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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_151.55', 'a10': [0.9443763702374811, -0.32886664673858323], 'a2': [0.6691306063588582, 0.7431448254773942], 'a3': [0.06279051952931337, 0.9980267284282716], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [0.387515586452103, -0.9218631515885005], 'a6': [-0.6996633405133654, 0.7144726796328034], 'a7': [0.9964928592495044, 0.0836778433323155], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [-0.9921147013144779, 0.12533323356430426], 'algebraic': True, 'analytic_conductor': 0.701241051920901, 'analytic_normalization': 0, 'bad_lfactors': [[151, [1]]], 'bad_primes': [151], 'central_character': '151.55', 'coeff_info': ['x^75 - 1', '0.996492859249504 + 0.0836778433323155*I', '\\\\zeta_{75}'], 'conductor': 151, 'conductor_radical': 151, 'conjugate': 'dirichlet_L_151.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^18', 'a^20', 'a^61', 'a^28', 'a^1', 'a^30', 'a^36', 'a^71', 'a^7', 'a^38', 'a^23', 'a^11', 'a^4', 'a^40', 'a^49', 'a^46', 'a^45', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-151-151.55-r0-0-0', 'leading_term': '0.959198835400656300134170904696+1.38348565400378792265734265786*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/151/55', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6834770448890186, 2.273051626272292, 3.212121476381049, 4.026662450602856, 4.298341988744772, 3.776877241645516, 2.4592457561982815, 0.6239872664883973, -1.2332673926032918, -2.570106705239331, -3.018474919102284, -2.556488389499833, -1.5331931538657355, -0.5094164688551475, 0.025083117841560518, -0.0842024462701792, -0.5660530925241484, -0.8816288400142858, -0.5644556635844888, 0.4488265072240485, 1.7110508447451, 2.481882452532039, 2.1731098645395557, 0.7588773766163945, -1.1281702713438575, -2.5234312926050055, 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'1.20248610437572889822929066122+0.972972388406760697772739483182*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.28831594145', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.34205130262', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.60360016766', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.701241051920901, 'bad_primes': [151], 'central_character': '151.55', 'conductor': 151, 'conductor_radical': 151, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/151/55'], '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': '1-151-151.55-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': '1-151-151.55-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.701241051920901, 'root_angle': 0.30703133711923053, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28831594145', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_151.55', 'Lhash_array': ['dirichlet_L_151.55'], 'label': '1-151-151.55-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/151/55'}