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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_139.28', 'a10': [0.20345601305263378, -0.9790840876823229], 'a2': [-0.7151095013548994, 0.6990124470078821], 'a3': [-0.9496396989003193, 0.31334396798488223], 'a4': [0.022763197856105682, -0.9997408848413492], 'a5': [-0.8298852919990252, 0.5579340481846333], 'a6': [0.46006503773115215, -0.8878852184023752], 'a7': [0.5388986359155754, -0.8423706192694116], 'a8': [0.6825531432186541, 0.7308359642781241], 'a9': [0.8036311154549782, -0.5951277428187898], 'algebraic': True, 'analytic_conductor': 0.6455132862053328, 'analytic_normalization': 0, 'bad_lfactors': [[139, [1]]], 'bad_primes': [139], 'central_character': '139.28', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 139, 'conductor_radical': 139, 'conjugate': 'dirichlet_L_139.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^31', 'a^52', 'a^28', 'a^57', 'a^58', 'a^9', 'a^62', 'a^54', 'a^44', 'a^14', 'a^8', 'a^15', 'a^59', 'a^35', 'a^22', 'a^19', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-139-139.28-r0-0-0', 'leading_term': '0.392632599860651729388395240848+0.298933211379485558013902783798*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/139/28', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4934788985751946, 0.6115421152711006, 0.6581612652766461, 0.3677620789865075, -0.44618262994321206, -1.7943237574767013, -3.4616485262585925, -5.027060586381059, -5.977772020002622, -5.899699064912682, -4.674999773144453, -2.5910873789861304, -0.28492928022917374, 1.4854591736858935, 2.160018856363602, 1.6384135985757062, 0.3410264631304288, -0.9872547084129975, -1.6515391514164557, -1.3693328843348422, -0.415092931084757, 0.5522922623759976, 0.896984461471635, 0.4137516341057354, -0.521457052304578, -1.1740841672115672, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6455132862053328, 'bad_primes': [139], 'central_character': '139.28', 'conductor': 139, 'conductor_radical': 139, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/139/28'], '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': '1-139-139.28-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': '1-139-139.28-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6455132862053328, 'root_angle': 0.20713362128920934, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1058208122', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_139.28', 'Lhash_array': ['dirichlet_L_139.28'], 'label': '1-139-139.28-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/139/28'}