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lfunc_lfunctions • Show schema
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{'Lhash': '153528096006372821746349478940', 'a10': [0, 0], 'a2': [0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.22474487139158905, 0.3892695359907653], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.451', 'coefficient_field': 'CDF', 'conductor': 1350, 'conductor_radical': 30, 'conjugate': '2378393271103502799962342266944', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.22474487139158905, -0.3892695359907653], [-3.5, -6.06217782649107]], [[1.0, 0], [1.724744871391589, -2.987345747344081], [-5.5, -9.526279441628825]], [[1.0, 0], 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'-0.426795877952249862525043321116773483590254132943237212 - 0.904347985325874566187049871646137538178860757285934705*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3201788602298741', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.12111231279244567161002258194', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13883850801006158997067615313', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40519117633578954543157586756', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.779804272872857, 'bad_primes': [2, 3, 5], 'central_character': '9.7', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/2/e/m/451/1'], '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': '2-1350-9.7-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1350-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2832612251955915, 'root_angle': -0.3201788602298741, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12111231279244567161002258194', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '153528096006372821746349478940', 'Lhash_array': ['153528096006372821746349478940'], 'label': '2-1350-9.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/2/e/m/451/1'}