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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.439', 'a10': [0.23575893550942723, -0.9718115683235417], 'a2': [-0.9283679330160726, 0.3716624556603275], 'a3': [0.5, -0.8660254037844386], 'a4': [0.7237340381050702, -0.690079011482112], 'a5': [-0.5800569095711982, 0.8145759520503357], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.41541501300188644, 0.9096319953545183], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.439', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.164', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^55', 'a^58', 'a^23', 'a^18', 0, 'a^21', 'a^44', 'a^52', 0, 'a^47', 'a^36', 0, 'a^12', 'a^50', 'a^46', 'a^7', 'a^20', 'a^15', 0, 0, 'a^50', 'a^10', 'a^46', 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'191.50214095428491074155467327231', '192.36895076074162011767786206359', '193.22417321223406011769933279724', '193.79960276468188351939209116079', '194.66391656874785172987599828076', '195.49812749320362078560784040440', '195.69344483488015424343081474792', '196.38107618875414399129870094228', '197.152034125278223564262906756881', '197.643092814190968446479868273915', '198.11513851857837673766516623587', '198.78290708171094366682084619749', '199.21841346985843260118043349035'], 'prelabel': '1-847-847.439-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.7241169038094631, 'root_number': '-0.647335935724697140962875284019+0.762204819139469080673250823988*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.362058451905', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.577059009767818733909778484715+0.0111318222262228870790843350001*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.28226332067', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.54458336499', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.05586335548', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.439', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/439'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-847-847.439-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-847-847.439-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.36205845190473157, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28226332067', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.439', 'Lhash_array': ['dirichlet_L_847.439'], 'label': '1-847-847.439-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/439'}