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lfunc_lfunctions • Show schema
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{'Lhash': '3521683887124452103116901700824', 'a10': [-0.10435607626104, 0.18075002616265368], 'a2': [-0.39564392373896, -0.22842512587392833], 'a3': [1.39564392373896, -2.4173261851906624], 'a4': [-0.89564392373896, -1.5513007814062236], 'a5': [0.0, -0.45685025174785665], 'a6': [-1.10435607626104, 0.6376002779105103], 'a7': [0.0, 0.0], 'a8': [0.0, 1.7320508075688772], 'a9': [-2.39564392373896, -4.14937699275954], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.5, -0.8660254037844386]]]], 'bad_primes': [7, 13], 'central_character': '637.589', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '702694735841133416466986237631', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.39564392373896, 0.22842512587392833], [1.0, 1.7320508075688772]], [[1.0, 0], [-1.39564392373896, 2.4173261851906624], 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True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.45731285763705, 'root_number': '-0.9642464765553398 - 0.26500704226607386*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.457312857637', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.77811873909924684767672166968', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.29498762492748357425125107314', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74073964159259720591452148693', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/f/589/1'], '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': '2-637-13.4-c1-0-42', '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': '2-637-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': -0.45731285763705, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77811873909924684767672166968', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3521683887124452103116901700824', 'Lhash_array': ['3521683887124452103116901700824'], 'factors': ['2-637-13.4-c1-0-42'], 'label': '2-637-13.4-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/f/589/1'}