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lfunc_lfunctions • Show schema
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{'Lhash': '2237551155569491526412399455209', 'a10': [-3.203615623775565, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.203615623775565, 0.0], 'a6': [1.0, 0.0], 'a7': [1.5133370916661353, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.344517601554408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '3174.1', 'coefficient_field': 'CDF', 'conductor': 3174, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.203615623775565, 0], [5.0, 0]], [[1.0, 0], [-1.5133370916661353, 0], [7.0, 0]], [[1.0, 0], [6.538428883010135, 0], [11.0, 0]], [[1.0, 0], [-2.8861226894379275, 0], [13.0, 0]], [[1.0, 0], [1.1964737553213483, 0], [17.0, 0]], [[1.0, 0], [-0.5555542078925406, 0], [19.0, 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'7.41437140859080479144146324707862', '8.293190842870513093471130608191052'], 'prelabel': '2-3174-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.034333878633241, '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': '1.76511663006087009650902968967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83924335984516125066128127720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59800487813110209066633600364', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.344517601554408, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 3174, 'conductor_radical': 138, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3174/2/a/bc/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': '2-3174-1.1-c1-0-77', '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': '2-3174-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.034333878633241, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76511663006087009650902968967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2237551155569491526412399455209', 'Lhash_array': ['2237551155569491526412399455209'], 'label': '2-3174-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3174/2/a/bc/1/1'}