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lfunc_lfunctions • Show schema
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{'Lhash': '275016508507307708934543936349,3810090549187949332961662410670', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -8, 'a5': -9, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -18, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.700655875543622, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[5, [1, 9, 25]], [19, [1, 38, 361]]], 'bad_primes': [5, 19], 'central_character': '95.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, 8, 0, 16], [1, 0, 18, 0, 81], [1, 9, 25], [1, 0, 73, 0, 2401], [1, 6, 251, 726, 14641], [1, 0, 338, 0, 28561], [1, 0, 353, 0, 83521], [1, 38, 361], [1, 0, 158, 0, 279841], [1, 0, -1682, 0, 707281], [1, 0, -1922, 0, 923521], [1, 0, 2738, 0, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3527, 0, 3418801], [1, 0, -1207, 0, 4879681], [1, 0, 5618, 0, 7890481], [1, 0, -6962, 0, 12117361], [1, 206, 18051, 766526, 13845841], [1, 0, 8978, 0, 20151121], [1, 0, -10082, 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'13.01776673187754855297668165522036', '13.39187719624353869399446367513209', '14.25157432388585649567356766633413'], 'prelabel': '4-95e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6089010259872485, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c2e2-0', 'trace_hash': 683528778041269516, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21694977185179685344681100031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00563147960642771695247642133', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63104032948032955842137086463', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 6.700655875543622, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -8, -9, 0, 0, 0, -18, 0, -6, 0, 0, 0, 0, 48, 0, 0, -38, 72, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 48, 162, 0, 0, 0, -73, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, -206, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 304, 0, 0, 0, -432, 243, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 342, 0, 0, 0, 108, -448], 'euler11': [1, 6, 251, 726, 14641], 'euler13': [1, 0, 338, 0, 28561], 'euler17': [1, 0, 353, 0, 83521], 'euler19': [1, 38, 361, 0, 0], 'euler2': [1, 0, 8, 0, 16], 'euler23': [1, 0, 158, 0, 279841], 'euler29': [1, 0, -1682, 0, 707281], 'euler3': [1, 0, 18, 0, 81], 'euler31': [1, 0, -1922, 0, 923521], 'euler37': [1, 0, 2738, 0, 1874161], 'euler41': [1, 0, -3362, 0, 2825761], 'euler43': [1, 0, -3527, 0, 3418801], 'euler47': [1, 0, -1207, 0, 4879681], 'euler5': [1, 9, 25, 0, 0], 'euler53': [1, 0, 5618, 0, 7890481], 'euler59': [1, 0, -6962, 0, 12117361], 'euler61': [1, 206, 18051, 766526, 13845841], 'euler67': [1, 0, 8978, 0, 20151121], 'euler7': [1, 0, 73, 0, 2401], 'euler71': [1, 0, -10082, 0, 25411681], 'euler73': [1, 0, 10033, 0, 28398241], 'euler79': [1, 0, -12482, 0, 38950081], 'euler83': [1, 0, 5678, 0, 47458321], 'euler89': [1, 0, -15842, 0, 62742241], 'euler97': [1, 0, 18818, 0, 88529281], 'euler_factors': [[1, 0, 8, 0, 16], [1, 0, 18, 0, 81], [1, 9, 25, 0, 0], [1, 0, 73, 0, 2401], [1, 6, 251, 726, 14641], [1, 0, 338, 0, 28561], [1, 0, 353, 0, 83521], [1, 38, 361, 0, 0], [1, 0, 158, 0, 279841], [1, 0, -1682, 0, 707281], [1, 0, -1922, 0, 923521], [1, 0, 2738, 0, 1874161], [1, 0, -3362, 0, 2825761], [1, 0, -3527, 0, 3418801], [1, 0, -1207, 0, 4879681], [1, 0, 5618, 0, 7890481], [1, 0, -6962, 0, 12117361], [1, 206, 18051, 766526, 13845841], [1, 0, 8978, 0, 20151121], [1, 0, -10082, 0, 25411681], [1, 0, 10033, 0, 28398241], [1, 0, -12482, 0, 38950081], [1, 0, 5678, 0, 47458321], [1, 0, -15842, 0, 62742241], [1, 0, 18818, 0, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/3/d/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': '4-95e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-95e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6089010259872485, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 683528778041269516, 'z1': {'__RealLiteral__': 0, 'data': '0.21694977185179685344681100031', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '275016508507307708934543936349,3810090549187949332961662410670', 'Lhash_array': ['275016508507307708934543936349', '3810090549187949332961662410670'], 'label': '4-95e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/3/d/a'}