Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(191,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.4 | ||
Character | \(\chi\) | \(=\) | 912.191 |
Dual form | 912.2.d.b.191.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57777 | + | 0.714595i | −0.910925 | + | 0.412572i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.85004i | 0.827365i | 0.910421 | + | 0.413683i | \(0.135758\pi\) | ||||
−0.910421 | + | 0.413683i | \(0.864242\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707624i | 0.267457i | 0.991018 | + | 0.133728i | \(0.0426949\pi\) | ||||
−0.991018 | + | 0.133728i | \(0.957305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.97871 | − | 2.25493i | 0.659569 | − | 0.751644i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.63214 | −1.39664 | −0.698321 | − | 0.715785i | \(-0.746069\pi\) | ||||
−0.698321 | + | 0.715785i | \(0.746069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.78223 | −0.494302 | −0.247151 | − | 0.968977i | \(-0.579494\pi\) | ||||
−0.247151 | + | 0.968977i | \(0.579494\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.32203 | − | 2.91894i | −0.341348 | − | 0.753668i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.47660i | 0.358128i | 0.983837 | + | 0.179064i | \(0.0573069\pi\) | ||||
−0.983837 | + | 0.179064i | \(0.942693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.505665 | − | 1.11647i | −0.110345 | − | 0.243633i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.68346 | −0.559540 | −0.279770 | − | 0.960067i | \(-0.590258\pi\) | ||||
−0.279770 | + | 0.960067i | \(0.590258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.57733 | 0.315467 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.51058 | + | 4.97174i | −0.290711 | + | 0.956811i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.44439i | − | 0.453913i | −0.973905 | − | 0.226956i | \(-0.927123\pi\) | ||
0.973905 | − | 0.226956i | \(-0.0728775\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.63667i | − | 1.19198i | −0.802991 | − | 0.595991i | \(-0.796759\pi\) | ||
0.802991 | − | 0.595991i | \(-0.203241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.30844 | − | 3.31010i | 1.27224 | − | 0.576215i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.30914 | −0.221284 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.04433 | −0.500484 | −0.250242 | − | 0.968183i | \(-0.580510\pi\) | ||||
−0.250242 | + | 0.968183i | \(0.580510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.81195 | − | 1.27357i | 0.450272 | − | 0.203935i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.95675i | − | 0.774114i | −0.922056 | − | 0.387057i | \(-0.873492\pi\) | ||
0.922056 | − | 0.387057i | \(-0.126508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.80404i | − | 1.03761i | −0.854894 | − | 0.518803i | \(-0.826378\pi\) | ||
0.854894 | − | 0.518803i | \(-0.173622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.17173 | + | 3.66070i | 0.621884 | + | 0.545704i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.19420 | −1.19525 | −0.597624 | − | 0.801777i | \(-0.703888\pi\) | ||||
−0.597624 | + | 0.801777i | \(0.703888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.49927 | 0.928467 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.05517 | − | 2.32973i | −0.147753 | − | 0.326228i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.89976i | − | 0.535674i | −0.963464 | − | 0.267837i | \(-0.913691\pi\) | ||
0.963464 | − | 0.267837i | \(-0.0863088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.56966i | − | 1.15553i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.714595 | − | 1.57777i | −0.0946505 | − | 0.208981i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.14537 | −1.06044 | −0.530218 | − | 0.847861i | \(-0.677890\pi\) | ||||
−0.530218 | + | 0.847861i | \(0.677890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9620 | −1.53158 | −0.765792 | − | 0.643089i | \(-0.777653\pi\) | ||||
−0.765792 | + | 0.643089i | \(0.777653\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.59564 | + | 1.40018i | 0.201032 | + | 0.176406i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.29720i | − | 0.408968i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.84424i | − | 0.591818i | −0.955216 | − | 0.295909i | \(-0.904378\pi\) | ||
0.955216 | − | 0.295909i | \(-0.0956224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.23388 | − | 1.91759i | 0.509699 | − | 0.230850i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.09961 | 0.723891 | 0.361945 | − | 0.932199i | \(-0.382113\pi\) | ||||
0.361945 | + | 0.932199i | \(0.382113\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0559 | −1.76215 | −0.881077 | − | 0.472973i | \(-0.843181\pi\) | ||||
−0.881077 | + | 0.472973i | \(0.843181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.48867 | + | 1.12716i | −0.287367 | + | 0.130153i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.27781i | − | 0.373541i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.21403i | 0.249098i | 0.992213 | + | 0.124549i | \(0.0397485\pi\) | ||||
−0.992213 | + | 0.124549i | \(0.960252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.16944 | − | 8.92370i | −0.129937 | − | 0.991522i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.65489 | 0.291412 | 0.145706 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145706 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73177 | −0.296302 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.74675 | + | 3.85669i | 0.187272 | + | 0.413480i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.9884i | − | 1.16477i | −0.812914 | − | 0.582384i | \(-0.802120\pi\) | ||
0.812914 | − | 0.582384i | \(-0.197880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.26115i | − | 0.132204i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.74253 | + | 10.4711i | 0.491778 | + | 1.08581i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85004 | −0.189811 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.45643 | −0.960155 | −0.480077 | − | 0.877226i | \(-0.659391\pi\) | ||||
−0.480077 | + | 0.877226i | \(0.659391\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.16564 | + | 10.4452i | −0.921182 | + | 1.04978i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.11881i | 0.310333i | 0.987888 | + | 0.155167i | \(0.0495915\pi\) | ||||
−0.987888 | + | 0.155167i | \(0.950409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3329i | 1.51080i | 0.655264 | + | 0.755400i | \(0.272557\pi\) | ||||
−0.655264 | + | 0.755400i | \(0.727443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.06551 | − | 0.935502i | 0.201573 | − | 0.0912957i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4792 | 1.30308 | 0.651542 | − | 0.758613i | \(-0.274122\pi\) | ||||
0.651542 | + | 0.758613i | \(0.274122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.05566 | 0.388461 | 0.194231 | − | 0.980956i | \(-0.437779\pi\) | ||||
0.194231 | + | 0.980956i | \(0.437779\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.80324 | − | 2.17546i | 0.455904 | − | 0.206486i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.64136i | 0.906983i | 0.891261 | + | 0.453491i | \(0.149822\pi\) | ||||
−0.891261 | + | 0.453491i | \(0.850178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.96452i | − | 0.462944i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.52651 | + | 4.01881i | −0.326026 | + | 0.371539i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.04488 | −0.0957837 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4567 | 0.950608 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.54207 | + | 7.82060i | 0.319378 | + | 0.705160i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1684i | 1.08837i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.70658i | 0.328905i | 0.986385 | + | 0.164453i | \(0.0525858\pi\) | ||||
−0.986385 | + | 0.164453i | \(0.947414\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.86214 | + | 10.7352i | 0.428087 | + | 0.945182i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0121090 | −0.00105797 | −0.000528983 | − | 1.00000i | \(-0.500168\pi\) | ||||
−0.000528983 | 1.00000i | \(0.500168\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.707624 | −0.0613588 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.19793 | − | 2.79464i | −0.791632 | − | 0.240524i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.5314i | − | 1.41237i | −0.708028 | − | 0.706184i | \(-0.750415\pi\) | ||
0.708028 | − | 0.706184i | \(-0.249585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.09796i | − | 0.347585i | −0.984782 | − | 0.173792i | \(-0.944398\pi\) | ||
0.984782 | − | 0.173792i | \(-0.0556022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9286 | − | 5.85554i | 1.08878 | − | 0.493125i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.25553 | 0.690362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.52224 | 0.375552 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.2543 | + | 4.64435i | −0.845764 | + | 0.383059i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.8009i | 1.78600i | 0.450059 | + | 0.892999i | \(0.351403\pi\) | ||||
−0.450059 | + | 0.892999i | \(0.648597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.6817i | − | 1.52030i | −0.649750 | − | 0.760148i | \(-0.725127\pi\) | ||
0.649750 | − | 0.760148i | \(-0.274873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.32963 | + | 2.92176i | 0.269185 | + | 0.236210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.2781 | 0.986204 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1885 | −0.813127 | −0.406564 | − | 0.913622i | \(-0.633273\pi\) | ||||
−0.406564 | + | 0.913622i | \(0.633273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.78675 | + | 6.15292i | 0.221004 | + | 0.487958i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.89888i | − | 0.149653i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.10007i | 0.399469i | 0.979850 | + | 0.199734i | \(0.0640079\pi\) | ||||
−0.979850 | + | 0.199734i | \(0.935992\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.12384 | + | 13.5209i | 0.476740 | + | 1.05260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8667 | 0.995655 | 0.497827 | − | 0.867276i | \(-0.334131\pi\) | ||||
0.497827 | + | 0.867276i | \(0.334131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.82366 | −0.755666 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.25493 | + | 1.97871i | 0.172439 | + | 0.151316i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9225i | 0.906454i | 0.891395 | + | 0.453227i | \(0.149727\pi\) | ||||
−0.891395 | + | 0.453227i | \(0.850273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.11616i | 0.0843737i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8515 | − | 5.82064i | 0.965978 | − | 0.437506i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.28974 | −0.0963997 | −0.0481998 | − | 0.998838i | \(-0.515348\pi\) | ||||
−0.0481998 | + | 0.998838i | \(0.515348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7046 | −1.09298 | −0.546491 | − | 0.837465i | \(-0.684037\pi\) | ||||
−0.546491 | + | 0.837465i | \(0.684037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.8733 | − | 8.54802i | 1.39516 | − | 0.631888i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.63214i | − | 0.414083i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.83981i | − | 0.500176i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.51812 | − | 1.06892i | −0.255905 | − | 0.0777525i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.82987 | −0.349477 | −0.174739 | − | 0.984615i | \(-0.555908\pi\) | ||||
−0.174739 | + | 0.984615i | \(0.555908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.27363 | −0.163659 | −0.0818297 | − | 0.996646i | \(-0.526076\pi\) | ||||
−0.0818297 | + | 0.996646i | \(0.526076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.35617 | + | 5.20223i | 0.168729 | + | 0.372539i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5158i | 1.31919i | 0.751619 | + | 0.659597i | \(0.229273\pi\) | ||||
−0.751619 | + | 0.659597i | \(0.770727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8189i | 0.908710i | 0.890821 | + | 0.454355i | \(0.150130\pi\) | ||||
−0.890821 | + | 0.454355i | \(0.849870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.46167 | + | 7.64308i | 0.244167 | + | 0.539101i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.72971 | 0.121402 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.17020 | 0.640475 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.30978 | + | 6.05102i | −0.369055 | + | 0.420575i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.63214i | − | 0.320412i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1596i | 1.04363i | 0.853059 | + | 0.521815i | \(0.174745\pi\) | ||||
−0.853059 | + | 0.521815i | \(0.825255\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.62378 | + | 4.35875i | −0.659410 | + | 0.298657i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.5878 | 0.858480 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.69627 | 0.318803 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.7546 | − | 10.7588i | 1.60519 | − | 0.727015i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.63164i | − | 0.177023i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0080i | 1.00501i | 0.864574 | + | 0.502505i | \(0.167588\pi\) | ||||
−0.864574 | + | 0.502505i | \(0.832412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.12108 | − | 3.55678i | 0.208072 | − | 0.237119i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5512 | 1.29766 | 0.648830 | − | 0.760933i | \(-0.275259\pi\) | ||||
0.648830 | + | 0.760933i | \(0.275259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3435 | −0.947845 | −0.473923 | − | 0.880566i | \(-0.657162\pi\) | ||||
−0.473923 | + | 0.880566i | \(0.657162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.34231 | + | 5.17162i | 0.154112 | + | 0.340268i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.893124i | 0.0585105i | 0.999572 | + | 0.0292553i | \(0.00931357\pi\) | ||||
−0.999572 | + | 0.0292553i | \(0.990686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 15.1596i | − | 0.988906i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.58214 | − | 3.49323i | −0.102771 | − | 0.226910i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.7339 | −1.79396 | −0.896978 | − | 0.442075i | \(-0.854243\pi\) | ||||
−0.896978 | + | 0.442075i | \(0.854243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8414 | −1.66459 | −0.832294 | − | 0.554334i | \(-0.812973\pi\) | ||||
−0.832294 | + | 0.554334i | \(0.812973\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.22193 | + | 13.2439i | 0.527437 | + | 0.849594i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0239i | 0.768181i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.78223i | − | 0.113401i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.18881 | + | 1.89717i | −0.265455 | + | 0.120229i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.39616 | 0.214363 | 0.107182 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107182 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4301 | 0.781477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.31011 | − | 1.95211i | 0.269909 | − | 0.122246i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6927i | 1.54029i | 0.637868 | + | 0.770145i | \(0.279816\pi\) | ||||
−0.637868 | + | 0.770145i | \(0.720184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.15424i | − | 0.133858i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.51194 | − | 4.83674i | −0.341181 | − | 0.299387i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.4827 | −1.07803 | −0.539014 | − | 0.842297i | \(-0.681203\pi\) | ||||
−0.539014 | + | 0.842297i | \(0.681203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.21473 | 0.443198 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.85226 | + | 17.3372i | 0.480551 | + | 1.06102i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 22.3903i | − | 1.36516i | −0.730809 | − | 0.682582i | \(-0.760857\pi\) | ||
0.730809 | − | 0.682582i | \(-0.239143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0813i | 1.88805i | 0.329868 | + | 0.944027i | \(0.392996\pi\) | ||||
−0.329868 | + | 0.944027i | \(0.607004\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.901210 | + | 1.98980i | 0.0545437 | + | 0.120428i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.30643 | −0.440594 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4125 | −1.40672 | −0.703360 | − | 0.710834i | \(-0.748318\pi\) | ||||
−0.703360 | + | 0.710834i | \(0.748318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9652 | − | 13.1320i | −0.895946 | − | 0.786194i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.8664i | − | 1.72203i | −0.508583 | − | 0.861013i | \(-0.669831\pi\) | ||
0.508583 | − | 0.861013i | \(-0.330169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.8054i | − | 0.642317i | −0.947025 | − | 0.321158i | \(-0.895928\pi\) | ||
0.947025 | − | 0.321158i | \(-0.104072\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.91894 | − | 1.32203i | 0.172903 | − | 0.0783105i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.50751 | 0.207042 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.8197 | 0.871744 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9201 | − | 6.75752i | 0.874629 | − | 0.396133i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.514137i | 0.0300362i | 0.999887 | + | 0.0150181i | \(0.00478059\pi\) | ||||
−0.999887 | + | 0.0150181i | \(0.995219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 15.0693i | − | 0.877368i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.99720 | − | 23.0298i | 0.406019 | − | 1.33632i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.78254 | 0.276581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.81470 | 0.277515 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.22869 | − | 4.92076i | −0.128035 | − | 0.282690i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 22.1303i | − | 1.26718i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2588i | − | 1.15623i | −0.815954 | − | 0.578116i | \(-0.803788\pi\) | ||
0.815954 | − | 0.578116i | \(-0.196212\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.9568 | − | 24.1918i | −0.623313 | − | 1.37623i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.4007 | 1.66716 | 0.833581 | − | 0.552397i | \(-0.186287\pi\) | ||||
0.833581 | + | 0.552397i | \(0.186287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.82563 | 0.442331 | 0.221165 | − | 0.975236i | \(-0.429014\pi\) | ||||
0.221165 | + | 0.975236i | \(0.429014\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.59040 | + | 2.95201i | −0.145952 | + | 0.166327i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.41538i | 0.472655i | 0.971674 | + | 0.236327i | \(0.0759438\pi\) | ||||
−0.971674 | + | 0.236327i | \(0.924056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3228i | 0.633953i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.2671 | + | 9.63218i | −1.18701 | + | 0.537616i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.47660 | −0.0821602 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.81117 | −0.155936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.39889 | + | 2.89815i | −0.353859 | + | 0.160268i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.79841i | − | 0.319677i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.7185i | − | 1.46858i | −0.678836 | − | 0.734290i | \(-0.737515\pi\) | ||
0.678836 | − | 0.734290i | \(-0.262485\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.02383 | + | 6.86475i | −0.330104 | + | 0.376186i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.96205 | 0.489649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1242 | −0.769395 | −0.384697 | − | 0.923043i | \(-0.625694\pi\) | ||||
−0.384697 | + | 0.923043i | \(0.625694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.88967 | − | 15.2118i | −0.374196 | − | 0.826194i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.7420i | 1.66477i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.55240i | 0.515781i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.54762 | + | 7.83286i | 0.190998 | + | 0.421707i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.67942 | −0.251204 | −0.125602 | − | 0.992081i | \(-0.540086\pi\) | ||||
−0.125602 | + | 0.992081i | \(0.540086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.52611 | 0.0816911 | 0.0408455 | − | 0.999165i | \(-0.486995\pi\) | ||||
0.0408455 | + | 0.999165i | \(0.486995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.69220 | − | 8.86077i | 0.143699 | − | 0.472953i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6720i | 1.20671i | 0.797474 | + | 0.603354i | \(0.206169\pi\) | ||||
−0.797474 | + | 0.603354i | \(0.793831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.2846i | 0.598922i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.64857 | − | 0.746664i | 0.0872517 | − | 0.0395176i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7942 | −1.04470 | −0.522350 | − | 0.852731i | \(-0.674945\pi\) | ||||
−0.522350 | + | 0.852731i | \(0.674945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.4982 | + | 7.47230i | −0.865932 | + | 0.392194i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 27.8540i | − | 1.45794i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7226i | 1.29051i | 0.763967 | + | 0.645255i | \(0.223249\pi\) | ||||
−0.763967 | + | 0.645255i | \(0.776751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.1771 | − | 9.80795i | −0.581858 | − | 0.510582i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.75956 | 0.143269 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9194 | 1.44561 | 0.722805 | − | 0.691052i | \(-0.242852\pi\) | ||||
0.722805 | + | 0.691052i | \(0.242852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.69545 | − | 19.1989i | −0.449031 | − | 0.991425i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.35647i | 0.224370i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.4837i | − | 1.25764i | −0.777550 | − | 0.628821i | \(-0.783538\pi\) | ||
0.777550 | − | 0.628821i | \(-0.216462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.64870 | − | 5.84812i | −0.135697 | − | 0.299608i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.9416 | −0.712382 | −0.356191 | − | 0.934413i | \(-0.615925\pi\) | ||||
−0.356191 | + | 0.934413i | \(0.615925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.06409 | 0.309055 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.3427 | − | 13.4632i | −0.779911 | − | 0.684373i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.11256i | − | 0.462025i | −0.972951 | − | 0.231013i | \(-0.925796\pi\) | ||
0.972951 | − | 0.231013i | \(-0.0742039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.96239i | − | 0.200387i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0191051 | − | 0.00865301i | 0.000963727 | − | 0.000436487i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.09606 | −0.206095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.45405 | 0.374108 | 0.187054 | − | 0.982350i | \(-0.440106\pi\) | ||||
0.187054 | + | 0.982350i | \(0.440106\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.11647 | − | 0.505665i | 0.0558932 | − | 0.0253149i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3076i | 1.51349i | 0.653711 | + | 0.756744i | \(0.273211\pi\) | ||||
−0.653711 | + | 0.756744i | \(0.726789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8281i | 0.589198i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 16.5092 | − | 2.16351i | 0.820351 | − | 0.107506i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.1017 | 0.698997 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.7359 | 1.71758 | 0.858790 | − | 0.512328i | \(-0.171217\pi\) | ||||
0.858790 | + | 0.512328i | \(0.171217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8132 | + | 26.0826i | 0.582703 | + | 1.28656i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.76385i | − | 0.283621i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.91167i | 0.241105i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.92839 | + | 6.46564i | 0.143404 | + | 0.316624i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.9232 | −0.973314 | −0.486657 | − | 0.873593i | \(-0.661784\pi\) | ||||
−0.486657 | + | 0.873593i | \(0.661784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.25156 | −0.450893 | −0.225447 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225447 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.2139 | + | 18.4774i | −0.788348 | + | 0.898400i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.32909i | 0.112977i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.46463i | − | 0.409632i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.0253 | + | 5.89936i | −0.628868 | + | 0.284824i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6084 | −0.848169 | −0.424084 | − | 0.905623i | \(-0.639404\pi\) | ||||
−0.424084 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.4409 | 1.12650 | 0.563248 | − | 0.826288i | \(-0.309551\pi\) | ||||
0.563248 | + | 0.826288i | \(0.309551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.13505 | + | 3.23157i | −0.342099 | + | 0.154942i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.68346i | − | 0.128367i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10.9049i | − | 0.520461i | −0.965547 | − | 0.260231i | \(-0.916201\pi\) | ||
0.965547 | − | 0.260231i | \(-0.0837986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.8601 | − | 14.6554i | 0.612388 | − | 0.697877i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.08004 | 0.193848 | 0.0969242 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969242 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.3290 | 0.963689 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.5788 | − | 34.3967i | −0.736852 | − | 1.62691i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.2291i | − | 1.28502i | −0.766277 | − | 0.642511i | \(-0.777893\pi\) | ||
0.766277 | − | 0.642511i | \(-0.222107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9603i | 1.08116i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.3499 | + | 29.4754i | 0.627231 | + | 1.38487i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.33318 | 0.109381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.10668 | 0.285658 | 0.142829 | − | 0.989747i | \(-0.454380\pi\) | ||||
0.142829 | + | 0.989747i | \(0.454380\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.34126 | − | 2.23052i | −0.342661 | − | 0.104112i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.8562i | − | 0.831648i | −0.909445 | − | 0.415824i | \(-0.863493\pi\) | ||
0.909445 | − | 0.415824i | \(-0.136507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.1434i | − | 0.657299i | −0.944452 | − | 0.328649i | \(-0.893407\pi\) | ||
0.944452 | − | 0.328649i | \(-0.106593\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.3721 | + | 8.77390i | −0.898358 | + | 0.406880i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.7322 | −1.88486 | −0.942430 | − | 0.334404i | \(-0.891465\pi\) | ||||
−0.942430 | + | 0.334404i | \(0.891465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.42790 | 0.158286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0750 | − | 7.28062i | 0.740698 | − | 0.335473i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.5172i | 1.44916i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.57733i | 0.0723730i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.79370 | − | 7.71649i | −0.402636 | − | 0.353314i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.94900 | 0.0890519 | 0.0445260 | − | 0.999008i | \(-0.485822\pi\) | ||||
0.0445260 | + | 0.999008i | \(0.485822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.42569 | 0.247390 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.35693 | + | 2.99599i | 0.0617425 | + | 0.136322i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 17.4948i | − | 0.794399i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.97691i | − | 0.0895824i | −0.998996 | − | 0.0447912i | \(-0.985738\pi\) | ||
0.998996 | − | 0.0447912i | \(-0.0142622\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.64449 | − | 8.04674i | −0.164809 | − | 0.363886i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.44538 | −0.381134 | −0.190567 | − | 0.981674i | \(-0.561033\pi\) | ||||
−0.190567 | + | 0.981674i | \(0.561033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.60939 | 0.162559 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.3240 | − | 16.9568i | −0.868549 | − | 0.762154i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.31623i | 0.193609i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.5057i | − | 0.783664i | −0.920037 | − | 0.391832i | \(-0.871841\pi\) | ||
0.920037 | − | 0.391832i | \(-0.128159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.3007 | + | 9.19448i | −0.906967 | + | 0.410779i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.6802 | −0.476209 | −0.238104 | − | 0.971240i | \(-0.576526\pi\) | ||||
−0.238104 | + | 0.971240i | \(0.576526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.76994 | −0.256759 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.4995 | − | 7.01994i | 0.688355 | − | 0.311766i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 39.2121i | − | 1.73804i | −0.494773 | − | 0.869022i | \(-0.664749\pi\) | ||
0.494773 | − | 0.869022i | \(-0.335251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.6539i | − | 0.471300i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.97174 | − | 1.51058i | −0.219507 | − | 0.0666937i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.3666 | −1.24998 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.9567 | 1.66933 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.51979 | − | 18.8110i | −0.373977 | − | 0.825711i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.9655i | − | 1.57568i | −0.615881 | − | 0.787839i | \(-0.711200\pi\) | ||
0.615881 | − | 0.787839i | \(-0.288800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0443i | 0.876477i | 0.898859 | + | 0.438238i | \(0.144397\pi\) | ||||
−0.898859 | + | 0.438238i | \(0.855603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.797602 | − | 1.76104i | −0.0348102 | − | 0.0768581i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.79970 | 0.426882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7990 | −0.686915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.1173 | + | 18.3672i | −0.699431 | + | 0.797071i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.83406i | 0.382646i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9371i | 1.07813i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.03491 | − | 0.921642i | 0.0878129 | − | 0.0397718i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.1055 | −1.29674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.27173 | −0.183656 | −0.0918280 | − | 0.995775i | \(-0.529271\pi\) | ||||
−0.0918280 | + | 0.995775i | \(0.529271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.2004 | − | 10.5078i | 0.995624 | − | 0.450933i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.50314i | 0.321399i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.68080i | − | 0.328407i | −0.986426 | − | 0.164204i | \(-0.947495\pi\) | ||
0.986426 | − | 0.164204i | \(-0.0525054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.6694 | + | 26.9736i | −1.01018 | + | 1.15121i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.44439 | 0.104135 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.56670 | −0.0666230 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.02470 | + | 8.88621i | 0.170839 | + | 0.377199i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 44.2479i | − | 1.87484i | −0.348197 | − | 0.937421i | \(-0.613206\pi\) | ||
0.348197 | − | 0.937421i | \(-0.386794\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1264i | 0.512891i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.88769 | + | 10.7916i | 0.206359 | + | 0.455623i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.1114 | 1.52191 | 0.760956 | − | 0.648803i | \(-0.224730\pi\) | ||||
0.760956 | + | 0.648803i | \(0.224730\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.8370 | −0.750406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.31462 | − | 0.827521i | 0.265189 | − | 0.0347526i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.27441i | 0.346881i | 0.984844 | + | 0.173441i | \(0.0554885\pi\) | ||||
−0.984844 | + | 0.173441i | \(0.944511\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.3137i | 1.14304i | 0.820587 | + | 0.571521i | \(0.193647\pi\) | ||||
−0.820587 | + | 0.571521i | \(0.806353\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.62042 | − | 3.45140i | 0.318347 | − | 0.144184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.23271 | −0.176516 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1555 | −0.464408 | −0.232204 | − | 0.972667i | \(-0.574594\pi\) | ||||
−0.232204 | + | 0.972667i | \(0.574594\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.58726 | − | 1.62472i | 0.149081 | − | 0.0675212i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.87867i | 0.0779402i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0642i | 0.748144i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.43497 | − | 6.52420i | −0.307398 | − | 0.269743i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.7699 | −0.981089 | −0.490545 | − | 0.871416i | \(-0.663202\pi\) | ||||
−0.490545 | + | 0.871416i | \(0.663202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.63667 | 0.273459 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2313 | − | 29.2136i | −0.544262 | − | 1.20169i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.1707i | 1.11577i | 0.829920 | + | 0.557883i | \(0.188386\pi\) | ||||
−0.829920 | + | 0.557883i | \(0.811614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.93307i | − | 0.0792481i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.16035 | − | 20.2253i | −0.374908 | − | 0.827767i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.2016 | −0.621122 | −0.310561 | − | 0.950554i | \(-0.600517\pi\) | ||||
−0.310561 | + | 0.950554i | \(0.600517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.7396 | 0.723614 | 0.361807 | − | 0.932253i | \(-0.382160\pi\) | ||||
0.361807 | + | 0.932253i | \(0.382160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9234 | − | 9.58532i | −0.444836 | − | 0.390345i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.3453i | 0.786500i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00873i | 0.0409429i | 0.999790 | + | 0.0204715i | \(0.00651672\pi\) | ||||
−0.999790 | + | 0.0204715i | \(0.993483\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.72908 | + | 1.23604i | −0.110588 | + | 0.0500870i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6039 | 0.590813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.7234 | 1.84675 | 0.923375 | − | 0.383899i | \(-0.125419\pi\) | ||||
0.923375 | + | 0.383899i | \(0.125419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.4685 | + | 6.55299i | −0.583425 | + | 0.264242i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.79096i | − | 0.313652i | −0.987626 | − | 0.156826i | \(-0.949874\pi\) | ||
0.987626 | − | 0.156826i | \(-0.0501262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.8993i | − | 0.759628i | −0.925063 | − | 0.379814i | \(-0.875988\pi\) | ||
0.925063 | − | 0.379814i | \(-0.124012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.05358 | − | 13.3415i | 0.162664 | − | 0.535374i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.77565 | 0.311525 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.6253 | −0.585014 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.31010 | + | 7.30844i | 0.132193 | + | 0.291871i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.49525i | − | 0.179237i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4573i | 0.495918i | 0.968771 | + | 0.247959i | \(0.0797598\pi\) | ||||
−0.968771 | + | 0.247959i | \(0.920240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.8330 | − | 23.9183i | −0.430572 | − | 0.950668i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.85733 | −0.272125 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.5832 | −0.458943 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0693 | − | 13.7542i | 0.477456 | − | 0.544108i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9.64878i | − | 0.381104i | −0.981677 | − | 0.190552i | \(-0.938972\pi\) | ||
0.981677 | − | 0.190552i | \(-0.0610278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1740i | 0.440659i | 0.975426 | + | 0.220329i | \(0.0707132\pi\) | ||||
−0.975426 | + | 0.220329i | \(0.929287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.8606 | + | 8.99517i | −0.782011 | + | 0.354185i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.9594 | 1.53165 | 0.765826 | − | 0.643048i | \(-0.222330\pi\) | ||||
0.765826 | + | 0.643048i | \(0.222330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.7304 | 1.48105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.40962 | + | 3.35593i | −0.290406 | + | 0.131529i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.77338i | − | 0.382462i | −0.981545 | − | 0.191231i | \(-0.938752\pi\) | ||
0.981545 | − | 0.191231i | \(-0.0612479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.0224021i | − | 0.000875324i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.7911 | + | 33.9499i | −1.16226 | + | 1.32451i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.05188 | 0.313657 | 0.156828 | − | 0.987626i | \(-0.449873\pi\) | ||||
0.156828 | + | 0.987626i | \(0.449873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6768 | 0.531967 | 0.265984 | − | 0.963978i | \(-0.414303\pi\) | ||||
0.265984 | + | 0.963978i | \(0.414303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.88056 | + | 4.15212i | 0.0730348 | + | 0.161255i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.30914i | − | 0.0507661i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.55943i | 0.253982i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7247 | − | 23.6792i | −0.414639 | − | 0.915489i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55.4098 | 2.13907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.9298 | −1.34644 | −0.673221 | − | 0.739441i | \(-0.735090\pi\) | ||||
−0.673221 | + | 0.739441i | \(0.735090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.38269 | + | 7.84209i | −0.0917096 | + | 0.301842i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 43.3133i | − | 1.66466i | −0.554277 | − | 0.832332i | \(-0.687005\pi\) | ||
0.554277 | − | 0.832332i | \(-0.312995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.69159i | − | 0.256800i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.8473 | + | 13.9712i | −1.18207 | + | 0.535378i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.37903 | −0.244087 | −0.122043 | − | 0.992525i | \(-0.538945\pi\) | ||||
−0.122043 | + | 0.992525i | \(0.538945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5837 | 1.16854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.6307 | − | 10.2498i | 0.863416 | − | 0.391054i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.95027i | 0.264784i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.0940i | − | 1.22091i | −0.792050 | − | 0.610456i | \(-0.790986\pi\) | ||
0.792050 | − | 0.610456i | \(-0.209014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.39124 | − | 6.48582i | −0.280770 | − | 0.246376i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.58142 | 0.287580 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.31913 | 0.277232 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.638222 | − | 1.40914i | −0.0241398 | − | 0.0532987i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.5578i | 1.34300i | 0.741004 | + | 0.671500i | \(0.234350\pi\) | ||||
−0.741004 | + | 0.671500i | \(0.765650\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.04433i | − | 0.114819i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.8330 | + | 23.9184i | 0.407995 | + | 0.900819i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.20694 | −0.0830007 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.04768 | −0.302237 | −0.151118 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151118 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.99250 | + | 4.38093i | 0.187233 | + | 0.164298i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.8092i | 0.666961i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.2731i | 0.571182i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.7577 | − | 19.8185i | 1.63416 | − | 0.740136i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.8564 | −1.07616 | −0.538082 | − | 0.842893i | \(-0.680851\pi\) | ||||
−0.538082 | + | 0.842893i | \(0.680851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8500 | −0.404073 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.7717 | − | 18.4661i | 1.51632 | − | 0.686762i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3.85563i | − | 0.143194i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.8395i | − | 1.25504i | −0.778602 | − | 0.627518i | \(-0.784071\pi\) | ||
0.778602 | − | 0.627518i | \(-0.215929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.4363 | − | 15.0204i | −0.830974 | − | 0.556311i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0468 | 0.371596 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6799 | −0.874639 | −0.437319 | − | 0.899306i | \(-0.644072\pi\) | ||||
−0.437319 | + | 0.899306i | \(0.644072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.59225 | − | 18.9710i | −0.316930 | − | 0.699756i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.4392i | 0.826557i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.9341i | − | 1.39543i | −0.716375 | − | 0.697715i | \(-0.754200\pi\) | ||
0.716375 | − | 0.697715i | \(-0.245800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.27357 | + | 2.81195i | 0.0467859 | + | 0.103299i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.47556 | 0.274252 | 0.137126 | − | 0.990554i | \(-0.456214\pi\) | ||||
0.137126 | + | 0.990554i | \(0.456214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.3326 | −1.47767 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.25326 | − | 5.98660i | 0.192207 | − | 0.219038i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.53820i | 0.348518i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.8763i | 1.92948i | 0.263198 | + | 0.964742i | \(0.415223\pi\) | ||||
−0.263198 | + | 0.964742i | \(0.584777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.35835 | + | 2.42688i | −0.195269 | + | 0.0884403i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.5620 | 1.25784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.02847 | 0.110071 | 0.0550357 | − | 0.998484i | \(-0.482473\pi\) | ||||
0.0550357 | + | 0.998484i | \(0.482473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.6119 | + | 8.88253i | −0.711867 | + | 0.322415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 12.3323i | − | 0.447046i | −0.974699 | − | 0.223523i | \(-0.928244\pi\) | ||
0.974699 | − | 0.223523i | \(-0.0717558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.86988i | 0.103897i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.40538 | + | 6.15996i | −0.195432 | + | 0.222714i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.5169 | 0.524175 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7181 | 1.28803 | 0.644015 | − | 0.765013i | \(-0.277268\pi\) | ||||
0.644015 | + | 0.765013i | \(0.277268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.6453 | − | 38.9594i | −0.635481 | − | 1.40309i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.3015i | 1.44954i | 0.688989 | + | 0.724771i | \(0.258055\pi\) | ||||
−0.688989 | + | 0.724771i | \(0.741945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.4682i | − | 0.376031i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.53941 | + | 3.39889i | 0.0552260 | + | 0.121934i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.95675 | 0.177594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.2542 | −1.01102 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.1529 | + | 3.69245i | 0.434309 | + | 0.131957i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 18.8491i | − | 0.672753i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5594i | 0.946742i | 0.880863 | + | 0.473371i | \(0.156963\pi\) | ||||
−0.880863 | + | 0.473371i | \(0.843037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.5836 | − | 12.4930i | 0.982004 | − | 0.444764i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.82246 | −0.242579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3191 | 0.757064 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3832 | + | 5.15562i | −0.403720 | + | 0.182851i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.4101i | 0.970915i | 0.874260 | + | 0.485457i | \(0.161347\pi\) | ||||
−0.874260 | + | 0.485457i | \(0.838653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.0995i | − | 0.428051i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.7781 | − | 21.7428i | −0.875491 | − | 0.768245i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 69.7407 | 2.46110 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.51301 | 0.123817 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.0000 | + | 35.3268i | 0.563228 | + | 1.24356i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.2725i | 0.958849i | 0.877583 | + | 0.479425i | \(0.159155\pi\) | ||||
−0.877583 | + | 0.479425i | \(0.840845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6173i | 0.653740i | 0.945069 | + | 0.326870i | \(0.105994\pi\) | ||||
−0.945069 | + | 0.326870i | \(0.894006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.2105 | − | 49.0391i | −0.778958 | − | 1.71988i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.43536 | −0.330506 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.80404 | 0.238043 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.84380 | − | 2.49544i | −0.0993705 | − | 0.0871978i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9352i | 0.486341i | 0.969984 | + | 0.243171i | \(0.0781875\pi\) | ||||
−0.969984 | + | 0.243171i | \(0.921812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.9501i | 1.74115i | 0.492035 | + | 0.870575i | \(0.336253\pi\) | ||||
−0.492035 | + | 0.870575i | \(0.663747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.5278 | − | 5.22114i | 0.401348 | − | 0.181777i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.1270 | −0.421697 | −0.210849 | − | 0.977519i | \(-0.567623\pi\) | ||||
−0.210849 | + | 0.977519i | \(0.567623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3614 | 0.637717 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.9395 | − | 16.7305i | 1.28142 | − | 0.580373i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.59681i | 0.332510i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.8040i | 0.823770i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.9958 | + | 10.0252i | 1.14050 | + | 0.346522i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.5183 | −1.88218 | −0.941090 | − | 0.338156i | \(-0.890197\pi\) | ||||
−0.941090 | + | 0.338156i | \(0.890197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0249 | 0.793963 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.6278 | + | 45.5445i | 0.710459 | + | 1.56864i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 18.1742i | − | 0.625212i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.39940i | 0.254246i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.72152 | + | 17.0485i | 0.265002 | + | 0.585103i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.16933 | 0.280041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.62135 | 0.123993 | 0.0619964 | − | 0.998076i | \(-0.480253\pi\) | ||||
0.0619964 | + | 0.998076i | \(0.480253\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.66070 | + | 4.17173i | −0.125193 | + | 0.142670i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 58.1816i | 1.98745i | 0.111869 | + | 0.993723i | \(0.464316\pi\) | ||||
−0.111869 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 11.0241i | − | 0.376136i | −0.982156 | − | 0.188068i | \(-0.939777\pi\) | ||
0.982156 | − | 0.188068i | \(-0.0602226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.53404 | + | 2.50645i | −0.188600 | + | 0.0854196i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.9330 | 1.90398 | 0.951991 | − | 0.306126i | \(-0.0990330\pi\) | ||||
0.951991 | + | 0.306126i | \(0.0990330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.0572 | −0.749968 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.3820 | + | 10.5901i | −0.794094 | + | 0.359657i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.2557i | − | 0.347901i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.63354i | 0.292536i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.7115 | + | 21.3236i | −0.633288 | + | 0.721694i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.61062 | −0.291092 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.6467 | 1.13617 | 0.568084 | − | 0.822971i | \(-0.307685\pi\) | ||||
0.568084 | + | 0.822971i | \(0.307685\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.367400 | − | 0.811190i | −0.0123921 | − | 0.0273608i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.7744i | 1.71063i | 0.518105 | + | 0.855317i | \(0.326638\pi\) | ||||
−0.518105 | + | 0.855317i | \(0.673362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.6602i | − | 0.527007i | −0.964658 | − | 0.263504i | \(-0.915122\pi\) | ||
0.964658 | − | 0.263504i | \(-0.0848781\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.7684 | + | 23.7759i | 0.361977 | + | 0.799217i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.98064 | −0.267964 | −0.133982 | − | 0.990984i | \(-0.542776\pi\) | ||||
−0.133982 | + | 0.990984i | \(0.542776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.62286 | −0.0879679 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.41699 | + | 41.3358i | 0.181476 | + | 1.38480i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.19420i | − | 0.274208i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.38608i | − | 0.0797577i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.54574 | + | 3.41758i | −0.251945 | + | 0.114110i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.2226 | −0.541055 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.75838 | 0.191840 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.59648 | + | 3.44056i | −0.252795 | + | 0.114495i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 27.2041i | − | 0.904295i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.9105i | 0.727527i | 0.931491 | + | 0.363764i | \(0.118508\pi\) | ||||
−0.931491 | + | 0.363764i | \(0.881492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.03271 | + | 6.17121i | 0.233260 | + | 0.204686i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.5173 | −1.40866 | −0.704330 | − | 0.709873i | \(-0.748752\pi\) | ||||
−0.704330 | + | 0.709873i | \(0.748752\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.2978 | −0.406999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15.8142 | + | 34.9165i | 0.522802 | + | 1.15430i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.00856859i | − | 0.000282960i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.2272i | 0.667234i | 0.942709 | + | 0.333617i | \(0.108269\pi\) | ||||
−0.942709 | + | 0.333617i | \(0.891731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.4769 | + | 31.9637i | 0.477029 | + | 1.05324i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8709 | −0.357820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.80192 | −0.157886 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.5747 | + | 30.3394i | 1.13558 | + | 0.996476i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.3458i | 1.58617i | 0.609109 | + | 0.793086i | \(0.291527\pi\) | ||||
−0.609109 | + | 0.793086i | \(0.708473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.49927i | 0.213005i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.3875 | + | 21.0096i | −1.51866 | + | 0.687824i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6539 | 0.413828 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.7559 | −1.62545 | −0.812727 | − | 0.582645i | \(-0.802018\pi\) | ||||
−0.812727 | + | 0.582645i | \(0.802018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.3470 | + | 5.59216i | −0.402930 | + | 0.182493i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 24.6221i | − | 0.802657i | −0.915934 | − | 0.401328i | \(-0.868549\pi\) | ||
0.915934 | − | 0.401328i | \(-0.131451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3012i | 0.433148i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.97755 | − | 6.50868i | 0.0643298 | − | 0.211727i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.29796 | −0.269647 | −0.134824 | − | 0.990870i | \(-0.543047\pi\) | ||||
−0.134824 | + | 0.990870i | \(0.543047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.8330 | 0.871035 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.01359 | − | 13.2775i | −0.195004 | − | 0.430553i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.5290i | 0.341069i | 0.985352 | + | 0.170534i | \(0.0545494\pi\) | ||||
−0.985352 | + | 0.170534i | \(0.945451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.93548i | − | 0.289145i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.09120 | − | 17.8647i | −0.261551 | − | 0.577484i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.6980 | 0.377747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0454 | −0.420820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.6714 | − | 30.3947i | 0.859474 | − | 0.979455i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.20631i | − | 0.135406i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.6937i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.32973 | − | 1.05517i | 0.0748417 | − | 0.0338970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.7513 | 1.30777 | 0.653886 | − | 0.756593i | \(-0.273137\pi\) | ||||
0.653886 | + | 0.756593i | \(0.273137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.89982 | 0.0929639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.43538 | − | 2.00885i | 0.142046 | − | 0.0643347i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 49.7877i | − | 1.59285i | −0.604737 | − | 0.796425i | \(-0.706722\pi\) | ||
0.604737 | − | 0.796425i | \(-0.293278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.8998i | 1.62676i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.02495 | − | 9.14523i | 0.256217 | − | 0.291985i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.1050 | 0.641250 | 0.320625 | − | 0.947206i | \(-0.396107\pi\) | ||||
0.320625 | + | 0.947206i | \(0.396107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.2550 | −1.09146 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.14352 | + | 9.14855i | 0.131890 | + | 0.291202i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.2584i | 0.580582i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.64260i | 0.147477i | 0.997278 | + | 0.0737384i | \(0.0234930\pi\) | ||||
−0.997278 | + | 0.0737384i | \(0.976507\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.0929 | + | 42.1556i | 0.605895 | + | 1.33777i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.7156 | −0.751835 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.1056 | −1.46018 | −0.730089 | − | 0.683352i | \(-0.760521\pi\) | ||||
−0.730089 | + | 0.683352i | \(0.760521\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.59869 | − | 15.1356i | 0.145496 | − | 0.478869i |
(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 | 912.2.d.b.191.4 | yes | 24 | |
3.2 | odd | 2 | inner | 912.2.d.b.191.22 | yes | 24 | |
4.3 | odd | 2 | inner | 912.2.d.b.191.21 | yes | 24 | |
12.11 | even | 2 | inner | 912.2.d.b.191.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.d.b.191.3 | ✓ | 24 | 12.11 | even | 2 | inner | |
912.2.d.b.191.4 | yes | 24 | 1.1 | even | 1 | trivial | |
912.2.d.b.191.21 | yes | 24 | 4.3 | odd | 2 | inner | |
912.2.d.b.191.22 | yes | 24 | 3.2 | odd | 2 | inner |