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lfunc_lfunctions • Show schema
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{'Lhash': '1574072119198285174245042608075,2070104153546350976897243894588', 'a10': 4, 'a2': -2, 'a3': 2, 'a4': 3, 'a5': -2, 'a6': -4, 'a7': 0, 'a8': -4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 931.3985971344308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, -2, 1]], [7, [1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '3822.1', 'coefficient_field': '1.1.1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -2, 1], [1, 2, 4, 10, 25], [1], [1, 4, 19, 44, 121], [1, -2, 1], [1, 8, 43, 136, 289], [1, -10, 63, -190, 361], [1, 10, 64, 230, 529], [1, 2, 31, 58, 841], [1, 4, 38, 124, 961], [1, -6, 76, -222, 1369], [1, 10, 100, 410, 1681], [1, 0, 58, 0, 1849], [1, -6, 103, -282, 2209], [1, 6, 115, 318, 2809], [1, 0, 55, 0, 3481], [1, 8, 75, 488, 3721], [1, 6, 31, 402, 4489], [1, -22, 235, -1562, 5041], [1, 22, 260, 1606, 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['1.24172395683391563791530561812339', '1.63302423646835084744839110438356', '2.28330578840492803100587690072810', '2.56525921700966039264616764806479', '3.18906377798137353750742715907410', '3.36099736752790372719097445675419', '4.14316911150518593870444560599538', '4.17317481185997228729501704676180', '4.83677546507183315512320937418411', '5.51237617004546589237254956116379', '5.70378190625531471709317989892932', '6.24092644997960384654825484800565', '6.89985659807353539749792378616465', '6.91843924780574986112825004723749', '7.61723073235035246849060056606885', '7.62761906499602603133425477888904', '8.075866292435197277483842580689408', '8.137268305236160172415194446148877'], 'prelabel': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, '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': 1763868354180211453, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24172395683391563791530561812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63302423646835084744839110438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.28330578840492803100587690073', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 931.3985971344308, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 14607684, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -2, 2, 3, -2, -4, 0, -4, 3, 4, -4, 6, 2, 0, -4, 5, -8, -6, 10, -6, 0, 8, -10, -8, 0, -4, 4, 0, -2, 8, -4, -6, -8, 16, 0, 9, 6, -20, 4, 8, -10, 0, 0, -12, -6, 20, 6, 10, 0, 0, -16, 6, -6, -8, 8, 0, 20, 4, 0, -12, -8, 8, 0, 7, -4, 16, -6, -24, -20, 0, 22, -12, -22, -12, 0, 30, 0, -8, -20, -10, 5, 20, -16, 0, 16, 0, -4, 16, 18, 12, 0, -30, -8, -12, -20, -12, -14, 0, -12, 0], 'euler11': [1, 4, 19, 44, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 8, 43, 136, 289], 'euler19': [1, -10, 63, -190, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 10, 64, 230, 529], 'euler29': [1, 2, 31, 58, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 4, 38, 124, 961], 'euler37': [1, -6, 76, -222, 1369], 'euler41': [1, 10, 100, 410, 1681], 'euler43': [1, 0, 58, 0, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 2, 4, 10, 25], 'euler53': [1, 6, 115, 318, 2809], 'euler59': [1, 0, 55, 0, 3481], 'euler61': [1, 8, 75, 488, 3721], 'euler67': [1, 6, 31, 402, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, -22, 235, -1562, 5041], 'euler73': [1, 22, 260, 1606, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 16, 202, 1328, 6889], 'euler89': [1, -18, 196, -1602, 7921], 'euler97': [1, 14, 180, 1358, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, 2, 4, 10, 25], [1, 0, 0, 0, 0], [1, 4, 19, 44, 121], [1, -2, 1, 0, 0], [1, 8, 43, 136, 289], [1, -10, 63, -190, 361], [1, 10, 64, 230, 529], [1, 2, 31, 58, 841], [1, 4, 38, 124, 961], [1, -6, 76, -222, 1369], [1, 10, 100, 410, 1681], [1, 0, 58, 0, 1849], [1, -6, 103, -282, 2209], [1, 6, 115, 318, 2809], [1, 0, 55, 0, 3481], [1, 8, 75, 488, 3721], [1, 6, 31, 402, 4489], [1, -22, 235, -1562, 5041], [1, 22, 260, 1606, 5329], [1, 20, 258, 1580, 6241], [1, 16, 202, 1328, 6889], [1, -18, 196, -1602, 7921], [1, 14, 180, 1358, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3822/2/a/bk'], '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': '4-3822e2-1.1-c1e2-0-10', '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': '4-3822e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.5243844591531985, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1763868354180211453, 'z1': {'__RealLiteral__': 0, 'data': '1.24172395683391563791530561812', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1574072119198285174245042608075,2070104153546350976897243894588', 'Lhash_array': ['1574072119198285174245042608075', '2070104153546350976897243894588'], 'label': '4-3822e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3822/2/a/bk'}