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lfunc_lfunctions • Show schema
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{'Lhash': '1159455284154478797254132339455', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.08224645010157838, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.166958296845591, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.9932355214456887, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.94420193864136, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '8008.1', 'coefficient_field': 'CDF', 'conductor': 8008, 'conductor_radical': 2002, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.08224645010157838, 0], [3.0, 0]], [[1.0, 0], [4.166958296845591, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.558351633619871, 0], [17.0, 0]], [[1.0, 0], [-5.095219738100832, 0], [19.0, 0]], [[1.0, 0], 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'5.33492430135165461647354519576741', '6.07476586076651330305426925490586', '7.02684571013490978346859200869965', '7.72618694905280351932706839883525'], 'prelabel': '2-8008-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.996511860720358, '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': '0.914648945021387609450356470762', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.50986716267567213031602799535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33410815836188963593938507222', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.94420193864136, 'bad_primes': [2, 7, 11, 13], 'central_character': '1.1', 'conductor': 8008, 'conductor_radical': 2002, 'degree': 2, 'index': 82, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8008/2/a/u/1/5'], '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': '2-8008-1.1-c1-0-82', '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': '2-8008-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.996511860720358, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.914648945021387609450356470762', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1159455284154478797254132339455', 'Lhash_array': ['1159455284154478797254132339455'], 'label': '2-8008-1.1-c1-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8008/2/a/u/1/5'}