Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.476800 | −0.337148 | −0.168574 | − | 0.985689i | \(-0.553916\pi\) | ||||
−0.168574 | + | 0.985689i | \(0.553916\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77266 | −0.886331 | ||||||||
\(5\) | −3.87912 | −1.73480 | −0.867398 | − | 0.497614i | \(-0.834209\pi\) | ||||
−0.867398 | + | 0.497614i | \(0.834209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.79880 | 0.635973 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.84956 | 0.584884 | ||||||||
\(11\) | 5.00409 | 1.50879 | 0.754394 | − | 0.656422i | \(-0.227931\pi\) | ||||
0.754394 | + | 0.656422i | \(0.227931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.407559 | −0.113037 | −0.0565183 | − | 0.998402i | \(-0.518000\pi\) | ||||
−0.0565183 | + | 0.998402i | \(0.518000\pi\) | |||||||
\(14\) | −0.476800 | −0.127430 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.68765 | 0.671914 | ||||||||
\(17\) | 0.710255 | 0.172262 | 0.0861310 | − | 0.996284i | \(-0.472550\pi\) | ||||
0.0861310 | + | 0.996284i | \(0.472550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.42156 | 1.93204 | 0.966020 | − | 0.258469i | \(-0.0832178\pi\) | ||||
0.966020 | + | 0.258469i | \(0.0832178\pi\) | |||||||
\(20\) | 6.87638 | 1.53760 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.38595 | −0.508685 | ||||||||
\(23\) | −5.39892 | −1.12575 | −0.562876 | − | 0.826541i | \(-0.690305\pi\) | ||||
−0.562876 | + | 0.826541i | \(0.690305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0476 | 2.00952 | ||||||||
\(26\) | 0.194324 | 0.0381101 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.77266 | −0.335002 | ||||||||
\(29\) | 8.15929 | 1.51514 | 0.757571 | − | 0.652753i | \(-0.226386\pi\) | ||||
0.757571 | + | 0.652753i | \(0.226386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.794645 | −0.142722 | −0.0713612 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713612 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(32\) | −4.87908 | −0.862508 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.338649 | −0.0580779 | ||||||||
\(35\) | −3.87912 | −0.655692 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.57907 | 1.08159 | 0.540796 | − | 0.841154i | \(-0.318123\pi\) | ||||
0.540796 | + | 0.841154i | \(0.318123\pi\) | |||||||
\(38\) | −4.01540 | −0.651384 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.97778 | −1.10328 | ||||||||
\(41\) | −2.29873 | −0.359001 | −0.179500 | − | 0.983758i | \(-0.557448\pi\) | ||||
−0.179500 | + | 0.983758i | \(0.557448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17556 | 0.636767 | 0.318384 | − | 0.947962i | \(-0.396860\pi\) | ||||
0.318384 | + | 0.947962i | \(0.396860\pi\) | |||||||
\(44\) | −8.87055 | −1.33729 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.57420 | 0.379545 | ||||||||
\(47\) | 9.25600 | 1.35013 | 0.675063 | − | 0.737760i | \(-0.264116\pi\) | ||||
0.675063 | + | 0.737760i | \(0.264116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.79069 | −0.677506 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.722464 | 0.100188 | ||||||||
\(53\) | 1.76295 | 0.242160 | 0.121080 | − | 0.992643i | \(-0.461364\pi\) | ||||
0.121080 | + | 0.992643i | \(0.461364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.4115 | −2.61744 | ||||||||
\(56\) | 1.79880 | 0.240375 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.89035 | −0.510827 | ||||||||
\(59\) | −1.08670 | −0.141477 | −0.0707384 | − | 0.997495i | \(-0.522536\pi\) | ||||
−0.0707384 | + | 0.997495i | \(0.522536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.11237 | 0.142424 | 0.0712120 | − | 0.997461i | \(-0.477313\pi\) | ||||
0.0712120 | + | 0.997461i | \(0.477313\pi\) | |||||||
\(62\) | 0.378886 | 0.0481186 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.04897 | −0.381121 | ||||||||
\(65\) | 1.58097 | 0.196095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.810556 | 0.0990251 | 0.0495126 | − | 0.998774i | \(-0.484233\pi\) | ||||
0.0495126 | + | 0.998774i | \(0.484233\pi\) | |||||||
\(68\) | −1.25904 | −0.152681 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.84956 | 0.221065 | ||||||||
\(71\) | 9.28378 | 1.10178 | 0.550891 | − | 0.834577i | \(-0.314288\pi\) | ||||
0.550891 | + | 0.834577i | \(0.314288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8007 | −1.38117 | −0.690586 | − | 0.723250i | \(-0.742647\pi\) | ||||
−0.690586 | + | 0.723250i | \(0.742647\pi\) | |||||||
\(74\) | −3.13690 | −0.364657 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9286 | −1.71243 | ||||||||
\(77\) | 5.00409 | 0.570268 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.16006 | 0.355535 | 0.177767 | − | 0.984073i | \(-0.443113\pi\) | ||||
0.177767 | + | 0.984073i | \(0.443113\pi\) | |||||||
\(80\) | −10.4257 | −1.16563 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.09603 | 0.121037 | ||||||||
\(83\) | 1.77907 | 0.195278 | 0.0976391 | − | 0.995222i | \(-0.468871\pi\) | ||||
0.0976391 | + | 0.995222i | \(0.468871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.75517 | −0.298840 | ||||||||
\(86\) | −1.99091 | −0.214685 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.00137 | 0.959549 | ||||||||
\(89\) | −7.40408 | −0.784831 | −0.392415 | − | 0.919788i | \(-0.628360\pi\) | ||||
−0.392415 | + | 0.919788i | \(0.628360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.407559 | −0.0427238 | ||||||||
\(92\) | 9.57046 | 0.997789 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.41326 | −0.455193 | ||||||||
\(95\) | −32.6683 | −3.35170 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.89293 | 0.192198 | 0.0960990 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0960990 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(98\) | −0.476800 | −0.0481640 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.8110 | −1.78110 | ||||||||
\(101\) | −19.4439 | −1.93474 | −0.967368 | − | 0.253376i | \(-0.918459\pi\) | ||||
−0.967368 | + | 0.253376i | \(0.918459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.9767 | 1.37717 | 0.688585 | − | 0.725156i | \(-0.258232\pi\) | ||||
0.688585 | + | 0.725156i | \(0.258232\pi\) | |||||||
\(104\) | −0.733119 | −0.0718882 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.840576 | −0.0816440 | ||||||||
\(107\) | −6.69599 | −0.647326 | −0.323663 | − | 0.946172i | \(-0.604914\pi\) | ||||
−0.323663 | + | 0.946172i | \(0.604914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.827402 | 0.0792507 | 0.0396254 | − | 0.999215i | \(-0.487384\pi\) | ||||
0.0396254 | + | 0.999215i | \(0.487384\pi\) | |||||||
\(110\) | 9.25538 | 0.882466 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.68765 | 0.253960 | ||||||||
\(113\) | −8.28680 | −0.779557 | −0.389778 | − | 0.920909i | \(-0.627448\pi\) | ||||
−0.389778 | + | 0.920909i | \(0.627448\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.9431 | 1.95295 | ||||||||
\(116\) | −14.4637 | −1.34292 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.518140 | 0.0476986 | ||||||||
\(119\) | 0.710255 | 0.0651089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0409 | 1.27644 | ||||||||
\(122\) | −0.530376 | −0.0480180 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.40864 | 0.126499 | ||||||||
\(125\) | −19.5803 | −1.75131 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 11.2119 | 0.991002 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.753807 | −0.0661132 | ||||||||
\(131\) | −21.3079 | −1.86168 | −0.930838 | − | 0.365432i | \(-0.880921\pi\) | ||||
−0.930838 | + | 0.365432i | \(0.880921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.42156 | 0.730242 | ||||||||
\(134\) | −0.386473 | −0.0333862 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.27761 | 0.109554 | ||||||||
\(137\) | −12.9060 | −1.10263 | −0.551316 | − | 0.834296i | \(-0.685874\pi\) | ||||
−0.551316 | + | 0.834296i | \(0.685874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3363 | 1.21599 | 0.607993 | − | 0.793943i | \(-0.291975\pi\) | ||||
0.607993 | + | 0.793943i | \(0.291975\pi\) | |||||||
\(140\) | 6.87638 | 0.581160 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.42650 | −0.371464 | ||||||||
\(143\) | −2.03946 | −0.170548 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −31.6509 | −2.62846 | ||||||||
\(146\) | 5.62659 | 0.465660 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.6625 | −0.958649 | ||||||||
\(149\) | 20.1914 | 1.65414 | 0.827070 | − | 0.562099i | \(-0.190006\pi\) | ||||
0.827070 | + | 0.562099i | \(0.190006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.64467 | −0.784872 | −0.392436 | − | 0.919779i | \(-0.628368\pi\) | ||||
−0.392436 | + | 0.919779i | \(0.628368\pi\) | |||||||
\(152\) | 15.1487 | 1.22873 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.38595 | −0.192265 | ||||||||
\(155\) | 3.08253 | 0.247594 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.48469 | −0.357917 | −0.178959 | − | 0.983857i | \(-0.557273\pi\) | ||||
−0.178959 | + | 0.983857i | \(0.557273\pi\) | |||||||
\(158\) | −1.50672 | −0.119868 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.9266 | 1.49628 | ||||||||
\(161\) | −5.39892 | −0.425494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.315541 | −0.0247151 | −0.0123575 | − | 0.999924i | \(-0.503934\pi\) | ||||
−0.0123575 | + | 0.999924i | \(0.503934\pi\) | |||||||
\(164\) | 4.07487 | 0.318194 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.848259 | −0.0658377 | ||||||||
\(167\) | −9.99045 | −0.773084 | −0.386542 | − | 0.922272i | \(-0.626331\pi\) | ||||
−0.386542 | + | 0.922272i | \(0.626331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8339 | −0.987223 | ||||||||
\(170\) | 1.31366 | 0.100753 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.40186 | −0.564387 | ||||||||
\(173\) | 3.81632 | 0.290149 | 0.145075 | − | 0.989421i | \(-0.453658\pi\) | ||||
0.145075 | + | 0.989421i | \(0.453658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0476 | 0.759527 | ||||||||
\(176\) | 13.4493 | 1.01378 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.53026 | 0.264604 | ||||||||
\(179\) | 2.61980 | 0.195813 | 0.0979064 | − | 0.995196i | \(-0.468785\pi\) | ||||
0.0979064 | + | 0.995196i | \(0.468785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6108 | 1.75498 | 0.877490 | − | 0.479594i | \(-0.159216\pi\) | ||||
0.877490 | + | 0.479594i | \(0.159216\pi\) | |||||||
\(182\) | 0.194324 | 0.0144043 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.71160 | −0.715948 | ||||||||
\(185\) | −25.5210 | −1.87634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.55417 | 0.259907 | ||||||||
\(188\) | −16.4078 | −1.19666 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.5762 | 1.13002 | ||||||||
\(191\) | 3.07391 | 0.222420 | 0.111210 | − | 0.993797i | \(-0.464527\pi\) | ||||
0.111210 | + | 0.993797i | \(0.464527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0691 | 0.724788 | 0.362394 | − | 0.932025i | \(-0.381959\pi\) | ||||
0.362394 | + | 0.932025i | \(0.381959\pi\) | |||||||
\(194\) | −0.902549 | −0.0647993 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.77266 | −0.126619 | ||||||||
\(197\) | 11.4982 | 0.819213 | 0.409607 | − | 0.912262i | \(-0.365666\pi\) | ||||
0.409607 | + | 0.912262i | \(0.365666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.67839 | 0.402531 | 0.201265 | − | 0.979537i | \(-0.435495\pi\) | ||||
0.201265 | + | 0.979537i | \(0.435495\pi\) | |||||||
\(200\) | 18.0737 | 1.27800 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.27082 | 0.652293 | ||||||||
\(203\) | 8.15929 | 0.572670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.91705 | 0.622793 | ||||||||
\(206\) | −6.66411 | −0.464311 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.09538 | −0.0759508 | ||||||||
\(209\) | 42.1422 | 2.91504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0929 | 0.763664 | 0.381832 | − | 0.924232i | \(-0.375293\pi\) | ||||
0.381832 | + | 0.924232i | \(0.375293\pi\) | |||||||
\(212\) | −3.12512 | −0.214634 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.19264 | 0.218245 | ||||||||
\(215\) | −16.1975 | −1.10466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.794645 | −0.0539440 | ||||||||
\(218\) | −0.394505 | −0.0267192 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 34.4100 | 2.31992 | ||||||||
\(221\) | −0.289471 | −0.0194719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.19491 | −0.146982 | −0.0734911 | − | 0.997296i | \(-0.523414\pi\) | ||||
−0.0734911 | + | 0.997296i | \(0.523414\pi\) | |||||||
\(224\) | −4.87908 | −0.325997 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.95114 | 0.262826 | ||||||||
\(227\) | −10.2975 | −0.683466 | −0.341733 | − | 0.939797i | \(-0.611014\pi\) | ||||
−0.341733 | + | 0.939797i | \(0.611014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.13681 | 0.471614 | 0.235807 | − | 0.971800i | \(-0.424227\pi\) | ||||
0.235807 | + | 0.971800i | \(0.424227\pi\) | |||||||
\(230\) | −9.98565 | −0.658434 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.6770 | 0.963590 | ||||||||
\(233\) | 8.96887 | 0.587570 | 0.293785 | − | 0.955871i | \(-0.405085\pi\) | ||||
0.293785 | + | 0.955871i | \(0.405085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9052 | −2.34219 | ||||||||
\(236\) | 1.92636 | 0.125395 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.338649 | −0.0219514 | ||||||||
\(239\) | −12.4853 | −0.807606 | −0.403803 | − | 0.914846i | \(-0.632312\pi\) | ||||
−0.403803 | + | 0.914846i | \(0.632312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.4848 | −1.31954 | −0.659771 | − | 0.751467i | \(-0.729347\pi\) | ||||
−0.659771 | + | 0.751467i | \(0.729347\pi\) | |||||||
\(242\) | −6.69468 | −0.430350 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.97185 | −0.126235 | ||||||||
\(245\) | −3.87912 | −0.247828 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.43228 | −0.218391 | ||||||||
\(248\) | −1.42941 | −0.0907676 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.33586 | 0.590452 | ||||||||
\(251\) | 13.5065 | 0.852526 | 0.426263 | − | 0.904599i | \(-0.359830\pi\) | ||||
0.426263 | + | 0.904599i | \(0.359830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.0166 | −1.69852 | ||||||||
\(254\) | 0.476800 | 0.0299171 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.752097 | 0.0470061 | ||||||||
\(257\) | −25.1877 | −1.57116 | −0.785582 | − | 0.618757i | \(-0.787636\pi\) | ||||
−0.785582 | + | 0.618757i | \(0.787636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.57907 | 0.408804 | ||||||||
\(260\) | −2.80253 | −0.173805 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.1596 | 0.627661 | ||||||||
\(263\) | 13.6271 | 0.840280 | 0.420140 | − | 0.907459i | \(-0.361981\pi\) | ||||
0.420140 | + | 0.907459i | \(0.361981\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.83872 | −0.420099 | ||||||||
\(266\) | −4.01540 | −0.246200 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.43684 | −0.0877690 | ||||||||
\(269\) | 9.37573 | 0.571648 | 0.285824 | − | 0.958282i | \(-0.407733\pi\) | ||||
0.285824 | + | 0.958282i | \(0.407733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4873 | 1.30526 | 0.652629 | − | 0.757677i | \(-0.273666\pi\) | ||||
0.652629 | + | 0.757677i | \(0.273666\pi\) | |||||||
\(272\) | 1.90892 | 0.115745 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.15357 | 0.371751 | ||||||||
\(275\) | 50.2790 | 3.03194 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.0287 | 1.92442 | 0.962209 | − | 0.272311i | \(-0.0877879\pi\) | ||||
0.962209 | + | 0.272311i | \(0.0877879\pi\) | |||||||
\(278\) | −6.83552 | −0.409967 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.97778 | −0.417002 | ||||||||
\(281\) | −3.17026 | −0.189122 | −0.0945610 | − | 0.995519i | \(-0.530145\pi\) | ||||
−0.0945610 | + | 0.995519i | \(0.530145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00390 | 0.178563 | 0.0892816 | − | 0.996006i | \(-0.471543\pi\) | ||||
0.0892816 | + | 0.996006i | \(0.471543\pi\) | |||||||
\(284\) | −16.4570 | −0.976543 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.972414 | 0.0575000 | ||||||||
\(287\) | −2.29873 | −0.135690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4955 | −0.970326 | ||||||||
\(290\) | 15.0911 | 0.886182 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.9187 | 1.22418 | ||||||||
\(293\) | 23.1537 | 1.35265 | 0.676327 | − | 0.736602i | \(-0.263571\pi\) | ||||
0.676327 | + | 0.736602i | \(0.263571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.21546 | 0.245433 | ||||||||
\(296\) | 11.8345 | 0.687864 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.62723 | −0.557691 | ||||||||
\(299\) | 2.20038 | 0.127251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.17556 | 0.240675 | ||||||||
\(302\) | 4.59858 | 0.264618 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 22.6343 | 1.29816 | ||||||||
\(305\) | −4.31501 | −0.247077 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6103 | 1.29044 | 0.645219 | − | 0.763998i | \(-0.276766\pi\) | ||||
0.645219 | + | 0.763998i | \(0.276766\pi\) | |||||||
\(308\) | −8.87055 | −0.505447 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.46975 | −0.0834760 | ||||||||
\(311\) | −17.3980 | −0.986550 | −0.493275 | − | 0.869873i | \(-0.664200\pi\) | ||||
−0.493275 | + | 0.869873i | \(0.664200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0319 | 0.567036 | 0.283518 | − | 0.958967i | \(-0.408498\pi\) | ||||
0.283518 | + | 0.958967i | \(0.408498\pi\) | |||||||
\(314\) | 2.13830 | 0.120671 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.60173 | −0.315122 | ||||||||
\(317\) | −18.7272 | −1.05182 | −0.525911 | − | 0.850540i | \(-0.676275\pi\) | ||||
−0.525911 | + | 0.850540i | \(0.676275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.8298 | 2.28603 | ||||||||
\(320\) | 11.8273 | 0.661167 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.57420 | 0.143455 | ||||||||
\(323\) | 5.98145 | 0.332817 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.09499 | −0.227149 | ||||||||
\(326\) | 0.150450 | 0.00833264 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.13496 | −0.228315 | ||||||||
\(329\) | 9.25600 | 0.510300 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.6572 | −1.19039 | −0.595193 | − | 0.803582i | \(-0.702925\pi\) | ||||
−0.595193 | + | 0.803582i | \(0.702925\pi\) | |||||||
\(332\) | −3.15369 | −0.173081 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.76344 | 0.260644 | ||||||||
\(335\) | −3.14425 | −0.171788 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.9302 | −1.79382 | −0.896912 | − | 0.442209i | \(-0.854195\pi\) | ||||
−0.896912 | + | 0.442209i | \(0.854195\pi\) | |||||||
\(338\) | 6.11920 | 0.332840 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.88398 | 0.264871 | ||||||||
\(341\) | −3.97647 | −0.215338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 7.51102 | 0.404967 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.81962 | −0.0978233 | ||||||||
\(347\) | −11.2049 | −0.601508 | −0.300754 | − | 0.953702i | \(-0.597238\pi\) | ||||
−0.300754 | + | 0.953702i | \(0.597238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.7169 | 1.80482 | 0.902412 | − | 0.430874i | \(-0.141795\pi\) | ||||
0.902412 | + | 0.430874i | \(0.141795\pi\) | |||||||
\(350\) | −4.79069 | −0.256073 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.4153 | −1.30134 | ||||||||
\(353\) | 11.0999 | 0.590786 | 0.295393 | − | 0.955376i | \(-0.404549\pi\) | ||||
0.295393 | + | 0.955376i | \(0.404549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −36.0129 | −1.91137 | ||||||||
\(356\) | 13.1249 | 0.695620 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.24912 | −0.0660179 | ||||||||
\(359\) | −0.385888 | −0.0203664 | −0.0101832 | − | 0.999948i | \(-0.503241\pi\) | ||||
−0.0101832 | + | 0.999948i | \(0.503241\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.9227 | 2.73278 | ||||||||
\(362\) | −11.2576 | −0.591689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.722464 | 0.0378674 | ||||||||
\(365\) | 45.7765 | 2.39605 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.4165 | −1.48333 | −0.741664 | − | 0.670772i | \(-0.765963\pi\) | ||||
−0.741664 | + | 0.670772i | \(0.765963\pi\) | |||||||
\(368\) | −14.5104 | −0.756409 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.1684 | 0.632606 | ||||||||
\(371\) | 1.76295 | 0.0915280 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0502 | 0.675712 | 0.337856 | − | 0.941198i | \(-0.390298\pi\) | ||||
0.337856 | + | 0.941198i | \(0.390298\pi\) | |||||||
\(374\) | −1.69463 | −0.0876272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.6497 | 0.858644 | ||||||||
\(377\) | −3.32539 | −0.171266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1620 | 1.34385 | 0.671926 | − | 0.740618i | \(-0.265467\pi\) | ||||
0.671926 | + | 0.740618i | \(0.265467\pi\) | |||||||
\(380\) | 57.9098 | 2.97071 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.46564 | −0.0749885 | ||||||||
\(383\) | −17.7855 | −0.908798 | −0.454399 | − | 0.890798i | \(-0.650146\pi\) | ||||
−0.454399 | + | 0.890798i | \(0.650146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.4115 | −0.989300 | ||||||||
\(386\) | −4.80093 | −0.244361 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.35553 | −0.170351 | ||||||||
\(389\) | 4.85940 | 0.246382 | 0.123191 | − | 0.992383i | \(-0.460687\pi\) | ||||
0.123191 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.83461 | −0.193924 | ||||||||
\(392\) | 1.79880 | 0.0908533 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.48234 | −0.276196 | ||||||||
\(395\) | −12.2583 | −0.616781 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9858 | 0.752116 | 0.376058 | − | 0.926596i | \(-0.377279\pi\) | ||||
0.376058 | + | 0.926596i | \(0.377279\pi\) | |||||||
\(398\) | −2.70746 | −0.135713 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27.0045 | 1.35022 | ||||||||
\(401\) | 36.5532 | 1.82538 | 0.912689 | − | 0.408655i | \(-0.134002\pi\) | ||||
0.912689 | + | 0.408655i | \(0.134002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.323865 | 0.0161328 | ||||||||
\(404\) | 34.4674 | 1.71482 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.89035 | −0.193075 | ||||||||
\(407\) | 32.9222 | 1.63189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9043 | −1.23144 | −0.615720 | − | 0.787965i | \(-0.711135\pi\) | ||||
−0.615720 | + | 0.787965i | \(0.711135\pi\) | |||||||
\(410\) | −4.25164 | −0.209974 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.7761 | −1.22063 | ||||||||
\(413\) | −1.08670 | −0.0534732 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.90123 | −0.338768 | ||||||||
\(416\) | 1.98851 | 0.0974949 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.0934 | −0.982800 | ||||||||
\(419\) | −0.748228 | −0.0365533 | −0.0182767 | − | 0.999833i | \(-0.505818\pi\) | ||||
−0.0182767 | + | 0.999833i | \(0.505818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3895 | −0.652562 | −0.326281 | − | 0.945273i | \(-0.605796\pi\) | ||||
−0.326281 | + | 0.945273i | \(0.605796\pi\) | |||||||
\(422\) | −5.28908 | −0.257468 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.17121 | 0.154008 | ||||||||
\(425\) | 7.13635 | 0.346164 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.11237 | 0.0538312 | ||||||||
\(428\) | 11.8697 | 0.573745 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.72298 | 0.372435 | ||||||||
\(431\) | 29.1853 | 1.40581 | 0.702904 | − | 0.711285i | \(-0.251886\pi\) | ||||
0.702904 | + | 0.711285i | \(0.251886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.0171978 | −0.000826473 0 | −0.000413236 | − | 1.00000i | \(-0.500132\pi\) | ||||
−0.000413236 | 1.00000i | \(0.500132\pi\) | ||||||||
\(434\) | 0.378886 | 0.0181871 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.46670 | −0.0702424 | ||||||||
\(437\) | −45.4673 | −2.17500 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5422 | 1.55316 | 0.776578 | − | 0.630021i | \(-0.216954\pi\) | ||||
0.776578 | + | 0.630021i | \(0.216954\pi\) | |||||||
\(440\) | −34.9174 | −1.66462 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.138020 | 0.00656492 | ||||||||
\(443\) | −18.6179 | −0.884561 | −0.442280 | − | 0.896877i | \(-0.645830\pi\) | ||||
−0.442280 | + | 0.896877i | \(0.645830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.7213 | 1.36152 | ||||||||
\(446\) | 1.04653 | 0.0495548 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.04897 | −0.144050 | ||||||||
\(449\) | −4.41081 | −0.208159 | −0.104080 | − | 0.994569i | \(-0.533190\pi\) | ||||
−0.104080 | + | 0.994569i | \(0.533190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.5030 | −0.541656 | ||||||||
\(452\) | 14.6897 | 0.690945 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.90982 | 0.230429 | ||||||||
\(455\) | 1.58097 | 0.0741171 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.9405 | 1.49411 | 0.747057 | − | 0.664760i | \(-0.231466\pi\) | ||||
0.747057 | + | 0.664760i | \(0.231466\pi\) | |||||||
\(458\) | −3.40283 | −0.159004 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −37.1250 | −1.73096 | ||||||||
\(461\) | −22.3641 | −1.04160 | −0.520799 | − | 0.853679i | \(-0.674366\pi\) | ||||
−0.520799 | + | 0.853679i | \(0.674366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.7564 | 1.05758 | 0.528790 | − | 0.848753i | \(-0.322646\pi\) | ||||
0.528790 | + | 0.848753i | \(0.322646\pi\) | |||||||
\(464\) | 21.9294 | 1.01804 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.27636 | −0.198098 | ||||||||
\(467\) | −13.5933 | −0.629023 | −0.314512 | − | 0.949254i | \(-0.601841\pi\) | ||||
−0.314512 | + | 0.949254i | \(0.601841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.810556 | 0.0374280 | ||||||||
\(470\) | 17.1196 | 0.789667 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.95477 | −0.0899754 | ||||||||
\(473\) | 20.8949 | 0.960747 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 84.6165 | 3.88247 | ||||||||
\(476\) | −1.25904 | −0.0577081 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.95298 | 0.272283 | ||||||||
\(479\) | −0.420777 | −0.0192258 | −0.00961289 | − | 0.999954i | \(-0.503060\pi\) | ||||
−0.00961289 | + | 0.999954i | \(0.503060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.68136 | −0.122259 | ||||||||
\(482\) | 9.76714 | 0.444881 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.8897 | −1.13135 | ||||||||
\(485\) | −7.34292 | −0.333425 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.04291 | 0.319145 | 0.159572 | − | 0.987186i | \(-0.448988\pi\) | ||||
0.159572 | + | 0.987186i | \(0.448988\pi\) | |||||||
\(488\) | 2.00093 | 0.0905779 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.84956 | 0.0835548 | ||||||||
\(491\) | 3.92441 | 0.177106 | 0.0885530 | − | 0.996071i | \(-0.471776\pi\) | ||||
0.0885530 | + | 0.996071i | \(0.471776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.79517 | 0.261001 | ||||||||
\(494\) | 1.63651 | 0.0736302 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13573 | −0.0958972 | ||||||||
\(497\) | 9.28378 | 0.416434 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5608 | −0.607065 | −0.303532 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303532 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(500\) | 34.7092 | 1.55224 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.43992 | −0.287428 | ||||||||
\(503\) | 1.31965 | 0.0588401 | 0.0294201 | − | 0.999567i | \(-0.490634\pi\) | ||||
0.0294201 | + | 0.999567i | \(0.490634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 75.4251 | 3.35637 | ||||||||
\(506\) | 12.8815 | 0.572654 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.77266 | 0.0786492 | ||||||||
\(509\) | −2.94653 | −0.130602 | −0.0653012 | − | 0.997866i | \(-0.520801\pi\) | ||||
−0.0653012 | + | 0.997866i | \(0.520801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.8007 | −0.522034 | ||||||||
\(512\) | −22.7824 | −1.00685 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0095 | 0.529715 | ||||||||
\(515\) | −54.2175 | −2.38911 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.3178 | 2.03705 | ||||||||
\(518\) | −3.13690 | −0.137827 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.84386 | 0.124711 | ||||||||
\(521\) | 24.2412 | 1.06203 | 0.531014 | − | 0.847363i | \(-0.321811\pi\) | ||||
0.531014 | + | 0.847363i | \(0.321811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6601 | −0.597315 | −0.298658 | − | 0.954360i | \(-0.596539\pi\) | ||||
−0.298658 | + | 0.954360i | \(0.596539\pi\) | |||||||
\(524\) | 37.7716 | 1.65006 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.49738 | −0.283299 | ||||||||
\(527\) | −0.564400 | −0.0245857 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.14832 | 0.267318 | ||||||||
\(530\) | 3.26070 | 0.141636 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9286 | −0.647236 | ||||||||
\(533\) | 0.936867 | 0.0405802 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.9746 | 1.12298 | ||||||||
\(536\) | 1.45803 | 0.0629773 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.47034 | −0.192730 | ||||||||
\(539\) | 5.00409 | 0.215541 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6037 | 1.48773 | 0.743865 | − | 0.668330i | \(-0.232991\pi\) | ||||
0.743865 | + | 0.668330i | \(0.232991\pi\) | |||||||
\(542\) | −10.2451 | −0.440066 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.46539 | −0.148577 | ||||||||
\(545\) | −3.20959 | −0.137484 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3891 | −1.38486 | −0.692428 | − | 0.721487i | \(-0.743459\pi\) | ||||
−0.692428 | + | 0.721487i | \(0.743459\pi\) | |||||||
\(548\) | 22.8780 | 0.977298 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.9730 | −1.02221 | ||||||||
\(551\) | 68.7140 | 2.92731 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.16006 | 0.134380 | ||||||||
\(554\) | −15.2713 | −0.648814 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.4133 | −1.07777 | ||||||||
\(557\) | 36.2257 | 1.53493 | 0.767467 | − | 0.641089i | \(-0.221517\pi\) | ||||
0.767467 | + | 0.641089i | \(0.221517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.70179 | −0.0719780 | ||||||||
\(560\) | −10.4257 | −0.440568 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.51158 | 0.0637622 | ||||||||
\(563\) | 1.20547 | 0.0508046 | 0.0254023 | − | 0.999677i | \(-0.491913\pi\) | ||||
0.0254023 | + | 0.999677i | \(0.491913\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.1455 | 1.35237 | ||||||||
\(566\) | −1.43226 | −0.0602023 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.6997 | 0.700704 | ||||||||
\(569\) | 30.1557 | 1.26419 | 0.632095 | − | 0.774891i | \(-0.282195\pi\) | ||||
0.632095 | + | 0.774891i | \(0.282195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.362635 | −0.0151758 | −0.00758791 | − | 0.999971i | \(-0.502415\pi\) | ||||
−0.00758791 | + | 0.999971i | \(0.502415\pi\) | |||||||
\(572\) | 3.61527 | 0.151162 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.09603 | 0.0457475 | ||||||||
\(575\) | −54.2462 | −2.26222 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0853 | −1.41899 | −0.709496 | − | 0.704710i | \(-0.751077\pi\) | ||||
−0.709496 | + | 0.704710i | \(0.751077\pi\) | |||||||
\(578\) | 7.86507 | 0.327144 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 56.1063 | 2.32969 | ||||||||
\(581\) | 1.77907 | 0.0738082 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.82197 | 0.365369 | ||||||||
\(584\) | −21.2272 | −0.878389 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0397 | −0.456045 | ||||||||
\(587\) | −35.1456 | −1.45062 | −0.725308 | − | 0.688425i | \(-0.758302\pi\) | ||||
−0.725308 | + | 0.688425i | \(0.758302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.69215 | −0.275745 | ||||||||
\(590\) | −2.00993 | −0.0827474 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.6823 | 0.726737 | ||||||||
\(593\) | −22.7973 | −0.936172 | −0.468086 | − | 0.883683i | \(-0.655056\pi\) | ||||
−0.468086 | + | 0.883683i | \(0.655056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.75517 | −0.112951 | ||||||||
\(596\) | −35.7924 | −1.46612 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.04914 | −0.0429025 | ||||||||
\(599\) | −24.3667 | −0.995595 | −0.497797 | − | 0.867293i | \(-0.665858\pi\) | ||||
−0.497797 | + | 0.867293i | \(0.665858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8415 | 0.523818 | 0.261909 | − | 0.965093i | \(-0.415648\pi\) | ||||
0.261909 | + | 0.965093i | \(0.415648\pi\) | |||||||
\(602\) | −1.99091 | −0.0811433 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.0967 | 0.695657 | ||||||||
\(605\) | −54.4663 | −2.21437 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5300 | −0.873875 | −0.436938 | − | 0.899492i | \(-0.643937\pi\) | ||||
−0.436938 | + | 0.899492i | \(0.643937\pi\) | |||||||
\(608\) | −41.0895 | −1.66640 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.05740 | 0.0833015 | ||||||||
\(611\) | −3.77237 | −0.152614 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1695 | −0.410743 | −0.205372 | − | 0.978684i | \(-0.565840\pi\) | ||||
−0.205372 | + | 0.978684i | \(0.565840\pi\) | |||||||
\(614\) | −10.7806 | −0.435069 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.00137 | 0.362675 | ||||||||
\(617\) | 31.1448 | 1.25384 | 0.626921 | − | 0.779083i | \(-0.284315\pi\) | ||||
0.626921 | + | 0.779083i | \(0.284315\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7319 | −0.551933 | −0.275967 | − | 0.961167i | \(-0.588998\pi\) | ||||
−0.275967 | + | 0.961167i | \(0.588998\pi\) | |||||||
\(620\) | −5.46428 | −0.219451 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.29536 | 0.332614 | ||||||||
\(623\) | −7.40408 | −0.296638 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.7162 | 1.02865 | ||||||||
\(626\) | −4.78320 | −0.191175 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.94984 | 0.317233 | ||||||||
\(629\) | 4.67282 | 0.186317 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.6765 | −0.823118 | −0.411559 | − | 0.911383i | \(-0.635016\pi\) | ||||
−0.411559 | + | 0.911383i | \(0.635016\pi\) | |||||||
\(632\) | 5.68434 | 0.226111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.92910 | 0.354620 | ||||||||
\(635\) | 3.87912 | 0.153938 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.407559 | −0.0161481 | ||||||||
\(638\) | −19.4676 | −0.770731 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −43.4924 | −1.71919 | ||||||||
\(641\) | 11.4317 | 0.451525 | 0.225763 | − | 0.974182i | \(-0.427513\pi\) | ||||
0.225763 | + | 0.974182i | \(0.427513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0657 | 0.396951 | 0.198475 | − | 0.980106i | \(-0.436401\pi\) | ||||
0.198475 | + | 0.980106i | \(0.436401\pi\) | |||||||
\(644\) | 9.57046 | 0.377129 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.85196 | −0.112209 | ||||||||
\(647\) | 3.59533 | 0.141347 | 0.0706735 | − | 0.997500i | \(-0.477485\pi\) | ||||
0.0706735 | + | 0.997500i | \(0.477485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.43796 | −0.213458 | ||||||||
\(650\) | 1.95249 | 0.0765830 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.559347 | 0.0219057 | ||||||||
\(653\) | 34.9356 | 1.36714 | 0.683569 | − | 0.729886i | \(-0.260427\pi\) | ||||
0.683569 | + | 0.729886i | \(0.260427\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 82.6558 | 3.22963 | ||||||||
\(656\) | −6.17818 | −0.241218 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.41326 | −0.172047 | ||||||||
\(659\) | −11.3713 | −0.442965 | −0.221482 | − | 0.975164i | \(-0.571090\pi\) | ||||
−0.221482 | + | 0.975164i | \(0.571090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.4734 | 0.407366 | 0.203683 | − | 0.979037i | \(-0.434709\pi\) | ||||
0.203683 | + | 0.979037i | \(0.434709\pi\) | |||||||
\(662\) | 10.3261 | 0.401337 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.20020 | 0.124192 | ||||||||
\(665\) | −32.6683 | −1.26682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.0513 | −1.70567 | ||||||||
\(668\) | 17.7097 | 0.685209 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.49918 | 0.0579182 | ||||||||
\(671\) | 5.56638 | 0.214888 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.72784 | −0.297886 | −0.148943 | − | 0.988846i | \(-0.547587\pi\) | ||||
−0.148943 | + | 0.988846i | \(0.547587\pi\) | |||||||
\(674\) | 15.7011 | 0.604785 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.7502 | 0.875006 | ||||||||
\(677\) | −47.4205 | −1.82252 | −0.911260 | − | 0.411832i | \(-0.864889\pi\) | ||||
−0.911260 | + | 0.411832i | \(0.864889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.89293 | 0.0726440 | ||||||||
\(680\) | −4.95600 | −0.190054 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.89598 | 0.0726008 | ||||||||
\(683\) | −25.1455 | −0.962167 | −0.481084 | − | 0.876675i | \(-0.659757\pi\) | ||||
−0.481084 | + | 0.876675i | \(0.659757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.0639 | 1.91284 | ||||||||
\(686\) | −0.476800 | −0.0182043 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.2225 | 0.427853 | ||||||||
\(689\) | −0.718508 | −0.0273730 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.2318 | −1.45441 | −0.727203 | − | 0.686422i | \(-0.759180\pi\) | ||||
−0.727203 | + | 0.686422i | \(0.759180\pi\) | |||||||
\(692\) | −6.76504 | −0.257168 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.34247 | 0.202798 | ||||||||
\(695\) | −55.6121 | −2.10949 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.63268 | −0.0618422 | ||||||||
\(698\) | −16.0762 | −0.608493 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.8110 | −0.673192 | ||||||||
\(701\) | 39.4939 | 1.49166 | 0.745832 | − | 0.666134i | \(-0.232052\pi\) | ||||
0.745832 | + | 0.666134i | \(0.232052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.4061 | 2.08968 | ||||||||
\(704\) | −15.2573 | −0.575031 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.29241 | −0.199182 | ||||||||
\(707\) | −19.4439 | −0.731261 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.2635 | 0.498120 | 0.249060 | − | 0.968488i | \(-0.419878\pi\) | ||||
0.249060 | + | 0.968488i | \(0.419878\pi\) | |||||||
\(710\) | 17.1709 | 0.644414 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.3185 | −0.499131 | ||||||||
\(713\) | 4.29022 | 0.160670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.91132 | 0.295867 | ||||||||
\(716\) | −4.64401 | −0.173555 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.183991 | 0.00686650 | ||||||||
\(719\) | −4.92349 | −0.183615 | −0.0918075 | − | 0.995777i | \(-0.529264\pi\) | ||||
−0.0918075 | + | 0.995777i | \(0.529264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.9767 | 0.520521 | ||||||||
\(722\) | −24.7567 | −0.921351 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −41.8541 | −1.55549 | ||||||||
\(725\) | 81.9813 | 3.04471 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.1568 | −0.970101 | −0.485050 | − | 0.874486i | \(-0.661199\pi\) | ||||
−0.485050 | + | 0.874486i | \(0.661199\pi\) | |||||||
\(728\) | −0.733119 | −0.0271712 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.8262 | −0.807825 | ||||||||
\(731\) | 2.96571 | 0.109691 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.2501 | −0.747955 | −0.373977 | − | 0.927438i | \(-0.622006\pi\) | ||||
−0.373977 | + | 0.927438i | \(0.622006\pi\) | |||||||
\(734\) | 13.5490 | 0.500101 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.3418 | 0.970970 | ||||||||
\(737\) | 4.05609 | 0.149408 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4553 | −0.605316 | −0.302658 | − | 0.953099i | \(-0.597874\pi\) | ||||
−0.302658 | + | 0.953099i | \(0.597874\pi\) | |||||||
\(740\) | 45.2402 | 1.66306 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.840576 | −0.0308585 | ||||||||
\(743\) | −33.0398 | −1.21211 | −0.606056 | − | 0.795422i | \(-0.707249\pi\) | ||||
−0.606056 | + | 0.795422i | \(0.707249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −78.3248 | −2.86960 | ||||||||
\(746\) | −6.22232 | −0.227815 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.30035 | −0.230364 | ||||||||
\(749\) | −6.69599 | −0.244666 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.64889 | −0.352093 | −0.176047 | − | 0.984382i | \(-0.556331\pi\) | ||||
−0.176047 | + | 0.984382i | \(0.556331\pi\) | |||||||
\(752\) | 24.8769 | 0.907168 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.58555 | 0.0577422 | ||||||||
\(755\) | 37.4129 | 1.36159 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.8217 | −0.902159 | −0.451079 | − | 0.892484i | \(-0.648961\pi\) | ||||
−0.451079 | + | 0.892484i | \(0.648961\pi\) | |||||||
\(758\) | −12.4740 | −0.453077 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −58.7638 | −2.13159 | ||||||||
\(761\) | 6.25290 | 0.226668 | 0.113334 | − | 0.993557i | \(-0.463847\pi\) | ||||
0.113334 | + | 0.993557i | \(0.463847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.827402 | 0.0299540 | ||||||||
\(764\) | −5.44900 | −0.197138 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.48014 | 0.306400 | ||||||||
\(767\) | 0.442896 | 0.0159920 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.5097 | 0.847782 | 0.423891 | − | 0.905713i | \(-0.360664\pi\) | ||||
0.423891 | + | 0.905713i | \(0.360664\pi\) | |||||||
\(770\) | 9.25538 | 0.333541 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8491 | −0.642402 | ||||||||
\(773\) | −17.0244 | −0.612326 | −0.306163 | − | 0.951979i | \(-0.599045\pi\) | ||||
−0.306163 | + | 0.951979i | \(0.599045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.98427 | −0.286804 | ||||||||
\(776\) | 3.40501 | 0.122233 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.31696 | −0.0830671 | ||||||||
\(779\) | −19.3589 | −0.693604 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.4568 | 1.66236 | ||||||||
\(782\) | 1.82834 | 0.0653813 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.68765 | 0.0959877 | ||||||||
\(785\) | 17.3967 | 0.620914 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.5601 | −1.23193 | −0.615966 | − | 0.787772i | \(-0.711234\pi\) | ||||
−0.615966 | + | 0.787772i | \(0.711234\pi\) | |||||||
\(788\) | −20.3824 | −0.726094 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.84474 | 0.207947 | ||||||||
\(791\) | −8.28680 | −0.294645 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.453355 | −0.0160991 | ||||||||
\(794\) | −7.14523 | −0.253575 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0659 | −0.356775 | ||||||||
\(797\) | 9.18832 | 0.325467 | 0.162734 | − | 0.986670i | \(-0.447969\pi\) | ||||
0.162734 | + | 0.986670i | \(0.447969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.57411 | 0.232575 | ||||||||
\(800\) | −49.0230 | −1.73323 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.4285 | −0.615423 | ||||||||
\(803\) | −59.0519 | −2.08390 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.9431 | 0.738146 | ||||||||
\(806\) | −0.154419 | −0.00543916 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34.9757 | −1.23044 | ||||||||
\(809\) | −52.9283 | −1.86086 | −0.930429 | − | 0.366472i | \(-0.880566\pi\) | ||||
−0.930429 | + | 0.366472i | \(0.880566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.1436 | 1.93635 | 0.968177 | − | 0.250268i | \(-0.0805188\pi\) | ||||
0.968177 | + | 0.250268i | \(0.0805188\pi\) | |||||||
\(812\) | −14.4637 | −0.507575 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.6973 | −0.550190 | ||||||||
\(815\) | 1.22402 | 0.0428756 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.1648 | 1.23026 | ||||||||
\(818\) | 11.8744 | 0.415178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.8069 | −0.552001 | ||||||||
\(821\) | 0.850062 | 0.0296674 | 0.0148337 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148337 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0436 | −0.942680 | −0.471340 | − | 0.881952i | \(-0.656230\pi\) | ||||
−0.471340 | + | 0.881952i | \(0.656230\pi\) | |||||||
\(824\) | 25.1414 | 0.875843 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.518140 | 0.0180284 | ||||||||
\(827\) | 46.5194 | 1.61764 | 0.808819 | − | 0.588058i | \(-0.200107\pi\) | ||||
0.808819 | + | 0.588058i | \(0.200107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.39637 | 0.222155 | 0.111078 | − | 0.993812i | \(-0.464570\pi\) | ||||
0.111078 | + | 0.993812i | \(0.464570\pi\) | |||||||
\(830\) | 3.29050 | 0.114215 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.24263 | 0.0430806 | ||||||||
\(833\) | 0.710255 | 0.0246089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.7542 | 1.34114 | ||||||||
\(836\) | −74.7039 | −2.58369 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.356755 | 0.0123239 | ||||||||
\(839\) | 13.0104 | 0.449169 | 0.224584 | − | 0.974455i | \(-0.427898\pi\) | ||||
0.224584 | + | 0.974455i | \(0.427898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.5740 | 1.29565 | ||||||||
\(842\) | 6.38409 | 0.220010 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.6639 | −0.676859 | ||||||||
\(845\) | 49.7843 | 1.71263 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0409 | 0.482450 | ||||||||
\(848\) | 4.73821 | 0.162711 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.40261 | −0.116709 | ||||||||
\(851\) | −35.5199 | −1.21761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.1861 | −1.64986 | −0.824930 | − | 0.565234i | \(-0.808786\pi\) | ||||
−0.824930 | + | 0.565234i | \(0.808786\pi\) | |||||||
\(854\) | −0.530376 | −0.0181491 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0448 | −0.411682 | ||||||||
\(857\) | −24.7884 | −0.846756 | −0.423378 | − | 0.905953i | \(-0.639156\pi\) | ||||
−0.423378 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.20536 | −0.109365 | −0.0546827 | − | 0.998504i | \(-0.517415\pi\) | ||||
−0.0546827 | + | 0.998504i | \(0.517415\pi\) | |||||||
\(860\) | 28.7127 | 0.979096 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.9156 | −0.473966 | ||||||||
\(863\) | −30.4040 | −1.03496 | −0.517482 | − | 0.855694i | \(-0.673131\pi\) | ||||
−0.517482 | + | 0.855694i | \(0.673131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.8040 | −0.503350 | ||||||||
\(866\) | 0.00819990 | 0.000278644 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.40864 | 0.0478122 | ||||||||
\(869\) | 15.8132 | 0.536427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.330349 | −0.0111935 | ||||||||
\(872\) | 1.48833 | 0.0504013 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.6788 | 0.733297 | ||||||||
\(875\) | −19.5803 | −0.661934 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.0743 | −1.04930 | −0.524652 | − | 0.851317i | \(-0.675805\pi\) | ||||
−0.524652 | + | 0.851317i | \(0.675805\pi\) | |||||||
\(878\) | −15.5161 | −0.523644 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −52.1713 | −1.75869 | ||||||||
\(881\) | 35.7896 | 1.20578 | 0.602890 | − | 0.797824i | \(-0.294016\pi\) | ||||
0.602890 | + | 0.797824i | \(0.294016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.5463 | 1.60006 | 0.800030 | − | 0.599959i | \(-0.204817\pi\) | ||||
0.800030 | + | 0.599959i | \(0.204817\pi\) | |||||||
\(884\) | 0.513134 | 0.0172586 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.87699 | 0.298228 | ||||||||
\(887\) | −52.6046 | −1.76629 | −0.883146 | − | 0.469099i | \(-0.844579\pi\) | ||||
−0.883146 | + | 0.469099i | \(0.844579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −13.6943 | −0.459035 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.89084 | 0.130275 | ||||||||
\(893\) | 77.9500 | 2.60850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.1625 | −0.339695 | ||||||||
\(896\) | 11.2119 | 0.374564 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.10307 | 0.0701805 | ||||||||
\(899\) | −6.48374 | −0.216245 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.25215 | 0.0417150 | ||||||||
\(902\) | 5.48464 | 0.182618 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.9063 | −0.495777 | ||||||||
\(905\) | −91.5894 | −3.04453 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.8180 | −1.45495 | −0.727477 | − | 0.686132i | \(-0.759307\pi\) | ||||
−0.727477 | + | 0.686132i | \(0.759307\pi\) | |||||||
\(908\) | 18.2539 | 0.605777 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.753807 | −0.0249885 | ||||||||
\(911\) | 32.7123 | 1.08381 | 0.541903 | − | 0.840441i | \(-0.317704\pi\) | ||||
0.541903 | + | 0.840441i | \(0.317704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.90261 | 0.294633 | ||||||||
\(914\) | −15.2292 | −0.503738 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.6512 | −0.418006 | ||||||||
\(917\) | −21.3079 | −0.703648 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.6840 | −1.60594 | −0.802969 | − | 0.596021i | \(-0.796748\pi\) | ||||
−0.802969 | + | 0.596021i | \(0.796748\pi\) | |||||||
\(920\) | 37.6725 | 1.24202 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.6632 | 0.351173 | ||||||||
\(923\) | −3.78369 | −0.124542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66.1039 | 2.17348 | ||||||||
\(926\) | −10.8502 | −0.356561 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −39.8098 | −1.30682 | ||||||||
\(929\) | −37.8583 | −1.24209 | −0.621045 | − | 0.783775i | \(-0.713292\pi\) | ||||
−0.621045 | + | 0.783775i | \(0.713292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.42156 | 0.276006 | ||||||||
\(932\) | −15.8988 | −0.520782 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.48128 | 0.212074 | ||||||||
\(935\) | −13.7871 | −0.450886 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.8499 | −0.387121 | −0.193560 | − | 0.981088i | \(-0.562004\pi\) | ||||
−0.193560 | + | 0.981088i | \(0.562004\pi\) | |||||||
\(938\) | −0.386473 | −0.0126188 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 63.6477 | 2.07596 | ||||||||
\(941\) | −8.12653 | −0.264917 | −0.132459 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132459 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4106 | 0.404146 | ||||||||
\(944\) | −2.92068 | −0.0950602 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.96267 | −0.323914 | ||||||||
\(947\) | 15.4114 | 0.500802 | 0.250401 | − | 0.968142i | \(-0.419438\pi\) | ||||
0.250401 | + | 0.968142i | \(0.419438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.80950 | 0.156123 | ||||||||
\(950\) | −40.3451 | −1.30897 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.27761 | 0.0414075 | ||||||||
\(953\) | 42.9768 | 1.39216 | 0.696078 | − | 0.717966i | \(-0.254927\pi\) | ||||
0.696078 | + | 0.717966i | \(0.254927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9241 | −0.385854 | ||||||||
\(956\) | 22.1322 | 0.715807 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.200626 | 0.00648194 | ||||||||
\(959\) | −12.9060 | −0.416756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3685 | −0.979630 | ||||||||
\(962\) | 1.27847 | 0.0412196 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 36.3126 | 1.16955 | ||||||||
\(965\) | −39.0592 | −1.25736 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.6077 | 1.11291 | 0.556454 | − | 0.830879i | \(-0.312162\pi\) | ||||
0.556454 | + | 0.830879i | \(0.312162\pi\) | |||||||
\(968\) | 25.2568 | 0.811783 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.50110 | 0.112414 | ||||||||
\(971\) | −2.44650 | −0.0785118 | −0.0392559 | − | 0.999229i | \(-0.512499\pi\) | ||||
−0.0392559 | + | 0.999229i | \(0.512499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.3363 | 0.459599 | ||||||||
\(974\) | −3.35806 | −0.107599 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.98966 | 0.0956967 | ||||||||
\(977\) | 46.9898 | 1.50334 | 0.751668 | − | 0.659542i | \(-0.229250\pi\) | ||||
0.751668 | + | 0.659542i | \(0.229250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.0506 | −1.18414 | ||||||||
\(980\) | 6.87638 | 0.219658 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.87116 | −0.0597110 | ||||||||
\(983\) | −3.47547 | −0.110850 | −0.0554251 | − | 0.998463i | \(-0.517651\pi\) | ||||
−0.0554251 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.6030 | −1.42117 | ||||||||
\(986\) | −2.76314 | −0.0879962 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.08428 | 0.193567 | ||||||||
\(989\) | −22.5435 | −0.716842 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.72105 | −0.118203 | −0.0591015 | − | 0.998252i | \(-0.518824\pi\) | ||||
−0.0591015 | + | 0.998252i | \(0.518824\pi\) | |||||||
\(992\) | 3.87714 | 0.123099 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.42650 | −0.140400 | ||||||||
\(995\) | −22.0272 | −0.698309 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.8809 | 0.851327 | 0.425664 | − | 0.904881i | \(-0.360041\pi\) | ||||
0.425664 | + | 0.904881i | \(0.360041\pi\) | |||||||
\(998\) | 6.46579 | 0.204671 | ||||||||
\(999\) | 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 | 8001.2.a.ba.1.17 | ✓ | 40 | |
3.2 | odd | 2 | inner | 8001.2.a.ba.1.24 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.ba.1.17 | ✓ | 40 | 1.1 | even | 1 | trivial | |
8001.2.a.ba.1.24 | yes | 40 | 3.2 | odd | 2 | inner |