-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1459068626227221787685406718718', 'a10': [-125.99962625596777, 0.0], 'a2': [1.722866782181628, 0.0], 'a3': [0.0, 0.0], 'a4': [-29.031730050855124, 0.0], 'a5': [-73.13370224505532, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-105.14954036369453, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.722866782181628, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [73.13370224505532, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-193.0704129055728, 0], [161051.0, 0]], [[1.0, 0], [-151.5003434469376, 0], [371293.0, 0]], [[1.0, 0], [-1760.1205121797293, 0], [1419857.0, 0]], [[1.0, 0], [-1126.7909492870822, 0], [2476099.0, 0]], [[1.0, 0], [-2413.3254946690445, 0], [6436343.0, 0]], [[1.0, 0], [7729.106650194871, 0], [20511149.0, 0]], [[1.0, 0], [8176.754180825752, 0], [28629151.0, 0]], [[1.0, 0], [-5932.376733425753, 0], [69343957.0, 0]], [[1.0, 0], [-4975.838722038296, 0], [115856201.0, 0]], [[1.0, 0], [5652.507680813682, 0], [147008443.0, 0]], [[1.0, 0], [-4720.9325545326865, 0], [229345007.0, 0]], [[1.0, 0], [32072.115745682157, 0], [418195493.0, 0]], [[1.0, 0], [28566.931080707855, 0], [714924299.0, 0]], [[1.0, 0], [-29003.65437237779, 0], [844596301.0, 0]], [[1.0, 0], [30517.384040684097, 0], [1350125107.0, 0]], [[1.0, 0], [-56944.50353881482, 0], [1804229351.0, 0]], [[1.0, 0], [-9726.786028454037, 0], [2073071593.0, 0]], [[1.0, 0], [98483.5215482197, 0], [3077056399.0, 0]], [[1.0, 0], [-50636.991775346156, 0], [3939040643.0, 0]], [[1.0, 0], [-59655.78977385894, 0], [5584059449.0, 0]], [[1.0, 0], [134206.1565426406, 0], [8587340257.0, 0]], [[1.0, 0], [-135280.90844532484, 0], [10510100501.0, 0]], [[1.0, 0], [-199409.56118008812, 0], [11592740743.0, 0]], [[1.0, 0], [-93298.08250670826, 0], [14025517307.0, 0]], [[1.0, 0], [41818.73079796579, 0], [15386239549.0, 0]], [[1.0, 0], [170560.04553562243, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-21e2-1.1-c5-0-46', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/441/6/a/be/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-9.212979649645987e-61, 0.19823513208026258, 0.3924511028187075, 0.5786809832529687, 0.7530619448397861, 0.9118863903480566, 1.0516519583699435, 1.1691099888193204, 1.2613120078762814, 1.3256537582724202, 1.3599162668050335, 1.362303408007012, 1.3314753936647585, 1.2665775951545617, 1.1672640921518023, 1.0337153398593266, 0.8666493600123478, 0.6673258907692997, 0.43754297902985934, 0.17962556710063513, -0.10359428522649929, -0.4088057920093708, -0.7322565641302845, -1.0697984322355512, -1.41694177068662, -1.7689179415829708, -2.120749284616377, -2.4673258779867258, -2.8034880925673495, -3.1241137612182874, -3.4242085933195536, -3.6989982872626834, -3.9440206369987583, -4.155215799002917, -4.329012789213174, -4.462410221303183, -4.553049283156347, -4.599276981956595, -4.600197773267797, -4.555711828054059, -4.466538384687603, -4.334222880018667, -4.16112685237402, -3.9503999560721397, -3.705933816156674, -3.4322978763300624, -3.134657843669742, -2.8186778002850166, -2.4904075229610987, -2.156157014295757, -1.822360689334625, -1.4954340662816863, -1.1816261644748085, -0.88687110381421, -0.6166426143735231, -0.3758152914470337, -0.16853645997067543, 0.0018875645398470661, 0.13308721870585768, 0.22370413775121886, 0.273441417168235, 0.28308731918768437, 0.2545106703674284, 0.190626900039806, 0.09533444414906143, -0.02657793346468224, -0.16955149158089128, -0.3274032573083019, -0.4934940432613115, -0.6609148111291389, -0.8226867284122255, -0.9719696370701413, -1.1022731504372898, -1.2076642411980105, -1.282964998387962, -1.3239342310742008, -1.3274267913800422, -1.2915248850324625, -1.2156362325881542, -1.1005547313267934, -0.9484802321114989, -0.7629951662081932, -0.5489970065793189, -0.3125868930412879, -0.06091615224160349, 0.1980061411730215, 0.4555400323894306, 0.7026701494188377, 0.9302827502540133, 1.1294563388434329, 1.2917570456030467, 1.4095294323689989, 1.4761731301076744, 1.4863957734101167, 1.4364330725340262, 1.3242275648726882, 1.1495586054829676, 0.9141174714849595, 0.6215230371049694, 0.27727528322544065, -0.11135411424071434, -0.5354927796199485, -0.9848967406234763, -1.4482320531527986, -1.913401354416951, -2.367905922822788, -2.7992322468272124, -3.1952508480894255, -3.5446142260903097, -3.837140340287226, -4.064168057012369, -4.218871481651179, -4.2965210753609, -4.294680905197619, -4.213333264431904, -4.054924175713349, -3.824325886517225, -3.5287153018646515, -3.177370278889733, -2.7813887270074815, -2.3533384056447826, -1.9068480759569089, -1.4561531329078243, -1.0156109151689536, -0.5992024688257381, -0.22003854805127326, 0.11011198852458003, 0.3812535215053161, 0.5855378689418872, 0.7175661047217818, 0.7746050480742555, 0.7567083298665609, 0.6667352759961316, 0.510264550742954, 0.2954034425314889, 0.03249770573287604, -0.2662491598393914, -0.5872345634878067, -0.9159774143647349, -1.2376818042949607, -1.5378227468422638, -1.8027315091382632, -2.020157492446969, -2.179783935792575, -2.2736759515009526, -2.296641532845972, -2.2464891455271427, -2.1241692334156297, -1.9337913079087128, -1.682513092340618, -1.380303276600686, -1.039584602817888, -0.6747690407849245, -0.3017015099273398, 0.0629672417665527, 0.4024545713472546, 0.7005401345388252, 0.94225229532463, 1.1145183394683449, 1.2067508844838777, 1.211344856283691, 1.1240625045513075, 0.9442880562785093, 0.6751386144573995, 0.3234236089685485, -0.10054872393698845, -0.5833129687519361, -1.108725059466066, -1.6585604864137795, -2.2132095281591893, -2.7524422647430695, -3.2562125974589318, -3.7054682092926985, -4.082932480760663, -4.373824903098016, -4.5664885179533155, -4.652896309187118, -4.629013163498414, -4.494995827233998, -4.255219987115833, -3.918130917122647, -3.495921751966575, -3.0040510373276046, -2.4606184287266255, -1.8856239330028552, -1.3001416004208524, -0.725442811064544, -0.182107037427992, 0.3108409500270505, 0.7367291202574968, 1.081935544537401, 1.336453234390901, 1.4942961888083024, 1.5537272611283692, 1.5172963319306396, 1.3916858052159984, 1.1873692477477094, 0.9180976609610044, 0.600236003768149, 0.25197978171276997, -0.10751257254234796, -0.45903148308286823, -0.7842296391688037, -1.0664939685519799, -1.2917346323779726, -1.4490530152563919, -1.5312560688759302, -1.5351913947453308, -1.4618858116145022, -1.316479465121673, -1.107957366245084, -0.8486901219936773, -0.5538050651943508, -0.24041753030830224, 0.07324077620685088, 0.36875387742938653, 0.6284681982329166, 0.8364066639327542, 0.9791041628607382, 1.0463217041069761, 1.0316021781207934, 0.9326381460114137, 0.7514311997229773, 0.4942327188009149, 0.17126680155748839, -0.20375277353633778, -0.6142890564798734, -1.041799744118748, -1.4666659812050324, -1.8691855883785784, -2.2305802248091404, -2.5339645925714342, -2.765227043080331, -2.913774836706005, -2.9731036819534955, -2.9411597554122397, -2.8204727730957826, -2.6180503411365743, -2.3450361748183552, -2.016147206528083, -1.648916455493345, -1.2627791721358799, -0.8780486150488517, -0.5148343688699495, -0.19195997713791565, 0.07406241026871865, 0.2699447959000998, 0.38637303310806614, 0.41855088852387196, 0.3665061966987208, 0.2351390486646318, 0.03400546513743432, -0.22315588781631568, -0.5191324215171097, -0.8341472030589145, -1.1469233603123514, -1.4358481035808293], 'positive_zeros': ['1.15100219726518430637131665897830', '3.33911309168299900069244889817388', '3.79672849118677358618601427159683', '4.93573759170980716997775427705504', '5.84318245635476395236018109378816', '7.36215894237170455214857026045391', '7.916837171262653904383861167192391', '9.013102509203953611807720118463451', '9.654850934421136744203856651008422'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15100219726518430637131665898', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33911309168299900069244889817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79672849118677358618601427160', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/be/1/5'], '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': '2-21e2-1.1-c5-0-46', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15100219726518430637131665898', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1459068626227221787685406718718', 'Lhash_array': ['1459068626227221787685406718718'], 'label': '2-21e2-1.1-c5-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/be/1/5'}