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lfunc_lfunctions • Show schema
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{'Lhash': '870561332725113642520221195138', 'a10': [0.0, 0.0], 'a2': [0.59861731450831, 1.8423546539302866], 'a3': [0.0, 0.0], 'a4': [-2.226910987254498, 1.617945538322797], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-2.7466964915371435, -1.9955918126248515], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6971938226483044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.42577929156507266, -0.9048270524660196]]], [127, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [11, 127], 'central_character': '1397.126', 'coefficient_field': 'CDF', 'conductor': 1397, 'conductor_radical': 1397, 'conjugate': '3093250258074798730365107348804', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.59861731450831, -1.8423546539302866], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], 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'positive_zeros': ['0.68675180098394359613356607627384', '2.14438922641477184279723965661890', '2.97690739319855480567415938743143', '3.99472798036209074277804230307001', '4.57608011519359539493901548178471', '5.68290190039428038847602288686872', '6.45457625419869206813673957238642', '7.895465255984451554859391961454998', '9.029038662017943925789303200948570', '9.491741575776288402410163674707332'], 'prelabel': '2-1397-1397.126-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8349813307184206, 'root_angle': 0.7545657398607865, 'root_number': '-0.71717621787780151192658428194628 + 0.69689186572271897556614869790404*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3772828699303932', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68675180098394359613356607627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14438922641477184279723965662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97690739319855480567415938743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6971938226483044, 'bad_primes': [11, 127], 'central_character': '1397.126', 'conductor': 1397, 'conductor_radical': 1397, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1397/1/l/a/126/5'], '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': '2-1397-1397.126-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1397-1397.126-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8349813307184206, 'root_angle': 0.3772828699303932, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68675180098394359613356607627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '870561332725113642520221195138', 'Lhash_array': ['870561332725113642520221195138'], 'label': '2-1397-1397.126-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1397/1/l/a/126/5'}