Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 625) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.66501\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66501 | 1.88445 | 0.942224 | − | 0.334983i | \(-0.108731\pi\) | ||||
0.942224 | + | 0.334983i | \(0.108731\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.10229 | 2.55115 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.04213 | 0.771852 | 0.385926 | − | 0.922530i | \(-0.373882\pi\) | ||||
0.385926 | + | 0.922530i | \(0.373882\pi\) | |||||||
\(8\) | 8.26764 | 2.92305 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.34867 | −0.406640 | −0.203320 | − | 0.979112i | \(-0.565173\pi\) | ||||
−0.203320 | + | 0.979112i | \(0.565173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.31964 | −0.366002 | −0.183001 | − | 0.983113i | \(-0.558581\pi\) | ||||
−0.183001 | + | 0.983113i | \(0.558581\pi\) | |||||||
\(14\) | 5.44230 | 1.45452 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.8288 | 2.95720 | ||||||||
\(17\) | 4.08717 | 0.991285 | 0.495643 | − | 0.868527i | \(-0.334933\pi\) | ||||
0.495643 | + | 0.868527i | \(0.334933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.88680 | −1.12111 | −0.560554 | − | 0.828118i | \(-0.689412\pi\) | ||||
−0.560554 | + | 0.828118i | \(0.689412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.59423 | −0.766292 | ||||||||
\(23\) | −2.73618 | −0.570532 | −0.285266 | − | 0.958448i | \(-0.592082\pi\) | ||||
−0.285266 | + | 0.958448i | \(0.592082\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.51685 | −0.689711 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.4195 | 1.96911 | ||||||||
\(29\) | 4.61914 | 0.857753 | 0.428876 | − | 0.903363i | \(-0.358910\pi\) | ||||
0.428876 | + | 0.903363i | \(0.358910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.15727 | 1.28548 | 0.642742 | − | 0.766083i | \(-0.277797\pi\) | ||||
0.642742 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(32\) | 14.9886 | 2.64963 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.8924 | 1.86803 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.64640 | 1.42146 | 0.710730 | − | 0.703465i | \(-0.248365\pi\) | ||||
0.710730 | + | 0.703465i | \(0.248365\pi\) | |||||||
\(38\) | −13.0234 | −2.11267 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0996 | 1.57729 | 0.788645 | − | 0.614849i | \(-0.210783\pi\) | ||||
0.788645 | + | 0.614849i | \(0.210783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.43460 | −0.371272 | −0.185636 | − | 0.982619i | \(-0.559435\pi\) | ||||
−0.185636 | + | 0.982619i | \(0.559435\pi\) | |||||||
\(44\) | −6.88131 | −1.03740 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.29194 | −1.07514 | ||||||||
\(47\) | 7.57192 | 1.10448 | 0.552239 | − | 0.833686i | \(-0.313774\pi\) | ||||
0.552239 | + | 0.833686i | \(0.313774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.82971 | −0.404244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.73317 | −0.933723 | ||||||||
\(53\) | −0.621245 | −0.0853345 | −0.0426673 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426673 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 16.8836 | 2.25616 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.3101 | 1.61639 | ||||||||
\(59\) | 11.3412 | 1.47650 | 0.738248 | − | 0.674530i | \(-0.235653\pi\) | ||||
0.738248 | + | 0.674530i | \(0.235653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.647513 | 0.0829056 | 0.0414528 | − | 0.999140i | \(-0.486801\pi\) | ||||
0.0414528 | + | 0.999140i | \(0.486801\pi\) | |||||||
\(62\) | 19.0742 | 2.42243 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16.2872 | 2.03590 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9389 | −1.33639 | −0.668197 | − | 0.743984i | \(-0.732934\pi\) | ||||
−0.668197 | + | 0.743984i | \(0.732934\pi\) | |||||||
\(68\) | 20.8539 | 2.52891 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.95230 | 0.350374 | 0.175187 | − | 0.984535i | \(-0.443947\pi\) | ||||
0.175187 | + | 0.984535i | \(0.443947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.5390 | −1.58462 | −0.792309 | − | 0.610120i | \(-0.791121\pi\) | ||||
−0.792309 | + | 0.610120i | \(0.791121\pi\) | |||||||
\(74\) | 23.0428 | 2.67867 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.9339 | −2.86011 | ||||||||
\(77\) | −2.75416 | −0.313866 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.88929 | 0.212562 | 0.106281 | − | 0.994336i | \(-0.466106\pi\) | ||||
0.106281 | + | 0.994336i | \(0.466106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.9155 | 2.97232 | ||||||||
\(83\) | 2.37481 | 0.260669 | 0.130335 | − | 0.991470i | \(-0.458395\pi\) | ||||
0.130335 | + | 0.991470i | \(0.458395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.48823 | −0.699644 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.1503 | −1.18863 | ||||||||
\(89\) | −7.33882 | −0.777913 | −0.388957 | − | 0.921256i | \(-0.627164\pi\) | ||||
−0.388957 | + | 0.921256i | \(0.627164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.69487 | −0.282499 | ||||||||
\(92\) | −13.9608 | −1.45551 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.1793 | 2.08133 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.79915 | −0.588814 | −0.294407 | − | 0.955680i | \(-0.595122\pi\) | ||||
−0.294407 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(98\) | −7.54121 | −0.761777 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.5536 | −1.14962 | −0.574812 | − | 0.818285i | \(-0.694925\pi\) | ||||
−0.574812 | + | 0.818285i | \(0.694925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6071 | −1.14368 | −0.571842 | − | 0.820364i | \(-0.693771\pi\) | ||||
−0.571842 | + | 0.820364i | \(0.693771\pi\) | |||||||
\(104\) | −10.9103 | −1.06984 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.65562 | −0.160808 | ||||||||
\(107\) | 10.1703 | 0.983204 | 0.491602 | − | 0.870820i | \(-0.336412\pi\) | ||||
0.491602 | + | 0.870820i | \(0.336412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.19475 | 0.114436 | 0.0572182 | − | 0.998362i | \(-0.481777\pi\) | ||||
0.0572182 | + | 0.998362i | \(0.481777\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 24.1559 | 2.28252 | ||||||||
\(113\) | 4.48257 | 0.421685 | 0.210842 | − | 0.977520i | \(-0.432379\pi\) | ||||
0.210842 | + | 0.977520i | \(0.432379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 23.5682 | 2.18825 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30.2244 | 2.78238 | ||||||||
\(119\) | 8.34653 | 0.765125 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.18108 | −0.834644 | ||||||||
\(122\) | 1.72563 | 0.156231 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 36.5185 | 3.27946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.17685 | 0.370635 | 0.185318 | − | 0.982679i | \(-0.440669\pi\) | ||||
0.185318 | + | 0.982679i | \(0.440669\pi\) | |||||||
\(128\) | 13.4284 | 1.18691 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.38914 | −0.296111 | −0.148055 | − | 0.988979i | \(-0.547301\pi\) | ||||
−0.148055 | + | 0.988979i | \(0.547301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.97947 | −0.865330 | ||||||||
\(134\) | −29.1522 | −2.51837 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.7913 | 2.89758 | ||||||||
\(137\) | −8.33597 | −0.712190 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.43355 | −0.291230 | −0.145615 | − | 0.989341i | \(-0.546516\pi\) | ||||
−0.145615 | + | 0.989341i | \(0.546516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.86792 | 0.660261 | ||||||||
\(143\) | 1.77976 | 0.148831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −36.0816 | −2.98613 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 44.1164 | 3.62635 | ||||||||
\(149\) | −9.96023 | −0.815974 | −0.407987 | − | 0.912988i | \(-0.633769\pi\) | ||||
−0.407987 | + | 0.912988i | \(0.633769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0404 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827134\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827134\pi\) | |||||||
\(152\) | −40.4023 | −3.27706 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.33987 | −0.591464 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.80843 | −0.623181 | −0.311590 | − | 0.950217i | \(-0.600862\pi\) | ||||
−0.311590 | + | 0.950217i | \(0.600862\pi\) | |||||||
\(158\) | 5.03499 | 0.400562 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.58762 | −0.440366 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6785 | 0.914734 | 0.457367 | − | 0.889278i | \(-0.348793\pi\) | ||||
0.457367 | + | 0.889278i | \(0.348793\pi\) | |||||||
\(164\) | 51.5310 | 4.02390 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.32890 | 0.491218 | ||||||||
\(167\) | 7.51198 | 0.581294 | 0.290647 | − | 0.956830i | \(-0.406129\pi\) | ||||
0.290647 | + | 0.956830i | \(0.406129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2586 | −0.866043 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.4220 | −0.947170 | ||||||||
\(173\) | 5.31381 | 0.404002 | 0.202001 | − | 0.979385i | \(-0.435256\pi\) | ||||
0.202001 | + | 0.979385i | \(0.435256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −15.9532 | −1.20251 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.5580 | −1.46594 | ||||||||
\(179\) | −1.30674 | −0.0976705 | −0.0488352 | − | 0.998807i | \(-0.515551\pi\) | ||||
−0.0488352 | + | 0.998807i | \(0.515551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.1627 | −1.49868 | −0.749341 | − | 0.662184i | \(-0.769630\pi\) | ||||
−0.749341 | + | 0.662184i | \(0.769630\pi\) | |||||||
\(182\) | −7.18186 | −0.532355 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.6217 | −1.66770 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.51225 | −0.403096 | ||||||||
\(188\) | 38.6342 | 2.81769 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2957 | −1.54090 | −0.770452 | − | 0.637498i | \(-0.779970\pi\) | ||||
−0.770452 | + | 0.637498i | \(0.779970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.99352 | 0.575386 | 0.287693 | − | 0.957723i | \(-0.407112\pi\) | ||||
0.287693 | + | 0.957723i | \(0.407112\pi\) | |||||||
\(194\) | −15.4548 | −1.10959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.4380 | −1.03129 | ||||||||
\(197\) | −21.7014 | −1.54616 | −0.773081 | − | 0.634307i | \(-0.781285\pi\) | ||||
−0.773081 | + | 0.634307i | \(0.781285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.34240 | 0.662265 | 0.331133 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331133 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30.7904 | −2.16641 | ||||||||
\(203\) | 9.43288 | 0.662058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −30.9331 | −2.15521 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.6097 | −1.08234 | ||||||||
\(209\) | 6.59069 | 0.455887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.88147 | −0.473740 | −0.236870 | − | 0.971541i | \(-0.576122\pi\) | ||||
−0.236870 | + | 0.971541i | \(0.576122\pi\) | |||||||
\(212\) | −3.16977 | −0.217701 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.1041 | 1.85280 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.6161 | 0.992203 | ||||||||
\(218\) | 3.18402 | 0.215649 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.39359 | −0.362812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.51496 | −0.570204 | −0.285102 | − | 0.958497i | \(-0.592028\pi\) | ||||
−0.285102 | + | 0.958497i | \(0.592028\pi\) | |||||||
\(224\) | 30.6086 | 2.04512 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.9461 | 0.794643 | ||||||||
\(227\) | 20.9836 | 1.39273 | 0.696364 | − | 0.717689i | \(-0.254800\pi\) | ||||
0.696364 | + | 0.717689i | \(0.254800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.7629 | 1.96679 | 0.983394 | − | 0.181485i | \(-0.0580904\pi\) | ||||
0.983394 | + | 0.181485i | \(0.0580904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.1894 | 2.50726 | ||||||||
\(233\) | −2.27154 | −0.148813 | −0.0744066 | − | 0.997228i | \(-0.523706\pi\) | ||||
−0.0744066 | + | 0.997228i | \(0.523706\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 57.8660 | 3.76676 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.2436 | 1.44184 | ||||||||
\(239\) | −15.4308 | −0.998135 | −0.499067 | − | 0.866563i | \(-0.666324\pi\) | ||||
−0.499067 | + | 0.866563i | \(0.666324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.84184 | −0.311890 | −0.155945 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155945 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(242\) | −24.4677 | −1.57284 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.30380 | 0.211504 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.44880 | 0.410328 | ||||||||
\(248\) | 59.1737 | 3.75754 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.8293 | 1.12537 | 0.562687 | − | 0.826670i | \(-0.309768\pi\) | ||||
0.562687 | + | 0.826670i | \(0.309768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.69020 | 0.232001 | ||||||||
\(254\) | 11.1313 | 0.698443 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.21240 | 0.200775 | ||||||||
\(257\) | 5.88929 | 0.367364 | 0.183682 | − | 0.982986i | \(-0.441198\pi\) | ||||
0.183682 | + | 0.982986i | \(0.441198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6571 | 1.09716 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.03210 | −0.558005 | ||||||||
\(263\) | 23.6773 | 1.46000 | 0.730002 | − | 0.683445i | \(-0.239519\pi\) | ||||
0.730002 | + | 0.683445i | \(0.239519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.5954 | −1.63067 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −55.8132 | −3.40934 | ||||||||
\(269\) | −13.7460 | −0.838111 | −0.419056 | − | 0.907961i | \(-0.637639\pi\) | ||||
−0.419056 | + | 0.907961i | \(0.637639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.49882 | 0.455521 | 0.227760 | − | 0.973717i | \(-0.426860\pi\) | ||||
0.227760 | + | 0.973717i | \(0.426860\pi\) | |||||||
\(272\) | 48.3463 | 2.93143 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.2155 | −1.34209 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.83798 | −0.170517 | −0.0852587 | − | 0.996359i | \(-0.527172\pi\) | ||||
−0.0852587 | + | 0.996359i | \(0.527172\pi\) | |||||||
\(278\) | −9.15045 | −0.548807 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9609 | 1.36974 | 0.684868 | − | 0.728667i | \(-0.259860\pi\) | ||||
0.684868 | + | 0.728667i | \(0.259860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.1247 | 1.49351 | 0.746753 | − | 0.665101i | \(-0.231612\pi\) | ||||
0.746753 | + | 0.665101i | \(0.231612\pi\) | |||||||
\(284\) | 15.0635 | 0.893854 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.74308 | 0.280464 | ||||||||
\(287\) | 20.6246 | 1.21743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.295018 | −0.0173540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −69.0798 | −4.04259 | ||||||||
\(293\) | −28.8755 | −1.68692 | −0.843461 | − | 0.537190i | \(-0.819486\pi\) | ||||
−0.843461 | + | 0.537190i | \(0.819486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 71.4853 | 4.15500 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.5441 | −1.53766 | ||||||||
\(299\) | 3.61076 | 0.208816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.97176 | −0.286567 | ||||||||
\(302\) | −56.0730 | −3.22664 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −57.8049 | −3.31534 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9526 | −1.36704 | −0.683522 | − | 0.729930i | \(-0.739553\pi\) | ||||
−0.683522 | + | 0.729930i | \(0.739553\pi\) | |||||||
\(308\) | −14.0525 | −0.800717 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.88835 | 0.560717 | 0.280358 | − | 0.959895i | \(-0.409547\pi\) | ||||
0.280358 | + | 0.959895i | \(0.409547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7786 | 1.06143 | 0.530713 | − | 0.847551i | \(-0.321924\pi\) | ||||
0.530713 | + | 0.847551i | \(0.321924\pi\) | |||||||
\(314\) | −20.8096 | −1.17435 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.63973 | 0.542277 | ||||||||
\(317\) | −25.8818 | −1.45367 | −0.726834 | − | 0.686813i | \(-0.759009\pi\) | ||||
−0.726834 | + | 0.686813i | \(0.759009\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.22970 | −0.348796 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.8911 | −0.829848 | ||||||||
\(323\) | −19.9732 | −1.11134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 31.1234 | 1.72377 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 83.4997 | 4.61050 | ||||||||
\(329\) | 15.4628 | 0.852494 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.29743 | 0.0713134 | 0.0356567 | − | 0.999364i | \(-0.488648\pi\) | ||||
0.0356567 | + | 0.999364i | \(0.488648\pi\) | |||||||
\(332\) | 12.1170 | 0.665006 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.0195 | 1.09542 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.2769 | 0.614293 | 0.307147 | − | 0.951662i | \(-0.400626\pi\) | ||||
0.307147 | + | 0.951662i | \(0.400626\pi\) | |||||||
\(338\) | −30.0042 | −1.63201 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.65281 | −0.522729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0735 | −1.08387 | ||||||||
\(344\) | −20.1284 | −1.08525 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.1614 | 0.761321 | ||||||||
\(347\) | 2.15501 | 0.115687 | 0.0578434 | − | 0.998326i | \(-0.481578\pi\) | ||||
0.0578434 | + | 0.998326i | \(0.481578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.60904 | 0.300245 | 0.150122 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150122 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.2147 | −1.07745 | ||||||||
\(353\) | −18.4969 | −0.984492 | −0.492246 | − | 0.870456i | \(-0.663824\pi\) | ||||
−0.492246 | + | 0.870456i | \(0.663824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −37.4448 | −1.98457 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.48248 | −0.184055 | ||||||||
\(359\) | −11.2450 | −0.593487 | −0.296743 | − | 0.954957i | \(-0.595901\pi\) | ||||
−0.296743 | + | 0.954957i | \(0.595901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.88081 | 0.256885 | ||||||||
\(362\) | −53.7339 | −2.82419 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.7500 | −0.720696 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5677 | 1.49122 | 0.745610 | − | 0.666383i | \(-0.232158\pi\) | ||||
0.745610 | + | 0.666383i | \(0.232158\pi\) | |||||||
\(368\) | −32.3656 | −1.68718 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26866 | −0.0658656 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0848 | −0.729284 | −0.364642 | − | 0.931148i | \(-0.618809\pi\) | ||||
−0.364642 | + | 0.931148i | \(0.618809\pi\) | |||||||
\(374\) | −14.6902 | −0.759613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 62.6020 | 3.22845 | ||||||||
\(377\) | −6.09559 | −0.313939 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9903 | 1.12957 | 0.564783 | − | 0.825239i | \(-0.308960\pi\) | ||||
0.564783 | + | 0.825239i | \(0.308960\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −56.7534 | −2.90376 | ||||||||
\(383\) | −14.7436 | −0.753363 | −0.376682 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376682 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.3028 | 1.08429 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −29.5889 | −1.50215 | ||||||||
\(389\) | 14.2568 | 0.722847 | 0.361423 | − | 0.932402i | \(-0.382291\pi\) | ||||
0.361423 | + | 0.932402i | \(0.382291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1832 | −0.565560 | ||||||||
\(392\) | −23.3950 | −1.18163 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −57.8345 | −2.91366 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.49065 | 0.275568 | 0.137784 | − | 0.990462i | \(-0.456002\pi\) | ||||
0.137784 | + | 0.990462i | \(0.456002\pi\) | |||||||
\(398\) | 24.8976 | 1.24800 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.7528 | −1.33597 | −0.667985 | − | 0.744175i | \(-0.732843\pi\) | ||||
−0.667985 | + | 0.744175i | \(0.732843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.44500 | −0.470489 | ||||||||
\(404\) | −58.9497 | −2.93286 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.1387 | 1.24761 | ||||||||
\(407\) | −11.6612 | −0.578022 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.13389 | 0.253854 | 0.126927 | − | 0.991912i | \(-0.459489\pi\) | ||||
0.126927 | + | 0.991912i | \(0.459489\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −59.2230 | −2.91771 | ||||||||
\(413\) | 23.1601 | 1.13964 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.7795 | −0.969769 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.5643 | 0.859096 | ||||||||
\(419\) | −31.8516 | −1.55605 | −0.778026 | − | 0.628231i | \(-0.783779\pi\) | ||||
−0.778026 | + | 0.628231i | \(0.783779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.08044 | 0.150132 | 0.0750658 | − | 0.997179i | \(-0.476083\pi\) | ||||
0.0750658 | + | 0.997179i | \(0.476083\pi\) | |||||||
\(422\) | −18.3392 | −0.892739 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.13623 | −0.249437 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32231 | 0.0639908 | ||||||||
\(428\) | 51.8920 | 2.50830 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.3471 | −1.12459 | −0.562295 | − | 0.826937i | \(-0.690081\pi\) | ||||
−0.562295 | + | 0.826937i | \(0.690081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.21415 | −0.394747 | −0.197374 | − | 0.980328i | \(-0.563241\pi\) | ||||
−0.197374 | + | 0.980328i | \(0.563241\pi\) | |||||||
\(434\) | 38.9520 | 1.86976 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.09596 | 0.291944 | ||||||||
\(437\) | 13.3711 | 0.639628 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.3117 | −1.16034 | −0.580168 | − | 0.814497i | \(-0.697013\pi\) | ||||
−0.580168 | + | 0.814497i | \(0.697013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.3740 | −0.683700 | ||||||||
\(443\) | 0.0631363 | 0.00299970 | 0.00149985 | − | 0.999999i | \(-0.499523\pi\) | ||||
0.00149985 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22.6925 | −1.07452 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 33.2605 | 1.57141 | ||||||||
\(449\) | 11.5711 | 0.546074 | 0.273037 | − | 0.962004i | \(-0.411972\pi\) | ||||
0.273037 | + | 0.962004i | \(0.411972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6210 | −0.641389 | ||||||||
\(452\) | 22.8714 | 1.07578 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 55.9215 | 2.62452 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.3967 | 1.93646 | 0.968228 | − | 0.250071i | \(-0.0804539\pi\) | ||||
0.968228 | + | 0.250071i | \(0.0804539\pi\) | |||||||
\(458\) | 79.3185 | 3.70631 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.3707 | −1.36793 | −0.683965 | − | 0.729515i | \(-0.739746\pi\) | ||||
−0.683965 | + | 0.729515i | \(0.739746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.5501 | 1.41978 | 0.709891 | − | 0.704311i | \(-0.248744\pi\) | ||||
0.709891 | + | 0.704311i | \(0.248744\pi\) | |||||||
\(464\) | 54.6388 | 2.53654 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.05367 | −0.280431 | ||||||||
\(467\) | 32.7149 | 1.51386 | 0.756932 | − | 0.653494i | \(-0.226697\pi\) | ||||
0.756932 | + | 0.653494i | \(0.226697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.3386 | −1.03150 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 93.7648 | 4.31588 | ||||||||
\(473\) | 3.28347 | 0.150974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 42.5864 | 1.95195 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −41.1233 | −1.88093 | ||||||||
\(479\) | 12.3353 | 0.563613 | 0.281807 | − | 0.959471i | \(-0.409066\pi\) | ||||
0.281807 | + | 0.959471i | \(0.409066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4101 | −0.520256 | ||||||||
\(482\) | −12.9036 | −0.587741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.8446 | −2.12930 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.2962 | −1.59942 | −0.799711 | − | 0.600385i | \(-0.795014\pi\) | ||||
−0.799711 | + | 0.600385i | \(0.795014\pi\) | |||||||
\(488\) | 5.35341 | 0.242337 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3156 | −0.691183 | −0.345591 | − | 0.938385i | \(-0.612322\pi\) | ||||
−0.345591 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.8792 | 0.850278 | ||||||||
\(494\) | 17.1861 | 0.773241 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 84.6618 | 3.80143 | ||||||||
\(497\) | 6.02898 | 0.270437 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.1777 | −1.57477 | −0.787386 | − | 0.616461i | \(-0.788566\pi\) | ||||
−0.787386 | + | 0.616461i | \(0.788566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 47.5152 | 2.12071 | ||||||||
\(503\) | 7.33494 | 0.327049 | 0.163524 | − | 0.986539i | \(-0.447714\pi\) | ||||
0.163524 | + | 0.986539i | \(0.447714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.83443 | 0.437194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.3115 | 0.945544 | ||||||||
\(509\) | −5.70697 | −0.252957 | −0.126479 | − | 0.991969i | \(-0.540367\pi\) | ||||
−0.126479 | + | 0.991969i | \(0.540367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.6484 | −1.22309 | ||||||||
\(512\) | −18.2956 | −0.808560 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.6950 | 0.692278 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2120 | −0.449125 | ||||||||
\(518\) | 47.0563 | 2.06753 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.0901 | 1.44970 | 0.724852 | − | 0.688905i | \(-0.241908\pi\) | ||||
0.724852 | + | 0.688905i | \(0.241908\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4719 | 1.37617 | 0.688086 | − | 0.725629i | \(-0.258451\pi\) | ||||
0.688086 | + | 0.725629i | \(0.258451\pi\) | |||||||
\(524\) | −17.2924 | −0.755421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 63.1002 | 2.75130 | ||||||||
\(527\) | 29.2530 | 1.27428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5133 | −0.674493 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −50.9182 | −2.20758 | ||||||||
\(533\) | −13.3278 | −0.577291 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −90.4386 | −3.90635 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.6334 | −1.57938 | ||||||||
\(539\) | 3.81635 | 0.164382 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.8759 | −0.983512 | −0.491756 | − | 0.870733i | \(-0.663645\pi\) | ||||
−0.491756 | + | 0.870733i | \(0.663645\pi\) | |||||||
\(542\) | 19.9844 | 0.858405 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 61.2609 | 2.62654 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7548 | −0.759139 | −0.379570 | − | 0.925163i | \(-0.623928\pi\) | ||||
−0.379570 | + | 0.925163i | \(0.623928\pi\) | |||||||
\(548\) | −42.5325 | −1.81690 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.5728 | −0.961634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.85818 | 0.164067 | ||||||||
\(554\) | −7.56324 | −0.321331 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.5190 | −0.742969 | ||||||||
\(557\) | −2.27448 | −0.0963727 | −0.0481864 | − | 0.998838i | \(-0.515344\pi\) | ||||
−0.0481864 | + | 0.998838i | \(0.515344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.21278 | 0.135886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 61.1912 | 2.58120 | ||||||||
\(563\) | −0.397699 | −0.0167610 | −0.00838050 | − | 0.999965i | \(-0.502668\pi\) | ||||
−0.00838050 | + | 0.999965i | \(0.502668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 66.9576 | 2.81444 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.4086 | 1.02416 | ||||||||
\(569\) | 11.1876 | 0.469010 | 0.234505 | − | 0.972115i | \(-0.424653\pi\) | ||||
0.234505 | + | 0.972115i | \(0.424653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.9124 | −0.791458 | −0.395729 | − | 0.918367i | \(-0.629508\pi\) | ||||
−0.395729 | + | 0.918367i | \(0.629508\pi\) | |||||||
\(572\) | 9.08084 | 0.379689 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 54.9649 | 2.29419 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.01809 | 0.250537 | 0.125268 | − | 0.992123i | \(-0.460021\pi\) | ||||
0.125268 | + | 0.992123i | \(0.460021\pi\) | |||||||
\(578\) | −0.786228 | −0.0327028 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.84967 | 0.201198 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.837855 | 0.0347004 | ||||||||
\(584\) | −111.935 | −4.63192 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −76.9535 | −3.17892 | ||||||||
\(587\) | −16.3326 | −0.674118 | −0.337059 | − | 0.941483i | \(-0.609432\pi\) | ||||
−0.337059 | + | 0.941483i | \(0.609432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.9761 | −1.44117 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 102.276 | 4.20354 | ||||||||
\(593\) | 8.40604 | 0.345195 | 0.172597 | − | 0.984992i | \(-0.444784\pi\) | ||||
0.172597 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −50.8200 | −2.08167 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.62272 | 0.393502 | ||||||||
\(599\) | −13.1918 | −0.539001 | −0.269501 | − | 0.963000i | \(-0.586859\pi\) | ||||
−0.269501 | + | 0.963000i | \(0.586859\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.06690 | −0.247474 | −0.123737 | − | 0.992315i | \(-0.539488\pi\) | ||||
−0.123737 | + | 0.992315i | \(0.539488\pi\) | |||||||
\(602\) | −13.2498 | −0.540021 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −107.354 | −4.36819 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9141 | 0.605345 | 0.302672 | − | 0.953095i | \(-0.402121\pi\) | ||||
0.302672 | + | 0.953095i | \(0.402121\pi\) | |||||||
\(608\) | −73.2462 | −2.97053 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.99219 | −0.404241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4772 | 1.47330 | 0.736651 | − | 0.676273i | \(-0.236406\pi\) | ||||
0.736651 | + | 0.676273i | \(0.236406\pi\) | |||||||
\(614\) | −63.8338 | −2.57612 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.7704 | −0.917446 | ||||||||
\(617\) | 16.2341 | 0.653559 | 0.326780 | − | 0.945101i | \(-0.394036\pi\) | ||||
0.326780 | + | 0.945101i | \(0.394036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0360 | −0.403382 | −0.201691 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201691 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.3526 | 1.05664 | ||||||||
\(623\) | −14.9868 | −0.600434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 50.0451 | 2.00020 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −39.8409 | −1.58982 | ||||||||
\(629\) | 35.3393 | 1.40907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.7580 | 1.14484 | 0.572420 | − | 0.819961i | \(-0.306005\pi\) | ||||
0.572420 | + | 0.819961i | \(0.306005\pi\) | |||||||
\(632\) | 15.6200 | 0.621330 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −68.9754 | −2.73936 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.73419 | 0.147954 | ||||||||
\(638\) | −16.6022 | −0.657289 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.2437 | 0.720582 | 0.360291 | − | 0.932840i | \(-0.382677\pi\) | ||||
0.360291 | + | 0.932840i | \(0.382677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.9734 | 1.33978 | 0.669890 | − | 0.742461i | \(-0.266341\pi\) | ||||
0.669890 | + | 0.742461i | \(0.266341\pi\) | |||||||
\(644\) | −28.5097 | −1.12344 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −53.2288 | −2.09426 | ||||||||
\(647\) | 47.3728 | 1.86242 | 0.931208 | − | 0.364488i | \(-0.118756\pi\) | ||||
0.931208 | + | 0.364488i | \(0.118756\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2955 | −0.600402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 59.5873 | 2.33362 | ||||||||
\(653\) | −37.3959 | −1.46342 | −0.731708 | − | 0.681618i | \(-0.761277\pi\) | ||||
−0.731708 | + | 0.681618i | \(0.761277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 119.466 | 4.66436 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 41.2087 | 1.60648 | ||||||||
\(659\) | 9.48154 | 0.369348 | 0.184674 | − | 0.982800i | \(-0.440877\pi\) | ||||
0.184674 | + | 0.982800i | \(0.440877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.78089 | −0.341537 | −0.170768 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170768 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(662\) | 3.45768 | 0.134386 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.6341 | 0.761951 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.6388 | −0.489375 | ||||||||
\(668\) | 38.3283 | 1.48297 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.873283 | −0.0337127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0259 | −1.85126 | −0.925631 | − | 0.378427i | \(-0.876465\pi\) | ||||
−0.925631 | + | 0.378427i | \(0.876465\pi\) | |||||||
\(674\) | 30.0531 | 1.15760 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.4444 | −2.20940 | ||||||||
\(677\) | −15.4151 | −0.592451 | −0.296226 | − | 0.955118i | \(-0.595728\pi\) | ||||
−0.296226 | + | 0.955118i | \(0.595728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8426 | −0.454478 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −25.7248 | −0.985055 | ||||||||
\(683\) | −27.8221 | −1.06458 | −0.532292 | − | 0.846561i | \(-0.678669\pi\) | ||||
−0.532292 | + | 0.846561i | \(0.678669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −53.4962 | −2.04249 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.7983 | −1.09793 | ||||||||
\(689\) | 0.819818 | 0.0312326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.1261 | −0.765634 | −0.382817 | − | 0.923824i | \(-0.625046\pi\) | ||||
−0.382817 | + | 0.923824i | \(0.625046\pi\) | |||||||
\(692\) | 27.1126 | 1.03067 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.74312 | 0.218006 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.2787 | 1.56354 | ||||||||
\(698\) | 14.9481 | 0.565796 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.6216 | −1.19433 | −0.597166 | − | 0.802118i | \(-0.703707\pi\) | ||||
−0.597166 | + | 0.802118i | \(0.703707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.2532 | −1.59361 | ||||||||
\(704\) | −21.9661 | −0.827877 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −49.2945 | −1.85522 | ||||||||
\(707\) | −23.5939 | −0.887340 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.76008 | −0.178768 | −0.0893842 | − | 0.995997i | \(-0.528490\pi\) | ||||
−0.0893842 | + | 0.995997i | \(0.528490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −60.6748 | −2.27388 | ||||||||
\(713\) | −19.5835 | −0.733409 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.66738 | −0.249172 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.9680 | −1.11840 | ||||||||
\(719\) | 23.0727 | 0.860467 | 0.430234 | − | 0.902718i | \(-0.358431\pi\) | ||||
0.430234 | + | 0.902718i | \(0.358431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7033 | −0.882755 | ||||||||
\(722\) | 13.0074 | 0.484086 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −102.876 | −3.82336 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.5807 | −0.577856 | −0.288928 | − | 0.957351i | \(-0.593299\pi\) | ||||
−0.288928 | + | 0.957351i | \(0.593299\pi\) | |||||||
\(728\) | −22.2802 | −0.825760 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.95061 | −0.368037 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.2215 | −0.636092 | −0.318046 | − | 0.948075i | \(-0.603027\pi\) | ||||
−0.318046 | + | 0.948075i | \(0.603027\pi\) | |||||||
\(734\) | 76.1331 | 2.81013 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.0114 | −1.51170 | ||||||||
\(737\) | 14.7529 | 0.543431 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.4878 | −1.01116 | −0.505578 | − | 0.862781i | \(-0.668721\pi\) | ||||
−0.505578 | + | 0.862781i | \(0.668721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.38100 | −0.124120 | ||||||||
\(743\) | 48.4801 | 1.77856 | 0.889280 | − | 0.457362i | \(-0.151206\pi\) | ||||
0.889280 | + | 0.457362i | \(0.151206\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −37.5362 | −1.37430 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.1251 | −1.02836 | ||||||||
\(749\) | 20.7691 | 0.758888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.29720 | 0.120316 | 0.0601582 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601582 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(752\) | 89.5667 | 3.26616 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.2448 | −0.591602 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.7934 | 1.30093 | 0.650466 | − | 0.759535i | \(-0.274574\pi\) | ||||
0.650466 | + | 0.759535i | \(0.274574\pi\) | |||||||
\(758\) | 58.6045 | 2.12861 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.664110 | 0.0240740 | 0.0120370 | − | 0.999928i | \(-0.496168\pi\) | ||||
0.0120370 | + | 0.999928i | \(0.496168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.43983 | 0.0883279 | ||||||||
\(764\) | −108.657 | −3.93107 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −39.2919 | −1.41967 | ||||||||
\(767\) | −14.9662 | −0.540400 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7090 | 0.927091 | 0.463545 | − | 0.886073i | \(-0.346577\pi\) | ||||
0.463545 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40.7853 | 1.46789 | ||||||||
\(773\) | −38.5458 | −1.38640 | −0.693199 | − | 0.720746i | \(-0.743799\pi\) | ||||
−0.693199 | + | 0.720746i | \(0.743799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −47.9453 | −1.72114 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.9944 | 1.36217 | ||||||||
\(779\) | −49.3546 | −1.76831 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.98169 | −0.142476 | ||||||||
\(782\) | −29.8034 | −1.06577 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −33.4720 | −1.19543 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.2312 | 1.29150 | 0.645751 | − | 0.763548i | \(-0.276544\pi\) | ||||
0.645751 | + | 0.763548i | \(0.276544\pi\) | |||||||
\(788\) | −110.727 | −3.94448 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.15398 | 0.325478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.854482 | −0.0303436 | ||||||||
\(794\) | 14.6326 | 0.519293 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 47.6676 | 1.68953 | ||||||||
\(797\) | 33.8276 | 1.19823 | 0.599117 | − | 0.800662i | \(-0.295518\pi\) | ||||
0.599117 | + | 0.800662i | \(0.295518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.9478 | 1.09485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −71.2965 | −2.51757 | ||||||||
\(803\) | 18.2596 | 0.644369 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25.1710 | −0.886612 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −95.5209 | −3.36041 | ||||||||
\(809\) | 1.46409 | 0.0514747 | 0.0257374 | − | 0.999669i | \(-0.491807\pi\) | ||||
0.0257374 | + | 0.999669i | \(0.491807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.6885 | −1.42877 | −0.714383 | − | 0.699755i | \(-0.753293\pi\) | ||||
−0.714383 | + | 0.699755i | \(0.753293\pi\) | |||||||
\(812\) | 48.1293 | 1.68901 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −31.0771 | −1.08925 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.8974 | 0.416237 | ||||||||
\(818\) | 13.6819 | 0.478375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.9533 | 1.04538 | 0.522689 | − | 0.852523i | \(-0.324929\pi\) | ||||
0.522689 | + | 0.852523i | \(0.324929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9369 | −0.660098 | −0.330049 | − | 0.943964i | \(-0.607065\pi\) | ||||
−0.330049 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(824\) | −95.9636 | −3.34305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 61.7221 | 2.14759 | ||||||||
\(827\) | 20.2639 | 0.704644 | 0.352322 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352322 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6400 | 0.577932 | 0.288966 | − | 0.957339i | \(-0.406689\pi\) | ||||
0.288966 | + | 0.957339i | \(0.406689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.4932 | −0.745142 | ||||||||
\(833\) | −11.5655 | −0.400721 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 33.6276 | 1.16304 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −84.8849 | −2.93230 | ||||||||
\(839\) | 7.13666 | 0.246385 | 0.123192 | − | 0.992383i | \(-0.460687\pi\) | ||||
0.123192 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.66354 | −0.264260 | ||||||||
\(842\) | 8.20942 | 0.282915 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.1113 | −1.20858 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.7490 | −0.644222 | ||||||||
\(848\) | −7.34857 | −0.252351 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.6581 | −0.810988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.8252 | −1.08968 | −0.544838 | − | 0.838541i | \(-0.683409\pi\) | ||||
−0.544838 | + | 0.838541i | \(0.683409\pi\) | |||||||
\(854\) | 3.52396 | 0.120587 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 84.0847 | 2.87396 | ||||||||
\(857\) | 43.1535 | 1.47409 | 0.737047 | − | 0.675842i | \(-0.236220\pi\) | ||||
0.737047 | + | 0.675842i | \(0.236220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.8915 | 1.05400 | 0.527002 | − | 0.849864i | \(-0.323316\pi\) | ||||
0.527002 | + | 0.849864i | \(0.323316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −62.2203 | −2.11923 | ||||||||
\(863\) | 38.1910 | 1.30004 | 0.650019 | − | 0.759918i | \(-0.274761\pi\) | ||||
0.650019 | + | 0.759918i | \(0.274761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.8908 | −0.743880 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 74.5754 | 2.53125 | ||||||||
\(869\) | −2.54804 | −0.0864362 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.4353 | 0.489123 | ||||||||
\(872\) | 9.87777 | 0.334504 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.6343 | 1.20535 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.7247 | 1.07127 | 0.535634 | − | 0.844450i | \(-0.320073\pi\) | ||||
0.535634 | + | 0.844450i | \(0.320073\pi\) | |||||||
\(878\) | −64.7911 | −2.18659 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4409 | 1.29511 | 0.647554 | − | 0.762020i | \(-0.275792\pi\) | ||||
0.647554 | + | 0.762020i | \(0.275792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1497 | 0.408871 | 0.204435 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204435 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(884\) | −27.5196 | −0.925586 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.168259 | 0.00565278 | ||||||||
\(887\) | 24.2431 | 0.814005 | 0.407002 | − | 0.913427i | \(-0.366574\pi\) | ||||
0.407002 | + | 0.913427i | \(0.366574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.52966 | 0.286075 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −43.4458 | −1.45467 | ||||||||
\(893\) | −37.0025 | −1.23824 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 27.4225 | 0.916120 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.8371 | 1.02905 | ||||||||
\(899\) | 33.0604 | 1.10263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.53913 | −0.0845908 | ||||||||
\(902\) | −36.3002 | −1.20866 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.0603 | 1.23261 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.5046 | −1.07930 | −0.539649 | − | 0.841890i | \(-0.681443\pi\) | ||||
−0.539649 | + | 0.841890i | \(0.681443\pi\) | |||||||
\(908\) | 107.064 | 3.55305 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.2258 | −1.46527 | −0.732633 | − | 0.680624i | \(-0.761709\pi\) | ||||
−0.732633 | + | 0.680624i | \(0.761709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.20284 | −0.105999 | ||||||||
\(914\) | 110.323 | 3.64915 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 151.859 | 5.01756 | ||||||||
\(917\) | −6.92106 | −0.228554 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.7936 | −1.31267 | −0.656335 | − | 0.754469i | \(-0.727894\pi\) | ||||
−0.656335 | + | 0.754469i | \(0.727894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −78.2732 | −2.57779 | ||||||||
\(923\) | −3.89597 | −0.128237 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 81.4163 | 2.67551 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 69.2344 | 2.27273 | ||||||||
\(929\) | 6.64622 | 0.218055 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8282 | 0.453202 | ||||||||
\(932\) | −11.5900 | −0.379644 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 87.1855 | 2.85280 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.229585 | 0.00750023 | 0.00375011 | − | 0.999993i | \(-0.498806\pi\) | ||||
0.00375011 | + | 0.999993i | \(0.498806\pi\) | |||||||
\(938\) | −59.5325 | −1.94381 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.3476 | −0.924106 | −0.462053 | − | 0.886852i | \(-0.652887\pi\) | ||||
−0.462053 | + | 0.886852i | \(0.652887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.6342 | −0.899894 | ||||||||
\(944\) | 134.152 | 4.36629 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.75049 | 0.284503 | ||||||||
\(947\) | −48.0036 | −1.55991 | −0.779954 | − | 0.625837i | \(-0.784758\pi\) | ||||
−0.779954 | + | 0.625837i | \(0.784758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.8666 | 0.579973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69.0062 | 2.23650 | ||||||||
\(953\) | 26.8885 | 0.871004 | 0.435502 | − | 0.900188i | \(-0.356571\pi\) | ||||
0.435502 | + | 0.900188i | \(0.356571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −78.7324 | −2.54639 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.8737 | 1.06210 | ||||||||
\(959\) | −17.0231 | −0.549705 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2265 | 0.652468 | ||||||||
\(962\) | −30.4081 | −0.980396 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.7045 | −0.795677 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.78016 | −0.121562 | −0.0607809 | − | 0.998151i | \(-0.519359\pi\) | ||||
−0.0607809 | + | 0.998151i | \(0.519359\pi\) | |||||||
\(968\) | −75.9059 | −2.43971 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.2875 | −0.362232 | −0.181116 | − | 0.983462i | \(-0.557971\pi\) | ||||
−0.181116 | + | 0.983462i | \(0.557971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.01175 | −0.224786 | ||||||||
\(974\) | −94.0648 | −3.01403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.65930 | 0.245168 | ||||||||
\(977\) | −20.2798 | −0.648807 | −0.324403 | − | 0.945919i | \(-0.605164\pi\) | ||||
−0.324403 | + | 0.945919i | \(0.605164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.89766 | 0.316331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.8162 | −1.30250 | ||||||||
\(983\) | 28.3127 | 0.903035 | 0.451517 | − | 0.892262i | \(-0.350883\pi\) | ||||
0.451517 | + | 0.892262i | \(0.350883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 50.3134 | 1.60230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.9037 | 1.04681 | ||||||||
\(989\) | 6.66148 | 0.211823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.8610 | 0.757970 | 0.378985 | − | 0.925403i | \(-0.376273\pi\) | ||||
0.378985 | + | 0.925403i | \(0.376273\pi\) | |||||||
\(992\) | 107.277 | 3.40606 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0673 | 0.509624 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.6720 | 0.432996 | 0.216498 | − | 0.976283i | \(-0.430536\pi\) | ||||
0.216498 | + | 0.976283i | \(0.430536\pi\) | |||||||
\(998\) | −93.7491 | −2.96757 | ||||||||
\(999\) | 0 | 0 |
(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 | 5625.2.a.be.1.8 | 8 | ||
3.2 | odd | 2 | 625.2.a.e.1.1 | ✓ | 8 | ||
5.4 | even | 2 | 5625.2.a.s.1.1 | 8 | |||
12.11 | even | 2 | 10000.2.a.bn.1.5 | 8 | |||
15.2 | even | 4 | 625.2.b.d.624.1 | 16 | |||
15.8 | even | 4 | 625.2.b.d.624.16 | 16 | |||
15.14 | odd | 2 | 625.2.a.g.1.8 | yes | 8 | ||
60.59 | even | 2 | 10000.2.a.be.1.4 | 8 | |||
75.2 | even | 20 | 625.2.e.j.124.1 | 32 | |||
75.8 | even | 20 | 625.2.e.k.374.1 | 32 | |||
75.11 | odd | 10 | 625.2.d.q.501.1 | 16 | |||
75.14 | odd | 10 | 625.2.d.m.501.4 | 16 | |||
75.17 | even | 20 | 625.2.e.k.374.8 | 32 | |||
75.23 | even | 20 | 625.2.e.j.124.8 | 32 | |||
75.29 | odd | 10 | 625.2.d.n.376.1 | 16 | |||
75.38 | even | 20 | 625.2.e.j.499.1 | 32 | |||
75.41 | odd | 10 | 625.2.d.q.126.1 | 16 | |||
75.44 | odd | 10 | 625.2.d.n.251.1 | 16 | |||
75.47 | even | 20 | 625.2.e.k.249.1 | 32 | |||
75.53 | even | 20 | 625.2.e.k.249.8 | 32 | |||
75.56 | odd | 10 | 625.2.d.p.251.4 | 16 | |||
75.59 | odd | 10 | 625.2.d.m.126.4 | 16 | |||
75.62 | even | 20 | 625.2.e.j.499.8 | 32 | |||
75.71 | odd | 10 | 625.2.d.p.376.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.1 | ✓ | 8 | 3.2 | odd | 2 | ||
625.2.a.g.1.8 | yes | 8 | 15.14 | odd | 2 | ||
625.2.b.d.624.1 | 16 | 15.2 | even | 4 | |||
625.2.b.d.624.16 | 16 | 15.8 | even | 4 | |||
625.2.d.m.126.4 | 16 | 75.59 | odd | 10 | |||
625.2.d.m.501.4 | 16 | 75.14 | odd | 10 | |||
625.2.d.n.251.1 | 16 | 75.44 | odd | 10 | |||
625.2.d.n.376.1 | 16 | 75.29 | odd | 10 | |||
625.2.d.p.251.4 | 16 | 75.56 | odd | 10 | |||
625.2.d.p.376.4 | 16 | 75.71 | odd | 10 | |||
625.2.d.q.126.1 | 16 | 75.41 | odd | 10 | |||
625.2.d.q.501.1 | 16 | 75.11 | odd | 10 | |||
625.2.e.j.124.1 | 32 | 75.2 | even | 20 | |||
625.2.e.j.124.8 | 32 | 75.23 | even | 20 | |||
625.2.e.j.499.1 | 32 | 75.38 | even | 20 | |||
625.2.e.j.499.8 | 32 | 75.62 | even | 20 | |||
625.2.e.k.249.1 | 32 | 75.47 | even | 20 | |||
625.2.e.k.249.8 | 32 | 75.53 | even | 20 | |||
625.2.e.k.374.1 | 32 | 75.8 | even | 20 | |||
625.2.e.k.374.8 | 32 | 75.17 | even | 20 | |||
5625.2.a.s.1.1 | 8 | 5.4 | even | 2 | |||
5625.2.a.be.1.8 | 8 | 1.1 | even | 1 | trivial | ||
10000.2.a.be.1.4 | 8 | 60.59 | even | 2 | |||
10000.2.a.bn.1.5 | 8 | 12.11 | even | 2 |