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{'Lhash': '886243406290104332790336199789,888723039543818984953356148273,2352147923955520570634490852798,2582071713967628693188813150861', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 476.1369573827687, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 0, 2, 0, 1]], [13, [1, 0, 26, 0, 169]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 117117950625, 'conductor_radical': 195, 'degree': 8, 'euler_factors': [[1, 0, 0, 0, 8, 0, 0, 0, 16], [1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 99, 0, -98, 0, 2401], [1, 0, -26, 0, 411, 0, -3146, 0, 14641], [1, 0, 26, 0, 169], [1, 0, 42, 0, 1019, 0, 12138, 0, 83521], [1, 0, 28, 0, 918, 0, 10108, 0, 130321], [1, 0, 66, 0, 2147, 0, 34914, 0, 279841], [1, 0, 12, 0, 1718, 0, 10092, 0, 707281], [1, 0, -20, 0, 2022, 0, -19220, 0, 923521], [1, 0, -122, 0, 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'10.83011117654957591658900061588047', '11.44201407773603800801142731519435'], 'prelabel': '8-585e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 671441193403961698, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69912277573216465176782182821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.70107886146530611510706438638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.85551754050527559636569970945', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 476.1369573827687, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 117117950625, 'conductor_radical': 195, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -26, 0, 411, 0, -3146, 0, 14641], 'euler13': [1, 0, 26, 0, 169, 0, 0, 0, 0], 'euler17': [1, 0, 42, 0, 1019, 0, 12138, 0, 83521], 'euler19': [1, 0, 28, 0, 918, 0, 10108, 0, 130321], 'euler2': [1, 0, 0, 0, 8, 0, 0, 0, 16], 'euler23': [1, 0, 66, 0, 2147, 0, 34914, 0, 279841], 'euler29': [1, 0, 12, 0, 1718, 0, 10092, 0, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -20, 0, 2022, 0, -19220, 0, 923521], 'euler37': [1, 0, -122, 0, 6459, 0, -167018, 0, 1874161], 'euler41': [1, 0, 78, 0, 4883, 0, 131118, 0, 2825761], 'euler43': [1, 16, 268, 2320, 19606, 99760, 495532, 1272112, 3418801], 'euler47': [1, 0, -156, 0, 10502, 0, -344604, 0, 4879681], 'euler5': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler53': [1, 0, -22, 0, 5739, 0, -61798, 0, 7890481], 'euler59': [1, 0, 52, 0, 7638, 0, 181012, 0, 12117361], 'euler61': [1, -52, 1258, -18304, 174595, -1116544, 4681018, -11803012, 13845841], 'euler67': [1, 0, -268, 0, 26934, 0, -1203052, 0, 20151121], 'euler7': [1, 0, -2, 0, 99, 0, -98, 0, 2401], 'euler71': [1, 0, -234, 0, 23771, 0, -1179594, 0, 25411681], 'euler73': [1, 0, -188, 0, 19494, 0, -1001852, 0, 28398241], 'euler79': [1, -52, 1330, -21112, 226219, -1667848, 8300530, -25638028, 38950081], 'euler83': [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], 'euler89': [1, 0, -338, 0, 44403, 0, -2677298, 0, 62742241], 'euler97': [1, 0, -362, 0, 51579, 0, -3406058, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 8, 0, 0, 0, 16], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -2, 0, 99, 0, -98, 0, 2401], [1, 0, -26, 0, 411, 0, -3146, 0, 14641], [1, 0, 26, 0, 169, 0, 0, 0, 0], [1, 0, 42, 0, 1019, 0, 12138, 0, 83521], [1, 0, 28, 0, 918, 0, 10108, 0, 130321], [1, 0, 66, 0, 2147, 0, 34914, 0, 279841], [1, 0, 12, 0, 1718, 0, 10092, 0, 707281], [1, 0, -20, 0, 2022, 0, -19220, 0, 923521], [1, 0, -122, 0, 6459, 0, -167018, 0, 1874161], [1, 0, 78, 0, 4883, 0, 131118, 0, 2825761], [1, 16, 268, 2320, 19606, 99760, 495532, 1272112, 3418801], [1, 0, -156, 0, 10502, 0, -344604, 0, 4879681], [1, 0, -22, 0, 5739, 0, -61798, 0, 7890481], [1, 0, 52, 0, 7638, 0, 181012, 0, 12117361], [1, -52, 1258, -18304, 174595, -1116544, 4681018, -11803012, 13845841], [1, 0, -268, 0, 26934, 0, -1203052, 0, 20151121], [1, 0, -234, 0, 23771, 0, -1179594, 0, 25411681], [1, 0, -188, 0, 19494, 0, -1001852, 0, 28398241], [1, -52, 1330, -21112, 226219, -1667848, 8300530, -25638028, 38950081], [1, 0, -260, 0, 30678, 0, -1791140, 0, 47458321], [1, 0, -338, 0, 44403, 0, -2677298, 0, 62742241], [1, 0, -362, 0, 51579, 0, -3406058, 0, 88529281]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/b/f'], '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': '8-585e4-1.1-c1e4-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-585e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 671441193403961698, 'z1': {'__RealLiteral__': 0, 'data': '0.69912277573216465176782182821', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '886243406290104332790336199789,888723039543818984953356148273,2352147923955520570634490852798,2582071713967628693188813150861', 'Lhash_array': ['886243406290104332790336199789', '888723039543818984953356148273', '2352147923955520570634490852798', '2582071713967628693188813150861'], 'label': '8-585e4-1.1-c1e4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/b/f'}