Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5239,2,Mod(1,5239)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5239, 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("5239.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5239 = 13^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5239.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: | \(41.8336256189\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.49 | ||
Character | \(\chi\) | \(=\) | 5239.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45438 | 1.73551 | 0.867755 | − | 0.496991i | \(-0.165562\pi\) | ||||
0.867755 | + | 0.496991i | \(0.165562\pi\) | |||||||
\(3\) | 0.207916 | 0.120041 | 0.0600203 | − | 0.998197i | \(-0.480883\pi\) | ||||
0.0600203 | + | 0.998197i | \(0.480883\pi\) | |||||||
\(4\) | 4.02400 | 2.01200 | ||||||||
\(5\) | −4.16467 | −1.86250 | −0.931249 | − | 0.364384i | \(-0.881279\pi\) | ||||
−0.931249 | + | 0.364384i | \(0.881279\pi\) | |||||||
\(6\) | 0.510306 | 0.208332 | ||||||||
\(7\) | −1.04008 | −0.393114 | −0.196557 | − | 0.980492i | \(-0.562976\pi\) | ||||
−0.196557 | + | 0.980492i | \(0.562976\pi\) | |||||||
\(8\) | 4.96766 | 1.75633 | ||||||||
\(9\) | −2.95677 | −0.985590 | ||||||||
\(10\) | −10.2217 | −3.23238 | ||||||||
\(11\) | 1.11808 | 0.337113 | 0.168556 | − | 0.985692i | \(-0.446089\pi\) | ||||
0.168556 | + | 0.985692i | \(0.446089\pi\) | |||||||
\(12\) | 0.836655 | 0.241521 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.55276 | −0.682253 | ||||||||
\(15\) | −0.865903 | −0.223575 | ||||||||
\(16\) | 4.14456 | 1.03614 | ||||||||
\(17\) | −1.34008 | −0.325016 | −0.162508 | − | 0.986707i | \(-0.551958\pi\) | ||||
−0.162508 | + | 0.986707i | \(0.551958\pi\) | |||||||
\(18\) | −7.25705 | −1.71050 | ||||||||
\(19\) | 4.31588 | 0.990130 | 0.495065 | − | 0.868856i | \(-0.335144\pi\) | ||||
0.495065 | + | 0.868856i | \(0.335144\pi\) | |||||||
\(20\) | −16.7586 | −3.74734 | ||||||||
\(21\) | −0.216250 | −0.0471896 | ||||||||
\(22\) | 2.74419 | 0.585063 | ||||||||
\(23\) | 5.72370 | 1.19347 | 0.596737 | − | 0.802437i | \(-0.296464\pi\) | ||||
0.596737 | + | 0.802437i | \(0.296464\pi\) | |||||||
\(24\) | 1.03286 | 0.210831 | ||||||||
\(25\) | 12.3445 | 2.46890 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23851 | −0.238351 | ||||||||
\(28\) | −4.18528 | −0.790944 | ||||||||
\(29\) | 0.344453 | 0.0639634 | 0.0319817 | − | 0.999488i | \(-0.489818\pi\) | ||||
0.0319817 | + | 0.999488i | \(0.489818\pi\) | |||||||
\(30\) | −2.12526 | −0.388017 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.237002 | 0.0418965 | ||||||||
\(33\) | 0.232466 | 0.0404672 | ||||||||
\(34\) | −3.28906 | −0.564069 | ||||||||
\(35\) | 4.33159 | 0.732173 | ||||||||
\(36\) | −11.8980 | −1.98301 | ||||||||
\(37\) | 4.86405 | 0.799645 | 0.399822 | − | 0.916593i | \(-0.369072\pi\) | ||||
0.399822 | + | 0.916593i | \(0.369072\pi\) | |||||||
\(38\) | 10.5928 | 1.71838 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.6887 | −3.27117 | ||||||||
\(41\) | 7.57660 | 1.18327 | 0.591633 | − | 0.806207i | \(-0.298483\pi\) | ||||
0.591633 | + | 0.806207i | \(0.298483\pi\) | |||||||
\(42\) | −0.530760 | −0.0818980 | ||||||||
\(43\) | 9.64063 | 1.47018 | 0.735091 | − | 0.677968i | \(-0.237139\pi\) | ||||
0.735091 | + | 0.677968i | \(0.237139\pi\) | |||||||
\(44\) | 4.49914 | 0.678270 | ||||||||
\(45\) | 12.3140 | 1.83566 | ||||||||
\(46\) | 14.0482 | 2.07129 | ||||||||
\(47\) | 3.74505 | 0.546272 | 0.273136 | − | 0.961975i | \(-0.411939\pi\) | ||||
0.273136 | + | 0.961975i | \(0.411939\pi\) | |||||||
\(48\) | 0.861721 | 0.124379 | ||||||||
\(49\) | −5.91823 | −0.845462 | ||||||||
\(50\) | 30.2981 | 4.28480 | ||||||||
\(51\) | −0.278624 | −0.0390151 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.64964 | 0.638677 | 0.319339 | − | 0.947641i | \(-0.396539\pi\) | ||||
0.319339 | + | 0.947641i | \(0.396539\pi\) | |||||||
\(54\) | −3.03978 | −0.413661 | ||||||||
\(55\) | −4.65642 | −0.627872 | ||||||||
\(56\) | −5.16677 | −0.690439 | ||||||||
\(57\) | 0.897342 | 0.118856 | ||||||||
\(58\) | 0.845420 | 0.111009 | ||||||||
\(59\) | 2.86318 | 0.372754 | 0.186377 | − | 0.982478i | \(-0.440325\pi\) | ||||
0.186377 | + | 0.982478i | \(0.440325\pi\) | |||||||
\(60\) | −3.48439 | −0.449833 | ||||||||
\(61\) | 14.2917 | 1.82986 | 0.914931 | − | 0.403611i | \(-0.132245\pi\) | ||||
0.914931 | + | 0.403611i | \(0.132245\pi\) | |||||||
\(62\) | −2.45438 | −0.311707 | ||||||||
\(63\) | 3.07528 | 0.387449 | ||||||||
\(64\) | −7.70742 | −0.963427 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.570562 | 0.0702313 | ||||||||
\(67\) | 2.50369 | 0.305875 | 0.152937 | − | 0.988236i | \(-0.451127\pi\) | ||||
0.152937 | + | 0.988236i | \(0.451127\pi\) | |||||||
\(68\) | −5.39246 | −0.653932 | ||||||||
\(69\) | 1.19005 | 0.143265 | ||||||||
\(70\) | 10.6314 | 1.27069 | ||||||||
\(71\) | 10.2197 | 1.21286 | 0.606429 | − | 0.795138i | \(-0.292601\pi\) | ||||
0.606429 | + | 0.795138i | \(0.292601\pi\) | |||||||
\(72\) | −14.6882 | −1.73103 | ||||||||
\(73\) | −14.1665 | −1.65806 | −0.829029 | − | 0.559206i | \(-0.811106\pi\) | ||||
−0.829029 | + | 0.559206i | \(0.811106\pi\) | |||||||
\(74\) | 11.9382 | 1.38779 | ||||||||
\(75\) | 2.56662 | 0.296368 | ||||||||
\(76\) | 17.3671 | 1.99214 | ||||||||
\(77\) | −1.16289 | −0.132524 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.53614 | 0.622864 | 0.311432 | − | 0.950268i | \(-0.399191\pi\) | ||||
0.311432 | + | 0.950268i | \(0.399191\pi\) | |||||||
\(80\) | −17.2607 | −1.92981 | ||||||||
\(81\) | 8.61281 | 0.956978 | ||||||||
\(82\) | 18.5959 | 2.05357 | ||||||||
\(83\) | −8.16087 | −0.895772 | −0.447886 | − | 0.894091i | \(-0.647823\pi\) | ||||
−0.447886 | + | 0.894091i | \(0.647823\pi\) | |||||||
\(84\) | −0.870189 | −0.0949453 | ||||||||
\(85\) | 5.58097 | 0.605341 | ||||||||
\(86\) | 23.6618 | 2.55152 | ||||||||
\(87\) | 0.0716175 | 0.00767820 | ||||||||
\(88\) | 5.55423 | 0.592083 | ||||||||
\(89\) | −16.1871 | −1.71582 | −0.857912 | − | 0.513796i | \(-0.828239\pi\) | ||||
−0.857912 | + | 0.513796i | \(0.828239\pi\) | |||||||
\(90\) | 30.2232 | 3.18581 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 23.0322 | 2.40127 | ||||||||
\(93\) | −0.207916 | −0.0215599 | ||||||||
\(94\) | 9.19179 | 0.948061 | ||||||||
\(95\) | −17.9742 | −1.84411 | ||||||||
\(96\) | 0.0492766 | 0.00502928 | ||||||||
\(97\) | −5.66833 | −0.575531 | −0.287766 | − | 0.957701i | \(-0.592912\pi\) | ||||
−0.287766 | + | 0.957701i | \(0.592912\pi\) | |||||||
\(98\) | −14.5256 | −1.46731 | ||||||||
\(99\) | −3.30590 | −0.332255 | ||||||||
\(100\) | 49.6741 | 4.96741 | ||||||||
\(101\) | 9.97672 | 0.992721 | 0.496360 | − | 0.868117i | \(-0.334669\pi\) | ||||
0.496360 | + | 0.868117i | \(0.334669\pi\) | |||||||
\(102\) | −0.683849 | −0.0677111 | ||||||||
\(103\) | −3.88745 | −0.383042 | −0.191521 | − | 0.981489i | \(-0.561342\pi\) | ||||
−0.191521 | + | 0.981489i | \(0.561342\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.900609 | 0.0878905 | ||||||||
\(106\) | 11.4120 | 1.10843 | ||||||||
\(107\) | 1.63569 | 0.158128 | 0.0790639 | − | 0.996870i | \(-0.474807\pi\) | ||||
0.0790639 | + | 0.996870i | \(0.474807\pi\) | |||||||
\(108\) | −4.98376 | −0.479563 | ||||||||
\(109\) | −11.0848 | −1.06174 | −0.530868 | − | 0.847455i | \(-0.678134\pi\) | ||||
−0.530868 | + | 0.847455i | \(0.678134\pi\) | |||||||
\(110\) | −11.4286 | −1.08968 | ||||||||
\(111\) | 1.01132 | 0.0959898 | ||||||||
\(112\) | −4.31067 | −0.407320 | ||||||||
\(113\) | 2.20404 | 0.207339 | 0.103669 | − | 0.994612i | \(-0.466942\pi\) | ||||
0.103669 | + | 0.994612i | \(0.466942\pi\) | |||||||
\(114\) | 2.20242 | 0.206276 | ||||||||
\(115\) | −23.8373 | −2.22284 | ||||||||
\(116\) | 1.38608 | 0.128694 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.02734 | 0.646919 | ||||||||
\(119\) | 1.39379 | 0.127768 | ||||||||
\(120\) | −4.30152 | −0.392673 | ||||||||
\(121\) | −9.74991 | −0.886355 | ||||||||
\(122\) | 35.0772 | 3.17574 | ||||||||
\(123\) | 1.57530 | 0.142040 | ||||||||
\(124\) | −4.02400 | −0.361366 | ||||||||
\(125\) | −30.5873 | −2.73582 | ||||||||
\(126\) | 7.54792 | 0.672422 | ||||||||
\(127\) | −17.5762 | −1.55963 | −0.779817 | − | 0.626008i | \(-0.784688\pi\) | ||||
−0.779817 | + | 0.626008i | \(0.784688\pi\) | |||||||
\(128\) | −19.3910 | −1.71394 | ||||||||
\(129\) | 2.00445 | 0.176482 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4714 | 1.61385 | 0.806927 | − | 0.590651i | \(-0.201129\pi\) | ||||
0.806927 | + | 0.590651i | \(0.201129\pi\) | |||||||
\(132\) | 0.935444 | 0.0814200 | ||||||||
\(133\) | −4.48886 | −0.389234 | ||||||||
\(134\) | 6.14503 | 0.530849 | ||||||||
\(135\) | 5.15799 | 0.443929 | ||||||||
\(136\) | −6.65704 | −0.570837 | ||||||||
\(137\) | −1.61293 | −0.137802 | −0.0689009 | − | 0.997624i | \(-0.521949\pi\) | ||||
−0.0689009 | + | 0.997624i | \(0.521949\pi\) | |||||||
\(138\) | 2.92084 | 0.248639 | ||||||||
\(139\) | 20.2596 | 1.71840 | 0.859199 | − | 0.511641i | \(-0.170962\pi\) | ||||
0.859199 | + | 0.511641i | \(0.170962\pi\) | |||||||
\(140\) | 17.4303 | 1.47313 | ||||||||
\(141\) | 0.778657 | 0.0655748 | ||||||||
\(142\) | 25.0831 | 2.10493 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.2545 | −1.02121 | ||||||||
\(145\) | −1.43453 | −0.119132 | ||||||||
\(146\) | −34.7699 | −2.87758 | ||||||||
\(147\) | −1.23050 | −0.101490 | ||||||||
\(148\) | 19.5729 | 1.60888 | ||||||||
\(149\) | 11.4008 | 0.933988 | 0.466994 | − | 0.884261i | \(-0.345337\pi\) | ||||
0.466994 | + | 0.884261i | \(0.345337\pi\) | |||||||
\(150\) | 6.29947 | 0.514349 | ||||||||
\(151\) | 19.6612 | 1.60000 | 0.800002 | − | 0.599997i | \(-0.204832\pi\) | ||||
0.800002 | + | 0.599997i | \(0.204832\pi\) | |||||||
\(152\) | 21.4398 | 1.73900 | ||||||||
\(153\) | 3.96229 | 0.320333 | ||||||||
\(154\) | −2.85418 | −0.229996 | ||||||||
\(155\) | 4.16467 | 0.334514 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.69774 | 0.135495 | 0.0677473 | − | 0.997703i | \(-0.478419\pi\) | ||||
0.0677473 | + | 0.997703i | \(0.478419\pi\) | |||||||
\(158\) | 13.5878 | 1.08099 | ||||||||
\(159\) | 0.966736 | 0.0766672 | ||||||||
\(160\) | −0.987036 | −0.0780320 | ||||||||
\(161\) | −5.95311 | −0.469171 | ||||||||
\(162\) | 21.1391 | 1.66085 | ||||||||
\(163\) | −18.6626 | −1.46177 | −0.730883 | − | 0.682503i | \(-0.760892\pi\) | ||||
−0.730883 | + | 0.682503i | \(0.760892\pi\) | |||||||
\(164\) | 30.4882 | 2.38073 | ||||||||
\(165\) | −0.968146 | −0.0753701 | ||||||||
\(166\) | −20.0299 | −1.55462 | ||||||||
\(167\) | −20.2665 | −1.56827 | −0.784134 | − | 0.620591i | \(-0.786893\pi\) | ||||
−0.784134 | + | 0.620591i | \(0.786893\pi\) | |||||||
\(168\) | −1.07426 | −0.0828807 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.6978 | 1.05058 | ||||||||
\(171\) | −12.7611 | −0.975863 | ||||||||
\(172\) | 38.7939 | 2.95801 | ||||||||
\(173\) | 13.8121 | 1.05012 | 0.525059 | − | 0.851066i | \(-0.324043\pi\) | ||||
0.525059 | + | 0.851066i | \(0.324043\pi\) | |||||||
\(174\) | 0.175777 | 0.0133256 | ||||||||
\(175\) | −12.8393 | −0.970556 | ||||||||
\(176\) | 4.63393 | 0.349296 | ||||||||
\(177\) | 0.595302 | 0.0447456 | ||||||||
\(178\) | −39.7292 | −2.97783 | ||||||||
\(179\) | 23.6415 | 1.76705 | 0.883524 | − | 0.468385i | \(-0.155164\pi\) | ||||
0.883524 | + | 0.468385i | \(0.155164\pi\) | |||||||
\(180\) | 49.5514 | 3.69334 | ||||||||
\(181\) | −3.71890 | −0.276423 | −0.138212 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138212 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.97147 | 0.219658 | ||||||||
\(184\) | 28.4334 | 2.09614 | ||||||||
\(185\) | −20.2572 | −1.48934 | ||||||||
\(186\) | −0.510306 | −0.0374175 | ||||||||
\(187\) | −1.49831 | −0.109567 | ||||||||
\(188\) | 15.0701 | 1.09910 | ||||||||
\(189\) | 1.28815 | 0.0936992 | ||||||||
\(190\) | −44.1156 | −3.20048 | ||||||||
\(191\) | 2.05593 | 0.148762 | 0.0743809 | − | 0.997230i | \(-0.476302\pi\) | ||||
0.0743809 | + | 0.997230i | \(0.476302\pi\) | |||||||
\(192\) | −1.60250 | −0.115650 | ||||||||
\(193\) | 15.5562 | 1.11976 | 0.559880 | − | 0.828574i | \(-0.310847\pi\) | ||||
0.559880 | + | 0.828574i | \(0.310847\pi\) | |||||||
\(194\) | −13.9122 | −0.998841 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.8149 | −1.70107 | ||||||||
\(197\) | −7.05414 | −0.502587 | −0.251293 | − | 0.967911i | \(-0.580856\pi\) | ||||
−0.251293 | + | 0.967911i | \(0.580856\pi\) | |||||||
\(198\) | −8.11393 | −0.576632 | ||||||||
\(199\) | −1.39696 | −0.0990279 | −0.0495140 | − | 0.998773i | \(-0.515767\pi\) | ||||
−0.0495140 | + | 0.998773i | \(0.515767\pi\) | |||||||
\(200\) | 61.3232 | 4.33621 | ||||||||
\(201\) | 0.520559 | 0.0367174 | ||||||||
\(202\) | 24.4867 | 1.72288 | ||||||||
\(203\) | −0.358259 | −0.0251449 | ||||||||
\(204\) | −1.12118 | −0.0784983 | ||||||||
\(205\) | −31.5540 | −2.20383 | ||||||||
\(206\) | −9.54129 | −0.664773 | ||||||||
\(207\) | −16.9237 | −1.17628 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.82548 | 0.333786 | ||||||||
\(210\) | 2.21044 | 0.152535 | ||||||||
\(211\) | 7.36580 | 0.507083 | 0.253541 | − | 0.967325i | \(-0.418405\pi\) | ||||
0.253541 | + | 0.967325i | \(0.418405\pi\) | |||||||
\(212\) | 18.7101 | 1.28502 | ||||||||
\(213\) | 2.12485 | 0.145592 | ||||||||
\(214\) | 4.01460 | 0.274432 | ||||||||
\(215\) | −40.1501 | −2.73821 | ||||||||
\(216\) | −6.15250 | −0.418625 | ||||||||
\(217\) | 1.04008 | 0.0706053 | ||||||||
\(218\) | −27.2065 | −1.84265 | ||||||||
\(219\) | −2.94544 | −0.199034 | ||||||||
\(220\) | −18.7374 | −1.26328 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.48216 | 0.166591 | ||||||||
\(223\) | −5.09963 | −0.341497 | −0.170748 | − | 0.985315i | \(-0.554618\pi\) | ||||
−0.170748 | + | 0.985315i | \(0.554618\pi\) | |||||||
\(224\) | −0.246501 | −0.0164701 | ||||||||
\(225\) | −36.4998 | −2.43332 | ||||||||
\(226\) | 5.40957 | 0.359839 | ||||||||
\(227\) | −0.399712 | −0.0265298 | −0.0132649 | − | 0.999912i | \(-0.504222\pi\) | ||||
−0.0132649 | + | 0.999912i | \(0.504222\pi\) | |||||||
\(228\) | 3.61090 | 0.239138 | ||||||||
\(229\) | −10.6028 | −0.700654 | −0.350327 | − | 0.936627i | \(-0.613930\pi\) | ||||
−0.350327 | + | 0.936627i | \(0.613930\pi\) | |||||||
\(230\) | −58.5059 | −3.85777 | ||||||||
\(231\) | −0.241784 | −0.0159082 | ||||||||
\(232\) | 1.71113 | 0.112341 | ||||||||
\(233\) | 9.25053 | 0.606022 | 0.303011 | − | 0.952987i | \(-0.402008\pi\) | ||||
0.303011 | + | 0.952987i | \(0.402008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.5969 | −1.01743 | ||||||||
\(236\) | 11.5214 | 0.749981 | ||||||||
\(237\) | 1.15105 | 0.0747690 | ||||||||
\(238\) | 3.42089 | 0.221743 | ||||||||
\(239\) | 24.1459 | 1.56187 | 0.780934 | − | 0.624613i | \(-0.214743\pi\) | ||||
0.780934 | + | 0.624613i | \(0.214743\pi\) | |||||||
\(240\) | −3.58878 | −0.231655 | ||||||||
\(241\) | −10.3073 | −0.663951 | −0.331975 | − | 0.943288i | \(-0.607715\pi\) | ||||
−0.331975 | + | 0.943288i | \(0.607715\pi\) | |||||||
\(242\) | −23.9300 | −1.53828 | ||||||||
\(243\) | 5.50627 | 0.353228 | ||||||||
\(244\) | 57.5096 | 3.68168 | ||||||||
\(245\) | 24.6475 | 1.57467 | ||||||||
\(246\) | 3.86639 | 0.246512 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.96766 | −0.315447 | ||||||||
\(249\) | −1.69678 | −0.107529 | ||||||||
\(250\) | −75.0731 | −4.74804 | ||||||||
\(251\) | 7.72955 | 0.487885 | 0.243942 | − | 0.969790i | \(-0.421559\pi\) | ||||
0.243942 | + | 0.969790i | \(0.421559\pi\) | |||||||
\(252\) | 12.3749 | 0.779546 | ||||||||
\(253\) | 6.39954 | 0.402335 | ||||||||
\(254\) | −43.1387 | −2.70676 | ||||||||
\(255\) | 1.16038 | 0.0726655 | ||||||||
\(256\) | −32.1780 | −2.01113 | ||||||||
\(257\) | 26.3276 | 1.64227 | 0.821137 | − | 0.570732i | \(-0.193340\pi\) | ||||
0.821137 | + | 0.570732i | \(0.193340\pi\) | |||||||
\(258\) | 4.91968 | 0.306286 | ||||||||
\(259\) | −5.05900 | −0.314351 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.01847 | −0.0630417 | ||||||||
\(262\) | 45.3359 | 2.80086 | ||||||||
\(263\) | 20.4973 | 1.26392 | 0.631959 | − | 0.775001i | \(-0.282251\pi\) | ||||
0.631959 | + | 0.775001i | \(0.282251\pi\) | |||||||
\(264\) | 1.15481 | 0.0710739 | ||||||||
\(265\) | −19.3642 | −1.18953 | ||||||||
\(266\) | −11.0174 | −0.675519 | ||||||||
\(267\) | −3.36555 | −0.205969 | ||||||||
\(268\) | 10.0749 | 0.615420 | ||||||||
\(269\) | −9.05361 | −0.552009 | −0.276004 | − | 0.961156i | \(-0.589010\pi\) | ||||
−0.276004 | + | 0.961156i | \(0.589010\pi\) | |||||||
\(270\) | 12.6597 | 0.770443 | ||||||||
\(271\) | −6.08790 | −0.369813 | −0.184907 | − | 0.982756i | \(-0.559198\pi\) | ||||
−0.184907 | + | 0.982756i | \(0.559198\pi\) | |||||||
\(272\) | −5.55402 | −0.336762 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.95875 | −0.239157 | ||||||||
\(275\) | 13.8021 | 0.832296 | ||||||||
\(276\) | 4.78876 | 0.288250 | ||||||||
\(277\) | −26.8138 | −1.61109 | −0.805543 | − | 0.592537i | \(-0.798126\pi\) | ||||
−0.805543 | + | 0.592537i | \(0.798126\pi\) | |||||||
\(278\) | 49.7249 | 2.98230 | ||||||||
\(279\) | 2.95677 | 0.177017 | ||||||||
\(280\) | 21.5179 | 1.28594 | ||||||||
\(281\) | 28.8217 | 1.71936 | 0.859678 | − | 0.510836i | \(-0.170664\pi\) | ||||
0.859678 | + | 0.510836i | \(0.170664\pi\) | |||||||
\(282\) | 1.91112 | 0.113806 | ||||||||
\(283\) | −0.150867 | −0.00896809 | −0.00448404 | − | 0.999990i | \(-0.501427\pi\) | ||||
−0.00448404 | + | 0.999990i | \(0.501427\pi\) | |||||||
\(284\) | 41.1241 | 2.44027 | ||||||||
\(285\) | −3.73713 | −0.221369 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.88027 | −0.465158 | ||||||||
\(288\) | −0.700761 | −0.0412927 | ||||||||
\(289\) | −15.2042 | −0.894365 | ||||||||
\(290\) | −3.52090 | −0.206754 | ||||||||
\(291\) | −1.17854 | −0.0690871 | ||||||||
\(292\) | −57.0058 | −3.33601 | ||||||||
\(293\) | −11.4871 | −0.671085 | −0.335543 | − | 0.942025i | \(-0.608920\pi\) | ||||
−0.335543 | + | 0.942025i | \(0.608920\pi\) | |||||||
\(294\) | −3.02011 | −0.176137 | ||||||||
\(295\) | −11.9242 | −0.694254 | ||||||||
\(296\) | 24.1630 | 1.40444 | ||||||||
\(297\) | −1.38475 | −0.0803513 | ||||||||
\(298\) | 27.9819 | 1.62095 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 10.3281 | 0.596291 | ||||||||
\(301\) | −10.0270 | −0.577949 | ||||||||
\(302\) | 48.2561 | 2.77683 | ||||||||
\(303\) | 2.07432 | 0.119167 | ||||||||
\(304\) | 17.8874 | 1.02591 | ||||||||
\(305\) | −59.5201 | −3.40811 | ||||||||
\(306\) | 9.72499 | 0.555941 | ||||||||
\(307\) | 19.5488 | 1.11571 | 0.557854 | − | 0.829939i | \(-0.311625\pi\) | ||||
0.557854 | + | 0.829939i | \(0.311625\pi\) | |||||||
\(308\) | −4.67946 | −0.266637 | ||||||||
\(309\) | −0.808264 | −0.0459805 | ||||||||
\(310\) | 10.2217 | 0.580553 | ||||||||
\(311\) | 5.53261 | 0.313726 | 0.156863 | − | 0.987620i | \(-0.449862\pi\) | ||||
0.156863 | + | 0.987620i | \(0.449862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.1821 | −1.02771 | −0.513855 | − | 0.857877i | \(-0.671783\pi\) | ||||
−0.513855 | + | 0.857877i | \(0.671783\pi\) | |||||||
\(314\) | 4.16691 | 0.235152 | ||||||||
\(315\) | −12.8075 | −0.721622 | ||||||||
\(316\) | 22.2774 | 1.25320 | ||||||||
\(317\) | 10.6759 | 0.599616 | 0.299808 | − | 0.954000i | \(-0.403077\pi\) | ||||
0.299808 | + | 0.954000i | \(0.403077\pi\) | |||||||
\(318\) | 2.37274 | 0.133057 | ||||||||
\(319\) | 0.385125 | 0.0215629 | ||||||||
\(320\) | 32.0989 | 1.79438 | ||||||||
\(321\) | 0.340086 | 0.0189817 | ||||||||
\(322\) | −14.6112 | −0.814251 | ||||||||
\(323\) | −5.78360 | −0.321808 | ||||||||
\(324\) | 34.6579 | 1.92544 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −45.8051 | −2.53691 | ||||||||
\(327\) | −2.30472 | −0.127451 | ||||||||
\(328\) | 37.6380 | 2.07821 | ||||||||
\(329\) | −3.89515 | −0.214747 | ||||||||
\(330\) | −2.37620 | −0.130806 | ||||||||
\(331\) | 20.8375 | 1.14533 | 0.572667 | − | 0.819788i | \(-0.305909\pi\) | ||||
0.572667 | + | 0.819788i | \(0.305909\pi\) | |||||||
\(332\) | −32.8393 | −1.80229 | ||||||||
\(333\) | −14.3819 | −0.788122 | ||||||||
\(334\) | −49.7417 | −2.72175 | ||||||||
\(335\) | −10.4271 | −0.569691 | ||||||||
\(336\) | −0.896259 | −0.0488950 | ||||||||
\(337\) | 4.66410 | 0.254070 | 0.127035 | − | 0.991898i | \(-0.459454\pi\) | ||||
0.127035 | + | 0.991898i | \(0.459454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.458257 | 0.0248891 | ||||||||
\(340\) | 22.4578 | 1.21795 | ||||||||
\(341\) | −1.11808 | −0.0605472 | ||||||||
\(342\) | −31.3205 | −1.69362 | ||||||||
\(343\) | 13.4360 | 0.725476 | ||||||||
\(344\) | 47.8914 | 2.58213 | ||||||||
\(345\) | −4.95617 | −0.266831 | ||||||||
\(346\) | 33.9003 | 1.82249 | ||||||||
\(347\) | −11.1380 | −0.597921 | −0.298961 | − | 0.954265i | \(-0.596640\pi\) | ||||
−0.298961 | + | 0.954265i | \(0.596640\pi\) | |||||||
\(348\) | 0.288188 | 0.0154485 | ||||||||
\(349\) | −33.6591 | −1.80173 | −0.900865 | − | 0.434100i | \(-0.857066\pi\) | ||||
−0.900865 | + | 0.434100i | \(0.857066\pi\) | |||||||
\(350\) | −31.5125 | −1.68441 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.264987 | 0.0141238 | ||||||||
\(353\) | 25.3844 | 1.35107 | 0.675537 | − | 0.737326i | \(-0.263912\pi\) | ||||
0.675537 | + | 0.737326i | \(0.263912\pi\) | |||||||
\(354\) | 1.46110 | 0.0776565 | ||||||||
\(355\) | −42.5618 | −2.25894 | ||||||||
\(356\) | −65.1366 | −3.45224 | ||||||||
\(357\) | 0.289791 | 0.0153374 | ||||||||
\(358\) | 58.0253 | 3.06673 | ||||||||
\(359\) | −16.0845 | −0.848905 | −0.424453 | − | 0.905450i | \(-0.639533\pi\) | ||||
−0.424453 | + | 0.905450i | \(0.639533\pi\) | |||||||
\(360\) | 61.1717 | 3.22403 | ||||||||
\(361\) | −0.373198 | −0.0196420 | ||||||||
\(362\) | −9.12759 | −0.479736 | ||||||||
\(363\) | −2.02716 | −0.106399 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.9986 | 3.08813 | ||||||||
\(366\) | 7.29313 | 0.381218 | ||||||||
\(367\) | 19.9241 | 1.04003 | 0.520015 | − | 0.854157i | \(-0.325926\pi\) | ||||
0.520015 | + | 0.854157i | \(0.325926\pi\) | |||||||
\(368\) | 23.7222 | 1.23661 | ||||||||
\(369\) | −22.4023 | −1.16622 | ||||||||
\(370\) | −49.7188 | −2.58476 | ||||||||
\(371\) | −4.83600 | −0.251073 | ||||||||
\(372\) | −0.836655 | −0.0433785 | ||||||||
\(373\) | 3.40010 | 0.176051 | 0.0880253 | − | 0.996118i | \(-0.471944\pi\) | ||||
0.0880253 | + | 0.996118i | \(0.471944\pi\) | |||||||
\(374\) | −3.67742 | −0.190155 | ||||||||
\(375\) | −6.35961 | −0.328409 | ||||||||
\(376\) | 18.6042 | 0.959436 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.16161 | 0.162616 | ||||||||
\(379\) | 34.0019 | 1.74656 | 0.873280 | − | 0.487219i | \(-0.161989\pi\) | ||||
0.873280 | + | 0.487219i | \(0.161989\pi\) | |||||||
\(380\) | −72.3282 | −3.71036 | ||||||||
\(381\) | −3.65437 | −0.187219 | ||||||||
\(382\) | 5.04604 | 0.258178 | ||||||||
\(383\) | 37.1546 | 1.89851 | 0.949255 | − | 0.314507i | \(-0.101839\pi\) | ||||
0.949255 | + | 0.314507i | \(0.101839\pi\) | |||||||
\(384\) | −4.03170 | −0.205742 | ||||||||
\(385\) | 4.84305 | 0.246825 | ||||||||
\(386\) | 38.1809 | 1.94336 | ||||||||
\(387\) | −28.5051 | −1.44900 | ||||||||
\(388\) | −22.8093 | −1.15797 | ||||||||
\(389\) | −21.5704 | −1.09366 | −0.546832 | − | 0.837243i | \(-0.684166\pi\) | ||||
−0.546832 | + | 0.837243i | \(0.684166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.67019 | −0.387898 | ||||||||
\(392\) | −29.3998 | −1.48491 | ||||||||
\(393\) | 3.84051 | 0.193728 | ||||||||
\(394\) | −17.3136 | −0.872245 | ||||||||
\(395\) | −23.0562 | −1.16008 | ||||||||
\(396\) | −13.3029 | −0.668497 | ||||||||
\(397\) | 17.4417 | 0.875376 | 0.437688 | − | 0.899127i | \(-0.355798\pi\) | ||||
0.437688 | + | 0.899127i | \(0.355798\pi\) | |||||||
\(398\) | −3.42868 | −0.171864 | ||||||||
\(399\) | −0.933308 | −0.0467238 | ||||||||
\(400\) | 51.1624 | 2.55812 | ||||||||
\(401\) | −21.7853 | −1.08791 | −0.543954 | − | 0.839115i | \(-0.683073\pi\) | ||||
−0.543954 | + | 0.839115i | \(0.683073\pi\) | |||||||
\(402\) | 1.27765 | 0.0637235 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 40.1463 | 1.99735 | ||||||||
\(405\) | −35.8695 | −1.78237 | ||||||||
\(406\) | −0.879305 | −0.0436392 | ||||||||
\(407\) | 5.43838 | 0.269570 | ||||||||
\(408\) | −1.38411 | −0.0685236 | ||||||||
\(409\) | −15.9720 | −0.789767 | −0.394883 | − | 0.918731i | \(-0.629215\pi\) | ||||
−0.394883 | + | 0.918731i | \(0.629215\pi\) | |||||||
\(410\) | −77.4457 | −3.82477 | ||||||||
\(411\) | −0.335354 | −0.0165418 | ||||||||
\(412\) | −15.6431 | −0.770679 | ||||||||
\(413\) | −2.97794 | −0.146535 | ||||||||
\(414\) | −41.5372 | −2.04144 | ||||||||
\(415\) | 33.9873 | 1.66837 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.21231 | 0.206278 | ||||||||
\(418\) | 11.8436 | 0.579288 | ||||||||
\(419\) | 29.9022 | 1.46082 | 0.730408 | − | 0.683011i | \(-0.239330\pi\) | ||||
0.730408 | + | 0.683011i | \(0.239330\pi\) | |||||||
\(420\) | 3.62405 | 0.176835 | ||||||||
\(421\) | −14.0954 | −0.686968 | −0.343484 | − | 0.939159i | \(-0.611607\pi\) | ||||
−0.343484 | + | 0.939159i | \(0.611607\pi\) | |||||||
\(422\) | 18.0785 | 0.880047 | ||||||||
\(423\) | −11.0733 | −0.538400 | ||||||||
\(424\) | 23.0978 | 1.12173 | ||||||||
\(425\) | −16.5425 | −0.802431 | ||||||||
\(426\) | 5.21519 | 0.252677 | ||||||||
\(427\) | −14.8645 | −0.719343 | ||||||||
\(428\) | 6.58199 | 0.318153 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −98.5436 | −4.75220 | ||||||||
\(431\) | −5.21700 | −0.251294 | −0.125647 | − | 0.992075i | \(-0.540101\pi\) | ||||
−0.125647 | + | 0.992075i | \(0.540101\pi\) | |||||||
\(432\) | −5.13308 | −0.246965 | ||||||||
\(433\) | 6.72834 | 0.323343 | 0.161672 | − | 0.986845i | \(-0.448311\pi\) | ||||
0.161672 | + | 0.986845i | \(0.448311\pi\) | |||||||
\(434\) | 2.55276 | 0.122536 | ||||||||
\(435\) | −0.298263 | −0.0143006 | ||||||||
\(436\) | −44.6054 | −2.13621 | ||||||||
\(437\) | 24.7028 | 1.18170 | ||||||||
\(438\) | −7.22923 | −0.345426 | ||||||||
\(439\) | 9.04469 | 0.431680 | 0.215840 | − | 0.976429i | \(-0.430751\pi\) | ||||
0.215840 | + | 0.976429i | \(0.430751\pi\) | |||||||
\(440\) | −23.1315 | −1.10275 | ||||||||
\(441\) | 17.4989 | 0.833279 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8251 | −0.751872 | −0.375936 | − | 0.926646i | \(-0.622679\pi\) | ||||
−0.375936 | + | 0.926646i | \(0.622679\pi\) | |||||||
\(444\) | 4.06953 | 0.193131 | ||||||||
\(445\) | 67.4137 | 3.19572 | ||||||||
\(446\) | −12.5164 | −0.592671 | ||||||||
\(447\) | 2.37041 | 0.112116 | ||||||||
\(448\) | 8.01634 | 0.378736 | ||||||||
\(449\) | −7.32916 | −0.345884 | −0.172942 | − | 0.984932i | \(-0.555327\pi\) | ||||
−0.172942 | + | 0.984932i | \(0.555327\pi\) | |||||||
\(450\) | −89.5845 | −4.22305 | ||||||||
\(451\) | 8.47122 | 0.398894 | ||||||||
\(452\) | 8.86906 | 0.417166 | ||||||||
\(453\) | 4.08788 | 0.192065 | ||||||||
\(454\) | −0.981047 | −0.0460428 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.45769 | 0.208751 | ||||||||
\(457\) | −21.2855 | −0.995692 | −0.497846 | − | 0.867265i | \(-0.665876\pi\) | ||||
−0.497846 | + | 0.867265i | \(0.665876\pi\) | |||||||
\(458\) | −26.0234 | −1.21599 | ||||||||
\(459\) | 1.65970 | 0.0774680 | ||||||||
\(460\) | −95.9213 | −4.47236 | ||||||||
\(461\) | −39.2985 | −1.83032 | −0.915158 | − | 0.403096i | \(-0.867934\pi\) | ||||
−0.915158 | + | 0.403096i | \(0.867934\pi\) | |||||||
\(462\) | −0.593430 | −0.0276089 | ||||||||
\(463\) | 39.2252 | 1.82295 | 0.911474 | − | 0.411358i | \(-0.134946\pi\) | ||||
0.911474 | + | 0.411358i | \(0.134946\pi\) | |||||||
\(464\) | 1.42761 | 0.0662749 | ||||||||
\(465\) | 0.865903 | 0.0401553 | ||||||||
\(466\) | 22.7043 | 1.05176 | ||||||||
\(467\) | 1.51386 | 0.0700531 | 0.0350266 | − | 0.999386i | \(-0.488848\pi\) | ||||
0.0350266 | + | 0.999386i | \(0.488848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.60404 | −0.120244 | ||||||||
\(470\) | −38.2808 | −1.76576 | ||||||||
\(471\) | 0.352989 | 0.0162649 | ||||||||
\(472\) | 14.2233 | 0.654681 | ||||||||
\(473\) | 10.7790 | 0.495617 | ||||||||
\(474\) | 2.82513 | 0.129762 | ||||||||
\(475\) | 53.2773 | 2.44453 | ||||||||
\(476\) | 5.60859 | 0.257069 | ||||||||
\(477\) | −13.7479 | −0.629474 | ||||||||
\(478\) | 59.2633 | 2.71064 | ||||||||
\(479\) | −31.1067 | −1.42130 | −0.710651 | − | 0.703545i | \(-0.751599\pi\) | ||||
−0.710651 | + | 0.703545i | \(0.751599\pi\) | |||||||
\(480\) | −0.205221 | −0.00936701 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −25.2980 | −1.15229 | ||||||||
\(483\) | −1.23775 | −0.0563195 | ||||||||
\(484\) | −39.2336 | −1.78334 | ||||||||
\(485\) | 23.6067 | 1.07193 | ||||||||
\(486\) | 13.5145 | 0.613030 | ||||||||
\(487\) | 5.43917 | 0.246472 | 0.123236 | − | 0.992377i | \(-0.460673\pi\) | ||||
0.123236 | + | 0.992377i | \(0.460673\pi\) | |||||||
\(488\) | 70.9962 | 3.21385 | ||||||||
\(489\) | −3.88026 | −0.175471 | ||||||||
\(490\) | 60.4944 | 2.73286 | ||||||||
\(491\) | −23.9384 | −1.08033 | −0.540163 | − | 0.841560i | \(-0.681637\pi\) | ||||
−0.540163 | + | 0.841560i | \(0.681637\pi\) | |||||||
\(492\) | 6.33900 | 0.285784 | ||||||||
\(493\) | −0.461593 | −0.0207891 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.7680 | 0.618824 | ||||||||
\(496\) | −4.14456 | −0.186096 | ||||||||
\(497\) | −10.6293 | −0.476791 | ||||||||
\(498\) | −4.16455 | −0.186618 | ||||||||
\(499\) | 39.9518 | 1.78849 | 0.894245 | − | 0.447578i | \(-0.147713\pi\) | ||||
0.894245 | + | 0.447578i | \(0.147713\pi\) | |||||||
\(500\) | −123.083 | −5.50446 | ||||||||
\(501\) | −4.21374 | −0.188256 | ||||||||
\(502\) | 18.9713 | 0.846729 | ||||||||
\(503\) | 10.4197 | 0.464590 | 0.232295 | − | 0.972645i | \(-0.425376\pi\) | ||||
0.232295 | + | 0.972645i | \(0.425376\pi\) | |||||||
\(504\) | 15.2770 | 0.680490 | ||||||||
\(505\) | −41.5498 | −1.84894 | ||||||||
\(506\) | 15.7069 | 0.698257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −70.7265 | −3.13798 | ||||||||
\(509\) | −27.2062 | −1.20589 | −0.602947 | − | 0.797781i | \(-0.706007\pi\) | ||||
−0.602947 | + | 0.797781i | \(0.706007\pi\) | |||||||
\(510\) | 2.84801 | 0.126112 | ||||||||
\(511\) | 14.7343 | 0.651805 | ||||||||
\(512\) | −40.1953 | −1.77640 | ||||||||
\(513\) | −5.34526 | −0.235999 | ||||||||
\(514\) | 64.6181 | 2.85018 | ||||||||
\(515\) | 16.1899 | 0.713414 | ||||||||
\(516\) | 8.06588 | 0.355081 | ||||||||
\(517\) | 4.18725 | 0.184155 | ||||||||
\(518\) | −12.4167 | −0.545560 | ||||||||
\(519\) | 2.87177 | 0.126057 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.34101 | −0.146372 | −0.0731862 | − | 0.997318i | \(-0.523317\pi\) | ||||
−0.0731862 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(522\) | −2.49971 | −0.109410 | ||||||||
\(523\) | −0.695895 | −0.0304294 | −0.0152147 | − | 0.999884i | \(-0.504843\pi\) | ||||
−0.0152147 | + | 0.999884i | \(0.504843\pi\) | |||||||
\(524\) | 74.3289 | 3.24707 | ||||||||
\(525\) | −2.66949 | −0.116506 | ||||||||
\(526\) | 50.3083 | 2.19355 | ||||||||
\(527\) | 1.34008 | 0.0583746 | ||||||||
\(528\) | 0.963470 | 0.0419297 | ||||||||
\(529\) | 9.76076 | 0.424381 | ||||||||
\(530\) | −47.5272 | −2.06445 | ||||||||
\(531\) | −8.46577 | −0.367383 | ||||||||
\(532\) | −18.0632 | −0.783137 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.26036 | −0.357461 | ||||||||
\(535\) | −6.81209 | −0.294512 | ||||||||
\(536\) | 12.4375 | 0.537219 | ||||||||
\(537\) | 4.91546 | 0.212118 | ||||||||
\(538\) | −22.2210 | −0.958017 | ||||||||
\(539\) | −6.61704 | −0.285016 | ||||||||
\(540\) | 20.7557 | 0.893184 | ||||||||
\(541\) | −11.2139 | −0.482124 | −0.241062 | − | 0.970510i | \(-0.577496\pi\) | ||||
−0.241062 | + | 0.970510i | \(0.577496\pi\) | |||||||
\(542\) | −14.9420 | −0.641815 | ||||||||
\(543\) | −0.773219 | −0.0331820 | ||||||||
\(544\) | −0.317601 | −0.0136170 | ||||||||
\(545\) | 46.1647 | 1.97748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5206 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(548\) | −6.49042 | −0.277257 | ||||||||
\(549\) | −42.2572 | −1.80349 | ||||||||
\(550\) | 33.8756 | 1.44446 | ||||||||
\(551\) | 1.48662 | 0.0633321 | ||||||||
\(552\) | 5.91177 | 0.251622 | ||||||||
\(553\) | −5.75803 | −0.244856 | ||||||||
\(554\) | −65.8114 | −2.79606 | ||||||||
\(555\) | −4.21180 | −0.178781 | ||||||||
\(556\) | 81.5246 | 3.45741 | ||||||||
\(557\) | 18.9343 | 0.802273 | 0.401136 | − | 0.916018i | \(-0.368615\pi\) | ||||
0.401136 | + | 0.916018i | \(0.368615\pi\) | |||||||
\(558\) | 7.25705 | 0.307215 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17.9525 | 0.758633 | ||||||||
\(561\) | −0.311522 | −0.0131525 | ||||||||
\(562\) | 70.7394 | 2.98396 | ||||||||
\(563\) | −34.1120 | −1.43765 | −0.718825 | − | 0.695191i | \(-0.755320\pi\) | ||||
−0.718825 | + | 0.695191i | \(0.755320\pi\) | |||||||
\(564\) | 3.13331 | 0.131936 | ||||||||
\(565\) | −9.17911 | −0.386168 | ||||||||
\(566\) | −0.370284 | −0.0155642 | ||||||||
\(567\) | −8.95801 | −0.376201 | ||||||||
\(568\) | 50.7681 | 2.13018 | ||||||||
\(569\) | 27.2991 | 1.14444 | 0.572219 | − | 0.820101i | \(-0.306083\pi\) | ||||
0.572219 | + | 0.820101i | \(0.306083\pi\) | |||||||
\(570\) | −9.17236 | −0.384188 | ||||||||
\(571\) | −4.86991 | −0.203800 | −0.101900 | − | 0.994795i | \(-0.532492\pi\) | ||||
−0.101900 | + | 0.994795i | \(0.532492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.427461 | 0.0178574 | ||||||||
\(574\) | −19.3412 | −0.807287 | ||||||||
\(575\) | 70.6561 | 2.94656 | ||||||||
\(576\) | 22.7891 | 0.949545 | ||||||||
\(577\) | 37.6235 | 1.56629 | 0.783144 | − | 0.621841i | \(-0.213615\pi\) | ||||
0.783144 | + | 0.621841i | \(0.213615\pi\) | |||||||
\(578\) | −37.3169 | −1.55218 | ||||||||
\(579\) | 3.23439 | 0.134417 | ||||||||
\(580\) | −5.77256 | −0.239693 | ||||||||
\(581\) | 8.48796 | 0.352140 | ||||||||
\(582\) | −2.89258 | −0.119901 | ||||||||
\(583\) | 5.19865 | 0.215306 | ||||||||
\(584\) | −70.3742 | −2.91210 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.1938 | −1.16468 | ||||||||
\(587\) | −6.78936 | −0.280227 | −0.140113 | − | 0.990135i | \(-0.544747\pi\) | ||||
−0.140113 | + | 0.990135i | \(0.544747\pi\) | |||||||
\(588\) | −4.95152 | −0.204197 | ||||||||
\(589\) | −4.31588 | −0.177833 | ||||||||
\(590\) | −29.2666 | −1.20488 | ||||||||
\(591\) | −1.46667 | −0.0603308 | ||||||||
\(592\) | 20.1593 | 0.828543 | ||||||||
\(593\) | −0.409434 | −0.0168134 | −0.00840671 | − | 0.999965i | \(-0.502676\pi\) | ||||
−0.00840671 | + | 0.999965i | \(0.502676\pi\) | |||||||
\(594\) | −3.39870 | −0.139451 | ||||||||
\(595\) | −5.80466 | −0.237968 | ||||||||
\(596\) | 45.8767 | 1.87918 | ||||||||
\(597\) | −0.290451 | −0.0118874 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.629813 | −0.0257335 | −0.0128667 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128667 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(600\) | 12.7501 | 0.520521 | ||||||||
\(601\) | −28.2438 | −1.15209 | −0.576045 | − | 0.817418i | \(-0.695405\pi\) | ||||
−0.576045 | + | 0.817418i | \(0.695405\pi\) | |||||||
\(602\) | −24.6102 | −1.00304 | ||||||||
\(603\) | −7.40285 | −0.301467 | ||||||||
\(604\) | 79.1165 | 3.21921 | ||||||||
\(605\) | 40.6051 | 1.65083 | ||||||||
\(606\) | 5.09119 | 0.206815 | ||||||||
\(607\) | −26.3757 | −1.07056 | −0.535279 | − | 0.844676i | \(-0.679793\pi\) | ||||
−0.535279 | + | 0.844676i | \(0.679793\pi\) | |||||||
\(608\) | 1.02287 | 0.0414830 | ||||||||
\(609\) | −0.0744879 | −0.00301840 | ||||||||
\(610\) | −146.085 | −5.91482 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.9443 | 0.644509 | ||||||||
\(613\) | −8.84762 | −0.357352 | −0.178676 | − | 0.983908i | \(-0.557181\pi\) | ||||
−0.178676 | + | 0.983908i | \(0.557181\pi\) | |||||||
\(614\) | 47.9802 | 1.93632 | ||||||||
\(615\) | −6.56060 | −0.264549 | ||||||||
\(616\) | −5.77684 | −0.232756 | ||||||||
\(617\) | −22.6953 | −0.913678 | −0.456839 | − | 0.889549i | \(-0.651018\pi\) | ||||
−0.456839 | + | 0.889549i | \(0.651018\pi\) | |||||||
\(618\) | −1.98379 | −0.0797997 | ||||||||
\(619\) | −4.67069 | −0.187731 | −0.0938655 | − | 0.995585i | \(-0.529922\pi\) | ||||
−0.0938655 | + | 0.995585i | \(0.529922\pi\) | |||||||
\(620\) | 16.7586 | 0.673042 | ||||||||
\(621\) | −7.08886 | −0.284466 | ||||||||
\(622\) | 13.5792 | 0.544474 | ||||||||
\(623\) | 16.8358 | 0.674514 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 65.6638 | 2.62655 | ||||||||
\(626\) | −44.6257 | −1.78360 | ||||||||
\(627\) | 1.00330 | 0.0400678 | ||||||||
\(628\) | 6.83171 | 0.272615 | ||||||||
\(629\) | −6.51819 | −0.259897 | ||||||||
\(630\) | −31.4346 | −1.25238 | ||||||||
\(631\) | 2.63073 | 0.104728 | 0.0523639 | − | 0.998628i | \(-0.483324\pi\) | ||||
0.0523639 | + | 0.998628i | \(0.483324\pi\) | |||||||
\(632\) | 27.5017 | 1.09396 | ||||||||
\(633\) | 1.53147 | 0.0608705 | ||||||||
\(634\) | 26.2027 | 1.04064 | ||||||||
\(635\) | 73.1990 | 2.90481 | ||||||||
\(636\) | 3.89014 | 0.154254 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.945244 | 0.0374226 | ||||||||
\(639\) | −30.2174 | −1.19538 | ||||||||
\(640\) | 80.7570 | 3.19220 | ||||||||
\(641\) | 37.7307 | 1.49027 | 0.745137 | − | 0.666912i | \(-0.232384\pi\) | ||||
0.745137 | + | 0.666912i | \(0.232384\pi\) | |||||||
\(642\) | 0.834701 | 0.0329430 | ||||||||
\(643\) | −24.6775 | −0.973186 | −0.486593 | − | 0.873629i | \(-0.661761\pi\) | ||||
−0.486593 | + | 0.873629i | \(0.661761\pi\) | |||||||
\(644\) | −23.9553 | −0.943971 | ||||||||
\(645\) | −8.34785 | −0.328696 | ||||||||
\(646\) | −14.1952 | −0.558502 | ||||||||
\(647\) | −38.9825 | −1.53256 | −0.766281 | − | 0.642506i | \(-0.777895\pi\) | ||||
−0.766281 | + | 0.642506i | \(0.777895\pi\) | |||||||
\(648\) | 42.7855 | 1.68077 | ||||||||
\(649\) | 3.20125 | 0.125660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.216250 | 0.00847550 | ||||||||
\(652\) | −75.0982 | −2.94107 | ||||||||
\(653\) | −31.1789 | −1.22012 | −0.610062 | − | 0.792353i | \(-0.708856\pi\) | ||||
−0.610062 | + | 0.792353i | \(0.708856\pi\) | |||||||
\(654\) | −5.65667 | −0.221193 | ||||||||
\(655\) | −76.9273 | −3.00580 | ||||||||
\(656\) | 31.4016 | 1.22603 | ||||||||
\(657\) | 41.8869 | 1.63417 | ||||||||
\(658\) | −9.56020 | −0.372695 | ||||||||
\(659\) | 37.6542 | 1.46680 | 0.733400 | − | 0.679797i | \(-0.237932\pi\) | ||||
0.733400 | + | 0.679797i | \(0.237932\pi\) | |||||||
\(660\) | −3.89582 | −0.151644 | ||||||||
\(661\) | −30.7355 | −1.19547 | −0.597735 | − | 0.801693i | \(-0.703933\pi\) | ||||
−0.597735 | + | 0.801693i | \(0.703933\pi\) | |||||||
\(662\) | 51.1432 | 1.98774 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.5405 | −1.57328 | ||||||||
\(665\) | 18.6946 | 0.724947 | ||||||||
\(666\) | −35.2986 | −1.36779 | ||||||||
\(667\) | 1.97155 | 0.0763386 | ||||||||
\(668\) | −81.5523 | −3.15535 | ||||||||
\(669\) | −1.06030 | −0.0409934 | ||||||||
\(670\) | −25.5920 | −0.988706 | ||||||||
\(671\) | 15.9792 | 0.616870 | ||||||||
\(672\) | −0.0512517 | −0.00197708 | ||||||||
\(673\) | −42.5188 | −1.63898 | −0.819489 | − | 0.573095i | \(-0.805743\pi\) | ||||
−0.819489 | + | 0.573095i | \(0.805743\pi\) | |||||||
\(674\) | 11.4475 | 0.440941 | ||||||||
\(675\) | −15.2888 | −0.588465 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.5135 | 0.673100 | 0.336550 | − | 0.941666i | \(-0.390740\pi\) | ||||
0.336550 | + | 0.941666i | \(0.390740\pi\) | |||||||
\(678\) | 1.12474 | 0.0431953 | ||||||||
\(679\) | 5.89552 | 0.226249 | ||||||||
\(680\) | 27.7244 | 1.06318 | ||||||||
\(681\) | −0.0831067 | −0.00318466 | ||||||||
\(682\) | −2.74419 | −0.105080 | ||||||||
\(683\) | 3.13849 | 0.120091 | 0.0600454 | − | 0.998196i | \(-0.480875\pi\) | ||||
0.0600454 | + | 0.998196i | \(0.480875\pi\) | |||||||
\(684\) | −51.3505 | −1.96343 | ||||||||
\(685\) | 6.71732 | 0.256656 | ||||||||
\(686\) | 32.9771 | 1.25907 | ||||||||
\(687\) | −2.20450 | −0.0841070 | ||||||||
\(688\) | 39.9561 | 1.52331 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −12.1643 | −0.463089 | ||||||||
\(691\) | 32.7355 | 1.24532 | 0.622659 | − | 0.782493i | \(-0.286052\pi\) | ||||
0.622659 | + | 0.782493i | \(0.286052\pi\) | |||||||
\(692\) | 55.5800 | 2.11283 | ||||||||
\(693\) | 3.43840 | 0.130614 | ||||||||
\(694\) | −27.3370 | −1.03770 | ||||||||
\(695\) | −84.3746 | −3.20051 | ||||||||
\(696\) | 0.355772 | 0.0134855 | ||||||||
\(697\) | −10.1532 | −0.384580 | ||||||||
\(698\) | −82.6123 | −3.12692 | ||||||||
\(699\) | 1.92334 | 0.0727473 | ||||||||
\(700\) | −51.6651 | −1.95276 | ||||||||
\(701\) | −0.516921 | −0.0195238 | −0.00976192 | − | 0.999952i | \(-0.503107\pi\) | ||||
−0.00976192 | + | 0.999952i | \(0.503107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9926 | 0.791752 | ||||||||
\(704\) | −8.61748 | −0.324784 | ||||||||
\(705\) | −3.24285 | −0.122133 | ||||||||
\(706\) | 62.3030 | 2.34481 | ||||||||
\(707\) | −10.3766 | −0.390252 | ||||||||
\(708\) | 2.39549 | 0.0900281 | ||||||||
\(709\) | 20.7453 | 0.779106 | 0.389553 | − | 0.921004i | \(-0.372629\pi\) | ||||
0.389553 | + | 0.921004i | \(0.372629\pi\) | |||||||
\(710\) | −104.463 | −3.92042 | ||||||||
\(711\) | −16.3691 | −0.613889 | ||||||||
\(712\) | −80.4118 | −3.01356 | ||||||||
\(713\) | −5.72370 | −0.214354 | ||||||||
\(714\) | 0.711258 | 0.0266182 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 95.1333 | 3.55530 | ||||||||
\(717\) | 5.02033 | 0.187488 | ||||||||
\(718\) | −39.4774 | −1.47328 | ||||||||
\(719\) | −24.1492 | −0.900612 | −0.450306 | − | 0.892874i | \(-0.648685\pi\) | ||||
−0.450306 | + | 0.892874i | \(0.648685\pi\) | |||||||
\(720\) | 51.0360 | 1.90200 | ||||||||
\(721\) | 4.04326 | 0.150579 | ||||||||
\(722\) | −0.915972 | −0.0340889 | ||||||||
\(723\) | −2.14305 | −0.0797011 | ||||||||
\(724\) | −14.9648 | −0.556163 | ||||||||
\(725\) | 4.25210 | 0.157919 | ||||||||
\(726\) | −4.97544 | −0.184656 | ||||||||
\(727\) | 3.70241 | 0.137315 | 0.0686574 | − | 0.997640i | \(-0.478128\pi\) | ||||
0.0686574 | + | 0.997640i | \(0.478128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.6936 | −0.914577 | ||||||||
\(730\) | 144.805 | 5.35948 | ||||||||
\(731\) | −12.9192 | −0.477833 | ||||||||
\(732\) | 11.9572 | 0.441951 | ||||||||
\(733\) | −31.7795 | −1.17380 | −0.586901 | − | 0.809659i | \(-0.699652\pi\) | ||||
−0.586901 | + | 0.809659i | \(0.699652\pi\) | |||||||
\(734\) | 48.9014 | 1.80498 | ||||||||
\(735\) | 5.12462 | 0.189024 | ||||||||
\(736\) | 1.35653 | 0.0500024 | ||||||||
\(737\) | 2.79932 | 0.103114 | ||||||||
\(738\) | −54.9837 | −2.02398 | ||||||||
\(739\) | −6.01212 | −0.221159 | −0.110580 | − | 0.993867i | \(-0.535271\pi\) | ||||
−0.110580 | + | 0.993867i | \(0.535271\pi\) | |||||||
\(740\) | −81.5148 | −2.99654 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.8694 | −0.435739 | ||||||||
\(743\) | 46.0440 | 1.68919 | 0.844596 | − | 0.535405i | \(-0.179841\pi\) | ||||
0.844596 | + | 0.535405i | \(0.179841\pi\) | |||||||
\(744\) | −1.03286 | −0.0378664 | ||||||||
\(745\) | −47.4805 | −1.73955 | ||||||||
\(746\) | 8.34515 | 0.305538 | ||||||||
\(747\) | 24.1298 | 0.882864 | ||||||||
\(748\) | −6.02918 | −0.220449 | ||||||||
\(749\) | −1.70125 | −0.0621621 | ||||||||
\(750\) | −15.6089 | −0.569957 | ||||||||
\(751\) | −24.8216 | −0.905754 | −0.452877 | − | 0.891573i | \(-0.649602\pi\) | ||||
−0.452877 | + | 0.891573i | \(0.649602\pi\) | |||||||
\(752\) | 15.5216 | 0.566014 | ||||||||
\(753\) | 1.60710 | 0.0585660 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −81.8823 | −2.98000 | ||||||||
\(756\) | 5.18351 | 0.188523 | ||||||||
\(757\) | −32.0615 | −1.16529 | −0.582647 | − | 0.812725i | \(-0.697983\pi\) | ||||
−0.582647 | + | 0.812725i | \(0.697983\pi\) | |||||||
\(758\) | 83.4537 | 3.03117 | ||||||||
\(759\) | 1.33057 | 0.0482966 | ||||||||
\(760\) | −89.2898 | −3.23888 | ||||||||
\(761\) | −36.4847 | −1.32257 | −0.661285 | − | 0.750135i | \(-0.729989\pi\) | ||||
−0.661285 | + | 0.750135i | \(0.729989\pi\) | |||||||
\(762\) | −8.96924 | −0.324921 | ||||||||
\(763\) | 11.5291 | 0.417383 | ||||||||
\(764\) | 8.27305 | 0.299308 | ||||||||
\(765\) | −16.5017 | −0.596618 | ||||||||
\(766\) | 91.1916 | 3.29489 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −6.69034 | −0.241417 | ||||||||
\(769\) | 14.0881 | 0.508028 | 0.254014 | − | 0.967201i | \(-0.418249\pi\) | ||||
0.254014 | + | 0.967201i | \(0.418249\pi\) | |||||||
\(770\) | 11.8867 | 0.428367 | ||||||||
\(771\) | 5.47395 | 0.197139 | ||||||||
\(772\) | 62.5981 | 2.25296 | ||||||||
\(773\) | −24.5626 | −0.883456 | −0.441728 | − | 0.897149i | \(-0.645634\pi\) | ||||
−0.441728 | + | 0.897149i | \(0.645634\pi\) | |||||||
\(774\) | −69.9625 | −2.51475 | ||||||||
\(775\) | −12.3445 | −0.443427 | ||||||||
\(776\) | −28.1583 | −1.01083 | ||||||||
\(777\) | −1.05185 | −0.0377349 | ||||||||
\(778\) | −52.9420 | −1.89806 | ||||||||
\(779\) | 32.6997 | 1.17159 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4264 | 0.408870 | ||||||||
\(782\) | −18.8256 | −0.673202 | ||||||||
\(783\) | −0.426609 | −0.0152458 | ||||||||
\(784\) | −24.5284 | −0.876016 | ||||||||
\(785\) | −7.07054 | −0.252358 | ||||||||
\(786\) | 9.42607 | 0.336217 | ||||||||
\(787\) | 40.6555 | 1.44921 | 0.724606 | − | 0.689163i | \(-0.242022\pi\) | ||||
0.724606 | + | 0.689163i | \(0.242022\pi\) | |||||||
\(788\) | −28.3858 | −1.01120 | ||||||||
\(789\) | 4.26173 | 0.151722 | ||||||||
\(790\) | −56.5887 | −2.01334 | ||||||||
\(791\) | −2.29238 | −0.0815077 | ||||||||
\(792\) | −16.4226 | −0.583551 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 42.8087 | 1.51922 | ||||||||
\(795\) | −4.02614 | −0.142792 | ||||||||
\(796\) | −5.62137 | −0.199244 | ||||||||
\(797\) | −42.5066 | −1.50566 | −0.752830 | − | 0.658215i | \(-0.771312\pi\) | ||||
−0.752830 | + | 0.658215i | \(0.771312\pi\) | |||||||
\(798\) | −2.29069 | −0.0810897 | ||||||||
\(799\) | −5.01865 | −0.177547 | ||||||||
\(800\) | 2.92567 | 0.103438 | ||||||||
\(801\) | 47.8614 | 1.69110 | ||||||||
\(802\) | −53.4696 | −1.88808 | ||||||||
\(803\) | −15.8392 | −0.558952 | ||||||||
\(804\) | 2.09473 | 0.0738754 | ||||||||
\(805\) | 24.7927 | 0.873830 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.88239 | −0.0662634 | ||||||||
\(808\) | 49.5610 | 1.74355 | ||||||||
\(809\) | 29.7674 | 1.04657 | 0.523283 | − | 0.852159i | \(-0.324707\pi\) | ||||
0.523283 | + | 0.852159i | \(0.324707\pi\) | |||||||
\(810\) | −88.0375 | −3.09332 | ||||||||
\(811\) | −4.12585 | −0.144878 | −0.0724391 | − | 0.997373i | \(-0.523078\pi\) | ||||
−0.0724391 | + | 0.997373i | \(0.523078\pi\) | |||||||
\(812\) | −1.44163 | −0.0505914 | ||||||||
\(813\) | −1.26577 | −0.0443926 | ||||||||
\(814\) | 13.3479 | 0.467842 | ||||||||
\(815\) | 77.7235 | 2.72254 | ||||||||
\(816\) | −1.15477 | −0.0404251 | ||||||||
\(817\) | 41.6078 | 1.45567 | ||||||||
\(818\) | −39.2015 | −1.37065 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −126.973 | −4.43410 | ||||||||
\(821\) | −7.42162 | −0.259016 | −0.129508 | − | 0.991578i | \(-0.541340\pi\) | ||||
−0.129508 | + | 0.991578i | \(0.541340\pi\) | |||||||
\(822\) | −0.823088 | −0.0287085 | ||||||||
\(823\) | 8.95935 | 0.312303 | 0.156152 | − | 0.987733i | \(-0.450091\pi\) | ||||
0.156152 | + | 0.987733i | \(0.450091\pi\) | |||||||
\(824\) | −19.3115 | −0.672749 | ||||||||
\(825\) | 2.86968 | 0.0999093 | ||||||||
\(826\) | −7.30900 | −0.254313 | ||||||||
\(827\) | 35.6188 | 1.23859 | 0.619293 | − | 0.785160i | \(-0.287419\pi\) | ||||
0.619293 | + | 0.785160i | \(0.287419\pi\) | |||||||
\(828\) | −68.1008 | −2.36667 | ||||||||
\(829\) | −2.80274 | −0.0973432 | −0.0486716 | − | 0.998815i | \(-0.515499\pi\) | ||||
−0.0486716 | + | 0.998815i | \(0.515499\pi\) | |||||||
\(830\) | 83.4180 | 2.89548 | ||||||||
\(831\) | −5.57503 | −0.193396 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.93088 | 0.274789 | ||||||||
\(834\) | 10.3386 | 0.357997 | ||||||||
\(835\) | 84.4033 | 2.92090 | ||||||||
\(836\) | 19.4177 | 0.671576 | ||||||||
\(837\) | 1.23851 | 0.0428092 | ||||||||
\(838\) | 73.3914 | 2.53526 | ||||||||
\(839\) | 50.7990 | 1.75378 | 0.876888 | − | 0.480695i | \(-0.159616\pi\) | ||||
0.876888 | + | 0.480695i | \(0.159616\pi\) | |||||||
\(840\) | 4.47392 | 0.154365 | ||||||||
\(841\) | −28.8814 | −0.995909 | ||||||||
\(842\) | −34.5955 | −1.19224 | ||||||||
\(843\) | 5.99250 | 0.206393 | ||||||||
\(844\) | 29.6400 | 1.02025 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.1780 | −0.934399 | ||||||||
\(847\) | 10.1407 | 0.348438 | ||||||||
\(848\) | 19.2707 | 0.661758 | ||||||||
\(849\) | −0.0313676 | −0.00107653 | ||||||||
\(850\) | −40.6017 | −1.39263 | ||||||||
\(851\) | 27.8404 | 0.954355 | ||||||||
\(852\) | 8.55038 | 0.292931 | ||||||||
\(853\) | −38.5243 | −1.31905 | −0.659524 | − | 0.751684i | \(-0.729242\pi\) | ||||
−0.659524 | + | 0.751684i | \(0.729242\pi\) | |||||||
\(854\) | −36.4832 | −1.24843 | ||||||||
\(855\) | 53.1456 | 1.81754 | ||||||||
\(856\) | 8.12554 | 0.277725 | ||||||||
\(857\) | 36.5220 | 1.24757 | 0.623784 | − | 0.781597i | \(-0.285594\pi\) | ||||
0.623784 | + | 0.781597i | \(0.285594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.2640 | 0.350203 | 0.175102 | − | 0.984550i | \(-0.443975\pi\) | ||||
0.175102 | + | 0.984550i | \(0.443975\pi\) | |||||||
\(860\) | −161.564 | −5.50928 | ||||||||
\(861\) | −1.63844 | −0.0558378 | ||||||||
\(862\) | −12.8045 | −0.436124 | ||||||||
\(863\) | −0.506664 | −0.0172471 | −0.00862353 | − | 0.999963i | \(-0.502745\pi\) | ||||
−0.00862353 | + | 0.999963i | \(0.502745\pi\) | |||||||
\(864\) | −0.293530 | −0.00998608 | ||||||||
\(865\) | −57.5230 | −1.95584 | ||||||||
\(866\) | 16.5139 | 0.561166 | ||||||||
\(867\) | −3.16120 | −0.107360 | ||||||||
\(868\) | 4.18528 | 0.142058 | ||||||||
\(869\) | 6.18983 | 0.209975 | ||||||||
\(870\) | −0.732052 | −0.0248189 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −55.0658 | −1.86476 | ||||||||
\(873\) | 16.7599 | 0.567238 | ||||||||
\(874\) | 60.6301 | 2.05084 | ||||||||
\(875\) | 31.8133 | 1.07549 | ||||||||
\(876\) | −11.8524 | −0.400457 | ||||||||
\(877\) | 13.4804 | 0.455200 | 0.227600 | − | 0.973755i | \(-0.426912\pi\) | ||||
0.227600 | + | 0.973755i | \(0.426912\pi\) | |||||||
\(878\) | 22.1991 | 0.749185 | ||||||||
\(879\) | −2.38836 | −0.0805575 | ||||||||
\(880\) | −19.2988 | −0.650562 | ||||||||
\(881\) | 43.1217 | 1.45281 | 0.726403 | − | 0.687269i | \(-0.241191\pi\) | ||||
0.726403 | + | 0.687269i | \(0.241191\pi\) | |||||||
\(882\) | 42.9489 | 1.44616 | ||||||||
\(883\) | −23.7848 | −0.800422 | −0.400211 | − | 0.916423i | \(-0.631063\pi\) | ||||
−0.400211 | + | 0.916423i | \(0.631063\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.47924 | −0.0833386 | ||||||||
\(886\) | −38.8408 | −1.30488 | ||||||||
\(887\) | −4.15323 | −0.139452 | −0.0697260 | − | 0.997566i | \(-0.522212\pi\) | ||||
−0.0697260 | + | 0.997566i | \(0.522212\pi\) | |||||||
\(888\) | 5.02387 | 0.168590 | ||||||||
\(889\) | 18.2806 | 0.613113 | ||||||||
\(890\) | 165.459 | 5.54620 | ||||||||
\(891\) | 9.62978 | 0.322610 | ||||||||
\(892\) | −20.5209 | −0.687091 | ||||||||
\(893\) | 16.1632 | 0.540880 | ||||||||
\(894\) | 5.81789 | 0.194579 | ||||||||
\(895\) | −98.4591 | −3.29112 | ||||||||
\(896\) | 20.1682 | 0.673771 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.9886 | −0.600286 | ||||||||
\(899\) | −0.344453 | −0.0114882 | ||||||||
\(900\) | −146.875 | −4.89584 | ||||||||
\(901\) | −6.23087 | −0.207580 | ||||||||
\(902\) | 20.7916 | 0.692285 | ||||||||
\(903\) | −2.08478 | −0.0693773 | ||||||||
\(904\) | 10.9489 | 0.364156 | ||||||||
\(905\) | 15.4880 | 0.514838 | ||||||||
\(906\) | 10.0332 | 0.333332 | ||||||||
\(907\) | 5.73296 | 0.190360 | 0.0951799 | − | 0.995460i | \(-0.469657\pi\) | ||||
0.0951799 | + | 0.995460i | \(0.469657\pi\) | |||||||
\(908\) | −1.60844 | −0.0533780 | ||||||||
\(909\) | −29.4989 | −0.978416 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.5918 | −0.649106 | −0.324553 | − | 0.945868i | \(-0.605214\pi\) | ||||
−0.324553 | + | 0.945868i | \(0.605214\pi\) | |||||||
\(912\) | 3.71908 | 0.123151 | ||||||||
\(913\) | −9.12448 | −0.301976 | ||||||||
\(914\) | −52.2427 | −1.72804 | ||||||||
\(915\) | −12.3752 | −0.409112 | ||||||||
\(916\) | −42.6657 | −1.40972 | ||||||||
\(917\) | −19.2117 | −0.634428 | ||||||||
\(918\) | 4.07353 | 0.134447 | ||||||||
\(919\) | −29.5074 | −0.973361 | −0.486680 | − | 0.873580i | \(-0.661792\pi\) | ||||
−0.486680 | + | 0.873580i | \(0.661792\pi\) | |||||||
\(920\) | −118.416 | −3.90405 | ||||||||
\(921\) | 4.06451 | 0.133930 | ||||||||
\(922\) | −96.4537 | −3.17653 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.972937 | −0.0320073 | ||||||||
\(925\) | 60.0442 | 1.97424 | ||||||||
\(926\) | 96.2736 | 3.16375 | ||||||||
\(927\) | 11.4943 | 0.377522 | ||||||||
\(928\) | 0.0816362 | 0.00267984 | ||||||||
\(929\) | 30.3220 | 0.994833 | 0.497417 | − | 0.867512i | \(-0.334282\pi\) | ||||
0.497417 | + | 0.867512i | \(0.334282\pi\) | |||||||
\(930\) | 2.12526 | 0.0696900 | ||||||||
\(931\) | −25.5424 | −0.837117 | ||||||||
\(932\) | 37.2241 | 1.21932 | ||||||||
\(933\) | 1.15032 | 0.0376598 | ||||||||
\(934\) | 3.71559 | 0.121578 | ||||||||
\(935\) | 6.23995 | 0.204068 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2399 | 1.57593 | 0.787964 | − | 0.615721i | \(-0.211135\pi\) | ||||
0.787964 | + | 0.615721i | \(0.211135\pi\) | |||||||
\(938\) | −6.39132 | −0.208684 | ||||||||
\(939\) | −3.78035 | −0.123367 | ||||||||
\(940\) | −62.7619 | −2.04707 | ||||||||
\(941\) | −22.9378 | −0.747752 | −0.373876 | − | 0.927479i | \(-0.621972\pi\) | ||||
−0.373876 | + | 0.927479i | \(0.621972\pi\) | |||||||
\(942\) | 0.866369 | 0.0282278 | ||||||||
\(943\) | 43.3662 | 1.41220 | ||||||||
\(944\) | 11.8666 | 0.386225 | ||||||||
\(945\) | −5.36472 | −0.174514 | ||||||||
\(946\) | 26.4557 | 0.860149 | ||||||||
\(947\) | 3.17540 | 0.103187 | 0.0515934 | − | 0.998668i | \(-0.483570\pi\) | ||||
0.0515934 | + | 0.998668i | \(0.483570\pi\) | |||||||
\(948\) | 4.63184 | 0.150435 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 130.763 | 4.24251 | ||||||||
\(951\) | 2.21969 | 0.0719783 | ||||||||
\(952\) | 6.92386 | 0.224404 | ||||||||
\(953\) | 49.7271 | 1.61082 | 0.805409 | − | 0.592720i | \(-0.201946\pi\) | ||||
0.805409 | + | 0.592720i | \(0.201946\pi\) | |||||||
\(954\) | −33.7427 | −1.09246 | ||||||||
\(955\) | −8.56226 | −0.277068 | ||||||||
\(956\) | 97.1631 | 3.14248 | ||||||||
\(957\) | 0.0800738 | 0.00258842 | ||||||||
\(958\) | −76.3478 | −2.46668 | ||||||||
\(959\) | 1.67758 | 0.0541718 | ||||||||
\(960\) | 6.67388 | 0.215398 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.83635 | −0.155849 | ||||||||
\(964\) | −41.4765 | −1.33587 | ||||||||
\(965\) | −64.7865 | −2.08555 | ||||||||
\(966\) | −3.03791 | −0.0977432 | ||||||||
\(967\) | 27.3485 | 0.879468 | 0.439734 | − | 0.898128i | \(-0.355073\pi\) | ||||
0.439734 | + | 0.898128i | \(0.355073\pi\) | |||||||
\(968\) | −48.4342 | −1.55674 | ||||||||
\(969\) | −1.20251 | −0.0386300 | ||||||||
\(970\) | 57.9399 | 1.86034 | ||||||||
\(971\) | 13.4045 | 0.430171 | 0.215085 | − | 0.976595i | \(-0.430997\pi\) | ||||
0.215085 | + | 0.976595i | \(0.430997\pi\) | |||||||
\(972\) | 22.1572 | 0.710693 | ||||||||
\(973\) | −21.0716 | −0.675526 | ||||||||
\(974\) | 13.3498 | 0.427756 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 59.2326 | 1.89599 | ||||||||
\(977\) | −17.2034 | −0.550386 | −0.275193 | − | 0.961389i | \(-0.588742\pi\) | ||||
−0.275193 | + | 0.961389i | \(0.588742\pi\) | |||||||
\(978\) | −9.52364 | −0.304532 | ||||||||
\(979\) | −18.0984 | −0.578426 | ||||||||
\(980\) | 99.1814 | 3.16823 | ||||||||
\(981\) | 32.7754 | 1.04644 | ||||||||
\(982\) | −58.7541 | −1.87492 | ||||||||
\(983\) | −3.44470 | −0.109869 | −0.0549344 | − | 0.998490i | \(-0.517495\pi\) | ||||
−0.0549344 | + | 0.998490i | \(0.517495\pi\) | |||||||
\(984\) | 7.82555 | 0.249470 | ||||||||
\(985\) | 29.3782 | 0.936067 | ||||||||
\(986\) | −1.13293 | −0.0360797 | ||||||||
\(987\) | −0.809866 | −0.0257783 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.1801 | 1.75463 | ||||||||
\(990\) | 33.7919 | 1.07398 | ||||||||
\(991\) | 12.3189 | 0.391322 | 0.195661 | − | 0.980672i | \(-0.437315\pi\) | ||||
0.195661 | + | 0.980672i | \(0.437315\pi\) | |||||||
\(992\) | −0.237002 | −0.00752483 | ||||||||
\(993\) | 4.33246 | 0.137486 | ||||||||
\(994\) | −26.0885 | −0.827476 | ||||||||
\(995\) | 5.81788 | 0.184439 | ||||||||
\(996\) | −6.82783 | −0.216348 | ||||||||
\(997\) | 4.03242 | 0.127708 | 0.0638540 | − | 0.997959i | \(-0.479661\pi\) | ||||
0.0638540 | + | 0.997959i | \(0.479661\pi\) | |||||||
\(998\) | 98.0571 | 3.10394 | ||||||||
\(999\) | −6.02417 | −0.190596 |
(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 | 5239.2.a.u.1.49 | ✓ | 54 | |
13.12 | even | 2 | 5239.2.a.v.1.6 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5239.2.a.u.1.49 | ✓ | 54 | 1.1 | even | 1 | trivial | |
5239.2.a.v.1.6 | yes | 54 | 13.12 | even | 2 |