Lfunction data - 4-10e2-1.1-c17e2-0-0

Formats: - HTML - YAML - JSON - 2025-01-14T12:16:15.812703

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '794655483524419038516246572752,1586520505141490713403804466537', 'a10': -400000000, 'a2': -512, 'a3': -1308, 'a4': 196608, 'a5': 781250, 'a6': 669696, 'a7': 603844, 'a8': -67108864, 'a9': -182044278, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 335.703332908975, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 512, 65536]], [5, [1, -781250, 152587890625]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': '1.1.1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, 512, 65536], [1, 1308, 183755142, 168915333204, 16677181699666569], [1, -781250, 152587890625], [1, -603844, -168048464563602, -140472540088091023708, 54116956037952111668959660849], [1, 471481296, 1064411254083979846, 238308820056195962235807216, 255476698618765889551019445759400441], [1, 1541834228, 17324849107520411262, 13337507350938235409534170724, 74829695578286078013428929473144712489], [1, -32139900564, 421210336401887678278, -26587419759564182670866297295828, 684326450885775034048946719925754910487329], [1, -128672529400, 11048947607205473212278, -705175239081688578143420244106600, 30034640110980377619945846078500632729311721], [1, -650359859292, 383505148553643242724622, -91733283881803801969015315425899076, 19895113660064588580108197261066338165074766609], [1, -2543054749980, 1300431386621219326561918, -18455324023198018947801747111170987820, 52666193272726422601456708224751866691705278695881], [1, -7839407998744, 44521666362170934473791806, -176779565811982655508563836524262263784, 508507766528375922442969666478706045897328683433921], [1, 27805209097556, 1056043531593171221644249518, 12692742645180677692584470114497609634852, 208381240119593773598371865160915107617069000520604889], [1, 37826364264156, 4086289739939014280958364246, 98882665468797247446152451559226973355836, 6833624772958324635768660320234188206281715423144834961], [1, -29630453926852, 8260351743625889653180108662, -174061230590768694366037742218442332121836, 34508611856016952192871159710674768120457665758914571449], [1, -220791583022004, 41012465711315987336383109278, -5883640085642034405519357474832599048884748, 710112520079088427392020925014421733344154169313556279969], [1, -1058306017600572, 674218448097611565545837650222, -217420779663701818618114861564876360926083436, 42206522052678945186203086745997960094176615418554557058169], [1, -1527820717235160, 1999279705617309064039688309638, -1943374915455692042866656843600040703709092040, 1617962292165351485107436017199696023447086893648213540833561], [1, 631738213122116, 3222776472482328887885492379006, 1416264413778395196487181426527318929857354036, 5025906331956386730429209354686389578016774520729003377125641], [1, 8843763493872596, 38731901316365470670193289745958, 97703194981714309497201188620649281944647988092, 122051547946915276501139298573834221091215046641684146917022729], [1, 3331901660912376, 57116338514874372652089886358926, 98647050187114186822237987658010191837786646216, 876564456148583685580741416193317498080031692578600918378223281], [1, 10026350574292028, 115441696003744941477346258124502, 476026913903723238845567166834077925765598118684, 2254121098958571461145959861189507961269267337119053041038240209], [1, -8263606842055120, 378980145174874501170652087605918, -1502554378891175287415471849260436671232507660080, 33061389635588795063368942081397460712933173476460004123495939681], [1, 10689526892336988, 867773035493778559635444660772582, 4500762067469803706154998822707353665293019168724, 177278121356160474500473255263998346371626331523159666001836231529], [1, -55878412521904980, 2796050833571225804846465104599958, -77068014867241220864545147306545765286385684346420, 1902217732808760980190430983601716818363305103120555045416541165041], [1, 56106580363859756, 4180618963917465835865973180665958, 334297618126446778543948724754858234903404842028972, 35500867454043477833550660611106142600066519938980258615297790898369], [1, 78995733009671316, 11578900477404242996226287191393966, 935549966629070190323861872009908941634785320668516, 140257698616957210495095340671758323626004183047357349291203589613401], [1, 372475381312287188, 65539144701344243915403757739086062, 6156450520815315419780850136035132725151190410823244, 273190529550633389204969454322733638418863819596995123034388064454769], [1, -170264625914641164, 34122272788609805023799454185975638, -5378344902284316145402132769533475569195214952767748, 997811353702376766257783294590159855719786937813437480923720110254649], [1, -389444706275611900, 121200747417947670726664855979116638, -16853739223641273491530094240513387522154859928001100, 1872841093441861984128915510720716694558810308158343526976129430640361], [1, -19137298135925892, -48331243191416251366238917800218, -1528319526618678185420135221964189429040933051693636, 6377743935089859685589857024410199291038836254257581172336605088542689]], 'euler_factors_factorization': [[[[1, 256], 2]], [[[1, 1308, 183755142, 168915333204, 16677181699666569], 1]], [[[1, -390625], 2]], [[[1, -603844, -168048464563602, -140472540088091023708, 54116956037952111668959660849], 1]], [[[1, 471481296, 1064411254083979846, 238308820056195962235807216, 255476698618765889551019445759400441], 1]], [[[1, 1541834228, 17324849107520411262, 13337507350938235409534170724, 74829695578286078013428929473144712489], 1]], [[[1, -32139900564, 421210336401887678278, -26587419759564182670866297295828, 684326450885775034048946719925754910487329], 1]], [[[1, -128672529400, 11048947607205473212278, -705175239081688578143420244106600, 30034640110980377619945846078500632729311721], 1]], [[[1, -650359859292, 383505148553643242724622, -91733283881803801969015315425899076, 19895113660064588580108197261066338165074766609], 1]], [[[1, -2543054749980, 1300431386621219326561918, -18455324023198018947801747111170987820, 52666193272726422601456708224751866691705278695881], 1]], [[[1, -7839407998744, 44521666362170934473791806, -176779565811982655508563836524262263784, 508507766528375922442969666478706045897328683433921], 1]], [[[1, 27805209097556, 1056043531593171221644249518, 12692742645180677692584470114497609634852, 208381240119593773598371865160915107617069000520604889], 1]], [[[1, 37826364264156, 4086289739939014280958364246, 98882665468797247446152451559226973355836, 6833624772958324635768660320234188206281715423144834961], 1]], [[[1, -29630453926852, 8260351743625889653180108662, -174061230590768694366037742218442332121836, 34508611856016952192871159710674768120457665758914571449], 1]], [[[1, -220791583022004, 41012465711315987336383109278, -5883640085642034405519357474832599048884748, 710112520079088427392020925014421733344154169313556279969], 1]], [[[1, -1058306017600572, 674218448097611565545837650222, -217420779663701818618114861564876360926083436, 42206522052678945186203086745997960094176615418554557058169], 1]], [[[1, -1527820717235160, 1999279705617309064039688309638, -1943374915455692042866656843600040703709092040, 1617962292165351485107436017199696023447086893648213540833561], 1]], [[[1, 631738213122116, 3222776472482328887885492379006, 1416264413778395196487181426527318929857354036, 5025906331956386730429209354686389578016774520729003377125641], 1]], [[[1, 8843763493872596, 38731901316365470670193289745958, 97703194981714309497201188620649281944647988092, 122051547946915276501139298573834221091215046641684146917022729], 1]], [[[1, 3331901660912376, 57116338514874372652089886358926, 98647050187114186822237987658010191837786646216, 876564456148583685580741416193317498080031692578600918378223281], 1]], [[[1, 10026350574292028, 115441696003744941477346258124502, 476026913903723238845567166834077925765598118684, 2254121098958571461145959861189507961269267337119053041038240209], 1]], [[[1, -8263606842055120, 378980145174874501170652087605918, -1502554378891175287415471849260436671232507660080, 33061389635588795063368942081397460712933173476460004123495939681], 1]], [[[1, 10689526892336988, 867773035493778559635444660772582, 4500762067469803706154998822707353665293019168724, 177278121356160474500473255263998346371626331523159666001836231529], 1]], [[[1, -55878412521904980, 2796050833571225804846465104599958, -77068014867241220864545147306545765286385684346420, 1902217732808760980190430983601716818363305103120555045416541165041], 1]], [[[1, 56106580363859756, 4180618963917465835865973180665958, 334297618126446778543948724754858234903404842028972, 35500867454043477833550660611106142600066519938980258615297790898369], 1]], [[[1, 78995733009671316, 11578900477404242996226287191393966, 935549966629070190323861872009908941634785320668516, 140257698616957210495095340671758323626004183047357349291203589613401], 1]], [[[1, 372475381312287188, 65539144701344243915403757739086062, 6156450520815315419780850136035132725151190410823244, 273190529550633389204969454322733638418863819596995123034388064454769], 1]], [[[1, -170264625914641164, 34122272788609805023799454185975638, -5378344902284316145402132769533475569195214952767748, 997811353702376766257783294590159855719786937813437480923720110254649], 1]], [[[1, -389444706275611900, 121200747417947670726664855979116638, -16853739223641273491530094240513387522154859928001100, 1872841093441861984128915510720716694558810308158343526976129430640361], 1]], [[[1, -19137298135925892, -48331243191416251366238917800218, -1528319526618678185420135221964189429040933051693636, 6377743935089859685589857024410199291038836254257581172336605088542689], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-10e2-1.1-c17e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17, 17], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/10/18/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.087890625', 'prec': 37}, 'plot_values': [1.376771223981786, 1.3243730246964183, 1.2265682333053927, 1.053379984533256, 0.8227413767495103, 0.5623310839098599, 0.2922359283194479, 0.0325175859395169, -0.19444023892725049, -0.3683971506395267, -0.4731131427574136, -0.4972966952494287, -0.43543285821103683, -0.28848496679201835, -0.06396827655296015, 0.22441559543566136, 0.557686470473157, 0.9127009039953795, 1.2640413262397896, 1.5854833071905148, 1.852526658958626, 2.0436832464425145, 2.143140491237665, 2.14134255675098, 2.037183446541717, 1.8375095718828782, 1.5583185436898985, 1.223072896092317, 0.862604600448191, 0.5124437908144972, 0.21145987290813287, -0.001307531959452446, -0.08888112590396133, -0.019352141564043832, 0.23169810399706658, 0.6790200341951769, 1.3259151078617994, 2.1633675824366074, 3.1696751882165386, 4.311032033653111, 5.543071330072896, 6.812620110521382, 8.06122485285403, 9.227407517117278, 10.251755204881187, 11.078759490406059, 11.662629475512762, 11.967780137470774, 11.974297245933812, 11.67638786766419, 11.08646799986601, 10.23135986298712, 9.154301803155843, 7.909262947990276, 6.5607213253274885, 5.1770102743887065, 3.8283350718638447, 2.58040421405816, 1.4916798536220002, 0.6085597460635196, -0.03688256563681594, -0.4292492391875617, -0.5704361488037865, -0.4792444087436576, -0.18966908553938042, 0.2517353989275321, 0.7898767129703176, 1.364844039253187, 1.9174795366424342, 2.3926694597295524, 2.745168552814276, 2.9410491898165456, 2.9623412501117916, 2.805777760374087, 2.4851450520240865, 2.0273196913679925, 1.4719491441605654, 0.8656707261997799, 0.2596378111971538, -0.2965543806197686, -0.7582215013045717, -1.0902967737458622, -1.2699428813740739, -1.2886726582800603, -1.1528264341496075, -0.8827862963154505, -0.5106764019204442, -0.07740447850775391, 0.37202885908070854, 0.7921008836031206, 1.142532709254669, 1.3906411388029558, 1.5164034192309972, 1.5121854626299513, 1.385552855307651, 1.1559728685271418, 0.8546852311831699, 0.5191903268499297, 0.19069049568012889, -0.09187650657895914, -0.2952648255171836, -0.39631715594808103, -0.38425782795516267, -0.2620740459212096, -0.04608052812532338, 0.23591902056000977, 0.5482379299143446, 0.851153910701616, 1.1066833173151405, 1.2822499147033108, 1.356520490841538, 1.3206491281729889, 1.1818516897003493, 0.9609518026925862, 0.692245404162133, 0.41772775141270396, 0.18347461640860693, 0.032556430564010384, -6.569334055561464e-05, 0.10688923234751478, 0.3574536671612783, 0.7367104165108138, 1.211455744398269, 1.7330259775009214, 2.243189757166829, 2.6799163544623545, 2.9870655275972737, 3.119754782051387, 3.0543509423311788, 2.78976110833255, 2.3536072263470147, 1.7972196543064543, 1.1952173350888424, 0.6347482271794039, 0.20862930469420854, 0.0022561980340993206, 0.08376114824938095, 0.4935780992854834, 1.2371732830044748, 2.2815300877533016, 3.555691227065935, 4.955459550445299, 6.354088715960973, 7.612457810384975, 8.597846389429101, 9.193610371346747, 9.320050156465646, 8.936917499198469, 8.05891378309854, 6.746866793180777, 5.112372298674398, 3.2983384604198602, 1.4720895485798238, -0.1989622865385945, -1.5608974635788153, -2.493961033163543, -2.924385736428026, -2.834011147607187, -2.262211242778935, -1.3018926269665254, -0.08772559410536265, 1.2176238158454187, 2.4462896883511105, 3.4399709433672325, 4.0756148767005955, 4.27158550815535, 4.006460027797808, 3.310944179866434, 2.2732265494233457, 1.017929555767122, -0.3019169389254626, -1.5310760964595151, -2.5267568281026462, -3.1794482273006426, -3.424183424280331, -3.2481492384189856, -2.6905205954939544, -1.8357530284188797, -0.800183816944789, 0.2827309625736479, 1.2836906918945643, 2.0901208484710927, 2.6258092764739236, 2.852627990248908, 2.7801915229853735, 2.454391322421808, 1.954566067515149, 1.374015953528634, 0.8092869422472213, 0.3422475773704421, 0.030310825688973322, -0.10156287779433176, -0.06205429963171829, 0.11070203432003001, 0.3583405052662694, 0.6135877757430509, 0.814855465075039, 0.9156071684359659, 0.8957340652816793, 0.7615984121794113, 0.5477215904069145, 0.3065434073256811, 0.10047636237608357, -0.012607023826870114, 0.00982392270569825, 0.18512466388727578, 0.5009777701861033, 0.9160074472066044, 1.3669273894495761, 1.7780086199364589, 2.0774439159252065, 2.2074251407485423, 2.140694549687521, 1.8817559762306155, 1.4738479387514338, 0.9872619497001894, 0.5130912805403886, 0.1434377350880748, -0.04246351230576072, 0.004827985762045341, 0.29517018541700224, 0.7946709052539335, 1.4300379091265314, 2.0987695812018186, 2.6886858341098203, 3.093770049239599, 3.2392680828246236, 3.0893412015531263, 2.6632832310051593, 2.0254204169936423, 1.2830723951005274, 0.5607713625152894, -0.01699572811958167, -0.35373731091875144, -0.39879083967692047, -0.16094792213394232, 0.29009161845994663, 0.8323313868156006, 1.3136123394107815, 1.5750786819659899, 1.487907794884762, 0.9724692166883927, 0.02892168380044104, -1.266503369224735, -2.7560416159248438, -4.231624366452012, -5.457965362083902, -6.21715243790643, -6.3436693201604335, -5.75744416001116, -4.483374595397331, -2.653715011527544, -0.4916273814471843, 1.7162668776386207, 3.6711253623677895, 5.096923419759972, 5.802558580251578, 5.694266159163707, 4.816372869689982, 3.3231228957024235, 1.4786697445917023, -0.4040732482908303, -1.9972336446169168, -3.022311966470414, -3.288198748736626, -2.725586839666003, -1.3963582445820593, 0.5162601850696772, 2.7409518776926265, 4.957917844133845, 6.860343540997846, 8.189862655125816, 8.793210393017416, 8.623125902890944, 7.761230112458625, 6.378076295991105, 4.716942366198022, 3.0347226406919576, 1.5676310024911566, 0.4869155270043159, -0.1222206961866312, -0.2677969770710699, -0.040091204546986496, 0.41390145938299805, 0.9270198570615631, 1.3438314634722155, 1.5574467898505335, 1.5198726678206531, 1.2551953662916344, 0.839540652044491, 0.38651433721941786, 0.01216862992839878, -0.18936449069589556, -0.169895189218997, 0.06338349769036646, 0.45018335392337444, 0.8938325161634596, 1.2825423594964223, 1.5210965728874946, 1.54799118796114, 1.3582559570635788, 0.9973427195751033, 0.5588840274446464, 0.15640281128397374, -0.09853713049126447, -0.12645120698530662, 0.10148576388053908, 0.5536687132213668, 1.143810668871341, 1.7461814040932224, 2.2267251564532202, 2.465813537279933, 2.394251098499153, 1.9984429155907601, 1.3363023990973142, 0.513900411306021, -0.3268049194664972, -1.0463520520476235, -1.532110477237248, -1.7245596562268501, -1.6271353643381583, -1.3028795467775465, -0.8562694390552085, -0.4080957567164133, -0.06138953694704164, 0.11838706402207803, 0.12574636371229522, 0.007102504462809699, -0.1464400235047163, -0.23220405104738784, -0.16320522611780108, 0.10070935904459387, 0.5360908309843587, 1.0540668863972014, 1.5184395135923434, 1.774498473500397, 1.695678297440882, 1.2138094547711773, 0.358831208025678, -0.7453740643937014, -1.883518016457366, -2.796807674125272, -3.2291940695727614, -2.989035844295728, -1.999261813056248, -0.3256146854557162, 1.8211749603842613, 4.113861383667122, 6.17428068445681, 7.632886244418148, 8.22806085938251, 7.8377458252297485, 6.547185732955088, 4.607669913842239, 2.428202195305504, 0.471126455907618, -0.8167301077675915, -1.1091625069294075, -0.262629145561153, 1.645608736952044, 4.329000918087752, 7.337882149606802, 10.155659250936955, 12.279103989957717, 13.343298725904603, 13.156500233959713, 11.77449562018057, 9.445230480228966, 6.593548142121242, 3.7026455178353754, 1.2414507343268832, -0.4397881716269599, -1.163908429735531, -0.9526222684696675, -0.006991098072748834, 1.3453520687253024, 2.7347868353762603, 3.8194011225371858, 4.372349070121855, 4.299289194005181, 3.6685914761408265, 2.6576409157866814, 1.5189812181755245, 0.49887746618811074, -0.21282432503265242, -0.5284351399712138, -0.472855039465342, -0.16701698017096253, 0.2147697542838832, 0.4929682952524723, 0.5403830393848168, 0.3063164443723344, -0.1613869890500112, -0.7436366971852928, -1.2772465531529902, -1.6094319564896018, -1.6388679751382713, -1.3480727611102514, -0.8094240964334316, -0.17066092815946618, 0.38886793444791434, 0.6957755315435262, 0.6426885338874461, 0.20095375231337914, -0.551582600310808, -1.466545401231793, -2.3458762297766085, -3.0019877774932247, -3.296351599623563, -3.1749184402189607, -2.678061586223747, -1.9261274837568112, -1.0852874207895171, -0.3263069706861956, 0.22372074855774007, 0.5018941068611358, 0.5283878291752578, 0.3824000002624251, 0.18007259100796394, 0.02903428915988244, -0.0024462227841132223, 0.09249002338946581, 0.26097787365225467, 0.4100845393131029, 0.44601001530637663, 0.30680298180109167, 0.0002745282532166794, -0.39570004563416805, -0.7382268489351573, -0.8633987857619744, -0.6308791498047617, 0.02620703101351119, 1.0683797222284037, 2.3445695140291236, 3.619650625023523, 4.620268480901667, 5.114851075079987, 4.958540507606351, 4.161480860395502, 2.8709315499160017, 1.3684402556737392, -0.016748182666814423, -0.9727859115517192, -1.2958028703144866, -0.9415120691024678, -0.04313247262578817, 1.1212999076528265, 2.193880444977667, 2.8451544902489925, 2.8477082003777485, 2.172365753021121, 0.9792349981911637, -0.3825862726844456, -1.4830536320674765, -1.9016007539262414, -1.3525512219686588, 0.23439953539925165, 2.676783200975047, 5.570794863996305, 8.366058980593355, 10.511572129819923, 11.554589280290605, 11.294645158613003, 9.785888184040672, 7.381160281202803, 4.6018952874262045, 2.056078618901086, 0.2647511421906453, -0.44247155425367196, -0.011107789913680588, 1.3364901092425678, 3.1579492694500977, 4.917962129778623, 6.104756749954671, 6.387817414514344, 5.6594352206002725, 4.0967203965621035, 2.0695565160398366, 0.07477189921272807, -1.4179844482650963, -2.0695633136326874, -1.7592056778306349, -0.6045385849358583, 1.075423263554089, 2.856433405027481, 4.306519813798759, 5.116312377649742, 5.139663181191465, 4.449102231583329, 3.2678908787513046, 1.9237380919254634, 0.7326805867138347, -0.07389130535679143, -0.4100007622264844, -0.3423477315740229, -0.05683720762993362, 0.21372042244486655, 0.2576108373540354, -0.03592312758820879, -0.6621171096927427, -1.4879261946610705, -2.3124371856162758, -2.9183356404536616, -3.145567959843377, -2.9353136065121017, -2.3443418486727214, -1.5258723706379407, -0.681658964424472, 0.010042032967846604, 0.4282137850358523, 0.5343730976643192, 0.3973916538869275], 'positive_zeros': ['0.62687264407191403541721810398874', '1.25154400183761327838886927624916', '2.72388181303130273758290534286006', '2.91054587554933684561382951428893', '5.26730866841669086707818893707479', '5.66588688571795440059821513093687', '6.89507437872306717036684652840044', '7.66158257804266450132459066985573', '8.670268548833463173601824657423738', '9.156191399489473612719585899751176', '10.32654301785782703697713516185057', '10.37125833178106857491133091067670', '11.86821136002649854971542806552063', '11.90456567292496176224001549305079', '13.43605969509634101210197496409547', '14.06847169365456172570887139250137', '14.92114101550407849727475476247621', '15.70921941218575105644057520023018', '16.71190426901195853340748588140571', '16.91331647796161257372432449622836'], 'prelabel': '4-10e2-1.1-c17e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.280444922488313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c17e2-0', 'trace_hash': 226374992719769199, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62687264407191403541721810399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.25154400183761327838886927625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72388181303130273758290534286', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 335.703332908975, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, -512, -1308, 196608, 781250, 669696, 603844, -67108864, -182044278, -400000000, -471481296, -257163264, -1541834228, -309168128, -1021875000, 21474836480, 32139900564, 93206670336, 128672529400, 153600000000, -789827952, 241398423552, 650359859292, 87778394112, 457763671875, 789419124736, 309550308156, 118720561152, 2543054749980, 523200000000, 7839407998744, -6597069766656, 616697535168, -16455629088768, 471753125000, -35791361409024, -27805209097556, -65880335052800, 2016719170224, -52428800000000, -37826364264156, 404391911424, 29630453926852, -92696994643968, -142222092187500, -332984247957504, 220791583022004, -28089086115840, 168413092139938, -234375000000000, -42038989937712, -303136943898624, 1058306017600572, -158489757775872, -368344762500000, -40523284873216, -168303668455200, -1302044031989760, 1527820717235160, -200908800000000, -631738213122116, -4013776895356928, -109926345004632, 1970324836974592, -1204557990625000, -315749138006016, -8843763493872596, 6318961570086912, -850670695953936, -241537600000000, -3331901660912376, 12216784694280192, -10026350574292028, 14236267057948672, -598754882812500, 25298048660275200, -284701151701824, -1032560215154688, 8263606842055120, 16777216000000000, 16590439907273691, 19367098503247872, -10689526892336988, -155286493986816, 25109297315625000, -15170792410548224, -3326315612973840, 31640574171807744, 55878412521904980, 72817711200000000, -931027347572432, 127865951215681536, -10253945662357152, -113045290507266048, 100525413593750000, 8628967254786048, -56106580363859756, -86227503175648256, 85830472120824288, 90000000000000000], 'euler11': [1, 471481296, 1064411254083979846, 238308820056195962235807216, 255476698618765889551019445759400441], 'euler13': [1, 1541834228, 17324849107520411262, 13337507350938235409534170724, 74829695578286078013428929473144712489], 'euler17': [1, -32139900564, 421210336401887678278, -26587419759564182670866297295828, 684326450885775034048946719925754910487329], 'euler19': [1, -128672529400, 11048947607205473212278, -705175239081688578143420244106600, 30034640110980377619945846078500632729311721], 'euler2': [1, 512, 65536, 0, 0], 'euler23': [1, -650359859292, 383505148553643242724622, -91733283881803801969015315425899076, 19895113660064588580108197261066338165074766609], 'euler29': [1, -2543054749980, 1300431386621219326561918, -18455324023198018947801747111170987820, 52666193272726422601456708224751866691705278695881], 'euler3': [1, 1308, 183755142, 168915333204, 16677181699666569], 'euler31': [1, -7839407998744, 44521666362170934473791806, -176779565811982655508563836524262263784, 508507766528375922442969666478706045897328683433921], 'euler37': [1, 27805209097556, 1056043531593171221644249518, 12692742645180677692584470114497609634852, 208381240119593773598371865160915107617069000520604889], 'euler41': [1, 37826364264156, 4086289739939014280958364246, 98882665468797247446152451559226973355836, 6833624772958324635768660320234188206281715423144834961], 'euler43': [1, -29630453926852, 8260351743625889653180108662, -174061230590768694366037742218442332121836, 34508611856016952192871159710674768120457665758914571449], 'euler47': [1, -220791583022004, 41012465711315987336383109278, -5883640085642034405519357474832599048884748, 710112520079088427392020925014421733344154169313556279969], 'euler5': [1, -781250, 152587890625, 0, 0], 'euler53': [1, -1058306017600572, 674218448097611565545837650222, -217420779663701818618114861564876360926083436, 42206522052678945186203086745997960094176615418554557058169], 'euler59': [1, -1527820717235160, 1999279705617309064039688309638, -1943374915455692042866656843600040703709092040, 1617962292165351485107436017199696023447086893648213540833561], 'euler61': [1, 631738213122116, 3222776472482328887885492379006, 1416264413778395196487181426527318929857354036, 5025906331956386730429209354686389578016774520729003377125641], 'euler67': [1, 8843763493872596, 38731901316365470670193289745958, 97703194981714309497201188620649281944647988092, 122051547946915276501139298573834221091215046641684146917022729], 'euler7': [1, -603844, -168048464563602, -140472540088091023708, 54116956037952111668959660849], 'euler71': [1, 3331901660912376, 57116338514874372652089886358926, 98647050187114186822237987658010191837786646216, 876564456148583685580741416193317498080031692578600918378223281], 'euler73': [1, 10026350574292028, 115441696003744941477346258124502, 476026913903723238845567166834077925765598118684, 2254121098958571461145959861189507961269267337119053041038240209], 'euler79': [1, -8263606842055120, 378980145174874501170652087605918, -1502554378891175287415471849260436671232507660080, 33061389635588795063368942081397460712933173476460004123495939681], 'euler83': [1, 10689526892336988, 867773035493778559635444660772582, 4500762067469803706154998822707353665293019168724, 177278121356160474500473255263998346371626331523159666001836231529], 'euler89': [1, -55878412521904980, 2796050833571225804846465104599958, -77068014867241220864545147306545765286385684346420, 1902217732808760980190430983601716818363305103120555045416541165041], 'euler97': [1, 56106580363859756, 4180618963917465835865973180665958, 334297618126446778543948724754858234903404842028972, 35500867454043477833550660611106142600066519938980258615297790898369], 'euler_factors': [[1, 512, 65536, 0, 0], [1, 1308, 183755142, 168915333204, 16677181699666569], [1, -781250, 152587890625, 0, 0], [1, -603844, -168048464563602, -140472540088091023708, 54116956037952111668959660849], [1, 471481296, 1064411254083979846, 238308820056195962235807216, 255476698618765889551019445759400441], [1, 1541834228, 17324849107520411262, 13337507350938235409534170724, 74829695578286078013428929473144712489], [1, -32139900564, 421210336401887678278, -26587419759564182670866297295828, 684326450885775034048946719925754910487329], [1, -128672529400, 11048947607205473212278, -705175239081688578143420244106600, 30034640110980377619945846078500632729311721], [1, -650359859292, 383505148553643242724622, -91733283881803801969015315425899076, 19895113660064588580108197261066338165074766609], [1, -2543054749980, 1300431386621219326561918, -18455324023198018947801747111170987820, 52666193272726422601456708224751866691705278695881], [1, -7839407998744, 44521666362170934473791806, -176779565811982655508563836524262263784, 508507766528375922442969666478706045897328683433921], [1, 27805209097556, 1056043531593171221644249518, 12692742645180677692584470114497609634852, 208381240119593773598371865160915107617069000520604889], [1, 37826364264156, 4086289739939014280958364246, 98882665468797247446152451559226973355836, 6833624772958324635768660320234188206281715423144834961], [1, -29630453926852, 8260351743625889653180108662, -174061230590768694366037742218442332121836, 34508611856016952192871159710674768120457665758914571449], [1, -220791583022004, 41012465711315987336383109278, -5883640085642034405519357474832599048884748, 710112520079088427392020925014421733344154169313556279969], [1, -1058306017600572, 674218448097611565545837650222, -217420779663701818618114861564876360926083436, 42206522052678945186203086745997960094176615418554557058169], [1, -1527820717235160, 1999279705617309064039688309638, -1943374915455692042866656843600040703709092040, 1617962292165351485107436017199696023447086893648213540833561], [1, 631738213122116, 3222776472482328887885492379006, 1416264413778395196487181426527318929857354036, 5025906331956386730429209354686389578016774520729003377125641], [1, 8843763493872596, 38731901316365470670193289745958, 97703194981714309497201188620649281944647988092, 122051547946915276501139298573834221091215046641684146917022729], [1, 3331901660912376, 57116338514874372652089886358926, 98647050187114186822237987658010191837786646216, 876564456148583685580741416193317498080031692578600918378223281], [1, 10026350574292028, 115441696003744941477346258124502, 476026913903723238845567166834077925765598118684, 2254121098958571461145959861189507961269267337119053041038240209], [1, -8263606842055120, 378980145174874501170652087605918, -1502554378891175287415471849260436671232507660080, 33061389635588795063368942081397460712933173476460004123495939681], [1, 10689526892336988, 867773035493778559635444660772582, 4500762067469803706154998822707353665293019168724, 177278121356160474500473255263998346371626331523159666001836231529], [1, -55878412521904980, 2796050833571225804846465104599958, -77068014867241220864545147306545765286385684346420, 1902217732808760980190430983601716818363305103120555045416541165041], [1, 56106580363859756, 4180618963917465835865973180665958, 334297618126446778543948724754858234903404842028972, 35500867454043477833550660611106142600066519938980258615297790898369]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/18/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-10e2-1.1-c17e2-0-0', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17, 17], 'order_of_vanishing': 0, 'prelabel': '4-10e2-1.1-c17e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.280444922488313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c17e2-0', 'trace_hash': 226374992719769199, 'z1': {'__RealLiteral__': 0, 'data': '0.62687264407191403541721810399', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '794655483524419038516246572752,1586520505141490713403804466537', 'Lhash_array': ['794655483524419038516246572752', '1586520505141490713403804466537'], 'label': '4-10e2-1.1-c17e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/18/a/c'}