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lfunc_lfunctions • Show schema
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{'Lhash': '1498749146095177044312751031377', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.062010346883029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [2, 7, 19], 'central_character': '2128.607', 'coefficient_field': 'CDF', 'conductor': 2128, 'conductor_radical': 266, 'conjugate': '2181376617867574513424663540202', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.5, -0.8660254037844386], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.5, 0.8660254037844386], [0.5, -0.8660254037844386]], 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'3.55317679433870760296363359253789', '4.16926382172128054001661105121861', '5.33911680886528468558921014472461', '6.08451828908086746233396723286666', '6.60070047556043472933429782229163', '7.52554980726921347994747031501433', '8.708506787600451563904095291911555', '9.262675324269625945857583643063761'], 'prelabel': '2-2128-532.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305388623836702, 'root_angle': -0.2929874272254411, 'root_number': '0.60546434364936736350712946050774 - 0.79587243234656694719841781696280*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14649371361272054', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18230460808785983394956349765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98778001504534548398865043734', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55317679433870760296363359254', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.062010346883029, 'bad_primes': [2, 7, 19], 'central_character': '532.75', 'conductor': 2128, 'conductor_radical': 266, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2128/1/cw/e/607/1'], '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': '2-2128-532.75-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2128-532.75-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0305388623836702, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18230460808785983394956349765', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1498749146095177044312751031377', 'Lhash_array': ['1498749146095177044312751031377'], 'label': '2-2128-532.75-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2128/1/cw/e/607/1'}