Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.350444 | −0.202329 | −0.101164 | − | 0.994870i | \(-0.532257\pi\) | ||||
−0.101164 | + | 0.994870i | \(0.532257\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.178230 | −0.0797067 | −0.0398534 | − | 0.999206i | \(-0.512689\pi\) | ||||
−0.0398534 | + | 0.999206i | \(0.512689\pi\) | |||||||
\(6\) | 0.350444 | 0.143068 | ||||||||
\(7\) | −3.90849 | −1.47727 | −0.738636 | − | 0.674105i | \(-0.764530\pi\) | ||||
−0.738636 | + | 0.674105i | \(0.764530\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.87719 | −0.959063 | ||||||||
\(10\) | 0.178230 | 0.0563612 | ||||||||
\(11\) | −1.52727 | −0.460488 | −0.230244 | − | 0.973133i | \(-0.573952\pi\) | ||||
−0.230244 | + | 0.973133i | \(0.573952\pi\) | |||||||
\(12\) | −0.350444 | −0.101164 | ||||||||
\(13\) | −0.315173 | −0.0874134 | −0.0437067 | − | 0.999044i | \(-0.513917\pi\) | ||||
−0.0437067 | + | 0.999044i | \(0.513917\pi\) | |||||||
\(14\) | 3.90849 | 1.04459 | ||||||||
\(15\) | 0.0624595 | 0.0161270 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.70888 | 1.62714 | 0.813571 | − | 0.581466i | \(-0.197520\pi\) | ||||
0.813571 | + | 0.581466i | \(0.197520\pi\) | |||||||
\(18\) | 2.87719 | 0.678160 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.178230 | −0.0398534 | ||||||||
\(21\) | 1.36971 | 0.298895 | ||||||||
\(22\) | 1.52727 | 0.325614 | ||||||||
\(23\) | −3.64189 | −0.759387 | −0.379693 | − | 0.925112i | \(-0.623971\pi\) | ||||
−0.379693 | + | 0.925112i | \(0.623971\pi\) | |||||||
\(24\) | 0.350444 | 0.0715340 | ||||||||
\(25\) | −4.96823 | −0.993647 | ||||||||
\(26\) | 0.315173 | 0.0618106 | ||||||||
\(27\) | 2.05962 | 0.396375 | ||||||||
\(28\) | −3.90849 | −0.738636 | ||||||||
\(29\) | 7.13883 | 1.32565 | 0.662824 | − | 0.748775i | \(-0.269358\pi\) | ||||
0.662824 | + | 0.748775i | \(0.269358\pi\) | |||||||
\(30\) | −0.0624595 | −0.0114035 | ||||||||
\(31\) | 7.92567 | 1.42349 | 0.711746 | − | 0.702436i | \(-0.247905\pi\) | ||||
0.711746 | + | 0.702436i | \(0.247905\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.535221 | 0.0931700 | ||||||||
\(34\) | −6.70888 | −1.15056 | ||||||||
\(35\) | 0.696609 | 0.117748 | ||||||||
\(36\) | −2.87719 | −0.479532 | ||||||||
\(37\) | 7.58524 | 1.24701 | 0.623503 | − | 0.781821i | \(-0.285709\pi\) | ||||
0.623503 | + | 0.781821i | \(0.285709\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0.110451 | 0.0176862 | ||||||||
\(40\) | 0.178230 | 0.0281806 | ||||||||
\(41\) | −5.82883 | −0.910310 | −0.455155 | − | 0.890412i | \(-0.650416\pi\) | ||||
−0.455155 | + | 0.890412i | \(0.650416\pi\) | |||||||
\(42\) | −1.36971 | −0.211350 | ||||||||
\(43\) | −4.70286 | −0.717180 | −0.358590 | − | 0.933495i | \(-0.616742\pi\) | ||||
−0.358590 | + | 0.933495i | \(0.616742\pi\) | |||||||
\(44\) | −1.52727 | −0.230244 | ||||||||
\(45\) | 0.512800 | 0.0764438 | ||||||||
\(46\) | 3.64189 | 0.536968 | ||||||||
\(47\) | −1.67658 | −0.244555 | −0.122277 | − | 0.992496i | \(-0.539020\pi\) | ||||
−0.122277 | + | 0.992496i | \(0.539020\pi\) | |||||||
\(48\) | −0.350444 | −0.0505822 | ||||||||
\(49\) | 8.27632 | 1.18233 | ||||||||
\(50\) | 4.96823 | 0.702614 | ||||||||
\(51\) | −2.35108 | −0.329218 | ||||||||
\(52\) | −0.315173 | −0.0437067 | ||||||||
\(53\) | 3.11276 | 0.427570 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(54\) | −2.05962 | −0.280279 | ||||||||
\(55\) | 0.272204 | 0.0367040 | ||||||||
\(56\) | 3.90849 | 0.522294 | ||||||||
\(57\) | 0.350444 | 0.0464174 | ||||||||
\(58\) | −7.13883 | −0.937375 | ||||||||
\(59\) | −13.1462 | −1.71149 | −0.855746 | − | 0.517397i | \(-0.826901\pi\) | ||||
−0.855746 | + | 0.517397i | \(0.826901\pi\) | |||||||
\(60\) | 0.0624595 | 0.00806348 | ||||||||
\(61\) | 3.19516 | 0.409098 | 0.204549 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204549 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(62\) | −7.92567 | −1.00656 | ||||||||
\(63\) | 11.2455 | 1.41680 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0561732 | 0.00696743 | ||||||||
\(66\) | −0.535221 | −0.0658811 | ||||||||
\(67\) | 2.05631 | 0.251218 | 0.125609 | − | 0.992080i | \(-0.459912\pi\) | ||||
0.125609 | + | 0.992080i | \(0.459912\pi\) | |||||||
\(68\) | 6.70888 | 0.813571 | ||||||||
\(69\) | 1.27628 | 0.153646 | ||||||||
\(70\) | −0.696609 | −0.0832607 | ||||||||
\(71\) | 5.71954 | 0.678785 | 0.339393 | − | 0.940645i | \(-0.389779\pi\) | ||||
0.339393 | + | 0.940645i | \(0.389779\pi\) | |||||||
\(72\) | 2.87719 | 0.339080 | ||||||||
\(73\) | 5.78654 | 0.677263 | 0.338631 | − | 0.940919i | \(-0.390036\pi\) | ||||
0.338631 | + | 0.940919i | \(0.390036\pi\) | |||||||
\(74\) | −7.58524 | −0.881766 | ||||||||
\(75\) | 1.74109 | 0.201043 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 5.96931 | 0.680266 | ||||||||
\(78\) | −0.110451 | −0.0125061 | ||||||||
\(79\) | −5.62658 | −0.633040 | −0.316520 | − | 0.948586i | \(-0.602514\pi\) | ||||
−0.316520 | + | 0.948586i | \(0.602514\pi\) | |||||||
\(80\) | −0.178230 | −0.0199267 | ||||||||
\(81\) | 7.90979 | 0.878865 | ||||||||
\(82\) | 5.82883 | 0.643686 | ||||||||
\(83\) | 5.96257 | 0.654478 | 0.327239 | − | 0.944942i | \(-0.393882\pi\) | ||||
0.327239 | + | 0.944942i | \(0.393882\pi\) | |||||||
\(84\) | 1.36971 | 0.149447 | ||||||||
\(85\) | −1.19572 | −0.129694 | ||||||||
\(86\) | 4.70286 | 0.507123 | ||||||||
\(87\) | −2.50176 | −0.268217 | ||||||||
\(88\) | 1.52727 | 0.162807 | ||||||||
\(89\) | 6.61534 | 0.701225 | 0.350613 | − | 0.936521i | \(-0.385973\pi\) | ||||
0.350613 | + | 0.936521i | \(0.385973\pi\) | |||||||
\(90\) | −0.512800 | −0.0540539 | ||||||||
\(91\) | 1.23185 | 0.129133 | ||||||||
\(92\) | −3.64189 | −0.379693 | ||||||||
\(93\) | −2.77750 | −0.288014 | ||||||||
\(94\) | 1.67658 | 0.172926 | ||||||||
\(95\) | 0.178230 | 0.0182860 | ||||||||
\(96\) | 0.350444 | 0.0357670 | ||||||||
\(97\) | 5.63552 | 0.572201 | 0.286100 | − | 0.958200i | \(-0.407641\pi\) | ||||
0.286100 | + | 0.958200i | \(0.407641\pi\) | |||||||
\(98\) | −8.27632 | −0.836034 | ||||||||
\(99\) | 4.39423 | 0.441637 | ||||||||
\(100\) | −4.96823 | −0.496823 | ||||||||
\(101\) | 3.83173 | 0.381272 | 0.190636 | − | 0.981661i | \(-0.438945\pi\) | ||||
0.190636 | + | 0.981661i | \(0.438945\pi\) | |||||||
\(102\) | 2.35108 | 0.232792 | ||||||||
\(103\) | −1.12275 | −0.110628 | −0.0553138 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553138 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(104\) | 0.315173 | 0.0309053 | ||||||||
\(105\) | −0.244122 | −0.0238239 | ||||||||
\(106\) | −3.11276 | −0.302338 | ||||||||
\(107\) | −0.421369 | −0.0407353 | −0.0203677 | − | 0.999793i | \(-0.506484\pi\) | ||||
−0.0203677 | + | 0.999793i | \(0.506484\pi\) | |||||||
\(108\) | 2.05962 | 0.198187 | ||||||||
\(109\) | 19.8217 | 1.89857 | 0.949287 | − | 0.314411i | \(-0.101807\pi\) | ||||
0.949287 | + | 0.314411i | \(0.101807\pi\) | |||||||
\(110\) | −0.272204 | −0.0259536 | ||||||||
\(111\) | −2.65820 | −0.252305 | ||||||||
\(112\) | −3.90849 | −0.369318 | ||||||||
\(113\) | 3.23659 | 0.304472 | 0.152236 | − | 0.988344i | \(-0.451353\pi\) | ||||
0.152236 | + | 0.988344i | \(0.451353\pi\) | |||||||
\(114\) | −0.350444 | −0.0328221 | ||||||||
\(115\) | 0.649093 | 0.0605282 | ||||||||
\(116\) | 7.13883 | 0.662824 | ||||||||
\(117\) | 0.906814 | 0.0838350 | ||||||||
\(118\) | 13.1462 | 1.21021 | ||||||||
\(119\) | −26.2216 | −2.40373 | ||||||||
\(120\) | −0.0624595 | −0.00570174 | ||||||||
\(121\) | −8.66746 | −0.787951 | ||||||||
\(122\) | −3.19516 | −0.289276 | ||||||||
\(123\) | 2.04268 | 0.184182 | ||||||||
\(124\) | 7.92567 | 0.711746 | ||||||||
\(125\) | 1.77663 | 0.158907 | ||||||||
\(126\) | −11.2455 | −1.00183 | ||||||||
\(127\) | −2.71343 | −0.240778 | −0.120389 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120389 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.64809 | 0.145106 | ||||||||
\(130\) | −0.0561732 | −0.00492672 | ||||||||
\(131\) | −5.20115 | −0.454427 | −0.227213 | − | 0.973845i | \(-0.572961\pi\) | ||||
−0.227213 | + | 0.973845i | \(0.572961\pi\) | |||||||
\(132\) | 0.535221 | 0.0465850 | ||||||||
\(133\) | 3.90849 | 0.338909 | ||||||||
\(134\) | −2.05631 | −0.177638 | ||||||||
\(135\) | −0.367086 | −0.0315937 | ||||||||
\(136\) | −6.70888 | −0.575282 | ||||||||
\(137\) | −10.8685 | −0.928556 | −0.464278 | − | 0.885690i | \(-0.653686\pi\) | ||||
−0.464278 | + | 0.885690i | \(0.653686\pi\) | |||||||
\(138\) | −1.27628 | −0.108644 | ||||||||
\(139\) | 0.716808 | 0.0607989 | 0.0303994 | − | 0.999538i | \(-0.490322\pi\) | ||||
0.0303994 | + | 0.999538i | \(0.490322\pi\) | |||||||
\(140\) | 0.696609 | 0.0588742 | ||||||||
\(141\) | 0.587547 | 0.0494804 | ||||||||
\(142\) | −5.71954 | −0.479973 | ||||||||
\(143\) | 0.481354 | 0.0402528 | ||||||||
\(144\) | −2.87719 | −0.239766 | ||||||||
\(145\) | −1.27235 | −0.105663 | ||||||||
\(146\) | −5.78654 | −0.478897 | ||||||||
\(147\) | −2.90038 | −0.239220 | ||||||||
\(148\) | 7.58524 | 0.623503 | ||||||||
\(149\) | −12.5612 | −1.02905 | −0.514527 | − | 0.857474i | \(-0.672032\pi\) | ||||
−0.514527 | + | 0.857474i | \(0.672032\pi\) | |||||||
\(150\) | −1.74109 | −0.142159 | ||||||||
\(151\) | 10.0366 | 0.816768 | 0.408384 | − | 0.912810i | \(-0.366092\pi\) | ||||
0.408384 | + | 0.912810i | \(0.366092\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −19.3027 | −1.56053 | ||||||||
\(154\) | −5.96931 | −0.481021 | ||||||||
\(155\) | −1.41259 | −0.113462 | ||||||||
\(156\) | 0.110451 | 0.00884312 | ||||||||
\(157\) | −10.5317 | −0.840524 | −0.420262 | − | 0.907403i | \(-0.638062\pi\) | ||||
−0.420262 | + | 0.907403i | \(0.638062\pi\) | |||||||
\(158\) | 5.62658 | 0.447627 | ||||||||
\(159\) | −1.09085 | −0.0865098 | ||||||||
\(160\) | 0.178230 | 0.0140903 | ||||||||
\(161\) | 14.2343 | 1.12182 | ||||||||
\(162\) | −7.90979 | −0.621451 | ||||||||
\(163\) | −2.70092 | −0.211552 | −0.105776 | − | 0.994390i | \(-0.533733\pi\) | ||||
−0.105776 | + | 0.994390i | \(0.533733\pi\) | |||||||
\(164\) | −5.82883 | −0.455155 | ||||||||
\(165\) | −0.0953922 | −0.00742627 | ||||||||
\(166\) | −5.96257 | −0.462786 | ||||||||
\(167\) | 13.5906 | 1.05167 | 0.525836 | − | 0.850586i | \(-0.323752\pi\) | ||||
0.525836 | + | 0.850586i | \(0.323752\pi\) | |||||||
\(168\) | −1.36971 | −0.105675 | ||||||||
\(169\) | −12.9007 | −0.992359 | ||||||||
\(170\) | 1.19572 | 0.0917076 | ||||||||
\(171\) | 2.87719 | 0.220024 | ||||||||
\(172\) | −4.70286 | −0.358590 | ||||||||
\(173\) | 18.5724 | 1.41204 | 0.706018 | − | 0.708194i | \(-0.250490\pi\) | ||||
0.706018 | + | 0.708194i | \(0.250490\pi\) | |||||||
\(174\) | 2.50176 | 0.189658 | ||||||||
\(175\) | 19.4183 | 1.46789 | ||||||||
\(176\) | −1.52727 | −0.115122 | ||||||||
\(177\) | 4.60701 | 0.346284 | ||||||||
\(178\) | −6.61534 | −0.495841 | ||||||||
\(179\) | 12.9704 | 0.969452 | 0.484726 | − | 0.874666i | \(-0.338919\pi\) | ||||
0.484726 | + | 0.874666i | \(0.338919\pi\) | |||||||
\(180\) | 0.512800 | 0.0382219 | ||||||||
\(181\) | −9.98409 | −0.742112 | −0.371056 | − | 0.928611i | \(-0.621004\pi\) | ||||
−0.371056 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(182\) | −1.23185 | −0.0913110 | ||||||||
\(183\) | −1.11972 | −0.0827723 | ||||||||
\(184\) | 3.64189 | 0.268484 | ||||||||
\(185\) | −1.35191 | −0.0993947 | ||||||||
\(186\) | 2.77750 | 0.203656 | ||||||||
\(187\) | −10.2462 | −0.749279 | ||||||||
\(188\) | −1.67658 | −0.122277 | ||||||||
\(189\) | −8.05003 | −0.585553 | ||||||||
\(190\) | −0.178230 | −0.0129301 | ||||||||
\(191\) | −0.371920 | −0.0269112 | −0.0134556 | − | 0.999909i | \(-0.504283\pi\) | ||||
−0.0134556 | + | 0.999909i | \(0.504283\pi\) | |||||||
\(192\) | −0.350444 | −0.0252911 | ||||||||
\(193\) | 3.37266 | 0.242770 | 0.121385 | − | 0.992606i | \(-0.461267\pi\) | ||||
0.121385 | + | 0.992606i | \(0.461267\pi\) | |||||||
\(194\) | −5.63552 | −0.404607 | ||||||||
\(195\) | −0.0196856 | −0.00140971 | ||||||||
\(196\) | 8.27632 | 0.591166 | ||||||||
\(197\) | −26.2737 | −1.87193 | −0.935963 | − | 0.352099i | \(-0.885468\pi\) | ||||
−0.935963 | + | 0.352099i | \(0.885468\pi\) | |||||||
\(198\) | −4.39423 | −0.312285 | ||||||||
\(199\) | −6.26480 | −0.444100 | −0.222050 | − | 0.975035i | \(-0.571275\pi\) | ||||
−0.222050 | + | 0.975035i | \(0.571275\pi\) | |||||||
\(200\) | 4.96823 | 0.351307 | ||||||||
\(201\) | −0.720620 | −0.0508286 | ||||||||
\(202\) | −3.83173 | −0.269600 | ||||||||
\(203\) | −27.9021 | −1.95834 | ||||||||
\(204\) | −2.35108 | −0.164609 | ||||||||
\(205\) | 1.03887 | 0.0725578 | ||||||||
\(206\) | 1.12275 | 0.0782255 | ||||||||
\(207\) | 10.4784 | 0.728300 | ||||||||
\(208\) | −0.315173 | −0.0218533 | ||||||||
\(209\) | 1.52727 | 0.105643 | ||||||||
\(210\) | 0.244122 | 0.0168460 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 3.11276 | 0.213785 | ||||||||
\(213\) | −2.00438 | −0.137338 | ||||||||
\(214\) | 0.421369 | 0.0288042 | ||||||||
\(215\) | 0.838189 | 0.0571640 | ||||||||
\(216\) | −2.05962 | −0.140140 | ||||||||
\(217\) | −30.9774 | −2.10289 | ||||||||
\(218\) | −19.8217 | −1.34249 | ||||||||
\(219\) | −2.02786 | −0.137030 | ||||||||
\(220\) | 0.272204 | 0.0183520 | ||||||||
\(221\) | −2.11446 | −0.142234 | ||||||||
\(222\) | 2.65820 | 0.178407 | ||||||||
\(223\) | 6.21424 | 0.416136 | 0.208068 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208068 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(224\) | 3.90849 | 0.261147 | ||||||||
\(225\) | 14.2945 | 0.952970 | ||||||||
\(226\) | −3.23659 | −0.215294 | ||||||||
\(227\) | −17.2456 | −1.14463 | −0.572314 | − | 0.820034i | \(-0.693954\pi\) | ||||
−0.572314 | + | 0.820034i | \(0.693954\pi\) | |||||||
\(228\) | 0.350444 | 0.0232087 | ||||||||
\(229\) | −0.785104 | −0.0518811 | −0.0259406 | − | 0.999663i | \(-0.508258\pi\) | ||||
−0.0259406 | + | 0.999663i | \(0.508258\pi\) | |||||||
\(230\) | −0.649093 | −0.0427999 | ||||||||
\(231\) | −2.09191 | −0.137637 | ||||||||
\(232\) | −7.13883 | −0.468687 | ||||||||
\(233\) | −11.8271 | −0.774821 | −0.387411 | − | 0.921907i | \(-0.626630\pi\) | ||||
−0.387411 | + | 0.921907i | \(0.626630\pi\) | |||||||
\(234\) | −0.906814 | −0.0592803 | ||||||||
\(235\) | 0.298817 | 0.0194926 | ||||||||
\(236\) | −13.1462 | −0.855746 | ||||||||
\(237\) | 1.97180 | 0.128082 | ||||||||
\(238\) | 26.2216 | 1.69969 | ||||||||
\(239\) | −5.54195 | −0.358479 | −0.179239 | − | 0.983805i | \(-0.557364\pi\) | ||||
−0.179239 | + | 0.983805i | \(0.557364\pi\) | |||||||
\(240\) | 0.0624595 | 0.00403174 | ||||||||
\(241\) | 16.5329 | 1.06498 | 0.532489 | − | 0.846437i | \(-0.321257\pi\) | ||||
0.532489 | + | 0.846437i | \(0.321257\pi\) | |||||||
\(242\) | 8.66746 | 0.557165 | ||||||||
\(243\) | −8.95081 | −0.574195 | ||||||||
\(244\) | 3.19516 | 0.204549 | ||||||||
\(245\) | −1.47509 | −0.0942397 | ||||||||
\(246\) | −2.04268 | −0.130236 | ||||||||
\(247\) | 0.315173 | 0.0200540 | ||||||||
\(248\) | −7.92567 | −0.503281 | ||||||||
\(249\) | −2.08955 | −0.132420 | ||||||||
\(250\) | −1.77663 | −0.112364 | ||||||||
\(251\) | −3.08097 | −0.194469 | −0.0972344 | − | 0.995262i | \(-0.531000\pi\) | ||||
−0.0972344 | + | 0.995262i | \(0.531000\pi\) | |||||||
\(252\) | 11.2455 | 0.708398 | ||||||||
\(253\) | 5.56214 | 0.349688 | ||||||||
\(254\) | 2.71343 | 0.170256 | ||||||||
\(255\) | 0.419033 | 0.0262409 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.207315 | 0.0129320 | 0.00646598 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646598 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(258\) | −1.64809 | −0.102605 | ||||||||
\(259\) | −29.6468 | −1.84217 | ||||||||
\(260\) | 0.0561732 | 0.00348372 | ||||||||
\(261\) | −20.5398 | −1.27138 | ||||||||
\(262\) | 5.20115 | 0.321328 | ||||||||
\(263\) | −13.4049 | −0.826583 | −0.413291 | − | 0.910599i | \(-0.635621\pi\) | ||||
−0.413291 | + | 0.910599i | \(0.635621\pi\) | |||||||
\(264\) | −0.535221 | −0.0329406 | ||||||||
\(265\) | −0.554786 | −0.0340802 | ||||||||
\(266\) | −3.90849 | −0.239645 | ||||||||
\(267\) | −2.31831 | −0.141878 | ||||||||
\(268\) | 2.05631 | 0.125609 | ||||||||
\(269\) | −11.2749 | −0.687441 | −0.343721 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343721 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(270\) | 0.367086 | 0.0223401 | ||||||||
\(271\) | −23.7771 | −1.44435 | −0.722177 | − | 0.691708i | \(-0.756859\pi\) | ||||
−0.722177 | + | 0.691708i | \(0.756859\pi\) | |||||||
\(272\) | 6.70888 | 0.406786 | ||||||||
\(273\) | −0.431695 | −0.0261274 | ||||||||
\(274\) | 10.8685 | 0.656588 | ||||||||
\(275\) | 7.58781 | 0.457562 | ||||||||
\(276\) | 1.27628 | 0.0768229 | ||||||||
\(277\) | −3.22032 | −0.193490 | −0.0967451 | − | 0.995309i | \(-0.530843\pi\) | ||||
−0.0967451 | + | 0.995309i | \(0.530843\pi\) | |||||||
\(278\) | −0.716808 | −0.0429913 | ||||||||
\(279\) | −22.8037 | −1.36522 | ||||||||
\(280\) | −0.696609 | −0.0416304 | ||||||||
\(281\) | −24.0598 | −1.43529 | −0.717643 | − | 0.696411i | \(-0.754779\pi\) | ||||
−0.717643 | + | 0.696411i | \(0.754779\pi\) | |||||||
\(282\) | −0.587547 | −0.0349879 | ||||||||
\(283\) | −17.9884 | −1.06930 | −0.534649 | − | 0.845074i | \(-0.679556\pi\) | ||||
−0.534649 | + | 0.845074i | \(0.679556\pi\) | |||||||
\(284\) | 5.71954 | 0.339393 | ||||||||
\(285\) | −0.0624595 | −0.00369978 | ||||||||
\(286\) | −0.481354 | −0.0284630 | ||||||||
\(287\) | 22.7819 | 1.34478 | ||||||||
\(288\) | 2.87719 | 0.169540 | ||||||||
\(289\) | 28.0090 | 1.64759 | ||||||||
\(290\) | 1.27235 | 0.0747151 | ||||||||
\(291\) | −1.97493 | −0.115773 | ||||||||
\(292\) | 5.78654 | 0.338631 | ||||||||
\(293\) | −6.08806 | −0.355668 | −0.177834 | − | 0.984060i | \(-0.556909\pi\) | ||||
−0.177834 | + | 0.984060i | \(0.556909\pi\) | |||||||
\(294\) | 2.90038 | 0.169154 | ||||||||
\(295\) | 2.34304 | 0.136417 | ||||||||
\(296\) | −7.58524 | −0.440883 | ||||||||
\(297\) | −3.14559 | −0.182526 | ||||||||
\(298\) | 12.5612 | 0.727651 | ||||||||
\(299\) | 1.14783 | 0.0663806 | ||||||||
\(300\) | 1.74109 | 0.100522 | ||||||||
\(301\) | 18.3811 | 1.05947 | ||||||||
\(302\) | −10.0366 | −0.577542 | ||||||||
\(303\) | −1.34281 | −0.0771422 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.569471 | −0.0326078 | ||||||||
\(306\) | 19.3027 | 1.10346 | ||||||||
\(307\) | −22.8889 | −1.30634 | −0.653169 | − | 0.757213i | \(-0.726561\pi\) | ||||
−0.653169 | + | 0.757213i | \(0.726561\pi\) | |||||||
\(308\) | 5.96931 | 0.340133 | ||||||||
\(309\) | 0.393460 | 0.0223831 | ||||||||
\(310\) | 1.41259 | 0.0802297 | ||||||||
\(311\) | 6.32785 | 0.358819 | 0.179410 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179410 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(312\) | −0.110451 | −0.00625303 | ||||||||
\(313\) | 8.71500 | 0.492601 | 0.246301 | − | 0.969194i | \(-0.420785\pi\) | ||||
0.246301 | + | 0.969194i | \(0.420785\pi\) | |||||||
\(314\) | 10.5317 | 0.594340 | ||||||||
\(315\) | −2.00428 | −0.112928 | ||||||||
\(316\) | −5.62658 | −0.316520 | ||||||||
\(317\) | −18.9379 | −1.06366 | −0.531830 | − | 0.846851i | \(-0.678496\pi\) | ||||
−0.531830 | + | 0.846851i | \(0.678496\pi\) | |||||||
\(318\) | 1.09085 | 0.0611717 | ||||||||
\(319\) | −10.9029 | −0.610445 | ||||||||
\(320\) | −0.178230 | −0.00996334 | ||||||||
\(321\) | 0.147666 | 0.00824192 | ||||||||
\(322\) | −14.2343 | −0.793247 | ||||||||
\(323\) | −6.70888 | −0.373292 | ||||||||
\(324\) | 7.90979 | 0.439433 | ||||||||
\(325\) | 1.56586 | 0.0868580 | ||||||||
\(326\) | 2.70092 | 0.149590 | ||||||||
\(327\) | −6.94639 | −0.384136 | ||||||||
\(328\) | 5.82883 | 0.321843 | ||||||||
\(329\) | 6.55291 | 0.361273 | ||||||||
\(330\) | 0.0953922 | 0.00525117 | ||||||||
\(331\) | −15.3285 | −0.842530 | −0.421265 | − | 0.906938i | \(-0.638414\pi\) | ||||
−0.421265 | + | 0.906938i | \(0.638414\pi\) | |||||||
\(332\) | 5.96257 | 0.327239 | ||||||||
\(333\) | −21.8242 | −1.19596 | ||||||||
\(334\) | −13.5906 | −0.743645 | ||||||||
\(335\) | −0.366495 | −0.0200237 | ||||||||
\(336\) | 1.36971 | 0.0747236 | ||||||||
\(337\) | 3.20160 | 0.174402 | 0.0872010 | − | 0.996191i | \(-0.472208\pi\) | ||||
0.0872010 | + | 0.996191i | \(0.472208\pi\) | |||||||
\(338\) | 12.9007 | 0.701704 | ||||||||
\(339\) | −1.13424 | −0.0616035 | ||||||||
\(340\) | −1.19572 | −0.0648471 | ||||||||
\(341\) | −12.1046 | −0.655501 | ||||||||
\(342\) | −2.87719 | −0.155581 | ||||||||
\(343\) | −4.98848 | −0.269353 | ||||||||
\(344\) | 4.70286 | 0.253561 | ||||||||
\(345\) | −0.227471 | −0.0122466 | ||||||||
\(346\) | −18.5724 | −0.998460 | ||||||||
\(347\) | −7.73645 | −0.415315 | −0.207657 | − | 0.978202i | \(-0.566584\pi\) | ||||
−0.207657 | + | 0.978202i | \(0.566584\pi\) | |||||||
\(348\) | −2.50176 | −0.134108 | ||||||||
\(349\) | 18.1960 | 0.974009 | 0.487004 | − | 0.873400i | \(-0.338090\pi\) | ||||
0.487004 | + | 0.873400i | \(0.338090\pi\) | |||||||
\(350\) | −19.4183 | −1.03795 | ||||||||
\(351\) | −0.649139 | −0.0346485 | ||||||||
\(352\) | 1.52727 | 0.0814035 | ||||||||
\(353\) | −11.8165 | −0.628927 | −0.314463 | − | 0.949270i | \(-0.601825\pi\) | ||||
−0.314463 | + | 0.949270i | \(0.601825\pi\) | |||||||
\(354\) | −4.60701 | −0.244860 | ||||||||
\(355\) | −1.01939 | −0.0541037 | ||||||||
\(356\) | 6.61534 | 0.350613 | ||||||||
\(357\) | 9.18920 | 0.486344 | ||||||||
\(358\) | −12.9704 | −0.685506 | ||||||||
\(359\) | −4.87578 | −0.257334 | −0.128667 | − | 0.991688i | \(-0.541070\pi\) | ||||
−0.128667 | + | 0.991688i | \(0.541070\pi\) | |||||||
\(360\) | −0.512800 | −0.0270270 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.98409 | 0.524752 | ||||||||
\(363\) | 3.03746 | 0.159425 | ||||||||
\(364\) | 1.23185 | 0.0645667 | ||||||||
\(365\) | −1.03133 | −0.0539824 | ||||||||
\(366\) | 1.11972 | 0.0585288 | ||||||||
\(367\) | −20.7486 | −1.08307 | −0.541534 | − | 0.840679i | \(-0.682156\pi\) | ||||
−0.541534 | + | 0.840679i | \(0.682156\pi\) | |||||||
\(368\) | −3.64189 | −0.189847 | ||||||||
\(369\) | 16.7706 | 0.873045 | ||||||||
\(370\) | 1.35191 | 0.0702827 | ||||||||
\(371\) | −12.1662 | −0.631638 | ||||||||
\(372\) | −2.77750 | −0.144007 | ||||||||
\(373\) | 3.88759 | 0.201292 | 0.100646 | − | 0.994922i | \(-0.467909\pi\) | ||||
0.100646 | + | 0.994922i | \(0.467909\pi\) | |||||||
\(374\) | 10.2462 | 0.529820 | ||||||||
\(375\) | −0.622610 | −0.0321515 | ||||||||
\(376\) | 1.67658 | 0.0864631 | ||||||||
\(377\) | −2.24997 | −0.115879 | ||||||||
\(378\) | 8.05003 | 0.414049 | ||||||||
\(379\) | 2.86778 | 0.147308 | 0.0736540 | − | 0.997284i | \(-0.476534\pi\) | ||||
0.0736540 | + | 0.997284i | \(0.476534\pi\) | |||||||
\(380\) | 0.178230 | 0.00914299 | ||||||||
\(381\) | 0.950905 | 0.0487163 | ||||||||
\(382\) | 0.371920 | 0.0190291 | ||||||||
\(383\) | 10.3522 | 0.528975 | 0.264487 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264487 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(384\) | 0.350444 | 0.0178835 | ||||||||
\(385\) | −1.06391 | −0.0542217 | ||||||||
\(386\) | −3.37266 | −0.171664 | ||||||||
\(387\) | 13.5310 | 0.687821 | ||||||||
\(388\) | 5.63552 | 0.286100 | ||||||||
\(389\) | 16.1807 | 0.820394 | 0.410197 | − | 0.911997i | \(-0.365460\pi\) | ||||
0.410197 | + | 0.911997i | \(0.365460\pi\) | |||||||
\(390\) | 0.0196856 | 0.000996817 0 | ||||||||
\(391\) | −24.4330 | −1.23563 | ||||||||
\(392\) | −8.27632 | −0.418017 | ||||||||
\(393\) | 1.82271 | 0.0919436 | ||||||||
\(394\) | 26.2737 | 1.32365 | ||||||||
\(395\) | 1.00282 | 0.0504575 | ||||||||
\(396\) | 4.39423 | 0.220819 | ||||||||
\(397\) | 7.66033 | 0.384461 | 0.192230 | − | 0.981350i | \(-0.438428\pi\) | ||||
0.192230 | + | 0.981350i | \(0.438428\pi\) | |||||||
\(398\) | 6.26480 | 0.314026 | ||||||||
\(399\) | −1.36971 | −0.0685711 | ||||||||
\(400\) | −4.96823 | −0.248412 | ||||||||
\(401\) | 36.2291 | 1.80920 | 0.904598 | − | 0.426266i | \(-0.140171\pi\) | ||||
0.904598 | + | 0.426266i | \(0.140171\pi\) | |||||||
\(402\) | 0.720620 | 0.0359412 | ||||||||
\(403\) | −2.49796 | −0.124432 | ||||||||
\(404\) | 3.83173 | 0.190636 | ||||||||
\(405\) | −1.40976 | −0.0700514 | ||||||||
\(406\) | 27.9021 | 1.38476 | ||||||||
\(407\) | −11.5847 | −0.574231 | ||||||||
\(408\) | 2.35108 | 0.116396 | ||||||||
\(409\) | −6.16561 | −0.304870 | −0.152435 | − | 0.988314i | \(-0.548711\pi\) | ||||
−0.152435 | + | 0.988314i | \(0.548711\pi\) | |||||||
\(410\) | −1.03887 | −0.0513061 | ||||||||
\(411\) | 3.80879 | 0.187874 | ||||||||
\(412\) | −1.12275 | −0.0553138 | ||||||||
\(413\) | 51.3819 | 2.52834 | ||||||||
\(414\) | −10.4784 | −0.514986 | ||||||||
\(415\) | −1.06271 | −0.0521663 | ||||||||
\(416\) | 0.315173 | 0.0154527 | ||||||||
\(417\) | −0.251201 | −0.0123014 | ||||||||
\(418\) | −1.52727 | −0.0747010 | ||||||||
\(419\) | 22.0812 | 1.07874 | 0.539369 | − | 0.842070i | \(-0.318663\pi\) | ||||
0.539369 | + | 0.842070i | \(0.318663\pi\) | |||||||
\(420\) | −0.244122 | −0.0119120 | ||||||||
\(421\) | −5.97402 | −0.291156 | −0.145578 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145578 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 4.82384 | 0.234543 | ||||||||
\(424\) | −3.11276 | −0.151169 | ||||||||
\(425\) | −33.3313 | −1.61680 | ||||||||
\(426\) | 2.00438 | 0.0971124 | ||||||||
\(427\) | −12.4882 | −0.604349 | ||||||||
\(428\) | −0.421369 | −0.0203677 | ||||||||
\(429\) | −0.168687 | −0.00814430 | ||||||||
\(430\) | −0.838189 | −0.0404211 | ||||||||
\(431\) | 30.4508 | 1.46676 | 0.733382 | − | 0.679817i | \(-0.237941\pi\) | ||||
0.733382 | + | 0.679817i | \(0.237941\pi\) | |||||||
\(432\) | 2.05962 | 0.0990937 | ||||||||
\(433\) | −13.8536 | −0.665759 | −0.332880 | − | 0.942969i | \(-0.608020\pi\) | ||||
−0.332880 | + | 0.942969i | \(0.608020\pi\) | |||||||
\(434\) | 30.9774 | 1.48696 | ||||||||
\(435\) | 0.445888 | 0.0213787 | ||||||||
\(436\) | 19.8217 | 0.949287 | ||||||||
\(437\) | 3.64189 | 0.174215 | ||||||||
\(438\) | 2.02786 | 0.0968947 | ||||||||
\(439\) | 2.92118 | 0.139420 | 0.0697102 | − | 0.997567i | \(-0.477793\pi\) | ||||
0.0697102 | + | 0.997567i | \(0.477793\pi\) | |||||||
\(440\) | −0.272204 | −0.0129768 | ||||||||
\(441\) | −23.8125 | −1.13393 | ||||||||
\(442\) | 2.11446 | 0.100575 | ||||||||
\(443\) | 26.4299 | 1.25572 | 0.627861 | − | 0.778325i | \(-0.283930\pi\) | ||||
0.627861 | + | 0.778325i | \(0.283930\pi\) | |||||||
\(444\) | −2.65820 | −0.126153 | ||||||||
\(445\) | −1.17905 | −0.0558924 | ||||||||
\(446\) | −6.21424 | −0.294253 | ||||||||
\(447\) | 4.40199 | 0.208207 | ||||||||
\(448\) | −3.90849 | −0.184659 | ||||||||
\(449\) | 14.6511 | 0.691429 | 0.345715 | − | 0.938340i | \(-0.387637\pi\) | ||||
0.345715 | + | 0.938340i | \(0.387637\pi\) | |||||||
\(450\) | −14.2945 | −0.673852 | ||||||||
\(451\) | 8.90217 | 0.419187 | ||||||||
\(452\) | 3.23659 | 0.152236 | ||||||||
\(453\) | −3.51727 | −0.165256 | ||||||||
\(454\) | 17.2456 | 0.809375 | ||||||||
\(455\) | −0.219553 | −0.0102928 | ||||||||
\(456\) | −0.350444 | −0.0164110 | ||||||||
\(457\) | −38.6663 | −1.80873 | −0.904367 | − | 0.426755i | \(-0.859657\pi\) | ||||
−0.904367 | + | 0.426755i | \(0.859657\pi\) | |||||||
\(458\) | 0.785104 | 0.0366855 | ||||||||
\(459\) | 13.8178 | 0.644958 | ||||||||
\(460\) | 0.649093 | 0.0302641 | ||||||||
\(461\) | 15.1128 | 0.703875 | 0.351937 | − | 0.936024i | \(-0.385523\pi\) | ||||
0.351937 | + | 0.936024i | \(0.385523\pi\) | |||||||
\(462\) | 2.09191 | 0.0973243 | ||||||||
\(463\) | −15.5067 | −0.720658 | −0.360329 | − | 0.932825i | \(-0.617336\pi\) | ||||
−0.360329 | + | 0.932825i | \(0.617336\pi\) | |||||||
\(464\) | 7.13883 | 0.331412 | ||||||||
\(465\) | 0.495033 | 0.0229566 | ||||||||
\(466\) | 11.8271 | 0.547881 | ||||||||
\(467\) | −32.0065 | −1.48108 | −0.740542 | − | 0.672010i | \(-0.765431\pi\) | ||||
−0.740542 | + | 0.672010i | \(0.765431\pi\) | |||||||
\(468\) | 0.906814 | 0.0419175 | ||||||||
\(469\) | −8.03706 | −0.371117 | ||||||||
\(470\) | −0.298817 | −0.0137834 | ||||||||
\(471\) | 3.69078 | 0.170062 | ||||||||
\(472\) | 13.1462 | 0.605103 | ||||||||
\(473\) | 7.18252 | 0.330253 | ||||||||
\(474\) | −1.97180 | −0.0905677 | ||||||||
\(475\) | 4.96823 | 0.227958 | ||||||||
\(476\) | −26.2216 | −1.20187 | ||||||||
\(477\) | −8.95600 | −0.410067 | ||||||||
\(478\) | 5.54195 | 0.253483 | ||||||||
\(479\) | 4.50579 | 0.205875 | 0.102937 | − | 0.994688i | \(-0.467176\pi\) | ||||
0.102937 | + | 0.994688i | \(0.467176\pi\) | |||||||
\(480\) | −0.0624595 | −0.00285087 | ||||||||
\(481\) | −2.39067 | −0.109005 | ||||||||
\(482\) | −16.5329 | −0.753053 | ||||||||
\(483\) | −4.98832 | −0.226977 | ||||||||
\(484\) | −8.66746 | −0.393975 | ||||||||
\(485\) | −1.00442 | −0.0456082 | ||||||||
\(486\) | 8.95081 | 0.406017 | ||||||||
\(487\) | −3.49804 | −0.158511 | −0.0792557 | − | 0.996854i | \(-0.525254\pi\) | ||||
−0.0792557 | + | 0.996854i | \(0.525254\pi\) | |||||||
\(488\) | −3.19516 | −0.144638 | ||||||||
\(489\) | 0.946519 | 0.0428031 | ||||||||
\(490\) | 1.47509 | 0.0666376 | ||||||||
\(491\) | −19.9387 | −0.899821 | −0.449910 | − | 0.893074i | \(-0.648544\pi\) | ||||
−0.449910 | + | 0.893074i | \(0.648544\pi\) | |||||||
\(492\) | 2.04268 | 0.0920910 | ||||||||
\(493\) | 47.8936 | 2.15702 | ||||||||
\(494\) | −0.315173 | −0.0141803 | ||||||||
\(495\) | −0.783182 | −0.0352014 | ||||||||
\(496\) | 7.92567 | 0.355873 | ||||||||
\(497\) | −22.3548 | −1.00275 | ||||||||
\(498\) | 2.08955 | 0.0936348 | ||||||||
\(499\) | −3.53741 | −0.158356 | −0.0791782 | − | 0.996860i | \(-0.525230\pi\) | ||||
−0.0791782 | + | 0.996860i | \(0.525230\pi\) | |||||||
\(500\) | 1.77663 | 0.0794535 | ||||||||
\(501\) | −4.76274 | −0.212784 | ||||||||
\(502\) | 3.08097 | 0.137510 | ||||||||
\(503\) | −14.5430 | −0.648442 | −0.324221 | − | 0.945981i | \(-0.605102\pi\) | ||||
−0.324221 | + | 0.945981i | \(0.605102\pi\) | |||||||
\(504\) | −11.2455 | −0.500913 | ||||||||
\(505\) | −0.682928 | −0.0303899 | ||||||||
\(506\) | −5.56214 | −0.247267 | ||||||||
\(507\) | 4.52096 | 0.200783 | ||||||||
\(508\) | −2.71343 | −0.120389 | ||||||||
\(509\) | −16.2845 | −0.721796 | −0.360898 | − | 0.932605i | \(-0.617530\pi\) | ||||
−0.360898 | + | 0.932605i | \(0.617530\pi\) | |||||||
\(510\) | −0.419033 | −0.0185551 | ||||||||
\(511\) | −22.6166 | −1.00050 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.05962 | −0.0909346 | ||||||||
\(514\) | −0.207315 | −0.00914427 | ||||||||
\(515\) | 0.200107 | 0.00881776 | ||||||||
\(516\) | 1.64809 | 0.0725530 | ||||||||
\(517\) | 2.56059 | 0.112614 | ||||||||
\(518\) | 29.6468 | 1.30261 | ||||||||
\(519\) | −6.50859 | −0.285695 | ||||||||
\(520\) | −0.0561732 | −0.00246336 | ||||||||
\(521\) | 39.4238 | 1.72719 | 0.863593 | − | 0.504189i | \(-0.168209\pi\) | ||||
0.863593 | + | 0.504189i | \(0.168209\pi\) | |||||||
\(522\) | 20.5398 | 0.899002 | ||||||||
\(523\) | 1.49680 | 0.0654503 | 0.0327251 | − | 0.999464i | \(-0.489581\pi\) | ||||
0.0327251 | + | 0.999464i | \(0.489581\pi\) | |||||||
\(524\) | −5.20115 | −0.227213 | ||||||||
\(525\) | −6.80502 | −0.296996 | ||||||||
\(526\) | 13.4049 | 0.584482 | ||||||||
\(527\) | 53.1724 | 2.31623 | ||||||||
\(528\) | 0.535221 | 0.0232925 | ||||||||
\(529\) | −9.73663 | −0.423332 | ||||||||
\(530\) | 0.554786 | 0.0240984 | ||||||||
\(531\) | 37.8241 | 1.64143 | ||||||||
\(532\) | 3.90849 | 0.169455 | ||||||||
\(533\) | 1.83709 | 0.0795733 | ||||||||
\(534\) | 2.31831 | 0.100323 | ||||||||
\(535\) | 0.0751005 | 0.00324688 | ||||||||
\(536\) | −2.05631 | −0.0888189 | ||||||||
\(537\) | −4.54539 | −0.196148 | ||||||||
\(538\) | 11.2749 | 0.486094 | ||||||||
\(539\) | −12.6401 | −0.544449 | ||||||||
\(540\) | −0.367086 | −0.0157969 | ||||||||
\(541\) | −0.0467454 | −0.00200974 | −0.00100487 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100487 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(542\) | 23.7771 | 1.02131 | ||||||||
\(543\) | 3.49886 | 0.150151 | ||||||||
\(544\) | −6.70888 | −0.287641 | ||||||||
\(545\) | −3.53281 | −0.151329 | ||||||||
\(546\) | 0.431695 | 0.0184749 | ||||||||
\(547\) | 19.6108 | 0.838498 | 0.419249 | − | 0.907871i | \(-0.362294\pi\) | ||||
0.419249 | + | 0.907871i | \(0.362294\pi\) | |||||||
\(548\) | −10.8685 | −0.464278 | ||||||||
\(549\) | −9.19307 | −0.392351 | ||||||||
\(550\) | −7.58781 | −0.323545 | ||||||||
\(551\) | −7.13883 | −0.304125 | ||||||||
\(552\) | −1.27628 | −0.0543220 | ||||||||
\(553\) | 21.9914 | 0.935171 | ||||||||
\(554\) | 3.22032 | 0.136818 | ||||||||
\(555\) | 0.473770 | 0.0201104 | ||||||||
\(556\) | 0.716808 | 0.0303994 | ||||||||
\(557\) | 21.6090 | 0.915602 | 0.457801 | − | 0.889055i | \(-0.348637\pi\) | ||||
0.457801 | + | 0.889055i | \(0.348637\pi\) | |||||||
\(558\) | 22.8037 | 0.965356 | ||||||||
\(559\) | 1.48222 | 0.0626911 | ||||||||
\(560\) | 0.696609 | 0.0294371 | ||||||||
\(561\) | 3.59073 | 0.151601 | ||||||||
\(562\) | 24.0598 | 1.01490 | ||||||||
\(563\) | −33.0227 | −1.39174 | −0.695870 | − | 0.718168i | \(-0.744981\pi\) | ||||
−0.695870 | + | 0.718168i | \(0.744981\pi\) | |||||||
\(564\) | 0.587547 | 0.0247402 | ||||||||
\(565\) | −0.576855 | −0.0242685 | ||||||||
\(566\) | 17.9884 | 0.756108 | ||||||||
\(567\) | −30.9153 | −1.29832 | ||||||||
\(568\) | −5.71954 | −0.239987 | ||||||||
\(569\) | −28.6710 | −1.20195 | −0.600975 | − | 0.799268i | \(-0.705221\pi\) | ||||
−0.600975 | + | 0.799268i | \(0.705221\pi\) | |||||||
\(570\) | 0.0624595 | 0.00261614 | ||||||||
\(571\) | 16.0721 | 0.672595 | 0.336298 | − | 0.941756i | \(-0.390825\pi\) | ||||
0.336298 | + | 0.941756i | \(0.390825\pi\) | |||||||
\(572\) | 0.481354 | 0.0201264 | ||||||||
\(573\) | 0.130337 | 0.00544490 | ||||||||
\(574\) | −22.7819 | −0.950900 | ||||||||
\(575\) | 18.0938 | 0.754562 | ||||||||
\(576\) | −2.87719 | −0.119883 | ||||||||
\(577\) | −24.4920 | −1.01962 | −0.509808 | − | 0.860288i | \(-0.670284\pi\) | ||||
−0.509808 | + | 0.860288i | \(0.670284\pi\) | |||||||
\(578\) | −28.0090 | −1.16502 | ||||||||
\(579\) | −1.18193 | −0.0491193 | ||||||||
\(580\) | −1.27235 | −0.0528315 | ||||||||
\(581\) | −23.3047 | −0.966841 | ||||||||
\(582\) | 1.97493 | 0.0818636 | ||||||||
\(583\) | −4.75401 | −0.196891 | ||||||||
\(584\) | −5.78654 | −0.239449 | ||||||||
\(585\) | −0.161621 | −0.00668221 | ||||||||
\(586\) | 6.08806 | 0.251496 | ||||||||
\(587\) | 1.70612 | 0.0704190 | 0.0352095 | − | 0.999380i | \(-0.488790\pi\) | ||||
0.0352095 | + | 0.999380i | \(0.488790\pi\) | |||||||
\(588\) | −2.90038 | −0.119610 | ||||||||
\(589\) | −7.92567 | −0.326572 | ||||||||
\(590\) | −2.34304 | −0.0964616 | ||||||||
\(591\) | 9.20746 | 0.378744 | ||||||||
\(592\) | 7.58524 | 0.311751 | ||||||||
\(593\) | −18.4026 | −0.755705 | −0.377852 | − | 0.925866i | \(-0.623337\pi\) | ||||
−0.377852 | + | 0.925866i | \(0.623337\pi\) | |||||||
\(594\) | 3.14559 | 0.129065 | ||||||||
\(595\) | 4.67347 | 0.191593 | ||||||||
\(596\) | −12.5612 | −0.514527 | ||||||||
\(597\) | 2.19546 | 0.0898542 | ||||||||
\(598\) | −1.14783 | −0.0469382 | ||||||||
\(599\) | 36.7569 | 1.50185 | 0.750923 | − | 0.660390i | \(-0.229609\pi\) | ||||
0.750923 | + | 0.660390i | \(0.229609\pi\) | |||||||
\(600\) | −1.74109 | −0.0710796 | ||||||||
\(601\) | 14.5290 | 0.592649 | 0.296324 | − | 0.955087i | \(-0.404239\pi\) | ||||
0.296324 | + | 0.955087i | \(0.404239\pi\) | |||||||
\(602\) | −18.3811 | −0.749158 | ||||||||
\(603\) | −5.91638 | −0.240934 | ||||||||
\(604\) | 10.0366 | 0.408384 | ||||||||
\(605\) | 1.54480 | 0.0628050 | ||||||||
\(606\) | 1.34281 | 0.0545478 | ||||||||
\(607\) | −17.9592 | −0.728942 | −0.364471 | − | 0.931215i | \(-0.618750\pi\) | ||||
−0.364471 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 9.77811 | 0.396229 | ||||||||
\(610\) | 0.569471 | 0.0230572 | ||||||||
\(611\) | 0.528414 | 0.0213773 | ||||||||
\(612\) | −19.3027 | −0.780266 | ||||||||
\(613\) | −14.1782 | −0.572652 | −0.286326 | − | 0.958132i | \(-0.592434\pi\) | ||||
−0.286326 | + | 0.958132i | \(0.592434\pi\) | |||||||
\(614\) | 22.8889 | 0.923720 | ||||||||
\(615\) | −0.364065 | −0.0146805 | ||||||||
\(616\) | −5.96931 | −0.240510 | ||||||||
\(617\) | 31.1767 | 1.25513 | 0.627563 | − | 0.778565i | \(-0.284052\pi\) | ||||
0.627563 | + | 0.778565i | \(0.284052\pi\) | |||||||
\(618\) | −0.393460 | −0.0158273 | ||||||||
\(619\) | −4.33432 | −0.174211 | −0.0871056 | − | 0.996199i | \(-0.527762\pi\) | ||||
−0.0871056 | + | 0.996199i | \(0.527762\pi\) | |||||||
\(620\) | −1.41259 | −0.0567310 | ||||||||
\(621\) | −7.50093 | −0.301002 | ||||||||
\(622\) | −6.32785 | −0.253724 | ||||||||
\(623\) | −25.8560 | −1.03590 | ||||||||
\(624\) | 0.110451 | 0.00442156 | ||||||||
\(625\) | 24.5245 | 0.980981 | ||||||||
\(626\) | −8.71500 | −0.348322 | ||||||||
\(627\) | −0.535221 | −0.0213747 | ||||||||
\(628\) | −10.5317 | −0.420262 | ||||||||
\(629\) | 50.8884 | 2.02905 | ||||||||
\(630\) | 2.00428 | 0.0798523 | ||||||||
\(631\) | −35.6623 | −1.41969 | −0.709847 | − | 0.704356i | \(-0.751236\pi\) | ||||
−0.709847 | + | 0.704356i | \(0.751236\pi\) | |||||||
\(632\) | 5.62658 | 0.223813 | ||||||||
\(633\) | 0.350444 | 0.0139289 | ||||||||
\(634\) | 18.9379 | 0.752122 | ||||||||
\(635\) | 0.483614 | 0.0191916 | ||||||||
\(636\) | −1.09085 | −0.0432549 | ||||||||
\(637\) | −2.60848 | −0.103352 | ||||||||
\(638\) | 10.9029 | 0.431650 | ||||||||
\(639\) | −16.4562 | −0.650998 | ||||||||
\(640\) | 0.178230 | 0.00704514 | ||||||||
\(641\) | −22.6249 | −0.893628 | −0.446814 | − | 0.894627i | \(-0.647442\pi\) | ||||
−0.446814 | + | 0.894627i | \(0.647442\pi\) | |||||||
\(642\) | −0.147666 | −0.00582792 | ||||||||
\(643\) | 9.33857 | 0.368277 | 0.184139 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184139 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(644\) | 14.2343 | 0.560910 | ||||||||
\(645\) | −0.293738 | −0.0115659 | ||||||||
\(646\) | 6.70888 | 0.263957 | ||||||||
\(647\) | 15.8243 | 0.622118 | 0.311059 | − | 0.950391i | \(-0.399316\pi\) | ||||
0.311059 | + | 0.950391i | \(0.399316\pi\) | |||||||
\(648\) | −7.90979 | −0.310726 | ||||||||
\(649\) | 20.0778 | 0.788121 | ||||||||
\(650\) | −1.56586 | −0.0614179 | ||||||||
\(651\) | 10.8558 | 0.425474 | ||||||||
\(652\) | −2.70092 | −0.105776 | ||||||||
\(653\) | −5.01270 | −0.196162 | −0.0980811 | − | 0.995178i | \(-0.531270\pi\) | ||||
−0.0980811 | + | 0.995178i | \(0.531270\pi\) | |||||||
\(654\) | 6.94639 | 0.271625 | ||||||||
\(655\) | 0.926999 | 0.0362209 | ||||||||
\(656\) | −5.82883 | −0.227578 | ||||||||
\(657\) | −16.6490 | −0.649538 | ||||||||
\(658\) | −6.55291 | −0.255459 | ||||||||
\(659\) | −20.6192 | −0.803211 | −0.401606 | − | 0.915813i | \(-0.631548\pi\) | ||||
−0.401606 | + | 0.915813i | \(0.631548\pi\) | |||||||
\(660\) | −0.0953922 | −0.00371314 | ||||||||
\(661\) | −23.0752 | −0.897521 | −0.448761 | − | 0.893652i | \(-0.648134\pi\) | ||||
−0.448761 | + | 0.893652i | \(0.648134\pi\) | |||||||
\(662\) | 15.3285 | 0.595759 | ||||||||
\(663\) | 0.740999 | 0.0287780 | ||||||||
\(664\) | −5.96257 | −0.231393 | ||||||||
\(665\) | −0.696609 | −0.0270133 | ||||||||
\(666\) | 21.8242 | 0.845669 | ||||||||
\(667\) | −25.9989 | −1.00668 | ||||||||
\(668\) | 13.5906 | 0.525836 | ||||||||
\(669\) | −2.17774 | −0.0841963 | ||||||||
\(670\) | 0.366495 | 0.0141589 | ||||||||
\(671\) | −4.87985 | −0.188385 | ||||||||
\(672\) | −1.36971 | −0.0528376 | ||||||||
\(673\) | −32.8708 | −1.26708 | −0.633538 | − | 0.773712i | \(-0.718398\pi\) | ||||
−0.633538 | + | 0.773712i | \(0.718398\pi\) | |||||||
\(674\) | −3.20160 | −0.123321 | ||||||||
\(675\) | −10.2327 | −0.393857 | ||||||||
\(676\) | −12.9007 | −0.496179 | ||||||||
\(677\) | −27.6238 | −1.06167 | −0.530835 | − | 0.847475i | \(-0.678121\pi\) | ||||
−0.530835 | + | 0.847475i | \(0.678121\pi\) | |||||||
\(678\) | 1.13424 | 0.0435603 | ||||||||
\(679\) | −22.0264 | −0.845296 | ||||||||
\(680\) | 1.19572 | 0.0458538 | ||||||||
\(681\) | 6.04360 | 0.231591 | ||||||||
\(682\) | 12.1046 | 0.463509 | ||||||||
\(683\) | 28.4349 | 1.08803 | 0.544016 | − | 0.839075i | \(-0.316903\pi\) | ||||
0.544016 | + | 0.839075i | \(0.316903\pi\) | |||||||
\(684\) | 2.87719 | 0.110012 | ||||||||
\(685\) | 1.93708 | 0.0740121 | ||||||||
\(686\) | 4.98848 | 0.190461 | ||||||||
\(687\) | 0.275135 | 0.0104970 | ||||||||
\(688\) | −4.70286 | −0.179295 | ||||||||
\(689\) | −0.981059 | −0.0373754 | ||||||||
\(690\) | 0.227471 | 0.00865966 | ||||||||
\(691\) | 8.57183 | 0.326088 | 0.163044 | − | 0.986619i | \(-0.447869\pi\) | ||||
0.163044 | + | 0.986619i | \(0.447869\pi\) | |||||||
\(692\) | 18.5724 | 0.706018 | ||||||||
\(693\) | −17.1748 | −0.652418 | ||||||||
\(694\) | 7.73645 | 0.293672 | ||||||||
\(695\) | −0.127756 | −0.00484608 | ||||||||
\(696\) | 2.50176 | 0.0948290 | ||||||||
\(697\) | −39.1049 | −1.48120 | ||||||||
\(698\) | −18.1960 | −0.688728 | ||||||||
\(699\) | 4.14475 | 0.156769 | ||||||||
\(700\) | 19.4183 | 0.733943 | ||||||||
\(701\) | 23.0686 | 0.871288 | 0.435644 | − | 0.900119i | \(-0.356521\pi\) | ||||
0.435644 | + | 0.900119i | \(0.356521\pi\) | |||||||
\(702\) | 0.649139 | 0.0245002 | ||||||||
\(703\) | −7.58524 | −0.286083 | ||||||||
\(704\) | −1.52727 | −0.0575610 | ||||||||
\(705\) | −0.104718 | −0.00394392 | ||||||||
\(706\) | 11.8165 | 0.444718 | ||||||||
\(707\) | −14.9763 | −0.563242 | ||||||||
\(708\) | 4.60701 | 0.173142 | ||||||||
\(709\) | −17.6685 | −0.663554 | −0.331777 | − | 0.943358i | \(-0.607648\pi\) | ||||
−0.331777 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(710\) | 1.01939 | 0.0382571 | ||||||||
\(711\) | 16.1887 | 0.607125 | ||||||||
\(712\) | −6.61534 | −0.247921 | ||||||||
\(713\) | −28.8644 | −1.08098 | ||||||||
\(714\) | −9.18920 | −0.343897 | ||||||||
\(715\) | −0.0857915 | −0.00320842 | ||||||||
\(716\) | 12.9704 | 0.484726 | ||||||||
\(717\) | 1.94214 | 0.0725306 | ||||||||
\(718\) | 4.87578 | 0.181963 | ||||||||
\(719\) | −39.2821 | −1.46498 | −0.732488 | − | 0.680779i | \(-0.761641\pi\) | ||||
−0.732488 | + | 0.680779i | \(0.761641\pi\) | |||||||
\(720\) | 0.512800 | 0.0191109 | ||||||||
\(721\) | 4.38825 | 0.163427 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −5.79385 | −0.215476 | ||||||||
\(724\) | −9.98409 | −0.371056 | ||||||||
\(725\) | −35.4674 | −1.31723 | ||||||||
\(726\) | −3.03746 | −0.112731 | ||||||||
\(727\) | 26.8301 | 0.995072 | 0.497536 | − | 0.867443i | \(-0.334238\pi\) | ||||
0.497536 | + | 0.867443i | \(0.334238\pi\) | |||||||
\(728\) | −1.23185 | −0.0456555 | ||||||||
\(729\) | −20.5926 | −0.762689 | ||||||||
\(730\) | 1.03133 | 0.0381713 | ||||||||
\(731\) | −31.5509 | −1.16695 | ||||||||
\(732\) | −1.11972 | −0.0413861 | ||||||||
\(733\) | −19.3579 | −0.715002 | −0.357501 | − | 0.933913i | \(-0.616371\pi\) | ||||
−0.357501 | + | 0.933913i | \(0.616371\pi\) | |||||||
\(734\) | 20.7486 | 0.765844 | ||||||||
\(735\) | 0.516934 | 0.0190674 | ||||||||
\(736\) | 3.64189 | 0.134242 | ||||||||
\(737\) | −3.14053 | −0.115683 | ||||||||
\(738\) | −16.7706 | −0.617336 | ||||||||
\(739\) | 5.60953 | 0.206350 | 0.103175 | − | 0.994663i | \(-0.467100\pi\) | ||||
0.103175 | + | 0.994663i | \(0.467100\pi\) | |||||||
\(740\) | −1.35191 | −0.0496973 | ||||||||
\(741\) | −0.110451 | −0.00405750 | ||||||||
\(742\) | 12.1662 | 0.446635 | ||||||||
\(743\) | −31.1987 | −1.14457 | −0.572285 | − | 0.820055i | \(-0.693943\pi\) | ||||
−0.572285 | + | 0.820055i | \(0.693943\pi\) | |||||||
\(744\) | 2.77750 | 0.101828 | ||||||||
\(745\) | 2.23878 | 0.0820225 | ||||||||
\(746\) | −3.88759 | −0.142335 | ||||||||
\(747\) | −17.1555 | −0.627685 | ||||||||
\(748\) | −10.2462 | −0.374640 | ||||||||
\(749\) | 1.64692 | 0.0601771 | ||||||||
\(750\) | 0.622610 | 0.0227345 | ||||||||
\(751\) | 1.29229 | 0.0471564 | 0.0235782 | − | 0.999722i | \(-0.492494\pi\) | ||||
0.0235782 | + | 0.999722i | \(0.492494\pi\) | |||||||
\(752\) | −1.67658 | −0.0611386 | ||||||||
\(753\) | 1.07970 | 0.0393466 | ||||||||
\(754\) | 2.24997 | 0.0819391 | ||||||||
\(755\) | −1.78882 | −0.0651019 | ||||||||
\(756\) | −8.05003 | −0.292777 | ||||||||
\(757\) | −28.4963 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(758\) | −2.86778 | −0.104163 | ||||||||
\(759\) | −1.94922 | −0.0707520 | ||||||||
\(760\) | −0.178230 | −0.00646507 | ||||||||
\(761\) | 34.8944 | 1.26492 | 0.632460 | − | 0.774593i | \(-0.282045\pi\) | ||||
0.632460 | + | 0.774593i | \(0.282045\pi\) | |||||||
\(762\) | −0.950905 | −0.0344477 | ||||||||
\(763\) | −77.4729 | −2.80471 | ||||||||
\(764\) | −0.371920 | −0.0134556 | ||||||||
\(765\) | 3.44032 | 0.124385 | ||||||||
\(766\) | −10.3522 | −0.374042 | ||||||||
\(767\) | 4.14334 | 0.149607 | ||||||||
\(768\) | −0.350444 | −0.0126455 | ||||||||
\(769\) | −23.3590 | −0.842346 | −0.421173 | − | 0.906980i | \(-0.638382\pi\) | ||||
−0.421173 | + | 0.906980i | \(0.638382\pi\) | |||||||
\(770\) | 1.06391 | 0.0383406 | ||||||||
\(771\) | −0.0726522 | −0.00261651 | ||||||||
\(772\) | 3.37266 | 0.121385 | ||||||||
\(773\) | 29.8991 | 1.07540 | 0.537698 | − | 0.843137i | \(-0.319294\pi\) | ||||
0.537698 | + | 0.843137i | \(0.319294\pi\) | |||||||
\(774\) | −13.5310 | −0.486363 | ||||||||
\(775\) | −39.3766 | −1.41445 | ||||||||
\(776\) | −5.63552 | −0.202303 | ||||||||
\(777\) | 10.3896 | 0.372723 | ||||||||
\(778\) | −16.1807 | −0.580106 | ||||||||
\(779\) | 5.82883 | 0.208839 | ||||||||
\(780\) | −0.0196856 | −0.000704856 0 | ||||||||
\(781\) | −8.73526 | −0.312572 | ||||||||
\(782\) | 24.4330 | 0.873722 | ||||||||
\(783\) | 14.7033 | 0.525454 | ||||||||
\(784\) | 8.27632 | 0.295583 | ||||||||
\(785\) | 1.87707 | 0.0669954 | ||||||||
\(786\) | −1.82271 | −0.0650140 | ||||||||
\(787\) | −41.2586 | −1.47071 | −0.735356 | − | 0.677681i | \(-0.762985\pi\) | ||||
−0.735356 | + | 0.677681i | \(0.762985\pi\) | |||||||
\(788\) | −26.2737 | −0.935963 | ||||||||
\(789\) | 4.69767 | 0.167242 | ||||||||
\(790\) | −1.00282 | −0.0356788 | ||||||||
\(791\) | −12.6502 | −0.449788 | ||||||||
\(792\) | −4.39423 | −0.156142 | ||||||||
\(793\) | −1.00703 | −0.0357606 | ||||||||
\(794\) | −7.66033 | −0.271855 | ||||||||
\(795\) | 0.194421 | 0.00689541 | ||||||||
\(796\) | −6.26480 | −0.222050 | ||||||||
\(797\) | −25.2412 | −0.894088 | −0.447044 | − | 0.894512i | \(-0.647523\pi\) | ||||
−0.447044 | + | 0.894512i | \(0.647523\pi\) | |||||||
\(798\) | 1.36971 | 0.0484871 | ||||||||
\(799\) | −11.2480 | −0.397925 | ||||||||
\(800\) | 4.96823 | 0.175654 | ||||||||
\(801\) | −19.0336 | −0.672519 | ||||||||
\(802\) | −36.2291 | −1.27929 | ||||||||
\(803\) | −8.83758 | −0.311871 | ||||||||
\(804\) | −0.720620 | −0.0254143 | ||||||||
\(805\) | −2.53698 | −0.0894166 | ||||||||
\(806\) | 2.49796 | 0.0879870 | ||||||||
\(807\) | 3.95121 | 0.139089 | ||||||||
\(808\) | −3.83173 | −0.134800 | ||||||||
\(809\) | 1.69656 | 0.0596478 | 0.0298239 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298239 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(810\) | 1.40976 | 0.0495339 | ||||||||
\(811\) | −23.1413 | −0.812600 | −0.406300 | − | 0.913740i | \(-0.633181\pi\) | ||||
−0.406300 | + | 0.913740i | \(0.633181\pi\) | |||||||
\(812\) | −27.9021 | −0.979171 | ||||||||
\(813\) | 8.33253 | 0.292235 | ||||||||
\(814\) | 11.5847 | 0.406043 | ||||||||
\(815\) | 0.481383 | 0.0168621 | ||||||||
\(816\) | −2.35108 | −0.0823044 | ||||||||
\(817\) | 4.70286 | 0.164532 | ||||||||
\(818\) | 6.16561 | 0.215575 | ||||||||
\(819\) | −3.54428 | −0.123847 | ||||||||
\(820\) | 1.03887 | 0.0362789 | ||||||||
\(821\) | 37.2451 | 1.29986 | 0.649931 | − | 0.759993i | \(-0.274798\pi\) | ||||
0.649931 | + | 0.759993i | \(0.274798\pi\) | |||||||
\(822\) | −3.80879 | −0.132847 | ||||||||
\(823\) | −18.5852 | −0.647839 | −0.323919 | − | 0.946085i | \(-0.605001\pi\) | ||||
−0.323919 | + | 0.946085i | \(0.605001\pi\) | |||||||
\(824\) | 1.12275 | 0.0391127 | ||||||||
\(825\) | −2.65910 | −0.0925780 | ||||||||
\(826\) | −51.3819 | −1.78780 | ||||||||
\(827\) | 11.8046 | 0.410486 | 0.205243 | − | 0.978711i | \(-0.434201\pi\) | ||||
0.205243 | + | 0.978711i | \(0.434201\pi\) | |||||||
\(828\) | 10.4784 | 0.364150 | ||||||||
\(829\) | −14.2287 | −0.494182 | −0.247091 | − | 0.968992i | \(-0.579475\pi\) | ||||
−0.247091 | + | 0.968992i | \(0.579475\pi\) | |||||||
\(830\) | 1.06271 | 0.0368871 | ||||||||
\(831\) | 1.12854 | 0.0391486 | ||||||||
\(832\) | −0.315173 | −0.0109267 | ||||||||
\(833\) | 55.5248 | 1.92382 | ||||||||
\(834\) | 0.251201 | 0.00869838 | ||||||||
\(835\) | −2.42225 | −0.0838254 | ||||||||
\(836\) | 1.52727 | 0.0528216 | ||||||||
\(837\) | 16.3239 | 0.564237 | ||||||||
\(838\) | −22.0812 | −0.762783 | ||||||||
\(839\) | −33.7128 | −1.16390 | −0.581948 | − | 0.813226i | \(-0.697709\pi\) | ||||
−0.581948 | + | 0.813226i | \(0.697709\pi\) | |||||||
\(840\) | 0.244122 | 0.00842302 | ||||||||
\(841\) | 21.9630 | 0.757343 | ||||||||
\(842\) | 5.97402 | 0.205878 | ||||||||
\(843\) | 8.43160 | 0.290400 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 2.29928 | 0.0790977 | ||||||||
\(846\) | −4.82384 | −0.165847 | ||||||||
\(847\) | 33.8767 | 1.16402 | ||||||||
\(848\) | 3.11276 | 0.106893 | ||||||||
\(849\) | 6.30391 | 0.216350 | ||||||||
\(850\) | 33.3313 | 1.14325 | ||||||||
\(851\) | −27.6246 | −0.946959 | ||||||||
\(852\) | −2.00438 | −0.0686689 | ||||||||
\(853\) | 5.09969 | 0.174610 | 0.0873050 | − | 0.996182i | \(-0.472175\pi\) | ||||
0.0873050 | + | 0.996182i | \(0.472175\pi\) | |||||||
\(854\) | 12.4882 | 0.427339 | ||||||||
\(855\) | −0.512800 | −0.0175374 | ||||||||
\(856\) | 0.421369 | 0.0144021 | ||||||||
\(857\) | 12.5681 | 0.429318 | 0.214659 | − | 0.976689i | \(-0.431136\pi\) | ||||
0.214659 | + | 0.976689i | \(0.431136\pi\) | |||||||
\(858\) | 0.168687 | 0.00575889 | ||||||||
\(859\) | −36.7667 | −1.25447 | −0.627233 | − | 0.778832i | \(-0.715812\pi\) | ||||
−0.627233 | + | 0.778832i | \(0.715812\pi\) | |||||||
\(860\) | 0.838189 | 0.0285820 | ||||||||
\(861\) | −7.98379 | −0.272087 | ||||||||
\(862\) | −30.4508 | −1.03716 | ||||||||
\(863\) | −3.51129 | −0.119526 | −0.0597629 | − | 0.998213i | \(-0.519034\pi\) | ||||
−0.0597629 | + | 0.998213i | \(0.519034\pi\) | |||||||
\(864\) | −2.05962 | −0.0700698 | ||||||||
\(865\) | −3.31016 | −0.112549 | ||||||||
\(866\) | 13.8536 | 0.470763 | ||||||||
\(867\) | −9.81560 | −0.333355 | ||||||||
\(868\) | −30.9774 | −1.05144 | ||||||||
\(869\) | 8.59328 | 0.291507 | ||||||||
\(870\) | −0.445888 | −0.0151170 | ||||||||
\(871\) | −0.648093 | −0.0219598 | ||||||||
\(872\) | −19.8217 | −0.671247 | ||||||||
\(873\) | −16.2145 | −0.548776 | ||||||||
\(874\) | −3.64189 | −0.123189 | ||||||||
\(875\) | −6.94396 | −0.234749 | ||||||||
\(876\) | −2.02786 | −0.0685149 | ||||||||
\(877\) | −26.0693 | −0.880297 | −0.440149 | − | 0.897925i | \(-0.645074\pi\) | ||||
−0.440149 | + | 0.897925i | \(0.645074\pi\) | |||||||
\(878\) | −2.92118 | −0.0985852 | ||||||||
\(879\) | 2.13352 | 0.0719620 | ||||||||
\(880\) | 0.272204 | 0.00917600 | ||||||||
\(881\) | −3.66429 | −0.123453 | −0.0617266 | − | 0.998093i | \(-0.519661\pi\) | ||||
−0.0617266 | + | 0.998093i | \(0.519661\pi\) | |||||||
\(882\) | 23.8125 | 0.801810 | ||||||||
\(883\) | −50.1886 | −1.68898 | −0.844490 | − | 0.535571i | \(-0.820096\pi\) | ||||
−0.844490 | + | 0.535571i | \(0.820096\pi\) | |||||||
\(884\) | −2.11446 | −0.0711170 | ||||||||
\(885\) | −0.821105 | −0.0276012 | ||||||||
\(886\) | −26.4299 | −0.887930 | ||||||||
\(887\) | 2.58173 | 0.0866861 | 0.0433431 | − | 0.999060i | \(-0.486199\pi\) | ||||
0.0433431 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(888\) | 2.65820 | 0.0892033 | ||||||||
\(889\) | 10.6054 | 0.355695 | ||||||||
\(890\) | 1.17905 | 0.0395219 | ||||||||
\(891\) | −12.0803 | −0.404707 | ||||||||
\(892\) | 6.21424 | 0.208068 | ||||||||
\(893\) | 1.67658 | 0.0561047 | ||||||||
\(894\) | −4.40199 | −0.147225 | ||||||||
\(895\) | −2.31171 | −0.0772718 | ||||||||
\(896\) | 3.90849 | 0.130574 | ||||||||
\(897\) | −0.402249 | −0.0134307 | ||||||||
\(898\) | −14.6511 | −0.488914 | ||||||||
\(899\) | 56.5801 | 1.88705 | ||||||||
\(900\) | 14.2945 | 0.476485 | ||||||||
\(901\) | 20.8831 | 0.695718 | ||||||||
\(902\) | −8.90217 | −0.296410 | ||||||||
\(903\) | −6.44154 | −0.214361 | ||||||||
\(904\) | −3.23659 | −0.107647 | ||||||||
\(905\) | 1.77946 | 0.0591513 | ||||||||
\(906\) | 3.51727 | 0.116853 | ||||||||
\(907\) | 57.4999 | 1.90925 | 0.954626 | − | 0.297808i | \(-0.0962555\pi\) | ||||
0.954626 | + | 0.297808i | \(0.0962555\pi\) | |||||||
\(908\) | −17.2456 | −0.572314 | ||||||||
\(909\) | −11.0246 | −0.365664 | ||||||||
\(910\) | 0.219553 | 0.00727810 | ||||||||
\(911\) | 0.499116 | 0.0165365 | 0.00826823 | − | 0.999966i | \(-0.497368\pi\) | ||||
0.00826823 | + | 0.999966i | \(0.497368\pi\) | |||||||
\(912\) | 0.350444 | 0.0116044 | ||||||||
\(913\) | −9.10644 | −0.301379 | ||||||||
\(914\) | 38.6663 | 1.27897 | ||||||||
\(915\) | 0.199568 | 0.00659750 | ||||||||
\(916\) | −0.785104 | −0.0259406 | ||||||||
\(917\) | 20.3287 | 0.671312 | ||||||||
\(918\) | −13.8178 | −0.456054 | ||||||||
\(919\) | 4.17123 | 0.137596 | 0.0687981 | − | 0.997631i | \(-0.478084\pi\) | ||||
0.0687981 | + | 0.997631i | \(0.478084\pi\) | |||||||
\(920\) | −0.649093 | −0.0214000 | ||||||||
\(921\) | 8.02126 | 0.264310 | ||||||||
\(922\) | −15.1128 | −0.497714 | ||||||||
\(923\) | −1.80265 | −0.0593349 | ||||||||
\(924\) | −2.09191 | −0.0688187 | ||||||||
\(925\) | −37.6852 | −1.23908 | ||||||||
\(926\) | 15.5067 | 0.509582 | ||||||||
\(927\) | 3.23036 | 0.106099 | ||||||||
\(928\) | −7.13883 | −0.234344 | ||||||||
\(929\) | −11.3410 | −0.372085 | −0.186042 | − | 0.982542i | \(-0.559566\pi\) | ||||
−0.186042 | + | 0.982542i | \(0.559566\pi\) | |||||||
\(930\) | −0.495033 | −0.0162328 | ||||||||
\(931\) | −8.27632 | −0.271245 | ||||||||
\(932\) | −11.8271 | −0.387411 | ||||||||
\(933\) | −2.21756 | −0.0725995 | ||||||||
\(934\) | 32.0065 | 1.04728 | ||||||||
\(935\) | 1.82618 | 0.0597226 | ||||||||
\(936\) | −0.906814 | −0.0296401 | ||||||||
\(937\) | 31.2345 | 1.02039 | 0.510194 | − | 0.860059i | \(-0.329574\pi\) | ||||
0.510194 | + | 0.860059i | \(0.329574\pi\) | |||||||
\(938\) | 8.03706 | 0.262419 | ||||||||
\(939\) | −3.05412 | −0.0996674 | ||||||||
\(940\) | 0.298817 | 0.00974632 | ||||||||
\(941\) | −8.50659 | −0.277307 | −0.138653 | − | 0.990341i | \(-0.544277\pi\) | ||||
−0.138653 | + | 0.990341i | \(0.544277\pi\) | |||||||
\(942\) | −3.69078 | −0.120252 | ||||||||
\(943\) | 21.2280 | 0.691277 | ||||||||
\(944\) | −13.1462 | −0.427873 | ||||||||
\(945\) | 1.43475 | 0.0466725 | ||||||||
\(946\) | −7.18252 | −0.233524 | ||||||||
\(947\) | 21.4703 | 0.697691 | 0.348846 | − | 0.937180i | \(-0.386574\pi\) | ||||
0.348846 | + | 0.937180i | \(0.386574\pi\) | |||||||
\(948\) | 1.97180 | 0.0640411 | ||||||||
\(949\) | −1.82376 | −0.0592019 | ||||||||
\(950\) | −4.96823 | −0.161191 | ||||||||
\(951\) | 6.63668 | 0.215209 | ||||||||
\(952\) | 26.2216 | 0.849847 | ||||||||
\(953\) | −25.9185 | −0.839582 | −0.419791 | − | 0.907621i | \(-0.637897\pi\) | ||||
−0.419791 | + | 0.907621i | \(0.637897\pi\) | |||||||
\(954\) | 8.95600 | 0.289961 | ||||||||
\(955\) | 0.0662871 | 0.00214500 | ||||||||
\(956\) | −5.54195 | −0.179239 | ||||||||
\(957\) | 3.82085 | 0.123511 | ||||||||
\(958\) | −4.50579 | −0.145575 | ||||||||
\(959\) | 42.4793 | 1.37173 | ||||||||
\(960\) | 0.0624595 | 0.00201587 | ||||||||
\(961\) | 31.8163 | 1.02633 | ||||||||
\(962\) | 2.39067 | 0.0770782 | ||||||||
\(963\) | 1.21236 | 0.0390677 | ||||||||
\(964\) | 16.5329 | 0.532489 | ||||||||
\(965\) | −0.601108 | −0.0193504 | ||||||||
\(966\) | 4.98832 | 0.160497 | ||||||||
\(967\) | 31.6303 | 1.01716 | 0.508580 | − | 0.861015i | \(-0.330171\pi\) | ||||
0.508580 | + | 0.861015i | \(0.330171\pi\) | |||||||
\(968\) | 8.66746 | 0.278583 | ||||||||
\(969\) | 2.35108 | 0.0755277 | ||||||||
\(970\) | 1.00442 | 0.0322499 | ||||||||
\(971\) | 47.7418 | 1.53211 | 0.766053 | − | 0.642777i | \(-0.222218\pi\) | ||||
0.766053 | + | 0.642777i | \(0.222218\pi\) | |||||||
\(972\) | −8.95081 | −0.287097 | ||||||||
\(973\) | −2.80164 | −0.0898165 | ||||||||
\(974\) | 3.49804 | 0.112085 | ||||||||
\(975\) | −0.548744 | −0.0175739 | ||||||||
\(976\) | 3.19516 | 0.102274 | ||||||||
\(977\) | 43.2744 | 1.38447 | 0.692236 | − | 0.721671i | \(-0.256626\pi\) | ||||
0.692236 | + | 0.721671i | \(0.256626\pi\) | |||||||
\(978\) | −0.946519 | −0.0302663 | ||||||||
\(979\) | −10.1034 | −0.322906 | ||||||||
\(980\) | −1.47509 | −0.0471199 | ||||||||
\(981\) | −57.0308 | −1.82085 | ||||||||
\(982\) | 19.9387 | 0.636269 | ||||||||
\(983\) | 12.5169 | 0.399228 | 0.199614 | − | 0.979875i | \(-0.436031\pi\) | ||||
0.199614 | + | 0.979875i | \(0.436031\pi\) | |||||||
\(984\) | −2.04268 | −0.0651181 | ||||||||
\(985\) | 4.68276 | 0.149205 | ||||||||
\(986\) | −47.8936 | −1.52524 | ||||||||
\(987\) | −2.29643 | −0.0730960 | ||||||||
\(988\) | 0.315173 | 0.0100270 | ||||||||
\(989\) | 17.1273 | 0.544617 | ||||||||
\(990\) | 0.783182 | 0.0248912 | ||||||||
\(991\) | −3.47662 | −0.110439 | −0.0552193 | − | 0.998474i | \(-0.517586\pi\) | ||||
−0.0552193 | + | 0.998474i | \(0.517586\pi\) | |||||||
\(992\) | −7.92567 | −0.251640 | ||||||||
\(993\) | 5.37177 | 0.170468 | ||||||||
\(994\) | 22.3548 | 0.709051 | ||||||||
\(995\) | 1.11657 | 0.0353977 | ||||||||
\(996\) | −2.08955 | −0.0662098 | ||||||||
\(997\) | −34.8244 | −1.10290 | −0.551450 | − | 0.834208i | \(-0.685925\pi\) | ||||
−0.551450 | + | 0.834208i | \(0.685925\pi\) | |||||||
\(998\) | 3.53741 | 0.111975 | ||||||||
\(999\) | 15.6227 | 0.494282 |
(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 | 8018.2.a.f.1.19 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.19 | ✓ | 34 | 1.1 | even | 1 | trivial |