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lfunc_lfunctions • Show schema
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{'Lhash': '2011984717979446017442960054803', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 1.7320508075688772], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.5, -2.598076211353316], 'a8': [0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.179056282979259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, 2.598076211353316]]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.401', 'coefficient_field': 'CDF', 'conductor': 1400, 'conductor_radical': 70, 'conjugate': '814551227536026988831096253938', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 2.598076211353316]], [[1.0, 0], [2.0, 3.4641016151377544], [-5.5, 9.526279441628825]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-8.5, 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-1.5993503863227927, -2.0154922712184216, -2.3305926582600742], 'positive_zeros': ['1.58717608591610793170014415323044', '2.31856820978026890140390153273379', '3.33129490705527477394992038942900', '4.65881410784362455438298351544852', '5.65265750840310458565433198324935', '6.48802365056284018082708748709955', '7.42881538663985532489250437751424', '7.88581045624189820291944312690326', '8.911438316034635997633731928727134', '9.316402721314430828805157942795356'], 'prelabel': '2-1400-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.25264152111754884, 'root_number': '0.7012145161459063422881052853594033060275307273817210712 + 0.7129503505478221262538366779721476646448806805958393603*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12632076055877442', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58717608591610793170014415323', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31856820978026890140390153273', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33129490705527477394992038943', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.179056282979259, 'bad_primes': [2, 5, 7], 'central_character': '7.2', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1400/2/q/f/401/1'], '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': '2-1400-7.2-c1-0-31', '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': '2-1400-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.343509575727167, 'root_angle': 0.12632076055877442, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58717608591610793170014415323', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2011984717979446017442960054803', 'Lhash_array': ['2011984717979446017442960054803'], 'label': '2-1400-7.2-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/q/f/401/1'}