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lfunc_lfunctions • Show schema
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{'Lhash': '1110769378514414293665615788775', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.20710678118654752, -0.3587194676071504], 'a4': [0.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.4142135623730951, -2.449489742783178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '980.961', 'coefficient_field': 'CDF', 'conductor': 980, 'conductor_radical': 70, 'conjugate': '1529920565522380080696009513550', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.20710678118654752, 0.3587194676071504], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9142135623730951, -3.3155151465676167], [-5.5, 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'root_analytic_conductor': 2.797380810344827, 'root_angle': -0.14354881026837107, 'root_number': '0.9000239394702093 - 0.43584046207359534*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0717744051342', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.876242537426661560987527842652', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.49531079680727329042369027709', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69273170515887622495671188114', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8253393980854815, 'bad_primes': [2, 5, 7], 'central_character': '7.2', 'conductor': 980, 'conductor_radical': 70, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/980/2/i/l/961/1'], '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': '2-980-7.2-c1-0-2', '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': '2-980-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.797380810344827, 'root_angle': -0.07177440513418554, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.876242537426661560987527842652', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1110769378514414293665615788775', 'Lhash_array': ['1110769378514414293665615788775'], 'label': '2-980-7.2-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/980/2/i/l/961/1'}