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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': -2, 'A4': 1, 'A5': 1, 'A6': 2, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '1367493627822148218', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1130.761543023352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1, -1]], [7, [1]], [17, [1]]], 'bad_primes': [2, 5, 7, 17], 'central_character': '141610.1', 'coefficient_field': '1.1.1.1', 'conductor': 141610, 'conductor_radical': 1190, 'degree': 2, 'euler_factors': [[1, 1], [1, 2, 3], [1, -1], [1], [1, -2, 11], [1, -6, 13], [1], [1, -8, 19], [1, -2, 23], [1, 6, 29], [1, 2, 31], [1, 6, 37], [1, -2, 41], [1, 4, 43], [1, 4, 47], [1, 10, 53], [1, 0, 59], [1, 10, 61], [1, -8, 67], [1, 14, 71], [1, -10, 73], [1, -14, 79], [1, -4, 83], [1, 6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 51, 'label': '2-141610-1.1-c1-0-51', 'leading_term': '4.39703445936', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/141610/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9612845617085132, 1.192083525773071, 0.4979032824521788, -0.3929221454518931, -0.3968895764953961, 0.4351377269688087, 0.3473234730025397, -2.204429673009581, -5.852844266530644, -6.825580108237197, -3.390920341832832, 1.084790673929134, 1.678707745139457, -1.41172492383935, -2.470477030795346, 1.94384706786557, 7.510291801762869, 7.633747078630689, 2.628240316327801, -1.039178028242141, -0.2523894261445129, 1.305067408633488, 0.4045331071875052, -0.7339361110337848, 0.2547321757497133, 1.022137413207118, -0.5150676294648026, -1.263832982211467, 1.365578779788087, 3.460128520451423, 0.9357641036227701, -2.449667474063965, -1.094940081082201, 2.472127777032204, 2.218611559009512, -0.6279477573596078, -0.8283592052916395, 0.566915532938603, -0.8457470199786357, -3.259192415690929, -2.16463928893715, 0.534075347284735, 0.6085809867650823, -0.2801060928526863, 0.6085671824906251, 0.8441258706026762, -0.6034895830721394, 0.3152277039509237, 3.032719778275837, 1.122038368272985, -3.832066127334567, -2.664770394532977, 3.161294718853817, 2.771004799465267, -2.610366271962888, -1.675321060155215, 3.310260831917345, -0.01486343883920929, -8.64427915624346, -8.603621320528921, -1.11542231434125, 1.270321329362761, -1.757678003024563, -1.850904809570591, 0.2772155942031881, -0.01151545000425751, -0.3235306098880185, 1.180875557630099, 1.006795050814691, -0.6048001563683567, -0.2364481545388165, 0.3568056980602067, -0.588766017045068, 0.04198230582249373, 1.022436306672472, -2.221296946170927, -4.792942780846882, -0.262410191255001, 3.916166379677751, 0.3422107709640267, -2.960536517839631, -0.4320451910555116, -0.01543110313644219, -2.757631071380197, 0.2530418837588565, 5.781677411625041, 3.950633271327641, -0.196580291035968, 1.202032904332498, 2.286131582807771, -0.03525721214772877, 1.100061458893974, 3.62557436752104, 0.4165624226585355, -2.346237192240418, 1.106918028394395, 2.243641271137173, -1.405852605958762, -0.5681539448798226, 3.045953022069266, 1.138943257321088, -0.8833945716687774, 2.440318305045953, 3.269798953603745, 0.03294505461982311, 0.8361990427128805, 2.847263956048498, -0.6933268985086667, -3.589771314575369, -1.113805367188177, 0.4759260389473904, -0.1851667283961219, 0.6714250138645065, 0.7821954292554226, -0.3948717271712287, 0.668686812415624, 1.146088015284235, -0.3550374302939523, 1.802121362365863, 4.295634481073022], 'positive_zeros': ['0.8754816217628506', '1.376523530084650', '1.805945423882578', '2.926598586488426', '3.396796413898017', '3.917373748420708', '4.891988962381617', '5.280000052751757', '5.810190196189840', '6.208662734709749', '6.685603026333322', '7.147635502598255', '7.805314271491378', '8.320702637944007', '8.936404814895969', '9.373735321471180', '9.665155297505744', '10.43623003211715', '10.87707165818835', '11.12577701531377', '11.64247765967087', '11.96940379653505', '12.55396010367318', '13.11023967659765', '13.62250035502200', '14.07480108379129', '14.49955217727354', '15.29756822399599', '15.61397501531708', '16.20260324407678', '16.49742172915573', '16.81622597938655', '17.39033558278005', '17.80061984559363', '18.10782387443329', '18.49393146608370', '18.86796718300363', '19.51004573951091'], 'prelabel': '2-141610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.62679798945109, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1367493627822148218, 'z1': {'__RealLiteral__': 0, 'data': '0.8754816217628506', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.376523530084650', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.805945423882578', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1130.761543023352, 'bad_primes': [2, 5, 7, 17], 'central_character': '1.1', 'conductor': 141610, 'conductor_radical': 1190, 'degree': 2, 'dirichlet_coefficients': [1, -1, -2, 1, 1, 2, 0, -1, 1, -1, 2, -2, 6, 0, -2, 1, 0, -1, 8, 1, 0, -2, 2, 2, 1, -6, 4, 0, -6, 2, -2, -1, -4, 0, 0, 1, -6, -8, -12, -1, 2, 0, -4, 2, 1, -2, -4, -2, 0, -1, 0, 6, -10, -4, 2, 0, -16, 6, 0, -2, -10, 2, 0, 1, 6, 4, 8, 0, -4, 0, -14, -1, 10, 6, -2, 8, 0, 12, 14, 1, -11, -2, 4, 0, 0, 4, 12, -2, -6, -1, 0, 2, 4, 4, 8, 2, -14, 0, 2, 1], 'euler11': [1, -2, 11], 'euler13': [1, -6, 13], 'euler17': [1, 0, 0], 'euler19': [1, -8, 19], 'euler2': [1, 1, 0], 'euler23': [1, -2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 2, 31], 'euler37': [1, 6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 14, 71], 'euler73': [1, -10, 73], 'euler79': [1, -14, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 2, 3], [1, -1, 0], [1, 0, 0], [1, -2, 11], [1, -6, 13], [1, 0, 0], [1, -8, 19], [1, -2, 23], [1, 6, 29], [1, 2, 31], [1, 6, 37], [1, -2, 41], [1, 4, 43], [1, 4, 47], [1, 10, 53], [1, 0, 59], [1, 10, 61], [1, -8, 67], [1, 14, 71], [1, -10, 73], [1, -14, 79], [1, -4, 83], [1, 6, 89], [1, 14, 97]], 'index': 51, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/141610/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-141610-1.1-c1-0-51', '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': '2-141610-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.62679798945109, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1367493627822148218, 'z1': {'__RealLiteral__': 0, 'data': '0.8754816217628506', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1367493627822148218', 'Lhash_array': ['1367493627822148218'], 'factors': ['2-141610-1.1-c1-0-51'], 'label': '2-141610-1.1-c1-0-51', 'type': 'ECQ', 'url': 'EllipticCurve/Q/141610/g'}