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lfunc_lfunctions • Show schema
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{'Lhash': '2646145564041565485011606297071', 'a10': [-28.0, 0.0], 'a2': [-2.6457513110645907, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [10.583005244258363, 0.0], 'a6': [0.0, 0.0], 'a7': [-22.0, 0.0], 'a8': [23.811761799581316, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.903223470671655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-13.0, 0]]]], 'bad_primes': [3, 13], 'central_character': '117.1', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '2646145564041565485011606297071', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6457513110645907, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-10.583005244258363, 0], [125.0, 0]], [[1.0, 0], [22.0, 0], [343.0, 0]], [[1.0, 0], [-5.291502622129181, 0], [1331.0, 0]], [[1.0, 0], [-13.0, 0]], [[1.0, 0], [116.41305768684198, 0], [4913.0, 0]], [[1.0, 0], [126.0, 0], [6859.0, 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'10.15143470278430850365840553124079', '11.06948416915141318041468229486111', '12.99150470352574584035942427316242'], 'prelabel': '2-117-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.08744078499639421461408287849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17973981511170068750084622342', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.97055871662157869782917407107', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.903223470671655, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/4/a/e/1/1'], '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': '2-117-1.1-c3-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-117-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.08744078499639421461408287849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2646145564041565485011606297071', 'Lhash_array': ['2646145564041565485011606297071'], 'label': '2-117-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/4/a/e/1/1'}