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lfunc_lfunctions • Show schema
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{'Lhash': '344775540199802577838413977772', 'a10': [-0.43704076642495576, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.7710336320654001, 0.0], 'a4': [1.0, 0.0], 'a5': [0.43704076642495576, 0.0], 'a6': [0.7710336320654001, 0.0], 'a7': [-4.611282743892725, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.405507138224037, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.86304007342658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 37], 'central_character': '2738.1', 'coefficient_field': 'CDF', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7710336320654001, 0], [3.0, 0]], [[1.0, 0], [-0.43704076642495576, 0], [5.0, 0]], [[1.0, 0], [4.611282743892725, 0], [7.0, 0]], [[1.0, 0], [1.8028301220776026, 0], [11.0, 0]], [[1.0, 0], [6.122788180618002, 0], [13.0, 0]], [[1.0, 0], [-2.2051886488478067, 0], [17.0, 0]], [[1.0, 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0], [109.0, 0]], [[1.0, 0], [4.868090461573502, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2738-1.1-c1-0-2', 'leading_term': '0.17839275353893525843067188506514', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2738/2/a/w/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.17839275353893524, 0.17222140896434004, 0.1536831545475984, 0.12270983782767537, 0.07920261749401884, 0.02305311225683271, -0.0458288280680929, -0.12748234681498644, -0.22185961388112094, -0.3287885477010167, -0.44793606310183604, -0.5787735635343537, -0.7205462315543899, -0.8722474862948594, -1.032599787860689, -1.2000427843394237, -1.3727296186611335, -1.548532036394551, -1.725054755968633, -1.8996593736778637, -2.069497872169604, 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'5.44864426149933870638332718646743', '5.60392241099342931126296534741890', '6.76381049221564551613615625102262', '7.15067429084720348214824483906814', '8.097584914603320397726306185329799', '8.983965051680315066163448298597158'], 'prelabel': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27197994474007960697630656115', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18301704180241458142084177434', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92237976467930596572244071911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.86304007342658, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 2738, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2738/2/a/w/1/7'], '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': '2-2738-1.1-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': '2-2738-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.675792988726787, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27197994474007960697630656115', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '344775540199802577838413977772', 'Lhash_array': ['344775540199802577838413977772'], 'label': '2-2738-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2738/2/a/w/1/7'}