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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2784.683', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.11196447610330786, 0.9937122098932426], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9749279121818236, 0.2225209339563144], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.928841646011845, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [29, [1]]], 'bad_primes': [2, 3, 29], 'central_character': '2784.683', 'coeff_info': ['x^56 - 1', '0.993712209893243 + 0.111964476103308*I', '\\\\zeta_{56}'], 'conductor': 2784, 'conductor_radical': 174, 'conjugate': 'dirichlet_L_2784.803', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^71', 0, 'a^82', 0, 0, 0, 'a^39', 0, 'a^53', 0, 0, 0, 'a^0', 0, 'a^65', 0, 0, 0, 'a^34', 0, 'a^30', 0, 0, 0, 0, 0, 'a^36', 0, 0, 0, 'a^41', 0, 'a^59', 0, 0, 0, 'a^70', 0, 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50}, 'spectral_label': 'r0-0', 'st_group': 'mu(56)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.940365322341374935454995196129+0.0518557739620267881788821618029*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.482091862403', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.77478108083', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00645852921', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 12.928841646011845, 'bad_primes': [2, 3, 29], 'central_character': '2784.683', 'conductor': 2784, 'conductor_radical': 174, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2784/683'], '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': '1-2784-2784.683-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': '1-2784-2784.683-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.928841646011845, 'root_angle': -0.0785434179609785, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.482091862403', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2784.683', 'Lhash_array': ['dirichlet_L_2784.683'], 'factors': ['1-2784-2784.683-r0-0-0'], 'label': '1-2784-2784.683-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2784/683'}
Lfunction data - 1-2784-2784.683-r0-0-0