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lfunc_lfunctions • Show schema
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{'Lhash': '1323915383525775330553067111333,2367318938959428575978609734083', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -4, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 257.34402396169924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [41, [1, -2, 1]]], 'bad_primes': [7, 41], 'central_character': '2009.1', 'coefficient_field': '1.1.1.1', 'conductor': 4036081, 'conductor_radical': 287, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 1, 3, 3, 9], [1, -1, 7, -5, 25], [1], [1, 5, 25, 55, 121], [1, -1, 23, -13, 169], [1, 3, 7, 51, 289], [1, 0, 25, 0, 361], [1, 4, 37, 92, 529], [1, -4, 49, -116, 841], [1, -1, 59, -31, 961], [1, 0, 22, 0, 1369], [1, -2, 1], [1, 12, 109, 516, 1849], [1, -18, 175, -846, 2209], [1, -9, 97, -477, 2809], [1, 8, 121, 472, 3481], [1, 0, 70, 0, 3721], [1, 6, 130, 402, 4489], [1, 0, 25, 0, 5041], [1, 15, 199, 1095, 5329], [1, 6, -41, 474, 6241], [1, 16, 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0.19058749267726385], 'positive_zeros': ['1.04438508788416614721215932321677', '1.86748536113438001741414829712067', '2.66115787201260131618437153258177', '2.97327408335083045607922851207244', '3.78605279638168857222091759104277', '4.04935865377997381264276759061314', '4.67960341094204373319430849008621', '4.79040531856481382664727393852959', '5.51138324868263757577110361822446', '5.64135080796154896978556221997582', '5.96693530228955912877585919748547', '6.27324694550977427497958356906571', '7.30630530579428335913130207459571', '7.30765305099540558791090349399741', '8.011964882236786287447004917188536', '8.292461396959523451698842973672542', '8.584337313748584171008274975841116', '8.964553996192192304835834185380906'], 'prelabel': '4-2009e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.005239788836024, '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': 620005391801734869, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04438508788416614721215932322', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86748536113438001741414829712', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66115787201260131618437153258', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 257.34402396169924, 'bad_primes': [7, 41], 'central_character': '1.1', 'conductor': 4036081, 'conductor_radical': 287, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -4, 1, 0, 0, 0, -2, 0, -5, 4, 1, 0, -1, 12, -3, 0, 0, -4, 0, 0, -4, 0, -6, 0, 2, 0, 4, 0, 1, 0, 5, 0, 0, 8, 0, 0, -1, 0, 2, 0, -12, 20, -2, 0, 18, -12, 0, 0, 3, -4, 9, 0, -5, 0, 0, 0, -8, 4, 0, 0, 0, -32, 1, 0, -6, 12, 4, 0, 0, 0, -15, 0, 6, 0, 0, 0, -6, 12, -2, 0, -16, 0, -3, 0, -4, 0, -8, 0, 0, 16, -1, 0, 0, 0, -15, 0, 10, 24], 'euler11': [1, 5, 25, 55, 121], 'euler13': [1, -1, 23, -13, 169], 'euler17': [1, 3, 7, 51, 289], 'euler19': [1, 0, 25, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 4, 37, 92, 529], 'euler29': [1, -4, 49, -116, 841], 'euler3': [1, 1, 3, 3, 9], 'euler31': [1, -1, 59, -31, 961], 'euler37': [1, 0, 22, 0, 1369], 'euler41': [1, -2, 1, 0, 0], 'euler43': [1, 12, 109, 516, 1849], 'euler47': [1, -18, 175, -846, 2209], 'euler5': [1, -1, 7, -5, 25], 'euler53': [1, -9, 97, -477, 2809], 'euler59': [1, 8, 121, 472, 3481], 'euler61': [1, 0, 70, 0, 3721], 'euler67': [1, 6, 130, 402, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 25, 0, 5041], 'euler73': [1, 15, 199, 1095, 5329], 'euler79': [1, 6, -41, 474, 6241], 'euler83': [1, 16, 217, 1328, 6889], 'euler89': [1, 8, 181, 712, 7921], 'euler97': [1, 15, 247, 1455, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 1, 3, 3, 9], [1, -1, 7, -5, 25], [1, 0, 0, 0, 0], [1, 5, 25, 55, 121], [1, -1, 23, -13, 169], [1, 3, 7, 51, 289], [1, 0, 25, 0, 361], [1, 4, 37, 92, 529], [1, -4, 49, -116, 841], [1, -1, 59, -31, 961], [1, 0, 22, 0, 1369], [1, -2, 1, 0, 0], [1, 12, 109, 516, 1849], [1, -18, 175, -846, 2209], [1, -9, 97, -477, 2809], [1, 8, 121, 472, 3481], [1, 0, 70, 0, 3721], [1, 6, 130, 402, 4489], [1, 0, 25, 0, 5041], [1, 15, 199, 1095, 5329], [1, 6, -41, 474, 6241], [1, 16, 217, 1328, 6889], [1, 8, 181, 712, 7921], [1, 15, 247, 1455, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2009/2/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': '4-2009e2-1.1-c1e2-0-1', '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': '4-2009e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.005239788836024, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 620005391801734869, 'z1': {'__RealLiteral__': 0, 'data': '1.04438508788416614721215932322', 'prec': 103}}
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{'Lhash': '1323915383525775330553067111333,2367318938959428575978609734083', 'Lhash_array': ['1323915383525775330553067111333', '2367318938959428575978609734083'], 'label': '4-2009e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2009/2/a/c'}