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: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 10 x^{11} + 53 x^{10} + 19 x^{9} - 242 x^{8} + 61 x^{7} + 467 x^{6} - 211 x^{5} - 372 x^{4} + 146 x^{3} + 116 x^{2} - 12 x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70878\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70878 | −1.91539 | −0.957697 | − | 0.287777i | \(-0.907084\pi\) | ||||
−0.957697 | + | 0.287777i | \(0.907084\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.33747 | 2.66874 | ||||||||
\(5\) | −2.87857 | −1.28734 | −0.643668 | − | 0.765305i | \(-0.722588\pi\) | ||||
−0.643668 | + | 0.765305i | \(0.722588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.04047 | −3.19629 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.79741 | 2.46576 | ||||||||
\(11\) | 1.50105 | 0.452584 | 0.226292 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226292 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.43745 | 1.50808 | 0.754039 | − | 0.656830i | \(-0.228103\pi\) | ||||
0.754039 | + | 0.656830i | \(0.228103\pi\) | |||||||
\(14\) | −2.70878 | −0.723951 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.8137 | 3.45342 | ||||||||
\(17\) | −1.68422 | −0.408484 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.30288 | −0.757733 | −0.378867 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378867 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(20\) | −15.3643 | −3.43556 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.06601 | −0.866877 | ||||||||
\(23\) | 5.07189 | 1.05756 | 0.528781 | − | 0.848758i | \(-0.322649\pi\) | ||||
0.528781 | + | 0.848758i | \(0.322649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.28617 | 0.657235 | ||||||||
\(26\) | −14.7288 | −2.88856 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.33747 | 1.00869 | ||||||||
\(29\) | 8.28010 | 1.53758 | 0.768788 | − | 0.639504i | \(-0.220860\pi\) | ||||
0.768788 | + | 0.639504i | \(0.220860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.29635 | −1.66967 | −0.834837 | − | 0.550498i | \(-0.814438\pi\) | ||||
−0.834837 | + | 0.550498i | \(0.814438\pi\) | |||||||
\(32\) | −19.3372 | −3.41837 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.56218 | 0.782408 | ||||||||
\(35\) | −2.87857 | −0.486567 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.22083 | −1.18710 | −0.593548 | − | 0.804798i | \(-0.702273\pi\) | ||||
−0.593548 | + | 0.804798i | \(0.702273\pi\) | |||||||
\(38\) | 8.94677 | 1.45136 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26.0237 | 4.11470 | ||||||||
\(41\) | 2.03090 | 0.317173 | 0.158586 | − | 0.987345i | \(-0.449306\pi\) | ||||
0.158586 | + | 0.987345i | \(0.449306\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.859629 | 0.131092 | 0.0655461 | − | 0.997850i | \(-0.479121\pi\) | ||||
0.0655461 | + | 0.997850i | \(0.479121\pi\) | |||||||
\(44\) | 8.01182 | 1.20783 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.7386 | −2.02565 | ||||||||
\(47\) | 6.92288 | 1.00981 | 0.504903 | − | 0.863176i | \(-0.331528\pi\) | ||||
0.504903 | + | 0.863176i | \(0.331528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.90151 | −1.25886 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29.0223 | 4.02466 | ||||||||
\(53\) | −8.32870 | −1.14404 | −0.572018 | − | 0.820241i | \(-0.693839\pi\) | ||||
−0.572018 | + | 0.820241i | \(0.693839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.32088 | −0.582628 | ||||||||
\(56\) | −9.04047 | −1.20808 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −22.4289 | −2.94506 | ||||||||
\(59\) | −8.94067 | −1.16398 | −0.581988 | − | 0.813197i | \(-0.697725\pi\) | ||||
−0.581988 | + | 0.813197i | \(0.697725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.99896 | 1.28024 | 0.640118 | − | 0.768277i | \(-0.278886\pi\) | ||||
0.640118 | + | 0.768277i | \(0.278886\pi\) | |||||||
\(62\) | 25.1817 | 3.19808 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 24.7529 | 3.09411 | ||||||||
\(65\) | −15.6521 | −1.94140 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.7116 | −1.91947 | −0.959736 | − | 0.280903i | \(-0.909366\pi\) | ||||
−0.959736 | + | 0.280903i | \(0.909366\pi\) | |||||||
\(68\) | −8.98949 | −1.09014 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.79741 | 0.931969 | ||||||||
\(71\) | −5.53761 | −0.657194 | −0.328597 | − | 0.944470i | \(-0.606576\pi\) | ||||
−0.328597 | + | 0.944470i | \(0.606576\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.56437 | 0.768302 | 0.384151 | − | 0.923270i | \(-0.374494\pi\) | ||||
0.384151 | + | 0.923270i | \(0.374494\pi\) | |||||||
\(74\) | 19.5596 | 2.27376 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.6290 | −2.02219 | ||||||||
\(77\) | 1.50105 | 0.171061 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.27964 | −1.04404 | −0.522021 | − | 0.852933i | \(-0.674822\pi\) | ||||
−0.522021 | + | 0.852933i | \(0.674822\pi\) | |||||||
\(80\) | −39.7637 | −4.44571 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.50124 | −0.607511 | ||||||||
\(83\) | −7.17857 | −0.787950 | −0.393975 | − | 0.919121i | \(-0.628900\pi\) | ||||
−0.393975 | + | 0.919121i | \(0.628900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.84815 | 0.525856 | ||||||||
\(86\) | −2.32854 | −0.251093 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.5702 | −1.44659 | ||||||||
\(89\) | −9.76491 | −1.03508 | −0.517539 | − | 0.855660i | \(-0.673152\pi\) | ||||
−0.517539 | + | 0.855660i | \(0.673152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.43745 | 0.570000 | ||||||||
\(92\) | 27.0711 | 2.82235 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.7525 | −1.93418 | ||||||||
\(95\) | 9.50758 | 0.975457 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.08877 | −0.922825 | −0.461412 | − | 0.887186i | \(-0.652657\pi\) | ||||
−0.461412 | + | 0.887186i | \(0.652657\pi\) | |||||||
\(98\) | −2.70878 | −0.273628 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 17.5399 | 1.75399 | ||||||||
\(101\) | 2.25398 | 0.224279 | 0.112140 | − | 0.993692i | \(-0.464230\pi\) | ||||
0.112140 | + | 0.993692i | \(0.464230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1074 | 1.68564 | 0.842820 | − | 0.538195i | \(-0.180894\pi\) | ||||
0.842820 | + | 0.538195i | \(0.180894\pi\) | |||||||
\(104\) | −49.1571 | −4.82025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.5606 | 2.19128 | ||||||||
\(107\) | 3.37485 | 0.326259 | 0.163130 | − | 0.986605i | \(-0.447841\pi\) | ||||
0.163130 | + | 0.986605i | \(0.447841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.18665 | 0.784139 | 0.392069 | − | 0.919936i | \(-0.371759\pi\) | ||||
0.392069 | + | 0.919936i | \(0.371759\pi\) | |||||||
\(110\) | 11.7043 | 1.11596 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.8137 | 1.30527 | ||||||||
\(113\) | 13.4635 | 1.26654 | 0.633269 | − | 0.773932i | \(-0.281713\pi\) | ||||
0.633269 | + | 0.773932i | \(0.281713\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.5998 | −1.36144 | ||||||||
\(116\) | 44.1948 | 4.10338 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.2183 | 2.22947 | ||||||||
\(119\) | −1.68422 | −0.154392 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.74685 | −0.795168 | ||||||||
\(122\) | −27.0850 | −2.45216 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −49.6190 | −4.45592 | ||||||||
\(125\) | 4.93337 | 0.441254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −28.3756 | −2.50808 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 42.3980 | 3.71855 | ||||||||
\(131\) | 0.496098 | 0.0433443 | 0.0216721 | − | 0.999765i | \(-0.493101\pi\) | ||||
0.0216721 | + | 0.999765i | \(0.493101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.30288 | −0.286396 | ||||||||
\(134\) | 42.5591 | 3.67655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.2262 | 1.30563 | ||||||||
\(137\) | −20.7815 | −1.77548 | −0.887741 | − | 0.460343i | \(-0.847726\pi\) | ||||
−0.887741 | + | 0.460343i | \(0.847726\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.210195 | 0.0178285 | 0.00891424 | − | 0.999960i | \(-0.497162\pi\) | ||||
0.00891424 | + | 0.999960i | \(0.497162\pi\) | |||||||
\(140\) | −15.3643 | −1.29852 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.0002 | 1.25879 | ||||||||
\(143\) | 8.16189 | 0.682531 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.8349 | −1.97938 | ||||||||
\(146\) | −17.7814 | −1.47160 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.5410 | −3.16805 | ||||||||
\(149\) | 9.61526 | 0.787713 | 0.393857 | − | 0.919172i | \(-0.371141\pi\) | ||||
0.393857 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.39942 | 0.358020 | 0.179010 | − | 0.983847i | \(-0.442711\pi\) | ||||
0.179010 | + | 0.983847i | \(0.442711\pi\) | |||||||
\(152\) | 29.8596 | 2.42194 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.06601 | −0.327649 | ||||||||
\(155\) | 26.7602 | 2.14943 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.08882 | −0.0868971 | −0.0434486 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434486 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(158\) | 25.1365 | 1.99975 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 55.6636 | 4.40060 | ||||||||
\(161\) | 5.07189 | 0.399721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.7282 | −1.07528 | −0.537638 | − | 0.843176i | \(-0.680683\pi\) | ||||
−0.537638 | + | 0.843176i | \(0.680683\pi\) | |||||||
\(164\) | 10.8398 | 0.846450 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.4451 | 1.50924 | ||||||||
\(167\) | −10.7070 | −0.828536 | −0.414268 | − | 0.910155i | \(-0.635962\pi\) | ||||
−0.414268 | + | 0.910155i | \(0.635962\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.5659 | 1.27430 | ||||||||
\(170\) | −13.1326 | −1.00722 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.58825 | 0.349851 | ||||||||
\(173\) | 5.28100 | 0.401507 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.28617 | 0.248411 | ||||||||
\(176\) | 20.7350 | 1.56296 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.4510 | 1.98258 | ||||||||
\(179\) | 3.05114 | 0.228053 | 0.114026 | − | 0.993478i | \(-0.463625\pi\) | ||||
0.114026 | + | 0.993478i | \(0.463625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8363 | 1.47442 | 0.737209 | − | 0.675664i | \(-0.236143\pi\) | ||||
0.737209 | + | 0.675664i | \(0.236143\pi\) | |||||||
\(182\) | −14.7288 | −1.09177 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −45.8523 | −3.38027 | ||||||||
\(185\) | 20.7857 | 1.52819 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.52810 | −0.184873 | ||||||||
\(188\) | 36.9507 | 2.69491 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.7539 | −1.86839 | ||||||||
\(191\) | −26.8779 | −1.94482 | −0.972410 | − | 0.233280i | \(-0.925054\pi\) | ||||
−0.972410 | + | 0.233280i | \(0.925054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4021 | 0.820739 | 0.410369 | − | 0.911919i | \(-0.365400\pi\) | ||||
0.410369 | + | 0.911919i | \(0.365400\pi\) | |||||||
\(194\) | 24.6194 | 1.76757 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.33747 | 0.381248 | ||||||||
\(197\) | 11.0512 | 0.787368 | 0.393684 | − | 0.919246i | \(-0.371200\pi\) | ||||
0.393684 | + | 0.919246i | \(0.371200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37619 | 0.310220 | 0.155110 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155110 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(200\) | −29.7086 | −2.10071 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.10553 | −0.429583 | ||||||||
\(203\) | 8.28010 | 0.581149 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.84608 | −0.408308 | ||||||||
\(206\) | −46.3401 | −3.22867 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 75.1112 | 5.20803 | ||||||||
\(209\) | −4.95779 | −0.342938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.47388 | −0.307994 | −0.153997 | − | 0.988071i | \(-0.549215\pi\) | ||||
−0.153997 | + | 0.988071i | \(0.549215\pi\) | |||||||
\(212\) | −44.4542 | −3.05313 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.14172 | −0.624915 | ||||||||
\(215\) | −2.47450 | −0.168760 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.29635 | −0.631077 | ||||||||
\(218\) | −22.1758 | −1.50193 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −23.0626 | −1.55488 | ||||||||
\(221\) | −9.15787 | −0.616025 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4884 | 1.63986 | 0.819932 | − | 0.572461i | \(-0.194011\pi\) | ||||
0.819932 | + | 0.572461i | \(0.194011\pi\) | |||||||
\(224\) | −19.3372 | −1.29202 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.4696 | −2.42592 | ||||||||
\(227\) | 0.513152 | 0.0340591 | 0.0170296 | − | 0.999855i | \(-0.494579\pi\) | ||||
0.0170296 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6982 | −1.30169 | −0.650847 | − | 0.759209i | \(-0.725586\pi\) | ||||
−0.650847 | + | 0.759209i | \(0.725586\pi\) | |||||||
\(230\) | 39.5476 | 2.60769 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −74.8560 | −4.91454 | ||||||||
\(233\) | 1.36091 | 0.0891564 | 0.0445782 | − | 0.999006i | \(-0.485806\pi\) | ||||
0.0445782 | + | 0.999006i | \(0.485806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.9280 | −1.29996 | ||||||||
\(236\) | −47.7206 | −3.10635 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.56218 | 0.295722 | ||||||||
\(239\) | −25.4879 | −1.64867 | −0.824336 | − | 0.566100i | \(-0.808451\pi\) | ||||
−0.824336 | + | 0.566100i | \(0.808451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9835 | 1.54492 | 0.772458 | − | 0.635066i | \(-0.219027\pi\) | ||||
0.772458 | + | 0.635066i | \(0.219027\pi\) | |||||||
\(242\) | 23.6933 | 1.52306 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 53.3692 | 3.41661 | ||||||||
\(245\) | −2.87857 | −0.183905 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.9593 | −1.14272 | ||||||||
\(248\) | 84.0434 | 5.33676 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.3634 | −0.845176 | ||||||||
\(251\) | −10.4969 | −0.662558 | −0.331279 | − | 0.943533i | \(-0.607480\pi\) | ||||
−0.331279 | + | 0.943533i | \(0.607480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.61316 | 0.478635 | ||||||||
\(254\) | 2.70878 | 0.169964 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27.3575 | 1.70984 | ||||||||
\(257\) | −3.96662 | −0.247431 | −0.123716 | − | 0.992318i | \(-0.539481\pi\) | ||||
−0.123716 | + | 0.992318i | \(0.539481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.22083 | −0.448680 | ||||||||
\(260\) | −83.5426 | −5.18109 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.34382 | −0.0830214 | ||||||||
\(263\) | 5.02765 | 0.310018 | 0.155009 | − | 0.987913i | \(-0.450459\pi\) | ||||
0.155009 | + | 0.987913i | \(0.450459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.9748 | 1.47276 | ||||||||
\(266\) | 8.94677 | 0.548562 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −83.8600 | −5.12257 | ||||||||
\(269\) | −16.7702 | −1.02250 | −0.511249 | − | 0.859432i | \(-0.670817\pi\) | ||||
−0.511249 | + | 0.859432i | \(0.670817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8503 | −1.50955 | −0.754773 | − | 0.655986i | \(-0.772253\pi\) | ||||
−0.754773 | + | 0.655986i | \(0.772253\pi\) | |||||||
\(272\) | −23.2653 | −1.41067 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 56.2924 | 3.40075 | ||||||||
\(275\) | 4.93271 | 0.297454 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.45207 | −0.327583 | −0.163791 | − | 0.986495i | \(-0.552372\pi\) | ||||
−0.163791 | + | 0.986495i | \(0.552372\pi\) | |||||||
\(278\) | −0.569371 | −0.0341486 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 26.0237 | 1.55521 | ||||||||
\(281\) | 9.96730 | 0.594600 | 0.297300 | − | 0.954784i | \(-0.403914\pi\) | ||||
0.297300 | + | 0.954784i | \(0.403914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.38116 | −0.379320 | −0.189660 | − | 0.981850i | \(-0.560739\pi\) | ||||
−0.189660 | + | 0.981850i | \(0.560739\pi\) | |||||||
\(284\) | −29.5569 | −1.75388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.1087 | −1.30732 | ||||||||
\(287\) | 2.03090 | 0.119880 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1634 | −0.833141 | ||||||||
\(290\) | 64.5633 | 3.79129 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 35.0372 | 2.05040 | ||||||||
\(293\) | 26.0774 | 1.52346 | 0.761728 | − | 0.647896i | \(-0.224351\pi\) | ||||
0.761728 | + | 0.647896i | \(0.224351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.7364 | 1.49843 | ||||||||
\(296\) | 65.2797 | 3.79431 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.0456 | −1.50878 | ||||||||
\(299\) | 27.5781 | 1.59489 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.859629 | 0.0495482 | ||||||||
\(302\) | −11.9171 | −0.685750 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −45.6250 | −2.61677 | ||||||||
\(305\) | −28.7827 | −1.64809 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.03900 | −0.344664 | −0.172332 | − | 0.985039i | \(-0.555130\pi\) | ||||
−0.172332 | + | 0.985039i | \(0.555130\pi\) | |||||||
\(308\) | 8.01182 | 0.456516 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −72.4874 | −4.11701 | ||||||||
\(311\) | 27.0222 | 1.53229 | 0.766144 | − | 0.642669i | \(-0.222173\pi\) | ||||
0.766144 | + | 0.642669i | \(0.222173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.2532 | −1.37087 | −0.685435 | − | 0.728134i | \(-0.740388\pi\) | ||||
−0.685435 | + | 0.728134i | \(0.740388\pi\) | |||||||
\(314\) | 2.94937 | 0.166442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −49.5298 | −2.78627 | ||||||||
\(317\) | −8.83443 | −0.496191 | −0.248095 | − | 0.968736i | \(-0.579805\pi\) | ||||
−0.248095 | + | 0.968736i | \(0.579805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4288 | 0.695882 | ||||||||
\(320\) | −71.2530 | −3.98317 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.7386 | −0.765623 | ||||||||
\(323\) | 5.56279 | 0.309522 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8684 | 0.991161 | ||||||||
\(326\) | 37.1867 | 2.05958 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.3603 | −1.01378 | ||||||||
\(329\) | 6.92288 | 0.381671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9974 | −0.934261 | −0.467130 | − | 0.884188i | \(-0.654712\pi\) | ||||
−0.467130 | + | 0.884188i | \(0.654712\pi\) | |||||||
\(332\) | −38.3154 | −2.10283 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.0030 | 1.58697 | ||||||||
\(335\) | 45.2268 | 2.47101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4361 | 0.677435 | 0.338718 | − | 0.940888i | \(-0.390007\pi\) | ||||
0.338718 | + | 0.940888i | \(0.390007\pi\) | |||||||
\(338\) | −44.8733 | −2.44078 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.8769 | 1.40337 | ||||||||
\(341\) | −13.9543 | −0.755667 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.77146 | −0.419009 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.3051 | −0.769045 | ||||||||
\(347\) | −10.2559 | −0.550567 | −0.275283 | − | 0.961363i | \(-0.588772\pi\) | ||||
−0.275283 | + | 0.961363i | \(0.588772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0536 | 1.50167 | 0.750836 | − | 0.660488i | \(-0.229651\pi\) | ||||
0.750836 | + | 0.660488i | \(0.229651\pi\) | |||||||
\(350\) | −8.90151 | −0.475806 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.0262 | −1.54710 | ||||||||
\(353\) | 0.120411 | 0.00640881 | 0.00320440 | − | 0.999995i | \(-0.498980\pi\) | ||||
0.00320440 | + | 0.999995i | \(0.498980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9404 | 0.846029 | ||||||||
\(356\) | −52.1199 | −2.76235 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.26485 | −0.436811 | ||||||||
\(359\) | −15.5091 | −0.818542 | −0.409271 | − | 0.912413i | \(-0.634217\pi\) | ||||
−0.409271 | + | 0.912413i | \(0.634217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.09097 | −0.425840 | ||||||||
\(362\) | −53.7320 | −2.82409 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 29.0223 | 1.52118 | ||||||||
\(365\) | −18.8960 | −0.989063 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.278621 | 0.0145439 | 0.00727195 | − | 0.999974i | \(-0.497685\pi\) | ||||
0.00727195 | + | 0.999974i | \(0.497685\pi\) | |||||||
\(368\) | 70.0615 | 3.65221 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −56.3038 | −2.92709 | ||||||||
\(371\) | −8.32870 | −0.432405 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5201 | 1.32138 | 0.660691 | − | 0.750658i | \(-0.270263\pi\) | ||||
0.660691 | + | 0.750658i | \(0.270263\pi\) | |||||||
\(374\) | 6.84807 | 0.354105 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −62.5861 | −3.22763 | ||||||||
\(377\) | 45.0226 | 2.31878 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1849 | −0.523161 | −0.261580 | − | 0.965182i | \(-0.584244\pi\) | ||||
−0.261580 | + | 0.965182i | \(0.584244\pi\) | |||||||
\(380\) | 50.7465 | 2.60324 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 72.8063 | 3.72510 | ||||||||
\(383\) | 27.7594 | 1.41844 | 0.709220 | − | 0.704987i | \(-0.249047\pi\) | ||||
0.709220 | + | 0.704987i | \(0.249047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.32088 | −0.220213 | ||||||||
\(386\) | −30.8857 | −1.57204 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −48.5111 | −2.46278 | ||||||||
\(389\) | −26.1982 | −1.32830 | −0.664151 | − | 0.747598i | \(-0.731207\pi\) | ||||
−0.664151 | + | 0.747598i | \(0.731207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.54219 | −0.431997 | ||||||||
\(392\) | −9.04047 | −0.456613 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.9353 | −1.50812 | ||||||||
\(395\) | 26.7121 | 1.34403 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.93868 | 0.448620 | 0.224310 | − | 0.974518i | \(-0.427987\pi\) | ||||
0.224310 | + | 0.974518i | \(0.427987\pi\) | |||||||
\(398\) | −11.8541 | −0.594193 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 45.3942 | 2.26971 | ||||||||
\(401\) | 35.2875 | 1.76217 | 0.881086 | − | 0.472956i | \(-0.156813\pi\) | ||||
0.881086 | + | 0.472956i | \(0.156813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.5484 | −2.51800 | ||||||||
\(404\) | 12.0306 | 0.598542 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.4289 | −1.11313 | ||||||||
\(407\) | −10.8388 | −0.537261 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.33933 | −0.313460 | −0.156730 | − | 0.987642i | \(-0.550095\pi\) | ||||
−0.156730 | + | 0.987642i | \(0.550095\pi\) | |||||||
\(410\) | 15.8357 | 0.782070 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 91.3102 | 4.49853 | ||||||||
\(413\) | −8.94067 | −0.439942 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.6640 | 1.01436 | ||||||||
\(416\) | −105.145 | −5.15517 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.4296 | 0.656861 | ||||||||
\(419\) | −36.2997 | −1.77335 | −0.886677 | − | 0.462388i | \(-0.846993\pi\) | ||||
−0.886677 | + | 0.462388i | \(0.846993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.45931 | −0.412282 | −0.206141 | − | 0.978522i | \(-0.566091\pi\) | ||||
−0.206141 | + | 0.978522i | \(0.566091\pi\) | |||||||
\(422\) | 12.1187 | 0.589931 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 75.2954 | 3.65667 | ||||||||
\(425\) | −5.53465 | −0.268470 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.99896 | 0.483884 | ||||||||
\(428\) | 18.0132 | 0.870700 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.70288 | 0.323242 | ||||||||
\(431\) | 29.6930 | 1.43026 | 0.715130 | − | 0.698991i | \(-0.246367\pi\) | ||||
0.715130 | + | 0.698991i | \(0.246367\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.0121 | 1.39423 | 0.697116 | − | 0.716958i | \(-0.254466\pi\) | ||||
0.697116 | + | 0.716958i | \(0.254466\pi\) | |||||||
\(434\) | 25.1817 | 1.20876 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 43.6960 | 2.09266 | ||||||||
\(437\) | −16.7519 | −0.801350 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.1917 | −0.725058 | −0.362529 | − | 0.931972i | \(-0.618087\pi\) | ||||
−0.362529 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(440\) | 39.0628 | 1.86225 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.8066 | 1.17993 | ||||||||
\(443\) | −21.9474 | −1.04275 | −0.521377 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521377 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.1090 | 1.33249 | ||||||||
\(446\) | −66.3336 | −3.14099 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 24.7529 | 1.16947 | ||||||||
\(449\) | −10.5308 | −0.496979 | −0.248490 | − | 0.968635i | \(-0.579934\pi\) | ||||
−0.248490 | + | 0.968635i | \(0.579934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.04848 | 0.143547 | ||||||||
\(452\) | 71.8610 | 3.38006 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.39002 | −0.0652366 | ||||||||
\(455\) | −15.6521 | −0.733781 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.7062 | −1.24926 | −0.624632 | − | 0.780920i | \(-0.714751\pi\) | ||||
−0.624632 | + | 0.780920i | \(0.714751\pi\) | |||||||
\(458\) | 53.3580 | 2.49326 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −77.9260 | −3.63332 | ||||||||
\(461\) | −5.08320 | −0.236748 | −0.118374 | − | 0.992969i | \(-0.537768\pi\) | ||||
−0.118374 | + | 0.992969i | \(0.537768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.56483 | −0.119198 | −0.0595988 | − | 0.998222i | \(-0.518982\pi\) | ||||
−0.0595988 | + | 0.998222i | \(0.518982\pi\) | |||||||
\(464\) | 114.379 | 5.30990 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.68641 | −0.170770 | ||||||||
\(467\) | 38.3764 | 1.77585 | 0.887925 | − | 0.459989i | \(-0.152147\pi\) | ||||
0.887925 | + | 0.459989i | \(0.152147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.7116 | −0.725492 | ||||||||
\(470\) | 53.9805 | 2.48994 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 80.8279 | 3.72041 | ||||||||
\(473\) | 1.29035 | 0.0593302 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8538 | −0.498009 | ||||||||
\(476\) | −8.98949 | −0.412033 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 69.0409 | 3.15786 | ||||||||
\(479\) | 9.38202 | 0.428675 | 0.214338 | − | 0.976760i | \(-0.431241\pi\) | ||||
0.214338 | + | 0.976760i | \(0.431241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.2629 | −1.79023 | ||||||||
\(482\) | −64.9661 | −2.95912 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.6861 | −2.12209 | ||||||||
\(485\) | 26.1627 | 1.18799 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0828 | 1.36318 | 0.681591 | − | 0.731733i | \(-0.261288\pi\) | ||||
0.681591 | + | 0.731733i | \(0.261288\pi\) | |||||||
\(488\) | −90.3953 | −4.09200 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.79741 | 0.352251 | ||||||||
\(491\) | −39.3902 | −1.77765 | −0.888827 | − | 0.458244i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458244i | \(0.848479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.9455 | −0.628075 | ||||||||
\(494\) | 48.6476 | 2.18876 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −128.417 | −5.76609 | ||||||||
\(497\) | −5.53761 | −0.248396 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.4929 | 0.872624 | 0.436312 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436312 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(500\) | 26.3317 | 1.17759 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.4337 | 1.26906 | ||||||||
\(503\) | 25.0033 | 1.11484 | 0.557421 | − | 0.830230i | \(-0.311791\pi\) | ||||
0.557421 | + | 0.830230i | \(0.311791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48824 | −0.288723 | ||||||||
\(506\) | −20.6224 | −0.916776 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.33747 | −0.236812 | ||||||||
\(509\) | −0.817857 | −0.0362509 | −0.0181254 | − | 0.999836i | \(-0.505770\pi\) | ||||
−0.0181254 | + | 0.999836i | \(0.505770\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.56437 | 0.290391 | ||||||||
\(512\) | −17.3540 | −0.766947 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.7447 | 0.473928 | ||||||||
\(515\) | −49.2448 | −2.16999 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3916 | 0.457022 | ||||||||
\(518\) | 19.5596 | 0.859400 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 141.502 | 6.20529 | ||||||||
\(521\) | −23.7258 | −1.03945 | −0.519723 | − | 0.854335i | \(-0.673965\pi\) | ||||
−0.519723 | + | 0.854335i | \(0.673965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8646 | −0.562530 | −0.281265 | − | 0.959630i | \(-0.590754\pi\) | ||||
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(524\) | 2.64791 | 0.115674 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6188 | −0.593807 | ||||||||
\(527\) | 15.6571 | 0.682035 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.72405 | 0.118437 | ||||||||
\(530\) | −64.9423 | −2.82091 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.6290 | −0.764316 | ||||||||
\(533\) | 11.0429 | 0.478321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.71475 | −0.420005 | ||||||||
\(536\) | 142.040 | 6.13519 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45.4268 | 1.95849 | ||||||||
\(539\) | 1.50105 | 0.0646548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.7136 | −1.19150 | −0.595751 | − | 0.803170i | \(-0.703145\pi\) | ||||
−0.595751 | + | 0.803170i | \(0.703145\pi\) | |||||||
\(542\) | 67.3139 | 2.89138 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.5682 | 1.39635 | ||||||||
\(545\) | −23.5658 | −1.00945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.1078 | 1.75764 | 0.878821 | − | 0.477152i | \(-0.158331\pi\) | ||||
0.878821 | + | 0.477152i | \(0.158331\pi\) | |||||||
\(548\) | −110.921 | −4.73829 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.3616 | −0.569742 | ||||||||
\(551\) | −27.3482 | −1.16507 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.27964 | −0.394610 | ||||||||
\(554\) | 14.7684 | 0.627451 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.12191 | 0.0475795 | ||||||||
\(557\) | 1.86702 | 0.0791083 | 0.0395541 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395541 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.67419 | 0.197697 | ||||||||
\(560\) | −39.7637 | −1.68032 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.9992 | −1.13889 | ||||||||
\(563\) | 8.31194 | 0.350306 | 0.175153 | − | 0.984541i | \(-0.443958\pi\) | ||||
0.175153 | + | 0.984541i | \(0.443958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.7556 | −1.63046 | ||||||||
\(566\) | 17.2851 | 0.726548 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 50.0626 | 2.10058 | ||||||||
\(569\) | −36.1817 | −1.51681 | −0.758407 | − | 0.651781i | \(-0.774022\pi\) | ||||
−0.758407 | + | 0.651781i | \(0.774022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8415 | 0.537398 | 0.268699 | − | 0.963224i | \(-0.413406\pi\) | ||||
0.268699 | + | 0.963224i | \(0.413406\pi\) | |||||||
\(572\) | 43.5639 | 1.82150 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.50124 | −0.229617 | ||||||||
\(575\) | 16.6671 | 0.695066 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.22429 | −0.175860 | −0.0879298 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879298 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(578\) | 38.3655 | 1.59579 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −127.218 | −5.28244 | ||||||||
\(581\) | −7.17857 | −0.297817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5018 | −0.517772 | ||||||||
\(584\) | −59.3451 | −2.45572 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −70.6378 | −2.91802 | ||||||||
\(587\) | 11.3497 | 0.468454 | 0.234227 | − | 0.972182i | \(-0.424744\pi\) | ||||
0.234227 | + | 0.972182i | \(0.424744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.7047 | 1.26517 | ||||||||
\(590\) | −69.7141 | −2.87008 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −99.7462 | −4.09955 | ||||||||
\(593\) | 40.4494 | 1.66106 | 0.830528 | − | 0.556977i | \(-0.188039\pi\) | ||||
0.830528 | + | 0.556977i | \(0.188039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.84815 | 0.198755 | ||||||||
\(596\) | 51.3212 | 2.10220 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −74.7031 | −3.05484 | ||||||||
\(599\) | −25.7241 | −1.05106 | −0.525530 | − | 0.850775i | \(-0.676133\pi\) | ||||
−0.525530 | + | 0.850775i | \(0.676133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.07077 | −0.288423 | −0.144211 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144211 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(602\) | −2.32854 | −0.0949044 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.4818 | 0.955461 | ||||||||
\(605\) | 25.1784 | 1.02365 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7490 | −0.963940 | −0.481970 | − | 0.876188i | \(-0.660079\pi\) | ||||
−0.481970 | + | 0.876188i | \(0.660079\pi\) | |||||||
\(608\) | 63.8686 | 2.59021 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 77.9660 | 3.15675 | ||||||||
\(611\) | 37.6428 | 1.52287 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.8791 | −1.48953 | −0.744767 | − | 0.667325i | \(-0.767439\pi\) | ||||
−0.744767 | + | 0.667325i | \(0.767439\pi\) | |||||||
\(614\) | 16.3583 | 0.660167 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.5702 | −0.546759 | ||||||||
\(617\) | −42.2547 | −1.70111 | −0.850555 | − | 0.525886i | \(-0.823734\pi\) | ||||
−0.850555 | + | 0.525886i | \(0.823734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0800 | 1.28941 | 0.644703 | − | 0.764433i | \(-0.276981\pi\) | ||||
0.644703 | + | 0.764433i | \(0.276981\pi\) | |||||||
\(620\) | 142.832 | 5.73627 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −73.1971 | −2.93494 | ||||||||
\(623\) | −9.76491 | −0.391223 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6319 | −1.22528 | ||||||||
\(626\) | 65.6964 | 2.62576 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.81154 | −0.231906 | ||||||||
\(629\) | 12.1615 | 0.484910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8436 | −0.511294 | −0.255647 | − | 0.966770i | \(-0.582288\pi\) | ||||
−0.255647 | + | 0.966770i | \(0.582288\pi\) | |||||||
\(632\) | 83.8924 | 3.33706 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.9305 | 0.950401 | ||||||||
\(635\) | 2.87857 | 0.114233 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.43745 | 0.215440 | ||||||||
\(638\) | −33.6670 | −1.33289 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 81.6813 | 3.22874 | ||||||||
\(641\) | 20.1359 | 0.795322 | 0.397661 | − | 0.917532i | \(-0.369822\pi\) | ||||
0.397661 | + | 0.917532i | \(0.369822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9635 | 1.45770 | 0.728848 | − | 0.684675i | \(-0.240056\pi\) | ||||
0.728848 | + | 0.684675i | \(0.240056\pi\) | |||||||
\(644\) | 27.0711 | 1.06675 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.0684 | −0.592856 | ||||||||
\(647\) | −12.1948 | −0.479426 | −0.239713 | − | 0.970844i | \(-0.577053\pi\) | ||||
−0.239713 | + | 0.970844i | \(0.577053\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4204 | −0.526797 | ||||||||
\(650\) | −48.4015 | −1.89846 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −73.2740 | −2.86963 | ||||||||
\(653\) | 11.5419 | 0.451669 | 0.225834 | − | 0.974166i | \(-0.427489\pi\) | ||||
0.225834 | + | 0.974166i | \(0.427489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.42805 | −0.0557987 | ||||||||
\(656\) | 28.0541 | 1.09533 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.7525 | −0.731050 | ||||||||
\(659\) | −13.9433 | −0.543156 | −0.271578 | − | 0.962416i | \(-0.587545\pi\) | ||||
−0.271578 | + | 0.962416i | \(0.587545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7279 | −1.81751 | −0.908753 | − | 0.417335i | \(-0.862964\pi\) | ||||
−0.908753 | + | 0.417335i | \(0.862964\pi\) | |||||||
\(662\) | 46.0421 | 1.78948 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64.8976 | 2.51852 | ||||||||
\(665\) | 9.50758 | 0.368688 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.9957 | 1.62608 | ||||||||
\(668\) | −57.1486 | −2.21114 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −122.509 | −4.73295 | ||||||||
\(671\) | 15.0089 | 0.579414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.4878 | −1.79197 | −0.895986 | − | 0.444083i | \(-0.853530\pi\) | ||||
−0.895986 | + | 0.444083i | \(0.853530\pi\) | |||||||
\(674\) | −33.6865 | −1.29756 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 88.4199 | 3.40077 | ||||||||
\(677\) | 17.3432 | 0.666555 | 0.333278 | − | 0.942829i | \(-0.391845\pi\) | ||||
0.333278 | + | 0.942829i | \(0.391845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.08877 | −0.348795 | ||||||||
\(680\) | −43.8296 | −1.68079 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 37.7991 | 1.44740 | ||||||||
\(683\) | −16.4433 | −0.629185 | −0.314593 | − | 0.949227i | \(-0.601868\pi\) | ||||
−0.314593 | + | 0.949227i | \(0.601868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.8210 | 2.28564 | ||||||||
\(686\) | −2.70878 | −0.103422 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.8746 | 0.452717 | ||||||||
\(689\) | −45.2869 | −1.72529 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.28341 | −0.315116 | −0.157558 | − | 0.987510i | \(-0.550362\pi\) | ||||
−0.157558 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(692\) | 28.1872 | 1.07152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.7810 | 1.05455 | ||||||||
\(695\) | −0.605061 | −0.0229513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.42048 | −0.129560 | ||||||||
\(698\) | −75.9908 | −2.87630 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.5399 | 0.662945 | ||||||||
\(701\) | 24.0456 | 0.908190 | 0.454095 | − | 0.890953i | \(-0.349963\pi\) | ||||
0.454095 | + | 0.890953i | \(0.349963\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.8495 | 0.899503 | ||||||||
\(704\) | 37.1554 | 1.40035 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.326165 | −0.0122754 | ||||||||
\(707\) | 2.25398 | 0.0847696 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4417 | −0.617480 | −0.308740 | − | 0.951146i | \(-0.599907\pi\) | ||||
−0.308740 | + | 0.951146i | \(0.599907\pi\) | |||||||
\(710\) | −43.1790 | −1.62048 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 88.2794 | 3.30841 | ||||||||
\(713\) | −47.1500 | −1.76578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.4946 | −0.878648 | ||||||||
\(716\) | 16.2854 | 0.608612 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 42.0108 | 1.56783 | ||||||||
\(719\) | 12.7441 | 0.475276 | 0.237638 | − | 0.971354i | \(-0.423627\pi\) | ||||
0.237638 | + | 0.971354i | \(0.423627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1074 | 0.637112 | ||||||||
\(722\) | 21.9166 | 0.815653 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 105.876 | 3.93484 | ||||||||
\(725\) | 27.2098 | 1.01055 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.9453 | −1.92654 | −0.963272 | − | 0.268528i | \(-0.913463\pi\) | ||||
−0.963272 | + | 0.268528i | \(0.913463\pi\) | |||||||
\(728\) | −49.1571 | −1.82188 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 51.1851 | 1.89445 | ||||||||
\(731\) | −1.44781 | −0.0535491 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.2902 | 0.934115 | 0.467057 | − | 0.884227i | \(-0.345314\pi\) | ||||
0.467057 | + | 0.884227i | \(0.345314\pi\) | |||||||
\(734\) | −0.754722 | −0.0278573 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −98.0763 | −3.61514 | ||||||||
\(737\) | −23.5838 | −0.868722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4581 | −0.642207 | −0.321103 | − | 0.947044i | \(-0.604054\pi\) | ||||
−0.321103 | + | 0.947044i | \(0.604054\pi\) | |||||||
\(740\) | 110.943 | 4.07835 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.5606 | 0.828226 | ||||||||
\(743\) | −21.0345 | −0.771680 | −0.385840 | − | 0.922566i | \(-0.626088\pi\) | ||||
−0.385840 | + | 0.922566i | \(0.626088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.6782 | −1.01405 | ||||||||
\(746\) | −69.1283 | −2.53097 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.4937 | −0.493378 | ||||||||
\(749\) | 3.37485 | 0.123314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.0063 | 1.13144 | 0.565718 | − | 0.824599i | \(-0.308599\pi\) | ||||
0.565718 | + | 0.824599i | \(0.308599\pi\) | |||||||
\(752\) | 95.6305 | 3.48729 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −121.956 | −4.44139 | ||||||||
\(755\) | −12.6641 | −0.460892 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.88141 | −0.104727 | −0.0523633 | − | 0.998628i | \(-0.516675\pi\) | ||||
−0.0523633 | + | 0.998628i | \(0.516675\pi\) | |||||||
\(758\) | 27.5885 | 1.00206 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −85.9531 | −3.11785 | ||||||||
\(761\) | −52.1088 | −1.88894 | −0.944470 | − | 0.328597i | \(-0.893424\pi\) | ||||
−0.944470 | + | 0.328597i | \(0.893424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.18665 | 0.296377 | ||||||||
\(764\) | −143.460 | −5.19021 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −75.1941 | −2.71687 | ||||||||
\(767\) | −48.6144 | −1.75537 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2692 | 0.803048 | 0.401524 | − | 0.915849i | \(-0.368481\pi\) | ||||
0.401524 | + | 0.915849i | \(0.368481\pi\) | |||||||
\(770\) | 11.7043 | 0.421794 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 60.8582 | 2.19034 | ||||||||
\(773\) | −33.9532 | −1.22121 | −0.610605 | − | 0.791935i | \(-0.709074\pi\) | ||||
−0.610605 | + | 0.791935i | \(0.709074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.5494 | −1.09737 | ||||||||
\(776\) | 82.1668 | 2.94962 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 70.9652 | 2.54422 | ||||||||
\(779\) | −6.70781 | −0.240332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.31224 | −0.297435 | ||||||||
\(782\) | 23.1389 | 0.827445 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.8137 | 0.493346 | ||||||||
\(785\) | 3.13424 | 0.111866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0039 | 0.820002 | 0.410001 | − | 0.912085i | \(-0.365528\pi\) | ||||
0.410001 | + | 0.912085i | \(0.365528\pi\) | |||||||
\(788\) | 58.9857 | 2.10128 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −72.3572 | −2.57435 | ||||||||
\(791\) | 13.4635 | 0.478706 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.3689 | 1.93069 | ||||||||
\(794\) | −24.2129 | −0.859284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.3578 | 0.827895 | ||||||||
\(797\) | 3.18430 | 0.112794 | 0.0563968 | − | 0.998408i | \(-0.482039\pi\) | ||||
0.0563968 | + | 0.998408i | \(0.482039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6597 | −0.412490 | ||||||||
\(800\) | −63.5455 | −2.24667 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −95.5859 | −3.37526 | ||||||||
\(803\) | 9.85346 | 0.347721 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.5998 | −0.514575 | ||||||||
\(806\) | 136.924 | 4.82296 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.3770 | −0.716862 | ||||||||
\(809\) | −0.519198 | −0.0182540 | −0.00912701 | − | 0.999958i | \(-0.502905\pi\) | ||||
−0.00912701 | + | 0.999958i | \(0.502905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7425 | 0.623023 | 0.311511 | − | 0.950242i | \(-0.399165\pi\) | ||||
0.311511 | + | 0.950242i | \(0.399165\pi\) | |||||||
\(812\) | 44.1948 | 1.55093 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.3600 | 1.02907 | ||||||||
\(815\) | 39.5176 | 1.38424 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.83925 | −0.0993329 | ||||||||
\(818\) | 17.1718 | 0.600399 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −31.2033 | −1.08967 | ||||||||
\(821\) | −13.1810 | −0.460021 | −0.230011 | − | 0.973188i | \(-0.573876\pi\) | ||||
−0.230011 | + | 0.973188i | \(0.573876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.7749 | 0.584736 | 0.292368 | − | 0.956306i | \(-0.405557\pi\) | ||||
0.292368 | + | 0.956306i | \(0.405557\pi\) | |||||||
\(824\) | −154.659 | −5.38780 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.2183 | 0.842662 | ||||||||
\(827\) | −8.15970 | −0.283740 | −0.141870 | − | 0.989885i | \(-0.545312\pi\) | ||||
−0.141870 | + | 0.989885i | \(0.545312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.84768 | −0.168367 | −0.0841834 | − | 0.996450i | \(-0.526828\pi\) | ||||
−0.0841834 | + | 0.996450i | \(0.526828\pi\) | |||||||
\(830\) | −55.9742 | −1.94289 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 134.593 | 4.66616 | ||||||||
\(833\) | −1.68422 | −0.0583548 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.8210 | 1.06660 | ||||||||
\(836\) | −26.4621 | −0.915211 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 98.3277 | 3.39667 | ||||||||
\(839\) | −35.2043 | −1.21539 | −0.607693 | − | 0.794172i | \(-0.707905\pi\) | ||||
−0.607693 | + | 0.794172i | \(0.707905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.5600 | 1.36414 | ||||||||
\(842\) | 22.9144 | 0.789682 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.8792 | −0.821956 | ||||||||
\(845\) | −47.6861 | −1.64045 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.74685 | −0.300545 | ||||||||
\(848\) | −115.050 | −3.95083 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 14.9921 | 0.514226 | ||||||||
\(851\) | −36.6232 | −1.25543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.9868 | −1.06097 | −0.530484 | − | 0.847695i | \(-0.677990\pi\) | ||||
−0.530484 | + | 0.847695i | \(0.677990\pi\) | |||||||
\(854\) | −27.0850 | −0.926828 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.5102 | −1.04282 | ||||||||
\(857\) | −30.4958 | −1.04172 | −0.520858 | − | 0.853643i | \(-0.674388\pi\) | ||||
−0.520858 | + | 0.853643i | \(0.674388\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.8062 | −0.846376 | −0.423188 | − | 0.906042i | \(-0.639089\pi\) | ||||
−0.423188 | + | 0.906042i | \(0.639089\pi\) | |||||||
\(860\) | −13.2076 | −0.450376 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −80.4317 | −2.73951 | ||||||||
\(863\) | −45.5391 | −1.55017 | −0.775084 | − | 0.631858i | \(-0.782293\pi\) | ||||
−0.775084 | + | 0.631858i | \(0.782293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2017 | −0.516875 | ||||||||
\(866\) | −78.5873 | −2.67050 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −49.6190 | −1.68418 | ||||||||
\(869\) | −13.9292 | −0.472516 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −85.4308 | −2.89471 | ||||||||
\(872\) | −74.0112 | −2.50633 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 45.3770 | 1.53490 | ||||||||
\(875\) | 4.93337 | 0.166778 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0252 | 1.28402 | 0.642010 | − | 0.766697i | \(-0.278101\pi\) | ||||
0.642010 | + | 0.766697i | \(0.278101\pi\) | |||||||
\(878\) | 41.1508 | 1.38877 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −59.6873 | −2.01206 | ||||||||
\(881\) | 18.1199 | 0.610476 | 0.305238 | − | 0.952276i | \(-0.401264\pi\) | ||||
0.305238 | + | 0.952276i | \(0.401264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.1982 | −1.35278 | −0.676388 | − | 0.736546i | \(-0.736456\pi\) | ||||
−0.676388 | + | 0.736546i | \(0.736456\pi\) | |||||||
\(884\) | −48.8799 | −1.64401 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.4507 | 1.99728 | ||||||||
\(887\) | −43.6325 | −1.46504 | −0.732518 | − | 0.680748i | \(-0.761655\pi\) | ||||
−0.732518 | + | 0.680748i | \(0.761655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −76.1410 | −2.55225 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 130.706 | 4.37637 | ||||||||
\(893\) | −22.8655 | −0.765164 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.78291 | −0.293580 | ||||||||
\(896\) | −28.3756 | −0.947964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.5256 | 0.951911 | ||||||||
\(899\) | −76.9747 | −2.56725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.0274 | 0.467320 | ||||||||
\(902\) | −8.25764 | −0.274949 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −121.716 | −4.04822 | ||||||||
\(905\) | −57.1001 | −1.89807 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8276 | −0.492341 | −0.246170 | − | 0.969227i | \(-0.579172\pi\) | ||||
−0.246170 | + | 0.969227i | \(0.579172\pi\) | |||||||
\(908\) | 2.73894 | 0.0908948 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 42.3980 | 1.40548 | ||||||||
\(911\) | −48.2909 | −1.59995 | −0.799975 | − | 0.600034i | \(-0.795154\pi\) | ||||
−0.799975 | + | 0.600034i | \(0.795154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.7754 | −0.356613 | ||||||||
\(914\) | 72.3411 | 2.39283 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −105.139 | −3.47388 | ||||||||
\(917\) | 0.496098 | 0.0163826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.0061 | −1.51760 | −0.758801 | − | 0.651322i | \(-0.774215\pi\) | ||||
−0.758801 | + | 0.651322i | \(0.774215\pi\) | |||||||
\(920\) | 131.989 | 4.35155 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.7693 | 0.453466 | ||||||||
\(923\) | −30.1105 | −0.991099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.7289 | −0.780201 | ||||||||
\(926\) | 6.94754 | 0.228310 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −160.114 | −5.25601 | ||||||||
\(929\) | −15.8115 | −0.518759 | −0.259379 | − | 0.965776i | \(-0.583518\pi\) | ||||
−0.259379 | + | 0.965776i | \(0.583518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.30288 | −0.108248 | ||||||||
\(932\) | 7.26384 | 0.237935 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −103.953 | −3.40145 | ||||||||
\(935\) | 7.27732 | 0.237994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.8913 | 0.747825 | 0.373913 | − | 0.927464i | \(-0.378016\pi\) | ||||
0.373913 | + | 0.927464i | \(0.378016\pi\) | |||||||
\(938\) | 42.5591 | 1.38960 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −106.365 | −3.46925 | ||||||||
\(941\) | −58.6620 | −1.91233 | −0.956163 | − | 0.292836i | \(-0.905401\pi\) | ||||
−0.956163 | + | 0.292836i | \(0.905401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3005 | 0.335430 | ||||||||
\(944\) | −123.504 | −4.01970 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.49526 | −0.113641 | ||||||||
\(947\) | 35.5721 | 1.15594 | 0.577969 | − | 0.816058i | \(-0.303845\pi\) | ||||
0.577969 | + | 0.816058i | \(0.303845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.6935 | 1.15866 | ||||||||
\(950\) | 29.4007 | 0.953883 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.2262 | 0.493483 | ||||||||
\(953\) | 56.3625 | 1.82576 | 0.912880 | − | 0.408229i | \(-0.133853\pi\) | ||||
0.912880 | + | 0.408229i | \(0.133853\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.3701 | 2.50364 | ||||||||
\(956\) | −136.041 | −4.39987 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.4138 | −0.821082 | ||||||||
\(959\) | −20.7815 | −0.671069 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.4221 | 1.78781 | ||||||||
\(962\) | 106.354 | 3.42901 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 128.012 | 4.12297 | ||||||||
\(965\) | −32.8217 | −1.05657 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.3294 | −1.03964 | −0.519822 | − | 0.854275i | \(-0.674002\pi\) | ||||
−0.519822 | + | 0.854275i | \(0.674002\pi\) | |||||||
\(968\) | 79.0756 | 2.54159 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −70.8688 | −2.27546 | ||||||||
\(971\) | −18.2980 | −0.587210 | −0.293605 | − | 0.955927i | \(-0.594855\pi\) | ||||
−0.293605 | + | 0.955927i | \(0.594855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.210195 | 0.00673853 | ||||||||
\(974\) | −81.4876 | −2.61103 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 138.122 | 4.42119 | ||||||||
\(977\) | −35.5195 | −1.13637 | −0.568185 | − | 0.822901i | \(-0.692354\pi\) | ||||
−0.568185 | + | 0.822901i | \(0.692354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6576 | −0.468460 | ||||||||
\(980\) | −15.3643 | −0.490795 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 106.699 | 3.40491 | ||||||||
\(983\) | −19.4569 | −0.620578 | −0.310289 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310289 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.8118 | −1.01361 | ||||||||
\(986\) | 37.7753 | 1.20301 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −95.8571 | −3.04962 | ||||||||
\(989\) | 4.35994 | 0.138638 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.5095 | 1.25506 | 0.627531 | − | 0.778592i | \(-0.284066\pi\) | ||||
0.627531 | + | 0.778592i | \(0.284066\pi\) | |||||||
\(992\) | 179.766 | 5.70757 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.0002 | 0.475776 | ||||||||
\(995\) | −12.5972 | −0.399357 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.2009 | −1.52654 | −0.763269 | − | 0.646080i | \(-0.776407\pi\) | ||||
−0.763269 | + | 0.646080i | \(0.776407\pi\) | |||||||
\(998\) | −52.8020 | −1.67142 | ||||||||
\(999\) | 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.o.1.1 | 13 | ||
3.2 | odd | 2 | 2667.2.a.l.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.l.1.13 | ✓ | 13 | 3.2 | odd | 2 | ||
8001.2.a.o.1.1 | 13 | 1.1 | even | 1 | trivial |