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lfunc_lfunctions • Show schema
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{'Lhash': '1252908011121154102348831887882', 'a10': [-0.975769248229062, -1.690081914396023], 'a2': [-1.9946873126213425, 1.1516332568910632], 'a3': [-0.7366804631721601, -1.2759679911575545], 'a4': [1.6525183167550355, -2.862245685057921], 'a5': [0.0, 0.847291655038895], 'a6': [2.9388943466910438, 1.6967714421819435], 'a7': [0.0, 0.0], 'a8': [0.0, 3.0058471772227042], 'a9': [0.41460379036090333, -0.7181148299157201], '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], [-2.9232860268708456, -2.1105446702454955]]]], 'bad_primes': [7, 13], 'central_character': '637.491', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '928636723792905032594478960278', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9946873126213425, -1.1516332568910632], [1.0, -1.7320508075688772]], [[1.0, 0], [0.7366804631721601, 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'9.277510319947689348671891209684749', '9.661240354816095298354385834810116', '10.60515330530239127868796417659791'], 'prelabel': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.03646195987102019, 'root_number': '0.9934464768716729 + 0.1142982834134477*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0182309799355', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.988370147811691151376066508461', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48932704501639980719271345451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78942018454969295189895153707', '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': '13.10', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/i/491/1'], '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': '2-637-13.10-c1-0-14', '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': '2-637-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.018230979935510094, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.988370147811691151376066508461', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1252908011121154102348831887882', 'Lhash_array': ['1252908011121154102348831887882'], 'label': '2-637-13.10-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/i/491/1'}