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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1141445514935970308', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [-0.020618556701030927, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [0.0, 0.0], 'a9': [0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 0.05081741102259204, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[797, [1, 15, 811, 797]]], 'bad_primes': [797], 'central_character': '797.1', 'coefficient_field': '1.1.1.1', 'conductor': 797, 'conductor_radical': 797, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 0, 3, 9], [1, 0, 2, 0, 25], [1, 1, 12, 7, 49], [1, 3, 10, 33, 121], [1, 1, -9, 13, 169], [1, -7, 39, -119, 289], [1, -3, 20, -57, 361], [1, 0, 16, 0, 529], [1, -7, 54, -203, 841], [1, 0, 60, 0, 961], [1, -1, 40, -37, 1369], [1, 5, 33, 205, 1681], [1, 3, -22, 129, 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4.798211052120008, 5.401286044488807, 6.452882737109843, 7.597803371540018, 8.191239003344633, 9.240564181573317, 10.00113942500061, 10.22126266014729, 11.39349941946995, 12.00080383381073, 12.66096753236767, 13.3009950213516, 13.79235729369329, 14.46503188895015, 15.20409319624618, 15.93791381069443, 16.41910614146522, 16.9725635964967, 17.77749404653778, 18.06697427206895, 18.59458196422723, 19.16878443947747, 19.66792272317577], 'prelabel': '4-797-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.47479171701214085, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1141445514935970308, 'z1': {'__RealLiteral__': 0, 'data': '3.37269439426', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.79821105212', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.40128604449', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.05081741102259204, 'bad_primes': [797], 'central_character': '1.1', 'conductor': 797, 'conductor_radical': 797, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, -1, 0, 1, 0, -3, 2, -1, 0, 0, 0, 7, 0, 3, 0, 1, 0, 0, 0, -2, 0, -4, 2, 7, 0, 0, 0, 3, 0, 0, -2, 1, 0, 1, 0, -5, 0, -3, 6, 0, 0, -8, 0, -11, 0, -7, 2, 7, 0, 0, 0, -3, 0, 0, 0, -4, 0, -1, 8, 0, 0, -8, -14, 0, 0, 8, 0, -1, 0, 2, -6, 3, 0, 2, 0, -2, 0, 19, -2, 0, 0, -7, 0, 1, 0, 1, 0, 0, 0, 0, 0, 10, 0, -3, 4], 'euler11': [1, 3, 10, 33, 121], 'euler13': [1, 1, -9, 13, 169], 'euler17': [1, -7, 39, -119, 289], 'euler19': [1, -3, 20, -57, 361], 'euler2': [1, 0, 2, 0, 4], 'euler23': [1, 0, 16, 0, 529], 'euler29': [1, -7, 54, -203, 841], 'euler3': [1, 1, 0, 3, 9], 'euler31': [1, 0, 60, 0, 961], 'euler37': [1, -1, 40, -37, 1369], 'euler41': [1, 5, 33, 205, 1681], 'euler43': [1, 3, -22, 129, 1849], 'euler47': [1, 8, 52, 376, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, -7, 46, -371, 2809], 'euler59': [1, 0, -38, 0, 3481], 'euler61': [1, 4, 62, 244, 3721], 'euler67': [1, 8, 34, 536, 4489], 'euler7': [1, 1, 12, 7, 49], 'euler71': [1, -8, 42, -568, 5041], 'euler73': [1, 1, 84, 73, 5329], 'euler79': [1, -2, -90, -158, 6241], 'euler83': [1, -19, 208, -1577, 6889], 'euler89': [1, -1, -27, -89, 7921], 'euler97': [1, -10, 82, -970, 9409], 'euler_factors': [[1, 0, 2, 0, 4], [1, 1, 0, 3, 9], [1, 0, 2, 0, 25], [1, 1, 12, 7, 49], [1, 3, 10, 33, 121], [1, 1, -9, 13, 169], [1, -7, 39, -119, 289], [1, -3, 20, -57, 361], [1, 0, 16, 0, 529], [1, -7, 54, -203, 841], [1, 0, 60, 0, 961], [1, -1, 40, -37, 1369], [1, 5, 33, 205, 1681], [1, 3, -22, 129, 1849], [1, 8, 52, 376, 2209], [1, -7, 46, -371, 2809], [1, 0, -38, 0, 3481], [1, 4, 62, 244, 3721], [1, 8, 34, 536, 4489], [1, -8, 42, -568, 5041], [1, 1, 84, 73, 5329], [1, -2, -90, -158, 6241], [1, -19, 208, -1577, 6889], [1, -1, -27, -89, 7921], [1, -10, 82, -970, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/797/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-797-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-797-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.47479171701214085, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1141445514935970308, 'z1': {'__RealLiteral__': 0, 'data': '3.37269439426', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1141445514935970308', 'Lhash_array': ['1141445514935970308'], 'label': '4-797-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/797/a'}