-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '259706415086962580616485248410', 'a10': [-4.0, 5.830951894845301], 'a2': [-0.7071067811865476, -1.224744871391589], 'a3': [0, 0], 'a4': [-1.0, 1.7320508075688772], 'a5': [-2.15650065189833, -4.511042555592009], 'a6': [0, 0], 'a7': [5.049752469181039, -2.9154759474226504], 'a8': [2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.07090141318405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 1.224744871391589]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.15650065189833, 4.511042555592009]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.539', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'conjugate': '1552571564670651214428458530302', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.15650065189833, 4.511042555592009]], [[1.0, 0], [-5.049752469181039, 2.9154759474226504], [24.5, -42.4352447854375]], [[1.0, 0], [14.2828568570857, -8.246211251235321], [60.5, -104.78907385791707]], [[1.0, 0], [0, 0], [84.5, 146.35829323957014]], [[1.0, 0], [11.313708498984761, 0], [289.0, 0]], [[1.0, 0], [-12.0, 0], [361.0, 0]], [[1.0, 0], [12.020815280171307, -20.820662813657012], [-264.5, -458.12743860196804]], [[1.0, 0], [0, 0], [420.5, -728.3273645827129]], [[1.0, 0], [-16.0, 27.712812921102035], [-480.5, -832.2504130368455]], [[1.0, 0], [0, -23.323807579381203], [-1369.0, 0]], [[1.0, 0], [49.98999899979995, 28.861739379323623], [840.5, 1455.7887037616413]], [[1.0, 0], [35.34826728426727, -20.40833163195855], [924.5, -1601.280971597427]], [[1.0, 0], [-17.67766952966369, -30.618621784789728], [-1104.5, 1913.050116959825]], [[1.0, 0], [-67.88225099390856, 0], [2809.0, 0]], [[1.0, 0], [-14.2828568570857, -8.246211251235321], [1740.5, 3014.634430573631]], [[1.0, 0], [-8.0, -13.856406460551018], [-1860.5, 3222.4805274818964]], [[1.0, 0], [-5.049752469181039, -2.9154759474226504], [2244.5, 3887.5880375883453]], [[1.0, 0], [0, 0], [-5041.0, 0]], [[1.0, 0], [0, -116.61903789690601], [-5329.0, 0]], [[1.0, 0], [-36.0, -62.353829072479584], [-3120.5, 5404.864545018681]], [[1.0, 0], [-21.920310216782973, -37.96709101313926], [-3444.5, 5966.049006670998]], [[1.0, 0], [0, -65.96969000988257], [-7921.0, 0]], [[1.0, 0], [141.3930691370691, -81.6333265278342], [4704.5, -8148.433024207783]], [[1.0, 0], [114.2628548566856, -65.96969000988257], [5100.5, -8834.325144005059]], [[1.0, 0], [-85.84579197607766, -49.563091106185055], [5304.5, 9187.66350874911]], [[1.0, 0], [55.154328932550705, 0], [11449.0, 0]], [[1.0, 0], [-80.0, 0], [11881.0, 0]], [[1.0, 0], [-76.36753236814714, 132.2724461102916], [-6384.5, -11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-810-45.14-c2-0-5', 'leading_term': '0.506569241405019143652585764074349501128368442821093814', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/810/3/j/c/539/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5065692414050191, 0.3663205210139169, 0.21316155731803071, 0.04794109634258383, -0.12839184727257463, -0.31475985960024544, -0.5099279196731854, -0.7124750850660375, -0.9207690475973586, -1.132945458204668, -1.346893770707437, -1.5602511472864737, -1.7704057174335743, -1.9745101980005586, -2.1695065730618626, -2.3521622041178096, -2.519117397191058, -2.6669440960674393, -2.792215002803659, -2.891582051133032, -2.961862780659474, -3.0001327868928116, -3.0038220635469064, -2.9708127204013897, -2.8995352653744746, -2.7890603973629227, -2.6391830814772503, -2.4504955849319763, -2.224446153473528, -1.9633801165303109, -1.6705604334269335, -1.3501650389525055, -1.00725881634211, -0.6477386168826313, -0.27825045054383507, 0.09392122126984088, 0.4609912693688569, 0.8148369842713611, 1.1471837110296033, 1.449809290147233, 1.7147626133697513, 1.934590725859445, 2.102568140793361, 2.2129214175491128, 2.261041627291915, 2.2436771233182733, 2.1590990760624296, 2.0072325454283244, 1.789746458807093, 1.5100967447018145, 1.1735180313477465, 0.7869607375224427, 0.35897202741132733, -0.10047907028375969, -0.5802301211028041, -1.0682030405851564, -1.5517248500958574, -2.0178832046489914, -2.453906699540753, -2.847558444610462, -3.1875302017755662, -3.4638235839012603, -3.66810447133936, -3.7940169629739695, -3.8374438707097656, -3.796701999773027, -3.672662220097174, -3.4687865917558396, -3.1910775021085596, -2.84793682386333, -2.449936410826058, -2.009504693070027, -1.5405375830084846, -1.0579452165637002, -0.5771490838018596, -0.11354670802162536, 0.3180369227156861, 0.7038906007723202, 1.0319296579332353, 1.292159326999123, 1.4770689264837944, 1.5819391005352854, 1.605047198662716, 1.547759494524263, 1.4145032026899285, 1.212616004038984, 0.9520758505004937, 0.6451189800823076, 0.30575910926458266, -0.05077454916537088, -0.4086586962520913, -0.7521317352011635, -1.0661565676117402, -1.3370618411263204, -1.553133146679912, -1.7051270129281888, -1.786683185161374, -1.7946145403563347, -1.7290589517367827, -1.5934832893119855, -1.3945362884829775, -1.1417539540362467, -0.847128176287312, -0.5245559857333778, -0.18919302518135026, 0.14325994968481454, 0.4573047121759633, 0.7383919620451944, 0.9736301794463508, 1.152421480888533, 1.26699165190799, 1.3127858841900533, 1.2887076706164888, 1.1971855723368285, 1.0440608508285643, 0.8382978721588994, 0.5915283078990105, 0.31744901562334454, 0.03110161331902163, -0.25193128428813577, -0.5163728318246789, -0.7480979468718846, -0.9349335005685299, -1.067368753096601, -1.1391355269300452, -1.1476233299849057, -1.09410241625662, -0.9837372653840658, -0.8253837301844561, -0.6311746103402697, -0.41591006636131267, -0.1962804631589897, 0.010040700335010125, 0.18538775282627942, 0.31312553933418635, 0.37864817859285443, 0.3702976783812099, 0.28014873010551977, 0.10461159826239884, -0.15518651703409725, -0.4932702975007423, -0.8989509992141874, -1.3572284178903504, -1.8494466388926458, -2.354175424644343, -2.8482754937005854, -3.3080942159033007, -3.7107291205069886, -4.035290703579902, -4.264093782745316, -4.383708344765495, -4.385806512733331, -4.267751746014286, -4.032889273009875, -3.6905124280662553, -3.2554972186868683, -2.7476161414714717, -2.1905609526065484, -1.6107216998618459, -1.035784779080377, -0.49322511581075545, -0.008775964829145838, 0.39503635988478264, 0.7002066461162062, 0.8943338487363535, 0.9714041330629444, 0.9322204146952748, 0.7844439832556089, 0.5422354888841773, 0.22550569141605764, -0.14119039663987473, -0.5300603730046364, -0.9117073512827796, -1.2568984247644956, -1.5383675710411924, -1.732546926142114, -1.8211215576537259, -1.7923103438036223, -1.641789068253176, -1.37319074561233, -0.9981415316434792, -0.5358170770503031, -0.012032355248690901, 0.542093814730276, 1.0918318185033946, 1.6008009570012083, 2.033086549645205, 2.35539287984749, 2.5391051360588763, 2.5621357030428062, 2.4104399254848157, 2.0791034054446236, 1.5729261612067655, 0.9064573103567447, 0.1034657410409893, -0.804134357039911, -1.777851223053107, -2.774594063899567, -3.7489537402363395, -4.6556568044414, -5.452051407208427, -6.100479286527231, -6.570392572156537, -6.840087375133777, -6.897947431309661, -6.743119255707918, -6.385573707920519, -5.845545570281041, -5.152380457300364, -4.342854756514546, -3.459067038221558, -2.5460263456525944, -1.6490821998718725, -0.8113516901819454, -0.07129988471698527, 0.5393791886581559, 0.9974521163936698, 1.28930404645048, 1.4114962075932305, 1.3706921788861886, 1.1829622456226752, 0.8725149195829714, 0.4699414242744437, 0.010090213018136413, -0.4702877063000649, -0.9349673499474426, -1.350592659310575, -1.6887804382500051, -1.9278485775166145, -2.0540575541256167, -2.0622874563063753, -1.9561113676804638, -1.747267255424427, -1.4545717391768906, -1.10235743827514, -0.7185483426932687, -0.33251252292576866, 0.027153296646817805, 0.33474835640567624, 0.5693494835639104, 0.7163150674752828, 0.7683039020121821, 0.7257363486630675, 0.5966655677247751, 0.3960693820963812, 0.14461563502732724, -0.13300736312184203, -0.4100713577739941, -0.6599521423385153, -0.8582765439362067, -0.9849105890320079, -1.0256375592557416, -0.9733963983155549, -0.8289824467892626, -0.6011515680454874, -0.3061126061374489, 0.033561385208983247], 'positive_zeros': ['0.20487223769720513872163339256786', '2.17169935596389801538577890399701', '3.29911784583145984509211723342570', '4.70342096140153723240161635152144', '5.55367799495795713612726075483830', '6.53531107107094703437885391265999', '7.38177114041431807554144959744811', '8.246773893891077187760081728809135', '8.652607676700973553795781441689050', '10.06372774615341020494590356557171'], 'prelabel': '2-810-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.69796779609908, 'root_angle': -0.3641672111780362, 'root_number': '0.4138974366126600489716146839446696344967652695529167554 - 0.9103235204944828057184345354021092237703439402282646473*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1820836055890181', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20487223769720513872163339257', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17169935596389801538577890400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29911784583145984509211723343', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.07090141318405, 'bad_primes': [2, 3, 5], 'central_character': '45.14', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/3/j/c/539/1'], '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': '2-810-45.14-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-810-45.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.69796779609908, 'root_angle': -0.1820836055890181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.20487223769720513872163339257', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '259706415086962580616485248410', 'Lhash_array': ['259706415086962580616485248410'], 'label': '2-810-45.14-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/3/j/c/539/1'}