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lfunc_lfunctions • Show schema
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{'Lhash': '413692174785471690900522005955', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.5809002169130673, 0.7076400950795659], 'a4': [0, 0], 'a5': [1.0, 0], 'a6': [0, 0], 'a7': [0, -1.3380251111548667], 'a8': [0, 0], 'a9': [1.9984909916715659, -2.2374167596153387], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5809002169130673, -0.7076400950795659]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-0.3644309916349752, -4.7819650827181865]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1241', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'conjugate': '1648399191537305006184176911391', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5809002169130673, -0.7076400950795659]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.3380251111548667], [-7.0, 0]], [[1.0, 0], [2.7498502257652713, 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-3.7341601299612512, -3.77350290393659, -3.62706819024949, -3.3051355716949224], 'positive_zeros': ['0.32634558348411623336970752636554', '1.97288324781133153244815648501759', '2.85164424167858998248949257620046', '4.53709785266006524961902855546529', '5.29792610445214455776997980570528', '5.81035060448969090072901603492481', '6.96411843169197286434573342189609', '7.42014965790013703679011800611923', '8.499269526420441896263717176583860', '9.406607609323005193706359239562147'], 'prelabel': '2-1380-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.6581790351117991, 'root_number': '-0.476732704511348422620055808335168559255695529256711705 - 0.879048308370646573838554028425853487167985017518180583*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32908951755589955', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32634558348411623336970752637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97288324781133153244815648502', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85164424167858998248949257620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/2/i/b/1241/4'], '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': '2-1380-69.68-c1-0-2', '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': '2-1380-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.32908951755589955, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32634558348411623336970752637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '413692174785471690900522005955', 'Lhash_array': ['413692174785471690900522005955'], 'label': '2-1380-69.68-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/i/b/1241/4'}