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lfunc_lfunctions • Show schema
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{'Lhash': '587644371999434798098797433473', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 77.78174593052023], 'a6': [0, 0], 'a7': [249.41531628991834, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.5111521650342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '576.449', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '1598526929207534534796328342304', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -77.78174593052023], [-15625.0, 0]], [[1.0, 0], [-249.41531628991834, 0], [117649.0, 0]], [[1.0, 0], [0, -2469.0856607254436], [-1771561.0, 0]], [[1.0, 0], [504.0, 0], [4826809.0, 0]], [[1.0, 0], [0, 2773.2727958136393], [-24137569.0, 0]], [[1.0, 0], [-6983.628856117713, 0], [47045881.0, 0]], [[1.0, 0], [0, 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0.7149600435740429], 'positive_zeros': ['0.46356967124350713791234614066865', '1.25436469355603442996465801252255', '2.66885505497787796340849958515913', '3.79747293573841310126645027932581', '4.91461682743830402768794405889404', '5.68424880586150379716699114041854', '6.67194266419958475759758162802664', '8.084049692548741797030031582228845', '8.367518076273160099317155703590757', '9.333617320478017717149257287290563'], 'prelabel': '2-24e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.511348842122464, 'root_angle': -0.6959132760153036, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46356967124350713791234614067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.25436469355603442996465801252', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.66885505497787796340849958516', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.5111521650342, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/7/e/o/449/4'], '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': '2-24e2-3.2-c6-0-16', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-24e2-3.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.511348842122464, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46356967124350713791234614067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '587644371999434798098797433473', 'Lhash_array': ['587644371999434798098797433473'], 'label': '2-24e2-3.2-c6-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/7/e/o/449/4'}