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lfunc_lfunctions • Show schema
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{'Lhash': '1290127266552554828480119980991', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7896168092868736, 1.7896168092868736], 'a4': [0, 0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [0, 3.4054566481642596], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.886490052766813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2240.1681', 'coefficient_field': 'CDF', 'conductor': 2240, 'conductor_radical': 70, 'conjugate': '1759900189046464251886163330594', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7896168092868736, -1.7896168092868736], [0, 3.0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-3.2040617017740427, 3.2040617017740427], [0, -11.0]], [[1.0, 0], 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'-0.2356963574647329', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01773096334295798844862574121', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71350639377938130072265183227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07054134286129646211658428442', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.886490052766813, 'bad_primes': [2, 5, 7], 'central_character': '16.13', 'conductor': 2240, 'conductor_radical': 70, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2240/2/bd/a/1681/21'], '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': '2-2240-16.13-c1-0-27', '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': '2-2240-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.22924225515243, 'root_angle': -0.2356963574647329, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01773096334295798844862574121', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1290127266552554828480119980991', 'Lhash_array': ['1290127266552554828480119980991'], 'label': '2-2240-16.13-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2240/2/bd/a/1681/21'}