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lfunc_lfunctions • Show schema
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{'Lhash': '594629368281596666398552601129', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.3826834323650898, -0.9238795325112867], 'a4': [0.0, 0.0], 'a5': [-2.508071481418116, -1.0388772230045638], 'a6': [0.0, 0.0], 'a7': [-2.2200982531418245, 0.9195948062521605], 'a8': [0.0, 0.0], 'a9': [-0.7071067811865476, -0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.515792804936482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.3826834323650898, 0.9238795325112867]]], [17, [[1.0, 0], [-3.255696088643214, 2.529909677912095]]]], 'bad_primes': [2, 3, 17], 'central_character': '816.433', 'coefficient_field': 'CDF', 'conductor': 816, 'conductor_radical': 102, 'conjugate': '1761200466773927422601028452740', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [2.508071481418116, 1.0388772230045638], 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'4.31508848105023015399172949490074', '5.80691515532617449395379977184601', '6.58732461479829780804112402747778', '7.65021861621831467658767013106064', '8.379910543577765416294128662630271', '9.210836482600147230622285672981634', '10.18820885369788438094812693234482'], 'prelabel': '2-816-17.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5526051016435116, 'root_angle': -0.35945502790340933, 'root_number': '0.4273278033853832 - 0.9040967583471491*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.179727513952', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46907986173361875133489661982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88963548744372233328289978952', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60737327096553328572215714633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.515792804936482, 'bad_primes': [2, 3, 17], 'central_character': '17.8', 'conductor': 816, 'conductor_radical': 102, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/816/2/bq/f/433/3'], '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': '2-816-17.8-c1-0-3', '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': '2-816-17.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5526051016435116, 'root_angle': -0.17972751395170466, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46907986173361875133489661982', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '594629368281596666398552601129', 'Lhash_array': ['594629368281596666398552601129'], 'label': '2-816-17.8-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/816/2/bq/f/433/3'}