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lfunc_lfunctions • Show schema
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{'Lhash': '3927368786833602873824520580801', 'a10': [-1.0, -2.0], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [0.2928932188134525, -0.2928932188134525], 'a4': [0.0, -1.0], 'a5': [0.7071067811865476, -2.1213203435596424], 'a6': [0.0, -0.41421356237309503], 'a7': [-2.1213203435596424, 2.1213203435596424], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [0.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-0.7071067811865476, 2.1213203435596424]]], [11, [[1.0, 0], [-1.4142135623730951, 3.0]]]], 'bad_primes': [2, 5, 11], 'central_character': '110.87', 'coefficient_field': 'CDF', 'conductor': 110, 'conductor_radical': 110, 'conjugate': '2538871897008657121207553706666', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 0.7071067811865476]], 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.09814769631830291355157683830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.24691816132634715133386340351', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.38135762585198493384827002430', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'bad_primes': [2, 5, 11], 'central_character': '55.32', 'conductor': 110, 'conductor_radical': 110, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/110/2/f/b/87/2'], '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': '2-110-55.32-c1-0-4', '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': '2-110-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9372056456477866, 'root_angle': 0.15821354508927757, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.09814769631830291355157683830', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3927368786833602873824520580801', 'Lhash_array': ['3927368786833602873824520580801'], 'factors': ['2-110-55.32-c1-0-4'], 'label': '2-110-55.32-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/110/2/f/b/87/2'}