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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_88.37', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.40867028191416754, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [11, [1]]], 'bad_primes': [2, 11], 'central_character': '88.37', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 88, 'conductor_radical': 22, 'conjugate': 'dirichlet_L_88.69', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 'a^13', 0, 'a^4', 0, 'a^2', 0, 0, 0, 'a^7', 0, 'a^4', 0, 'a^8', 0, 'a^11', 0, 'a^5', 0, 'a^0', 0, 'a^6', 0, 'a^13', 0, 'a^9', 0, 'a^2', 0, 0, 0, 'a^7', 0, 'a^9', 0, 'a^8', 0, 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'189.73965878078901497217281790312', '190.6904992201295568499511612080', '191.25738258166853970112086199367', '191.83074938361860699151433222490', '193.19341290897022547041513978228', '193.446411133183008316181290497993', '194.16249566915794193377486900069', '195.290867772071630905601815779581', '196.17250928424954439308674460009', '197.00506599013933504310424449883', '197.60388097210616267025830773477', '198.393781353901723454282148497274', '199.12114712614378395913809530043', '199.69112672501448976768589503920'], 'prelabel': '1-88-88.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40867028191416754, 'root_angle': 0.20378373710217174, 'root_number': '0.286321457385842763640011748955+0.958133614398559250513700436076*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.203783737102', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07033514048537215880882869926+0.441639799047043206172305275655*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.72019739627', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.40682081031', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.2511552132', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.40867028191416754, 'bad_primes': [2, 11], 'central_character': '88.37', 'conductor': 88, 'conductor_radical': 22, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/88/37'], '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': '1-88-88.37-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': '1-88-88.37-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40867028191416754, 'root_angle': 0.20378373710217174, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.72019739627', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_88.37', 'Lhash_array': ['dirichlet_L_88.37'], 'factors': ['1-88-88.37-r0-0-0'], 'label': '1-88-88.37-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/88/37'}
Lfunction data - 1-88-88.37-r0-0-0