Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34979 | −1.66155 | −0.830777 | − | 0.556605i | \(-0.812104\pi\) | ||||
−0.830777 | + | 0.556605i | \(0.812104\pi\) | |||||||
\(3\) | −2.55203 | −1.47342 | −0.736708 | − | 0.676211i | \(-0.763621\pi\) | ||||
−0.736708 | + | 0.676211i | \(0.763621\pi\) | |||||||
\(4\) | 3.52153 | 1.76076 | ||||||||
\(5\) | 3.27958 | 1.46667 | 0.733336 | − | 0.679866i | \(-0.237962\pi\) | ||||
0.733336 | + | 0.679866i | \(0.237962\pi\) | |||||||
\(6\) | 5.99675 | 2.44816 | ||||||||
\(7\) | 4.82178 | 1.82246 | 0.911231 | − | 0.411896i | \(-0.135133\pi\) | ||||
0.911231 | + | 0.411896i | \(0.135133\pi\) | |||||||
\(8\) | −3.57528 | −1.26405 | ||||||||
\(9\) | 3.51287 | 1.17096 | ||||||||
\(10\) | −7.70633 | −2.43696 | ||||||||
\(11\) | 3.08273 | 0.929479 | 0.464739 | − | 0.885447i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885447i | \(0.346148\pi\) | |||||||
\(12\) | −8.98706 | −2.59434 | ||||||||
\(13\) | −3.47250 | −0.963099 | −0.481549 | − | 0.876419i | \(-0.659926\pi\) | ||||
−0.481549 | + | 0.876419i | \(0.659926\pi\) | |||||||
\(14\) | −11.3302 | −3.02812 | ||||||||
\(15\) | −8.36959 | −2.16102 | ||||||||
\(16\) | 1.35811 | 0.339528 | ||||||||
\(17\) | −4.04990 | −0.982246 | −0.491123 | − | 0.871090i | \(-0.663413\pi\) | ||||
−0.491123 | + | 0.871090i | \(0.663413\pi\) | |||||||
\(18\) | −8.25452 | −1.94561 | ||||||||
\(19\) | 3.40481 | 0.781118 | 0.390559 | − | 0.920578i | \(-0.372282\pi\) | ||||
0.390559 | + | 0.920578i | \(0.372282\pi\) | |||||||
\(20\) | 11.5491 | 2.58246 | ||||||||
\(21\) | −12.3053 | −2.68525 | ||||||||
\(22\) | −7.24379 | −1.54438 | ||||||||
\(23\) | −8.59467 | −1.79211 | −0.896056 | − | 0.443940i | \(-0.853580\pi\) | ||||
−0.896056 | + | 0.443940i | \(0.853580\pi\) | |||||||
\(24\) | 9.12423 | 1.86248 | ||||||||
\(25\) | 5.75564 | 1.15113 | ||||||||
\(26\) | 8.15966 | 1.60024 | ||||||||
\(27\) | −1.30887 | −0.251891 | ||||||||
\(28\) | 16.9800 | 3.20893 | ||||||||
\(29\) | −0.344181 | −0.0639128 | −0.0319564 | − | 0.999489i | \(-0.510174\pi\) | ||||
−0.0319564 | + | 0.999489i | \(0.510174\pi\) | |||||||
\(30\) | 19.6668 | 3.59065 | ||||||||
\(31\) | −2.73850 | −0.491848 | −0.245924 | − | 0.969289i | \(-0.579091\pi\) | ||||
−0.245924 | + | 0.969289i | \(0.579091\pi\) | |||||||
\(32\) | 3.95928 | 0.699908 | ||||||||
\(33\) | −7.86724 | −1.36951 | ||||||||
\(34\) | 9.51643 | 1.63205 | ||||||||
\(35\) | 15.8134 | 2.67295 | ||||||||
\(36\) | 12.3707 | 2.06178 | ||||||||
\(37\) | −8.28001 | −1.36123 | −0.680613 | − | 0.732643i | \(-0.738286\pi\) | ||||
−0.680613 | + | 0.732643i | \(0.738286\pi\) | |||||||
\(38\) | −8.00061 | −1.29787 | ||||||||
\(39\) | 8.86194 | 1.41905 | ||||||||
\(40\) | −11.7254 | −1.85395 | ||||||||
\(41\) | 2.78767 | 0.435361 | 0.217680 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217680 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(42\) | 28.9150 | 4.46168 | ||||||||
\(43\) | −12.7978 | −1.95165 | −0.975826 | − | 0.218549i | \(-0.929868\pi\) | ||||
−0.975826 | + | 0.218549i | \(0.929868\pi\) | |||||||
\(44\) | 10.8559 | 1.63659 | ||||||||
\(45\) | 11.5207 | 1.71741 | ||||||||
\(46\) | 20.1957 | 2.97769 | ||||||||
\(47\) | −1.37067 | −0.199933 | −0.0999666 | − | 0.994991i | \(-0.531874\pi\) | ||||
−0.0999666 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(48\) | −3.46595 | −0.500266 | ||||||||
\(49\) | 16.2496 | 2.32137 | ||||||||
\(50\) | −13.5246 | −1.91266 | ||||||||
\(51\) | 10.3355 | 1.44726 | ||||||||
\(52\) | −12.2285 | −1.69579 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 3.07556 | 0.418531 | ||||||||
\(55\) | 10.1101 | 1.36324 | ||||||||
\(56\) | −17.2392 | −2.30369 | ||||||||
\(57\) | −8.68920 | −1.15091 | ||||||||
\(58\) | 0.808754 | 0.106195 | ||||||||
\(59\) | 14.2547 | 1.85580 | 0.927902 | − | 0.372825i | \(-0.121611\pi\) | ||||
0.927902 | + | 0.372825i | \(0.121611\pi\) | |||||||
\(60\) | −29.4738 | −3.80505 | ||||||||
\(61\) | 12.5301 | 1.60431 | 0.802156 | − | 0.597114i | \(-0.203686\pi\) | ||||
0.802156 | + | 0.597114i | \(0.203686\pi\) | |||||||
\(62\) | 6.43490 | 0.817233 | ||||||||
\(63\) | 16.9383 | 2.13402 | ||||||||
\(64\) | −12.0197 | −1.50246 | ||||||||
\(65\) | −11.3883 | −1.41255 | ||||||||
\(66\) | 18.4864 | 2.27552 | ||||||||
\(67\) | −4.86324 | −0.594139 | −0.297069 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297069 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(68\) | −14.2619 | −1.72950 | ||||||||
\(69\) | 21.9339 | 2.64053 | ||||||||
\(70\) | −37.1582 | −4.44126 | ||||||||
\(71\) | −13.6656 | −1.62180 | −0.810902 | − | 0.585182i | \(-0.801023\pi\) | ||||
−0.810902 | + | 0.585182i | \(0.801023\pi\) | |||||||
\(72\) | −12.5595 | −1.48015 | ||||||||
\(73\) | 4.28647 | 0.501693 | 0.250847 | − | 0.968027i | \(-0.419291\pi\) | ||||
0.250847 | + | 0.968027i | \(0.419291\pi\) | |||||||
\(74\) | 19.4563 | 2.26175 | ||||||||
\(75\) | −14.6886 | −1.69609 | ||||||||
\(76\) | 11.9902 | 1.37537 | ||||||||
\(77\) | 14.8643 | 1.69394 | ||||||||
\(78\) | −20.8237 | −2.35782 | ||||||||
\(79\) | −13.2510 | −1.49085 | −0.745427 | − | 0.666588i | \(-0.767754\pi\) | ||||
−0.745427 | + | 0.666588i | \(0.767754\pi\) | |||||||
\(80\) | 4.45404 | 0.497976 | ||||||||
\(81\) | −7.19835 | −0.799816 | ||||||||
\(82\) | −6.55045 | −0.723376 | ||||||||
\(83\) | 4.59159 | 0.503993 | 0.251996 | − | 0.967728i | \(-0.418913\pi\) | ||||
0.251996 | + | 0.967728i | \(0.418913\pi\) | |||||||
\(84\) | −43.3336 | −4.72809 | ||||||||
\(85\) | −13.2820 | −1.44063 | ||||||||
\(86\) | 30.0723 | 3.24278 | ||||||||
\(87\) | 0.878361 | 0.0941702 | ||||||||
\(88\) | −11.0216 | −1.17491 | ||||||||
\(89\) | −8.51377 | −0.902458 | −0.451229 | − | 0.892408i | \(-0.649014\pi\) | ||||
−0.451229 | + | 0.892408i | \(0.649014\pi\) | |||||||
\(90\) | −27.0714 | −2.85357 | ||||||||
\(91\) | −16.7436 | −1.75521 | ||||||||
\(92\) | −30.2664 | −3.15549 | ||||||||
\(93\) | 6.98873 | 0.724698 | ||||||||
\(94\) | 3.22080 | 0.332200 | ||||||||
\(95\) | 11.1664 | 1.14564 | ||||||||
\(96\) | −10.1042 | −1.03126 | ||||||||
\(97\) | 7.60135 | 0.771800 | 0.385900 | − | 0.922541i | \(-0.373891\pi\) | ||||
0.385900 | + | 0.922541i | \(0.373891\pi\) | |||||||
\(98\) | −38.1831 | −3.85708 | ||||||||
\(99\) | 10.8292 | 1.08838 | ||||||||
\(100\) | 20.2686 | 2.02686 | ||||||||
\(101\) | 1.21450 | 0.120847 | 0.0604237 | − | 0.998173i | \(-0.480755\pi\) | ||||
0.0604237 | + | 0.998173i | \(0.480755\pi\) | |||||||
\(102\) | −24.2863 | −2.40470 | ||||||||
\(103\) | −7.85027 | −0.773510 | −0.386755 | − | 0.922182i | \(-0.626404\pi\) | ||||
−0.386755 | + | 0.922182i | \(0.626404\pi\) | |||||||
\(104\) | 12.4152 | 1.21741 | ||||||||
\(105\) | −40.3563 | −3.93838 | ||||||||
\(106\) | 2.34979 | 0.228232 | ||||||||
\(107\) | 7.83343 | 0.757286 | 0.378643 | − | 0.925543i | \(-0.376391\pi\) | ||||
0.378643 | + | 0.925543i | \(0.376391\pi\) | |||||||
\(108\) | −4.60921 | −0.443521 | ||||||||
\(109\) | −6.10668 | −0.584914 | −0.292457 | − | 0.956279i | \(-0.594473\pi\) | ||||
−0.292457 | + | 0.956279i | \(0.594473\pi\) | |||||||
\(110\) | −23.7566 | −2.26510 | ||||||||
\(111\) | 21.1309 | 2.00565 | ||||||||
\(112\) | 6.54852 | 0.618777 | ||||||||
\(113\) | 0.695341 | 0.0654122 | 0.0327061 | − | 0.999465i | \(-0.489587\pi\) | ||||
0.0327061 | + | 0.999465i | \(0.489587\pi\) | |||||||
\(114\) | 20.4178 | 1.91230 | ||||||||
\(115\) | −28.1869 | −2.62844 | ||||||||
\(116\) | −1.21204 | −0.112535 | ||||||||
\(117\) | −12.1985 | −1.12775 | ||||||||
\(118\) | −33.4956 | −3.08352 | ||||||||
\(119\) | −19.5277 | −1.79011 | ||||||||
\(120\) | 29.9236 | 2.73164 | ||||||||
\(121\) | −1.49676 | −0.136069 | ||||||||
\(122\) | −29.4431 | −2.66565 | ||||||||
\(123\) | −7.11422 | −0.641468 | ||||||||
\(124\) | −9.64369 | −0.866029 | ||||||||
\(125\) | 2.47817 | 0.221654 | ||||||||
\(126\) | −39.8015 | −3.54580 | ||||||||
\(127\) | −11.3199 | −1.00448 | −0.502241 | − | 0.864728i | \(-0.667491\pi\) | ||||
−0.502241 | + | 0.864728i | \(0.667491\pi\) | |||||||
\(128\) | 20.3253 | 1.79652 | ||||||||
\(129\) | 32.6605 | 2.87560 | ||||||||
\(130\) | 26.7602 | 2.34703 | ||||||||
\(131\) | 6.17924 | 0.539883 | 0.269941 | − | 0.962877i | \(-0.412996\pi\) | ||||
0.269941 | + | 0.962877i | \(0.412996\pi\) | |||||||
\(132\) | −27.7047 | −2.41138 | ||||||||
\(133\) | 16.4173 | 1.42356 | ||||||||
\(134\) | 11.4276 | 0.987195 | ||||||||
\(135\) | −4.29253 | −0.369442 | ||||||||
\(136\) | 14.4795 | 1.24161 | ||||||||
\(137\) | −18.3273 | −1.56580 | −0.782902 | − | 0.622145i | \(-0.786261\pi\) | ||||
−0.782902 | + | 0.622145i | \(0.786261\pi\) | |||||||
\(138\) | −51.5401 | −4.38738 | ||||||||
\(139\) | −12.8690 | −1.09153 | −0.545766 | − | 0.837938i | \(-0.683761\pi\) | ||||
−0.545766 | + | 0.837938i | \(0.683761\pi\) | |||||||
\(140\) | 55.6874 | 4.70644 | ||||||||
\(141\) | 3.49800 | 0.294585 | ||||||||
\(142\) | 32.1113 | 2.69472 | ||||||||
\(143\) | −10.7048 | −0.895180 | ||||||||
\(144\) | 4.77087 | 0.397573 | ||||||||
\(145\) | −1.12877 | −0.0937391 | ||||||||
\(146\) | −10.0723 | −0.833591 | ||||||||
\(147\) | −41.4694 | −3.42034 | ||||||||
\(148\) | −29.1583 | −2.39680 | ||||||||
\(149\) | 1.74075 | 0.142608 | 0.0713038 | − | 0.997455i | \(-0.477284\pi\) | ||||
0.0713038 | + | 0.997455i | \(0.477284\pi\) | |||||||
\(150\) | 34.5151 | 2.81815 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | −12.1732 | −0.987374 | ||||||||
\(153\) | −14.2268 | −1.15017 | ||||||||
\(154\) | −34.9279 | −2.81457 | ||||||||
\(155\) | −8.98111 | −0.721380 | ||||||||
\(156\) | 31.2076 | 2.49861 | ||||||||
\(157\) | −7.11405 | −0.567763 | −0.283881 | − | 0.958859i | \(-0.591622\pi\) | ||||
−0.283881 | + | 0.958859i | \(0.591622\pi\) | |||||||
\(158\) | 31.1371 | 2.47713 | ||||||||
\(159\) | 2.55203 | 0.202389 | ||||||||
\(160\) | 12.9848 | 1.02654 | ||||||||
\(161\) | −41.4416 | −3.26606 | ||||||||
\(162\) | 16.9146 | 1.32894 | ||||||||
\(163\) | 23.5364 | 1.84351 | 0.921756 | − | 0.387771i | \(-0.126755\pi\) | ||||
0.921756 | + | 0.387771i | \(0.126755\pi\) | |||||||
\(164\) | 9.81686 | 0.766568 | ||||||||
\(165\) | −25.8012 | −2.00862 | ||||||||
\(166\) | −10.7893 | −0.837412 | ||||||||
\(167\) | −22.3933 | −1.73284 | −0.866422 | − | 0.499312i | \(-0.833586\pi\) | ||||
−0.866422 | + | 0.499312i | \(0.833586\pi\) | |||||||
\(168\) | 43.9951 | 3.39429 | ||||||||
\(169\) | −0.941736 | −0.0724412 | ||||||||
\(170\) | 31.2099 | 2.39369 | ||||||||
\(171\) | 11.9607 | 0.914656 | ||||||||
\(172\) | −45.0680 | −3.43640 | ||||||||
\(173\) | 14.2454 | 1.08306 | 0.541529 | − | 0.840682i | \(-0.317846\pi\) | ||||
0.541529 | + | 0.840682i | \(0.317846\pi\) | |||||||
\(174\) | −2.06397 | −0.156469 | ||||||||
\(175\) | 27.7524 | 2.09789 | ||||||||
\(176\) | 4.18670 | 0.315584 | ||||||||
\(177\) | −36.3785 | −2.73437 | ||||||||
\(178\) | 20.0056 | 1.49948 | ||||||||
\(179\) | −2.61927 | −0.195774 | −0.0978868 | − | 0.995198i | \(-0.531208\pi\) | ||||
−0.0978868 | + | 0.995198i | \(0.531208\pi\) | |||||||
\(180\) | 40.5706 | 3.02396 | ||||||||
\(181\) | −5.17426 | −0.384599 | −0.192300 | − | 0.981336i | \(-0.561595\pi\) | ||||
−0.192300 | + | 0.981336i | \(0.561595\pi\) | |||||||
\(182\) | 39.3441 | 2.91638 | ||||||||
\(183\) | −31.9772 | −2.36382 | ||||||||
\(184\) | 30.7284 | 2.26532 | ||||||||
\(185\) | −27.1550 | −1.99647 | ||||||||
\(186\) | −16.4221 | −1.20412 | ||||||||
\(187\) | −12.4848 | −0.912977 | ||||||||
\(188\) | −4.82687 | −0.352035 | ||||||||
\(189\) | −6.31106 | −0.459062 | ||||||||
\(190\) | −26.2386 | −1.90355 | ||||||||
\(191\) | 23.6082 | 1.70823 | 0.854114 | − | 0.520086i | \(-0.174100\pi\) | ||||
0.854114 | + | 0.520086i | \(0.174100\pi\) | |||||||
\(192\) | 30.6747 | 2.21376 | ||||||||
\(193\) | −4.40647 | −0.317184 | −0.158592 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158592 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(194\) | −17.8616 | −1.28239 | ||||||||
\(195\) | 29.0634 | 2.08127 | ||||||||
\(196\) | 57.2233 | 4.08738 | ||||||||
\(197\) | −11.7995 | −0.840681 | −0.420340 | − | 0.907366i | \(-0.638089\pi\) | ||||
−0.420340 | + | 0.907366i | \(0.638089\pi\) | |||||||
\(198\) | −25.4465 | −1.80840 | ||||||||
\(199\) | 5.83666 | 0.413750 | 0.206875 | − | 0.978367i | \(-0.433671\pi\) | ||||
0.206875 | + | 0.978367i | \(0.433671\pi\) | |||||||
\(200\) | −20.5780 | −1.45509 | ||||||||
\(201\) | 12.4111 | 0.875414 | ||||||||
\(202\) | −2.85383 | −0.200795 | ||||||||
\(203\) | −1.65956 | −0.116479 | ||||||||
\(204\) | 36.3967 | 2.54828 | ||||||||
\(205\) | 9.14238 | 0.638532 | ||||||||
\(206\) | 18.4465 | 1.28523 | ||||||||
\(207\) | −30.1920 | −2.09849 | ||||||||
\(208\) | −4.71605 | −0.326999 | ||||||||
\(209\) | 10.4961 | 0.726033 | ||||||||
\(210\) | 94.8291 | 6.54383 | ||||||||
\(211\) | −26.1322 | −1.79901 | −0.899507 | − | 0.436906i | \(-0.856074\pi\) | ||||
−0.899507 | + | 0.436906i | \(0.856074\pi\) | |||||||
\(212\) | −3.52153 | −0.241860 | ||||||||
\(213\) | 34.8750 | 2.38959 | ||||||||
\(214\) | −18.4069 | −1.25827 | ||||||||
\(215\) | −41.9715 | −2.86243 | ||||||||
\(216\) | 4.67956 | 0.318404 | ||||||||
\(217\) | −13.2044 | −0.896375 | ||||||||
\(218\) | 14.3494 | 0.971866 | ||||||||
\(219\) | −10.9392 | −0.739203 | ||||||||
\(220\) | 35.6029 | 2.40035 | ||||||||
\(221\) | 14.0633 | 0.945999 | ||||||||
\(222\) | −49.6532 | −3.33250 | ||||||||
\(223\) | 11.3643 | 0.761007 | 0.380504 | − | 0.924779i | \(-0.375751\pi\) | ||||
0.380504 | + | 0.924779i | \(0.375751\pi\) | |||||||
\(224\) | 19.0908 | 1.27556 | ||||||||
\(225\) | 20.2188 | 1.34792 | ||||||||
\(226\) | −1.63391 | −0.108686 | ||||||||
\(227\) | −18.2321 | −1.21010 | −0.605052 | − | 0.796186i | \(-0.706848\pi\) | ||||
−0.605052 | + | 0.796186i | \(0.706848\pi\) | |||||||
\(228\) | −30.5993 | −2.02649 | ||||||||
\(229\) | 13.6210 | 0.900102 | 0.450051 | − | 0.893003i | \(-0.351406\pi\) | ||||
0.450051 | + | 0.893003i | \(0.351406\pi\) | |||||||
\(230\) | 66.2334 | 4.36730 | ||||||||
\(231\) | −37.9341 | −2.49588 | ||||||||
\(232\) | 1.23054 | 0.0807891 | ||||||||
\(233\) | 14.3590 | 0.940692 | 0.470346 | − | 0.882482i | \(-0.344129\pi\) | ||||
0.470346 | + | 0.882482i | \(0.344129\pi\) | |||||||
\(234\) | 28.6638 | 1.87381 | ||||||||
\(235\) | −4.49523 | −0.293236 | ||||||||
\(236\) | 50.1983 | 3.26763 | ||||||||
\(237\) | 33.8170 | 2.19665 | ||||||||
\(238\) | 45.8862 | 2.97436 | ||||||||
\(239\) | −25.7499 | −1.66563 | −0.832813 | − | 0.553555i | \(-0.813271\pi\) | ||||
−0.832813 | + | 0.553555i | \(0.813271\pi\) | |||||||
\(240\) | −11.3668 | −0.733727 | ||||||||
\(241\) | −11.3817 | −0.733158 | −0.366579 | − | 0.930387i | \(-0.619471\pi\) | ||||
−0.366579 | + | 0.930387i | \(0.619471\pi\) | |||||||
\(242\) | 3.51707 | 0.226086 | ||||||||
\(243\) | 22.2970 | 1.43035 | ||||||||
\(244\) | 44.1251 | 2.82482 | ||||||||
\(245\) | 53.2917 | 3.40468 | ||||||||
\(246\) | 16.7170 | 1.06583 | ||||||||
\(247\) | −11.8232 | −0.752294 | ||||||||
\(248\) | 9.79089 | 0.621722 | ||||||||
\(249\) | −11.7179 | −0.742592 | ||||||||
\(250\) | −5.82318 | −0.368290 | ||||||||
\(251\) | 22.0126 | 1.38942 | 0.694712 | − | 0.719288i | \(-0.255532\pi\) | ||||
0.694712 | + | 0.719288i | \(0.255532\pi\) | |||||||
\(252\) | 59.6487 | 3.75752 | ||||||||
\(253\) | −26.4951 | −1.66573 | ||||||||
\(254\) | 26.5995 | 1.66900 | ||||||||
\(255\) | 33.8960 | 2.12265 | ||||||||
\(256\) | −23.7208 | −1.48255 | ||||||||
\(257\) | 1.24375 | 0.0775829 | 0.0387914 | − | 0.999247i | \(-0.487649\pi\) | ||||
0.0387914 | + | 0.999247i | \(0.487649\pi\) | |||||||
\(258\) | −76.7454 | −4.77796 | ||||||||
\(259\) | −39.9244 | −2.48078 | ||||||||
\(260\) | −40.1044 | −2.48717 | ||||||||
\(261\) | −1.20906 | −0.0748391 | ||||||||
\(262\) | −14.5199 | −0.897045 | ||||||||
\(263\) | 28.3305 | 1.74693 | 0.873467 | − | 0.486883i | \(-0.161866\pi\) | ||||
0.873467 | + | 0.486883i | \(0.161866\pi\) | |||||||
\(264\) | 28.1276 | 1.73113 | ||||||||
\(265\) | −3.27958 | −0.201463 | ||||||||
\(266\) | −38.5772 | −2.36532 | ||||||||
\(267\) | 21.7274 | 1.32970 | ||||||||
\(268\) | −17.1260 | −1.04614 | ||||||||
\(269\) | 4.85106 | 0.295774 | 0.147887 | − | 0.989004i | \(-0.452753\pi\) | ||||
0.147887 | + | 0.989004i | \(0.452753\pi\) | |||||||
\(270\) | 10.0866 | 0.613848 | ||||||||
\(271\) | 4.70926 | 0.286067 | 0.143034 | − | 0.989718i | \(-0.454314\pi\) | ||||
0.143034 | + | 0.989718i | \(0.454314\pi\) | |||||||
\(272\) | −5.50022 | −0.333500 | ||||||||
\(273\) | 42.7303 | 2.58616 | ||||||||
\(274\) | 43.0653 | 2.60167 | ||||||||
\(275\) | 17.7431 | 1.06995 | ||||||||
\(276\) | 77.2408 | 4.64935 | ||||||||
\(277\) | −4.56836 | −0.274486 | −0.137243 | − | 0.990537i | \(-0.543824\pi\) | ||||
−0.137243 | + | 0.990537i | \(0.543824\pi\) | |||||||
\(278\) | 30.2394 | 1.81364 | ||||||||
\(279\) | −9.61998 | −0.575933 | ||||||||
\(280\) | −56.5374 | −3.37875 | ||||||||
\(281\) | −3.77999 | −0.225495 | −0.112748 | − | 0.993624i | \(-0.535965\pi\) | ||||
−0.112748 | + | 0.993624i | \(0.535965\pi\) | |||||||
\(282\) | −8.21958 | −0.489469 | ||||||||
\(283\) | 0.740790 | 0.0440354 | 0.0220177 | − | 0.999758i | \(-0.492991\pi\) | ||||
0.0220177 | + | 0.999758i | \(0.492991\pi\) | |||||||
\(284\) | −48.1237 | −2.85562 | ||||||||
\(285\) | −28.4969 | −1.68801 | ||||||||
\(286\) | 25.1541 | 1.48739 | ||||||||
\(287\) | 13.4415 | 0.793428 | ||||||||
\(288\) | 13.9084 | 0.819562 | ||||||||
\(289\) | −0.598292 | −0.0351937 | ||||||||
\(290\) | 2.65237 | 0.155753 | ||||||||
\(291\) | −19.3989 | −1.13718 | ||||||||
\(292\) | 15.0949 | 0.883363 | ||||||||
\(293\) | −2.09295 | −0.122272 | −0.0611358 | − | 0.998129i | \(-0.519472\pi\) | ||||
−0.0611358 | + | 0.998129i | \(0.519472\pi\) | |||||||
\(294\) | 97.4446 | 5.68309 | ||||||||
\(295\) | 46.7494 | 2.72186 | ||||||||
\(296\) | 29.6034 | 1.72066 | ||||||||
\(297\) | −4.03488 | −0.234128 | ||||||||
\(298\) | −4.09040 | −0.236950 | ||||||||
\(299\) | 29.8450 | 1.72598 | ||||||||
\(300\) | −51.7262 | −2.98642 | ||||||||
\(301\) | −61.7084 | −3.55681 | ||||||||
\(302\) | 2.34979 | 0.135215 | ||||||||
\(303\) | −3.09945 | −0.178059 | ||||||||
\(304\) | 4.62412 | 0.265211 | ||||||||
\(305\) | 41.0934 | 2.35300 | ||||||||
\(306\) | 33.4300 | 1.91107 | ||||||||
\(307\) | 24.8316 | 1.41721 | 0.708607 | − | 0.705604i | \(-0.249324\pi\) | ||||
0.708607 | + | 0.705604i | \(0.249324\pi\) | |||||||
\(308\) | 52.3449 | 2.98263 | ||||||||
\(309\) | 20.0342 | 1.13970 | ||||||||
\(310\) | 21.1038 | 1.19861 | ||||||||
\(311\) | 32.4115 | 1.83789 | 0.918944 | − | 0.394389i | \(-0.129044\pi\) | ||||
0.918944 | + | 0.394389i | \(0.129044\pi\) | |||||||
\(312\) | −31.6839 | −1.79375 | ||||||||
\(313\) | −21.4248 | −1.21100 | −0.605499 | − | 0.795846i | \(-0.707027\pi\) | ||||
−0.605499 | + | 0.795846i | \(0.707027\pi\) | |||||||
\(314\) | 16.7165 | 0.943369 | ||||||||
\(315\) | 55.5505 | 3.12991 | ||||||||
\(316\) | −46.6638 | −2.62504 | ||||||||
\(317\) | −29.4016 | −1.65136 | −0.825679 | − | 0.564141i | \(-0.809207\pi\) | ||||
−0.825679 | + | 0.564141i | \(0.809207\pi\) | |||||||
\(318\) | −5.99675 | −0.336281 | ||||||||
\(319\) | −1.06102 | −0.0594056 | ||||||||
\(320\) | −39.4196 | −2.20362 | ||||||||
\(321\) | −19.9912 | −1.11580 | ||||||||
\(322\) | 97.3792 | 5.42673 | ||||||||
\(323\) | −13.7892 | −0.767250 | ||||||||
\(324\) | −25.3492 | −1.40829 | ||||||||
\(325\) | −19.9865 | −1.10865 | ||||||||
\(326\) | −55.3056 | −3.06310 | ||||||||
\(327\) | 15.5844 | 0.861822 | ||||||||
\(328\) | −9.96670 | −0.550319 | ||||||||
\(329\) | −6.60908 | −0.364371 | ||||||||
\(330\) | 60.6275 | 3.33744 | ||||||||
\(331\) | −18.3859 | −1.01058 | −0.505290 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505290 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(332\) | 16.1694 | 0.887413 | ||||||||
\(333\) | −29.0866 | −1.59394 | ||||||||
\(334\) | 52.6196 | 2.87922 | ||||||||
\(335\) | −15.9494 | −0.871407 | ||||||||
\(336\) | −16.7120 | −0.911716 | ||||||||
\(337\) | −11.6946 | −0.637045 | −0.318522 | − | 0.947915i | \(-0.603187\pi\) | ||||
−0.318522 | + | 0.947915i | \(0.603187\pi\) | |||||||
\(338\) | 2.21288 | 0.120365 | ||||||||
\(339\) | −1.77453 | −0.0963794 | ||||||||
\(340\) | −46.7729 | −2.53661 | ||||||||
\(341\) | −8.44205 | −0.457163 | ||||||||
\(342\) | −28.1051 | −1.51975 | ||||||||
\(343\) | 44.5994 | 2.40814 | ||||||||
\(344\) | 45.7559 | 2.46699 | ||||||||
\(345\) | 71.9339 | 3.87279 | ||||||||
\(346\) | −33.4738 | −1.79956 | ||||||||
\(347\) | 12.2023 | 0.655053 | 0.327527 | − | 0.944842i | \(-0.393785\pi\) | ||||
0.327527 | + | 0.944842i | \(0.393785\pi\) | |||||||
\(348\) | 3.09317 | 0.165811 | ||||||||
\(349\) | −35.7783 | −1.91517 | −0.957584 | − | 0.288153i | \(-0.906959\pi\) | ||||
−0.957584 | + | 0.288153i | \(0.906959\pi\) | |||||||
\(350\) | −65.2124 | −3.48575 | ||||||||
\(351\) | 4.54504 | 0.242596 | ||||||||
\(352\) | 12.2054 | 0.650550 | ||||||||
\(353\) | −26.5979 | −1.41566 | −0.707831 | − | 0.706381i | \(-0.750326\pi\) | ||||
−0.707831 | + | 0.706381i | \(0.750326\pi\) | |||||||
\(354\) | 85.4819 | 4.54331 | ||||||||
\(355\) | −44.8173 | −2.37865 | ||||||||
\(356\) | −29.9815 | −1.58902 | ||||||||
\(357\) | 49.8354 | 2.63757 | ||||||||
\(358\) | 6.15475 | 0.325289 | ||||||||
\(359\) | −35.4096 | −1.86884 | −0.934422 | − | 0.356167i | \(-0.884083\pi\) | ||||
−0.934422 | + | 0.356167i | \(0.884083\pi\) | |||||||
\(360\) | −41.1899 | −2.17090 | ||||||||
\(361\) | −7.40724 | −0.389855 | ||||||||
\(362\) | 12.1584 | 0.639033 | ||||||||
\(363\) | 3.81978 | 0.200486 | ||||||||
\(364\) | −58.9632 | −3.09051 | ||||||||
\(365\) | 14.0578 | 0.735819 | ||||||||
\(366\) | 75.1398 | 3.92762 | ||||||||
\(367\) | 3.80542 | 0.198641 | 0.0993206 | − | 0.995055i | \(-0.468333\pi\) | ||||
0.0993206 | + | 0.995055i | \(0.468333\pi\) | |||||||
\(368\) | −11.6725 | −0.608473 | ||||||||
\(369\) | 9.79272 | 0.509789 | ||||||||
\(370\) | 63.8085 | 3.31725 | ||||||||
\(371\) | −4.82178 | −0.250334 | ||||||||
\(372\) | 24.6110 | 1.27602 | ||||||||
\(373\) | 8.36767 | 0.433261 | 0.216631 | − | 0.976254i | \(-0.430493\pi\) | ||||
0.216631 | + | 0.976254i | \(0.430493\pi\) | |||||||
\(374\) | 29.3366 | 1.51696 | ||||||||
\(375\) | −6.32436 | −0.326589 | ||||||||
\(376\) | 4.90054 | 0.252726 | ||||||||
\(377\) | 1.19517 | 0.0615543 | ||||||||
\(378\) | 14.8297 | 0.762757 | ||||||||
\(379\) | −29.8927 | −1.53548 | −0.767742 | − | 0.640760i | \(-0.778620\pi\) | ||||
−0.767742 | + | 0.640760i | \(0.778620\pi\) | |||||||
\(380\) | 39.3227 | 2.01721 | ||||||||
\(381\) | 28.8889 | 1.48002 | ||||||||
\(382\) | −55.4744 | −2.83831 | ||||||||
\(383\) | 8.91615 | 0.455594 | 0.227797 | − | 0.973709i | \(-0.426848\pi\) | ||||
0.227797 | + | 0.973709i | \(0.426848\pi\) | |||||||
\(384\) | −51.8708 | −2.64702 | ||||||||
\(385\) | 48.7485 | 2.48445 | ||||||||
\(386\) | 10.3543 | 0.527019 | ||||||||
\(387\) | −44.9572 | −2.28530 | ||||||||
\(388\) | 26.7684 | 1.35896 | ||||||||
\(389\) | −2.03711 | −0.103285 | −0.0516427 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516427 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(390\) | −68.2930 | −3.45815 | ||||||||
\(391\) | 34.8076 | 1.76029 | ||||||||
\(392\) | −58.0968 | −2.93433 | ||||||||
\(393\) | −15.7696 | −0.795473 | ||||||||
\(394\) | 27.7264 | 1.39684 | ||||||||
\(395\) | −43.4577 | −2.18659 | ||||||||
\(396\) | 38.1355 | 1.91638 | ||||||||
\(397\) | 10.4502 | 0.524481 | 0.262240 | − | 0.965003i | \(-0.415539\pi\) | ||||
0.262240 | + | 0.965003i | \(0.415539\pi\) | |||||||
\(398\) | −13.7149 | −0.687468 | ||||||||
\(399\) | −41.8974 | −2.09749 | ||||||||
\(400\) | 7.81680 | 0.390840 | ||||||||
\(401\) | 6.54172 | 0.326678 | 0.163339 | − | 0.986570i | \(-0.447774\pi\) | ||||
0.163339 | + | 0.986570i | \(0.447774\pi\) | |||||||
\(402\) | −29.1636 | −1.45455 | ||||||||
\(403\) | 9.50943 | 0.473698 | ||||||||
\(404\) | 4.27690 | 0.212784 | ||||||||
\(405\) | −23.6075 | −1.17307 | ||||||||
\(406\) | 3.89963 | 0.193536 | ||||||||
\(407\) | −25.5251 | −1.26523 | ||||||||
\(408\) | −36.9523 | −1.82941 | ||||||||
\(409\) | −17.7146 | −0.875930 | −0.437965 | − | 0.898992i | \(-0.644301\pi\) | ||||
−0.437965 | + | 0.898992i | \(0.644301\pi\) | |||||||
\(410\) | −21.4827 | −1.06096 | ||||||||
\(411\) | 46.7718 | 2.30708 | ||||||||
\(412\) | −27.6450 | −1.36197 | ||||||||
\(413\) | 68.7330 | 3.38213 | ||||||||
\(414\) | 70.9449 | 3.48675 | ||||||||
\(415\) | 15.0585 | 0.739192 | ||||||||
\(416\) | −13.7486 | −0.674080 | ||||||||
\(417\) | 32.8420 | 1.60828 | ||||||||
\(418\) | −24.6637 | −1.20634 | ||||||||
\(419\) | −14.5429 | −0.710466 | −0.355233 | − | 0.934778i | \(-0.615598\pi\) | ||||
−0.355233 | + | 0.934778i | \(0.615598\pi\) | |||||||
\(420\) | −142.116 | −6.93455 | ||||||||
\(421\) | 23.3232 | 1.13670 | 0.568350 | − | 0.822787i | \(-0.307582\pi\) | ||||
0.568350 | + | 0.822787i | \(0.307582\pi\) | |||||||
\(422\) | 61.4053 | 2.98916 | ||||||||
\(423\) | −4.81500 | −0.234113 | ||||||||
\(424\) | 3.57528 | 0.173631 | ||||||||
\(425\) | −23.3098 | −1.13069 | ||||||||
\(426\) | −81.9490 | −3.97044 | ||||||||
\(427\) | 60.4173 | 2.92380 | ||||||||
\(428\) | 27.5857 | 1.33340 | ||||||||
\(429\) | 27.3190 | 1.31897 | ||||||||
\(430\) | 98.6244 | 4.75609 | ||||||||
\(431\) | 3.86468 | 0.186155 | 0.0930775 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930775 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(432\) | −1.77759 | −0.0855241 | ||||||||
\(433\) | −11.6182 | −0.558333 | −0.279167 | − | 0.960243i | \(-0.590058\pi\) | ||||
−0.279167 | + | 0.960243i | \(0.590058\pi\) | |||||||
\(434\) | 31.0277 | 1.48938 | ||||||||
\(435\) | 2.88065 | 0.138117 | ||||||||
\(436\) | −21.5049 | −1.02990 | ||||||||
\(437\) | −29.2633 | −1.39985 | ||||||||
\(438\) | 25.7049 | 1.22823 | ||||||||
\(439\) | −17.9477 | −0.856596 | −0.428298 | − | 0.903638i | \(-0.640887\pi\) | ||||
−0.428298 | + | 0.903638i | \(0.640887\pi\) | |||||||
\(440\) | −36.1463 | −1.72321 | ||||||||
\(441\) | 57.0827 | 2.71822 | ||||||||
\(442\) | −33.0458 | −1.57183 | ||||||||
\(443\) | −26.3122 | −1.25013 | −0.625066 | − | 0.780572i | \(-0.714928\pi\) | ||||
−0.625066 | + | 0.780572i | \(0.714928\pi\) | |||||||
\(444\) | 74.4130 | 3.53148 | ||||||||
\(445\) | −27.9216 | −1.32361 | ||||||||
\(446\) | −26.7037 | −1.26446 | ||||||||
\(447\) | −4.44244 | −0.210120 | ||||||||
\(448\) | −57.9564 | −2.73818 | ||||||||
\(449\) | 20.5011 | 0.967506 | 0.483753 | − | 0.875205i | \(-0.339273\pi\) | ||||
0.483753 | + | 0.875205i | \(0.339273\pi\) | |||||||
\(450\) | −47.5100 | −2.23964 | ||||||||
\(451\) | 8.59364 | 0.404659 | ||||||||
\(452\) | 2.44866 | 0.115176 | ||||||||
\(453\) | 2.55203 | 0.119905 | ||||||||
\(454\) | 42.8416 | 2.01065 | ||||||||
\(455\) | −54.9121 | −2.57432 | ||||||||
\(456\) | 31.0663 | 1.45481 | ||||||||
\(457\) | −28.1733 | −1.31789 | −0.658946 | − | 0.752190i | \(-0.728998\pi\) | ||||
−0.658946 | + | 0.752190i | \(0.728998\pi\) | |||||||
\(458\) | −32.0066 | −1.49557 | ||||||||
\(459\) | 5.30078 | 0.247419 | ||||||||
\(460\) | −99.2610 | −4.62807 | ||||||||
\(461\) | 18.7101 | 0.871416 | 0.435708 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435708 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(462\) | 89.1373 | 4.14704 | ||||||||
\(463\) | 16.0866 | 0.747607 | 0.373803 | − | 0.927508i | \(-0.378054\pi\) | ||||
0.373803 | + | 0.927508i | \(0.378054\pi\) | |||||||
\(464\) | −0.467436 | −0.0217002 | ||||||||
\(465\) | 22.9201 | 1.06289 | ||||||||
\(466\) | −33.7408 | −1.56301 | ||||||||
\(467\) | 5.53290 | 0.256032 | 0.128016 | − | 0.991772i | \(-0.459139\pi\) | ||||
0.128016 | + | 0.991772i | \(0.459139\pi\) | |||||||
\(468\) | −42.9572 | −1.98570 | ||||||||
\(469\) | −23.4495 | −1.08280 | ||||||||
\(470\) | 10.5629 | 0.487228 | ||||||||
\(471\) | 18.1553 | 0.836551 | ||||||||
\(472\) | −50.9645 | −2.34583 | ||||||||
\(473\) | −39.4523 | −1.81402 | ||||||||
\(474\) | −79.4629 | −3.64985 | ||||||||
\(475\) | 19.5969 | 0.899166 | ||||||||
\(476\) | −68.7675 | −3.15195 | ||||||||
\(477\) | −3.51287 | −0.160843 | ||||||||
\(478\) | 60.5070 | 2.76753 | ||||||||
\(479\) | 3.68528 | 0.168385 | 0.0841924 | − | 0.996450i | \(-0.473169\pi\) | ||||
0.0841924 | + | 0.996450i | \(0.473169\pi\) | |||||||
\(480\) | −33.1375 | −1.51252 | ||||||||
\(481\) | 28.7524 | 1.31099 | ||||||||
\(482\) | 26.7446 | 1.21818 | ||||||||
\(483\) | 105.760 | 4.81226 | ||||||||
\(484\) | −5.27088 | −0.239585 | ||||||||
\(485\) | 24.9292 | 1.13198 | ||||||||
\(486\) | −52.3934 | −2.37661 | ||||||||
\(487\) | −10.5871 | −0.479749 | −0.239874 | − | 0.970804i | \(-0.577106\pi\) | ||||
−0.239874 | + | 0.970804i | \(0.577106\pi\) | |||||||
\(488\) | −44.7986 | −2.02794 | ||||||||
\(489\) | −60.0656 | −2.71626 | ||||||||
\(490\) | −125.225 | −5.65707 | ||||||||
\(491\) | −18.0523 | −0.814688 | −0.407344 | − | 0.913275i | \(-0.633545\pi\) | ||||
−0.407344 | + | 0.913275i | \(0.633545\pi\) | |||||||
\(492\) | −25.0530 | −1.12947 | ||||||||
\(493\) | 1.39390 | 0.0627780 | ||||||||
\(494\) | 27.7821 | 1.24998 | ||||||||
\(495\) | 35.5154 | 1.59630 | ||||||||
\(496\) | −3.71918 | −0.166996 | ||||||||
\(497\) | −65.8924 | −2.95568 | ||||||||
\(498\) | 27.5346 | 1.23386 | ||||||||
\(499\) | −25.8090 | −1.15537 | −0.577685 | − | 0.816260i | \(-0.696044\pi\) | ||||
−0.577685 | + | 0.816260i | \(0.696044\pi\) | |||||||
\(500\) | 8.72694 | 0.390281 | ||||||||
\(501\) | 57.1484 | 2.55320 | ||||||||
\(502\) | −51.7251 | −2.30860 | ||||||||
\(503\) | −29.1621 | −1.30027 | −0.650136 | − | 0.759818i | \(-0.725288\pi\) | ||||
−0.650136 | + | 0.759818i | \(0.725288\pi\) | |||||||
\(504\) | −60.5592 | −2.69752 | ||||||||
\(505\) | 3.98305 | 0.177244 | ||||||||
\(506\) | 62.2579 | 2.76770 | ||||||||
\(507\) | 2.40334 | 0.106736 | ||||||||
\(508\) | −39.8635 | −1.76866 | ||||||||
\(509\) | −19.8330 | −0.879083 | −0.439542 | − | 0.898222i | \(-0.644859\pi\) | ||||
−0.439542 | + | 0.898222i | \(0.644859\pi\) | |||||||
\(510\) | −79.6487 | −3.52690 | ||||||||
\(511\) | 20.6684 | 0.914316 | ||||||||
\(512\) | 15.0884 | 0.666820 | ||||||||
\(513\) | −4.45644 | −0.196757 | ||||||||
\(514\) | −2.92255 | −0.128908 | ||||||||
\(515\) | −25.7456 | −1.13449 | ||||||||
\(516\) | 115.015 | 5.06325 | ||||||||
\(517\) | −4.22542 | −0.185834 | ||||||||
\(518\) | 93.8141 | 4.12196 | ||||||||
\(519\) | −36.3548 | −1.59580 | ||||||||
\(520\) | 40.7165 | 1.78554 | ||||||||
\(521\) | 5.54609 | 0.242979 | 0.121489 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121489 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(522\) | 2.84105 | 0.124349 | ||||||||
\(523\) | 28.4244 | 1.24291 | 0.621456 | − | 0.783449i | \(-0.286542\pi\) | ||||
0.621456 | + | 0.783449i | \(0.286542\pi\) | |||||||
\(524\) | 21.7604 | 0.950607 | ||||||||
\(525\) | −70.8251 | −3.09106 | ||||||||
\(526\) | −66.5709 | −2.90263 | ||||||||
\(527\) | 11.0906 | 0.483116 | ||||||||
\(528\) | −10.6846 | −0.464987 | ||||||||
\(529\) | 50.8684 | 2.21167 | ||||||||
\(530\) | 7.70633 | 0.334742 | ||||||||
\(531\) | 50.0749 | 2.17307 | ||||||||
\(532\) | 57.8139 | 2.50655 | ||||||||
\(533\) | −9.68019 | −0.419295 | ||||||||
\(534\) | −51.0549 | −2.20936 | ||||||||
\(535\) | 25.6903 | 1.11069 | ||||||||
\(536\) | 17.3874 | 0.751023 | ||||||||
\(537\) | 6.68447 | 0.288456 | ||||||||
\(538\) | −11.3990 | −0.491445 | ||||||||
\(539\) | 50.0931 | 2.15766 | ||||||||
\(540\) | −15.1163 | −0.650500 | ||||||||
\(541\) | −12.5006 | −0.537443 | −0.268722 | − | 0.963218i | \(-0.586601\pi\) | ||||
−0.268722 | + | 0.963218i | \(0.586601\pi\) | |||||||
\(542\) | −11.0658 | −0.475317 | ||||||||
\(543\) | 13.2049 | 0.566675 | ||||||||
\(544\) | −16.0347 | −0.687482 | ||||||||
\(545\) | −20.0273 | −0.857877 | ||||||||
\(546\) | −100.407 | −4.29704 | ||||||||
\(547\) | −25.1384 | −1.07484 | −0.537420 | − | 0.843314i | \(-0.680601\pi\) | ||||
−0.537420 | + | 0.843314i | \(0.680601\pi\) | |||||||
\(548\) | −64.5400 | −2.75701 | ||||||||
\(549\) | 44.0166 | 1.87858 | ||||||||
\(550\) | −41.6926 | −1.77778 | ||||||||
\(551\) | −1.17187 | −0.0499234 | ||||||||
\(552\) | −78.4198 | −3.33777 | ||||||||
\(553\) | −63.8934 | −2.71702 | ||||||||
\(554\) | 10.7347 | 0.456074 | ||||||||
\(555\) | 69.3003 | 2.94164 | ||||||||
\(556\) | −45.3184 | −1.92193 | ||||||||
\(557\) | −21.9044 | −0.928117 | −0.464059 | − | 0.885804i | \(-0.653607\pi\) | ||||
−0.464059 | + | 0.885804i | \(0.653607\pi\) | |||||||
\(558\) | 22.6050 | 0.956945 | ||||||||
\(559\) | 44.4405 | 1.87963 | ||||||||
\(560\) | 21.4764 | 0.907543 | ||||||||
\(561\) | 31.8615 | 1.34520 | ||||||||
\(562\) | 8.88219 | 0.374672 | ||||||||
\(563\) | 34.0753 | 1.43610 | 0.718052 | − | 0.695990i | \(-0.245034\pi\) | ||||
0.718052 | + | 0.695990i | \(0.245034\pi\) | |||||||
\(564\) | 12.3183 | 0.518695 | ||||||||
\(565\) | 2.28043 | 0.0959382 | ||||||||
\(566\) | −1.74070 | −0.0731672 | ||||||||
\(567\) | −34.7089 | −1.45763 | ||||||||
\(568\) | 48.8582 | 2.05005 | ||||||||
\(569\) | 10.2760 | 0.430794 | 0.215397 | − | 0.976527i | \(-0.430896\pi\) | ||||
0.215397 | + | 0.976527i | \(0.430896\pi\) | |||||||
\(570\) | 66.9618 | 2.80472 | ||||||||
\(571\) | −6.82983 | −0.285819 | −0.142910 | − | 0.989736i | \(-0.545646\pi\) | ||||
−0.142910 | + | 0.989736i | \(0.545646\pi\) | |||||||
\(572\) | −37.6972 | −1.57620 | ||||||||
\(573\) | −60.2489 | −2.51693 | ||||||||
\(574\) | −31.5848 | −1.31832 | ||||||||
\(575\) | −49.4678 | −2.06295 | ||||||||
\(576\) | −42.2237 | −1.75932 | ||||||||
\(577\) | −25.5250 | −1.06262 | −0.531309 | − | 0.847178i | \(-0.678300\pi\) | ||||
−0.531309 | + | 0.847178i | \(0.678300\pi\) | |||||||
\(578\) | 1.40586 | 0.0584762 | ||||||||
\(579\) | 11.2455 | 0.467345 | ||||||||
\(580\) | −3.97499 | −0.165052 | ||||||||
\(581\) | 22.1397 | 0.918508 | ||||||||
\(582\) | 45.5834 | 1.88949 | ||||||||
\(583\) | −3.08273 | −0.127674 | ||||||||
\(584\) | −15.3253 | −0.634166 | ||||||||
\(585\) | −40.0058 | −1.65404 | ||||||||
\(586\) | 4.91801 | 0.203161 | ||||||||
\(587\) | 29.0087 | 1.19732 | 0.598658 | − | 0.801005i | \(-0.295701\pi\) | ||||
0.598658 | + | 0.801005i | \(0.295701\pi\) | |||||||
\(588\) | −146.036 | −6.02242 | ||||||||
\(589\) | −9.32407 | −0.384192 | ||||||||
\(590\) | −109.851 | −4.52251 | ||||||||
\(591\) | 30.1128 | 1.23867 | ||||||||
\(592\) | −11.2452 | −0.462174 | ||||||||
\(593\) | 26.7625 | 1.09900 | 0.549502 | − | 0.835492i | \(-0.314817\pi\) | ||||
0.549502 | + | 0.835492i | \(0.314817\pi\) | |||||||
\(594\) | 9.48114 | 0.389016 | ||||||||
\(595\) | −64.0428 | −2.62550 | ||||||||
\(596\) | 6.13009 | 0.251098 | ||||||||
\(597\) | −14.8953 | −0.609626 | ||||||||
\(598\) | −70.1296 | −2.86781 | ||||||||
\(599\) | −0.661074 | −0.0270107 | −0.0135054 | − | 0.999909i | \(-0.504299\pi\) | ||||
−0.0135054 | + | 0.999909i | \(0.504299\pi\) | |||||||
\(600\) | 52.5158 | 2.14395 | ||||||||
\(601\) | 28.3595 | 1.15681 | 0.578404 | − | 0.815750i | \(-0.303676\pi\) | ||||
0.578404 | + | 0.815750i | \(0.303676\pi\) | |||||||
\(602\) | 145.002 | 5.90984 | ||||||||
\(603\) | −17.0839 | −0.695711 | ||||||||
\(604\) | −3.52153 | −0.143289 | ||||||||
\(605\) | −4.90874 | −0.199569 | ||||||||
\(606\) | 7.28306 | 0.295854 | ||||||||
\(607\) | 9.81288 | 0.398292 | 0.199146 | − | 0.979970i | \(-0.436183\pi\) | ||||
0.199146 | + | 0.979970i | \(0.436183\pi\) | |||||||
\(608\) | 13.4806 | 0.546711 | ||||||||
\(609\) | 4.23526 | 0.171622 | ||||||||
\(610\) | −96.5610 | −3.90964 | ||||||||
\(611\) | 4.75966 | 0.192555 | ||||||||
\(612\) | −50.1001 | −2.02517 | ||||||||
\(613\) | −19.1643 | −0.774040 | −0.387020 | − | 0.922071i | \(-0.626496\pi\) | ||||
−0.387020 | + | 0.922071i | \(0.626496\pi\) | |||||||
\(614\) | −58.3491 | −2.35478 | ||||||||
\(615\) | −23.3317 | −0.940823 | ||||||||
\(616\) | −53.1439 | −2.14123 | ||||||||
\(617\) | 3.29263 | 0.132556 | 0.0662781 | − | 0.997801i | \(-0.478888\pi\) | ||||
0.0662781 | + | 0.997801i | \(0.478888\pi\) | |||||||
\(618\) | −47.0761 | −1.89368 | ||||||||
\(619\) | 13.1219 | 0.527412 | 0.263706 | − | 0.964603i | \(-0.415055\pi\) | ||||
0.263706 | + | 0.964603i | \(0.415055\pi\) | |||||||
\(620\) | −31.6273 | −1.27018 | ||||||||
\(621\) | 11.2493 | 0.451418 | ||||||||
\(622\) | −76.1603 | −3.05375 | ||||||||
\(623\) | −41.0515 | −1.64469 | ||||||||
\(624\) | 12.0355 | 0.481806 | ||||||||
\(625\) | −20.6508 | −0.826033 | ||||||||
\(626\) | 50.3438 | 2.01214 | ||||||||
\(627\) | −26.7865 | −1.06975 | ||||||||
\(628\) | −25.0523 | −0.999697 | ||||||||
\(629\) | 33.5332 | 1.33706 | ||||||||
\(630\) | −130.532 | −5.20053 | ||||||||
\(631\) | 48.7161 | 1.93936 | 0.969679 | − | 0.244384i | \(-0.0785856\pi\) | ||||
0.969679 | + | 0.244384i | \(0.0785856\pi\) | |||||||
\(632\) | 47.3760 | 1.88452 | ||||||||
\(633\) | 66.6902 | 2.65070 | ||||||||
\(634\) | 69.0876 | 2.74382 | ||||||||
\(635\) | −37.1246 | −1.47325 | ||||||||
\(636\) | 8.98706 | 0.356360 | ||||||||
\(637\) | −56.4267 | −2.23571 | ||||||||
\(638\) | 2.49317 | 0.0987056 | ||||||||
\(639\) | −48.0054 | −1.89906 | ||||||||
\(640\) | 66.6584 | 2.63490 | ||||||||
\(641\) | 41.5587 | 1.64147 | 0.820736 | − | 0.571308i | \(-0.193564\pi\) | ||||
0.820736 | + | 0.571308i | \(0.193564\pi\) | |||||||
\(642\) | 46.9751 | 1.85396 | ||||||||
\(643\) | 31.4097 | 1.23868 | 0.619338 | − | 0.785124i | \(-0.287401\pi\) | ||||
0.619338 | + | 0.785124i | \(0.287401\pi\) | |||||||
\(644\) | −145.938 | −5.75076 | ||||||||
\(645\) | 107.113 | 4.21756 | ||||||||
\(646\) | 32.4017 | 1.27483 | ||||||||
\(647\) | 32.1926 | 1.26562 | 0.632811 | − | 0.774306i | \(-0.281901\pi\) | ||||
0.632811 | + | 0.774306i | \(0.281901\pi\) | |||||||
\(648\) | 25.7361 | 1.01101 | ||||||||
\(649\) | 43.9434 | 1.72493 | ||||||||
\(650\) | 46.9640 | 1.84208 | ||||||||
\(651\) | 33.6981 | 1.32073 | ||||||||
\(652\) | 82.8840 | 3.24599 | ||||||||
\(653\) | −47.1808 | −1.84633 | −0.923163 | − | 0.384408i | \(-0.874406\pi\) | ||||
−0.923163 | + | 0.384408i | \(0.874406\pi\) | |||||||
\(654\) | −36.6202 | −1.43196 | ||||||||
\(655\) | 20.2653 | 0.791831 | ||||||||
\(656\) | 3.78597 | 0.147817 | ||||||||
\(657\) | 15.0578 | 0.587461 | ||||||||
\(658\) | 15.5300 | 0.605422 | ||||||||
\(659\) | −9.56067 | −0.372431 | −0.186215 | − | 0.982509i | \(-0.559622\pi\) | ||||
−0.186215 | + | 0.982509i | \(0.559622\pi\) | |||||||
\(660\) | −90.8598 | −3.53671 | ||||||||
\(661\) | −40.2832 | −1.56683 | −0.783417 | − | 0.621496i | \(-0.786525\pi\) | ||||
−0.783417 | + | 0.621496i | \(0.786525\pi\) | |||||||
\(662\) | 43.2031 | 1.67914 | ||||||||
\(663\) | −35.8900 | −1.39385 | ||||||||
\(664\) | −16.4162 | −0.637074 | ||||||||
\(665\) | 53.8417 | 2.08789 | ||||||||
\(666\) | 68.3476 | 2.64841 | ||||||||
\(667\) | 2.95812 | 0.114539 | ||||||||
\(668\) | −78.8586 | −3.05113 | ||||||||
\(669\) | −29.0020 | −1.12128 | ||||||||
\(670\) | 37.4777 | 1.44789 | ||||||||
\(671\) | 38.6269 | 1.49117 | ||||||||
\(672\) | −48.7203 | −1.87943 | ||||||||
\(673\) | 17.4256 | 0.671709 | 0.335855 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335855 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(674\) | 27.4799 | 1.05849 | ||||||||
\(675\) | −7.53335 | −0.289959 | ||||||||
\(676\) | −3.31635 | −0.127552 | ||||||||
\(677\) | −40.0720 | −1.54009 | −0.770047 | − | 0.637988i | \(-0.779767\pi\) | ||||
−0.770047 | + | 0.637988i | \(0.779767\pi\) | |||||||
\(678\) | 4.16979 | 0.160140 | ||||||||
\(679\) | 36.6521 | 1.40658 | ||||||||
\(680\) | 47.4868 | 1.82103 | ||||||||
\(681\) | 46.5288 | 1.78299 | ||||||||
\(682\) | 19.8371 | 0.759601 | ||||||||
\(683\) | −35.8465 | −1.37163 | −0.685814 | − | 0.727777i | \(-0.740554\pi\) | ||||
−0.685814 | + | 0.727777i | \(0.740554\pi\) | |||||||
\(684\) | 42.1199 | 1.61049 | ||||||||
\(685\) | −60.1057 | −2.29652 | ||||||||
\(686\) | −104.799 | −4.00126 | ||||||||
\(687\) | −34.7613 | −1.32622 | ||||||||
\(688\) | −17.3809 | −0.662641 | ||||||||
\(689\) | 3.47250 | 0.132292 | ||||||||
\(690\) | −169.030 | −6.43485 | ||||||||
\(691\) | −16.3774 | −0.623025 | −0.311512 | − | 0.950242i | \(-0.600836\pi\) | ||||
−0.311512 | + | 0.950242i | \(0.600836\pi\) | |||||||
\(692\) | 50.1656 | 1.90701 | ||||||||
\(693\) | 52.2162 | 1.98353 | ||||||||
\(694\) | −28.6729 | −1.08841 | ||||||||
\(695\) | −42.2048 | −1.60092 | ||||||||
\(696\) | −3.14039 | −0.119036 | ||||||||
\(697\) | −11.2898 | −0.427631 | ||||||||
\(698\) | 84.0716 | 3.18216 | ||||||||
\(699\) | −36.6448 | −1.38603 | ||||||||
\(700\) | 97.7310 | 3.69388 | ||||||||
\(701\) | 37.6420 | 1.42172 | 0.710860 | − | 0.703334i | \(-0.248306\pi\) | ||||
0.710860 | + | 0.703334i | \(0.248306\pi\) | |||||||
\(702\) | −10.6799 | −0.403087 | ||||||||
\(703\) | −28.1919 | −1.06328 | ||||||||
\(704\) | −37.0536 | −1.39651 | ||||||||
\(705\) | 11.4720 | 0.432060 | ||||||||
\(706\) | 62.4996 | 2.35220 | ||||||||
\(707\) | 5.85606 | 0.220240 | ||||||||
\(708\) | −128.108 | −4.81459 | ||||||||
\(709\) | −15.5997 | −0.585861 | −0.292930 | − | 0.956134i | \(-0.594630\pi\) | ||||
−0.292930 | + | 0.956134i | \(0.594630\pi\) | |||||||
\(710\) | 105.311 | 3.95227 | ||||||||
\(711\) | −46.5490 | −1.74573 | ||||||||
\(712\) | 30.4391 | 1.14075 | ||||||||
\(713\) | 23.5365 | 0.881448 | ||||||||
\(714\) | −117.103 | −4.38247 | ||||||||
\(715\) | −35.1072 | −1.31294 | ||||||||
\(716\) | −9.22385 | −0.344711 | ||||||||
\(717\) | 65.7147 | 2.45416 | ||||||||
\(718\) | 83.2051 | 3.10519 | ||||||||
\(719\) | 45.1328 | 1.68317 | 0.841586 | − | 0.540124i | \(-0.181623\pi\) | ||||
0.841586 | + | 0.540124i | \(0.181623\pi\) | |||||||
\(720\) | 15.6465 | 0.583109 | ||||||||
\(721\) | −37.8523 | −1.40969 | ||||||||
\(722\) | 17.4055 | 0.647765 | ||||||||
\(723\) | 29.0464 | 1.08025 | ||||||||
\(724\) | −18.2213 | −0.677189 | ||||||||
\(725\) | −1.98098 | −0.0735717 | ||||||||
\(726\) | −8.97569 | −0.333119 | ||||||||
\(727\) | 37.2070 | 1.37993 | 0.689965 | − | 0.723843i | \(-0.257626\pi\) | ||||
0.689965 | + | 0.723843i | \(0.257626\pi\) | |||||||
\(728\) | 59.8632 | 2.21868 | ||||||||
\(729\) | −35.3077 | −1.30769 | ||||||||
\(730\) | −33.0329 | −1.22260 | ||||||||
\(731\) | 51.8300 | 1.91700 | ||||||||
\(732\) | −112.609 | −4.16213 | ||||||||
\(733\) | −12.1531 | −0.448883 | −0.224442 | − | 0.974488i | \(-0.572056\pi\) | ||||
−0.224442 | + | 0.974488i | \(0.572056\pi\) | |||||||
\(734\) | −8.94195 | −0.330053 | ||||||||
\(735\) | −136.002 | −5.01652 | ||||||||
\(736\) | −34.0287 | −1.25431 | ||||||||
\(737\) | −14.9921 | −0.552240 | ||||||||
\(738\) | −23.0109 | −0.847042 | ||||||||
\(739\) | 32.8362 | 1.20790 | 0.603949 | − | 0.797023i | \(-0.293593\pi\) | ||||
0.603949 | + | 0.797023i | \(0.293593\pi\) | |||||||
\(740\) | −95.6270 | −3.51532 | ||||||||
\(741\) | 30.1732 | 1.10844 | ||||||||
\(742\) | 11.3302 | 0.415944 | ||||||||
\(743\) | −13.2548 | −0.486270 | −0.243135 | − | 0.969992i | \(-0.578176\pi\) | ||||
−0.243135 | + | 0.969992i | \(0.578176\pi\) | |||||||
\(744\) | −24.9867 | −0.916056 | ||||||||
\(745\) | 5.70892 | 0.209158 | ||||||||
\(746\) | −19.6623 | −0.719888 | ||||||||
\(747\) | 16.1297 | 0.590154 | ||||||||
\(748\) | −43.9655 | −1.60754 | ||||||||
\(749\) | 37.7711 | 1.38013 | ||||||||
\(750\) | 14.8610 | 0.542645 | ||||||||
\(751\) | −11.3269 | −0.413323 | −0.206662 | − | 0.978412i | \(-0.566260\pi\) | ||||
−0.206662 | + | 0.978412i | \(0.566260\pi\) | |||||||
\(752\) | −1.86153 | −0.0678829 | ||||||||
\(753\) | −56.1769 | −2.04720 | ||||||||
\(754\) | −2.80840 | −0.102276 | ||||||||
\(755\) | −3.27958 | −0.119356 | ||||||||
\(756\) | −22.2246 | −0.808301 | ||||||||
\(757\) | 39.7099 | 1.44328 | 0.721640 | − | 0.692268i | \(-0.243388\pi\) | ||||
0.721640 | + | 0.692268i | \(0.243388\pi\) | |||||||
\(758\) | 70.2416 | 2.55129 | ||||||||
\(759\) | 67.6163 | 2.45432 | ||||||||
\(760\) | −39.9229 | −1.44815 | ||||||||
\(761\) | 13.0738 | 0.473924 | 0.236962 | − | 0.971519i | \(-0.423848\pi\) | ||||
0.236962 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(762\) | −67.8829 | −2.45914 | ||||||||
\(763\) | −29.4451 | −1.06598 | ||||||||
\(764\) | 83.1369 | 3.00779 | ||||||||
\(765\) | −46.6579 | −1.68692 | ||||||||
\(766\) | −20.9511 | −0.756994 | ||||||||
\(767\) | −49.4995 | −1.78732 | ||||||||
\(768\) | 60.5363 | 2.18441 | ||||||||
\(769\) | −0.692477 | −0.0249713 | −0.0124857 | − | 0.999922i | \(-0.503974\pi\) | ||||
−0.0124857 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(770\) | −114.549 | −4.12806 | ||||||||
\(771\) | −3.17409 | −0.114312 | ||||||||
\(772\) | −15.5175 | −0.558487 | ||||||||
\(773\) | −20.6488 | −0.742684 | −0.371342 | − | 0.928496i | \(-0.621102\pi\) | ||||
−0.371342 | + | 0.928496i | \(0.621102\pi\) | |||||||
\(774\) | 105.640 | 3.79715 | ||||||||
\(775\) | −15.7618 | −0.566180 | ||||||||
\(776\) | −27.1770 | −0.975596 | ||||||||
\(777\) | 101.888 | 3.65523 | ||||||||
\(778\) | 4.78678 | 0.171614 | ||||||||
\(779\) | 9.49150 | 0.340068 | ||||||||
\(780\) | 102.348 | 3.66464 | ||||||||
\(781\) | −42.1273 | −1.50743 | ||||||||
\(782\) | −81.7906 | −2.92483 | ||||||||
\(783\) | 0.450486 | 0.0160991 | ||||||||
\(784\) | 22.0687 | 0.788169 | ||||||||
\(785\) | −23.3311 | −0.832722 | ||||||||
\(786\) | 37.0554 | 1.32172 | ||||||||
\(787\) | −54.4542 | −1.94108 | −0.970541 | − | 0.240935i | \(-0.922546\pi\) | ||||
−0.970541 | + | 0.240935i | \(0.922546\pi\) | |||||||
\(788\) | −41.5524 | −1.48024 | ||||||||
\(789\) | −72.3004 | −2.57396 | ||||||||
\(790\) | 102.117 | 3.63314 | ||||||||
\(791\) | 3.35278 | 0.119211 | ||||||||
\(792\) | −38.7176 | −1.37577 | ||||||||
\(793\) | −43.5107 | −1.54511 | ||||||||
\(794\) | −24.5558 | −0.871454 | ||||||||
\(795\) | 8.36959 | 0.296839 | ||||||||
\(796\) | 20.5540 | 0.728516 | ||||||||
\(797\) | 4.76060 | 0.168629 | 0.0843145 | − | 0.996439i | \(-0.473130\pi\) | ||||
0.0843145 | + | 0.996439i | \(0.473130\pi\) | |||||||
\(798\) | 98.4503 | 3.48510 | ||||||||
\(799\) | 5.55109 | 0.196383 | ||||||||
\(800\) | 22.7882 | 0.805683 | ||||||||
\(801\) | −29.9078 | −1.05674 | ||||||||
\(802\) | −15.3717 | −0.542793 | ||||||||
\(803\) | 13.2140 | 0.466313 | ||||||||
\(804\) | 43.7062 | 1.54140 | ||||||||
\(805\) | −135.911 | −4.79023 | ||||||||
\(806\) | −22.3452 | −0.787076 | ||||||||
\(807\) | −12.3801 | −0.435799 | ||||||||
\(808\) | −4.34218 | −0.152757 | ||||||||
\(809\) | 16.0485 | 0.564234 | 0.282117 | − | 0.959380i | \(-0.408963\pi\) | ||||
0.282117 | + | 0.959380i | \(0.408963\pi\) | |||||||
\(810\) | 55.4729 | 1.94912 | ||||||||
\(811\) | −17.3718 | −0.610007 | −0.305004 | − | 0.952351i | \(-0.598658\pi\) | ||||
−0.305004 | + | 0.952351i | \(0.598658\pi\) | |||||||
\(812\) | −5.84421 | −0.205091 | ||||||||
\(813\) | −12.0182 | −0.421497 | ||||||||
\(814\) | 59.9786 | 2.10225 | ||||||||
\(815\) | 77.1894 | 2.70383 | ||||||||
\(816\) | 14.0367 | 0.491384 | ||||||||
\(817\) | −43.5743 | −1.52447 | ||||||||
\(818\) | 41.6256 | 1.45541 | ||||||||
\(819\) | −58.8183 | −2.05528 | ||||||||
\(820\) | 32.1952 | 1.12430 | ||||||||
\(821\) | −32.1024 | −1.12038 | −0.560191 | − | 0.828363i | \(-0.689272\pi\) | ||||
−0.560191 | + | 0.828363i | \(0.689272\pi\) | |||||||
\(822\) | −109.904 | −3.83334 | ||||||||
\(823\) | 17.3917 | 0.606237 | 0.303118 | − | 0.952953i | \(-0.401972\pi\) | ||||
0.303118 | + | 0.952953i | \(0.401972\pi\) | |||||||
\(824\) | 28.0669 | 0.977758 | ||||||||
\(825\) | −45.2809 | −1.57648 | ||||||||
\(826\) | −161.508 | −5.61960 | ||||||||
\(827\) | −7.67010 | −0.266716 | −0.133358 | − | 0.991068i | \(-0.542576\pi\) | ||||
−0.133358 | + | 0.991068i | \(0.542576\pi\) | |||||||
\(828\) | −106.322 | −3.69494 | ||||||||
\(829\) | −20.8625 | −0.724584 | −0.362292 | − | 0.932065i | \(-0.618006\pi\) | ||||
−0.362292 | + | 0.932065i | \(0.618006\pi\) | |||||||
\(830\) | −35.3844 | −1.22821 | ||||||||
\(831\) | 11.6586 | 0.404433 | ||||||||
\(832\) | 41.7385 | 1.44702 | ||||||||
\(833\) | −65.8092 | −2.28015 | ||||||||
\(834\) | −77.1720 | −2.67225 | ||||||||
\(835\) | −73.4405 | −2.54151 | ||||||||
\(836\) | 36.9624 | 1.27837 | ||||||||
\(837\) | 3.58432 | 0.123892 | ||||||||
\(838\) | 34.1728 | 1.18048 | ||||||||
\(839\) | 34.5548 | 1.19296 | 0.596482 | − | 0.802626i | \(-0.296565\pi\) | ||||
0.596482 | + | 0.802626i | \(0.296565\pi\) | |||||||
\(840\) | 144.285 | 4.97831 | ||||||||
\(841\) | −28.8815 | −0.995915 | ||||||||
\(842\) | −54.8046 | −1.88869 | ||||||||
\(843\) | 9.64665 | 0.332248 | ||||||||
\(844\) | −92.0253 | −3.16764 | ||||||||
\(845\) | −3.08850 | −0.106247 | ||||||||
\(846\) | 11.3143 | 0.388992 | ||||||||
\(847\) | −7.21704 | −0.247980 | ||||||||
\(848\) | −1.35811 | −0.0466378 | ||||||||
\(849\) | −1.89052 | −0.0648825 | ||||||||
\(850\) | 54.7731 | 1.87870 | ||||||||
\(851\) | 71.1640 | 2.43947 | ||||||||
\(852\) | 122.813 | 4.20751 | ||||||||
\(853\) | −34.8325 | −1.19264 | −0.596322 | − | 0.802746i | \(-0.703372\pi\) | ||||
−0.596322 | + | 0.802746i | \(0.703372\pi\) | |||||||
\(854\) | −141.968 | −4.85805 | ||||||||
\(855\) | 39.2260 | 1.34150 | ||||||||
\(856\) | −28.0067 | −0.957250 | ||||||||
\(857\) | 29.9372 | 1.02264 | 0.511318 | − | 0.859391i | \(-0.329157\pi\) | ||||
0.511318 | + | 0.859391i | \(0.329157\pi\) | |||||||
\(858\) | −64.1940 | −2.19155 | ||||||||
\(859\) | 49.1525 | 1.67706 | 0.838532 | − | 0.544853i | \(-0.183415\pi\) | ||||
0.838532 | + | 0.544853i | \(0.183415\pi\) | |||||||
\(860\) | −147.804 | −5.04007 | ||||||||
\(861\) | −34.3032 | −1.16905 | ||||||||
\(862\) | −9.08120 | −0.309307 | ||||||||
\(863\) | −12.4598 | −0.424135 | −0.212068 | − | 0.977255i | \(-0.568020\pi\) | ||||
−0.212068 | + | 0.977255i | \(0.568020\pi\) | |||||||
\(864\) | −5.18216 | −0.176301 | ||||||||
\(865\) | 46.7189 | 1.58849 | ||||||||
\(866\) | 27.3003 | 0.927701 | ||||||||
\(867\) | 1.52686 | 0.0518549 | ||||||||
\(868\) | −46.4998 | −1.57831 | ||||||||
\(869\) | −40.8493 | −1.38572 | ||||||||
\(870\) | −6.76894 | −0.229489 | ||||||||
\(871\) | 16.8876 | 0.572214 | ||||||||
\(872\) | 21.8331 | 0.739362 | ||||||||
\(873\) | 26.7026 | 0.903745 | ||||||||
\(874\) | 68.7626 | 2.32593 | ||||||||
\(875\) | 11.9492 | 0.403956 | ||||||||
\(876\) | −38.5227 | −1.30156 | ||||||||
\(877\) | −49.2618 | −1.66345 | −0.831726 | − | 0.555186i | \(-0.812647\pi\) | ||||
−0.831726 | + | 0.555186i | \(0.812647\pi\) | |||||||
\(878\) | 42.1733 | 1.42328 | ||||||||
\(879\) | 5.34129 | 0.180157 | ||||||||
\(880\) | 13.7306 | 0.462859 | ||||||||
\(881\) | 27.4367 | 0.924365 | 0.462183 | − | 0.886785i | \(-0.347066\pi\) | ||||
0.462183 | + | 0.886785i | \(0.347066\pi\) | |||||||
\(882\) | −134.132 | −4.51647 | ||||||||
\(883\) | 7.02371 | 0.236367 | 0.118183 | − | 0.992992i | \(-0.462293\pi\) | ||||
0.118183 | + | 0.992992i | \(0.462293\pi\) | |||||||
\(884\) | 49.5243 | 1.66568 | ||||||||
\(885\) | −119.306 | −4.01043 | ||||||||
\(886\) | 61.8283 | 2.07716 | ||||||||
\(887\) | 4.20107 | 0.141058 | 0.0705290 | − | 0.997510i | \(-0.477531\pi\) | ||||
0.0705290 | + | 0.997510i | \(0.477531\pi\) | |||||||
\(888\) | −75.5488 | −2.53525 | ||||||||
\(889\) | −54.5823 | −1.83063 | ||||||||
\(890\) | 65.6099 | 2.19925 | ||||||||
\(891\) | −22.1906 | −0.743412 | ||||||||
\(892\) | 40.0196 | 1.33995 | ||||||||
\(893\) | −4.66689 | −0.156171 | ||||||||
\(894\) | 10.4388 | 0.349127 | ||||||||
\(895\) | −8.59011 | −0.287136 | ||||||||
\(896\) | 98.0041 | 3.27409 | ||||||||
\(897\) | −76.1654 | −2.54309 | ||||||||
\(898\) | −48.1733 | −1.60756 | ||||||||
\(899\) | 0.942538 | 0.0314354 | ||||||||
\(900\) | 71.2011 | 2.37337 | ||||||||
\(901\) | 4.04990 | 0.134922 | ||||||||
\(902\) | −20.1933 | −0.672363 | ||||||||
\(903\) | 157.482 | 5.24067 | ||||||||
\(904\) | −2.48604 | −0.0826845 | ||||||||
\(905\) | −16.9694 | −0.564081 | ||||||||
\(906\) | −5.99675 | −0.199229 | ||||||||
\(907\) | −9.41590 | −0.312650 | −0.156325 | − | 0.987706i | \(-0.549965\pi\) | ||||
−0.156325 | + | 0.987706i | \(0.549965\pi\) | |||||||
\(908\) | −64.2047 | −2.13071 | ||||||||
\(909\) | 4.26639 | 0.141507 | ||||||||
\(910\) | 129.032 | 4.27737 | ||||||||
\(911\) | 46.9174 | 1.55444 | 0.777221 | − | 0.629228i | \(-0.216629\pi\) | ||||
0.777221 | + | 0.629228i | \(0.216629\pi\) | |||||||
\(912\) | −11.8009 | −0.390767 | ||||||||
\(913\) | 14.1547 | 0.468451 | ||||||||
\(914\) | 66.2015 | 2.18975 | ||||||||
\(915\) | −104.872 | −3.46695 | ||||||||
\(916\) | 47.9668 | 1.58487 | ||||||||
\(917\) | 29.7950 | 0.983916 | ||||||||
\(918\) | −12.4557 | −0.411100 | ||||||||
\(919\) | −27.2302 | −0.898243 | −0.449121 | − | 0.893471i | \(-0.648263\pi\) | ||||
−0.449121 | + | 0.893471i | \(0.648263\pi\) | |||||||
\(920\) | 100.776 | 3.32249 | ||||||||
\(921\) | −63.3710 | −2.08815 | ||||||||
\(922\) | −43.9648 | −1.44791 | ||||||||
\(923\) | 47.4537 | 1.56196 | ||||||||
\(924\) | −133.586 | −4.39466 | ||||||||
\(925\) | −47.6567 | −1.56694 | ||||||||
\(926\) | −37.8001 | −1.24219 | ||||||||
\(927\) | −27.5770 | −0.905748 | ||||||||
\(928\) | −1.36271 | −0.0447331 | ||||||||
\(929\) | −9.10301 | −0.298660 | −0.149330 | − | 0.988787i | \(-0.547712\pi\) | ||||
−0.149330 | + | 0.988787i | \(0.547712\pi\) | |||||||
\(930\) | −53.8575 | −1.76606 | ||||||||
\(931\) | 55.3268 | 1.81326 | ||||||||
\(932\) | 50.5658 | 1.65634 | ||||||||
\(933\) | −82.7152 | −2.70797 | ||||||||
\(934\) | −13.0012 | −0.425412 | ||||||||
\(935\) | −40.9448 | −1.33904 | ||||||||
\(936\) | 43.6129 | 1.42553 | ||||||||
\(937\) | 26.6909 | 0.871953 | 0.435977 | − | 0.899958i | \(-0.356403\pi\) | ||||
0.435977 | + | 0.899958i | \(0.356403\pi\) | |||||||
\(938\) | 55.1014 | 1.79912 | ||||||||
\(939\) | 54.6767 | 1.78431 | ||||||||
\(940\) | −15.8301 | −0.516320 | ||||||||
\(941\) | 16.3756 | 0.533830 | 0.266915 | − | 0.963720i | \(-0.413996\pi\) | ||||
0.266915 | + | 0.963720i | \(0.413996\pi\) | |||||||
\(942\) | −42.6612 | −1.38998 | ||||||||
\(943\) | −23.9591 | −0.780216 | ||||||||
\(944\) | 19.3595 | 0.630097 | ||||||||
\(945\) | −20.6976 | −0.673294 | ||||||||
\(946\) | 92.7048 | 3.01409 | ||||||||
\(947\) | 12.7835 | 0.415407 | 0.207704 | − | 0.978192i | \(-0.433401\pi\) | ||||
0.207704 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(948\) | 119.087 | 3.86778 | ||||||||
\(949\) | −14.8848 | −0.483180 | ||||||||
\(950\) | −46.0486 | −1.49401 | ||||||||
\(951\) | 75.0338 | 2.43314 | ||||||||
\(952\) | 69.8172 | 2.26279 | ||||||||
\(953\) | 19.3786 | 0.627736 | 0.313868 | − | 0.949467i | \(-0.398375\pi\) | ||||
0.313868 | + | 0.949467i | \(0.398375\pi\) | |||||||
\(954\) | 8.25452 | 0.267250 | ||||||||
\(955\) | 77.4249 | 2.50541 | ||||||||
\(956\) | −90.6792 | −2.93277 | ||||||||
\(957\) | 2.70775 | 0.0875292 | ||||||||
\(958\) | −8.65965 | −0.279780 | ||||||||
\(959\) | −88.3700 | −2.85362 | ||||||||
\(960\) | 100.600 | 3.24685 | ||||||||
\(961\) | −23.5006 | −0.758085 | ||||||||
\(962\) | −67.5621 | −2.17829 | ||||||||
\(963\) | 27.5178 | 0.886750 | ||||||||
\(964\) | −40.0809 | −1.29092 | ||||||||
\(965\) | −14.4514 | −0.465206 | ||||||||
\(966\) | −248.515 | −7.99584 | ||||||||
\(967\) | 25.2675 | 0.812547 | 0.406273 | − | 0.913752i | \(-0.366828\pi\) | ||||
0.406273 | + | 0.913752i | \(0.366828\pi\) | |||||||
\(968\) | 5.35133 | 0.171998 | ||||||||
\(969\) | 35.1904 | 1.13048 | ||||||||
\(970\) | −58.5786 | −1.88084 | ||||||||
\(971\) | −29.0931 | −0.933642 | −0.466821 | − | 0.884352i | \(-0.654601\pi\) | ||||
−0.466821 | + | 0.884352i | \(0.654601\pi\) | |||||||
\(972\) | 78.5196 | 2.51852 | ||||||||
\(973\) | −62.0513 | −1.98927 | ||||||||
\(974\) | 24.8776 | 0.797129 | ||||||||
\(975\) | 51.0061 | 1.63350 | ||||||||
\(976\) | 17.0173 | 0.544709 | ||||||||
\(977\) | −5.47042 | −0.175014 | −0.0875072 | − | 0.996164i | \(-0.527890\pi\) | ||||
−0.0875072 | + | 0.996164i | \(0.527890\pi\) | |||||||
\(978\) | 141.142 | 4.51322 | ||||||||
\(979\) | −26.2457 | −0.838815 | ||||||||
\(980\) | 187.668 | 5.99485 | ||||||||
\(981\) | −21.4520 | −0.684909 | ||||||||
\(982\) | 42.4191 | 1.35365 | ||||||||
\(983\) | 51.5729 | 1.64492 | 0.822460 | − | 0.568824i | \(-0.192601\pi\) | ||||
0.822460 | + | 0.568824i | \(0.192601\pi\) | |||||||
\(984\) | 25.4353 | 0.810849 | ||||||||
\(985\) | −38.6974 | −1.23300 | ||||||||
\(986\) | −3.27537 | −0.104309 | ||||||||
\(987\) | 16.8666 | 0.536870 | ||||||||
\(988\) | −41.6358 | −1.32461 | ||||||||
\(989\) | 109.993 | 3.49758 | ||||||||
\(990\) | −83.4538 | −2.65233 | ||||||||
\(991\) | −5.97771 | −0.189888 | −0.0949441 | − | 0.995483i | \(-0.530267\pi\) | ||||
−0.0949441 | + | 0.995483i | \(0.530267\pi\) | |||||||
\(992\) | −10.8425 | −0.344249 | ||||||||
\(993\) | 46.9214 | 1.48901 | ||||||||
\(994\) | 154.833 | 4.91102 | ||||||||
\(995\) | 19.1418 | 0.606835 | ||||||||
\(996\) | −41.2649 | −1.30753 | ||||||||
\(997\) | −39.6857 | −1.25686 | −0.628429 | − | 0.777867i | \(-0.716302\pi\) | ||||
−0.628429 | + | 0.777867i | \(0.716302\pi\) | |||||||
\(998\) | 60.6458 | 1.91971 | ||||||||
\(999\) | 10.8374 | 0.342881 |
(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 | 8003.2.a.b.1.18 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.18 | ✓ | 153 | 1.1 | even | 1 | trivial |