Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62246 | −1.85436 | −0.927179 | − | 0.374618i | \(-0.877774\pi\) | ||||
−0.927179 | + | 0.374618i | \(0.877774\pi\) | |||||||
\(3\) | −2.12328 | −1.22588 | −0.612939 | − | 0.790130i | \(-0.710013\pi\) | ||||
−0.612939 | + | 0.790130i | \(0.710013\pi\) | |||||||
\(4\) | 4.87729 | 2.43864 | ||||||||
\(5\) | 2.57436 | 1.15129 | 0.575644 | − | 0.817700i | \(-0.304751\pi\) | ||||
0.575644 | + | 0.817700i | \(0.304751\pi\) | |||||||
\(6\) | 5.56822 | 2.27322 | ||||||||
\(7\) | −3.69406 | −1.39622 | −0.698111 | − | 0.715990i | \(-0.745976\pi\) | ||||
−0.698111 | + | 0.715990i | \(0.745976\pi\) | |||||||
\(8\) | −7.54557 | −2.66776 | ||||||||
\(9\) | 1.50833 | 0.502777 | ||||||||
\(10\) | −6.75115 | −2.13490 | ||||||||
\(11\) | −0.495298 | −0.149338 | −0.0746691 | − | 0.997208i | \(-0.523790\pi\) | ||||
−0.0746691 | + | 0.997208i | \(0.523790\pi\) | |||||||
\(12\) | −10.3559 | −2.98948 | ||||||||
\(13\) | 5.97668 | 1.65763 | 0.828816 | − | 0.559521i | \(-0.189015\pi\) | ||||
0.828816 | + | 0.559521i | \(0.189015\pi\) | |||||||
\(14\) | 9.68751 | 2.58910 | ||||||||
\(15\) | −5.46609 | −1.41134 | ||||||||
\(16\) | 10.0334 | 2.50834 | ||||||||
\(17\) | −3.51722 | −0.853052 | −0.426526 | − | 0.904475i | \(-0.640263\pi\) | ||||
−0.426526 | + | 0.904475i | \(0.640263\pi\) | |||||||
\(18\) | −3.95553 | −0.932328 | ||||||||
\(19\) | −8.34345 | −1.91412 | −0.957059 | − | 0.289892i | \(-0.906380\pi\) | ||||
−0.957059 | + | 0.289892i | \(0.906380\pi\) | |||||||
\(20\) | 12.5559 | 2.80758 | ||||||||
\(21\) | 7.84353 | 1.71160 | ||||||||
\(22\) | 1.29890 | 0.276926 | ||||||||
\(23\) | −5.47494 | −1.14160 | −0.570802 | − | 0.821088i | \(-0.693367\pi\) | ||||
−0.570802 | + | 0.821088i | \(0.693367\pi\) | |||||||
\(24\) | 16.0214 | 3.27035 | ||||||||
\(25\) | 1.62732 | 0.325465 | ||||||||
\(26\) | −15.6736 | −3.07384 | ||||||||
\(27\) | 3.16724 | 0.609535 | ||||||||
\(28\) | −18.0170 | −3.40489 | ||||||||
\(29\) | 6.95494 | 1.29150 | 0.645750 | − | 0.763549i | \(-0.276545\pi\) | ||||
0.645750 | + | 0.763549i | \(0.276545\pi\) | |||||||
\(30\) | 14.3346 | 2.61713 | ||||||||
\(31\) | 1.64309 | 0.295107 | 0.147554 | − | 0.989054i | \(-0.452860\pi\) | ||||
0.147554 | + | 0.989054i | \(0.452860\pi\) | |||||||
\(32\) | −11.2210 | −1.98360 | ||||||||
\(33\) | 1.05166 | 0.183070 | ||||||||
\(34\) | 9.22377 | 1.58186 | ||||||||
\(35\) | −9.50983 | −1.60745 | ||||||||
\(36\) | 7.35656 | 1.22609 | ||||||||
\(37\) | 0.114816 | 0.0188756 | 0.00943781 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943781 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(38\) | 21.8803 | 3.54946 | ||||||||
\(39\) | −12.6902 | −2.03205 | ||||||||
\(40\) | −19.4250 | −3.07136 | ||||||||
\(41\) | −7.14150 | −1.11531 | −0.557657 | − | 0.830071i | \(-0.688300\pi\) | ||||
−0.557657 | + | 0.830071i | \(0.688300\pi\) | |||||||
\(42\) | −20.5693 | −3.17392 | ||||||||
\(43\) | −4.66431 | −0.711301 | −0.355650 | − | 0.934619i | \(-0.615741\pi\) | ||||
−0.355650 | + | 0.934619i | \(0.615741\pi\) | |||||||
\(44\) | −2.41571 | −0.364183 | ||||||||
\(45\) | 3.88298 | 0.578841 | ||||||||
\(46\) | 14.3578 | 2.11694 | ||||||||
\(47\) | −3.97553 | −0.579891 | −0.289946 | − | 0.957043i | \(-0.593637\pi\) | ||||
−0.289946 | + | 0.957043i | \(0.593637\pi\) | |||||||
\(48\) | −21.3037 | −3.07492 | ||||||||
\(49\) | 6.64605 | 0.949436 | ||||||||
\(50\) | −4.26759 | −0.603529 | ||||||||
\(51\) | 7.46806 | 1.04574 | ||||||||
\(52\) | 29.1500 | 4.04237 | ||||||||
\(53\) | 4.37021 | 0.600294 | 0.300147 | − | 0.953893i | \(-0.402964\pi\) | ||||
0.300147 | + | 0.953893i | \(0.402964\pi\) | |||||||
\(54\) | −8.30595 | −1.13030 | ||||||||
\(55\) | −1.27508 | −0.171931 | ||||||||
\(56\) | 27.8738 | 3.72479 | ||||||||
\(57\) | 17.7155 | 2.34648 | ||||||||
\(58\) | −18.2390 | −2.39490 | ||||||||
\(59\) | −6.50881 | −0.847375 | −0.423687 | − | 0.905809i | \(-0.639264\pi\) | ||||
−0.423687 | + | 0.905809i | \(0.639264\pi\) | |||||||
\(60\) | −26.6597 | −3.44175 | ||||||||
\(61\) | −1.38885 | −0.177824 | −0.0889119 | − | 0.996039i | \(-0.528339\pi\) | ||||
−0.0889119 | + | 0.996039i | \(0.528339\pi\) | |||||||
\(62\) | −4.30893 | −0.547235 | ||||||||
\(63\) | −5.57185 | −0.701988 | ||||||||
\(64\) | 9.35975 | 1.16997 | ||||||||
\(65\) | 15.3861 | 1.90841 | ||||||||
\(66\) | −2.75793 | −0.339478 | ||||||||
\(67\) | −5.99388 | −0.732269 | −0.366135 | − | 0.930562i | \(-0.619319\pi\) | ||||
−0.366135 | + | 0.930562i | \(0.619319\pi\) | |||||||
\(68\) | −17.1545 | −2.08029 | ||||||||
\(69\) | 11.6248 | 1.39947 | ||||||||
\(70\) | 24.9391 | 2.98080 | ||||||||
\(71\) | 16.5048 | 1.95876 | 0.979380 | − | 0.202027i | \(-0.0647528\pi\) | ||||
0.979380 | + | 0.202027i | \(0.0647528\pi\) | |||||||
\(72\) | −11.3812 | −1.34129 | ||||||||
\(73\) | −12.4975 | −1.46272 | −0.731360 | − | 0.681991i | \(-0.761114\pi\) | ||||
−0.731360 | + | 0.681991i | \(0.761114\pi\) | |||||||
\(74\) | −0.301100 | −0.0350022 | ||||||||
\(75\) | −3.45527 | −0.398980 | ||||||||
\(76\) | −40.6934 | −4.66785 | ||||||||
\(77\) | 1.82966 | 0.208509 | ||||||||
\(78\) | 33.2795 | 3.76816 | ||||||||
\(79\) | 0.963915 | 0.108449 | 0.0542245 | − | 0.998529i | \(-0.482731\pi\) | ||||
0.0542245 | + | 0.998529i | \(0.482731\pi\) | |||||||
\(80\) | 25.8295 | 2.88783 | ||||||||
\(81\) | −11.2499 | −1.24999 | ||||||||
\(82\) | 18.7283 | 2.06819 | ||||||||
\(83\) | −8.20641 | −0.900770 | −0.450385 | − | 0.892834i | \(-0.648713\pi\) | ||||
−0.450385 | + | 0.892834i | \(0.648713\pi\) | |||||||
\(84\) | 38.2551 | 4.17398 | ||||||||
\(85\) | −9.05459 | −0.982108 | ||||||||
\(86\) | 12.2320 | 1.31901 | ||||||||
\(87\) | −14.7673 | −1.58322 | ||||||||
\(88\) | 3.73731 | 0.398399 | ||||||||
\(89\) | −1.76787 | −0.187394 | −0.0936969 | − | 0.995601i | \(-0.529868\pi\) | ||||
−0.0936969 | + | 0.995601i | \(0.529868\pi\) | |||||||
\(90\) | −10.1830 | −1.07338 | ||||||||
\(91\) | −22.0782 | −2.31442 | ||||||||
\(92\) | −26.7028 | −2.78396 | ||||||||
\(93\) | −3.48874 | −0.361765 | ||||||||
\(94\) | 10.4257 | 1.07533 | ||||||||
\(95\) | −21.4790 | −2.20370 | ||||||||
\(96\) | 23.8253 | 2.43166 | ||||||||
\(97\) | −1.36444 | −0.138538 | −0.0692691 | − | 0.997598i | \(-0.522067\pi\) | ||||
−0.0692691 | + | 0.997598i | \(0.522067\pi\) | |||||||
\(98\) | −17.4290 | −1.76059 | ||||||||
\(99\) | −0.747073 | −0.0750837 | ||||||||
\(100\) | 7.93693 | 0.793693 | ||||||||
\(101\) | 8.06225 | 0.802223 | 0.401112 | − | 0.916029i | \(-0.368624\pi\) | ||||
0.401112 | + | 0.916029i | \(0.368624\pi\) | |||||||
\(102\) | −19.5847 | −1.93917 | ||||||||
\(103\) | −5.00940 | −0.493591 | −0.246795 | − | 0.969068i | \(-0.579378\pi\) | ||||
−0.246795 | + | 0.969068i | \(0.579378\pi\) | |||||||
\(104\) | −45.0974 | −4.42217 | ||||||||
\(105\) | 20.1921 | 1.97054 | ||||||||
\(106\) | −11.4607 | −1.11316 | ||||||||
\(107\) | −10.7604 | −1.04024 | −0.520122 | − | 0.854092i | \(-0.674114\pi\) | ||||
−0.520122 | + | 0.854092i | \(0.674114\pi\) | |||||||
\(108\) | 15.4475 | 1.48644 | ||||||||
\(109\) | 17.7083 | 1.69615 | 0.848073 | − | 0.529880i | \(-0.177763\pi\) | ||||
0.848073 | + | 0.529880i | \(0.177763\pi\) | |||||||
\(110\) | 3.34383 | 0.318822 | ||||||||
\(111\) | −0.243787 | −0.0231392 | ||||||||
\(112\) | −37.0638 | −3.50220 | ||||||||
\(113\) | −18.8603 | −1.77422 | −0.887112 | − | 0.461554i | \(-0.847292\pi\) | ||||
−0.887112 | + | 0.461554i | \(0.847292\pi\) | |||||||
\(114\) | −46.4582 | −4.35121 | ||||||||
\(115\) | −14.0945 | −1.31431 | ||||||||
\(116\) | 33.9213 | 3.14951 | ||||||||
\(117\) | 9.01480 | 0.833418 | ||||||||
\(118\) | 17.0691 | 1.57134 | ||||||||
\(119\) | 12.9928 | 1.19105 | ||||||||
\(120\) | 41.2448 | 3.76512 | ||||||||
\(121\) | −10.7547 | −0.977698 | ||||||||
\(122\) | 3.64220 | 0.329749 | ||||||||
\(123\) | 15.1634 | 1.36724 | ||||||||
\(124\) | 8.01381 | 0.719662 | ||||||||
\(125\) | −8.68248 | −0.776584 | ||||||||
\(126\) | 14.6120 | 1.30174 | ||||||||
\(127\) | 13.8862 | 1.23220 | 0.616100 | − | 0.787668i | \(-0.288712\pi\) | ||||
0.616100 | + | 0.787668i | \(0.288712\pi\) | |||||||
\(128\) | −2.10365 | −0.185938 | ||||||||
\(129\) | 9.90365 | 0.871968 | ||||||||
\(130\) | −40.3494 | −3.53888 | ||||||||
\(131\) | 14.7953 | 1.29267 | 0.646337 | − | 0.763052i | \(-0.276300\pi\) | ||||
0.646337 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(132\) | 5.12924 | 0.446443 | ||||||||
\(133\) | 30.8212 | 2.67253 | ||||||||
\(134\) | 15.7187 | 1.35789 | ||||||||
\(135\) | 8.15361 | 0.701751 | ||||||||
\(136\) | 26.5394 | 2.27574 | ||||||||
\(137\) | −18.2090 | −1.55570 | −0.777849 | − | 0.628451i | \(-0.783689\pi\) | ||||
−0.777849 | + | 0.628451i | \(0.783689\pi\) | |||||||
\(138\) | −30.4857 | −2.59511 | ||||||||
\(139\) | −0.751610 | −0.0637507 | −0.0318754 | − | 0.999492i | \(-0.510148\pi\) | ||||
−0.0318754 | + | 0.999492i | \(0.510148\pi\) | |||||||
\(140\) | −46.3822 | −3.92001 | ||||||||
\(141\) | 8.44118 | 0.710876 | ||||||||
\(142\) | −43.2832 | −3.63224 | ||||||||
\(143\) | −2.96024 | −0.247548 | ||||||||
\(144\) | 15.1336 | 1.26114 | ||||||||
\(145\) | 17.9045 | 1.48689 | ||||||||
\(146\) | 32.7741 | 2.71241 | ||||||||
\(147\) | −14.1114 | −1.16389 | ||||||||
\(148\) | 0.559990 | 0.0460309 | ||||||||
\(149\) | 9.02651 | 0.739481 | 0.369740 | − | 0.929135i | \(-0.379447\pi\) | ||||
0.369740 | + | 0.929135i | \(0.379447\pi\) | |||||||
\(150\) | 9.06130 | 0.739852 | ||||||||
\(151\) | 10.5635 | 0.859649 | 0.429825 | − | 0.902912i | \(-0.358575\pi\) | ||||
0.429825 | + | 0.902912i | \(0.358575\pi\) | |||||||
\(152\) | 62.9561 | 5.10641 | ||||||||
\(153\) | −5.30513 | −0.428894 | ||||||||
\(154\) | −4.79821 | −0.386651 | ||||||||
\(155\) | 4.22990 | 0.339754 | ||||||||
\(156\) | −61.8937 | −4.95546 | ||||||||
\(157\) | −6.66893 | −0.532239 | −0.266119 | − | 0.963940i | \(-0.585742\pi\) | ||||
−0.266119 | + | 0.963940i | \(0.585742\pi\) | |||||||
\(158\) | −2.52783 | −0.201103 | ||||||||
\(159\) | −9.27918 | −0.735887 | ||||||||
\(160\) | −28.8868 | −2.28370 | ||||||||
\(161\) | 20.2247 | 1.59393 | ||||||||
\(162\) | 29.5025 | 2.31793 | ||||||||
\(163\) | 6.19594 | 0.485303 | 0.242652 | − | 0.970113i | \(-0.421983\pi\) | ||||
0.242652 | + | 0.970113i | \(0.421983\pi\) | |||||||
\(164\) | −34.8312 | −2.71986 | ||||||||
\(165\) | 2.70735 | 0.210767 | ||||||||
\(166\) | 21.5210 | 1.67035 | ||||||||
\(167\) | 8.85709 | 0.685383 | 0.342691 | − | 0.939448i | \(-0.388662\pi\) | ||||
0.342691 | + | 0.939448i | \(0.388662\pi\) | |||||||
\(168\) | −59.1839 | −4.56614 | ||||||||
\(169\) | 22.7207 | 1.74774 | ||||||||
\(170\) | 23.7453 | 1.82118 | ||||||||
\(171\) | −12.5847 | −0.962374 | ||||||||
\(172\) | −22.7492 | −1.73461 | ||||||||
\(173\) | 6.87287 | 0.522535 | 0.261267 | − | 0.965266i | \(-0.415860\pi\) | ||||
0.261267 | + | 0.965266i | \(0.415860\pi\) | |||||||
\(174\) | 38.7267 | 2.93586 | ||||||||
\(175\) | −6.01143 | −0.454421 | ||||||||
\(176\) | −4.96951 | −0.374591 | ||||||||
\(177\) | 13.8200 | 1.03878 | ||||||||
\(178\) | 4.63617 | 0.347495 | ||||||||
\(179\) | 4.94169 | 0.369359 | 0.184679 | − | 0.982799i | \(-0.440875\pi\) | ||||
0.184679 | + | 0.982799i | \(0.440875\pi\) | |||||||
\(180\) | 18.9384 | 1.41159 | ||||||||
\(181\) | −6.80310 | −0.505671 | −0.252835 | − | 0.967509i | \(-0.581363\pi\) | ||||
−0.252835 | + | 0.967509i | \(0.581363\pi\) | |||||||
\(182\) | 57.8991 | 4.29177 | ||||||||
\(183\) | 2.94892 | 0.217990 | ||||||||
\(184\) | 41.3115 | 3.04553 | ||||||||
\(185\) | 0.295577 | 0.0217313 | ||||||||
\(186\) | 9.14908 | 0.670843 | ||||||||
\(187\) | 1.74207 | 0.127393 | ||||||||
\(188\) | −19.3898 | −1.41415 | ||||||||
\(189\) | −11.7000 | −0.851046 | ||||||||
\(190\) | 56.3279 | 4.08645 | ||||||||
\(191\) | 5.60597 | 0.405633 | 0.202817 | − | 0.979217i | \(-0.434990\pi\) | ||||
0.202817 | + | 0.979217i | \(0.434990\pi\) | |||||||
\(192\) | −19.8734 | −1.43424 | ||||||||
\(193\) | 19.9563 | 1.43649 | 0.718243 | − | 0.695792i | \(-0.244947\pi\) | ||||
0.718243 | + | 0.695792i | \(0.244947\pi\) | |||||||
\(194\) | 3.57820 | 0.256900 | ||||||||
\(195\) | −32.6691 | −2.33948 | ||||||||
\(196\) | 32.4147 | 2.31534 | ||||||||
\(197\) | 20.8896 | 1.48832 | 0.744160 | − | 0.668001i | \(-0.232850\pi\) | ||||
0.744160 | + | 0.668001i | \(0.232850\pi\) | |||||||
\(198\) | 1.95917 | 0.139232 | ||||||||
\(199\) | −5.19715 | −0.368416 | −0.184208 | − | 0.982887i | \(-0.558972\pi\) | ||||
−0.184208 | + | 0.982887i | \(0.558972\pi\) | |||||||
\(200\) | −12.2791 | −0.868263 | ||||||||
\(201\) | 12.7267 | 0.897672 | ||||||||
\(202\) | −21.1429 | −1.48761 | ||||||||
\(203\) | −25.6919 | −1.80322 | ||||||||
\(204\) | 36.4239 | 2.55018 | ||||||||
\(205\) | −18.3848 | −1.28405 | ||||||||
\(206\) | 13.1369 | 0.915294 | ||||||||
\(207\) | −8.25801 | −0.573971 | ||||||||
\(208\) | 59.9662 | 4.15791 | ||||||||
\(209\) | 4.13250 | 0.285851 | ||||||||
\(210\) | −52.9528 | −3.65409 | ||||||||
\(211\) | 20.4682 | 1.40909 | 0.704546 | − | 0.709658i | \(-0.251151\pi\) | ||||
0.704546 | + | 0.709658i | \(0.251151\pi\) | |||||||
\(212\) | 21.3148 | 1.46390 | ||||||||
\(213\) | −35.0444 | −2.40120 | ||||||||
\(214\) | 28.2186 | 1.92899 | ||||||||
\(215\) | −12.0076 | −0.818912 | ||||||||
\(216\) | −23.8986 | −1.62610 | ||||||||
\(217\) | −6.06966 | −0.412035 | ||||||||
\(218\) | −46.4392 | −3.14526 | ||||||||
\(219\) | 26.5357 | 1.79312 | ||||||||
\(220\) | −6.21892 | −0.419279 | ||||||||
\(221\) | −21.0213 | −1.41405 | ||||||||
\(222\) | 0.639320 | 0.0429084 | ||||||||
\(223\) | −25.2565 | −1.69130 | −0.845650 | − | 0.533739i | \(-0.820787\pi\) | ||||
−0.845650 | + | 0.533739i | \(0.820787\pi\) | |||||||
\(224\) | 41.4508 | 2.76955 | ||||||||
\(225\) | 2.45454 | 0.163636 | ||||||||
\(226\) | 49.4603 | 3.29005 | ||||||||
\(227\) | −14.5384 | −0.964950 | −0.482475 | − | 0.875910i | \(-0.660262\pi\) | ||||
−0.482475 | + | 0.875910i | \(0.660262\pi\) | |||||||
\(228\) | 86.4036 | 5.72222 | ||||||||
\(229\) | −8.14567 | −0.538281 | −0.269141 | − | 0.963101i | \(-0.586740\pi\) | ||||
−0.269141 | + | 0.963101i | \(0.586740\pi\) | |||||||
\(230\) | 36.9621 | 2.43721 | ||||||||
\(231\) | −3.88489 | −0.255607 | ||||||||
\(232\) | −52.4790 | −3.44542 | ||||||||
\(233\) | 16.4477 | 1.07752 | 0.538762 | − | 0.842458i | \(-0.318892\pi\) | ||||
0.538762 | + | 0.842458i | \(0.318892\pi\) | |||||||
\(234\) | −23.6409 | −1.54546 | ||||||||
\(235\) | −10.2344 | −0.667622 | ||||||||
\(236\) | −31.7453 | −2.06645 | ||||||||
\(237\) | −2.04666 | −0.132945 | ||||||||
\(238\) | −34.0731 | −2.20863 | ||||||||
\(239\) | 9.99532 | 0.646543 | 0.323272 | − | 0.946306i | \(-0.395217\pi\) | ||||
0.323272 | + | 0.946306i | \(0.395217\pi\) | |||||||
\(240\) | −54.8433 | −3.54012 | ||||||||
\(241\) | −24.0020 | −1.54610 | −0.773052 | − | 0.634342i | \(-0.781271\pi\) | ||||
−0.773052 | + | 0.634342i | \(0.781271\pi\) | |||||||
\(242\) | 28.2037 | 1.81300 | ||||||||
\(243\) | 14.3851 | 0.922803 | ||||||||
\(244\) | −6.77381 | −0.433649 | ||||||||
\(245\) | 17.1093 | 1.09307 | ||||||||
\(246\) | −39.7655 | −2.53535 | ||||||||
\(247\) | −49.8661 | −3.17290 | ||||||||
\(248\) | −12.3980 | −0.787276 | ||||||||
\(249\) | 17.4245 | 1.10423 | ||||||||
\(250\) | 22.7694 | 1.44007 | ||||||||
\(251\) | −17.3855 | −1.09736 | −0.548681 | − | 0.836032i | \(-0.684870\pi\) | ||||
−0.548681 | + | 0.836032i | \(0.684870\pi\) | |||||||
\(252\) | −27.1755 | −1.71190 | ||||||||
\(253\) | 2.71173 | 0.170485 | ||||||||
\(254\) | −36.4160 | −2.28494 | ||||||||
\(255\) | 19.2255 | 1.20394 | ||||||||
\(256\) | −13.2028 | −0.825173 | ||||||||
\(257\) | 25.8083 | 1.60987 | 0.804937 | − | 0.593360i | \(-0.202199\pi\) | ||||
0.804937 | + | 0.593360i | \(0.202199\pi\) | |||||||
\(258\) | −25.9719 | −1.61694 | ||||||||
\(259\) | −0.424137 | −0.0263546 | ||||||||
\(260\) | 75.0425 | 4.65394 | ||||||||
\(261\) | 10.4903 | 0.649336 | ||||||||
\(262\) | −38.8001 | −2.39708 | ||||||||
\(263\) | −21.8763 | −1.34895 | −0.674475 | − | 0.738297i | \(-0.735630\pi\) | ||||
−0.674475 | + | 0.738297i | \(0.735630\pi\) | |||||||
\(264\) | −7.93537 | −0.488388 | ||||||||
\(265\) | 11.2505 | 0.691111 | ||||||||
\(266\) | −80.8272 | −4.95584 | ||||||||
\(267\) | 3.75369 | 0.229722 | ||||||||
\(268\) | −29.2339 | −1.78574 | ||||||||
\(269\) | 2.17383 | 0.132541 | 0.0662705 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662705 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(270\) | −21.3825 | −1.30130 | ||||||||
\(271\) | −27.7046 | −1.68293 | −0.841467 | − | 0.540308i | \(-0.818308\pi\) | ||||
−0.841467 | + | 0.540308i | \(0.818308\pi\) | |||||||
\(272\) | −35.2896 | −2.13975 | ||||||||
\(273\) | 46.8782 | 2.83720 | ||||||||
\(274\) | 47.7523 | 2.88482 | ||||||||
\(275\) | −0.806011 | −0.0486043 | ||||||||
\(276\) | 56.6977 | 3.41280 | ||||||||
\(277\) | −12.2117 | −0.733730 | −0.366865 | − | 0.930274i | \(-0.619569\pi\) | ||||
−0.366865 | + | 0.930274i | \(0.619569\pi\) | |||||||
\(278\) | 1.97107 | 0.118217 | ||||||||
\(279\) | 2.47832 | 0.148373 | ||||||||
\(280\) | 71.7571 | 4.28831 | ||||||||
\(281\) | 29.9597 | 1.78725 | 0.893624 | − | 0.448817i | \(-0.148154\pi\) | ||||
0.893624 | + | 0.448817i | \(0.148154\pi\) | |||||||
\(282\) | −22.1366 | −1.31822 | ||||||||
\(283\) | −17.7801 | −1.05692 | −0.528460 | − | 0.848958i | \(-0.677230\pi\) | ||||
−0.528460 | + | 0.848958i | \(0.677230\pi\) | |||||||
\(284\) | 80.4987 | 4.77672 | ||||||||
\(285\) | 45.6061 | 2.70147 | ||||||||
\(286\) | 7.76310 | 0.459042 | ||||||||
\(287\) | 26.3811 | 1.55723 | ||||||||
\(288\) | −16.9249 | −0.997309 | ||||||||
\(289\) | −4.62915 | −0.272303 | ||||||||
\(290\) | −46.9539 | −2.75723 | ||||||||
\(291\) | 2.89710 | 0.169831 | ||||||||
\(292\) | −60.9539 | −3.56706 | ||||||||
\(293\) | −8.28073 | −0.483766 | −0.241883 | − | 0.970305i | \(-0.577765\pi\) | ||||
−0.241883 | + | 0.970305i | \(0.577765\pi\) | |||||||
\(294\) | 37.0067 | 2.15827 | ||||||||
\(295\) | −16.7560 | −0.975573 | ||||||||
\(296\) | −0.866352 | −0.0503557 | ||||||||
\(297\) | −1.56873 | −0.0910268 | ||||||||
\(298\) | −23.6716 | −1.37126 | ||||||||
\(299\) | −32.7219 | −1.89236 | ||||||||
\(300\) | −16.8524 | −0.972971 | ||||||||
\(301\) | 17.2302 | 0.993133 | ||||||||
\(302\) | −27.7025 | −1.59410 | ||||||||
\(303\) | −17.1184 | −0.983428 | ||||||||
\(304\) | −83.7129 | −4.80126 | ||||||||
\(305\) | −3.57539 | −0.204726 | ||||||||
\(306\) | 13.9125 | 0.795324 | ||||||||
\(307\) | 12.7718 | 0.728926 | 0.364463 | − | 0.931218i | \(-0.381253\pi\) | ||||
0.364463 | + | 0.931218i | \(0.381253\pi\) | |||||||
\(308\) | 8.92378 | 0.508480 | ||||||||
\(309\) | 10.6364 | 0.605082 | ||||||||
\(310\) | −11.0927 | −0.630025 | ||||||||
\(311\) | −24.2820 | −1.37691 | −0.688453 | − | 0.725281i | \(-0.741710\pi\) | ||||
−0.688453 | + | 0.725281i | \(0.741710\pi\) | |||||||
\(312\) | 95.7546 | 5.42104 | ||||||||
\(313\) | 14.4328 | 0.815790 | 0.407895 | − | 0.913029i | \(-0.366263\pi\) | ||||
0.407895 | + | 0.913029i | \(0.366263\pi\) | |||||||
\(314\) | 17.4890 | 0.986962 | ||||||||
\(315\) | −14.3440 | −0.808190 | ||||||||
\(316\) | 4.70129 | 0.264468 | ||||||||
\(317\) | 5.31540 | 0.298542 | 0.149271 | − | 0.988796i | \(-0.452307\pi\) | ||||
0.149271 | + | 0.988796i | \(0.452307\pi\) | |||||||
\(318\) | 24.3343 | 1.36460 | ||||||||
\(319\) | −3.44477 | −0.192870 | ||||||||
\(320\) | 24.0954 | 1.34697 | ||||||||
\(321\) | 22.8473 | 1.27521 | ||||||||
\(322\) | −53.0385 | −2.95572 | ||||||||
\(323\) | 29.3458 | 1.63284 | ||||||||
\(324\) | −54.8692 | −3.04829 | ||||||||
\(325\) | 9.72599 | 0.539501 | ||||||||
\(326\) | −16.2486 | −0.899926 | ||||||||
\(327\) | −37.5997 | −2.07927 | ||||||||
\(328\) | 53.8867 | 2.97540 | ||||||||
\(329\) | 14.6858 | 0.809657 | ||||||||
\(330\) | −7.09991 | −0.390837 | ||||||||
\(331\) | −11.8664 | −0.652237 | −0.326119 | − | 0.945329i | \(-0.605741\pi\) | ||||
−0.326119 | + | 0.945329i | \(0.605741\pi\) | |||||||
\(332\) | −40.0250 | −2.19666 | ||||||||
\(333\) | 0.173180 | 0.00949022 | ||||||||
\(334\) | −23.2274 | −1.27094 | ||||||||
\(335\) | −15.4304 | −0.843053 | ||||||||
\(336\) | 78.6970 | 4.29327 | ||||||||
\(337\) | −11.1479 | −0.607265 | −0.303632 | − | 0.952789i | \(-0.598199\pi\) | ||||
−0.303632 | + | 0.952789i | \(0.598199\pi\) | |||||||
\(338\) | −59.5840 | −3.24094 | ||||||||
\(339\) | 40.0457 | 2.17498 | ||||||||
\(340\) | −44.1619 | −2.39501 | ||||||||
\(341\) | −0.813819 | −0.0440708 | ||||||||
\(342\) | 33.0028 | 1.78459 | ||||||||
\(343\) | 1.30751 | 0.0705987 | ||||||||
\(344\) | 35.1949 | 1.89758 | ||||||||
\(345\) | 29.9265 | 1.61119 | ||||||||
\(346\) | −18.0238 | −0.968967 | ||||||||
\(347\) | 11.6908 | 0.627595 | 0.313798 | − | 0.949490i | \(-0.398399\pi\) | ||||
0.313798 | + | 0.949490i | \(0.398399\pi\) | |||||||
\(348\) | −72.0244 | −3.86091 | ||||||||
\(349\) | −9.79573 | −0.524353 | −0.262177 | − | 0.965020i | \(-0.584440\pi\) | ||||
−0.262177 | + | 0.965020i | \(0.584440\pi\) | |||||||
\(350\) | 15.7647 | 0.842660 | ||||||||
\(351\) | 18.9296 | 1.01039 | ||||||||
\(352\) | 5.55772 | 0.296228 | ||||||||
\(353\) | −21.0312 | −1.11938 | −0.559689 | − | 0.828703i | \(-0.689079\pi\) | ||||
−0.559689 | + | 0.828703i | \(0.689079\pi\) | |||||||
\(354\) | −36.2425 | −1.92627 | ||||||||
\(355\) | 42.4893 | 2.25510 | ||||||||
\(356\) | −8.62241 | −0.456987 | ||||||||
\(357\) | −27.5874 | −1.46008 | ||||||||
\(358\) | −12.9594 | −0.684924 | ||||||||
\(359\) | −23.6567 | −1.24855 | −0.624277 | − | 0.781203i | \(-0.714606\pi\) | ||||
−0.624277 | + | 0.781203i | \(0.714606\pi\) | |||||||
\(360\) | −29.2993 | −1.54421 | ||||||||
\(361\) | 50.6131 | 2.66385 | ||||||||
\(362\) | 17.8409 | 0.937695 | ||||||||
\(363\) | 22.8352 | 1.19854 | ||||||||
\(364\) | −107.682 | −5.64405 | ||||||||
\(365\) | −32.1730 | −1.68401 | ||||||||
\(366\) | −7.73341 | −0.404232 | ||||||||
\(367\) | 1.30702 | 0.0682259 | 0.0341130 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341130 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(368\) | −54.9321 | −2.86353 | ||||||||
\(369\) | −10.7717 | −0.560754 | ||||||||
\(370\) | −0.775140 | −0.0402976 | ||||||||
\(371\) | −16.1438 | −0.838144 | ||||||||
\(372\) | −17.0156 | −0.882217 | ||||||||
\(373\) | −27.2531 | −1.41111 | −0.705555 | − | 0.708655i | \(-0.749302\pi\) | ||||
−0.705555 | + | 0.708655i | \(0.749302\pi\) | |||||||
\(374\) | −4.56852 | −0.236232 | ||||||||
\(375\) | 18.4354 | 0.951998 | ||||||||
\(376\) | 29.9977 | 1.54701 | ||||||||
\(377\) | 41.5674 | 2.14083 | ||||||||
\(378\) | 30.6826 | 1.57815 | ||||||||
\(379\) | 12.3670 | 0.635250 | 0.317625 | − | 0.948216i | \(-0.397115\pi\) | ||||
0.317625 | + | 0.948216i | \(0.397115\pi\) | |||||||
\(380\) | −104.759 | −5.37405 | ||||||||
\(381\) | −29.4843 | −1.51053 | ||||||||
\(382\) | −14.7014 | −0.752190 | ||||||||
\(383\) | 21.6502 | 1.10628 | 0.553138 | − | 0.833090i | \(-0.313430\pi\) | ||||
0.553138 | + | 0.833090i | \(0.313430\pi\) | |||||||
\(384\) | 4.46664 | 0.227937 | ||||||||
\(385\) | 4.71020 | 0.240054 | ||||||||
\(386\) | −52.3346 | −2.66376 | ||||||||
\(387\) | −7.03532 | −0.357625 | ||||||||
\(388\) | −6.65478 | −0.337845 | ||||||||
\(389\) | −33.1177 | −1.67913 | −0.839567 | − | 0.543256i | \(-0.817191\pi\) | ||||
−0.839567 | + | 0.543256i | \(0.817191\pi\) | |||||||
\(390\) | 85.6733 | 4.33823 | ||||||||
\(391\) | 19.2566 | 0.973846 | ||||||||
\(392\) | −50.1483 | −2.53287 | ||||||||
\(393\) | −31.4147 | −1.58466 | ||||||||
\(394\) | −54.7820 | −2.75988 | ||||||||
\(395\) | 2.48146 | 0.124856 | ||||||||
\(396\) | −3.64369 | −0.183102 | ||||||||
\(397\) | −10.8938 | −0.546743 | −0.273371 | − | 0.961909i | \(-0.588139\pi\) | ||||
−0.273371 | + | 0.961909i | \(0.588139\pi\) | |||||||
\(398\) | 13.6293 | 0.683176 | ||||||||
\(399\) | −65.4421 | −3.27620 | ||||||||
\(400\) | 16.3276 | 0.816378 | ||||||||
\(401\) | 0.640899 | 0.0320050 | 0.0160025 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160025 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(402\) | −33.3753 | −1.66461 | ||||||||
\(403\) | 9.82020 | 0.489179 | ||||||||
\(404\) | 39.3219 | 1.95634 | ||||||||
\(405\) | −28.9614 | −1.43910 | ||||||||
\(406\) | 67.3761 | 3.34382 | ||||||||
\(407\) | −0.0568682 | −0.00281885 | ||||||||
\(408\) | −56.3507 | −2.78978 | ||||||||
\(409\) | −20.6544 | −1.02129 | −0.510646 | − | 0.859791i | \(-0.670594\pi\) | ||||
−0.510646 | + | 0.859791i | \(0.670594\pi\) | |||||||
\(410\) | 48.2133 | 2.38109 | ||||||||
\(411\) | 38.6628 | 1.90710 | ||||||||
\(412\) | −24.4323 | −1.20369 | ||||||||
\(413\) | 24.0439 | 1.18312 | ||||||||
\(414\) | 21.6563 | 1.06435 | ||||||||
\(415\) | −21.1262 | −1.03705 | ||||||||
\(416\) | −67.0640 | −3.28808 | ||||||||
\(417\) | 1.59588 | 0.0781506 | ||||||||
\(418\) | −10.8373 | −0.530070 | ||||||||
\(419\) | 11.8486 | 0.578842 | 0.289421 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289421 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(420\) | 98.4825 | 4.80545 | ||||||||
\(421\) | −7.66252 | −0.373448 | −0.186724 | − | 0.982412i | \(-0.559787\pi\) | ||||
−0.186724 | + | 0.982412i | \(0.559787\pi\) | |||||||
\(422\) | −53.6771 | −2.61296 | ||||||||
\(423\) | −5.99641 | −0.291556 | ||||||||
\(424\) | −32.9757 | −1.60144 | ||||||||
\(425\) | −5.72366 | −0.277638 | ||||||||
\(426\) | 91.9024 | 4.45269 | ||||||||
\(427\) | 5.13048 | 0.248281 | ||||||||
\(428\) | −52.4814 | −2.53679 | ||||||||
\(429\) | 6.28542 | 0.303463 | ||||||||
\(430\) | 31.4895 | 1.51856 | ||||||||
\(431\) | 13.5323 | 0.651826 | 0.325913 | − | 0.945400i | \(-0.394328\pi\) | ||||
0.325913 | + | 0.945400i | \(0.394328\pi\) | |||||||
\(432\) | 31.7781 | 1.52892 | ||||||||
\(433\) | −6.82557 | −0.328016 | −0.164008 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164008 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(434\) | 15.9174 | 0.764061 | ||||||||
\(435\) | −38.0164 | −1.82274 | ||||||||
\(436\) | 86.3684 | 4.13630 | ||||||||
\(437\) | 45.6799 | 2.18516 | ||||||||
\(438\) | −69.5888 | −3.32508 | ||||||||
\(439\) | 14.1805 | 0.676799 | 0.338400 | − | 0.941003i | \(-0.390114\pi\) | ||||
0.338400 | + | 0.941003i | \(0.390114\pi\) | |||||||
\(440\) | 9.62118 | 0.458672 | ||||||||
\(441\) | 10.0244 | 0.477354 | ||||||||
\(442\) | 55.1275 | 2.62215 | ||||||||
\(443\) | 38.2677 | 1.81816 | 0.909078 | − | 0.416627i | \(-0.136788\pi\) | ||||
0.909078 | + | 0.416627i | \(0.136788\pi\) | |||||||
\(444\) | −1.18902 | −0.0564283 | ||||||||
\(445\) | −4.55113 | −0.215744 | ||||||||
\(446\) | 66.2341 | 3.13627 | ||||||||
\(447\) | −19.1658 | −0.906513 | ||||||||
\(448\) | −34.5754 | −1.63354 | ||||||||
\(449\) | 22.4203 | 1.05808 | 0.529040 | − | 0.848597i | \(-0.322552\pi\) | ||||
0.529040 | + | 0.848597i | \(0.322552\pi\) | |||||||
\(450\) | −6.43694 | −0.303440 | ||||||||
\(451\) | 3.53717 | 0.166559 | ||||||||
\(452\) | −91.9869 | −4.32670 | ||||||||
\(453\) | −22.4294 | −1.05383 | ||||||||
\(454\) | 38.1265 | 1.78936 | ||||||||
\(455\) | −56.8372 | −2.66457 | ||||||||
\(456\) | −133.674 | −6.25984 | ||||||||
\(457\) | −12.0090 | −0.561757 | −0.280879 | − | 0.959743i | \(-0.590626\pi\) | ||||
−0.280879 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(458\) | 21.3617 | 0.998166 | ||||||||
\(459\) | −11.1399 | −0.519965 | ||||||||
\(460\) | −68.7427 | −3.20515 | ||||||||
\(461\) | 12.8426 | 0.598141 | 0.299070 | − | 0.954231i | \(-0.403323\pi\) | ||||
0.299070 | + | 0.954231i | \(0.403323\pi\) | |||||||
\(462\) | 10.1880 | 0.473987 | ||||||||
\(463\) | −25.5790 | −1.18876 | −0.594379 | − | 0.804185i | \(-0.702602\pi\) | ||||
−0.594379 | + | 0.804185i | \(0.702602\pi\) | |||||||
\(464\) | 69.7815 | 3.23952 | ||||||||
\(465\) | −8.98127 | −0.416496 | ||||||||
\(466\) | −43.1334 | −1.99812 | ||||||||
\(467\) | −30.1067 | −1.39317 | −0.696586 | − | 0.717473i | \(-0.745299\pi\) | ||||
−0.696586 | + | 0.717473i | \(0.745299\pi\) | |||||||
\(468\) | 43.9678 | 2.03241 | ||||||||
\(469\) | 22.1417 | 1.02241 | ||||||||
\(470\) | 26.8394 | 1.23801 | ||||||||
\(471\) | 14.1600 | 0.652460 | ||||||||
\(472\) | 49.1127 | 2.26059 | ||||||||
\(473\) | 2.31023 | 0.106224 | ||||||||
\(474\) | 5.36729 | 0.246528 | ||||||||
\(475\) | −13.5775 | −0.622978 | ||||||||
\(476\) | 63.3697 | 2.90455 | ||||||||
\(477\) | 6.59171 | 0.301814 | ||||||||
\(478\) | −26.2123 | −1.19892 | ||||||||
\(479\) | 22.1949 | 1.01411 | 0.507055 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(480\) | 61.3348 | 2.79954 | ||||||||
\(481\) | 0.686218 | 0.0312888 | ||||||||
\(482\) | 62.9442 | 2.86703 | ||||||||
\(483\) | −42.9428 | −1.95397 | ||||||||
\(484\) | −52.4537 | −2.38426 | ||||||||
\(485\) | −3.51257 | −0.159497 | ||||||||
\(486\) | −37.7243 | −1.71121 | ||||||||
\(487\) | −10.3416 | −0.468625 | −0.234312 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234312 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(488\) | 10.4796 | 0.474391 | ||||||||
\(489\) | −13.1557 | −0.594923 | ||||||||
\(490\) | −44.8685 | −2.02695 | ||||||||
\(491\) | 28.4685 | 1.28476 | 0.642382 | − | 0.766385i | \(-0.277946\pi\) | ||||
0.642382 | + | 0.766385i | \(0.277946\pi\) | |||||||
\(492\) | 73.9564 | 3.33421 | ||||||||
\(493\) | −24.4621 | −1.10172 | ||||||||
\(494\) | 130.772 | 5.88370 | ||||||||
\(495\) | −1.92324 | −0.0864430 | ||||||||
\(496\) | 16.4857 | 0.740230 | ||||||||
\(497\) | −60.9697 | −2.73486 | ||||||||
\(498\) | −45.6951 | −2.04765 | ||||||||
\(499\) | −29.2362 | −1.30879 | −0.654395 | − | 0.756153i | \(-0.727077\pi\) | ||||
−0.654395 | + | 0.756153i | \(0.727077\pi\) | |||||||
\(500\) | −42.3470 | −1.89381 | ||||||||
\(501\) | −18.8061 | −0.840195 | ||||||||
\(502\) | 45.5927 | 2.03490 | ||||||||
\(503\) | 34.1701 | 1.52357 | 0.761784 | − | 0.647831i | \(-0.224324\pi\) | ||||
0.761784 | + | 0.647831i | \(0.224324\pi\) | |||||||
\(504\) | 42.0428 | 1.87274 | ||||||||
\(505\) | 20.7551 | 0.923591 | ||||||||
\(506\) | −7.11139 | −0.316140 | ||||||||
\(507\) | −48.2424 | −2.14252 | ||||||||
\(508\) | 67.7270 | 3.00490 | ||||||||
\(509\) | −15.3626 | −0.680937 | −0.340469 | − | 0.940256i | \(-0.610586\pi\) | ||||
−0.340469 | + | 0.940256i | \(0.610586\pi\) | |||||||
\(510\) | −50.4180 | −2.23255 | ||||||||
\(511\) | 46.1664 | 2.04228 | ||||||||
\(512\) | 38.8310 | 1.71610 | ||||||||
\(513\) | −26.4257 | −1.16672 | ||||||||
\(514\) | −67.6811 | −2.98528 | ||||||||
\(515\) | −12.8960 | −0.568266 | ||||||||
\(516\) | 48.3030 | 2.12642 | ||||||||
\(517\) | 1.96908 | 0.0865998 | ||||||||
\(518\) | 1.11228 | 0.0488708 | ||||||||
\(519\) | −14.5931 | −0.640564 | ||||||||
\(520\) | −116.097 | −5.09119 | ||||||||
\(521\) | −21.3254 | −0.934282 | −0.467141 | − | 0.884183i | \(-0.654716\pi\) | ||||
−0.467141 | + | 0.884183i | \(0.654716\pi\) | |||||||
\(522\) | −27.5105 | −1.20410 | ||||||||
\(523\) | 39.0138 | 1.70596 | 0.852978 | − | 0.521948i | \(-0.174794\pi\) | ||||
0.852978 | + | 0.521948i | \(0.174794\pi\) | |||||||
\(524\) | 72.1611 | 3.15237 | ||||||||
\(525\) | 12.7640 | 0.557065 | ||||||||
\(526\) | 57.3697 | 2.50144 | ||||||||
\(527\) | −5.77910 | −0.251742 | ||||||||
\(528\) | 10.5517 | 0.459203 | ||||||||
\(529\) | 6.97493 | 0.303258 | ||||||||
\(530\) | −29.5039 | −1.28157 | ||||||||
\(531\) | −9.81743 | −0.426040 | ||||||||
\(532\) | 150.324 | 6.51736 | ||||||||
\(533\) | −42.6824 | −1.84878 | ||||||||
\(534\) | −9.84389 | −0.425987 | ||||||||
\(535\) | −27.7011 | −1.19762 | ||||||||
\(536\) | 45.2273 | 1.95352 | ||||||||
\(537\) | −10.4926 | −0.452789 | ||||||||
\(538\) | −5.70079 | −0.245779 | ||||||||
\(539\) | −3.29178 | −0.141787 | ||||||||
\(540\) | 39.7675 | 1.71132 | ||||||||
\(541\) | 30.5151 | 1.31195 | 0.655973 | − | 0.754785i | \(-0.272259\pi\) | ||||
0.655973 | + | 0.754785i | \(0.272259\pi\) | |||||||
\(542\) | 72.6542 | 3.12076 | ||||||||
\(543\) | 14.4449 | 0.619890 | ||||||||
\(544\) | 39.4666 | 1.69212 | ||||||||
\(545\) | 45.5875 | 1.95275 | ||||||||
\(546\) | −122.936 | −5.26118 | ||||||||
\(547\) | 15.6078 | 0.667343 | 0.333671 | − | 0.942689i | \(-0.391712\pi\) | ||||
0.333671 | + | 0.942689i | \(0.391712\pi\) | |||||||
\(548\) | −88.8105 | −3.79379 | ||||||||
\(549\) | −2.09484 | −0.0894056 | ||||||||
\(550\) | 2.11373 | 0.0901298 | ||||||||
\(551\) | −58.0282 | −2.47208 | ||||||||
\(552\) | −87.7160 | −3.73344 | ||||||||
\(553\) | −3.56076 | −0.151419 | ||||||||
\(554\) | 32.0247 | 1.36060 | ||||||||
\(555\) | −0.627594 | −0.0266399 | ||||||||
\(556\) | −3.66582 | −0.155465 | ||||||||
\(557\) | −7.65266 | −0.324254 | −0.162127 | − | 0.986770i | \(-0.551835\pi\) | ||||
−0.162127 | + | 0.986770i | \(0.551835\pi\) | |||||||
\(558\) | −6.49929 | −0.275137 | ||||||||
\(559\) | −27.8771 | −1.17907 | ||||||||
\(560\) | −95.4156 | −4.03205 | ||||||||
\(561\) | −3.69892 | −0.156168 | ||||||||
\(562\) | −78.5681 | −3.31420 | ||||||||
\(563\) | −43.7816 | −1.84518 | −0.922588 | − | 0.385787i | \(-0.873930\pi\) | ||||
−0.922588 | + | 0.385787i | \(0.873930\pi\) | |||||||
\(564\) | 41.1701 | 1.73357 | ||||||||
\(565\) | −48.5531 | −2.04264 | ||||||||
\(566\) | 46.6277 | 1.95991 | ||||||||
\(567\) | 41.5579 | 1.74527 | ||||||||
\(568\) | −124.538 | −5.22551 | ||||||||
\(569\) | −4.26891 | −0.178962 | −0.0894810 | − | 0.995989i | \(-0.528521\pi\) | ||||
−0.0894810 | + | 0.995989i | \(0.528521\pi\) | |||||||
\(570\) | −119.600 | −5.00949 | ||||||||
\(571\) | −36.3894 | −1.52285 | −0.761424 | − | 0.648255i | \(-0.775499\pi\) | ||||
−0.761424 | + | 0.648255i | \(0.775499\pi\) | |||||||
\(572\) | −14.4379 | −0.603681 | ||||||||
\(573\) | −11.9030 | −0.497257 | ||||||||
\(574\) | −69.1834 | −2.88766 | ||||||||
\(575\) | −8.90950 | −0.371552 | ||||||||
\(576\) | 14.1176 | 0.588233 | ||||||||
\(577\) | 5.30055 | 0.220665 | 0.110332 | − | 0.993895i | \(-0.464808\pi\) | ||||
0.110332 | + | 0.993895i | \(0.464808\pi\) | |||||||
\(578\) | 12.1398 | 0.504948 | ||||||||
\(579\) | −42.3729 | −1.76096 | ||||||||
\(580\) | 87.3255 | 3.62599 | ||||||||
\(581\) | 30.3149 | 1.25768 | ||||||||
\(582\) | −7.59752 | −0.314927 | ||||||||
\(583\) | −2.16456 | −0.0896468 | ||||||||
\(584\) | 94.3007 | 3.90219 | ||||||||
\(585\) | 23.2073 | 0.959505 | ||||||||
\(586\) | 21.7159 | 0.897075 | ||||||||
\(587\) | −40.2217 | −1.66013 | −0.830064 | − | 0.557668i | \(-0.811696\pi\) | ||||
−0.830064 | + | 0.557668i | \(0.811696\pi\) | |||||||
\(588\) | −68.8256 | −2.83832 | ||||||||
\(589\) | −13.7090 | −0.564870 | ||||||||
\(590\) | 43.9419 | 1.80906 | ||||||||
\(591\) | −44.3545 | −1.82450 | ||||||||
\(592\) | 1.15199 | 0.0473465 | ||||||||
\(593\) | 23.9449 | 0.983298 | 0.491649 | − | 0.870793i | \(-0.336394\pi\) | ||||
0.491649 | + | 0.870793i | \(0.336394\pi\) | |||||||
\(594\) | 4.11392 | 0.168796 | ||||||||
\(595\) | 33.4482 | 1.37124 | ||||||||
\(596\) | 44.0249 | 1.80333 | ||||||||
\(597\) | 11.0350 | 0.451633 | ||||||||
\(598\) | 85.8119 | 3.50911 | ||||||||
\(599\) | 28.4448 | 1.16222 | 0.581111 | − | 0.813825i | \(-0.302618\pi\) | ||||
0.581111 | + | 0.813825i | \(0.302618\pi\) | |||||||
\(600\) | 26.0720 | 1.06438 | ||||||||
\(601\) | 16.5880 | 0.676640 | 0.338320 | − | 0.941031i | \(-0.390141\pi\) | ||||
0.338320 | + | 0.941031i | \(0.390141\pi\) | |||||||
\(602\) | −45.1855 | −1.84163 | ||||||||
\(603\) | −9.04075 | −0.368168 | ||||||||
\(604\) | 51.5215 | 2.09638 | ||||||||
\(605\) | −27.6864 | −1.12561 | ||||||||
\(606\) | 44.8924 | 1.82363 | ||||||||
\(607\) | 10.2001 | 0.414009 | 0.207004 | − | 0.978340i | \(-0.433629\pi\) | ||||
0.207004 | + | 0.978340i | \(0.433629\pi\) | |||||||
\(608\) | 93.6215 | 3.79685 | ||||||||
\(609\) | 54.5513 | 2.21053 | ||||||||
\(610\) | 9.37632 | 0.379636 | ||||||||
\(611\) | −23.7605 | −0.961246 | ||||||||
\(612\) | −25.8747 | −1.04592 | ||||||||
\(613\) | −3.26789 | −0.131989 | −0.0659945 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659945 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(614\) | −33.4935 | −1.35169 | ||||||||
\(615\) | 39.0361 | 1.57409 | ||||||||
\(616\) | −13.8058 | −0.556253 | ||||||||
\(617\) | 26.3219 | 1.05968 | 0.529841 | − | 0.848097i | \(-0.322252\pi\) | ||||
0.529841 | + | 0.848097i | \(0.322252\pi\) | |||||||
\(618\) | −27.8935 | −1.12204 | ||||||||
\(619\) | 7.61212 | 0.305957 | 0.152978 | − | 0.988230i | \(-0.451113\pi\) | ||||
0.152978 | + | 0.988230i | \(0.451113\pi\) | |||||||
\(620\) | 20.6304 | 0.828538 | ||||||||
\(621\) | −17.3404 | −0.695847 | ||||||||
\(622\) | 63.6785 | 2.55328 | ||||||||
\(623\) | 6.53061 | 0.261643 | ||||||||
\(624\) | −127.325 | −5.09709 | ||||||||
\(625\) | −30.4884 | −1.21954 | ||||||||
\(626\) | −37.8494 | −1.51277 | ||||||||
\(627\) | −8.77446 | −0.350418 | ||||||||
\(628\) | −32.5263 | −1.29794 | ||||||||
\(629\) | −0.403833 | −0.0161019 | ||||||||
\(630\) | 37.6164 | 1.49867 | ||||||||
\(631\) | 34.9343 | 1.39071 | 0.695355 | − | 0.718666i | \(-0.255247\pi\) | ||||
0.695355 | + | 0.718666i | \(0.255247\pi\) | |||||||
\(632\) | −7.27329 | −0.289316 | ||||||||
\(633\) | −43.4599 | −1.72737 | ||||||||
\(634\) | −13.9394 | −0.553605 | ||||||||
\(635\) | 35.7480 | 1.41862 | ||||||||
\(636\) | −45.2573 | −1.79457 | ||||||||
\(637\) | 39.7213 | 1.57382 | ||||||||
\(638\) | 9.03377 | 0.357650 | ||||||||
\(639\) | 24.8947 | 0.984819 | ||||||||
\(640\) | −5.41554 | −0.214068 | ||||||||
\(641\) | 39.1496 | 1.54632 | 0.773158 | − | 0.634214i | \(-0.218676\pi\) | ||||
0.773158 | + | 0.634214i | \(0.218676\pi\) | |||||||
\(642\) | −59.9161 | −2.36470 | ||||||||
\(643\) | −28.6390 | −1.12941 | −0.564705 | − | 0.825293i | \(-0.691010\pi\) | ||||
−0.564705 | + | 0.825293i | \(0.691010\pi\) | |||||||
\(644\) | 98.6418 | 3.88703 | ||||||||
\(645\) | 25.4955 | 1.00389 | ||||||||
\(646\) | −76.9580 | −3.02787 | ||||||||
\(647\) | 11.7241 | 0.460920 | 0.230460 | − | 0.973082i | \(-0.425977\pi\) | ||||
0.230460 | + | 0.973082i | \(0.425977\pi\) | |||||||
\(648\) | 84.8872 | 3.33468 | ||||||||
\(649\) | 3.22380 | 0.126545 | ||||||||
\(650\) | −25.5060 | −1.00043 | ||||||||
\(651\) | 12.8876 | 0.505105 | ||||||||
\(652\) | 30.2194 | 1.18348 | ||||||||
\(653\) | −13.7044 | −0.536296 | −0.268148 | − | 0.963378i | \(-0.586412\pi\) | ||||
−0.268148 | + | 0.963378i | \(0.586412\pi\) | |||||||
\(654\) | 98.6036 | 3.85571 | ||||||||
\(655\) | 38.0885 | 1.48824 | ||||||||
\(656\) | −71.6533 | −2.79759 | ||||||||
\(657\) | −18.8503 | −0.735422 | ||||||||
\(658\) | −38.5130 | −1.50139 | ||||||||
\(659\) | 35.6349 | 1.38814 | 0.694069 | − | 0.719909i | \(-0.255816\pi\) | ||||
0.694069 | + | 0.719909i | \(0.255816\pi\) | |||||||
\(660\) | 13.2045 | 0.513985 | ||||||||
\(661\) | 26.3826 | 1.02616 | 0.513082 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513082 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(662\) | 31.1192 | 1.20948 | ||||||||
\(663\) | 44.6342 | 1.73345 | ||||||||
\(664\) | 61.9220 | 2.40304 | ||||||||
\(665\) | 79.3448 | 3.07686 | ||||||||
\(666\) | −0.454158 | −0.0175983 | ||||||||
\(667\) | −38.0779 | −1.47438 | ||||||||
\(668\) | 43.1986 | 1.67140 | ||||||||
\(669\) | 53.6267 | 2.07333 | ||||||||
\(670\) | 40.4656 | 1.56332 | ||||||||
\(671\) | 0.687894 | 0.0265559 | ||||||||
\(672\) | −88.0119 | −3.39513 | ||||||||
\(673\) | 11.6934 | 0.450747 | 0.225373 | − | 0.974272i | \(-0.427640\pi\) | ||||
0.225373 | + | 0.974272i | \(0.427640\pi\) | |||||||
\(674\) | 29.2349 | 1.12609 | ||||||||
\(675\) | 5.15412 | 0.198382 | ||||||||
\(676\) | 110.815 | 4.26213 | ||||||||
\(677\) | 20.1776 | 0.775487 | 0.387744 | − | 0.921767i | \(-0.373255\pi\) | ||||
0.387744 | + | 0.921767i | \(0.373255\pi\) | |||||||
\(678\) | −105.018 | −4.03320 | ||||||||
\(679\) | 5.04033 | 0.193430 | ||||||||
\(680\) | 68.3221 | 2.62003 | ||||||||
\(681\) | 30.8692 | 1.18291 | ||||||||
\(682\) | 2.13421 | 0.0817230 | ||||||||
\(683\) | −10.6885 | −0.408984 | −0.204492 | − | 0.978868i | \(-0.565554\pi\) | ||||
−0.204492 | + | 0.978868i | \(0.565554\pi\) | |||||||
\(684\) | −61.3791 | −2.34689 | ||||||||
\(685\) | −46.8765 | −1.79106 | ||||||||
\(686\) | −3.42888 | −0.130915 | ||||||||
\(687\) | 17.2956 | 0.659867 | ||||||||
\(688\) | −46.7987 | −1.78419 | ||||||||
\(689\) | 26.1193 | 0.995066 | ||||||||
\(690\) | −78.4810 | −2.98772 | ||||||||
\(691\) | 30.8960 | 1.17534 | 0.587669 | − | 0.809101i | \(-0.300046\pi\) | ||||
0.587669 | + | 0.809101i | \(0.300046\pi\) | |||||||
\(692\) | 33.5210 | 1.27428 | ||||||||
\(693\) | 2.75973 | 0.104834 | ||||||||
\(694\) | −30.6587 | −1.16379 | ||||||||
\(695\) | −1.93491 | −0.0733955 | ||||||||
\(696\) | 111.428 | 4.22366 | ||||||||
\(697\) | 25.1182 | 0.951421 | ||||||||
\(698\) | 25.6889 | 0.972339 | ||||||||
\(699\) | −34.9231 | −1.32091 | ||||||||
\(700\) | −29.3195 | −1.10817 | ||||||||
\(701\) | 50.2952 | 1.89962 | 0.949812 | − | 0.312822i | \(-0.101274\pi\) | ||||
0.949812 | + | 0.312822i | \(0.101274\pi\) | |||||||
\(702\) | −49.6420 | −1.87362 | ||||||||
\(703\) | −0.957961 | −0.0361302 | ||||||||
\(704\) | −4.63587 | −0.174721 | ||||||||
\(705\) | 21.7306 | 0.818423 | ||||||||
\(706\) | 55.1534 | 2.07573 | ||||||||
\(707\) | −29.7824 | −1.12008 | ||||||||
\(708\) | 67.4043 | 2.53321 | ||||||||
\(709\) | −3.11713 | −0.117066 | −0.0585332 | − | 0.998285i | \(-0.518642\pi\) | ||||
−0.0585332 | + | 0.998285i | \(0.518642\pi\) | |||||||
\(710\) | −111.426 | −4.18176 | ||||||||
\(711\) | 1.45390 | 0.0545256 | ||||||||
\(712\) | 13.3396 | 0.499922 | ||||||||
\(713\) | −8.99580 | −0.336895 | ||||||||
\(714\) | 72.3469 | 2.70751 | ||||||||
\(715\) | −7.62072 | −0.284999 | ||||||||
\(716\) | 24.1020 | 0.900735 | ||||||||
\(717\) | −21.2229 | −0.792583 | ||||||||
\(718\) | 62.0388 | 2.31527 | ||||||||
\(719\) | −8.87317 | −0.330913 | −0.165457 | − | 0.986217i | \(-0.552910\pi\) | ||||
−0.165457 | + | 0.986217i | \(0.552910\pi\) | |||||||
\(720\) | 38.9594 | 1.45193 | ||||||||
\(721\) | 18.5050 | 0.689163 | ||||||||
\(722\) | −132.731 | −4.93973 | ||||||||
\(723\) | 50.9630 | 1.89534 | ||||||||
\(724\) | −33.1807 | −1.23315 | ||||||||
\(725\) | 11.3179 | 0.420338 | ||||||||
\(726\) | −59.8844 | −2.22252 | ||||||||
\(727\) | 19.5032 | 0.723334 | 0.361667 | − | 0.932307i | \(-0.382208\pi\) | ||||
0.361667 | + | 0.932307i | \(0.382208\pi\) | |||||||
\(728\) | 166.592 | 6.17433 | ||||||||
\(729\) | 3.20622 | 0.118749 | ||||||||
\(730\) | 84.3724 | 3.12276 | ||||||||
\(731\) | 16.4054 | 0.606776 | ||||||||
\(732\) | 14.3827 | 0.531600 | ||||||||
\(733\) | −0.853618 | −0.0315291 | −0.0157646 | − | 0.999876i | \(-0.505018\pi\) | ||||
−0.0157646 | + | 0.999876i | \(0.505018\pi\) | |||||||
\(734\) | −3.42761 | −0.126515 | ||||||||
\(735\) | −36.3279 | −1.33998 | ||||||||
\(736\) | 61.4340 | 2.26449 | ||||||||
\(737\) | 2.96876 | 0.109356 | ||||||||
\(738\) | 28.2484 | 1.03984 | ||||||||
\(739\) | −25.1255 | −0.924258 | −0.462129 | − | 0.886813i | \(-0.652914\pi\) | ||||
−0.462129 | + | 0.886813i | \(0.652914\pi\) | |||||||
\(740\) | 1.44162 | 0.0529949 | ||||||||
\(741\) | 105.880 | 3.88959 | ||||||||
\(742\) | 42.3364 | 1.55422 | ||||||||
\(743\) | −14.7403 | −0.540769 | −0.270384 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270384 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(744\) | 26.3245 | 0.965104 | ||||||||
\(745\) | 23.2375 | 0.851355 | ||||||||
\(746\) | 71.4700 | 2.61670 | ||||||||
\(747\) | −12.3780 | −0.452886 | ||||||||
\(748\) | 8.49660 | 0.310666 | ||||||||
\(749\) | 39.7494 | 1.45241 | ||||||||
\(750\) | −48.3460 | −1.76534 | ||||||||
\(751\) | 17.1548 | 0.625989 | 0.312995 | − | 0.949755i | \(-0.398668\pi\) | ||||
0.312995 | + | 0.949755i | \(0.398668\pi\) | |||||||
\(752\) | −39.8880 | −1.45457 | ||||||||
\(753\) | 36.9143 | 1.34523 | ||||||||
\(754\) | −109.009 | −3.96987 | ||||||||
\(755\) | 27.1944 | 0.989704 | ||||||||
\(756\) | −57.0641 | −2.07540 | ||||||||
\(757\) | 4.46359 | 0.162232 | 0.0811159 | − | 0.996705i | \(-0.474152\pi\) | ||||
0.0811159 | + | 0.996705i | \(0.474152\pi\) | |||||||
\(758\) | −32.4319 | −1.17798 | ||||||||
\(759\) | −5.75777 | −0.208994 | ||||||||
\(760\) | 162.072 | 5.87895 | ||||||||
\(761\) | 1.40186 | 0.0508175 | 0.0254087 | − | 0.999677i | \(-0.491911\pi\) | ||||
0.0254087 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(762\) | 77.3214 | 2.80106 | ||||||||
\(763\) | −65.4154 | −2.36820 | ||||||||
\(764\) | 27.3419 | 0.989196 | ||||||||
\(765\) | −13.6573 | −0.493781 | ||||||||
\(766\) | −56.7769 | −2.05143 | ||||||||
\(767\) | −38.9010 | −1.40464 | ||||||||
\(768\) | 28.0332 | 1.01156 | ||||||||
\(769\) | 22.6490 | 0.816743 | 0.408372 | − | 0.912816i | \(-0.366097\pi\) | ||||
0.408372 | + | 0.912816i | \(0.366097\pi\) | |||||||
\(770\) | −12.3523 | −0.445146 | ||||||||
\(771\) | −54.7982 | −1.97351 | ||||||||
\(772\) | 97.3326 | 3.50308 | ||||||||
\(773\) | −24.6865 | −0.887910 | −0.443955 | − | 0.896049i | \(-0.646425\pi\) | ||||
−0.443955 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(774\) | 18.4498 | 0.663165 | ||||||||
\(775\) | 2.67384 | 0.0960471 | ||||||||
\(776\) | 10.2955 | 0.369587 | ||||||||
\(777\) | 0.900562 | 0.0323075 | ||||||||
\(778\) | 86.8498 | 3.11372 | ||||||||
\(779\) | 59.5847 | 2.13485 | ||||||||
\(780\) | −159.336 | −5.70516 | ||||||||
\(781\) | −8.17481 | −0.292518 | ||||||||
\(782\) | −50.4995 | −1.80586 | ||||||||
\(783\) | 22.0280 | 0.787215 | ||||||||
\(784\) | 66.6823 | 2.38151 | ||||||||
\(785\) | −17.1682 | −0.612760 | ||||||||
\(786\) | 82.3836 | 2.93853 | ||||||||
\(787\) | 36.9055 | 1.31554 | 0.657770 | − | 0.753219i | \(-0.271500\pi\) | ||||
0.657770 | + | 0.753219i | \(0.271500\pi\) | |||||||
\(788\) | 101.884 | 3.62948 | ||||||||
\(789\) | 46.4496 | 1.65365 | ||||||||
\(790\) | −6.50754 | −0.231528 | ||||||||
\(791\) | 69.6709 | 2.47721 | ||||||||
\(792\) | 5.63710 | 0.200305 | ||||||||
\(793\) | −8.30069 | −0.294766 | ||||||||
\(794\) | 28.5685 | 1.01386 | ||||||||
\(795\) | −23.8879 | −0.847218 | ||||||||
\(796\) | −25.3480 | −0.898436 | ||||||||
\(797\) | −4.79724 | −0.169927 | −0.0849634 | − | 0.996384i | \(-0.527077\pi\) | ||||
−0.0849634 | + | 0.996384i | \(0.527077\pi\) | |||||||
\(798\) | 171.619 | 6.07525 | ||||||||
\(799\) | 13.9828 | 0.494677 | ||||||||
\(800\) | −18.2601 | −0.645593 | ||||||||
\(801\) | −2.66653 | −0.0942172 | ||||||||
\(802\) | −1.68073 | −0.0593487 | ||||||||
\(803\) | 6.18999 | 0.218440 | ||||||||
\(804\) | 62.0718 | 2.18910 | ||||||||
\(805\) | 52.0657 | 1.83507 | ||||||||
\(806\) | −25.7531 | −0.907114 | ||||||||
\(807\) | −4.61567 | −0.162479 | ||||||||
\(808\) | −60.8343 | −2.14014 | ||||||||
\(809\) | −29.9285 | −1.05223 | −0.526116 | − | 0.850413i | \(-0.676352\pi\) | ||||
−0.526116 | + | 0.850413i | \(0.676352\pi\) | |||||||
\(810\) | 75.9500 | 2.66861 | ||||||||
\(811\) | 14.4777 | 0.508381 | 0.254191 | − | 0.967154i | \(-0.418191\pi\) | ||||
0.254191 | + | 0.967154i | \(0.418191\pi\) | |||||||
\(812\) | −125.307 | −4.39741 | ||||||||
\(813\) | 58.8247 | 2.06307 | ||||||||
\(814\) | 0.149134 | 0.00522716 | ||||||||
\(815\) | 15.9506 | 0.558724 | ||||||||
\(816\) | 74.9298 | 2.62307 | ||||||||
\(817\) | 38.9164 | 1.36151 | ||||||||
\(818\) | 54.1652 | 1.89384 | ||||||||
\(819\) | −33.3012 | −1.16364 | ||||||||
\(820\) | −89.6679 | −3.13134 | ||||||||
\(821\) | −21.4614 | −0.749009 | −0.374505 | − | 0.927225i | \(-0.622187\pi\) | ||||
−0.374505 | + | 0.927225i | \(0.622187\pi\) | |||||||
\(822\) | −101.392 | −3.53644 | ||||||||
\(823\) | 30.7576 | 1.07214 | 0.536071 | − | 0.844173i | \(-0.319908\pi\) | ||||
0.536071 | + | 0.844173i | \(0.319908\pi\) | |||||||
\(824\) | 37.7988 | 1.31678 | ||||||||
\(825\) | 1.71139 | 0.0595830 | ||||||||
\(826\) | −63.0541 | −2.19393 | ||||||||
\(827\) | −13.3096 | −0.462820 | −0.231410 | − | 0.972856i | \(-0.574334\pi\) | ||||
−0.231410 | + | 0.972856i | \(0.574334\pi\) | |||||||
\(828\) | −40.2767 | −1.39971 | ||||||||
\(829\) | −49.0060 | −1.70205 | −0.851024 | − | 0.525127i | \(-0.824018\pi\) | ||||
−0.851024 | + | 0.525127i | \(0.824018\pi\) | |||||||
\(830\) | 55.4027 | 1.92306 | ||||||||
\(831\) | 25.9289 | 0.899463 | ||||||||
\(832\) | 55.9402 | 1.93938 | ||||||||
\(833\) | −23.3756 | −0.809918 | ||||||||
\(834\) | −4.18513 | −0.144919 | ||||||||
\(835\) | 22.8013 | 0.789073 | ||||||||
\(836\) | 20.1554 | 0.697089 | ||||||||
\(837\) | 5.20405 | 0.179878 | ||||||||
\(838\) | −31.0725 | −1.07338 | ||||||||
\(839\) | −10.5379 | −0.363810 | −0.181905 | − | 0.983316i | \(-0.558226\pi\) | ||||
−0.181905 | + | 0.983316i | \(0.558226\pi\) | |||||||
\(840\) | −152.361 | −5.25694 | ||||||||
\(841\) | 19.3712 | 0.667973 | ||||||||
\(842\) | 20.0946 | 0.692507 | ||||||||
\(843\) | −63.6130 | −2.19095 | ||||||||
\(844\) | 99.8295 | 3.43627 | ||||||||
\(845\) | 58.4912 | 2.01216 | ||||||||
\(846\) | 15.7253 | 0.540649 | ||||||||
\(847\) | 39.7284 | 1.36508 | ||||||||
\(848\) | 43.8479 | 1.50574 | ||||||||
\(849\) | 37.7523 | 1.29565 | ||||||||
\(850\) | 15.0101 | 0.514841 | ||||||||
\(851\) | −0.628610 | −0.0215485 | ||||||||
\(852\) | −170.922 | −5.85567 | ||||||||
\(853\) | −12.5306 | −0.429039 | −0.214520 | − | 0.976720i | \(-0.568819\pi\) | ||||
−0.214520 | + | 0.976720i | \(0.568819\pi\) | |||||||
\(854\) | −13.4545 | −0.460403 | ||||||||
\(855\) | −32.3975 | −1.10797 | ||||||||
\(856\) | 81.1931 | 2.77512 | ||||||||
\(857\) | 47.6658 | 1.62823 | 0.814117 | − | 0.580701i | \(-0.197221\pi\) | ||||
0.814117 | + | 0.580701i | \(0.197221\pi\) | |||||||
\(858\) | −16.4833 | −0.562729 | ||||||||
\(859\) | −36.1047 | −1.23188 | −0.615939 | − | 0.787794i | \(-0.711223\pi\) | ||||
−0.615939 | + | 0.787794i | \(0.711223\pi\) | |||||||
\(860\) | −58.5646 | −1.99704 | ||||||||
\(861\) | −56.0145 | −1.90897 | ||||||||
\(862\) | −35.4878 | −1.20872 | ||||||||
\(863\) | 50.2612 | 1.71091 | 0.855456 | − | 0.517875i | \(-0.173277\pi\) | ||||
0.855456 | + | 0.517875i | \(0.173277\pi\) | |||||||
\(864\) | −35.5394 | −1.20908 | ||||||||
\(865\) | 17.6932 | 0.601588 | ||||||||
\(866\) | 17.8998 | 0.608259 | ||||||||
\(867\) | 9.82900 | 0.333810 | ||||||||
\(868\) | −29.6035 | −1.00481 | ||||||||
\(869\) | −0.477426 | −0.0161956 | ||||||||
\(870\) | 99.6963 | 3.38002 | ||||||||
\(871\) | −35.8235 | −1.21383 | ||||||||
\(872\) | −133.619 | −4.52491 | ||||||||
\(873\) | −2.05803 | −0.0696538 | ||||||||
\(874\) | −119.794 | −4.05208 | ||||||||
\(875\) | 32.0736 | 1.08428 | ||||||||
\(876\) | 129.422 | 4.37277 | ||||||||
\(877\) | −50.4153 | −1.70240 | −0.851202 | − | 0.524838i | \(-0.824126\pi\) | ||||
−0.851202 | + | 0.524838i | \(0.824126\pi\) | |||||||
\(878\) | −37.1878 | −1.25503 | ||||||||
\(879\) | 17.5823 | 0.593038 | ||||||||
\(880\) | −12.7933 | −0.431262 | ||||||||
\(881\) | −20.8921 | −0.703872 | −0.351936 | − | 0.936024i | \(-0.614477\pi\) | ||||
−0.351936 | + | 0.936024i | \(0.614477\pi\) | |||||||
\(882\) | −26.2887 | −0.885186 | ||||||||
\(883\) | 12.0556 | 0.405703 | 0.202851 | − | 0.979210i | \(-0.434979\pi\) | ||||
0.202851 | + | 0.979210i | \(0.434979\pi\) | |||||||
\(884\) | −102.527 | −3.44835 | ||||||||
\(885\) | 35.5777 | 1.19593 | ||||||||
\(886\) | −100.356 | −3.37151 | ||||||||
\(887\) | 42.0475 | 1.41182 | 0.705908 | − | 0.708304i | \(-0.250539\pi\) | ||||
0.705908 | + | 0.708304i | \(0.250539\pi\) | |||||||
\(888\) | 1.83951 | 0.0617299 | ||||||||
\(889\) | −51.2964 | −1.72042 | ||||||||
\(890\) | 11.9352 | 0.400067 | ||||||||
\(891\) | 5.57207 | 0.186671 | ||||||||
\(892\) | −123.183 | −4.12448 | ||||||||
\(893\) | 33.1697 | 1.10998 | ||||||||
\(894\) | 50.2616 | 1.68100 | ||||||||
\(895\) | 12.7217 | 0.425239 | ||||||||
\(896\) | 7.77099 | 0.259610 | ||||||||
\(897\) | 69.4779 | 2.31980 | ||||||||
\(898\) | −58.7964 | −1.96206 | ||||||||
\(899\) | 11.4276 | 0.381131 | ||||||||
\(900\) | 11.9715 | 0.399050 | ||||||||
\(901\) | −15.3710 | −0.512082 | ||||||||
\(902\) | −9.27609 | −0.308860 | ||||||||
\(903\) | −36.5846 | −1.21746 | ||||||||
\(904\) | 142.311 | 4.73321 | ||||||||
\(905\) | −17.5136 | −0.582173 | ||||||||
\(906\) | 58.8202 | 1.95417 | ||||||||
\(907\) | −29.0309 | −0.963955 | −0.481978 | − | 0.876183i | \(-0.660081\pi\) | ||||
−0.481978 | + | 0.876183i | \(0.660081\pi\) | |||||||
\(908\) | −70.9082 | −2.35317 | ||||||||
\(909\) | 12.1605 | 0.403339 | ||||||||
\(910\) | 149.053 | 4.94106 | ||||||||
\(911\) | −2.69669 | −0.0893453 | −0.0446727 | − | 0.999002i | \(-0.514224\pi\) | ||||
−0.0446727 | + | 0.999002i | \(0.514224\pi\) | |||||||
\(912\) | 177.746 | 5.88576 | ||||||||
\(913\) | 4.06462 | 0.134519 | ||||||||
\(914\) | 31.4931 | 1.04170 | ||||||||
\(915\) | 7.59157 | 0.250970 | ||||||||
\(916\) | −39.7288 | −1.31268 | ||||||||
\(917\) | −54.6548 | −1.80486 | ||||||||
\(918\) | 29.2139 | 0.964201 | ||||||||
\(919\) | 38.4948 | 1.26983 | 0.634913 | − | 0.772584i | \(-0.281036\pi\) | ||||
0.634913 | + | 0.772584i | \(0.281036\pi\) | |||||||
\(920\) | 106.351 | 3.50628 | ||||||||
\(921\) | −27.1182 | −0.893574 | ||||||||
\(922\) | −33.6792 | −1.10917 | ||||||||
\(923\) | 98.6439 | 3.24690 | ||||||||
\(924\) | −18.9477 | −0.623334 | ||||||||
\(925\) | 0.186843 | 0.00614335 | ||||||||
\(926\) | 67.0800 | 2.20438 | ||||||||
\(927\) | −7.55583 | −0.248166 | ||||||||
\(928\) | −78.0411 | −2.56182 | ||||||||
\(929\) | −10.3990 | −0.341180 | −0.170590 | − | 0.985342i | \(-0.554567\pi\) | ||||
−0.170590 | + | 0.985342i | \(0.554567\pi\) | |||||||
\(930\) | 23.5530 | 0.772334 | ||||||||
\(931\) | −55.4510 | −1.81733 | ||||||||
\(932\) | 80.2202 | 2.62770 | ||||||||
\(933\) | 51.5575 | 1.68792 | ||||||||
\(934\) | 78.9536 | 2.58344 | ||||||||
\(935\) | 4.48473 | 0.146666 | ||||||||
\(936\) | −68.0218 | −2.22336 | ||||||||
\(937\) | 6.69629 | 0.218758 | 0.109379 | − | 0.994000i | \(-0.465114\pi\) | ||||
0.109379 | + | 0.994000i | \(0.465114\pi\) | |||||||
\(938\) | −58.0658 | −1.89591 | ||||||||
\(939\) | −30.6449 | −1.00006 | ||||||||
\(940\) | −49.9164 | −1.62809 | ||||||||
\(941\) | 19.9735 | 0.651119 | 0.325559 | − | 0.945522i | \(-0.394447\pi\) | ||||
0.325559 | + | 0.945522i | \(0.394447\pi\) | |||||||
\(942\) | −37.1341 | −1.20989 | ||||||||
\(943\) | 39.0993 | 1.27325 | ||||||||
\(944\) | −65.3053 | −2.12551 | ||||||||
\(945\) | −30.1199 | −0.979800 | ||||||||
\(946\) | −6.05847 | −0.196978 | ||||||||
\(947\) | 49.1728 | 1.59790 | 0.798951 | − | 0.601397i | \(-0.205389\pi\) | ||||
0.798951 | + | 0.601397i | \(0.205389\pi\) | |||||||
\(948\) | −9.98218 | −0.324206 | ||||||||
\(949\) | −74.6934 | −2.42465 | ||||||||
\(950\) | 35.6064 | 1.15523 | ||||||||
\(951\) | −11.2861 | −0.365976 | ||||||||
\(952\) | −98.0382 | −3.17744 | ||||||||
\(953\) | 39.8727 | 1.29160 | 0.645801 | − | 0.763506i | \(-0.276524\pi\) | ||||
0.645801 | + | 0.763506i | \(0.276524\pi\) | |||||||
\(954\) | −17.2865 | −0.559671 | ||||||||
\(955\) | 14.4318 | 0.467001 | ||||||||
\(956\) | 48.7501 | 1.57669 | ||||||||
\(957\) | 7.31422 | 0.236435 | ||||||||
\(958\) | −58.2051 | −1.88052 | ||||||||
\(959\) | 67.2650 | 2.17210 | ||||||||
\(960\) | −51.1613 | −1.65122 | ||||||||
\(961\) | −28.3003 | −0.912912 | ||||||||
\(962\) | −1.79958 | −0.0580207 | ||||||||
\(963\) | −16.2302 | −0.523010 | ||||||||
\(964\) | −117.065 | −3.77040 | ||||||||
\(965\) | 51.3747 | 1.65381 | ||||||||
\(966\) | 112.616 | 3.62335 | ||||||||
\(967\) | −24.2306 | −0.779203 | −0.389601 | − | 0.920984i | \(-0.627387\pi\) | ||||
−0.389601 | + | 0.920984i | \(0.627387\pi\) | |||||||
\(968\) | 81.1502 | 2.60827 | ||||||||
\(969\) | −62.3093 | −2.00166 | ||||||||
\(970\) | 9.21156 | 0.295765 | ||||||||
\(971\) | 52.7038 | 1.69134 | 0.845672 | − | 0.533702i | \(-0.179200\pi\) | ||||
0.845672 | + | 0.533702i | \(0.179200\pi\) | |||||||
\(972\) | 70.1601 | 2.25039 | ||||||||
\(973\) | 2.77649 | 0.0890102 | ||||||||
\(974\) | 27.1205 | 0.868998 | ||||||||
\(975\) | −20.6510 | −0.661362 | ||||||||
\(976\) | −13.9348 | −0.446043 | ||||||||
\(977\) | 60.8726 | 1.94749 | 0.973744 | − | 0.227648i | \(-0.0731035\pi\) | ||||
0.973744 | + | 0.227648i | \(0.0731035\pi\) | |||||||
\(978\) | 34.5003 | 1.10320 | ||||||||
\(979\) | 0.875623 | 0.0279850 | ||||||||
\(980\) | 83.4471 | 2.66562 | ||||||||
\(981\) | 26.7099 | 0.852782 | ||||||||
\(982\) | −74.6574 | −2.38241 | ||||||||
\(983\) | −51.3243 | −1.63699 | −0.818495 | − | 0.574514i | \(-0.805191\pi\) | ||||
−0.818495 | + | 0.574514i | \(0.805191\pi\) | |||||||
\(984\) | −114.417 | −3.64747 | ||||||||
\(985\) | 53.7773 | 1.71349 | ||||||||
\(986\) | 64.1508 | 2.04298 | ||||||||
\(987\) | −31.1822 | −0.992540 | ||||||||
\(988\) | −243.211 | −7.73758 | ||||||||
\(989\) | 25.5368 | 0.812023 | ||||||||
\(990\) | 5.04360 | 0.160296 | ||||||||
\(991\) | 48.3760 | 1.53671 | 0.768357 | − | 0.640022i | \(-0.221075\pi\) | ||||
0.768357 | + | 0.640022i | \(0.221075\pi\) | |||||||
\(992\) | −18.4370 | −0.585376 | ||||||||
\(993\) | 25.1958 | 0.799563 | ||||||||
\(994\) | 159.890 | 5.07142 | ||||||||
\(995\) | −13.3793 | −0.424153 | ||||||||
\(996\) | 84.9844 | 2.69283 | ||||||||
\(997\) | 29.2455 | 0.926213 | 0.463106 | − | 0.886303i | \(-0.346735\pi\) | ||||
0.463106 | + | 0.886303i | \(0.346735\pi\) | |||||||
\(998\) | 76.6706 | 2.42697 | ||||||||
\(999\) | 0.363649 | 0.0115054 |
(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 | 8011.2.a.b.1.12 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.12 | ✓ | 358 | 1.1 | even | 1 | trivial |