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lfunc_lfunctions • Show schema
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{'Lhash': '1535715117951650876747620904267,2402061971551522154712575873190', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 338.4692067138067, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2304.1', 'coefficient_field': '1.1.1.1', 'conductor': 5308416, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -6, 0, 25], [1, 8, 30, 56, 49], [1, 0, -18, 0, 121], [1, 0, -22, 0, 169], [1, -4, 38, -68, 289], [1, 0, -34, 0, 361], [1, 8, 62, 184, 529], [1, 0, -22, 0, 841], [1, 0, 62, 0, 961], [1, 0, 26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -50, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, -70, 0, 2809], [1, 0, 78, 0, 3481], [1, 0, -118, 0, 3721], [1, 0, -34, 0, 4489], [1, 24, 286, 1704, 5041], [1, 28, 342, 2044, 5329], [1, -16, 222, -1264, 6241], [1, 0, -130, 0, 6889], [1, 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'1.89489278127510207413757070938359', '2.76949698107409344784867387251804', '3.02134894909850940868110394782222', '3.51512988593556574794619540592964', '3.54504386175201089083978945511281', '4.43840339046971541107811169446073', '4.65041292432824869473491905227497', '5.54545642580210773785881917935839', '5.75245531885267310765400026045503', '6.05413092799802394714867394530796', '6.63217600020591710133260327070657', '6.88483364047604802017468384205263', '6.90658693472445454577262700351023', '7.78807401181537754550940713268650', '7.927597082960768217010357813250628', '8.537883598187149394139660939031038', '8.901283822911148933219274961961185'], 'prelabel': '4-48e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1131153389031153573, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21146561810893222769175172833', 'prec': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 338.4692067138067, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5308416, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -8, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -16, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -28, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, -18, 0, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 0, -34, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 62, 184, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -50, 0, 1849], 'euler47': [1, 16, 158, 752, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, 0, 78, 0, 3481], 'euler61': [1, 0, -118, 0, 3721], 'euler67': [1, 0, -34, 0, 4489], 'euler7': [1, 8, 30, 56, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, -16, 222, -1264, 6241], 'euler83': [1, 0, -130, 0, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 25], [1, 8, 30, 56, 49], [1, 0, -18, 0, 121], [1, 0, -22, 0, 169], [1, -4, 38, -68, 289], [1, 0, -34, 0, 361], [1, 8, 62, 184, 529], [1, 0, -22, 0, 841], [1, 0, 62, 0, 961], [1, 0, 26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -50, 0, 1849], [1, 16, 158, 752, 2209], [1, 0, -70, 0, 2809], [1, 0, 78, 0, 3481], [1, 0, -118, 0, 3721], [1, 0, -34, 0, 4489], [1, 24, 286, 1704, 5041], [1, 28, 342, 2044, 5329], [1, -16, 222, -1264, 6241], [1, 0, -130, 0, 6889], [1, 4, 182, 356, 7921], [1, 4, 198, 388, 9409]], 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/2/d/b'], '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': '4-48e4-1.1-c1e2-0-28', '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': 2, 'prelabel': '4-48e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1131153389031153573, 'z1': {'__RealLiteral__': 0, 'data': '1.21146561810893222769175172833', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1535715117951650876747620904267,2402061971551522154712575873190', 'Lhash_array': ['1535715117951650876747620904267', '2402061971551522154712575873190'], 'label': '4-48e4-1.1-c1e2-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/d/b'}