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lfunc_lfunctions • Show schema
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{'Lhash': '1882312828303997950098186008410', 'a10': [3.170888828022142, 0], 'a2': [0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.585444414011071, -2.7460702776434407], 'a6': [0, 0], 'a7': [1.8628869276297246, -1.0755382691368565], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.678879007511487, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [-4.103672215313193, 4.9152695093215915]]]], 'bad_primes': [2, 3, 41], 'central_character': '2214.901', 'coefficient_field': 'CDF', 'conductor': 2214, 'conductor_radical': 246, 'conjugate': '1153800793289020338510788962255', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.585444414011071, 2.7460702776434407], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.8628869276297246, 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'8.278308073561860766774399843794088', '9.252834818900711344800851854751265'], 'prelabel': '2-2214-369.40-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.204625905774673, 'root_angle': 0.05853369616037395, 'root_number': '0.93312853139213483704819980522249247002649707829979222783 + 0.3595429653072878993118142300826454102115029414192810802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05853369616037395', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48488300164501479456572348933', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16876200036391851996308151727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43439687863290717864002197363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.678879007511487, 'bad_primes': [2, 3, 41], 'central_character': '369.40', 'conductor': 2214, 'conductor_radical': 246, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2214/2/i/b/901/15'], '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': '2-2214-369.40-c1-0-36', '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': '2-2214-369.40-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.204625905774673, 'root_angle': 0.05853369616037395, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48488300164501479456572348933', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1882312828303997950098186008410', 'Lhash_array': ['1882312828303997950098186008410'], 'factors': ['2-2214-369.40-c1-0-36'], 'label': '2-2214-369.40-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2214/2/i/b/901/15'}