Lfunction data - 8-3e16-1.1-c7e4-0-4

Formats: - HTML - YAML - JSON - 2025-09-03T19:00:57.356313

• 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
  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': '599315060729431002716903192491,1202974596879005758274388005133,1720572227968293037989134371025,1840122637793055862936423343928', 'a10': 1620, 'a2': 9, 'a3': 0, 'a4': 130, 'a5': 180, 'a6': 0, 'a7': -700, 'a8': 477, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 409921.6959158787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.1', 'coefficient_field': '1.1.1.1', 'conductor': 43046721, 'conductor_radical': 3, 'degree': 8, 'euler_factors': [[1, -9, -49, 1134, -9852, 145152, -802816, -18874368, 268435456], [1], [1, -180, -131365, -1352700, 18184209600, -105679687500, -801788330078125, -85830688476562500, 37252902984619140625], [1, 700, -94961, -743487500, -739579771328, -612293926212500, -64404741220813889, 390982104858298804900, 459986536544739960976801], [1, -10890, 50203733, -320318732250, 1986194375394348, -6242105909858964750, 19064859252007464438653, -80588721892971363502187790, 144209936106499234037676064081], [1, -5480, -27158234, 374330032000, -2551199591830133, 23488654376562544000, -106932189228895544295626, -1353913619322508152020183240, 15502932802662396215269535105521], [1, 32832, 427500356, 16066218476736, 564158142422065734, 6592590769871931611328, 71981580796650152294230724, 2268426374231902717943319188544, 28351092476867700887730107366063041], [1, -32048, 3547821700, -81382636750448, 4764807384912655414, -72745639036528262789072, 2834733258265597773069225700, -22888985917981224495432545716112, 638411683925748518131605316913942641], [1, -24372, -2311612066, 95149371189168, -5172734676275436957, 323967000290927857158096, -26798140326966865943039595394, -962001448189590382044046998291756, 134393854047545109686936775588697536481], [1, 143280, -19092997318, 733937916168000, 918231547937772286443, 12660338272383211263912000, -5681278538427859119748571943958, 735433703256999157707187225263003120, 88540901833145211536614766025207452637361], [1, -38708, -24998494289, 1104278262087652, -96085741293891320816, 30381581695983290734057372, -18922458641710262767576733146769, -806113701475400146164705242505916748, 572964121067545096123347421337293637543041], [1, -911240, 554643085132, -244630239722188760, 87549393525276764783734, -23223207860323159418153625080, 4998477480609361639011452596123948, -779594884607107628289906530325328099880, 81217248802771228597652036390959994837496721], [1, -731880, 62715601538, -61056492590988000, 81416340195765222102483, -11891012880278524264384428000, 2378754299400597645392937849323618, -5406309076595959345271776833254168791080, 1438626275603521989270100382252682485138269921], [1, -1088840, 434479093486, -225886641364316000, 167995333752804683324347, -61400193123273390711057812000, 32101643080770469651640679087765214, -21867625822077903641880006286149706100120, 5459046029871041534743397034507955551606171601], [1, -1561500, 1014040055534, -641770181452710000, 536508680245115269940787, -325135611947677666667804730000, 260270604927486670707345450734848046, -203047200105271806223495121926424480590500, 65877941798660252683780571409941608871644628161], [1, 5220936, 14680769827514, 26667624626206420752, 34239512516067315219951339, 31326755721396195582829930697424, 20258673447599243563427990544204259466, 8463336938084708770029145151417869124360808, 1904251686165483303166544735375573842653419591761], [1, -1731960, -1329825064438, 1121950635256656000, 5086103380773827735924283, 2792144114325097245552705264000, -8236120219648276524305337208150393318, -26695010877351121543745262394725002575577640, 38358032782038398419973086399760468678777161743121], [1, -620192, -5918398022954, -10884659710932992, 28642613360255532163202539, -34207686329061069337974904832, -58455026138493372262252976144728970714, -19250973451996130376171891929899889348974112, 97551820892064552722266841889541788960852432978481], [1, 346600, -12016990578146, 5441248271500000, 109849425893519278692502987, 32977836546523763949194500000, -441410803696869415949716286303154574034, 77161278527601396100643017358066824010342200, 1349256365417755877454657051946796697206085388680241], [1, -8484480, 47293476367964, -201451744961585447040, 707381642276777629071514086, -1832227826543158367292925342112640, 3912173623160326229839546212115826688284, -6383377865725885358547728452511332070613790080, 6842798698940938981814244812733146152009703886272161], [1, 6290380, 47602415172538, 188098063023211820080, 818171326665306797962526179, 2077994262887644435888338008067760, 5809637428058246241269345359394793478042, 8481192963696115274290954359643153312618925740, 14894985451961941943846586557477384171894488107677281], [1, 10110616, 44597210011234, 194321266458985636864, 989009806128422563565118499, 3731727915153511753584481176165376, 16447010447258271649194823910488652238754, 71605525013919412362685266393240317379004780264, 136006152866792691625201101984747368303641150837104961], [1, -644202, -52162543092091, 1091640661370608518, 2016771017967066782917429788, 29622816649302974065085095842786, -38410684779012174068188980853123772388739, -12872473567103361093965484307544510522734098366, 542233801012015735135407853098133122208235840693558641], [1, 12042000, 225939967485116, 1674742331778843654000, 16115149116594091289608763046, 74076088940629173429430514622966000, 442031434709065045991483988993155245906556, 1042050490641450316607921159811872786331745338000, 3827543948647425430322045212330289877339037312647605281], [1, 4098670, 11066174414449, -638833656515967139250, -7852834506260402499354615068, -51616663513370239469607643848235250, 72244001104587043648054510307133126671281, 2161968552737864046241709412110643854098146466990, 42619520516862344959898006540158454742326868747150111361], [1, 1143900, -116309935257277, -110739389516723587500, 2199066192219135415096673328, -11872761437162777544319989109837500, -1336952713215772678278128570594919945515077, 1409733140563444043031074852685247958941593333900, 132129096689825080931822600853816049099831724850779782801], [1, 5643640, -220426095083774, 35566187948768176000, 44600439224339817005181523507, 4374192505097894487991337493712000, -3334142465136523037448295012255611360387806, 10498832856682581281523624985456547399461703822920, 228792767573726113549107350198718474022130892363602038561], [1, -16289100, 365288792960642, -5050528250368829837400, 95217704341588739347005843339, -811004471087328135151697126150728200, 9419096273348081449014015398975114869840658, -67446034580335473084080711844155416394420775533700, 664883836375406516433586250657527435394385613490936917201], [1, 22860568, 662268093455980, 10255531135928891480008, 185255791046491925778907107094, 1874751212123164088709108829576773352, 22131191871780756329926893828872603112304780, 139650814667833358418068412984528236419154016803512, 1116713952456127112240969687448211536647543601817400964721], [1, 16651800, -224633522994094, 522781098671519028000, 131338492134508277604280357347, 122989767780933119018868812277876000, -12432909634511007618937912722778973779033966, 216824572709901378235182598842345418067681037173400, 3063348575248001425954190006610728401266477888045839853121]], 'euler_factors_factorization': [[[[1, -9, -49, 1134, -9852, 145152, -802816, -18874368, 268435456], 1]], [1], [[[1, -180, -131365, -1352700, 18184209600, -105679687500, -801788330078125, -85830688476562500, 37252902984619140625], 1]], [[[1, 700, -94961, -743487500, -739579771328, -612293926212500, -64404741220813889, 390982104858298804900, 459986536544739960976801], 1]], [[[1, -10890, 50203733, -320318732250, 1986194375394348, -6242105909858964750, 19064859252007464438653, -80588721892971363502187790, 144209936106499234037676064081], 1]], [[[1, -5480, -27158234, 374330032000, -2551199591830133, 23488654376562544000, -106932189228895544295626, -1353913619322508152020183240, 15502932802662396215269535105521], 1]], [[[1, 16416, 79007650, 6736119655968, 168377826559400929], 2]], [[[1, -16024, 1645526562, -14323400745736, 799006685782884121], 2]], [[[1, -24372, -2311612066, 95149371189168, -5172734676275436957, 323967000290927857158096, -26798140326966865943039595394, -962001448189590382044046998291756, 134393854047545109686936775588697536481], 1]], [[[1, 143280, -19092997318, 733937916168000, 918231547937772286443, 12660338272383211263912000, -5681278538427859119748571943958, 735433703256999157707187225263003120, 88540901833145211536614766025207452637361], 1]], [[[1, -38708, -24998494289, 1104278262087652, -96085741293891320816, 30381581695983290734057372, -18922458641710262767576733146769, -806113701475400146164705242505916748, 572964121067545096123347421337293637543041], 1]], [[[1, -455620, 173526750366, -43252861859337460, 9012061295995008299689], 2]], [[[1, -731880, 62715601538, -61056492590988000, 81416340195765222102483, -11891012880278524264384428000, 2378754299400597645392937849323618, -5406309076595959345271776833254168791080, 1438626275603521989270100382252682485138269921], 1]], [[[1, -1088840, 434479093486, -225886641364316000, 167995333752804683324347, -61400193123273390711057812000, 32101643080770469651640679087765214, -21867625822077903641880006286149706100120, 5459046029871041534743397034507955551606171601], 1]], [[[1, -1561500, 1014040055534, -641770181452710000, 536508680245115269940787, -325135611947677666667804730000, 260270604927486670707345450734848046, -203047200105271806223495121926424480590500, 65877941798660252683780571409941608871644628161], 1]], [[[1, 2610468, 3933113324245, 3066545839788013716, 1379946262057143768386569], 2]], [[[1, -1731960, -1329825064438, 1121950635256656000, 5086103380773827735924283, 2792144114325097245552705264000, -8236120219648276524305337208150393318, -26695010877351121543745262394725002575577640, 38358032782038398419973086399760468678777161743121], 1]], [[[1, -620192, -5918398022954, -10884659710932992, 28642613360255532163202539, -34207686329061069337974904832, -58455026138493372262252976144728970714, -19250973451996130376171891929899889348974112, 97551820892064552722266841889541788960852432978481], 1]], [[[1, 346600, -12016990578146, 5441248271500000, 109849425893519278692502987, 32977836546523763949194500000, -441410803696869415949716286303154574034, 77161278527601396100643017358066824010342200, 1349256365417755877454657051946796697206085388680241], 1]], [[[1, -4242240, 14648438075182, -38583682540732635840, 82721210695570328927708881], 2]], [[[1, 3145190, 18855097518219, 34746167348278693430, 122045014039746588673695409], 2]], [[[1, 10110616, 44597210011234, 194321266458985636864, 989009806128422563565118499, 3731727915153511753584481176165376, 16447010447258271649194823910488652238754, 71605525013919412362685266393240317379004780264, 136006152866792691625201101984747368303641150837104961], 1]], [[[1, -644202, -52162543092091, 1091640661370608518, 2016771017967066782917429788, 29622816649302974065085095842786, -38410684779012174068188980853123772388739, -12872473567103361093965484307544510522734098366, 542233801012015735135407853098133122208235840693558641], 1]], [[[1, 6021000, 94843763242558, 266316867405980109000, 1956410986640441413344189841], 2]], [[[1, 4098670, 11066174414449, -638833656515967139250, -7852834506260402499354615068, -51616663513370239469607643848235250, 72244001104587043648054510307133126671281, 2161968552737864046241709412110643854098146466990, 42619520516862344959898006540158454742326868747150111361], 1]], [[[1, 1143900, -116309935257277, -110739389516723587500, 2199066192219135415096673328, -11872761437162777544319989109837500, -1336952713215772678278128570594919945515077, 1409733140563444043031074852685247958941593333900, 132129096689825080931822600853816049099831724850779782801], 1]], [[[1, 5643640, -220426095083774, 35566187948768176000, 44600439224339817005181523507, 4374192505097894487991337493712000, -3334142465136523037448295012255611360387806, 10498832856682581281523624985456547399461703822920, 228792767573726113549107350198718474022130892363602038561], 1]], [[[1, -8144550, 149477549129071, -1307836752425239705650, 25785341502012466393542552649], 2]], [[[1, 11430284, 265808350567662, 2089500631404507863996, 33417270272362569384925825561], 2]], [[[1, 16651800, -224633522994094, 522781098671519028000, 131338492134508277604280357347, 122989767780933119018868812277876000, -12432909634511007618937912722778973779033966, 216824572709901378235182598842345418067681037173400, 3063348575248001425954190006610728401266477888045839853121], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '8-3e16-1.1-c7e4-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7, 7, 7, 7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/81/8/c/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [15.33167037412215, 15.104965107400115, 14.767784178971239, 14.27557522511743, 13.590073227057946, 12.692610403748631, 11.613528139396044, 10.396364253532532, 9.085114622534423, 7.720601993378585, 6.335033958596948, 4.958761281585535, 3.621626839842225, 2.352571363119554, 1.179439990707569, 0.12617626465603068, -0.7882198066542154, -1.550053242558589, -2.1511360780431743, -2.588732443923643, -2.8653784284088926, -2.9885899237372513, -2.970526352572756, -2.8273623926192983, -2.5784952429004186, -2.2457128832124185, -1.85235875365272, -1.4222926401348666, -0.9789179102170432, -0.5443049449005581, -0.13840518086099524, 0.22175698150370304, 0.5226917840199486, 0.7548688544269968, 0.9129794662783172, 0.9960563000776606, 1.007378069683832, 0.9541898047319021, 0.8472574862997481, 0.7002868159427819, 0.5292131445199884, 0.35138979789211194, 0.18470313625300122, 0.04670719169190058, -0.04624080028490219, -0.0798114029080074, -0.042435918595329275, 0.07412311212568949, 0.27430267582414875, 0.5584374319826112, 0.9227443897652751, 1.3593966383930687, 1.8567292514921616, 2.3996994165474845, 2.970760936388419, 3.5504388648260785, 4.118016577774289, 4.652503759234737, 5.134035804884718, 5.544373834981328, 5.867512414612594, 6.090560165106102, 6.204967463663316, 6.20632516760928, 6.094345374935902, 5.8731156470899, 5.551579631064267, 5.142424523681501, 4.661310541248276, 4.126407931764735, 3.558080280241844, 2.9772864881732466, 2.4044974566525457, 1.858967737727731, 1.358145770146033, 0.9164193909959603, 0.5444456836538041, 0.24883803116066688, 0.032015548239274674, -0.10804670332419884, -0.17759539625385506, -0.18661648141549977, -0.148218354137281, -0.0778928051058109, 0.007429382819701719, 0.09038865664006708, 0.15420942935645046, 0.18370601824725338, 0.16620595212361877, 0.09232368808747277, -0.043459333009336104, -0.24240791520721286, -0.501383812141785, -0.8129736341520634, -1.1659515188145433, -1.5458273720175613, -1.935595285856139, -2.316737786728211, -2.670542499401927, -2.9790144251875144, -3.2258504780953676, -3.397543708121199, -3.48462003363717, -3.4819000188842475, -3.388760028098869, -3.2094185209560755, -2.953156604242489, -2.6333824499232104, -2.26681520377775, -1.8727174366148762, -1.4720130755227296, -1.0856738496906142, -0.7334550366198954, -0.4328147358159704, -0.19786097210490075, -0.03830779129345809, 0.041093866138179024, 0.04083764865544453, -0.03327261277860757, -0.17052186442248848, -0.3560116216965592, -0.5716029983626122, -0.7970945325292589, -1.0116570745554492, -1.1952404274508939, -1.3299518887695763, -1.401450384790731, -1.399966421621715, -1.3210029837785473, -1.1657841348520848, -0.9414457048586373, -0.6604798334666888, -0.339897969141877, -0.00015715807711200866, 0.3362075862684187, 0.6463446618605152, 0.9087795681140393, 1.1050639120739743, 1.2214187103144871, 1.2499768404909948, 1.189619176754641, 1.0464617321976082, 0.8339625534068795, 0.5722107380757278, 0.2868259550498431, 0.007502404309318272, -0.23384673027393998, -0.40530907477225814, -0.4771914701127947, -0.4242138130934628, -0.22758799138331848, 0.12335405761684, 0.6299437136026911, 1.2834890989954635, 2.0654360153319526, 2.947981901627704, 3.895160184622829, 4.86470768997363, 5.811160501125185, 6.687954586267688, 7.449745495217719, 8.055399707407469, 8.471963395198594, 8.675526134394762, 8.652201521129998, 8.399577937928738, 7.928567260759425, 7.2610859467986275, 6.42827319652042, 5.469229491543602, 4.429817089234765, 3.3582955244359556, 2.302209646034977, 1.3060706841122884, 0.40921757419017746, -0.3572004960722057, -0.971698531683218, -1.4230729816679961, -1.710648723285222, -1.843726264997091, -1.8400928999419344, -1.7241551012243246, -1.5249247495142364, -1.2732322920000063, -0.99912101876131, -0.7296254753553014, -0.4869559541424676, -0.2868859286896601, -0.13798655024604148, -0.04159880915571221, 0.007561052367740309, 0.02023555987345392, 0.010934308574496671, -0.004066620276278195, -0.008840836077371355, 0.010184744171621978, 0.06250398871730405, 0.15225100602128477, 0.27759538857722665, 0.43074316987968253, 0.5985218494968659, 0.7636487864148693, 0.9068063511721983, 1.008533089027403, 1.051232221635806, 1.0213527009133798, 0.9116091660013002, 0.7217024357476118, 0.45869327331627147, 0.13699652296854087, -0.22235877049491773, -0.593922449097312, -0.9500264333060775, -1.2631933922408252, -1.5090810216809853, -1.6690409869225622, -1.7319072234367472, -1.695344111551711, -1.5668630221971374, -1.3628497460691071, -1.1067963625844373, -0.8270491056455398, -0.5540463174976785, -0.31626328118654007, -0.13651118763993222, -0.02873561165261108, 0.004634012046603815, -0.02548076796466893, -0.09444623994497534, -0.16496179260578347, -0.18953552999555942, -0.11430563353655564, 0.11606882978180419, 0.5527830741595184, 1.2370582073088068, 2.194713036899908, 3.431352825226865, 4.928981337581204, 6.645483597519397, 8.514815428589383, 10.448909492970051, 12.342746678584868, 14.08442798557235, 15.560940753263889, 16.66517125091266, 17.305932644493158, 17.42191767719361, 16.983210042575656, 15.993556421013393, 14.494504221227672, 12.570397910358684, 10.337444980059853, 7.935192554169794, 5.519827436456458, 3.256726262102695, 1.3029730908897705, -0.2046298145592071, -1.158398259766691, -1.488155114136255, -1.1694134042963338, -0.2251469386842149, 1.275975356971796, 3.2232435510106994, 5.472255915915516, 7.856335741955113, 10.199141457797841, 12.327891760078234, 14.086728165694835, 15.34835771979888, 16.02358194980952, 16.068455845298928, 15.485578430580627, 14.32241987154993, 12.666877525208092, 10.639685964246437, 8.382252566387338, 6.044750420779414, 3.7741217249624603, 1.7017002760276032, -0.06662363370550739, -1.4569290578097749, -2.4314367652684856, -2.9902960261141205, -3.167260155649578, -3.0234275479771555, -2.6396960503333244, -2.1077659132188815, -1.519173724121888, -0.9563242155653786, -0.48522277815678905, -0.1498920494174904, 0.029977248127085587, 0.05832289460371468, -0.04027925655367043, -0.22594375582950688, -0.4507938914754725, -0.6662128744709194, -0.8297738845297951, -0.9117942203975877, -0.8988116408018695, -0.7944710438465966, -0.618377927385878, -0.40297111589704754, -0.18674029803153971, -0.006809442356234265, 0.10839032153920829, 0.14597016223020615, 0.11438417292957938, 0.046290132975786796, -0.0016100042699136558, 0.0481592766104191, 0.2874246094292401, 0.8132576403943327, 1.7171241940872581, 3.073783114946186, 4.930397457083636, 7.296909051251451, 10.139743017939324, 13.382244260866386, 16.905105945453364, 20.550332831171293, 24.13188223221627, 27.456591037174288, 30.333456767602392, 32.58510975284151, 34.06490584786485, 34.680972816531614, 34.39372364663248, 33.21539606902851, 31.213522218862934, 28.516466285483556, 25.290557948429875, 21.723793922539045, 18.01486853513407, 14.363789480590865, 10.94770137547103, 7.907776831827368, 5.343192158605598, 3.3085377396263427, 1.8102428130151353, 0.811553220303719, 0.2418113456826453, 0.007548997417569495, 0.00440643646624232, 0.12974005183260295, 0.2937336460244221, 0.42792042214042714, 0.4902808990220217, 0.4666452036028775, 0.36847792988450606, 0.2274101167381083, 0.08751589832151663, -0.003491932475006359, -0.0032024413915506342, 0.11788352468939048, 0.3712203408096667, 0.7474041921956772, 1.2164997510646525, 1.7329025033037422, 2.2408789012262567, 2.6811227713426002, 2.99908165044667, 3.155232350445849, 3.128567028319484, 2.9186738817569453, 2.5470898025586863, 2.057022924542712, 1.5048489049709421, 0.9521622666552525, 0.4583211949492047, 0.07257407265101037, -0.17469648360885642, -0.27657170272317105, -0.25114892048227555, -0.14054551221358225, -0.006081822753987471, 0.07943502789285904, 0.04091787462748669, -0.18899524243262758, -0.6601561656248489, -1.3970855564043096, -2.3940383274641412, -3.614131253108472, -4.9912677569562565, -6.435243860948157, -7.840762704968399, -9.101207883830776, -10.117409108499151, -10.80649688788605, -11.111871260428858, -11.013955846666747, -10.526757948875836, -9.694312849720822, -8.587563805368648, -7.300325882241437, -5.933522405042382, -4.5840386617586075, -3.3369467661870247, -2.2593777091580094, -1.3924430199163846, -0.749897053297369, -0.32080056330046375, -0.07448333718817295, 0.03319263246511692, 0.05158917127705778, 0.02721237265369841, -0.0030408393176715436, -0.01630659054566361, -0.005446449708698478, 0.022146210270715918, 0.0484597536756676, 0.05083534856165093, 0.00880274928480313, -0.0891957770672684, -0.2404525820198892, -0.42505740579763057, -0.6056786169133247, -0.7304845103776443, -0.7397023223444689, -0.5734817999172735, -0.18075991759479612, 0.47159149124535504, 1.391000933409154, 2.5550236720630157, 3.9097737016163645, 5.372461831964847, 6.840650226812816, 8.200595614094699, 9.337095046411854, 10.146690589974094, 10.555259745283829, 10.521725195436607, 10.040901465243085, 9.14683453616383, 7.915343853262336, 6.449390032589111, 4.866885317638881, 3.2904067589187385, 1.8366338783334697, 0.6006021936261963, -0.35282562789958055, -0.9928844148481155, -1.32397128396072, -1.3821361058798858, -1.227222477841487, -0.9332026586179161, -0.5777178358676043, -0.23076894284702262, 0.05370957661606594, 0.24310341558489118, 0.3281789063354688, 0.32102769676186554, 0.24963531340578166, 0.15042905562078226, 0.059807569985896196, 0.005824241266156478, 0.001964443781292379, 0.043707782113581825, 0.1085948285213855, 0.15980181981088717, 0.15240195719054067, 0.04165005072028543, -0.20770311301124036, -0.6139624871968226, -1.1730637454402304, -1.856005314660194, -2.6110129791693093, -3.3693565731387363, -4.053158315983024, -4.585716963546958, -4.905025846502009, -4.9715776086812475, -4.773516834768312, -4.330018112476904, -3.692320425005461, -2.93403630454141, -2.1401823253174572, -1.3958690977537977, -0.7744380789560887, -0.3241534770627545, -0.06021616525520864, 0.038258728502313204, 0.026436006561047627, -0.013440073764335382, 0.016071276802273302, 0.21288346839043112, 0.6598709239907767, 1.4107945200365286, 2.4792567885895784, 3.8329034723054902, 5.396448123840996, 7.057686375823943, 8.677760091573628, 10.107912597310767, 11.214646090292424, 11.891232831460798, 12.068031983767662, 11.723909595565265, 10.897502137869392, 9.67309308577897, 8.167549501175808, 6.518939629350359, 4.874068367697592, 3.3633243436308033, 2.085774256304607, 1.1015182707557243, 0.4284536152448808, 0.042467606594676584, -0.11326747150698775, -0.1147030102532609, -0.04179225591657144, 0.03687032324270829, 0.07672601623537538, 0.06496925346399175, 0.022309061664002445, -0.0015291695085685706, 0.061972353527109954, 0.28584219039589776, 0.7321824224691996, 1.4376917507499385, 2.401883689847274, 3.5811574935048394, 4.89346567494856, 6.224947628661707, 7.441088464165619, 8.40512815084016, 9.005374003542386, 9.165595483057682, 8.853711234029733, 8.090841669135838, 6.958228349019195, 5.57780055624154, 4.0943694047706956, 2.6594558894200064, 1.4134900667941124, 0.4607122899532599, -0.14396827512077942, -0.3997506557085896, -0.35869437201728327, -0.11630449137368017, 0.20585931407708324, 0.48081392233040166, 0.5976143048970576, 0.4803013311598167, 0.10073199342827166, -0.5164394981545666, -1.2980621819157445, -2.1347560952476488, -2.898656688746956, -3.465841579456311, -3.7418371433104207, -3.6758946018337046, -3.26990025845326, -2.5821050132722005, -1.7232043774820376, -0.833225413627439, -0.058141312221666464, 0.47313217323510404, 0.6712140890400375, 0.5076195526633781, 0.022816673200227434, -0.6768976056538243, -1.4343315727156525, -2.064124621262799, -2.381897770730455, -2.2361686228381745, -1.5401506251526604, -0.28998608576197815, 1.4273527946014486, 3.4376238852078496, 5.498186336907562, 7.330042607803016, 8.654051238413745, 9.23065661695302, 8.903033089702124, 7.619652064916958, 5.444547180453717, 2.5563743002103942, -0.7656033371032286, -4.181277255253568, -7.332977229933872, -9.890825180163846, -11.598896929071064, -12.308193807122523, -11.994554435467712, -10.763084333413634, -8.837206178302477, -6.520620891896235, -4.154631995112176, -2.0729928881081268, -0.5569002426704259, 0.20521827617420474, 0.14074320976543092, -0.7001621403253455, -2.1581798297307957, -3.991615254444959, -5.91180950015423, -7.626053969520876, -8.889053184811388, -9.532320413853242, -9.481317409062488, -8.763767917469854, -7.508488489596759, -5.912617955182633, -4.205177425043437, -2.61125196220875, -1.3179349225177728, -0.4422594107635664, -0.015043796485630671, 0.020164051229330876, -0.2061964383982898, -0.5152390584576789, -0.7124071322416257, -0.6232736555008136, -0.12589436003518034, 0.8275376561633645, 2.1992089937885377, 3.8679336755308897, 5.652242453736852, 7.335945767374771, 8.696434557667917, 9.539864899789755, 9.744447199306729, 9.268059275225557, 8.14923326139269, 6.50614484561864, 4.530022605586539, 2.443237853397892, 0.4660451063737795, -1.2089775844635005, -2.439518192953566, -3.155587992441738, -3.362239928013571, -3.130633299286427, -2.5824373572706887, -1.8657598430857087, -1.1285166358894814, -0.4950618829879791, -0.04919565939144384, 0.17500976902810916, 0.19265174073226682, 0.0585863059972772, -0.14928811698775477, -0.3488437850484914, -0.47133210875355475, -0.47580601616525997, -0.3572748032983329, -0.14467056587811697, 0.10697389974591008, 0.32939625640270237, 0.4586263534799581, 0.4499945604726967, 0.2882240203743267, -0.007323084380772976, -0.38409408420316304, -0.7684518615245991, -1.080829201214647, -1.2524030059782445, -1.2427019279276186, -1.0509202284468486, -0.718966787600714, -0.327450728169779, 0.015794994807275704, 0.19674940395606916, 0.11740878516630249, -0.2837013483650398, -1.014249294064283, -2.0199332369638117, -3.1875226692853316, -4.358003774397885, -5.34728438217258, -5.973922260067554, -6.089051851600819, -5.602985410687809, -4.49899674426367, -2.840712416820453, -0.7710381599271959, 1.5040820738697442, 3.755629621790568, 5.754974304319586, 7.297304222435357, 8.231863609036438, 8.499798639439762, 8.123726055477164, 7.195277496554393, 5.864946892810032, 4.330022411179075, 2.7910336179492754, 1.422197274463765, 0.35313513898349214, -0.342963095485755, -0.6575449669051043, -0.639718166896336, -0.38074810045020446, 0.005787263468355112, 0.40634441842614105, 0.7265684029113573, 0.9051079120358025, 0.920357291885856, 0.788102331032247, 0.5529798162959473, 0.27570832195469913, 0.017150231862668352, -0.17498100048253146, -0.2743949163388856, -0.280166479278432, -0.21588429050144461, -0.12006421619690046, -0.03525311307385055, 0.0022020407887656406, -0.02868531486564253, -0.12779380439925228, -0.27487661636471483, -0.435179724056175, -0.5677779571246245, -0.636892086666554, -0.6219514116091401, -0.5236287010831945, -0.36443624688400367, -0.1846022338815076, -0.032623183885377084, 0.04769985403637565, 0.029908657651435237, -0.0857772881384083, -0.2674884887505509, -0.45367960557383585, -0.5656008054060286, -0.5228687793916585, -0.26124026350118257, 0.24857830673043052, 0.9844586772192743, 1.8684133834738101, 2.7706681464969476, 3.52413211931141, 3.9522954031204387, 3.8956184269434013, 3.2391386825659763, 1.940476536390946, 0.052055515317253206, -2.2846600827298515, -4.850717641807807, -7.370975903370357, -9.554553679511198, -11.136743750229886, -11.911666707075025, -11.76366434667308, -10.7010057356326, -8.844435991602374, -6.40504692674789, -3.6596899178279494, -0.922907105050352, 1.5112180639516821, 3.4106446953957703, 4.630963590167528, 5.12825451922522, 4.9626615129157585, 4.280555097465927, 3.283611932885715, 2.1910427341471586, 1.2024656747237885, 0.4665936174207462, 0.059945596285136016, -0.020160724907364033, 0.1541700276393043, 0.4612633440952142, 0.7576475211014035, 0.9112197915967023, 0.8271952230614384, 0.46518501966400033, -0.15281648151140054, -0.9472159180452691, -1.8003908885406161, -2.579574043637774, -3.1618275089936, -3.4611017434307736, -3.4422240435225198, -3.123808281837238, -2.5733582612473938, -1.895230171007073, -1.2053646811408305, -0.6075317086756378, -0.17430165978676324, 0.06565621988405923, 0.13134016471089463, 0.08237657638489526, 0.0037157288053283823, -0.014817735886286347, 0.10051160042443694, 0.39009000401131433, 0.8505845148514949, 1.4362083536398857, 2.0675458071170727, 2.645749800260905, 3.072858154938131, 3.277934568840761, 3.2270613043941503, 2.9275467768327896, 2.428531666494903, 1.815776492395723, 1.1871253664857717, 0.6323338907651878, 0.21793972683845933, -0.02408526768233038, -0.10260993609581777, -0.06062033059547267, 0.03898785307490481, 0.13138791897674534, 0.16916701573935555, 0.1373216660072535, 0.059968256908194545, -0.0027968994463256984, 0.032220623064984306, 0.2505399691445687, 0.7157547517096947, 1.4492676724873945, 2.4163875319157144, 3.5214579396193453, 4.617834692037365, 5.539332959985634, 6.126147511749123, 6.252987204864054, 5.861844099828835, 4.994564946320974, 3.781448623836046, 2.422933078494872, 1.1656848435383782, 0.26555525101729444, -0.06999120575802922, 0.2791654869430073, 1.3211623289569654, 2.938412187438827, 4.901259838485774, 6.905188714259118, 8.619710760317746, 9.742657378600592, 10.056656759458976, 9.470355086878817, 8.03756739312164, 5.949301578466065, 3.503993448073925, 1.0596562218324102, -1.0286129395709724, -2.4778909176912345, -3.1183831963155693, -2.9192093058824127, -1.9959330773780732, -0.5884690884121415, 0.9949749335507696, 2.43378438203906, 3.453472024168923, 3.8877021711920605, 3.7038827973747432, 3.0017352224295233, 1.9945971938938798, 0.9716663640474127, 0.2273231556674798, -0.00024343529240624835, 0.4237166991180121, 1.4983008926379813, 3.082410479744035, 4.921482101595294, 6.696048528445922, 8.086112721038837, 8.834213575277824, 8.795684957996848, 7.970212881683424, 6.508039705718384, 4.67238284865271, 2.7846027124156554, 1.1585831197953573, 0.030443948033653804, -0.5001849416639172, -0.4983674830087633, -0.19156139081096255, 0.06645113988632036, -0.13690322487242512, -1.1916844900898411, -3.381314459042135, -6.8114481809668534, -11.371352220571515, -16.727584450065724, -22.356256240403084, -27.628922017151925, -31.90074245518516, -34.59940030633595, -35.31913758299837, -33.91761524106679, -30.517014387303785, -25.47773663664999, -19.354926017221114, -12.83268446720305, -6.599845893266406, -1.250679724444983, 2.78854805304453, 5.309275587277369, 6.3356541016152566, 6.096721331757359, 4.969014112183833, 3.3996858421050873, 1.8246148131197604, 0.5981588906439028, -0.05835940420241883, -0.07836701128808278, 0.4637257951914248, 1.3841573990224527, 2.438301086315067, 3.386286229182276, 4.038041217892833, 4.280497539043936, 4.093514928027097, 3.552480706559461, 2.789896619034901, 1.957517541047855, 1.1945512537018548, 0.6012890554728781, 0.21811353607904804, 0.027948559043774284, -0.026405264768199817, -0.016815009458916067, -0.0013260578435884244, -0.0004081280607060914, 0.015108125212880548, 0.12128824794759391, 0.4236843897962986, 1.0285851576708973, 2.0095123564174013, 3.3804666018141263, 5.07737811227033, 6.951948689186462, 8.786492703288003, 10.340045395020693, 11.38028702873285, 11.71746178397141, 11.245980548640057, 9.989804833907295, 8.082189131846247, 5.741057618280238, 3.244128138944785, 0.895668303554752, -1.0408662124179242, -2.3833317021251497, -3.0510076662045784, -3.071826003903766, -2.5742674574391344, -1.7554620674300887, -0.8395305859548675, -0.03539778069631104, 0.4991073827779394, 0.6817365545255292, 0.5141439457111117, 0.07089669454536986, -0.524841528890496, -1.130237210898705, -1.6146960522816016, -1.8909164791930777, -1.925205222447603, -1.7366883067350327, -1.3886092071527822, -0.9711034494032835, -0.5728109726606886, -0.2604819026029617, -0.06673955521019442, 0.013968422735965826, 0.018616738371204127, 7.663085147018577e-05, 0.008717929964356623, 0.07525136000195416, 0.19981889048040852, 0.3505431181610085, 0.47143950367094206, 0.499260772440466, 0.3829510718529186, 0.10073069002426159, -0.32842850491560793, -0.8419970072208223, -1.3453745968923232, -1.7315130493866604, -1.9051717100967136, -1.8066889568465487, -1.4289636612431467, -0.8241376101845709, -0.09674838581424797, 0.6208199378877576, 1.1952791467814439, 1.5198771369480564, 1.5419594258165406, 1.285442319210729, 0.84030960455357, 0.3421393619071501, -0.055598611292496394, -0.21862510490037995, -0.07580464282212893, 0.3554783703869907, 0.9612691724767239, 1.5404786818299048, 1.8383532009241494, 1.5961713921540372, 0.6058332380053605, -1.2419373858988734, -3.920470633693751, -7.251326681005766, -10.9191045149141, -14.52778866363744, -17.65048788575761, -19.887991199662046, -20.93959137986588, -20.67990538620829, -19.155082900569923, -16.56860801811694, -13.260236749075858, -9.666914105197117, -6.224635778696583, -3.300661742422938, -1.1465506500733569, 0.13239336043250716, 0.5745133034850542, 0.33641124308867, -0.3428873160117459, -1.1770635542630676, -1.8948741248050278, -2.300669266893728, -2.323209637948033, -2.0399925453143086, -1.576669644238149], 'positive_zeros': ['0.47277622131960460452056500386576', '0.948979629451854245493220394136610', '1.35729216525320073169786058207509', '1.45160080976710607710921842289049', '2.44337210471920643119098780892511', '2.62233453003962693047894731134468', '2.80394686992945066770321098049264', '3.60513770763791984470470695146548', '3.67675125820217519040409566759464', '4.15626497689373217558523284511176', '4.53213403965099846041649382476756', '4.70924464777523734253800048000529', '5.45345918739039282150495541183211', '5.93035627402637886080380259786893', '6.02199072790136231819718268544797', '6.08264685069164416558688674614534', '6.54344262097206123906175491818634', '7.05021905278371807614594404257823', '7.07389507520542995188969958166999', '7.23726401240407476905593892751100', '7.995041841250873261047577050086711', '8.130469170762493019243330713546725', '8.717442245752585103139702473012230', '9.085976549780191183495623436938635', '9.147000163318842966502704820346206', '9.501421087559634505642325944026162', '9.653406022499396712242101462470954', '9.666911919440458896662098094921544', '10.69007959094685656574883304753089', '10.71687778891284670132152218826441', '10.99799773756371992190908133911586', '11.03289941595770332262026320567235', '11.56999984533582764836686790519317', '11.72032515424199548975913977890407', '11.78971366658769306590611256834025', '12.58009097112933608322711711328640', '12.68372106825080849747720957057866', '12.75726244421185054636291333617890', '12.87878789771925781381537447781712', '13.13505930950806929280070297167301'], 'prelabel': '8-3e16-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.030227337229787, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e4-0', 'trace_hash': 1953467583553935495, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47277622131960460452056500386576', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '0.948979629451854245493220394136610', 'prec': 117}, 'z3': {'__RealLiteral__': 0, 'data': '1.35729216525320073169786058207509', 'prec': 113}}
• 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': 409921.6959158787, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 43046721, 'conductor_radical': 3, 'degree': 8, 'dirichlet_coefficients': [1, 9, 0, 130, 180, 0, -700, 477, 0, 1620, 10890, 0, 5480, -6300, 0, 10309, -32832, 0, 32048, 23400, 0, 98010, 24372, 0, 163765, 49320, 0, -91000, -143280, 0, 38708, -87750, 0, -295488, -126000, 0, 911240, 288432, 0, 85860, 731880, 0, 1088840, 1415700, 0, 219348, 1561500, 0, 584961, 1473885, 0, 712400, -5220936, 0, 1960200, -333900, 0, -1289520, 1731960, 0, 620192, 348372, 0, -48319, 986400, 0, -346600, -4268160, 0, -1134000, 8484480, 0, -6290380, 8201160, 0, 4166240, -7623000, 0, -10110616, 1855620, 0, 6586920, 644202, 0, -5909760, 9799560, 0, 5194530, -12042000, 0, -3836000, 3168360, 0, 14053500, 5768640, 0, -4098670, 5264649, 0, 21289450], 'euler11': [1, -10890, 50203733, -320318732250, 1986194375394348, -6242105909858964750, 19064859252007464438653, -80588721892971363502187790, 144209936106499234037676064081], 'euler13': [1, -5480, -27158234, 374330032000, -2551199591830133, 23488654376562544000, -106932189228895544295626, -1353913619322508152020183240, 15502932802662396215269535105521], 'euler17': [1, 32832, 427500356, 16066218476736, 564158142422065734, 6592590769871931611328, 71981580796650152294230724, 2268426374231902717943319188544, 28351092476867700887730107366063041], 'euler19': [1, -32048, 3547821700, -81382636750448, 4764807384912655414, -72745639036528262789072, 2834733258265597773069225700, -22888985917981224495432545716112, 638411683925748518131605316913942641], 'euler2': [1, -9, -49, 1134, -9852, 145152, -802816, -18874368, 268435456], 'euler23': [1, -24372, -2311612066, 95149371189168, -5172734676275436957, 323967000290927857158096, -26798140326966865943039595394, -962001448189590382044046998291756, 134393854047545109686936775588697536481], 'euler29': [1, 143280, -19092997318, 733937916168000, 918231547937772286443, 12660338272383211263912000, -5681278538427859119748571943958, 735433703256999157707187225263003120, 88540901833145211536614766025207452637361], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -38708, -24998494289, 1104278262087652, -96085741293891320816, 30381581695983290734057372, -18922458641710262767576733146769, -806113701475400146164705242505916748, 572964121067545096123347421337293637543041], 'euler37': [1, -911240, 554643085132, -244630239722188760, 87549393525276764783734, -23223207860323159418153625080, 4998477480609361639011452596123948, -779594884607107628289906530325328099880, 81217248802771228597652036390959994837496721], 'euler41': [1, -731880, 62715601538, -61056492590988000, 81416340195765222102483, -11891012880278524264384428000, 2378754299400597645392937849323618, -5406309076595959345271776833254168791080, 1438626275603521989270100382252682485138269921], 'euler43': [1, -1088840, 434479093486, -225886641364316000, 167995333752804683324347, -61400193123273390711057812000, 32101643080770469651640679087765214, -21867625822077903641880006286149706100120, 5459046029871041534743397034507955551606171601], 'euler47': [1, -1561500, 1014040055534, -641770181452710000, 536508680245115269940787, -325135611947677666667804730000, 260270604927486670707345450734848046, -203047200105271806223495121926424480590500, 65877941798660252683780571409941608871644628161], 'euler5': [1, -180, -131365, -1352700, 18184209600, -105679687500, -801788330078125, -85830688476562500, 37252902984619140625], 'euler53': [1, 5220936, 14680769827514, 26667624626206420752, 34239512516067315219951339, 31326755721396195582829930697424, 20258673447599243563427990544204259466, 8463336938084708770029145151417869124360808, 1904251686165483303166544735375573842653419591761], 'euler59': [1, -1731960, -1329825064438, 1121950635256656000, 5086103380773827735924283, 2792144114325097245552705264000, -8236120219648276524305337208150393318, -26695010877351121543745262394725002575577640, 38358032782038398419973086399760468678777161743121], 'euler61': [1, -620192, -5918398022954, -10884659710932992, 28642613360255532163202539, -34207686329061069337974904832, -58455026138493372262252976144728970714, -19250973451996130376171891929899889348974112, 97551820892064552722266841889541788960852432978481], 'euler67': [1, 346600, -12016990578146, 5441248271500000, 109849425893519278692502987, 32977836546523763949194500000, -441410803696869415949716286303154574034, 77161278527601396100643017358066824010342200, 1349256365417755877454657051946796697206085388680241], 'euler7': [1, 700, -94961, -743487500, -739579771328, -612293926212500, -64404741220813889, 390982104858298804900, 459986536544739960976801], 'euler71': [1, -8484480, 47293476367964, -201451744961585447040, 707381642276777629071514086, -1832227826543158367292925342112640, 3912173623160326229839546212115826688284, -6383377865725885358547728452511332070613790080, 6842798698940938981814244812733146152009703886272161], 'euler73': [1, 6290380, 47602415172538, 188098063023211820080, 818171326665306797962526179, 2077994262887644435888338008067760, 5809637428058246241269345359394793478042, 8481192963696115274290954359643153312618925740, 14894985451961941943846586557477384171894488107677281], 'euler79': [1, 10110616, 44597210011234, 194321266458985636864, 989009806128422563565118499, 3731727915153511753584481176165376, 16447010447258271649194823910488652238754, 71605525013919412362685266393240317379004780264, 136006152866792691625201101984747368303641150837104961], 'euler83': [1, -644202, -52162543092091, 1091640661370608518, 2016771017967066782917429788, 29622816649302974065085095842786, -38410684779012174068188980853123772388739, -12872473567103361093965484307544510522734098366, 542233801012015735135407853098133122208235840693558641], 'euler89': [1, 12042000, 225939967485116, 1674742331778843654000, 16115149116594091289608763046, 74076088940629173429430514622966000, 442031434709065045991483988993155245906556, 1042050490641450316607921159811872786331745338000, 3827543948647425430322045212330289877339037312647605281], 'euler97': [1, 4098670, 11066174414449, -638833656515967139250, -7852834506260402499354615068, -51616663513370239469607643848235250, 72244001104587043648054510307133126671281, 2161968552737864046241709412110643854098146466990, 42619520516862344959898006540158454742326868747150111361], 'euler_factors': [[1, -9, -49, 1134, -9852, 145152, -802816, -18874368, 268435456], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -180, -131365, -1352700, 18184209600, -105679687500, -801788330078125, -85830688476562500, 37252902984619140625], [1, 700, -94961, -743487500, -739579771328, -612293926212500, -64404741220813889, 390982104858298804900, 459986536544739960976801], [1, -10890, 50203733, -320318732250, 1986194375394348, -6242105909858964750, 19064859252007464438653, -80588721892971363502187790, 144209936106499234037676064081], [1, -5480, -27158234, 374330032000, -2551199591830133, 23488654376562544000, -106932189228895544295626, -1353913619322508152020183240, 15502932802662396215269535105521], [1, 32832, 427500356, 16066218476736, 564158142422065734, 6592590769871931611328, 71981580796650152294230724, 2268426374231902717943319188544, 28351092476867700887730107366063041], [1, -32048, 3547821700, -81382636750448, 4764807384912655414, -72745639036528262789072, 2834733258265597773069225700, -22888985917981224495432545716112, 638411683925748518131605316913942641], [1, -24372, -2311612066, 95149371189168, -5172734676275436957, 323967000290927857158096, -26798140326966865943039595394, -962001448189590382044046998291756, 134393854047545109686936775588697536481], [1, 143280, -19092997318, 733937916168000, 918231547937772286443, 12660338272383211263912000, -5681278538427859119748571943958, 735433703256999157707187225263003120, 88540901833145211536614766025207452637361], [1, -38708, -24998494289, 1104278262087652, -96085741293891320816, 30381581695983290734057372, -18922458641710262767576733146769, -806113701475400146164705242505916748, 572964121067545096123347421337293637543041], [1, -911240, 554643085132, -244630239722188760, 87549393525276764783734, -23223207860323159418153625080, 4998477480609361639011452596123948, -779594884607107628289906530325328099880, 81217248802771228597652036390959994837496721], [1, -731880, 62715601538, -61056492590988000, 81416340195765222102483, -11891012880278524264384428000, 2378754299400597645392937849323618, -5406309076595959345271776833254168791080, 1438626275603521989270100382252682485138269921], [1, -1088840, 434479093486, -225886641364316000, 167995333752804683324347, -61400193123273390711057812000, 32101643080770469651640679087765214, -21867625822077903641880006286149706100120, 5459046029871041534743397034507955551606171601], [1, -1561500, 1014040055534, -641770181452710000, 536508680245115269940787, -325135611947677666667804730000, 260270604927486670707345450734848046, -203047200105271806223495121926424480590500, 65877941798660252683780571409941608871644628161], [1, 5220936, 14680769827514, 26667624626206420752, 34239512516067315219951339, 31326755721396195582829930697424, 20258673447599243563427990544204259466, 8463336938084708770029145151417869124360808, 1904251686165483303166544735375573842653419591761], [1, -1731960, -1329825064438, 1121950635256656000, 5086103380773827735924283, 2792144114325097245552705264000, -8236120219648276524305337208150393318, -26695010877351121543745262394725002575577640, 38358032782038398419973086399760468678777161743121], [1, -620192, -5918398022954, -10884659710932992, 28642613360255532163202539, -34207686329061069337974904832, -58455026138493372262252976144728970714, -19250973451996130376171891929899889348974112, 97551820892064552722266841889541788960852432978481], [1, 346600, -12016990578146, 5441248271500000, 109849425893519278692502987, 32977836546523763949194500000, -441410803696869415949716286303154574034, 77161278527601396100643017358066824010342200, 1349256365417755877454657051946796697206085388680241], [1, -8484480, 47293476367964, -201451744961585447040, 707381642276777629071514086, -1832227826543158367292925342112640, 3912173623160326229839546212115826688284, -6383377865725885358547728452511332070613790080, 6842798698940938981814244812733146152009703886272161], [1, 6290380, 47602415172538, 188098063023211820080, 818171326665306797962526179, 2077994262887644435888338008067760, 5809637428058246241269345359394793478042, 8481192963696115274290954359643153312618925740, 14894985451961941943846586557477384171894488107677281], [1, 10110616, 44597210011234, 194321266458985636864, 989009806128422563565118499, 3731727915153511753584481176165376, 16447010447258271649194823910488652238754, 71605525013919412362685266393240317379004780264, 136006152866792691625201101984747368303641150837104961], [1, -644202, -52162543092091, 1091640661370608518, 2016771017967066782917429788, 29622816649302974065085095842786, -38410684779012174068188980853123772388739, -12872473567103361093965484307544510522734098366, 542233801012015735135407853098133122208235840693558641], [1, 12042000, 225939967485116, 1674742331778843654000, 16115149116594091289608763046, 74076088940629173429430514622966000, 442031434709065045991483988993155245906556, 1042050490641450316607921159811872786331745338000, 3827543948647425430322045212330289877339037312647605281], [1, 4098670, 11066174414449, -638833656515967139250, -7852834506260402499354615068, -51616663513370239469607643848235250, 72244001104587043648054510307133126671281, 2161968552737864046241709412110643854098146466990, 42619520516862344959898006540158454742326868747150111361]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/8/c/h'], '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': '8-3e16-1.1-c7e4-0-4', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7, 7, 7, 7], 'order_of_vanishing': 0, 'prelabel': '8-3e16-1.1-c7e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.030227337229787, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e4-0', 'trace_hash': 1953467583553935495, 'z1': {'__RealLiteral__': 0, 'data': '0.47277622131960460452056500386576', 'prec': 113}}
• lfunc_instances •

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

  
  {'Lhash': '599315060729431002716903192491,1202974596879005758274388005133,1720572227968293037989134371025,1840122637793055862936423343928', 'Lhash_array': ['599315060729431002716903192491', '1202974596879005758274388005133', '1720572227968293037989134371025', '1840122637793055862936423343928'], 'factors': ['2-3e4-9.4-c7-0-5', '2-3e4-9.7-c7-0-12', '2-3e4-9.4-c7-0-18', '2-3e4-9.7-c7-0-19'], 'label': '8-3e16-1.1-c7e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/8/c/h'}