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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_847.670', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [-0.0475819158237423, 0.998867339183008], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.9954719225730846, -0.09505604330418266], 'a5': [0.7860530947427875, -0.6181589862206052], 'a6': [0.8412535328311812, 0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.14231483827328514, -0.9898214418809327], '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': '847.670', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.780', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^55', 'a^34', 'a^59', 'a^6', 0, 'a^51', 'a^44', 'a^10', 0, 'a^23', 'a^12', 0, 'a^48', 'a^2', 'a^52', 'a^61', 'a^14', 'a^27', 0, 0, 'a^2', 'a^40', 'a^52', 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'191.61157471793738605956112699682', '192.16197897064282591621096827275', '193.091108412382925707433882139180', '193.60501371796397187429255507253', '194.45460513425869158840048659667', '195.225181715653631610557067002626', '195.714653268391117430350936270811', '196.00432605032655161123627929141', '196.8009669446171636386090294858', '197.28083525624904033116244899447', '197.754695133381728451637835136591', '198.154404548640818410744405907677', '199.16342132435042431691642986275', '199.93446209032147949525983119032'], 'prelabel': '1-847-847.670-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.11885830280210713, 'root_number': '0.931090872218855818251127842235-0.364787318407219724769655988089*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0594291514011', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.29632018598610088363091277137+0.0233829758642203631664257477956*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.892820222923', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.83356302831', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.20533258866', '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': '847.670', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/670'], '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': '1-847-847.670-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': '1-847-847.670-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.059429151401053565, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.892820222923', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.670', 'Lhash_array': ['dirichlet_L_847.670'], 'label': '1-847-847.670-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/670'}