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lfunc_lfunctions • Show schema
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{'Lhash': '310567933379474235419185122141', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.15206734782503536, 0.26338837260520986], 'a4': [0, 0], 'a5': [-17.760336739125176, -30.761805591696962], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [121.45375104345092, 210.36406757707854], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.87045736668842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '392.361', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '1667554481309451668540382115774', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.15206734782503536, -0.26338837260520986], [-121.5, -210.4441731196186]], [[1.0, 0], [17.760336739125176, 30.761805591696962], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [282.91240408695023, -490.0186579700547], [-80525.5, 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[-422298150.5, 731441852.6083683]], [[1.0, 0], [5989.436488696956, -10374.008307130063], [-675062553.5, -1169242640.9491835]], [[1.0, 0], [12924.89428695505, 0], [1804229351.0, 0]], [[1.0, 0], [40588.60485825955, -70301.5258228425], [-1036535796.5, -1795332663.4018745]], [[1.0, 0], [23499.400254433156, 40702.15518807522], [-1538528199.5, 2664809010.4114656]], [[1.0, 0], [111544.23762964121, 0], [3939040643.0, 0]], [[1.0, 0], [-17363.42029182852, -30074.326138619417], [-2792029724.5, 4835937339.076535]], [[1.0, 0], [-92655.55285652248, 0], [8587340257.0, 0]], [[1.0, 0], [-77382.57640238605, 134030.5539495131], [-5255050250.5, -9102014030.193556]], [[1.0, 0], [-98572.84249591063, -170733.17144940177], [-5796370371.5, 10039607982.924889]], [[1.0, 0], [31950.63640121595, 55340.12558106565], [-7012758653.5, 12146454289.080307]], [[1.0, 0], [33455.21717887042, -57946.13593205469], [-7693119774.5, -13324874318.146824]], [[1.0, 0], [100523.56478346881, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-392-7.4-c5-0-6', 'leading_term': '0.963257940404920689077593807539210157265463473064168162', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/392/6/i/l/361/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.9632579404049207, 0.7284704720222492, 0.4835441417169651, 0.2325773359610938, -0.020209870708269056, -0.27053467375795465, -0.5141120211417641, -0.7467161879014891, -0.9642429608124629, -1.1627718889417358, -1.33862798403124, -1.488442175883967, -1.6092097461785602, -1.6983458836528083, -1.7537374290550782, -1.7737898145778452, -1.7574681546441941, -1.7043314177990099, -1.6145586076617118, -1.488965908563917, -1.3290138121195858, -1.1368033372423172, -0.9150605897508617, -0.6671090792959983, 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'6.27200422067160980007821737102718', '7.37383921156472908246912794408676', '8.307212191726908302964814862190001', '9.200377333353941144476590467733976', '10.29333922633703244510159768507566'], 'prelabel': '2-392-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': -0.707012572774559, 'root_number': '-0.6054643436493673635071294605077551469423497523567868621 - 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3535062863872795', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24499490105835093343614847017', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58528541862157101033574369158', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37285792841901014882664435243', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.87045736668842, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/6/i/l/361/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-392-7.4-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-392-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.929089315090883, 'root_angle': -0.3535062863872795, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24499490105835093343614847017', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '310567933379474235419185122141', 'Lhash_array': ['310567933379474235419185122141'], 'label': '2-392-7.4-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/6/i/l/361/1'}