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lfunc_lfunctions • Show schema
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{'Lhash': '1673984179646939089366397051773', 'a10': [2.235857911289395, 0.03064964150890418], 'a2': [0.7071067811865476, -0.7071067811865476], 'a3': [1.5958851880575038, 0.673164516696079], 'a4': [0.0, -1.0], 'a5': [1.5593177214904386, 1.6026628601942041], 'a6': [1.604460433080592, -0.6524620438606673], 'a7': [-0.7002508406730334, -0.7002508406730334], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [2.0936990669226687, 2.1485865626423215], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.5958851880575038, -0.673164516696079]]], [5, [[1.0, 0], [-1.5593177214904386, -1.6026628601942041]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.497', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': 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2.7250848405103056, 'root_angle': -0.022392969622328292, 'root_number': '0.9901181887512507 - 0.1402354174377595*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0223929696223', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32054067528193721629189323031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73325794132892970803593814024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62753455090804047031174161185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '15.2', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/j/g/497/19'], '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': '2-930-15.2-c1-0-30', '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': '2-930-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.022392969622328292, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32054067528193721629189323031', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1673984179646939089366397051773', 'Lhash_array': ['1673984179646939089366397051773'], 'factors': ['2-930-15.2-c1-0-30'], 'label': '2-930-15.2-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/j/g/497/19'}