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lfunc_lfunctions • Show schema
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{'Lhash': '580317782440179065393258080019', 'a10': 0, 'a2': -5, 'a3': -3, 'a4': 17, 'a5': 0, 'a6': 15, 'a7': -3, 'a8': -45, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.67657575473603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3]], [5, [1]], [11, [1, 11]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 5, 8], [1, 3], [1], [1, 3, 343], [1, 11], [1, 32, 2197], [1, 33, 4913], [1, -47, 6859], [1, 113, 12167], [1, 54, 24389], [1, -178, 29791], [1, 19, 50653], [1, -139, 68921], [1, -308, 79507], [1, 195, 103823], [1, 152, 148877], [1, 625, 205379], [1, -320, 226981], [1, 200, 300763], [1, 947, 357911], [1, -448, 389017], [1, 721, 493039], [1, 142, 571787], [1, -404, 704969], [1, 79, 912673], [1, 545, 1030301], [1, -1306, 1092727], [1, 1938, 1225043], [1, 576, 1295029], [1, -1104, 1442897]], 'euler_factors_factorization': [[[[1, 5, 8], 1]], [[[1, 3], 1]], [1], [[[1, 3, 343], 1]], [[[1, 11], 1]], [[[1, 32, 2197], 1]], [[[1, 33, 4913], 1]], [[[1, -47, 6859], 1]], [[[1, 113, 12167], 1]], [[[1, 54, 24389], 1]], [[[1, -178, 29791], 1]], [[[1, 19, 50653], 1]], [[[1, -139, 68921], 1]], [[[1, -308, 79507], 1]], [[[1, 195, 103823], 1]], [[[1, 152, 148877], 1]], [[[1, 625, 205379], 1]], [[[1, -320, 226981], 1]], [[[1, 200, 300763], 1]], [[[1, 947, 357911], 1]], [[[1, -448, 389017], 1]], [[[1, 721, 493039], 1]], [[[1, 142, 571787], 1]], [[[1, -404, 704969], 1]], [[[1, 79, 912673], 1]], [[[1, 545, 1030301], 1]], [[[1, -1306, 1092727], 1]], [[[1, 1938, 1225043], 1]], [[[1, 576, 1295029], 1]], [[[1, -1104, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-825-1.1-c3-0-5', 'leading_term': '0.384854049322166385702819922975990000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': 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8.767737478617057, 7.861765590273475, 6.679257887676075, 5.256129689196938, 3.638966345067767, 1.8831448752430615, 0.05051173493006392, -1.7932753884569086, -3.5816150345361417, -5.249899553459623, -6.738378428607722, -7.9948052622087955, -8.97673620242489, -9.653364557156506, -10.006799583183177, -10.032725763245184, -9.740410793324157, -9.152064283971868, -8.301582994773591, -7.2327504100463855, -5.996986851147224, -4.650769517840246, -3.252858550016679, -1.8614744524586904, -0.5315734973845834, 0.6876390675629336, 1.7548326433604617, 2.6382076928101363], 'positive_zeros': ['0.45779001117160984669781443764031', '1.72245949754762610921239561275816', '2.84679337150766418326259469436832', '4.51068218999076718561587436021612', '5.80548181248261029059555322521029', '6.64322727489192114310104377908134', '7.50506055730627607780729180908004', '8.115806408807401130792124009830368', '9.164068148390571035206558399273550', '9.811021672104947389089780926872590'], 'prelabel': '2-825-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 504412438111374439, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45779001117160984669781443764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.72245949754762610921239561276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84679337150766418326259469437', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.67657575473603, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, -5, -3, 17, 0, 15, -3, -45, 9, 0, -11, -51, -32, 15, 0, 89, -33, -45, 47, 0, 9, 55, -113, 135, 0, 160, -27, -51, -54, 0, 178, -85, 33, 165, 0, 153, -19, -235, 96, 0, 139, -45, 308, -187, 0, 565, -195, -267, -334, 0, 99, -544, -152, 135, 0, 135, -141, 270, -625, 0, 320, -890, -27, -287, 0, -165, -200, -561, 339, 0, -947, -405, 448, 95, 0, 799, 33, -480, -721, 0, 81, -695, -142, 153, 0, -1540, 162, 495, 404, 0, 96, -1921, -534, 975, 0, 255, -79, 1670, -99, 0], 'euler11': [1, 11, 0], 'euler13': [1, 32, 2197], 'euler17': [1, 33, 4913], 'euler19': [1, -47, 6859], 'euler2': [1, 5, 8], 'euler23': [1, 113, 12167], 'euler29': [1, 54, 24389], 'euler3': [1, 3, 0], 'euler31': [1, -178, 29791], 'euler37': [1, 19, 50653], 'euler41': [1, -139, 68921], 'euler43': [1, -308, 79507], 'euler47': [1, 195, 103823], 'euler5': [1, 0, 0], 'euler53': [1, 152, 148877], 'euler59': [1, 625, 205379], 'euler61': [1, -320, 226981], 'euler67': [1, 200, 300763], 'euler7': [1, 3, 343], 'euler71': [1, 947, 357911], 'euler73': [1, -448, 389017], 'euler79': [1, 721, 493039], 'euler83': [1, 142, 571787], 'euler89': [1, -404, 704969], 'euler97': [1, 79, 912673], 'euler_factors': [[1, 5, 8], [1, 3, 0], [1, 0, 0], [1, 3, 343], [1, 11, 0], [1, 32, 2197], [1, 33, 4913], [1, -47, 6859], [1, 113, 12167], [1, 54, 24389], [1, -178, 29791], [1, 19, 50653], [1, -139, 68921], [1, -308, 79507], [1, 195, 103823], [1, 152, 148877], [1, 625, 205379], [1, -320, 226981], [1, 200, 300763], [1, 947, 357911], [1, -448, 389017], [1, 721, 493039], [1, 142, 571787], [1, -404, 704969], [1, 79, 912673]], 'index': 5, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/4/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/825/4/a/a'], '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': '2-825-1.1-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.976860021151064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 504412438111374439, 'z1': {'__RealLiteral__': 0, 'data': '0.45779001117160984669781443764', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19979121
{'Lhash': '580317782440179065393258080019', 'Lhash_array': ['580317782440179065393258080019'], 'label': '2-825-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/a'}
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id: 24573461
{'Lhash': '580317782440179065393258080019', 'Lhash_array': ['580317782440179065393258080019'], 'label': '2-825-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/4/a/a/1/1'}