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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_185.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.3420201433256687, 0.9396926207859084], 'a3': [0.3420201433256687, -0.9396926207859084], 'a4': [-0.766044443118978, 0.6427876096865394], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, 0.0], 'a7': [0.984807753012208, -0.17364817766693036], 'a8': [-0.8660254037844386, -0.5], 'a9': [-0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 19.88101108700563, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '185.83', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 185, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_185.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^29', 'a^14', 0, 'a^0', 'a^35', 'a^21', 'a^22', 0, 'a^12', 'a^7', 'a^5', 'a^6', 0, 'a^28', 'a^31', 'a^29', 'a^2', 0, 'a^28', 'a^19', 'a^33', 'a^14', 0, 'a^12', 'a^15', 'a^13', 'a^30', 0, 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'187.58271942191775914995594426336', '188.60642163934192807735877761893', '189.001962593589550772824241680909', '189.62546044573482403114316463367', '190.48685448408489202718934321481', '191.0949302176424102208990172939', '191.70226034520368719989116096686', '192.85419015661861411603455267996', '193.5298716294832209764325156432', '194.62770426322280131879671704014', '195.16771300384600356894708435314', '195.62639284125395813191747290935', '196.26725372832732488328840291746', '197.03908706847403431795919820556', '197.68101741751052935720082322053', '198.36457138428595282993154760966', '198.943263448589706782112196833191'], 'prelabel': '1-185-185.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': 0.16849236323207636, 'root_number': '0.863143377248258078788256848696+0.504958919430552526558438984159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.084246181616', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.47084657774843991913675474258+0.339407286675341655175641453916*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.07630803811', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.74109338822', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.34065622263', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.88101108700563, 'bad_primes': [5, 37], 'central_character': '185.83', 'conductor': 185, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/185/83'], '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': '1-185-185.83-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-185-185.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.88101108700563, 'root_angle': 0.08424618161603818, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07630803811', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_185.83', 'Lhash_array': ['dirichlet_L_185.83'], 'label': '1-185-185.83-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/185/83'}
Lfunction data - 1-185-185.83-r1-0-0