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lfunc_lfunctions • Show schema
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{'Lhash': '478839485656409687627955489793', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.532088886237956, -1.2855752193730787], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.766044443118978, 0.6427876096865394], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.568', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1904465907277225216436527053633', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.532088886237956, 1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-4.698463103929542, -1.7101007166283437]], [[1.0, 0], [0.766044443118978, -0.6427876096865394], [1.2155372436685123, -6.893654271085456]], [[1.0, 0], [0, 0], [-10.336618828644992, 3.762221576582356]], [[1.0, 0], [4.698463103929542, 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'-0.058144828910475774 - 0.9983081582712682*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.259259259259', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37773775011047904446030288029', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60294011361708084539319257101', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57735746289543123429592203540', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/f/568/1'], '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': '2-3e6-27.4-c1-0-3', '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': '2-3e6-27.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.25925925925925924, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37773775011047904446030288029', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '478839485656409687627955489793', 'Lhash_array': ['478839485656409687627955489793'], 'label': '2-3e6-27.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/f/568/1'}