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lfunc_lfunctions • Show schema
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{'Lhash': '2654064483766529073501512790986', 'a10': [0.5, -0.8660254037844386], 'a2': [0.0, 1.0], 'a3': [0.8660254037844386, 0.5], 'a4': [0.0, 0.0], 'a5': [-0.8660254037844386, -0.5], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 1.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8660254037844386, -0.5]]], [7, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.107', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '3498603378964340963271376793878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 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5.0603143325626965, 5.415136972668031, 5.524767839724684, 5.406414516795647, 5.088503385480103, 4.608373948333561], 'positive_zeros': ['2.09368771117900151686760285035503', '3.08829971249185133363349303392141', '3.99770012676609839692866788023304', '6.11384775433892806220920232724135', '7.22864699467596249750084034109382', '8.007607814910001464625463047681043', '9.337069498874731396699529351393682', '9.946932265950353662835940003386026', '11.28242428730413389059665891949038', '11.90363920371632228224238796992843'], 'prelabel': '2-273-273.107-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': -0.4388805711131795, 'root_number': '0.19083464627323151065483336636232 - 0.98162219707062992163401295235658*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21944028555658973', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09368771117900151686760285036', 'prec': 103}, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.107', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/s/b/107/2'], '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': '2-273-273.107-c0-0-1', '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': '2-273-273.107-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': -0.21944028555658976, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09368771117900151686760285036', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2654064483766529073501512790986', 'Lhash_array': ['2654064483766529073501512790986'], 'label': '2-273-273.107-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/s/b/107/2'}