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lfunc_lfunctions • Show schema
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{'Lhash': '1741433627666974359037492930318,2441222058417965906385738083055', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 428.3750897471616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2592.1', 'coefficient_field': '1.1.1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, -1, 10, 25], [1, -4, 9, -28, 49], [1, 4, 5, 44, 121], [1, -2, -9, -26, 169], [1, 12, 70, 204, 289], [1, 8, 54, 152, 361], [1, 0, -23, 0, 529], [1, 2, -25, 58, 841], [1, 4, -15, 124, 961], [1, 4, 78, 148, 1369], [1, 2, -37, 82, 1681], [1, 4, -27, 172, 1849], [1, 8, 17, 376, 2209], [1, -20, 206, -1060, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, 4, -51, 268, 4489], [1, 32, 398, 2272, 5041], [1, 12, 182, 876, 5329], [1, 4, -63, 316, 6241], [1, 12, 61, 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'trace_hash': 951750521190737145, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37374890790367982153748551298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92578464284909834771248956834', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.33559924612471592659008956244', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 428.3750897471616, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 4, 0, 0, 0, -4, 0, 2, 0, 0, 0, -12, 0, -8, 0, 0, 0, 0, 0, 5, 0, 0, 0, -2, 0, -4, 0, 0, 0, -8, 0, -4, 0, 0, 0, -2, 0, -4, 0, 0, 0, -8, 0, 7, 0, 0, 0, 20, 0, 8, 0, 0, 0, 4, 0, -6, 0, 0, 0, -4, 0, -4, 0, 0, 0, -32, 0, -12, 0, 0, 0, -16, 0, -4, 0, 0, 0, -12, 0, 24, 0, 0, 0, 20, 0, 8, 0, 0, 0, 16, 0, 14, 0, 0, 0], 'euler11': [1, 4, 5, 44, 121], 'euler13': [1, -2, -9, -26, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, 2, -25, 58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, -15, 124, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 2, -37, 82, 1681], 'euler43': [1, 4, -27, 172, 1849], 'euler47': [1, 8, 17, 376, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, -20, 206, -1060, 2809], 'euler59': [1, -4, -43, -236, 3481], 'euler61': [1, 6, -25, 366, 3721], 'euler67': [1, 4, -51, 268, 4489], 'euler7': [1, -4, 9, -28, 49], 'euler71': [1, 32, 398, 2272, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 4, -63, 316, 6241], 'euler83': [1, 12, 61, 996, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -14, 99, -1358, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, -4, 9, -28, 49], [1, 4, 5, 44, 121], [1, -2, -9, -26, 169], [1, 12, 70, 204, 289], [1, 8, 54, 152, 361], [1, 0, -23, 0, 529], [1, 2, -25, 58, 841], [1, 4, -15, 124, 961], [1, 4, 78, 148, 1369], [1, 2, -37, 82, 1681], [1, 4, -27, 172, 1849], [1, 8, 17, 376, 2209], [1, -20, 206, -1060, 2809], [1, -4, -43, -236, 3481], [1, 6, -25, 366, 3721], [1, 4, -51, 268, 4489], [1, 32, 398, 2272, 5041], [1, 12, 182, 876, 5329], [1, 4, -63, 316, 6241], [1, 12, 61, 996, 6889], [1, -20, 278, -1780, 7921], [1, -14, 99, -1358, 9409]], 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/i/h'], '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': '4-2592e2-1.1-c1e2-0-34', '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': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 951750521190737145, 'z1': {'__RealLiteral__': 0, 'data': '1.37374890790367982153748551298', 'prec': 103}}
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{'Lhash': '1741433627666974359037492930318,2441222058417965906385738083055', 'Lhash_array': ['1741433627666974359037492930318', '2441222058417965906385738083055'], 'label': '4-2592e2-1.1-c1e2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/i/h'}