-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1808900639723665387049222027755', 'a10': [-2.453051372115214, 0.0], 'a2': [-1.0, 0.0], 'a3': [-2.144894625503444, 0.0], 'a4': [1.0, 0.0], 'a5': [2.453051372115214, 0.0], 'a6': [2.144894625503444, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.6005729545135596, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [2.144894625503444, 0], [3.0, 0]], [[1.0, 0], [-2.453051372115214, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.660963749620213, 0], [11.0, 0]], [[1.0, 0], [-1.9691204962319826, 0], [13.0, 0]], [[1.0, 0], [1.6793312452250946, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.37117449861332436, 0], [23.0, 0]], [[1.0, 0], [6.250745191496991, 0], [29.0, 0]], [[1.0, 0], [7.32289387707488, 0], [31.0, 0]], [[1.0, 0], [-0.646286535623011, 0], [37.0, 0]], [[1.0, 0], [-1.1058505659935471, 0], [41.0, 0]], [[1.0, 0], [9.922500453753985, 0], [43.0, 0]], [[1.0, 0], [12.644821376315305, 0], [47.0, 0]], [[1.0, 0], [5.55238927985344, 0], [53.0, 0]], [[1.0, 0], [2.0204227536824577, 0], [59.0, 0]], [[1.0, 0], [11.696063717299872, 0], [61.0, 0]], [[1.0, 0], [-6.752471864167779, 0], [67.0, 0]], [[1.0, 0], [8.289789251006889, 0], [71.0, 0]], [[1.0, 0], [2.512086475878023, 0], [73.0, 0]], [[1.0, 0], [9.581773749479131, 0], [79.0, 0]], [[1.0, 0], [-9.73987890367598, 0], [83.0, 0]], [[1.0, 0], [-1.9654232258431745, 0], [89.0, 0]], [[1.0, 0], [10.894533284730805, 0], [97.0, 0]], [[1.0, 0], [18.097932664896426, 0], [101.0, 0]], [[1.0, 0], [-19.37895578650949, 0], [103.0, 0]], [[1.0, 0], [20.108852692038912, 0], [107.0, 0]], [[1.0, 0], [12.34540088426274, 0], [109.0, 0]], [[1.0, 0], [5.920505112142317, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 133, 'label': '2-5054-1.1-c1-0-133', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5054/2/a/z/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.8225357517330646e-61, 0.11907957246942721, 0.237412867149958, 0.3542309825725831, 0.4687217066784216, 0.5800125655109613, 0.6871591476784773, 0.789139896033051, 0.8848581570061187, 0.9731518625722823, 1.052810821835269, 1.122601241255858, 1.1812967867498732, 1.2277152504292839, 1.2607596863917738, 1.2794627270172894, 1.2830326762512534, 1.2708998929881932, 1.2427619217034194, 1.198625797158006, 1.13884594581197, 1.0641561307284184, 0.975693942497307, 0.875016429686483, 0.7641055919319577, 0.6453626296348116, 0.5215900577825094, 0.39596104760732836, 0.2719756568749017, 0.15340394396704352, 0.04421632710984895, -0.05149805922474324, -0.129623852620928, -0.1861212267371214, -0.21713495840310698, -0.21910844174310695, -0.18889994378151126, -0.12389809437740607, -0.022133363362095516, 0.11761788750274667, 0.2957402687823581, 0.5117006167410925, 0.7639869858126421, 1.050068497130113, 1.3663788147078815, 1.7083255643340116, 2.07032744741099, 2.4458801415959917, 2.8276513347473626, 3.2076044247822066, 3.5771495555542456, 3.9273197709243073, 4.248969181646169, 4.532989180381809, 4.770537938198852, 4.953277700768326, 5.073613803061466, 5.12492886491805, 5.101805341047943, 5.000229498765165, 4.817770001297246, 4.553724594547076, 4.2092289350503735, 3.7873223539599232, 3.292966316229833, 2.7330124882639155, 2.1161186461624433, 1.4526121082588515, 0.7543019212853328, 0.03424262503253263, -0.693545982899598, -1.4143971144711749, -2.1133458804775405, -2.7755001058078252, -3.3864232965940735, -3.93251916130746, -4.4014065591888025, -4.782273549062193, -5.066199363384125, -5.246433649407059, -5.318623202848493, -5.280977658171277, -5.134367169356099, -4.882346979016613, -4.531105882891442, -4.0893378911385945, -3.56803879798037, -2.9802318201481692, -2.340628870210593, -1.6652363087981426, -0.9709160860781841, -0.27491495733044324, 0.40562413338533093, 1.05415342743635, 1.6551989098848725, 2.194810494572869, 2.6609688306638315, 3.043934812823818, 3.3365294812624944, 3.5343340795576452, 3.635802539614491, 3.642281508547245, 3.5579361302937365, 3.3895830410374668, 3.1464353181496447, 2.839767317927912, 2.4825103272005173, 2.088792620516411, 1.6734397487709427, 1.2514525898773112, 0.8374817874333507, 0.4453176297741883, 0.08741414357083052, -0.22553481651313195, -0.4849513899952289, -0.6846476931992006, -0.8210071305914619, -0.8930656040755077, -0.9024889520929998, -0.8534469366719685, -0.7523881553014297, -0.6077242267542922, -0.42943532523442673, -0.22861245990588544, -0.01695467280611848, 0.19375856910929964, 0.39219818544983126, 0.5679974190228901, 0.7122232355583324, 0.8177868395023185, 0.8797751420593091, 0.8956880015939773, 0.8655697384349303, 0.7920276711391603, 0.680135066896113, 0.5372207608525517, 0.3725525790373705, 0.19692639195071618, 0.022176927333132514, -0.13936981165698392, -0.27547971626572226, -0.37460446672352526, -0.42646024736793064, -0.42256542445409373, -0.35671248946810186, -0.22535182547168411, -0.027868134653695132, 0.23326544263711388, 0.552465540850599, 0.9211536318169836, 1.3280066136163498, 1.7593356717283555, 2.1995803943120116, 2.6318997819391754, 3.0388371178320948, 3.4030318796639882, 3.7079491671908653, 3.9385956378445037, 4.08219078116723, 4.128763562891781, 4.071647011492161, 3.9078471248943, 3.6382674051478574, 3.2677761928513283, 2.805110532962353, 2.2626172840782193, 1.65583928331999, 1.002961284728787, 0.32413678775986554, -0.35927753349530545, -1.0255485686093992, -1.6534202227469048, -2.2229573775344638, -2.716343986208384, -3.1186003791158217, -3.4181878939189203, -3.607473464087051, -3.6830326226548578, -3.6457762652240695, -3.500894172149028, -3.2576163784578136, -2.9288016380535744, -2.5303700822415083, -2.080604354428917, -1.599349669797588, -1.107148098438329, -0.6243456563604622, -0.1702123332197863, 0.23788511048536576, 0.5852198945697956, 0.8603177679375401, 1.0554171571118969, 1.166755651455202, 1.1946695691112437, 1.1435020607605388, 1.021324220802607, 0.8394825597797793, 0.6119945189776423, 0.354821069292447, 0.08505146296420976, -0.179960411027061, -0.4234661135302147, -0.6301567504266874, -0.7869202375715243, -0.8834845116862078, -0.9129149456910984, -0.8719413277911636, -0.761098149897876, -0.5846712201228903, -0.3504533129668831, -0.06932121752798434, 0.24534434838795757, 0.5783663894431434, 0.9135706100784288, 1.2346345971406225, 1.5259432667232267, 1.7734060469962718, 1.9651929749669332, 2.0923508277888927, 2.149266415399512, 2.133951948287706, 2.048136582317608, 1.8971583726002132, 1.6896614241356962, 1.4371134606565161, 1.1531687936267199, 0.8529102348048314, 0.5520103856022958, 0.2658575613636156, 0.008694076955568916, -0.2071854408962347, -0.37213068103718033, -0.4796872905196754, -0.5269709659532171, -0.5148406817920961, -0.44785843395214964, -0.3340344549769889, -0.18436871531364715, -0.012211028646080046, 0.16752740279085723, 0.33926922604451204, 0.4877243377728912, 0.5988484988946653, 0.6607526972266223, 0.66451023130168, 0.604812877815186, 0.4804346764718932, 0.29447149712324044, 0.05433618161181948, -0.22849790636332218, -0.5389983100443926, -0.8592994860623873, -1.1696199426568914, -1.4493254913595488, -1.6780841625597174, -1.8370516154061303, -1.9100223020606952], 'positive_zeros': ['1.42697099610727802334058262190106', '1.78961552068974456284501372531330', '3.23658438021552824838533835798562', '4.28436804831562626579064699805518', '5.26238033404640770254939869532968', '5.81622986732728877465323957805548', '6.47488974074484787373644879020517', '6.84933778786212944799807441046205', '7.897180289071156284304031969321906'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42697099610727802334058262190', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78961552068974456284501372531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23658438021552824838533835799', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 133, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/z/1/2'], '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': '2-5054-1.1-c1-0-133', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42697099610727802334058262190', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1808900639723665387049222027755', 'Lhash_array': ['1808900639723665387049222027755'], 'label': '2-5054-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/z/1/2'}