psi_G(x)^{-2}\right|_{x_{N_G}=1}\,dx_1\cdots dx_{N_G-1}$ [1].
Parameters
$\ell$
—   Loop order ($\ell\geq5$ is the loop order of the uncompleted non-$\phi^4$ graph.)
$k$
—   Census index ($k\geq1$ is an index present at loop order $\ell$ in the non-$\phi^4$ census of Panzer and Schnetz.)
Formulas
(1)
$\Psi_G(x)=\sum_{T\text{ spanning tree of }G}\prod_{e\notin T}x_e.$
(2)
For the wheel $W_n$ with $n\geq3$ spokes, $P(W_n)=\binom{2n-2}{n-1}\zeta(2n-3)$, where $\zeta$ is the Riemann zeta function [2], equation (3.47). The wheels in this table have labels $(\ell,k)=(5,1),(6,1),(7,21),(8,162)$.
Comments
(3)
Write $N_G$ for the number of edges and $h_G$ for the first Betti number of $G$. Primitive logarithmic divergence means $N_G=2h_G$ and $N_\gamma>2h_\gamma$ for every nonempty strict edge subgraph $\gamma$. The graph polynomial $\Psi_G$ has one variable $x_e$ per edge and is defined in (1).
(4)
The normalization is that of [1], equation (1.3), in which the three-loop wheel has period $6\zeta(3)$. The three-loop wheel belongs to the companion $\phi^4$ census.
(5)
The label $P^{\mathrm{non}\text{-}\phi^4}_{\ell,k}$ denotes PeriodNonPhi4[loops,index] in [3]. These indices are separate from those of the $\phi^4$ periods. Distinct census labels remain separate rows when the source expressions coincide; declared equalities include equal periods of different graphs in the two censuses.
(6)
The edge lists in the attached source file describe completed graphs. Curly-braced pairs represent edges of weight $+1$, and square-bracketed pairs represent edges of weight $-1$; repeated pairs retain their multiplicity. The vertex with the largest label is the completion vertex. Deleting it gives the unweighted graph used in the defining integral. Negative-weight edges belong to the completion, and the weighted degree at each completed vertex is four [1], Section 5.1.
(7)
The source uses $\zeta(s_1,\ldots,s_r)=\sum_{n_1>\cdots>n_r>0}\prod_j n_j^{-s_j}$, with $s_1\geq2$, as do the multiple zeta values of length 2 and length 3. Its notation $\mathtt{zeta}[[-1,s_1],s_2,\ldots,s_r]$ means $\sum_{n_1>\cdots>n_r>0}(-1)^{n_1}\prod_j n_j^{-s_j}$ [1], equations (2.2) and Section 6. Sage represents the nonalternating value as Multizeta(sr,...,s1), whereas PARI zetamult([s1,...,sr]) uses the displayed order.
(8)
The 118 eight-loop entries marked FAIL in the source are omitted.
Programs
(P1)
Sage
# Non-phi4 period P_{7,2}, including a depth-two zeta value.
import numberdb.sage as numberdb
from sage.libs.pari import pari
from sage.rings.rational_field import QQ
from sage.rings.real_mpfr import RealField
R = RealField(numberdb.bits(150, losing=32))
zeta = lambda *s: R(pari.zetamult(list(s), precision=R.precision()))
P_7_2 = -5598*zeta(5)**2 - 846*zeta(7,3) - 756*zeta(3)*zeta(7) + QQ(793)/10395*R.pi()**10
print(P_7_2)
References
[1]
Erik Panzer and Oliver Schnetz, The Galois coaction on $\phi^4$ periods, Communications in Number Theory and Physics 11 (2017), 657–705. (arXiv) (doi)
[2]
Oliver Schnetz, Graphical functions and single-valued multiple polylogarithms, Communications in Number Theory and Physics 8 (2014), 589–675. (arXiv) (doi)
Links
Similar tables
Feynman periods of primitive log-divergent $\phi^4$ graphs —   The companion census uses the same integral normalization and contains 25 values also represented here.
Multiple zeta values of length 2 —   Depth-two values occurring in the nonalternating period expressions.
Multiple zeta values of length 3 —   Depth-three values occurring in the nonalternating period expressions.
Values of the Riemann zeta function at rational numbers —   Single zeta values occurring in wheel periods.
Data properties
Entries are of type: real number
Table is complete: no (it holds all 511 evaluated labels in the version-2 non-$\phi^4$ ancillary census through eight loops: one at five loops, three at six loops, fifty at seven loops, and 457 at eight loops; the source covers every non-$\phi^4$ period through seven loops, and 118 eight-loop labels have no evaluated period)
digits: 100 (Unknown key)
How well the digits are known: heuristic (agreement-checked)
How they were obtained:

The attached generator parses [3], pinned by SHA-256, and recomputes its 191 distinct expressions using PARI zetamult and polylogmult [4]. Rational coefficients are exact. Both runs use 32 guard bits beyond 150 and 200 decimal working digits. The smallest measured agreement is 155.35 significant digits, and the stored values have 100 significant digits. All 511 recomputations agree with the independent source decimals within 0.498 units of the last printed place. These checks support heuristic agreement, not a certified enclosure of each graph integral.

more

The attached checks independently evaluate the 129 entries involving only single zeta values with Arb, identify and check all four wheel graphs against (2), and check the multiple-zeta argument order and alternating signs using nonzero identities and a bounded finite nested sum. They verify primitiveness and the non-$\phi^4$ degree condition for all 629 source graphs after deleting the completion vertex, as well as weighted degree four for every completion. Exact polynomial comparisons of source expressions justify the declared internal and cross-table equalities. The numerical comparisons are repeated on values read back from the draft; the calculation does not independently integrate all graphs.



API Python package Skill for AI Privacy Legal notice Source
Data licensed CC BY-SA 4.0. No tracking, no analytics, essential cookies only.