Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,8,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.12385025484\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 28.0000 | 0.598734 | 0.299367 | − | 0.954138i | \(-0.403225\pi\) | ||||
0.299367 | + | 0.954138i | \(0.403225\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 125.000 | 0.447214 | ||||||||
\(6\) | 224.000 | 0.423369 | ||||||||
\(7\) | 104.000 | 0.114601 | 0.0573007 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0573007 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | −1403.00 | −0.641518 | ||||||||
\(10\) | 1000.00 | 0.316228 | ||||||||
\(11\) | −5148.00 | −1.16618 | −0.583088 | − | 0.812409i | \(-0.698156\pi\) | ||||
−0.583088 | + | 0.812409i | \(0.698156\pi\) | |||||||
\(12\) | 1792.00 | 0.299367 | ||||||||
\(13\) | −8602.00 | −1.08592 | −0.542960 | − | 0.839759i | \(-0.682696\pi\) | ||||
−0.542960 | + | 0.839759i | \(0.682696\pi\) | |||||||
\(14\) | 832.000 | 0.0810355 | ||||||||
\(15\) | 3500.00 | 0.267762 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 20274.0 | 1.00085 | 0.500424 | − | 0.865780i | \(-0.333177\pi\) | ||||
0.500424 | + | 0.865780i | \(0.333177\pi\) | |||||||
\(18\) | −11224.0 | −0.453622 | ||||||||
\(19\) | 45500.0 | 1.52186 | 0.760928 | − | 0.648836i | \(-0.224744\pi\) | ||||
0.760928 | + | 0.648836i | \(0.224744\pi\) | |||||||
\(20\) | 8000.00 | 0.223607 | ||||||||
\(21\) | 2912.00 | 0.0686158 | ||||||||
\(22\) | −41184.0 | −0.824611 | ||||||||
\(23\) | −72072.0 | −1.23515 | −0.617574 | − | 0.786513i | \(-0.711884\pi\) | ||||
−0.617574 | + | 0.786513i | \(0.711884\pi\) | |||||||
\(24\) | 14336.0 | 0.211684 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −68816.0 | −0.767861 | ||||||||
\(27\) | −100520. | −0.982832 | ||||||||
\(28\) | 6656.00 | 0.0573007 | ||||||||
\(29\) | 231510. | 1.76269 | 0.881347 | − | 0.472470i | \(-0.156638\pi\) | ||||
0.881347 | + | 0.472470i | \(0.156638\pi\) | |||||||
\(30\) | 28000.0 | 0.189336 | ||||||||
\(31\) | −80128.0 | −0.483079 | −0.241540 | − | 0.970391i | \(-0.577652\pi\) | ||||
−0.241540 | + | 0.970391i | \(0.577652\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −144144. | −0.698229 | ||||||||
\(34\) | 162192. | 0.707707 | ||||||||
\(35\) | 13000.0 | 0.0512513 | ||||||||
\(36\) | −89792.0 | −0.320759 | ||||||||
\(37\) | 104654. | 0.339664 | 0.169832 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169832 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(38\) | 364000. | 1.07612 | ||||||||
\(39\) | −240856. | −0.650177 | ||||||||
\(40\) | 64000.0 | 0.158114 | ||||||||
\(41\) | 584922. | 1.32542 | 0.662711 | − | 0.748875i | \(-0.269406\pi\) | ||||
0.662711 | + | 0.748875i | \(0.269406\pi\) | |||||||
\(42\) | 23296.0 | 0.0485187 | ||||||||
\(43\) | −795532. | −1.52587 | −0.762936 | − | 0.646474i | \(-0.776243\pi\) | ||||
−0.762936 | + | 0.646474i | \(0.776243\pi\) | |||||||
\(44\) | −329472. | −0.583088 | ||||||||
\(45\) | −175375. | −0.286896 | ||||||||
\(46\) | −576576. | −0.873382 | ||||||||
\(47\) | 425664. | 0.598032 | 0.299016 | − | 0.954248i | \(-0.403342\pi\) | ||||
0.299016 | + | 0.954248i | \(0.403342\pi\) | |||||||
\(48\) | 114688. | 0.149683 | ||||||||
\(49\) | −812727. | −0.986867 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | 567672. | 0.599241 | ||||||||
\(52\) | −550528. | −0.542960 | ||||||||
\(53\) | 1.50080e6 | 1.38470 | 0.692352 | − | 0.721560i | \(-0.256575\pi\) | ||||
0.692352 | + | 0.721560i | \(0.256575\pi\) | |||||||
\(54\) | −804160. | −0.694967 | ||||||||
\(55\) | −643500. | −0.521530 | ||||||||
\(56\) | 53248.0 | 0.0405177 | ||||||||
\(57\) | 1.27400e6 | 0.911187 | ||||||||
\(58\) | 1.85208e6 | 1.24641 | ||||||||
\(59\) | 246420. | 0.156205 | 0.0781023 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781023 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(60\) | 224000. | 0.133881 | ||||||||
\(61\) | 893942. | 0.504260 | 0.252130 | − | 0.967693i | \(-0.418869\pi\) | ||||
0.252130 | + | 0.967693i | \(0.418869\pi\) | |||||||
\(62\) | −641024. | −0.341589 | ||||||||
\(63\) | −145912. | −0.0735189 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −1.07525e6 | −0.485638 | ||||||||
\(66\) | −1.15315e6 | −0.493722 | ||||||||
\(67\) | −2.33684e6 | −0.949219 | −0.474610 | − | 0.880196i | \(-0.657411\pi\) | ||||
−0.474610 | + | 0.880196i | \(0.657411\pi\) | |||||||
\(68\) | 1.29754e6 | 0.500424 | ||||||||
\(69\) | −2.01802e6 | −0.739525 | ||||||||
\(70\) | 104000. | 0.0362402 | ||||||||
\(71\) | −203688. | −0.0675400 | −0.0337700 | − | 0.999430i | \(-0.510751\pi\) | ||||
−0.0337700 | + | 0.999430i | \(0.510751\pi\) | |||||||
\(72\) | −718336. | −0.226811 | ||||||||
\(73\) | −3.80570e6 | −1.14500 | −0.572499 | − | 0.819905i | \(-0.694026\pi\) | ||||
−0.572499 | + | 0.819905i | \(0.694026\pi\) | |||||||
\(74\) | 837232. | 0.240179 | ||||||||
\(75\) | 437500. | 0.119747 | ||||||||
\(76\) | 2.91200e6 | 0.760928 | ||||||||
\(77\) | −535392. | −0.133645 | ||||||||
\(78\) | −1.92685e6 | −0.459744 | ||||||||
\(79\) | 5.05304e6 | 1.15308 | 0.576538 | − | 0.817070i | \(-0.304403\pi\) | ||||
0.576538 | + | 0.817070i | \(0.304403\pi\) | |||||||
\(80\) | 512000. | 0.111803 | ||||||||
\(81\) | 253801. | 0.0530635 | ||||||||
\(82\) | 4.67938e6 | 0.937215 | ||||||||
\(83\) | −45492.0 | −0.00873296 | −0.00436648 | − | 0.999990i | \(-0.501390\pi\) | ||||
−0.00436648 | + | 0.999990i | \(0.501390\pi\) | |||||||
\(84\) | 186368. | 0.0343079 | ||||||||
\(85\) | 2.53425e6 | 0.447593 | ||||||||
\(86\) | −6.36426e6 | −1.07895 | ||||||||
\(87\) | 6.48228e6 | 1.05538 | ||||||||
\(88\) | −2.63578e6 | −0.412306 | ||||||||
\(89\) | 980010. | 0.147355 | 0.0736776 | − | 0.997282i | \(-0.476526\pi\) | ||||
0.0736776 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(90\) | −1.40300e6 | −0.202866 | ||||||||
\(91\) | −894608. | −0.124448 | ||||||||
\(92\) | −4.61261e6 | −0.617574 | ||||||||
\(93\) | −2.24358e6 | −0.289236 | ||||||||
\(94\) | 3.40531e6 | 0.422872 | ||||||||
\(95\) | 5.68750e6 | 0.680595 | ||||||||
\(96\) | 917504. | 0.105842 | ||||||||
\(97\) | −5.24765e6 | −0.583799 | −0.291900 | − | 0.956449i | \(-0.594287\pi\) | ||||
−0.291900 | + | 0.956449i | \(0.594287\pi\) | |||||||
\(98\) | −6.50182e6 | −0.697820 | ||||||||
\(99\) | 7.22264e6 | 0.748123 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | −1.53807e7 | −1.48542 | −0.742711 | − | 0.669612i | \(-0.766461\pi\) | ||||
−0.742711 | + | 0.669612i | \(0.766461\pi\) | |||||||
\(102\) | 4.54138e6 | 0.423728 | ||||||||
\(103\) | 3.25681e6 | 0.293672 | 0.146836 | − | 0.989161i | \(-0.453091\pi\) | ||||
0.146836 | + | 0.989161i | \(0.453091\pi\) | |||||||
\(104\) | −4.40422e6 | −0.383931 | ||||||||
\(105\) | 364000. | 0.0306859 | ||||||||
\(106\) | 1.20064e7 | 0.979133 | ||||||||
\(107\) | −1.48329e7 | −1.17053 | −0.585264 | − | 0.810842i | \(-0.699009\pi\) | ||||
−0.585264 | + | 0.810842i | \(0.699009\pi\) | |||||||
\(108\) | −6.43328e6 | −0.491416 | ||||||||
\(109\) | −7.03225e6 | −0.520118 | −0.260059 | − | 0.965593i | \(-0.583742\pi\) | ||||
−0.260059 | + | 0.965593i | \(0.583742\pi\) | |||||||
\(110\) | −5.14800e6 | −0.368777 | ||||||||
\(111\) | 2.93031e6 | 0.203368 | ||||||||
\(112\) | 425984. | 0.0286504 | ||||||||
\(113\) | 1.46074e7 | 0.952352 | 0.476176 | − | 0.879350i | \(-0.342022\pi\) | ||||
0.476176 | + | 0.879350i | \(0.342022\pi\) | |||||||
\(114\) | 1.01920e7 | 0.644306 | ||||||||
\(115\) | −9.00900e6 | −0.552375 | ||||||||
\(116\) | 1.48166e7 | 0.881347 | ||||||||
\(117\) | 1.20686e7 | 0.696637 | ||||||||
\(118\) | 1.97136e6 | 0.110453 | ||||||||
\(119\) | 2.10850e6 | 0.114699 | ||||||||
\(120\) | 1.79200e6 | 0.0946681 | ||||||||
\(121\) | 7.01473e6 | 0.359967 | ||||||||
\(122\) | 7.15154e6 | 0.356566 | ||||||||
\(123\) | 1.63778e7 | 0.793575 | ||||||||
\(124\) | −5.12819e6 | −0.241540 | ||||||||
\(125\) | 1.95312e6 | 0.0894427 | ||||||||
\(126\) | −1.16730e6 | −0.0519857 | ||||||||
\(127\) | −1.51661e7 | −0.656993 | −0.328497 | − | 0.944505i | \(-0.606542\pi\) | ||||
−0.328497 | + | 0.944505i | \(0.606542\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −2.22749e7 | −0.913591 | ||||||||
\(130\) | −8.60200e6 | −0.343398 | ||||||||
\(131\) | −2.45985e7 | −0.956005 | −0.478002 | − | 0.878359i | \(-0.658639\pi\) | ||||
−0.478002 | + | 0.878359i | \(0.658639\pi\) | |||||||
\(132\) | −9.22522e6 | −0.349114 | ||||||||
\(133\) | 4.73200e6 | 0.174407 | ||||||||
\(134\) | −1.86947e7 | −0.671199 | ||||||||
\(135\) | −1.25650e7 | −0.439536 | ||||||||
\(136\) | 1.03803e7 | 0.353853 | ||||||||
\(137\) | 3.51725e7 | 1.16864 | 0.584320 | − | 0.811523i | \(-0.301361\pi\) | ||||
0.584320 | + | 0.811523i | \(0.301361\pi\) | |||||||
\(138\) | −1.61441e7 | −0.522923 | ||||||||
\(139\) | −4.47137e7 | −1.41217 | −0.706087 | − | 0.708125i | \(-0.749541\pi\) | ||||
−0.706087 | + | 0.708125i | \(0.749541\pi\) | |||||||
\(140\) | 832000. | 0.0256257 | ||||||||
\(141\) | 1.19186e7 | 0.358062 | ||||||||
\(142\) | −1.62950e6 | −0.0477580 | ||||||||
\(143\) | 4.42831e7 | 1.26637 | ||||||||
\(144\) | −5.74669e6 | −0.160380 | ||||||||
\(145\) | 2.89388e7 | 0.788300 | ||||||||
\(146\) | −3.04456e7 | −0.809636 | ||||||||
\(147\) | −2.27564e7 | −0.590870 | ||||||||
\(148\) | 6.69786e6 | 0.169832 | ||||||||
\(149\) | 1.73348e7 | 0.429305 | 0.214652 | − | 0.976691i | \(-0.431138\pi\) | ||||
0.214652 | + | 0.976691i | \(0.431138\pi\) | |||||||
\(150\) | 3.50000e6 | 0.0846737 | ||||||||
\(151\) | 5.92382e7 | 1.40017 | 0.700087 | − | 0.714057i | \(-0.253144\pi\) | ||||
0.700087 | + | 0.714057i | \(0.253144\pi\) | |||||||
\(152\) | 2.32960e7 | 0.538058 | ||||||||
\(153\) | −2.84444e7 | −0.642062 | ||||||||
\(154\) | −4.28314e6 | −0.0945016 | ||||||||
\(155\) | −1.00160e7 | −0.216040 | ||||||||
\(156\) | −1.54148e7 | −0.325088 | ||||||||
\(157\) | 2.73945e7 | 0.564955 | 0.282478 | − | 0.959274i | \(-0.408844\pi\) | ||||
0.282478 | + | 0.959274i | \(0.408844\pi\) | |||||||
\(158\) | 4.04243e7 | 0.815348 | ||||||||
\(159\) | 4.20223e7 | 0.829068 | ||||||||
\(160\) | 4.09600e6 | 0.0790569 | ||||||||
\(161\) | −7.49549e6 | −0.141550 | ||||||||
\(162\) | 2.03041e6 | 0.0375215 | ||||||||
\(163\) | −8.85387e7 | −1.60131 | −0.800657 | − | 0.599123i | \(-0.795516\pi\) | ||||
−0.800657 | + | 0.599123i | \(0.795516\pi\) | |||||||
\(164\) | 3.74350e7 | 0.662711 | ||||||||
\(165\) | −1.80180e7 | −0.312257 | ||||||||
\(166\) | −363936. | −0.00617514 | ||||||||
\(167\) | −2.85309e7 | −0.474033 | −0.237016 | − | 0.971506i | \(-0.576170\pi\) | ||||
−0.237016 | + | 0.971506i | \(0.576170\pi\) | |||||||
\(168\) | 1.49094e6 | 0.0242593 | ||||||||
\(169\) | 1.12459e7 | 0.179222 | ||||||||
\(170\) | 2.02740e7 | 0.316496 | ||||||||
\(171\) | −6.38365e7 | −0.976299 | ||||||||
\(172\) | −5.09140e7 | −0.762936 | ||||||||
\(173\) | −1.04351e8 | −1.53227 | −0.766134 | − | 0.642681i | \(-0.777822\pi\) | ||||
−0.766134 | + | 0.642681i | \(0.777822\pi\) | |||||||
\(174\) | 5.18582e7 | 0.746269 | ||||||||
\(175\) | 1.62500e6 | 0.0229203 | ||||||||
\(176\) | −2.10862e7 | −0.291544 | ||||||||
\(177\) | 6.89976e6 | 0.0935250 | ||||||||
\(178\) | 7.84008e6 | 0.104196 | ||||||||
\(179\) | 1.00761e8 | 1.31313 | 0.656565 | − | 0.754270i | \(-0.272009\pi\) | ||||
0.656565 | + | 0.754270i | \(0.272009\pi\) | |||||||
\(180\) | −1.12240e7 | −0.143448 | ||||||||
\(181\) | 3.56842e7 | 0.447302 | 0.223651 | − | 0.974669i | \(-0.428202\pi\) | ||||
0.223651 | + | 0.974669i | \(0.428202\pi\) | |||||||
\(182\) | −7.15686e6 | −0.0879980 | ||||||||
\(183\) | 2.50304e7 | 0.301918 | ||||||||
\(184\) | −3.69009e7 | −0.436691 | ||||||||
\(185\) | 1.30818e7 | 0.151902 | ||||||||
\(186\) | −1.79487e7 | −0.204521 | ||||||||
\(187\) | −1.04371e8 | −1.16717 | ||||||||
\(188\) | 2.72425e7 | 0.299016 | ||||||||
\(189\) | −1.04541e7 | −0.112634 | ||||||||
\(190\) | 4.55000e7 | 0.481253 | ||||||||
\(191\) | 5.27892e7 | 0.548186 | 0.274093 | − | 0.961703i | \(-0.411622\pi\) | ||||
0.274093 | + | 0.961703i | \(0.411622\pi\) | |||||||
\(192\) | 7.34003e6 | 0.0748417 | ||||||||
\(193\) | −3.20893e7 | −0.321300 | −0.160650 | − | 0.987011i | \(-0.551359\pi\) | ||||
−0.160650 | + | 0.987011i | \(0.551359\pi\) | |||||||
\(194\) | −4.19812e7 | −0.412808 | ||||||||
\(195\) | −3.01070e7 | −0.290768 | ||||||||
\(196\) | −5.20145e7 | −0.493433 | ||||||||
\(197\) | 1.67464e8 | 1.56059 | 0.780294 | − | 0.625412i | \(-0.215069\pi\) | ||||
0.780294 | + | 0.625412i | \(0.215069\pi\) | |||||||
\(198\) | 5.77812e7 | 0.529003 | ||||||||
\(199\) | 1.61770e8 | 1.45517 | 0.727583 | − | 0.686020i | \(-0.240644\pi\) | ||||
0.727583 | + | 0.686020i | \(0.240644\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | −6.54314e7 | −0.568329 | ||||||||
\(202\) | −1.23045e8 | −1.05035 | ||||||||
\(203\) | 2.40770e7 | 0.202007 | ||||||||
\(204\) | 3.63310e7 | 0.299621 | ||||||||
\(205\) | 7.31152e7 | 0.592747 | ||||||||
\(206\) | 2.60545e7 | 0.207657 | ||||||||
\(207\) | 1.01117e8 | 0.792370 | ||||||||
\(208\) | −3.52338e7 | −0.271480 | ||||||||
\(209\) | −2.34234e8 | −1.77475 | ||||||||
\(210\) | 2.91200e6 | 0.0216982 | ||||||||
\(211\) | 1.78419e8 | 1.30753 | 0.653766 | − | 0.756697i | \(-0.273188\pi\) | ||||
0.653766 | + | 0.756697i | \(0.273188\pi\) | |||||||
\(212\) | 9.60511e7 | 0.692352 | ||||||||
\(213\) | −5.70326e6 | −0.0404385 | ||||||||
\(214\) | −1.18663e8 | −0.827689 | ||||||||
\(215\) | −9.94415e7 | −0.682391 | ||||||||
\(216\) | −5.14662e7 | −0.347484 | ||||||||
\(217\) | −8.33331e6 | −0.0553616 | ||||||||
\(218\) | −5.62580e7 | −0.367779 | ||||||||
\(219\) | −1.06560e8 | −0.685549 | ||||||||
\(220\) | −4.11840e7 | −0.260765 | ||||||||
\(221\) | −1.74397e8 | −1.08684 | ||||||||
\(222\) | 2.34425e7 | 0.143803 | ||||||||
\(223\) | 1.26953e8 | 0.766611 | 0.383305 | − | 0.923622i | \(-0.374786\pi\) | ||||
0.383305 | + | 0.923622i | \(0.374786\pi\) | |||||||
\(224\) | 3.40787e6 | 0.0202589 | ||||||||
\(225\) | −2.19219e7 | −0.128304 | ||||||||
\(226\) | 1.16859e8 | 0.673415 | ||||||||
\(227\) | −1.57656e8 | −0.894582 | −0.447291 | − | 0.894389i | \(-0.647611\pi\) | ||||
−0.447291 | + | 0.894389i | \(0.647611\pi\) | |||||||
\(228\) | 8.15360e7 | 0.455593 | ||||||||
\(229\) | −3.38259e8 | −1.86134 | −0.930670 | − | 0.365861i | \(-0.880775\pi\) | ||||
−0.930670 | + | 0.365861i | \(0.880775\pi\) | |||||||
\(230\) | −7.20720e7 | −0.390588 | ||||||||
\(231\) | −1.49910e7 | −0.0800181 | ||||||||
\(232\) | 1.18533e8 | 0.623206 | ||||||||
\(233\) | −3.56382e7 | −0.184574 | −0.0922868 | − | 0.995732i | \(-0.529418\pi\) | ||||
−0.0922868 | + | 0.995732i | \(0.529418\pi\) | |||||||
\(234\) | 9.65488e7 | 0.492597 | ||||||||
\(235\) | 5.32080e7 | 0.267448 | ||||||||
\(236\) | 1.57709e7 | 0.0781023 | ||||||||
\(237\) | 1.41485e8 | 0.690385 | ||||||||
\(238\) | 1.68680e7 | 0.0811042 | ||||||||
\(239\) | 2.16045e8 | 1.02365 | 0.511825 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511825 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(240\) | 1.43360e7 | 0.0669405 | ||||||||
\(241\) | 3.84299e8 | 1.76852 | 0.884260 | − | 0.466995i | \(-0.154663\pi\) | ||||
0.884260 | + | 0.466995i | \(0.154663\pi\) | |||||||
\(242\) | 5.61179e7 | 0.254535 | ||||||||
\(243\) | 2.26944e8 | 1.01460 | ||||||||
\(244\) | 5.72123e7 | 0.252130 | ||||||||
\(245\) | −1.01591e8 | −0.441340 | ||||||||
\(246\) | 1.31023e8 | 0.561142 | ||||||||
\(247\) | −3.91391e8 | −1.65261 | ||||||||
\(248\) | −4.10255e7 | −0.170794 | ||||||||
\(249\) | −1.27378e6 | −0.00522872 | ||||||||
\(250\) | 1.56250e7 | 0.0632456 | ||||||||
\(251\) | −2.36430e8 | −0.943724 | −0.471862 | − | 0.881672i | \(-0.656418\pi\) | ||||
−0.471862 | + | 0.881672i | \(0.656418\pi\) | |||||||
\(252\) | −9.33837e6 | −0.0367595 | ||||||||
\(253\) | 3.71027e8 | 1.44040 | ||||||||
\(254\) | −1.21329e8 | −0.464564 | ||||||||
\(255\) | 7.09590e7 | 0.267989 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.37832e7 | −0.0873985 | −0.0436992 | − | 0.999045i | \(-0.513914\pi\) | ||||
−0.0436992 | + | 0.999045i | \(0.513914\pi\) | |||||||
\(258\) | −1.78199e8 | −0.646006 | ||||||||
\(259\) | 1.08840e7 | 0.0389260 | ||||||||
\(260\) | −6.88160e7 | −0.242819 | ||||||||
\(261\) | −3.24809e8 | −1.13080 | ||||||||
\(262\) | −1.96788e8 | −0.675997 | ||||||||
\(263\) | −7.98963e7 | −0.270821 | −0.135410 | − | 0.990790i | \(-0.543235\pi\) | ||||
−0.135410 | + | 0.990790i | \(0.543235\pi\) | |||||||
\(264\) | −7.38017e7 | −0.246861 | ||||||||
\(265\) | 1.87600e8 | 0.619258 | ||||||||
\(266\) | 3.78560e7 | 0.123324 | ||||||||
\(267\) | 2.74403e7 | 0.0882265 | ||||||||
\(268\) | −1.49558e8 | −0.474610 | ||||||||
\(269\) | 2.33547e8 | 0.731545 | 0.365772 | − | 0.930704i | \(-0.380805\pi\) | ||||
0.365772 | + | 0.930704i | \(0.380805\pi\) | |||||||
\(270\) | −1.00520e8 | −0.310799 | ||||||||
\(271\) | −2.79282e8 | −0.852414 | −0.426207 | − | 0.904626i | \(-0.640150\pi\) | ||||
−0.426207 | + | 0.904626i | \(0.640150\pi\) | |||||||
\(272\) | 8.30423e7 | 0.250212 | ||||||||
\(273\) | −2.50490e7 | −0.0745112 | ||||||||
\(274\) | 2.81380e8 | 0.826354 | ||||||||
\(275\) | −8.04375e7 | −0.233235 | ||||||||
\(276\) | −1.29153e8 | −0.369762 | ||||||||
\(277\) | 1.63825e8 | 0.463127 | 0.231564 | − | 0.972820i | \(-0.425616\pi\) | ||||
0.231564 | + | 0.972820i | \(0.425616\pi\) | |||||||
\(278\) | −3.57709e8 | −0.998558 | ||||||||
\(279\) | 1.12420e8 | 0.309904 | ||||||||
\(280\) | 6.65600e6 | 0.0181201 | ||||||||
\(281\) | 1.28061e8 | 0.344307 | 0.172153 | − | 0.985070i | \(-0.444928\pi\) | ||||
0.172153 | + | 0.985070i | \(0.444928\pi\) | |||||||
\(282\) | 9.53487e7 | 0.253188 | ||||||||
\(283\) | −2.69379e8 | −0.706498 | −0.353249 | − | 0.935529i | \(-0.614923\pi\) | ||||
−0.353249 | + | 0.935529i | \(0.614923\pi\) | |||||||
\(284\) | −1.30360e7 | −0.0337700 | ||||||||
\(285\) | 1.59250e8 | 0.407495 | ||||||||
\(286\) | 3.54265e8 | 0.895461 | ||||||||
\(287\) | 6.08319e7 | 0.151895 | ||||||||
\(288\) | −4.59735e7 | −0.113405 | ||||||||
\(289\) | 696403. | 0.00169714 | ||||||||
\(290\) | 2.31510e8 | 0.557413 | ||||||||
\(291\) | −1.46934e8 | −0.349540 | ||||||||
\(292\) | −2.43565e8 | −0.572499 | ||||||||
\(293\) | −1.55781e8 | −0.361808 | −0.180904 | − | 0.983501i | \(-0.557902\pi\) | ||||
−0.180904 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(294\) | −1.82051e8 | −0.417808 | ||||||||
\(295\) | 3.08025e7 | 0.0698568 | ||||||||
\(296\) | 5.35828e7 | 0.120089 | ||||||||
\(297\) | 5.17477e8 | 1.14616 | ||||||||
\(298\) | 1.38678e8 | 0.303564 | ||||||||
\(299\) | 6.19963e8 | 1.34127 | ||||||||
\(300\) | 2.80000e7 | 0.0598734 | ||||||||
\(301\) | −8.27353e7 | −0.174867 | ||||||||
\(302\) | 4.73905e8 | 0.990073 | ||||||||
\(303\) | −4.30658e8 | −0.889373 | ||||||||
\(304\) | 1.86368e8 | 0.380464 | ||||||||
\(305\) | 1.11743e8 | 0.225512 | ||||||||
\(306\) | −2.27555e8 | −0.454007 | ||||||||
\(307\) | −4.87126e8 | −0.960852 | −0.480426 | − | 0.877035i | \(-0.659518\pi\) | ||||
−0.480426 | + | 0.877035i | \(0.659518\pi\) | |||||||
\(308\) | −3.42651e7 | −0.0668227 | ||||||||
\(309\) | 9.11906e7 | 0.175831 | ||||||||
\(310\) | −8.01280e7 | −0.152763 | ||||||||
\(311\) | 2.88891e8 | 0.544595 | 0.272297 | − | 0.962213i | \(-0.412217\pi\) | ||||
0.272297 | + | 0.962213i | \(0.412217\pi\) | |||||||
\(312\) | −1.23318e8 | −0.229872 | ||||||||
\(313\) | −4.09453e8 | −0.754743 | −0.377371 | − | 0.926062i | \(-0.623172\pi\) | ||||
−0.377371 | + | 0.926062i | \(0.623172\pi\) | |||||||
\(314\) | 2.19156e8 | 0.399484 | ||||||||
\(315\) | −1.82390e7 | −0.0328787 | ||||||||
\(316\) | 3.23395e8 | 0.576538 | ||||||||
\(317\) | −2.69274e8 | −0.474774 | −0.237387 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237387 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(318\) | 3.36179e8 | 0.586240 | ||||||||
\(319\) | −1.19181e9 | −2.05561 | ||||||||
\(320\) | 3.27680e7 | 0.0559017 | ||||||||
\(321\) | −4.15321e8 | −0.700835 | ||||||||
\(322\) | −5.99639e7 | −0.100091 | ||||||||
\(323\) | 9.22467e8 | 1.52315 | ||||||||
\(324\) | 1.62433e7 | 0.0265317 | ||||||||
\(325\) | −1.34406e8 | −0.217184 | ||||||||
\(326\) | −7.08310e8 | −1.13230 | ||||||||
\(327\) | −1.96903e8 | −0.311412 | ||||||||
\(328\) | 2.99480e8 | 0.468608 | ||||||||
\(329\) | 4.42691e7 | 0.0685353 | ||||||||
\(330\) | −1.44144e8 | −0.220799 | ||||||||
\(331\) | 4.05515e8 | 0.614624 | 0.307312 | − | 0.951609i | \(-0.400570\pi\) | ||||
0.307312 | + | 0.951609i | \(0.400570\pi\) | |||||||
\(332\) | −2.91149e6 | −0.00436648 | ||||||||
\(333\) | −1.46830e8 | −0.217901 | ||||||||
\(334\) | −2.28247e8 | −0.335192 | ||||||||
\(335\) | −2.92104e8 | −0.424504 | ||||||||
\(336\) | 1.19276e7 | 0.0171539 | ||||||||
\(337\) | −3.83013e8 | −0.545141 | −0.272570 | − | 0.962136i | \(-0.587874\pi\) | ||||
−0.272570 | + | 0.962136i | \(0.587874\pi\) | |||||||
\(338\) | 8.99671e7 | 0.126729 | ||||||||
\(339\) | 4.09007e8 | 0.570205 | ||||||||
\(340\) | 1.62192e8 | 0.223796 | ||||||||
\(341\) | 4.12499e8 | 0.563355 | ||||||||
\(342\) | −5.10692e8 | −0.690347 | ||||||||
\(343\) | −1.70172e8 | −0.227698 | ||||||||
\(344\) | −4.07312e8 | −0.539477 | ||||||||
\(345\) | −2.52252e8 | −0.330726 | ||||||||
\(346\) | −8.34807e8 | −1.08348 | ||||||||
\(347\) | 1.17574e9 | 1.51063 | 0.755317 | − | 0.655359i | \(-0.227483\pi\) | ||||
0.755317 | + | 0.655359i | \(0.227483\pi\) | |||||||
\(348\) | 4.14866e8 | 0.527692 | ||||||||
\(349\) | 2.88405e8 | 0.363173 | 0.181586 | − | 0.983375i | \(-0.441877\pi\) | ||||
0.181586 | + | 0.983375i | \(0.441877\pi\) | |||||||
\(350\) | 1.30000e7 | 0.0162071 | ||||||||
\(351\) | 8.64673e8 | 1.06728 | ||||||||
\(352\) | −1.68690e8 | −0.206153 | ||||||||
\(353\) | 7.65131e8 | 0.925816 | 0.462908 | − | 0.886406i | \(-0.346806\pi\) | ||||
0.462908 | + | 0.886406i | \(0.346806\pi\) | |||||||
\(354\) | 5.51981e7 | 0.0661321 | ||||||||
\(355\) | −2.54610e7 | −0.0302048 | ||||||||
\(356\) | 6.27206e7 | 0.0736776 | ||||||||
\(357\) | 5.90379e7 | 0.0686740 | ||||||||
\(358\) | 8.06089e8 | 0.928523 | ||||||||
\(359\) | −5.25904e8 | −0.599896 | −0.299948 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299948 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(360\) | −8.97920e7 | −0.101433 | ||||||||
\(361\) | 1.17638e9 | 1.31605 | ||||||||
\(362\) | 2.85474e8 | 0.316291 | ||||||||
\(363\) | 1.96413e8 | 0.215524 | ||||||||
\(364\) | −5.72549e7 | −0.0622240 | ||||||||
\(365\) | −4.75713e8 | −0.512059 | ||||||||
\(366\) | 2.00243e8 | 0.213488 | ||||||||
\(367\) | 8.93571e8 | 0.943621 | 0.471811 | − | 0.881700i | \(-0.343601\pi\) | ||||
0.471811 | + | 0.881700i | \(0.343601\pi\) | |||||||
\(368\) | −2.95207e8 | −0.308787 | ||||||||
\(369\) | −8.20646e8 | −0.850283 | ||||||||
\(370\) | 1.04654e8 | 0.107411 | ||||||||
\(371\) | 1.56083e8 | 0.158689 | ||||||||
\(372\) | −1.43589e8 | −0.144618 | ||||||||
\(373\) | −8.13329e8 | −0.811494 | −0.405747 | − | 0.913985i | \(-0.632989\pi\) | ||||
−0.405747 | + | 0.913985i | \(0.632989\pi\) | |||||||
\(374\) | −8.34964e8 | −0.825310 | ||||||||
\(375\) | 5.46875e7 | 0.0535524 | ||||||||
\(376\) | 2.17940e8 | 0.211436 | ||||||||
\(377\) | −1.99145e9 | −1.91414 | ||||||||
\(378\) | −8.36326e7 | −0.0796443 | ||||||||
\(379\) | −1.02095e9 | −0.963309 | −0.481655 | − | 0.876361i | \(-0.659964\pi\) | ||||
−0.481655 | + | 0.876361i | \(0.659964\pi\) | |||||||
\(380\) | 3.64000e8 | 0.340298 | ||||||||
\(381\) | −4.24651e8 | −0.393364 | ||||||||
\(382\) | 4.22313e8 | 0.387626 | ||||||||
\(383\) | −9.14343e8 | −0.831598 | −0.415799 | − | 0.909457i | \(-0.636498\pi\) | ||||
−0.415799 | + | 0.909457i | \(0.636498\pi\) | |||||||
\(384\) | 5.87203e7 | 0.0529211 | ||||||||
\(385\) | −6.69240e7 | −0.0597681 | ||||||||
\(386\) | −2.56715e8 | −0.227193 | ||||||||
\(387\) | 1.11613e9 | 0.978874 | ||||||||
\(388\) | −3.35849e8 | −0.291900 | ||||||||
\(389\) | 2.23944e8 | 0.192893 | 0.0964463 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964463 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(390\) | −2.40856e8 | −0.205604 | ||||||||
\(391\) | −1.46119e9 | −1.23620 | ||||||||
\(392\) | −4.16116e8 | −0.348910 | ||||||||
\(393\) | −6.88759e8 | −0.572392 | ||||||||
\(394\) | 1.33971e9 | 1.10350 | ||||||||
\(395\) | 6.31630e8 | 0.515671 | ||||||||
\(396\) | 4.62249e8 | 0.374062 | ||||||||
\(397\) | 1.80757e9 | 1.44987 | 0.724934 | − | 0.688818i | \(-0.241870\pi\) | ||||
0.724934 | + | 0.688818i | \(0.241870\pi\) | |||||||
\(398\) | 1.29416e9 | 1.02896 | ||||||||
\(399\) | 1.32496e8 | 0.104423 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | −1.63569e9 | −1.26676 | −0.633381 | − | 0.773840i | \(-0.718333\pi\) | ||||
−0.633381 | + | 0.773840i | \(0.718333\pi\) | |||||||
\(402\) | −5.23451e8 | −0.401870 | ||||||||
\(403\) | 6.89261e8 | 0.524585 | ||||||||
\(404\) | −9.84362e8 | −0.742711 | ||||||||
\(405\) | 3.17251e7 | 0.0237307 | ||||||||
\(406\) | 1.92616e8 | 0.142841 | ||||||||
\(407\) | −5.38759e8 | −0.396108 | ||||||||
\(408\) | 2.90648e8 | 0.211864 | ||||||||
\(409\) | 2.27381e9 | 1.64332 | 0.821661 | − | 0.569977i | \(-0.193048\pi\) | ||||
0.821661 | + | 0.569977i | \(0.193048\pi\) | |||||||
\(410\) | 5.84922e8 | 0.419136 | ||||||||
\(411\) | 9.84829e8 | 0.699704 | ||||||||
\(412\) | 2.08436e8 | 0.146836 | ||||||||
\(413\) | 2.56277e7 | 0.0179013 | ||||||||
\(414\) | 8.08936e8 | 0.560290 | ||||||||
\(415\) | −5.68650e6 | −0.00390550 | ||||||||
\(416\) | −2.81870e8 | −0.191965 | ||||||||
\(417\) | −1.25198e9 | −0.845516 | ||||||||
\(418\) | −1.87387e9 | −1.25494 | ||||||||
\(419\) | 4.04353e8 | 0.268542 | 0.134271 | − | 0.990945i | \(-0.457131\pi\) | ||||
0.134271 | + | 0.990945i | \(0.457131\pi\) | |||||||
\(420\) | 2.32960e7 | 0.0153429 | ||||||||
\(421\) | 8.37294e6 | 0.00546878 | 0.00273439 | − | 0.999996i | \(-0.499130\pi\) | ||||
0.00273439 | + | 0.999996i | \(0.499130\pi\) | |||||||
\(422\) | 1.42735e9 | 0.924565 | ||||||||
\(423\) | −5.97207e8 | −0.383648 | ||||||||
\(424\) | 7.68409e8 | 0.489567 | ||||||||
\(425\) | 3.16781e8 | 0.200170 | ||||||||
\(426\) | −4.56261e7 | −0.0285943 | ||||||||
\(427\) | 9.29700e7 | 0.0577890 | ||||||||
\(428\) | −9.49304e8 | −0.585264 | ||||||||
\(429\) | 1.23993e9 | 0.758220 | ||||||||
\(430\) | −7.95532e8 | −0.482523 | ||||||||
\(431\) | −2.77413e8 | −0.166900 | −0.0834499 | − | 0.996512i | \(-0.526594\pi\) | ||||
−0.0834499 | + | 0.996512i | \(0.526594\pi\) | |||||||
\(432\) | −4.11730e8 | −0.245708 | ||||||||
\(433\) | 8.78768e8 | 0.520196 | 0.260098 | − | 0.965582i | \(-0.416245\pi\) | ||||
0.260098 | + | 0.965582i | \(0.416245\pi\) | |||||||
\(434\) | −6.66665e7 | −0.0391466 | ||||||||
\(435\) | 8.10285e8 | 0.471982 | ||||||||
\(436\) | −4.50064e8 | −0.260059 | ||||||||
\(437\) | −3.27928e9 | −1.87972 | ||||||||
\(438\) | −8.52477e8 | −0.484756 | ||||||||
\(439\) | 8.96007e8 | 0.505458 | 0.252729 | − | 0.967537i | \(-0.418672\pi\) | ||||
0.252729 | + | 0.967537i | \(0.418672\pi\) | |||||||
\(440\) | −3.29472e8 | −0.184389 | ||||||||
\(441\) | 1.14026e9 | 0.633093 | ||||||||
\(442\) | −1.39518e9 | −0.768512 | ||||||||
\(443\) | −3.83067e7 | −0.0209344 | −0.0104672 | − | 0.999945i | \(-0.503332\pi\) | ||||
−0.0104672 | + | 0.999945i | \(0.503332\pi\) | |||||||
\(444\) | 1.87540e8 | 0.101684 | ||||||||
\(445\) | 1.22501e8 | 0.0658993 | ||||||||
\(446\) | 1.01562e9 | 0.542076 | ||||||||
\(447\) | 4.85373e8 | 0.257039 | ||||||||
\(448\) | 2.72630e7 | 0.0143252 | ||||||||
\(449\) | 7.55714e8 | 0.393999 | 0.197000 | − | 0.980404i | \(-0.436880\pi\) | ||||
0.197000 | + | 0.980404i | \(0.436880\pi\) | |||||||
\(450\) | −1.75375e8 | −0.0907244 | ||||||||
\(451\) | −3.01118e9 | −1.54568 | ||||||||
\(452\) | 9.34872e8 | 0.476176 | ||||||||
\(453\) | 1.65867e9 | 0.838332 | ||||||||
\(454\) | −1.26125e9 | −0.632565 | ||||||||
\(455\) | −1.11826e8 | −0.0556548 | ||||||||
\(456\) | 6.52288e8 | 0.322153 | ||||||||
\(457\) | 2.22407e9 | 1.09004 | 0.545019 | − | 0.838424i | \(-0.316522\pi\) | ||||
0.545019 | + | 0.838424i | \(0.316522\pi\) | |||||||
\(458\) | −2.70607e9 | −1.31617 | ||||||||
\(459\) | −2.03794e9 | −0.983666 | ||||||||
\(460\) | −5.76576e8 | −0.276188 | ||||||||
\(461\) | 1.19504e9 | 0.568107 | 0.284054 | − | 0.958808i | \(-0.408321\pi\) | ||||
0.284054 | + | 0.958808i | \(0.408321\pi\) | |||||||
\(462\) | −1.19928e8 | −0.0565813 | ||||||||
\(463\) | −3.83431e9 | −1.79537 | −0.897686 | − | 0.440636i | \(-0.854753\pi\) | ||||
−0.897686 | + | 0.440636i | \(0.854753\pi\) | |||||||
\(464\) | 9.48265e8 | 0.440673 | ||||||||
\(465\) | −2.80448e8 | −0.129350 | ||||||||
\(466\) | −2.85105e8 | −0.130513 | ||||||||
\(467\) | −1.64554e9 | −0.747653 | −0.373826 | − | 0.927499i | \(-0.621954\pi\) | ||||
−0.373826 | + | 0.927499i | \(0.621954\pi\) | |||||||
\(468\) | 7.72391e8 | 0.348319 | ||||||||
\(469\) | −2.43031e8 | −0.108782 | ||||||||
\(470\) | 4.25664e8 | 0.189114 | ||||||||
\(471\) | 7.67045e8 | 0.338258 | ||||||||
\(472\) | 1.26167e8 | 0.0552267 | ||||||||
\(473\) | 4.09540e9 | 1.77944 | ||||||||
\(474\) | 1.13188e9 | 0.488176 | ||||||||
\(475\) | 7.10937e8 | 0.304371 | ||||||||
\(476\) | 1.34944e8 | 0.0573493 | ||||||||
\(477\) | −2.10562e9 | −0.888312 | ||||||||
\(478\) | 1.72836e9 | 0.723830 | ||||||||
\(479\) | −7.80831e8 | −0.324626 | −0.162313 | − | 0.986739i | \(-0.551895\pi\) | ||||
−0.162313 | + | 0.986739i | \(0.551895\pi\) | |||||||
\(480\) | 1.14688e8 | 0.0473340 | ||||||||
\(481\) | −9.00234e8 | −0.368848 | ||||||||
\(482\) | 3.07439e9 | 1.25053 | ||||||||
\(483\) | −2.09874e8 | −0.0847506 | ||||||||
\(484\) | 4.48943e8 | 0.179983 | ||||||||
\(485\) | −6.55956e8 | −0.261083 | ||||||||
\(486\) | 1.81555e9 | 0.717433 | ||||||||
\(487\) | 4.79803e9 | 1.88240 | 0.941200 | − | 0.337849i | \(-0.109699\pi\) | ||||
0.941200 | + | 0.337849i | \(0.109699\pi\) | |||||||
\(488\) | 4.57698e8 | 0.178283 | ||||||||
\(489\) | −2.47908e9 | −0.958760 | ||||||||
\(490\) | −8.12727e8 | −0.312075 | ||||||||
\(491\) | −1.41644e9 | −0.540022 | −0.270011 | − | 0.962857i | \(-0.587027\pi\) | ||||
−0.270011 | + | 0.962857i | \(0.587027\pi\) | |||||||
\(492\) | 1.04818e9 | 0.396788 | ||||||||
\(493\) | 4.69363e9 | 1.76419 | ||||||||
\(494\) | −3.13113e9 | −1.16857 | ||||||||
\(495\) | 9.02830e8 | 0.334571 | ||||||||
\(496\) | −3.28204e8 | −0.120770 | ||||||||
\(497\) | −2.11836e7 | −0.00774019 | ||||||||
\(498\) | −1.01902e7 | −0.00369726 | ||||||||
\(499\) | −4.18128e9 | −1.50646 | −0.753230 | − | 0.657758i | \(-0.771505\pi\) | ||||
−0.753230 | + | 0.657758i | \(0.771505\pi\) | |||||||
\(500\) | 1.25000e8 | 0.0447214 | ||||||||
\(501\) | −7.98866e8 | −0.283819 | ||||||||
\(502\) | −1.89144e9 | −0.667314 | ||||||||
\(503\) | 2.85222e9 | 0.999298 | 0.499649 | − | 0.866228i | \(-0.333462\pi\) | ||||
0.499649 | + | 0.866228i | \(0.333462\pi\) | |||||||
\(504\) | −7.47069e7 | −0.0259929 | ||||||||
\(505\) | −1.92258e9 | −0.664301 | ||||||||
\(506\) | 2.96821e9 | 1.01852 | ||||||||
\(507\) | 3.14885e8 | 0.107306 | ||||||||
\(508\) | −9.70630e8 | −0.328497 | ||||||||
\(509\) | 8.51999e8 | 0.286369 | 0.143185 | − | 0.989696i | \(-0.454266\pi\) | ||||
0.143185 | + | 0.989696i | \(0.454266\pi\) | |||||||
\(510\) | 5.67672e8 | 0.189497 | ||||||||
\(511\) | −3.95793e8 | −0.131218 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −4.57366e9 | −1.49573 | ||||||||
\(514\) | −1.90265e8 | −0.0618000 | ||||||||
\(515\) | 4.07101e8 | 0.131334 | ||||||||
\(516\) | −1.42559e9 | −0.456795 | ||||||||
\(517\) | −2.19132e9 | −0.697411 | ||||||||
\(518\) | 8.70721e7 | 0.0275249 | ||||||||
\(519\) | −2.92182e9 | −0.917420 | ||||||||
\(520\) | −5.50528e8 | −0.171699 | ||||||||
\(521\) | 2.86477e9 | 0.887479 | 0.443740 | − | 0.896156i | \(-0.353652\pi\) | ||||
0.443740 | + | 0.896156i | \(0.353652\pi\) | |||||||
\(522\) | −2.59847e9 | −0.799596 | ||||||||
\(523\) | 2.86816e9 | 0.876693 | 0.438347 | − | 0.898806i | \(-0.355564\pi\) | ||||
0.438347 | + | 0.898806i | \(0.355564\pi\) | |||||||
\(524\) | −1.57431e9 | −0.478002 | ||||||||
\(525\) | 4.55000e7 | 0.0137232 | ||||||||
\(526\) | −6.39170e8 | −0.191499 | ||||||||
\(527\) | −1.62452e9 | −0.483489 | ||||||||
\(528\) | −5.90414e8 | −0.174557 | ||||||||
\(529\) | 1.78955e9 | 0.525592 | ||||||||
\(530\) | 1.50080e9 | 0.437882 | ||||||||
\(531\) | −3.45727e8 | −0.100208 | ||||||||
\(532\) | 3.02848e8 | 0.0872035 | ||||||||
\(533\) | −5.03150e9 | −1.43930 | ||||||||
\(534\) | 2.19522e8 | 0.0623856 | ||||||||
\(535\) | −1.85411e9 | −0.523476 | ||||||||
\(536\) | −1.19646e9 | −0.335600 | ||||||||
\(537\) | 2.82131e9 | 0.786215 | ||||||||
\(538\) | 1.86837e9 | 0.517280 | ||||||||
\(539\) | 4.18392e9 | 1.15086 | ||||||||
\(540\) | −8.04160e8 | −0.219768 | ||||||||
\(541\) | 2.71353e8 | 0.0736792 | 0.0368396 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368396 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(542\) | −2.23426e9 | −0.602747 | ||||||||
\(543\) | 9.99158e8 | 0.267815 | ||||||||
\(544\) | 6.64338e8 | 0.176927 | ||||||||
\(545\) | −8.79031e8 | −0.232604 | ||||||||
\(546\) | −2.00392e8 | −0.0526874 | ||||||||
\(547\) | 3.76596e9 | 0.983829 | 0.491915 | − | 0.870643i | \(-0.336297\pi\) | ||||
0.491915 | + | 0.870643i | \(0.336297\pi\) | |||||||
\(548\) | 2.25104e9 | 0.584320 | ||||||||
\(549\) | −1.25420e9 | −0.323492 | ||||||||
\(550\) | −6.43500e8 | −0.164922 | ||||||||
\(551\) | 1.05337e10 | 2.68257 | ||||||||
\(552\) | −1.03322e9 | −0.261462 | ||||||||
\(553\) | 5.25516e8 | 0.132144 | ||||||||
\(554\) | 1.31060e9 | 0.327480 | ||||||||
\(555\) | 3.66289e8 | 0.0909491 | ||||||||
\(556\) | −2.86167e9 | −0.706087 | ||||||||
\(557\) | −1.23789e9 | −0.303520 | −0.151760 | − | 0.988417i | \(-0.548494\pi\) | ||||
−0.151760 | + | 0.988417i | \(0.548494\pi\) | |||||||
\(558\) | 8.99357e8 | 0.219135 | ||||||||
\(559\) | 6.84317e9 | 1.65697 | ||||||||
\(560\) | 5.32480e7 | 0.0128128 | ||||||||
\(561\) | −2.92238e9 | −0.698821 | ||||||||
\(562\) | 1.02449e9 | 0.243462 | ||||||||
\(563\) | −3.72192e9 | −0.878998 | −0.439499 | − | 0.898243i | \(-0.644844\pi\) | ||||
−0.439499 | + | 0.898243i | \(0.644844\pi\) | |||||||
\(564\) | 7.62790e8 | 0.179031 | ||||||||
\(565\) | 1.82592e9 | 0.425905 | ||||||||
\(566\) | −2.15503e9 | −0.499569 | ||||||||
\(567\) | 2.63953e7 | 0.00608115 | ||||||||
\(568\) | −1.04288e8 | −0.0238790 | ||||||||
\(569\) | 3.89118e9 | 0.885499 | 0.442749 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442749 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(570\) | 1.27400e9 | 0.288143 | ||||||||
\(571\) | −7.43685e9 | −1.67172 | −0.835858 | − | 0.548946i | \(-0.815029\pi\) | ||||
−0.835858 | + | 0.548946i | \(0.815029\pi\) | |||||||
\(572\) | 2.83412e9 | 0.633187 | ||||||||
\(573\) | 1.47810e9 | 0.328217 | ||||||||
\(574\) | 4.86655e8 | 0.107406 | ||||||||
\(575\) | −1.12612e9 | −0.247030 | ||||||||
\(576\) | −3.67788e8 | −0.0801898 | ||||||||
\(577\) | −5.38224e9 | −1.16640 | −0.583200 | − | 0.812329i | \(-0.698200\pi\) | ||||
−0.583200 | + | 0.812329i | \(0.698200\pi\) | |||||||
\(578\) | 5.57122e6 | 0.00120006 | ||||||||
\(579\) | −8.98502e8 | −0.192373 | ||||||||
\(580\) | 1.85208e9 | 0.394150 | ||||||||
\(581\) | −4.73117e6 | −0.00100081 | ||||||||
\(582\) | −1.17547e9 | −0.247162 | ||||||||
\(583\) | −7.72611e9 | −1.61481 | ||||||||
\(584\) | −1.94852e9 | −0.404818 | ||||||||
\(585\) | 1.50858e9 | 0.311546 | ||||||||
\(586\) | −1.24625e9 | −0.255837 | ||||||||
\(587\) | −4.92134e9 | −1.00427 | −0.502135 | − | 0.864790i | \(-0.667452\pi\) | ||||
−0.502135 | + | 0.864790i | \(0.667452\pi\) | |||||||
\(588\) | −1.45641e9 | −0.295435 | ||||||||
\(589\) | −3.64582e9 | −0.735177 | ||||||||
\(590\) | 2.46420e8 | 0.0493962 | ||||||||
\(591\) | 4.68898e9 | 0.934377 | ||||||||
\(592\) | 4.28663e8 | 0.0849161 | ||||||||
\(593\) | −7.30205e9 | −1.43798 | −0.718991 | − | 0.695019i | \(-0.755396\pi\) | ||||
−0.718991 | + | 0.695019i | \(0.755396\pi\) | |||||||
\(594\) | 4.13982e9 | 0.810454 | ||||||||
\(595\) | 2.63562e8 | 0.0512948 | ||||||||
\(596\) | 1.10942e9 | 0.214652 | ||||||||
\(597\) | 4.52956e9 | 0.871256 | ||||||||
\(598\) | 4.95971e9 | 0.948423 | ||||||||
\(599\) | −2.56041e8 | −0.0486761 | −0.0243381 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243381 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(600\) | 2.24000e8 | 0.0423369 | ||||||||
\(601\) | −3.57507e9 | −0.671775 | −0.335888 | − | 0.941902i | \(-0.609036\pi\) | ||||
−0.335888 | + | 0.941902i | \(0.609036\pi\) | |||||||
\(602\) | −6.61883e8 | −0.123650 | ||||||||
\(603\) | 3.27858e9 | 0.608941 | ||||||||
\(604\) | 3.79124e9 | 0.700087 | ||||||||
\(605\) | 8.76842e8 | 0.160982 | ||||||||
\(606\) | −3.44527e9 | −0.628881 | ||||||||
\(607\) | 6.27324e9 | 1.13850 | 0.569248 | − | 0.822166i | \(-0.307234\pi\) | ||||
0.569248 | + | 0.822166i | \(0.307234\pi\) | |||||||
\(608\) | 1.49094e9 | 0.269029 | ||||||||
\(609\) | 6.74157e8 | 0.120949 | ||||||||
\(610\) | 8.93942e8 | 0.159461 | ||||||||
\(611\) | −3.66156e9 | −0.649415 | ||||||||
\(612\) | −1.82044e9 | −0.321031 | ||||||||
\(613\) | −8.70805e9 | −1.52690 | −0.763448 | − | 0.645870i | \(-0.776495\pi\) | ||||
−0.763448 | + | 0.645870i | \(0.776495\pi\) | |||||||
\(614\) | −3.89700e9 | −0.679425 | ||||||||
\(615\) | 2.04723e9 | 0.354898 | ||||||||
\(616\) | −2.74121e8 | −0.0472508 | ||||||||
\(617\) | 3.92214e8 | 0.0672241 | 0.0336121 | − | 0.999435i | \(-0.489299\pi\) | ||||
0.0336121 | + | 0.999435i | \(0.489299\pi\) | |||||||
\(618\) | 7.29525e8 | 0.124331 | ||||||||
\(619\) | −6.39170e7 | −0.0108318 | −0.00541588 | − | 0.999985i | \(-0.501724\pi\) | ||||
−0.00541588 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(620\) | −6.41024e8 | −0.108020 | ||||||||
\(621\) | 7.24468e9 | 1.21394 | ||||||||
\(622\) | 2.31113e9 | 0.385087 | ||||||||
\(623\) | 1.01921e8 | 0.0168871 | ||||||||
\(624\) | −9.86546e8 | −0.162544 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −3.27562e9 | −0.533684 | ||||||||
\(627\) | −6.55855e9 | −1.06260 | ||||||||
\(628\) | 1.75325e9 | 0.282478 | ||||||||
\(629\) | 2.12176e9 | 0.339952 | ||||||||
\(630\) | −1.45912e8 | −0.0232487 | ||||||||
\(631\) | 5.26547e9 | 0.834324 | 0.417162 | − | 0.908832i | \(-0.363025\pi\) | ||||
0.417162 | + | 0.908832i | \(0.363025\pi\) | |||||||
\(632\) | 2.58716e9 | 0.407674 | ||||||||
\(633\) | 4.99573e9 | 0.782864 | ||||||||
\(634\) | −2.15419e9 | −0.335716 | ||||||||
\(635\) | −1.89576e9 | −0.293816 | ||||||||
\(636\) | 2.68943e9 | 0.414534 | ||||||||
\(637\) | 6.99108e9 | 1.07166 | ||||||||
\(638\) | −9.53451e9 | −1.45354 | ||||||||
\(639\) | 2.85774e8 | 0.0433281 | ||||||||
\(640\) | 2.62144e8 | 0.0395285 | ||||||||
\(641\) | −2.37074e9 | −0.355534 | −0.177767 | − | 0.984073i | \(-0.556887\pi\) | ||||
−0.177767 | + | 0.984073i | \(0.556887\pi\) | |||||||
\(642\) | −3.32256e9 | −0.495565 | ||||||||
\(643\) | 9.35246e9 | 1.38735 | 0.693677 | − | 0.720286i | \(-0.255989\pi\) | ||||
0.693677 | + | 0.720286i | \(0.255989\pi\) | |||||||
\(644\) | −4.79711e8 | −0.0707749 | ||||||||
\(645\) | −2.78436e9 | −0.408570 | ||||||||
\(646\) | 7.37974e9 | 1.07703 | ||||||||
\(647\) | 9.02598e9 | 1.31017 | 0.655087 | − | 0.755553i | \(-0.272632\pi\) | ||||
0.655087 | + | 0.755553i | \(0.272632\pi\) | |||||||
\(648\) | 1.29946e8 | 0.0187608 | ||||||||
\(649\) | −1.26857e9 | −0.182162 | ||||||||
\(650\) | −1.07525e9 | −0.153572 | ||||||||
\(651\) | −2.33333e8 | −0.0331468 | ||||||||
\(652\) | −5.66648e9 | −0.800657 | ||||||||
\(653\) | 6.74203e9 | 0.947533 | 0.473767 | − | 0.880650i | \(-0.342894\pi\) | ||||
0.473767 | + | 0.880650i | \(0.342894\pi\) | |||||||
\(654\) | −1.57522e9 | −0.220201 | ||||||||
\(655\) | −3.07482e9 | −0.427538 | ||||||||
\(656\) | 2.39584e9 | 0.331356 | ||||||||
\(657\) | 5.33940e9 | 0.734537 | ||||||||
\(658\) | 3.54152e8 | 0.0484618 | ||||||||
\(659\) | −5.50026e9 | −0.748660 | −0.374330 | − | 0.927296i | \(-0.622127\pi\) | ||||
−0.374330 | + | 0.927296i | \(0.622127\pi\) | |||||||
\(660\) | −1.15315e9 | −0.156129 | ||||||||
\(661\) | −3.20844e9 | −0.432104 | −0.216052 | − | 0.976382i | \(-0.569318\pi\) | ||||
−0.216052 | + | 0.976382i | \(0.569318\pi\) | |||||||
\(662\) | 3.24412e9 | 0.434605 | ||||||||
\(663\) | −4.88311e9 | −0.650728 | ||||||||
\(664\) | −2.32919e7 | −0.00308757 | ||||||||
\(665\) | 5.91500e8 | 0.0779972 | ||||||||
\(666\) | −1.17464e9 | −0.154079 | ||||||||
\(667\) | −1.66854e10 | −2.17719 | ||||||||
\(668\) | −1.82598e9 | −0.237016 | ||||||||
\(669\) | 3.55468e9 | 0.458996 | ||||||||
\(670\) | −2.33684e9 | −0.300169 | ||||||||
\(671\) | −4.60201e9 | −0.588057 | ||||||||
\(672\) | 9.54204e7 | 0.0121297 | ||||||||
\(673\) | 6.24821e9 | 0.790138 | 0.395069 | − | 0.918651i | \(-0.370721\pi\) | ||||
0.395069 | + | 0.918651i | \(0.370721\pi\) | |||||||
\(674\) | −3.06410e9 | −0.385473 | ||||||||
\(675\) | −1.57062e9 | −0.196566 | ||||||||
\(676\) | 7.19737e8 | 0.0896108 | ||||||||
\(677\) | −8.32469e9 | −1.03112 | −0.515558 | − | 0.856855i | \(-0.672415\pi\) | ||||
−0.515558 | + | 0.856855i | \(0.672415\pi\) | |||||||
\(678\) | 3.27205e9 | 0.403196 | ||||||||
\(679\) | −5.45755e8 | −0.0669042 | ||||||||
\(680\) | 1.29754e9 | 0.158248 | ||||||||
\(681\) | −4.41437e9 | −0.535616 | ||||||||
\(682\) | 3.29999e9 | 0.398352 | ||||||||
\(683\) | 9.99323e9 | 1.20014 | 0.600072 | − | 0.799946i | \(-0.295139\pi\) | ||||
0.600072 | + | 0.799946i | \(0.295139\pi\) | |||||||
\(684\) | −4.08554e9 | −0.488149 | ||||||||
\(685\) | 4.39656e9 | 0.522632 | ||||||||
\(686\) | −1.36138e9 | −0.161007 | ||||||||
\(687\) | −9.47126e9 | −1.11445 | ||||||||
\(688\) | −3.25850e9 | −0.381468 | ||||||||
\(689\) | −1.29099e10 | −1.50368 | ||||||||
\(690\) | −2.01802e9 | −0.233858 | ||||||||
\(691\) | 1.54902e9 | 0.178601 | 0.0893004 | − | 0.996005i | \(-0.471537\pi\) | ||||
0.0893004 | + | 0.996005i | \(0.471537\pi\) | |||||||
\(692\) | −6.67845e9 | −0.766134 | ||||||||
\(693\) | 7.51155e8 | 0.0857360 | ||||||||
\(694\) | 9.40595e9 | 1.06818 | ||||||||
\(695\) | −5.58921e9 | −0.631544 | ||||||||
\(696\) | 3.31893e9 | 0.373135 | ||||||||
\(697\) | 1.18587e10 | 1.32655 | ||||||||
\(698\) | 2.30724e9 | 0.256802 | ||||||||
\(699\) | −9.97869e8 | −0.110510 | ||||||||
\(700\) | 1.04000e8 | 0.0114601 | ||||||||
\(701\) | 1.27712e10 | 1.40029 | 0.700143 | − | 0.714002i | \(-0.253119\pi\) | ||||
0.700143 | + | 0.714002i | \(0.253119\pi\) | |||||||
\(702\) | 6.91738e9 | 0.754679 | ||||||||
\(703\) | 4.76176e9 | 0.516920 | ||||||||
\(704\) | −1.34952e9 | −0.145772 | ||||||||
\(705\) | 1.48982e9 | 0.160130 | ||||||||
\(706\) | 6.12105e9 | 0.654650 | ||||||||
\(707\) | −1.59959e9 | −0.170232 | ||||||||
\(708\) | 4.41585e8 | 0.0467625 | ||||||||
\(709\) | −1.34411e10 | −1.41636 | −0.708178 | − | 0.706034i | \(-0.750482\pi\) | ||||
−0.708178 | + | 0.706034i | \(0.750482\pi\) | |||||||
\(710\) | −2.03688e8 | −0.0213580 | ||||||||
\(711\) | −7.08942e9 | −0.739719 | ||||||||
\(712\) | 5.01765e8 | 0.0520979 | ||||||||
\(713\) | 5.77499e9 | 0.596675 | ||||||||
\(714\) | 4.72303e8 | 0.0485598 | ||||||||
\(715\) | 5.53539e9 | 0.566339 | ||||||||
\(716\) | 6.44872e9 | 0.656565 | ||||||||
\(717\) | 6.04926e9 | 0.612893 | ||||||||
\(718\) | −4.20723e9 | −0.424190 | ||||||||
\(719\) | 8.53708e9 | 0.856561 | 0.428281 | − | 0.903646i | \(-0.359120\pi\) | ||||
0.428281 | + | 0.903646i | \(0.359120\pi\) | |||||||
\(720\) | −7.18336e8 | −0.0717239 | ||||||||
\(721\) | 3.38708e8 | 0.0336552 | ||||||||
\(722\) | 9.41103e9 | 0.930587 | ||||||||
\(723\) | 1.07604e10 | 1.05887 | ||||||||
\(724\) | 2.28379e9 | 0.223651 | ||||||||
\(725\) | 3.61734e9 | 0.352539 | ||||||||
\(726\) | 1.57130e9 | 0.152399 | ||||||||
\(727\) | −1.07165e10 | −1.03439 | −0.517194 | − | 0.855868i | \(-0.673023\pi\) | ||||
−0.517194 | + | 0.855868i | \(0.673023\pi\) | |||||||
\(728\) | −4.58039e8 | −0.0439990 | ||||||||
\(729\) | 5.79936e9 | 0.554413 | ||||||||
\(730\) | −3.80570e9 | −0.362080 | ||||||||
\(731\) | −1.61286e10 | −1.52717 | ||||||||
\(732\) | 1.60194e9 | 0.150959 | ||||||||
\(733\) | −1.44465e10 | −1.35487 | −0.677435 | − | 0.735583i | \(-0.736908\pi\) | ||||
−0.677435 | + | 0.735583i | \(0.736908\pi\) | |||||||
\(734\) | 7.14856e9 | 0.667241 | ||||||||
\(735\) | −2.84454e9 | −0.264245 | ||||||||
\(736\) | −2.36166e9 | −0.218345 | ||||||||
\(737\) | 1.20300e10 | 1.10696 | ||||||||
\(738\) | −6.56516e9 | −0.601241 | ||||||||
\(739\) | 4.70532e9 | 0.428878 | 0.214439 | − | 0.976737i | \(-0.431208\pi\) | ||||
0.214439 | + | 0.976737i | \(0.431208\pi\) | |||||||
\(740\) | 8.37232e8 | 0.0759512 | ||||||||
\(741\) | −1.09589e10 | −0.989476 | ||||||||
\(742\) | 1.24866e9 | 0.112210 | ||||||||
\(743\) | −1.70883e10 | −1.52840 | −0.764201 | − | 0.644978i | \(-0.776867\pi\) | ||||
−0.764201 | + | 0.644978i | \(0.776867\pi\) | |||||||
\(744\) | −1.14872e9 | −0.102260 | ||||||||
\(745\) | 2.16684e9 | 0.191991 | ||||||||
\(746\) | −6.50663e9 | −0.573813 | ||||||||
\(747\) | 6.38253e7 | 0.00560235 | ||||||||
\(748\) | −6.67972e9 | −0.583583 | ||||||||
\(749\) | −1.54262e9 | −0.134144 | ||||||||
\(750\) | 4.37500e8 | 0.0378672 | ||||||||
\(751\) | 2.08836e10 | 1.79914 | 0.899569 | − | 0.436778i | \(-0.143881\pi\) | ||||
0.899569 | + | 0.436778i | \(0.143881\pi\) | |||||||
\(752\) | 1.74352e9 | 0.149508 | ||||||||
\(753\) | −6.62005e9 | −0.565040 | ||||||||
\(754\) | −1.59316e10 | −1.35350 | ||||||||
\(755\) | 7.40477e9 | 0.626177 | ||||||||
\(756\) | −6.69061e8 | −0.0563170 | ||||||||
\(757\) | −5.69959e9 | −0.477538 | −0.238769 | − | 0.971076i | \(-0.576744\pi\) | ||||
−0.238769 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(758\) | −8.16757e9 | −0.681163 | ||||||||
\(759\) | 1.03887e10 | 0.862416 | ||||||||
\(760\) | 2.91200e9 | 0.240627 | ||||||||
\(761\) | −3.00610e9 | −0.247262 | −0.123631 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123631 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(762\) | −3.39721e9 | −0.278150 | ||||||||
\(763\) | −7.31354e8 | −0.0596062 | ||||||||
\(764\) | 3.37851e9 | 0.274093 | ||||||||
\(765\) | −3.55555e9 | −0.287139 | ||||||||
\(766\) | −7.31474e9 | −0.588028 | ||||||||
\(767\) | −2.11970e9 | −0.169626 | ||||||||
\(768\) | 4.69762e8 | 0.0374209 | ||||||||
\(769\) | −1.11669e10 | −0.885500 | −0.442750 | − | 0.896645i | \(-0.645997\pi\) | ||||
−0.442750 | + | 0.896645i | \(0.645997\pi\) | |||||||
\(770\) | −5.35392e8 | −0.0422624 | ||||||||
\(771\) | −6.65929e8 | −0.0523284 | ||||||||
\(772\) | −2.05372e9 | −0.160650 | ||||||||
\(773\) | 1.67216e10 | 1.30212 | 0.651058 | − | 0.759028i | \(-0.274325\pi\) | ||||
0.651058 | + | 0.759028i | \(0.274325\pi\) | |||||||
\(774\) | 8.92905e9 | 0.692169 | ||||||||
\(775\) | −1.25200e9 | −0.0966158 | ||||||||
\(776\) | −2.68679e9 | −0.206404 | ||||||||
\(777\) | 3.04752e8 | 0.0233063 | ||||||||
\(778\) | 1.79155e9 | 0.136396 | ||||||||
\(779\) | 2.66140e10 | 2.01710 | ||||||||
\(780\) | −1.92685e9 | −0.145384 | ||||||||
\(781\) | 1.04859e9 | 0.0787636 | ||||||||
\(782\) | −1.16895e10 | −0.874123 | ||||||||
\(783\) | −2.32714e10 | −1.73243 | ||||||||
\(784\) | −3.32893e9 | −0.246717 | ||||||||
\(785\) | 3.42431e9 | 0.252656 | ||||||||
\(786\) | −5.51007e9 | −0.404742 | ||||||||
\(787\) | 4.20103e9 | 0.307216 | 0.153608 | − | 0.988132i | \(-0.450911\pi\) | ||||
0.153608 | + | 0.988132i | \(0.450911\pi\) | |||||||
\(788\) | 1.07177e10 | 0.780294 | ||||||||
\(789\) | −2.23710e9 | −0.162149 | ||||||||
\(790\) | 5.05304e9 | 0.364635 | ||||||||
\(791\) | 1.51917e9 | 0.109141 | ||||||||
\(792\) | 3.69799e9 | 0.264501 | ||||||||
\(793\) | −7.68969e9 | −0.547586 | ||||||||
\(794\) | 1.44606e10 | 1.02521 | ||||||||
\(795\) | 5.25279e9 | 0.370771 | ||||||||
\(796\) | 1.03533e10 | 0.727583 | ||||||||
\(797\) | 8.80492e9 | 0.616058 | 0.308029 | − | 0.951377i | \(-0.400331\pi\) | ||||
0.308029 | + | 0.951377i | \(0.400331\pi\) | |||||||
\(798\) | 1.05997e9 | 0.0738385 | ||||||||
\(799\) | 8.62991e9 | 0.598539 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | −1.37495e9 | −0.0945310 | ||||||||
\(802\) | −1.30855e10 | −0.895736 | ||||||||
\(803\) | 1.95918e10 | 1.33527 | ||||||||
\(804\) | −4.18761e9 | −0.284165 | ||||||||
\(805\) | −9.36936e8 | −0.0633030 | ||||||||
\(806\) | 5.51409e9 | 0.370938 | ||||||||
\(807\) | 6.53931e9 | 0.438000 | ||||||||
\(808\) | −7.87490e9 | −0.525176 | ||||||||
\(809\) | 7.27057e9 | 0.482779 | 0.241390 | − | 0.970428i | \(-0.422397\pi\) | ||||
0.241390 | + | 0.970428i | \(0.422397\pi\) | |||||||
\(810\) | 2.53801e8 | 0.0167801 | ||||||||
\(811\) | 3.53384e9 | 0.232634 | 0.116317 | − | 0.993212i | \(-0.462891\pi\) | ||||
0.116317 | + | 0.993212i | \(0.462891\pi\) | |||||||
\(812\) | 1.54093e9 | 0.101004 | ||||||||
\(813\) | −7.81990e9 | −0.510369 | ||||||||
\(814\) | −4.31007e9 | −0.280091 | ||||||||
\(815\) | −1.10673e10 | −0.716129 | ||||||||
\(816\) | 2.32518e9 | 0.149810 | ||||||||
\(817\) | −3.61967e10 | −2.32216 | ||||||||
\(818\) | 1.81905e10 | 1.16200 | ||||||||
\(819\) | 1.25514e9 | 0.0798356 | ||||||||
\(820\) | 4.67938e9 | 0.296374 | ||||||||
\(821\) | −2.76875e10 | −1.74615 | −0.873077 | − | 0.487583i | \(-0.837879\pi\) | ||||
−0.873077 | + | 0.487583i | \(0.837879\pi\) | |||||||
\(822\) | 7.87863e9 | 0.494766 | ||||||||
\(823\) | 1.16831e10 | 0.730562 | 0.365281 | − | 0.930897i | \(-0.380973\pi\) | ||||
0.365281 | + | 0.930897i | \(0.380973\pi\) | |||||||
\(824\) | 1.66749e9 | 0.103829 | ||||||||
\(825\) | −2.25225e9 | −0.139646 | ||||||||
\(826\) | 2.05021e8 | 0.0126581 | ||||||||
\(827\) | 2.45526e9 | 0.150948 | 0.0754741 | − | 0.997148i | \(-0.475953\pi\) | ||||
0.0754741 | + | 0.997148i | \(0.475953\pi\) | |||||||
\(828\) | 6.47149e9 | 0.396185 | ||||||||
\(829\) | 4.71294e9 | 0.287310 | 0.143655 | − | 0.989628i | \(-0.454114\pi\) | ||||
0.143655 | + | 0.989628i | \(0.454114\pi\) | |||||||
\(830\) | −4.54920e7 | −0.00276161 | ||||||||
\(831\) | 4.58709e9 | 0.277290 | ||||||||
\(832\) | −2.25496e9 | −0.135740 | ||||||||
\(833\) | −1.64772e10 | −0.987704 | ||||||||
\(834\) | −1.00159e10 | −0.597870 | ||||||||
\(835\) | −3.56637e9 | −0.211994 | ||||||||
\(836\) | −1.49910e10 | −0.887377 | ||||||||
\(837\) | 8.05447e9 | 0.474786 | ||||||||
\(838\) | 3.23483e9 | 0.189888 | ||||||||
\(839\) | −2.77058e10 | −1.61958 | −0.809792 | − | 0.586717i | \(-0.800420\pi\) | ||||
−0.809792 | + | 0.586717i | \(0.800420\pi\) | |||||||
\(840\) | 1.86368e8 | 0.0108491 | ||||||||
\(841\) | 3.63470e10 | 2.10709 | ||||||||
\(842\) | 6.69835e7 | 0.00386701 | ||||||||
\(843\) | 3.58571e9 | 0.206148 | ||||||||
\(844\) | 1.14188e10 | 0.653766 | ||||||||
\(845\) | 1.40574e9 | 0.0801503 | ||||||||
\(846\) | −4.77765e9 | −0.271280 | ||||||||
\(847\) | 7.29532e8 | 0.0412527 | ||||||||
\(848\) | 6.14727e9 | 0.346176 | ||||||||
\(849\) | −7.54261e9 | −0.423004 | ||||||||
\(850\) | 2.53425e9 | 0.141541 | ||||||||
\(851\) | −7.54262e9 | −0.419536 | ||||||||
\(852\) | −3.65009e8 | −0.0202192 | ||||||||
\(853\) | −9.59318e9 | −0.529226 | −0.264613 | − | 0.964355i | \(-0.585244\pi\) | ||||
−0.264613 | + | 0.964355i | \(0.585244\pi\) | |||||||
\(854\) | 7.43760e8 | 0.0408630 | ||||||||
\(855\) | −7.97956e9 | −0.436614 | ||||||||
\(856\) | −7.59443e9 | −0.413844 | ||||||||
\(857\) | 2.00524e10 | 1.08826 | 0.544131 | − | 0.839000i | \(-0.316859\pi\) | ||||
0.544131 | + | 0.839000i | \(0.316859\pi\) | |||||||
\(858\) | 9.91941e9 | 0.536143 | ||||||||
\(859\) | −1.40320e9 | −0.0755344 | −0.0377672 | − | 0.999287i | \(-0.512025\pi\) | ||||
−0.0377672 | + | 0.999287i | \(0.512025\pi\) | |||||||
\(860\) | −6.36426e9 | −0.341195 | ||||||||
\(861\) | 1.70329e9 | 0.0909449 | ||||||||
\(862\) | −2.21930e9 | −0.118016 | ||||||||
\(863\) | −3.50518e10 | −1.85640 | −0.928201 | − | 0.372079i | \(-0.878645\pi\) | ||||
−0.928201 | + | 0.372079i | \(0.878645\pi\) | |||||||
\(864\) | −3.29384e9 | −0.173742 | ||||||||
\(865\) | −1.30439e10 | −0.685251 | ||||||||
\(866\) | 7.03014e9 | 0.367834 | ||||||||
\(867\) | 1.94993e7 | 0.00101614 | ||||||||
\(868\) | −5.33332e8 | −0.0276808 | ||||||||
\(869\) | −2.60130e10 | −1.34469 | ||||||||
\(870\) | 6.48228e9 | 0.333742 | ||||||||
\(871\) | 2.01015e10 | 1.03078 | ||||||||
\(872\) | −3.60051e9 | −0.183889 | ||||||||
\(873\) | 7.36245e9 | 0.374518 | ||||||||
\(874\) | −2.62342e10 | −1.32916 | ||||||||
\(875\) | 2.03125e8 | 0.0102503 | ||||||||
\(876\) | −6.81982e9 | −0.342774 | ||||||||
\(877\) | 1.87881e10 | 0.940556 | 0.470278 | − | 0.882518i | \(-0.344154\pi\) | ||||
0.470278 | + | 0.882518i | \(0.344154\pi\) | |||||||
\(878\) | 7.16805e9 | 0.357413 | ||||||||
\(879\) | −4.36187e9 | −0.216626 | ||||||||
\(880\) | −2.63578e9 | −0.130382 | ||||||||
\(881\) | 7.29040e9 | 0.359199 | 0.179600 | − | 0.983740i | \(-0.442520\pi\) | ||||
0.179600 | + | 0.983740i | \(0.442520\pi\) | |||||||
\(882\) | 9.12205e9 | 0.447664 | ||||||||
\(883\) | 3.83994e10 | 1.87699 | 0.938496 | − | 0.345291i | \(-0.112220\pi\) | ||||
0.938496 | + | 0.345291i | \(0.112220\pi\) | |||||||
\(884\) | −1.11614e10 | −0.543420 | ||||||||
\(885\) | 8.62470e8 | 0.0418256 | ||||||||
\(886\) | −3.06453e8 | −0.0148029 | ||||||||
\(887\) | −1.17256e10 | −0.564159 | −0.282079 | − | 0.959391i | \(-0.591024\pi\) | ||||
−0.282079 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(888\) | 1.50032e9 | 0.0719016 | ||||||||
\(889\) | −1.57727e9 | −0.0752924 | ||||||||
\(890\) | 9.80010e8 | 0.0465978 | ||||||||
\(891\) | −1.30657e9 | −0.0618814 | ||||||||
\(892\) | 8.12497e9 | 0.383305 | ||||||||
\(893\) | 1.93677e10 | 0.910119 | ||||||||
\(894\) | 3.88298e9 | 0.181754 | ||||||||
\(895\) | 1.25951e10 | 0.587249 | ||||||||
\(896\) | 2.18104e8 | 0.0101294 | ||||||||
\(897\) | 1.73590e10 | 0.803065 | ||||||||
\(898\) | 6.04571e9 | 0.278600 | ||||||||
\(899\) | −1.85504e10 | −0.851521 | ||||||||
\(900\) | −1.40300e9 | −0.0641518 | ||||||||
\(901\) | 3.04272e10 | 1.38588 | ||||||||
\(902\) | −2.40894e10 | −1.09296 | ||||||||
\(903\) | −2.31659e9 | −0.104699 | ||||||||
\(904\) | 7.47898e9 | 0.336707 | ||||||||
\(905\) | 4.46053e9 | 0.200040 | ||||||||
\(906\) | 1.32693e10 | 0.592790 | ||||||||
\(907\) | 5.31183e9 | 0.236384 | 0.118192 | − | 0.992991i | \(-0.462290\pi\) | ||||
0.118192 | + | 0.992991i | \(0.462290\pi\) | |||||||
\(908\) | −1.00900e10 | −0.447291 | ||||||||
\(909\) | 2.15791e10 | 0.952926 | ||||||||
\(910\) | −8.94608e8 | −0.0393539 | ||||||||
\(911\) | 1.84585e10 | 0.808877 | 0.404439 | − | 0.914565i | \(-0.367467\pi\) | ||||
0.404439 | + | 0.914565i | \(0.367467\pi\) | |||||||
\(912\) | 5.21830e9 | 0.227797 | ||||||||
\(913\) | 2.34193e8 | 0.0101842 | ||||||||
\(914\) | 1.77926e10 | 0.770773 | ||||||||
\(915\) | 3.12880e9 | 0.135022 | ||||||||
\(916\) | −2.16486e10 | −0.930670 | ||||||||
\(917\) | −2.55825e9 | −0.109560 | ||||||||
\(918\) | −1.63035e10 | −0.695557 | ||||||||
\(919\) | −2.59035e9 | −0.110092 | −0.0550459 | − | 0.998484i | \(-0.517531\pi\) | ||||
−0.0550459 | + | 0.998484i | \(0.517531\pi\) | |||||||
\(920\) | −4.61261e9 | −0.195294 | ||||||||
\(921\) | −1.36395e10 | −0.575295 | ||||||||
\(922\) | 9.56035e9 | 0.401713 | ||||||||
\(923\) | 1.75212e9 | 0.0733430 | ||||||||
\(924\) | −9.59422e8 | −0.0400090 | ||||||||
\(925\) | 1.63522e9 | 0.0679328 | ||||||||
\(926\) | −3.06745e10 | −1.26952 | ||||||||
\(927\) | −4.56930e9 | −0.188396 | ||||||||
\(928\) | 7.58612e9 | 0.311603 | ||||||||
\(929\) | 1.64437e9 | 0.0672893 | 0.0336446 | − | 0.999434i | \(-0.489289\pi\) | ||||
0.0336446 | + | 0.999434i | \(0.489289\pi\) | |||||||
\(930\) | −2.24358e9 | −0.0914644 | ||||||||
\(931\) | −3.69791e10 | −1.50187 | ||||||||
\(932\) | −2.28084e9 | −0.0922868 | ||||||||
\(933\) | 8.08896e9 | 0.326067 | ||||||||
\(934\) | −1.31643e10 | −0.528670 | ||||||||
\(935\) | −1.30463e10 | −0.521972 | ||||||||
\(936\) | 6.17913e9 | 0.246298 | ||||||||
\(937\) | −4.12858e10 | −1.63950 | −0.819751 | − | 0.572720i | \(-0.805888\pi\) | ||||
−0.819751 | + | 0.572720i | \(0.805888\pi\) | |||||||
\(938\) | −1.94425e9 | −0.0769204 | ||||||||
\(939\) | −1.14647e10 | −0.451890 | ||||||||
\(940\) | 3.40531e9 | 0.133724 | ||||||||
\(941\) | −2.22631e10 | −0.871009 | −0.435504 | − | 0.900187i | \(-0.643430\pi\) | ||||
−0.435504 | + | 0.900187i | \(0.643430\pi\) | |||||||
\(942\) | 6.13636e9 | 0.239184 | ||||||||
\(943\) | −4.21565e10 | −1.63709 | ||||||||
\(944\) | 1.00934e9 | 0.0390512 | ||||||||
\(945\) | −1.30676e9 | −0.0503715 | ||||||||
\(946\) | 3.27632e10 | 1.25825 | ||||||||
\(947\) | 5.66138e9 | 0.216619 | 0.108310 | − | 0.994117i | \(-0.465456\pi\) | ||||
0.108310 | + | 0.994117i | \(0.465456\pi\) | |||||||
\(948\) | 9.05505e9 | 0.345193 | ||||||||
\(949\) | 3.27366e10 | 1.24338 | ||||||||
\(950\) | 5.68750e9 | 0.215223 | ||||||||
\(951\) | −7.53968e9 | −0.284263 | ||||||||
\(952\) | 1.07955e9 | 0.0405521 | ||||||||
\(953\) | 4.12640e9 | 0.154435 | 0.0772176 | − | 0.997014i | \(-0.475396\pi\) | ||||
0.0772176 | + | 0.997014i | \(0.475396\pi\) | |||||||
\(954\) | −1.68450e10 | −0.628132 | ||||||||
\(955\) | 6.59864e9 | 0.245156 | ||||||||
\(956\) | 1.38269e10 | 0.511825 | ||||||||
\(957\) | −3.33708e10 | −1.23076 | ||||||||
\(958\) | −6.24665e9 | −0.229545 | ||||||||
\(959\) | 3.65794e9 | 0.133928 | ||||||||
\(960\) | 9.17504e8 | 0.0334702 | ||||||||
\(961\) | −2.10921e10 | −0.766634 | ||||||||
\(962\) | −7.20187e9 | −0.260815 | ||||||||
\(963\) | 2.08105e10 | 0.750915 | ||||||||
\(964\) | 2.45952e10 | 0.884260 | ||||||||
\(965\) | −4.01117e9 | −0.143690 | ||||||||
\(966\) | −1.67899e9 | −0.0599278 | ||||||||
\(967\) | 1.68951e10 | 0.600853 | 0.300426 | − | 0.953805i | \(-0.402871\pi\) | ||||
0.300426 | + | 0.953805i | \(0.402871\pi\) | |||||||
\(968\) | 3.59154e9 | 0.127267 | ||||||||
\(969\) | 2.58291e10 | 0.911960 | ||||||||
\(970\) | −5.24765e9 | −0.184614 | ||||||||
\(971\) | −2.00638e9 | −0.0703309 | −0.0351655 | − | 0.999382i | \(-0.511196\pi\) | ||||
−0.0351655 | + | 0.999382i | \(0.511196\pi\) | |||||||
\(972\) | 1.45244e10 | 0.507301 | ||||||||
\(973\) | −4.65022e9 | −0.161837 | ||||||||
\(974\) | 3.83843e10 | 1.33106 | ||||||||
\(975\) | −3.76337e9 | −0.130035 | ||||||||
\(976\) | 3.66159e9 | 0.126065 | ||||||||
\(977\) | −3.75233e9 | −0.128727 | −0.0643636 | − | 0.997927i | \(-0.520502\pi\) | ||||
−0.0643636 | + | 0.997927i | \(0.520502\pi\) | |||||||
\(978\) | −1.98327e10 | −0.677946 | ||||||||
\(979\) | −5.04509e9 | −0.171842 | ||||||||
\(980\) | −6.50182e9 | −0.220670 | ||||||||
\(981\) | 9.86625e9 | 0.333665 | ||||||||
\(982\) | −1.13315e10 | −0.381853 | ||||||||
\(983\) | −2.82796e10 | −0.949591 | −0.474795 | − | 0.880096i | \(-0.657478\pi\) | ||||
−0.474795 | + | 0.880096i | \(0.657478\pi\) | |||||||
\(984\) | 8.38544e9 | 0.280571 | ||||||||
\(985\) | 2.09329e10 | 0.697916 | ||||||||
\(986\) | 3.75491e10 | 1.24747 | ||||||||
\(987\) | 1.23953e9 | 0.0410344 | ||||||||
\(988\) | −2.50490e10 | −0.826307 | ||||||||
\(989\) | 5.73356e10 | 1.88468 | ||||||||
\(990\) | 7.22264e9 | 0.236577 | ||||||||
\(991\) | −1.43828e10 | −0.469447 | −0.234723 | − | 0.972062i | \(-0.575418\pi\) | ||||
−0.234723 | + | 0.972062i | \(0.575418\pi\) | |||||||
\(992\) | −2.62563e9 | −0.0853972 | ||||||||
\(993\) | 1.13544e10 | 0.367996 | ||||||||
\(994\) | −1.69468e8 | −0.00547314 | ||||||||
\(995\) | 2.02213e10 | 0.650770 | ||||||||
\(996\) | −8.15217e7 | −0.00261436 | ||||||||
\(997\) | −1.74539e10 | −0.557775 | −0.278887 | − | 0.960324i | \(-0.589966\pi\) | ||||
−0.278887 | + | 0.960324i | \(0.589966\pi\) | |||||||
\(998\) | −3.34502e10 | −1.06523 | ||||||||
\(999\) | −1.05198e10 | −0.333833 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.8.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 80.8.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 50.8.b.d.49.2 | 2 | |||
5.3 | odd | 4 | 50.8.b.d.49.1 | 2 | |||
5.4 | even | 2 | 50.8.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 490.8.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 320.8.a.f.1.1 | 1 | |||
8.5 | even | 2 | 320.8.a.c.1.1 | 1 | |||
15.2 | even | 4 | 450.8.c.p.199.1 | 2 | |||
15.8 | even | 4 | 450.8.c.p.199.2 | 2 | |||
15.14 | odd | 2 | 450.8.a.t.1.1 | 1 | |||
20.3 | even | 4 | 400.8.c.i.49.1 | 2 | |||
20.7 | even | 4 | 400.8.c.i.49.2 | 2 | |||
20.19 | odd | 2 | 400.8.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
50.8.a.b.1.1 | 1 | 5.4 | even | 2 | |||
50.8.b.d.49.1 | 2 | 5.3 | odd | 4 | |||
50.8.b.d.49.2 | 2 | 5.2 | odd | 4 | |||
80.8.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
90.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
320.8.a.c.1.1 | 1 | 8.5 | even | 2 | |||
320.8.a.f.1.1 | 1 | 8.3 | odd | 2 | |||
400.8.a.m.1.1 | 1 | 20.19 | odd | 2 | |||
400.8.c.i.49.1 | 2 | 20.3 | even | 4 | |||
400.8.c.i.49.2 | 2 | 20.7 | even | 4 | |||
450.8.a.t.1.1 | 1 | 15.14 | odd | 2 | |||
450.8.c.p.199.1 | 2 | 15.2 | even | 4 | |||
450.8.c.p.199.2 | 2 | 15.8 | even | 4 | |||
490.8.a.b.1.1 | 1 | 7.6 | odd | 2 |