Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + \cdots + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.3 | ||
Root | \(0.294251 - 1.09816i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.95 |
Dual form | 224.3.r.c.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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −2.25843 | − | 1.30391i | −0.752812 | − | 0.434636i | 0.0738973 | − | 0.997266i | \(-0.476456\pi\) |
−0.826709 | + | 0.562630i | \(0.809790\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.59965 | − | 6.23477i | −0.719930 | − | 1.24695i | −0.961027 | − | 0.276454i | \(-0.910841\pi\) |
0.241098 | − | 0.970501i | \(-0.422493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.36875 | + | 4.49183i | 0.766964 | + | 0.641690i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.09965 | − | 1.90465i | −0.122183 | − | 0.211627i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.81789 | + | 2.20426i | 0.347081 | + | 0.200387i | 0.663399 | − | 0.748266i | \(-0.269113\pi\) |
−0.316318 | + | 0.948653i | \(0.602447\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.1993 | −1.39995 | −0.699973 | − | 0.714169i | \(-0.746805\pi\) | ||||
−0.699973 | + | 0.714169i | \(0.746805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.7744i | 1.25163i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.58331 | + | 14.8667i | −0.504901 | + | 0.874514i | 0.495083 | + | 0.868846i | \(0.335138\pi\) |
−0.999984 | + | 0.00566806i | \(0.998196\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.4174 | + | 11.2107i | −1.02197 | + | 0.590035i | −0.914674 | − | 0.404192i | \(-0.867553\pi\) |
−0.107297 | + | 0.994227i | \(0.534219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.26803 | − | 17.1449i | −0.298478 | − | 0.816422i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.53183 | + | 5.50320i | −0.414427 | + | 0.239270i | −0.692690 | − | 0.721235i | \(-0.743575\pi\) |
0.278263 | + | 0.960505i | \(0.410241\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.4149 | + | 23.2353i | −0.536597 | + | 0.929413i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.2057i | 1.08169i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.4931 | 1.29287 | 0.646433 | − | 0.762971i | \(-0.276260\pi\) | ||||
0.646433 | + | 0.762971i | \(0.276260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40.5472 | − | 23.4100i | −1.30798 | − | 0.755160i | −0.326218 | − | 0.945295i | \(-0.605774\pi\) |
−0.981758 | + | 0.190135i | \(0.939108\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.74831 | − | 9.95636i | −0.174191 | − | 0.301708i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.67995 | − | 49.6419i | 0.247999 | − | 1.41834i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −31.3135 | − | 54.2366i | −0.846311 | − | 1.46585i | −0.884478 | − | 0.466583i | \(-0.845485\pi\) |
0.0381662 | − | 0.999271i | \(-0.487848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.1019 | + | 23.7302i | 1.05390 | + | 0.608467i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.97085 | 0.0724597 | 0.0362299 | − | 0.999343i | \(-0.488465\pi\) | ||||
0.0362299 | + | 0.999343i | \(0.488465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.9347i | 1.02174i | 0.859659 | + | 0.510868i | \(0.170676\pi\) | ||||
−0.859659 | + | 0.510868i | \(0.829324\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.91669 | + | 13.7121i | −0.175926 | + | 0.304713i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18.9763 | − | 10.9560i | 0.403750 | − | 0.233105i | −0.284351 | − | 0.958720i | \(-0.591778\pi\) |
0.688101 | + | 0.725615i | \(0.258445\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.64690 | + | 48.2310i | 0.176467 | + | 0.984307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 38.7697 | − | 22.3837i | 0.760190 | − | 0.438896i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.03606 | − | 3.52656i | 0.0384163 | − | 0.0665389i | −0.846178 | − | 0.532900i | \(-0.821102\pi\) |
0.884594 | + | 0.466361i | \(0.154435\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 31.7382i | − | 0.577059i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 58.4707 | 1.02580 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2884 | + | 7.09468i | 0.208277 | + | 0.120249i | 0.600510 | − | 0.799617i | \(-0.294964\pi\) |
−0.392233 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.4837 | − | 70.1198i | −0.663667 | − | 1.14950i | −0.979645 | − | 0.200738i | \(-0.935666\pi\) |
0.315978 | − | 0.948766i | \(-0.397667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.65162 | − | 15.1650i | 0.0420892 | − | 0.240714i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 65.5111 | + | 113.468i | 1.00786 | + | 1.74567i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.4791 | − | 11.8236i | −0.305659 | − | 0.176472i | 0.339323 | − | 0.940670i | \(-0.389802\pi\) |
−0.644982 | + | 0.764198i | \(0.723135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28.7027 | 0.415981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 96.3589i | − | 1.35717i | −0.734523 | − | 0.678584i | \(-0.762594\pi\) | ||
0.734523 | − | 0.678584i | \(-0.237406\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3462 | − | 28.3124i | 0.223920 | − | 0.387842i | −0.732075 | − | 0.681224i | \(-0.761448\pi\) |
0.955995 | + | 0.293383i | \(0.0947811\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 60.5935 | − | 34.9837i | 0.807913 | − | 0.466449i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.5961 | + | 28.9834i | 0.137612 | + | 0.376408i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −73.2664 | + | 42.3004i | −0.927423 | + | 0.535448i | −0.885996 | − | 0.463694i | \(-0.846524\pi\) |
−0.0414274 | + | 0.999142i | \(0.513191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.1847 | − | 48.8174i | 0.347960 | − | 0.602684i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 41.1048i | − | 0.495239i | −0.968857 | − | 0.247619i | \(-0.920352\pi\) | ||
0.968857 | − | 0.247619i | \(-0.0796482\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 123.588 | 1.45397 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −84.6757 | − | 48.8875i | −0.973284 | − | 0.561926i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −49.9313 | − | 86.4835i | −0.561025 | − | 0.971725i | −0.997407 | − | 0.0719630i | \(-0.977074\pi\) |
0.436382 | − | 0.899762i | \(-0.356260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −97.7074 | − | 81.7482i | −1.07371 | − | 0.898332i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 61.0489 | + | 105.740i | 0.656440 | + | 1.13699i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 139.792 | + | 80.7089i | 1.47149 | + | 0.849567i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61.8520 | 0.637649 | 0.318825 | − | 0.947814i | \(-0.396712\pi\) | ||||
0.318825 | + | 0.947814i | \(0.396712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9.69564i | − | 0.0979358i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −59.2920 | + | 102.697i | −0.587050 | + | 1.01680i | 0.407567 | + | 0.913175i | \(0.366377\pi\) |
−0.994616 | + | 0.103625i | \(0.966956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 147.524 | − | 85.1728i | 1.43227 | − | 0.826921i | 0.434975 | − | 0.900442i | \(-0.356757\pi\) |
0.997294 | + | 0.0735216i | \(0.0234238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −84.3316 | + | 100.795i | −0.803158 | + | 0.959954i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −142.676 | + | 82.3738i | −1.33342 | + | 0.769848i | −0.985822 | − | 0.167797i | \(-0.946335\pi\) |
−0.347595 | + | 0.937645i | \(0.613001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 21.8153 | − | 37.7852i | 0.200140 | − | 0.346653i | −0.748433 | − | 0.663210i | \(-0.769194\pi\) |
0.948573 | + | 0.316557i | \(0.102527\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 163.320i | 1.47135i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −176.707 | −1.56378 | −0.781891 | − | 0.623415i | \(-0.785745\pi\) | ||||
−0.781891 | + | 0.623415i | \(0.785745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 68.6224 | + | 39.6192i | 0.596717 | + | 0.344515i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.0128 | + | 34.6632i | 0.171050 | + | 0.296267i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −112.860 | + | 41.2609i | −0.948407 | + | 0.346731i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50.7825 | − | 87.9578i | −0.419690 | − | 0.726924i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.70947 | − | 3.87371i | −0.0545485 | − | 0.0314936i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.1737 | 0.105389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 157.837i | 1.24281i | 0.783490 | + | 0.621404i | \(0.213437\pi\) | ||||
−0.783490 | + | 0.621404i | \(0.786563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 57.2867 | − | 99.2236i | 0.444083 | − | 0.769175i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 141.518 | − | 81.7054i | 1.08029 | − | 0.623705i | 0.149315 | − | 0.988790i | \(-0.452293\pi\) |
0.930974 | + | 0.365085i | \(0.118960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −154.604 | − | 27.0327i | −1.16243 | − | 0.203253i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 182.091 | − | 105.130i | 1.34882 | − | 0.778743i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 74.3375 | − | 128.756i | 0.542610 | − | 0.939827i | −0.456144 | − | 0.889906i | \(-0.650770\pi\) |
0.998753 | − | 0.0499212i | \(-0.0158970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 53.7059i | 0.386374i | 0.981162 | + | 0.193187i | \(0.0618824\pi\) | ||||
−0.981162 | + | 0.193187i | \(0.938118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −57.1422 | −0.405264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −69.4829 | − | 40.1160i | −0.485895 | − | 0.280531i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −134.962 | − | 233.761i | −0.930772 | − | 1.61214i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 43.3604 | − | 120.201i | 0.294968 | − | 0.817696i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3023 | + | 24.7724i | 0.0959888 | + | 0.166257i | 0.910021 | − | 0.414562i | \(-0.136065\pi\) |
−0.814032 | + | 0.580820i | \(0.802732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −210.547 | − | 121.559i | −1.39435 | − | 0.805028i | −0.400556 | − | 0.916272i | \(-0.631183\pi\) |
−0.993793 | + | 0.111244i | \(0.964516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 37.7545 | 0.246761 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 337.070i | 2.17465i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −46.5817 | + | 80.6818i | −0.296699 | + | 0.513897i | −0.975379 | − | 0.220537i | \(-0.929219\pi\) |
0.678680 | + | 0.734434i | \(0.262552\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.19663 | + | 5.30968i | −0.0578404 | + | 0.0333942i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.8934 | − | 13.2701i | −0.471388 | − | 0.0824227i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −239.198 | + | 138.101i | −1.46747 | + | 0.847246i | −0.999337 | − | 0.0364104i | \(-0.988408\pi\) |
−0.468136 | + | 0.883656i | \(0.655074\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −41.3837 | + | 71.6788i | −0.250811 | + | 0.434417i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 29.2913i | 0.175397i | 0.996147 | + | 0.0876984i | \(0.0279512\pi\) | ||||
−0.996147 | + | 0.0876984i | \(0.972049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 162.214 | 0.959848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42.7047 | + | 24.6556i | 0.249735 | + | 0.144185i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.2062 | − | 38.4623i | −0.128360 | − | 0.222325i | 0.794682 | − | 0.607027i | \(-0.207638\pi\) |
−0.923041 | + | 0.384701i | \(0.874304\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −176.391 | + | 64.4871i | −1.00795 | + | 0.368497i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.5016 | − | 32.0458i | −0.104529 | − | 0.181049i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 136.879 | + | 79.0271i | 0.764687 | + | 0.441492i | 0.830976 | − | 0.556308i | \(-0.187783\pi\) |
−0.0662893 | + | 0.997800i | \(0.521116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −75.4380 | −0.416785 | −0.208392 | − | 0.978045i | \(-0.566823\pi\) | ||||
−0.208392 | + | 0.978045i | \(0.566823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 211.148i | 1.15381i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −225.435 | + | 390.465i | −1.21857 | + | 2.11062i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −65.5403 | + | 37.8397i | −0.350483 | + | 0.202351i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −131.187 | + | 156.798i | −0.694112 | + | 0.829619i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 98.5940 | − | 56.9233i | 0.516199 | − | 0.298028i | −0.219179 | − | 0.975685i | \(-0.570338\pi\) |
0.735378 | + | 0.677657i | \(0.237005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 71.6871 | − | 124.166i | 0.371436 | − | 0.643346i | −0.618351 | − | 0.785902i | \(-0.712199\pi\) |
0.989787 | + | 0.142557i | \(0.0455323\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 341.682i | − | 1.75221i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 290.812 | 1.47620 | 0.738101 | − | 0.674690i | \(-0.235723\pi\) | ||||
0.738101 | + | 0.674690i | \(0.235723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −168.125 | − | 97.0672i | −0.844851 | − | 0.487775i | 0.0140595 | − | 0.999901i | \(-0.495525\pi\) |
−0.858910 | + | 0.512126i | \(0.828858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.8339 | + | 53.4058i | 0.153402 | + | 0.265701i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 201.291 | + | 168.413i | 0.991581 | + | 0.829619i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6940 | − | 18.5226i | −0.0521659 | − | 0.0903540i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.9633 | + | 12.1032i | 0.101272 | + | 0.0584694i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −98.8449 | −0.472942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 29.7854i | 0.141163i | 0.997506 | + | 0.0705815i | \(0.0224855\pi\) | ||||
−0.997506 | + | 0.0705815i | \(0.977515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −125.643 | + | 217.620i | −0.589874 | + | 1.02169i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 273.923 | − | 158.149i | 1.27406 | − | 0.735578i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −112.534 | − | 307.814i | −0.518591 | − | 1.41850i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −73.8336 | + | 42.6279i | −0.337140 | + | 0.194648i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 156.210 | − | 270.564i | 0.706834 | − | 1.22427i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 294.019i | 1.31847i | 0.751937 | + | 0.659234i | \(0.229120\pi\) | ||||
−0.751937 | + | 0.659234i | \(0.770880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 59.0068 | 0.262252 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −147.997 | − | 85.4459i | −0.651968 | − | 0.376414i | 0.137242 | − | 0.990538i | \(-0.456176\pi\) |
−0.789210 | + | 0.614124i | \(0.789510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 61.4423 | + | 106.421i | 0.268307 | + | 0.464721i | 0.968425 | − | 0.249306i | \(-0.0802025\pi\) |
−0.700118 | + | 0.714027i | \(0.746869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.8611 | − | 79.2736i | 0.0600047 | − | 0.343176i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 97.8057 | + | 169.404i | 0.419767 | + | 0.727058i | 0.995916 | − | 0.0902870i | \(-0.0287784\pi\) |
−0.576149 | + | 0.817345i | \(0.695445\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −136.616 | − | 78.8752i | −0.581344 | − | 0.335639i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 220.623 | 0.930900 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 229.735i | − | 0.961233i | −0.876931 | − | 0.480616i | \(-0.840413\pi\) | ||
0.876931 | − | 0.480616i | \(-0.159587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.409 | − | 217.214i | 0.520368 | − | 0.901304i | −0.479351 | − | 0.877623i | \(-0.659128\pi\) |
0.999720 | − | 0.0236812i | \(-0.00753866\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 100.329 | − | 57.9251i | 0.412877 | − | 0.238375i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 269.584 | − | 227.526i | 1.10034 | − | 0.928678i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 353.384 | − | 204.026i | 1.43070 | − | 0.826017i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −53.5969 | + | 92.8325i | −0.215248 | + | 0.372821i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 481.380i | − | 1.91785i | −0.283664 | − | 0.958924i | \(-0.591550\pi\) | ||
0.283664 | − | 0.958924i | \(-0.408450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −48.5220 | −0.191786 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −279.115 | − | 161.147i | −1.09457 | − | 0.631948i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 154.913 | + | 268.317i | 0.602774 | + | 1.04404i | 0.992399 | + | 0.123062i | \(0.0392715\pi\) |
−0.389625 | + | 0.920974i | \(0.627395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 75.5073 | − | 431.838i | 0.291534 | − | 1.66733i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −41.2292 | − | 71.4111i | −0.157966 | − | 0.273606i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 244.337 | + | 141.068i | 0.929036 | + | 0.536379i | 0.886507 | − | 0.462716i | \(-0.153125\pi\) |
0.0425297 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.3164 | −0.110628 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 260.423i | 0.975367i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 147.169 | − | 254.904i | 0.547097 | − | 0.947599i | −0.451375 | − | 0.892334i | \(-0.649066\pi\) |
0.998472 | − | 0.0552649i | \(-0.0176003\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −193.033 | + | 111.447i | −0.712297 | + | 0.411245i | −0.811911 | − | 0.583781i | \(-0.801573\pi\) |
0.0996137 | + | 0.995026i | \(0.468239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 114.074 | + | 312.024i | 0.417853 | + | 1.14295i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −102.433 | + | 59.1400i | −0.372485 | + | 0.215054i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1994 | + | 40.1826i | −0.0837525 | + | 0.145064i | −0.904859 | − | 0.425712i | \(-0.860024\pi\) |
0.821106 | + | 0.570775i | \(0.193357\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 102.971i | 0.369071i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 523.027 | 1.86131 | 0.930653 | − | 0.365902i | \(-0.119240\pi\) | ||||
0.930653 | + | 0.365902i | \(0.119240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 344.794 | + | 199.067i | 1.21835 | + | 0.703416i | 0.964565 | − | 0.263844i | \(-0.0849904\pi\) |
0.253787 | + | 0.967260i | \(0.418324\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −210.474 | − | 364.552i | −0.738505 | − | 1.27913i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.9497 | + | 13.3446i | 0.0555740 | + | 0.0464967i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.84646 | − | 4.93021i | −0.00984934 | − | 0.0170596i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −139.689 | − | 80.6493i | −0.480030 | − | 0.277145i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −81.0068 | −0.276474 | −0.138237 | − | 0.990399i | \(-0.544144\pi\) | ||||
−0.138237 | + | 0.990399i | \(0.544144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 102.153i | − | 0.346283i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −64.3770 | + | 111.504i | −0.216757 | + | 0.375435i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 173.473 | − | 100.154i | 0.580176 | − | 0.334965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −197.347 | + | 235.874i | −0.655638 | + | 0.783635i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 267.814 | − | 154.623i | 0.883876 | − | 0.510306i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −291.454 | + | 504.813i | −0.955586 | + | 1.65512i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 214.075i | 0.697312i | 0.937251 | + | 0.348656i | \(0.113362\pi\) | ||||
−0.937251 | + | 0.348656i | \(0.886638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −444.230 | −1.43764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −167.737 | − | 96.8432i | −0.539349 | − | 0.311393i | 0.205466 | − | 0.978664i | \(-0.434129\pi\) |
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 73.9149 | + | 128.024i | 0.236150 | + | 0.409024i | 0.959606 | − | 0.281346i | \(-0.0907810\pi\) |
−0.723456 | + | 0.690370i | \(0.757448\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −104.095 | + | 38.0564i | −0.330461 | + | 0.120814i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 71.0408 | + | 123.046i | 0.224104 | + | 0.388159i | 0.956050 | − | 0.293203i | \(-0.0947213\pi\) |
−0.731947 | + | 0.681362i | \(0.761388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 143.145 | + | 82.6445i | 0.448729 | + | 0.259074i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 429.631 | 1.33842 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 384.899i | − | 1.19164i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 244.142 | − | 422.867i | 0.751207 | − | 1.30113i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −98.5368 | + | 56.8902i | −0.301336 | + | 0.173976i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 151.091 | + | 26.4185i | 0.459243 | + | 0.0802993i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −265.954 | + | 153.549i | −0.803487 | + | 0.463893i | −0.844689 | − | 0.535258i | \(-0.820215\pi\) |
0.0412021 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −68.8677 | + | 119.282i | −0.206810 | + | 0.358205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 170.244i | 0.508190i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −100.940 | −0.299524 | −0.149762 | − | 0.988722i | \(-0.547851\pi\) | ||||
−0.149762 | + | 0.988722i | \(0.547851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 399.082 | + | 230.410i | 1.17723 | + | 0.679676i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −103.203 | − | 178.753i | −0.302649 | − | 0.524203i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −170.223 | + | 297.781i | −0.496276 | + | 0.868165i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −103.320 | − | 178.955i | −0.299477 | − | 0.518709i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −271.926 | − | 156.996i | −0.783647 | − | 0.452439i | 0.0540741 | − | 0.998537i | \(-0.482779\pi\) |
−0.837721 | + | 0.546098i | \(0.816113\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 69.1392 | 0.198107 | 0.0990534 | − | 0.995082i | \(-0.468419\pi\) | ||||
0.0990534 | + | 0.995082i | \(0.468419\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 531.523i | − | 1.51431i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −172.017 | + | 297.942i | −0.487300 | + | 0.844028i | −0.999893 | − | 0.0146034i | \(-0.995351\pi\) |
0.512594 | + | 0.858631i | \(0.328685\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −600.776 | + | 346.858i | −1.69233 | + | 0.977065i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 308.689 | + | 53.9746i | 0.864674 | + | 0.151189i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −466.067 | + | 269.084i | −1.29824 | + | 0.749537i | −0.980099 | − | 0.198508i | \(-0.936390\pi\) |
−0.318137 | + | 0.948045i | \(0.603057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 70.8581 | − | 122.730i | 0.196283 | − | 0.339972i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 264.863i | 0.729649i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −235.362 | −0.644828 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 111.276 | + | 64.2450i | 0.303203 | + | 0.175054i | 0.643881 | − | 0.765126i | \(-0.277323\pi\) |
−0.340678 | + | 0.940180i | \(0.610657\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.26689 | − | 5.65842i | −0.00885335 | − | 0.0153345i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.7718 | − | 9.78758i | 0.0721613 | − | 0.0263816i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −39.7402 | − | 68.8321i | −0.106542 | − | 0.184537i | 0.807825 | − | 0.589422i | \(-0.200645\pi\) |
−0.914367 | + | 0.404886i | \(0.867311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.7519 | − | 17.1773i | −0.0793383 | − | 0.0458060i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −682.348 | −1.80994 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 421.203i | − | 1.11135i | −0.831399 | − | 0.555676i | \(-0.812459\pi\) | ||
0.831399 | − | 0.555676i | \(-0.187541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 205.804 | − | 356.464i | 0.540169 | − | 0.935600i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −200.635 | + | 115.837i | −0.523851 | + | 0.302446i | −0.738509 | − | 0.674244i | \(-0.764470\pi\) |
0.214658 | + | 0.976689i | \(0.431136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 142.563 | − | 170.395i | 0.370293 | − | 0.442583i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 83.6800 | − | 48.3126i | 0.216227 | − | 0.124839i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 40.0992 | − | 69.4539i | 0.103083 | − | 0.178545i | −0.809870 | − | 0.586609i | \(-0.800463\pi\) |
0.912953 | + | 0.408064i | \(0.133796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 188.943i | − | 0.483230i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −426.145 | −1.08434 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 527.467 | + | 304.533i | 1.33536 | + | 0.770970i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −56.0008 | − | 96.9961i | −0.141060 | − | 0.244323i | 0.786836 | − | 0.617162i | \(-0.211718\pi\) |
−0.927896 | + | 0.372839i | \(0.878384\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 313.915 | + | 262.641i | 0.786753 | + | 0.658247i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −77.1126 | − | 133.563i | −0.192301 | − | 0.333075i | 0.753712 | − | 0.657205i | \(-0.228262\pi\) |
−0.946012 | + | 0.324131i | \(0.894928\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 737.931 | + | 426.045i | 1.83110 | + | 1.05718i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.820 | −1.00203 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 276.093i | − | 0.678360i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 51.6192 | − | 89.4071i | 0.126208 | − | 0.218599i | −0.795996 | − | 0.605302i | \(-0.793053\pi\) |
0.922205 | + | 0.386702i | \(0.126386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −335.773 | + | 193.859i | −0.816966 | + | 0.471675i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.1049 | + | 93.2868i | 0.0825785 | + | 0.225876i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −256.279 | + | 147.963i | −0.617540 | + | 0.356537i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 70.0276 | − | 121.291i | 0.167932 | − | 0.290867i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 384.000i | 0.916468i | 0.888832 | + | 0.458234i | \(0.151518\pi\) | ||||
−0.888832 | + | 0.458234i | \(0.848482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −385.061 | −0.914635 | −0.457317 | − | 0.889304i | \(-0.651190\pi\) | ||||
−0.457317 | + | 0.889304i | \(0.651190\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −41.7344 | − | 24.0954i | −0.0986629 | − | 0.0569631i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −230.289 | − | 398.872i | −0.541856 | − | 0.938523i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 97.6196 | − | 558.301i | 0.228617 | − | 1.30750i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 104.615 | + | 181.199i | 0.243858 | + | 0.422375i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 445.945 | + | 257.467i | 1.03468 | + | 0.597370i | 0.918321 | − | 0.395837i | \(-0.129546\pi\) |
0.116355 | + | 0.993208i | \(0.462879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −439.034 | −1.01393 | −0.506967 | − | 0.861965i | \(-0.669234\pi\) | ||||
−0.506967 | + | 0.861965i | \(0.669234\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 703.912i | 1.61819i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 123.389 | − | 213.716i | 0.282355 | − | 0.489053i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 200.608 | − | 115.821i | 0.456965 | − | 0.263829i | −0.253802 | − | 0.967256i | \(-0.581681\pi\) |
0.710767 | + | 0.703427i | \(0.248348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 82.3545 | − | 69.5064i | 0.186745 | − | 0.157611i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 110.163 | − | 63.6026i | 0.248675 | − | 0.143572i | −0.370483 | − | 0.928839i | \(-0.620808\pi\) |
0.619157 | + | 0.785267i | \(0.287474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −359.470 | + | 622.620i | −0.807798 | + | 1.39915i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 74.5957i | − | 0.166881i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −736.977 | −1.64137 | −0.820687 | − | 0.571378i | \(-0.806409\pi\) | ||||
−0.820687 | + | 0.571378i | \(0.806409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3424 | + | 6.54853i | 0.0251494 | + | 0.0145200i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 317.004 | + | 549.067i | 0.699788 | + | 1.21207i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −157.969 | + | 903.448i | −0.347185 | + | 1.98560i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 59.8757 | + | 103.708i | 0.131019 | + | 0.226932i | 0.924070 | − | 0.382224i | \(-0.124842\pi\) |
−0.793051 | + | 0.609156i | \(0.791508\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −434.193 | − | 250.682i | −0.945955 | − | 0.546147i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 213.385 | 0.462875 | 0.231438 | − | 0.972850i | \(-0.425657\pi\) | ||||
0.231438 | + | 0.972850i | \(0.425657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 140.406i | − | 0.303253i | −0.988438 | − | 0.151627i | \(-0.951549\pi\) | ||
0.988438 | − | 0.151627i | \(-0.0484511\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 439.509 | − | 761.252i | 0.945180 | − | 1.63710i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −443.927 | + | 256.302i | −0.950594 | + | 0.548826i | −0.893265 | − | 0.449530i | \(-0.851592\pi\) |
−0.0573286 | + | 0.998355i | \(0.518258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −56.8375 | − | 155.467i | −0.121189 | − | 0.331486i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 210.403 | − | 121.476i | 0.446716 | − | 0.257912i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −96.8434 | + | 167.738i | −0.204743 | + | 0.354625i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 601.561i | − | 1.26644i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.95581 | −0.0187753 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −432.197 | − | 249.529i | −0.902289 | − | 0.520937i | −0.0243471 | − | 0.999704i | \(-0.507751\pi\) |
−0.877942 | + | 0.478767i | \(0.841084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 569.884 | + | 987.068i | 1.18479 | + | 2.05212i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 154.097 | + | 128.928i | 0.319042 | + | 0.266931i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −222.645 | − | 385.633i | −0.459062 | − | 0.795119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −606.787 | − | 350.329i | −1.24597 | − | 0.719360i | −0.275666 | − | 0.961254i | \(-0.588898\pi\) |
−0.970303 | + | 0.241893i | \(0.922232\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 720.284 | 1.47297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 276.736i | − | 0.563618i | −0.959471 | − | 0.281809i | \(-0.909066\pi\) | ||
0.959471 | − | 0.281809i | \(-0.0909344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −321.815 | + | 557.400i | −0.652768 | + | 1.13063i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60.4501 | + | 34.9009i | −0.122121 | + | 0.0705068i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 432.828 | − | 517.326i | 0.870881 | − | 1.04090i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 143.156 | − | 82.6513i | 0.286886 | − | 0.165634i | −0.349650 | − | 0.936880i | \(-0.613700\pi\) |
0.636537 | + | 0.771246i | \(0.280366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.1931 | − | 66.1525i | 0.0762338 | − | 0.132041i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 140.294i | 0.278914i | 0.990228 | + | 0.139457i | \(0.0445356\pi\) | ||||
−0.990228 | + | 0.139457i | \(0.955464\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 853.722 | 1.69054 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −366.351 | − | 211.513i | −0.722585 | − | 0.417185i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 315.443 | + | 546.363i | 0.619730 | + | 1.07340i | 0.989535 | + | 0.144295i | \(0.0460914\pi\) |
−0.369804 | + | 0.929110i | \(0.620575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 214.933 | − | 78.5780i | 0.420613 | − | 0.153773i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −327.415 | − | 567.100i | −0.638237 | − | 1.10546i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1062.07 | − | 613.184i | −2.06227 | − | 1.19065i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 96.5991 | 0.186845 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 115.819i | 0.223159i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9121 | − | 39.6850i | 0.0439773 | − | 0.0761708i | −0.843199 | − | 0.537602i | \(-0.819330\pi\) |
0.887176 | + | 0.461431i | \(0.152664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 131.869 | − | 76.1344i | 0.252139 | − | 0.145572i | −0.368604 | − | 0.929586i | \(-0.620164\pi\) |
0.620743 | + | 0.784014i | \(0.286831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 482.452 | + | 84.3573i | 0.918956 | + | 0.160681i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 696.059 | − | 401.870i | 1.32080 | − | 0.762562i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −203.930 | + | 353.216i | −0.385500 | + | 0.667706i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.2066i | − | 0.0587695i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −54.0674 | −0.101440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1027.16 | + | 593.033i | 1.91993 | + | 1.10847i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −206.088 | − | 356.955i | −0.383777 | − | 0.664721i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −73.3008 | + | 203.201i | −0.135994 | + | 0.376996i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 94.2832 | + | 163.303i | 0.174276 | + | 0.301855i | 0.939910 | − | 0.341421i | \(-0.110908\pi\) |
−0.765635 | + | 0.643276i | \(0.777575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 170.372 | + | 98.3643i | 0.313760 | + | 0.181150i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −314.109 | −0.576347 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 469.901i | − | 0.859052i | −0.903055 | − | 0.429526i | \(-0.858681\pi\) | ||
0.903055 | − | 0.429526i | \(-0.141319\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −89.0355 | + | 154.214i | −0.162178 | + | 0.280900i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −728.020 | + | 420.323i | −1.32127 | + | 0.762836i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −583.355 | − | 102.000i | −1.05489 | − | 0.184449i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1018.26 | − | 587.894i | 1.83471 | − | 1.05927i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 263.848 | − | 456.998i | 0.473695 | − | 0.820463i | −0.525852 | − | 0.850576i | \(-0.676253\pi\) |
0.999547 | + | 0.0301129i | \(0.00958669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 799.580i | − | 1.43038i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 197.358 | 0.351797 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 453.298 | + | 261.712i | 0.805148 | + | 0.464852i | 0.845268 | − | 0.534342i | \(-0.179441\pi\) |
−0.0401201 | + | 0.999195i | \(0.512774\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 636.085 | + | 1101.73i | 1.12581 | + | 1.94997i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 370.596 | − | 135.487i | 0.653609 | − | 0.238954i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −199.215 | − | 345.051i | −0.350115 | − | 0.606417i | 0.636154 | − | 0.771562i | \(-0.280524\pi\) |
−0.986269 | + | 0.165145i | \(0.947191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −154.445 | − | 89.1690i | −0.270482 | − | 0.156163i | 0.358625 | − | 0.933482i | \(-0.383246\pi\) |
−0.629107 | + | 0.777319i | \(0.716579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −296.891 | −0.518134 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 295.300i | − | 0.513566i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.4369 | − | 78.6991i | 0.0787469 | − | 0.136394i | −0.823963 | − | 0.566644i | \(-0.808241\pi\) |
0.902710 | + | 0.430251i | \(0.141575\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −323.801 | + | 186.947i | −0.559242 | + | 0.322879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 184.636 | − | 220.681i | 0.317790 | − | 0.379830i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5469 | − | 8.97602i | 0.0266671 | − | 0.0153963i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 144.078 | − | 249.551i | 0.246287 | − | 0.426582i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18.9786i | − | 0.0323315i | −0.999869 | − | 0.0161658i | \(-0.994854\pi\) | ||
0.999869 | − | 0.0161658i | \(-0.00514594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1049.77 | 1.78228 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −656.780 | − | 379.192i | −1.11130 | − | 0.641611i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 228.806 | + | 396.304i | 0.385845 | + | 0.668303i | 0.991886 | − | 0.127130i | \(-0.0405767\pi\) |
−0.606041 | + | 0.795433i | \(0.707243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 663.511 | + | 555.135i | 1.11514 | + | 0.932999i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 253.133 | + | 438.440i | 0.424009 | + | 0.734405i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −109.568 | − | 63.2589i | −0.182918 | − | 0.105608i | 0.405745 | − | 0.913986i | \(-0.367012\pi\) |
−0.588663 | + | 0.808379i | \(0.700345\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 333.744 | 0.555315 | 0.277658 | − | 0.960680i | \(-0.410442\pi\) | ||||
0.277658 | + | 0.960680i | \(0.410442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.0073i | 0.0862476i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −365.598 | + | 633.234i | −0.604294 | + | 1.04667i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 503.950 | − | 290.956i | 0.830231 | − | 0.479334i | −0.0237005 | − | 0.999719i | \(-0.507545\pi\) |
0.853932 | + | 0.520385i | \(0.174211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −235.008 | − | 642.814i | −0.385891 | − | 1.05552i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −345.355 | + | 199.391i | −0.565229 | + | 0.326335i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −379.921 | + | 658.043i | −0.619774 | + | 1.07348i | 0.369753 | + | 0.929130i | \(0.379442\pi\) |
−0.989527 | + | 0.144350i | \(0.953891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 55.7760i | 0.0906927i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −906.461 | −1.46914 | −0.734571 | − | 0.678532i | \(-0.762617\pi\) | ||||
−0.734571 | + | 0.678532i | \(0.762617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 410.119 | + | 236.783i | 0.662552 | + | 0.382524i | 0.793248 | − | 0.608898i | \(-0.208388\pi\) |
−0.130697 | + | 0.991422i | \(0.541721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −160.725 | − | 278.384i | −0.258816 | − | 0.448283i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 120.401 | − | 688.591i | 0.193260 | − | 1.10528i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 287.953 | + | 498.749i | 0.460724 | + | 0.797998i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 223.235 | + | 128.885i | 0.356036 | + | 0.205558i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1075.09 | 1.70921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 523.166i | 0.829106i | 0.910025 | + | 0.414553i | \(0.136062\pi\) | ||||
−0.910025 | + | 0.414553i | \(0.863938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.8374 | − | 67.2683i | 0.0613545 | − | 0.106269i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 984.076 | − | 568.156i | 1.54973 | − | 0.894734i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −157.367 | − | 877.771i | −0.247045 | − | 1.37798i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −183.530 | + | 105.961i | −0.287214 | + | 0.165823i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 595.150 | − | 1030.83i | 0.928472 | − | 1.60816i | 0.142591 | − | 0.989782i | \(-0.454457\pi\) |
0.785880 | − | 0.618379i | \(-0.212210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 739.763i | − | 1.15049i | −0.817982 | − | 0.575243i | \(-0.804907\pi\) | ||
0.817982 | − | 0.575243i | \(-0.195093\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −824.848 | −1.27883 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −190.375 | − | 109.913i | −0.294243 | − | 0.169882i | 0.345611 | − | 0.938378i | \(-0.387672\pi\) |
−0.639854 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.2771 | + | 54.1734i | 0.0481927 | + | 0.0834722i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −147.209 | + | 841.911i | −0.226128 | + | 1.29326i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −424.090 | − | 734.546i | −0.649449 | − | 1.12488i | −0.983255 | − | 0.182236i | \(-0.941666\pi\) |
0.333806 | − | 0.942642i | \(-0.391667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1018.83 | − | 588.221i | −1.55546 | − | 0.898048i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −71.9002 | −0.109437 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 18.3735i | − | 0.0278809i | −0.999903 | − | 0.0139404i | \(-0.995562\pi\) | ||
0.999903 | − | 0.0139404i | \(-0.00443752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 456.940 | − | 791.444i | 0.691286 | − | 1.19734i | −0.280130 | − | 0.959962i | \(-0.590378\pi\) |
0.971417 | − | 0.237381i | \(-0.0762890\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −705.581 | + | 407.368i | −1.06423 | + | 0.614431i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 387.977 | + | 1061.23i | 0.583424 | + | 1.59583i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −357.378 | + | 206.332i | −0.535799 | + | 0.309343i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 383.373 | − | 664.022i | 0.573054 | − | 0.992559i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 356.946i | − | 0.531961i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1018.88 | −1.51393 | −0.756966 | − | 0.653455i | \(-0.773319\pi\) | ||||
−0.756966 | + | 0.653455i | \(0.773319\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −678.604 | − | 391.792i | −1.00534 | − | 0.580433i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 231.944 | + | 401.739i | 0.342606 | + | 0.593410i | 0.984916 | − | 0.173035i | \(-0.0553572\pi\) |
−0.642310 | + | 0.766445i | \(0.722024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 332.068 | + | 277.829i | 0.489054 | + | 0.409173i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 222.827 | + | 385.948i | 0.327206 | + | 0.566737i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 368.311 | + | 212.645i | 0.539255 | + | 0.311339i | 0.744777 | − | 0.667313i | \(-0.232556\pi\) |
−0.205522 | + | 0.978653i | \(0.565889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1070.36 | −1.56256 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 320.461i | − | 0.466464i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.0549 | + | 64.1810i | −0.0537807 | + | 0.0931509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −221.337 | + | 127.789i | −0.320314 | + | 0.184933i | −0.651533 | − | 0.758621i | \(-0.725874\pi\) |
0.331219 | + | 0.943554i | \(0.392540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.5512 | − | 52.0534i | 0.0628444 | − | 0.0751132i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 334.844 | − | 193.322i | 0.481790 | − | 0.278162i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.4997 | + | 44.1668i | −0.0365850 | + | 0.0633670i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 510.119i | − | 0.729783i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 354.151 | 0.505208 | 0.252604 | − | 0.967570i | \(-0.418713\pi\) | ||||
0.252604 | + | 0.967570i | \(0.418713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1216.06 | + | 702.091i | 1.72981 | + | 0.998707i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 205.692 | + | 356.269i | 0.291762 | + | 0.505346i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −779.621 | + | 285.023i | −1.10272 | + | 0.403145i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.2143 | − | 35.0122i | −0.0285110 | − | 0.0493825i | 0.851418 | − | 0.524488i | \(-0.175743\pi\) |
−0.879929 | + | 0.475106i | \(0.842410\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 161.134 | + | 93.0310i | 0.226631 | + | 0.130845i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 515.319 | 0.722748 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 577.614i | 0.807851i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −299.553 | + | 518.841i | −0.417786 | + | 0.723627i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −364.833 | + | 210.636i | −0.507417 | + | 0.292957i | −0.731771 | − | 0.681551i | \(-0.761306\pi\) |
0.224355 | + | 0.974508i | \(0.427973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1174.60 | + | 205.380i | 1.62913 | + | 0.284855i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −566.455 | + | 327.043i | −0.783479 | + | 0.452342i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −502.967 | + | 871.165i | −0.693748 | + | 1.20161i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1056.48i | 1.45321i | 0.687057 | + | 0.726603i | \(0.258902\pi\) | ||||
−0.687057 | + | 0.726603i | \(0.741098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −809.441 | −1.11034 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −653.165 | − | 377.105i | −0.893522 | − | 0.515875i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −333.330 | − | 577.344i | −0.454747 | − | 0.787645i | 0.543927 | − | 0.839133i | \(-0.316937\pi\) |
−0.998674 | + | 0.0514878i | \(0.983604\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −905.510 | + | 162.341i | −1.23199 | + | 0.220872i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −52.1247 | − | 90.2827i | −0.0707256 | − | 0.122500i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 654.379 | + | 377.806i | 0.885492 | + | 0.511239i | 0.872465 | − | 0.488676i | \(-0.162520\pi\) |
0.0130267 | + | 0.999915i | \(0.495853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1064.13 | −1.43607 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 616.726i | 0.830048i | 0.909810 | + | 0.415024i | \(0.136227\pi\) | ||||
−0.909810 | + | 0.415024i | \(0.863773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 102.967 | − | 178.344i | 0.138210 | − | 0.239387i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −78.2901 | + | 45.2008i | −0.104806 | + | 0.0605098i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1136.00 | − | 198.631i | −1.51669 | − | 0.265194i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −315.176 | + | 181.967i | −0.419675 | + | 0.242299i | −0.694938 | − | 0.719069i | \(-0.744568\pi\) |
0.275263 | + | 0.961369i | \(0.411235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −627.675 | + | 1087.16i | −0.833566 | + | 1.44378i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1750.28i | 2.31825i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −730.440 | −0.964915 | −0.482457 | − | 0.875919i | \(-0.660256\pi\) | ||||
−0.482457 | + | 0.875919i | \(0.660256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 109.584 | + | 63.2682i | 0.144379 | + | 0.0833573i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −183.675 | − | 318.134i | −0.241359 | − | 0.418047i | 0.719742 | − | 0.694241i | \(-0.244260\pi\) |
−0.961102 | + | 0.276194i | \(0.910927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 286.845 | − | 104.868i | 0.375944 | − | 0.137442i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −135.903 | − | 235.391i | −0.177651 | − | 0.307700i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −223.639 | − | 129.118i | −0.291577 | − | 0.168342i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −903.272 | −1.17461 | −0.587303 | − | 0.809367i | \(-0.699810\pi\) | ||||
−0.587303 | + | 0.809367i | \(0.699810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 807.969i | − | 1.04795i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 555.526 | − | 962.200i | 0.718663 | − | 1.24476i | −0.242867 | − | 0.970060i | \(-0.578088\pi\) |
0.961530 | − | 0.274701i | \(-0.0885787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1087.88 | − | 628.086i | 1.40371 | − | 0.810433i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −733.605 | + | 876.823i | −0.944151 | + | 1.12847i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.6863 | + | 33.3052i | −0.0740517 | + | 0.0427538i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 212.400 | − | 367.888i | 0.271959 | − | 0.471047i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1095.01i | 1.39848i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 670.711 | 0.854408 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 568.705 | + | 328.342i | 0.722623 | + | 0.417207i | 0.815717 | − | 0.578451i | \(-0.196342\pi\) |
−0.0930942 | + | 0.995657i | \(0.529676\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −367.879 | − | 637.185i | −0.466260 | − | 0.807585i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −948.698 | − | 793.740i | −1.19936 | − | 1.00346i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 736.774 | + | 1276.13i | 0.929097 | + | 1.60924i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 66.2093 | + | 38.2259i | 0.0832821 | + | 0.0480829i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 820.253 | 1.02918 | 0.514588 | − | 0.857438i | \(-0.327945\pi\) | ||||
0.514588 | + | 0.857438i | \(0.327945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 376.153i | 0.470780i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −109.814 | + | 190.203i | −0.137096 | + | 0.237457i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 124.816 | − | 72.0625i | 0.155437 | − | 0.0897416i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 190.454 | + | 520.946i | 0.236589 | + | 0.647138i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −664.743 | + | 383.790i | −0.823721 | + | 0.475576i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 76.3989 | − | 132.327i | 0.0944363 | − | 0.163568i | −0.814937 | − | 0.579550i | \(-0.803228\pi\) |
0.909373 | + | 0.415981i | \(0.136562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 203.504i | − | 0.250930i | −0.992098 | − | 0.125465i | \(-0.959958\pi\) | ||
0.992098 | − | 0.125465i | \(-0.0400423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 581.269 | 0.714968 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1722.06 | + | 994.231i | 2.11295 | + | 1.21991i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −492.537 | − | 853.099i | −0.602860 | − | 1.04418i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48.2576 | + | 275.992i | −0.0589225 | + | 0.336987i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −716.357 | − | 1240.77i | −0.872542 | − | 1.51129i | −0.859358 | − | 0.511374i | \(-0.829137\pi\) |
−0.0131839 | − | 0.999913i | \(-0.504197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −141.907 | − | 81.9300i | −0.172426 | − | 0.0995504i | 0.411303 | − | 0.911499i | \(-0.365074\pi\) |
−0.583729 | + | 0.811948i | \(0.698407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 308.452 | 0.373882 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1380.58i | − | 1.66939i | −0.550715 | − | 0.834693i | \(-0.685645\pi\) | ||
0.550715 | − | 0.834693i | \(-0.314355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.77609 | − | 13.4686i | 0.00938009 | − | 0.0162468i | −0.861297 | − | 0.508101i | \(-0.830348\pi\) |
0.870677 | + | 0.491855i | \(0.163681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 104.789 | − | 60.4998i | 0.126100 | − | 0.0728037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −791.257 | − | 285.431i | −0.949888 | − | 0.342654i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 182.624 | − | 105.438i | 0.218712 | − | 0.126273i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 683.704 | − | 1184.21i | 0.816851 | − | 1.41483i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 843.862i | − | 1.00580i | −0.864346 | − | 0.502898i | \(-0.832267\pi\) | ||
0.864346 | − | 0.502898i | \(-0.167733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 564.732 | 0.671500 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1181.22 | − | 681.979i | −1.40121 | − | 0.808991i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −583.915 | − | 1011.37i | −0.691023 | − | 1.19689i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 122.453 | − | 700.330i | 0.144573 | − | 0.826835i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −519.130 | − | 899.159i | −0.611460 | − | 1.05908i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 596.950 | + | 344.649i | 0.701469 | + | 0.404993i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 507.417 | 0.594862 | 0.297431 | − | 0.954743i | \(-0.403870\pi\) | ||||
0.297431 | + | 0.954743i | \(0.403870\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 355.005i | − | 0.415211i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 204.793 | − | 354.713i | 0.238966 | − | 0.413900i | −0.721452 | − | 0.692464i | \(-0.756525\pi\) |
0.960418 | + | 0.278564i | \(0.0898584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −543.757 | + | 313.938i | −0.633011 | + | 0.365469i | −0.781917 | − | 0.623382i | \(-0.785758\pi\) |
0.148906 | + | 0.988851i | \(0.452425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.6214 | − | 50.9348i | −0.0216276 | − | 0.0591577i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 334.919 | − | 193.365i | 0.388086 | − | 0.224062i | −0.293244 | − | 0.956038i | \(-0.594735\pi\) |
0.681331 | + | 0.731976i | \(0.261402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −159.869 | + | 276.901i | −0.184820 | + | 0.320117i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8461i | 0.0171235i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −372.964 | −0.429188 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 372.706 | + | 215.182i | 0.427906 | + | 0.247051i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −68.0154 | − | 117.806i | −0.0779099 | − | 0.134944i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 70.7261 | + | 59.1739i | 0.0808298 | + | 0.0676273i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 648.580 | + | 1123.37i | 0.739544 | + | 1.28093i | 0.952701 | + | 0.303909i | \(0.0982920\pi\) |
−0.213157 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 182.949 | + | 105.625i | 0.208133 | + | 0.120165i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 869.810 | 0.987299 | 0.493649 | − | 0.869661i | \(-0.335663\pi\) | ||||
0.493649 | + | 0.869661i | \(0.335663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 350.462i | 0.396899i | 0.980111 | + | 0.198450i | \(0.0635906\pi\) | ||||
−0.980111 | + | 0.198450i | \(0.936409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −133.199 | + | 230.707i | −0.150507 | + | 0.260686i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1043.07 | + | 602.215i | −1.17595 | + | 0.678935i | −0.955074 | − | 0.296367i | \(-0.904225\pi\) |
−0.220876 | + | 0.975302i | \(0.570891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −708.976 | + | 847.385i | −0.797498 | + | 0.953189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 215.212 | − | 124.253i | 0.241540 | − | 0.139453i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −245.647 | + | 425.473i | −0.275081 | + | 0.476454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1137.88i | − | 1.27137i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −522.369 | −0.582351 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1520.24 | − | 877.712i | −1.69104 | − | 0.976320i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9523 | + | 60.5392i | 0.0387928 | + | 0.0671911i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 753.254 | − | 275.384i | 0.834168 | − | 0.304965i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 271.550 | + | 470.339i | 0.300056 | + | 0.519712i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 938.261 | + | 541.705i | 1.03447 | + | 0.597250i | 0.918261 | − | 0.395976i | \(-0.129594\pi\) |
0.116206 | + | 0.993225i | \(0.462927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 260.801 | 0.286910 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 677.413i | 0.743593i | 0.928314 | + | 0.371797i | \(0.121258\pi\) | ||||
−0.928314 | + | 0.371797i | \(0.878742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 90.6057 | − | 156.934i | 0.0992395 | − | 0.171888i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1316.46 | − | 760.058i | 1.43875 | − | 0.830665i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1126.78 | + | 197.019i | 1.22877 | + | 0.214852i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −834.480 | + | 481.787i | −0.908031 | + | 0.524252i | −0.879797 | − | 0.475349i | \(-0.842322\pi\) |
−0.0282338 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 279.134 | − | 483.474i | 0.303077 | − | 0.524945i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1753.66i | 1.89996i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1680.27 | 1.81651 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −324.448 | − | 187.320i | −0.349998 | − | 0.202071i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 489.329 | + | 847.543i | 0.526727 | + | 0.912318i | 0.999515 | + | 0.0311416i | \(0.00991428\pi\) |
−0.472788 | + | 0.881176i | \(0.656752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −708.603 | − | 839.586i | −0.761120 | − | 0.901811i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 252.549 | + | 437.428i | 0.270685 | + | 0.468841i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 471.844 | + | 272.419i | 0.504646 | + | 0.291357i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −653.549 | −0.697490 | −0.348745 | − | 0.937218i | \(-0.613392\pi\) | ||||
−0.348745 | + | 0.937218i | \(0.613392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 385.513i | − | 0.410557i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −771.643 | + | 1336.53i | −0.820025 | + | 1.42032i | 0.0856385 | + | 0.996326i | \(0.472707\pi\) |
−0.905663 | + | 0.423998i | \(0.860626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.3176 | + | 16.3492i | −0.0300293 | + | 0.0173374i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1449.83 | + | 253.504i | 1.53421 | + | 0.268258i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1031.64 | − | 595.615i | 1.08937 | − | 0.628949i | 0.155963 | − | 0.987763i | \(-0.450152\pi\) |
0.933409 | + | 0.358814i | \(0.116819\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −297.489 | + | 515.266i | −0.313476 | + | 0.542957i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 370.523i | − | 0.389614i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 895.795 | 0.939974 | 0.469987 | − | 0.882673i | \(-0.344259\pi\) | ||||
0.469987 | + | 0.882673i | \(0.344259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −709.807 | − | 409.808i | −0.743254 | − | 0.429118i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −215.522 | − | 373.295i | −0.225206 | − | 0.390067i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 977.451 | − | 357.349i | 1.01924 | − | 0.372626i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 615.553 | + | 1066.17i | 0.640534 | + | 1.10944i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 313.786 | + | 181.164i | 0.325842 | + | 0.188125i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1032.19 | −1.06963 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 160.933i | − | 0.166425i | −0.996532 | − | 0.0832125i | \(-0.973482\pi\) | ||
0.996532 | − | 0.0832125i | \(-0.0265180\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −501.872 | + | 869.268i | −0.517928 | + | 0.897078i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 93.6821 | − | 54.0874i | 0.0964801 | − | 0.0557028i | −0.450984 | − | 0.892532i | \(-0.648927\pi\) |
0.547464 | + | 0.836829i | \(0.315593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −241.238 | + | 288.334i | −0.247932 | + | 0.296335i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1102.76 | + | 636.678i | −1.13103 | + | 0.653003i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −587.879 | + | 1018.24i | −0.601718 | + | 1.04221i | 0.390843 | + | 0.920457i | \(0.372184\pi\) |
−0.992561 | + | 0.121749i | \(0.961150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 440.246i | − | 0.449689i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.9565 | −0.0978150 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1445.70 | − | 834.675i | −1.47070 | − | 0.849109i | −0.471242 | − | 0.882004i | \(-0.656194\pi\) |
−0.999459 | + | 0.0328947i | \(0.989527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1046.82 | − | 1813.15i | −1.06276 | − | 1.84076i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −306.782 | − | 256.673i | −0.310823 | − | 0.260054i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −241.781 | − | 418.778i | −0.244471 | − | 0.423435i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 186.089 | + | 107.439i | 0.187779 | + | 0.108414i | 0.590943 | − | 0.806714i | \(-0.298756\pi\) |
−0.403163 | + | 0.915128i | \(0.632089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 800.853 | 0.806499 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1397.63i | 1.40465i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 245.695 | − | 425.557i | 0.246435 | − | 0.426837i | −0.716099 | − | 0.697998i | \(-0.754074\pi\) |
0.962534 | + | 0.271161i | \(0.0874076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1584.02 | − | 914.533i | 1.58560 | − | 0.915449i |
(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 | 224.3.r.c.95.3 | ✓ | 12 | |
4.3 | odd | 2 | inner | 224.3.r.c.95.4 | yes | 12 | |
7.2 | even | 3 | inner | 224.3.r.c.191.4 | yes | 12 | |
7.3 | odd | 6 | 1568.3.d.k.1471.3 | 6 | |||
7.4 | even | 3 | 1568.3.d.j.1471.4 | 6 | |||
8.3 | odd | 2 | 448.3.r.g.319.3 | 12 | |||
8.5 | even | 2 | 448.3.r.g.319.4 | 12 | |||
28.3 | even | 6 | 1568.3.d.k.1471.4 | 6 | |||
28.11 | odd | 6 | 1568.3.d.j.1471.3 | 6 | |||
28.23 | odd | 6 | inner | 224.3.r.c.191.3 | yes | 12 | |
56.37 | even | 6 | 448.3.r.g.191.3 | 12 | |||
56.51 | odd | 6 | 448.3.r.g.191.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.c.95.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
224.3.r.c.95.4 | yes | 12 | 4.3 | odd | 2 | inner | |
224.3.r.c.191.3 | yes | 12 | 28.23 | odd | 6 | inner | |
224.3.r.c.191.4 | yes | 12 | 7.2 | even | 3 | inner | |
448.3.r.g.191.3 | 12 | 56.37 | even | 6 | |||
448.3.r.g.191.4 | 12 | 56.51 | odd | 6 | |||
448.3.r.g.319.3 | 12 | 8.3 | odd | 2 | |||
448.3.r.g.319.4 | 12 | 8.5 | even | 2 | |||
1568.3.d.j.1471.3 | 6 | 28.11 | odd | 6 | |||
1568.3.d.j.1471.4 | 6 | 7.4 | even | 3 | |||
1568.3.d.k.1471.3 | 6 | 7.3 | odd | 6 | |||
1568.3.d.k.1471.4 | 6 | 28.3 | even | 6 |