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lfunc_lfunctions • Show schema
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{'Lhash': '476061740430657414775516246269', 'a10': [0.6839691391292742, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.1642479384602111, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.6839691391292742, 0.0], 'a6': [1.1642479384602111, 0.0], 'a7': [-0.3160308608707258, 0.0], 'a8': [-1.0, 0.0], 'a9': [-1.6445267377911483, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.417189285300914, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '7942.1', 'coefficient_field': 'CDF', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.1642479384602111, 0], [3.0, 0]], [[1.0, 0], [0.6839691391292742, 0], [5.0, 0]], [[1.0, 0], [0.3160308608707258, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.3160308608707258, 0], [13.0, 0]], [[1.0, 0], [1.8482170775894855, 0], [17.0, 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'2.51896623093295714311668866992885', '3.50906568857825699452902708015191', '4.25942378600726445877104908585261', '5.21049197326161583910976847410706', '6.02202630097050379836892775554353', '6.31186176379087708586335139108256', '7.28077589003246979403689859411177', '7.81775204581138292433829291465042'], 'prelabel': '2-7942-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37554649549721876270480340782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60758992607344691037154983004', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.51896623093295714311668866993', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.417189285300914, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 7942, 'conductor_radical': 418, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7942/2/a/bf/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': '2-7942-1.1-c1-0-11', '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': '2-7942-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.9634910237471175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37554649549721876270480340782', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '476061740430657414775516246269', 'Lhash_array': ['476061740430657414775516246269'], 'label': '2-7942-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7942/2/a/bf/1/1'}