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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_83.14', 'a10': [0.8961655569610556, 0.4437198378669597], 'a2': [0.7714891798219429, 0.6362424423265598], 'a3': [0.8179293607667176, -0.5753186602186205], 'a4': [0.19039110916466837, 0.9817083199968549], 'a5': [0.9736954238777791, -0.22785350890313757], 'a6': [0.9970658011837404, 0.07654925283649565], 'a7': [0.720521593600787, -0.6934325007922417], 'a8': [-0.4777198185122629, 0.8785122509109424], 'a9': [0.33801687840850275, -0.9411400479795615], 'algebraic': True, 'analytic_conductor': 8.919588757953877, 'analytic_normalization': 0, 'bad_lfactors': [[83, [1]]], 'bad_primes': [83], 'central_character': '83.14', 'coeff_info': ['x^82 - 1', '0.997065801183740 + 0.0765492528364956*I', '\\\\zeta_{82}'], 'conductor': 83, 'conductor_radical': 83, 'conjugate': 'dirichlet_L_83.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^74', 'a^18', 'a^79', 'a^1', 'a^72', 'a^27', 'a^66', 'a^6', 'a^52', 'a^10', 'a^37', 'a^81', 'a^71', 'a^36', 'a^12', 'a^75', 'a^13', 'a^15', 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0.08879015499589041, 'root_number': '0.961347147350313238023038664093+0.275339176800932429565031455138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0443950774979', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(82)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.31460972587860413554501039615+0.313670344114199861290610131836*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.76235476668', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.28540613912', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.93532743733', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.919588757953877, 'bad_primes': [83], 'central_character': '83.14', 'conductor': 83, 'conductor_radical': 83, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/83/14'], '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': '1-83-83.14-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': '1-83-83.14-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.919588757953877, 'root_angle': 0.044395077497945204, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76235476668', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_83.14', 'Lhash_array': ['dirichlet_L_83.14'], 'label': '1-83-83.14-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/83/14'}
Lfunction data - 1-83-83.14-r1-0-0