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lfunc_lfunctions • Show schema
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{'Lhash': '1549170400173951425561430075044', 'a10': [2.39564392373896, 4.14937699275954], 'a2': [0.0, -2.1889010593167337], 'a3': [0.89564392373896, 1.5513007814062236], 'a4': [-2.79128784747792, 0.0], 'a5': [-1.89564392373896, 1.0944505296583669], 'a6': [3.39564392373896, -1.9604759334428057], 'a7': [0.0, 0.0], 'a8': [0.0, 1.7320508075688772], 'a9': [-0.10435607626104, 0.18075002616265368], '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': '637.459', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '1457303604592262246103183977163', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.1889010593167337], [-2.0, 0]], [[1.0, 0], [-0.89564392373896, -1.5513007814062236], [-1.5, 2.598076211353316]], [[1.0, 0], 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'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.3783617119513411, 'root_number': '0.37290506072652435 + 0.9278695035857937*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.189180855976', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22207996422282042602728488688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19851392988863822957567174270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.56578541770108484399372854762', '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': '91.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/d/459/1'], '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': '2-637-91.4-c1-0-15', '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': '2-637-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.18918085597567055, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22207996422282042602728488688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1549170400173951425561430075044', 'Lhash_array': ['1549170400173951425561430075044'], 'label': '2-637-91.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/d/459/1'}