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lfunc_lfunctions • Show schema
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{'Lhash': '1787704546215465882968612796603', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 4, 'a5': 5, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.3133651550257905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 3]], [5, [1, -5]], [13, [1, -13]]], 'bad_primes': [3, 5, 13], 'central_character': '195.194', 'coefficient_field': '1.1.1.1', 'conductor': 195, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, 0, -4], [1, 3], [1, -5], [1, 1, 49], [1, 17, 121], [1, -13], [1, -31, 289], [1, 0, -361], [1, -19, 529], [1, 0, -841], [1, 0, -961], [1, 61, 1369], [1, -43, 1681], [1, 0, -1849], [1, 0, -2209], [1, 41, 2809], [1, 38, 3481], [1, 73, 3721], [1, -74, 4489], [1, -103, 5041], [1, 94, 5329], [1, 37, 6241], [1, 0, -6889], [1, 173, 7921], [1, 181, 9409], [1, 0, -10201], [1, 0, -10609], [1, 149, 11449], [1, 0, -11881], [1, -34, 12769]], 'euler_factors_factorization': [[[[1, -2], 1], [[1, 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'1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2-0', 'trace_hash': 1823062942804208270, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41025022659525055073707903900', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06763453592803290747245242836', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27727475927254964577085556976', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.3133651550257905, 'bad_primes': [3, 5, 13], 'central_character': '195.194', 'conductor': 195, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 4, 5, 0, -1, 0, 9, 0, -17, -12, 13, 0, -15, 16, 31, 0, 0, 20, 3, 0, 19, 0, 25, 0, -27, -4, 0, 0, 0, 0, 51, 0, -5, 36, -61, 0, -39, 0, 43, 0, 0, -68, 45, 0, 0, -48, -48, 0, -93, 52, -41, 0, -85, 0, 0, 0, -38, -60, -73, 0, -9, 64, 65, 0, 74, 124, -57, 0, 103, 0, -94, 0, -75, 0, 17, 0, -37, 80, 81, 0, 0, 12, 155, 0, 0, 0, -173, 0, -13, 76, 0, 0, 0, 0, -181, 0, -153, 100], 'euler11': [1, 17, 121], 'euler13': [1, -13, 0], 'euler17': [1, -31, 289], 'euler19': [1, 0, -361], 'euler2': [1, 0, -4], 'euler23': [1, -19, 529], 'euler29': [1, 0, -841], 'euler3': [1, 3, 0], 'euler31': [1, 0, -961], 'euler37': [1, 61, 1369], 'euler41': [1, -43, 1681], 'euler43': [1, 0, -1849], 'euler47': [1, 0, -2209], 'euler5': [1, -5, 0], 'euler53': [1, 41, 2809], 'euler59': [1, 38, 3481], 'euler61': [1, 73, 3721], 'euler67': [1, -74, 4489], 'euler7': [1, 1, 49], 'euler71': [1, -103, 5041], 'euler73': [1, 94, 5329], 'euler79': [1, 37, 6241], 'euler83': [1, 0, -6889], 'euler89': [1, 173, 7921], 'euler97': [1, 181, 9409], 'euler_factors': [[1, 0, -4], [1, 3, 0], [1, -5, 0], [1, 1, 49], [1, 17, 121], [1, -13, 0], [1, -31, 289], [1, 0, -361], [1, -19, 529], [1, 0, -841], [1, 0, -961], [1, 61, 1369], [1, -43, 1681], [1, 0, -1849], [1, 0, -2209], [1, 41, 2809], [1, 38, 3481], [1, 73, 3721], [1, -74, 4489], [1, -103, 5041], [1, 94, 5329], [1, 37, 6241], [1, 0, -6889], [1, 173, 7921], [1, 181, 9409]], 'index': 20, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/195/3/e/b/194/1', 'ModularForm/GL2/Q/holomorphic/195/3/e/b'], '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': '2-195-195.194-c2-0-20', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-195-195.194-c2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3050737851586858, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2-0', 'trace_hash': 1823062942804208270, 'z1': {'__RealLiteral__': 0, 'data': '1.41025022659525055073707903900', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10770221
{'Lhash': '1787704546215465882968612796603', 'Lhash_array': ['1787704546215465882968612796603'], 'factors': ['2-195-195.194-c2-0-20'], 'label': '2-195-195.194-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/195/3/e/b'}
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id: 24550114
{'Lhash': '1787704546215465882968612796603', 'Lhash_array': ['1787704546215465882968612796603'], 'factors': ['2-195-195.194-c2-0-20'], 'label': '2-195-195.194-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/195/3/e/b/194/1'}