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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_731.419', 'a10': [-0.9609173219450995, 0.2768355114248494], 'a2': [0.8467241992282841, -0.5320320765153366], 'a3': [-0.5786712961798057, -0.8155608689592602], 'a4': [0.4338837391175581, -0.9009688679024191], 'a5': [-0.9609173219450995, -0.2768355114248494], 'a6': [-0.9238795325112867, -0.3826834323650898], 'a7': [-0.3826834323650898, 0.9238795325112867], 'a8': [-0.11196447610330786, -0.9937122098932426], 'a9': [-0.3302790619551671, 0.9438833303083676], 'algebraic': True, 'analytic_conductor': 3.3947497281733687, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [43, [1]]], 'bad_primes': [17, 43], 'central_character': '731.419', 'coeff_info': ['x^112 - 1', '0.998426815017817 + 0.0560704472371918*I', '\\\\zeta_{112}'], 'conductor': 731, 'conductor_radical': 731, 'conjugate': 'dirichlet_L_731.82', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^102', 'a^73', 'a^92', 'a^61', 'a^63', 'a^35', 'a^82', 'a^34', 'a^51', 'a^55', 'a^53', 'a^68', 'a^25', 'a^22', 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[[0], []], 'index': 0, 'label': '1-731-731.419-r0-0-0', 'leading_term': '0.544480964774592171462518139125+0.166795857265688208945197371354*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/731/419', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5694562134201948, 1.1315224370096328, 1.4054170543187765, 0.9672389991190364, -0.16765211828381138, -1.3842356329830015, -1.8815851347357408, -1.3062226186534474, -0.1211415750671484, 0.6559438919298919, 0.24099834285386842, -1.2050926694860713, -2.599997878709718, -2.795676044297424, -1.5939782956875244, 0.014283792906756026, 0.7124913123638744, 0.10851656874070956, -0.832587699414932, -0.7119186410604873, 0.8174207413349758, 2.5058434371389824, 2.634893832888892, 0.8642923673749829, -1.0913759774757466, -0.9003692604849715, 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'193.04856012355884902040685135422', '193.74284405204603067354380605383', '193.90381429753016160404755226500', '194.67026751884784827981750897473', '195.52623072033073765082601203808', '195.866358528967693129792631523133', '196.0582026747223175107504593938', '196.94185283161840263286167921783', '197.40054674063370828182503925249', '198.856122062967526464113848296654', '199.19958017447280889522715733007', '199.774428709342175755639140348386'], 'prelabel': '1-731-731.419-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3947497281733687, 'root_angle': 0.18924310222646878, 'root_number': '0.828414792862013348726920454401+0.560115105105537675396313619879*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0946215511132', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(112)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.792034722663461392241444059219-0.383502944281893048714119959560*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20986875277', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.53330062329', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.18984814009', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3947497281733687, 'bad_primes': [17, 43], 'central_character': '731.419', 'conductor': 731, 'conductor_radical': 731, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/731/419'], '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': '1-731-731.419-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': '1-731-731.419-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3947497281733687, 'root_angle': 0.09462155111323439, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20986875277', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_731.419', 'Lhash_array': ['dirichlet_L_731.419'], 'label': '1-731-731.419-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/731/419'}