Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29894 | −1.62559 | −0.812797 | − | 0.582547i | \(-0.802056\pi\) | ||||
−0.812797 | + | 0.582547i | \(0.802056\pi\) | |||||||
\(3\) | 0.676824 | 0.390764 | 0.195382 | − | 0.980727i | \(-0.437405\pi\) | ||||
0.195382 | + | 0.980727i | \(0.437405\pi\) | |||||||
\(4\) | 3.28511 | 1.64255 | ||||||||
\(5\) | −3.14176 | −1.40504 | −0.702519 | − | 0.711665i | \(-0.747941\pi\) | ||||
−0.702519 | + | 0.711665i | \(0.747941\pi\) | |||||||
\(6\) | −1.55598 | −0.635224 | ||||||||
\(7\) | −3.61058 | −1.36467 | −0.682336 | − | 0.731039i | \(-0.739036\pi\) | ||||
−0.682336 | + | 0.731039i | \(0.739036\pi\) | |||||||
\(8\) | −2.95439 | −1.04453 | ||||||||
\(9\) | −2.54191 | −0.847303 | ||||||||
\(10\) | 7.22271 | 2.28402 | ||||||||
\(11\) | −5.00307 | −1.50848 | −0.754241 | − | 0.656598i | \(-0.771995\pi\) | ||||
−0.754241 | + | 0.656598i | \(0.771995\pi\) | |||||||
\(12\) | 2.22344 | 0.641852 | ||||||||
\(13\) | 3.46811 | 0.961881 | 0.480940 | − | 0.876753i | \(-0.340295\pi\) | ||||
0.480940 | + | 0.876753i | \(0.340295\pi\) | |||||||
\(14\) | 8.30050 | 2.21840 | ||||||||
\(15\) | −2.12642 | −0.549039 | ||||||||
\(16\) | 0.221727 | 0.0554319 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.84369 | 1.37737 | ||||||||
\(19\) | −2.21471 | −0.508089 | −0.254044 | − | 0.967193i | \(-0.581761\pi\) | ||||
−0.254044 | + | 0.967193i | \(0.581761\pi\) | |||||||
\(20\) | −10.3210 | −2.30785 | ||||||||
\(21\) | −2.44373 | −0.533265 | ||||||||
\(22\) | 11.5017 | 2.45218 | ||||||||
\(23\) | −4.03171 | −0.840671 | −0.420335 | − | 0.907369i | \(-0.638088\pi\) | ||||
−0.420335 | + | 0.907369i | \(0.638088\pi\) | |||||||
\(24\) | −1.99960 | −0.408166 | ||||||||
\(25\) | 4.87066 | 0.974131 | ||||||||
\(26\) | −7.97297 | −1.56363 | ||||||||
\(27\) | −3.75090 | −0.721860 | ||||||||
\(28\) | −11.8612 | −2.24155 | ||||||||
\(29\) | 6.02696 | 1.11918 | 0.559589 | − | 0.828770i | \(-0.310959\pi\) | ||||
0.559589 | + | 0.828770i | \(0.310959\pi\) | |||||||
\(30\) | 4.88850 | 0.892514 | ||||||||
\(31\) | 7.26825 | 1.30542 | 0.652708 | − | 0.757609i | \(-0.273633\pi\) | ||||
0.652708 | + | 0.757609i | \(0.273633\pi\) | |||||||
\(32\) | 5.39904 | 0.954424 | ||||||||
\(33\) | −3.38620 | −0.589461 | ||||||||
\(34\) | −2.29894 | −0.394264 | ||||||||
\(35\) | 11.3436 | 1.91741 | ||||||||
\(36\) | −8.35045 | −1.39174 | ||||||||
\(37\) | 8.52411 | 1.40135 | 0.700677 | − | 0.713478i | \(-0.252881\pi\) | ||||
0.700677 | + | 0.713478i | \(0.252881\pi\) | |||||||
\(38\) | 5.09147 | 0.825946 | ||||||||
\(39\) | 2.34730 | 0.375869 | ||||||||
\(40\) | 9.28197 | 1.46761 | ||||||||
\(41\) | −3.54127 | −0.553054 | −0.276527 | − | 0.961006i | \(-0.589184\pi\) | ||||
−0.276527 | + | 0.961006i | \(0.589184\pi\) | |||||||
\(42\) | 5.61797 | 0.866872 | ||||||||
\(43\) | −4.72382 | −0.720376 | −0.360188 | − | 0.932880i | \(-0.617288\pi\) | ||||
−0.360188 | + | 0.932880i | \(0.617288\pi\) | |||||||
\(44\) | −16.4356 | −2.47776 | ||||||||
\(45\) | 7.98607 | 1.19049 | ||||||||
\(46\) | 9.26866 | 1.36659 | ||||||||
\(47\) | 2.95722 | 0.431355 | 0.215677 | − | 0.976465i | \(-0.430804\pi\) | ||||
0.215677 | + | 0.976465i | \(0.430804\pi\) | |||||||
\(48\) | 0.150070 | 0.0216608 | ||||||||
\(49\) | 6.03629 | 0.862328 | ||||||||
\(50\) | −11.1973 | −1.58354 | ||||||||
\(51\) | 0.676824 | 0.0947743 | ||||||||
\(52\) | 11.3931 | 1.57994 | ||||||||
\(53\) | −1.45415 | −0.199743 | −0.0998714 | − | 0.995000i | \(-0.531843\pi\) | ||||
−0.0998714 | + | 0.995000i | \(0.531843\pi\) | |||||||
\(54\) | 8.62307 | 1.17345 | ||||||||
\(55\) | 15.7184 | 2.11947 | ||||||||
\(56\) | 10.6671 | 1.42544 | ||||||||
\(57\) | −1.49897 | −0.198543 | ||||||||
\(58\) | −13.8556 | −1.81933 | ||||||||
\(59\) | −4.01062 | −0.522138 | −0.261069 | − | 0.965320i | \(-0.584075\pi\) | ||||
−0.261069 | + | 0.965320i | \(0.584075\pi\) | |||||||
\(60\) | −6.98552 | −0.901826 | ||||||||
\(61\) | 7.07630 | 0.906028 | 0.453014 | − | 0.891503i | \(-0.350349\pi\) | ||||
0.453014 | + | 0.891503i | \(0.350349\pi\) | |||||||
\(62\) | −16.7093 | −2.12208 | ||||||||
\(63\) | 9.17777 | 1.15629 | ||||||||
\(64\) | −12.8555 | −1.60694 | ||||||||
\(65\) | −10.8960 | −1.35148 | ||||||||
\(66\) | 7.78465 | 0.958224 | ||||||||
\(67\) | 2.33224 | 0.284928 | 0.142464 | − | 0.989800i | \(-0.454497\pi\) | ||||
0.142464 | + | 0.989800i | \(0.454497\pi\) | |||||||
\(68\) | 3.28511 | 0.398378 | ||||||||
\(69\) | −2.72876 | −0.328504 | ||||||||
\(70\) | −26.0782 | −3.11694 | ||||||||
\(71\) | −4.74504 | −0.563133 | −0.281566 | − | 0.959542i | \(-0.590854\pi\) | ||||
−0.281566 | + | 0.959542i | \(0.590854\pi\) | |||||||
\(72\) | 7.50978 | 0.885036 | ||||||||
\(73\) | −2.40867 | −0.281914 | −0.140957 | − | 0.990016i | \(-0.545018\pi\) | ||||
−0.140957 | + | 0.990016i | \(0.545018\pi\) | |||||||
\(74\) | −19.5964 | −2.27803 | ||||||||
\(75\) | 3.29658 | 0.380656 | ||||||||
\(76\) | −7.27555 | −0.834563 | ||||||||
\(77\) | 18.0640 | 2.05858 | ||||||||
\(78\) | −5.39629 | −0.611010 | ||||||||
\(79\) | 10.8731 | 1.22332 | 0.611662 | − | 0.791119i | \(-0.290501\pi\) | ||||
0.611662 | + | 0.791119i | \(0.290501\pi\) | |||||||
\(80\) | −0.696615 | −0.0778839 | ||||||||
\(81\) | 5.08703 | 0.565226 | ||||||||
\(82\) | 8.14116 | 0.899041 | ||||||||
\(83\) | −0.0418311 | −0.00459156 | −0.00229578 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229578 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(84\) | −8.02791 | −0.875917 | ||||||||
\(85\) | −3.14176 | −0.340772 | ||||||||
\(86\) | 10.8598 | 1.17104 | ||||||||
\(87\) | 4.07919 | 0.437335 | ||||||||
\(88\) | 14.7810 | 1.57566 | ||||||||
\(89\) | 4.18620 | 0.443737 | 0.221868 | − | 0.975077i | \(-0.428784\pi\) | ||||
0.221868 | + | 0.975077i | \(0.428784\pi\) | |||||||
\(90\) | −18.3595 | −1.93526 | ||||||||
\(91\) | −12.5219 | −1.31265 | ||||||||
\(92\) | −13.2446 | −1.38085 | ||||||||
\(93\) | 4.91933 | 0.510110 | ||||||||
\(94\) | −6.79846 | −0.701208 | ||||||||
\(95\) | 6.95808 | 0.713884 | ||||||||
\(96\) | 3.65420 | 0.372955 | ||||||||
\(97\) | −0.739229 | −0.0750573 | −0.0375286 | − | 0.999296i | \(-0.511949\pi\) | ||||
−0.0375286 | + | 0.999296i | \(0.511949\pi\) | |||||||
\(98\) | −13.8771 | −1.40179 | ||||||||
\(99\) | 12.7173 | 1.27814 | ||||||||
\(100\) | 16.0006 | 1.60006 | ||||||||
\(101\) | 17.2598 | 1.71741 | 0.858707 | − | 0.512468i | \(-0.171269\pi\) | ||||
0.858707 | + | 0.512468i | \(0.171269\pi\) | |||||||
\(102\) | −1.55598 | −0.154064 | ||||||||
\(103\) | 17.1913 | 1.69391 | 0.846956 | − | 0.531664i | \(-0.178433\pi\) | ||||
0.846956 | + | 0.531664i | \(0.178433\pi\) | |||||||
\(104\) | −10.2461 | −1.00472 | ||||||||
\(105\) | 7.67760 | 0.749257 | ||||||||
\(106\) | 3.34300 | 0.324701 | ||||||||
\(107\) | −7.85975 | −0.759831 | −0.379916 | − | 0.925021i | \(-0.624047\pi\) | ||||
−0.379916 | + | 0.925021i | \(0.624047\pi\) | |||||||
\(108\) | −12.3221 | −1.18570 | ||||||||
\(109\) | 6.61226 | 0.633340 | 0.316670 | − | 0.948536i | \(-0.397435\pi\) | ||||
0.316670 | + | 0.948536i | \(0.397435\pi\) | |||||||
\(110\) | −36.1357 | −3.44540 | ||||||||
\(111\) | 5.76932 | 0.547600 | ||||||||
\(112\) | −0.800565 | −0.0756463 | ||||||||
\(113\) | −0.0902512 | −0.00849012 | −0.00424506 | − | 0.999991i | \(-0.501351\pi\) | ||||
−0.00424506 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(114\) | 3.44603 | 0.322750 | ||||||||
\(115\) | 12.6667 | 1.18117 | ||||||||
\(116\) | 19.7992 | 1.83831 | ||||||||
\(117\) | −8.81562 | −0.815005 | ||||||||
\(118\) | 9.22016 | 0.848784 | ||||||||
\(119\) | −3.61058 | −0.330981 | ||||||||
\(120\) | 6.28226 | 0.573489 | ||||||||
\(121\) | 14.0307 | 1.27552 | ||||||||
\(122\) | −16.2680 | −1.47283 | ||||||||
\(123\) | −2.39682 | −0.216114 | ||||||||
\(124\) | 23.8770 | 2.14422 | ||||||||
\(125\) | 0.406364 | 0.0363463 | ||||||||
\(126\) | −21.0991 | −1.87966 | ||||||||
\(127\) | −22.0076 | −1.95286 | −0.976429 | − | 0.215839i | \(-0.930751\pi\) | ||||
−0.976429 | + | 0.215839i | \(0.930751\pi\) | |||||||
\(128\) | 18.7559 | 1.65780 | ||||||||
\(129\) | −3.19720 | −0.281497 | ||||||||
\(130\) | 25.0492 | 2.19696 | ||||||||
\(131\) | 9.51275 | 0.831133 | 0.415566 | − | 0.909563i | \(-0.363583\pi\) | ||||
0.415566 | + | 0.909563i | \(0.363583\pi\) | |||||||
\(132\) | −11.1240 | −0.968222 | ||||||||
\(133\) | 7.99638 | 0.693374 | ||||||||
\(134\) | −5.36166 | −0.463177 | ||||||||
\(135\) | 11.7844 | 1.01424 | ||||||||
\(136\) | −2.95439 | −0.253337 | ||||||||
\(137\) | −13.4583 | −1.14982 | −0.574911 | − | 0.818216i | \(-0.694963\pi\) | ||||
−0.574911 | + | 0.818216i | \(0.694963\pi\) | |||||||
\(138\) | 6.27325 | 0.534014 | ||||||||
\(139\) | −20.4663 | −1.73593 | −0.867966 | − | 0.496623i | \(-0.834573\pi\) | ||||
−0.867966 | + | 0.496623i | \(0.834573\pi\) | |||||||
\(140\) | 37.2649 | 3.14946 | ||||||||
\(141\) | 2.00152 | 0.168558 | ||||||||
\(142\) | 10.9086 | 0.915425 | ||||||||
\(143\) | −17.3512 | −1.45098 | ||||||||
\(144\) | −0.563611 | −0.0469676 | ||||||||
\(145\) | −18.9353 | −1.57249 | ||||||||
\(146\) | 5.53739 | 0.458277 | ||||||||
\(147\) | 4.08551 | 0.336967 | ||||||||
\(148\) | 28.0026 | 2.30180 | ||||||||
\(149\) | −0.129244 | −0.0105881 | −0.00529404 | − | 0.999986i | \(-0.501685\pi\) | ||||
−0.00529404 | + | 0.999986i | \(0.501685\pi\) | |||||||
\(150\) | −7.57862 | −0.618792 | ||||||||
\(151\) | 23.6820 | 1.92722 | 0.963608 | − | 0.267319i | \(-0.0861376\pi\) | ||||
0.963608 | + | 0.267319i | \(0.0861376\pi\) | |||||||
\(152\) | 6.54310 | 0.530715 | ||||||||
\(153\) | −2.54191 | −0.205501 | ||||||||
\(154\) | −41.5279 | −3.34642 | ||||||||
\(155\) | −22.8351 | −1.83416 | ||||||||
\(156\) | 7.71114 | 0.617385 | ||||||||
\(157\) | 13.1085 | 1.04617 | 0.523085 | − | 0.852280i | \(-0.324781\pi\) | ||||
0.523085 | + | 0.852280i | \(0.324781\pi\) | |||||||
\(158\) | −24.9967 | −1.98863 | ||||||||
\(159\) | −0.984203 | −0.0780524 | ||||||||
\(160\) | −16.9625 | −1.34100 | ||||||||
\(161\) | 14.5568 | 1.14724 | ||||||||
\(162\) | −11.6948 | −0.918828 | ||||||||
\(163\) | −0.653299 | −0.0511703 | −0.0255852 | − | 0.999673i | \(-0.508145\pi\) | ||||
−0.0255852 | + | 0.999673i | \(0.508145\pi\) | |||||||
\(164\) | −11.6335 | −0.908422 | ||||||||
\(165\) | 10.6386 | 0.828215 | ||||||||
\(166\) | 0.0961671 | 0.00746401 | ||||||||
\(167\) | −16.7110 | −1.29313 | −0.646567 | − | 0.762858i | \(-0.723796\pi\) | ||||
−0.646567 | + | 0.762858i | \(0.723796\pi\) | |||||||
\(168\) | 7.21971 | 0.557013 | ||||||||
\(169\) | −0.972207 | −0.0747852 | ||||||||
\(170\) | 7.22271 | 0.553956 | ||||||||
\(171\) | 5.62958 | 0.430505 | ||||||||
\(172\) | −15.5183 | −1.18326 | ||||||||
\(173\) | 3.02851 | 0.230254 | 0.115127 | − | 0.993351i | \(-0.463273\pi\) | ||||
0.115127 | + | 0.993351i | \(0.463273\pi\) | |||||||
\(174\) | −9.37780 | −0.710929 | ||||||||
\(175\) | −17.5859 | −1.32937 | ||||||||
\(176\) | −1.10932 | −0.0836180 | ||||||||
\(177\) | −2.71448 | −0.204033 | ||||||||
\(178\) | −9.62382 | −0.721336 | ||||||||
\(179\) | −1.50324 | −0.112358 | −0.0561789 | − | 0.998421i | \(-0.517892\pi\) | ||||
−0.0561789 | + | 0.998421i | \(0.517892\pi\) | |||||||
\(180\) | 26.2351 | 1.95545 | ||||||||
\(181\) | −6.54968 | −0.486834 | −0.243417 | − | 0.969922i | \(-0.578268\pi\) | ||||
−0.243417 | + | 0.969922i | \(0.578268\pi\) | |||||||
\(182\) | 28.7870 | 2.13384 | ||||||||
\(183\) | 4.78941 | 0.354043 | ||||||||
\(184\) | 11.9112 | 0.878108 | ||||||||
\(185\) | −26.7807 | −1.96896 | ||||||||
\(186\) | −11.3092 | −0.829232 | ||||||||
\(187\) | −5.00307 | −0.365861 | ||||||||
\(188\) | 9.71479 | 0.708524 | ||||||||
\(189\) | 13.5429 | 0.985102 | ||||||||
\(190\) | −15.9962 | −1.16048 | ||||||||
\(191\) | 1.71593 | 0.124160 | 0.0620801 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620801 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(192\) | −8.70091 | −0.627934 | ||||||||
\(193\) | −11.2622 | −0.810671 | −0.405335 | − | 0.914168i | \(-0.632845\pi\) | ||||
−0.405335 | + | 0.914168i | \(0.632845\pi\) | |||||||
\(194\) | 1.69944 | 0.122013 | ||||||||
\(195\) | −7.37465 | −0.528110 | ||||||||
\(196\) | 19.8299 | 1.41642 | ||||||||
\(197\) | −19.1442 | −1.36397 | −0.681983 | − | 0.731368i | \(-0.738882\pi\) | ||||
−0.681983 | + | 0.731368i | \(0.738882\pi\) | |||||||
\(198\) | −29.2364 | −2.07774 | ||||||||
\(199\) | −17.9354 | −1.27140 | −0.635702 | − | 0.771934i | \(-0.719289\pi\) | ||||
−0.635702 | + | 0.771934i | \(0.719289\pi\) | |||||||
\(200\) | −14.3898 | −1.01751 | ||||||||
\(201\) | 1.57851 | 0.111340 | ||||||||
\(202\) | −39.6792 | −2.79182 | ||||||||
\(203\) | −21.7608 | −1.52731 | ||||||||
\(204\) | 2.22344 | 0.155672 | ||||||||
\(205\) | 11.1258 | 0.777062 | ||||||||
\(206\) | −39.5218 | −2.75361 | ||||||||
\(207\) | 10.2483 | 0.712303 | ||||||||
\(208\) | 0.768975 | 0.0533189 | ||||||||
\(209\) | 11.0803 | 0.766442 | ||||||||
\(210\) | −17.6503 | −1.21799 | ||||||||
\(211\) | −1.89961 | −0.130774 | −0.0653872 | − | 0.997860i | \(-0.520828\pi\) | ||||
−0.0653872 | + | 0.997860i | \(0.520828\pi\) | |||||||
\(212\) | −4.77704 | −0.328088 | ||||||||
\(213\) | −3.21156 | −0.220052 | ||||||||
\(214\) | 18.0691 | 1.23518 | ||||||||
\(215\) | 14.8411 | 1.01216 | ||||||||
\(216\) | 11.0816 | 0.754007 | ||||||||
\(217\) | −26.2426 | −1.78146 | ||||||||
\(218\) | −15.2012 | −1.02955 | ||||||||
\(219\) | −1.63025 | −0.110162 | ||||||||
\(220\) | 51.6368 | 3.48135 | ||||||||
\(221\) | 3.46811 | 0.233290 | ||||||||
\(222\) | −13.2633 | −0.890174 | ||||||||
\(223\) | 10.6679 | 0.714375 | 0.357187 | − | 0.934033i | \(-0.383736\pi\) | ||||
0.357187 | + | 0.934033i | \(0.383736\pi\) | |||||||
\(224\) | −19.4937 | −1.30247 | ||||||||
\(225\) | −12.3808 | −0.825385 | ||||||||
\(226\) | 0.207482 | 0.0138015 | ||||||||
\(227\) | −25.3126 | −1.68005 | −0.840027 | − | 0.542545i | \(-0.817461\pi\) | ||||
−0.840027 | + | 0.542545i | \(0.817461\pi\) | |||||||
\(228\) | −4.92427 | −0.326118 | ||||||||
\(229\) | 7.39467 | 0.488653 | 0.244327 | − | 0.969693i | \(-0.421433\pi\) | ||||
0.244327 | + | 0.969693i | \(0.421433\pi\) | |||||||
\(230\) | −29.1199 | −1.92011 | ||||||||
\(231\) | 12.2261 | 0.804420 | ||||||||
\(232\) | −17.8060 | −1.16902 | ||||||||
\(233\) | 19.3484 | 1.26756 | 0.633779 | − | 0.773515i | \(-0.281503\pi\) | ||||
0.633779 | + | 0.773515i | \(0.281503\pi\) | |||||||
\(234\) | 20.2666 | 1.32487 | ||||||||
\(235\) | −9.29087 | −0.606070 | ||||||||
\(236\) | −13.1753 | −0.857640 | ||||||||
\(237\) | 7.35920 | 0.478031 | ||||||||
\(238\) | 8.30050 | 0.538041 | ||||||||
\(239\) | 1.37499 | 0.0889404 | 0.0444702 | − | 0.999011i | \(-0.485840\pi\) | ||||
0.0444702 | + | 0.999011i | \(0.485840\pi\) | |||||||
\(240\) | −0.471485 | −0.0304342 | ||||||||
\(241\) | −9.27995 | −0.597774 | −0.298887 | − | 0.954288i | \(-0.596615\pi\) | ||||
−0.298887 | + | 0.954288i | \(0.596615\pi\) | |||||||
\(242\) | −32.2557 | −2.07347 | ||||||||
\(243\) | 14.6957 | 0.942730 | ||||||||
\(244\) | 23.2464 | 1.48820 | ||||||||
\(245\) | −18.9646 | −1.21160 | ||||||||
\(246\) | 5.51013 | 0.351313 | ||||||||
\(247\) | −7.68085 | −0.488721 | ||||||||
\(248\) | −21.4732 | −1.36355 | ||||||||
\(249\) | −0.0283123 | −0.00179422 | ||||||||
\(250\) | −0.934206 | −0.0590844 | ||||||||
\(251\) | −13.4357 | −0.848052 | −0.424026 | − | 0.905650i | \(-0.639383\pi\) | ||||
−0.424026 | + | 0.905650i | \(0.639383\pi\) | |||||||
\(252\) | 30.1500 | 1.89927 | ||||||||
\(253\) | 20.1709 | 1.26814 | ||||||||
\(254\) | 50.5941 | 3.17455 | ||||||||
\(255\) | −2.12642 | −0.133161 | ||||||||
\(256\) | −17.4076 | −1.08798 | ||||||||
\(257\) | 27.1753 | 1.69515 | 0.847574 | − | 0.530677i | \(-0.178062\pi\) | ||||
0.847574 | + | 0.530677i | \(0.178062\pi\) | |||||||
\(258\) | 7.35015 | 0.457601 | ||||||||
\(259\) | −30.7770 | −1.91239 | ||||||||
\(260\) | −35.7945 | −2.21988 | ||||||||
\(261\) | −15.3200 | −0.948283 | ||||||||
\(262\) | −21.8692 | −1.35108 | ||||||||
\(263\) | 23.5773 | 1.45384 | 0.726919 | − | 0.686723i | \(-0.240951\pi\) | ||||
0.726919 | + | 0.686723i | \(0.240951\pi\) | |||||||
\(264\) | 10.0041 | 0.615712 | ||||||||
\(265\) | 4.56859 | 0.280646 | ||||||||
\(266\) | −18.3832 | −1.12714 | ||||||||
\(267\) | 2.83332 | 0.173397 | ||||||||
\(268\) | 7.66165 | 0.468010 | ||||||||
\(269\) | −23.9470 | −1.46008 | −0.730038 | − | 0.683406i | \(-0.760498\pi\) | ||||
−0.730038 | + | 0.683406i | \(0.760498\pi\) | |||||||
\(270\) | −27.0916 | −1.64874 | ||||||||
\(271\) | −12.4315 | −0.755161 | −0.377581 | − | 0.925977i | \(-0.623244\pi\) | ||||
−0.377581 | + | 0.925977i | \(0.623244\pi\) | |||||||
\(272\) | 0.221727 | 0.0134442 | ||||||||
\(273\) | −8.47512 | −0.512937 | ||||||||
\(274\) | 30.9398 | 1.86914 | ||||||||
\(275\) | −24.3682 | −1.46946 | ||||||||
\(276\) | −8.96428 | −0.539586 | ||||||||
\(277\) | 23.7653 | 1.42792 | 0.713959 | − | 0.700188i | \(-0.246900\pi\) | ||||
0.713959 | + | 0.700188i | \(0.246900\pi\) | |||||||
\(278\) | 47.0508 | 2.82192 | ||||||||
\(279\) | −18.4752 | −1.10608 | ||||||||
\(280\) | −33.5133 | −2.00280 | ||||||||
\(281\) | 21.0050 | 1.25306 | 0.626528 | − | 0.779399i | \(-0.284475\pi\) | ||||
0.626528 | + | 0.779399i | \(0.284475\pi\) | |||||||
\(282\) | −4.60136 | −0.274007 | ||||||||
\(283\) | 11.4954 | 0.683331 | 0.341666 | − | 0.939822i | \(-0.389009\pi\) | ||||
0.341666 | + | 0.939822i | \(0.389009\pi\) | |||||||
\(284\) | −15.5880 | −0.924977 | ||||||||
\(285\) | 4.70939 | 0.278960 | ||||||||
\(286\) | 39.8893 | 2.35870 | ||||||||
\(287\) | 12.7861 | 0.754737 | ||||||||
\(288\) | −13.7239 | −0.808686 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 43.5310 | 2.55623 | ||||||||
\(291\) | −0.500328 | −0.0293297 | ||||||||
\(292\) | −7.91275 | −0.463059 | ||||||||
\(293\) | −18.7639 | −1.09620 | −0.548098 | − | 0.836414i | \(-0.684648\pi\) | ||||
−0.548098 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(294\) | −9.39232 | −0.547771 | ||||||||
\(295\) | 12.6004 | 0.733624 | ||||||||
\(296\) | −25.1835 | −1.46376 | ||||||||
\(297\) | 18.7660 | 1.08891 | ||||||||
\(298\) | 0.297124 | 0.0172119 | ||||||||
\(299\) | −13.9824 | −0.808625 | ||||||||
\(300\) | 10.8296 | 0.625248 | ||||||||
\(301\) | 17.0557 | 0.983077 | ||||||||
\(302\) | −54.4435 | −3.13287 | ||||||||
\(303\) | 11.6818 | 0.671104 | ||||||||
\(304\) | −0.491061 | −0.0281643 | ||||||||
\(305\) | −22.2321 | −1.27300 | ||||||||
\(306\) | 5.84369 | 0.334061 | ||||||||
\(307\) | 8.95426 | 0.511047 | 0.255523 | − | 0.966803i | \(-0.417752\pi\) | ||||
0.255523 | + | 0.966803i | \(0.417752\pi\) | |||||||
\(308\) | 59.3422 | 3.38133 | ||||||||
\(309\) | 11.6355 | 0.661920 | ||||||||
\(310\) | 52.4965 | 2.98160 | ||||||||
\(311\) | −4.87181 | −0.276255 | −0.138128 | − | 0.990414i | \(-0.544108\pi\) | ||||
−0.138128 | + | 0.990414i | \(0.544108\pi\) | |||||||
\(312\) | −6.93483 | −0.392608 | ||||||||
\(313\) | 18.9843 | 1.07305 | 0.536527 | − | 0.843883i | \(-0.319736\pi\) | ||||
0.536527 | + | 0.843883i | \(0.319736\pi\) | |||||||
\(314\) | −30.1356 | −1.70065 | ||||||||
\(315\) | −28.8344 | −1.62463 | ||||||||
\(316\) | 35.7194 | 2.00938 | ||||||||
\(317\) | −24.5905 | −1.38114 | −0.690571 | − | 0.723264i | \(-0.742641\pi\) | ||||
−0.690571 | + | 0.723264i | \(0.742641\pi\) | |||||||
\(318\) | 2.26262 | 0.126881 | ||||||||
\(319\) | −30.1533 | −1.68826 | ||||||||
\(320\) | 40.3889 | 2.25781 | ||||||||
\(321\) | −5.31967 | −0.296915 | ||||||||
\(322\) | −33.4652 | −1.86494 | ||||||||
\(323\) | −2.21471 | −0.123230 | ||||||||
\(324\) | 16.7115 | 0.928415 | ||||||||
\(325\) | 16.8920 | 0.936998 | ||||||||
\(326\) | 1.50189 | 0.0831822 | ||||||||
\(327\) | 4.47533 | 0.247487 | ||||||||
\(328\) | 10.4623 | 0.577683 | ||||||||
\(329\) | −10.6773 | −0.588657 | ||||||||
\(330\) | −24.4575 | −1.34634 | ||||||||
\(331\) | −20.5671 | −1.13047 | −0.565236 | − | 0.824929i | \(-0.691215\pi\) | ||||
−0.565236 | + | 0.824929i | \(0.691215\pi\) | |||||||
\(332\) | −0.137420 | −0.00754189 | ||||||||
\(333\) | −21.6675 | −1.18737 | ||||||||
\(334\) | 38.4174 | 2.10211 | ||||||||
\(335\) | −7.32733 | −0.400335 | ||||||||
\(336\) | −0.541841 | −0.0295599 | ||||||||
\(337\) | 19.6308 | 1.06936 | 0.534679 | − | 0.845055i | \(-0.320433\pi\) | ||||
0.534679 | + | 0.845055i | \(0.320433\pi\) | |||||||
\(338\) | 2.23504 | 0.121570 | ||||||||
\(339\) | −0.0610842 | −0.00331764 | ||||||||
\(340\) | −10.3210 | −0.559736 | ||||||||
\(341\) | −36.3636 | −1.96920 | ||||||||
\(342\) | −12.9421 | −0.699826 | ||||||||
\(343\) | 3.47954 | 0.187878 | ||||||||
\(344\) | 13.9560 | 0.752457 | ||||||||
\(345\) | 8.57311 | 0.461561 | ||||||||
\(346\) | −6.96236 | −0.374299 | ||||||||
\(347\) | −17.9500 | −0.963604 | −0.481802 | − | 0.876280i | \(-0.660018\pi\) | ||||
−0.481802 | + | 0.876280i | \(0.660018\pi\) | |||||||
\(348\) | 13.4006 | 0.718347 | ||||||||
\(349\) | −11.8813 | −0.635992 | −0.317996 | − | 0.948092i | \(-0.603010\pi\) | ||||
−0.317996 | + | 0.948092i | \(0.603010\pi\) | |||||||
\(350\) | 40.4289 | 2.16101 | ||||||||
\(351\) | −13.0085 | −0.694344 | ||||||||
\(352\) | −27.0117 | −1.43973 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 6.24042 | 0.331675 | ||||||||
\(355\) | 14.9078 | 0.791223 | ||||||||
\(356\) | 13.7521 | 0.728862 | ||||||||
\(357\) | −2.44373 | −0.129336 | ||||||||
\(358\) | 3.45586 | 0.182648 | ||||||||
\(359\) | −23.7131 | −1.25153 | −0.625765 | − | 0.780011i | \(-0.715213\pi\) | ||||
−0.625765 | + | 0.780011i | \(0.715213\pi\) | |||||||
\(360\) | −23.5939 | −1.24351 | ||||||||
\(361\) | −14.0951 | −0.741846 | ||||||||
\(362\) | 15.0573 | 0.791394 | ||||||||
\(363\) | 9.49630 | 0.498427 | ||||||||
\(364\) | −41.1358 | −2.15610 | ||||||||
\(365\) | 7.56747 | 0.396100 | ||||||||
\(366\) | −11.0106 | −0.575531 | ||||||||
\(367\) | 0.638015 | 0.0333041 | 0.0166521 | − | 0.999861i | \(-0.494699\pi\) | ||||
0.0166521 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(368\) | −0.893942 | −0.0465999 | ||||||||
\(369\) | 9.00160 | 0.468604 | ||||||||
\(370\) | 61.5671 | 3.20072 | ||||||||
\(371\) | 5.25032 | 0.272583 | ||||||||
\(372\) | 16.1605 | 0.837884 | ||||||||
\(373\) | 3.01159 | 0.155934 | 0.0779671 | − | 0.996956i | \(-0.475157\pi\) | ||||
0.0779671 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(374\) | 11.5017 | 0.594741 | ||||||||
\(375\) | 0.275037 | 0.0142028 | ||||||||
\(376\) | −8.73677 | −0.450564 | ||||||||
\(377\) | 20.9022 | 1.07652 | ||||||||
\(378\) | −31.1343 | −1.60138 | ||||||||
\(379\) | 24.4279 | 1.25478 | 0.627389 | − | 0.778706i | \(-0.284124\pi\) | ||||
0.627389 | + | 0.778706i | \(0.284124\pi\) | |||||||
\(380\) | 22.8580 | 1.17259 | ||||||||
\(381\) | −14.8953 | −0.763107 | ||||||||
\(382\) | −3.94481 | −0.201834 | ||||||||
\(383\) | 2.65014 | 0.135416 | 0.0677078 | − | 0.997705i | \(-0.478431\pi\) | ||||
0.0677078 | + | 0.997705i | \(0.478431\pi\) | |||||||
\(384\) | 12.6944 | 0.647810 | ||||||||
\(385\) | −56.7527 | −2.89239 | ||||||||
\(386\) | 25.8911 | 1.31782 | ||||||||
\(387\) | 12.0075 | 0.610377 | ||||||||
\(388\) | −2.42845 | −0.123286 | ||||||||
\(389\) | 36.1883 | 1.83482 | 0.917409 | − | 0.397946i | \(-0.130277\pi\) | ||||
0.917409 | + | 0.397946i | \(0.130277\pi\) | |||||||
\(390\) | 16.9539 | 0.858492 | ||||||||
\(391\) | −4.03171 | −0.203893 | ||||||||
\(392\) | −17.8335 | −0.900730 | ||||||||
\(393\) | 6.43846 | 0.324777 | ||||||||
\(394\) | 44.0113 | 2.21726 | ||||||||
\(395\) | −34.1608 | −1.71882 | ||||||||
\(396\) | 41.7779 | 2.09942 | ||||||||
\(397\) | 28.4096 | 1.42584 | 0.712918 | − | 0.701247i | \(-0.247373\pi\) | ||||
0.712918 | + | 0.701247i | \(0.247373\pi\) | |||||||
\(398\) | 41.2323 | 2.06679 | ||||||||
\(399\) | 5.41214 | 0.270946 | ||||||||
\(400\) | 1.07996 | 0.0539979 | ||||||||
\(401\) | −14.3720 | −0.717702 | −0.358851 | − | 0.933395i | \(-0.616831\pi\) | ||||
−0.358851 | + | 0.933395i | \(0.616831\pi\) | |||||||
\(402\) | −3.62890 | −0.180993 | ||||||||
\(403\) | 25.2071 | 1.25566 | ||||||||
\(404\) | 56.7003 | 2.82095 | ||||||||
\(405\) | −15.9822 | −0.794164 | ||||||||
\(406\) | 50.0267 | 2.48279 | ||||||||
\(407\) | −42.6467 | −2.11392 | ||||||||
\(408\) | −1.99960 | −0.0989949 | ||||||||
\(409\) | 13.6809 | 0.676479 | 0.338240 | − | 0.941060i | \(-0.390169\pi\) | ||||
0.338240 | + | 0.941060i | \(0.390169\pi\) | |||||||
\(410\) | −25.5776 | −1.26319 | ||||||||
\(411\) | −9.10892 | −0.449310 | ||||||||
\(412\) | 56.4754 | 2.78234 | ||||||||
\(413\) | 14.4807 | 0.712547 | ||||||||
\(414\) | −23.5601 | −1.15792 | ||||||||
\(415\) | 0.131423 | 0.00645132 | ||||||||
\(416\) | 18.7245 | 0.918042 | ||||||||
\(417\) | −13.8521 | −0.678341 | ||||||||
\(418\) | −25.4730 | −1.24592 | ||||||||
\(419\) | −0.0799622 | −0.00390641 | −0.00195320 | − | 0.999998i | \(-0.500622\pi\) | ||||
−0.00195320 | + | 0.999998i | \(0.500622\pi\) | |||||||
\(420\) | 25.2218 | 1.23070 | ||||||||
\(421\) | 8.39663 | 0.409227 | 0.204613 | − | 0.978843i | \(-0.434406\pi\) | ||||
0.204613 | + | 0.978843i | \(0.434406\pi\) | |||||||
\(422\) | 4.36708 | 0.212586 | ||||||||
\(423\) | −7.51698 | −0.365488 | ||||||||
\(424\) | 4.29612 | 0.208638 | ||||||||
\(425\) | 4.87066 | 0.236262 | ||||||||
\(426\) | 7.38317 | 0.357716 | ||||||||
\(427\) | −25.5496 | −1.23643 | ||||||||
\(428\) | −25.8202 | −1.24806 | ||||||||
\(429\) | −11.7437 | −0.566991 | ||||||||
\(430\) | −34.1188 | −1.64535 | ||||||||
\(431\) | 4.95307 | 0.238581 | 0.119291 | − | 0.992859i | \(-0.461938\pi\) | ||||
0.119291 | + | 0.992859i | \(0.461938\pi\) | |||||||
\(432\) | −0.831677 | −0.0400141 | ||||||||
\(433\) | 39.0135 | 1.87487 | 0.937436 | − | 0.348159i | \(-0.113193\pi\) | ||||
0.937436 | + | 0.348159i | \(0.113193\pi\) | |||||||
\(434\) | 60.3301 | 2.89594 | ||||||||
\(435\) | −12.8158 | −0.614472 | ||||||||
\(436\) | 21.7220 | 1.04030 | ||||||||
\(437\) | 8.92906 | 0.427135 | ||||||||
\(438\) | 3.74783 | 0.179078 | ||||||||
\(439\) | −25.8330 | −1.23294 | −0.616472 | − | 0.787377i | \(-0.711439\pi\) | ||||
−0.616472 | + | 0.787377i | \(0.711439\pi\) | |||||||
\(440\) | −46.4383 | −2.21386 | ||||||||
\(441\) | −15.3437 | −0.730653 | ||||||||
\(442\) | −7.97297 | −0.379235 | ||||||||
\(443\) | 19.1949 | 0.911978 | 0.455989 | − | 0.889986i | \(-0.349286\pi\) | ||||
0.455989 | + | 0.889986i | \(0.349286\pi\) | |||||||
\(444\) | 18.9528 | 0.899462 | ||||||||
\(445\) | −13.1520 | −0.623467 | ||||||||
\(446\) | −24.5248 | −1.16128 | ||||||||
\(447\) | −0.0874754 | −0.00413744 | ||||||||
\(448\) | 46.4158 | 2.19294 | ||||||||
\(449\) | −30.7152 | −1.44954 | −0.724770 | − | 0.688991i | \(-0.758054\pi\) | ||||
−0.724770 | + | 0.688991i | \(0.758054\pi\) | |||||||
\(450\) | 28.4626 | 1.34174 | ||||||||
\(451\) | 17.7172 | 0.834272 | ||||||||
\(452\) | −0.296485 | −0.0139455 | ||||||||
\(453\) | 16.0286 | 0.753088 | ||||||||
\(454\) | 58.1920 | 2.73109 | ||||||||
\(455\) | 39.3408 | 1.84432 | ||||||||
\(456\) | 4.42853 | 0.207385 | ||||||||
\(457\) | −6.61176 | −0.309285 | −0.154643 | − | 0.987970i | \(-0.549423\pi\) | ||||
−0.154643 | + | 0.987970i | \(0.549423\pi\) | |||||||
\(458\) | −16.9999 | −0.794352 | ||||||||
\(459\) | −3.75090 | −0.175077 | ||||||||
\(460\) | 41.6114 | 1.94014 | ||||||||
\(461\) | −14.2456 | −0.663485 | −0.331742 | − | 0.943370i | \(-0.607637\pi\) | ||||
−0.331742 | + | 0.943370i | \(0.607637\pi\) | |||||||
\(462\) | −28.1071 | −1.30766 | ||||||||
\(463\) | −40.9274 | −1.90206 | −0.951029 | − | 0.309103i | \(-0.899971\pi\) | ||||
−0.951029 | + | 0.309103i | \(0.899971\pi\) | |||||||
\(464\) | 1.33634 | 0.0620381 | ||||||||
\(465\) | −15.4553 | −0.716724 | ||||||||
\(466\) | −44.4808 | −2.06053 | ||||||||
\(467\) | 5.55279 | 0.256952 | 0.128476 | − | 0.991713i | \(-0.458991\pi\) | ||||
0.128476 | + | 0.991713i | \(0.458991\pi\) | |||||||
\(468\) | −28.9603 | −1.33869 | ||||||||
\(469\) | −8.42073 | −0.388833 | ||||||||
\(470\) | 21.3591 | 0.985223 | ||||||||
\(471\) | 8.87213 | 0.408806 | ||||||||
\(472\) | 11.8489 | 0.545390 | ||||||||
\(473\) | 23.6336 | 1.08667 | ||||||||
\(474\) | −16.9183 | −0.777085 | ||||||||
\(475\) | −10.7871 | −0.494945 | ||||||||
\(476\) | −11.8612 | −0.543655 | ||||||||
\(477\) | 3.69632 | 0.169243 | ||||||||
\(478\) | −3.16100 | −0.144581 | ||||||||
\(479\) | −23.9135 | −1.09264 | −0.546319 | − | 0.837577i | \(-0.683971\pi\) | ||||
−0.546319 | + | 0.837577i | \(0.683971\pi\) | |||||||
\(480\) | −11.4806 | −0.524016 | ||||||||
\(481\) | 29.5626 | 1.34794 | ||||||||
\(482\) | 21.3340 | 0.971738 | ||||||||
\(483\) | 9.85241 | 0.448300 | ||||||||
\(484\) | 46.0923 | 2.09511 | ||||||||
\(485\) | 2.32248 | 0.105458 | ||||||||
\(486\) | −33.7845 | −1.53250 | ||||||||
\(487\) | 11.9983 | 0.543695 | 0.271848 | − | 0.962340i | \(-0.412365\pi\) | ||||
0.271848 | + | 0.962340i | \(0.412365\pi\) | |||||||
\(488\) | −20.9061 | −0.946376 | ||||||||
\(489\) | −0.442168 | −0.0199955 | ||||||||
\(490\) | 43.5984 | 1.96957 | ||||||||
\(491\) | 12.9861 | 0.586056 | 0.293028 | − | 0.956104i | \(-0.405337\pi\) | ||||
0.293028 | + | 0.956104i | \(0.405337\pi\) | |||||||
\(492\) | −7.87381 | −0.354979 | ||||||||
\(493\) | 6.02696 | 0.271440 | ||||||||
\(494\) | 17.6578 | 0.794461 | ||||||||
\(495\) | −39.9549 | −1.79584 | ||||||||
\(496\) | 1.61157 | 0.0723617 | ||||||||
\(497\) | 17.1324 | 0.768491 | ||||||||
\(498\) | 0.0650881 | 0.00291667 | ||||||||
\(499\) | −19.0751 | −0.853919 | −0.426960 | − | 0.904271i | \(-0.640415\pi\) | ||||
−0.426960 | + | 0.904271i | \(0.640415\pi\) | |||||||
\(500\) | 1.33495 | 0.0597008 | ||||||||
\(501\) | −11.3104 | −0.505310 | ||||||||
\(502\) | 30.8877 | 1.37859 | ||||||||
\(503\) | 27.4287 | 1.22298 | 0.611492 | − | 0.791251i | \(-0.290570\pi\) | ||||
0.611492 | + | 0.791251i | \(0.290570\pi\) | |||||||
\(504\) | −27.1147 | −1.20778 | ||||||||
\(505\) | −54.2261 | −2.41303 | ||||||||
\(506\) | −46.3717 | −2.06147 | ||||||||
\(507\) | −0.658013 | −0.0292234 | ||||||||
\(508\) | −72.2974 | −3.20768 | ||||||||
\(509\) | 10.8322 | 0.480130 | 0.240065 | − | 0.970757i | \(-0.422831\pi\) | ||||
0.240065 | + | 0.970757i | \(0.422831\pi\) | |||||||
\(510\) | 4.88850 | 0.216466 | ||||||||
\(511\) | 8.69671 | 0.384720 | ||||||||
\(512\) | 2.50725 | 0.110806 | ||||||||
\(513\) | 8.30713 | 0.366769 | ||||||||
\(514\) | −62.4743 | −2.75562 | ||||||||
\(515\) | −54.0110 | −2.38001 | ||||||||
\(516\) | −10.5031 | −0.462375 | ||||||||
\(517\) | −14.7952 | −0.650691 | ||||||||
\(518\) | 70.7543 | 3.10877 | ||||||||
\(519\) | 2.04977 | 0.0899749 | ||||||||
\(520\) | 32.1909 | 1.41166 | ||||||||
\(521\) | 10.3149 | 0.451906 | 0.225953 | − | 0.974138i | \(-0.427450\pi\) | ||||
0.225953 | + | 0.974138i | \(0.427450\pi\) | |||||||
\(522\) | 35.2197 | 1.54152 | ||||||||
\(523\) | 12.1984 | 0.533399 | 0.266699 | − | 0.963780i | \(-0.414067\pi\) | ||||
0.266699 | + | 0.963780i | \(0.414067\pi\) | |||||||
\(524\) | 31.2504 | 1.36518 | ||||||||
\(525\) | −11.9026 | −0.519470 | ||||||||
\(526\) | −54.2027 | −2.36335 | ||||||||
\(527\) | 7.26825 | 0.316610 | ||||||||
\(528\) | −0.750813 | −0.0326749 | ||||||||
\(529\) | −6.74528 | −0.293273 | ||||||||
\(530\) | −10.5029 | −0.456217 | ||||||||
\(531\) | 10.1946 | 0.442409 | ||||||||
\(532\) | 26.2690 | 1.13890 | ||||||||
\(533\) | −12.2815 | −0.531972 | ||||||||
\(534\) | −6.51363 | −0.281872 | ||||||||
\(535\) | 24.6935 | 1.06759 | ||||||||
\(536\) | −6.89033 | −0.297617 | ||||||||
\(537\) | −1.01743 | −0.0439054 | ||||||||
\(538\) | 55.0527 | 2.37349 | ||||||||
\(539\) | −30.2000 | −1.30081 | ||||||||
\(540\) | 38.7131 | 1.66595 | ||||||||
\(541\) | −28.4394 | −1.22271 | −0.611353 | − | 0.791358i | \(-0.709374\pi\) | ||||
−0.611353 | + | 0.791358i | \(0.709374\pi\) | |||||||
\(542\) | 28.5793 | 1.22759 | ||||||||
\(543\) | −4.43298 | −0.190237 | ||||||||
\(544\) | 5.39904 | 0.231482 | ||||||||
\(545\) | −20.7741 | −0.889866 | ||||||||
\(546\) | 19.4838 | 0.833828 | ||||||||
\(547\) | 3.91466 | 0.167379 | 0.0836893 | − | 0.996492i | \(-0.473330\pi\) | ||||
0.0836893 | + | 0.996492i | \(0.473330\pi\) | |||||||
\(548\) | −44.2121 | −1.88865 | ||||||||
\(549\) | −17.9873 | −0.767680 | ||||||||
\(550\) | 56.0210 | 2.38874 | ||||||||
\(551\) | −13.3479 | −0.568641 | ||||||||
\(552\) | 8.06181 | 0.343134 | ||||||||
\(553\) | −39.2583 | −1.66943 | ||||||||
\(554\) | −54.6349 | −2.32121 | ||||||||
\(555\) | −18.1258 | −0.769398 | ||||||||
\(556\) | −67.2342 | −2.85137 | ||||||||
\(557\) | 29.5323 | 1.25132 | 0.625662 | − | 0.780095i | \(-0.284829\pi\) | ||||
0.625662 | + | 0.780095i | \(0.284829\pi\) | |||||||
\(558\) | 42.4734 | 1.79804 | ||||||||
\(559\) | −16.3827 | −0.692916 | ||||||||
\(560\) | 2.51518 | 0.106286 | ||||||||
\(561\) | −3.38620 | −0.142965 | ||||||||
\(562\) | −48.2893 | −2.03696 | ||||||||
\(563\) | −3.30634 | −0.139345 | −0.0696727 | − | 0.997570i | \(-0.522196\pi\) | ||||
−0.0696727 | + | 0.997570i | \(0.522196\pi\) | |||||||
\(564\) | 6.57520 | 0.276866 | ||||||||
\(565\) | 0.283548 | 0.0119289 | ||||||||
\(566\) | −26.4272 | −1.11082 | ||||||||
\(567\) | −18.3671 | −0.771347 | ||||||||
\(568\) | 14.0187 | 0.588211 | ||||||||
\(569\) | 16.3949 | 0.687311 | 0.343655 | − | 0.939096i | \(-0.388335\pi\) | ||||
0.343655 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(570\) | −10.8266 | −0.453476 | ||||||||
\(571\) | −32.4486 | −1.35793 | −0.678965 | − | 0.734171i | \(-0.737571\pi\) | ||||
−0.678965 | + | 0.734171i | \(0.737571\pi\) | |||||||
\(572\) | −57.0006 | −2.38331 | ||||||||
\(573\) | 1.16138 | 0.0485174 | ||||||||
\(574\) | −29.3943 | −1.22690 | ||||||||
\(575\) | −19.6371 | −0.818924 | ||||||||
\(576\) | 32.6775 | 1.36156 | ||||||||
\(577\) | 43.3846 | 1.80612 | 0.903061 | − | 0.429512i | \(-0.141314\pi\) | ||||
0.903061 | + | 0.429512i | \(0.141314\pi\) | |||||||
\(578\) | −2.29894 | −0.0956232 | ||||||||
\(579\) | −7.62252 | −0.316781 | ||||||||
\(580\) | −62.2044 | −2.58290 | ||||||||
\(581\) | 0.151035 | 0.00626597 | ||||||||
\(582\) | 1.15022 | 0.0476782 | ||||||||
\(583\) | 7.27521 | 0.301308 | ||||||||
\(584\) | 7.11615 | 0.294468 | ||||||||
\(585\) | 27.6966 | 1.14511 | ||||||||
\(586\) | 43.1369 | 1.78197 | ||||||||
\(587\) | −1.31121 | −0.0541195 | −0.0270598 | − | 0.999634i | \(-0.508614\pi\) | ||||
−0.0270598 | + | 0.999634i | \(0.508614\pi\) | |||||||
\(588\) | 13.4213 | 0.553487 | ||||||||
\(589\) | −16.0970 | −0.663267 | ||||||||
\(590\) | −28.9675 | −1.19257 | ||||||||
\(591\) | −12.9572 | −0.532990 | ||||||||
\(592\) | 1.89003 | 0.0776797 | ||||||||
\(593\) | −28.3916 | −1.16590 | −0.582952 | − | 0.812506i | \(-0.698103\pi\) | ||||
−0.582952 | + | 0.812506i | \(0.698103\pi\) | |||||||
\(594\) | −43.1418 | −1.77013 | ||||||||
\(595\) | 11.3436 | 0.465041 | ||||||||
\(596\) | −0.424581 | −0.0173915 | ||||||||
\(597\) | −12.1391 | −0.496820 | ||||||||
\(598\) | 32.1447 | 1.31450 | ||||||||
\(599\) | 0.907711 | 0.0370881 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(600\) | −9.73936 | −0.397608 | ||||||||
\(601\) | 15.2212 | 0.620884 | 0.310442 | − | 0.950592i | \(-0.399523\pi\) | ||||
0.310442 | + | 0.950592i | \(0.399523\pi\) | |||||||
\(602\) | −39.2101 | −1.59808 | ||||||||
\(603\) | −5.92833 | −0.241420 | ||||||||
\(604\) | 77.7981 | 3.16556 | ||||||||
\(605\) | −44.0811 | −1.79215 | ||||||||
\(606\) | −26.8558 | −1.09094 | ||||||||
\(607\) | −7.57408 | −0.307423 | −0.153711 | − | 0.988116i | \(-0.549123\pi\) | ||||
−0.153711 | + | 0.988116i | \(0.549123\pi\) | |||||||
\(608\) | −11.9573 | −0.484932 | ||||||||
\(609\) | −14.7282 | −0.596818 | ||||||||
\(610\) | 51.1101 | 2.06939 | ||||||||
\(611\) | 10.2560 | 0.414912 | ||||||||
\(612\) | −8.35045 | −0.337547 | ||||||||
\(613\) | −15.3428 | −0.619688 | −0.309844 | − | 0.950787i | \(-0.600277\pi\) | ||||
−0.309844 | + | 0.950787i | \(0.600277\pi\) | |||||||
\(614\) | −20.5853 | −0.830754 | ||||||||
\(615\) | 7.53023 | 0.303648 | ||||||||
\(616\) | −53.3680 | −2.15026 | ||||||||
\(617\) | −13.4506 | −0.541499 | −0.270749 | − | 0.962650i | \(-0.587271\pi\) | ||||
−0.270749 | + | 0.962650i | \(0.587271\pi\) | |||||||
\(618\) | −26.7493 | −1.07601 | ||||||||
\(619\) | 29.0423 | 1.16731 | 0.583654 | − | 0.812003i | \(-0.301623\pi\) | ||||
0.583654 | + | 0.812003i | \(0.301623\pi\) | |||||||
\(620\) | −75.0158 | −3.01271 | ||||||||
\(621\) | 15.1225 | 0.606847 | ||||||||
\(622\) | 11.2000 | 0.449079 | ||||||||
\(623\) | −15.1146 | −0.605555 | ||||||||
\(624\) | 0.520461 | 0.0208351 | ||||||||
\(625\) | −25.6300 | −1.02520 | ||||||||
\(626\) | −43.6437 | −1.74435 | ||||||||
\(627\) | 7.49943 | 0.299498 | ||||||||
\(628\) | 43.0628 | 1.71839 | ||||||||
\(629\) | 8.52411 | 0.339878 | ||||||||
\(630\) | 66.2883 | 2.64099 | ||||||||
\(631\) | −27.7666 | −1.10537 | −0.552685 | − | 0.833390i | \(-0.686397\pi\) | ||||
−0.552685 | + | 0.833390i | \(0.686397\pi\) | |||||||
\(632\) | −32.1234 | −1.27780 | ||||||||
\(633\) | −1.28570 | −0.0511020 | ||||||||
\(634\) | 56.5321 | 2.24518 | ||||||||
\(635\) | 69.1426 | 2.74384 | ||||||||
\(636\) | −3.23321 | −0.128205 | ||||||||
\(637\) | 20.9345 | 0.829456 | ||||||||
\(638\) | 69.3205 | 2.74442 | ||||||||
\(639\) | 12.0615 | 0.477144 | ||||||||
\(640\) | −58.9265 | −2.32928 | ||||||||
\(641\) | −11.2254 | −0.443378 | −0.221689 | − | 0.975117i | \(-0.571157\pi\) | ||||
−0.221689 | + | 0.975117i | \(0.571157\pi\) | |||||||
\(642\) | 12.2296 | 0.482663 | ||||||||
\(643\) | 38.8931 | 1.53379 | 0.766897 | − | 0.641770i | \(-0.221800\pi\) | ||||
0.766897 | + | 0.641770i | \(0.221800\pi\) | |||||||
\(644\) | 47.8208 | 1.88440 | ||||||||
\(645\) | 10.0448 | 0.395515 | ||||||||
\(646\) | 5.09147 | 0.200321 | ||||||||
\(647\) | 12.2230 | 0.480537 | 0.240269 | − | 0.970706i | \(-0.422764\pi\) | ||||
0.240269 | + | 0.970706i | \(0.422764\pi\) | |||||||
\(648\) | −15.0291 | −0.590397 | ||||||||
\(649\) | 20.0654 | 0.787636 | ||||||||
\(650\) | −38.8336 | −1.52318 | ||||||||
\(651\) | −17.7616 | −0.696133 | ||||||||
\(652\) | −2.14616 | −0.0840501 | ||||||||
\(653\) | −30.9004 | −1.20923 | −0.604613 | − | 0.796519i | \(-0.706672\pi\) | ||||
−0.604613 | + | 0.796519i | \(0.706672\pi\) | |||||||
\(654\) | −10.2885 | −0.402313 | ||||||||
\(655\) | −29.8868 | −1.16777 | ||||||||
\(656\) | −0.785198 | −0.0306568 | ||||||||
\(657\) | 6.12263 | 0.238866 | ||||||||
\(658\) | 24.5464 | 0.956918 | ||||||||
\(659\) | −7.30415 | −0.284529 | −0.142265 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142265 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(660\) | 34.9490 | 1.36039 | ||||||||
\(661\) | −30.6933 | −1.19383 | −0.596916 | − | 0.802303i | \(-0.703608\pi\) | ||||
−0.596916 | + | 0.802303i | \(0.703608\pi\) | |||||||
\(662\) | 47.2825 | 1.83769 | ||||||||
\(663\) | 2.34730 | 0.0911616 | ||||||||
\(664\) | 0.123585 | 0.00479604 | ||||||||
\(665\) | −25.1227 | −0.974216 | ||||||||
\(666\) | 49.8122 | 1.93019 | ||||||||
\(667\) | −24.2990 | −0.940860 | ||||||||
\(668\) | −54.8973 | −2.12404 | ||||||||
\(669\) | 7.22028 | 0.279152 | ||||||||
\(670\) | 16.8451 | 0.650782 | ||||||||
\(671\) | −35.4032 | −1.36673 | ||||||||
\(672\) | −13.1938 | −0.508961 | ||||||||
\(673\) | 25.0745 | 0.966552 | 0.483276 | − | 0.875468i | \(-0.339447\pi\) | ||||
0.483276 | + | 0.875468i | \(0.339447\pi\) | |||||||
\(674\) | −45.1300 | −1.73834 | ||||||||
\(675\) | −18.2693 | −0.703187 | ||||||||
\(676\) | −3.19381 | −0.122839 | ||||||||
\(677\) | −13.4478 | −0.516840 | −0.258420 | − | 0.966033i | \(-0.583202\pi\) | ||||
−0.258420 | + | 0.966033i | \(0.583202\pi\) | |||||||
\(678\) | 0.140429 | 0.00539313 | ||||||||
\(679\) | 2.66904 | 0.102429 | ||||||||
\(680\) | 9.28197 | 0.355947 | ||||||||
\(681\) | −17.1321 | −0.656505 | ||||||||
\(682\) | 83.5975 | 3.20111 | ||||||||
\(683\) | −43.9040 | −1.67994 | −0.839971 | − | 0.542632i | \(-0.817428\pi\) | ||||
−0.839971 | + | 0.542632i | \(0.817428\pi\) | |||||||
\(684\) | 18.4938 | 0.707128 | ||||||||
\(685\) | 42.2828 | 1.61554 | ||||||||
\(686\) | −7.99925 | −0.305413 | ||||||||
\(687\) | 5.00489 | 0.190948 | ||||||||
\(688\) | −1.04740 | −0.0399318 | ||||||||
\(689\) | −5.04315 | −0.192129 | ||||||||
\(690\) | −19.7090 | −0.750310 | ||||||||
\(691\) | 38.9391 | 1.48131 | 0.740656 | − | 0.671884i | \(-0.234515\pi\) | ||||
0.740656 | + | 0.671884i | \(0.234515\pi\) | |||||||
\(692\) | 9.94900 | 0.378204 | ||||||||
\(693\) | −45.9170 | −1.74424 | ||||||||
\(694\) | 41.2658 | 1.56643 | ||||||||
\(695\) | 64.3004 | 2.43905 | ||||||||
\(696\) | −12.0515 | −0.456811 | ||||||||
\(697\) | −3.54127 | −0.134135 | ||||||||
\(698\) | 27.3144 | 1.03386 | ||||||||
\(699\) | 13.0955 | 0.495316 | ||||||||
\(700\) | −57.7716 | −2.18356 | ||||||||
\(701\) | −5.69168 | −0.214972 | −0.107486 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107486 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(702\) | 29.9058 | 1.12872 | ||||||||
\(703\) | −18.8784 | −0.712012 | ||||||||
\(704\) | 64.3169 | 2.42403 | ||||||||
\(705\) | −6.28828 | −0.236831 | ||||||||
\(706\) | −2.29894 | −0.0865216 | ||||||||
\(707\) | −62.3179 | −2.34370 | ||||||||
\(708\) | −8.91737 | −0.335135 | ||||||||
\(709\) | −0.603496 | −0.0226648 | −0.0113324 | − | 0.999936i | \(-0.503607\pi\) | ||||
−0.0113324 | + | 0.999936i | \(0.503607\pi\) | |||||||
\(710\) | −34.2721 | −1.28621 | ||||||||
\(711\) | −27.6385 | −1.03653 | ||||||||
\(712\) | −12.3677 | −0.463498 | ||||||||
\(713\) | −29.3035 | −1.09743 | ||||||||
\(714\) | 5.61797 | 0.210247 | ||||||||
\(715\) | 54.5133 | 2.03868 | ||||||||
\(716\) | −4.93832 | −0.184554 | ||||||||
\(717\) | 0.930623 | 0.0347547 | ||||||||
\(718\) | 54.5150 | 2.03448 | ||||||||
\(719\) | 28.9927 | 1.08124 | 0.540622 | − | 0.841266i | \(-0.318189\pi\) | ||||
0.540622 | + | 0.841266i | \(0.318189\pi\) | |||||||
\(720\) | 1.77073 | 0.0659913 | ||||||||
\(721\) | −62.0707 | −2.31163 | ||||||||
\(722\) | 32.4037 | 1.20594 | ||||||||
\(723\) | −6.28089 | −0.233589 | ||||||||
\(724\) | −21.5164 | −0.799651 | ||||||||
\(725\) | 29.3552 | 1.09023 | ||||||||
\(726\) | −21.8314 | −0.810239 | ||||||||
\(727\) | −28.1318 | −1.04335 | −0.521676 | − | 0.853144i | \(-0.674693\pi\) | ||||
−0.521676 | + | 0.853144i | \(0.674693\pi\) | |||||||
\(728\) | 36.9945 | 1.37111 | ||||||||
\(729\) | −5.31469 | −0.196840 | ||||||||
\(730\) | −17.3971 | −0.643897 | ||||||||
\(731\) | −4.72382 | −0.174717 | ||||||||
\(732\) | 15.7337 | 0.581536 | ||||||||
\(733\) | −29.6995 | −1.09698 | −0.548489 | − | 0.836158i | \(-0.684797\pi\) | ||||
−0.548489 | + | 0.836158i | \(0.684797\pi\) | |||||||
\(734\) | −1.46676 | −0.0541390 | ||||||||
\(735\) | −12.8357 | −0.473451 | ||||||||
\(736\) | −21.7674 | −0.802356 | ||||||||
\(737\) | −11.6683 | −0.429809 | ||||||||
\(738\) | −20.6941 | −0.761760 | ||||||||
\(739\) | 30.6203 | 1.12639 | 0.563194 | − | 0.826325i | \(-0.309573\pi\) | ||||
0.563194 | + | 0.826325i | \(0.309573\pi\) | |||||||
\(740\) | −87.9776 | −3.23412 | ||||||||
\(741\) | −5.19858 | −0.190975 | ||||||||
\(742\) | −12.0702 | −0.443110 | ||||||||
\(743\) | −8.73139 | −0.320324 | −0.160162 | − | 0.987091i | \(-0.551202\pi\) | ||||
−0.160162 | + | 0.987091i | \(0.551202\pi\) | |||||||
\(744\) | −14.5336 | −0.532827 | ||||||||
\(745\) | 0.406053 | 0.0148766 | ||||||||
\(746\) | −6.92346 | −0.253486 | ||||||||
\(747\) | 0.106331 | 0.00389044 | ||||||||
\(748\) | −16.4356 | −0.600946 | ||||||||
\(749\) | 28.3783 | 1.03692 | ||||||||
\(750\) | −0.632293 | −0.0230881 | ||||||||
\(751\) | 4.57804 | 0.167055 | 0.0835275 | − | 0.996505i | \(-0.473381\pi\) | ||||
0.0835275 | + | 0.996505i | \(0.473381\pi\) | |||||||
\(752\) | 0.655697 | 0.0239108 | ||||||||
\(753\) | −9.09358 | −0.331388 | ||||||||
\(754\) | −48.0527 | −1.74998 | ||||||||
\(755\) | −74.4033 | −2.70781 | ||||||||
\(756\) | 44.4900 | 1.61808 | ||||||||
\(757\) | −10.4326 | −0.379181 | −0.189590 | − | 0.981863i | \(-0.560716\pi\) | ||||
−0.189590 | + | 0.981863i | \(0.560716\pi\) | |||||||
\(758\) | −56.1582 | −2.03976 | ||||||||
\(759\) | 13.6522 | 0.495542 | ||||||||
\(760\) | −20.5568 | −0.745675 | ||||||||
\(761\) | 0.724565 | 0.0262655 | 0.0131327 | − | 0.999914i | \(-0.495820\pi\) | ||||
0.0131327 | + | 0.999914i | \(0.495820\pi\) | |||||||
\(762\) | 34.2433 | 1.24050 | ||||||||
\(763\) | −23.8741 | −0.864300 | ||||||||
\(764\) | 5.63701 | 0.203940 | ||||||||
\(765\) | 7.98607 | 0.288737 | ||||||||
\(766\) | −6.09249 | −0.220131 | ||||||||
\(767\) | −13.9093 | −0.502235 | ||||||||
\(768\) | −11.7819 | −0.425143 | ||||||||
\(769\) | 0.441772 | 0.0159307 | 0.00796535 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796535 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(770\) | 130.471 | 4.70184 | ||||||||
\(771\) | 18.3929 | 0.662404 | ||||||||
\(772\) | −36.9976 | −1.33157 | ||||||||
\(773\) | −20.0461 | −0.721007 | −0.360503 | − | 0.932758i | \(-0.617395\pi\) | ||||
−0.360503 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(774\) | −27.6046 | −0.992225 | ||||||||
\(775\) | 35.4012 | 1.27165 | ||||||||
\(776\) | 2.18397 | 0.0783998 | ||||||||
\(777\) | −20.8306 | −0.747293 | ||||||||
\(778\) | −83.1945 | −2.98267 | ||||||||
\(779\) | 7.84288 | 0.281000 | ||||||||
\(780\) | −24.2265 | −0.867450 | ||||||||
\(781\) | 23.7398 | 0.849476 | ||||||||
\(782\) | 9.26866 | 0.331446 | ||||||||
\(783\) | −22.6065 | −0.807890 | ||||||||
\(784\) | 1.33841 | 0.0478004 | ||||||||
\(785\) | −41.1837 | −1.46991 | ||||||||
\(786\) | −14.8016 | −0.527956 | ||||||||
\(787\) | −11.4148 | −0.406892 | −0.203446 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203446 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(788\) | −62.8908 | −2.24039 | ||||||||
\(789\) | 15.9577 | 0.568108 | ||||||||
\(790\) | 78.5335 | 2.79410 | ||||||||
\(791\) | 0.325859 | 0.0115862 | ||||||||
\(792\) | −37.5720 | −1.33506 | ||||||||
\(793\) | 24.5414 | 0.871491 | ||||||||
\(794\) | −65.3118 | −2.31783 | ||||||||
\(795\) | 3.09213 | 0.109667 | ||||||||
\(796\) | −58.9196 | −2.08835 | ||||||||
\(797\) | 43.3706 | 1.53626 | 0.768132 | − | 0.640291i | \(-0.221186\pi\) | ||||
0.768132 | + | 0.640291i | \(0.221186\pi\) | |||||||
\(798\) | −12.4422 | −0.440448 | ||||||||
\(799\) | 2.95722 | 0.104619 | ||||||||
\(800\) | 26.2969 | 0.929734 | ||||||||
\(801\) | −10.6410 | −0.375980 | ||||||||
\(802\) | 33.0403 | 1.16669 | ||||||||
\(803\) | 12.0508 | 0.425262 | ||||||||
\(804\) | 5.18559 | 0.182882 | ||||||||
\(805\) | −45.7341 | −1.61191 | ||||||||
\(806\) | −57.9495 | −2.04119 | ||||||||
\(807\) | −16.2079 | −0.570546 | ||||||||
\(808\) | −50.9921 | −1.79390 | ||||||||
\(809\) | −26.6505 | −0.936982 | −0.468491 | − | 0.883468i | \(-0.655202\pi\) | ||||
−0.468491 | + | 0.883468i | \(0.655202\pi\) | |||||||
\(810\) | 36.7422 | 1.29099 | ||||||||
\(811\) | −50.9075 | −1.78761 | −0.893803 | − | 0.448460i | \(-0.851973\pi\) | ||||
−0.893803 | + | 0.448460i | \(0.851973\pi\) | |||||||
\(812\) | −71.4867 | −2.50869 | ||||||||
\(813\) | −8.41395 | −0.295090 | ||||||||
\(814\) | 98.0420 | 3.43637 | ||||||||
\(815\) | 2.05251 | 0.0718963 | ||||||||
\(816\) | 0.150070 | 0.00525352 | ||||||||
\(817\) | 10.4619 | 0.366015 | ||||||||
\(818\) | −31.4516 | −1.09968 | ||||||||
\(819\) | 31.8295 | 1.11221 | ||||||||
\(820\) | 36.5496 | 1.27637 | ||||||||
\(821\) | 4.18614 | 0.146097 | 0.0730487 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730487 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(822\) | 20.9408 | 0.730395 | ||||||||
\(823\) | 31.6078 | 1.10178 | 0.550889 | − | 0.834578i | \(-0.314289\pi\) | ||||
0.550889 | + | 0.834578i | \(0.314289\pi\) | |||||||
\(824\) | −50.7898 | −1.76935 | ||||||||
\(825\) | −16.4930 | −0.574212 | ||||||||
\(826\) | −33.2901 | −1.15831 | ||||||||
\(827\) | 19.9084 | 0.692284 | 0.346142 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346142 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(828\) | 33.6666 | 1.17000 | ||||||||
\(829\) | −20.2717 | −0.704064 | −0.352032 | − | 0.935988i | \(-0.614509\pi\) | ||||
−0.352032 | + | 0.935988i | \(0.614509\pi\) | |||||||
\(830\) | −0.302134 | −0.0104872 | ||||||||
\(831\) | 16.0849 | 0.557980 | ||||||||
\(832\) | −44.5843 | −1.54568 | ||||||||
\(833\) | 6.03629 | 0.209145 | ||||||||
\(834\) | 31.8451 | 1.10271 | ||||||||
\(835\) | 52.5018 | 1.81690 | ||||||||
\(836\) | 36.4001 | 1.25892 | ||||||||
\(837\) | −27.2625 | −0.942329 | ||||||||
\(838\) | 0.183828 | 0.00635023 | ||||||||
\(839\) | 31.2137 | 1.07761 | 0.538807 | − | 0.842429i | \(-0.318875\pi\) | ||||
0.538807 | + | 0.842429i | \(0.318875\pi\) | |||||||
\(840\) | −22.6826 | −0.782624 | ||||||||
\(841\) | 7.32421 | 0.252559 | ||||||||
\(842\) | −19.3033 | −0.665237 | ||||||||
\(843\) | 14.2167 | 0.489650 | ||||||||
\(844\) | −6.24042 | −0.214804 | ||||||||
\(845\) | 3.05444 | 0.105076 | ||||||||
\(846\) | 17.2811 | 0.594135 | ||||||||
\(847\) | −50.6589 | −1.74066 | ||||||||
\(848\) | −0.322425 | −0.0110721 | ||||||||
\(849\) | 7.78037 | 0.267022 | ||||||||
\(850\) | −11.1973 | −0.384065 | ||||||||
\(851\) | −34.3668 | −1.17808 | ||||||||
\(852\) | −10.5503 | −0.361448 | ||||||||
\(853\) | 33.6167 | 1.15101 | 0.575507 | − | 0.817797i | \(-0.304805\pi\) | ||||
0.575507 | + | 0.817797i | \(0.304805\pi\) | |||||||
\(854\) | 58.7368 | 2.00993 | ||||||||
\(855\) | −17.6868 | −0.604876 | ||||||||
\(856\) | 23.2208 | 0.793669 | ||||||||
\(857\) | 8.88779 | 0.303601 | 0.151801 | − | 0.988411i | \(-0.451493\pi\) | ||||
0.151801 | + | 0.988411i | \(0.451493\pi\) | |||||||
\(858\) | 26.9980 | 0.921697 | ||||||||
\(859\) | −29.8631 | −1.01892 | −0.509458 | − | 0.860496i | \(-0.670154\pi\) | ||||
−0.509458 | + | 0.860496i | \(0.670154\pi\) | |||||||
\(860\) | 48.7547 | 1.66252 | ||||||||
\(861\) | 8.65391 | 0.294924 | ||||||||
\(862\) | −11.3868 | −0.387836 | ||||||||
\(863\) | −26.2242 | −0.892683 | −0.446341 | − | 0.894863i | \(-0.647273\pi\) | ||||
−0.446341 | + | 0.894863i | \(0.647273\pi\) | |||||||
\(864\) | −20.2512 | −0.688961 | ||||||||
\(865\) | −9.51486 | −0.323515 | ||||||||
\(866\) | −89.6897 | −3.04778 | ||||||||
\(867\) | 0.676824 | 0.0229861 | ||||||||
\(868\) | −86.2099 | −2.92615 | ||||||||
\(869\) | −54.3990 | −1.84536 | ||||||||
\(870\) | 29.4628 | 0.998882 | ||||||||
\(871\) | 8.08845 | 0.274067 | ||||||||
\(872\) | −19.5352 | −0.661544 | ||||||||
\(873\) | 1.87905 | 0.0635963 | ||||||||
\(874\) | −20.5274 | −0.694348 | ||||||||
\(875\) | −1.46721 | −0.0496008 | ||||||||
\(876\) | −5.35554 | −0.180947 | ||||||||
\(877\) | −36.4614 | −1.23121 | −0.615606 | − | 0.788054i | \(-0.711089\pi\) | ||||
−0.615606 | + | 0.788054i | \(0.711089\pi\) | |||||||
\(878\) | 59.3885 | 2.00427 | ||||||||
\(879\) | −12.6998 | −0.428354 | ||||||||
\(880\) | 3.48521 | 0.117486 | ||||||||
\(881\) | −46.5762 | −1.56919 | −0.784595 | − | 0.620008i | \(-0.787129\pi\) | ||||
−0.784595 | + | 0.620008i | \(0.787129\pi\) | |||||||
\(882\) | 35.2742 | 1.18774 | ||||||||
\(883\) | 26.9522 | 0.907013 | 0.453507 | − | 0.891253i | \(-0.350173\pi\) | ||||
0.453507 | + | 0.891253i | \(0.350173\pi\) | |||||||
\(884\) | 11.3931 | 0.383192 | ||||||||
\(885\) | 8.52825 | 0.286674 | ||||||||
\(886\) | −44.1279 | −1.48251 | ||||||||
\(887\) | 53.4339 | 1.79413 | 0.897067 | − | 0.441895i | \(-0.145694\pi\) | ||||
0.897067 | + | 0.441895i | \(0.145694\pi\) | |||||||
\(888\) | −17.0448 | −0.571986 | ||||||||
\(889\) | 79.4602 | 2.66501 | ||||||||
\(890\) | 30.2357 | 1.01350 | ||||||||
\(891\) | −25.4508 | −0.852633 | ||||||||
\(892\) | 35.0452 | 1.17340 | ||||||||
\(893\) | −6.54937 | −0.219166 | ||||||||
\(894\) | 0.201100 | 0.00672580 | ||||||||
\(895\) | 4.72283 | 0.157867 | ||||||||
\(896\) | −67.7197 | −2.26236 | ||||||||
\(897\) | −9.46364 | −0.315982 | ||||||||
\(898\) | 70.6123 | 2.35636 | ||||||||
\(899\) | 43.8054 | 1.46099 | ||||||||
\(900\) | −40.6722 | −1.35574 | ||||||||
\(901\) | −1.45415 | −0.0484447 | ||||||||
\(902\) | −40.7308 | −1.35619 | ||||||||
\(903\) | 11.5437 | 0.384151 | ||||||||
\(904\) | 0.266637 | 0.00886821 | ||||||||
\(905\) | 20.5775 | 0.684020 | ||||||||
\(906\) | −36.8487 | −1.22421 | ||||||||
\(907\) | 20.4132 | 0.677809 | 0.338904 | − | 0.940821i | \(-0.389944\pi\) | ||||
0.338904 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(908\) | −83.1546 | −2.75958 | ||||||||
\(909\) | −43.8728 | −1.45517 | ||||||||
\(910\) | −90.4420 | −2.99812 | ||||||||
\(911\) | −14.8722 | −0.492737 | −0.246369 | − | 0.969176i | \(-0.579237\pi\) | ||||
−0.246369 | + | 0.969176i | \(0.579237\pi\) | |||||||
\(912\) | −0.332362 | −0.0110056 | ||||||||
\(913\) | 0.209284 | 0.00692628 | ||||||||
\(914\) | 15.2000 | 0.502772 | ||||||||
\(915\) | −15.0472 | −0.497445 | ||||||||
\(916\) | 24.2923 | 0.802640 | ||||||||
\(917\) | −34.3466 | −1.13422 | ||||||||
\(918\) | 8.62307 | 0.284604 | ||||||||
\(919\) | −43.6636 | −1.44033 | −0.720165 | − | 0.693803i | \(-0.755934\pi\) | ||||
−0.720165 | + | 0.693803i | \(0.755934\pi\) | |||||||
\(920\) | −37.4223 | −1.23378 | ||||||||
\(921\) | 6.06046 | 0.199699 | ||||||||
\(922\) | 32.7498 | 1.07856 | ||||||||
\(923\) | −16.4563 | −0.541667 | ||||||||
\(924\) | 40.1642 | 1.32130 | ||||||||
\(925\) | 41.5180 | 1.36510 | ||||||||
\(926\) | 94.0895 | 3.09197 | ||||||||
\(927\) | −43.6988 | −1.43526 | ||||||||
\(928\) | 32.5398 | 1.06817 | ||||||||
\(929\) | 8.52875 | 0.279819 | 0.139910 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139910 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(930\) | 35.5309 | 1.16510 | ||||||||
\(931\) | −13.3686 | −0.438139 | ||||||||
\(932\) | 63.5617 | 2.08203 | ||||||||
\(933\) | −3.29736 | −0.107951 | ||||||||
\(934\) | −12.7655 | −0.417700 | ||||||||
\(935\) | 15.7184 | 0.514048 | ||||||||
\(936\) | 26.0448 | 0.851300 | ||||||||
\(937\) | −9.45609 | −0.308917 | −0.154458 | − | 0.987999i | \(-0.549363\pi\) | ||||
−0.154458 | + | 0.987999i | \(0.549363\pi\) | |||||||
\(938\) | 19.3587 | 0.632085 | ||||||||
\(939\) | 12.8490 | 0.419312 | ||||||||
\(940\) | −30.5215 | −0.995503 | ||||||||
\(941\) | 37.6423 | 1.22710 | 0.613551 | − | 0.789655i | \(-0.289740\pi\) | ||||
0.613551 | + | 0.789655i | \(0.289740\pi\) | |||||||
\(942\) | −20.3965 | −0.664553 | ||||||||
\(943\) | 14.2774 | 0.464936 | ||||||||
\(944\) | −0.889264 | −0.0289431 | ||||||||
\(945\) | −42.5486 | −1.38411 | ||||||||
\(946\) | −54.3322 | −1.76649 | ||||||||
\(947\) | 31.5419 | 1.02497 | 0.512486 | − | 0.858695i | \(-0.328725\pi\) | ||||
0.512486 | + | 0.858695i | \(0.328725\pi\) | |||||||
\(948\) | 24.1758 | 0.785193 | ||||||||
\(949\) | −8.35354 | −0.271167 | ||||||||
\(950\) | 24.7988 | 0.804580 | ||||||||
\(951\) | −16.6435 | −0.539701 | ||||||||
\(952\) | 10.6671 | 0.345721 | ||||||||
\(953\) | 21.0411 | 0.681588 | 0.340794 | − | 0.940138i | \(-0.389304\pi\) | ||||
0.340794 | + | 0.940138i | \(0.389304\pi\) | |||||||
\(954\) | −8.49760 | −0.275120 | ||||||||
\(955\) | −5.39103 | −0.174450 | ||||||||
\(956\) | 4.51698 | 0.146089 | ||||||||
\(957\) | −20.4085 | −0.659712 | ||||||||
\(958\) | 54.9757 | 1.77618 | ||||||||
\(959\) | 48.5924 | 1.56913 | ||||||||
\(960\) | 27.3362 | 0.882271 | ||||||||
\(961\) | 21.8275 | 0.704113 | ||||||||
\(962\) | −67.9624 | −2.19120 | ||||||||
\(963\) | 19.9788 | 0.643807 | ||||||||
\(964\) | −30.4857 | −0.981877 | ||||||||
\(965\) | 35.3831 | 1.13902 | ||||||||
\(966\) | −22.6501 | −0.728754 | ||||||||
\(967\) | 4.58049 | 0.147299 | 0.0736493 | − | 0.997284i | \(-0.476535\pi\) | ||||
0.0736493 | + | 0.997284i | \(0.476535\pi\) | |||||||
\(968\) | −41.4521 | −1.33232 | ||||||||
\(969\) | −1.49897 | −0.0481537 | ||||||||
\(970\) | −5.33923 | −0.171432 | ||||||||
\(971\) | −4.26831 | −0.136976 | −0.0684882 | − | 0.997652i | \(-0.521818\pi\) | ||||
−0.0684882 | + | 0.997652i | \(0.521818\pi\) | |||||||
\(972\) | 48.2770 | 1.54849 | ||||||||
\(973\) | 73.8954 | 2.36898 | ||||||||
\(974\) | −27.5834 | −0.883828 | ||||||||
\(975\) | 11.4329 | 0.366146 | ||||||||
\(976\) | 1.56901 | 0.0502228 | ||||||||
\(977\) | −6.20038 | −0.198368 | −0.0991838 | − | 0.995069i | \(-0.531623\pi\) | ||||
−0.0991838 | + | 0.995069i | \(0.531623\pi\) | |||||||
\(978\) | 1.01652 | 0.0325046 | ||||||||
\(979\) | −20.9439 | −0.669369 | ||||||||
\(980\) | −62.3007 | −1.99012 | ||||||||
\(981\) | −16.8078 | −0.536631 | ||||||||
\(982\) | −29.8543 | −0.952688 | ||||||||
\(983\) | 21.5731 | 0.688076 | 0.344038 | − | 0.938956i | \(-0.388205\pi\) | ||||
0.344038 | + | 0.938956i | \(0.388205\pi\) | |||||||
\(984\) | 7.08113 | 0.225738 | ||||||||
\(985\) | 60.1464 | 1.91642 | ||||||||
\(986\) | −13.8556 | −0.441252 | ||||||||
\(987\) | −7.22664 | −0.230026 | ||||||||
\(988\) | −25.2324 | −0.802751 | ||||||||
\(989\) | 19.0451 | 0.605599 | ||||||||
\(990\) | 91.8537 | 2.91930 | ||||||||
\(991\) | −2.23436 | −0.0709766 | −0.0354883 | − | 0.999370i | \(-0.511299\pi\) | ||||
−0.0354883 | + | 0.999370i | \(0.511299\pi\) | |||||||
\(992\) | 39.2416 | 1.24592 | ||||||||
\(993\) | −13.9203 | −0.441748 | ||||||||
\(994\) | −39.3862 | −1.24925 | ||||||||
\(995\) | 56.3486 | 1.78637 | ||||||||
\(996\) | −0.0930090 | −0.00294710 | ||||||||
\(997\) | −23.3745 | −0.740278 | −0.370139 | − | 0.928976i | \(-0.620690\pi\) | ||||
−0.370139 | + | 0.928976i | \(0.620690\pi\) | |||||||
\(998\) | 43.8525 | 1.38813 | ||||||||
\(999\) | −31.9730 | −1.01158 |
(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 | 6001.2.a.b.1.15 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.15 | ✓ | 114 | 1.1 | even | 1 | trivial |