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lfunc_lfunctions • Show schema
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{'Lhash': '1565772802050433552235550590438', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 13.198663731711221], 'a6': [0, 0], 'a7': [0, -4.490912811363259], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 101.95530048991984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.1727', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '366544795193660981412772979381', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -13.198663731711221], [-125.0, 0]], [[1.0, 0], [0, 4.490912811363259], [-343.0, 0]], [[1.0, 0], [-22.351932773860586, 0], [1331.0, 0]], [[1.0, 0], [-73.54019178771861, 0], [2197.0, 0]], [[1.0, 0], [0, 42.619940172656094], [-4913.0, 0]], [[1.0, 0], [0, 122.56286417844275], [-6859.0, 0]], [[1.0, 0], 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'3.53018457049056108514049935628076', '4.04231608452586400799286671786088', '5.12694863637537294004348892680010', '5.97260620103225914181919270973921', '6.50091905325774426582816669629851', '7.933710827851882393855958039503551', '8.419956023782091760359641406547324', '8.939962023384485714724465134464965'], 'prelabel': '2-12e3-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.5, 'root_number': '0.e-55 + 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23517694999594514150464862171', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75778430987209610408677528963', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53018457049056108514049935628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 101.95530048991984, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/4/c/i/1727/9'], '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': '2-12e3-12.11-c3-0-78', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-12e3-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23517694999594514150464862171', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1565772802050433552235550590438', 'Lhash_array': ['1565772802050433552235550590438'], 'label': '2-12e3-12.11-c3-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/4/c/i/1727/9'}