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lfunc_lfunctions • Show schema
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{'Lhash': '2723751909739876585715329899682', 'a10': [3.1583722945790362, 0.1571128538202791], 'a2': [0.9798814432847255, -1.0197217057149677], 'a3': [-0.5823091415492235, -0.5823091415492235], 'a4': [-0.07966471421248657, -1.9984127534894893], 'a5': [1.4673095075776175, 1.6873063767355143], 'a6': [-1.1643871931331353, 0.023199349014850143], 'a7': [-0.9729329838188646, 0.9729329838188646], 'a8': [-2.115886836852244, -1.876971734905831], 'a9': [0.0, -2.3218321273364126], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9798814432847255, 1.0197217057149677]]], [5, [[1.0, 0], [-1.4673095075776175, -1.6873063767355143]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.267', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1436350767392700271719851990540', 'degree': 2, 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'root_number': '-0.25863249825101414 + 0.9659757920612914*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.291635930264', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14866139711485868506095888771', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.11239192123751600550281775170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.71863284363260243148835630229', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '20.7', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/k/d/267/20'], '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': '2-380-20.7-c1-0-45', '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': '2-380-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.2916359302635691, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14866139711485868506095888771', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2723751909739876585715329899682', 'Lhash_array': ['2723751909739876585715329899682'], 'label': '2-380-20.7-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/k/d/267/20'}