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lfunc_lfunctions • Show schema
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{'Lhash': '2854646542639980009224686741957', 'a10': [-1702.37870704476, 6863.08288874618], 'a2': [-8.0, 8.0], 'a3': [-25.94933459514875, -25.94933459514875], 'a4': [0.0, -128.0], 'a5': [535.3413497369338, -322.54401135633873], 'a6': [415.18935352238, 0.0], 'a7': [2031.0107411137762, -2031.0107411137762], 'a8': [1024.0, 1024.0], 'a9': [0.0, -5214.264068138033], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.073786100611273, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [8.0, -8.0]]], [5, [[1.0, 0], [-535.3413497369338, 322.54401135633873]]]], 'bad_primes': [2, 5], 'central_character': '10.3', 'coefficient_field': 'CDF', 'conductor': 10, 'conductor_radical': 10, 'conjugate': '1383288807000119284640565995676', 'degree': 2, 'euler_factors': [[[1.0, 0], [8.0, -8.0]], [[1.0, 0], [25.94933459514875, 25.94933459514875], [0, 6561.0]], [[1.0, 0], [-535.3413497369338, 322.54401135633873]], [[1.0, 0], [-2031.0107411137762, 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'root_analytic_conductor': 2.018362232259431, 'root_angle': 0.1268012342021021, 'root_number': '0.6990589947252025 + 0.7150639984601304*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.126801234202', 'prec': 47}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25191905571300630546010570399', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.45269018885786286140952283594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.154952320465890285594692637568', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.073786100611273, 'bad_primes': [2, 5], 'central_character': '5.3', 'conductor': 10, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/9/c/a/3/1'], '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': '2-10-5.3-c8-0-2', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-10-5.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018362232259431, 'root_angle': 0.1268012342021021, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25191905571300630546010570399', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2854646542639980009224686741957', 'Lhash_array': ['2854646542639980009224686741957'], 'factors': ['2-10-5.3-c8-0-2'], 'label': '2-10-5.3-c8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/9/c/a/3/1'}