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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_83.69', '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': 0.38545037953268074, 'analytic_normalization': 0, 'bad_lfactors': [[83, [1]]], 'bad_primes': [83], 'central_character': '83.69', 'coeff_info': ['x^41 - 1', '0.988280423780349 + 0.152649284218874*I', '\\\\zeta_{41}'], 'conductor': 83, 'conductor_radical': 83, 'conjugate': 'dirichlet_L_83.77', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 'a^37', 'a^9', 'a^19', 'a^21', 'a^36', 'a^34', 'a^33', 'a^3', 'a^26', 'a^5', 'a^39', 'a^20', 'a^15', 'a^18', 'a^6', 'a^17', 'a^27', 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-0.5205575728945254, 'root_number': '-0.0645386326988522049769318305659-0.997915209268484215416308119354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.260278786447', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(41)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.735114280351136501057534590788-0.433940943062348527763985628540*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.17190879688', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.97368666448', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.03795885934', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38545037953268074, 'bad_primes': [83], 'central_character': '83.69', 'conductor': 83, 'conductor_radical': 83, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/83/69'], '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': '1-83-83.69-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': '1-83-83.69-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.38545037953268074, 'root_angle': -0.2602787864472627, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17190879688', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_83.69', 'Lhash_array': ['dirichlet_L_83.69'], 'label': '1-83-83.69-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/83/69'}