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lfunc_lfunctions • Show schema
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{'Lhash': '1246136248842414698158508809485', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.91807566263978, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1]]], 'bad_primes': [2, 11], 'central_character': '3872.1', 'coefficient_field': '1.1.1.1', 'conductor': 3872, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 3, 5], [1, 4, 7], [1], [1, -2, 13], [1, -8, 17], [1, -6, 19], [1, 5, 23], [1, 4, 29], [1, 1, 31], [1, -3, 37], [1, -6, 41], [1, 6, 43], [1, -12, 47], [1, 6, 53], [1, 3, 59], [1, 0, 61], [1, 11, 67], [1, -5, 71], [1, -10, 73], [1, 2, 79], [1, 2, 83], [1, 5, 89], [1, -13, 97], [1, -4, 101], [1, 16, 103], [1, 16, 107], [1, 2, 109], [1, -1, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, 3, 5], 1]], [[[1, 4, 7], 1]], [1], [[[1, -2, 13], 1]], [[[1, -8, 17], 1]], [[[1, -6, 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0.2468291510227459, 0.48701470215426157, 0.6903458973966464, 0.8463584238141642, 0.9478898036983614, 0.9914971305573161, 0.977669784701045, 0.9108233671461538], 'positive_zeros': ['0.983028169290543283320284215782112', '2.89719888783107338887618151319241', '3.45638227499885283826740836493381', '4.03192176008940410390660094974735', '5.34340324995592983674267035014187', '5.84688954059027242125847376557291', '6.55308364199828309630932268800750', '7.62722480655714859723348506404693', '7.78122525591253568263543482389512'], 'prelabel': '2-3872-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.5604024730805035, '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': 1048816032710607661, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983028169290543283320284215782', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.89719888783107338887618151319', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45638227499885283826740836493', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.91807566263978, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 3872, 'conductor_radical': 22, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -3, 0, -4, 0, -2, 0, 0, 0, 2, 0, 3, 0, 8, 0, 6, 0, 4, 0, -5, 0, 4, 0, 5, 0, -4, 0, -1, 0, 0, 0, 12, 0, 3, 0, -2, 0, 6, 0, -6, 0, 6, 0, 12, 0, 9, 0, -8, 0, -6, 0, 0, 0, -6, 0, -3, 0, 0, 0, 8, 0, -6, 0, -11, 0, 5, 0, 5, 0, 10, 0, -4, 0, 0, 0, -2, 0, 1, 0, -2, 0, -24, 0, 4, 0, -5, 0, -8, 0, 1, 0, -18, 0, 13, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, -8, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 5, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 3], 'euler31': [1, 1, 31], 'euler37': [1, -3, 37], 'euler41': [1, -6, 41], 'euler43': [1, 6, 43], 'euler47': [1, -12, 47], 'euler5': [1, 3, 5], 'euler53': [1, 6, 53], 'euler59': [1, 3, 59], 'euler61': [1, 0, 61], 'euler67': [1, 11, 67], 'euler7': [1, 4, 7], 'euler71': [1, -5, 71], 'euler73': [1, -10, 73], 'euler79': [1, 2, 79], 'euler83': [1, 2, 83], 'euler89': [1, 5, 89], 'euler97': [1, -13, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 3, 5], [1, 4, 7], [1, 0, 0], [1, -2, 13], [1, -8, 17], [1, -6, 19], [1, 5, 23], [1, 4, 29], [1, 1, 31], [1, -3, 37], [1, -6, 41], [1, 6, 43], [1, -12, 47], [1, 6, 53], [1, 3, 59], [1, 0, 61], [1, 11, 67], [1, -5, 71], [1, -10, 73], [1, 2, 79], [1, 2, 83], [1, 5, 89], [1, -13, 97]], 'index': 45, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3872/d', 'ModularForm/GL2/Q/holomorphic/3872/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/3872/2/a/d'], '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': '2-3872-1.1-c1-0-45', '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': '2-3872-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.5604024730805035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1048816032710607661, 'z1': {'__RealLiteral__': 0, 'data': '0.983028169290543283320284215782', 'prec': 107}}
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lfunc_instances • Show schema
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id: 20513934
{'Lhash': '1246136248842414698158508809485', 'Lhash_array': ['1246136248842414698158508809485'], 'label': '2-3872-1.1-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3872/2/a/d'}
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id: 24563442
{'Lhash': '1246136248842414698158508809485', 'Lhash_array': ['1246136248842414698158508809485'], 'label': '2-3872-1.1-c1-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3872/2/a/d/1/1'}
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id: 88759
{'Lhash': '1048816032710607661', 'Lhash_array': ['1048816032710607661'], 'label': '2-3872-1.1-c1-0-45', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3872/d'}