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lfunc_lfunctions • Show schema
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{'Lhash': '1543653086085394489705106373615', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.2912940054082746, -1.7073803918322372], 'a4': [0.0, 0.0], 'a5': [3.5098622126164782, 2.026419893272619], 'a6': [0.0, 0.0], 'a7': [0.0, 0.19666497188073775], 'a8': [0.0, 0.0], 'a9': [-2.830295604826408, 0.9946993461847236], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.2912940054082746, 1.7073803918322372]]], [19, [[1.0, 0], [-2.7521875691704167, 3.3801573312648974]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.239', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1672825368627680295795295511690', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2912940054082746, 1.7073803918322372]], [[1.0, 0], [-3.5098622126164782, -2.026419893272619], [2.5, 4.330127018922194]], 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'9.981873641235902136018526612988464'], 'prelabel': '2-912-228.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.04798776667605495, 'root_number': '0.9548873738016908 + 0.29696818576088263*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0479877666761', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21772757083653275991590288775', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65593678162223266565433555124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94020230290772688352322308281', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '228.11', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bh/g/239/5'], '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': '2-912-228.11-c1-0-20', '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': '2-912-228.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.04798776667605495, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21772757083653275991590288775', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1543653086085394489705106373615', 'Lhash_array': ['1543653086085394489705106373615'], 'factors': ['2-912-228.11-c1-0-20'], 'label': '2-912-228.11-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bh/g/239/5'}