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lfunc_lfunctions • Show schema
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{'Lhash': '2847842055764173899382162915792', 'a10': [30957.037876309158, 25976.039064352102], 'a2': [-12.256711089903648, 10.28460175498463], 'a3': [-33.702454004008516, -12.266690079184889], 'a4': [44.45393348273417, -252.11078477112525], 'a5': [-438.5869238294564, -2487.350047436053], 'a6': [539.2392640641363, -196.26704126695822], 'a7': [2232.688109786096, -3867.1292436044373], 'a8': [2048.0, 3547.2400539010605], 'a9': [-14092.669053517307, -11825.15340510984], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.571361774227185, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [12.256711089903648, -10.28460175498463]]], [19, [[1.0, 0], [-157492.85990778945, 545787.2267258235]]]], 'bad_primes': [2, 19], 'central_character': '38.25', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '274014486443230925765630888680', 'degree': 2, 'euler_factors': [[[1.0, 0], [12.256711089903648, 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'-0.9926219551521792 - 0.12125037793699879*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48065480298', 'prec': 47}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.24655126203659340311588063022', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47149429636799386176803403465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.85935212394758806799701416973', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.571361774227185, 'bad_primes': [2, 19], 'central_character': '19.6', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/10/e/a/25/5'], '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': '2-38-19.6-c9-0-12', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-38-19.6-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.423953184000389, 'root_angle': -0.4806548029798212, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24655126203659340311588063022', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2847842055764173899382162915792', 'Lhash_array': ['2847842055764173899382162915792'], 'label': '2-38-19.6-c9-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/10/e/a/25/5'}