Lfunction data - 8-540e4-1.1-c1e4-0-2

Formats: - HTML - YAML - JSON - 2025-01-28T12:49:58.575901

• 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': '447890473375835721351846516642,1408883257627542509270045667337,2132463474780117645245509475996,2586798939007558672282069011331', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 345.6873340670527, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 0, 0, 0, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '540.1', 'coefficient_field': '1.1.1.1', 'conductor': 85030560000, 'conductor_radical': 30, 'degree': 8, 'euler_factors': [[1], [1], [1, 0, 0, 0, 25], [1, 0, -26, 0, 267, 0, -1274, 0, 2401], [1, 0, 24, 0, 386, 0, 2904, 0, 14641], [1, 0, -34, 0, 627, 0, -5746, 0, 28561], [1, 0, 12, 0, 614, 0, 3468, 0, 83521], [1, 12, 130, 792, 4299, 15048, 46930, 82308, 130321], [1, 0, -72, 0, 2354, 0, -38088, 0, 279841], [1, 0, -64, 0, 2706, 0, -53824, 0, 707281], [1, 8, 148, 776, 7270, 24056, 142228, 238328, 923521], [1, 0, -146, 0, 8067, 0, -199874, 0, 1874161], [1, 0, 144, 0, 8546, 0, 242064, 0, 2825761], [1, 0, 28, 0, 3894, 0, 51772, 0, 3418801], [1, 0, -108, 0, 7334, 0, -238572, 0, 4879681], [1, 0, -32, 0, 5874, 0, -89888, 0, 7890481], [1, 0, 156, 0, 13046, 0, 543036, 0, 12117361], [1, 4, 250, 736, 23059, 44896, 930250, 907924, 13845841], [1, 0, -26, 0, 9147, 0, -116714, 0, 20151121], [1, 0, 104, 0, 12786, 0, 524264, 0, 25411681], [1, 0, 46, 0, 11187, 0, 245134, 0, 28398241], [1, -12, 370, -2952, 46059, -233208, 2309170, -5916468, 38950081], [1, 0, 168, 0, 20834, 0, 1157352, 0, 47458321], [1, 0, 36, 0, 16166, 0, 285156, 0, 62742241], [1, 0, -386, 0, 56067, 0, -3631874, 0, 88529281], [1, 0, 324, 0, 46646, 0, 3305124, 0, 104060401], [1, 0, 166, 0, 28107, 0, 1761094, 0, 112550881], [1, 0, -248, 0, 38274, 0, -2839352, 0, 131079601], [1, 64, 1972, 37312, 471670, 4067008, 23429332, 82881856, 141158161], [1, 0, -272, 0, 44034, 0, -3473168, 0, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 0, 0, 25], 1]], [[[1, 0, -13, 0, 49], 2]], [[[1, 0, 12, 0, 121], 2]], [[[1, 0, -17, 0, 169], 2]], [[[1, 0, 6, 0, 289], 2]], [[[1, 3, 19], 4]], [[[1, 0, -36, 0, 529], 2]], [[[1, 0, -32, 0, 841], 2]], [[[1, 2, 31], 4]], [[[1, 0, -73, 0, 1369], 2]], [[[1, 0, 72, 0, 1681], 2]], [[[1, 0, 14, 0, 1849], 2]], [[[1, 0, -54, 0, 2209], 2]], [[[1, 0, -16, 0, 2809], 2]], [[[1, 0, 78, 0, 3481], 2]], [[[1, 1, 61], 4]], [[[1, 0, -13, 0, 4489], 2]], [[[1, 0, 52, 0, 5041], 2]], [[[1, 0, 23, 0, 5329], 2]], [[[1, -3, 79], 4]], [[[1, 0, 84, 0, 6889], 2]], [[[1, 0, 18, 0, 7921], 2]], [[[1, 0, -193, 0, 9409], 2]], [[[1, 0, 162, 0, 10201], 2]], [[[1, 0, 83, 0, 10609], 2]], [[[1, 0, -124, 0, 11449], 2]], [[[1, 16, 109], 4]], [[[1, 0, -136, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '8-540e4-1.1-c1e4-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, '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': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/540/2/d/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [1.135720732484823, 1.1260175116340034, 1.0995809098161171, 1.0558870122569612, 0.9944171053503267, 0.914757830849186, 0.8168238159109479, 0.7006868868526386, 0.5665317384020798, 0.4146675967895205, 0.2455626499125165, 0.0599736073115321, -0.14099436008586927, -0.35581267536701555, -0.5823716160728644, -0.8180204109521038, -1.0595764011782713, -1.3032731958430557, -1.544635008005183, -1.7786162905790448, -1.9996933670843362, -2.2019102221645728, -2.3789190691013546, -2.5242385924251804, -2.6314540169550362, -2.694413088499089, -2.707503616651116, -2.665940799644832, -2.566010034013502, -2.4053540211845124, -2.183396045711118, -1.901453930045291, -1.562841721137467, -1.1730408595322297, -0.7399790628487245, -0.2737344517517386, 0.21371848511906572, 0.7087006690798242, 1.1960159104430284, 1.6597074290010112, 2.0836953609936453, 2.45237020246765, 2.7512814898196605, 2.967996699016277, 3.092769398742642, 3.1191647651177257, 3.04477923905168, 2.871502006177104, 2.6055917115548843, 2.257705343737089, 1.8429110648482498, 1.3798418658283278, 0.8898208765886101, 0.39598523555548115, -0.07769572233766786, -0.5080073099111496, -0.8738287130273337, -1.1573398332285516, -1.3452479796597179, -1.4297992753264595, -1.4093466541366448, -1.2886508528403886, -1.078975727138307, -0.7973205030746159, -0.4653446554048725, -0.10808042472440471, 0.24764185968837552, 0.5753313296950674, 0.8508014833707296, 1.0540254925654884, 1.1709807624113076, 1.194953407079457, 1.1272484142931536, 0.9774537165540417, 0.7632401366542976, 0.5089411076096468, 0.24370113579351096, -0.000726099546388527, -0.1926302797934875, -0.3034470327244417, -0.3105362645064575, -0.1996771995548851, 0.03275094613225238, 0.3786238631078722, 0.8178350074660429, 1.3189298393573514, 1.8408820674106983, 2.3359738193628403, 2.753201751851776, 3.0423283662435923, 3.1588429244375194, 3.0678254984787716, 2.7472965820818724, 2.191250426346772, 1.4122235587054706, 0.44065430906292585, -0.6766100868048756, -1.8787006149345968, -3.094618389799686, -4.248996215675387, -5.267644916134148, -6.083373502050655, -6.642662789516315, -6.909751640888206, -6.869359295451873, -6.528712700689912, -5.918906223088993, -5.090962057588535, -4.111281384550014, -3.0567371370210425, -2.0089609654289675, -1.0459621439531033, -0.23543797759219795, 0.3706780426841709, 0.7408005036063378, 0.8661772765852707, 0.7608100328351295, 0.45951668008514823, 0.014136544913354763, -0.5127630828181152, -1.0545669614118762, -1.5474907605401713, -1.9377826126814153, -2.1869456878911153, -2.274872832056945, -2.2014205805264626, -1.9864362466312024, -1.665326873055475, -1.2835422063944926, -0.8905585066822999, -0.5333994569042989, -0.24914045204264207, -0.05964320330322753, 0.03157208778072034, 0.040285118699606506, -5.753693994742991e-05, -0.04271465358642987, -0.03401070558043975, 0.07884785108651582, 0.339729634218684, 0.7762337367715832, 1.3938798984035037, 2.1731686398448473, 3.0696955414362797, 4.016989757191598, 4.932743442795606, 5.729620848149913, 6.324426460904365, 6.647350647574626, 6.65197618006564, 6.325935597937058, 5.691457303632018, 4.803787412329993, 3.7480526523816646, 2.633550962906124, 1.5790586587008957, 0.6994587349005665, 0.09357834917246516, -0.16715884467557454, -0.048829353003580114, 0.4404077639757899, 1.2505765606349086, 2.2955983123660317, 3.4625705020523894, 4.623838191747742, 5.651816007791751, 6.436932789439052, 6.897879080412647, 6.989115439788866, 6.706761513734734, 6.0922879864231065, 5.2214680719863376, 4.192714876084319, 3.1155866401566157, 2.0985405419276217, 1.2309897385655302, 0.5721690707063426, 0.14545770257499643, -0.0629465681796443, -0.10138994967155172, -0.04365258448221987, 0.023806930343623463, 0.01621204366912217, -0.13565509601830142, -0.4735994769120546, -1.004174128238883, -1.6972491182970926, -2.4895797872302667, -3.292759182985867, -4.0061270576561645, -4.5353083555279605, -4.805136194368547, -4.770536714344327, -4.425932617254717, -3.81191619198407, -3.007099233842083, -2.117295072823891, -1.2628006978135737, -0.5629703064998446, -0.1164305945942898, 0.013209722817138171, -0.19346817170129255, -0.7081657930497404, -1.4582596939982122, -2.3365930725911785, -3.2165145951674696, -3.972128748345668, -4.495267278887741, -4.709673106877722, -4.582578888636844, -4.132435522224308, -3.421544651027889, -2.5450908401667056, -1.6176359718712312, -0.756323864319616, -0.06017582294230933, 0.40405022685305775, 0.6105008791607717, 0.5776915130502807, 0.36274004789631925, 0.049026111147475765, -0.26968520865413187, -0.5070550436707965, -0.6019371421903498, -0.5306589872280395, -0.31274712710986513, -0.00889888571881076, 0.289189038071104, 0.47491437932207975, 0.4467832943783959, 0.12987681063016468, -0.5077000560728195, -1.4441258966171415, -2.600782718849042, -3.850621526445591, -5.034610346146508, -5.9825177497459086, -6.538491844947235, -6.591381080335641, -6.090647454706545, -5.055363622747732, -3.577037393004867, -1.8133104782488993, 0.03719107110364061, 1.7615629381071363, 3.1607702494425833, 4.080103670924368, 4.430152062598477, 4.196999710990716, 3.443923058035136, 2.3035553750837208, 0.9525154602840709, -0.4157546782393853, -1.6187085159909382, -2.5129585044569764, -3.0134107703060704, -3.1006805276232385, -2.819900951132246, -2.2710666944013793, -1.5840999359994072, -0.8935457159251804, -0.31547470912286224, 0.07243839178889601, 0.24375916116796106, 0.22364371494278354, 0.07971248311298706, -0.09478511772120582, -0.20408888952413803, -0.17268181420318696, 0.03613576563545907, 0.40945483152704487, 0.8842710060117006, 1.3568951532487887, 1.7013790542012737, 1.7960517256987945, 1.5472716607795511, 0.9093721828054149, -0.10120641288073791, -1.402131105238538, -2.857377704819043, -4.2960649364853545, -5.538075002302463, -6.4276119234261495, -6.856662369111789, -6.7800920851554105, -6.224340551846839, -5.288303346468226, -4.119292416636131, -2.8863968136415843, -1.7539835375016182, -0.8558899912891627, -0.2716221792878015, -0.01706209223725168, -0.04730570401902369, -0.27076585635362965, -0.5720653247616275, -0.8377833559541875, -0.9810388596146722, -0.9611848827792587, -0.7886993453854867, -0.5185798497215542, -0.23402872193712576, -0.02135475628957483, 0.059985860631339795, 0.0015671526212202701, -0.1386068507635899, -0.23401556099054477, -0.10400771892888838, 0.45895954110337317, 1.652236678336145, 3.6197241460116247, 6.416144999444591, 9.981718643311892, 14.132438602842933, 18.57637917134266, 22.942978550673907, 26.822941082584116, 29.822952064008014, 31.638824222374037, 32.08362001752053, 31.10586668819084, 28.803171493273442, 25.426833495728264, 21.323736832113116, 16.884489646508566, 12.497852590693869, 8.506307002767032, 5.158270431702574, 2.5891403685323424, 0.8207290341627158, -0.22618363869642144, -0.6986076646945144, -0.7744930254375687, -0.6294503678775502, -0.4095410349489196, -0.21133413667027845, -0.07963760931654536, -0.017003858020695522, -0.00036260039288048913, -0.0005852638112917951, 0.0006863724318630525, 0.0018375192807726535, -0.018137822196377253, -0.08957220676323731, -0.23567489830269336, -0.45429937839393225, -0.7047410095934492, -0.9033401241116202, -0.9297269205373188, -0.6457427892536912, 0.07162682358016502, 1.3000750259404286, 3.0449080498245222, 5.219109359589144, 7.639685478878654, 10.046848156024145, 12.135232562222388, 13.599129610069816, 14.19420643450063, 13.775469702853151, 12.3232449230578, 9.958684233425315, 6.942090329073733, 3.6226579942721924, 0.3854326593066083, -2.4038243684414256, -4.458297909306202, -5.614924947738427, -5.851458933464893, -5.283511200877178, -4.1422508408158905, -2.718756398717674, -1.3072399701646447, -0.15364618017709564, 0.5871618726850492, 0.8741097802133392, 0.7754719292266055, 0.4442795015571892, 0.07759042972515952, -0.13430068818024676, -0.05223212328361081, 0.3800955629916065, 1.1238136864998025, 2.056122617062791, 2.998308118498918, 3.756452253532366, 4.171580653772543, 4.153202304675685, 3.697508240329048, 2.8908076383543078, 1.8950836823030448, 0.9059657618418279, 0.1096536577274267, -0.35640636749389937, -0.4348949355451185, -0.1602486937912784, 0.35116020808294, 0.9278315776761372, 1.3846192030981128, 1.5665285366350634, 1.3834665158126689, 0.8323616876353845, 0.0008275755305318681, -0.9559530580800253, -1.8499296520423707, -2.5020536517253102, -2.787899620517862, -2.6652925085494763, -2.182647470581782, -1.4704593215104045, -0.714895338506253, -0.1109087866753345, 0.18196041038040459, 0.07560394428042749, -0.4244876876600115, -1.2202323174346044, -2.1421693762509713, -2.9864628462054044, -3.5647388618849885, -3.7443311605505927, -3.4750301633392087, -2.8012563903842405, -1.8551142827700002, -0.8182331941785147, 0.12043142291605159, 0.8058131024086931, 1.1532249039113045, 1.1644757653842028, 0.9198905804035686, 0.5525887334507885, 0.20873724087677986, -0.0006438618611328776, -0.03673569150428674, 0.047577603032248415, 0.11125315453606309, -0.04576366375970178, -0.635186631784996, -1.8240316401046368, -3.6826279696220534, -6.151583481229357, -9.031465448902921, -12.00271161271843, -14.688193399862723, -16.714346959689063, -17.772530411427898, -17.682247560530087, -16.450614719464777, -14.254665465054867, -11.404276888193058, -8.29226622420955, -5.329238752450997, -2.857873513319961, -1.0961602832124868, -0.1073568370786614, 0.20086824982144919, 0.03760344680832591, -0.3265197341835909, -0.6225786297035332, -0.6501585861463156, -0.31805299110635865, 0.34671574848990067, 1.2121244095856143, 2.0744099779643257, 2.7216229273153205, 2.9893473952888003, 2.799457051918386, 2.177639210871177, 1.2495888347426598, 0.20955325994543328, -0.7282612141982807, -1.3849745542528782, -1.6540681069712349, -1.5223324657634463, -1.0705861047726346, -0.44929808095840673, 0.1675364522571112, 0.6267078260908628, 0.834164122286344, 0.7812891348280079, 0.5405436506988802, 0.24066768478369122, 0.02920653185190941, 0.02833187246745855, 0.29606172483483206, 0.8069647685637957, 1.4551428948898135, 2.0834541052879225, 2.5258050839948627, 2.651790511221088, 2.4079127444817217, 1.8461817171976755, 1.110708735278191, 0.40540603374221246, -0.05177318838439317, -0.08593252230130359, 0.3822387175303504, 1.311036681867751, 2.539030212728052, 3.8157767106837905, 4.860454797087654, 5.427565847234058, 5.368583211334207, 4.6782487390786445, 3.4980674079937173, 2.087856768363671, 0.7706617164762479, -0.1442541066059289, -0.4390315988425011, -0.04239472489986865, 0.944249469772415, 2.262466968410892, 3.553636028921471, 4.43436251446907, 4.582822744529685, 3.8258256267478044, 2.175880102126073, -0.16742870167680993, -2.8496603837505234, -5.434730604871939, -7.498407283098614, -8.708450494537656, -8.89040309002023, -8.072618244866254, -6.457698543660085, -4.369142578932504, -2.184481418724787, -0.2567419881098447, 1.1612305060968653, 1.9528492631224854, 2.1432748140918285, 1.8781461433742705, 1.3639031629321667, 0.8063160188379359, 0.36064690647595277, 0.09984389251105313, 0.007323659441609845, 0.0009782952561555038, -0.025088269432593766, -0.1542184273270525, -0.41033236227507763, -0.741085079583774, -1.026604699445011, -1.116022204535283, -0.8734592018938, -0.22327332751660206, 0.814705434257886, 2.1143016755998256, 3.4674760683700523, 4.62662305828645, 5.361522745168136, 5.527020540078428, 5.095952818845743, 4.165433626295936, 2.940381992735085, 1.6920045798047556, 0.6826765100452745, 0.1030082368380105, 0.02854026247546422, 0.40375989352613395, 1.0610872489368484, 1.7682406758345188, 2.292680908369698, 2.472327801876873, 2.255303088894104, 1.7091252977203997, 1.000606305140329, 0.3444828623125603, -0.07491494831362014, -0.16949082089629888, 0.009243492573390464, 0.2613234741321819, 0.2757460074250836, -0.29840616814736437, -1.761548018787199, -4.271195757753892, -7.781377317975217, -12.020893565666077, -16.520796815150334, -20.709177769357723, -24.009493678793888, -25.93804693750465, -26.204123449293185, -24.804263003822676, -21.982534050733907, -18.16646148185643, -13.894054075199398, -9.727662121959222, -6.121651988839396, -3.353224219364456, -1.5038573792987964, -0.4792271974941873, -0.06076411610134054, 0.017717066472842283, -0.004860459463496496, 0.028604233121881387, 0.1727049348788226, 0.3913413192079617, 0.5950200857041696, 0.6946518185980868, 0.6433942107726737, 0.4572745294587621, 0.2125677653840658, 0.01801336467529956, -0.03522026989703841, 0.08182944922946608, 0.30804440433528574, 0.4922697840242971, 0.42539414374438456, -0.10383899381146199, -1.2413415721341192, -3.006619310591093, -5.265135142756478, -7.733068001247047, -10.021666461038745, -11.732072593367658, -12.537601525928926, -12.251589672723732, -10.882038009530177, -8.661665725400024, -5.975199287894927, -3.272000934791669, -0.9774684445721976, 0.5933874266940525, 1.311742575702841, 1.2502273457750765, 0.6499572264533142, -0.15218818740896242, -0.8144956929465592, -1.0753597429769393, -0.8162162090910385, -0.08594827404288106, 0.9306201362619967, 1.971033402341032, 2.769978143415746, 3.1419218809870118, 3.0239598329537767, 2.480385031419988, 1.6787866442147994, 0.840831662284033, 0.16438457242307083, -0.23213889822188308, -0.33533332466498544, -0.22961972423430377, -0.057107582952563136, 0.043458567363108026, -0.0026439182653177355, -0.16601207560134146, -0.3106435664676748, -0.22918628744654482, 0.28975241905663385, 1.378523565929938, 3.024518813757159, 5.033640207713868, 7.0383987794378156, 8.57580705920241, 9.184929168637815, 8.508670405756359, 6.394395494030081, 2.975813863181754, -1.3513726634630063, -5.997186841427283, -10.282992814238831, -13.589551076088503, -15.474674237791186, -15.746458288409576, -14.500348306160292, -12.11059898257648, -9.10029676375672, -6.020319408689379, -3.345952953116494, -1.3903665137423713, -0.2511272020282744, 0.16857930929679316, 0.09851810400083297, -0.18112452048653177, -0.4288435596493763, -0.5016548333884905, -0.3763165486411857, -0.1317117403394145, 0.10161170010994942, 0.2022547970117714, 0.10908404166241664, -0.15122394515592802, -0.47473035605412583, -0.7205735470918406, -0.766737191198751, -0.5595033703868885, -0.14365680418489413, 0.33732192961108454, 0.6779464477704774, 0.6880663278522373, 0.2516325281522941, -0.6312910587168893, -1.8223858341440449, -3.056276963054053, -4.020222036717374, -4.439126506980141, -4.150030223518915, -3.1514223313711343, -1.618564634629317, 0.13137300768831686, 1.7193160365546294, 2.8225228610030073, 3.2422790805957113, 2.9452402256418733, 2.079070056621069, 0.9480336306924529, -0.10690114236031888, -0.8076779852741931, -1.0094931304788184, -0.7413956396156388, -0.20690044373095487, 0.28349636263484307, 0.412621802023176, -0.04412402974924256, -1.1431062505531264, -2.737864440360725, -4.505147356798939, -6.046040459016678, -6.986102423358728, -7.068915512905128, -6.237729321693817, -4.683895918407522, -2.77270981768082, -0.9432202994750442, 0.39929540138611475, 0.9895904547692701, 0.7861993029261111, -0.02077211941716048, -1.0647701206945117, -1.9105244156883339, -2.1764121721886056, -1.640960597480323, -0.31175398414162947, 1.5679042348325376, 3.589546015296717, 5.282176004285482, 6.232891752036534, 6.208587943192211, 5.2042482260250384, 3.43525797974781, 1.2843971169020887, -0.7973085610444247, -2.412113984612259, -3.3020888486705773, -3.3982904588922485, -2.8267548430922114, -1.8442748301622012, -0.7557720586152094, 0.1673146343558378, 0.755796418063811, 0.9685812809302281, 0.8748824321397132, 0.6109750791039856, 0.32392191277090965, 0.11523959632578516, 0.017209960760921704, 0.00038095742523779313, 0.005393733443233947, -0.013892388356252233, -0.05593937619363525, -0.06168149484903975, 0.06223723519359659, 0.39464533046080214, 0.9419948100510979, 1.5911844757346798, 2.101213622931612, 2.139877449866468, 1.3571847950659015, -0.5111764848310378, -3.52901368856578, -7.505129125626773, -11.988350070469416, -16.324819877090057, -19.801765561087738, -21.797466020456774, -21.912718723471432, -20.083746766198477, -16.65463480349093, -12.267398514893564, -7.717744637097333, -3.798578530120905, -1.134720421515319, -0.029163452940541058, -0.4188382885410969, -1.9170409574264489, -3.931083712697091, -5.82251536295351, -7.061542632568694, -7.347083264157847, -6.6690437157505205, -5.263512769661081, -3.5178589030117204, -1.851251806159462, -0.5913323265821144, 0.10797284500682387, 0.28253820637331223, 0.1198802911904967, -0.12381554871581218, -0.2251290882989689, -0.0682807152556919, 0.3200651894349665, 0.7888116131014187, 1.1280565405081735, 1.1493906379974181, 0.760798114836811, 0.014952031646353591, -0.9054633011558596, -1.7410225472348357, -2.2345105616641443, -2.2234451547764955, -1.6917076724072004, -0.7752821990582833, 0.271297636416277, 1.1480993952959917, 1.6116430968723936, 1.5457065499151053, 0.9937613221131089, 0.14880070843454762, -0.7159166162033146, -1.3382532372566303, -1.5512153793838965, -1.337747144086895, -0.8360929790611618, -0.29136811904774423, 0.0305431819905255, -0.06178905652911687, -0.6149144982324702, -1.5013093119152454, -2.444778118977998, -3.116787613410058, -3.2360913457104945, -2.652474330199054, -1.406387493892559, 0.2544072696486999, 1.9542781999684466, 3.29483938847291, 3.965090538450988, 3.8386784101941167, 3.001226182041886, 1.7187700042766756, 0.36037704401498566, -0.7158678712471409, -1.277461219199055, -1.2755856126390517, -0.8474746151274108, -0.2594130080325453, 0.20701326342553764, 0.3682793411654077, 0.22231056042340233, -0.02326072133647685, -0.002426975335992555, 0.7000472287838891, 2.410939887724431, 5.23994119367393, 9.008930541545427, 13.252098040937566, 17.298691810398164, 20.453773405877453, 22.147696915804183, 22.05571983376811, 20.188148934519305, 16.928774289789686, 12.888454124373204, 8.748775180193526, 5.119700158250742, 2.417008043134062, 0.7773062029321881, 0.07544377057806582, 0.006954045859882063, 0.20725983136941706, 0.3715891463016899, 0.3336344624763251, 0.08959036159282746, -0.2371143203170329, -0.47704976303971, -0.5001091935595754, -0.28013924827102143, 0.083398179360645, 0.40320571533355487, 0.47544759562920347, 0.1625305698168697, -0.5378551768660083, -1.4767584536822038, -2.388566684584984, -2.9681629131301164, -2.979405740969107, -2.3357662379966144, -1.1372374138031638, 0.3421074063244401, 1.7264259429051882, 2.655603591838181, 2.8886486387516164, 2.377672421194024, 1.2930739085108707, -0.036983163154814626, -1.2254685862235948, -1.939359802112359, -2.005447558355266, -1.4552951573964952, -0.5051076564065302, 0.5151065828763173, 1.2717171363601807, 1.536754568456393, 1.251958306156747, 0.5405695860811355, -0.34024599971447544, -1.0993595337058164, -1.5097075720614428, -1.4822302342267581, -1.0956560964614086, -0.5501296717076021, -0.08193534278538898, 0.13194343056846006, 0.052162301950749945, -0.2000786605115073, -0.38845636765163644, -0.2599167936649198, 0.32857089162927056, 1.3085158770834722, 2.3577593484859243, 2.9375256226763042, 2.4258381807827334, 0.2920800565031867, -3.730602251325123, -9.510433393754276, -16.48237453114172, -23.73708704656138, -30.178274204888904, -34.74916178783151, -36.726665907762964, -35.83632355025628, -32.28072166093641, -26.704078815055155, -20.076201400520258, -13.418649918679177, -7.596970904805517, -3.1768490855228917, -0.3419976278440477, 1.0572360868002277, 1.3889387949029919, 1.109403153455734, 0.6375770370443327, 0.24409110673011483, 0.032845700486353345, -0.020523765858419977, -0.0033016190242331762, 0.0021065385278067382, -0.0357145255351563, -0.0909104391277358, -0.10973757423292506, -0.055371545100790724, 0.055435112436456664, 0.14359013527205067, 0.09939619691739286, -0.1614279414969975, -0.6379657005711314, -1.2023507143049903, -1.6087529205858315, -1.5549112102242635, -0.772726422463973, 0.8662633960262266, 3.257893340185689, 6.059614375521571, 8.746755080977382, 10.728264339100637, 11.521359119641822, 10.884115862216353, 8.88866214822845, 5.931376516321172, 2.6579905883997776, -0.22944285715827184, -2.1516781655784674, -2.7969780050464252, -2.208770597584348, -0.7537055977088126, 0.9978617086011474, 2.438124269192093, 3.1063477949167564, 2.8139054389374025, 1.6773404697590577, 0.06751098338686393, -1.5201037566219227, -2.6324505728247365, -2.9898995557228476, -2.5621005844305658, -1.5679146255462495, -0.3699831761021034, 0.6541330390332429, 1.2329578714865508, 1.2899999204661476, 0.9448060027970555, 0.43989373134547677, 0.03174170984535362, -0.12416718059775075, -0.056032823047004215, 0.022047901699025037, -0.21725180798811186, -1.0919091899972004, -2.777615591855642, -5.2058172457757035, -8.034486146584447, -10.737885795597414, -12.73166752906145, -13.516594192344446, -12.828655795448542, -10.76083864190327, -7.709843549225736, -4.2681888191604616, -1.0816064700426644, 1.322728917840798, 2.6663377105050086, 2.9564362284043364, 2.4521166499807774, 1.5652716381999212, 0.6979013995935152, 0.13253841075898495, -0.024287032470628852, 0.15212590208715845, 0.46017865362845817, 0.6779282855947038, 0.6710699371818741, 0.46447772770660517, 0.19445970059732795], 'positive_zeros': ['0.35332328426712925442445266470562', '1.11141292196279116917135978452872', '1.68221706706578788417056345829750', '2.04062455265025563980423584218811', '2.40614944817258005486158744738130', '2.55891320612509104968977451474841', '2.98148059706059539763732947130663', '3.51083706802360544452006946189403', '3.68838905701190899944937263707096', '4.14142567463601568673380914961975', '4.21871151075220772968317566885985', '4.29503185762542678734933904785618', '4.91354576492017427015098996358248', '4.97329274697948220646736498621456', '5.54945835612603859208996413079124', '5.64314905237052058772885131641755', '5.69349141421041870368883655237244', '6.23697560124964681076913275600469', '6.25582017012099008313409589400852', '6.72201669085319595487951365472905', '6.87961662612998868504155277168362', '7.06336344421532421814038642601409', '7.19536141654616463916172647648529', '7.59311716056863857875950867392109', '7.86528528412522724079353843836079', '8.180086797143006838135397086890998', '8.295158528276832617736283795132208', '8.402305423639278671659480762567621', '8.653527773618160145538112893086930', '9.133847116070031301149343471843201', '9.138971882917032325124576494721142', '9.442163148021534276849440910948368', '9.500423991163577270739730049516686', '9.602449061266310040709086096207379', '10.30376404642834083141339154613325', '10.56641163195596602543201659096798', '10.58032583879914652172345147997861', '10.61786359226985500153371548653828', '10.66394558388108740158397214785120', '10.93517731343346390211662927955659'], 'prelabel': '8-540e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0765167249866163, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1765298151140775927, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35332328426712925442445266471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11141292196279116917135978453', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.68221706706578788417056345830', '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': 345.6873340670527, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 85030560000, 'conductor_radical': 30, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 24, 0, 386, 0, 2904, 0, 14641], 'euler13': [1, 0, -34, 0, 627, 0, -5746, 0, 28561], 'euler17': [1, 0, 12, 0, 614, 0, 3468, 0, 83521], 'euler19': [1, 12, 130, 792, 4299, 15048, 46930, 82308, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -72, 0, 2354, 0, -38088, 0, 279841], 'euler29': [1, 0, -64, 0, 2706, 0, -53824, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 8, 148, 776, 7270, 24056, 142228, 238328, 923521], 'euler37': [1, 0, -146, 0, 8067, 0, -199874, 0, 1874161], 'euler41': [1, 0, 144, 0, 8546, 0, 242064, 0, 2825761], 'euler43': [1, 0, 28, 0, 3894, 0, 51772, 0, 3418801], 'euler47': [1, 0, -108, 0, 7334, 0, -238572, 0, 4879681], 'euler5': [1, 0, 0, 0, 25, 0, 0, 0, 0], 'euler53': [1, 0, -32, 0, 5874, 0, -89888, 0, 7890481], 'euler59': [1, 0, 156, 0, 13046, 0, 543036, 0, 12117361], 'euler61': [1, 4, 250, 736, 23059, 44896, 930250, 907924, 13845841], 'euler67': [1, 0, -26, 0, 9147, 0, -116714, 0, 20151121], 'euler7': [1, 0, -26, 0, 267, 0, -1274, 0, 2401], 'euler71': [1, 0, 104, 0, 12786, 0, 524264, 0, 25411681], 'euler73': [1, 0, 46, 0, 11187, 0, 245134, 0, 28398241], 'euler79': [1, -12, 370, -2952, 46059, -233208, 2309170, -5916468, 38950081], 'euler83': [1, 0, 168, 0, 20834, 0, 1157352, 0, 47458321], 'euler89': [1, 0, 36, 0, 16166, 0, 285156, 0, 62742241], 'euler97': [1, 0, -386, 0, 56067, 0, -3631874, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 25, 0, 0, 0, 0], [1, 0, -26, 0, 267, 0, -1274, 0, 2401], [1, 0, 24, 0, 386, 0, 2904, 0, 14641], [1, 0, -34, 0, 627, 0, -5746, 0, 28561], [1, 0, 12, 0, 614, 0, 3468, 0, 83521], [1, 12, 130, 792, 4299, 15048, 46930, 82308, 130321], [1, 0, -72, 0, 2354, 0, -38088, 0, 279841], [1, 0, -64, 0, 2706, 0, -53824, 0, 707281], [1, 8, 148, 776, 7270, 24056, 142228, 238328, 923521], [1, 0, -146, 0, 8067, 0, -199874, 0, 1874161], [1, 0, 144, 0, 8546, 0, 242064, 0, 2825761], [1, 0, 28, 0, 3894, 0, 51772, 0, 3418801], [1, 0, -108, 0, 7334, 0, -238572, 0, 4879681], [1, 0, -32, 0, 5874, 0, -89888, 0, 7890481], [1, 0, 156, 0, 13046, 0, 543036, 0, 12117361], [1, 4, 250, 736, 23059, 44896, 930250, 907924, 13845841], [1, 0, -26, 0, 9147, 0, -116714, 0, 20151121], [1, 0, 104, 0, 12786, 0, 524264, 0, 25411681], [1, 0, 46, 0, 11187, 0, 245134, 0, 28398241], [1, -12, 370, -2952, 46059, -233208, 2309170, -5916468, 38950081], [1, 0, 168, 0, 20834, 0, 1157352, 0, 47458321], [1, 0, 36, 0, 16166, 0, 285156, 0, 62742241], [1, 0, -386, 0, 56067, 0, -3631874, 0, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/540/2/d/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': '8-540e4-1.1-c1e4-0-2', 'motivic_weight': 1, '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': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-540e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0765167249866163, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1765298151140775927, 'z1': {'__RealLiteral__': 0, 'data': '0.35332328426712925442445266471', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '447890473375835721351846516642,1408883257627542509270045667337,2132463474780117645245509475996,2586798939007558672282069011331', 'Lhash_array': ['447890473375835721351846516642', '1408883257627542509270045667337', '2132463474780117645245509475996', '2586798939007558672282069011331'], 'label': '8-540e4-1.1-c1e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/540/2/d/c'}