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lfunc_lfunctions • Show schema
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{'Lhash': '3837428796723830343816199138199', 'a10': [-2.9112199758821093, -2.761849580070541], 'a2': [0.6746257748366975, -1.242932043164865], 'a3': [-0.8395053862092143, -3.1330767545605203], 'a4': [-1.089760127851971, -1.677027985378913], 'a5': [0.734403654760781, -2.740831752831508], 'a6': [-4.460553463589224, -1.0702061882393088], 'a7': [0.0, 0.0], 'a8': [-2.819612090949944, 0.22313147821158003], 'a9': [-6.513324445139886, 3.760469621720883], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.260271518468385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6746257748366975, 1.242932043164865]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.165', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'conjugate': '1071255503776409676393837214616', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6746257748366975, 1.242932043164865]], [[1.0, 0], [0.8395053862092143, 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[2.037296740700007, 7.603294946386902], [-94.39676901250381, 54.5]], [[1.0, 0], [-7.180603215217992, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 75, 'label': '2-28e2-112.53-c1-0-75', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/784/2/x/n/165/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6025430558875613, 1.9820531871636702, 2.418129585715239, 2.9172374122035523, 3.481153653919143, 4.105380160247223, 4.778213563587322, 5.480443716264181, 6.185657504045546, 6.861169634772263, 7.469622340584661, 7.971269209978491, 8.326889770560848, 8.501186775512052, 8.466415435547095, 8.205901072820417, 7.717036242426711, 7.013326083332898, 6.125083956942439, 5.098475052318023, 3.992762374417432, 2.87581660250154, 1.8181879115891444, 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'7.06088550939033360653776745529926', '8.496331988209638565848692127395738', '9.323092112154266209324582093272061', '9.953454425083414982354031577946676', '10.74997582791420255648506511091324'], 'prelabel': '2-28e2-112.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.502053460353792, 'root_angle': -0.30776444195324415, 'root_number': '-0.3550286307563741 - 0.9348554280439592*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.307764441953', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.02719755430473890659219888947', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77032975531153694992014006662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.58049923647379682571992739662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.260271518468385, 'bad_primes': [2, 7], 'central_character': '112.53', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/2/x/n/165/7'], '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': '2-28e2-112.53-c1-0-75', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-28e2-112.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.502053460353792, 'root_angle': -0.30776444195324415, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.02719755430473890659219888947', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3837428796723830343816199138199', 'Lhash_array': ['3837428796723830343816199138199'], 'factors': ['2-28e2-112.53-c1-0-75'], 'label': '2-28e2-112.53-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/2/x/n/165/7'}