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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_920.517', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.28173255684142967, -0.9594929736144974], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9898214418809327, 0.14231483827328514], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8412535328311812, -0.5406408174555976], 'algebraic': True, 'analytic_conductor': 4.272462038193569, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '920.517', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 920, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_920.573', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^35', 0, 0, 0, 'a^1', 0, 'a^26', 0, 'a^52', 0, 'a^43', 0, 0, 0, 'a^5', 0, 'a^50', 0, 'a^36', 0, 0, 0, 0, 0, 'a^61', 0, 'a^60', 0, 'a^20', 0, 'a^43', 0, 0, 0, 'a^59', 0, 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'193.975828185237808211753907733457', '194.75080410372397769967411801579', '195.276974907271025820217685563275', '195.677538544799849908334194901915', '196.24334165784858711548272054077', '196.931861851372490008764388919245', '197.55085396698327546468142295146', '198.10008498770933691227076697128', '198.76335954193925097694935405821', '199.39178480715495979582492333589'], 'prelabel': '1-920-920.517-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': -0.03782795300830779, 'root_number': '0.971886821312280749935084671862-0.235448522100927336176872687756*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0378279530083', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.35241990710495361864263190295-0.219546332000676004234209025203*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.40593029469', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.66399547453', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.09493541348', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.272462038193569, 'bad_primes': [2, 5, 23], 'central_character': '920.517', 'conductor': 920, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/920/517'], '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': '1-920-920.517-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': '1-920-920.517-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.272462038193569, 'root_angle': -0.03782795300830779, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40593029469', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_920.517', 'Lhash_array': ['dirichlet_L_920.517'], 'factors': ['1-920-920.517-r0-0-0'], 'label': '1-920-920.517-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/920/517'}
Lfunction data - 1-920-920.517-r0-0-0