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lfunc_lfunctions • Show schema
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{'Lhash': '1797619153187711389143913902192', 'a10': [-1.522504346351936, 1.6892463972414662], 'a2': [-1.0505014948077294, -0.9468086445563993], 'a3': [0, 0], 'a4': [0.20710678118654752, 1.9892477928067553], 'a5': [0, -1.6080380709507176], 'a6': [0, 0], 'a7': [0, 0], 'a8': [1.6658710231728877, -2.2857982706601465], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.085610916553867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0505014948077294, 0.9468086445563993]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.1567', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '243618515442250940823341237556', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0505014948077294, 0.9468086445563993]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.6080380709507176], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.677979252207494], 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'positive_zeros': ['1.41807147242628669580759384892585', '2.74746829229275986244338460090972', '3.78919641479799300272165655377691', '5.14946993899483747619889937148587', '5.90751954937582563562301368357334', '6.51029265074244070887682033563621', '7.53435027845827727217944983939406', '7.937623720113277097167391184740206', '8.925612128149389243726696005138727', '9.506758426588787569950933777218189'], 'prelabel': '2-42e2-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': -0.9829814480181135, 'root_number': '-0.9985710681907458734712610135067853748450375226260643995 - 0.053439889337392482909183897271900599244194833404301091*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.49149072400905675', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41807147242628669580759384893', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74746829229275986244338460091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78919641479799300272165655378', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.085610916553867, 'bad_primes': [2, 3, 7], 'central_character': '28.27', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 73, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/2/b/n/1567/1'], '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': '2-42e2-28.27-c1-0-73', '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': '2-42e2-28.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': -0.49149072400905675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41807147242628669580759384893', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1797619153187711389143913902192', 'Lhash_array': ['1797619153187711389143913902192'], 'label': '2-42e2-28.27-c1-0-73', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/2/b/n/1567/1'}