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lfunc_lfunctions • Show schema
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{'Lhash': '2817534233770208511821576148381', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -4.295800470680297], 'a4': [0, 0], 'a5': [2.3288172861599326, 0], 'a6': [0, 0], 'a7': [2.957403781604451, 0], 'a8': [0, 0], 'a9': [-9.453901683897062, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.56680007310605, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-10.575559534275596, 15.784724911666737]]]], 'bad_primes': [2, 19], 'central_character': '608.417', 'coefficient_field': 'CDF', 'conductor': 608, 'conductor_radical': 38, 'conjugate': '218871288133693898291063922703', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.295800470680297], [-9.0, 0]], [[1.0, 0], [-2.3288172861599326, 0], [25.0, 0]], [[1.0, 0], [-2.957403781604451, 0], [49.0, 0]], [[1.0, 0], [19.485889700231514, 0], [121.0, 0]], [[1.0, 0], [0, -14.023540835189708], [-169.0, 0]], [[1.0, 0], [22.273066937555228, 0], 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['2.22264260614315657648917682506764', '3.40536091738980733712858919387650', '4.56953475925931473890076636094446', '5.30275818886988848323609005294970', '6.08329048141029533783325278586814', '7.79628815666360117748122926689484', '8.287297629380430924615503731806652', '9.525866174382483346167757648546108', '10.22836373014059934466676983016160', '10.55095650436336487473375410819514'], 'prelabel': '2-608-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.070233417521169, 'root_angle': -0.8121023958594414, 'root_number': '-0.83077499535088095384113805493259373532724119530230152014 - 0.5566083965408209052944845516362968638288139332106201685*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4060511979297207', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22264260614315657648917682507', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40536091738980733712858919388', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.56953475925931473890076636094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.56680007310605, 'bad_primes': [2, 19], 'central_character': '19.18', 'conductor': 608, 'conductor_radical': 38, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/608/3/e/b/417/4'], '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': '2-608-19.18-c2-0-38', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-608-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.070233417521169, 'root_angle': -0.4060511979297207, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22264260614315657648917682507', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2817534233770208511821576148381', 'Lhash_array': ['2817534233770208511821576148381'], 'label': '2-608-19.18-c2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/608/3/e/b/417/4'}