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lfunc_lfunctions • Show schema
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{'Lhash': '2551567198875132225571175856554', 'a10': [-3.741830175924028, 1.485679323208676], 'a2': [1.0328763076400334, -0.9660054519079545], 'a3': [0.16738276424578835, 1.1105120803072395], 'a4': [0.1336669337682174, -1.9955282886536594], 'a5': [-2.6500110309654836, -1.0400526881816952], 'a6': [1.2456464154832096, 0.9853289542805383], 'a7': [2.564985563874447, 0.648728800898869], 'a8': [-1.789629797271904, -2.190256877335744], 'a9': [1.6614983266166705, -0.5125043597723793], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0328763076400334, 0.9660054519079545]]], [7, [[1.0, 0], [-2.564985563874447, -0.648728800898869]]]], 'bad_primes': [2, 7], 'central_character': '392.109', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '1483326405838083035120799635531', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.97312305167128*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.213016956729', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01283161023687826271148197292', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86877861977159131603135439981', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38581290947264230156508993502', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'bad_primes': [2, 7], 'central_character': '392.109', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/2/z/a/109/42'], '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': '2-392-392.109-c1-0-39', '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': '2-392-392.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': 0.21301695672867166, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01283161023687826271148197292', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2551567198875132225571175856554', 'Lhash_array': ['2551567198875132225571175856554'], 'label': '2-392-392.109-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/2/z/a/109/42'}