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lfunc_lfunctions • Show schema
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{'Lhash': '1394541091103180547689737968278', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.35027811608699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 7, 11], 'central_character': '4928.1', 'coefficient_field': '1.1.1.1', 'conductor': 4928, 'conductor_radical': 154, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 0, 5], [1, 1], [1, -1], [1, 0, 13], [1, 6, 17], [1, -6, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -2, 59], [1, 4, 61], [1, 8, 67], [1, -16, 71], [1, 2, 73], [1, -8, 79], [1, 2, 83], [1, 14, 89], [1, -6, 97], [1, -12, 101], [1, 8, 103], [1, -8, 107], [1, -6, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, 2, 3], 1]], [[[1, 0, 5], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 13], 1]], [[[1, 6, 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0.7524933919918824, 0.5575348099657473, 0.3286220001799144, 0.08112963796245432, -0.16792068688316333, -0.4008562146762237, -0.6004066454380881], 'positive_zeros': ['1.10009894749555249949447812962225', '2.37155344399764906447695687329544', '3.36774462290951527375178815830193', '4.35081123763063332649398662910394', '5.01653479082931599488789500378801', '5.80110530492159745680366439654373', '6.38244450193543748318009116986424', '6.95985663952059687310261569779954', '7.78424852053449074989340887434039'], 'prelabel': '2-4928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.2729800028445, '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': 199182711063629401, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10009894749555249949447812962', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37155344399764906447695687330', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36774462290951527375178815830', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.35027811608699, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 4928, 'conductor_radical': 154, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, -6, 0, 6, 0, 2, 0, 0, 0, -5, 0, 4, 0, 6, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 1, 0, 12, 0, -6, 0, 0, 0, -12, 0, 2, 0, -4, 0, -1, 0, 0, 0, -8, 0, 0, 0, 16, 0, -2, 0, 10, 0, -1, 0, 8, 0, -11, 0, -2, 0, 0, 0, -12, 0, -14, 0, 0, 0, 0, 0, 0, 0, 6, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, -2, 59], 'euler61': [1, 4, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 2, 83], 'euler89': [1, 14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 5], [1, 1, 0], [1, -1, 0], [1, 0, 13], [1, 6, 17], [1, -6, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -2, 59], [1, 4, 61], [1, 8, 67], [1, -16, 71], [1, 2, 73], [1, -8, 79], [1, 2, 83], [1, 14, 89], [1, -6, 97]], 'index': 67, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4928/f', 'ModularForm/GL2/Q/holomorphic/4928/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/4928/2/a/f'], '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': '2-4928-1.1-c1-0-67', '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': '2-4928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.2729800028445, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 199182711063629401, 'z1': {'__RealLiteral__': 0, 'data': '1.10009894749555249949447812962', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20051347
{'Lhash': '1394541091103180547689737968278', 'Lhash_array': ['1394541091103180547689737968278'], 'label': '2-4928-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4928/2/a/f'}
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id: 24568110
{'Lhash': '1394541091103180547689737968278', 'Lhash_array': ['1394541091103180547689737968278'], 'label': '2-4928-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4928/2/a/f/1/1'}
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id: 42105
{'Lhash': '199182711063629401', 'Lhash_array': ['199182711063629401'], 'label': '2-4928-1.1-c1-0-67', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4928/f'}