Table lfunc_lfunctions
L-functions
{'Lhash': '2272035697418710018556413669820', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [0.0, 0.0], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [1.3449970239279148, 0.4370160244488211], 'a8': [0.0, 0.0], 'a9': [1.1082614755937437e-79, 6.356751333032792e-81], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.48309493222874633, 'analytic_normalization': 0, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11], 'central_character': '968.481', 'coefficient_field': 'CDF', 'conductor': 968, 'conductor_radical': 22, 'conjugate': '1319015882575002536051499584582', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.30901699437494745, 0.9510565162951535], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-1.3449970239279148, -0.4370160244488211], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.8312538755549068, 1.1441228056353685], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-0.8090169943749475, -0.5877852522924731], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.8312538755549068, -1.1441228056353685], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.8312538755549068, -1.1441228056353685], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-0.8090169943749475, 0.5877852522924731], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.8312538755549068, -1.1441228056353685], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-1.3449970239279148, 0.4370160244488211], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-0.30901699437494745, -0.9510565162951535], [-0.8090169943749475, 0.5877852522924731]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19441700, 'index': 0, 'label': '2-968-11.8-c0-0-0', 'leading_term': '0.91946723379044874752488401104396', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/968/1/j/a/481/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [0.9194672337904487, 0.9650341118038422, 1.0231252037614547, 1.093891982923509, 1.1765512077124134, 1.2695732208284083, 1.3708908927366612, 1.4780739749917609, 1.5884504863410616, 1.6991816084580307, 1.8073058846293752, 1.909768161792763, 2.003444767344353, 2.085172218110427, 2.1517834801125315, 2.200153529848406, 2.227254468652235, 2.230219446119782, 2.206413960056921, 2.1535125956317525, 2.069578876666716, 1.9531455940987572, 1.8032927388553814, 1.6197199993362494, 1.4028106944537715, 1.1536840117004032, 0.8742325163025154, 0.5671421012141309, 0.23589186495000972, -0.11526816204515576, -0.48136297306299347, -0.856763095934883, -1.2352797774063335, -1.6102841245840938, -1.9748485940088698, -2.3219082951726873, -2.6444386524126924, -2.935645082259321, -3.189159530142946, -3.3992380096501247, -3.5609527376593846, -3.6703720960017585, -3.724721507270373, -3.7225184158994296, -3.6636749351205764, -3.5495623663730416, -3.3830327203150192, -3.16839355644396, -2.911333888060282, -2.6188005351680967, -2.298826102175785, -1.9603116511237395, -1.61276906620043, -1.2660299855376542, -0.9299299307873916, -0.6139778110088435, -0.3270222337851729, -0.07692694744431804, 0.12973180283114594, 0.2879332489828448, 0.39443319766164414, 0.44792713471581586, 0.4491458452228732, 0.40087619009792735, 0.30790226664555403, 0.17686514332285647, 0.016042598285870967, -0.16494631327727058, -0.3555036230104358, -0.5444702177171103, -0.7205844803121981, -0.8729647001835413, -0.9915961558884274, -1.067802484888952, -1.094680477733453, -1.0674778435002545, -0.9838948299236683, -0.8442928460668975, -0.651796385506794, -0.41227849758101737, -0.134224674052174, 0.17152486074907713, 0.4921490507634293, 0.8133252118742431, 1.1197973524371965, 1.396012569095164, 1.6268003159397042, 1.798066115963384, 1.8974691922713622, 1.9150527074146753, 1.8437959247275968, 1.6800596965481758, 1.4239002236528184, 1.0792309297532898, 0.6538183945979297, 0.15910536116967208, -0.39013841211760036, -0.9763285834273401, -1.5797250037217532, -2.1792122534157086, -2.753170532763991, -3.280399873491987, -3.7410565473490323, -4.117558267381086, -4.395414511382386, -4.563940154770291, -4.616814590834158, -4.552454540897889, -4.37417660776409, -4.090134991536701, -3.7130302631712557, -3.259596196644422, -2.7498828585459654, -2.206364876870542, -1.6529134894460822, -1.1136790652916408, -0.6119368157245504, -0.1689519692224885, 0.1970785102256764, 0.4719526798529599, 0.6462088763756206, 0.7156472709105044, 0.6815957429621904, 0.55090033539772, 0.33563423115051305, 0.0525336366293665, -0.27781657614607014, -0.6320109004149493, -0.9850161282626724, -1.311470439542479, -1.5870227629544746, -1.789642715487569, -1.9008312598805484, -1.9066658265797298, -1.7986209516052916, -1.5741162009685066, -1.2367568011424004, -0.7962483075988132, -0.26798400306091863, 0.32767840244954766, 0.9664167838190496, 1.6211713860623223, 2.2635348943308014, 2.8652319928573915, 3.3996082286856977, 3.843046000764005, 4.17622812722675, 4.385176676470475, 4.462006284932295, 4.4053464692895785, 4.220405679063781, 3.91867003523666, 3.517250723705481, 3.0379146388598497, 2.505851869735521, 1.9482498181675287, 1.392756098539374, 0.8659200570671503, 0.3917051889145173, -0.009838349915190614, -0.3236604867930774, -0.5404902066207391, -0.6572577137017187, -0.6771320809518704, -0.6091701468382037, -0.46759659479123455, -0.2707585485575921, -0.039819157498009995, 0.20272785439061713, 0.43462803533953154, 0.6354188956396541, 0.7878633116422707, 0.879167472477582, 0.9018994745328693, 0.8545426403869454, 0.7416402988711321, 0.5735147740790306, 0.36557110165626616, 0.1372237686797814, -0.08948924489999058, -0.29151840042778565, -0.44653644170995666, -0.5346791046455505, -0.5401739618901992, -0.4527427001573217, -0.2686738438008999, 0.008518206203406365, 0.3679069841278556, 0.7914701771386718, 1.254905357586197, 1.7289091109430585, 2.1808515966456987, 2.5767502587538926, 2.8834235767159497, 3.070690079236361, 3.1134705774776963, 2.9936534290915486, 2.701593760110862, 2.237137475971127, 1.6100885178877045, 0.840071555950139, -0.044219905646567616, -1.0063605898219103, -2.004047707062217, -2.991369372620654, -3.9213549395194605, -4.748653760697227, -5.432177197687164, -5.937537544741436, -6.239127251802618, -6.321702001530519, -6.181360707231845, -5.825852578782639, -5.2741837318911, -4.555540667141239, -3.707592365705324, -2.774273753128839, -1.8031880577144694, -0.8427916909429551, 0.060459195985072635, 0.8648175857156509, 1.5356354790357374, 2.04728065470777, 2.384457039150483, 2.5428448991276595, 2.5290225544893734, 2.359679734126515, 2.0601807513668082, 1.6625800155568025, 1.2032298956923733, 0.7201489163889782, 0.25033463711083087, -0.17279092502118754, -0.5216251919693253, -0.7761624942900747, -0.9251829439406317, -0.9667730035948573, -0.9081464217146736, -0.7647850534283728, -0.5589687493888778, -0.317808342639046, -0.07093247454031472, 0.15199519635079817, 0.3237389715948298, 0.42174595780021734, 0.4300196359172758, 0.3404672721401427, 0.15361566880964364, -0.12136256645789813, -0.4673175603772675, -0.8604374359916245, -1.2721119034220922, -1.6712024369354619, -2.026544292958245, -2.3094856248583664, -2.4962636705490957, -2.5700280524953345], 'positive_zeros': ['1.79232013696017646061738422107079', '3.58418886820362785195632855123042', '4.13077820116991630063198439689471', '5.02798958301002478672233356594316', '5.95616984084919423972195366782373', '7.33957599405351662728484509097074', '7.82294678613158328617213124503778', '8.653850844395604142085851973840052', '9.935796356815212136996426776718345', '10.44781039295252739501896378935452'], 'prelabel': '2-968-11.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6950503091350628, 'root_angle': 0.2410676202934349, 'root_number': '0.056094337694120088440287305383750 + 0.99842547307180520382925103642483*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2410676202934349', 'prec': 54}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79232013696017646061738422107', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.58418886820362785195632855123', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.13077820116991630063198439689', 'prec': 100}}