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lfunc_lfunctions • Show schema
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{'Lhash': '1188277911562039553161921407079', 'a10': [0.0, 0.0], 'a2': [0.7531363768225959, 0.0], 'a3': [-0.8855101980975775, 0.0], 'a4': [-1.4327855979065327, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.6669099422346687, 0.0], 'a7': [1.0, 0.0], 'a8': [-2.585355707616115, 0.0], 'a9': [-2.2158716890651893, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.986910176862037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '875.1', 'coefficient_field': 'CDF', 'conductor': 875, 'conductor_radical': 35, 'conjugate': '1188277911562039553161921407079', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7531363768225959, 0], [2.0, 0]], [[1.0, 0], [0.8855101980975775, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.6513858537694417, 0], [11.0, 0]], [[1.0, 0], [-0.9165021322097924, 0], [13.0, 0]], [[1.0, 0], [-1.5850984214660262, 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'4.90687800399370423865555418038442', '5.62555498579545660464847209765139', '6.41079699426416548103566077391477', '7.56752892774227223292549979070675', '8.727113655596282211996328497039159', '9.091641732745179641268833707154067', '10.20805358625892457357502115745460'], 'prelabel': '2-875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.643276409470269, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937385988968963932118313623538', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.88462179164816194604585329242', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93125573874472580107989503683', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.986910176862037, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 875, 'conductor_radical': 35, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/875/2/a/g/1/4'], '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': '2-875-1.1-c1-0-12', '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': '2-875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.643276409470269, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937385988968963932118313623538', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1188277911562039553161921407079', 'Lhash_array': ['1188277911562039553161921407079'], 'factors': ['2-875-1.1-c1-0-12'], 'label': '2-875-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/875/2/a/g/1/4'}