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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4235.1952', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.22649676742576438, 0.9740119169423335], 'a3': [-0.9510565162951535, 0.30901699437494745], 'a4': [-0.8973984286913584, -0.4412211012432213], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.08557500847883974, -0.9963317308626913], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.6330124538088704, -0.7741416106390825], 'a9': [0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.1952', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.1868', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^63', 'a^99', 'a^126', 0, 'a^162', 0, 'a^189', 'a^198', 0, 0, 'a^5', 'a^203', 0, 0, 'a^32', 'a^117', 'a^41', 'a^4', 0, 0, 0, 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'193.60706666616485011420782823500', '194.40632437766057985741170598574', '194.588260038014823795548599491696', '195.30180426699102437785989381688', '195.66391074805870743600039300583', '196.07812158606009809977935059500', '196.97136421587691328335478194562', '197.32079699031231237902994944070', '197.79960578580474594712965323239', '198.41439983109434993546245825102', '199.020624867542261970832660895115', '199.45714632462719329879788089856', '199.72969723776564988673905143770'], 'prelabel': '1-4235-4235.1952-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.9175305052243702, 'root_number': '-0.966624659067273228357035754754+0.256196737846284444361169437142*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(220)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.536378363519718999574273078205+0.326608236206841609405472794942*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.864084669531', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66931116583', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.27911401399', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.1952', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/1952'], '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': '1-4235-4235.1952-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': '1-4235-4235.1952-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.4587652526121851, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.864084669531', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4235.1952', 'Lhash_array': ['dirichlet_L_4235.1952'], 'label': '1-4235-4235.1952-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/1952'}
Lfunction data - 1-4235-4235.1952-r0-0-0