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lfunc_lfunctions • Show schema
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{'Lhash': '794023440816077854805586342553', 'a10': [-0.6415196266365629, 0.0], 'a2': [-1.3536599559369042, 0.0], 'a3': [-2.8275748588805687, 0.0], 'a4': [-0.16760472369289856, 0.0], 'a5': [0.47391490294366434, 0.0], 'a6': [3.8275748588805687, 0.0], 'a7': [1.0, 0.0], 'a8': [2.9341997147627543, 0.0], 'a9': [4.995179582573467, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.99302524233017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.1', 'coefficient_field': 'CDF', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3536599559369042, 0], [2.0, 0]], [[1.0, 0], [2.8275748588805687, 0], [3.0, 0]], [[1.0, 0], [-0.47391490294366434, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.1812348148174727, 0], 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'5.05242752356995650772065130454460', '5.53085123654131352949144828790290', '6.69162171767787445390324627410282', '7.45356254626022438183549175851543', '8.301155165617694081897401529299526', '9.419876211145011839127308502396645', '9.970115597779079513202603240154878'], 'prelabel': '2-1001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62637405028887366928638761304', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90428416060025497711539930512', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99020954848054038023803854705', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.99302524233017, 'bad_primes': [7, 11, 13], 'central_character': '1.1', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1001/2/a/g/1/2'], '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': '2-1001-1.1-c1-0-7', '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': '2-1001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.827193881277011, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62637405028887366928638761304', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '794023440816077854805586342553', 'Lhash_array': ['794023440816077854805586342553'], 'label': '2-1001-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1001/2/a/g/1/2'}