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lfunc_lfunctions • Show schema
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{'Lhash': '1659898877827263495925049379481', 'a10': [0.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.5, 0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [-1.0, 3.9689140359382235e-80], 'a9': [-4.582907173931562e-80, -2.6459426907612794e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.3051', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '693277659446429585055546785602', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], 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-0.106929618287112, 0.08095663081526726, 0.26493511245043133], 'positive_zeros': ['1.30942933133815676285840403259440', '2.61457635491670598605040696977004', '3.69640326728159162261851970047194', '4.40672017324912073846013203006384', '5.58269055062843969766651745156236', '5.91220156149461080410026856877652', '6.53633365398466010734190753222975', '7.46696163752520357293982429056357', '7.908190608243251120909372638082192', '8.455486710762704136513495198752950'], 'prelabel': '2-3800-152.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': 0.5989133786043899, 'root_number': '-0.30576855776155245201166452061865 + 0.95210587073309245599954997573793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.29945668930219493', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30942933133815676285840403259', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'bad_primes': [2, 5, 19], 'central_character': '152.11', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 5, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/bd/c/3051/1', 'ArtinRepresentation/2.3800.12t18.d.a'], 'is_instance_Artin': True, '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': '2-3800-152.11-c0-0-5', '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': '2-3800-152.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': 0.29945668930219493, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30942933133815676285840403259', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24609445
{'Lhash': '1659898877827263495925049379481', 'Lhash_array': ['1659898877827263495925049379481'], 'label': '2-3800-152.11-c0-0-5', 'type': 'Artin', 'url': 'ArtinRepresentation/2.3800.12t18.d.a'}
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id: 19954724
{'Lhash': '1659898877827263495925049379481', 'Lhash_array': ['1659898877827263495925049379481'], 'label': '2-3800-152.11-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/bd/c/3051/1'}