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lfunc_lfunctions • Show schema
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{'Lhash': '1901451657020131673109390381693', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 14, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 81, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.615677637366039, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '64.63', 'coefficient_field': '1.1.1.1', 'conductor': 64, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[1], [1, 0, -81], [1, -14, 625], [1, 0, -2401], [1, 0, -14641], [1, -238, 28561], [1, -322, 83521], [1, 0, -130321], [1, 0, -279841], [1, 82, 707281], [1, 0, -923521], [1, 2162, 1874161], [1, 3038, 2825761], [1, 0, -3418801], [1, 0, -4879681], [1, 2482, 7890481], [1, 0, -12117361], [1, -6958, 13845841], [1, 0, -20151121], [1, 0, -25411681], [1, -1442, 28398241], [1, 0, -38950081], [1, 0, -47458321], [1, 9758, 62742241], [1, 1918, 88529281], [1, 18802, 104060401], [1, 0, -112550881], [1, 0, -131079601], [1, 9362, 141158161], [1, 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'13.98854262116414467487283372784694'], 'prelabel': '2-2e6-4.3-c4-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5720959619279444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c4-0', 'trace_hash': 1313820879685019631, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.49998087539089393848938004561', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71181906572610660469945677070', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.49397901031855704077965920800', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.615677637366039, 'bad_primes': [2], 'central_character': '4.3', 'conductor': 64, 'conductor_radical': 2, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 14, 0, 0, 0, 81, 0, 0, 0, 238, 0, 0, 0, 322, 0, 0, 0, 0, 0, 0, 0, -429, 0, 0, 0, -82, 0, 0, 0, 0, 0, 0, 0, -2162, 0, 0, 0, -3038, 0, 0, 0, 1134, 0, 0, 0, 2401, 0, 0, 0, -2482, 0, 0, 0, 0, 0, 0, 0, 6958, 0, 0, 0, 3332, 0, 0, 0, 0, 0, 0, 0, 1442, 0, 0, 0, 0, 0, 0, 0, 6561, 0, 0, 0, 4508, 0, 0, 0, -9758, 0, 0, 0, 0, 0, 0, 0, -1918, 0, 0, 0], 'euler11': [1, 0, -14641], 'euler13': [1, -238, 28561], 'euler17': [1, -322, 83521], 'euler19': [1, 0, -130321], 'euler2': [1, 0, 0], 'euler23': [1, 0, -279841], 'euler29': [1, 82, 707281], 'euler3': [1, 0, -81], 'euler31': [1, 0, -923521], 'euler37': [1, 2162, 1874161], 'euler41': [1, 3038, 2825761], 'euler43': [1, 0, -3418801], 'euler47': [1, 0, -4879681], 'euler5': [1, -14, 625], 'euler53': [1, 2482, 7890481], 'euler59': [1, 0, -12117361], 'euler61': [1, -6958, 13845841], 'euler67': [1, 0, -20151121], 'euler7': [1, 0, -2401], 'euler71': [1, 0, -25411681], 'euler73': [1, -1442, 28398241], 'euler79': [1, 0, -38950081], 'euler83': [1, 0, -47458321], 'euler89': [1, 9758, 62742241], 'euler97': [1, 1918, 88529281], 'euler_factors': [[1, 0, 0], [1, 0, -81], [1, -14, 625], [1, 0, -2401], [1, 0, -14641], [1, -238, 28561], [1, -322, 83521], [1, 0, -130321], [1, 0, -279841], [1, 82, 707281], [1, 0, -923521], [1, 2162, 1874161], [1, 3038, 2825761], [1, 0, -3418801], [1, 0, -4879681], [1, 2482, 7890481], [1, 0, -12117361], [1, -6958, 13845841], [1, 0, -20151121], [1, 0, -25411681], [1, -1442, 28398241], [1, 0, -38950081], [1, 0, -47458321], [1, 9758, 62742241], [1, 1918, 88529281]], 'index': 3, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/64/5/c/a/63/1', 'ModularForm/GL2/Q/holomorphic/64/5/c/a'], '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': '2-2e6-4.3-c4-0-3', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-2e6-4.3-c4-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5720959619279444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4-0', 'trace_hash': 1313820879685019631, 'z1': {'__RealLiteral__': 0, 'data': '1.49998087539089393848938004561', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10571422
{'Lhash': '1901451657020131673109390381693', 'Lhash_array': ['1901451657020131673109390381693'], 'factors': ['2-2e6-4.3-c4-0-3'], 'label': '2-2e6-4.3-c4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/64/5/c/a'}
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id: 24550698
{'Lhash': '1901451657020131673109390381693', 'Lhash_array': ['1901451657020131673109390381693'], 'factors': ['2-2e6-4.3-c4-0-3'], 'label': '2-2e6-4.3-c4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/64/5/c/a/63/1'}