Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [343,2,Mod(1,343)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(343, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("343.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 343 = 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 343.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: | \(2.73886878933\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1279733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.0849355\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 343.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33192 | −1.64891 | −0.824456 | − | 0.565925i | \(-0.808519\pi\) | ||||
−0.824456 | + | 0.565925i | \(0.808519\pi\) | |||||||
\(3\) | 2.95499 | 1.70606 | 0.853031 | − | 0.521860i | \(-0.174762\pi\) | ||||
0.853031 | + | 0.521860i | \(0.174762\pi\) | |||||||
\(4\) | 3.43783 | 1.71891 | ||||||||
\(5\) | 1.95286 | 0.873348 | 0.436674 | − | 0.899620i | \(-0.356156\pi\) | ||||
0.436674 | + | 0.899620i | \(0.356156\pi\) | |||||||
\(6\) | −6.89078 | −2.81315 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.35289 | −1.18543 | ||||||||
\(9\) | 5.73194 | 1.91065 | ||||||||
\(10\) | −4.55391 | −1.44007 | ||||||||
\(11\) | 2.65101 | 0.799310 | 0.399655 | − | 0.916666i | \(-0.369130\pi\) | ||||
0.399655 | + | 0.916666i | \(0.369130\pi\) | |||||||
\(12\) | 10.1587 | 2.93257 | ||||||||
\(13\) | −1.50061 | −0.416194 | −0.208097 | − | 0.978108i | \(-0.566727\pi\) | ||||
−0.208097 | + | 0.978108i | \(0.566727\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.77069 | 1.48999 | ||||||||
\(16\) | 0.943005 | 0.235751 | ||||||||
\(17\) | 2.09215 | 0.507421 | 0.253710 | − | 0.967280i | \(-0.418349\pi\) | ||||
0.253710 | + | 0.967280i | \(0.418349\pi\) | |||||||
\(18\) | −13.3664 | −3.15049 | ||||||||
\(19\) | −6.38881 | −1.46569 | −0.732847 | − | 0.680394i | \(-0.761809\pi\) | ||||
−0.732847 | + | 0.680394i | \(0.761809\pi\) | |||||||
\(20\) | 6.71361 | 1.50121 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.18193 | −1.31799 | ||||||||
\(23\) | −2.12424 | −0.442936 | −0.221468 | − | 0.975168i | \(-0.571085\pi\) | ||||
−0.221468 | + | 0.975168i | \(0.571085\pi\) | |||||||
\(24\) | −9.90775 | −2.02241 | ||||||||
\(25\) | −1.18632 | −0.237264 | ||||||||
\(26\) | 3.49929 | 0.686268 | ||||||||
\(27\) | 8.07285 | 1.55362 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.42740 | −1.37923 | −0.689617 | − | 0.724174i | \(-0.742221\pi\) | ||||
−0.689617 | + | 0.724174i | \(0.742221\pi\) | |||||||
\(30\) | −13.4568 | −2.45686 | ||||||||
\(31\) | −0.0654672 | −0.0117582 | −0.00587912 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587912 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(32\) | 4.50678 | 0.796693 | ||||||||
\(33\) | 7.83370 | 1.36367 | ||||||||
\(34\) | −4.87871 | −0.836693 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.7054 | 3.28424 | ||||||||
\(37\) | 0.537796 | 0.0884130 | 0.0442065 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442065 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(38\) | 14.8982 | 2.41680 | ||||||||
\(39\) | −4.43428 | −0.710053 | ||||||||
\(40\) | −6.54774 | −1.03529 | ||||||||
\(41\) | 11.8724 | 1.85416 | 0.927082 | − | 0.374858i | \(-0.122309\pi\) | ||||
0.927082 | + | 0.374858i | \(0.122309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.588754 | −0.0897842 | −0.0448921 | − | 0.998992i | \(-0.514294\pi\) | ||||
−0.0448921 | + | 0.998992i | \(0.514294\pi\) | |||||||
\(44\) | 9.11372 | 1.37394 | ||||||||
\(45\) | 11.1937 | 1.66866 | ||||||||
\(46\) | 4.95356 | 0.730362 | ||||||||
\(47\) | 3.02880 | 0.441796 | 0.220898 | − | 0.975297i | \(-0.429101\pi\) | ||||
0.220898 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(48\) | 2.78657 | 0.402206 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.76640 | 0.391228 | ||||||||
\(51\) | 6.18227 | 0.865691 | ||||||||
\(52\) | −5.15883 | −0.715402 | ||||||||
\(53\) | 1.04162 | 0.143078 | 0.0715390 | − | 0.997438i | \(-0.477209\pi\) | ||||
0.0715390 | + | 0.997438i | \(0.477209\pi\) | |||||||
\(54\) | −18.8252 | −2.56179 | ||||||||
\(55\) | 5.17707 | 0.698075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.8788 | −2.50056 | ||||||||
\(58\) | 17.3201 | 2.27424 | ||||||||
\(59\) | −2.27140 | −0.295711 | −0.147855 | − | 0.989009i | \(-0.547237\pi\) | ||||
−0.147855 | + | 0.989009i | \(0.547237\pi\) | |||||||
\(60\) | 19.8386 | 2.56116 | ||||||||
\(61\) | −10.2767 | −1.31580 | −0.657898 | − | 0.753107i | \(-0.728554\pi\) | ||||
−0.657898 | + | 0.753107i | \(0.728554\pi\) | |||||||
\(62\) | 0.152664 | 0.0193883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.3954 | −1.54943 | ||||||||
\(65\) | −2.93048 | −0.363482 | ||||||||
\(66\) | −18.2675 | −2.24858 | ||||||||
\(67\) | −0.221714 | −0.0270867 | −0.0135434 | − | 0.999908i | \(-0.504311\pi\) | ||||
−0.0135434 | + | 0.999908i | \(0.504311\pi\) | |||||||
\(68\) | 7.19245 | 0.872213 | ||||||||
\(69\) | −6.27711 | −0.755676 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7708 | 1.27826 | 0.639131 | − | 0.769098i | \(-0.279294\pi\) | ||||
0.639131 | + | 0.769098i | \(0.279294\pi\) | |||||||
\(72\) | −19.2186 | −2.26493 | ||||||||
\(73\) | 10.2207 | 1.19624 | 0.598122 | − | 0.801405i | \(-0.295914\pi\) | ||||
0.598122 | + | 0.801405i | \(0.295914\pi\) | |||||||
\(74\) | −1.25409 | −0.145785 | ||||||||
\(75\) | −3.50556 | −0.404787 | ||||||||
\(76\) | −21.9636 | −2.51940 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.3404 | 1.17081 | ||||||||
\(79\) | −13.2859 | −1.49478 | −0.747392 | − | 0.664383i | \(-0.768694\pi\) | ||||
−0.747392 | + | 0.664383i | \(0.768694\pi\) | |||||||
\(80\) | 1.84156 | 0.205893 | ||||||||
\(81\) | 6.65934 | 0.739927 | ||||||||
\(82\) | −27.6855 | −3.05736 | ||||||||
\(83\) | −11.8543 | −1.30118 | −0.650592 | − | 0.759428i | \(-0.725479\pi\) | ||||
−0.650592 | + | 0.759428i | \(0.725479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.08568 | 0.443155 | ||||||||
\(86\) | 1.37293 | 0.148046 | ||||||||
\(87\) | −21.9479 | −2.35306 | ||||||||
\(88\) | −8.88855 | −0.947523 | ||||||||
\(89\) | 3.51020 | 0.372080 | 0.186040 | − | 0.982542i | \(-0.440435\pi\) | ||||
0.186040 | + | 0.982542i | \(0.440435\pi\) | |||||||
\(90\) | −26.1028 | −2.75147 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.30279 | −0.761368 | ||||||||
\(93\) | −0.193455 | −0.0200603 | ||||||||
\(94\) | −7.06291 | −0.728484 | ||||||||
\(95\) | −12.4765 | −1.28006 | ||||||||
\(96\) | 13.3175 | 1.35921 | ||||||||
\(97\) | 14.6497 | 1.48746 | 0.743728 | − | 0.668483i | \(-0.233056\pi\) | ||||
0.743728 | + | 0.668483i | \(0.233056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.1954 | 1.52720 | ||||||||
\(100\) | −4.07837 | −0.407837 | ||||||||
\(101\) | 0.324269 | 0.0322659 | 0.0161330 | − | 0.999870i | \(-0.494864\pi\) | ||||
0.0161330 | + | 0.999870i | \(0.494864\pi\) | |||||||
\(102\) | −14.4165 | −1.42745 | ||||||||
\(103\) | 10.1971 | 1.00475 | 0.502377 | − | 0.864648i | \(-0.332459\pi\) | ||||
0.502377 | + | 0.864648i | \(0.332459\pi\) | |||||||
\(104\) | 5.03138 | 0.493367 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.42898 | −0.235923 | ||||||||
\(107\) | −15.3684 | −1.48572 | −0.742861 | − | 0.669446i | \(-0.766532\pi\) | ||||
−0.742861 | + | 0.669446i | \(0.766532\pi\) | |||||||
\(108\) | 27.7531 | 2.67054 | ||||||||
\(109\) | −14.2387 | −1.36382 | −0.681911 | − | 0.731435i | \(-0.738851\pi\) | ||||
−0.681911 | + | 0.731435i | \(0.738851\pi\) | |||||||
\(110\) | −12.0725 | −1.15107 | ||||||||
\(111\) | 1.58918 | 0.150838 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.22812 | −0.774037 | −0.387018 | − | 0.922072i | \(-0.626495\pi\) | ||||
−0.387018 | + | 0.922072i | \(0.626495\pi\) | |||||||
\(114\) | 44.0239 | 4.12321 | ||||||||
\(115\) | −4.14836 | −0.386837 | ||||||||
\(116\) | −25.5341 | −2.37078 | ||||||||
\(117\) | −8.60140 | −0.795200 | ||||||||
\(118\) | 5.29670 | 0.487601 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −19.3485 | −1.76627 | ||||||||
\(121\) | −3.97214 | −0.361104 | ||||||||
\(122\) | 23.9644 | 2.16963 | ||||||||
\(123\) | 35.0829 | 3.16332 | ||||||||
\(124\) | −0.225065 | −0.0202114 | ||||||||
\(125\) | −12.0810 | −1.08056 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.7450 | 1.39714 | 0.698572 | − | 0.715540i | \(-0.253819\pi\) | ||||
0.698572 | + | 0.715540i | \(0.253819\pi\) | |||||||
\(128\) | 19.8915 | 1.75818 | ||||||||
\(129\) | −1.73976 | −0.153177 | ||||||||
\(130\) | 6.83364 | 0.599350 | ||||||||
\(131\) | 8.25951 | 0.721636 | 0.360818 | − | 0.932636i | \(-0.382497\pi\) | ||||
0.360818 | + | 0.932636i | \(0.382497\pi\) | |||||||
\(132\) | 26.9309 | 2.34404 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.517019 | 0.0446636 | ||||||||
\(135\) | 15.7652 | 1.35685 | ||||||||
\(136\) | −7.01475 | −0.601510 | ||||||||
\(137\) | 0.0780530 | 0.00666851 | 0.00333426 | − | 0.999994i | \(-0.498939\pi\) | ||||
0.00333426 | + | 0.999994i | \(0.498939\pi\) | |||||||
\(138\) | 14.6377 | 1.24604 | ||||||||
\(139\) | 15.6375 | 1.32635 | 0.663177 | − | 0.748463i | \(-0.269208\pi\) | ||||
0.663177 | + | 0.748463i | \(0.269208\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.95007 | 0.753732 | ||||||||
\(142\) | −25.1166 | −2.10774 | ||||||||
\(143\) | −3.97813 | −0.332668 | ||||||||
\(144\) | 5.40525 | 0.450437 | ||||||||
\(145\) | −14.5047 | −1.20455 | ||||||||
\(146\) | −23.8339 | −1.97250 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.84885 | 0.151974 | ||||||||
\(149\) | −6.26566 | −0.513303 | −0.256652 | − | 0.966504i | \(-0.582619\pi\) | ||||
−0.256652 | + | 0.966504i | \(0.582619\pi\) | |||||||
\(150\) | 8.17467 | 0.667459 | ||||||||
\(151\) | −16.3222 | −1.32828 | −0.664142 | − | 0.747606i | \(-0.731203\pi\) | ||||
−0.664142 | + | 0.747606i | \(0.731203\pi\) | |||||||
\(152\) | 21.4210 | 1.73747 | ||||||||
\(153\) | 11.9921 | 0.969502 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.127848 | −0.0102690 | ||||||||
\(156\) | −15.2443 | −1.22052 | ||||||||
\(157\) | −13.3664 | −1.06675 | −0.533376 | − | 0.845878i | \(-0.679077\pi\) | ||||
−0.533376 | + | 0.845878i | \(0.679077\pi\) | |||||||
\(158\) | 30.9817 | 2.46477 | ||||||||
\(159\) | 3.07798 | 0.244100 | ||||||||
\(160\) | 8.80113 | 0.695790 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −15.5290 | −1.22008 | ||||||||
\(163\) | −11.1164 | −0.870700 | −0.435350 | − | 0.900261i | \(-0.643375\pi\) | ||||
−0.435350 | + | 0.900261i | \(0.643375\pi\) | |||||||
\(164\) | 40.8154 | 3.18715 | ||||||||
\(165\) | 15.2982 | 1.19096 | ||||||||
\(166\) | 27.6433 | 2.14554 | ||||||||
\(167\) | −8.91212 | −0.689640 | −0.344820 | − | 0.938669i | \(-0.612060\pi\) | ||||
−0.344820 | + | 0.938669i | \(0.612060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7482 | −0.826783 | ||||||||
\(170\) | −9.52747 | −0.730723 | ||||||||
\(171\) | −36.6203 | −2.80042 | ||||||||
\(172\) | −2.02404 | −0.154331 | ||||||||
\(173\) | 3.24509 | 0.246720 | 0.123360 | − | 0.992362i | \(-0.460633\pi\) | ||||
0.123360 | + | 0.992362i | \(0.460633\pi\) | |||||||
\(174\) | 51.1806 | 3.87999 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.49992 | 0.188438 | ||||||||
\(177\) | −6.71194 | −0.504501 | ||||||||
\(178\) | −8.18548 | −0.613528 | ||||||||
\(179\) | −4.04711 | −0.302495 | −0.151248 | − | 0.988496i | \(-0.548329\pi\) | ||||
−0.151248 | + | 0.988496i | \(0.548329\pi\) | |||||||
\(180\) | 38.4820 | 2.86828 | ||||||||
\(181\) | 8.66577 | 0.644121 | 0.322061 | − | 0.946719i | \(-0.395624\pi\) | ||||
0.322061 | + | 0.946719i | \(0.395624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.3675 | −2.24483 | ||||||||
\(184\) | 7.12236 | 0.525068 | ||||||||
\(185\) | 1.05024 | 0.0772153 | ||||||||
\(186\) | 0.451120 | 0.0330777 | ||||||||
\(187\) | 5.54631 | 0.405586 | ||||||||
\(188\) | 10.4125 | 0.759410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 29.0941 | 2.11071 | ||||||||
\(191\) | 15.2165 | 1.10102 | 0.550512 | − | 0.834827i | \(-0.314433\pi\) | ||||
0.550512 | + | 0.834827i | \(0.314433\pi\) | |||||||
\(192\) | −36.6283 | −2.64342 | ||||||||
\(193\) | 10.2716 | 0.739364 | 0.369682 | − | 0.929158i | \(-0.379467\pi\) | ||||
0.369682 | + | 0.929158i | \(0.379467\pi\) | |||||||
\(194\) | −34.1619 | −2.45268 | ||||||||
\(195\) | −8.65954 | −0.620123 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.72522 | 0.550399 | 0.275200 | − | 0.961387i | \(-0.411256\pi\) | ||||
0.275200 | + | 0.961387i | \(0.411256\pi\) | |||||||
\(198\) | −35.4345 | −2.51822 | ||||||||
\(199\) | −14.7692 | −1.04696 | −0.523482 | − | 0.852037i | \(-0.675367\pi\) | ||||
−0.523482 | + | 0.852037i | \(0.675367\pi\) | |||||||
\(200\) | 3.97761 | 0.281259 | ||||||||
\(201\) | −0.655163 | −0.0462116 | ||||||||
\(202\) | −0.756167 | −0.0532037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 21.2536 | 1.48805 | ||||||||
\(205\) | 23.1853 | 1.61933 | ||||||||
\(206\) | −23.7789 | −1.65675 | ||||||||
\(207\) | −12.1760 | −0.846294 | ||||||||
\(208\) | −1.41508 | −0.0981182 | ||||||||
\(209\) | −16.9368 | −1.17154 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.88834 | −0.336527 | −0.168264 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168264 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(212\) | 3.58092 | 0.245939 | ||||||||
\(213\) | 31.8276 | 2.18079 | ||||||||
\(214\) | 35.8379 | 2.44983 | ||||||||
\(215\) | −1.14976 | −0.0784128 | ||||||||
\(216\) | −27.0674 | −1.84170 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 33.2035 | 2.24883 | ||||||||
\(219\) | 30.2021 | 2.04087 | ||||||||
\(220\) | 17.7979 | 1.19993 | ||||||||
\(221\) | −3.13950 | −0.211185 | ||||||||
\(222\) | −3.70583 | −0.248719 | ||||||||
\(223\) | 1.74696 | 0.116985 | 0.0584925 | − | 0.998288i | \(-0.481371\pi\) | ||||
0.0584925 | + | 0.998288i | \(0.481371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.79992 | −0.453328 | ||||||||
\(226\) | 19.1873 | 1.27632 | ||||||||
\(227\) | 23.6939 | 1.57262 | 0.786311 | − | 0.617831i | \(-0.211988\pi\) | ||||
0.786311 | + | 0.617831i | \(0.211988\pi\) | |||||||
\(228\) | −64.9022 | −4.29825 | ||||||||
\(229\) | 13.1910 | 0.871685 | 0.435843 | − | 0.900023i | \(-0.356450\pi\) | ||||
0.435843 | + | 0.900023i | \(0.356450\pi\) | |||||||
\(230\) | 9.67363 | 0.637860 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.9033 | 1.63498 | ||||||||
\(233\) | 21.2901 | 1.39476 | 0.697379 | − | 0.716703i | \(-0.254349\pi\) | ||||
0.697379 | + | 0.716703i | \(0.254349\pi\) | |||||||
\(234\) | 20.0577 | 1.31122 | ||||||||
\(235\) | 5.91484 | 0.385842 | ||||||||
\(236\) | −7.80867 | −0.508301 | ||||||||
\(237\) | −39.2598 | −2.55020 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2612 | −0.728429 | −0.364215 | − | 0.931315i | \(-0.618663\pi\) | ||||
−0.364215 | + | 0.931315i | \(0.618663\pi\) | |||||||
\(240\) | 5.44178 | 0.351266 | ||||||||
\(241\) | 9.26049 | 0.596521 | 0.298260 | − | 0.954485i | \(-0.403594\pi\) | ||||
0.298260 | + | 0.954485i | \(0.403594\pi\) | |||||||
\(242\) | 9.26269 | 0.595428 | ||||||||
\(243\) | −4.54030 | −0.291260 | ||||||||
\(244\) | −35.3295 | −2.26174 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −81.8104 | −5.21604 | ||||||||
\(247\) | 9.58710 | 0.610013 | ||||||||
\(248\) | 0.219504 | 0.0139385 | ||||||||
\(249\) | −35.0294 | −2.21990 | ||||||||
\(250\) | 28.1720 | 1.78175 | ||||||||
\(251\) | −19.8599 | −1.25355 | −0.626773 | − | 0.779202i | \(-0.715625\pi\) | ||||
−0.626773 | + | 0.779202i | \(0.715625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.63140 | −0.354043 | ||||||||
\(254\) | −36.7160 | −2.30377 | ||||||||
\(255\) | 12.0731 | 0.756049 | ||||||||
\(256\) | −21.5945 | −1.34966 | ||||||||
\(257\) | 25.1574 | 1.56927 | 0.784637 | − | 0.619955i | \(-0.212849\pi\) | ||||
0.784637 | + | 0.619955i | \(0.212849\pi\) | |||||||
\(258\) | 4.05698 | 0.252576 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −10.0745 | −0.624794 | ||||||||
\(261\) | −42.5735 | −2.63523 | ||||||||
\(262\) | −19.2605 | −1.18992 | ||||||||
\(263\) | −10.3286 | −0.636887 | −0.318444 | − | 0.947942i | \(-0.603160\pi\) | ||||
−0.318444 | + | 0.947942i | \(0.603160\pi\) | |||||||
\(264\) | −26.2656 | −1.61653 | ||||||||
\(265\) | 2.03415 | 0.124957 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3726 | 0.634792 | ||||||||
\(268\) | −0.762215 | −0.0465597 | ||||||||
\(269\) | −0.448329 | −0.0273351 | −0.0136676 | − | 0.999907i | \(-0.504351\pi\) | ||||
−0.0136676 | + | 0.999907i | \(0.504351\pi\) | |||||||
\(270\) | −36.7631 | −2.23733 | ||||||||
\(271\) | −23.9630 | −1.45565 | −0.727825 | − | 0.685763i | \(-0.759469\pi\) | ||||
−0.727825 | + | 0.685763i | \(0.759469\pi\) | |||||||
\(272\) | 1.97291 | 0.119625 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.182013 | −0.0109958 | ||||||||
\(275\) | −3.14495 | −0.189648 | ||||||||
\(276\) | −21.5796 | −1.29894 | ||||||||
\(277\) | 15.1757 | 0.911822 | 0.455911 | − | 0.890025i | \(-0.349314\pi\) | ||||
0.455911 | + | 0.890025i | \(0.349314\pi\) | |||||||
\(278\) | −36.4653 | −2.18704 | ||||||||
\(279\) | −0.375254 | −0.0224659 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0320 | 0.598460 | 0.299230 | − | 0.954181i | \(-0.403270\pi\) | ||||
0.299230 | + | 0.954181i | \(0.403270\pi\) | |||||||
\(282\) | −20.8708 | −1.24284 | ||||||||
\(283\) | −2.10305 | −0.125014 | −0.0625068 | − | 0.998045i | \(-0.519910\pi\) | ||||
−0.0625068 | + | 0.998045i | \(0.519910\pi\) | |||||||
\(284\) | 37.0282 | 2.19722 | ||||||||
\(285\) | −36.8678 | −2.18386 | ||||||||
\(286\) | 9.27666 | 0.548540 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 25.8326 | 1.52220 | ||||||||
\(289\) | −12.6229 | −0.742524 | ||||||||
\(290\) | 33.8238 | 1.98620 | ||||||||
\(291\) | 43.2898 | 2.53769 | ||||||||
\(292\) | 35.1371 | 2.05624 | ||||||||
\(293\) | 18.6487 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.43573 | −0.258258 | ||||||||
\(296\) | −1.80317 | −0.104807 | ||||||||
\(297\) | 21.4012 | 1.24183 | ||||||||
\(298\) | 14.6110 | 0.846392 | ||||||||
\(299\) | 3.18766 | 0.184347 | ||||||||
\(300\) | −12.0515 | −0.695795 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 38.0620 | 2.19022 | ||||||||
\(303\) | 0.958209 | 0.0550477 | ||||||||
\(304\) | −6.02468 | −0.345539 | ||||||||
\(305\) | −20.0690 | −1.14915 | ||||||||
\(306\) | −27.9645 | −1.59862 | ||||||||
\(307\) | 9.72652 | 0.555122 | 0.277561 | − | 0.960708i | \(-0.410474\pi\) | ||||
0.277561 | + | 0.960708i | \(0.410474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.1324 | 1.71417 | ||||||||
\(310\) | 0.298132 | 0.0169327 | ||||||||
\(311\) | −27.8427 | −1.57881 | −0.789406 | − | 0.613871i | \(-0.789611\pi\) | ||||
−0.789406 | + | 0.613871i | \(0.789611\pi\) | |||||||
\(312\) | 14.8677 | 0.841715 | ||||||||
\(313\) | 20.2150 | 1.14262 | 0.571311 | − | 0.820734i | \(-0.306435\pi\) | ||||
0.571311 | + | 0.820734i | \(0.306435\pi\) | |||||||
\(314\) | 31.1692 | 1.75898 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −45.6748 | −2.56941 | ||||||||
\(317\) | 11.8535 | 0.665760 | 0.332880 | − | 0.942969i | \(-0.391980\pi\) | ||||
0.332880 | + | 0.942969i | \(0.391980\pi\) | |||||||
\(318\) | −7.17759 | −0.402499 | ||||||||
\(319\) | −19.6901 | −1.10244 | ||||||||
\(320\) | −24.2066 | −1.35319 | ||||||||
\(321\) | −45.4135 | −2.53473 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.3663 | −0.743723 | ||||||||
\(324\) | 22.8937 | 1.27187 | ||||||||
\(325\) | 1.78020 | 0.0987479 | ||||||||
\(326\) | 25.9224 | 1.43571 | ||||||||
\(327\) | −42.0752 | −2.32677 | ||||||||
\(328\) | −39.8070 | −2.19798 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −35.6740 | −1.96379 | ||||||||
\(331\) | 12.6856 | 0.697261 | 0.348631 | − | 0.937260i | \(-0.386647\pi\) | ||||
0.348631 | + | 0.937260i | \(0.386647\pi\) | |||||||
\(332\) | −40.7532 | −2.23662 | ||||||||
\(333\) | 3.08261 | 0.168926 | ||||||||
\(334\) | 20.7823 | 1.13716 | ||||||||
\(335\) | −0.432978 | −0.0236561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.8310 | 1.57053 | 0.785264 | − | 0.619162i | \(-0.212527\pi\) | ||||
0.785264 | + | 0.619162i | \(0.212527\pi\) | |||||||
\(338\) | 25.0638 | 1.36329 | ||||||||
\(339\) | −24.3140 | −1.32055 | ||||||||
\(340\) | 14.0459 | 0.761745 | ||||||||
\(341\) | −0.173554 | −0.00939848 | ||||||||
\(342\) | 85.3954 | 4.61766 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.97403 | 0.106433 | ||||||||
\(345\) | −12.2583 | −0.659967 | ||||||||
\(346\) | −7.56728 | −0.406819 | ||||||||
\(347\) | 15.5749 | 0.836103 | 0.418052 | − | 0.908423i | \(-0.362713\pi\) | ||||
0.418052 | + | 0.908423i | \(0.362713\pi\) | |||||||
\(348\) | −75.4530 | −4.04471 | ||||||||
\(349\) | 9.08484 | 0.486300 | 0.243150 | − | 0.969989i | \(-0.421819\pi\) | ||||
0.243150 | + | 0.969989i | \(0.421819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.1142 | −0.646608 | ||||||||
\(352\) | 11.9475 | 0.636805 | ||||||||
\(353\) | 22.9922 | 1.22375 | 0.611876 | − | 0.790954i | \(-0.290415\pi\) | ||||
0.611876 | + | 0.790954i | \(0.290415\pi\) | |||||||
\(354\) | 15.6517 | 0.831877 | ||||||||
\(355\) | 21.0340 | 1.11637 | ||||||||
\(356\) | 12.0674 | 0.639573 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.43751 | 0.498788 | ||||||||
\(359\) | −14.1163 | −0.745030 | −0.372515 | − | 0.928026i | \(-0.621504\pi\) | ||||
−0.372515 | + | 0.928026i | \(0.621504\pi\) | |||||||
\(360\) | −37.5313 | −1.97807 | ||||||||
\(361\) | 21.8169 | 1.14826 | ||||||||
\(362\) | −20.2078 | −1.06210 | ||||||||
\(363\) | −11.7376 | −0.616065 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.9597 | 1.04474 | ||||||||
\(366\) | 70.8145 | 3.70153 | ||||||||
\(367\) | 13.1892 | 0.688469 | 0.344235 | − | 0.938884i | \(-0.388138\pi\) | ||||
0.344235 | + | 0.938884i | \(0.388138\pi\) | |||||||
\(368\) | −2.00317 | −0.104423 | ||||||||
\(369\) | 68.0522 | 3.54265 | ||||||||
\(370\) | −2.44907 | −0.127321 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.665063 | −0.0344819 | ||||||||
\(373\) | 9.15428 | 0.473991 | 0.236995 | − | 0.971511i | \(-0.423837\pi\) | ||||
0.236995 | + | 0.971511i | \(0.423837\pi\) | |||||||
\(374\) | −12.9335 | −0.668777 | ||||||||
\(375\) | −35.6993 | −1.84351 | ||||||||
\(376\) | −10.1553 | −0.523717 | ||||||||
\(377\) | 11.1456 | 0.574029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.07480 | 0.157942 | 0.0789710 | − | 0.996877i | \(-0.474837\pi\) | ||||
0.0789710 | + | 0.996877i | \(0.474837\pi\) | |||||||
\(380\) | −42.8920 | −2.20031 | ||||||||
\(381\) | 46.5263 | 2.38361 | ||||||||
\(382\) | −35.4835 | −1.81549 | ||||||||
\(383\) | 1.09321 | 0.0558605 | 0.0279303 | − | 0.999610i | \(-0.491108\pi\) | ||||
0.0279303 | + | 0.999610i | \(0.491108\pi\) | |||||||
\(384\) | 58.7792 | 2.99956 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.9524 | −1.21915 | ||||||||
\(387\) | −3.37471 | −0.171546 | ||||||||
\(388\) | 50.3633 | 2.55681 | ||||||||
\(389\) | −11.8335 | −0.599981 | −0.299991 | − | 0.953942i | \(-0.596984\pi\) | ||||
−0.299991 | + | 0.953942i | \(0.596984\pi\) | |||||||
\(390\) | 20.1933 | 1.02253 | ||||||||
\(391\) | −4.44424 | −0.224755 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.4067 | 1.23116 | ||||||||
\(394\) | −18.0146 | −0.907561 | ||||||||
\(395\) | −25.9456 | −1.30547 | ||||||||
\(396\) | 52.2393 | 2.62512 | ||||||||
\(397\) | −28.2609 | −1.41838 | −0.709188 | − | 0.705020i | \(-0.750938\pi\) | ||||
−0.709188 | + | 0.705020i | \(0.750938\pi\) | |||||||
\(398\) | 34.4406 | 1.72635 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.11871 | −0.0559353 | ||||||||
\(401\) | −6.66256 | −0.332713 | −0.166356 | − | 0.986066i | \(-0.553200\pi\) | ||||
−0.166356 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(402\) | 1.52778 | 0.0761989 | ||||||||
\(403\) | 0.0982406 | 0.00489371 | ||||||||
\(404\) | 1.11478 | 0.0554623 | ||||||||
\(405\) | 13.0048 | 0.646213 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.42570 | 0.0706694 | ||||||||
\(408\) | −20.7285 | −1.02621 | ||||||||
\(409\) | 11.7556 | 0.581276 | 0.290638 | − | 0.956833i | \(-0.406132\pi\) | ||||
0.290638 | + | 0.956833i | \(0.406132\pi\) | |||||||
\(410\) | −54.0661 | −2.67013 | ||||||||
\(411\) | 0.230645 | 0.0113769 | ||||||||
\(412\) | 35.0560 | 1.72709 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 28.3935 | 1.39546 | ||||||||
\(415\) | −23.1499 | −1.13639 | ||||||||
\(416\) | −6.76291 | −0.331579 | ||||||||
\(417\) | 46.2085 | 2.26284 | ||||||||
\(418\) | 39.4952 | 1.93177 | ||||||||
\(419\) | 6.77442 | 0.330952 | 0.165476 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165476 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.52728 | −0.0744351 | −0.0372175 | − | 0.999307i | \(-0.511849\pi\) | ||||
−0.0372175 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(422\) | 11.3992 | 0.554904 | ||||||||
\(423\) | 17.3609 | 0.844117 | ||||||||
\(424\) | −3.49245 | −0.169608 | ||||||||
\(425\) | −2.48196 | −0.120393 | ||||||||
\(426\) | −74.2193 | −3.59594 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −52.8340 | −2.55383 | ||||||||
\(429\) | −11.7553 | −0.567552 | ||||||||
\(430\) | 2.68114 | 0.129296 | ||||||||
\(431\) | 3.78461 | 0.182298 | 0.0911491 | − | 0.995837i | \(-0.470946\pi\) | ||||
0.0911491 | + | 0.995837i | \(0.470946\pi\) | |||||||
\(432\) | 7.61274 | 0.366268 | ||||||||
\(433\) | 3.53219 | 0.169746 | 0.0848730 | − | 0.996392i | \(-0.472952\pi\) | ||||
0.0848730 | + | 0.996392i | \(0.472952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −42.8612 | −2.05504 | ||||||||
\(436\) | −48.9503 | −2.34429 | ||||||||
\(437\) | 13.5714 | 0.649208 | ||||||||
\(438\) | −70.4287 | −3.36521 | ||||||||
\(439\) | 11.4480 | 0.546381 | 0.273190 | − | 0.961960i | \(-0.411921\pi\) | ||||
0.273190 | + | 0.961960i | \(0.411921\pi\) | |||||||
\(440\) | −17.3581 | −0.827517 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.32104 | 0.348226 | ||||||||
\(443\) | −13.5209 | −0.642400 | −0.321200 | − | 0.947011i | \(-0.604086\pi\) | ||||
−0.321200 | + | 0.947011i | \(0.604086\pi\) | |||||||
\(444\) | 5.46332 | 0.259278 | ||||||||
\(445\) | 6.85494 | 0.324955 | ||||||||
\(446\) | −4.07376 | −0.192898 | ||||||||
\(447\) | −18.5150 | −0.875727 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0667 | −0.852621 | −0.426310 | − | 0.904577i | \(-0.640187\pi\) | ||||
−0.426310 | + | 0.904577i | \(0.640187\pi\) | |||||||
\(450\) | 15.8568 | 0.747499 | ||||||||
\(451\) | 31.4740 | 1.48205 | ||||||||
\(452\) | −28.2869 | −1.33050 | ||||||||
\(453\) | −48.2320 | −2.26614 | ||||||||
\(454\) | −55.2523 | −2.59312 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 63.2987 | 2.96424 | ||||||||
\(457\) | 27.8916 | 1.30471 | 0.652357 | − | 0.757912i | \(-0.273780\pi\) | ||||
0.652357 | + | 0.757912i | \(0.273780\pi\) | |||||||
\(458\) | −30.7603 | −1.43733 | ||||||||
\(459\) | 16.8896 | 0.788340 | ||||||||
\(460\) | −14.2614 | −0.664939 | ||||||||
\(461\) | 27.9948 | 1.30385 | 0.651925 | − | 0.758284i | \(-0.273962\pi\) | ||||
0.651925 | + | 0.758284i | \(0.273962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.3527 | −1.73593 | −0.867964 | − | 0.496627i | \(-0.834572\pi\) | ||||
−0.867964 | + | 0.496627i | \(0.834572\pi\) | |||||||
\(464\) | −7.00408 | −0.325156 | ||||||||
\(465\) | −0.377790 | −0.0175196 | ||||||||
\(466\) | −49.6466 | −2.29983 | ||||||||
\(467\) | −28.8663 | −1.33577 | −0.667886 | − | 0.744264i | \(-0.732801\pi\) | ||||
−0.667886 | + | 0.744264i | \(0.732801\pi\) | |||||||
\(468\) | −29.5701 | −1.36688 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.7929 | −0.636220 | ||||||||
\(471\) | −39.4974 | −1.81995 | ||||||||
\(472\) | 7.61575 | 0.350543 | ||||||||
\(473\) | −1.56079 | −0.0717654 | ||||||||
\(474\) | 91.5504 | 4.20505 | ||||||||
\(475\) | 7.57918 | 0.347757 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.97052 | 0.273372 | ||||||||
\(478\) | 26.2603 | 1.20112 | ||||||||
\(479\) | 25.0973 | 1.14672 | 0.573362 | − | 0.819302i | \(-0.305639\pi\) | ||||
0.573362 | + | 0.819302i | \(0.305639\pi\) | |||||||
\(480\) | 26.0072 | 1.18706 | ||||||||
\(481\) | −0.807021 | −0.0367970 | ||||||||
\(482\) | −21.5947 | −0.983611 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.6555 | −0.620706 | ||||||||
\(485\) | 28.6089 | 1.29907 | ||||||||
\(486\) | 10.5876 | 0.480263 | ||||||||
\(487\) | −41.0234 | −1.85895 | −0.929474 | − | 0.368888i | \(-0.879738\pi\) | ||||
−0.929474 | + | 0.368888i | \(0.879738\pi\) | |||||||
\(488\) | 34.4567 | 1.55978 | ||||||||
\(489\) | −32.8487 | −1.48547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.985019 | 0.0444533 | 0.0222266 | − | 0.999753i | \(-0.492924\pi\) | ||||
0.0222266 | + | 0.999753i | \(0.492924\pi\) | |||||||
\(492\) | 120.609 | 5.43747 | ||||||||
\(493\) | −15.5392 | −0.699852 | ||||||||
\(494\) | −22.3563 | −1.00586 | ||||||||
\(495\) | 29.6746 | 1.33378 | ||||||||
\(496\) | −0.0617358 | −0.00277202 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 81.6856 | 3.66042 | ||||||||
\(499\) | −9.68113 | −0.433387 | −0.216693 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216693 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(500\) | −41.5326 | −1.85739 | ||||||||
\(501\) | −26.3352 | −1.17657 | ||||||||
\(502\) | 46.3116 | 2.06699 | ||||||||
\(503\) | −12.4080 | −0.553243 | −0.276622 | − | 0.960979i | \(-0.589215\pi\) | ||||
−0.276622 | + | 0.960979i | \(0.589215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.633252 | 0.0281794 | ||||||||
\(506\) | 13.1319 | 0.583786 | ||||||||
\(507\) | −31.7607 | −1.41054 | ||||||||
\(508\) | 54.1287 | 2.40157 | ||||||||
\(509\) | 13.7199 | 0.608122 | 0.304061 | − | 0.952653i | \(-0.401657\pi\) | ||||
0.304061 | + | 0.952653i | \(0.401657\pi\) | |||||||
\(510\) | −28.1535 | −1.24666 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.5735 | 0.467287 | ||||||||
\(513\) | −51.5759 | −2.27713 | ||||||||
\(514\) | −58.6649 | −2.58760 | ||||||||
\(515\) | 19.9136 | 0.877500 | ||||||||
\(516\) | −5.98100 | −0.263299 | ||||||||
\(517\) | 8.02939 | 0.353132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.58920 | 0.420919 | ||||||||
\(520\) | 9.82560 | 0.430881 | ||||||||
\(521\) | −34.1034 | −1.49410 | −0.747049 | − | 0.664769i | \(-0.768530\pi\) | ||||
−0.747049 | + | 0.664769i | \(0.768530\pi\) | |||||||
\(522\) | 99.2777 | 4.34527 | ||||||||
\(523\) | 5.24558 | 0.229373 | 0.114687 | − | 0.993402i | \(-0.463414\pi\) | ||||
0.114687 | + | 0.993402i | \(0.463414\pi\) | |||||||
\(524\) | 28.3948 | 1.24043 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0854 | 1.05017 | ||||||||
\(527\) | −0.136967 | −0.00596638 | ||||||||
\(528\) | 7.38722 | 0.321487 | ||||||||
\(529\) | −18.4876 | −0.803808 | ||||||||
\(530\) | −4.74346 | −0.206043 | ||||||||
\(531\) | −13.0195 | −0.564999 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.8159 | −0.771692 | ||||||||
\(534\) | −24.1880 | −1.04672 | ||||||||
\(535\) | −30.0125 | −1.29755 | ||||||||
\(536\) | 0.743384 | 0.0321093 | ||||||||
\(537\) | −11.9592 | −0.516075 | ||||||||
\(538\) | 1.04547 | 0.0450732 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 54.1980 | 2.33231 | ||||||||
\(541\) | 43.6622 | 1.87719 | 0.938593 | − | 0.345027i | \(-0.112130\pi\) | ||||
0.938593 | + | 0.345027i | \(0.112130\pi\) | |||||||
\(542\) | 55.8797 | 2.40024 | ||||||||
\(543\) | 25.6072 | 1.09891 | ||||||||
\(544\) | 9.42885 | 0.404259 | ||||||||
\(545\) | −27.8063 | −1.19109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.2818 | −1.55130 | −0.775648 | − | 0.631166i | \(-0.782577\pi\) | ||||
−0.775648 | + | 0.631166i | \(0.782577\pi\) | |||||||
\(548\) | 0.268333 | 0.0114626 | ||||||||
\(549\) | −58.9055 | −2.51402 | ||||||||
\(550\) | 7.33375 | 0.312712 | ||||||||
\(551\) | 47.4523 | 2.02153 | ||||||||
\(552\) | 21.0465 | 0.895798 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35.3885 | −1.50352 | ||||||||
\(555\) | 3.10345 | 0.131734 | ||||||||
\(556\) | 53.7589 | 2.27989 | ||||||||
\(557\) | −7.19093 | −0.304689 | −0.152345 | − | 0.988327i | \(-0.548682\pi\) | ||||
−0.152345 | + | 0.988327i | \(0.548682\pi\) | |||||||
\(558\) | 0.875061 | 0.0370443 | ||||||||
\(559\) | 0.883490 | 0.0373676 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3893 | 0.691956 | ||||||||
\(562\) | −23.3938 | −0.986808 | ||||||||
\(563\) | 11.6990 | 0.493053 | 0.246527 | − | 0.969136i | \(-0.420711\pi\) | ||||
0.246527 | + | 0.969136i | \(0.420711\pi\) | |||||||
\(564\) | 30.7688 | 1.29560 | ||||||||
\(565\) | −16.0684 | −0.676003 | ||||||||
\(566\) | 4.90414 | 0.206136 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.1134 | −1.51528 | ||||||||
\(569\) | 24.2886 | 1.01823 | 0.509115 | − | 0.860698i | \(-0.329973\pi\) | ||||
0.509115 | + | 0.860698i | \(0.329973\pi\) | |||||||
\(570\) | 85.9726 | 3.60100 | ||||||||
\(571\) | 1.58477 | 0.0663206 | 0.0331603 | − | 0.999450i | \(-0.489443\pi\) | ||||
0.0331603 | + | 0.999450i | \(0.489443\pi\) | |||||||
\(572\) | −13.6761 | −0.571828 | ||||||||
\(573\) | 44.9644 | 1.87842 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.52004 | 0.105093 | ||||||||
\(576\) | −71.0499 | −2.96041 | ||||||||
\(577\) | −17.9000 | −0.745188 | −0.372594 | − | 0.927994i | \(-0.621532\pi\) | ||||
−0.372594 | + | 0.927994i | \(0.621532\pi\) | |||||||
\(578\) | 29.4356 | 1.22436 | ||||||||
\(579\) | 30.3523 | 1.26140 | ||||||||
\(580\) | −49.8647 | −2.07052 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −100.948 | −4.18443 | ||||||||
\(583\) | 2.76135 | 0.114364 | ||||||||
\(584\) | −34.2690 | −1.41806 | ||||||||
\(585\) | −16.7974 | −0.694486 | ||||||||
\(586\) | −43.4873 | −1.79644 | ||||||||
\(587\) | −1.07134 | −0.0442189 | −0.0221094 | − | 0.999756i | \(-0.507038\pi\) | ||||
−0.0221094 | + | 0.999756i | \(0.507038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.418257 | 0.0172340 | ||||||||
\(590\) | 10.3437 | 0.425845 | ||||||||
\(591\) | 22.8279 | 0.939015 | ||||||||
\(592\) | 0.507144 | 0.0208435 | ||||||||
\(593\) | −5.21037 | −0.213964 | −0.106982 | − | 0.994261i | \(-0.534119\pi\) | ||||
−0.106982 | + | 0.994261i | \(0.534119\pi\) | |||||||
\(594\) | −49.9058 | −2.04766 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.5403 | −0.882324 | ||||||||
\(597\) | −43.6429 | −1.78619 | ||||||||
\(598\) | −7.43335 | −0.303972 | ||||||||
\(599\) | 19.3597 | 0.791015 | 0.395508 | − | 0.918463i | \(-0.370569\pi\) | ||||
0.395508 | + | 0.918463i | \(0.370569\pi\) | |||||||
\(600\) | 11.7538 | 0.479846 | ||||||||
\(601\) | −15.0693 | −0.614689 | −0.307345 | − | 0.951598i | \(-0.599440\pi\) | ||||
−0.307345 | + | 0.951598i | \(0.599440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.27085 | −0.0517532 | ||||||||
\(604\) | −56.1130 | −2.28321 | ||||||||
\(605\) | −7.75705 | −0.315369 | ||||||||
\(606\) | −2.23446 | −0.0907688 | ||||||||
\(607\) | −30.9662 | −1.25688 | −0.628440 | − | 0.777858i | \(-0.716306\pi\) | ||||
−0.628440 | + | 0.777858i | \(0.716306\pi\) | |||||||
\(608\) | −28.7930 | −1.16771 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 46.7992 | 1.89484 | ||||||||
\(611\) | −4.54505 | −0.183873 | ||||||||
\(612\) | 41.2267 | 1.66649 | ||||||||
\(613\) | 3.75434 | 0.151636 | 0.0758182 | − | 0.997122i | \(-0.475843\pi\) | ||||
0.0758182 | + | 0.997122i | \(0.475843\pi\) | |||||||
\(614\) | −22.6814 | −0.915348 | ||||||||
\(615\) | 68.5122 | 2.76268 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.0758 | 1.13029 | 0.565145 | − | 0.824991i | \(-0.308820\pi\) | ||||
0.565145 | + | 0.824991i | \(0.308820\pi\) | |||||||
\(618\) | −70.2663 | −2.82652 | ||||||||
\(619\) | −19.3674 | −0.778441 | −0.389221 | − | 0.921145i | \(-0.627256\pi\) | ||||
−0.389221 | + | 0.921145i | \(0.627256\pi\) | |||||||
\(620\) | −0.439521 | −0.0176516 | ||||||||
\(621\) | −17.1487 | −0.688154 | ||||||||
\(622\) | 64.9267 | 2.60332 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.18154 | −0.167396 | ||||||||
\(625\) | −17.6610 | −0.706442 | ||||||||
\(626\) | −47.1398 | −1.88408 | ||||||||
\(627\) | −50.0480 | −1.99873 | ||||||||
\(628\) | −45.9513 | −1.83366 | ||||||||
\(629\) | 1.12515 | 0.0448626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.7248 | 1.62123 | 0.810615 | − | 0.585580i | \(-0.199133\pi\) | ||||
0.810615 | + | 0.585580i | \(0.199133\pi\) | |||||||
\(632\) | 44.5463 | 1.77196 | ||||||||
\(633\) | −14.4450 | −0.574136 | ||||||||
\(634\) | −27.6414 | −1.09778 | ||||||||
\(635\) | 30.7479 | 1.22019 | ||||||||
\(636\) | 10.5816 | 0.419587 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 45.9157 | 1.81782 | ||||||||
\(639\) | 61.7377 | 2.44231 | ||||||||
\(640\) | 38.8455 | 1.53550 | ||||||||
\(641\) | 0.706513 | 0.0279056 | 0.0139528 | − | 0.999903i | \(-0.495559\pi\) | ||||
0.0139528 | + | 0.999903i | \(0.495559\pi\) | |||||||
\(642\) | 105.900 | 4.17956 | ||||||||
\(643\) | 16.5495 | 0.652650 | 0.326325 | − | 0.945258i | \(-0.394190\pi\) | ||||
0.326325 | + | 0.945258i | \(0.394190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.39752 | −0.133777 | ||||||||
\(646\) | 31.1692 | 1.22634 | ||||||||
\(647\) | −11.7596 | −0.462317 | −0.231159 | − | 0.972916i | \(-0.574252\pi\) | ||||
−0.231159 | + | 0.972916i | \(0.574252\pi\) | |||||||
\(648\) | −22.3281 | −0.877129 | ||||||||
\(649\) | −6.02150 | −0.236364 | ||||||||
\(650\) | −4.15128 | −0.162827 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.2161 | −1.49666 | ||||||||
\(653\) | 22.5877 | 0.883925 | 0.441962 | − | 0.897034i | \(-0.354282\pi\) | ||||
0.441962 | + | 0.897034i | \(0.354282\pi\) | |||||||
\(654\) | 98.1159 | 3.83664 | ||||||||
\(655\) | 16.1297 | 0.630239 | ||||||||
\(656\) | 11.1958 | 0.437121 | ||||||||
\(657\) | 58.5846 | 2.28560 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0135 | 0.701705 | 0.350852 | − | 0.936431i | \(-0.385892\pi\) | ||||
0.350852 | + | 0.936431i | \(0.385892\pi\) | |||||||
\(660\) | 52.5924 | 2.04716 | ||||||||
\(661\) | 37.6880 | 1.46590 | 0.732948 | − | 0.680285i | \(-0.238144\pi\) | ||||
0.732948 | + | 0.680285i | \(0.238144\pi\) | |||||||
\(662\) | −29.5816 | −1.14972 | ||||||||
\(663\) | −9.27717 | −0.360295 | ||||||||
\(664\) | 39.7463 | 1.54246 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.18839 | −0.278545 | ||||||||
\(667\) | 15.7776 | 0.610912 | ||||||||
\(668\) | −30.6383 | −1.18543 | ||||||||
\(669\) | 5.16223 | 0.199584 | ||||||||
\(670\) | 1.00967 | 0.0390069 | ||||||||
\(671\) | −27.2436 | −1.05173 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.7754 | −0.723738 | −0.361869 | − | 0.932229i | \(-0.617861\pi\) | ||||
−0.361869 | + | 0.932229i | \(0.617861\pi\) | |||||||
\(674\) | −67.2316 | −2.58966 | ||||||||
\(675\) | −9.57699 | −0.368619 | ||||||||
\(676\) | −36.9504 | −1.42117 | ||||||||
\(677\) | −3.85662 | −0.148222 | −0.0741110 | − | 0.997250i | \(-0.523612\pi\) | ||||
−0.0741110 | + | 0.997250i | \(0.523612\pi\) | |||||||
\(678\) | 56.6982 | 2.17748 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.6989 | −0.525327 | ||||||||
\(681\) | 70.0153 | 2.68299 | ||||||||
\(682\) | 0.404714 | 0.0154973 | ||||||||
\(683\) | 40.0543 | 1.53264 | 0.766318 | − | 0.642461i | \(-0.222087\pi\) | ||||
0.766318 | + | 0.642461i | \(0.222087\pi\) | |||||||
\(684\) | −125.894 | −4.81369 | ||||||||
\(685\) | 0.152427 | 0.00582393 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.9792 | 1.48715 | ||||||||
\(688\) | −0.555198 | −0.0211667 | ||||||||
\(689\) | −1.56307 | −0.0595482 | ||||||||
\(690\) | 28.5854 | 1.08823 | ||||||||
\(691\) | −33.8236 | −1.28671 | −0.643356 | − | 0.765567i | \(-0.722458\pi\) | ||||
−0.643356 | + | 0.765567i | \(0.722458\pi\) | |||||||
\(692\) | 11.1561 | 0.424090 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.3193 | −1.37866 | ||||||||
\(695\) | 30.5379 | 1.15837 | ||||||||
\(696\) | 73.5889 | 2.78938 | ||||||||
\(697\) | 24.8389 | 0.940842 | ||||||||
\(698\) | −21.1851 | −0.801867 | ||||||||
\(699\) | 62.9118 | 2.37954 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0095 | 1.54891 | 0.774453 | − | 0.632631i | \(-0.218025\pi\) | ||||
0.774453 | + | 0.632631i | \(0.218025\pi\) | |||||||
\(702\) | 28.2493 | 1.06620 | ||||||||
\(703\) | −3.43587 | −0.129586 | ||||||||
\(704\) | −32.8604 | −1.23847 | ||||||||
\(705\) | 17.4783 | 0.658270 | ||||||||
\(706\) | −53.6159 | −2.01786 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −23.0745 | −0.867193 | ||||||||
\(709\) | −24.8640 | −0.933787 | −0.466893 | − | 0.884314i | \(-0.654627\pi\) | ||||
−0.466893 | + | 0.884314i | \(0.654627\pi\) | |||||||
\(710\) | −49.0494 | −1.84079 | ||||||||
\(711\) | −76.1542 | −2.85601 | ||||||||
\(712\) | −11.7693 | −0.441073 | ||||||||
\(713\) | 0.139068 | 0.00520815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.76875 | −0.290535 | ||||||||
\(716\) | −13.9133 | −0.519963 | ||||||||
\(717\) | −33.2768 | −1.24275 | ||||||||
\(718\) | 32.9180 | 1.22849 | ||||||||
\(719\) | 20.1550 | 0.751654 | 0.375827 | − | 0.926690i | \(-0.377359\pi\) | ||||
0.375827 | + | 0.926690i | \(0.377359\pi\) | |||||||
\(720\) | 10.5557 | 0.393388 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −50.8752 | −1.89338 | ||||||||
\(723\) | 27.3646 | 1.01770 | ||||||||
\(724\) | 29.7914 | 1.10719 | ||||||||
\(725\) | 8.81128 | 0.327243 | ||||||||
\(726\) | 27.3711 | 1.01584 | ||||||||
\(727\) | 39.6430 | 1.47028 | 0.735138 | − | 0.677918i | \(-0.237117\pi\) | ||||
0.735138 | + | 0.677918i | \(0.237117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.3945 | −1.23683 | ||||||||
\(730\) | −46.5443 | −1.72268 | ||||||||
\(731\) | −1.23176 | −0.0455584 | ||||||||
\(732\) | −104.398 | −3.85867 | ||||||||
\(733\) | −4.69321 | −0.173348 | −0.0866738 | − | 0.996237i | \(-0.527624\pi\) | ||||
−0.0866738 | + | 0.996237i | \(0.527624\pi\) | |||||||
\(734\) | −30.7560 | −1.13523 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.57350 | −0.352884 | ||||||||
\(737\) | −0.587767 | −0.0216507 | ||||||||
\(738\) | −158.692 | −5.84153 | ||||||||
\(739\) | 24.4235 | 0.898433 | 0.449216 | − | 0.893423i | \(-0.351703\pi\) | ||||
0.449216 | + | 0.893423i | \(0.351703\pi\) | |||||||
\(740\) | 3.61055 | 0.132726 | ||||||||
\(741\) | 28.3298 | 1.04072 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.1516 | 1.03278 | 0.516391 | − | 0.856353i | \(-0.327275\pi\) | ||||
0.516391 | + | 0.856353i | \(0.327275\pi\) | |||||||
\(744\) | 0.648632 | 0.0237800 | ||||||||
\(745\) | −12.2360 | −0.448292 | ||||||||
\(746\) | −21.3470 | −0.781570 | ||||||||
\(747\) | −67.9484 | −2.48610 | ||||||||
\(748\) | 19.0673 | 0.697168 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 83.2478 | 3.03978 | ||||||||
\(751\) | −28.7070 | −1.04753 | −0.523766 | − | 0.851862i | \(-0.675474\pi\) | ||||
−0.523766 | + | 0.851862i | \(0.675474\pi\) | |||||||
\(752\) | 2.85618 | 0.104154 | ||||||||
\(753\) | −58.6858 | −2.13863 | ||||||||
\(754\) | −25.9906 | −0.946524 | ||||||||
\(755\) | −31.8751 | −1.16005 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9823 | −1.27145 | −0.635726 | − | 0.771915i | \(-0.719299\pi\) | ||||
−0.635726 | + | 0.771915i | \(0.719299\pi\) | |||||||
\(758\) | −7.17018 | −0.260433 | ||||||||
\(759\) | −16.6407 | −0.604019 | ||||||||
\(760\) | 41.8323 | 1.51742 | ||||||||
\(761\) | 47.2861 | 1.71412 | 0.857060 | − | 0.515216i | \(-0.172288\pi\) | ||||
0.857060 | + | 0.515216i | \(0.172288\pi\) | |||||||
\(762\) | −108.495 | −3.93037 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 52.3116 | 1.89257 | ||||||||
\(765\) | 23.4189 | 0.846712 | ||||||||
\(766\) | −2.54928 | −0.0921091 | ||||||||
\(767\) | 3.40848 | 0.123073 | ||||||||
\(768\) | −63.8115 | −2.30260 | ||||||||
\(769\) | −41.8758 | −1.51008 | −0.755040 | − | 0.655678i | \(-0.772383\pi\) | ||||
−0.755040 | + | 0.655678i | \(0.772383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 74.3397 | 2.67728 | ||||||||
\(772\) | 35.3119 | 1.27090 | ||||||||
\(773\) | −21.0942 | −0.758706 | −0.379353 | − | 0.925252i | \(-0.623853\pi\) | ||||
−0.379353 | + | 0.925252i | \(0.623853\pi\) | |||||||
\(774\) | 7.86953 | 0.282864 | ||||||||
\(775\) | 0.0776650 | 0.00278981 | ||||||||
\(776\) | −49.1190 | −1.76327 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.5947 | 0.989317 | ||||||||
\(779\) | −75.8508 | −2.71764 | ||||||||
\(780\) | −29.7700 | −1.06594 | ||||||||
\(781\) | 28.5536 | 1.02173 | ||||||||
\(782\) | 10.3636 | 0.370601 | ||||||||
\(783\) | −59.9603 | −2.14281 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.1027 | −0.931646 | ||||||||
\(786\) | −56.9144 | −2.03007 | ||||||||
\(787\) | 40.2501 | 1.43476 | 0.717380 | − | 0.696682i | \(-0.245341\pi\) | ||||
0.717380 | + | 0.696682i | \(0.245341\pi\) | |||||||
\(788\) | 26.5580 | 0.946089 | ||||||||
\(789\) | −30.5208 | −1.08657 | ||||||||
\(790\) | 60.5030 | 2.15260 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −50.9487 | −1.81038 | ||||||||
\(793\) | 15.4213 | 0.547627 | ||||||||
\(794\) | 65.9021 | 2.33878 | ||||||||
\(795\) | 6.01088 | 0.213184 | ||||||||
\(796\) | −50.7741 | −1.79964 | ||||||||
\(797\) | −5.32667 | −0.188680 | −0.0943401 | − | 0.995540i | \(-0.530074\pi\) | ||||
−0.0943401 | + | 0.995540i | \(0.530074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.33671 | 0.224177 | ||||||||
\(800\) | −5.34648 | −0.189027 | ||||||||
\(801\) | 20.1202 | 0.710914 | ||||||||
\(802\) | 15.5365 | 0.548614 | ||||||||
\(803\) | 27.0952 | 0.956170 | ||||||||
\(804\) | −2.25234 | −0.0794338 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.229089 | −0.00806930 | ||||||||
\(807\) | −1.32481 | −0.0466354 | ||||||||
\(808\) | −1.08724 | −0.0382489 | ||||||||
\(809\) | 38.3657 | 1.34887 | 0.674434 | − | 0.738335i | \(-0.264388\pi\) | ||||
0.674434 | + | 0.738335i | \(0.264388\pi\) | |||||||
\(810\) | −30.3261 | −1.06555 | ||||||||
\(811\) | 33.5120 | 1.17676 | 0.588382 | − | 0.808583i | \(-0.299765\pi\) | ||||
0.588382 | + | 0.808583i | \(0.299765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −70.8104 | −2.48343 | ||||||||
\(814\) | −3.32462 | −0.116528 | ||||||||
\(815\) | −21.7087 | −0.760424 | ||||||||
\(816\) | 5.82991 | 0.204088 | ||||||||
\(817\) | 3.76144 | 0.131596 | ||||||||
\(818\) | −27.4130 | −0.958473 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 79.7070 | 2.78349 | ||||||||
\(821\) | −36.9875 | −1.29087 | −0.645437 | − | 0.763814i | \(-0.723325\pi\) | ||||
−0.645437 | + | 0.763814i | \(0.723325\pi\) | |||||||
\(822\) | −0.537846 | −0.0187595 | ||||||||
\(823\) | 8.10944 | 0.282677 | 0.141339 | − | 0.989961i | \(-0.454859\pi\) | ||||
0.141339 | + | 0.989961i | \(0.454859\pi\) | |||||||
\(824\) | −34.1899 | −1.19106 | ||||||||
\(825\) | −9.29328 | −0.323551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.9413 | −1.66708 | −0.833541 | − | 0.552458i | \(-0.813690\pi\) | ||||
−0.833541 | + | 0.552458i | \(0.813690\pi\) | |||||||
\(828\) | −41.8592 | −1.45471 | ||||||||
\(829\) | 29.4695 | 1.02352 | 0.511758 | − | 0.859129i | \(-0.328994\pi\) | ||||
0.511758 | + | 0.859129i | \(0.328994\pi\) | |||||||
\(830\) | 53.9837 | 1.87380 | ||||||||
\(831\) | 44.8441 | 1.55562 | ||||||||
\(832\) | 18.6007 | 0.644863 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −107.754 | −3.73123 | ||||||||
\(835\) | −17.4042 | −0.602296 | ||||||||
\(836\) | −58.2258 | −2.01378 | ||||||||
\(837\) | −0.528507 | −0.0182679 | ||||||||
\(838\) | −15.7974 | −0.545711 | ||||||||
\(839\) | 42.6216 | 1.47146 | 0.735731 | − | 0.677274i | \(-0.236839\pi\) | ||||
0.735731 | + | 0.677274i | \(0.236839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.1663 | 0.902287 | ||||||||
\(842\) | 3.56149 | 0.122737 | ||||||||
\(843\) | 29.6445 | 1.02101 | ||||||||
\(844\) | −16.8053 | −0.578461 | ||||||||
\(845\) | −20.9897 | −0.722069 | ||||||||
\(846\) | −40.4842 | −1.39188 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.982255 | 0.0337308 | ||||||||
\(849\) | −6.21449 | −0.213281 | ||||||||
\(850\) | 5.78772 | 0.198517 | ||||||||
\(851\) | −1.14241 | −0.0391613 | ||||||||
\(852\) | 109.418 | 3.74860 | ||||||||
\(853\) | −44.8312 | −1.53499 | −0.767496 | − | 0.641054i | \(-0.778498\pi\) | ||||
−0.767496 | + | 0.641054i | \(0.778498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −71.5145 | −2.44574 | ||||||||
\(856\) | 51.5287 | 1.76121 | ||||||||
\(857\) | 32.5489 | 1.11185 | 0.555924 | − | 0.831233i | \(-0.312364\pi\) | ||||
0.555924 | + | 0.831233i | \(0.312364\pi\) | |||||||
\(858\) | 27.4124 | 0.935844 | ||||||||
\(859\) | −34.8831 | −1.19020 | −0.595099 | − | 0.803653i | \(-0.702887\pi\) | ||||
−0.595099 | + | 0.803653i | \(0.702887\pi\) | |||||||
\(860\) | −3.95267 | −0.134785 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.82539 | −0.300594 | ||||||||
\(863\) | −1.66021 | −0.0565141 | −0.0282571 | − | 0.999601i | \(-0.508996\pi\) | ||||
−0.0282571 | + | 0.999601i | \(0.508996\pi\) | |||||||
\(864\) | 36.3826 | 1.23776 | ||||||||
\(865\) | 6.33722 | 0.215472 | ||||||||
\(866\) | −8.23676 | −0.279897 | ||||||||
\(867\) | −37.3005 | −1.26679 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.2212 | −1.19480 | ||||||||
\(870\) | 99.9487 | 3.38858 | ||||||||
\(871\) | 0.332706 | 0.0112733 | ||||||||
\(872\) | 47.7409 | 1.61671 | ||||||||
\(873\) | 83.9714 | 2.84200 | ||||||||
\(874\) | −31.6473 | −1.07049 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 103.830 | 3.50808 | ||||||||
\(877\) | 30.5981 | 1.03323 | 0.516613 | − | 0.856219i | \(-0.327193\pi\) | ||||
0.516613 | + | 0.856219i | \(0.327193\pi\) | |||||||
\(878\) | −26.6957 | −0.900935 | ||||||||
\(879\) | 55.1067 | 1.85870 | ||||||||
\(880\) | 4.88200 | 0.164572 | ||||||||
\(881\) | 51.9678 | 1.75084 | 0.875419 | − | 0.483365i | \(-0.160586\pi\) | ||||
0.875419 | + | 0.483365i | \(0.160586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.8041 | 0.767420 | 0.383710 | − | 0.923454i | \(-0.374646\pi\) | ||||
0.383710 | + | 0.923454i | \(0.374646\pi\) | |||||||
\(884\) | −10.7931 | −0.363010 | ||||||||
\(885\) | −13.1075 | −0.440604 | ||||||||
\(886\) | 31.5297 | 1.05926 | ||||||||
\(887\) | −14.9208 | −0.500993 | −0.250496 | − | 0.968118i | \(-0.580594\pi\) | ||||
−0.250496 | + | 0.968118i | \(0.580594\pi\) | |||||||
\(888\) | −5.32834 | −0.178808 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.9851 | −0.535823 | ||||||||
\(891\) | 17.6540 | 0.591431 | ||||||||
\(892\) | 6.00574 | 0.201087 | ||||||||
\(893\) | −19.3505 | −0.647538 | ||||||||
\(894\) | 43.1753 | 1.44400 | ||||||||
\(895\) | −7.90346 | −0.264183 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.41949 | 0.314508 | ||||||||
\(898\) | 42.1300 | 1.40590 | ||||||||
\(899\) | 0.486251 | 0.0162174 | ||||||||
\(900\) | −23.3770 | −0.779232 | ||||||||
\(901\) | 2.17923 | 0.0726007 | ||||||||
\(902\) | −73.3947 | −2.44377 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.5880 | 0.917564 | ||||||||
\(905\) | 16.9231 | 0.562542 | ||||||||
\(906\) | 112.473 | 3.73666 | ||||||||
\(907\) | −41.6207 | −1.38199 | −0.690996 | − | 0.722858i | \(-0.742828\pi\) | ||||
−0.690996 | + | 0.722858i | \(0.742828\pi\) | |||||||
\(908\) | 81.4557 | 2.70320 | ||||||||
\(909\) | 1.85869 | 0.0616488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.8850 | 0.725083 | 0.362541 | − | 0.931968i | \(-0.381909\pi\) | ||||
0.362541 | + | 0.931968i | \(0.381909\pi\) | |||||||
\(912\) | −17.8028 | −0.589511 | ||||||||
\(913\) | −31.4260 | −1.04005 | ||||||||
\(914\) | −65.0409 | −2.15136 | ||||||||
\(915\) | −59.3036 | −1.96052 | ||||||||
\(916\) | 45.3484 | 1.49835 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −39.3852 | −1.29990 | ||||||||
\(919\) | 4.45638 | 0.147002 | 0.0735012 | − | 0.997295i | \(-0.476583\pi\) | ||||
0.0735012 | + | 0.997295i | \(0.476583\pi\) | |||||||
\(920\) | 13.9090 | 0.458566 | ||||||||
\(921\) | 28.7417 | 0.947072 | ||||||||
\(922\) | −65.2816 | −2.14993 | ||||||||
\(923\) | −16.1628 | −0.532005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.637998 | −0.0209772 | ||||||||
\(926\) | 87.1034 | 2.86239 | ||||||||
\(927\) | 58.4495 | 1.91973 | ||||||||
\(928\) | −33.4737 | −1.09883 | ||||||||
\(929\) | 18.0749 | 0.593019 | 0.296509 | − | 0.955030i | \(-0.404177\pi\) | ||||
0.296509 | + | 0.955030i | \(0.404177\pi\) | |||||||
\(930\) | 0.880975 | 0.0288883 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 73.1916 | 2.39747 | ||||||||
\(933\) | −82.2747 | −2.69355 | ||||||||
\(934\) | 67.3137 | 2.20257 | ||||||||
\(935\) | 10.8312 | 0.354218 | ||||||||
\(936\) | 28.8396 | 0.942651 | ||||||||
\(937\) | −23.0218 | −0.752088 | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.7352 | 1.94938 | ||||||||
\(940\) | 20.3342 | 0.663229 | ||||||||
\(941\) | −11.2388 | −0.366373 | −0.183186 | − | 0.983078i | \(-0.558641\pi\) | ||||
−0.183186 | + | 0.983078i | \(0.558641\pi\) | |||||||
\(942\) | 92.1047 | 3.00093 | ||||||||
\(943\) | −25.2200 | −0.821275 | ||||||||
\(944\) | −2.14194 | −0.0697141 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.63964 | 0.118335 | ||||||||
\(947\) | 8.60672 | 0.279681 | 0.139840 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139840 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(948\) | −134.968 | −4.38357 | ||||||||
\(949\) | −15.3373 | −0.497870 | ||||||||
\(950\) | −17.6740 | −0.573420 | ||||||||
\(951\) | 35.0270 | 1.13583 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0513 | −0.519951 | −0.259976 | − | 0.965615i | \(-0.583715\pi\) | ||||
−0.259976 | + | 0.965615i | \(0.583715\pi\) | |||||||
\(954\) | −13.9228 | −0.450766 | ||||||||
\(955\) | 29.7157 | 0.961577 | ||||||||
\(956\) | −38.7142 | −1.25211 | ||||||||
\(957\) | −58.1841 | −1.88082 | ||||||||
\(958\) | −58.5247 | −1.89085 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −71.5302 | −2.30863 | ||||||||
\(961\) | −30.9957 | −0.999862 | ||||||||
\(962\) | 1.88190 | 0.0606750 | ||||||||
\(963\) | −88.0909 | −2.83869 | ||||||||
\(964\) | 31.8360 | 1.02537 | ||||||||
\(965\) | 20.0590 | 0.645721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.6295 | 0.502610 | 0.251305 | − | 0.967908i | \(-0.419140\pi\) | ||||
0.251305 | + | 0.967908i | \(0.419140\pi\) | |||||||
\(968\) | 13.3182 | 0.428062 | ||||||||
\(969\) | −39.4974 | −1.26884 | ||||||||
\(970\) | −66.7136 | −2.14205 | ||||||||
\(971\) | 5.03310 | 0.161520 | 0.0807600 | − | 0.996734i | \(-0.474265\pi\) | ||||
0.0807600 | + | 0.996734i | \(0.474265\pi\) | |||||||
\(972\) | −15.6088 | −0.500651 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 95.6631 | 3.06524 | ||||||||
\(975\) | 5.26047 | 0.168470 | ||||||||
\(976\) | −9.69098 | −0.310201 | ||||||||
\(977\) | 17.0593 | 0.545776 | 0.272888 | − | 0.962046i | \(-0.412021\pi\) | ||||
0.272888 | + | 0.962046i | \(0.412021\pi\) | |||||||
\(978\) | 76.6003 | 2.44941 | ||||||||
\(979\) | 9.30557 | 0.297407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −81.6156 | −2.60578 | ||||||||
\(982\) | −2.29698 | −0.0732996 | ||||||||
\(983\) | 26.8870 | 0.857561 | 0.428781 | − | 0.903409i | \(-0.358943\pi\) | ||||
0.428781 | + | 0.903409i | \(0.358943\pi\) | |||||||
\(984\) | −117.629 | −3.74988 | ||||||||
\(985\) | 15.0863 | 0.480690 | ||||||||
\(986\) | 36.2362 | 1.15400 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.9588 | 1.04856 | ||||||||
\(989\) | 1.25066 | 0.0397686 | ||||||||
\(990\) | −69.1987 | −2.19928 | ||||||||
\(991\) | 30.0379 | 0.954184 | 0.477092 | − | 0.878853i | \(-0.341691\pi\) | ||||
0.477092 | + | 0.878853i | \(0.341691\pi\) | |||||||
\(992\) | −0.295046 | −0.00936772 | ||||||||
\(993\) | 37.4857 | 1.18957 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.8423 | −0.914364 | ||||||||
\(996\) | −120.425 | −3.81582 | ||||||||
\(997\) | −42.6067 | −1.34937 | −0.674684 | − | 0.738107i | \(-0.735720\pi\) | ||||
−0.674684 | + | 0.738107i | \(0.735720\pi\) | |||||||
\(998\) | 22.5756 | 0.714617 | ||||||||
\(999\) | 4.34155 | 0.137360 |
(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 | 343.2.a.d.1.1 | yes | 6 | |
3.2 | odd | 2 | 3087.2.a.j.1.6 | 6 | |||
4.3 | odd | 2 | 5488.2.a.h.1.1 | 6 | |||
5.4 | even | 2 | 8575.2.a.n.1.6 | 6 | |||
7.2 | even | 3 | 343.2.c.d.18.6 | 12 | |||
7.3 | odd | 6 | 343.2.c.e.324.6 | 12 | |||
7.4 | even | 3 | 343.2.c.d.324.6 | 12 | |||
7.5 | odd | 6 | 343.2.c.e.18.6 | 12 | |||
7.6 | odd | 2 | 343.2.a.c.1.1 | ✓ | 6 | ||
21.20 | even | 2 | 3087.2.a.k.1.6 | 6 | |||
28.27 | even | 2 | 5488.2.a.p.1.6 | 6 | |||
35.34 | odd | 2 | 8575.2.a.o.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
343.2.a.c.1.1 | ✓ | 6 | 7.6 | odd | 2 | ||
343.2.a.d.1.1 | yes | 6 | 1.1 | even | 1 | trivial | |
343.2.c.d.18.6 | 12 | 7.2 | even | 3 | |||
343.2.c.d.324.6 | 12 | 7.4 | even | 3 | |||
343.2.c.e.18.6 | 12 | 7.5 | odd | 6 | |||
343.2.c.e.324.6 | 12 | 7.3 | odd | 6 | |||
3087.2.a.j.1.6 | 6 | 3.2 | odd | 2 | |||
3087.2.a.k.1.6 | 6 | 21.20 | even | 2 | |||
5488.2.a.h.1.1 | 6 | 4.3 | odd | 2 | |||
5488.2.a.p.1.6 | 6 | 28.27 | even | 2 | |||
8575.2.a.n.1.6 | 6 | 5.4 | even | 2 | |||
8575.2.a.o.1.6 | 6 | 35.34 | odd | 2 |