Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 42.2698 | 1.86808 | 0.934039 | − | 0.357172i | \(-0.116259\pi\) | ||||
0.934039 | + | 0.357172i | \(0.116259\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 1274.73 | 2.48971 | ||||||||
\(5\) | −60.0153 | −0.0429434 | −0.0214717 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214717 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(6\) | 3423.85 | 1.07853 | ||||||||
\(7\) | 8826.78 | 1.38951 | 0.694754 | − | 0.719247i | \(-0.255513\pi\) | ||||
0.694754 | + | 0.719247i | \(0.255513\pi\) | |||||||
\(8\) | 32240.5 | 2.78290 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −2536.83 | −0.0802217 | ||||||||
\(11\) | 16200.8 | 0.333633 | 0.166816 | − | 0.985988i | \(-0.446651\pi\) | ||||
0.166816 | + | 0.985988i | \(0.446651\pi\) | |||||||
\(12\) | 103253. | 1.43744 | ||||||||
\(13\) | 123272. | 1.19707 | 0.598536 | − | 0.801096i | \(-0.295749\pi\) | ||||
0.598536 | + | 0.801096i | \(0.295749\pi\) | |||||||
\(14\) | 373106. | 2.59571 | ||||||||
\(15\) | −4861.24 | −0.0247934 | ||||||||
\(16\) | 710136. | 2.70896 | ||||||||
\(17\) | −165876. | −0.481685 | −0.240842 | − | 0.970564i | \(-0.577424\pi\) | ||||
−0.240842 | + | 0.970564i | \(0.577424\pi\) | |||||||
\(18\) | 277332. | 0.622692 | ||||||||
\(19\) | −692496. | −1.21906 | −0.609532 | − | 0.792762i | \(-0.708643\pi\) | ||||
−0.609532 | + | 0.792762i | \(0.708643\pi\) | |||||||
\(20\) | −76503.4 | −0.106917 | ||||||||
\(21\) | 714969. | 0.802233 | ||||||||
\(22\) | 684803. | 0.623251 | ||||||||
\(23\) | −387376. | −0.288641 | −0.144320 | − | 0.989531i | \(-0.546100\pi\) | ||||
−0.144320 | + | 0.989531i | \(0.546100\pi\) | |||||||
\(24\) | 2.61148e6 | 1.60671 | ||||||||
\(25\) | −1.94952e6 | −0.998156 | ||||||||
\(26\) | 5.21069e6 | 2.23622 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 1.12518e7 | 3.45947 | ||||||||
\(29\) | −1.66452e6 | −0.437017 | −0.218509 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218509 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(30\) | −205483. | −0.0463160 | ||||||||
\(31\) | −1.05783e6 | −0.205726 | −0.102863 | − | 0.994696i | \(-0.532800\pi\) | ||||
−0.102863 | + | 0.994696i | \(0.532800\pi\) | |||||||
\(32\) | 1.35101e7 | 2.27764 | ||||||||
\(33\) | 1.31226e6 | 0.192623 | ||||||||
\(34\) | −7.01153e6 | −0.899825 | ||||||||
\(35\) | −529742. | −0.0596702 | ||||||||
\(36\) | 8.36352e6 | 0.829904 | ||||||||
\(37\) | 5.42244e6 | 0.475650 | 0.237825 | − | 0.971308i | \(-0.423566\pi\) | ||||
0.237825 | + | 0.971308i | \(0.423566\pi\) | |||||||
\(38\) | −2.92717e7 | −2.27730 | ||||||||
\(39\) | 9.98505e6 | 0.691130 | ||||||||
\(40\) | −1.93492e6 | −0.119507 | ||||||||
\(41\) | −2.48157e7 | −1.37151 | −0.685755 | − | 0.727832i | \(-0.740528\pi\) | ||||
−0.685755 | + | 0.727832i | \(0.740528\pi\) | |||||||
\(42\) | 3.02216e7 | 1.49863 | ||||||||
\(43\) | 1.30273e7 | 0.581094 | 0.290547 | − | 0.956861i | \(-0.406163\pi\) | ||||
0.290547 | + | 0.956861i | \(0.406163\pi\) | |||||||
\(44\) | 2.06516e7 | 0.830649 | ||||||||
\(45\) | −393760. | −0.0143145 | ||||||||
\(46\) | −1.63743e7 | −0.539203 | ||||||||
\(47\) | 2.22102e7 | 0.663915 | 0.331958 | − | 0.943294i | \(-0.392291\pi\) | ||||
0.331958 | + | 0.943294i | \(0.392291\pi\) | |||||||
\(48\) | 5.75210e7 | 1.56402 | ||||||||
\(49\) | 3.75584e7 | 0.930732 | ||||||||
\(50\) | −8.24059e7 | −1.86463 | ||||||||
\(51\) | −1.34359e7 | −0.278101 | ||||||||
\(52\) | 1.57139e8 | 2.98036 | ||||||||
\(53\) | 9.05128e7 | 1.57568 | 0.787841 | − | 0.615879i | \(-0.211199\pi\) | ||||
0.787841 | + | 0.615879i | \(0.211199\pi\) | |||||||
\(54\) | 2.24639e7 | 0.359512 | ||||||||
\(55\) | −972293. | −0.0143273 | ||||||||
\(56\) | 2.84580e8 | 3.86686 | ||||||||
\(57\) | −5.60922e7 | −0.703827 | ||||||||
\(58\) | −7.03589e7 | −0.816382 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −6.19678e6 | −0.0617284 | ||||||||
\(61\) | 5.78319e7 | 0.534790 | 0.267395 | − | 0.963587i | \(-0.413837\pi\) | ||||
0.267395 | + | 0.963587i | \(0.413837\pi\) | |||||||
\(62\) | −4.47143e7 | −0.384312 | ||||||||
\(63\) | 5.79125e7 | 0.463169 | ||||||||
\(64\) | 2.07481e8 | 1.54585 | ||||||||
\(65\) | −7.39822e6 | −0.0514064 | ||||||||
\(66\) | 5.54690e7 | 0.359834 | ||||||||
\(67\) | −2.31519e8 | −1.40362 | −0.701810 | − | 0.712364i | \(-0.747624\pi\) | ||||
−0.701810 | + | 0.712364i | \(0.747624\pi\) | |||||||
\(68\) | −2.11447e8 | −1.19926 | ||||||||
\(69\) | −3.13775e7 | −0.166647 | ||||||||
\(70\) | −2.23920e7 | −0.111469 | ||||||||
\(71\) | 1.74344e7 | 0.0814227 | 0.0407114 | − | 0.999171i | \(-0.487038\pi\) | ||||
0.0407114 | + | 0.999171i | \(0.487038\pi\) | |||||||
\(72\) | 2.11530e8 | 0.927633 | ||||||||
\(73\) | 1.14788e8 | 0.473092 | 0.236546 | − | 0.971620i | \(-0.423985\pi\) | ||||
0.236546 | + | 0.971620i | \(0.423985\pi\) | |||||||
\(74\) | 2.29205e8 | 0.888551 | ||||||||
\(75\) | −1.57911e8 | −0.576286 | ||||||||
\(76\) | −8.82748e8 | −3.03512 | ||||||||
\(77\) | 1.43001e8 | 0.463585 | ||||||||
\(78\) | 4.22066e8 | 1.29108 | ||||||||
\(79\) | −1.84489e8 | −0.532905 | −0.266452 | − | 0.963848i | \(-0.585852\pi\) | ||||
−0.266452 | + | 0.963848i | \(0.585852\pi\) | |||||||
\(80\) | −4.26190e7 | −0.116332 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.04895e9 | −2.56209 | ||||||||
\(83\) | 5.49192e8 | 1.27020 | 0.635101 | − | 0.772429i | \(-0.280959\pi\) | ||||
0.635101 | + | 0.772429i | \(0.280959\pi\) | |||||||
\(84\) | 9.11394e8 | 1.99733 | ||||||||
\(85\) | 9.95509e6 | 0.0206852 | ||||||||
\(86\) | 5.50661e8 | 1.08553 | ||||||||
\(87\) | −1.34826e8 | −0.252312 | ||||||||
\(88\) | 5.22321e8 | 0.928465 | ||||||||
\(89\) | 1.64838e8 | 0.278485 | 0.139242 | − | 0.990258i | \(-0.455533\pi\) | ||||
0.139242 | + | 0.990258i | \(0.455533\pi\) | |||||||
\(90\) | −1.66442e7 | −0.0267406 | ||||||||
\(91\) | 1.08810e9 | 1.66334 | ||||||||
\(92\) | −4.93801e8 | −0.718632 | ||||||||
\(93\) | −8.56843e7 | −0.118776 | ||||||||
\(94\) | 9.38821e8 | 1.24025 | ||||||||
\(95\) | 4.15604e7 | 0.0523508 | ||||||||
\(96\) | 1.09432e9 | 1.31500 | ||||||||
\(97\) | −1.37978e9 | −1.58248 | −0.791239 | − | 0.611507i | \(-0.790564\pi\) | ||||
−0.791239 | + | 0.611507i | \(0.790564\pi\) | |||||||
\(98\) | 1.58758e9 | 1.73868 | ||||||||
\(99\) | 1.06293e8 | 0.111211 | ||||||||
\(100\) | −2.48512e9 | −2.48512 | ||||||||
\(101\) | 7.27601e8 | 0.695740 | 0.347870 | − | 0.937543i | \(-0.386905\pi\) | ||||
0.347870 | + | 0.937543i | \(0.386905\pi\) | |||||||
\(102\) | −5.67934e8 | −0.519514 | ||||||||
\(103\) | 2.84037e8 | 0.248661 | 0.124330 | − | 0.992241i | \(-0.460322\pi\) | ||||
0.124330 | + | 0.992241i | \(0.460322\pi\) | |||||||
\(104\) | 3.97436e9 | 3.33133 | ||||||||
\(105\) | −4.29091e7 | −0.0344506 | ||||||||
\(106\) | 3.82595e9 | 2.94350 | ||||||||
\(107\) | 7.20470e8 | 0.531360 | 0.265680 | − | 0.964061i | \(-0.414404\pi\) | ||||
0.265680 | + | 0.964061i | \(0.414404\pi\) | |||||||
\(108\) | 6.77445e8 | 0.479145 | ||||||||
\(109\) | −2.76564e9 | −1.87662 | −0.938312 | − | 0.345790i | \(-0.887611\pi\) | ||||
−0.938312 | + | 0.345790i | \(0.887611\pi\) | |||||||
\(110\) | −4.10986e7 | −0.0267646 | ||||||||
\(111\) | 4.39218e8 | 0.274617 | ||||||||
\(112\) | 6.26822e9 | 3.76411 | ||||||||
\(113\) | −1.41911e9 | −0.818773 | −0.409386 | − | 0.912361i | \(-0.634257\pi\) | ||||
−0.409386 | + | 0.912361i | \(0.634257\pi\) | |||||||
\(114\) | −2.37100e9 | −1.31480 | ||||||||
\(115\) | 2.32485e7 | 0.0123952 | ||||||||
\(116\) | −2.12182e9 | −1.08805 | ||||||||
\(117\) | 8.08789e8 | 0.399024 | ||||||||
\(118\) | −5.12198e8 | −0.243203 | ||||||||
\(119\) | −1.46415e9 | −0.669305 | ||||||||
\(120\) | −1.56729e8 | −0.0689975 | ||||||||
\(121\) | −2.09548e9 | −0.888689 | ||||||||
\(122\) | 2.44454e9 | 0.999029 | ||||||||
\(123\) | −2.01007e9 | −0.791842 | ||||||||
\(124\) | −1.34845e9 | −0.512198 | ||||||||
\(125\) | 2.34219e8 | 0.0858077 | ||||||||
\(126\) | 2.44795e9 | 0.865236 | ||||||||
\(127\) | −4.50001e9 | −1.53496 | −0.767479 | − | 0.641074i | \(-0.778489\pi\) | ||||
−0.767479 | + | 0.641074i | \(0.778489\pi\) | |||||||
\(128\) | 1.85297e9 | 0.610130 | ||||||||
\(129\) | 1.05521e9 | 0.335495 | ||||||||
\(130\) | −3.12721e8 | −0.0960311 | ||||||||
\(131\) | −2.56225e8 | −0.0760151 | −0.0380076 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380076 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(132\) | 1.67278e9 | 0.479576 | ||||||||
\(133\) | −6.11251e9 | −1.69390 | ||||||||
\(134\) | −9.78624e9 | −2.62207 | ||||||||
\(135\) | −3.18946e7 | −0.00826447 | ||||||||
\(136\) | −5.34793e9 | −1.34048 | ||||||||
\(137\) | 7.23263e9 | 1.75410 | 0.877048 | − | 0.480402i | \(-0.159509\pi\) | ||||
0.877048 | + | 0.480402i | \(0.159509\pi\) | |||||||
\(138\) | −1.32632e9 | −0.311309 | ||||||||
\(139\) | 6.75360e9 | 1.53451 | 0.767253 | − | 0.641344i | \(-0.221623\pi\) | ||||
0.767253 | + | 0.641344i | \(0.221623\pi\) | |||||||
\(140\) | −6.75279e8 | −0.148562 | ||||||||
\(141\) | 1.79903e9 | 0.383312 | ||||||||
\(142\) | 7.36950e8 | 0.152104 | ||||||||
\(143\) | 1.99710e9 | 0.399382 | ||||||||
\(144\) | 4.65920e9 | 0.902985 | ||||||||
\(145\) | 9.98967e7 | 0.0187670 | ||||||||
\(146\) | 4.85208e9 | 0.883772 | ||||||||
\(147\) | 3.04223e9 | 0.537359 | ||||||||
\(148\) | 6.91217e9 | 1.18423 | ||||||||
\(149\) | −8.62282e9 | −1.43321 | −0.716607 | − | 0.697477i | \(-0.754306\pi\) | ||||
−0.716607 | + | 0.697477i | \(0.754306\pi\) | |||||||
\(150\) | −6.67488e9 | −1.07655 | ||||||||
\(151\) | −4.09088e9 | −0.640355 | −0.320178 | − | 0.947358i | \(-0.603743\pi\) | ||||
−0.320178 | + | 0.947358i | \(0.603743\pi\) | |||||||
\(152\) | −2.23265e10 | −3.39253 | ||||||||
\(153\) | −1.08831e9 | −0.160562 | ||||||||
\(154\) | 6.04460e9 | 0.866013 | ||||||||
\(155\) | 6.34860e7 | 0.00883457 | ||||||||
\(156\) | 1.27283e10 | 1.72071 | ||||||||
\(157\) | −3.74731e9 | −0.492234 | −0.246117 | − | 0.969240i | \(-0.579155\pi\) | ||||
−0.246117 | + | 0.969240i | \(0.579155\pi\) | |||||||
\(158\) | −7.79833e9 | −0.995507 | ||||||||
\(159\) | 7.33154e9 | 0.909720 | ||||||||
\(160\) | −8.10815e8 | −0.0978097 | ||||||||
\(161\) | −3.41928e9 | −0.401068 | ||||||||
\(162\) | 1.81957e9 | 0.207564 | ||||||||
\(163\) | 1.62523e9 | 0.180332 | 0.0901658 | − | 0.995927i | \(-0.471260\pi\) | ||||
0.0901658 | + | 0.995927i | \(0.471260\pi\) | |||||||
\(164\) | −3.16334e10 | −3.41467 | ||||||||
\(165\) | −7.87558e7 | −0.00827189 | ||||||||
\(166\) | 2.32142e10 | 2.37283 | ||||||||
\(167\) | −8.68516e9 | −0.864080 | −0.432040 | − | 0.901854i | \(-0.642206\pi\) | ||||
−0.432040 | + | 0.901854i | \(0.642206\pi\) | |||||||
\(168\) | 2.30510e10 | 2.23253 | ||||||||
\(169\) | 4.59154e9 | 0.432980 | ||||||||
\(170\) | 4.20799e8 | 0.0386416 | ||||||||
\(171\) | −4.54347e9 | −0.406355 | ||||||||
\(172\) | 1.66063e10 | 1.44676 | ||||||||
\(173\) | −5.57213e9 | −0.472948 | −0.236474 | − | 0.971638i | \(-0.575992\pi\) | ||||
−0.236474 | + | 0.971638i | \(0.575992\pi\) | |||||||
\(174\) | −5.69907e9 | −0.471338 | ||||||||
\(175\) | −1.72080e10 | −1.38695 | ||||||||
\(176\) | 1.15048e10 | 0.903796 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 6.96765e9 | 0.520231 | ||||||||
\(179\) | 2.83494e9 | 0.206398 | 0.103199 | − | 0.994661i | \(-0.467092\pi\) | ||||
0.103199 | + | 0.994661i | \(0.467092\pi\) | |||||||
\(180\) | −5.01939e8 | −0.0356389 | ||||||||
\(181\) | −6.81693e8 | −0.0472101 | −0.0236051 | − | 0.999721i | \(-0.507514\pi\) | ||||
−0.0236051 | + | 0.999721i | \(0.507514\pi\) | |||||||
\(182\) | 4.59936e10 | 3.10725 | ||||||||
\(183\) | 4.68439e9 | 0.308761 | ||||||||
\(184\) | −1.24892e10 | −0.803257 | ||||||||
\(185\) | −3.25430e8 | −0.0204260 | ||||||||
\(186\) | −3.62186e9 | −0.221882 | ||||||||
\(187\) | −2.68732e9 | −0.160706 | ||||||||
\(188\) | 2.83121e10 | 1.65296 | ||||||||
\(189\) | 4.69091e9 | 0.267411 | ||||||||
\(190\) | 1.75675e9 | 0.0977953 | ||||||||
\(191\) | 3.50450e9 | 0.190535 | 0.0952676 | − | 0.995452i | \(-0.469629\pi\) | ||||
0.0952676 | + | 0.995452i | \(0.469629\pi\) | |||||||
\(192\) | 1.68059e10 | 0.892498 | ||||||||
\(193\) | 3.04202e10 | 1.57817 | 0.789085 | − | 0.614285i | \(-0.210555\pi\) | ||||
0.789085 | + | 0.614285i | \(0.210555\pi\) | |||||||
\(194\) | −5.83231e10 | −2.95619 | ||||||||
\(195\) | −5.99256e8 | −0.0296795 | ||||||||
\(196\) | 4.78769e10 | 2.31726 | ||||||||
\(197\) | 2.76245e10 | 1.30676 | 0.653380 | − | 0.757030i | \(-0.273350\pi\) | ||||
0.653380 | + | 0.757030i | \(0.273350\pi\) | |||||||
\(198\) | 4.49299e9 | 0.207750 | ||||||||
\(199\) | 1.23928e10 | 0.560185 | 0.280093 | − | 0.959973i | \(-0.409635\pi\) | ||||
0.280093 | + | 0.959973i | \(0.409635\pi\) | |||||||
\(200\) | −6.28537e10 | −2.77777 | ||||||||
\(201\) | −1.87530e10 | −0.810380 | ||||||||
\(202\) | 3.07555e10 | 1.29970 | ||||||||
\(203\) | −1.46924e10 | −0.607239 | ||||||||
\(204\) | −1.71272e10 | −0.692391 | ||||||||
\(205\) | 1.48932e9 | 0.0588974 | ||||||||
\(206\) | 1.20062e10 | 0.464517 | ||||||||
\(207\) | −2.54157e9 | −0.0962135 | ||||||||
\(208\) | 8.75401e10 | 3.24281 | ||||||||
\(209\) | −1.12190e10 | −0.406719 | ||||||||
\(210\) | −1.81376e9 | −0.0643564 | ||||||||
\(211\) | 2.58153e10 | 0.896615 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(212\) | 1.15380e11 | 3.92299 | ||||||||
\(213\) | 1.41219e9 | 0.0470094 | ||||||||
\(214\) | 3.04541e10 | 0.992621 | ||||||||
\(215\) | −7.81837e8 | −0.0249542 | ||||||||
\(216\) | 1.71339e10 | 0.535569 | ||||||||
\(217\) | −9.33724e9 | −0.285858 | ||||||||
\(218\) | −1.16903e11 | −3.50568 | ||||||||
\(219\) | 9.29786e9 | 0.273140 | ||||||||
\(220\) | −1.23941e9 | −0.0356709 | ||||||||
\(221\) | −2.04479e10 | −0.576611 | ||||||||
\(222\) | 1.85656e10 | 0.513005 | ||||||||
\(223\) | −2.78289e9 | −0.0753572 | −0.0376786 | − | 0.999290i | \(-0.511996\pi\) | ||||
−0.0376786 | + | 0.999290i | \(0.511996\pi\) | |||||||
\(224\) | 1.19251e11 | 3.16480 | ||||||||
\(225\) | −1.27908e10 | −0.332719 | ||||||||
\(226\) | −5.99855e10 | −1.52953 | ||||||||
\(227\) | −2.66911e10 | −0.667191 | −0.333595 | − | 0.942716i | \(-0.608262\pi\) | ||||
−0.333595 | + | 0.942716i | \(0.608262\pi\) | |||||||
\(228\) | −7.15026e10 | −1.75233 | ||||||||
\(229\) | −2.17020e10 | −0.521482 | −0.260741 | − | 0.965409i | \(-0.583967\pi\) | ||||
−0.260741 | + | 0.965409i | \(0.583967\pi\) | |||||||
\(230\) | 9.82707e8 | 0.0231552 | ||||||||
\(231\) | 1.15830e10 | 0.267651 | ||||||||
\(232\) | −5.36650e10 | −1.21617 | ||||||||
\(233\) | 8.26830e10 | 1.83787 | 0.918935 | − | 0.394409i | \(-0.129051\pi\) | ||||
0.918935 | + | 0.394409i | \(0.129051\pi\) | |||||||
\(234\) | 3.41873e10 | 0.745407 | ||||||||
\(235\) | −1.33295e9 | −0.0285108 | ||||||||
\(236\) | −1.54464e10 | −0.324133 | ||||||||
\(237\) | −1.49436e10 | −0.307673 | ||||||||
\(238\) | −6.18892e10 | −1.25031 | ||||||||
\(239\) | −4.38699e10 | −0.869713 | −0.434857 | − | 0.900500i | \(-0.643201\pi\) | ||||
−0.434857 | + | 0.900500i | \(0.643201\pi\) | |||||||
\(240\) | −3.45214e9 | −0.0671642 | ||||||||
\(241\) | 2.06071e10 | 0.393495 | 0.196748 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196748 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(242\) | −8.85756e10 | −1.66014 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 7.37202e10 | 1.33147 | ||||||||
\(245\) | −2.25408e9 | −0.0399688 | ||||||||
\(246\) | −8.49652e10 | −1.47922 | ||||||||
\(247\) | −8.53656e10 | −1.45931 | ||||||||
\(248\) | −3.41050e10 | −0.572514 | ||||||||
\(249\) | 4.44845e10 | 0.733351 | ||||||||
\(250\) | 9.90036e9 | 0.160295 | ||||||||
\(251\) | 4.19417e10 | 0.666983 | 0.333492 | − | 0.942753i | \(-0.391773\pi\) | ||||
0.333492 | + | 0.942753i | \(0.391773\pi\) | |||||||
\(252\) | 7.38229e10 | 1.15316 | ||||||||
\(253\) | −6.27579e9 | −0.0962999 | ||||||||
\(254\) | −1.90214e11 | −2.86742 | ||||||||
\(255\) | 8.06362e8 | 0.0119426 | ||||||||
\(256\) | −2.79057e10 | −0.406081 | ||||||||
\(257\) | −1.08931e11 | −1.55759 | −0.778796 | − | 0.627277i | \(-0.784169\pi\) | ||||
−0.778796 | + | 0.627277i | \(0.784169\pi\) | |||||||
\(258\) | 4.46035e10 | 0.626730 | ||||||||
\(259\) | 4.78627e10 | 0.660919 | ||||||||
\(260\) | −9.43075e9 | −0.127987 | ||||||||
\(261\) | −1.09209e10 | −0.145672 | ||||||||
\(262\) | −1.08306e10 | −0.142002 | ||||||||
\(263\) | −1.51234e11 | −1.94916 | −0.974581 | − | 0.224037i | \(-0.928076\pi\) | ||||
−0.974581 | + | 0.224037i | \(0.928076\pi\) | |||||||
\(264\) | 4.23080e10 | 0.536050 | ||||||||
\(265\) | −5.43215e9 | −0.0676652 | ||||||||
\(266\) | −2.58374e11 | −3.16433 | ||||||||
\(267\) | 1.33518e10 | 0.160783 | ||||||||
\(268\) | −2.95124e11 | −3.49461 | ||||||||
\(269\) | −4.01575e10 | −0.467607 | −0.233804 | − | 0.972284i | \(-0.575117\pi\) | ||||
−0.233804 | + | 0.972284i | \(0.575117\pi\) | |||||||
\(270\) | −1.34818e9 | −0.0154387 | ||||||||
\(271\) | −3.70127e10 | −0.416859 | −0.208429 | − | 0.978037i | \(-0.566835\pi\) | ||||
−0.208429 | + | 0.978037i | \(0.566835\pi\) | |||||||
\(272\) | −1.17794e11 | −1.30486 | ||||||||
\(273\) | 8.81358e10 | 0.960330 | ||||||||
\(274\) | 3.05721e11 | 3.27679 | ||||||||
\(275\) | −3.15838e10 | −0.333017 | ||||||||
\(276\) | −3.99979e10 | −0.414902 | ||||||||
\(277\) | 8.72178e10 | 0.890115 | 0.445057 | − | 0.895502i | \(-0.353183\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353183\pi\) | |||||||
\(278\) | 2.85473e11 | 2.86658 | ||||||||
\(279\) | −6.94043e9 | −0.0685753 | ||||||||
\(280\) | −1.70791e10 | −0.166056 | ||||||||
\(281\) | −8.67326e10 | −0.829859 | −0.414929 | − | 0.909854i | \(-0.636194\pi\) | ||||
−0.414929 | + | 0.909854i | \(0.636194\pi\) | |||||||
\(282\) | 7.60445e10 | 0.716056 | ||||||||
\(283\) | 3.51750e10 | 0.325983 | 0.162992 | − | 0.986627i | \(-0.447886\pi\) | ||||
0.162992 | + | 0.986627i | \(0.447886\pi\) | |||||||
\(284\) | 2.22243e10 | 0.202719 | ||||||||
\(285\) | 3.36639e9 | 0.0302247 | ||||||||
\(286\) | 8.44171e10 | 0.746077 | ||||||||
\(287\) | −2.19043e11 | −1.90572 | ||||||||
\(288\) | 8.86400e10 | 0.759213 | ||||||||
\(289\) | −9.10731e10 | −0.767980 | ||||||||
\(290\) | 4.22261e9 | 0.0350582 | ||||||||
\(291\) | −1.11762e11 | −0.913644 | ||||||||
\(292\) | 1.46325e11 | 1.17786 | ||||||||
\(293\) | 1.83113e11 | 1.45149 | 0.725746 | − | 0.687963i | \(-0.241495\pi\) | ||||
0.725746 | + | 0.687963i | \(0.241495\pi\) | |||||||
\(294\) | 1.28594e11 | 1.00383 | ||||||||
\(295\) | 7.27227e8 | 0.00559076 | ||||||||
\(296\) | 1.74822e11 | 1.32368 | ||||||||
\(297\) | 8.60975e9 | 0.0642076 | ||||||||
\(298\) | −3.64484e11 | −2.67735 | ||||||||
\(299\) | −4.77527e10 | −0.345523 | ||||||||
\(300\) | −2.01295e11 | −1.43479 | ||||||||
\(301\) | 1.14989e11 | 0.807434 | ||||||||
\(302\) | −1.72921e11 | −1.19623 | ||||||||
\(303\) | 5.89357e10 | 0.401686 | ||||||||
\(304\) | −4.91767e11 | −3.30239 | ||||||||
\(305\) | −3.47080e9 | −0.0229657 | ||||||||
\(306\) | −4.60027e10 | −0.299942 | ||||||||
\(307\) | −1.30126e11 | −0.836068 | −0.418034 | − | 0.908431i | \(-0.637281\pi\) | ||||
−0.418034 | + | 0.908431i | \(0.637281\pi\) | |||||||
\(308\) | 1.82287e11 | 1.15419 | ||||||||
\(309\) | 2.30070e10 | 0.143564 | ||||||||
\(310\) | 2.68354e9 | 0.0165037 | ||||||||
\(311\) | 2.36559e11 | 1.43390 | 0.716948 | − | 0.697127i | \(-0.245538\pi\) | ||||
0.716948 | + | 0.697127i | \(0.245538\pi\) | |||||||
\(312\) | 3.21923e11 | 1.92334 | ||||||||
\(313\) | −2.09703e11 | −1.23497 | −0.617483 | − | 0.786584i | \(-0.711848\pi\) | ||||
−0.617483 | + | 0.786584i | \(0.711848\pi\) | |||||||
\(314\) | −1.58398e11 | −0.919531 | ||||||||
\(315\) | −3.47563e9 | −0.0198901 | ||||||||
\(316\) | −2.35175e11 | −1.32678 | ||||||||
\(317\) | 2.01816e11 | 1.12251 | 0.561253 | − | 0.827645i | \(-0.310320\pi\) | ||||
0.561253 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(318\) | 3.09902e11 | 1.69943 | ||||||||
\(319\) | −2.69665e10 | −0.145803 | ||||||||
\(320\) | −1.24520e10 | −0.0663842 | ||||||||
\(321\) | 5.83581e10 | 0.306781 | ||||||||
\(322\) | −1.44532e11 | −0.749227 | ||||||||
\(323\) | 1.14868e11 | 0.587205 | ||||||||
\(324\) | 5.48731e10 | 0.276635 | ||||||||
\(325\) | −2.40322e11 | −1.19486 | ||||||||
\(326\) | 6.86983e10 | 0.336873 | ||||||||
\(327\) | −2.24017e11 | −1.08347 | ||||||||
\(328\) | −8.00071e11 | −3.81677 | ||||||||
\(329\) | 1.96045e11 | 0.922516 | ||||||||
\(330\) | −3.32899e9 | −0.0154525 | ||||||||
\(331\) | −3.32010e11 | −1.52029 | −0.760144 | − | 0.649755i | \(-0.774871\pi\) | ||||
−0.760144 | + | 0.649755i | \(0.774871\pi\) | |||||||
\(332\) | 7.00073e11 | 3.16244 | ||||||||
\(333\) | 3.55767e10 | 0.158550 | ||||||||
\(334\) | −3.67120e11 | −1.61417 | ||||||||
\(335\) | 1.38947e10 | 0.0602763 | ||||||||
\(336\) | 5.07725e11 | 2.17321 | ||||||||
\(337\) | −5.50980e10 | −0.232703 | −0.116351 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116351 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(338\) | 1.94083e11 | 0.808841 | ||||||||
\(339\) | −1.14948e11 | −0.472719 | ||||||||
\(340\) | 1.26901e10 | 0.0515002 | ||||||||
\(341\) | −1.71377e10 | −0.0686368 | ||||||||
\(342\) | −1.92051e11 | −0.759102 | ||||||||
\(343\) | −2.46726e10 | −0.0962481 | ||||||||
\(344\) | 4.20007e11 | 1.61712 | ||||||||
\(345\) | 1.88313e9 | 0.00715638 | ||||||||
\(346\) | −2.35533e11 | −0.883504 | ||||||||
\(347\) | −3.11529e11 | −1.15349 | −0.576747 | − | 0.816923i | \(-0.695678\pi\) | ||||
−0.576747 | + | 0.816923i | \(0.695678\pi\) | |||||||
\(348\) | −1.71867e11 | −0.628184 | ||||||||
\(349\) | −3.19139e11 | −1.15150 | −0.575751 | − | 0.817625i | \(-0.695290\pi\) | ||||
−0.575751 | + | 0.817625i | \(0.695290\pi\) | |||||||
\(350\) | −7.27378e11 | −2.59092 | ||||||||
\(351\) | 6.55119e10 | 0.230377 | ||||||||
\(352\) | 2.18875e11 | 0.759895 | ||||||||
\(353\) | −1.33725e11 | −0.458382 | −0.229191 | − | 0.973382i | \(-0.573608\pi\) | ||||
−0.229191 | + | 0.973382i | \(0.573608\pi\) | |||||||
\(354\) | −4.14880e10 | −0.140413 | ||||||||
\(355\) | −1.04633e9 | −0.00349657 | ||||||||
\(356\) | 2.10124e11 | 0.693347 | ||||||||
\(357\) | −1.18596e11 | −0.386423 | ||||||||
\(358\) | 1.19832e11 | 0.385567 | ||||||||
\(359\) | −1.61952e11 | −0.514590 | −0.257295 | − | 0.966333i | \(-0.582831\pi\) | ||||
−0.257295 | + | 0.966333i | \(0.582831\pi\) | |||||||
\(360\) | −1.26950e10 | −0.0398357 | ||||||||
\(361\) | 1.56864e11 | 0.486116 | ||||||||
\(362\) | −2.88150e10 | −0.0881921 | ||||||||
\(363\) | −1.69734e11 | −0.513085 | ||||||||
\(364\) | 1.38703e12 | 4.14124 | ||||||||
\(365\) | −6.88906e9 | −0.0203162 | ||||||||
\(366\) | 1.98008e11 | 0.576790 | ||||||||
\(367\) | −2.17085e11 | −0.624643 | −0.312322 | − | 0.949976i | \(-0.601107\pi\) | ||||
−0.312322 | + | 0.949976i | \(0.601107\pi\) | |||||||
\(368\) | −2.75090e11 | −0.781914 | ||||||||
\(369\) | −1.62816e11 | −0.457170 | ||||||||
\(370\) | −1.37558e10 | −0.0381574 | ||||||||
\(371\) | 7.98936e11 | 2.18942 | ||||||||
\(372\) | −1.09225e11 | −0.295718 | ||||||||
\(373\) | −3.00669e11 | −0.804265 | −0.402132 | − | 0.915581i | \(-0.631731\pi\) | ||||
−0.402132 | + | 0.915581i | \(0.631731\pi\) | |||||||
\(374\) | −1.13592e11 | −0.300211 | ||||||||
\(375\) | 1.89717e10 | 0.0495411 | ||||||||
\(376\) | 7.16070e11 | 1.84761 | ||||||||
\(377\) | −2.05189e11 | −0.523141 | ||||||||
\(378\) | 1.98284e11 | 0.499544 | ||||||||
\(379\) | 3.67439e11 | 0.914763 | 0.457381 | − | 0.889271i | \(-0.348787\pi\) | ||||
0.457381 | + | 0.889271i | \(0.348787\pi\) | |||||||
\(380\) | 5.29784e10 | 0.130338 | ||||||||
\(381\) | −3.64501e11 | −0.886209 | ||||||||
\(382\) | 1.48134e11 | 0.355935 | ||||||||
\(383\) | 3.85840e11 | 0.916247 | 0.458124 | − | 0.888888i | \(-0.348522\pi\) | ||||
0.458124 | + | 0.888888i | \(0.348522\pi\) | |||||||
\(384\) | 1.50090e11 | 0.352259 | ||||||||
\(385\) | −8.58222e9 | −0.0199079 | ||||||||
\(386\) | 1.28585e12 | 2.94814 | ||||||||
\(387\) | 8.54721e10 | 0.193698 | ||||||||
\(388\) | −1.75885e12 | −3.93992 | ||||||||
\(389\) | 4.01764e11 | 0.889606 | 0.444803 | − | 0.895628i | \(-0.353274\pi\) | ||||
0.444803 | + | 0.895628i | \(0.353274\pi\) | |||||||
\(390\) | −2.53304e10 | −0.0554436 | ||||||||
\(391\) | 6.42563e10 | 0.139034 | ||||||||
\(392\) | 1.21090e12 | 2.59013 | ||||||||
\(393\) | −2.07542e10 | −0.0438874 | ||||||||
\(394\) | 1.16768e12 | 2.44113 | ||||||||
\(395\) | 1.10722e10 | 0.0228848 | ||||||||
\(396\) | 1.35495e11 | 0.276883 | ||||||||
\(397\) | 1.01154e11 | 0.204374 | 0.102187 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102187 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(398\) | 5.23842e11 | 1.04647 | ||||||||
\(399\) | −4.95113e11 | −0.977973 | ||||||||
\(400\) | −1.38443e12 | −2.70396 | ||||||||
\(401\) | 2.50446e11 | 0.483687 | 0.241844 | − | 0.970315i | \(-0.422248\pi\) | ||||
0.241844 | + | 0.970315i | \(0.422248\pi\) | |||||||
\(402\) | −7.92685e11 | −1.51385 | ||||||||
\(403\) | −1.30401e11 | −0.246269 | ||||||||
\(404\) | 9.27497e11 | 1.73219 | ||||||||
\(405\) | −2.58346e9 | −0.00477149 | ||||||||
\(406\) | −6.21043e11 | −1.13437 | ||||||||
\(407\) | 8.78478e10 | 0.158692 | ||||||||
\(408\) | −4.33182e11 | −0.773926 | ||||||||
\(409\) | 1.11159e12 | 1.96421 | 0.982106 | − | 0.188329i | \(-0.0603070\pi\) | ||||
0.982106 | + | 0.188329i | \(0.0603070\pi\) | |||||||
\(410\) | 6.29532e10 | 0.110025 | ||||||||
\(411\) | 5.85843e11 | 1.01273 | ||||||||
\(412\) | 3.62071e11 | 0.619094 | ||||||||
\(413\) | −1.06957e11 | −0.180899 | ||||||||
\(414\) | −1.07432e11 | −0.179734 | ||||||||
\(415\) | −3.29599e10 | −0.0545468 | ||||||||
\(416\) | 1.66543e12 | 2.72650 | ||||||||
\(417\) | 5.47042e11 | 0.885948 | ||||||||
\(418\) | −4.74223e11 | −0.759783 | ||||||||
\(419\) | 1.33843e11 | 0.212145 | 0.106072 | − | 0.994358i | \(-0.466173\pi\) | ||||
0.106072 | + | 0.994358i | \(0.466173\pi\) | |||||||
\(420\) | −5.46976e10 | −0.0857722 | ||||||||
\(421\) | 1.05335e12 | 1.63419 | 0.817095 | − | 0.576504i | \(-0.195583\pi\) | ||||
0.817095 | + | 0.576504i | \(0.195583\pi\) | |||||||
\(422\) | 1.09121e12 | 1.67495 | ||||||||
\(423\) | 1.45721e11 | 0.221305 | ||||||||
\(424\) | 2.91818e12 | 4.38496 | ||||||||
\(425\) | 3.23379e11 | 0.480797 | ||||||||
\(426\) | 5.96929e10 | 0.0878172 | ||||||||
\(427\) | 5.10470e11 | 0.743095 | ||||||||
\(428\) | 9.18406e11 | 1.32293 | ||||||||
\(429\) | 1.61765e11 | 0.230583 | ||||||||
\(430\) | −3.30481e10 | −0.0466163 | ||||||||
\(431\) | −1.21469e12 | −1.69558 | −0.847792 | − | 0.530330i | \(-0.822068\pi\) | ||||
−0.847792 | + | 0.530330i | \(0.822068\pi\) | |||||||
\(432\) | 3.77396e11 | 0.521339 | ||||||||
\(433\) | −4.80989e11 | −0.657567 | −0.328783 | − | 0.944405i | \(-0.606639\pi\) | ||||
−0.328783 | + | 0.944405i | \(0.606639\pi\) | |||||||
\(434\) | −3.94683e11 | −0.534004 | ||||||||
\(435\) | 8.09163e9 | 0.0108351 | ||||||||
\(436\) | −3.52546e12 | −4.67225 | ||||||||
\(437\) | 2.68256e11 | 0.351871 | ||||||||
\(438\) | 3.93018e11 | 0.510246 | ||||||||
\(439\) | 6.73221e11 | 0.865101 | 0.432551 | − | 0.901610i | \(-0.357614\pi\) | ||||
0.432551 | + | 0.901610i | \(0.357614\pi\) | |||||||
\(440\) | −3.13473e10 | −0.0398715 | ||||||||
\(441\) | 2.46421e11 | 0.310244 | ||||||||
\(442\) | −8.64327e11 | −1.07715 | ||||||||
\(443\) | −1.33274e12 | −1.64411 | −0.822054 | − | 0.569410i | \(-0.807172\pi\) | ||||
−0.822054 | + | 0.569410i | \(0.807172\pi\) | |||||||
\(444\) | 5.59886e11 | 0.683716 | ||||||||
\(445\) | −9.89278e9 | −0.0119591 | ||||||||
\(446\) | −1.17632e11 | −0.140773 | ||||||||
\(447\) | −6.98448e11 | −0.827466 | ||||||||
\(448\) | 1.83139e12 | 2.14797 | ||||||||
\(449\) | 9.05955e11 | 1.05196 | 0.525979 | − | 0.850498i | \(-0.323699\pi\) | ||||
0.525979 | + | 0.850498i | \(0.323699\pi\) | |||||||
\(450\) | −5.40665e11 | −0.621544 | ||||||||
\(451\) | −4.02033e11 | −0.457581 | ||||||||
\(452\) | −1.80899e12 | −2.03851 | ||||||||
\(453\) | −3.31362e11 | −0.369709 | ||||||||
\(454\) | −1.12823e12 | −1.24636 | ||||||||
\(455\) | −6.53024e10 | −0.0714296 | ||||||||
\(456\) | −1.80844e12 | −1.95868 | ||||||||
\(457\) | 1.69512e12 | 1.81793 | 0.908965 | − | 0.416872i | \(-0.136874\pi\) | ||||
0.908965 | + | 0.416872i | \(0.136874\pi\) | |||||||
\(458\) | −9.17337e11 | −0.974168 | ||||||||
\(459\) | −8.81532e10 | −0.0927003 | ||||||||
\(460\) | 2.96356e10 | 0.0308605 | ||||||||
\(461\) | 1.26008e12 | 1.29940 | 0.649702 | − | 0.760189i | \(-0.274894\pi\) | ||||
0.649702 | + | 0.760189i | \(0.274894\pi\) | |||||||
\(462\) | 4.89613e11 | 0.499993 | ||||||||
\(463\) | 5.71530e11 | 0.577996 | 0.288998 | − | 0.957330i | \(-0.406678\pi\) | ||||
0.288998 | + | 0.957330i | \(0.406678\pi\) | |||||||
\(464\) | −1.18204e12 | −1.18386 | ||||||||
\(465\) | 5.14237e9 | 0.00510064 | ||||||||
\(466\) | 3.49499e12 | 3.43328 | ||||||||
\(467\) | 1.03056e12 | 1.00264 | 0.501322 | − | 0.865261i | \(-0.332847\pi\) | ||||
0.501322 | + | 0.865261i | \(0.332847\pi\) | |||||||
\(468\) | 1.03099e12 | 0.993455 | ||||||||
\(469\) | −2.04356e12 | −1.95034 | ||||||||
\(470\) | −5.63436e10 | −0.0532604 | ||||||||
\(471\) | −3.03532e11 | −0.284191 | ||||||||
\(472\) | −3.90670e11 | −0.362302 | ||||||||
\(473\) | 2.11052e11 | 0.193872 | ||||||||
\(474\) | −6.31664e11 | −0.574756 | ||||||||
\(475\) | 1.35004e12 | 1.21682 | ||||||||
\(476\) | −1.86640e12 | −1.66638 | ||||||||
\(477\) | 5.93854e11 | 0.525227 | ||||||||
\(478\) | −1.85437e12 | −1.62469 | ||||||||
\(479\) | −1.20661e12 | −1.04727 | −0.523634 | − | 0.851943i | \(-0.675424\pi\) | ||||
−0.523634 | + | 0.851943i | \(0.675424\pi\) | |||||||
\(480\) | −6.56760e10 | −0.0564704 | ||||||||
\(481\) | 6.68437e11 | 0.569387 | ||||||||
\(482\) | 8.71056e11 | 0.735079 | ||||||||
\(483\) | −2.76962e11 | −0.231557 | ||||||||
\(484\) | −2.67118e12 | −2.21258 | ||||||||
\(485\) | 8.28080e10 | 0.0679571 | ||||||||
\(486\) | 1.47386e11 | 0.119837 | ||||||||
\(487\) | −1.26332e12 | −1.01773 | −0.508867 | − | 0.860845i | \(-0.669935\pi\) | ||||
−0.508867 | + | 0.860845i | \(0.669935\pi\) | |||||||
\(488\) | 1.86453e12 | 1.48827 | ||||||||
\(489\) | 1.31644e11 | 0.104115 | ||||||||
\(490\) | −9.52793e10 | −0.0746649 | ||||||||
\(491\) | −7.81392e11 | −0.606740 | −0.303370 | − | 0.952873i | \(-0.598112\pi\) | ||||
−0.303370 | + | 0.952873i | \(0.598112\pi\) | |||||||
\(492\) | −2.56230e12 | −1.97146 | ||||||||
\(493\) | 2.76104e11 | 0.210505 | ||||||||
\(494\) | −3.60838e12 | −2.72610 | ||||||||
\(495\) | −6.37922e9 | −0.00477578 | ||||||||
\(496\) | −7.51205e11 | −0.557302 | ||||||||
\(497\) | 1.53890e11 | 0.113137 | ||||||||
\(498\) | 1.88035e12 | 1.36996 | ||||||||
\(499\) | 2.09499e12 | 1.51262 | 0.756309 | − | 0.654215i | \(-0.227001\pi\) | ||||
0.756309 | + | 0.654215i | \(0.227001\pi\) | |||||||
\(500\) | 2.98566e11 | 0.213636 | ||||||||
\(501\) | −7.03498e11 | −0.498877 | ||||||||
\(502\) | 1.77287e12 | 1.24598 | ||||||||
\(503\) | −7.43670e11 | −0.517993 | −0.258997 | − | 0.965878i | \(-0.583392\pi\) | ||||
−0.258997 | + | 0.965878i | \(0.583392\pi\) | |||||||
\(504\) | 1.86713e12 | 1.28895 | ||||||||
\(505\) | −4.36672e10 | −0.0298775 | ||||||||
\(506\) | −2.65276e11 | −0.179896 | ||||||||
\(507\) | 3.71915e11 | 0.249981 | ||||||||
\(508\) | −5.73631e12 | −3.82161 | ||||||||
\(509\) | 2.21983e12 | 1.46585 | 0.732926 | − | 0.680308i | \(-0.238154\pi\) | ||||
0.732926 | + | 0.680308i | \(0.238154\pi\) | |||||||
\(510\) | 3.40847e10 | 0.0223097 | ||||||||
\(511\) | 1.01321e12 | 0.657364 | ||||||||
\(512\) | −2.12829e12 | −1.36872 | ||||||||
\(513\) | −3.68021e11 | −0.234609 | ||||||||
\(514\) | −4.60450e12 | −2.90970 | ||||||||
\(515\) | −1.70465e10 | −0.0106783 | ||||||||
\(516\) | 1.34511e12 | 0.835285 | ||||||||
\(517\) | 3.59823e11 | 0.221504 | ||||||||
\(518\) | 2.02315e12 | 1.23465 | ||||||||
\(519\) | −4.51343e11 | −0.273057 | ||||||||
\(520\) | −2.38522e11 | −0.143059 | ||||||||
\(521\) | 8.40218e9 | 0.00499600 | 0.00249800 | − | 0.999997i | \(-0.499205\pi\) | ||||
0.00249800 | + | 0.999997i | \(0.499205\pi\) | |||||||
\(522\) | −4.61625e11 | −0.272127 | ||||||||
\(523\) | 2.60435e12 | 1.52209 | 0.761047 | − | 0.648697i | \(-0.224686\pi\) | ||||
0.761047 | + | 0.648697i | \(0.224686\pi\) | |||||||
\(524\) | −3.26618e11 | −0.189256 | ||||||||
\(525\) | −1.39385e12 | −0.800753 | ||||||||
\(526\) | −6.39261e12 | −3.64118 | ||||||||
\(527\) | 1.75469e11 | 0.0990950 | ||||||||
\(528\) | 9.31885e11 | 0.521807 | ||||||||
\(529\) | −1.65109e12 | −0.916687 | ||||||||
\(530\) | −2.29616e11 | −0.126404 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −7.79182e12 | −4.21732 | ||||||||
\(533\) | −3.05909e12 | −1.64180 | ||||||||
\(534\) | 5.64379e11 | 0.300355 | ||||||||
\(535\) | −4.32392e10 | −0.0228184 | ||||||||
\(536\) | −7.46429e12 | −3.90613 | ||||||||
\(537\) | 2.29630e11 | 0.119164 | ||||||||
\(538\) | −1.69745e12 | −0.873526 | ||||||||
\(539\) | 6.08475e11 | 0.310523 | ||||||||
\(540\) | −4.06571e10 | −0.0205761 | ||||||||
\(541\) | 8.34995e11 | 0.419079 | 0.209540 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209540 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(542\) | −1.56452e12 | −0.778724 | ||||||||
\(543\) | −5.52171e10 | −0.0272568 | ||||||||
\(544\) | −2.24101e12 | −1.09710 | ||||||||
\(545\) | 1.65981e11 | 0.0805887 | ||||||||
\(546\) | 3.72548e12 | 1.79397 | ||||||||
\(547\) | −6.95891e11 | −0.332352 | −0.166176 | − | 0.986096i | \(-0.553142\pi\) | ||||
−0.166176 | + | 0.986096i | \(0.553142\pi\) | |||||||
\(548\) | 9.21967e12 | 4.36720 | ||||||||
\(549\) | 3.79435e11 | 0.178263 | ||||||||
\(550\) | −1.33504e12 | −0.622102 | ||||||||
\(551\) | 1.15268e12 | 0.532752 | ||||||||
\(552\) | −1.01163e12 | −0.463761 | ||||||||
\(553\) | −1.62845e12 | −0.740476 | ||||||||
\(554\) | 3.68667e12 | 1.66280 | ||||||||
\(555\) | −2.63598e10 | −0.0117930 | ||||||||
\(556\) | 8.60904e12 | 3.82048 | ||||||||
\(557\) | 1.76865e12 | 0.778562 | 0.389281 | − | 0.921119i | \(-0.372724\pi\) | ||||
0.389281 | + | 0.921119i | \(0.372724\pi\) | |||||||
\(558\) | −2.93370e11 | −0.128104 | ||||||||
\(559\) | 1.60590e12 | 0.695611 | ||||||||
\(560\) | −3.76189e11 | −0.161644 | ||||||||
\(561\) | −2.17673e11 | −0.0927835 | ||||||||
\(562\) | −3.66617e12 | −1.55024 | ||||||||
\(563\) | 2.10069e12 | 0.881201 | 0.440600 | − | 0.897703i | \(-0.354766\pi\) | ||||
0.440600 | + | 0.897703i | \(0.354766\pi\) | |||||||
\(564\) | 2.29328e12 | 0.954336 | ||||||||
\(565\) | 8.51683e10 | 0.0351609 | ||||||||
\(566\) | 1.48684e12 | 0.608962 | ||||||||
\(567\) | 3.79964e11 | 0.154390 | ||||||||
\(568\) | 5.62096e11 | 0.226591 | ||||||||
\(569\) | 1.35737e12 | 0.542867 | 0.271434 | − | 0.962457i | \(-0.412502\pi\) | ||||
0.271434 | + | 0.962457i | \(0.412502\pi\) | |||||||
\(570\) | 1.42296e11 | 0.0564621 | ||||||||
\(571\) | 3.13960e12 | 1.23598 | 0.617991 | − | 0.786185i | \(-0.287947\pi\) | ||||
0.617991 | + | 0.786185i | \(0.287947\pi\) | |||||||
\(572\) | 2.54577e12 | 0.994347 | ||||||||
\(573\) | 2.83864e11 | 0.110006 | ||||||||
\(574\) | −9.25888e12 | −3.56004 | ||||||||
\(575\) | 7.55198e11 | 0.288108 | ||||||||
\(576\) | 1.36128e12 | 0.515284 | ||||||||
\(577\) | 2.09516e12 | 0.786913 | 0.393456 | − | 0.919343i | \(-0.371279\pi\) | ||||
0.393456 | + | 0.919343i | \(0.371279\pi\) | |||||||
\(578\) | −3.84964e12 | −1.43465 | ||||||||
\(579\) | 2.46403e12 | 0.911156 | ||||||||
\(580\) | 1.27342e11 | 0.0467245 | ||||||||
\(581\) | 4.84759e12 | 1.76496 | ||||||||
\(582\) | −4.72417e12 | −1.70676 | ||||||||
\(583\) | 1.46638e12 | 0.525699 | ||||||||
\(584\) | 3.70084e12 | 1.31657 | ||||||||
\(585\) | −4.85397e10 | −0.0171355 | ||||||||
\(586\) | 7.74014e12 | 2.71150 | ||||||||
\(587\) | 4.64609e12 | 1.61516 | 0.807581 | − | 0.589757i | \(-0.200776\pi\) | ||||
0.807581 | + | 0.589757i | \(0.200776\pi\) | |||||||
\(588\) | 3.87803e12 | 1.33787 | ||||||||
\(589\) | 7.32545e11 | 0.250793 | ||||||||
\(590\) | 3.07397e10 | 0.0104440 | ||||||||
\(591\) | 2.23758e12 | 0.754458 | ||||||||
\(592\) | 3.85067e12 | 1.28851 | ||||||||
\(593\) | 4.34209e12 | 1.44196 | 0.720979 | − | 0.692957i | \(-0.243693\pi\) | ||||
0.720979 | + | 0.692957i | \(0.243693\pi\) | |||||||
\(594\) | 3.63932e11 | 0.119945 | ||||||||
\(595\) | 8.78713e10 | 0.0287423 | ||||||||
\(596\) | −1.09918e13 | −3.56829 | ||||||||
\(597\) | 1.00382e12 | 0.323423 | ||||||||
\(598\) | −2.01849e12 | −0.645464 | ||||||||
\(599\) | 4.84567e12 | 1.53792 | 0.768958 | − | 0.639299i | \(-0.220775\pi\) | ||||
0.768958 | + | 0.639299i | \(0.220775\pi\) | |||||||
\(600\) | −5.09115e12 | −1.60374 | ||||||||
\(601\) | −2.85729e12 | −0.893344 | −0.446672 | − | 0.894698i | \(-0.647391\pi\) | ||||
−0.446672 | + | 0.894698i | \(0.647391\pi\) | |||||||
\(602\) | 4.86056e12 | 1.50835 | ||||||||
\(603\) | −1.51899e12 | −0.467873 | ||||||||
\(604\) | −5.21478e12 | −1.59430 | ||||||||
\(605\) | 1.25761e11 | 0.0381634 | ||||||||
\(606\) | 2.49120e12 | 0.750380 | ||||||||
\(607\) | −6.02059e11 | −0.180007 | −0.0900036 | − | 0.995941i | \(-0.528688\pi\) | ||||
−0.0900036 | + | 0.995941i | \(0.528688\pi\) | |||||||
\(608\) | −9.35572e12 | −2.77659 | ||||||||
\(609\) | −1.19008e12 | −0.350589 | ||||||||
\(610\) | −1.46710e11 | −0.0429017 | ||||||||
\(611\) | 2.73790e12 | 0.794754 | ||||||||
\(612\) | −1.38731e12 | −0.399752 | ||||||||
\(613\) | −3.72672e12 | −1.06599 | −0.532997 | − | 0.846117i | \(-0.678934\pi\) | ||||
−0.532997 | + | 0.846117i | \(0.678934\pi\) | |||||||
\(614\) | −5.50040e12 | −1.56184 | ||||||||
\(615\) | 1.20635e11 | 0.0340044 | ||||||||
\(616\) | 4.61041e12 | 1.29011 | ||||||||
\(617\) | −5.71905e12 | −1.58869 | −0.794347 | − | 0.607464i | \(-0.792187\pi\) | ||||
−0.794347 | + | 0.607464i | \(0.792187\pi\) | |||||||
\(618\) | 9.72500e11 | 0.268189 | ||||||||
\(619\) | −2.32367e12 | −0.636159 | −0.318080 | − | 0.948064i | \(-0.603038\pi\) | ||||
−0.318080 | + | 0.948064i | \(0.603038\pi\) | |||||||
\(620\) | 8.09277e10 | 0.0219955 | ||||||||
\(621\) | −2.05867e11 | −0.0555489 | ||||||||
\(622\) | 9.99929e12 | 2.67863 | ||||||||
\(623\) | 1.45499e12 | 0.386957 | ||||||||
\(624\) | 7.09075e12 | 1.87224 | ||||||||
\(625\) | 3.79361e12 | 0.994471 | ||||||||
\(626\) | −8.86410e12 | −2.30701 | ||||||||
\(627\) | −9.08737e11 | −0.234820 | ||||||||
\(628\) | −4.77682e12 | −1.22552 | ||||||||
\(629\) | −8.99453e11 | −0.229113 | ||||||||
\(630\) | −1.46914e11 | −0.0371562 | ||||||||
\(631\) | −4.04352e12 | −1.01538 | −0.507689 | − | 0.861541i | \(-0.669500\pi\) | ||||
−0.507689 | + | 0.861541i | \(0.669500\pi\) | |||||||
\(632\) | −5.94804e12 | −1.48302 | ||||||||
\(633\) | 2.09104e12 | 0.517661 | ||||||||
\(634\) | 8.53070e12 | 2.09693 | ||||||||
\(635\) | 2.70069e11 | 0.0659164 | ||||||||
\(636\) | 9.34575e12 | 2.26494 | ||||||||
\(637\) | 4.62991e12 | 1.11415 | ||||||||
\(638\) | −1.13987e12 | −0.272371 | ||||||||
\(639\) | 1.14387e11 | 0.0271409 | ||||||||
\(640\) | −1.11206e11 | −0.0262011 | ||||||||
\(641\) | 8.23067e11 | 0.192563 | 0.0962817 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962817 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(642\) | 2.46678e12 | 0.573090 | ||||||||
\(643\) | 2.70737e12 | 0.624594 | 0.312297 | − | 0.949985i | \(-0.398902\pi\) | ||||
0.312297 | + | 0.949985i | \(0.398902\pi\) | |||||||
\(644\) | −4.35867e12 | −0.998545 | ||||||||
\(645\) | −6.33288e10 | −0.0144073 | ||||||||
\(646\) | 4.85546e12 | 1.09694 | ||||||||
\(647\) | 5.65228e12 | 1.26810 | 0.634051 | − | 0.773291i | \(-0.281391\pi\) | ||||
0.634051 | + | 0.773291i | \(0.281391\pi\) | |||||||
\(648\) | 1.38785e12 | 0.309211 | ||||||||
\(649\) | −1.96311e11 | −0.0434353 | ||||||||
\(650\) | −1.01584e13 | −2.23210 | ||||||||
\(651\) | −7.56317e11 | −0.165040 | ||||||||
\(652\) | 2.07174e12 | 0.448974 | ||||||||
\(653\) | −5.64503e11 | −0.121495 | −0.0607473 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607473 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(654\) | −9.46915e12 | −2.02400 | ||||||||
\(655\) | 1.53774e10 | 0.00326435 | ||||||||
\(656\) | −1.76225e13 | −3.71536 | ||||||||
\(657\) | 7.53127e11 | 0.157697 | ||||||||
\(658\) | 8.28677e12 | 1.72333 | ||||||||
\(659\) | 8.34085e11 | 0.172276 | 0.0861382 | − | 0.996283i | \(-0.472547\pi\) | ||||
0.0861382 | + | 0.996283i | \(0.472547\pi\) | |||||||
\(660\) | −1.00393e11 | −0.0205946 | ||||||||
\(661\) | −4.09602e12 | −0.834555 | −0.417278 | − | 0.908779i | \(-0.637016\pi\) | ||||
−0.417278 | + | 0.908779i | \(0.637016\pi\) | |||||||
\(662\) | −1.40340e13 | −2.84001 | ||||||||
\(663\) | −1.65628e12 | −0.332907 | ||||||||
\(664\) | 1.77062e13 | 3.53484 | ||||||||
\(665\) | 3.66844e11 | 0.0727418 | ||||||||
\(666\) | 1.50382e12 | 0.296184 | ||||||||
\(667\) | 6.44796e11 | 0.126141 | ||||||||
\(668\) | −1.10713e13 | −2.15131 | ||||||||
\(669\) | −2.25414e11 | −0.0435075 | ||||||||
\(670\) | 5.87324e11 | 0.112601 | ||||||||
\(671\) | 9.36921e11 | 0.178423 | ||||||||
\(672\) | 9.65933e12 | 1.82720 | ||||||||
\(673\) | 6.26288e12 | 1.17681 | 0.588405 | − | 0.808566i | \(-0.299756\pi\) | ||||
0.588405 | + | 0.808566i | \(0.299756\pi\) | |||||||
\(674\) | −2.32898e12 | −0.434707 | ||||||||
\(675\) | −1.03606e12 | −0.192095 | ||||||||
\(676\) | 5.85299e12 | 1.07800 | ||||||||
\(677\) | 5.43978e11 | 0.0995250 | 0.0497625 | − | 0.998761i | \(-0.484154\pi\) | ||||
0.0497625 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(678\) | −4.85882e12 | −0.883075 | ||||||||
\(679\) | −1.21790e13 | −2.19887 | ||||||||
\(680\) | 3.20957e11 | 0.0575648 | ||||||||
\(681\) | −2.16198e12 | −0.385203 | ||||||||
\(682\) | −7.24406e11 | −0.128219 | ||||||||
\(683\) | −7.39909e12 | −1.30102 | −0.650512 | − | 0.759496i | \(-0.725446\pi\) | ||||
−0.650512 | + | 0.759496i | \(0.725446\pi\) | |||||||
\(684\) | −5.79171e12 | −1.01171 | ||||||||
\(685\) | −4.34068e11 | −0.0753269 | ||||||||
\(686\) | −1.04291e12 | −0.179799 | ||||||||
\(687\) | −1.75786e12 | −0.301078 | ||||||||
\(688\) | 9.25116e12 | 1.57416 | ||||||||
\(689\) | 1.11577e13 | 1.88620 | ||||||||
\(690\) | 7.95993e10 | 0.0133687 | ||||||||
\(691\) | −4.12021e12 | −0.687493 | −0.343746 | − | 0.939063i | \(-0.611696\pi\) | ||||
−0.343746 | + | 0.939063i | \(0.611696\pi\) | |||||||
\(692\) | −7.10298e12 | −1.17751 | ||||||||
\(693\) | 9.38227e11 | 0.154528 | ||||||||
\(694\) | −1.31682e13 | −2.15482 | ||||||||
\(695\) | −4.05319e11 | −0.0658970 | ||||||||
\(696\) | −4.34687e12 | −0.702158 | ||||||||
\(697\) | 4.11632e12 | 0.660636 | ||||||||
\(698\) | −1.34899e13 | −2.15110 | ||||||||
\(699\) | 6.69733e12 | 1.06109 | ||||||||
\(700\) | −2.19356e13 | −3.45310 | ||||||||
\(701\) | −1.38815e12 | −0.217123 | −0.108561 | − | 0.994090i | \(-0.534624\pi\) | ||||
−0.108561 | + | 0.994090i | \(0.534624\pi\) | |||||||
\(702\) | 2.76917e12 | 0.430361 | ||||||||
\(703\) | −3.75502e12 | −0.579847 | ||||||||
\(704\) | 3.36135e12 | 0.515746 | ||||||||
\(705\) | −1.07969e11 | −0.0164607 | ||||||||
\(706\) | −5.65253e12 | −0.856292 | ||||||||
\(707\) | 6.42237e12 | 0.966737 | ||||||||
\(708\) | −1.25116e12 | −0.187138 | ||||||||
\(709\) | −6.66867e12 | −0.991131 | −0.495565 | − | 0.868571i | \(-0.665039\pi\) | ||||
−0.495565 | + | 0.868571i | \(0.665039\pi\) | |||||||
\(710\) | −4.42282e10 | −0.00653186 | ||||||||
\(711\) | −1.21044e12 | −0.177635 | ||||||||
\(712\) | 5.31445e12 | 0.774994 | ||||||||
\(713\) | 4.09778e11 | 0.0593808 | ||||||||
\(714\) | −5.01303e12 | −0.721869 | ||||||||
\(715\) | −1.19857e11 | −0.0171508 | ||||||||
\(716\) | 3.61379e12 | 0.513871 | ||||||||
\(717\) | −3.55346e12 | −0.502129 | ||||||||
\(718\) | −6.84568e12 | −0.961294 | ||||||||
\(719\) | −1.00413e12 | −0.140123 | −0.0700616 | − | 0.997543i | \(-0.522320\pi\) | ||||
−0.0700616 | + | 0.997543i | \(0.522320\pi\) | |||||||
\(720\) | −2.79623e11 | −0.0387773 | ||||||||
\(721\) | 2.50713e12 | 0.345516 | ||||||||
\(722\) | 6.63059e12 | 0.908102 | ||||||||
\(723\) | 1.66917e12 | 0.227185 | ||||||||
\(724\) | −8.68976e11 | −0.117540 | ||||||||
\(725\) | 3.24502e12 | 0.436211 | ||||||||
\(726\) | −7.17462e12 | −0.958482 | ||||||||
\(727\) | 1.41169e13 | 1.87428 | 0.937139 | − | 0.348958i | \(-0.113464\pi\) | ||||
0.937139 | + | 0.348958i | \(0.113464\pi\) | |||||||
\(728\) | 3.50808e13 | 4.62891 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −2.91199e11 | −0.0379522 | ||||||||
\(731\) | −2.16091e12 | −0.279904 | ||||||||
\(732\) | 5.97134e12 | 0.768727 | ||||||||
\(733\) | 7.89551e12 | 1.01021 | 0.505106 | − | 0.863057i | \(-0.331453\pi\) | ||||
0.505106 | + | 0.863057i | \(0.331453\pi\) | |||||||
\(734\) | −9.17612e12 | −1.16688 | ||||||||
\(735\) | −1.82580e11 | −0.0230760 | ||||||||
\(736\) | −5.23350e12 | −0.657419 | ||||||||
\(737\) | −3.75078e12 | −0.468293 | ||||||||
\(738\) | −6.88218e12 | −0.854029 | ||||||||
\(739\) | 5.28001e12 | 0.651231 | 0.325615 | − | 0.945502i | \(-0.394429\pi\) | ||||
0.325615 | + | 0.945502i | \(0.394429\pi\) | |||||||
\(740\) | −4.14836e11 | −0.0508550 | ||||||||
\(741\) | −6.91461e12 | −0.842531 | ||||||||
\(742\) | 3.37708e13 | 4.09001 | ||||||||
\(743\) | 7.69938e12 | 0.926843 | 0.463422 | − | 0.886138i | \(-0.346622\pi\) | ||||
0.463422 | + | 0.886138i | \(0.346622\pi\) | |||||||
\(744\) | −2.76251e12 | −0.330541 | ||||||||
\(745\) | 5.17501e11 | 0.0615471 | ||||||||
\(746\) | −1.27092e13 | −1.50243 | ||||||||
\(747\) | 3.60325e12 | 0.423401 | ||||||||
\(748\) | −3.42561e12 | −0.400111 | ||||||||
\(749\) | 6.35943e12 | 0.738329 | ||||||||
\(750\) | 8.01929e11 | 0.0925466 | ||||||||
\(751\) | −1.35739e13 | −1.55713 | −0.778563 | − | 0.627566i | \(-0.784051\pi\) | ||||
−0.778563 | + | 0.627566i | \(0.784051\pi\) | |||||||
\(752\) | 1.57723e13 | 1.79852 | ||||||||
\(753\) | 3.39728e12 | 0.385083 | ||||||||
\(754\) | −8.67330e12 | −0.977267 | ||||||||
\(755\) | 2.45516e11 | 0.0274991 | ||||||||
\(756\) | 5.97966e12 | 0.665776 | ||||||||
\(757\) | −9.32404e12 | −1.03198 | −0.515992 | − | 0.856594i | \(-0.672577\pi\) | ||||
−0.515992 | + | 0.856594i | \(0.672577\pi\) | |||||||
\(758\) | 1.55315e13 | 1.70885 | ||||||||
\(759\) | −5.08339e11 | −0.0555988 | ||||||||
\(760\) | 1.33993e12 | 0.145687 | ||||||||
\(761\) | −6.42108e12 | −0.694028 | −0.347014 | − | 0.937860i | \(-0.612804\pi\) | ||||
−0.347014 | + | 0.937860i | \(0.612804\pi\) | |||||||
\(762\) | −1.54074e13 | −1.65551 | ||||||||
\(763\) | −2.44117e13 | −2.60758 | ||||||||
\(764\) | 4.46729e12 | 0.474378 | ||||||||
\(765\) | 6.53153e10 | 0.00689507 | ||||||||
\(766\) | 1.63094e13 | 1.71162 | ||||||||
\(767\) | −1.49373e12 | −0.155845 | ||||||||
\(768\) | −2.26036e12 | −0.234451 | ||||||||
\(769\) | −5.58942e12 | −0.576366 | −0.288183 | − | 0.957575i | \(-0.593051\pi\) | ||||
−0.288183 | + | 0.957575i | \(0.593051\pi\) | |||||||
\(770\) | −3.62768e11 | −0.0371896 | ||||||||
\(771\) | −8.82344e12 | −0.899276 | ||||||||
\(772\) | 3.87776e13 | 3.92919 | ||||||||
\(773\) | 8.17454e12 | 0.823485 | 0.411742 | − | 0.911300i | \(-0.364920\pi\) | ||||
0.411742 | + | 0.911300i | \(0.364920\pi\) | |||||||
\(774\) | 3.61288e12 | 0.361843 | ||||||||
\(775\) | 2.06227e12 | 0.205346 | ||||||||
\(776\) | −4.44849e13 | −4.40388 | ||||||||
\(777\) | 3.87688e12 | 0.381582 | ||||||||
\(778\) | 1.69825e13 | 1.66185 | ||||||||
\(779\) | 1.71848e13 | 1.67196 | ||||||||
\(780\) | −7.63891e11 | −0.0738934 | ||||||||
\(781\) | 2.82451e11 | 0.0271653 | ||||||||
\(782\) | 2.71610e12 | 0.259726 | ||||||||
\(783\) | −8.84595e11 | −0.0841040 | ||||||||
\(784\) | 2.66716e13 | 2.52131 | ||||||||
\(785\) | 2.24896e11 | 0.0211382 | ||||||||
\(786\) | −8.77275e11 | −0.0819850 | ||||||||
\(787\) | −3.35172e12 | −0.311445 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(788\) | 3.52138e13 | 3.25346 | ||||||||
\(789\) | −1.22499e13 | −1.12535 | ||||||||
\(790\) | 4.68019e11 | 0.0427505 | ||||||||
\(791\) | −1.25262e13 | −1.13769 | ||||||||
\(792\) | 3.42695e12 | 0.309488 | ||||||||
\(793\) | 7.12907e12 | 0.640182 | ||||||||
\(794\) | 4.27575e12 | 0.381786 | ||||||||
\(795\) | −4.40004e11 | −0.0390665 | ||||||||
\(796\) | 1.57975e13 | 1.39470 | ||||||||
\(797\) | −1.48041e13 | −1.29963 | −0.649817 | − | 0.760091i | \(-0.725154\pi\) | ||||
−0.649817 | + | 0.760091i | \(0.725154\pi\) | |||||||
\(798\) | −2.09283e13 | −1.82693 | ||||||||
\(799\) | −3.68414e12 | −0.319798 | ||||||||
\(800\) | −2.63383e13 | −2.27344 | ||||||||
\(801\) | 1.08150e12 | 0.0928282 | ||||||||
\(802\) | 1.05863e13 | 0.903565 | ||||||||
\(803\) | 1.85966e12 | 0.157839 | ||||||||
\(804\) | −2.39051e13 | −2.01761 | ||||||||
\(805\) | 2.05209e11 | 0.0172233 | ||||||||
\(806\) | −5.51203e12 | −0.460049 | ||||||||
\(807\) | −3.25276e12 | −0.269973 | ||||||||
\(808\) | 2.34582e13 | 1.93617 | ||||||||
\(809\) | 1.05150e13 | 0.863058 | 0.431529 | − | 0.902099i | \(-0.357974\pi\) | ||||
0.431529 | + | 0.902099i | \(0.357974\pi\) | |||||||
\(810\) | −1.09202e11 | −0.00891352 | ||||||||
\(811\) | −2.07754e13 | −1.68638 | −0.843191 | − | 0.537615i | \(-0.819326\pi\) | ||||
−0.843191 | + | 0.537615i | \(0.819326\pi\) | |||||||
\(812\) | −1.87288e13 | −1.51185 | ||||||||
\(813\) | −2.99803e12 | −0.240673 | ||||||||
\(814\) | 3.71330e12 | 0.296449 | ||||||||
\(815\) | −9.75389e10 | −0.00774406 | ||||||||
\(816\) | −9.54135e12 | −0.753363 | ||||||||
\(817\) | −9.02136e12 | −0.708390 | ||||||||
\(818\) | 4.69865e13 | 3.66930 | ||||||||
\(819\) | 7.13900e12 | 0.554447 | ||||||||
\(820\) | 1.89849e12 | 0.146637 | ||||||||
\(821\) | 7.67497e12 | 0.589566 | 0.294783 | − | 0.955564i | \(-0.404753\pi\) | ||||
0.294783 | + | 0.955564i | \(0.404753\pi\) | |||||||
\(822\) | 2.47634e13 | 1.89185 | ||||||||
\(823\) | −9.08768e12 | −0.690484 | −0.345242 | − | 0.938514i | \(-0.612203\pi\) | ||||
−0.345242 | + | 0.938514i | \(0.612203\pi\) | |||||||
\(824\) | 9.15750e12 | 0.691997 | ||||||||
\(825\) | −2.55829e12 | −0.192268 | ||||||||
\(826\) | −4.52106e12 | −0.337932 | ||||||||
\(827\) | −1.56022e13 | −1.15988 | −0.579938 | − | 0.814660i | \(-0.696923\pi\) | ||||
−0.579938 | + | 0.814660i | \(0.696923\pi\) | |||||||
\(828\) | −3.23983e12 | −0.239544 | ||||||||
\(829\) | 2.64563e13 | 1.94551 | 0.972754 | − | 0.231840i | \(-0.0744747\pi\) | ||||
0.972754 | + | 0.231840i | \(0.0744747\pi\) | |||||||
\(830\) | −1.39321e12 | −0.101898 | ||||||||
\(831\) | 7.06464e12 | 0.513908 | ||||||||
\(832\) | 2.55766e13 | 1.85049 | ||||||||
\(833\) | −6.23003e12 | −0.448320 | ||||||||
\(834\) | 2.31233e13 | 1.65502 | ||||||||
\(835\) | 5.21243e11 | 0.0371066 | ||||||||
\(836\) | −1.43012e13 | −1.01261 | ||||||||
\(837\) | −5.62175e11 | −0.0395920 | ||||||||
\(838\) | 5.65750e12 | 0.396302 | ||||||||
\(839\) | 8.86025e12 | 0.617329 | 0.308665 | − | 0.951171i | \(-0.400118\pi\) | ||||
0.308665 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(840\) | −1.38341e12 | −0.0958726 | ||||||||
\(841\) | −1.17365e13 | −0.809016 | ||||||||
\(842\) | 4.45248e13 | 3.05279 | ||||||||
\(843\) | −7.02534e12 | −0.479119 | ||||||||
\(844\) | 3.29076e13 | 2.23231 | ||||||||
\(845\) | −2.75563e11 | −0.0185937 | ||||||||
\(846\) | 6.15961e12 | 0.413415 | ||||||||
\(847\) | −1.84964e13 | −1.23484 | ||||||||
\(848\) | 6.42764e13 | 4.26845 | ||||||||
\(849\) | 2.84918e12 | 0.188207 | ||||||||
\(850\) | 1.36691e13 | 0.898165 | ||||||||
\(851\) | −2.10052e12 | −0.137292 | ||||||||
\(852\) | 1.80016e12 | 0.117040 | ||||||||
\(853\) | −1.33799e13 | −0.865332 | −0.432666 | − | 0.901554i | \(-0.642427\pi\) | ||||
−0.432666 | + | 0.901554i | \(0.642427\pi\) | |||||||
\(854\) | 2.15774e13 | 1.38816 | ||||||||
\(855\) | 2.72678e11 | 0.0174503 | ||||||||
\(856\) | 2.32283e13 | 1.47872 | ||||||||
\(857\) | −7.75808e12 | −0.491293 | −0.245646 | − | 0.969360i | \(-0.579000\pi\) | ||||
−0.245646 | + | 0.969360i | \(0.579000\pi\) | |||||||
\(858\) | 6.83779e12 | 0.430748 | ||||||||
\(859\) | −1.43176e13 | −0.897222 | −0.448611 | − | 0.893727i | \(-0.648081\pi\) | ||||
−0.448611 | + | 0.893727i | \(0.648081\pi\) | |||||||
\(860\) | −9.96633e11 | −0.0621287 | ||||||||
\(861\) | −1.77425e13 | −1.10027 | ||||||||
\(862\) | −5.13448e13 | −3.16748 | ||||||||
\(863\) | 6.99759e12 | 0.429437 | 0.214719 | − | 0.976676i | \(-0.431117\pi\) | ||||
0.214719 | + | 0.976676i | \(0.431117\pi\) | |||||||
\(864\) | 7.17984e12 | 0.438332 | ||||||||
\(865\) | 3.34413e11 | 0.0203100 | ||||||||
\(866\) | −2.03313e13 | −1.22839 | ||||||||
\(867\) | −7.37692e12 | −0.443393 | ||||||||
\(868\) | −1.19025e13 | −0.711703 | ||||||||
\(869\) | −2.98887e12 | −0.177794 | ||||||||
\(870\) | 3.42031e11 | 0.0202409 | ||||||||
\(871\) | −2.85398e13 | −1.68023 | ||||||||
\(872\) | −8.91659e13 | −5.22245 | ||||||||
\(873\) | −9.05275e12 | −0.527493 | ||||||||
\(874\) | 1.13391e13 | 0.657323 | ||||||||
\(875\) | 2.06739e12 | 0.119230 | ||||||||
\(876\) | 1.18523e13 | 0.680039 | ||||||||
\(877\) | 3.15194e13 | 1.79920 | 0.899600 | − | 0.436714i | \(-0.143858\pi\) | ||||
0.899600 | + | 0.436714i | \(0.143858\pi\) | |||||||
\(878\) | 2.84569e13 | 1.61608 | ||||||||
\(879\) | 1.48321e13 | 0.838019 | ||||||||
\(880\) | −6.90461e11 | −0.0388121 | ||||||||
\(881\) | −1.72449e13 | −0.964424 | −0.482212 | − | 0.876055i | \(-0.660166\pi\) | ||||
−0.482212 | + | 0.876055i | \(0.660166\pi\) | |||||||
\(882\) | 1.04161e13 | 0.579560 | ||||||||
\(883\) | −1.01246e13 | −0.560472 | −0.280236 | − | 0.959931i | \(-0.590413\pi\) | ||||
−0.280236 | + | 0.959931i | \(0.590413\pi\) | |||||||
\(884\) | −2.60656e13 | −1.43560 | ||||||||
\(885\) | 5.89054e10 | 0.00322783 | ||||||||
\(886\) | −5.63348e13 | −3.07132 | ||||||||
\(887\) | −1.50249e12 | −0.0814995 | −0.0407497 | − | 0.999169i | \(-0.512975\pi\) | ||||
−0.0407497 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(888\) | 1.41606e13 | 0.764230 | ||||||||
\(889\) | −3.97206e13 | −2.13284 | ||||||||
\(890\) | −4.18165e11 | −0.0223405 | ||||||||
\(891\) | 6.97390e11 | 0.0370703 | ||||||||
\(892\) | −3.54745e12 | −0.187618 | ||||||||
\(893\) | −1.53805e13 | −0.809355 | ||||||||
\(894\) | −2.95232e13 | −1.54577 | ||||||||
\(895\) | −1.70140e11 | −0.00886343 | ||||||||
\(896\) | 1.63557e13 | 0.847781 | ||||||||
\(897\) | −3.86797e12 | −0.199488 | ||||||||
\(898\) | 3.82945e13 | 1.96514 | ||||||||
\(899\) | 1.76078e12 | 0.0899057 | ||||||||
\(900\) | −1.63049e13 | −0.828374 | ||||||||
\(901\) | −1.50139e13 | −0.758982 | ||||||||
\(902\) | −1.69938e13 | −0.854796 | ||||||||
\(903\) | 9.31411e12 | 0.466172 | ||||||||
\(904\) | −4.57529e13 | −2.27856 | ||||||||
\(905\) | 4.09120e10 | 0.00202736 | ||||||||
\(906\) | −1.40066e13 | −0.690645 | ||||||||
\(907\) | 2.46747e13 | 1.21065 | 0.605326 | − | 0.795977i | \(-0.293043\pi\) | ||||
0.605326 | + | 0.795977i | \(0.293043\pi\) | |||||||
\(908\) | −3.40240e13 | −1.66111 | ||||||||
\(909\) | 4.77379e12 | 0.231913 | ||||||||
\(910\) | −2.76032e12 | −0.133436 | ||||||||
\(911\) | −2.96700e13 | −1.42720 | −0.713599 | − | 0.700554i | \(-0.752936\pi\) | ||||
−0.713599 | + | 0.700554i | \(0.752936\pi\) | |||||||
\(912\) | −3.98331e13 | −1.90663 | ||||||||
\(913\) | 8.89733e12 | 0.423781 | ||||||||
\(914\) | 7.16523e13 | 3.39603 | ||||||||
\(915\) | −2.81135e11 | −0.0132593 | ||||||||
\(916\) | −2.76642e13 | −1.29834 | ||||||||
\(917\) | −2.26164e12 | −0.105624 | ||||||||
\(918\) | −3.72622e12 | −0.173171 | ||||||||
\(919\) | −6.41468e11 | −0.0296658 | −0.0148329 | − | 0.999890i | \(-0.504722\pi\) | ||||
−0.0148329 | + | 0.999890i | \(0.504722\pi\) | |||||||
\(920\) | 7.49543e11 | 0.0344946 | ||||||||
\(921\) | −1.05402e13 | −0.482704 | ||||||||
\(922\) | 5.32633e13 | 2.42739 | ||||||||
\(923\) | 2.14918e12 | 0.0974688 | ||||||||
\(924\) | 1.47653e13 | 0.666374 | ||||||||
\(925\) | −1.05712e13 | −0.474773 | ||||||||
\(926\) | 2.41584e13 | 1.07974 | ||||||||
\(927\) | 1.86357e12 | 0.0828869 | ||||||||
\(928\) | −2.24879e13 | −0.995367 | ||||||||
\(929\) | 2.78508e13 | 1.22678 | 0.613391 | − | 0.789779i | \(-0.289805\pi\) | ||||
0.613391 | + | 0.789779i | \(0.289805\pi\) | |||||||
\(930\) | 2.17367e11 | 0.00952840 | ||||||||
\(931\) | −2.60091e13 | −1.13462 | ||||||||
\(932\) | 1.05399e14 | 4.57577 | ||||||||
\(933\) | 1.91613e13 | 0.827860 | ||||||||
\(934\) | 4.35614e13 | 1.87302 | ||||||||
\(935\) | 1.61280e11 | 0.00690126 | ||||||||
\(936\) | 2.60758e13 | 1.11044 | ||||||||
\(937\) | 2.19926e13 | 0.932071 | 0.466035 | − | 0.884766i | \(-0.345682\pi\) | ||||
0.466035 | + | 0.884766i | \(0.345682\pi\) | |||||||
\(938\) | −8.63810e13 | −3.64339 | ||||||||
\(939\) | −1.69859e13 | −0.713008 | ||||||||
\(940\) | −1.69916e12 | −0.0709837 | ||||||||
\(941\) | 3.39798e13 | 1.41276 | 0.706378 | − | 0.707835i | \(-0.250328\pi\) | ||||
0.706378 | + | 0.707835i | \(0.250328\pi\) | |||||||
\(942\) | −1.28302e13 | −0.530892 | ||||||||
\(943\) | 9.61300e12 | 0.395874 | ||||||||
\(944\) | −8.60498e12 | −0.352676 | ||||||||
\(945\) | −2.81526e11 | −0.0114835 | ||||||||
\(946\) | 8.92113e12 | 0.362168 | ||||||||
\(947\) | 3.01777e13 | 1.21930 | 0.609650 | − | 0.792671i | \(-0.291310\pi\) | ||||
0.609650 | + | 0.792671i | \(0.291310\pi\) | |||||||
\(948\) | −1.90492e13 | −0.766017 | ||||||||
\(949\) | 1.41502e13 | 0.566324 | ||||||||
\(950\) | 5.70658e13 | 2.27311 | ||||||||
\(951\) | 1.63471e13 | 0.648079 | ||||||||
\(952\) | −4.72050e13 | −1.86261 | ||||||||
\(953\) | 8.09006e12 | 0.317712 | 0.158856 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158856 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(954\) | 2.51021e13 | 0.981165 | ||||||||
\(955\) | −2.10323e11 | −0.00818224 | ||||||||
\(956\) | −5.59224e13 | −2.16534 | ||||||||
\(957\) | −2.18429e12 | −0.0841795 | ||||||||
\(958\) | −5.10032e13 | −1.95638 | ||||||||
\(959\) | 6.38408e13 | 2.43733 | ||||||||
\(960\) | −1.00861e12 | −0.0383269 | ||||||||
\(961\) | −2.53206e13 | −0.957677 | ||||||||
\(962\) | 2.82547e13 | 1.06366 | ||||||||
\(963\) | 4.72700e12 | 0.177120 | ||||||||
\(964\) | 2.62685e13 | 0.979690 | ||||||||
\(965\) | −1.82567e12 | −0.0677720 | ||||||||
\(966\) | −1.17071e13 | −0.432566 | ||||||||
\(967\) | 1.06043e13 | 0.389998 | 0.194999 | − | 0.980803i | \(-0.437530\pi\) | ||||
0.194999 | + | 0.980803i | \(0.437530\pi\) | |||||||
\(968\) | −6.75595e13 | −2.47313 | ||||||||
\(969\) | 9.30434e12 | 0.339023 | ||||||||
\(970\) | 3.50028e12 | 0.126949 | ||||||||
\(971\) | 3.83413e13 | 1.38414 | 0.692071 | − | 0.721830i | \(-0.256699\pi\) | ||||
0.692071 | + | 0.721830i | \(0.256699\pi\) | |||||||
\(972\) | 4.44472e12 | 0.159715 | ||||||||
\(973\) | 5.96125e13 | 2.13221 | ||||||||
\(974\) | −5.34003e13 | −1.90120 | ||||||||
\(975\) | −1.94661e13 | −0.689855 | ||||||||
\(976\) | 4.10685e13 | 1.44872 | ||||||||
\(977\) | 1.97686e12 | 0.0694145 | 0.0347073 | − | 0.999398i | \(-0.488950\pi\) | ||||
0.0347073 | + | 0.999398i | \(0.488950\pi\) | |||||||
\(978\) | 5.56456e12 | 0.194494 | ||||||||
\(979\) | 2.67050e12 | 0.0929116 | ||||||||
\(980\) | −2.87335e12 | −0.0995109 | ||||||||
\(981\) | −1.81454e13 | −0.625541 | ||||||||
\(982\) | −3.30293e13 | −1.13344 | ||||||||
\(983\) | 5.58570e12 | 0.190804 | 0.0954019 | − | 0.995439i | \(-0.469586\pi\) | ||||
0.0954019 | + | 0.995439i | \(0.469586\pi\) | |||||||
\(984\) | −6.48058e13 | −2.20361 | ||||||||
\(985\) | −1.65789e12 | −0.0561168 | ||||||||
\(986\) | 1.16708e13 | 0.393239 | ||||||||
\(987\) | 1.58796e13 | 0.532615 | ||||||||
\(988\) | −1.08818e14 | −3.63325 | ||||||||
\(989\) | −5.04646e12 | −0.167727 | ||||||||
\(990\) | −2.69648e11 | −0.00892152 | ||||||||
\(991\) | −4.45379e10 | −0.00146689 | −0.000733447 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000733447 | 1.00000i | \(0.500233\pi\) | ||||||||
\(992\) | −1.42915e13 | −0.468569 | ||||||||
\(993\) | −2.68928e13 | −0.877738 | ||||||||
\(994\) | 6.50489e12 | 0.211350 | ||||||||
\(995\) | −7.43759e11 | −0.0240563 | ||||||||
\(996\) | 5.67059e13 | 1.82583 | ||||||||
\(997\) | −5.30115e13 | −1.69919 | −0.849595 | − | 0.527436i | \(-0.823154\pi\) | ||||
−0.849595 | + | 0.527436i | \(0.823154\pi\) | |||||||
\(998\) | 8.85547e13 | 2.82569 | ||||||||
\(999\) | 2.88171e12 | 0.0915389 |
(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 | 177.10.a.d.1.21 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.21 | ✓ | 22 | 1.1 | even | 1 | trivial |