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lfunc_lfunctions • Show schema
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{'Lhash': '1683594540780551824177022416463,2024105483767474344424729902512', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 288.73369008297294, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 7, 19], 'central_character': '2128.1', 'coefficient_field': '1.1.1.1', 'conductor': 4528384, 'conductor_radical': 266, 'degree': 4, 'euler_factors': [[1], [1, 3, 7, 9, 9], [1, -2, 11, -10, 25], [1, 2, 1], [1, -1, 21, -11, 121], [1, 2, 27, 26, 169], [1, -1, 23, -17, 289], [1, -2, 1], [1, -2, 27, -46, 529], [1, -5, 63, -145, 841], [1, -1, -39, -31, 961], [1, 14, 103, 518, 1369], [1, -9, 71, -369, 1681], [1, 8, 82, 344, 1849], [1, 6, 83, 282, 2209], [1, -3, 97, -159, 2809], [1, 20, 213, 1180, 3481], [1, 6, 51, 366, 3721], [1, 11, 103, 737, 4489], [1, 4, 101, 284, 5041], [1, 7, 97, 511, 5329], [1, 0, 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['1.32812191346529978745892661600720', '1.59673768418762382821840388724128', '2.63799976163539761420749992767815', '2.85931159964067051249689273960125', '3.52551643625639084960069568012229', '4.03470858277818001569700588154995', '4.79041835012383709587946987796190', '4.91711529117347146996794830065195', '5.53323163616067750542999721510063', '5.66256735557282101752380578082857', '6.21507577375541435408955903766330', '6.30870163837418532801635703301963', '6.76956516264692419252188916430276', '7.14164500255635955891571988887538', '7.78700496104395038634388329438543', '7.899184365174266849623141662943489', '8.833983926835018067458552718469695', '8.839575968020472540194575750239078'], 'prelabel': '4-2128e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.122155449534682, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1422347276529037806, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32812191346529978745892661601', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59673768418762382821840388724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63799976163539761420749992768', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 288.73369008297294, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 4528384, 'conductor_radical': 266, 'degree': 4, 'dirichlet_coefficients': [1, 0, -3, 0, 2, 0, -2, 0, 2, 0, 1, 0, -2, 0, -6, 0, 1, 0, 2, 0, 6, 0, 2, 0, -7, 0, 6, 0, 5, 0, 1, 0, -3, 0, -4, 0, -14, 0, 6, 0, 9, 0, -8, 0, 4, 0, -6, 0, 3, 0, -3, 0, 3, 0, 2, 0, -6, 0, -20, 0, -6, 0, -4, 0, -4, 0, -11, 0, -6, 0, -4, 0, -7, 0, 21, 0, -2, 0, 0, 0, -14, 0, -13, 0, 2, 0, -15, 0, 10, 0, 4, 0, -3, 0, 4, 0, 6, 0, 2, 0], 'euler11': [1, -1, 21, -11, 121], 'euler13': [1, 2, 27, 26, 169], 'euler17': [1, -1, 23, -17, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 27, -46, 529], 'euler29': [1, -5, 63, -145, 841], 'euler3': [1, 3, 7, 9, 9], 'euler31': [1, -1, -39, -31, 961], 'euler37': [1, 14, 103, 518, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 8, 82, 344, 1849], 'euler47': [1, 6, 83, 282, 2209], 'euler5': [1, -2, 11, -10, 25], 'euler53': [1, -3, 97, -159, 2809], 'euler59': [1, 20, 213, 1180, 3481], 'euler61': [1, 6, 51, 366, 3721], 'euler67': [1, 11, 103, 737, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 4, 101, 284, 5041], 'euler73': [1, 7, 97, 511, 5329], 'euler79': [1, 0, 138, 0, 6241], 'euler83': [1, 13, 197, 1079, 6889], 'euler89': [1, -10, 198, -890, 7921], 'euler97': [1, -6, 183, -582, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 3, 7, 9, 9], [1, -2, 11, -10, 25], [1, 2, 1, 0, 0], [1, -1, 21, -11, 121], [1, 2, 27, 26, 169], [1, -1, 23, -17, 289], [1, -2, 1, 0, 0], [1, -2, 27, -46, 529], [1, -5, 63, -145, 841], [1, -1, -39, -31, 961], [1, 14, 103, 518, 1369], [1, -9, 71, -369, 1681], [1, 8, 82, 344, 1849], [1, 6, 83, 282, 2209], [1, -3, 97, -159, 2809], [1, 20, 213, 1180, 3481], [1, 6, 51, 366, 3721], [1, 11, 103, 737, 4489], [1, 4, 101, 284, 5041], [1, 7, 97, 511, 5329], [1, 0, 138, 0, 6241], [1, 13, 197, 1079, 6889], [1, -10, 198, -890, 7921], [1, -6, 183, -582, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2128/2/a/c'], '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': '4-2128e2-1.1-c1e2-0-14', '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': '4-2128e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.122155449534682, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1422347276529037806, 'z1': {'__RealLiteral__': 0, 'data': '1.32812191346529978745892661601', 'prec': 103}}
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{'Lhash': '1683594540780551824177022416463,2024105483767474344424729902512', 'Lhash_array': ['1683594540780551824177022416463', '2024105483767474344424729902512'], 'label': '4-2128e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2128/2/a/c'}