Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22059 | −1.57020 | −0.785099 | − | 0.619371i | \(-0.787388\pi\) | ||||
−0.785099 | + | 0.619371i | \(0.787388\pi\) | |||||||
\(3\) | −3.23881 | −1.86993 | −0.934964 | − | 0.354741i | \(-0.884569\pi\) | ||||
−0.934964 | + | 0.354741i | \(0.884569\pi\) | |||||||
\(4\) | 2.93104 | 1.46552 | ||||||||
\(5\) | −1.33112 | −0.595294 | −0.297647 | − | 0.954676i | \(-0.596202\pi\) | ||||
−0.297647 | + | 0.954676i | \(0.596202\pi\) | |||||||
\(6\) | 7.19209 | 2.93616 | ||||||||
\(7\) | −0.932335 | −0.352389 | −0.176195 | − | 0.984355i | \(-0.556379\pi\) | ||||
−0.176195 | + | 0.984355i | \(0.556379\pi\) | |||||||
\(8\) | −2.06746 | −0.730958 | ||||||||
\(9\) | 7.48990 | 2.49663 | ||||||||
\(10\) | 2.95587 | 0.934729 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −9.49308 | −2.74042 | ||||||||
\(13\) | 4.80259 | 1.33200 | 0.666000 | − | 0.745952i | \(-0.268005\pi\) | ||||
0.666000 | + | 0.745952i | \(0.268005\pi\) | |||||||
\(14\) | 2.07034 | 0.553321 | ||||||||
\(15\) | 4.31124 | 1.11316 | ||||||||
\(16\) | −1.27109 | −0.317772 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −16.6320 | −3.92021 | ||||||||
\(19\) | 0.807270 | 0.185201 | 0.0926003 | − | 0.995703i | \(-0.470482\pi\) | ||||
0.0926003 | + | 0.995703i | \(0.470482\pi\) | |||||||
\(20\) | −3.90156 | −0.872415 | ||||||||
\(21\) | 3.01966 | 0.658943 | ||||||||
\(22\) | −2.22059 | −0.473432 | ||||||||
\(23\) | −8.62067 | −1.79753 | −0.898767 | − | 0.438427i | \(-0.855536\pi\) | ||||
−0.898767 | + | 0.438427i | \(0.855536\pi\) | |||||||
\(24\) | 6.69612 | 1.36684 | ||||||||
\(25\) | −3.22813 | −0.645625 | ||||||||
\(26\) | −10.6646 | −2.09150 | ||||||||
\(27\) | −14.5419 | −2.79860 | ||||||||
\(28\) | −2.73271 | −0.516434 | ||||||||
\(29\) | −7.30946 | −1.35733 | −0.678667 | − | 0.734446i | \(-0.737442\pi\) | ||||
−0.678667 | + | 0.734446i | \(0.737442\pi\) | |||||||
\(30\) | −9.57351 | −1.74788 | ||||||||
\(31\) | 8.01755 | 1.43999 | 0.719997 | − | 0.693977i | \(-0.244143\pi\) | ||||
0.719997 | + | 0.693977i | \(0.244143\pi\) | |||||||
\(32\) | 6.95749 | 1.22992 | ||||||||
\(33\) | −3.23881 | −0.563805 | ||||||||
\(34\) | −2.22059 | −0.380829 | ||||||||
\(35\) | 1.24105 | 0.209775 | ||||||||
\(36\) | 21.9532 | 3.65887 | ||||||||
\(37\) | −10.7508 | −1.76742 | −0.883712 | − | 0.468030i | \(-0.844964\pi\) | ||||
−0.883712 | + | 0.468030i | \(0.844964\pi\) | |||||||
\(38\) | −1.79262 | −0.290801 | ||||||||
\(39\) | −15.5547 | −2.49074 | ||||||||
\(40\) | 2.75203 | 0.435135 | ||||||||
\(41\) | 8.36668 | 1.30666 | 0.653328 | − | 0.757075i | \(-0.273372\pi\) | ||||
0.653328 | + | 0.757075i | \(0.273372\pi\) | |||||||
\(42\) | −6.70543 | −1.03467 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 2.93104 | 0.441871 | ||||||||
\(45\) | −9.96994 | −1.48623 | ||||||||
\(46\) | 19.1430 | 2.82248 | ||||||||
\(47\) | 11.5760 | 1.68854 | 0.844268 | − | 0.535920i | \(-0.180035\pi\) | ||||
0.844268 | + | 0.535920i | \(0.180035\pi\) | |||||||
\(48\) | 4.11681 | 0.594211 | ||||||||
\(49\) | −6.13075 | −0.875822 | ||||||||
\(50\) | 7.16836 | 1.01376 | ||||||||
\(51\) | −3.23881 | −0.453524 | ||||||||
\(52\) | 14.0766 | 1.95207 | ||||||||
\(53\) | 10.7135 | 1.47162 | 0.735808 | − | 0.677190i | \(-0.236803\pi\) | ||||
0.735808 | + | 0.677190i | \(0.236803\pi\) | |||||||
\(54\) | 32.2918 | 4.39435 | ||||||||
\(55\) | −1.33112 | −0.179488 | ||||||||
\(56\) | 1.92757 | 0.257582 | ||||||||
\(57\) | −2.61460 | −0.346312 | ||||||||
\(58\) | 16.2314 | 2.13128 | ||||||||
\(59\) | 10.2059 | 1.32870 | 0.664349 | − | 0.747423i | \(-0.268709\pi\) | ||||
0.664349 | + | 0.747423i | \(0.268709\pi\) | |||||||
\(60\) | 12.6364 | 1.63135 | ||||||||
\(61\) | −0.149587 | −0.0191527 | −0.00957636 | − | 0.999954i | \(-0.503048\pi\) | ||||
−0.00957636 | + | 0.999954i | \(0.503048\pi\) | |||||||
\(62\) | −17.8037 | −2.26108 | ||||||||
\(63\) | −6.98310 | −0.879788 | ||||||||
\(64\) | −12.9076 | −1.61345 | ||||||||
\(65\) | −6.39281 | −0.792931 | ||||||||
\(66\) | 7.19209 | 0.885285 | ||||||||
\(67\) | −9.07168 | −1.10828 | −0.554141 | − | 0.832423i | \(-0.686953\pi\) | ||||
−0.554141 | + | 0.832423i | \(0.686953\pi\) | |||||||
\(68\) | 2.93104 | 0.355441 | ||||||||
\(69\) | 27.9207 | 3.36126 | ||||||||
\(70\) | −2.75586 | −0.329389 | ||||||||
\(71\) | 10.2411 | 1.21540 | 0.607700 | − | 0.794167i | \(-0.292093\pi\) | ||||
0.607700 | + | 0.794167i | \(0.292093\pi\) | |||||||
\(72\) | −15.4851 | −1.82493 | ||||||||
\(73\) | 13.5574 | 1.58677 | 0.793387 | − | 0.608718i | \(-0.208316\pi\) | ||||
0.793387 | + | 0.608718i | \(0.208316\pi\) | |||||||
\(74\) | 23.8732 | 2.77521 | ||||||||
\(75\) | 10.4553 | 1.20727 | ||||||||
\(76\) | 2.36614 | 0.271415 | ||||||||
\(77\) | −0.932335 | −0.106249 | ||||||||
\(78\) | 34.5407 | 3.91096 | ||||||||
\(79\) | 2.14236 | 0.241034 | 0.120517 | − | 0.992711i | \(-0.461545\pi\) | ||||
0.120517 | + | 0.992711i | \(0.461545\pi\) | |||||||
\(80\) | 1.69197 | 0.189168 | ||||||||
\(81\) | 24.6289 | 2.73655 | ||||||||
\(82\) | −18.5790 | −2.05171 | ||||||||
\(83\) | 8.57869 | 0.941634 | 0.470817 | − | 0.882231i | \(-0.343959\pi\) | ||||
0.470817 | + | 0.882231i | \(0.343959\pi\) | |||||||
\(84\) | 8.85073 | 0.965694 | ||||||||
\(85\) | −1.33112 | −0.144380 | ||||||||
\(86\) | −2.22059 | −0.239453 | ||||||||
\(87\) | 23.6740 | 2.53812 | ||||||||
\(88\) | −2.06746 | −0.220392 | ||||||||
\(89\) | −8.59733 | −0.911315 | −0.455658 | − | 0.890155i | \(-0.650596\pi\) | ||||
−0.455658 | + | 0.890155i | \(0.650596\pi\) | |||||||
\(90\) | 22.1392 | 2.33368 | ||||||||
\(91\) | −4.47762 | −0.469383 | ||||||||
\(92\) | −25.2675 | −2.63432 | ||||||||
\(93\) | −25.9673 | −2.69269 | ||||||||
\(94\) | −25.7057 | −2.65134 | ||||||||
\(95\) | −1.07457 | −0.110249 | ||||||||
\(96\) | −22.5340 | −2.29987 | ||||||||
\(97\) | −19.2144 | −1.95092 | −0.975461 | − | 0.220170i | \(-0.929339\pi\) | ||||
−0.975461 | + | 0.220170i | \(0.929339\pi\) | |||||||
\(98\) | 13.6139 | 1.37521 | ||||||||
\(99\) | 7.48990 | 0.752763 | ||||||||
\(100\) | −9.46176 | −0.946176 | ||||||||
\(101\) | 11.7453 | 1.16870 | 0.584349 | − | 0.811503i | \(-0.301350\pi\) | ||||
0.584349 | + | 0.811503i | \(0.301350\pi\) | |||||||
\(102\) | 7.19209 | 0.712123 | ||||||||
\(103\) | 0.676477 | 0.0666553 | 0.0333276 | − | 0.999444i | \(-0.489390\pi\) | ||||
0.0333276 | + | 0.999444i | \(0.489390\pi\) | |||||||
\(104\) | −9.92917 | −0.973635 | ||||||||
\(105\) | −4.01952 | −0.392265 | ||||||||
\(106\) | −23.7904 | −2.31073 | ||||||||
\(107\) | −7.43546 | −0.718813 | −0.359406 | − | 0.933181i | \(-0.617021\pi\) | ||||
−0.359406 | + | 0.933181i | \(0.617021\pi\) | |||||||
\(108\) | −42.6230 | −4.10140 | ||||||||
\(109\) | −14.3239 | −1.37198 | −0.685990 | − | 0.727611i | \(-0.740630\pi\) | ||||
−0.685990 | + | 0.727611i | \(0.740630\pi\) | |||||||
\(110\) | 2.95587 | 0.281831 | ||||||||
\(111\) | 34.8199 | 3.30496 | ||||||||
\(112\) | 1.18508 | 0.111979 | ||||||||
\(113\) | −12.6686 | −1.19176 | −0.595879 | − | 0.803074i | \(-0.703196\pi\) | ||||
−0.595879 | + | 0.803074i | \(0.703196\pi\) | |||||||
\(114\) | 5.80596 | 0.543778 | ||||||||
\(115\) | 11.4751 | 1.07006 | ||||||||
\(116\) | −21.4243 | −1.98920 | ||||||||
\(117\) | 35.9709 | 3.32551 | ||||||||
\(118\) | −22.6632 | −2.08632 | ||||||||
\(119\) | −0.932335 | −0.0854670 | ||||||||
\(120\) | −8.91332 | −0.813671 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.332173 | 0.0300735 | ||||||||
\(123\) | −27.0981 | −2.44336 | ||||||||
\(124\) | 23.4998 | 2.11034 | ||||||||
\(125\) | 10.9526 | 0.979631 | ||||||||
\(126\) | 15.5066 | 1.38144 | ||||||||
\(127\) | 10.5483 | 0.936013 | 0.468007 | − | 0.883725i | \(-0.344972\pi\) | ||||
0.468007 | + | 0.883725i | \(0.344972\pi\) | |||||||
\(128\) | 14.7475 | 1.30351 | ||||||||
\(129\) | −3.23881 | −0.285161 | ||||||||
\(130\) | 14.1958 | 1.24506 | ||||||||
\(131\) | 9.37849 | 0.819403 | 0.409701 | − | 0.912220i | \(-0.365633\pi\) | ||||
0.409701 | + | 0.912220i | \(0.365633\pi\) | |||||||
\(132\) | −9.49308 | −0.826267 | ||||||||
\(133\) | −0.752646 | −0.0652627 | ||||||||
\(134\) | 20.1445 | 1.74022 | ||||||||
\(135\) | 19.3570 | 1.66599 | ||||||||
\(136\) | −2.06746 | −0.177283 | ||||||||
\(137\) | −5.92747 | −0.506418 | −0.253209 | − | 0.967412i | \(-0.581486\pi\) | ||||
−0.253209 | + | 0.967412i | \(0.581486\pi\) | |||||||
\(138\) | −62.0006 | −5.27784 | ||||||||
\(139\) | −1.05055 | −0.0891066 | −0.0445533 | − | 0.999007i | \(-0.514186\pi\) | ||||
−0.0445533 | + | 0.999007i | \(0.514186\pi\) | |||||||
\(140\) | 3.63756 | 0.307430 | ||||||||
\(141\) | −37.4926 | −3.15744 | ||||||||
\(142\) | −22.7414 | −1.90842 | ||||||||
\(143\) | 4.80259 | 0.401613 | ||||||||
\(144\) | −9.52032 | −0.793360 | ||||||||
\(145\) | 9.72975 | 0.808012 | ||||||||
\(146\) | −30.1055 | −2.49155 | ||||||||
\(147\) | 19.8564 | 1.63772 | ||||||||
\(148\) | −31.5111 | −2.59020 | ||||||||
\(149\) | 8.26366 | 0.676985 | 0.338493 | − | 0.940969i | \(-0.390083\pi\) | ||||
0.338493 | + | 0.940969i | \(0.390083\pi\) | |||||||
\(150\) | −23.2170 | −1.89566 | ||||||||
\(151\) | 9.80243 | 0.797710 | 0.398855 | − | 0.917014i | \(-0.369408\pi\) | ||||
0.398855 | + | 0.917014i | \(0.369408\pi\) | |||||||
\(152\) | −1.66900 | −0.135374 | ||||||||
\(153\) | 7.48990 | 0.605523 | ||||||||
\(154\) | 2.07034 | 0.166833 | ||||||||
\(155\) | −10.6723 | −0.857220 | ||||||||
\(156\) | −45.5914 | −3.65023 | ||||||||
\(157\) | −10.6114 | −0.846884 | −0.423442 | − | 0.905923i | \(-0.639178\pi\) | ||||
−0.423442 | + | 0.905923i | \(0.639178\pi\) | |||||||
\(158\) | −4.75731 | −0.378471 | ||||||||
\(159\) | −34.6991 | −2.75182 | ||||||||
\(160\) | −9.26124 | −0.732165 | ||||||||
\(161\) | 8.03735 | 0.633432 | ||||||||
\(162\) | −54.6909 | −4.29692 | ||||||||
\(163\) | −17.3561 | −1.35943 | −0.679716 | − | 0.733475i | \(-0.737897\pi\) | ||||
−0.679716 | + | 0.733475i | \(0.737897\pi\) | |||||||
\(164\) | 24.5231 | 1.91493 | ||||||||
\(165\) | 4.31124 | 0.335630 | ||||||||
\(166\) | −19.0498 | −1.47855 | ||||||||
\(167\) | −21.3077 | −1.64884 | −0.824421 | − | 0.565978i | \(-0.808499\pi\) | ||||
−0.824421 | + | 0.565978i | \(0.808499\pi\) | |||||||
\(168\) | −6.24302 | −0.481660 | ||||||||
\(169\) | 10.0649 | 0.774222 | ||||||||
\(170\) | 2.95587 | 0.226705 | ||||||||
\(171\) | 6.04638 | 0.462378 | ||||||||
\(172\) | 2.93104 | 0.223490 | ||||||||
\(173\) | 24.2718 | 1.84535 | 0.922676 | − | 0.385575i | \(-0.125997\pi\) | ||||
0.922676 | + | 0.385575i | \(0.125997\pi\) | |||||||
\(174\) | −52.5703 | −3.98534 | ||||||||
\(175\) | 3.00969 | 0.227512 | ||||||||
\(176\) | −1.27109 | −0.0958118 | ||||||||
\(177\) | −33.0551 | −2.48457 | ||||||||
\(178\) | 19.0912 | 1.43094 | ||||||||
\(179\) | 11.1232 | 0.831389 | 0.415694 | − | 0.909504i | \(-0.363539\pi\) | ||||
0.415694 | + | 0.909504i | \(0.363539\pi\) | |||||||
\(180\) | −29.2223 | −2.17810 | ||||||||
\(181\) | −6.48195 | −0.481799 | −0.240900 | − | 0.970550i | \(-0.577442\pi\) | ||||
−0.240900 | + | 0.970550i | \(0.577442\pi\) | |||||||
\(182\) | 9.94299 | 0.737023 | ||||||||
\(183\) | 0.484486 | 0.0358142 | ||||||||
\(184\) | 17.8229 | 1.31392 | ||||||||
\(185\) | 14.3106 | 1.05214 | ||||||||
\(186\) | 57.6629 | 4.22805 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 33.9298 | 2.47458 | ||||||||
\(189\) | 13.5580 | 0.986197 | ||||||||
\(190\) | 2.38619 | 0.173112 | ||||||||
\(191\) | 5.43991 | 0.393618 | 0.196809 | − | 0.980442i | \(-0.436942\pi\) | ||||
0.196809 | + | 0.980442i | \(0.436942\pi\) | |||||||
\(192\) | 41.8053 | 3.01703 | ||||||||
\(193\) | −4.53753 | −0.326619 | −0.163309 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163309 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(194\) | 42.6673 | 3.06333 | ||||||||
\(195\) | 20.7051 | 1.48272 | ||||||||
\(196\) | −17.9695 | −1.28353 | ||||||||
\(197\) | −16.0137 | −1.14093 | −0.570466 | − | 0.821322i | \(-0.693237\pi\) | ||||
−0.570466 | + | 0.821322i | \(0.693237\pi\) | |||||||
\(198\) | −16.6320 | −1.18199 | ||||||||
\(199\) | 8.62260 | 0.611240 | 0.305620 | − | 0.952154i | \(-0.401136\pi\) | ||||
0.305620 | + | 0.952154i | \(0.401136\pi\) | |||||||
\(200\) | 6.67402 | 0.471925 | ||||||||
\(201\) | 29.3815 | 2.07241 | ||||||||
\(202\) | −26.0815 | −1.83509 | ||||||||
\(203\) | 6.81487 | 0.478310 | ||||||||
\(204\) | −9.49308 | −0.664649 | ||||||||
\(205\) | −11.1370 | −0.777845 | ||||||||
\(206\) | −1.50218 | −0.104662 | ||||||||
\(207\) | −64.5680 | −4.48778 | ||||||||
\(208\) | −6.10451 | −0.423272 | ||||||||
\(209\) | 0.807270 | 0.0558401 | ||||||||
\(210\) | 8.92572 | 0.615933 | ||||||||
\(211\) | 17.3751 | 1.19615 | 0.598074 | − | 0.801441i | \(-0.295933\pi\) | ||||
0.598074 | + | 0.801441i | \(0.295933\pi\) | |||||||
\(212\) | 31.4018 | 2.15668 | ||||||||
\(213\) | −33.1691 | −2.27271 | ||||||||
\(214\) | 16.5111 | 1.12868 | ||||||||
\(215\) | −1.33112 | −0.0907815 | ||||||||
\(216\) | 30.0649 | 2.04566 | ||||||||
\(217\) | −7.47504 | −0.507439 | ||||||||
\(218\) | 31.8075 | 2.15428 | ||||||||
\(219\) | −43.9099 | −2.96715 | ||||||||
\(220\) | −3.90156 | −0.263043 | ||||||||
\(221\) | 4.80259 | 0.323057 | ||||||||
\(222\) | −77.3209 | −5.18944 | ||||||||
\(223\) | 15.5189 | 1.03922 | 0.519611 | − | 0.854403i | \(-0.326077\pi\) | ||||
0.519611 | + | 0.854403i | \(0.326077\pi\) | |||||||
\(224\) | −6.48671 | −0.433412 | ||||||||
\(225\) | −24.1783 | −1.61189 | ||||||||
\(226\) | 28.1318 | 1.87130 | ||||||||
\(227\) | −1.61241 | −0.107019 | −0.0535097 | − | 0.998567i | \(-0.517041\pi\) | ||||
−0.0535097 | + | 0.998567i | \(0.517041\pi\) | |||||||
\(228\) | −7.66349 | −0.507527 | ||||||||
\(229\) | −14.9324 | −0.986759 | −0.493380 | − | 0.869814i | \(-0.664239\pi\) | ||||
−0.493380 | + | 0.869814i | \(0.664239\pi\) | |||||||
\(230\) | −25.4816 | −1.68021 | ||||||||
\(231\) | 3.01966 | 0.198679 | ||||||||
\(232\) | 15.1120 | 0.992153 | ||||||||
\(233\) | 13.9882 | 0.916398 | 0.458199 | − | 0.888850i | \(-0.348495\pi\) | ||||
0.458199 | + | 0.888850i | \(0.348495\pi\) | |||||||
\(234\) | −79.8769 | −5.22171 | ||||||||
\(235\) | −15.4091 | −1.00518 | ||||||||
\(236\) | 29.9140 | 1.94723 | ||||||||
\(237\) | −6.93870 | −0.450717 | ||||||||
\(238\) | 2.07034 | 0.134200 | ||||||||
\(239\) | 2.07630 | 0.134304 | 0.0671522 | − | 0.997743i | \(-0.478609\pi\) | ||||
0.0671522 | + | 0.997743i | \(0.478609\pi\) | |||||||
\(240\) | −5.47996 | −0.353730 | ||||||||
\(241\) | 16.4376 | 1.05884 | 0.529421 | − | 0.848359i | \(-0.322409\pi\) | ||||
0.529421 | + | 0.848359i | \(0.322409\pi\) | |||||||
\(242\) | −2.22059 | −0.142745 | ||||||||
\(243\) | −36.1426 | −2.31855 | ||||||||
\(244\) | −0.438447 | −0.0280687 | ||||||||
\(245\) | 8.16075 | 0.521371 | ||||||||
\(246\) | 60.1739 | 3.83655 | ||||||||
\(247\) | 3.87699 | 0.246687 | ||||||||
\(248\) | −16.5760 | −1.05257 | ||||||||
\(249\) | −27.7848 | −1.76079 | ||||||||
\(250\) | −24.3213 | −1.53821 | ||||||||
\(251\) | −23.5430 | −1.48602 | −0.743010 | − | 0.669281i | \(-0.766602\pi\) | ||||
−0.743010 | + | 0.669281i | \(0.766602\pi\) | |||||||
\(252\) | −20.4677 | −1.28935 | ||||||||
\(253\) | −8.62067 | −0.541977 | ||||||||
\(254\) | −23.4236 | −1.46973 | ||||||||
\(255\) | 4.31124 | 0.269980 | ||||||||
\(256\) | −6.93312 | −0.433320 | ||||||||
\(257\) | −1.99334 | −0.124341 | −0.0621705 | − | 0.998066i | \(-0.519802\pi\) | ||||
−0.0621705 | + | 0.998066i | \(0.519802\pi\) | |||||||
\(258\) | 7.19209 | 0.447760 | ||||||||
\(259\) | 10.0234 | 0.622822 | ||||||||
\(260\) | −18.7376 | −1.16206 | ||||||||
\(261\) | −54.7472 | −3.38876 | ||||||||
\(262\) | −20.8258 | −1.28662 | ||||||||
\(263\) | −18.8731 | −1.16376 | −0.581882 | − | 0.813273i | \(-0.697684\pi\) | ||||
−0.581882 | + | 0.813273i | \(0.697684\pi\) | |||||||
\(264\) | 6.69612 | 0.412117 | ||||||||
\(265\) | −14.2610 | −0.876044 | ||||||||
\(266\) | 1.67132 | 0.102475 | ||||||||
\(267\) | 27.8451 | 1.70409 | ||||||||
\(268\) | −26.5894 | −1.62421 | ||||||||
\(269\) | −19.1525 | −1.16775 | −0.583873 | − | 0.811845i | \(-0.698463\pi\) | ||||
−0.583873 | + | 0.811845i | \(0.698463\pi\) | |||||||
\(270\) | −42.9841 | −2.61593 | ||||||||
\(271\) | 9.31968 | 0.566130 | 0.283065 | − | 0.959101i | \(-0.408649\pi\) | ||||
0.283065 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(272\) | −1.27109 | −0.0770710 | ||||||||
\(273\) | 14.5022 | 0.877712 | ||||||||
\(274\) | 13.1625 | 0.795176 | ||||||||
\(275\) | −3.22813 | −0.194663 | ||||||||
\(276\) | 81.8367 | 4.92599 | ||||||||
\(277\) | 9.57319 | 0.575197 | 0.287599 | − | 0.957751i | \(-0.407143\pi\) | ||||
0.287599 | + | 0.957751i | \(0.407143\pi\) | |||||||
\(278\) | 2.33285 | 0.139915 | ||||||||
\(279\) | 60.0507 | 3.59514 | ||||||||
\(280\) | −2.56582 | −0.153337 | ||||||||
\(281\) | 3.93684 | 0.234852 | 0.117426 | − | 0.993082i | \(-0.462536\pi\) | ||||
0.117426 | + | 0.993082i | \(0.462536\pi\) | |||||||
\(282\) | 83.2558 | 4.95781 | ||||||||
\(283\) | 21.8578 | 1.29931 | 0.649654 | − | 0.760230i | \(-0.274914\pi\) | ||||
0.649654 | + | 0.760230i | \(0.274914\pi\) | |||||||
\(284\) | 30.0172 | 1.78119 | ||||||||
\(285\) | 3.48034 | 0.206157 | ||||||||
\(286\) | −10.6646 | −0.630612 | ||||||||
\(287\) | −7.80055 | −0.460452 | ||||||||
\(288\) | 52.1109 | 3.07067 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −21.6058 | −1.26874 | ||||||||
\(291\) | 62.2317 | 3.64809 | ||||||||
\(292\) | 39.7373 | 2.32545 | ||||||||
\(293\) | −17.4790 | −1.02113 | −0.510567 | − | 0.859838i | \(-0.670565\pi\) | ||||
−0.510567 | + | 0.859838i | \(0.670565\pi\) | |||||||
\(294\) | −44.0929 | −2.57155 | ||||||||
\(295\) | −13.5853 | −0.790966 | ||||||||
\(296\) | 22.2269 | 1.29191 | ||||||||
\(297\) | −14.5419 | −0.843809 | ||||||||
\(298\) | −18.3502 | −1.06300 | ||||||||
\(299\) | −41.4015 | −2.39431 | ||||||||
\(300\) | 30.6449 | 1.76928 | ||||||||
\(301\) | −0.932335 | −0.0537389 | ||||||||
\(302\) | −21.7672 | −1.25256 | ||||||||
\(303\) | −38.0407 | −2.18538 | ||||||||
\(304\) | −1.02611 | −0.0588515 | ||||||||
\(305\) | 0.199119 | 0.0114015 | ||||||||
\(306\) | −16.6320 | −0.950790 | ||||||||
\(307\) | 3.32392 | 0.189706 | 0.0948530 | − | 0.995491i | \(-0.469762\pi\) | ||||
0.0948530 | + | 0.995491i | \(0.469762\pi\) | |||||||
\(308\) | −2.73271 | −0.155711 | ||||||||
\(309\) | −2.19098 | −0.124641 | ||||||||
\(310\) | 23.6988 | 1.34600 | ||||||||
\(311\) | 14.0796 | 0.798379 | 0.399190 | − | 0.916868i | \(-0.369291\pi\) | ||||
0.399190 | + | 0.916868i | \(0.369291\pi\) | |||||||
\(312\) | 32.1587 | 1.82063 | ||||||||
\(313\) | −1.65434 | −0.0935086 | −0.0467543 | − | 0.998906i | \(-0.514888\pi\) | ||||
−0.0467543 | + | 0.998906i | \(0.514888\pi\) | |||||||
\(314\) | 23.5637 | 1.32977 | ||||||||
\(315\) | 9.29532 | 0.523732 | ||||||||
\(316\) | 6.27934 | 0.353240 | ||||||||
\(317\) | 9.77596 | 0.549072 | 0.274536 | − | 0.961577i | \(-0.411476\pi\) | ||||
0.274536 | + | 0.961577i | \(0.411476\pi\) | |||||||
\(318\) | 77.0526 | 4.32090 | ||||||||
\(319\) | −7.30946 | −0.409251 | ||||||||
\(320\) | 17.1815 | 0.960476 | ||||||||
\(321\) | 24.0820 | 1.34413 | ||||||||
\(322\) | −17.8477 | −0.994613 | ||||||||
\(323\) | 0.807270 | 0.0449177 | ||||||||
\(324\) | 72.1884 | 4.01046 | ||||||||
\(325\) | −15.5034 | −0.859972 | ||||||||
\(326\) | 38.5408 | 2.13458 | ||||||||
\(327\) | 46.3924 | 2.56550 | ||||||||
\(328\) | −17.2978 | −0.955111 | ||||||||
\(329\) | −10.7927 | −0.595023 | ||||||||
\(330\) | −9.57351 | −0.527005 | ||||||||
\(331\) | −7.80926 | −0.429236 | −0.214618 | − | 0.976698i | \(-0.568851\pi\) | ||||
−0.214618 | + | 0.976698i | \(0.568851\pi\) | |||||||
\(332\) | 25.1445 | 1.37998 | ||||||||
\(333\) | −80.5226 | −4.41261 | ||||||||
\(334\) | 47.3158 | 2.58901 | ||||||||
\(335\) | 12.0755 | 0.659753 | ||||||||
\(336\) | −3.83825 | −0.209394 | ||||||||
\(337\) | −8.72374 | −0.475213 | −0.237606 | − | 0.971362i | \(-0.576363\pi\) | ||||
−0.237606 | + | 0.971362i | \(0.576363\pi\) | |||||||
\(338\) | −22.3500 | −1.21568 | ||||||||
\(339\) | 41.0311 | 2.22850 | ||||||||
\(340\) | −3.90156 | −0.211592 | ||||||||
\(341\) | 8.01755 | 0.434175 | ||||||||
\(342\) | −13.4266 | −0.726025 | ||||||||
\(343\) | 12.2423 | 0.661020 | ||||||||
\(344\) | −2.06746 | −0.111470 | ||||||||
\(345\) | −37.1658 | −2.00094 | ||||||||
\(346\) | −53.8979 | −2.89757 | ||||||||
\(347\) | 14.5666 | 0.781976 | 0.390988 | − | 0.920396i | \(-0.372133\pi\) | ||||
0.390988 | + | 0.920396i | \(0.372133\pi\) | |||||||
\(348\) | 69.3894 | 3.71966 | ||||||||
\(349\) | −25.6913 | −1.37522 | −0.687612 | − | 0.726079i | \(-0.741341\pi\) | ||||
−0.687612 | + | 0.726079i | \(0.741341\pi\) | |||||||
\(350\) | −6.68331 | −0.357238 | ||||||||
\(351\) | −69.8390 | −3.72773 | ||||||||
\(352\) | 6.95749 | 0.370835 | ||||||||
\(353\) | 18.5988 | 0.989915 | 0.494958 | − | 0.868917i | \(-0.335184\pi\) | ||||
0.494958 | + | 0.868917i | \(0.335184\pi\) | |||||||
\(354\) | 73.4019 | 3.90126 | ||||||||
\(355\) | −13.6322 | −0.723520 | ||||||||
\(356\) | −25.1991 | −1.33555 | ||||||||
\(357\) | 3.01966 | 0.159817 | ||||||||
\(358\) | −24.7002 | −1.30544 | ||||||||
\(359\) | 3.74162 | 0.197475 | 0.0987375 | − | 0.995114i | \(-0.468520\pi\) | ||||
0.0987375 | + | 0.995114i | \(0.468520\pi\) | |||||||
\(360\) | 20.6125 | 1.08637 | ||||||||
\(361\) | −18.3483 | −0.965701 | ||||||||
\(362\) | 14.3938 | 0.756520 | ||||||||
\(363\) | −3.23881 | −0.169994 | ||||||||
\(364\) | −13.1241 | −0.687889 | ||||||||
\(365\) | −18.0465 | −0.944596 | ||||||||
\(366\) | −1.07585 | −0.0562354 | ||||||||
\(367\) | −13.3254 | −0.695581 | −0.347790 | − | 0.937572i | \(-0.613068\pi\) | ||||
−0.347790 | + | 0.937572i | \(0.613068\pi\) | |||||||
\(368\) | 10.9576 | 0.571205 | ||||||||
\(369\) | 62.6657 | 3.26224 | ||||||||
\(370\) | −31.7781 | −1.65206 | ||||||||
\(371\) | −9.98860 | −0.518582 | ||||||||
\(372\) | −76.1113 | −3.94619 | ||||||||
\(373\) | −26.2400 | −1.35866 | −0.679328 | − | 0.733834i | \(-0.737729\pi\) | ||||
−0.679328 | + | 0.733834i | \(0.737729\pi\) | |||||||
\(374\) | −2.22059 | −0.114824 | ||||||||
\(375\) | −35.4734 | −1.83184 | ||||||||
\(376\) | −23.9330 | −1.23425 | ||||||||
\(377\) | −35.1044 | −1.80797 | ||||||||
\(378\) | −30.1067 | −1.54852 | ||||||||
\(379\) | 25.4656 | 1.30808 | 0.654040 | − | 0.756460i | \(-0.273073\pi\) | ||||
0.654040 | + | 0.756460i | \(0.273073\pi\) | |||||||
\(380\) | −3.14961 | −0.161572 | ||||||||
\(381\) | −34.1641 | −1.75028 | ||||||||
\(382\) | −12.0798 | −0.618059 | ||||||||
\(383\) | −7.17364 | −0.366556 | −0.183278 | − | 0.983061i | \(-0.558671\pi\) | ||||
−0.183278 | + | 0.983061i | \(0.558671\pi\) | |||||||
\(384\) | −47.7645 | −2.43747 | ||||||||
\(385\) | 1.24105 | 0.0632496 | ||||||||
\(386\) | 10.0760 | 0.512856 | ||||||||
\(387\) | 7.48990 | 0.380733 | ||||||||
\(388\) | −56.3181 | −2.85912 | ||||||||
\(389\) | 16.9227 | 0.858012 | 0.429006 | − | 0.903302i | \(-0.358864\pi\) | ||||
0.429006 | + | 0.903302i | \(0.358864\pi\) | |||||||
\(390\) | −45.9777 | −2.32817 | ||||||||
\(391\) | −8.62067 | −0.435966 | ||||||||
\(392\) | 12.6751 | 0.640189 | ||||||||
\(393\) | −30.3752 | −1.53222 | ||||||||
\(394\) | 35.5600 | 1.79149 | ||||||||
\(395\) | −2.85173 | −0.143486 | ||||||||
\(396\) | 21.9532 | 1.10319 | ||||||||
\(397\) | −17.5239 | −0.879498 | −0.439749 | − | 0.898121i | \(-0.644933\pi\) | ||||
−0.439749 | + | 0.898121i | \(0.644933\pi\) | |||||||
\(398\) | −19.1473 | −0.959768 | ||||||||
\(399\) | 2.43768 | 0.122037 | ||||||||
\(400\) | 4.10323 | 0.205161 | ||||||||
\(401\) | −10.5042 | −0.524554 | −0.262277 | − | 0.964993i | \(-0.584473\pi\) | ||||
−0.262277 | + | 0.964993i | \(0.584473\pi\) | |||||||
\(402\) | −65.2443 | −3.25409 | ||||||||
\(403\) | 38.5050 | 1.91807 | ||||||||
\(404\) | 34.4258 | 1.71275 | ||||||||
\(405\) | −32.7840 | −1.62905 | ||||||||
\(406\) | −15.1331 | −0.751041 | ||||||||
\(407\) | −10.7508 | −0.532899 | ||||||||
\(408\) | 6.69612 | 0.331507 | ||||||||
\(409\) | −15.4454 | −0.763724 | −0.381862 | − | 0.924219i | \(-0.624717\pi\) | ||||
−0.381862 | + | 0.924219i | \(0.624717\pi\) | |||||||
\(410\) | 24.7309 | 1.22137 | ||||||||
\(411\) | 19.1980 | 0.946965 | ||||||||
\(412\) | 1.98278 | 0.0976846 | ||||||||
\(413\) | −9.51533 | −0.468219 | ||||||||
\(414\) | 143.379 | 7.04671 | ||||||||
\(415\) | −11.4192 | −0.560549 | ||||||||
\(416\) | 33.4140 | 1.63826 | ||||||||
\(417\) | 3.40254 | 0.166623 | ||||||||
\(418\) | −1.79262 | −0.0876799 | ||||||||
\(419\) | 11.3979 | 0.556826 | 0.278413 | − | 0.960461i | \(-0.410192\pi\) | ||||
0.278413 | + | 0.960461i | \(0.410192\pi\) | |||||||
\(420\) | −11.7814 | −0.574872 | ||||||||
\(421\) | −25.9949 | −1.26691 | −0.633457 | − | 0.773778i | \(-0.718365\pi\) | ||||
−0.633457 | + | 0.773778i | \(0.718365\pi\) | |||||||
\(422\) | −38.5830 | −1.87819 | ||||||||
\(423\) | 86.7033 | 4.21566 | ||||||||
\(424\) | −22.1498 | −1.07569 | ||||||||
\(425\) | −3.22813 | −0.156587 | ||||||||
\(426\) | 73.6551 | 3.56860 | ||||||||
\(427\) | 0.139466 | 0.00674921 | ||||||||
\(428\) | −21.7936 | −1.05343 | ||||||||
\(429\) | −15.5547 | −0.750988 | ||||||||
\(430\) | 2.95587 | 0.142545 | ||||||||
\(431\) | 22.2699 | 1.07271 | 0.536353 | − | 0.843994i | \(-0.319802\pi\) | ||||
0.536353 | + | 0.843994i | \(0.319802\pi\) | |||||||
\(432\) | 18.4841 | 0.889316 | ||||||||
\(433\) | 37.6567 | 1.80966 | 0.904832 | − | 0.425769i | \(-0.139996\pi\) | ||||
0.904832 | + | 0.425769i | \(0.139996\pi\) | |||||||
\(434\) | 16.5990 | 0.796779 | ||||||||
\(435\) | −31.5128 | −1.51093 | ||||||||
\(436\) | −41.9839 | −2.01066 | ||||||||
\(437\) | −6.95921 | −0.332904 | ||||||||
\(438\) | 97.5060 | 4.65902 | ||||||||
\(439\) | 15.9729 | 0.762347 | 0.381173 | − | 0.924504i | \(-0.375520\pi\) | ||||
0.381173 | + | 0.924504i | \(0.375520\pi\) | |||||||
\(440\) | 2.75203 | 0.131198 | ||||||||
\(441\) | −45.9187 | −2.18661 | ||||||||
\(442\) | −10.6646 | −0.507264 | ||||||||
\(443\) | −2.44955 | −0.116382 | −0.0581908 | − | 0.998305i | \(-0.518533\pi\) | ||||
−0.0581908 | + | 0.998305i | \(0.518533\pi\) | |||||||
\(444\) | 102.058 | 4.84348 | ||||||||
\(445\) | 11.4441 | 0.542500 | ||||||||
\(446\) | −34.4612 | −1.63178 | ||||||||
\(447\) | −26.7644 | −1.26591 | ||||||||
\(448\) | 12.0342 | 0.568562 | ||||||||
\(449\) | −20.0298 | −0.945265 | −0.472632 | − | 0.881260i | \(-0.656696\pi\) | ||||
−0.472632 | + | 0.881260i | \(0.656696\pi\) | |||||||
\(450\) | 53.6903 | 2.53099 | ||||||||
\(451\) | 8.36668 | 0.393972 | ||||||||
\(452\) | −37.1321 | −1.74655 | ||||||||
\(453\) | −31.7482 | −1.49166 | ||||||||
\(454\) | 3.58051 | 0.168041 | ||||||||
\(455\) | 5.96024 | 0.279421 | ||||||||
\(456\) | 5.40558 | 0.253139 | ||||||||
\(457\) | −22.2696 | −1.04173 | −0.520864 | − | 0.853640i | \(-0.674390\pi\) | ||||
−0.520864 | + | 0.853640i | \(0.674390\pi\) | |||||||
\(458\) | 33.1588 | 1.54941 | ||||||||
\(459\) | −14.5419 | −0.678760 | ||||||||
\(460\) | 33.6340 | 1.56819 | ||||||||
\(461\) | 1.41068 | 0.0657018 | 0.0328509 | − | 0.999460i | \(-0.489541\pi\) | ||||
0.0328509 | + | 0.999460i | \(0.489541\pi\) | |||||||
\(462\) | −6.70543 | −0.311965 | ||||||||
\(463\) | −25.3233 | −1.17687 | −0.588436 | − | 0.808544i | \(-0.700256\pi\) | ||||
−0.588436 | + | 0.808544i | \(0.700256\pi\) | |||||||
\(464\) | 9.29096 | 0.431322 | ||||||||
\(465\) | 34.5656 | 1.60294 | ||||||||
\(466\) | −31.0621 | −1.43893 | ||||||||
\(467\) | 0.313198 | 0.0144931 | 0.00724654 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724654 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(468\) | 105.432 | 4.87361 | ||||||||
\(469\) | 8.45784 | 0.390547 | ||||||||
\(470\) | 34.2173 | 1.57832 | ||||||||
\(471\) | 34.3684 | 1.58361 | ||||||||
\(472\) | −21.1003 | −0.971222 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 15.4080 | 0.707715 | ||||||||
\(475\) | −2.60597 | −0.119570 | ||||||||
\(476\) | −2.73271 | −0.125254 | ||||||||
\(477\) | 80.2433 | 3.67409 | ||||||||
\(478\) | −4.61061 | −0.210884 | ||||||||
\(479\) | −1.08888 | −0.0497524 | −0.0248762 | − | 0.999691i | \(-0.507919\pi\) | ||||
−0.0248762 | + | 0.999691i | \(0.507919\pi\) | |||||||
\(480\) | 29.9954 | 1.36910 | ||||||||
\(481\) | −51.6318 | −2.35421 | ||||||||
\(482\) | −36.5013 | −1.66259 | ||||||||
\(483\) | −26.0315 | −1.18447 | ||||||||
\(484\) | 2.93104 | 0.133229 | ||||||||
\(485\) | 25.5766 | 1.16137 | ||||||||
\(486\) | 80.2581 | 3.64058 | ||||||||
\(487\) | −37.3112 | −1.69073 | −0.845367 | − | 0.534186i | \(-0.820618\pi\) | ||||
−0.845367 | + | 0.534186i | \(0.820618\pi\) | |||||||
\(488\) | 0.309266 | 0.0139998 | ||||||||
\(489\) | 56.2131 | 2.54204 | ||||||||
\(490\) | −18.1217 | −0.818656 | ||||||||
\(491\) | −30.7080 | −1.38583 | −0.692917 | − | 0.721017i | \(-0.743675\pi\) | ||||
−0.692917 | + | 0.721017i | \(0.743675\pi\) | |||||||
\(492\) | −79.4256 | −3.58078 | ||||||||
\(493\) | −7.30946 | −0.329202 | ||||||||
\(494\) | −8.60922 | −0.387347 | ||||||||
\(495\) | −9.96994 | −0.448115 | ||||||||
\(496\) | −10.1910 | −0.457590 | ||||||||
\(497\) | −9.54817 | −0.428294 | ||||||||
\(498\) | 61.6987 | 2.76479 | ||||||||
\(499\) | 22.7886 | 1.02016 | 0.510080 | − | 0.860127i | \(-0.329616\pi\) | ||||
0.510080 | + | 0.860127i | \(0.329616\pi\) | |||||||
\(500\) | 32.1025 | 1.43567 | ||||||||
\(501\) | 69.0117 | 3.08322 | ||||||||
\(502\) | 52.2794 | 2.33334 | ||||||||
\(503\) | −20.9566 | −0.934408 | −0.467204 | − | 0.884149i | \(-0.654739\pi\) | ||||
−0.467204 | + | 0.884149i | \(0.654739\pi\) | |||||||
\(504\) | 14.4373 | 0.643087 | ||||||||
\(505\) | −15.6343 | −0.695718 | ||||||||
\(506\) | 19.1430 | 0.851010 | ||||||||
\(507\) | −32.5983 | −1.44774 | ||||||||
\(508\) | 30.9176 | 1.37175 | ||||||||
\(509\) | −35.8907 | −1.59083 | −0.795414 | − | 0.606066i | \(-0.792747\pi\) | ||||
−0.795414 | + | 0.606066i | \(0.792747\pi\) | |||||||
\(510\) | −9.57351 | −0.423922 | ||||||||
\(511\) | −12.6400 | −0.559162 | ||||||||
\(512\) | −14.0994 | −0.623112 | ||||||||
\(513\) | −11.7393 | −0.518302 | ||||||||
\(514\) | 4.42639 | 0.195240 | ||||||||
\(515\) | −0.900471 | −0.0396795 | ||||||||
\(516\) | −9.49308 | −0.417910 | ||||||||
\(517\) | 11.5760 | 0.509113 | ||||||||
\(518\) | −22.2578 | −0.977953 | ||||||||
\(519\) | −78.6119 | −3.45068 | ||||||||
\(520\) | 13.2169 | 0.579599 | ||||||||
\(521\) | −4.88369 | −0.213958 | −0.106979 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106979 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(522\) | 121.571 | 5.32103 | ||||||||
\(523\) | −3.63027 | −0.158741 | −0.0793704 | − | 0.996845i | \(-0.525291\pi\) | ||||
−0.0793704 | + | 0.996845i | \(0.525291\pi\) | |||||||
\(524\) | 27.4887 | 1.20085 | ||||||||
\(525\) | −9.74783 | −0.425430 | ||||||||
\(526\) | 41.9095 | 1.82734 | ||||||||
\(527\) | 8.01755 | 0.349250 | ||||||||
\(528\) | 4.11681 | 0.179161 | ||||||||
\(529\) | 51.3159 | 2.23113 | ||||||||
\(530\) | 31.6678 | 1.37556 | ||||||||
\(531\) | 76.4413 | 3.31727 | ||||||||
\(532\) | −2.20604 | −0.0956438 | ||||||||
\(533\) | 40.1818 | 1.74047 | ||||||||
\(534\) | −61.8328 | −2.67576 | ||||||||
\(535\) | 9.89747 | 0.427905 | ||||||||
\(536\) | 18.7553 | 0.810107 | ||||||||
\(537\) | −36.0260 | −1.55464 | ||||||||
\(538\) | 42.5298 | 1.83359 | ||||||||
\(539\) | −6.13075 | −0.264070 | ||||||||
\(540\) | 56.7363 | 2.44154 | ||||||||
\(541\) | 27.6169 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(542\) | −20.6952 | −0.888936 | ||||||||
\(543\) | 20.9938 | 0.900931 | ||||||||
\(544\) | 6.95749 | 0.298300 | ||||||||
\(545\) | 19.0668 | 0.816731 | ||||||||
\(546\) | −32.2035 | −1.37818 | ||||||||
\(547\) | −5.88658 | −0.251692 | −0.125846 | − | 0.992050i | \(-0.540165\pi\) | ||||
−0.125846 | + | 0.992050i | \(0.540165\pi\) | |||||||
\(548\) | −17.3736 | −0.742165 | ||||||||
\(549\) | −1.12040 | −0.0478173 | ||||||||
\(550\) | 7.16836 | 0.305660 | ||||||||
\(551\) | −5.90071 | −0.251379 | ||||||||
\(552\) | −57.7250 | −2.45694 | ||||||||
\(553\) | −1.99740 | −0.0849379 | ||||||||
\(554\) | −21.2582 | −0.903174 | ||||||||
\(555\) | −46.3494 | −1.96742 | ||||||||
\(556\) | −3.07921 | −0.130588 | ||||||||
\(557\) | −17.7215 | −0.750886 | −0.375443 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375443 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(558\) | −133.348 | −5.64508 | ||||||||
\(559\) | 4.80259 | 0.203128 | ||||||||
\(560\) | −1.57748 | −0.0666607 | ||||||||
\(561\) | −3.23881 | −0.136743 | ||||||||
\(562\) | −8.74213 | −0.368765 | ||||||||
\(563\) | −19.5992 | −0.826006 | −0.413003 | − | 0.910730i | \(-0.635520\pi\) | ||||
−0.413003 | + | 0.910730i | \(0.635520\pi\) | |||||||
\(564\) | −109.892 | −4.62730 | ||||||||
\(565\) | 16.8634 | 0.709447 | ||||||||
\(566\) | −48.5372 | −2.04017 | ||||||||
\(567\) | −22.9624 | −0.964330 | ||||||||
\(568\) | −21.1731 | −0.888405 | ||||||||
\(569\) | 23.8377 | 0.999327 | 0.499664 | − | 0.866219i | \(-0.333457\pi\) | ||||
0.499664 | + | 0.866219i | \(0.333457\pi\) | |||||||
\(570\) | −7.72842 | −0.323708 | ||||||||
\(571\) | −15.1843 | −0.635445 | −0.317722 | − | 0.948184i | \(-0.602918\pi\) | ||||
−0.317722 | + | 0.948184i | \(0.602918\pi\) | |||||||
\(572\) | 14.0766 | 0.588572 | ||||||||
\(573\) | −17.6189 | −0.736038 | ||||||||
\(574\) | 17.3219 | 0.723001 | ||||||||
\(575\) | 27.8286 | 1.16053 | ||||||||
\(576\) | −96.6766 | −4.02819 | ||||||||
\(577\) | −12.8644 | −0.535552 | −0.267776 | − | 0.963481i | \(-0.586289\pi\) | ||||
−0.267776 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(578\) | −2.22059 | −0.0923645 | ||||||||
\(579\) | 14.6962 | 0.610754 | ||||||||
\(580\) | 28.5183 | 1.18416 | ||||||||
\(581\) | −7.99822 | −0.331822 | ||||||||
\(582\) | −138.191 | −5.72822 | ||||||||
\(583\) | 10.7135 | 0.443709 | ||||||||
\(584\) | −28.0294 | −1.15986 | ||||||||
\(585\) | −47.8816 | −1.97966 | ||||||||
\(586\) | 38.8138 | 1.60338 | ||||||||
\(587\) | 27.1321 | 1.11986 | 0.559931 | − | 0.828539i | \(-0.310827\pi\) | ||||
0.559931 | + | 0.828539i | \(0.310827\pi\) | |||||||
\(588\) | 58.1997 | 2.40012 | ||||||||
\(589\) | 6.47233 | 0.266688 | ||||||||
\(590\) | 30.1674 | 1.24197 | ||||||||
\(591\) | 51.8655 | 2.13346 | ||||||||
\(592\) | 13.6652 | 0.561638 | ||||||||
\(593\) | 18.9468 | 0.778054 | 0.389027 | − | 0.921226i | \(-0.372811\pi\) | ||||
0.389027 | + | 0.921226i | \(0.372811\pi\) | |||||||
\(594\) | 32.2918 | 1.32495 | ||||||||
\(595\) | 1.24105 | 0.0508780 | ||||||||
\(596\) | 24.2211 | 0.992135 | ||||||||
\(597\) | −27.9270 | −1.14298 | ||||||||
\(598\) | 91.9360 | 3.75954 | ||||||||
\(599\) | 4.37119 | 0.178602 | 0.0893010 | − | 0.996005i | \(-0.471537\pi\) | ||||
0.0893010 | + | 0.996005i | \(0.471537\pi\) | |||||||
\(600\) | −21.6159 | −0.882466 | ||||||||
\(601\) | 31.4728 | 1.28380 | 0.641901 | − | 0.766787i | \(-0.278146\pi\) | ||||
0.641901 | + | 0.766787i | \(0.278146\pi\) | |||||||
\(602\) | 2.07034 | 0.0843807 | ||||||||
\(603\) | −67.9460 | −2.76697 | ||||||||
\(604\) | 28.7313 | 1.16906 | ||||||||
\(605\) | −1.33112 | −0.0541176 | ||||||||
\(606\) | 84.4729 | 3.43148 | ||||||||
\(607\) | 13.6521 | 0.554121 | 0.277061 | − | 0.960852i | \(-0.410640\pi\) | ||||
0.277061 | + | 0.960852i | \(0.410640\pi\) | |||||||
\(608\) | 5.61658 | 0.227782 | ||||||||
\(609\) | −22.0721 | −0.894406 | ||||||||
\(610\) | −0.442161 | −0.0179026 | ||||||||
\(611\) | 55.5949 | 2.24913 | ||||||||
\(612\) | 21.9532 | 0.887405 | ||||||||
\(613\) | 7.09513 | 0.286570 | 0.143285 | − | 0.989681i | \(-0.454234\pi\) | ||||
0.143285 | + | 0.989681i | \(0.454234\pi\) | |||||||
\(614\) | −7.38107 | −0.297876 | ||||||||
\(615\) | 36.0708 | 1.45451 | ||||||||
\(616\) | 1.92757 | 0.0776638 | ||||||||
\(617\) | 25.3337 | 1.01990 | 0.509949 | − | 0.860205i | \(-0.329664\pi\) | ||||
0.509949 | + | 0.860205i | \(0.329664\pi\) | |||||||
\(618\) | 4.86528 | 0.195710 | ||||||||
\(619\) | 25.3955 | 1.02073 | 0.510366 | − | 0.859957i | \(-0.329510\pi\) | ||||
0.510366 | + | 0.859957i | \(0.329510\pi\) | |||||||
\(620\) | −31.2809 | −1.25627 | ||||||||
\(621\) | 125.361 | 5.03058 | ||||||||
\(622\) | −31.2650 | −1.25361 | ||||||||
\(623\) | 8.01559 | 0.321138 | ||||||||
\(624\) | 19.7714 | 0.791488 | ||||||||
\(625\) | 1.56143 | 0.0624571 | ||||||||
\(626\) | 3.67361 | 0.146827 | ||||||||
\(627\) | −2.61460 | −0.104417 | ||||||||
\(628\) | −31.1025 | −1.24113 | ||||||||
\(629\) | −10.7508 | −0.428663 | ||||||||
\(630\) | −20.6411 | −0.822363 | ||||||||
\(631\) | −24.7758 | −0.986310 | −0.493155 | − | 0.869941i | \(-0.664156\pi\) | ||||
−0.493155 | + | 0.869941i | \(0.664156\pi\) | |||||||
\(632\) | −4.42924 | −0.176186 | ||||||||
\(633\) | −56.2746 | −2.23671 | ||||||||
\(634\) | −21.7084 | −0.862152 | ||||||||
\(635\) | −14.0411 | −0.557203 | ||||||||
\(636\) | −101.704 | −4.03284 | ||||||||
\(637\) | −29.4435 | −1.16659 | ||||||||
\(638\) | 16.2314 | 0.642605 | ||||||||
\(639\) | 76.7051 | 3.03441 | ||||||||
\(640\) | −19.6307 | −0.775972 | ||||||||
\(641\) | −19.9885 | −0.789497 | −0.394748 | − | 0.918789i | \(-0.629168\pi\) | ||||
−0.394748 | + | 0.918789i | \(0.629168\pi\) | |||||||
\(642\) | −53.4765 | −2.11055 | ||||||||
\(643\) | −31.7736 | −1.25303 | −0.626514 | − | 0.779410i | \(-0.715519\pi\) | ||||
−0.626514 | + | 0.779410i | \(0.715519\pi\) | |||||||
\(644\) | 23.5578 | 0.928307 | ||||||||
\(645\) | 4.31124 | 0.169755 | ||||||||
\(646\) | −1.79262 | −0.0705297 | ||||||||
\(647\) | 42.1715 | 1.65793 | 0.828966 | − | 0.559300i | \(-0.188930\pi\) | ||||
0.828966 | + | 0.559300i | \(0.188930\pi\) | |||||||
\(648\) | −50.9193 | −2.00030 | ||||||||
\(649\) | 10.2059 | 0.400617 | ||||||||
\(650\) | 34.4267 | 1.35033 | ||||||||
\(651\) | 24.2102 | 0.948874 | ||||||||
\(652\) | −50.8713 | −1.99228 | ||||||||
\(653\) | −45.5674 | −1.78319 | −0.891595 | − | 0.452833i | \(-0.850413\pi\) | ||||
−0.891595 | + | 0.452833i | \(0.850413\pi\) | |||||||
\(654\) | −103.019 | −4.02835 | ||||||||
\(655\) | −12.4839 | −0.487785 | ||||||||
\(656\) | −10.6348 | −0.415219 | ||||||||
\(657\) | 101.544 | 3.96159 | ||||||||
\(658\) | 23.9663 | 0.934303 | ||||||||
\(659\) | 6.89142 | 0.268452 | 0.134226 | − | 0.990951i | \(-0.457145\pi\) | ||||
0.134226 | + | 0.990951i | \(0.457145\pi\) | |||||||
\(660\) | 12.6364 | 0.491872 | ||||||||
\(661\) | −16.1336 | −0.627526 | −0.313763 | − | 0.949501i | \(-0.601590\pi\) | ||||
−0.313763 | + | 0.949501i | \(0.601590\pi\) | |||||||
\(662\) | 17.3412 | 0.673985 | ||||||||
\(663\) | −15.5547 | −0.604094 | ||||||||
\(664\) | −17.7361 | −0.688295 | ||||||||
\(665\) | 1.00186 | 0.0388505 | ||||||||
\(666\) | 178.808 | 6.92867 | ||||||||
\(667\) | 63.0124 | 2.43985 | ||||||||
\(668\) | −62.4538 | −2.41641 | ||||||||
\(669\) | −50.2628 | −1.94327 | ||||||||
\(670\) | −26.8147 | −1.03594 | ||||||||
\(671\) | −0.149587 | −0.00577476 | ||||||||
\(672\) | 21.0092 | 0.810449 | ||||||||
\(673\) | 9.63893 | 0.371554 | 0.185777 | − | 0.982592i | \(-0.440520\pi\) | ||||
0.185777 | + | 0.982592i | \(0.440520\pi\) | |||||||
\(674\) | 19.3719 | 0.746178 | ||||||||
\(675\) | 46.9432 | 1.80685 | ||||||||
\(676\) | 29.5006 | 1.13464 | ||||||||
\(677\) | 30.9794 | 1.19064 | 0.595318 | − | 0.803490i | \(-0.297026\pi\) | ||||
0.595318 | + | 0.803490i | \(0.297026\pi\) | |||||||
\(678\) | −91.1135 | −3.49919 | ||||||||
\(679\) | 17.9142 | 0.687485 | ||||||||
\(680\) | 2.75203 | 0.105536 | ||||||||
\(681\) | 5.22229 | 0.200119 | ||||||||
\(682\) | −17.8037 | −0.681740 | ||||||||
\(683\) | 9.47005 | 0.362361 | 0.181181 | − | 0.983450i | \(-0.442008\pi\) | ||||
0.181181 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(684\) | 17.7222 | 0.677624 | ||||||||
\(685\) | 7.89016 | 0.301467 | ||||||||
\(686\) | −27.1851 | −1.03793 | ||||||||
\(687\) | 48.3632 | 1.84517 | ||||||||
\(688\) | −1.27109 | −0.0484597 | ||||||||
\(689\) | 51.4527 | 1.96019 | ||||||||
\(690\) | 82.5301 | 3.14187 | ||||||||
\(691\) | −12.7430 | −0.484766 | −0.242383 | − | 0.970181i | \(-0.577929\pi\) | ||||
−0.242383 | + | 0.970181i | \(0.577929\pi\) | |||||||
\(692\) | 71.1417 | 2.70440 | ||||||||
\(693\) | −6.98310 | −0.265266 | ||||||||
\(694\) | −32.3465 | −1.22786 | ||||||||
\(695\) | 1.39841 | 0.0530446 | ||||||||
\(696\) | −48.9450 | −1.85526 | ||||||||
\(697\) | 8.36668 | 0.316911 | ||||||||
\(698\) | 57.0499 | 2.15937 | ||||||||
\(699\) | −45.3052 | −1.71360 | ||||||||
\(700\) | 8.82153 | 0.333423 | ||||||||
\(701\) | 0.760299 | 0.0287161 | 0.0143580 | − | 0.999897i | \(-0.495430\pi\) | ||||
0.0143580 | + | 0.999897i | \(0.495430\pi\) | |||||||
\(702\) | 155.084 | 5.85328 | ||||||||
\(703\) | −8.67882 | −0.327328 | ||||||||
\(704\) | −12.9076 | −0.486473 | ||||||||
\(705\) | 49.9070 | 1.87961 | ||||||||
\(706\) | −41.3004 | −1.55436 | ||||||||
\(707\) | −10.9505 | −0.411837 | ||||||||
\(708\) | −96.8857 | −3.64119 | ||||||||
\(709\) | 31.7702 | 1.19316 | 0.596578 | − | 0.802555i | \(-0.296527\pi\) | ||||
0.596578 | + | 0.802555i | \(0.296527\pi\) | |||||||
\(710\) | 30.2715 | 1.13607 | ||||||||
\(711\) | 16.0461 | 0.601774 | ||||||||
\(712\) | 17.7746 | 0.666133 | ||||||||
\(713\) | −69.1166 | −2.58844 | ||||||||
\(714\) | −6.70543 | −0.250945 | ||||||||
\(715\) | −6.39281 | −0.239078 | ||||||||
\(716\) | 32.6026 | 1.21842 | ||||||||
\(717\) | −6.72473 | −0.251140 | ||||||||
\(718\) | −8.30861 | −0.310075 | ||||||||
\(719\) | −36.0100 | −1.34295 | −0.671474 | − | 0.741028i | \(-0.734338\pi\) | ||||
−0.671474 | + | 0.741028i | \(0.734338\pi\) | |||||||
\(720\) | 12.6727 | 0.472282 | ||||||||
\(721\) | −0.630703 | −0.0234886 | ||||||||
\(722\) | 40.7442 | 1.51634 | ||||||||
\(723\) | −53.2384 | −1.97996 | ||||||||
\(724\) | −18.9988 | −0.706087 | ||||||||
\(725\) | 23.5959 | 0.876329 | ||||||||
\(726\) | 7.19209 | 0.266923 | ||||||||
\(727\) | −38.0910 | −1.41272 | −0.706359 | − | 0.707854i | \(-0.749664\pi\) | ||||
−0.706359 | + | 0.707854i | \(0.749664\pi\) | |||||||
\(728\) | 9.25731 | 0.343099 | ||||||||
\(729\) | 43.1724 | 1.59898 | ||||||||
\(730\) | 40.0739 | 1.48320 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 1.42005 | 0.0524864 | ||||||||
\(733\) | 28.7771 | 1.06291 | 0.531454 | − | 0.847087i | \(-0.321646\pi\) | ||||
0.531454 | + | 0.847087i | \(0.321646\pi\) | |||||||
\(734\) | 29.5903 | 1.09220 | ||||||||
\(735\) | −26.4311 | −0.974927 | ||||||||
\(736\) | −59.9782 | −2.21083 | ||||||||
\(737\) | −9.07168 | −0.334159 | ||||||||
\(738\) | −139.155 | −5.12237 | ||||||||
\(739\) | −24.1005 | −0.886549 | −0.443275 | − | 0.896386i | \(-0.646183\pi\) | ||||
−0.443275 | + | 0.896386i | \(0.646183\pi\) | |||||||
\(740\) | 41.9450 | 1.54193 | ||||||||
\(741\) | −12.5568 | −0.461287 | ||||||||
\(742\) | 22.1806 | 0.814276 | ||||||||
\(743\) | −22.3442 | −0.819728 | −0.409864 | − | 0.912147i | \(-0.634424\pi\) | ||||
−0.409864 | + | 0.912147i | \(0.634424\pi\) | |||||||
\(744\) | 53.6864 | 1.96824 | ||||||||
\(745\) | −10.9999 | −0.403005 | ||||||||
\(746\) | 58.2684 | 2.13336 | ||||||||
\(747\) | 64.2536 | 2.35092 | ||||||||
\(748\) | 2.93104 | 0.107169 | ||||||||
\(749\) | 6.93234 | 0.253302 | ||||||||
\(750\) | 78.7721 | 2.87635 | ||||||||
\(751\) | 28.9494 | 1.05638 | 0.528189 | − | 0.849127i | \(-0.322871\pi\) | ||||
0.528189 | + | 0.849127i | \(0.322871\pi\) | |||||||
\(752\) | −14.7141 | −0.536569 | ||||||||
\(753\) | 76.2512 | 2.77875 | ||||||||
\(754\) | 77.9526 | 2.83886 | ||||||||
\(755\) | −13.0482 | −0.474872 | ||||||||
\(756\) | 39.7389 | 1.44529 | ||||||||
\(757\) | −20.4138 | −0.741952 | −0.370976 | − | 0.928642i | \(-0.620977\pi\) | ||||
−0.370976 | + | 0.928642i | \(0.620977\pi\) | |||||||
\(758\) | −56.5488 | −2.05394 | ||||||||
\(759\) | 27.9207 | 1.01346 | ||||||||
\(760\) | 2.22164 | 0.0805872 | ||||||||
\(761\) | 46.3201 | 1.67910 | 0.839551 | − | 0.543280i | \(-0.182818\pi\) | ||||
0.839551 | + | 0.543280i | \(0.182818\pi\) | |||||||
\(762\) | 75.8645 | 2.74828 | ||||||||
\(763\) | 13.3547 | 0.483471 | ||||||||
\(764\) | 15.9446 | 0.576856 | ||||||||
\(765\) | −9.96994 | −0.360464 | ||||||||
\(766\) | 15.9297 | 0.575565 | ||||||||
\(767\) | 49.0149 | 1.76982 | ||||||||
\(768\) | 22.4551 | 0.810278 | ||||||||
\(769\) | −20.9153 | −0.754223 | −0.377112 | − | 0.926168i | \(-0.623083\pi\) | ||||
−0.377112 | + | 0.926168i | \(0.623083\pi\) | |||||||
\(770\) | −2.75586 | −0.0993144 | ||||||||
\(771\) | 6.45604 | 0.232509 | ||||||||
\(772\) | −13.2997 | −0.478666 | ||||||||
\(773\) | −14.1945 | −0.510542 | −0.255271 | − | 0.966870i | \(-0.582165\pi\) | ||||
−0.255271 | + | 0.966870i | \(0.582165\pi\) | |||||||
\(774\) | −16.6320 | −0.597826 | ||||||||
\(775\) | −25.8817 | −0.929697 | ||||||||
\(776\) | 39.7249 | 1.42604 | ||||||||
\(777\) | −32.4638 | −1.16463 | ||||||||
\(778\) | −37.5783 | −1.34725 | ||||||||
\(779\) | 6.75418 | 0.241994 | ||||||||
\(780\) | 60.6875 | 2.17296 | ||||||||
\(781\) | 10.2411 | 0.366457 | ||||||||
\(782\) | 19.1430 | 0.684552 | ||||||||
\(783\) | 106.294 | 3.79863 | ||||||||
\(784\) | 7.79272 | 0.278311 | ||||||||
\(785\) | 14.1251 | 0.504145 | ||||||||
\(786\) | 67.4509 | 2.40590 | ||||||||
\(787\) | 22.0557 | 0.786201 | 0.393100 | − | 0.919496i | \(-0.371402\pi\) | ||||
0.393100 | + | 0.919496i | \(0.371402\pi\) | |||||||
\(788\) | −46.9369 | −1.67206 | ||||||||
\(789\) | 61.1264 | 2.17616 | ||||||||
\(790\) | 6.33254 | 0.225302 | ||||||||
\(791\) | 11.8114 | 0.419963 | ||||||||
\(792\) | −15.4851 | −0.550238 | ||||||||
\(793\) | −0.718408 | −0.0255114 | ||||||||
\(794\) | 38.9134 | 1.38099 | ||||||||
\(795\) | 46.1886 | 1.63814 | ||||||||
\(796\) | 25.2732 | 0.895784 | ||||||||
\(797\) | 1.90962 | 0.0676423 | 0.0338212 | − | 0.999428i | \(-0.489232\pi\) | ||||
0.0338212 | + | 0.999428i | \(0.489232\pi\) | |||||||
\(798\) | −5.41310 | −0.191622 | ||||||||
\(799\) | 11.5760 | 0.409530 | ||||||||
\(800\) | −22.4597 | −0.794069 | ||||||||
\(801\) | −64.3932 | −2.27522 | ||||||||
\(802\) | 23.3255 | 0.823654 | ||||||||
\(803\) | 13.5574 | 0.478430 | ||||||||
\(804\) | 86.1182 | 3.03715 | ||||||||
\(805\) | −10.6987 | −0.377078 | ||||||||
\(806\) | −85.5040 | −3.01175 | ||||||||
\(807\) | 62.0312 | 2.18360 | ||||||||
\(808\) | −24.2829 | −0.854268 | ||||||||
\(809\) | −16.0469 | −0.564180 | −0.282090 | − | 0.959388i | \(-0.591028\pi\) | ||||
−0.282090 | + | 0.959388i | \(0.591028\pi\) | |||||||
\(810\) | 72.8000 | 2.55793 | ||||||||
\(811\) | −17.8474 | −0.626708 | −0.313354 | − | 0.949636i | \(-0.601453\pi\) | ||||
−0.313354 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(812\) | 19.9746 | 0.700973 | ||||||||
\(813\) | −30.1847 | −1.05862 | ||||||||
\(814\) | 23.8732 | 0.836756 | ||||||||
\(815\) | 23.1030 | 0.809262 | ||||||||
\(816\) | 4.11681 | 0.144117 | ||||||||
\(817\) | 0.807270 | 0.0282428 | ||||||||
\(818\) | 34.2979 | 1.19920 | ||||||||
\(819\) | −33.5370 | −1.17188 | ||||||||
\(820\) | −32.6431 | −1.13995 | ||||||||
\(821\) | 27.8197 | 0.970915 | 0.485458 | − | 0.874260i | \(-0.338653\pi\) | ||||
0.485458 | + | 0.874260i | \(0.338653\pi\) | |||||||
\(822\) | −42.6309 | −1.48692 | ||||||||
\(823\) | −28.2474 | −0.984643 | −0.492321 | − | 0.870413i | \(-0.663852\pi\) | ||||
−0.492321 | + | 0.870413i | \(0.663852\pi\) | |||||||
\(824\) | −1.39859 | −0.0487222 | ||||||||
\(825\) | 10.4553 | 0.364007 | ||||||||
\(826\) | 21.1297 | 0.735196 | ||||||||
\(827\) | −13.0110 | −0.452436 | −0.226218 | − | 0.974077i | \(-0.572636\pi\) | ||||
−0.226218 | + | 0.974077i | \(0.572636\pi\) | |||||||
\(828\) | −189.251 | −6.57693 | ||||||||
\(829\) | −0.125222 | −0.00434914 | −0.00217457 | − | 0.999998i | \(-0.500692\pi\) | ||||
−0.00217457 | + | 0.999998i | \(0.500692\pi\) | |||||||
\(830\) | 25.3575 | 0.880172 | ||||||||
\(831\) | −31.0058 | −1.07558 | ||||||||
\(832\) | −61.9899 | −2.14911 | ||||||||
\(833\) | −6.13075 | −0.212418 | ||||||||
\(834\) | −7.55566 | −0.261631 | ||||||||
\(835\) | 28.3631 | 0.981545 | ||||||||
\(836\) | 2.36614 | 0.0818347 | ||||||||
\(837\) | −116.591 | −4.02997 | ||||||||
\(838\) | −25.3102 | −0.874327 | ||||||||
\(839\) | 44.9381 | 1.55143 | 0.775717 | − | 0.631080i | \(-0.217388\pi\) | ||||
0.775717 | + | 0.631080i | \(0.217388\pi\) | |||||||
\(840\) | 8.31020 | 0.286729 | ||||||||
\(841\) | 24.4282 | 0.842353 | ||||||||
\(842\) | 57.7241 | 1.98931 | ||||||||
\(843\) | −12.7507 | −0.439157 | ||||||||
\(844\) | 50.9270 | 1.75298 | ||||||||
\(845\) | −13.3976 | −0.460890 | ||||||||
\(846\) | −192.533 | −6.61942 | ||||||||
\(847\) | −0.932335 | −0.0320354 | ||||||||
\(848\) | −13.6178 | −0.467638 | ||||||||
\(849\) | −70.7932 | −2.42961 | ||||||||
\(850\) | 7.16836 | 0.245873 | ||||||||
\(851\) | 92.6793 | 3.17701 | ||||||||
\(852\) | −97.2200 | −3.33070 | ||||||||
\(853\) | −10.8932 | −0.372977 | −0.186488 | − | 0.982457i | \(-0.559711\pi\) | ||||
−0.186488 | + | 0.982457i | \(0.559711\pi\) | |||||||
\(854\) | −0.309697 | −0.0105976 | ||||||||
\(855\) | −8.04844 | −0.275251 | ||||||||
\(856\) | 15.3725 | 0.525422 | ||||||||
\(857\) | −19.4913 | −0.665809 | −0.332904 | − | 0.942961i | \(-0.608029\pi\) | ||||
−0.332904 | + | 0.942961i | \(0.608029\pi\) | |||||||
\(858\) | 34.5407 | 1.17920 | ||||||||
\(859\) | −37.7299 | −1.28733 | −0.643664 | − | 0.765308i | \(-0.722587\pi\) | ||||
−0.643664 | + | 0.765308i | \(0.722587\pi\) | |||||||
\(860\) | −3.90156 | −0.133042 | ||||||||
\(861\) | 25.2645 | 0.861013 | ||||||||
\(862\) | −49.4525 | −1.68436 | ||||||||
\(863\) | 54.9779 | 1.87147 | 0.935734 | − | 0.352707i | \(-0.114739\pi\) | ||||
0.935734 | + | 0.352707i | \(0.114739\pi\) | |||||||
\(864\) | −101.175 | −3.44206 | ||||||||
\(865\) | −32.3087 | −1.09853 | ||||||||
\(866\) | −83.6202 | −2.84153 | ||||||||
\(867\) | −3.23881 | −0.109996 | ||||||||
\(868\) | −21.9096 | −0.743662 | ||||||||
\(869\) | 2.14236 | 0.0726746 | ||||||||
\(870\) | 69.9772 | 2.37245 | ||||||||
\(871\) | −43.5676 | −1.47623 | ||||||||
\(872\) | 29.6141 | 1.00286 | ||||||||
\(873\) | −143.914 | −4.87074 | ||||||||
\(874\) | 15.4536 | 0.522725 | ||||||||
\(875\) | −10.2115 | −0.345212 | ||||||||
\(876\) | −128.701 | −4.34842 | ||||||||
\(877\) | −10.5383 | −0.355852 | −0.177926 | − | 0.984044i | \(-0.556939\pi\) | ||||
−0.177926 | + | 0.984044i | \(0.556939\pi\) | |||||||
\(878\) | −35.4694 | −1.19704 | ||||||||
\(879\) | 56.6112 | 1.90945 | ||||||||
\(880\) | 1.69197 | 0.0570362 | ||||||||
\(881\) | −1.28919 | −0.0434338 | −0.0217169 | − | 0.999764i | \(-0.506913\pi\) | ||||
−0.0217169 | + | 0.999764i | \(0.506913\pi\) | |||||||
\(882\) | 101.967 | 3.43340 | ||||||||
\(883\) | 13.3197 | 0.448245 | 0.224122 | − | 0.974561i | \(-0.428048\pi\) | ||||
0.224122 | + | 0.974561i | \(0.428048\pi\) | |||||||
\(884\) | 14.0766 | 0.473447 | ||||||||
\(885\) | 44.0002 | 1.47905 | ||||||||
\(886\) | 5.43946 | 0.182742 | ||||||||
\(887\) | 31.0808 | 1.04359 | 0.521796 | − | 0.853070i | \(-0.325262\pi\) | ||||
0.521796 | + | 0.853070i | \(0.325262\pi\) | |||||||
\(888\) | −71.9888 | −2.41579 | ||||||||
\(889\) | −9.83458 | −0.329841 | ||||||||
\(890\) | −25.4126 | −0.851833 | ||||||||
\(891\) | 24.6289 | 0.825100 | ||||||||
\(892\) | 45.4865 | 1.52300 | ||||||||
\(893\) | 9.34498 | 0.312718 | ||||||||
\(894\) | 59.4330 | 1.98774 | ||||||||
\(895\) | −14.8063 | −0.494921 | ||||||||
\(896\) | −13.7496 | −0.459343 | ||||||||
\(897\) | 134.092 | 4.47720 | ||||||||
\(898\) | 44.4781 | 1.48425 | ||||||||
\(899\) | −58.6040 | −1.95455 | ||||||||
\(900\) | −70.8677 | −2.36226 | ||||||||
\(901\) | 10.7135 | 0.356919 | ||||||||
\(902\) | −18.5790 | −0.618613 | ||||||||
\(903\) | 3.01966 | 0.100488 | ||||||||
\(904\) | 26.1918 | 0.871125 | ||||||||
\(905\) | 8.62824 | 0.286812 | ||||||||
\(906\) | 70.4999 | 2.34220 | ||||||||
\(907\) | −31.0511 | −1.03104 | −0.515518 | − | 0.856879i | \(-0.672400\pi\) | ||||
−0.515518 | + | 0.856879i | \(0.672400\pi\) | |||||||
\(908\) | −4.72603 | −0.156839 | ||||||||
\(909\) | 87.9709 | 2.91781 | ||||||||
\(910\) | −13.2353 | −0.438745 | ||||||||
\(911\) | 1.94022 | 0.0642823 | 0.0321411 | − | 0.999483i | \(-0.489767\pi\) | ||||
0.0321411 | + | 0.999483i | \(0.489767\pi\) | |||||||
\(912\) | 3.32338 | 0.110048 | ||||||||
\(913\) | 8.57869 | 0.283913 | ||||||||
\(914\) | 49.4517 | 1.63572 | ||||||||
\(915\) | −0.644907 | −0.0213200 | ||||||||
\(916\) | −43.7674 | −1.44612 | ||||||||
\(917\) | −8.74390 | −0.288749 | ||||||||
\(918\) | 32.2918 | 1.06579 | ||||||||
\(919\) | 6.35911 | 0.209768 | 0.104884 | − | 0.994484i | \(-0.466553\pi\) | ||||
0.104884 | + | 0.994484i | \(0.466553\pi\) | |||||||
\(920\) | −23.7244 | −0.782169 | ||||||||
\(921\) | −10.7655 | −0.354737 | ||||||||
\(922\) | −3.13254 | −0.103165 | ||||||||
\(923\) | 49.1840 | 1.61891 | ||||||||
\(924\) | 8.85073 | 0.291168 | ||||||||
\(925\) | 34.7050 | 1.14109 | ||||||||
\(926\) | 56.2327 | 1.84792 | ||||||||
\(927\) | 5.06675 | 0.166414 | ||||||||
\(928\) | −50.8555 | −1.66941 | ||||||||
\(929\) | 4.10078 | 0.134542 | 0.0672712 | − | 0.997735i | \(-0.478571\pi\) | ||||
0.0672712 | + | 0.997735i | \(0.478571\pi\) | |||||||
\(930\) | −76.7561 | −2.51693 | ||||||||
\(931\) | −4.94917 | −0.162203 | ||||||||
\(932\) | 41.0000 | 1.34300 | ||||||||
\(933\) | −45.6011 | −1.49291 | ||||||||
\(934\) | −0.695486 | −0.0227570 | ||||||||
\(935\) | −1.33112 | −0.0435322 | ||||||||
\(936\) | −74.3685 | −2.43081 | ||||||||
\(937\) | 31.6315 | 1.03335 | 0.516677 | − | 0.856180i | \(-0.327169\pi\) | ||||
0.516677 | + | 0.856180i | \(0.327169\pi\) | |||||||
\(938\) | −18.7814 | −0.613235 | ||||||||
\(939\) | 5.35808 | 0.174854 | ||||||||
\(940\) | −45.1645 | −1.47310 | ||||||||
\(941\) | −19.8860 | −0.648266 | −0.324133 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324133 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(942\) | −76.3183 | −2.48658 | ||||||||
\(943\) | −72.1264 | −2.34876 | ||||||||
\(944\) | −12.9726 | −0.422223 | ||||||||
\(945\) | −18.0472 | −0.587077 | ||||||||
\(946\) | −2.22059 | −0.0721978 | ||||||||
\(947\) | 31.8193 | 1.03399 | 0.516994 | − | 0.855989i | \(-0.327051\pi\) | ||||
0.516994 | + | 0.855989i | \(0.327051\pi\) | |||||||
\(948\) | −20.3376 | −0.660535 | ||||||||
\(949\) | 65.1106 | 2.11358 | ||||||||
\(950\) | 5.78680 | 0.187749 | ||||||||
\(951\) | −31.6625 | −1.02673 | ||||||||
\(952\) | 1.92757 | 0.0624728 | ||||||||
\(953\) | −39.9062 | −1.29269 | −0.646344 | − | 0.763046i | \(-0.723703\pi\) | ||||
−0.646344 | + | 0.763046i | \(0.723703\pi\) | |||||||
\(954\) | −178.188 | −5.76904 | ||||||||
\(955\) | −7.24117 | −0.234319 | ||||||||
\(956\) | 6.08571 | 0.196826 | ||||||||
\(957\) | 23.6740 | 0.765271 | ||||||||
\(958\) | 2.41797 | 0.0781211 | ||||||||
\(959\) | 5.52639 | 0.178456 | ||||||||
\(960\) | −55.6477 | −1.79602 | ||||||||
\(961\) | 33.2811 | 1.07358 | ||||||||
\(962\) | 114.653 | 3.69657 | ||||||||
\(963\) | −55.6908 | −1.79461 | ||||||||
\(964\) | 48.1794 | 1.55175 | ||||||||
\(965\) | 6.03999 | 0.194434 | ||||||||
\(966\) | 57.8053 | 1.85986 | ||||||||
\(967\) | 0.987880 | 0.0317681 | 0.0158840 | − | 0.999874i | \(-0.494944\pi\) | ||||
0.0158840 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(968\) | −2.06746 | −0.0664507 | ||||||||
\(969\) | −2.61460 | −0.0839930 | ||||||||
\(970\) | −56.7952 | −1.82358 | ||||||||
\(971\) | −6.56596 | −0.210712 | −0.105356 | − | 0.994435i | \(-0.533598\pi\) | ||||
−0.105356 | + | 0.994435i | \(0.533598\pi\) | |||||||
\(972\) | −105.935 | −3.39788 | ||||||||
\(973\) | 0.979466 | 0.0314002 | ||||||||
\(974\) | 82.8531 | 2.65479 | ||||||||
\(975\) | 50.2125 | 1.60809 | ||||||||
\(976\) | 0.190139 | 0.00608619 | ||||||||
\(977\) | 23.3104 | 0.745765 | 0.372882 | − | 0.927879i | \(-0.378369\pi\) | ||||
0.372882 | + | 0.927879i | \(0.378369\pi\) | |||||||
\(978\) | −124.826 | −3.99151 | ||||||||
\(979\) | −8.59733 | −0.274772 | ||||||||
\(980\) | 23.9195 | 0.764080 | ||||||||
\(981\) | −107.284 | −3.42533 | ||||||||
\(982\) | 68.1901 | 2.17603 | ||||||||
\(983\) | 2.26795 | 0.0723365 | 0.0361682 | − | 0.999346i | \(-0.488485\pi\) | ||||
0.0361682 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(984\) | 56.0243 | 1.78599 | ||||||||
\(985\) | 21.3162 | 0.679189 | ||||||||
\(986\) | 16.2314 | 0.516912 | ||||||||
\(987\) | 34.9556 | 1.11265 | ||||||||
\(988\) | 11.3636 | 0.361525 | ||||||||
\(989\) | −8.62067 | −0.274121 | ||||||||
\(990\) | 22.1392 | 0.703630 | ||||||||
\(991\) | 10.1142 | 0.321289 | 0.160645 | − | 0.987012i | \(-0.448643\pi\) | ||||
0.160645 | + | 0.987012i | \(0.448643\pi\) | |||||||
\(992\) | 55.7820 | 1.77108 | ||||||||
\(993\) | 25.2927 | 0.802641 | ||||||||
\(994\) | 21.2026 | 0.672506 | ||||||||
\(995\) | −11.4777 | −0.363868 | ||||||||
\(996\) | −81.4383 | −2.58047 | ||||||||
\(997\) | 40.8609 | 1.29408 | 0.647038 | − | 0.762458i | \(-0.276007\pi\) | ||||
0.647038 | + | 0.762458i | \(0.276007\pi\) | |||||||
\(998\) | −50.6043 | −1.60185 | ||||||||
\(999\) | 156.338 | 4.94631 |
(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 | 8041.2.a.j.1.13 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.13 | ✓ | 82 | 1.1 | even | 1 | trivial |