Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1456,2,Mod(1,1456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1456, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1456.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1456 = 2^{4} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1456.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: | \(11.6262185343\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.64268.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 6x + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 728) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.65932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1456.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.65932 | 1.53536 | 0.767681 | − | 0.640833i | \(-0.221411\pi\) | ||||
0.767681 | + | 0.640833i | \(0.221411\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.96141 | −1.32438 | −0.662190 | − | 0.749336i | \(-0.730373\pi\) | ||||
−0.662190 | + | 0.749336i | \(0.730373\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.07200 | 1.35733 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.80333 | 1.44826 | 0.724130 | − | 0.689664i | \(-0.242242\pi\) | ||||
0.724130 | + | 0.689664i | \(0.242242\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.87534 | −2.03340 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.268672 | 0.0651625 | 0.0325812 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325812 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.50125 | 1.49149 | 0.745745 | − | 0.666232i | \(-0.232094\pi\) | ||||
0.745745 | + | 0.666232i | \(0.232094\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.65932 | 0.580312 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.30208 | −0.480017 | −0.240009 | − | 0.970771i | \(-0.577150\pi\) | ||||
−0.240009 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.76992 | 0.753985 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.85081 | 0.548638 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.54873 | 1.21607 | 0.608034 | − | 0.793911i | \(-0.291958\pi\) | ||||
0.608034 | + | 0.793911i | \(0.291958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.03341 | −0.724422 | −0.362211 | − | 0.932096i | \(-0.617978\pi\) | ||||
−0.362211 | + | 0.932096i | \(0.617978\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.7736 | 2.22360 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.96141 | −0.500569 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51532 | 0.413515 | 0.206758 | − | 0.978392i | \(-0.433709\pi\) | ||||
0.206758 | + | 0.978392i | \(0.433709\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.65932 | −0.425833 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.46784 | 0.697760 | 0.348880 | − | 0.937167i | \(-0.386562\pi\) | ||||
0.348880 | + | 0.937167i | \(0.386562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6927 | −1.63063 | −0.815313 | − | 0.579020i | \(-0.803435\pi\) | ||||
−0.815313 | + | 0.579020i | \(0.803435\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0589 | −1.79763 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.63757 | 1.25992 | 0.629960 | − | 0.776628i | \(-0.283071\pi\) | ||||
0.629960 | + | 0.776628i | \(0.283071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.714485 | 0.100048 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.37409 | −0.463466 | −0.231733 | − | 0.972779i | \(-0.574440\pi\) | ||||
−0.231733 | + | 0.972779i | \(0.574440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.2246 | −1.91805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.2889 | 2.28998 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7788 | 1.53347 | 0.766735 | − | 0.641964i | \(-0.221880\pi\) | ||||
0.766735 | + | 0.641964i | \(0.221880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.13882 | 1.17011 | 0.585053 | − | 0.810995i | \(-0.301074\pi\) | ||||
0.585053 | + | 0.810995i | \(0.301074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.07200 | 0.513024 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.96141 | 0.367317 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.7093 | −1.67486 | −0.837429 | − | 0.546546i | \(-0.815942\pi\) | ||||
−0.837429 | + | 0.546546i | \(0.815942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.12198 | −0.737000 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2583 | 1.92951 | 0.964753 | − | 0.263158i | \(-0.0847640\pi\) | ||||
0.964753 | + | 0.263158i | \(0.0847640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.03341 | 0.706157 | 0.353079 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353079 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.0254 | 1.15764 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.80333 | 0.547391 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.76474 | 0.648584 | 0.324292 | − | 0.945957i | \(-0.394874\pi\) | ||||
0.324292 | + | 0.945957i | \(0.394874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.63479 | −0.514977 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.56557 | 0.171843 | 0.0859217 | − | 0.996302i | \(-0.472616\pi\) | ||||
0.0859217 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.795646 | −0.0862999 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.4152 | 1.86710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.64526 | 0.704396 | 0.352198 | − | 0.935925i | \(-0.385434\pi\) | ||||
0.352198 | + | 0.935925i | \(0.385434\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.7261 | −1.11225 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.2528 | −1.97530 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74789 | −0.279006 | −0.139503 | − | 0.990222i | \(-0.544551\pi\) | ||||
−0.139503 | + | 0.990222i | \(0.544551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.5592 | 1.96577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.59501 | −0.556724 | −0.278362 | − | 0.960476i | \(-0.589791\pi\) | ||||
−0.278362 | + | 0.960476i | \(0.589791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.78130 | 0.865248 | 0.432624 | − | 0.901575i | \(-0.357588\pi\) | ||||
0.432624 | + | 0.901575i | \(0.357588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.87534 | −0.768554 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.3855 | −1.68072 | −0.840358 | − | 0.542031i | \(-0.817655\pi\) | ||||
−0.840358 | + | 0.542031i | \(0.817655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.04998 | −0.866831 | −0.433415 | − | 0.901194i | \(-0.642692\pi\) | ||||
−0.433415 | + | 0.901194i | \(0.642692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.68904 | 0.634895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9394 | −1.02909 | −0.514545 | − | 0.857463i | \(-0.672039\pi\) | ||||
−0.514545 | + | 0.857463i | \(0.672039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.81740 | 0.635726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.07200 | −0.376457 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.268672 | 0.0246291 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.0720 | 1.09745 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.8814 | 1.07131 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.64276 | 0.325818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9176 | −1.67867 | −0.839334 | − | 0.543616i | \(-0.817055\pi\) | ||||
−0.839334 | + | 0.543616i | \(0.817055\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.4354 | −2.50360 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.75067 | −0.677180 | −0.338590 | − | 0.940934i | \(-0.609950\pi\) | ||||
−0.338590 | + | 0.940934i | \(0.609950\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.50125 | 0.563730 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.44240 | −0.726606 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.95253 | −0.337687 | −0.168844 | − | 0.985643i | \(-0.554003\pi\) | ||||
−0.168844 | + | 0.985643i | \(0.554003\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.04998 | −0.597971 | −0.298986 | − | 0.954258i | \(-0.596648\pi\) | ||||
−0.298986 | + | 0.954258i | \(0.596648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.9701 | 1.93443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.80333 | −0.401675 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.3934 | −1.61054 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.65932 | 0.219337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.3738 | −1.09563 | −0.547813 | − | 0.836601i | \(-0.684539\pi\) | ||||
−0.547813 | + | 0.836601i | \(0.684539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.5126 | −1.50654 | −0.753268 | − | 0.657713i | \(-0.771524\pi\) | ||||
−0.753268 | + | 0.657713i | \(0.771524\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.09403 | 0.0884473 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.9446 | 0.959410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.7568 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.97279 | −0.711588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.30208 | −0.181429 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.6710 | −1.30577 | −0.652886 | − | 0.757456i | \(-0.726442\pi\) | ||||
−0.652886 | + | 0.757456i | \(0.726442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −37.8279 | −2.94490 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.2054 | −1.33139 | −0.665696 | − | 0.746223i | \(-0.731865\pi\) | ||||
−0.665696 | + | 0.746223i | \(0.731865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.4731 | 2.02445 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.58732 | −0.728910 | −0.364455 | − | 0.931221i | \(-0.618745\pi\) | ||||
−0.364455 | + | 0.931221i | \(0.618745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.76992 | 0.284979 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 31.3237 | 2.35443 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3766 | 0.775583 | 0.387791 | − | 0.921747i | \(-0.373238\pi\) | ||||
0.387791 | + | 0.921747i | \(0.373238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.121981 | 0.00906675 | 0.00453338 | − | 0.999990i | \(-0.498557\pi\) | ||||
0.00453338 | + | 0.999990i | \(0.498557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.3031 | 1.79654 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.44887 | −0.547652 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.29052 | 0.0943721 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.85081 | 0.207366 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.3855 | 0.968538 | 0.484269 | − | 0.874919i | \(-0.339086\pi\) | ||||
0.484269 | + | 0.874919i | \(0.339086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6067 | −1.12339 | −0.561696 | − | 0.827344i | \(-0.689851\pi\) | ||||
−0.561696 | + | 0.827344i | \(0.689851\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.87534 | 0.563965 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2798 | 0.732404 | 0.366202 | − | 0.930535i | \(-0.380658\pi\) | ||||
0.366202 | + | 0.930535i | \(0.380658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.66451 | −0.117994 | −0.0589969 | − | 0.998258i | \(-0.518790\pi\) | ||||
−0.0589969 | + | 0.998258i | \(0.518790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.4575 | −2.57151 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.54873 | 0.459630 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.2311 | −0.924099 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.37409 | −0.651544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.2277 | 2.16006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2197 | 1.18545 | 0.592727 | − | 0.805404i | \(-0.298051\pi\) | ||||
0.592727 | + | 0.805404i | \(0.298051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 43.2361 | 2.96249 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.6655 | 2.15957 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.03341 | −0.273806 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0448 | 1.08421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.268672 | −0.0180728 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1002 | −1.34601 | −0.673005 | − | 0.739638i | \(-0.734997\pi\) | ||||
−0.673005 | + | 0.739638i | \(0.734997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.3511 | 1.02341 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.9456 | −1.72207 | −0.861034 | − | 0.508547i | \(-0.830183\pi\) | ||||
−0.861034 | + | 0.508547i | \(0.830183\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.24146 | 0.610693 | 0.305346 | − | 0.952241i | \(-0.401228\pi\) | ||||
0.305346 | + | 0.952241i | \(0.401228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.7736 | 0.840442 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.6539 | 1.54962 | 0.774808 | − | 0.632197i | \(-0.217846\pi\) | ||||
0.774808 | + | 0.632197i | \(0.217846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.5794 | −1.66861 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.3303 | 0.995810 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.68135 | −0.173442 | −0.0867211 | − | 0.996233i | \(-0.527639\pi\) | ||||
−0.0867211 | + | 0.996233i | \(0.527639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.6680 | 1.97550 | 0.987751 | − | 0.156041i | \(-0.0498733\pi\) | ||||
0.987751 | + | 0.156041i | \(0.0498733\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.8778 | −1.33931 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.96141 | −0.189197 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.50125 | −0.413665 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.16335 | 0.263842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.90078 | −0.624932 | −0.312466 | − | 0.949929i | \(-0.601155\pi\) | ||||
−0.312466 | + | 0.949929i | \(0.601155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0577 | −0.695189 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.11588 | −0.132502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.98316 | 0.560354 | 0.280177 | − | 0.959948i | \(-0.409607\pi\) | ||||
0.280177 | + | 0.959948i | \(0.409607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.51532 | 0.156294 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.6664 | 1.65061 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.77243 | 0.602594 | 0.301297 | − | 0.953530i | \(-0.402581\pi\) | ||||
0.301297 | + | 0.953530i | \(0.402581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.99204 | 0.613806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.6719 | 1.08150 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.4213 | −1.18414 | −0.592068 | − | 0.805888i | \(-0.701688\pi\) | ||||
−0.592068 | + | 0.805888i | \(0.701688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.56279 | 0.398661 | 0.199331 | − | 0.979932i | \(-0.436123\pi\) | ||||
0.199331 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.65932 | −0.160950 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.1082 | 1.09197 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.61304 | −0.337255 | −0.168628 | − | 0.985680i | \(-0.553934\pi\) | ||||
−0.168628 | + | 0.985680i | \(0.553934\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16.4241 | −0.983283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.65664 | −0.397102 | −0.198551 | − | 0.980091i | \(-0.563624\pi\) | ||||
−0.198551 | + | 0.980091i | \(0.563624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.46784 | −0.146698 | −0.0733490 | − | 0.997306i | \(-0.523369\pi\) | ||||
−0.0733490 | + | 0.997306i | \(0.523369\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −51.1995 | −3.03280 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.46784 | 0.263728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9278 | −0.995754 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.30754 | −0.428376 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.00796359 | −0.000465238 0 | −0.000232619 | − | 1.00000i | \(-0.500074\pi\) | ||||
−0.000232619 | 1.00000i | \(0.500074\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.8818 | −2.03090 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.6934 | 0.794570 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.30208 | 0.133133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6927 | −0.616319 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.8789 | −0.854773 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.0638 | −1.54967 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7224 | −0.611962 | −0.305981 | − | 0.952038i | \(-0.598984\pi\) | ||||
−0.305981 | + | 0.952038i | \(0.598984\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.3523 | 1.32847 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.11429 | −0.119891 | −0.0599453 | − | 0.998202i | \(-0.519093\pi\) | ||||
−0.0599453 | + | 0.998202i | \(0.519093\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2608 | 1.31478 | 0.657389 | − | 0.753551i | \(-0.271661\pi\) | ||||
0.657389 | + | 0.753551i | \(0.271661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0589 | −0.679440 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8870 | 0.892303 | 0.446151 | − | 0.894958i | \(-0.352794\pi\) | ||||
0.446151 | + | 0.894958i | \(0.352794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.4557 | 1.76118 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −46.2336 | −2.58051 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.74670 | 0.0971891 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.76992 | −0.209118 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0668 | −1.33090 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.63757 | 0.476205 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1566 | 0.943011 | 0.471506 | − | 0.881863i | \(-0.343711\pi\) | ||||
0.471506 | + | 0.881863i | \(0.343711\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2424 | 0.561279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.5988 | 2.21815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9394 | −0.595906 | −0.297953 | − | 0.954581i | \(-0.596304\pi\) | ||||
−0.297953 | + | 0.954581i | \(0.596304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.0913 | −1.58003 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3738 | −1.04915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.1297 | 0.976068 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.71699 | −0.521635 | −0.260818 | − | 0.965388i | \(-0.583992\pi\) | ||||
−0.260818 | + | 0.965388i | \(0.583992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.4137 | −1.30684 | −0.653418 | − | 0.756998i | \(-0.726665\pi\) | ||||
−0.653418 | + | 0.756998i | \(0.726665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.85081 | −0.152165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 37.3160 | 1.98613 | 0.993064 | − | 0.117573i | \(-0.0375115\pi\) | ||||
0.993064 | + | 0.117573i | \(0.0375115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.1474 | −2.55540 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.714485 | 0.0378146 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.9703 | −0.631767 | −0.315884 | − | 0.948798i | \(-0.602301\pi\) | ||||
−0.315884 | + | 0.948798i | \(0.602301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2663 | 1.22454 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.1034 | 1.68499 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8674 | −0.935221 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.84165 | −0.304932 | −0.152466 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152466 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.1931 | 0.947093 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.37409 | −0.175174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.31615 | −0.119925 | −0.0599627 | − | 0.998201i | \(-0.519098\pi\) | ||||
−0.0599627 | + | 0.998201i | \(0.519098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.68727 | 0.500249 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.54873 | −0.337277 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.9318 | −1.53749 | −0.768746 | − | 0.639554i | \(-0.779119\pi\) | ||||
−0.768746 | + | 0.639554i | \(0.779119\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −50.3081 | −2.57736 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.3932 | 1.70631 | 0.853155 | − | 0.521657i | \(-0.174686\pi\) | ||||
0.853155 | + | 0.521657i | \(0.174686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2246 | −0.724954 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −43.5409 | −2.21331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.9174 | 1.82109 | 0.910543 | − | 0.413413i | \(-0.135664\pi\) | ||||
0.910543 | + | 0.413413i | \(0.135664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.618504 | −0.0312791 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.6116 | −1.03972 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.0717 | −0.858972 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4603 | 1.27781 | 0.638907 | − | 0.769284i | \(-0.279387\pi\) | ||||
0.638907 | + | 0.769284i | \(0.279387\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.2889 | 0.865529 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.3212 | −0.815039 | −0.407520 | − | 0.913196i | \(-0.633606\pi\) | ||||
−0.407520 | + | 0.913196i | \(0.633606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.03341 | 0.200918 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.7255 | 0.682026 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0819 | 0.598877 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.2029 | 1.09786 | 0.548931 | − | 0.835868i | \(-0.315035\pi\) | ||||
0.548931 | + | 0.835868i | \(0.315035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.5110 | −0.518472 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7788 | 0.579597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.63628 | −0.227586 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7482 | −0.918102 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.3634 | −1.04367 | −0.521836 | − | 0.853046i | \(-0.674753\pi\) | ||||
−0.521836 | + | 0.853046i | \(0.674753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9370 | −0.533035 | −0.266518 | − | 0.963830i | \(-0.585873\pi\) | ||||
−0.266518 | + | 0.963830i | \(0.585873\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.1722 | 1.71013 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.01287 | 0.0491315 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.13882 | 0.442259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.7736 | −0.616716 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7451 | 0.854752 | 0.427376 | − | 0.904074i | \(-0.359438\pi\) | ||||
0.427376 | + | 0.904074i | \(0.359438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.46516 | −0.310696 | −0.155348 | − | 0.987860i | \(-0.549650\pi\) | ||||
−0.155348 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −51.5734 | −2.47276 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.9664 | −0.715940 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.85849 | −0.327338 | −0.163669 | − | 0.986515i | \(-0.552333\pi\) | ||||
−0.163669 | + | 0.986515i | \(0.552333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.07200 | 0.193905 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.05794 | −0.240310 | −0.120155 | − | 0.992755i | \(-0.538339\pi\) | ||||
−0.120155 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6793 | −0.932889 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −35.5653 | −1.68218 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.7734 | −1.02755 | −0.513776 | − | 0.857924i | \(-0.671754\pi\) | ||||
−0.513776 | + | 0.857924i | \(0.671754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.4605 | 1.01054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −49.2311 | −2.31308 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.96141 | 0.138833 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0267 | 1.49815 | 0.749074 | − | 0.662487i | \(-0.230499\pi\) | ||||
0.749074 | + | 0.662487i | \(0.230499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.765931 | 0.0357506 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.6729 | 1.47516 | 0.737578 | − | 0.675262i | \(-0.235970\pi\) | ||||
0.737578 | + | 0.675262i | \(0.235970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.3221 | 1.82745 | 0.913726 | − | 0.406332i | \(-0.133192\pi\) | ||||
0.913726 | + | 0.406332i | \(0.133192\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.7645 | 1.47304 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.7210 | −1.65297 | −0.826484 | − | 0.562960i | \(-0.809663\pi\) | ||||
−0.826484 | + | 0.562960i | \(0.809663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7093 | −0.633037 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −47.2210 | −2.17583 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −51.3608 | −2.36157 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.5092 | 1.12456 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.7393 | −0.629079 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.3365 | −1.29473 | −0.647364 | − | 0.762181i | \(-0.724129\pi\) | ||||
−0.647364 | + | 0.762181i | \(0.724129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.51532 | −0.114689 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.12198 | −0.278560 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.13763 | 0.369511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.3364 | −1.60125 | −0.800623 | − | 0.599169i | \(-0.795498\pi\) | ||||
−0.800623 | + | 0.599169i | \(0.795498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.3335 | −2.00483 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9975 | 0.676828 | 0.338414 | − | 0.940997i | \(-0.390110\pi\) | ||||
0.338414 | + | 0.940997i | \(0.390110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75946 | 0.0792420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −57.9227 | −2.60343 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.2583 | 0.729285 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.9008 | −1.33854 | −0.669271 | − | 0.743018i | \(-0.733394\pi\) | ||||
−0.669271 | + | 0.743018i | \(0.733394\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.7546 | −2.04417 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.0975 | 1.11904 | 0.559520 | − | 0.828817i | \(-0.310986\pi\) | ||||
0.559520 | + | 0.828817i | \(0.310986\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.5691 | 0.737315 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.65932 | 0.118105 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.5111 | −1.13076 | −0.565381 | − | 0.824830i | \(-0.691271\pi\) | ||||
−0.565381 | + | 0.824830i | \(0.691271\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.03341 | 0.266902 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.5338 | 0.818288 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.0050 | −1.14592 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.4891 | 1.82469 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.4958 | −1.11914 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.17714 | 0.270625 | 0.135313 | − | 0.990803i | \(-0.456796\pi\) | ||||
0.135313 | + | 0.990803i | \(0.456796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6756 | 0.685447 | 0.342723 | − | 0.939436i | \(-0.388651\pi\) | ||||
0.342723 | + | 0.939436i | \(0.388651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.0254 | 0.437546 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.08366 | −0.0472051 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7004 | −0.769584 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 47.9633 | 2.08143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.46784 | −0.193524 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 51.4854 | 2.22591 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.5947 | 1.19080 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.80333 | 0.206894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3815 | −0.747289 | −0.373644 | − | 0.927572i | \(-0.621892\pi\) | ||||
−0.373644 | + | 0.927572i | \(0.621892\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.324386 | 0.0139207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.8007 | 1.14801 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1579 | 1.16119 | 0.580594 | − | 0.814193i | \(-0.302820\pi\) | ||||
0.580594 | + | 0.814193i | \(0.302820\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.2133 | 1.58823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.5749 | 1.81375 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.76474 | 0.245142 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.8090 | −0.840843 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3699 | 1.28681 | 0.643407 | − | 0.765524i | \(-0.277520\pi\) | ||||
0.643407 | + | 0.765524i | \(0.277520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6927 | 0.452254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.43191 | 0.144895 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6321 | 0.490235 | 0.245118 | − | 0.969493i | \(-0.421173\pi\) | ||||
0.245118 | + | 0.969493i | \(0.421173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.3959 | 1.36291 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.63479 | −0.194643 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6979 | 0.993468 | 0.496734 | − | 0.867903i | \(-0.334532\pi\) | ||||
0.496734 | + | 0.867903i | \(0.334532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.0751 | −1.30045 | −0.650227 | − | 0.759740i | \(-0.725326\pi\) | ||||
−0.650227 | + | 0.759740i | \(0.725326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.5963 | 1.48706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.67867 | −0.361926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2880 | −0.428296 | −0.214148 | − | 0.976801i | \(-0.568697\pi\) | ||||
−0.214148 | + | 0.976801i | \(0.568697\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.5032 | −1.72481 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.56557 | 0.0649507 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.2069 | −0.671219 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0589 | 0.498572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2262 | 1.33012 | 0.665058 | − | 0.746791i | \(-0.268407\pi\) | ||||
0.665058 | + | 0.746791i | \(0.268407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.2222 | −1.08047 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.3373 | 1.12450 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.3340 | −0.876082 | −0.438041 | − | 0.898955i | \(-0.644328\pi\) | ||||
−0.438041 | + | 0.898955i | \(0.644328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.795646 | −0.0326183 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.42647 | −0.181163 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0859 | −1.31099 | −0.655497 | − | 0.755198i | \(-0.727541\pi\) | ||||
−0.655497 | + | 0.755198i | \(0.727541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5626 | 0.471649 | 0.235824 | − | 0.971796i | \(-0.424221\pi\) | ||||
0.235824 | + | 0.971796i | \(0.424221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −55.8243 | −2.27334 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.7501 | −1.45345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.4276 | 1.11325 | 0.556626 | − | 0.830764i | \(-0.312096\pi\) | ||||
0.556626 | + | 0.830764i | \(0.312096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.4152 | 0.705699 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.63757 | −0.349439 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8839 | 0.924274 | 0.462137 | − | 0.886809i | \(-0.347083\pi\) | ||||
0.462137 | + | 0.886809i | \(0.347083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.1858 | −1.41883 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.5576 | −1.18994 | −0.594972 | − | 0.803746i | \(-0.702837\pi\) | ||||
−0.594972 | + | 0.803746i | \(0.702837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.5730 | 1.26903 | 0.634513 | − | 0.772913i | \(-0.281201\pi\) | ||||
0.634513 | + | 0.772913i | \(0.281201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.56279 | −0.263356 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.64526 | 0.266237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6373 | −1.18549 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 83.0445 | 3.31648 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.675794 | 0.0269457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.6092 | 1.53701 | 0.768503 | − | 0.639846i | \(-0.221002\pi\) | ||||
0.768503 | + | 0.639846i | \(0.221002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.7928 | 1.82010 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.0228 | 2.22320 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 66.2039 | 2.61898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7463 | 0.898425 | 0.449213 | − | 0.893425i | \(-0.351705\pi\) | ||||
0.449213 | + | 0.893425i | \(0.351705\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.9406 | 0.944124 | 0.472062 | − | 0.881565i | \(-0.343510\pi\) | ||||
0.472062 | + | 0.881565i | \(0.343510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 84.2089 | 3.31572 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.5329 | −1.16106 | −0.580529 | − | 0.814240i | \(-0.697154\pi\) | ||||
−0.580529 | + | 0.814240i | \(0.697154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.5775 | 2.22086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.7261 | −0.420391 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.57298 | −0.374620 | −0.187310 | − | 0.982301i | \(-0.559977\pi\) | ||||
−0.187310 | + | 0.982301i | \(0.559977\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.9529 | 0.896844 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.5681 | 0.958492 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5947 | −0.841211 | −0.420606 | − | 0.907244i | \(-0.638182\pi\) | ||||
−0.420606 | + | 0.907244i | \(0.638182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.9302 | −0.541823 | −0.270911 | − | 0.962604i | \(-0.587325\pi\) | ||||
−0.270911 | + | 0.962604i | \(0.587325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.714485 | −0.0277483 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.2528 | −0.746593 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0757 | −0.583733 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −53.4530 | −2.06661 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.8968 | 1.69462 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.83692 | 0.147902 | 0.0739512 | − | 0.997262i | \(-0.476439\pi\) | ||||
0.0739512 | + | 0.997262i | \(0.476439\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.7473 | 0.413665 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3047 | −0.857239 | −0.428619 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428619 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.74789 | −0.105455 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −68.9977 | −2.64400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.8305 | 0.758795 | 0.379397 | − | 0.925234i | \(-0.376131\pi\) | ||||
0.379397 | + | 0.925234i | \(0.376131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7050 | 0.447226 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.5760 | 0.937634 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.37409 | 0.128542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.8996 | −1.17548 | −0.587738 | − | 0.809051i | \(-0.699981\pi\) | ||||
−0.587738 | + | 0.809051i | \(0.699981\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.5592 | 0.742992 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.8778 | 0.791942 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.20038 | 0.0454677 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 62.9033 | 2.37922 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.62341 | −0.136854 | −0.0684272 | − | 0.997656i | \(-0.521798\pi\) | ||||
−0.0684272 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3527 | 0.616754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −68.0238 | −2.56192 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.59501 | −0.210422 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0602 | −1.57960 | −0.789801 | − | 0.613363i | \(-0.789816\pi\) | ||||
−0.789801 | + | 0.613363i | \(0.789816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.4740 | 0.880345 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.28524 | 0.347735 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.2246 | 0.531970 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.13058 | −0.266297 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.9110 | −0.705260 | −0.352630 | − | 0.935763i | \(-0.614713\pi\) | ||||
−0.352630 | + | 0.935763i | \(0.614713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.78130 | 0.327033 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 81.5562 | 3.03311 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.6882 | 0.916896 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.23645 | −0.194209 | −0.0971047 | − | 0.995274i | \(-0.530958\pi\) | ||||
−0.0971047 | + | 0.995274i | \(0.530958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.6166 | −1.54135 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.87283 | −0.106256 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.77584 | −0.361079 | −0.180540 | − | 0.983568i | \(-0.557784\pi\) | ||||
−0.180540 | + | 0.983568i | \(0.557784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.87534 | −0.290486 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −65.8503 | −2.42563 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8318 | −0.876668 | −0.438334 | − | 0.898812i | \(-0.644431\pi\) | ||||
−0.438334 | + | 0.898812i | \(0.644431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.2889 | −0.635125 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.5492 | 1.56098 | 0.780489 | − | 0.625169i | \(-0.214970\pi\) | ||||
0.780489 | + | 0.625169i | \(0.214970\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.6053 | 1.45102 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.37500 | 0.233249 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.3855 | −0.635251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.8903 | 0.397393 | 0.198697 | − | 0.980061i | \(-0.436329\pi\) | ||||
0.198697 | + | 0.980061i | \(0.436329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.3294 | −0.959496 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.8234 | 1.99523 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.58186 | 0.166530 | 0.0832652 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832652 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.4059 | −1.06737 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.0537 | 1.48819 | 0.744097 | − | 0.668071i | \(-0.232880\pi\) | ||||
0.744097 | + | 0.668071i | \(0.232880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.04998 | −0.327631 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.23987 | −0.117138 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.7788 | −0.425308 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.6173 | −0.418931 | −0.209465 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209465 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8891 | 0.860346 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.9663 | 0.574268 | 0.287134 | − | 0.957890i | \(-0.407297\pi\) | ||||
0.287134 | + | 0.957890i | \(0.407297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.2056 | −0.546203 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.68904 | 0.239968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.0466 | 1.04070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78.0940 | 2.79442 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.6692 | 0.667181 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.5850 | 1.87684 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.2256 | 1.29130 | 0.645652 | − | 0.763632i | \(-0.276586\pi\) | ||||
0.645652 | + | 0.763632i | \(0.276586\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.9880 | 0.925199 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9394 | −0.388959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.13882 | −0.324529 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.5721 | 0.942414 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.2725 | −1.03688 | −0.518442 | − | 0.855113i | \(-0.673488\pi\) | ||||
−0.518442 | + | 0.855113i | \(0.673488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32067 | 0.0820994 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.0595 | 0.956101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.9805 | 1.02270 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.81740 | 0.240282 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −51.6475 | −1.81808 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.16631 | 0.216796 | 0.108398 | − | 0.994108i | \(-0.465428\pi\) | ||||
0.108398 | + | 0.994108i | \(0.465428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.9843 | −1.05289 | −0.526445 | − | 0.850209i | \(-0.676475\pi\) | ||||
−0.526445 | + | 0.850209i | \(0.676475\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.4526 | 0.612089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.3695 | 1.72934 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.5161 | −2.43206 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.07200 | −0.142287 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8119 | −0.412239 | −0.206120 | − | 0.978527i | \(-0.566084\pi\) | ||||
−0.206120 | + | 0.978527i | \(0.566084\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.5212 | −1.51705 | −0.758527 | − | 0.651641i | \(-0.774081\pi\) | ||||
−0.758527 | + | 0.651641i | \(0.774081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.1556 | 1.67656 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2470 | −0.877925 | −0.438962 | − | 0.898505i | \(-0.644654\pi\) | ||||
−0.438962 | + | 0.898505i | \(0.644654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.79314 | 0.0622784 | 0.0311392 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311392 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9269 | −0.517808 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.268672 | 0.00930892 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50.9521 | 1.76327 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.4985 | −0.397445 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.9588 | −1.79382 | −0.896909 | − | 0.442215i | \(-0.854193\pi\) | ||||
−0.896909 | + | 0.442215i | \(0.854193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8858 | 0.478821 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.7022 | −0.609695 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.96141 | −0.101875 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.0720 | 0.414799 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.56279 | −0.225234 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.79046 | −0.198494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.9976 | 0.479269 | 0.239634 | − | 0.970863i | \(-0.422972\pi\) | ||||
0.239634 | + | 0.970863i | \(0.422972\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −78.3977 | −2.68114 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.3830 | 0.627950 | 0.313975 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313975 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.4496 | 0.936568 | 0.468284 | − | 0.883578i | \(-0.344872\pi\) | ||||
0.468284 | + | 0.883578i | \(0.344872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8814 | 0.404918 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.7170 | 0.466932 | 0.233466 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233466 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.3919 | 0.965355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −45.0165 | −1.52884 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.6900 | 0.939317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.7093 | 0.464522 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.1894 | −0.378705 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.64276 | 0.123148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.4100 | 1.36455 | 0.682274 | − | 0.731096i | \(-0.260991\pi\) | ||||
0.682274 | + | 0.731096i | \(0.260991\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0211778 | −0.000714308 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.5239 | 0.792541 | 0.396270 | − | 0.918134i | \(-0.370304\pi\) | ||||
0.396270 | + | 0.918134i | \(0.370304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.6502 | −0.593975 | −0.296988 | − | 0.954881i | \(-0.595982\pi\) | ||||
−0.296988 | + | 0.954881i | \(0.595982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92.7620 | −3.11816 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.8763 | 0.432342 | 0.216171 | − | 0.976355i | \(-0.430643\pi\) | ||||
0.216171 | + | 0.976355i | \(0.430643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.9176 | −0.634477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.2625 | −0.745820 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 56.1550 | 1.87916 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.7293 | −1.02717 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.12198 | 0.204407 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.4137 | −0.880946 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.906521 | −0.0302006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.4354 | −0.946272 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.361234 | −0.0120078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.8342 | −1.18986 | −0.594928 | − | 0.803779i | \(-0.702820\pi\) | ||||
−0.594928 | + | 0.803779i | \(0.702820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.7829 | −0.755661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.8214 | 0.424791 | 0.212395 | − | 0.977184i | \(-0.431874\pi\) | ||||
0.212395 | + | 0.977184i | \(0.431874\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.51995 | 0.248874 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −71.9713 | −2.37930 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.75067 | −0.255950 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.6352 | −0.944587 | −0.472294 | − | 0.881441i | \(-0.656574\pi\) | ||||
−0.472294 | + | 0.881441i | \(0.656574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.5145 | −0.939584 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.2583 | −0.535149 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.48254 | 0.311784 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35.7575 | 1.17443 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1744 | 0.366619 | 0.183309 | − | 0.983055i | \(-0.441319\pi\) | ||||
0.183309 | + | 0.983055i | \(0.441319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50125 | 0.213070 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.62259 | −0.184075 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.82175 | −0.124985 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.5433 | −1.61851 | −0.809254 | − | 0.587459i | \(-0.800128\pi\) | ||||
−0.809254 | + | 0.587459i | \(0.800128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 61.8580 | 2.01866 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.1029 | −0.394544 | −0.197272 | − | 0.980349i | \(-0.563208\pi\) | ||||
−0.197272 | + | 0.980349i | \(0.563208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2853 | −0.334937 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.44240 | −0.274631 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.9228 | 0.712396 | 0.356198 | − | 0.934411i | \(-0.384073\pi\) | ||||
0.356198 | + | 0.934411i | \(0.384073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.03341 | −0.195853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.2487 | 1.37001 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.7105 | 0.735665 | 0.367833 | − | 0.929892i | \(-0.380100\pi\) | ||||
0.367833 | + | 0.929892i | \(0.380100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.6398 | −1.28271 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 83.6509 | 2.70405 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.95253 | −0.127634 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.7316 | −0.475213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −70.7937 | −2.28130 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.2177 | 1.48780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0574 | −0.998738 | −0.499369 | − | 0.866390i | \(-0.666435\pi\) | ||||
−0.499369 | + | 0.866390i | \(0.666435\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.64505 | 0.149220 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.871738 | 0.0279754 | 0.0139877 | − | 0.999902i | \(-0.495547\pi\) | ||||
0.0139877 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.04998 | −0.226012 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.0254 | −0.321071 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.9090 | −0.764917 | −0.382459 | − | 0.923973i | \(-0.624923\pi\) | ||||
−0.382459 | + | 0.923973i | \(0.624923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.9194 | 1.02015 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36.8515 | −1.17658 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.2466 | 1.34746 | 0.673728 | − | 0.738979i | \(-0.264692\pi\) | ||||
0.673728 | + | 0.738979i | \(0.264692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.4426 | −0.969982 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.9701 | 0.731147 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.6155 | 0.782729 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.70930 | 0.0542977 | 0.0271489 | − | 0.999631i | \(-0.491357\pi\) | ||||
0.0271489 | + | 0.999631i | \(0.491357\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.6249 | 1.44786 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.92929 | 0.156269 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7479 | 0.783773 | 0.391887 | − | 0.920014i | \(-0.371823\pi\) | ||||
0.391887 | + | 0.920014i | \(0.371823\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.17068 | 0.226870 |
(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 | 1456.2.a.v.1.4 | 4 | ||
4.3 | odd | 2 | 728.2.a.i.1.1 | ✓ | 4 | ||
8.3 | odd | 2 | 5824.2.a.cb.1.4 | 4 | |||
8.5 | even | 2 | 5824.2.a.ce.1.1 | 4 | |||
12.11 | even | 2 | 6552.2.a.br.1.4 | 4 | |||
28.27 | even | 2 | 5096.2.a.s.1.4 | 4 | |||
52.51 | odd | 2 | 9464.2.a.z.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
728.2.a.i.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
1456.2.a.v.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5096.2.a.s.1.4 | 4 | 28.27 | even | 2 | |||
5824.2.a.cb.1.4 | 4 | 8.3 | odd | 2 | |||
5824.2.a.ce.1.1 | 4 | 8.5 | even | 2 | |||
6552.2.a.br.1.4 | 4 | 12.11 | even | 2 | |||
9464.2.a.z.1.1 | 4 | 52.51 | odd | 2 |