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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1521.743', 'a10': [-0.6927243535095994, 0.7212024473438146], 'a2': [0.9034504346103823, 0.4286925614030542], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6324453755953773, 0.7746049618276546], 'a5': [-0.3166679938014725, 0.9485364419471455], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.23931566428755777, -0.970941817426052], 'a8': [0.23931566428755777, 0.970941817426052], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 7.063494304448282, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1521.743', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1521, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1521.956', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 'a^47', 0, 'a^111', 'a^33', 0, 'a^58', 'a^41', 0, 0, 'a^122', 0, 'a^44', 'a^20', 0, 'a^65', 'a^69', 0, 'a^52', 'a^0', 0, 'a^94', 0, 0, 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'198.797548180408220004888944044823', '199.519742549992675861730647305027'], 'prelabel': '1-39e2-1521.743-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.063494304448282, 'root_angle': 0.4291584483892177, 'root_number': '-0.902563052862218451949156788557+0.430557702994653505586750768576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.429158448389', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.26224401421762232608034064391+0.871098276939244566597388929030*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.63178090009', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.67425359193', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.65097661371', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.063494304448282, 'bad_primes': [3, 13], 'central_character': '1521.743', 'conductor': 1521, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1521/743'], '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': '1-39e2-1521.743-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': '1-39e2-1521.743-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.063494304448282, 'root_angle': 0.4291584483892177, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63178090009', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1521.743', 'Lhash_array': ['dirichlet_L_1521.743'], 'factors': ['1-39e2-1521.743-r0-0-0'], 'label': '1-39e2-1521.743-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1521/743'}
Lfunction data - 1-39e2-1521.743-r0-0-0