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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.84', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.6691306063588582, 0.7431448254773942], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.6691306063588582, -0.7431448254773942], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.84', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.734', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^22', 0, 'a^19', 'a^12', 'a^3', 'a^16', 0, 0, 'a^0', 'a^1', 'a^23', 0, 'a^14', 'a^14', 'a^27', 0, 0, 'a^20', 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'189.194794540824261855354682011447', '189.461058903437011127518560919455', '190.39149067544322685483020154534', '190.83697287959428516472139274703', '191.33767271519731525137976905603', '192.33405940684505415402855060746', '192.72544964359767404821690655209', '192.97795789851757566453401391667', '194.13906826220251324857002005040', '194.439461367702058796721462334392', '195.22995748160909572750940836640', '195.86086852128941478076486176840', '196.705151283372262305081311219767', '197.09685783209835499149638700437', '197.59232663952302164164398419980', '198.14314699923092634850258828897', '198.91310312599575093249307357593', '199.49264788160904103254258221415', '199.65439376283870540039017983314'], 'prelabel': '1-1045-1045.84-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.05763979018968345, 'root_number': '0.983649633585741991205123950714-0.180092749289457850992939389689*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0288198950948', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.490669831798535985425888334882+0.291993553750463515465233208622*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.247345825222', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.98043686491', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.18856116864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.84', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/84'], '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': '1-1045-1045.84-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': '1-1045-1045.84-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.028819895094841726, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.247345825222', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.84', 'Lhash_array': ['dirichlet_L_1045.84'], 'label': '1-1045-1045.84-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/84'}
Lfunction data - 1-1045-1045.84-r0-0-0