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lfunc_lfunctions • Show schema
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{'Lhash': '841973207978045440503571255900', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-5.196152422706632, 0.0], 'a4': [0.0, 8.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-25.588457268119896, 25.588457268119896], 'a8': [0.0, 0.0], 'a9': [27.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [5.196152422706632, 0]]], [13, [[1.0, 0], [-31.176914536239792, 35.0]]]], 'bad_primes': [3, 13], 'central_character': '39.8', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '4168140608005224104770987134221', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, -8.0]], [[1.0, 0], [5.196152422706632, 0]], [[1.0, 0], [0, 0], [0, -125.0]], [[1.0, 0], [25.588457268119896, -25.588457268119896], [0, -343.0]], [[1.0, 0], [0, 0], [0, 1331.0]], [[1.0, 0], [-31.176914536239792, 35.0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], 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'6.96658573105494420842171104875965', '9.606147852636555739952188230440820', '10.38085660668039823711397929569965', '11.47602965085814111631916940222783', '13.11492955502056318331339053988740', '13.95877025949219821621648341834863', '15.74919646684040088193110665381454'], 'prelabel': '2-39-39.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.6747850416276008, 'root_number': '-0.5219226477873236 - 0.8529928192702851*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.337392520814', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66419974701740016513030352077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.29787692687587276082604923756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.12679362412166326822274238597', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '39.8', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/f/a/8/1'], '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': '2-39-39.8-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39-39.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.3373925208138004, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66419974701740016513030352077', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '841973207978045440503571255900', 'Lhash_array': ['841973207978045440503571255900'], 'label': '2-39-39.8-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/f/a/8/1'}