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lfunc_lfunctions • Show schema
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{'Lhash': '1780156543071969818448508066180', 'a10': [-0.4777783265535196, -0.4398259336179839], 'a2': [0.6772815716257411, -0.7357239106731316], 'a3': [0.0, 1.674332956525057], 'a4': [-0.08257934547233232, -0.9965844930066698], 'a5': [0.0, -0.649398938409367], 'a6': [1.2318467905435215, 1.1339948562200644], 'a7': [0.0, 0.0], 'a8': [-0.7891405093963936, -0.6142127126896678], 'a9': [-1.803390849305939, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.433314716281983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6772815716257411, 0.7357239106731316]]], [359, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 359], 'central_character': '2872.717', 'coefficient_field': 'CDF', 'conductor': 2872, 'conductor_radical': 718, 'conjugate': '1255401228727075012608757118124', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6772815716257411, 0.7357239106731316]], [[1.0, 0], [0, -1.674332956525057], [-1.0, 0]], [[1.0, 0], [0, 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'0.10526315789473684', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40429590200286120261381336293', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61001464650444071727125508692', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22073343544648402547199734988', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.433314716281983, 'bad_primes': [2, 359], 'central_character': '2872.717', 'conductor': 2872, 'conductor_radical': 718, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2872/1/b/e/717/13'], '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': '2-2872-2872.717-c0-0-13', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2872-2872.717-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1972112245890376, 'root_angle': 0.10526315789473685, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40429590200286120261381336293', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1780156543071969818448508066180', 'Lhash_array': ['1780156543071969818448508066180'], 'label': '2-2872-2872.717-c0-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2872/1/b/e/717/13'}