Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(161,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 13x^{10} + 129x^{8} - 512x^{6} + 1548x^{4} - 160x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.1 | ||
Root | \(-0.278546 + 0.160819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.161 |
Dual form | 1728.3.h.i.161.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.03816 | −1.80763 | −0.903816 | − | 0.427920i | \(-0.859246\pi\) | ||||
−0.903816 | + | 0.427920i | \(0.859246\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.92398 | 1.13200 | 0.565999 | − | 0.824406i | \(-0.308491\pi\) | ||||
0.565999 | + | 0.824406i | \(0.308491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.07018 | −0.0972888 | −0.0486444 | − | 0.998816i | \(-0.515490\pi\) | ||||
−0.0486444 | + | 0.998816i | \(0.515490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 15.7264i | − 1.20972i | −0.796330 | − | 0.604862i | \(-0.793228\pi\) | ||||
0.796330 | − | 0.604862i | \(-0.206772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 23.3793i | − 1.37525i | −0.726065 | − | 0.687626i | \(-0.758653\pi\) | ||||
0.726065 | − | 0.687626i | \(-0.241347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 31.2389i | 1.64415i | 0.569376 | + | 0.822077i | \(0.307185\pi\) | ||||
−0.569376 | + | 0.822077i | \(0.692815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.34147i | 0.188760i | 0.995536 | + | 0.0943798i | \(0.0300868\pi\) | ||||
−0.995536 | + | 0.0943798i | \(0.969913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56.6884 | 2.26754 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.634271 | 0.0218714 | 0.0109357 | − | 0.999940i | \(-0.496519\pi\) | ||||
0.0109357 | + | 0.999940i | \(0.496519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.1947 | 0.586927 | 0.293463 | − | 0.955970i | \(-0.405192\pi\) | ||||
0.293463 | + | 0.955970i | \(0.405192\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −71.6182 | −2.04624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.79821i | 0.237789i | 0.992907 | + | 0.118895i | \(0.0379351\pi\) | ||||
−0.992907 | + | 0.118895i | \(0.962065\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.2389i | 0.957047i | 0.878075 | + | 0.478524i | \(0.158828\pi\) | ||||
−0.878075 | + | 0.478524i | \(0.841172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 62.8989i | 1.46277i | 0.681967 | + | 0.731383i | \(0.261125\pi\) | ||||
−0.681967 | + | 0.731383i | \(0.738875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 71.0368i | − 1.51142i | −0.654906 | − | 0.755710i | \(-0.727292\pi\) | ||||
0.654906 | − | 0.755710i | \(-0.272708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7895 | 0.281418 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −90.1026 | −1.70005 | −0.850024 | − | 0.526743i | \(-0.823413\pi\) | ||||
−0.850024 | + | 0.526743i | \(0.823413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.67244 | 0.175862 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28.7586 | 0.487434 | 0.243717 | − | 0.969846i | \(-0.421633\pi\) | ||||
0.243717 | + | 0.969846i | \(0.421633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 108.701i | − 1.78198i | −0.454018 | − | 0.890992i | \(-0.650010\pi\) | ||||
0.454018 | − | 0.890992i | \(-0.349990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 142.138i | 2.18674i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 70.8989i | − 1.05819i | −0.848562 | − | 0.529097i | \(-0.822531\pi\) | ||||
0.848562 | − | 0.529097i | \(-0.177469\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2930i | 0.201309i | 0.994921 | + | 0.100655i | \(0.0320937\pi\) | ||||
−0.994921 | + | 0.100655i | \(0.967906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −73.6884 | −1.00943 | −0.504715 | − | 0.863286i | \(-0.668402\pi\) | ||||
−0.504715 | + | 0.863286i | \(0.668402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.48006 | −0.110131 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.35100 | −0.0171012 | −0.00855061 | − | 0.999963i | \(-0.502722\pi\) | ||||
−0.00855061 | + | 0.999963i | \(0.502722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 119.065 | 1.43452 | 0.717261 | − | 0.696805i | \(-0.245396\pi\) | ||||
0.717261 | + | 0.696805i | \(0.245396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 211.306i | 2.48595i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 100.815i | − 1.13276i | −0.824145 | − | 0.566379i | \(-0.808344\pi\) | ||||
0.824145 | − | 0.566379i | \(-0.191656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 124.616i | − 1.36940i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 282.343i | − 2.97203i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −83.0568 | −0.856256 | −0.428128 | − | 0.903718i | \(-0.640827\pi\) | ||||
−0.428128 | + | 0.903718i | \(0.640827\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −43.9984 | −0.435628 | −0.217814 | − | 0.975990i | \(-0.569893\pi\) | ||||
−0.217814 | + | 0.975990i | \(0.569893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −75.9629 | −0.737504 | −0.368752 | − | 0.929528i | \(-0.620215\pi\) | ||||
−0.368752 | + | 0.929528i | \(0.620215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −204.096 | −1.90744 | −0.953720 | − | 0.300695i | \(-0.902781\pi\) | ||||
−0.953720 | + | 0.300695i | \(0.902781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 77.5940i | − 0.711872i | −0.934510 | − | 0.355936i | \(-0.884162\pi\) | ||||
0.934510 | − | 0.355936i | \(-0.115838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 151.520i | 1.34088i | 0.741963 | + | 0.670441i | \(0.233895\pi\) | ||||
−0.741963 | + | 0.670441i | \(0.766105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 39.2389i | − 0.341208i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 185.257i | − 1.55678i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.855 | −0.990535 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −286.405 | −2.29124 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −225.793 | −1.77790 | −0.888951 | − | 0.458003i | \(-0.848565\pi\) | ||||
−0.888951 | + | 0.458003i | \(0.848565\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −114.039 | −0.870529 | −0.435265 | − | 0.900303i | \(-0.643345\pi\) | ||||
−0.435265 | + | 0.900303i | \(0.643345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 247.537i | 1.86118i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 132.535i | 0.967407i | 0.875232 | + | 0.483703i | \(0.160709\pi\) | ||||
−0.875232 | + | 0.483703i | \(0.839291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 104.000i | − 0.748201i | −0.927388 | − | 0.374101i | \(-0.877951\pi\) | ||||
0.927388 | − | 0.374101i | \(-0.122049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.8300i | 0.117693i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.73264 | −0.0395355 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −122.450 | −0.821810 | −0.410905 | − | 0.911678i | \(-0.634787\pi\) | ||||
−0.410905 | + | 0.911678i | \(0.634787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8183 | 0.0782672 | 0.0391336 | − | 0.999234i | \(-0.487540\pi\) | ||||
0.0391336 | + | 0.999234i | \(0.487540\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −164.447 | −1.06095 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 82.5781i | − 0.525975i | −0.964799 | − | 0.262988i | \(-0.915292\pi\) | ||||
0.964799 | − | 0.262988i | \(-0.0847078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 34.4017i | 0.213675i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 49.1821i | 0.301731i | 0.988554 | + | 0.150865i | \(0.0482060\pi\) | ||||
−0.988554 | + | 0.150865i | \(0.951794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 174.465i | 1.04470i | 0.852731 | + | 0.522351i | \(0.174945\pi\) | ||||
−0.852731 | + | 0.522351i | \(0.825055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −78.3200 | −0.463432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −153.801 | −0.889024 | −0.444512 | − | 0.895773i | \(-0.646623\pi\) | ||||
−0.444512 | + | 0.895773i | \(0.646623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 449.198 | 2.56685 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −212.658 | −1.18803 | −0.594015 | − | 0.804454i | \(-0.702458\pi\) | ||||
−0.594015 | + | 0.804454i | \(0.702458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 161.359i | − 0.891487i | −0.895161 | − | 0.445743i | \(-0.852939\pi\) | ||||
0.895161 | − | 0.445743i | \(-0.147061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 79.5197i | − 0.429836i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0200i | 0.133797i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 40.6465i | − 0.212809i | −0.994323 | − | 0.106404i | \(-0.966066\pi\) | ||||
0.994323 | − | 0.106404i | \(-0.0339338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 301.486 | 1.56211 | 0.781053 | − | 0.624465i | \(-0.214683\pi\) | ||||
0.781053 | + | 0.624465i | \(0.214683\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.0193 | −0.121925 | −0.0609627 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609627 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −56.8231 | −0.285543 | −0.142772 | − | 0.989756i | \(-0.545601\pi\) | ||||
−0.142772 | + | 0.989756i | \(0.545601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.02595 | 0.0247584 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 354.648i | − 1.72999i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 33.4312i | − 0.159958i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 116.357i | 0.551454i | 0.961236 | + | 0.275727i | \(0.0889186\pi\) | ||||
−0.961236 | + | 0.275727i | \(0.911081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 568.491i | − 2.64414i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 144.175 | 0.664400 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −367.672 | −1.66368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −341.311 | −1.53054 | −0.765270 | − | 0.643709i | \(-0.777395\pi\) | ||||
−0.765270 | + | 0.643709i | \(0.777395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −174.956 | −0.770730 | −0.385365 | − | 0.922764i | \(-0.625925\pi\) | ||||
−0.385365 | + | 0.922764i | \(0.625925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 211.520i | 0.923670i | 0.886966 | + | 0.461835i | \(0.152809\pi\) | ||||
−0.886966 | + | 0.461835i | \(0.847191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 60.9776i | 0.261706i | 0.991402 | + | 0.130853i | \(0.0417716\pi\) | ||||
−0.991402 | + | 0.130853i | \(0.958228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 642.042i | 2.73209i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 331.136i | − 1.38551i | −0.721174 | − | 0.692754i | \(-0.756397\pi\) | ||||
0.721174 | − | 0.692754i | \(-0.243603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6842 | −0.0982749 | −0.0491374 | − | 0.998792i | \(-0.515647\pi\) | ||||
−0.0491374 | + | 0.998792i | \(0.515647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −124.631 | −0.508700 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 491.276 | 1.98897 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 389.429 | 1.55151 | 0.775754 | − | 0.631035i | \(-0.217370\pi\) | ||||
0.775754 | + | 0.631035i | \(0.217370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.64614i | − 0.0183642i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 326.419i | 1.27011i | 0.772466 | + | 0.635056i | \(0.219023\pi\) | ||||
−0.772466 | + | 0.635056i | \(0.780977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 69.7168i | 0.269177i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 178.610i | − 0.679124i | −0.940584 | − | 0.339562i | \(-0.889721\pi\) | ||||
0.940584 | − | 0.339562i | \(-0.110279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 814.362 | 3.07306 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 403.038 | 1.49828 | 0.749142 | − | 0.662409i | \(-0.230466\pi\) | ||||
0.749142 | + | 0.662409i | \(0.230466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 178.330 | 0.658044 | 0.329022 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329022 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −60.6666 | −0.220606 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 140.359i | − 0.506712i | −0.967373 | − | 0.253356i | \(-0.918466\pi\) | ||||
0.967373 | − | 0.253356i | \(-0.0815344\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 396.335i | − 1.41045i | −0.708986 | − | 0.705223i | \(-0.750847\pi\) | ||||
0.708986 | − | 0.705223i | \(-0.249153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 178.283i | − 0.629976i | −0.949096 | − | 0.314988i | \(-0.898000\pi\) | ||||
0.949096 | − | 0.314988i | \(-0.102000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 310.929i | 1.08338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −257.592 | −0.891320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 47.6578 | 0.162655 | 0.0813273 | − | 0.996687i | \(-0.474084\pi\) | ||||
0.0813273 | + | 0.996687i | \(0.474084\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −259.925 | −0.881101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 68.2758 | 0.228347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 498.410i | 1.65585i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 982.458i | 3.22117i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 74.5421i | 0.242808i | 0.992603 | + | 0.121404i | \(0.0387397\pi\) | ||||
−0.992603 | + | 0.121404i | \(0.961260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 322.453i | 1.03683i | 0.855130 | + | 0.518414i | \(0.173477\pi\) | ||||
−0.855130 | + | 0.518414i | \(0.826523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −239.324 | −0.764614 | −0.382307 | − | 0.924035i | \(-0.624870\pi\) | ||||
−0.382307 | + | 0.924035i | \(0.624870\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −93.5590 | −0.295139 | −0.147569 | − | 0.989052i | \(-0.547145\pi\) | ||||
−0.147569 | + | 0.989052i | \(0.547145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.678782 | −0.00212784 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 730.345 | 2.26113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 891.505i | − 2.74309i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 562.894i | − 1.71092i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 338.042i | − 1.02128i | −0.859796 | − | 0.510638i | \(-0.829409\pi\) | ||||
0.859796 | − | 0.510638i | \(-0.170591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 640.796i | 1.91282i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −235.507 | −0.698835 | −0.349417 | − | 0.936967i | \(-0.613620\pi\) | ||||
−0.349417 | + | 0.936967i | \(0.613620\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.4716 | −0.0571014 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −279.008 | −0.813433 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −449.450 | −1.29524 | −0.647622 | − | 0.761962i | \(-0.724236\pi\) | ||||
−0.647622 | + | 0.761962i | \(0.724236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 208.735i | 0.598095i | 0.954238 | + | 0.299048i | \(0.0966689\pi\) | ||||
−0.954238 | + | 0.299048i | \(0.903331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 404.076i | 1.14469i | 0.820012 | + | 0.572346i | \(0.193966\pi\) | ||||
−0.820012 | + | 0.572346i | \(0.806034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 129.182i | − 0.363893i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 605.760i | − 1.68735i | −0.536852 | − | 0.843677i | \(-0.680386\pi\) | ||||
0.536852 | − | 0.843677i | \(-0.319614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −614.872 | −1.70325 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 666.008 | 1.82468 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 346.991 | 0.945481 | 0.472740 | − | 0.881202i | \(-0.343265\pi\) | ||||
0.472740 | + | 0.881202i | \(0.343265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −713.971 | −1.92445 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 413.336i | 1.10814i | 0.832470 | + | 0.554070i | \(0.186926\pi\) | ||||
−0.832470 | + | 0.554070i | \(0.813074\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 9.97480i | − 0.0264584i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 348.503i | − 0.919533i | −0.888040 | − | 0.459767i | \(-0.847933\pi\) | ||||
0.888040 | − | 0.459767i | \(-0.152067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 236.283i | − 0.616927i | −0.951236 | − | 0.308464i | \(-0.900185\pi\) | ||||
0.951236 | − | 0.308464i | \(-0.0998148\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 76.6442 | 0.199076 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −138.591 | −0.356276 | −0.178138 | − | 0.984005i | \(-0.557007\pi\) | ||||
−0.178138 | + | 0.984005i | \(0.557007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 101.501 | 0.259592 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.2105 | 0.0309127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 512.390i | 1.29065i | 0.763906 | + | 0.645327i | \(0.223279\pi\) | ||||
−0.763906 | + | 0.645327i | \(0.776721\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 442.345i | − 1.10310i | −0.834141 | − | 0.551552i | \(-0.814036\pi\) | ||||
0.834141 | − | 0.551552i | \(-0.185964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 286.138i | − 0.710020i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 9.41564i | − 0.0231342i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −260.305 | −0.636443 | −0.318222 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318222 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 227.883 | 0.551774 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1076.13 | −2.59309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 460.986 | 1.10020 | 0.550102 | − | 0.835097i | \(-0.314589\pi\) | ||||
0.550102 | + | 0.835097i | \(0.314589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 215.681i | − 0.512307i | −0.966636 | − | 0.256153i | \(-0.917545\pi\) | ||||
0.966636 | − | 0.256153i | \(-0.0824552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1325.34i | − 3.11844i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 861.345i | − 2.01720i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 621.965i | 1.44307i | 0.692376 | + | 0.721537i | \(0.256564\pi\) | ||||
−0.692376 | + | 0.721537i | \(0.743436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −117.566 | −0.271516 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −135.623 | −0.310350 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −235.424 | −0.536273 | −0.268136 | − | 0.963381i | \(-0.586408\pi\) | ||||
−0.268136 | + | 0.963381i | \(0.586408\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 325.320 | 0.734357 | 0.367178 | − | 0.930151i | \(-0.380324\pi\) | ||||
0.367178 | + | 0.930151i | \(0.380324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 911.186i | 2.04761i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 430.658i | − 0.959149i | −0.877501 | − | 0.479574i | \(-0.840791\pi\) | ||||
0.877501 | − | 0.479574i | \(-0.159209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 41.9926i | − 0.0931100i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1126.30i | 2.47538i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −544.402 | −1.19125 | −0.595626 | − | 0.803262i | \(-0.703096\pi\) | ||||
−0.595626 | + | 0.803262i | \(0.703096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 304.995 | 0.661594 | 0.330797 | − | 0.943702i | \(-0.392682\pi\) | ||||
0.330797 | + | 0.943702i | \(0.392682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 591.711 | 1.27799 | 0.638997 | − | 0.769209i | \(-0.279350\pi\) | ||||
0.638997 | + | 0.769209i | \(0.279350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 327.438 | 0.701152 | 0.350576 | − | 0.936534i | \(-0.385986\pi\) | ||||
0.350576 | + | 0.936534i | \(0.385986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 561.802i | − 1.19787i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 67.3130i | − 0.142311i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1770.89i | 3.72818i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 745.601i | 1.55658i | 0.627906 | + | 0.778289i | \(0.283912\pi\) | ||||
−0.627906 | + | 0.778289i | \(0.716088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 138.364 | 0.287660 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 750.681 | 1.54780 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −804.238 | −1.65141 | −0.825707 | − | 0.564099i | \(-0.809223\pi\) | ||||
−0.825707 | + | 0.564099i | \(0.809223\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −152.679 | −0.310956 | −0.155478 | − | 0.987839i | \(-0.549692\pi\) | ||||
−0.155478 | + | 0.987839i | \(0.549692\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14.8288i | − 0.0300787i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 113.257i | 0.227882i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 753.686i | − 1.51039i | −0.655498 | − | 0.755197i | \(-0.727541\pi\) | ||||
0.655498 | − | 0.755197i | \(-0.272459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 429.795i | 0.854463i | 0.904142 | + | 0.427232i | \(0.140511\pi\) | ||||
−0.904142 | + | 0.427232i | \(0.859489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 397.665 | 0.787456 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −491.207 | −0.965042 | −0.482521 | − | 0.875884i | \(-0.660279\pi\) | ||||
−0.482521 | + | 0.875884i | \(0.660279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −583.906 | −1.14267 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 686.565 | 1.33314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 76.0219i | 0.147044i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 666.985i | − 1.28020i | −0.768291 | − | 0.640101i | \(-0.778893\pi\) | ||||
0.768291 | − | 0.640101i | \(-0.221107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 443.127i | − 0.847280i | −0.905831 | − | 0.423640i | \(-0.860752\pi\) | ||||
0.905831 | − | 0.423640i | \(-0.139248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 425.380i | − 0.807173i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 510.152 | 0.964370 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 617.088 | 1.15776 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1844.65 | 3.44795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.7572 | −0.0273788 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 172.653i | − 0.319137i | −0.987187 | − | 0.159569i | \(-0.948990\pi\) | ||||
0.987187 | − | 0.159569i | \(-0.0510103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 701.308i | 1.28680i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 55.1084i | − 0.100747i | −0.998730 | − | 0.0503733i | \(-0.983959\pi\) | ||||
0.998730 | − | 0.0503733i | \(-0.0160411\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.8140i | 0.0359600i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7053 | −0.0193585 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 49.5862 | 0.0890237 | 0.0445119 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445119 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 989.175 | 1.76954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 172.517 | 0.306425 | 0.153213 | − | 0.988193i | \(-0.451038\pi\) | ||||
0.153213 | + | 0.988193i | \(0.451038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1369.46i | − 2.42382i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 572.646i | 1.00641i | 0.864168 | + | 0.503203i | \(0.167845\pi\) | ||||
−0.864168 | + | 0.503203i | \(0.832155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 132.517i | − 0.232079i | −0.993245 | − | 0.116039i | \(-0.962980\pi\) | ||||
0.993245 | − | 0.116039i | \(-0.0370199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 246.111i | 0.428019i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −198.324 | −0.343716 | −0.171858 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171858 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 943.471 | 1.62387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 96.4257 | 0.165396 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −60.3600 | −0.102828 | −0.0514140 | − | 0.998677i | \(-0.516373\pi\) | ||||
−0.0514140 | + | 0.998677i | \(0.516373\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 568.384i | 0.964999i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 462.144i | 0.779332i | 0.920956 | + | 0.389666i | \(0.127410\pi\) | ||||
−0.920956 | + | 0.389666i | \(0.872590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1674.38i | 2.81409i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 965.054i | 1.61111i | 0.592522 | + | 0.805554i | \(0.298132\pi\) | ||||
−0.592522 | + | 0.805554i | \(0.701868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 822.800 | 1.36905 | 0.684526 | − | 0.728989i | \(-0.260009\pi\) | ||||
0.684526 | + | 0.728989i | \(0.260009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1083.27 | 1.79052 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −512.002 | −0.843496 | −0.421748 | − | 0.906713i | \(-0.638583\pi\) | ||||
−0.421748 | + | 0.906713i | \(0.638583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1117.15 | −1.82840 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 430.232i | − 0.701846i | −0.936404 | − | 0.350923i | \(-0.885868\pi\) | ||||
0.936404 | − | 0.350923i | \(-0.114132\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 840.028i | − 1.36147i | −0.732529 | − | 0.680736i | \(-0.761660\pi\) | ||||
0.732529 | − | 0.680736i | \(-0.238340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 662.138i | 1.06969i | 0.844950 | + | 0.534845i | \(0.179630\pi\) | ||||
−0.844950 | + | 0.534845i | \(0.820370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 798.859i | − 1.28228i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1171.37 | 1.87419 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 205.696 | 0.327021 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −594.485 | −0.942131 | −0.471065 | − | 0.882098i | \(-0.656130\pi\) | ||||
−0.471065 | + | 0.882098i | \(0.656130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2040.76 | 3.21379 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 216.859i | − 0.340438i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 393.431i | 0.613777i | 0.951745 | + | 0.306889i | \(0.0992879\pi\) | ||||
−0.951745 | + | 0.306889i | \(0.900712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 945.265i | 1.47009i | 0.678021 | + | 0.735043i | \(0.262838\pi\) | ||||
−0.678021 | + | 0.735043i | \(0.737162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 460.952i | 0.712446i | 0.934401 | + | 0.356223i | \(0.115936\pi\) | ||||
−0.934401 | + | 0.356223i | \(0.884064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.7768 | −0.0474219 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1163.60 | 1.78192 | 0.890961 | − | 0.454080i | \(-0.150032\pi\) | ||||
0.890961 | + | 0.454080i | \(0.150032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1030.71 | 1.57360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 894.773 | 1.35777 | 0.678887 | − | 0.734243i | \(-0.262463\pi\) | ||||
0.678887 | + | 0.734243i | \(0.262463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 571.283i | 0.864271i | 0.901809 | + | 0.432136i | \(0.142240\pi\) | ||||
−0.901809 | + | 0.432136i | \(0.857760\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2237.28i | − 3.36433i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.75367i | 0.00412844i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 116.329i | 0.173367i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −521.714 | −0.775206 | −0.387603 | − | 0.921826i | \(-0.626697\pi\) | ||||
−0.387603 | + | 0.921826i | \(0.626697\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 735.979 | 1.08712 | 0.543559 | − | 0.839371i | \(-0.317076\pi\) | ||||
0.543559 | + | 0.839371i | \(0.317076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −658.141 | −0.969279 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.32560 | −0.0121898 | −0.00609488 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609488 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1197.87i | − 1.74872i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1416.99i | 2.05659i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 833.459i | − 1.20616i | −0.797679 | − | 0.603082i | \(-0.793939\pi\) | ||||
0.797679 | − | 0.603082i | \(-0.206061\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 939.969i | 1.35247i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 917.379 | 1.31618 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −748.081 | −1.06716 | −0.533581 | − | 0.845749i | \(-0.679154\pi\) | ||||
−0.533581 | + | 0.845749i | \(0.679154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −274.847 | −0.390963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −348.643 | −0.493130 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 870.918i | 1.22837i | 0.789160 | + | 0.614187i | \(0.210516\pi\) | ||||
−0.789160 | + | 0.614187i | \(0.789484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 78.9919i | 0.110788i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 152.113i | − 0.212745i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 734.578i | 1.02167i | 0.859680 | + | 0.510833i | \(0.170663\pi\) | ||||
−0.859680 | + | 0.510833i | \(0.829337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −601.928 | −0.834852 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.9558 | 0.0495942 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.8359 | 0.0286601 | 0.0143300 | − | 0.999897i | \(-0.495438\pi\) | ||||
0.0143300 | + | 0.999897i | \(0.495438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1470.53 | 2.01167 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.75355i | − 0.0133063i | −0.999978 | − | 0.00665317i | \(-0.997882\pi\) | ||||
0.999978 | − | 0.00665317i | \(-0.00211779\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 75.8744i | 0.102950i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 352.340i | 0.476779i | 0.971170 | + | 0.238390i | \(0.0766196\pi\) | ||||
−0.971170 | + | 0.238390i | \(0.923380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1063.07i | − 1.43078i | −0.698726 | − | 0.715390i | \(-0.746249\pi\) | ||||
0.698726 | − | 0.715390i | \(-0.253751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1106.72 | 1.48553 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1617.25 | −2.15922 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 421.237 | 0.560902 | 0.280451 | − | 0.959868i | \(-0.409516\pi\) | ||||
0.280451 | + | 0.959868i | \(0.409516\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −106.816 | −0.141478 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1155.52i | 1.52644i | 0.646137 | + | 0.763221i | \(0.276383\pi\) | ||||
−0.646137 | + | 0.763221i | \(0.723617\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1281.10i | − 1.68345i | −0.539909 | − | 0.841723i | \(-0.681541\pi\) | ||||
0.539909 | − | 0.841723i | \(-0.318459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 614.854i | − 0.805837i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 452.269i | − 0.589660i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −156.377 | −0.203351 | −0.101676 | − | 0.994818i | \(-0.532420\pi\) | ||||
−0.101676 | + | 0.994818i | \(0.532420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1063.74 | −1.37612 | −0.688058 | − | 0.725656i | \(-0.741537\pi\) | ||||
−0.688058 | + | 0.725656i | \(0.741537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1031.43 | 1.33088 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1225.78 | −1.57353 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 15.2960i | − 0.0195851i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 746.354i | 0.950770i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 133.863i | − 0.170093i | −0.996377 | − | 0.0850464i | \(-0.972896\pi\) | ||||
0.996377 | − | 0.0850464i | \(-0.0271039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1200.64i | 1.51787i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1709.48 | −2.15571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −287.344 | −0.360532 | −0.180266 | − | 0.983618i | \(-0.557696\pi\) | ||||
−0.180266 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1660.79 | −2.07859 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 78.8596 | 0.0982063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 310.929i | − 0.386247i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 427.228i | − 0.528094i | −0.964510 | − | 0.264047i | \(-0.914943\pi\) | ||||
0.964510 | − | 0.264047i | \(-0.0850574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 257.702i | 0.317758i | 0.987298 | + | 0.158879i | \(0.0507880\pi\) | ||||
−0.987298 | + | 0.158879i | \(0.949212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 444.516i | − 0.545418i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1964.90 | −2.40501 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 514.687 | 0.626903 | 0.313452 | − | 0.949604i | \(-0.398515\pi\) | ||||
0.313452 | + | 0.949604i | \(0.398515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 271.043 | 0.329335 | 0.164667 | − | 0.986349i | \(-0.447345\pi\) | ||||
0.164667 | + | 0.986349i | \(0.447345\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1266.64 | −1.53161 | −0.765804 | − | 0.643073i | \(-0.777659\pi\) | ||||
−0.765804 | + | 0.643073i | \(0.777659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1076.89i | − 1.29902i | −0.760354 | − | 0.649509i | \(-0.774975\pi\) | ||||
0.760354 | − | 0.649509i | \(-0.225025\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 322.388i | − 0.387021i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1576.84i | − 1.88844i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 311.036i | − 0.370723i | −0.982670 | − | 0.185361i | \(-0.940654\pi\) | ||||
0.982670 | − | 0.185361i | \(-0.0593456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −840.598 | −0.999522 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 707.869 | 0.837715 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −949.726 | −1.12128 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.1972 | −0.0448851 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 97.6779i | 0.114511i | 0.998360 | + | 0.0572555i | \(0.0182350\pi\) | ||||
−0.998360 | + | 0.0572555i | \(0.981765\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 738.242i | − 0.861426i | −0.902489 | − | 0.430713i | \(-0.858262\pi\) | ||||
0.902489 | − | 0.430713i | \(-0.141738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1325.05i | − 1.54255i | −0.636499 | − | 0.771277i | \(-0.719618\pi\) | ||||
0.636499 | − | 0.771277i | \(-0.280382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 111.255i | − 0.128917i | −0.997920 | − | 0.0644584i | \(-0.979468\pi\) | ||||
0.997920 | − | 0.0644584i | \(-0.0205320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1390.08 | 1.60703 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.44581 | 0.00166376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1114.99 | −1.28012 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2269.47 | −2.59368 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 15.1739i | − 0.0173021i | −0.999963 | − | 0.00865105i | \(-0.997246\pi\) | ||||
0.999963 | − | 0.00865105i | \(-0.00275375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 965.029i | − 1.09538i | −0.836682 | − | 0.547690i | \(-0.815507\pi\) | ||||
0.836682 | − | 0.547690i | \(-0.184493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1588.94i | − 1.79948i | −0.436423 | − | 0.899742i | \(-0.643755\pi\) | ||||
0.436423 | − | 0.899742i | \(-0.356245\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 99.4993i | − 0.112175i | −0.998426 | − | 0.0560876i | \(-0.982137\pi\) | ||||
0.998426 | − | 0.0560876i | \(-0.0178626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1789.18 | −2.01258 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2219.11 | 2.48501 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1922.03 | 2.14752 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.5404 | 0.0128369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2106.54i | 2.33800i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1458.39i | 1.61148i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 763.643i | 0.841944i | 0.907074 | + | 0.420972i | \(0.138311\pi\) | ||||
−0.907074 | + | 0.420972i | \(0.861689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 484.661i | 0.532010i | 0.963972 | + | 0.266005i | \(0.0857038\pi\) | ||||
−0.963972 | + | 0.266005i | \(0.914296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −127.421 | −0.139563 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −903.645 | −0.985436 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −518.271 | −0.563951 | −0.281975 | − | 0.959422i | \(-0.590990\pi\) | ||||
−0.281975 | + | 0.959422i | \(0.590990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 224.777 | 0.243529 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 498.756i | 0.539196i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 709.355i | 0.763568i | 0.924251 | + | 0.381784i | \(0.124690\pi\) | ||||
−0.924251 | + | 0.381784i | \(0.875310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 430.768i | 0.462694i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 226.135i | − 0.241855i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1308.30 | 1.39626 | 0.698132 | − | 0.715969i | \(-0.254015\pi\) | ||||
0.698132 | + | 0.715969i | \(0.254015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −256.150 | −0.272211 | −0.136105 | − | 0.990694i | \(-0.543459\pi\) | ||||
−0.136105 | + | 0.990694i | \(0.543459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −170.355 | −0.180652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 542.855 | 0.573237 | 0.286618 | − | 0.958045i | \(-0.407469\pi\) | ||||
0.286618 | + | 0.958045i | \(0.407469\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1158.85i | 1.22113i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1161.82i | 1.21912i | 0.792742 | + | 0.609558i | \(0.208653\pi\) | ||||
−0.792742 | + | 0.609558i | \(0.791347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 367.369i | 0.384680i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1050.20i | 1.09510i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −629.952 | −0.655517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2724.88 | −2.82371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −682.976 | −0.706283 | −0.353142 | − | 0.935570i | \(-0.614887\pi\) | ||||
−0.353142 | + | 0.935570i | \(0.614887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 252.827 | 0.260378 | 0.130189 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130189 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 824.094i | − 0.846962i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 208.186i | − 0.213087i | −0.994308 | − | 0.106543i | \(-0.966022\pi\) | ||||
0.994308 | − | 0.106543i | \(-0.0339783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 107.890i | 0.110205i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1154.92i | − 1.17489i | −0.809264 | − | 0.587446i | \(-0.800134\pi\) | ||||
0.809264 | − | 0.587446i | \(-0.199866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 217.090 | 0.220396 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −273.074 | −0.276111 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −668.987 | −0.675062 | −0.337531 | − | 0.941314i | \(-0.609592\pi\) | ||||
−0.337531 | + | 0.941314i | \(0.609592\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 513.577 | 0.516158 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 846.458i | 0.849005i | 0.905427 | + | 0.424502i | \(0.139551\pi\) | ||||
−0.905427 | + | 0.424502i | \(0.860449\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.h.i.161.1 | ✓ | 12 | |
3.2 | odd | 2 | 1728.3.h.j.161.11 | yes | 12 | ||
4.3 | odd | 2 | 1728.3.h.j.161.1 | yes | 12 | ||
8.3 | odd | 2 | inner | 1728.3.h.i.161.12 | yes | 12 | |
8.5 | even | 2 | 1728.3.h.j.161.12 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.3.h.i.161.11 | yes | 12 | |
24.5 | odd | 2 | inner | 1728.3.h.i.161.2 | yes | 12 | |
24.11 | even | 2 | 1728.3.h.j.161.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.h.i.161.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1728.3.h.i.161.2 | yes | 12 | 24.5 | odd | 2 | inner | |
1728.3.h.i.161.11 | yes | 12 | 12.11 | even | 2 | inner | |
1728.3.h.i.161.12 | yes | 12 | 8.3 | odd | 2 | inner | |
1728.3.h.j.161.1 | yes | 12 | 4.3 | odd | 2 | ||
1728.3.h.j.161.2 | yes | 12 | 24.11 | even | 2 | ||
1728.3.h.j.161.11 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.h.j.161.12 | yes | 12 | 8.5 | even | 2 |