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lfunc_lfunctions • Show schema
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{'Lhash': '2099334649698169045588091759567', 'a10': [-3.982709502839758, 1.5751732496768431], 'a2': [-1.1079869867321832, -0.8788428967865286], 'a3': [-0.6628271480711836, 0.3826834323650898], 'a4': [0.4552703255357262, 1.9474929860429777], 'a5': [1.5142302396972043, -2.622723709512757], 'a6': [1.0707224707676244, 0.1585126677811072], 'a7': [0.0, 0.0], 'a8': [1.2071067811865475, -2.5579079770025843], 'a9': [-1.2071067811865475, 2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1079869867321832, 0.8788428967865286]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '392.19', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '968295314980260161865617497413', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1079869867321832, 0.8788428967865286]], [[1.0, 0], [0.6628271480711836, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-392-56.19-c1-0-21', '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/392/2/m/h/19/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8191706547441562, 0.9203814519410823, 1.0186240772622925, 1.1121307838287338, 1.1963291657071558, 1.2640786487922673, 1.30621579350225, 1.3123095428632257, 1.2715713587236606, 1.173896865102478, 1.0110186950418858, 0.7777303634856743, 0.4731100688509787, 0.10164157154975374, -0.3258960189379859, -0.7919113351266004, -1.2719964177868521, -1.7355539886728193, -2.1471347432065384, -2.468503151717596, -2.6613741671642264, -2.6906768726175727, -2.528113014640101, -2.155699256735241, -1.5689237334558475, -0.7791217909118625, 0.18530748255862733, 1.2791569673564818, 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'10.43436290831621813997749909311090', '11.26376010328238243871889133051616'], 'prelabel': '2-392-56.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': 0.2899916447611415, 'root_number': '-0.24863903861409056 + 0.9685962153947644*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.289991644761', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65608303212273335123879941200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22742176376032711163280035871', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.28176035418384452308491569752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'bad_primes': [2, 7], 'central_character': '56.19', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/2/m/h/19/3'], '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': '2-392-56.19-c1-0-21', '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': '2-392-56.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': 0.2899916447611415, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65608303212273335123879941200', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2099334649698169045588091759567', 'Lhash_array': ['2099334649698169045588091759567'], 'factors': ['2-392-56.19-c1-0-21'], 'label': '2-392-56.19-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/2/m/h/19/3'}