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lfunc_lfunctions • Show schema
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{'Lhash': '1871299378823531144998858048629', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.6180339887498949, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.427097670511378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': 'CDF', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [11.0, 0]], [[1.0, 0], [-0.38196601125010515, 0], [13.0, 0]], [[1.0, 0], [2.23606797749979, 0], [17.0, 0]], [[1.0, 0], [-3.4721359549995796, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-1932-1.1-c1-0-12', '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/1932/2/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.0355486360815806e-60, 0.12503261339031127, 0.2497632045627028, 0.3738528671179899, 0.49689096103962205, 0.6183641735520599, 0.7376310735031116, 0.8539033622665151, 0.9662346090381079, 1.0735168573791602, 1.1744851390531714, 1.2677296498390664, 1.351715133210508, 1.4248068726115901, 1.4853025958720436, 1.5314695286747235, 1.5615857823873822, 1.5739852134123884, 1.5671048395198817, 1.53953384077924, 1.4900631096072887, 1.417734249608213, 1.3218868614398036, 1.2022029019135072, 1.0587468661693298, 0.8920005280786867, 0.7028909864643998, 0.49281080890983314, 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'7.12560688888952564741987005991595', '7.976278093522204236014832747717567', '8.835997115331228201459127588499201'], 'prelabel': '2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47619492191824786851912018750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87585854646542638452068144525', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85544166182386658974120333312', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.427097670511378, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 1932, 'conductor_radical': 966, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/d/1/1'], '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': '2-1932-1.1-c1-0-12', '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': '2-1932-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47619492191824786851912018750', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1871299378823531144998858048629', 'Lhash_array': ['1871299378823531144998858048629'], 'label': '2-1932-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/d/1/1'}