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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2349.1525', 'a10': [0.3420201433256687, -0.9396926207859084], 'a2': [-0.918216106880274, -0.39607976603915684], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6862416378687336, 0.7273736415730487], 'a5': [0.05814482891047583, 0.9983081582712682], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9730448705798238, 0.23061587074244017], 'a8': [-0.3420201433256687, -0.9396926207859084], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 252.43510834257418, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '2349.1525', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 2349, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_2349.2158', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^61', 0, 'a^14', 'a^26', 0, 'a^4', 'a^75', 0, 'a^87', 'a^37', 0, 'a^2', 'a^65', 0, 'a^28', 'a^69', 0, 'a^93', 'a^40', 0, 'a^98', 'a^104', 0, 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'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.805956978491682291458909571488+0.136208172175928701650132594421*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.936233461971', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.91495762487', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.60829420189', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 252.43510834257418, 'bad_primes': [3, 29], 'central_character': '2349.1525', 'conductor': 2349, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2349/1525'], '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': '1-2349-2349.1525-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': '1-2349-2349.1525-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 252.43510834257418, 'root_angle': 0.29688075842944966, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936233461971', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2349.1525', 'Lhash_array': ['dirichlet_L_2349.1525'], 'factors': ['1-2349-2349.1525-r1-0-0'], 'label': '1-2349-2349.1525-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2349/1525'}
Lfunction data - 1-2349-2349.1525-r1-0-0