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lfunc_lfunctions • Show schema
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{'Lhash': '2361059312053878932868570026758', 'a10': [1.138347128085596, 4.868692413367194], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [-2.996107310529937, 0.15277756310749852], 'a4': [0.0, -3.0], 'a5': [4.247618394616997, 2.6377524473898846], 'a6': [-2.2265978473247756, -2.01053774555184], 'a7': [4.334015535778487, -5.4969363590668125], 'a8': [4.949747468305833, -4.949747468305833], 'a9': [8.953318032421869, -0.9154759474226503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8610427757831176, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.996107310529937, -0.15277756310749852]]], [5, [[1.0, 0], [-4.247618394616997, -2.6377524473898846]]], [7, [[1.0, 0], [-4.334015535778487, 5.4969363590668125]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.83', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '1824255588278874999872136230705', 'degree': 2, 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[-3481.0, 0]], [[1.0, 0], [0, -21.07170871718489], [-3721.0, 0]], [[1.0, 0], [32.478567053607705, -32.478567053607705], [0, -4489.0]], [[1.0, 0], [0, -16.034489432110544], [-5041.0, 0]], [[1.0, 0], [-57.35968291792892, 57.35968291792892], [0, -5329.0]], [[1.0, 0], [0, 75.8023746329889], [-6241.0, 0]], [[1.0, 0], [51.967492200700796, 51.967492200700796], [0, 6889.0]], [[1.0, 0], [0, -174.29430140959755], [-7921.0, 0]], [[1.0, 0], [16.665762376058883, 16.665762376058883], [0, 9409.0]], [[1.0, 0], [113.1135205786325, 0], [10201.0, 0]], [[1.0, 0], [16.182596745225638, -16.182596745225638], [0, -10609.0]], [[1.0, 0], [139.01044783163061, 139.01044783163061], [0, 11449.0]], [[1.0, 0], [0, 3.0142886309281973], [-11881.0, 0]], [[1.0, 0], [-80.11182563361352, 80.11182563361352], [0, -12769.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-105-105.83-c2-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 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1.6914617275549328, 'root_angle': 0.0494011425943645, 'root_number': '0.9879809029296013 + 0.15457598599526953*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0247005712972', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86254738618732232498433600067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.08239974258686348291179754543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.43398939493534927974766409194', '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': '105.83', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/3/k/c/83/5'], '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': '2-105-105.83-c2-0-11', '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': '2-105-105.83-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.02470057129718225, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86254738618732232498433600067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2361059312053878932868570026758', 'Lhash_array': ['2361059312053878932868570026758'], 'label': '2-105-105.83-c2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/3/k/c/83/5'}