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lfunc_lfunctions • Show schema
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{'Lhash': '464672767923454494332034958089,716789739546323048194816647477,808323237039092392757180237936,1499604475062479444760854448710', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37498399.429420754, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '9800.1', 'coefficient_field': '1.1.1.1', 'conductor': 9223681600000000, 'conductor_radical': 70, 'degree': 8, 'euler_factors': [[1], [1, 0, 1, 0, -8, 0, 9, 0, 81], [1], [1], [1, -4, 50, -136, 859, -1496, 6050, -5324, 14641], [1, 0, -4, 0, 342, 0, -676, 0, 28561], [1, 0, 29, 0, 552, 0, 8381, 0, 83521], [1, 0, 5, 0, 492, 0, 1805, 0, 130321], [1, -10, 77, -490, 2884, -11270, 40733, -121670, 279841], [1, 2, 65, 122, 2764, 3538, 54665, 48778, 707281], [1, 0, 80, 0, 3102, 0, 76880, 0, 923521], [1, 10, 133, 910, 7504, 33670, 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{'algebraic': True, 'analytic_conductor': 37498399.429420754, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 9223681600000000, 'conductor_radical': 70, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 2, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0], 'euler11': [1, -4, 50, -136, 859, -1496, 6050, -5324, 14641], 'euler13': [1, 0, -4, 0, 342, 0, -676, 0, 28561], 'euler17': [1, 0, 29, 0, 552, 0, 8381, 0, 83521], 'euler19': [1, 0, 5, 0, 492, 0, 1805, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -10, 77, -490, 2884, -11270, 40733, -121670, 279841], 'euler29': [1, 2, 65, 122, 2764, 3538, 54665, 48778, 707281], 'euler3': [1, 0, 1, 0, -8, 0, 9, 0, 81], 'euler31': [1, 0, 80, 0, 3102, 0, 76880, 0, 923521], 'euler37': [1, 10, 133, 910, 7504, 33670, 182077, 506530, 1874161], 'euler41': [1, 0, 65, 0, 2292, 0, 109265, 0, 2825761], 'euler43': [1, 26, 373, 3770, 28636, 162110, 689677, 2067182, 3418801], 'euler47': [1, 0, 144, 0, 9182, 0, 318096, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -4, 8, -220, 6046, -11660, 22472, -595508, 7890481], 'euler59': [1, 0, 180, 0, 15062, 0, 626580, 0, 12117361], 'euler61': [1, 0, 124, 0, 11286, 0, 461404, 0, 13845841], 'euler67': [1, -8, 82, -800, 12211, -53600, 368098, -2406104, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -30, 569, -7290, 71616, -517590, 2868329, -10737330, 25411681], 'euler73': [1, 0, 17, 0, -5676, 0, 90593, 0, 28398241], 'euler79': [1, -2, 265, -422, 30064, -33338, 1653865, -986078, 38950081], 'euler83': [1, 0, 177, 0, 15704, 0, 1219353, 0, 47458321], 'euler89': [1, 0, 201, 0, 20036, 0, 1592121, 0, 62742241], 'euler97': [1, 0, 104, 0, 17742, 0, 978536, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, -8, 0, 9, 0, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 50, -136, 859, -1496, 6050, -5324, 14641], [1, 0, -4, 0, 342, 0, -676, 0, 28561], [1, 0, 29, 0, 552, 0, 8381, 0, 83521], [1, 0, 5, 0, 492, 0, 1805, 0, 130321], [1, -10, 77, -490, 2884, -11270, 40733, -121670, 279841], [1, 2, 65, 122, 2764, 3538, 54665, 48778, 707281], [1, 0, 80, 0, 3102, 0, 76880, 0, 923521], [1, 10, 133, 910, 7504, 33670, 182077, 506530, 1874161], [1, 0, 65, 0, 2292, 0, 109265, 0, 2825761], [1, 26, 373, 3770, 28636, 162110, 689677, 2067182, 3418801], [1, 0, 144, 0, 9182, 0, 318096, 0, 4879681], [1, -4, 8, -220, 6046, -11660, 22472, -595508, 7890481], [1, 0, 180, 0, 15062, 0, 626580, 0, 12117361], [1, 0, 124, 0, 11286, 0, 461404, 0, 13845841], [1, -8, 82, -800, 12211, -53600, 368098, -2406104, 20151121], [1, -30, 569, -7290, 71616, -517590, 2868329, -10737330, 25411681], [1, 0, 17, 0, -5676, 0, 90593, 0, 28398241], [1, -2, 265, -422, 30064, -33338, 1653865, -986078, 38950081], [1, 0, 177, 0, 15704, 0, 1219353, 0, 47458321], [1, 0, 201, 0, 20036, 0, 1592121, 0, 62742241], [1, 0, 104, 0, 17742, 0, 978536, 0, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9800/2/a/cr'], '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': '8-9800e4-1.1-c1e4-0-2', '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': '8-9800e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1079251284880226061, 'z1': {'__RealLiteral__': 0, 'data': '0.36656218033564945048951429922', 'prec': 103}}
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{'Lhash': '464672767923454494332034958089,716789739546323048194816647477,808323237039092392757180237936,1499604475062479444760854448710', 'Lhash_array': ['464672767923454494332034958089', '716789739546323048194816647477', '808323237039092392757180237936', '1499604475062479444760854448710'], 'label': '8-9800e4-1.1-c1e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9800/2/a/cr'}