Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(155\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76547 | −1.95548 | −0.977740 | − | 0.209819i | \(-0.932713\pi\) | ||||
−0.977740 | + | 0.209819i | \(0.932713\pi\) | |||||||
\(3\) | 1.71486 | 0.990075 | 0.495038 | − | 0.868872i | \(-0.335154\pi\) | ||||
0.495038 | + | 0.868872i | \(0.335154\pi\) | |||||||
\(4\) | 5.64781 | 2.82390 | ||||||||
\(5\) | −3.60382 | −1.61168 | −0.805839 | − | 0.592135i | \(-0.798285\pi\) | ||||
−0.805839 | + | 0.592135i | \(0.798285\pi\) | |||||||
\(6\) | −4.74239 | −1.93607 | ||||||||
\(7\) | −5.22895 | −1.97636 | −0.988178 | − | 0.153312i | \(-0.951006\pi\) | ||||
−0.988178 | + | 0.153312i | \(0.951006\pi\) | |||||||
\(8\) | −10.0879 | −3.56661 | ||||||||
\(9\) | −0.0592525 | −0.0197508 | ||||||||
\(10\) | 9.96624 | 3.15160 | ||||||||
\(11\) | 4.65816 | 1.40449 | 0.702244 | − | 0.711937i | \(-0.252182\pi\) | ||||
0.702244 | + | 0.711937i | \(0.252182\pi\) | |||||||
\(12\) | 9.68521 | 2.79588 | ||||||||
\(13\) | 3.15368 | 0.874675 | 0.437337 | − | 0.899298i | \(-0.355922\pi\) | ||||
0.437337 | + | 0.899298i | \(0.355922\pi\) | |||||||
\(14\) | 14.4605 | 3.86473 | ||||||||
\(15\) | −6.18005 | −1.59568 | ||||||||
\(16\) | 16.6021 | 4.15053 | ||||||||
\(17\) | −4.13977 | −1.00404 | −0.502020 | − | 0.864856i | \(-0.667410\pi\) | ||||
−0.502020 | + | 0.864856i | \(0.667410\pi\) | |||||||
\(18\) | 0.163861 | 0.0386224 | ||||||||
\(19\) | −3.95842 | −0.908123 | −0.454062 | − | 0.890970i | \(-0.650025\pi\) | ||||
−0.454062 | + | 0.890970i | \(0.650025\pi\) | |||||||
\(20\) | −20.3537 | −4.55122 | ||||||||
\(21\) | −8.96691 | −1.95674 | ||||||||
\(22\) | −12.8820 | −2.74645 | ||||||||
\(23\) | 3.55199 | 0.740640 | 0.370320 | − | 0.928904i | \(-0.379248\pi\) | ||||
0.370320 | + | 0.928904i | \(0.379248\pi\) | |||||||
\(24\) | −17.2993 | −3.53121 | ||||||||
\(25\) | 7.98751 | 1.59750 | ||||||||
\(26\) | −8.72141 | −1.71041 | ||||||||
\(27\) | −5.24619 | −1.00963 | ||||||||
\(28\) | −29.5321 | −5.58104 | ||||||||
\(29\) | −2.64348 | −0.490883 | −0.245441 | − | 0.969411i | \(-0.578933\pi\) | ||||
−0.245441 | + | 0.969411i | \(0.578933\pi\) | |||||||
\(30\) | 17.0907 | 3.12032 | ||||||||
\(31\) | 4.89331 | 0.878864 | 0.439432 | − | 0.898276i | \(-0.355180\pi\) | ||||
0.439432 | + | 0.898276i | \(0.355180\pi\) | |||||||
\(32\) | −25.7368 | −4.54967 | ||||||||
\(33\) | 7.98809 | 1.39055 | ||||||||
\(34\) | 11.4484 | 1.96338 | ||||||||
\(35\) | 18.8442 | 3.18525 | ||||||||
\(36\) | −0.334647 | −0.0557745 | ||||||||
\(37\) | 0.163772 | 0.0269240 | 0.0134620 | − | 0.999909i | \(-0.495715\pi\) | ||||
0.0134620 | + | 0.999909i | \(0.495715\pi\) | |||||||
\(38\) | 10.9469 | 1.77582 | ||||||||
\(39\) | 5.40813 | 0.865994 | ||||||||
\(40\) | 36.3550 | 5.74822 | ||||||||
\(41\) | 4.13772 | 0.646203 | 0.323101 | − | 0.946364i | \(-0.395275\pi\) | ||||
0.323101 | + | 0.946364i | \(0.395275\pi\) | |||||||
\(42\) | 24.7977 | 3.82637 | ||||||||
\(43\) | −4.26841 | −0.650927 | −0.325463 | − | 0.945555i | \(-0.605520\pi\) | ||||
−0.325463 | + | 0.945555i | \(0.605520\pi\) | |||||||
\(44\) | 26.3084 | 3.96614 | ||||||||
\(45\) | 0.213535 | 0.0318320 | ||||||||
\(46\) | −9.82290 | −1.44831 | ||||||||
\(47\) | −10.6972 | −1.56035 | −0.780177 | − | 0.625559i | \(-0.784871\pi\) | ||||
−0.780177 | + | 0.625559i | \(0.784871\pi\) | |||||||
\(48\) | 28.4703 | 4.10934 | ||||||||
\(49\) | 20.3419 | 2.90598 | ||||||||
\(50\) | −22.0892 | −3.12389 | ||||||||
\(51\) | −7.09912 | −0.994076 | ||||||||
\(52\) | 17.8114 | 2.47000 | ||||||||
\(53\) | 9.86100 | 1.35451 | 0.677256 | − | 0.735747i | \(-0.263169\pi\) | ||||
0.677256 | + | 0.735747i | \(0.263169\pi\) | |||||||
\(54\) | 14.5082 | 1.97431 | ||||||||
\(55\) | −16.7872 | −2.26358 | ||||||||
\(56\) | 52.7491 | 7.04889 | ||||||||
\(57\) | −6.78813 | −0.899110 | ||||||||
\(58\) | 7.31047 | 0.959912 | ||||||||
\(59\) | −3.58420 | −0.466623 | −0.233312 | − | 0.972402i | \(-0.574956\pi\) | ||||
−0.233312 | + | 0.972402i | \(0.574956\pi\) | |||||||
\(60\) | −34.9037 | −4.50605 | ||||||||
\(61\) | −7.46176 | −0.955380 | −0.477690 | − | 0.878528i | \(-0.658526\pi\) | ||||
−0.477690 | + | 0.878528i | \(0.658526\pi\) | |||||||
\(62\) | −13.5323 | −1.71860 | ||||||||
\(63\) | 0.309828 | 0.0390347 | ||||||||
\(64\) | 37.9702 | 4.74627 | ||||||||
\(65\) | −11.3653 | −1.40969 | ||||||||
\(66\) | −22.0908 | −2.71919 | ||||||||
\(67\) | 4.54903 | 0.555753 | 0.277876 | − | 0.960617i | \(-0.410369\pi\) | ||||
0.277876 | + | 0.960617i | \(0.410369\pi\) | |||||||
\(68\) | −23.3806 | −2.83532 | ||||||||
\(69\) | 6.09116 | 0.733290 | ||||||||
\(70\) | −52.1129 | −6.22869 | ||||||||
\(71\) | 1.00000 | 0.118678 | ||||||||
\(72\) | 0.597733 | 0.0704435 | ||||||||
\(73\) | 12.6498 | 1.48055 | 0.740275 | − | 0.672304i | \(-0.234695\pi\) | ||||
0.740275 | + | 0.672304i | \(0.234695\pi\) | |||||||
\(74\) | −0.452906 | −0.0526493 | ||||||||
\(75\) | 13.6975 | 1.58165 | ||||||||
\(76\) | −22.3564 | −2.56445 | ||||||||
\(77\) | −24.3573 | −2.77577 | ||||||||
\(78\) | −14.9560 | −1.69343 | ||||||||
\(79\) | 12.5963 | 1.41720 | 0.708598 | − | 0.705613i | \(-0.249328\pi\) | ||||
0.708598 | + | 0.705613i | \(0.249328\pi\) | |||||||
\(80\) | −59.8311 | −6.68932 | ||||||||
\(81\) | −8.81873 | −0.979859 | ||||||||
\(82\) | −11.4427 | −1.26364 | ||||||||
\(83\) | 3.80676 | 0.417846 | 0.208923 | − | 0.977932i | \(-0.433004\pi\) | ||||
0.208923 | + | 0.977932i | \(0.433004\pi\) | |||||||
\(84\) | −50.6434 | −5.52565 | ||||||||
\(85\) | 14.9190 | 1.61819 | ||||||||
\(86\) | 11.8042 | 1.27287 | ||||||||
\(87\) | −4.53321 | −0.486011 | ||||||||
\(88\) | −46.9910 | −5.00926 | ||||||||
\(89\) | −8.70056 | −0.922258 | −0.461129 | − | 0.887333i | \(-0.652555\pi\) | ||||
−0.461129 | + | 0.887333i | \(0.652555\pi\) | |||||||
\(90\) | −0.590525 | −0.0622468 | ||||||||
\(91\) | −16.4904 | −1.72867 | ||||||||
\(92\) | 20.0609 | 2.09150 | ||||||||
\(93\) | 8.39134 | 0.870141 | ||||||||
\(94\) | 29.5829 | 3.05124 | ||||||||
\(95\) | 14.2654 | 1.46360 | ||||||||
\(96\) | −44.1351 | −4.50452 | ||||||||
\(97\) | −14.2906 | −1.45099 | −0.725493 | − | 0.688230i | \(-0.758388\pi\) | ||||
−0.725493 | + | 0.688230i | \(0.758388\pi\) | |||||||
\(98\) | −56.2548 | −5.68259 | ||||||||
\(99\) | −0.276008 | −0.0277398 | ||||||||
\(100\) | 45.1120 | 4.51120 | ||||||||
\(101\) | 9.94010 | 0.989077 | 0.494538 | − | 0.869156i | \(-0.335337\pi\) | ||||
0.494538 | + | 0.869156i | \(0.335337\pi\) | |||||||
\(102\) | 19.6324 | 1.94390 | ||||||||
\(103\) | 3.50256 | 0.345118 | 0.172559 | − | 0.984999i | \(-0.444797\pi\) | ||||
0.172559 | + | 0.984999i | \(0.444797\pi\) | |||||||
\(104\) | −31.8140 | −3.11962 | ||||||||
\(105\) | 32.3151 | 3.15363 | ||||||||
\(106\) | −27.2703 | −2.64872 | ||||||||
\(107\) | 2.81493 | 0.272130 | 0.136065 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136065 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(108\) | −29.6295 | −2.85110 | ||||||||
\(109\) | 5.93745 | 0.568705 | 0.284352 | − | 0.958720i | \(-0.408221\pi\) | ||||
0.284352 | + | 0.958720i | \(0.408221\pi\) | |||||||
\(110\) | 46.4243 | 4.42639 | ||||||||
\(111\) | 0.280846 | 0.0266567 | ||||||||
\(112\) | −86.8116 | −8.20293 | ||||||||
\(113\) | 1.00000 | 0.0940721 | ||||||||
\(114\) | 18.7724 | 1.75819 | ||||||||
\(115\) | −12.8007 | −1.19367 | ||||||||
\(116\) | −14.9299 | −1.38621 | ||||||||
\(117\) | −0.186864 | −0.0172756 | ||||||||
\(118\) | 9.91199 | 0.912473 | ||||||||
\(119\) | 21.6466 | 1.98434 | ||||||||
\(120\) | 62.3437 | 5.69117 | ||||||||
\(121\) | 10.6984 | 0.972585 | ||||||||
\(122\) | 20.6353 | 1.86823 | ||||||||
\(123\) | 7.09561 | 0.639789 | ||||||||
\(124\) | 27.6365 | 2.48183 | ||||||||
\(125\) | −10.7665 | −0.962982 | ||||||||
\(126\) | −0.856819 | −0.0763315 | ||||||||
\(127\) | 19.8850 | 1.76451 | 0.882254 | − | 0.470775i | \(-0.156025\pi\) | ||||
0.882254 | + | 0.470775i | \(0.156025\pi\) | |||||||
\(128\) | −53.5315 | −4.73156 | ||||||||
\(129\) | −7.31973 | −0.644466 | ||||||||
\(130\) | 31.4304 | 2.75663 | ||||||||
\(131\) | −6.35089 | −0.554880 | −0.277440 | − | 0.960743i | \(-0.589486\pi\) | ||||
−0.277440 | + | 0.960743i | \(0.589486\pi\) | |||||||
\(132\) | 45.1152 | 3.92678 | ||||||||
\(133\) | 20.6983 | 1.79477 | ||||||||
\(134\) | −12.5802 | −1.08676 | ||||||||
\(135\) | 18.9063 | 1.62720 | ||||||||
\(136\) | 41.7615 | 3.58102 | ||||||||
\(137\) | −10.0216 | −0.856205 | −0.428103 | − | 0.903730i | \(-0.640818\pi\) | ||||
−0.428103 | + | 0.903730i | \(0.640818\pi\) | |||||||
\(138\) | −16.8449 | −1.43393 | ||||||||
\(139\) | −12.4234 | −1.05374 | −0.526868 | − | 0.849947i | \(-0.676634\pi\) | ||||
−0.526868 | + | 0.849947i | \(0.676634\pi\) | |||||||
\(140\) | 106.428 | 8.99483 | ||||||||
\(141\) | −18.3443 | −1.54487 | ||||||||
\(142\) | −2.76547 | −0.232073 | ||||||||
\(143\) | 14.6904 | 1.22847 | ||||||||
\(144\) | −0.983718 | −0.0819765 | ||||||||
\(145\) | 9.52664 | 0.791144 | ||||||||
\(146\) | −34.9827 | −2.89519 | ||||||||
\(147\) | 34.8835 | 2.87714 | ||||||||
\(148\) | 0.924953 | 0.0760307 | ||||||||
\(149\) | 3.53692 | 0.289756 | 0.144878 | − | 0.989450i | \(-0.453721\pi\) | ||||
0.144878 | + | 0.989450i | \(0.453721\pi\) | |||||||
\(150\) | −37.8799 | −3.09288 | ||||||||
\(151\) | 23.3839 | 1.90295 | 0.951476 | − | 0.307724i | \(-0.0995672\pi\) | ||||
0.951476 | + | 0.307724i | \(0.0995672\pi\) | |||||||
\(152\) | 39.9321 | 3.23892 | ||||||||
\(153\) | 0.245292 | 0.0198306 | ||||||||
\(154\) | 67.3592 | 5.42796 | ||||||||
\(155\) | −17.6346 | −1.41644 | ||||||||
\(156\) | 30.5441 | 2.44548 | ||||||||
\(157\) | 16.2604 | 1.29772 | 0.648860 | − | 0.760907i | \(-0.275246\pi\) | ||||
0.648860 | + | 0.760907i | \(0.275246\pi\) | |||||||
\(158\) | −34.8347 | −2.77130 | ||||||||
\(159\) | 16.9102 | 1.34107 | ||||||||
\(160\) | 92.7509 | 7.33261 | ||||||||
\(161\) | −18.5731 | −1.46377 | ||||||||
\(162\) | 24.3879 | 1.91610 | ||||||||
\(163\) | 9.67616 | 0.757895 | 0.378948 | − | 0.925418i | \(-0.376286\pi\) | ||||
0.378948 | + | 0.925418i | \(0.376286\pi\) | |||||||
\(164\) | 23.3690 | 1.82481 | ||||||||
\(165\) | −28.7876 | −2.24112 | ||||||||
\(166\) | −10.5275 | −0.817089 | ||||||||
\(167\) | −12.8593 | −0.995079 | −0.497540 | − | 0.867441i | \(-0.665763\pi\) | ||||
−0.497540 | + | 0.867441i | \(0.665763\pi\) | |||||||
\(168\) | 90.4573 | 6.97893 | ||||||||
\(169\) | −3.05427 | −0.234944 | ||||||||
\(170\) | −41.2579 | −3.16434 | ||||||||
\(171\) | 0.234546 | 0.0179362 | ||||||||
\(172\) | −24.1072 | −1.83815 | ||||||||
\(173\) | −21.5031 | −1.63485 | −0.817425 | − | 0.576035i | \(-0.804599\pi\) | ||||
−0.817425 | + | 0.576035i | \(0.804599\pi\) | |||||||
\(174\) | 12.5364 | 0.950385 | ||||||||
\(175\) | −41.7663 | −3.15723 | ||||||||
\(176\) | 77.3353 | 5.82937 | ||||||||
\(177\) | −6.14640 | −0.461992 | ||||||||
\(178\) | 24.0611 | 1.80346 | ||||||||
\(179\) | 11.4261 | 0.854030 | 0.427015 | − | 0.904244i | \(-0.359565\pi\) | ||||
0.427015 | + | 0.904244i | \(0.359565\pi\) | |||||||
\(180\) | 1.20601 | 0.0898904 | ||||||||
\(181\) | 23.4309 | 1.74161 | 0.870803 | − | 0.491633i | \(-0.163600\pi\) | ||||
0.870803 | + | 0.491633i | \(0.163600\pi\) | |||||||
\(182\) | 45.6038 | 3.38038 | ||||||||
\(183\) | −12.7959 | −0.945899 | ||||||||
\(184\) | −35.8321 | −2.64157 | ||||||||
\(185\) | −0.590205 | −0.0433927 | ||||||||
\(186\) | −23.2060 | −1.70154 | ||||||||
\(187\) | −19.2837 | −1.41016 | ||||||||
\(188\) | −60.4160 | −4.40629 | ||||||||
\(189\) | 27.4321 | 1.99539 | ||||||||
\(190\) | −39.4506 | −2.86204 | ||||||||
\(191\) | 7.30726 | 0.528735 | 0.264367 | − | 0.964422i | \(-0.414837\pi\) | ||||
0.264367 | + | 0.964422i | \(0.414837\pi\) | |||||||
\(192\) | 65.1135 | 4.69916 | ||||||||
\(193\) | 1.72952 | 0.124493 | 0.0622467 | − | 0.998061i | \(-0.480173\pi\) | ||||
0.0622467 | + | 0.998061i | \(0.480173\pi\) | |||||||
\(194\) | 39.5201 | 2.83737 | ||||||||
\(195\) | −19.4899 | −1.39570 | ||||||||
\(196\) | 114.887 | 8.20621 | ||||||||
\(197\) | −14.8370 | −1.05709 | −0.528545 | − | 0.848905i | \(-0.677262\pi\) | ||||
−0.528545 | + | 0.848905i | \(0.677262\pi\) | |||||||
\(198\) | 0.763290 | 0.0542446 | ||||||||
\(199\) | 23.6181 | 1.67424 | 0.837120 | − | 0.547020i | \(-0.184238\pi\) | ||||
0.837120 | + | 0.547020i | \(0.184238\pi\) | |||||||
\(200\) | −80.5772 | −5.69767 | ||||||||
\(201\) | 7.80095 | 0.550237 | ||||||||
\(202\) | −27.4890 | −1.93412 | ||||||||
\(203\) | 13.8226 | 0.970159 | ||||||||
\(204\) | −40.0945 | −2.80718 | ||||||||
\(205\) | −14.9116 | −1.04147 | ||||||||
\(206\) | −9.68622 | −0.674871 | ||||||||
\(207\) | −0.210464 | −0.0146283 | ||||||||
\(208\) | 52.3579 | 3.63037 | ||||||||
\(209\) | −18.4389 | −1.27545 | ||||||||
\(210\) | −89.3665 | −6.16687 | ||||||||
\(211\) | −18.8933 | −1.30067 | −0.650335 | − | 0.759648i | \(-0.725371\pi\) | ||||
−0.650335 | + | 0.759648i | \(0.725371\pi\) | |||||||
\(212\) | 55.6930 | 3.82501 | ||||||||
\(213\) | 1.71486 | 0.117500 | ||||||||
\(214\) | −7.78460 | −0.532144 | ||||||||
\(215\) | 15.3826 | 1.04908 | ||||||||
\(216\) | 52.9230 | 3.60096 | ||||||||
\(217\) | −25.5868 | −1.73695 | ||||||||
\(218\) | −16.4198 | −1.11209 | ||||||||
\(219\) | 21.6927 | 1.46586 | ||||||||
\(220\) | −94.8107 | −6.39213 | ||||||||
\(221\) | −13.0555 | −0.878209 | ||||||||
\(222\) | −0.776671 | −0.0521267 | ||||||||
\(223\) | −18.7263 | −1.25401 | −0.627004 | − | 0.779016i | \(-0.715719\pi\) | ||||
−0.627004 | + | 0.779016i | \(0.715719\pi\) | |||||||
\(224\) | 134.577 | 8.99178 | ||||||||
\(225\) | −0.473280 | −0.0315520 | ||||||||
\(226\) | −2.76547 | −0.183956 | ||||||||
\(227\) | 14.1276 | 0.937682 | 0.468841 | − | 0.883283i | \(-0.344672\pi\) | ||||
0.468841 | + | 0.883283i | \(0.344672\pi\) | |||||||
\(228\) | −38.3381 | −2.53900 | ||||||||
\(229\) | 12.6243 | 0.834240 | 0.417120 | − | 0.908851i | \(-0.363039\pi\) | ||||
0.417120 | + | 0.908851i | \(0.363039\pi\) | |||||||
\(230\) | 35.4000 | 2.33420 | ||||||||
\(231\) | −41.7693 | −2.74822 | ||||||||
\(232\) | 26.6672 | 1.75079 | ||||||||
\(233\) | −8.58335 | −0.562314 | −0.281157 | − | 0.959662i | \(-0.590718\pi\) | ||||
−0.281157 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(234\) | 0.516765 | 0.0337820 | ||||||||
\(235\) | 38.5509 | 2.51479 | ||||||||
\(236\) | −20.2429 | −1.31770 | ||||||||
\(237\) | 21.6009 | 1.40313 | ||||||||
\(238\) | −59.8630 | −3.88034 | ||||||||
\(239\) | −24.1510 | −1.56220 | −0.781101 | − | 0.624405i | \(-0.785341\pi\) | ||||
−0.781101 | + | 0.624405i | \(0.785341\pi\) | |||||||
\(240\) | −102.602 | −6.62293 | ||||||||
\(241\) | −6.53769 | −0.421130 | −0.210565 | − | 0.977580i | \(-0.567530\pi\) | ||||
−0.210565 | + | 0.977580i | \(0.567530\pi\) | |||||||
\(242\) | −29.5862 | −1.90187 | ||||||||
\(243\) | 0.615679 | 0.0394958 | ||||||||
\(244\) | −42.1426 | −2.69790 | ||||||||
\(245\) | −73.3084 | −4.68350 | ||||||||
\(246\) | −19.6227 | −1.25110 | ||||||||
\(247\) | −12.4836 | −0.794312 | ||||||||
\(248\) | −49.3632 | −3.13456 | ||||||||
\(249\) | 6.52806 | 0.413699 | ||||||||
\(250\) | 29.7743 | 1.88309 | ||||||||
\(251\) | 9.67000 | 0.610365 | 0.305182 | − | 0.952294i | \(-0.401283\pi\) | ||||
0.305182 | + | 0.952294i | \(0.401283\pi\) | |||||||
\(252\) | 1.74985 | 0.110230 | ||||||||
\(253\) | 16.5457 | 1.04022 | ||||||||
\(254\) | −54.9913 | −3.45046 | ||||||||
\(255\) | 25.5840 | 1.60213 | ||||||||
\(256\) | 72.0993 | 4.50621 | ||||||||
\(257\) | −20.3720 | −1.27077 | −0.635385 | − | 0.772195i | \(-0.719159\pi\) | ||||
−0.635385 | + | 0.772195i | \(0.719159\pi\) | |||||||
\(258\) | 20.2425 | 1.26024 | ||||||||
\(259\) | −0.856355 | −0.0532113 | ||||||||
\(260\) | −64.1891 | −3.98084 | ||||||||
\(261\) | 0.156633 | 0.00969534 | ||||||||
\(262\) | 17.5632 | 1.08506 | ||||||||
\(263\) | 4.67398 | 0.288210 | 0.144105 | − | 0.989562i | \(-0.453970\pi\) | ||||
0.144105 | + | 0.989562i | \(0.453970\pi\) | |||||||
\(264\) | −80.5831 | −4.95954 | ||||||||
\(265\) | −35.5373 | −2.18304 | ||||||||
\(266\) | −57.2406 | −3.50965 | ||||||||
\(267\) | −14.9203 | −0.913105 | ||||||||
\(268\) | 25.6921 | 1.56939 | ||||||||
\(269\) | 21.5654 | 1.31486 | 0.657431 | − | 0.753514i | \(-0.271643\pi\) | ||||
0.657431 | + | 0.753514i | \(0.271643\pi\) | |||||||
\(270\) | −52.2848 | −3.18195 | ||||||||
\(271\) | −2.48617 | −0.151024 | −0.0755122 | − | 0.997145i | \(-0.524059\pi\) | ||||
−0.0755122 | + | 0.997145i | \(0.524059\pi\) | |||||||
\(272\) | −68.7289 | −4.16730 | ||||||||
\(273\) | −28.2788 | −1.71151 | ||||||||
\(274\) | 27.7145 | 1.67429 | ||||||||
\(275\) | 37.2071 | 2.24367 | ||||||||
\(276\) | 34.4017 | 2.07074 | ||||||||
\(277\) | −24.5430 | −1.47464 | −0.737322 | − | 0.675541i | \(-0.763910\pi\) | ||||
−0.737322 | + | 0.675541i | \(0.763910\pi\) | |||||||
\(278\) | 34.3564 | 2.06056 | ||||||||
\(279\) | −0.289941 | −0.0173583 | ||||||||
\(280\) | −190.098 | −11.3605 | ||||||||
\(281\) | 4.81026 | 0.286956 | 0.143478 | − | 0.989654i | \(-0.454171\pi\) | ||||
0.143478 | + | 0.989654i | \(0.454171\pi\) | |||||||
\(282\) | 50.7305 | 3.02096 | ||||||||
\(283\) | −10.6271 | −0.631718 | −0.315859 | − | 0.948806i | \(-0.602293\pi\) | ||||
−0.315859 | + | 0.948806i | \(0.602293\pi\) | |||||||
\(284\) | 5.64781 | 0.335136 | ||||||||
\(285\) | 24.4632 | 1.44908 | ||||||||
\(286\) | −40.6257 | −2.40225 | ||||||||
\(287\) | −21.6359 | −1.27713 | ||||||||
\(288\) | 1.52497 | 0.0898599 | ||||||||
\(289\) | 0.137665 | 0.00809796 | ||||||||
\(290\) | −26.3456 | −1.54707 | ||||||||
\(291\) | −24.5063 | −1.43659 | ||||||||
\(292\) | 71.4438 | 4.18093 | ||||||||
\(293\) | −15.3014 | −0.893916 | −0.446958 | − | 0.894555i | \(-0.647493\pi\) | ||||
−0.446958 | + | 0.894555i | \(0.647493\pi\) | |||||||
\(294\) | −96.4691 | −5.62619 | ||||||||
\(295\) | 12.9168 | 0.752046 | ||||||||
\(296\) | −1.65211 | −0.0960272 | ||||||||
\(297\) | −24.4376 | −1.41801 | ||||||||
\(298\) | −9.78124 | −0.566612 | ||||||||
\(299\) | 11.2018 | 0.647819 | ||||||||
\(300\) | 77.3607 | 4.46642 | ||||||||
\(301\) | 22.3193 | 1.28646 | ||||||||
\(302\) | −64.6673 | −3.72118 | ||||||||
\(303\) | 17.0459 | 0.979260 | ||||||||
\(304\) | −65.7181 | −3.76919 | ||||||||
\(305\) | 26.8908 | 1.53976 | ||||||||
\(306\) | −0.678346 | −0.0387784 | ||||||||
\(307\) | 4.56716 | 0.260662 | 0.130331 | − | 0.991471i | \(-0.458396\pi\) | ||||
0.130331 | + | 0.991471i | \(0.458396\pi\) | |||||||
\(308\) | −137.565 | −7.83850 | ||||||||
\(309\) | 6.00641 | 0.341692 | ||||||||
\(310\) | 48.7679 | 2.76983 | ||||||||
\(311\) | −12.0484 | −0.683204 | −0.341602 | − | 0.939845i | \(-0.610970\pi\) | ||||
−0.341602 | + | 0.939845i | \(0.610970\pi\) | |||||||
\(312\) | −54.5567 | −3.08866 | ||||||||
\(313\) | 13.7004 | 0.774390 | 0.387195 | − | 0.921998i | \(-0.373444\pi\) | ||||
0.387195 | + | 0.921998i | \(0.373444\pi\) | |||||||
\(314\) | −44.9676 | −2.53767 | ||||||||
\(315\) | −1.11656 | −0.0629113 | ||||||||
\(316\) | 71.1415 | 4.00202 | ||||||||
\(317\) | 22.2269 | 1.24839 | 0.624193 | − | 0.781271i | \(-0.285428\pi\) | ||||
0.624193 | + | 0.781271i | \(0.285428\pi\) | |||||||
\(318\) | −46.7647 | −2.62243 | ||||||||
\(319\) | −12.3138 | −0.689439 | ||||||||
\(320\) | −136.838 | −7.64945 | ||||||||
\(321\) | 4.82722 | 0.269429 | ||||||||
\(322\) | 51.3634 | 2.86237 | ||||||||
\(323\) | 16.3869 | 0.911793 | ||||||||
\(324\) | −49.8065 | −2.76703 | ||||||||
\(325\) | 25.1901 | 1.39730 | ||||||||
\(326\) | −26.7591 | −1.48205 | ||||||||
\(327\) | 10.1819 | 0.563060 | ||||||||
\(328\) | −41.7409 | −2.30475 | ||||||||
\(329\) | 55.9353 | 3.08381 | ||||||||
\(330\) | 79.6113 | 4.38246 | ||||||||
\(331\) | −25.2741 | −1.38919 | −0.694596 | − | 0.719400i | \(-0.744417\pi\) | ||||
−0.694596 | + | 0.719400i | \(0.744417\pi\) | |||||||
\(332\) | 21.4998 | 1.17996 | ||||||||
\(333\) | −0.00970390 | −0.000531770 0 | ||||||||
\(334\) | 35.5619 | 1.94586 | ||||||||
\(335\) | −16.3939 | −0.895694 | ||||||||
\(336\) | −148.870 | −8.12152 | ||||||||
\(337\) | 21.3645 | 1.16380 | 0.581899 | − | 0.813261i | \(-0.302310\pi\) | ||||
0.581899 | + | 0.813261i | \(0.302310\pi\) | |||||||
\(338\) | 8.44649 | 0.459429 | ||||||||
\(339\) | 1.71486 | 0.0931385 | ||||||||
\(340\) | 84.2595 | 4.56961 | ||||||||
\(341\) | 22.7938 | 1.23435 | ||||||||
\(342\) | −0.648630 | −0.0350739 | ||||||||
\(343\) | −69.7639 | −3.76690 | ||||||||
\(344\) | 43.0593 | 2.32160 | ||||||||
\(345\) | −21.9514 | −1.18183 | ||||||||
\(346\) | 59.4661 | 3.19692 | ||||||||
\(347\) | −30.3960 | −1.63174 | −0.815871 | − | 0.578234i | \(-0.803742\pi\) | ||||
−0.815871 | + | 0.578234i | \(0.803742\pi\) | |||||||
\(348\) | −25.6027 | −1.37245 | ||||||||
\(349\) | −20.5264 | −1.09875 | −0.549377 | − | 0.835574i | \(-0.685135\pi\) | ||||
−0.549377 | + | 0.835574i | \(0.685135\pi\) | |||||||
\(350\) | 115.503 | 6.17391 | ||||||||
\(351\) | −16.5448 | −0.883098 | ||||||||
\(352\) | −119.886 | −6.38996 | ||||||||
\(353\) | −24.9856 | −1.32985 | −0.664925 | − | 0.746910i | \(-0.731536\pi\) | ||||
−0.664925 | + | 0.746910i | \(0.731536\pi\) | |||||||
\(354\) | 16.9977 | 0.903417 | ||||||||
\(355\) | −3.60382 | −0.191271 | ||||||||
\(356\) | −49.1391 | −2.60437 | ||||||||
\(357\) | 37.1209 | 1.96465 | ||||||||
\(358\) | −31.5986 | −1.67004 | ||||||||
\(359\) | −7.40394 | −0.390765 | −0.195383 | − | 0.980727i | \(-0.562595\pi\) | ||||
−0.195383 | + | 0.980727i | \(0.562595\pi\) | |||||||
\(360\) | −2.15412 | −0.113532 | ||||||||
\(361\) | −3.33093 | −0.175312 | ||||||||
\(362\) | −64.7974 | −3.40567 | ||||||||
\(363\) | 18.3463 | 0.962933 | ||||||||
\(364\) | −93.1349 | −4.88159 | ||||||||
\(365\) | −45.5877 | −2.38617 | ||||||||
\(366\) | 35.3866 | 1.84969 | ||||||||
\(367\) | −22.2691 | −1.16244 | −0.581219 | − | 0.813747i | \(-0.697424\pi\) | ||||
−0.581219 | + | 0.813747i | \(0.697424\pi\) | |||||||
\(368\) | 58.9705 | 3.07405 | ||||||||
\(369\) | −0.245170 | −0.0127630 | ||||||||
\(370\) | 1.63219 | 0.0848536 | ||||||||
\(371\) | −51.5626 | −2.67700 | ||||||||
\(372\) | 47.3927 | 2.45720 | ||||||||
\(373\) | 27.6798 | 1.43321 | 0.716603 | − | 0.697481i | \(-0.245696\pi\) | ||||
0.716603 | + | 0.697481i | \(0.245696\pi\) | |||||||
\(374\) | 53.3284 | 2.75755 | ||||||||
\(375\) | −18.4630 | −0.953424 | ||||||||
\(376\) | 107.913 | 5.56517 | ||||||||
\(377\) | −8.33672 | −0.429363 | ||||||||
\(378\) | −75.8624 | −3.90194 | ||||||||
\(379\) | −2.61110 | −0.134123 | −0.0670616 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670616 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(380\) | 80.5684 | 4.13307 | ||||||||
\(381\) | 34.1000 | 1.74699 | ||||||||
\(382\) | −20.2080 | −1.03393 | ||||||||
\(383\) | 11.6605 | 0.595826 | 0.297913 | − | 0.954593i | \(-0.403709\pi\) | ||||
0.297913 | + | 0.954593i | \(0.403709\pi\) | |||||||
\(384\) | −91.7991 | −4.68460 | ||||||||
\(385\) | 87.7792 | 4.47364 | ||||||||
\(386\) | −4.78293 | −0.243445 | ||||||||
\(387\) | 0.252914 | 0.0128563 | ||||||||
\(388\) | −80.7103 | −4.09745 | ||||||||
\(389\) | −0.429804 | −0.0217919 | −0.0108960 | − | 0.999941i | \(-0.503468\pi\) | ||||
−0.0108960 | + | 0.999941i | \(0.503468\pi\) | |||||||
\(390\) | 53.8987 | 2.72927 | ||||||||
\(391\) | −14.7044 | −0.743633 | ||||||||
\(392\) | −205.207 | −10.3645 | ||||||||
\(393\) | −10.8909 | −0.549373 | ||||||||
\(394\) | 41.0311 | 2.06712 | ||||||||
\(395\) | −45.3948 | −2.28406 | ||||||||
\(396\) | −1.55884 | −0.0783345 | ||||||||
\(397\) | 4.47107 | 0.224396 | 0.112198 | − | 0.993686i | \(-0.464211\pi\) | ||||
0.112198 | + | 0.993686i | \(0.464211\pi\) | |||||||
\(398\) | −65.3150 | −3.27394 | ||||||||
\(399\) | 35.4948 | 1.77696 | ||||||||
\(400\) | 132.610 | 6.63049 | ||||||||
\(401\) | −23.9135 | −1.19418 | −0.597092 | − | 0.802173i | \(-0.703677\pi\) | ||||
−0.597092 | + | 0.802173i | \(0.703677\pi\) | |||||||
\(402\) | −21.5733 | −1.07598 | ||||||||
\(403\) | 15.4319 | 0.768720 | ||||||||
\(404\) | 56.1398 | 2.79306 | ||||||||
\(405\) | 31.7811 | 1.57922 | ||||||||
\(406\) | −38.2260 | −1.89713 | ||||||||
\(407\) | 0.762876 | 0.0378144 | ||||||||
\(408\) | 71.6152 | 3.54548 | ||||||||
\(409\) | −30.6639 | −1.51623 | −0.758115 | − | 0.652121i | \(-0.773880\pi\) | ||||
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(410\) | 41.2375 | 2.03657 | ||||||||
\(411\) | −17.1857 | −0.847708 | ||||||||
\(412\) | 19.7818 | 0.974579 | ||||||||
\(413\) | 18.7416 | 0.922213 | ||||||||
\(414\) | 0.582031 | 0.0286053 | ||||||||
\(415\) | −13.7189 | −0.673432 | ||||||||
\(416\) | −81.1659 | −3.97949 | ||||||||
\(417\) | −21.3043 | −1.04328 | ||||||||
\(418\) | 50.9923 | 2.49411 | ||||||||
\(419\) | −33.6937 | −1.64605 | −0.823023 | − | 0.568008i | \(-0.807714\pi\) | ||||
−0.823023 | + | 0.568008i | \(0.807714\pi\) | |||||||
\(420\) | 182.510 | 8.90556 | ||||||||
\(421\) | 30.0506 | 1.46458 | 0.732288 | − | 0.680995i | \(-0.238453\pi\) | ||||
0.732288 | + | 0.680995i | \(0.238453\pi\) | |||||||
\(422\) | 52.2488 | 2.54343 | ||||||||
\(423\) | 0.633838 | 0.0308183 | ||||||||
\(424\) | −99.4767 | −4.83102 | ||||||||
\(425\) | −33.0664 | −1.60396 | ||||||||
\(426\) | −4.74239 | −0.229770 | ||||||||
\(427\) | 39.0171 | 1.88817 | ||||||||
\(428\) | 15.8982 | 0.768468 | ||||||||
\(429\) | 25.1919 | 1.21628 | ||||||||
\(430\) | −42.5400 | −2.05146 | ||||||||
\(431\) | 19.1766 | 0.923704 | 0.461852 | − | 0.886957i | \(-0.347185\pi\) | ||||
0.461852 | + | 0.886957i | \(0.347185\pi\) | |||||||
\(432\) | −87.0979 | −4.19050 | ||||||||
\(433\) | 1.40570 | 0.0675536 | 0.0337768 | − | 0.999429i | \(-0.489246\pi\) | ||||
0.0337768 | + | 0.999429i | \(0.489246\pi\) | |||||||
\(434\) | 70.7595 | 3.39657 | ||||||||
\(435\) | 16.3369 | 0.783293 | ||||||||
\(436\) | 33.5336 | 1.60597 | ||||||||
\(437\) | −14.0602 | −0.672593 | ||||||||
\(438\) | −59.9904 | −2.86645 | ||||||||
\(439\) | 2.27194 | 0.108434 | 0.0542170 | − | 0.998529i | \(-0.482734\pi\) | ||||
0.0542170 | + | 0.998529i | \(0.482734\pi\) | |||||||
\(440\) | 169.347 | 8.07331 | ||||||||
\(441\) | −1.20531 | −0.0573956 | ||||||||
\(442\) | 36.1046 | 1.71732 | ||||||||
\(443\) | 11.2504 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(444\) | 1.58617 | 0.0752761 | ||||||||
\(445\) | 31.3553 | 1.48638 | ||||||||
\(446\) | 51.7870 | 2.45219 | ||||||||
\(447\) | 6.06533 | 0.286880 | ||||||||
\(448\) | −198.544 | −9.38032 | ||||||||
\(449\) | 10.1819 | 0.480511 | 0.240256 | − | 0.970710i | \(-0.422769\pi\) | ||||
0.240256 | + | 0.970710i | \(0.422769\pi\) | |||||||
\(450\) | 1.30884 | 0.0616993 | ||||||||
\(451\) | 19.2741 | 0.907584 | ||||||||
\(452\) | 5.64781 | 0.265651 | ||||||||
\(453\) | 40.1001 | 1.88407 | ||||||||
\(454\) | −39.0694 | −1.83362 | ||||||||
\(455\) | 59.4286 | 2.78606 | ||||||||
\(456\) | 68.4780 | 3.20678 | ||||||||
\(457\) | −28.1358 | −1.31614 | −0.658068 | − | 0.752958i | \(-0.728626\pi\) | ||||
−0.658068 | + | 0.752958i | \(0.728626\pi\) | |||||||
\(458\) | −34.9122 | −1.63134 | ||||||||
\(459\) | 21.7180 | 1.01371 | ||||||||
\(460\) | −72.2960 | −3.37082 | ||||||||
\(461\) | −23.0105 | −1.07170 | −0.535852 | − | 0.844312i | \(-0.680010\pi\) | ||||
−0.535852 | + | 0.844312i | \(0.680010\pi\) | |||||||
\(462\) | 115.512 | 5.37409 | ||||||||
\(463\) | 16.5418 | 0.768761 | 0.384381 | − | 0.923175i | \(-0.374415\pi\) | ||||
0.384381 | + | 0.923175i | \(0.374415\pi\) | |||||||
\(464\) | −43.8875 | −2.03742 | ||||||||
\(465\) | −30.2409 | −1.40239 | ||||||||
\(466\) | 23.7370 | 1.09959 | ||||||||
\(467\) | 20.6829 | 0.957089 | 0.478544 | − | 0.878063i | \(-0.341165\pi\) | ||||
0.478544 | + | 0.878063i | \(0.341165\pi\) | |||||||
\(468\) | −1.05537 | −0.0487845 | ||||||||
\(469\) | −23.7866 | −1.09836 | ||||||||
\(470\) | −106.611 | −4.91761 | ||||||||
\(471\) | 27.8843 | 1.28484 | ||||||||
\(472\) | 36.1570 | 1.66426 | ||||||||
\(473\) | −19.8829 | −0.914218 | ||||||||
\(474\) | −59.7366 | −2.74379 | ||||||||
\(475\) | −31.6179 | −1.45073 | ||||||||
\(476\) | 122.256 | 5.60359 | ||||||||
\(477\) | −0.584289 | −0.0267527 | ||||||||
\(478\) | 66.7889 | 3.05485 | ||||||||
\(479\) | −20.0057 | −0.914083 | −0.457041 | − | 0.889445i | \(-0.651091\pi\) | ||||
−0.457041 | + | 0.889445i | \(0.651091\pi\) | |||||||
\(480\) | 159.055 | 7.25983 | ||||||||
\(481\) | 0.516485 | 0.0235497 | ||||||||
\(482\) | 18.0798 | 0.823511 | ||||||||
\(483\) | −31.8503 | −1.44924 | ||||||||
\(484\) | 60.4227 | 2.74649 | ||||||||
\(485\) | 51.5006 | 2.33852 | ||||||||
\(486\) | −1.70264 | −0.0772334 | ||||||||
\(487\) | −17.8331 | −0.808094 | −0.404047 | − | 0.914738i | \(-0.632397\pi\) | ||||
−0.404047 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(488\) | 75.2735 | 3.40747 | ||||||||
\(489\) | 16.5933 | 0.750374 | ||||||||
\(490\) | 202.732 | 9.15850 | ||||||||
\(491\) | 37.0479 | 1.67195 | 0.835975 | − | 0.548768i | \(-0.184903\pi\) | ||||
0.835975 | + | 0.548768i | \(0.184903\pi\) | |||||||
\(492\) | 40.0746 | 1.80670 | ||||||||
\(493\) | 10.9434 | 0.492866 | ||||||||
\(494\) | 34.5230 | 1.55326 | ||||||||
\(495\) | 0.994681 | 0.0447076 | ||||||||
\(496\) | 81.2393 | 3.64775 | ||||||||
\(497\) | −5.22895 | −0.234550 | ||||||||
\(498\) | −18.0531 | −0.808980 | ||||||||
\(499\) | 13.8040 | 0.617952 | 0.308976 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308976 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(500\) | −60.8069 | −2.71937 | ||||||||
\(501\) | −22.0518 | −0.985204 | ||||||||
\(502\) | −26.7421 | −1.19356 | ||||||||
\(503\) | 19.1957 | 0.855894 | 0.427947 | − | 0.903804i | \(-0.359237\pi\) | ||||
0.427947 | + | 0.903804i | \(0.359237\pi\) | |||||||
\(504\) | −3.12551 | −0.139221 | ||||||||
\(505\) | −35.8223 | −1.59407 | ||||||||
\(506\) | −45.7566 | −2.03413 | ||||||||
\(507\) | −5.23765 | −0.232612 | ||||||||
\(508\) | 112.307 | 4.98280 | ||||||||
\(509\) | −35.7007 | −1.58241 | −0.791203 | − | 0.611554i | \(-0.790545\pi\) | ||||
−0.791203 | + | 0.611554i | \(0.790545\pi\) | |||||||
\(510\) | −70.7516 | −3.13293 | ||||||||
\(511\) | −66.1453 | −2.92609 | ||||||||
\(512\) | −92.3253 | −4.08024 | ||||||||
\(513\) | 20.7666 | 0.916869 | ||||||||
\(514\) | 56.3381 | 2.48497 | ||||||||
\(515\) | −12.6226 | −0.556218 | ||||||||
\(516\) | −41.3404 | −1.81991 | ||||||||
\(517\) | −49.8294 | −2.19150 | ||||||||
\(518\) | 2.36822 | 0.104054 | ||||||||
\(519\) | −36.8748 | −1.61863 | ||||||||
\(520\) | 114.652 | 5.02783 | ||||||||
\(521\) | 2.07701 | 0.0909956 | 0.0454978 | − | 0.998964i | \(-0.485513\pi\) | ||||
0.0454978 | + | 0.998964i | \(0.485513\pi\) | |||||||
\(522\) | −0.433164 | −0.0189591 | ||||||||
\(523\) | −42.4656 | −1.85689 | −0.928447 | − | 0.371466i | \(-0.878855\pi\) | ||||
−0.928447 | + | 0.371466i | \(0.878855\pi\) | |||||||
\(524\) | −35.8686 | −1.56693 | ||||||||
\(525\) | −71.6234 | −3.12590 | ||||||||
\(526\) | −12.9257 | −0.563589 | ||||||||
\(527\) | −20.2571 | −0.882415 | ||||||||
\(528\) | 132.619 | 5.77152 | ||||||||
\(529\) | −10.3834 | −0.451452 | ||||||||
\(530\) | 98.2771 | 4.26888 | ||||||||
\(531\) | 0.212373 | 0.00921620 | ||||||||
\(532\) | 116.900 | 5.06827 | ||||||||
\(533\) | 13.0491 | 0.565217 | ||||||||
\(534\) | 41.2615 | 1.78556 | ||||||||
\(535\) | −10.1445 | −0.438585 | ||||||||
\(536\) | −45.8901 | −1.98215 | ||||||||
\(537\) | 19.5943 | 0.845554 | ||||||||
\(538\) | −59.6383 | −2.57119 | ||||||||
\(539\) | 94.7557 | 4.08142 | ||||||||
\(540\) | 106.779 | 4.59505 | ||||||||
\(541\) | 5.64948 | 0.242890 | 0.121445 | − | 0.992598i | \(-0.461247\pi\) | ||||
0.121445 | + | 0.992598i | \(0.461247\pi\) | |||||||
\(542\) | 6.87543 | 0.295325 | ||||||||
\(543\) | 40.1807 | 1.72432 | ||||||||
\(544\) | 106.545 | 4.56806 | ||||||||
\(545\) | −21.3975 | −0.916568 | ||||||||
\(546\) | 78.2041 | 3.34683 | ||||||||
\(547\) | −15.4825 | −0.661984 | −0.330992 | − | 0.943634i | \(-0.607383\pi\) | ||||
−0.330992 | + | 0.943634i | \(0.607383\pi\) | |||||||
\(548\) | −56.6002 | −2.41784 | ||||||||
\(549\) | 0.442128 | 0.0188696 | ||||||||
\(550\) | −102.895 | −4.38746 | ||||||||
\(551\) | 10.4640 | 0.445782 | ||||||||
\(552\) | −61.4470 | −2.61536 | ||||||||
\(553\) | −65.8654 | −2.80088 | ||||||||
\(554\) | 67.8728 | 2.88364 | ||||||||
\(555\) | −1.01212 | −0.0429621 | ||||||||
\(556\) | −70.1648 | −2.97565 | ||||||||
\(557\) | −19.1853 | −0.812908 | −0.406454 | − | 0.913671i | \(-0.633235\pi\) | ||||
−0.406454 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(558\) | 0.801821 | 0.0339438 | ||||||||
\(559\) | −13.4612 | −0.569349 | ||||||||
\(560\) | 312.853 | 13.2205 | ||||||||
\(561\) | −33.0688 | −1.39617 | ||||||||
\(562\) | −13.3026 | −0.561137 | ||||||||
\(563\) | 1.14992 | 0.0484634 | 0.0242317 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242317 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(564\) | −103.605 | −4.36256 | ||||||||
\(565\) | −3.60382 | −0.151614 | ||||||||
\(566\) | 29.3890 | 1.23531 | ||||||||
\(567\) | 46.1127 | 1.93655 | ||||||||
\(568\) | −10.0879 | −0.423279 | ||||||||
\(569\) | −21.1540 | −0.886821 | −0.443411 | − | 0.896319i | \(-0.646232\pi\) | ||||
−0.443411 | + | 0.896319i | \(0.646232\pi\) | |||||||
\(570\) | −67.6522 | −2.83364 | ||||||||
\(571\) | −0.667874 | −0.0279497 | −0.0139748 | − | 0.999902i | \(-0.504448\pi\) | ||||
−0.0139748 | + | 0.999902i | \(0.504448\pi\) | |||||||
\(572\) | 82.9684 | 3.46908 | ||||||||
\(573\) | 12.5309 | 0.523487 | ||||||||
\(574\) | 59.8334 | 2.49740 | ||||||||
\(575\) | 28.3715 | 1.18317 | ||||||||
\(576\) | −2.24983 | −0.0937428 | ||||||||
\(577\) | 38.1625 | 1.58873 | 0.794364 | − | 0.607443i | \(-0.207805\pi\) | ||||
0.794364 | + | 0.607443i | \(0.207805\pi\) | |||||||
\(578\) | −0.380709 | −0.0158354 | ||||||||
\(579\) | 2.96588 | 0.123258 | ||||||||
\(580\) | 53.8046 | 2.23412 | ||||||||
\(581\) | −19.9053 | −0.825812 | ||||||||
\(582\) | 67.7714 | 2.80921 | ||||||||
\(583\) | 45.9341 | 1.90240 | ||||||||
\(584\) | −127.610 | −5.28055 | ||||||||
\(585\) | 0.673423 | 0.0278426 | ||||||||
\(586\) | 42.3154 | 1.74803 | ||||||||
\(587\) | 6.80014 | 0.280672 | 0.140336 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140336 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(588\) | 197.015 | 8.12477 | ||||||||
\(589\) | −19.3697 | −0.798116 | ||||||||
\(590\) | −35.7210 | −1.47061 | ||||||||
\(591\) | −25.4433 | −1.04660 | ||||||||
\(592\) | 2.71896 | 0.111749 | ||||||||
\(593\) | −8.46786 | −0.347734 | −0.173867 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173867 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(594\) | 67.5814 | 2.77290 | ||||||||
\(595\) | −78.0105 | −3.19812 | ||||||||
\(596\) | 19.9758 | 0.818243 | ||||||||
\(597\) | 40.5017 | 1.65762 | ||||||||
\(598\) | −30.9783 | −1.26680 | ||||||||
\(599\) | −34.2014 | −1.39743 | −0.698715 | − | 0.715400i | \(-0.746244\pi\) | ||||
−0.698715 | + | 0.715400i | \(0.746244\pi\) | |||||||
\(600\) | −138.179 | −5.64112 | ||||||||
\(601\) | 26.2495 | 1.07074 | 0.535369 | − | 0.844618i | \(-0.320173\pi\) | ||||
0.535369 | + | 0.844618i | \(0.320173\pi\) | |||||||
\(602\) | −61.7233 | −2.51565 | ||||||||
\(603\) | −0.269541 | −0.0109766 | ||||||||
\(604\) | 132.068 | 5.37375 | ||||||||
\(605\) | −38.5552 | −1.56749 | ||||||||
\(606\) | −47.1398 | −1.91492 | ||||||||
\(607\) | −48.6074 | −1.97291 | −0.986456 | − | 0.164025i | \(-0.947552\pi\) | ||||
−0.986456 | + | 0.164025i | \(0.947552\pi\) | |||||||
\(608\) | 101.877 | 4.13167 | ||||||||
\(609\) | 23.7039 | 0.960530 | ||||||||
\(610\) | −74.3657 | −3.01098 | ||||||||
\(611\) | −33.7357 | −1.36480 | ||||||||
\(612\) | 1.38536 | 0.0559998 | ||||||||
\(613\) | −45.9740 | −1.85687 | −0.928435 | − | 0.371494i | \(-0.878846\pi\) | ||||
−0.928435 | + | 0.371494i | \(0.878846\pi\) | |||||||
\(614\) | −12.6303 | −0.509719 | ||||||||
\(615\) | −25.5713 | −1.03113 | ||||||||
\(616\) | 245.713 | 9.90008 | ||||||||
\(617\) | −25.6330 | −1.03195 | −0.515973 | − | 0.856605i | \(-0.672570\pi\) | ||||
−0.515973 | + | 0.856605i | \(0.672570\pi\) | |||||||
\(618\) | −16.6105 | −0.668173 | ||||||||
\(619\) | 20.0863 | 0.807336 | 0.403668 | − | 0.914906i | \(-0.367735\pi\) | ||||
0.403668 | + | 0.914906i | \(0.367735\pi\) | |||||||
\(620\) | −99.5968 | −3.99990 | ||||||||
\(621\) | −18.6344 | −0.747773 | ||||||||
\(622\) | 33.3196 | 1.33599 | ||||||||
\(623\) | 45.4948 | 1.82271 | ||||||||
\(624\) | 89.7865 | 3.59434 | ||||||||
\(625\) | −1.13719 | −0.0454874 | ||||||||
\(626\) | −37.8879 | −1.51431 | ||||||||
\(627\) | −31.6202 | −1.26279 | ||||||||
\(628\) | 91.8356 | 3.66464 | ||||||||
\(629\) | −0.677978 | −0.0270327 | ||||||||
\(630\) | 3.08782 | 0.123022 | ||||||||
\(631\) | −17.5775 | −0.699750 | −0.349875 | − | 0.936796i | \(-0.613776\pi\) | ||||
−0.349875 | + | 0.936796i | \(0.613776\pi\) | |||||||
\(632\) | −127.070 | −5.05458 | ||||||||
\(633\) | −32.3994 | −1.28776 | ||||||||
\(634\) | −61.4677 | −2.44119 | ||||||||
\(635\) | −71.6619 | −2.84382 | ||||||||
\(636\) | 95.5058 | 3.78705 | ||||||||
\(637\) | 64.1518 | 2.54179 | ||||||||
\(638\) | 34.0533 | 1.34818 | ||||||||
\(639\) | −0.0592525 | −0.00234399 | ||||||||
\(640\) | 192.918 | 7.62575 | ||||||||
\(641\) | −0.0789430 | −0.00311806 | −0.00155903 | − | 0.999999i | \(-0.500496\pi\) | ||||
−0.00155903 | + | 0.999999i | \(0.500496\pi\) | |||||||
\(642\) | −13.3495 | −0.526863 | ||||||||
\(643\) | −35.1457 | −1.38601 | −0.693005 | − | 0.720933i | \(-0.743713\pi\) | ||||
−0.693005 | + | 0.720933i | \(0.743713\pi\) | |||||||
\(644\) | −104.898 | −4.13354 | ||||||||
\(645\) | 26.3790 | 1.03867 | ||||||||
\(646\) | −45.3175 | −1.78299 | ||||||||
\(647\) | 8.41572 | 0.330856 | 0.165428 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165428 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(648\) | 88.9624 | 3.49477 | ||||||||
\(649\) | −16.6958 | −0.655366 | ||||||||
\(650\) | −69.6624 | −2.73238 | ||||||||
\(651\) | −43.8779 | −1.71971 | ||||||||
\(652\) | 54.6491 | 2.14022 | ||||||||
\(653\) | 7.12071 | 0.278655 | 0.139327 | − | 0.990246i | \(-0.455506\pi\) | ||||
0.139327 | + | 0.990246i | \(0.455506\pi\) | |||||||
\(654\) | −28.1577 | −1.10105 | ||||||||
\(655\) | 22.8875 | 0.894287 | ||||||||
\(656\) | 68.6949 | 2.68209 | ||||||||
\(657\) | −0.749534 | −0.0292421 | ||||||||
\(658\) | −154.687 | −6.03034 | ||||||||
\(659\) | −1.80686 | −0.0703851 | −0.0351925 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351925 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(660\) | −162.587 | −6.32869 | ||||||||
\(661\) | 14.1155 | 0.549028 | 0.274514 | − | 0.961583i | \(-0.411483\pi\) | ||||
0.274514 | + | 0.961583i | \(0.411483\pi\) | |||||||
\(662\) | 69.8948 | 2.71654 | ||||||||
\(663\) | −22.3884 | −0.869493 | ||||||||
\(664\) | −38.4022 | −1.49029 | ||||||||
\(665\) | −74.5931 | −2.89260 | ||||||||
\(666\) | 0.0268358 | 0.00103987 | ||||||||
\(667\) | −9.38962 | −0.363567 | ||||||||
\(668\) | −72.6266 | −2.81001 | ||||||||
\(669\) | −32.1130 | −1.24156 | ||||||||
\(670\) | 45.3367 | 1.75151 | ||||||||
\(671\) | −34.7581 | −1.34182 | ||||||||
\(672\) | 230.780 | 8.90253 | ||||||||
\(673\) | −1.51990 | −0.0585877 | −0.0292939 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292939 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(674\) | −59.0828 | −2.27579 | ||||||||
\(675\) | −41.9040 | −1.61289 | ||||||||
\(676\) | −17.2500 | −0.663460 | ||||||||
\(677\) | −42.4817 | −1.63271 | −0.816353 | − | 0.577554i | \(-0.804007\pi\) | ||||
−0.816353 | + | 0.577554i | \(0.804007\pi\) | |||||||
\(678\) | −4.74239 | −0.182130 | ||||||||
\(679\) | 74.7245 | 2.86766 | ||||||||
\(680\) | −150.501 | −5.77145 | ||||||||
\(681\) | 24.2269 | 0.928376 | ||||||||
\(682\) | −63.0355 | −2.41375 | ||||||||
\(683\) | 5.98137 | 0.228871 | 0.114435 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114435 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(684\) | 1.32467 | 0.0506501 | ||||||||
\(685\) | 36.1161 | 1.37993 | ||||||||
\(686\) | 192.930 | 7.36610 | ||||||||
\(687\) | 21.6490 | 0.825961 | ||||||||
\(688\) | −70.8647 | −2.70169 | ||||||||
\(689\) | 31.0985 | 1.18476 | ||||||||
\(690\) | 60.7060 | 2.31104 | ||||||||
\(691\) | −1.62066 | −0.0616528 | −0.0308264 | − | 0.999525i | \(-0.509814\pi\) | ||||
−0.0308264 | + | 0.999525i | \(0.509814\pi\) | |||||||
\(692\) | −121.445 | −4.61666 | ||||||||
\(693\) | 1.44323 | 0.0548237 | ||||||||
\(694\) | 84.0591 | 3.19084 | ||||||||
\(695\) | 44.7716 | 1.69828 | ||||||||
\(696\) | 45.7305 | 1.73341 | ||||||||
\(697\) | −17.1292 | −0.648814 | ||||||||
\(698\) | 56.7652 | 2.14859 | ||||||||
\(699\) | −14.7193 | −0.556733 | ||||||||
\(700\) | −235.888 | −8.91573 | ||||||||
\(701\) | 17.3195 | 0.654148 | 0.327074 | − | 0.944999i | \(-0.393937\pi\) | ||||
0.327074 | + | 0.944999i | \(0.393937\pi\) | |||||||
\(702\) | 45.7542 | 1.72688 | ||||||||
\(703\) | −0.648278 | −0.0244503 | ||||||||
\(704\) | 176.871 | 6.66608 | ||||||||
\(705\) | 66.1095 | 2.48983 | ||||||||
\(706\) | 69.0969 | 2.60050 | ||||||||
\(707\) | −51.9762 | −1.95477 | ||||||||
\(708\) | −34.7137 | −1.30462 | ||||||||
\(709\) | 14.3440 | 0.538702 | 0.269351 | − | 0.963042i | \(-0.413191\pi\) | ||||
0.269351 | + | 0.963042i | \(0.413191\pi\) | |||||||
\(710\) | 9.96624 | 0.374026 | ||||||||
\(711\) | −0.746363 | −0.0279908 | ||||||||
\(712\) | 87.7704 | 3.28933 | ||||||||
\(713\) | 17.3810 | 0.650922 | ||||||||
\(714\) | −102.657 | −3.84183 | ||||||||
\(715\) | −52.9414 | −1.97990 | ||||||||
\(716\) | 64.5327 | 2.41170 | ||||||||
\(717\) | −41.4157 | −1.54670 | ||||||||
\(718\) | 20.4754 | 0.764134 | ||||||||
\(719\) | −27.3999 | −1.02184 | −0.510922 | − | 0.859627i | \(-0.670696\pi\) | ||||
−0.510922 | + | 0.859627i | \(0.670696\pi\) | |||||||
\(720\) | 3.54514 | 0.132120 | ||||||||
\(721\) | −18.3147 | −0.682075 | ||||||||
\(722\) | 9.21158 | 0.342820 | ||||||||
\(723\) | −11.2112 | −0.416950 | ||||||||
\(724\) | 132.333 | 4.91813 | ||||||||
\(725\) | −21.1149 | −0.784187 | ||||||||
\(726\) | −50.7362 | −1.88300 | ||||||||
\(727\) | −39.0786 | −1.44935 | −0.724673 | − | 0.689093i | \(-0.758009\pi\) | ||||
−0.724673 | + | 0.689093i | \(0.758009\pi\) | |||||||
\(728\) | 166.354 | 6.16549 | ||||||||
\(729\) | 27.5120 | 1.01896 | ||||||||
\(730\) | 126.071 | 4.66611 | ||||||||
\(731\) | 17.6702 | 0.653557 | ||||||||
\(732\) | −72.2687 | −2.67113 | ||||||||
\(733\) | −24.8531 | −0.917969 | −0.458985 | − | 0.888444i | \(-0.651787\pi\) | ||||
−0.458985 | + | 0.888444i | \(0.651787\pi\) | |||||||
\(734\) | 61.5845 | 2.27313 | ||||||||
\(735\) | −125.714 | −4.63702 | ||||||||
\(736\) | −91.4169 | −3.36967 | ||||||||
\(737\) | 21.1901 | 0.780547 | ||||||||
\(738\) | 0.678010 | 0.0249579 | ||||||||
\(739\) | 3.31251 | 0.121853 | 0.0609263 | − | 0.998142i | \(-0.480595\pi\) | ||||
0.0609263 | + | 0.998142i | \(0.480595\pi\) | |||||||
\(740\) | −3.33336 | −0.122537 | ||||||||
\(741\) | −21.4076 | −0.786429 | ||||||||
\(742\) | 142.595 | 5.23482 | ||||||||
\(743\) | 36.0903 | 1.32402 | 0.662012 | − | 0.749493i | \(-0.269703\pi\) | ||||
0.662012 | + | 0.749493i | \(0.269703\pi\) | |||||||
\(744\) | −84.6509 | −3.10345 | ||||||||
\(745\) | −12.7464 | −0.466993 | ||||||||
\(746\) | −76.5476 | −2.80261 | ||||||||
\(747\) | −0.225560 | −0.00825280 | ||||||||
\(748\) | −108.911 | −3.98217 | ||||||||
\(749\) | −14.7191 | −0.537825 | ||||||||
\(750\) | 51.0588 | 1.86440 | ||||||||
\(751\) | −28.7424 | −1.04883 | −0.524413 | − | 0.851464i | \(-0.675715\pi\) | ||||
−0.524413 | + | 0.851464i | \(0.675715\pi\) | |||||||
\(752\) | −177.597 | −6.47630 | ||||||||
\(753\) | 16.5827 | 0.604307 | ||||||||
\(754\) | 23.0549 | 0.839610 | ||||||||
\(755\) | −84.2712 | −3.06694 | ||||||||
\(756\) | 154.931 | 5.63479 | ||||||||
\(757\) | −28.2415 | −1.02645 | −0.513227 | − | 0.858253i | \(-0.671550\pi\) | ||||
−0.513227 | + | 0.858253i | \(0.671550\pi\) | |||||||
\(758\) | 7.22091 | 0.262275 | ||||||||
\(759\) | 28.3736 | 1.02990 | ||||||||
\(760\) | −143.908 | −5.22009 | ||||||||
\(761\) | 18.9696 | 0.687647 | 0.343824 | − | 0.939034i | \(-0.388278\pi\) | ||||
0.343824 | + | 0.939034i | \(0.388278\pi\) | |||||||
\(762\) | −94.3024 | −3.41621 | ||||||||
\(763\) | −31.0466 | −1.12396 | ||||||||
\(764\) | 41.2700 | 1.49310 | ||||||||
\(765\) | −0.883986 | −0.0319606 | ||||||||
\(766\) | −32.2469 | −1.16513 | ||||||||
\(767\) | −11.3034 | −0.408143 | ||||||||
\(768\) | 123.640 | 4.46149 | ||||||||
\(769\) | 4.46954 | 0.161176 | 0.0805878 | − | 0.996748i | \(-0.474320\pi\) | ||||
0.0805878 | + | 0.996748i | \(0.474320\pi\) | |||||||
\(770\) | −242.750 | −8.74812 | ||||||||
\(771\) | −34.9351 | −1.25816 | ||||||||
\(772\) | 9.76799 | 0.351558 | ||||||||
\(773\) | 18.6811 | 0.671914 | 0.335957 | − | 0.941877i | \(-0.390940\pi\) | ||||
0.335957 | + | 0.941877i | \(0.390940\pi\) | |||||||
\(774\) | −0.699425 | −0.0251403 | ||||||||
\(775\) | 39.0854 | 1.40399 | ||||||||
\(776\) | 144.162 | 5.17510 | ||||||||
\(777\) | −1.46853 | −0.0526832 | ||||||||
\(778\) | 1.18861 | 0.0426137 | ||||||||
\(779\) | −16.3788 | −0.586832 | ||||||||
\(780\) | −110.075 | −3.94133 | ||||||||
\(781\) | 4.65816 | 0.166682 | ||||||||
\(782\) | 40.6645 | 1.45416 | ||||||||
\(783\) | 13.8682 | 0.495610 | ||||||||
\(784\) | 337.718 | 12.0614 | ||||||||
\(785\) | −58.5995 | −2.09151 | ||||||||
\(786\) | 30.1184 | 1.07429 | ||||||||
\(787\) | −6.14304 | −0.218976 | −0.109488 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109488 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(788\) | −83.7964 | −2.98512 | ||||||||
\(789\) | 8.01522 | 0.285349 | ||||||||
\(790\) | 125.538 | 4.46644 | ||||||||
\(791\) | −5.22895 | −0.185920 | ||||||||
\(792\) | 2.78434 | 0.0989370 | ||||||||
\(793\) | −23.5320 | −0.835647 | ||||||||
\(794\) | −12.3646 | −0.438803 | ||||||||
\(795\) | −60.9414 | −2.16137 | ||||||||
\(796\) | 133.390 | 4.72789 | ||||||||
\(797\) | 15.3512 | 0.543769 | 0.271885 | − | 0.962330i | \(-0.412353\pi\) | ||||
0.271885 | + | 0.962330i | \(0.412353\pi\) | |||||||
\(798\) | −98.1597 | −3.47481 | ||||||||
\(799\) | 44.2841 | 1.56666 | ||||||||
\(800\) | −205.573 | −7.26812 | ||||||||
\(801\) | 0.515530 | 0.0182154 | ||||||||
\(802\) | 66.1320 | 2.33520 | ||||||||
\(803\) | 58.9249 | 2.07941 | ||||||||
\(804\) | 44.0583 | 1.55382 | ||||||||
\(805\) | 66.9342 | 2.35912 | ||||||||
\(806\) | −42.6765 | −1.50322 | ||||||||
\(807\) | 36.9816 | 1.30181 | ||||||||
\(808\) | −100.275 | −3.52765 | ||||||||
\(809\) | 21.8813 | 0.769306 | 0.384653 | − | 0.923061i | \(-0.374321\pi\) | ||||
0.384653 | + | 0.923061i | \(0.374321\pi\) | |||||||
\(810\) | −87.8896 | −3.08813 | ||||||||
\(811\) | −11.3827 | −0.399699 | −0.199850 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199850 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(812\) | 78.0676 | 2.73964 | ||||||||
\(813\) | −4.26344 | −0.149525 | ||||||||
\(814\) | −2.10971 | −0.0739452 | ||||||||
\(815\) | −34.8711 | −1.22148 | ||||||||
\(816\) | −117.861 | −4.12594 | ||||||||
\(817\) | 16.8962 | 0.591122 | ||||||||
\(818\) | 84.7999 | 2.96496 | ||||||||
\(819\) | 0.977100 | 0.0341426 | ||||||||
\(820\) | −84.2178 | −2.94101 | ||||||||
\(821\) | −46.0663 | −1.60773 | −0.803863 | − | 0.594814i | \(-0.797226\pi\) | ||||
−0.803863 | + | 0.594814i | \(0.797226\pi\) | |||||||
\(822\) | 47.5265 | 1.65768 | ||||||||
\(823\) | 8.08494 | 0.281823 | 0.140912 | − | 0.990022i | \(-0.454997\pi\) | ||||
0.140912 | + | 0.990022i | \(0.454997\pi\) | |||||||
\(824\) | −35.3335 | −1.23090 | ||||||||
\(825\) | 63.8050 | 2.22141 | ||||||||
\(826\) | −51.8293 | −1.80337 | ||||||||
\(827\) | −11.6961 | −0.406712 | −0.203356 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203356 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(828\) | −1.18866 | −0.0413088 | ||||||||
\(829\) | 13.8619 | 0.481445 | 0.240722 | − | 0.970594i | \(-0.422616\pi\) | ||||
0.240722 | + | 0.970594i | \(0.422616\pi\) | |||||||
\(830\) | 37.9391 | 1.31688 | ||||||||
\(831\) | −42.0878 | −1.46001 | ||||||||
\(832\) | 119.746 | 4.15144 | ||||||||
\(833\) | −84.2106 | −2.91772 | ||||||||
\(834\) | 58.9165 | 2.04011 | ||||||||
\(835\) | 46.3424 | 1.60375 | ||||||||
\(836\) | −104.140 | −3.60174 | ||||||||
\(837\) | −25.6712 | −0.887327 | ||||||||
\(838\) | 93.1789 | 3.21881 | ||||||||
\(839\) | 26.4799 | 0.914189 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(840\) | −325.992 | −11.2478 | ||||||||
\(841\) | −22.0120 | −0.759034 | ||||||||
\(842\) | −83.1039 | −2.86395 | ||||||||
\(843\) | 8.24893 | 0.284108 | ||||||||
\(844\) | −106.706 | −3.67297 | ||||||||
\(845\) | 11.0070 | 0.378654 | ||||||||
\(846\) | −1.75286 | −0.0602645 | ||||||||
\(847\) | −55.9416 | −1.92217 | ||||||||
\(848\) | 163.714 | 5.62195 | ||||||||
\(849\) | −18.2241 | −0.625449 | ||||||||
\(850\) | 91.4442 | 3.13651 | ||||||||
\(851\) | 0.581716 | 0.0199410 | ||||||||
\(852\) | 9.68521 | 0.331810 | ||||||||
\(853\) | −11.0461 | −0.378212 | −0.189106 | − | 0.981957i | \(-0.560559\pi\) | ||||
−0.189106 | + | 0.981957i | \(0.560559\pi\) | |||||||
\(854\) | −107.901 | −3.69228 | ||||||||
\(855\) | −0.845262 | −0.0289073 | ||||||||
\(856\) | −28.3967 | −0.970581 | ||||||||
\(857\) | 4.68870 | 0.160163 | 0.0800815 | − | 0.996788i | \(-0.474482\pi\) | ||||
0.0800815 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(858\) | −69.6674 | −2.37841 | ||||||||
\(859\) | −54.8407 | −1.87114 | −0.935570 | − | 0.353142i | \(-0.885113\pi\) | ||||
−0.935570 | + | 0.353142i | \(0.885113\pi\) | |||||||
\(860\) | 86.8779 | 2.96251 | ||||||||
\(861\) | −37.1025 | −1.26445 | ||||||||
\(862\) | −53.0322 | −1.80628 | ||||||||
\(863\) | 21.8944 | 0.745295 | 0.372647 | − | 0.927973i | \(-0.378450\pi\) | ||||
0.372647 | + | 0.927973i | \(0.378450\pi\) | |||||||
\(864\) | 135.020 | 4.59349 | ||||||||
\(865\) | 77.4933 | 2.63485 | ||||||||
\(866\) | −3.88741 | −0.132100 | ||||||||
\(867\) | 0.236077 | 0.00801759 | ||||||||
\(868\) | −144.510 | −4.90497 | ||||||||
\(869\) | 58.6756 | 1.99043 | ||||||||
\(870\) | −45.1791 | −1.53171 | ||||||||
\(871\) | 14.3462 | 0.486103 | ||||||||
\(872\) | −59.8964 | −2.02835 | ||||||||
\(873\) | 0.846751 | 0.0286582 | ||||||||
\(874\) | 38.8831 | 1.31524 | ||||||||
\(875\) | 56.2972 | 1.90319 | ||||||||
\(876\) | 122.516 | 4.13944 | ||||||||
\(877\) | 27.0585 | 0.913699 | 0.456850 | − | 0.889544i | \(-0.348978\pi\) | ||||
0.456850 | + | 0.889544i | \(0.348978\pi\) | |||||||
\(878\) | −6.28298 | −0.212040 | ||||||||
\(879\) | −26.2397 | −0.885044 | ||||||||
\(880\) | −278.703 | −9.39506 | ||||||||
\(881\) | 41.4136 | 1.39526 | 0.697629 | − | 0.716459i | \(-0.254238\pi\) | ||||
0.697629 | + | 0.716459i | \(0.254238\pi\) | |||||||
\(882\) | 3.33324 | 0.112236 | ||||||||
\(883\) | 10.5273 | 0.354271 | 0.177135 | − | 0.984187i | \(-0.443317\pi\) | ||||
0.177135 | + | 0.984187i | \(0.443317\pi\) | |||||||
\(884\) | −73.7351 | −2.47998 | ||||||||
\(885\) | 22.1505 | 0.744582 | ||||||||
\(886\) | −31.1126 | −1.04525 | ||||||||
\(887\) | −47.5602 | −1.59691 | −0.798457 | − | 0.602052i | \(-0.794350\pi\) | ||||
−0.798457 | + | 0.602052i | \(0.794350\pi\) | |||||||
\(888\) | −2.83315 | −0.0950742 | ||||||||
\(889\) | −103.978 | −3.48729 | ||||||||
\(890\) | −86.7119 | −2.90659 | ||||||||
\(891\) | −41.0790 | −1.37620 | ||||||||
\(892\) | −105.763 | −3.54120 | ||||||||
\(893\) | 42.3441 | 1.41699 | ||||||||
\(894\) | −16.7735 | −0.560988 | ||||||||
\(895\) | −41.1778 | −1.37642 | ||||||||
\(896\) | 279.913 | 9.35125 | ||||||||
\(897\) | 19.2096 | 0.641390 | ||||||||
\(898\) | −28.1576 | −0.939631 | ||||||||
\(899\) | −12.9354 | −0.431419 | ||||||||
\(900\) | −2.67300 | −0.0890999 | ||||||||
\(901\) | −40.8222 | −1.35999 | ||||||||
\(902\) | −53.3020 | −1.77476 | ||||||||
\(903\) | 38.2745 | 1.27369 | ||||||||
\(904\) | −10.0879 | −0.335518 | ||||||||
\(905\) | −84.4407 | −2.80690 | ||||||||
\(906\) | −110.895 | −3.68425 | ||||||||
\(907\) | −4.84484 | −0.160870 | −0.0804351 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804351 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(908\) | 79.7900 | 2.64793 | ||||||||
\(909\) | −0.588976 | −0.0195351 | ||||||||
\(910\) | −164.348 | −5.44808 | ||||||||
\(911\) | 10.8648 | 0.359968 | 0.179984 | − | 0.983670i | \(-0.442395\pi\) | ||||
0.179984 | + | 0.983670i | \(0.442395\pi\) | |||||||
\(912\) | −112.697 | −3.73179 | ||||||||
\(913\) | 17.7325 | 0.586859 | ||||||||
\(914\) | 77.8086 | 2.57368 | ||||||||
\(915\) | 46.1140 | 1.52448 | ||||||||
\(916\) | 71.2999 | 2.35581 | ||||||||
\(917\) | 33.2085 | 1.09664 | ||||||||
\(918\) | −60.0604 | −1.98229 | ||||||||
\(919\) | 26.1625 | 0.863020 | 0.431510 | − | 0.902108i | \(-0.357981\pi\) | ||||
0.431510 | + | 0.902108i | \(0.357981\pi\) | |||||||
\(920\) | 129.132 | 4.25737 | ||||||||
\(921\) | 7.83205 | 0.258075 | ||||||||
\(922\) | 63.6347 | 2.09570 | ||||||||
\(923\) | 3.15368 | 0.103805 | ||||||||
\(924\) | −235.905 | −7.76071 | ||||||||
\(925\) | 1.30813 | 0.0430111 | ||||||||
\(926\) | −45.7457 | −1.50330 | ||||||||
\(927\) | −0.207536 | −0.00681636 | ||||||||
\(928\) | 68.0350 | 2.23336 | ||||||||
\(929\) | 28.4562 | 0.933619 | 0.466810 | − | 0.884358i | \(-0.345403\pi\) | ||||
0.466810 | + | 0.884358i | \(0.345403\pi\) | |||||||
\(930\) | 83.6301 | 2.74234 | ||||||||
\(931\) | −80.5216 | −2.63899 | ||||||||
\(932\) | −48.4771 | −1.58792 | ||||||||
\(933\) | −20.6614 | −0.676424 | ||||||||
\(934\) | −57.1978 | −1.87157 | ||||||||
\(935\) | 69.4949 | 2.27273 | ||||||||
\(936\) | 1.88506 | 0.0616152 | ||||||||
\(937\) | 19.7018 | 0.643631 | 0.321815 | − | 0.946802i | \(-0.395707\pi\) | ||||
0.321815 | + | 0.946802i | \(0.395707\pi\) | |||||||
\(938\) | 65.7811 | 2.14783 | ||||||||
\(939\) | 23.4942 | 0.766705 | ||||||||
\(940\) | 217.728 | 7.10151 | ||||||||
\(941\) | −4.46392 | −0.145519 | −0.0727597 | − | 0.997349i | \(-0.523181\pi\) | ||||
−0.0727597 | + | 0.997349i | \(0.523181\pi\) | |||||||
\(942\) | −77.1132 | −2.51248 | ||||||||
\(943\) | 14.6971 | 0.478604 | ||||||||
\(944\) | −59.5054 | −1.93673 | ||||||||
\(945\) | −98.8602 | −3.21592 | ||||||||
\(946\) | 54.9856 | 1.78774 | ||||||||
\(947\) | 16.3653 | 0.531800 | 0.265900 | − | 0.964001i | \(-0.414331\pi\) | ||||
0.265900 | + | 0.964001i | \(0.414331\pi\) | |||||||
\(948\) | 121.998 | 3.96231 | ||||||||
\(949\) | 39.8936 | 1.29500 | ||||||||
\(950\) | 87.4383 | 2.83687 | ||||||||
\(951\) | 38.1160 | 1.23600 | ||||||||
\(952\) | −218.369 | −7.07737 | ||||||||
\(953\) | −25.9709 | −0.841281 | −0.420640 | − | 0.907227i | \(-0.638195\pi\) | ||||
−0.420640 | + | 0.907227i | \(0.638195\pi\) | |||||||
\(954\) | 1.61583 | 0.0523145 | ||||||||
\(955\) | −26.3340 | −0.852150 | ||||||||
\(956\) | −136.400 | −4.41151 | ||||||||
\(957\) | −21.1164 | −0.682596 | ||||||||
\(958\) | 55.3251 | 1.78747 | ||||||||
\(959\) | 52.4025 | 1.69217 | ||||||||
\(960\) | −234.657 | −7.57353 | ||||||||
\(961\) | −7.05556 | −0.227599 | ||||||||
\(962\) | −1.42832 | −0.0460510 | ||||||||
\(963\) | −0.166792 | −0.00537479 | ||||||||
\(964\) | −36.9236 | −1.18923 | ||||||||
\(965\) | −6.23287 | −0.200643 | ||||||||
\(966\) | 88.0811 | 2.83396 | ||||||||
\(967\) | 50.3073 | 1.61777 | 0.808886 | − | 0.587965i | \(-0.200071\pi\) | ||||
0.808886 | + | 0.587965i | \(0.200071\pi\) | |||||||
\(968\) | −107.925 | −3.46883 | ||||||||
\(969\) | 28.1013 | 0.902744 | ||||||||
\(970\) | −142.423 | −4.57293 | ||||||||
\(971\) | 4.13076 | 0.132562 | 0.0662811 | − | 0.997801i | \(-0.478887\pi\) | ||||
0.0662811 | + | 0.997801i | \(0.478887\pi\) | |||||||
\(972\) | 3.47724 | 0.111533 | ||||||||
\(973\) | 64.9611 | 2.08256 | ||||||||
\(974\) | 49.3168 | 1.58021 | ||||||||
\(975\) | 43.1975 | 1.38343 | ||||||||
\(976\) | −123.881 | −3.96534 | ||||||||
\(977\) | 8.97941 | 0.287277 | 0.143638 | − | 0.989630i | \(-0.454120\pi\) | ||||
0.143638 | + | 0.989630i | \(0.454120\pi\) | |||||||
\(978\) | −45.8881 | −1.46734 | ||||||||
\(979\) | −40.5286 | −1.29530 | ||||||||
\(980\) | −414.032 | −13.2258 | ||||||||
\(981\) | −0.351809 | −0.0112324 | ||||||||
\(982\) | −102.455 | −3.26947 | ||||||||
\(983\) | 34.7871 | 1.10953 | 0.554767 | − | 0.832005i | \(-0.312807\pi\) | ||||
0.554767 | + | 0.832005i | \(0.312807\pi\) | |||||||
\(984\) | −71.5798 | −2.28188 | ||||||||
\(985\) | 53.4698 | 1.70369 | ||||||||
\(986\) | −30.2636 | −0.963790 | ||||||||
\(987\) | 95.9212 | 3.05321 | ||||||||
\(988\) | −70.5050 | −2.24306 | ||||||||
\(989\) | −15.1613 | −0.482102 | ||||||||
\(990\) | −2.75076 | −0.0874248 | ||||||||
\(991\) | 35.6277 | 1.13175 | 0.565876 | − | 0.824490i | \(-0.308538\pi\) | ||||
0.565876 | + | 0.824490i | \(0.308538\pi\) | |||||||
\(992\) | −125.938 | −3.99854 | ||||||||
\(993\) | −43.3416 | −1.37540 | ||||||||
\(994\) | 14.4605 | 0.458658 | ||||||||
\(995\) | −85.1152 | −2.69833 | ||||||||
\(996\) | 36.8692 | 1.16825 | ||||||||
\(997\) | 13.1334 | 0.415940 | 0.207970 | − | 0.978135i | \(-0.433314\pi\) | ||||
0.207970 | + | 0.978135i | \(0.433314\pi\) | |||||||
\(998\) | −38.1745 | −1.20839 | ||||||||
\(999\) | −0.859179 | −0.0271832 |
(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 | 8023.2.a.b.1.5 | ✓ | 155 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.b.1.5 | ✓ | 155 | 1.1 | even | 1 | trivial |