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lfunc_lfunctions • Show schema
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{'Lhash': '1445605496826686853686675012814', 'a10': 0, 'a2': -1, 'a3': -2, 'a4': 1, 'a5': 0, 'a6': 2, 'a7': -4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.772324373936879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [37, [1, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '1850.1', 'coefficient_field': '1.1.1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, 1], [1, 2, 3], [1], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, 0, 17], [1, -5, 19], [1, -3, 23], [1, -6, 29], [1, 4, 31], [1, -1], [1, 9, 41], [1, 7, 43], [1, 6, 47], [1, -9, 53], [1, -3, 59], [1, -2, 61], [1, -2, 67], [1, 6, 71], [1, -11, 73], [1, 1, 79], [1, 0, 83], [1, 6, 89], [1, 4, 97], [1, -3, 101], [1, 13, 103], [1, 18, 107], [1, 16, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 2, 3], 1]], [1], [[[1, 4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -2, 13], 1]], [[[1, 0, 17], 1]], [[[1, -5, 19], 1]], [[[1, -3, 23], 1]], [[[1, -6, 29], 1]], [[[1, 4, 31], 1]], [[[1, -1], 1]], [[[1, 9, 41], 1]], [[[1, 7, 43], 1]], [[[1, 6, 47], 1]], [[[1, -9, 53], 1]], [[[1, -3, 59], 1]], [[[1, -2, 61], 1]], [[[1, -2, 67], 1]], [[[1, 6, 71], 1]], [[[1, -11, 73], 1]], [[[1, 1, 79], 1]], [[[1, 0, 83], 1]], [[[1, 6, 89], 1]], [[[1, 4, 97], 1]], [[[1, -3, 101], 1]], [[[1, 13, 103], 1]], [[[1, 18, 107], 1]], [[[1, 16, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-1850-1.1-c1-0-23', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1850/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.362176779625909e-61, 0.0708813593904042, 0.14124692876045336, 0.21055476216334043, 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1.9528346962720553, 2.33322999838077, 2.646122629741869, 2.8715070346708034, 2.9930578023350907, 2.999153154080941, 2.8836971743010724, 2.646691971406172, 2.294522145644851, 1.8399273603203001, 1.30165383800899], 'positive_zeros': ['1.14038166081917070031765794792576', '2.83749787001167205838664871215192', '3.62796544975618918664823760269456', '5.08878963109633340704817996247657', '5.76363456125624493960662199148048', '6.70418920425587068396749595738808', '6.86419083445922055821059928858019', '8.158659130909600647167541378736200', '8.975525571255412788416014295149039'], 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 406122692682033712, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14038166081917070031765794793', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83749787001167205838664871215', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62796544975618918664823760269', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.772324373936879, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 1850, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, -1, -2, 1, 0, 2, -4, -1, 1, 0, 0, -2, 2, 4, 0, 1, 0, -1, 5, 0, 8, 0, 3, 2, 0, -2, 4, -4, 6, 0, -4, -1, 0, 0, 0, 1, 1, -5, -4, 0, -9, -8, -7, 0, 0, -3, -6, -2, 9, 0, 0, 2, 9, -4, 0, 4, -10, -6, 3, 0, 2, 4, -4, 1, 0, 0, 2, 0, -6, 0, -6, -1, 11, -1, 0, 5, 0, 4, -1, 0, -11, 9, 0, 8, 0, 7, -12, 0, -6, 0, -8, 3, 8, 6, 0, 2, -4, -9, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -1, 0], 'euler41': [1, 9, 41], 'euler43': [1, 7, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -3, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, -11, 73], 'euler79': [1, 1, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 1, 0], [1, 2, 3], [1, 0, 0], [1, 4, 7], [1, 0, 11], [1, -2, 13], [1, 0, 17], [1, -5, 19], [1, -3, 23], [1, -6, 29], [1, 4, 31], [1, -1, 0], [1, 9, 41], [1, 7, 43], [1, 6, 47], [1, -9, 53], [1, -3, 59], [1, -2, 61], [1, -2, 67], [1, 6, 71], [1, -11, 73], [1, 1, 79], [1, 0, 83], [1, 6, 89], [1, 4, 97]], 'index': 23, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1850/a', 'ModularForm/GL2/Q/holomorphic/1850/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1850/2/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': True, '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': '2-1850-1.1-c1-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.8434781609808684, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 406122692682033712, 'z1': {'__RealLiteral__': 0, 'data': '1.14038166081917070031765794793', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20590943
{'Lhash': '1445605496826686853686675012814', 'Lhash_array': ['1445605496826686853686675012814'], 'label': '2-1850-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/a'}
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id: 24554793
{'Lhash': '1445605496826686853686675012814', 'Lhash_array': ['1445605496826686853686675012814'], 'label': '2-1850-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1850/2/a/a/1/1'}
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id: 37901
{'Lhash': '406122692682033712', 'Lhash_array': ['406122692682033712'], 'label': '2-1850-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1850/a'}