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lfunc_lfunctions • Show schema
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{'Lhash': '968846984499538425615981609183', 'a10': [0.8090169943749475, 0.5877852522924731], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-1.0, 0.0], 'a6': [-0.30901699437494745, -0.9510565162951535], 'a7': [0.0, 0.0], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1379', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '1896097365833586609135850672241', 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'4.35711757772140610690028697234086', '5.42868939354976063403352338766636', '6.57621769153610561090583422930173', '7.21349042034613693592827418803819', '7.67107302251207786555335136624263', '8.593651513844829349233608557950552', '8.907706102515296388969169680520326'], 'prelabel': '2-1860-1860.1379-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.15364727042335866, 'root_number': '0.56909272118240398061655780599830 - 0.82227335764769042142673341348985*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15364727042335866', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76428550921295347572565042270', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18009902994333449570581966654', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24364145005132855106014252961', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1379', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/bt/b/1379/1'], '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': '2-1860-1860.1379-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1860-1860.1379-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.15364727042335866, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76428550921295347572565042270', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '968846984499538425615981609183', 'Lhash_array': ['968846984499538425615981609183'], 'factors': ['2-1860-1860.1379-c0-0-0'], 'label': '2-1860-1860.1379-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/bt/b/1379/1'}