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lfunc_lfunctions • Show schema
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{'Lhash': '2706688703536928604829286564158', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [0.8446135760657543, 0.0], 'a6': [0.0, 0.0], 'a7': [-5.065620741595587, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 19], 'central_character': '1216.1', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [-0.8446135760657543, 0], [5.0, 0]], [[1.0, 0], [5.065620741595587, 0], [7.0, 0]], [[1.0, 0], [2.8446135760657545, 0], [11.0, 0]], [[1.0, 0], [2.9020984600878283, 0], [13.0, 0]], [[1.0, 0], [-7.725075094316588, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'7.02582000669406280081917585506045', '7.62387672380210063374364330677948', '8.657368615509975712270509004309677', '9.421686688117026628823697301022381'], 'prelabel': '2-1216-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, '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': '2.13520090082362835718224590119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21257579409725015130037056997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49136246005741852509466705711', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/a/w/1/4'], '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': '2-1216-1.1-c1-0-33', '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': '2-1216-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13520090082362835718224590119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2706688703536928604829286564158', 'Lhash_array': ['2706688703536928604829286564158'], 'label': '2-1216-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/a/w/1/4'}