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lfunc_lfunctions • Show schema
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{'Lhash': '2506511359356097979406713790318', 'a10': [-0.7593725692717678, -9.465976283269166], 'a2': [-0.949638634925816, -1.644822364521866], 'a3': [-2.6503468472153466, 1.4055822955116046], 'a4': [0.19637292611246526, -0.34012788525775894], 'a5': [4.516171679471548, 2.1457384187125728], 'a6': [4.828804956902992, 3.024554515654284], 'a7': [4.609607990458835, -5.2679705935301175], 'a8': [-8.343042349365847, 0.0], 'a9': [5.048676821088656, -7.450561210821782], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.6503468472153466, -1.4055822955116046]]], [5, [[1.0, 0], [-4.516171679471548, -2.1457384187125728]]], [7, [[1.0, 0], [-4.609607990458835, 5.2679705935301175]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.74', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '1202892551935546060552892299737', 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[-39.80167782245177, -68.93852821497386], [-5724.5, 9915.124847928038]], [[1.0, 0], [70.78485284672556, -122.60296153681516], [-5940.5, -10289.247822362915]], [[1.0, 0], [-99.60306560799907, 0], [12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-105-105.74-c2-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/105/3/o/b/74/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9274789658951684, 1.0169999536087513, 1.1013627224320763, 1.179888349792753, 1.2509642966756862, 1.3119955500923606, 1.3594200416276343, 1.3887848004015946, 1.3948792495319846, 1.3719234969463308, 1.3138108036491782, 1.2144034558108716, 1.0678795119784477, 0.869124394829342, 0.6141564380703771, 0.3005698320715534, -0.07202745262307907, -0.5016086113156393, 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'5.03103233399995265292139218946476', '5.96324009444984287587291229748678', '7.02983178865043003558138267563403', '8.228555575400302036792194771177445', '9.253381051632133109302830510427972', '10.62819121840921634929061655708922', '11.97407342480196223726217203067969', '12.54900763045933829940020548976074', '13.82118125595232408699785560060588'], 'prelabel': '2-105-105.74-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.5682922847684752, 'root_number': '-0.21290438678798831 + 0.9770730382558055*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.284146142384', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97728881988840027011974878174', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.03103233399995265292139218946', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.96324009444984287587291229749', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'bad_primes': [3, 5, 7], 'central_character': '105.74', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/3/o/b/74/5'], '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': '2-105-105.74-c2-0-12', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-105-105.74-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.2841461423842376, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97728881988840027011974878174', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2506511359356097979406713790318', 'Lhash_array': ['2506511359356097979406713790318'], 'label': '2-105-105.74-c2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/3/o/b/74/5'}