Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(809,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.b (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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.17 | ||
Character | \(\chi\) | \(=\) | 1620.809 |
Dual form | 1620.3.b.a.809.18 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 2.82619 | − | 4.12464i | 0.565237 | − | 0.824928i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.52777i | 1.07540i | 0.843137 | + | 0.537698i | \(0.180706\pi\) | ||||
−0.843137 | + | 0.537698i | \(0.819294\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.67363i | − | 0.606694i | −0.952880 | − | 0.303347i | \(-0.901896\pi\) | ||
0.952880 | − | 0.303347i | \(-0.0981041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5692i | 1.19763i | 0.800888 | + | 0.598814i | \(0.204361\pi\) | ||||
−0.800888 | + | 0.598814i | \(0.795639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.9462 | 1.11448 | 0.557242 | − | 0.830350i | \(-0.311860\pi\) | ||||
0.557242 | + | 0.830350i | \(0.311860\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −27.1064 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.6113 | 0.852665 | 0.426333 | − | 0.904567i | \(-0.359805\pi\) | ||||
0.426333 | + | 0.904567i | \(0.359805\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.02534 | − | 23.3140i | −0.361014 | − | 0.932560i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.97175i | 0.240405i | 0.992749 | + | 0.120203i | \(0.0383544\pi\) | ||||
−0.992749 | + | 0.120203i | \(0.961646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.5191 | 0.952228 | 0.476114 | − | 0.879383i | \(-0.342045\pi\) | ||||
0.476114 | + | 0.879383i | \(0.342045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.0494 | + | 21.2749i | 0.887125 | + | 0.607854i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52.2126i | 1.41115i | 0.708634 | + | 0.705576i | \(0.249312\pi\) | ||||
−0.708634 | + | 0.705576i | \(0.750688\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.8539i | 1.48424i | 0.670266 | + | 0.742121i | \(0.266180\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6611i | 0.247934i | 0.992286 | + | 0.123967i | \(0.0395616\pi\) | ||||
−0.992286 | + | 0.123967i | \(0.960438\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −75.8093 | −1.61296 | −0.806482 | − | 0.591259i | \(-0.798631\pi\) | ||||
−0.806482 | + | 0.591259i | \(0.798631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.66737 | −0.156477 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −47.3234 | −0.892895 | −0.446447 | − | 0.894810i | \(-0.647311\pi\) | ||||
−0.446447 | + | 0.894810i | \(0.647311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −27.5263 | − | 18.8609i | −0.500479 | − | 0.342926i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 24.4204i | − | 0.413905i | −0.978351 | − | 0.206952i | \(-0.933646\pi\) | ||
0.978351 | − | 0.206952i | \(-0.0663545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.7094 | 0.667367 | 0.333683 | − | 0.942685i | \(-0.391708\pi\) | ||||
0.333683 | + | 0.942685i | \(0.391708\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 64.2172 | + | 44.0013i | 0.987957 | + | 0.676944i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 58.9100i | − | 0.879254i | −0.898180 | − | 0.439627i | \(-0.855111\pi\) | ||
0.898180 | − | 0.439627i | \(-0.144889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33.9404i | 0.478034i | 0.971015 | + | 0.239017i | \(0.0768252\pi\) | ||||
−0.971015 | + | 0.239017i | \(0.923175\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 79.8213i | 1.09344i | 0.837315 | + | 0.546722i | \(0.184124\pi\) | ||||
−0.837315 | + | 0.546722i | \(0.815876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 50.2376 | 0.652436 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.0506 | 1.08925 | 0.544624 | − | 0.838680i | \(-0.316672\pi\) | ||||
0.544624 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 153.076 | 1.84429 | 0.922143 | − | 0.386850i | \(-0.126437\pi\) | ||||
0.922143 | + | 0.386850i | \(0.126437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 53.5456 | − | 78.1464i | 0.629948 | − | 0.919370i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 83.3156i | 0.936130i | 0.883694 | + | 0.468065i | \(0.155049\pi\) | ||||
−0.883694 | + | 0.468065i | \(0.844951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −117.201 | −1.28792 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −76.6077 | + | 111.804i | −0.806397 | + | 1.17689i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2175i | 0.167190i | 0.996500 | + | 0.0835952i | \(0.0266403\pi\) | ||||
−0.996500 | + | 0.0835952i | \(0.973360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127.041i | 1.25783i | 0.777473 | + | 0.628916i | \(0.216501\pi\) | ||||
−0.777473 | + | 0.628916i | \(0.783499\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 131.249i | − | 1.27426i | −0.770755 | − | 0.637132i | \(-0.780121\pi\) | ||
0.770755 | − | 0.637132i | \(-0.219879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 131.922 | 1.23292 | 0.616458 | − | 0.787388i | \(-0.288567\pi\) | ||||
0.616458 | + | 0.787388i | \(0.288567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −201.576 | −1.84932 | −0.924662 | − | 0.380790i | \(-0.875652\pi\) | ||||
−0.924662 | + | 0.380790i | \(0.875652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 33.6972 | 0.298205 | 0.149102 | − | 0.988822i | \(-0.452362\pi\) | ||||
0.149102 | + | 0.988822i | \(0.452362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 55.4252 | − | 80.8896i | 0.481958 | − | 0.703388i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 142.623i | 1.19851i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 76.4626 | 0.631923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −121.669 | − | 28.6634i | −0.973354 | − | 0.229307i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 118.081i | 0.929768i | 0.885372 | + | 0.464884i | \(0.153904\pi\) | ||||
−0.885372 | + | 0.464884i | \(0.846096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 28.0634i | − | 0.214224i | −0.994247 | − | 0.107112i | \(-0.965840\pi\) | ||
0.994247 | − | 0.107112i | \(-0.0341604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 204.051i | − | 1.53422i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 107.772 | 0.786656 | 0.393328 | − | 0.919398i | \(-0.371324\pi\) | ||||
0.393328 | + | 0.919398i | \(0.371324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 170.944 | 1.22981 | 0.614907 | − | 0.788600i | \(-0.289194\pi\) | ||||
0.614907 | + | 0.788600i | \(0.289194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 103.903 | 0.726593 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.7560 | + | 19.7035i | 0.198317 | + | 0.135886i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 81.6965i | 0.548299i | 0.961687 | + | 0.274149i | \(0.0883963\pi\) | ||||
−0.961687 | + | 0.274149i | \(0.911604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.21306 | 0.0610136 | 0.0305068 | − | 0.999535i | \(-0.490288\pi\) | ||||
0.0305068 | + | 0.999535i | \(0.490288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 83.4264 | − | 121.756i | 0.538235 | − | 0.785520i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 288.365i | 1.83672i | 0.395749 | + | 0.918359i | \(0.370485\pi\) | ||||
−0.395749 | + | 0.918359i | \(0.629515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 147.629i | 0.916953i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 69.1070i | 0.423970i | 0.977273 | + | 0.211985i | \(0.0679927\pi\) | ||||
−0.977273 | + | 0.211985i | \(0.932007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 195.225 | 1.16901 | 0.584507 | − | 0.811389i | \(-0.301288\pi\) | ||||
0.584507 | + | 0.811389i | \(0.301288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −73.3987 | −0.434312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −59.3786 | −0.343229 | −0.171614 | − | 0.985164i | \(-0.554898\pi\) | ||||
−0.171614 | + | 0.985164i | \(0.554898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.503 | − | 67.9407i | 1.00287 | − | 0.388233i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 82.1619i | 0.459005i | 0.973308 | + | 0.229503i | \(0.0737099\pi\) | ||||
−0.973308 | + | 0.229503i | \(0.926290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −242.120 | −1.33768 | −0.668840 | − | 0.743407i | \(-0.733209\pi\) | ||||
−0.668840 | + | 0.743407i | \(0.733209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 215.358 | + | 147.563i | 1.16410 | + | 0.797636i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 126.440i | − | 0.676151i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 27.4015i | − | 0.143463i | −0.997424 | − | 0.0717317i | \(-0.977147\pi\) | ||
0.997424 | − | 0.0717317i | \(-0.0228525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 139.702i | − | 0.723844i | −0.932208 | − | 0.361922i | \(-0.882121\pi\) | ||
0.932208 | − | 0.361922i | \(-0.117879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 125.291 | 0.635994 | 0.317997 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317997 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −242.646 | −1.21933 | −0.609664 | − | 0.792660i | \(-0.708696\pi\) | ||||
−0.609664 | + | 0.792660i | \(0.708696\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −52.4818 | −0.258531 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 251.001 | + | 171.984i | 1.22439 | + | 0.838949i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 180.898i | 0.865541i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 163.529 | 0.775018 | 0.387509 | − | 0.921866i | \(-0.373336\pi\) | ||||
0.387509 | + | 0.921866i | \(0.373336\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 43.9734 | + | 30.1304i | 0.204528 | + | 0.140141i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 222.213i | 1.02402i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 294.977i | 1.33474i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 201.029i | 0.901477i | 0.892656 | + | 0.450739i | \(0.148839\pi\) | ||||
−0.892656 | + | 0.450739i | \(0.851161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −155.168 | −0.683559 | −0.341780 | − | 0.939780i | \(-0.611030\pi\) | ||||
−0.341780 | + | 0.939780i | \(0.611030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −310.150 | −1.35437 | −0.677183 | − | 0.735814i | \(-0.736800\pi\) | ||||
−0.677183 | + | 0.735814i | \(0.736800\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 375.988 | 1.61368 | 0.806842 | − | 0.590768i | \(-0.201175\pi\) | ||||
0.806842 | + | 0.590768i | \(0.201175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −214.251 | + | 312.686i | −0.911707 | + | 1.33058i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 308.019i | − | 1.28878i | −0.764696 | − | 0.644391i | \(-0.777111\pi\) | ||
0.764696 | − | 0.644391i | \(-0.222889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 300.232 | 1.24577 | 0.622887 | − | 0.782312i | \(-0.285959\pi\) | ||||
0.622887 | + | 0.782312i | \(0.285959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.6694 | + | 31.6251i | −0.0884466 | + | 0.129082i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 422.024i | − | 1.70860i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 153.779i | − | 0.612666i | −0.951924 | − | 0.306333i | \(-0.900898\pi\) | ||
0.951924 | − | 0.306333i | \(-0.0991021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 130.879i | − | 0.517307i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.5779 | 0.115089 | 0.0575446 | − | 0.998343i | \(-0.481673\pi\) | ||||
0.0575446 | + | 0.998343i | \(0.481673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −393.045 | −1.51755 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −258.391 | −0.982475 | −0.491237 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491237 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −133.745 | + | 195.192i | −0.504697 | + | 0.736574i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 443.969i | 1.65044i | 0.564810 | + | 0.825221i | \(0.308949\pi\) | ||||
−0.564810 | + | 0.825221i | \(0.691051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 233.582 | 0.861928 | 0.430964 | − | 0.902369i | \(-0.358174\pi\) | ||||
0.430964 | + | 0.902369i | \(0.358174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −155.589 | + | 60.2318i | −0.565779 | + | 0.219025i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 199.108i | 0.718802i | 0.933183 | + | 0.359401i | \(0.117019\pi\) | ||||
−0.933183 | + | 0.359401i | \(0.882981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 173.925i | − | 0.618949i | −0.950908 | − | 0.309474i | \(-0.899847\pi\) | ||
0.950908 | − | 0.309474i | \(-0.100153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 221.755i | 0.783587i | 0.920053 | + | 0.391793i | \(0.128145\pi\) | ||||
−0.920053 | + | 0.391793i | \(0.871855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −458.094 | −1.59615 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 69.9596 | 0.242075 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −100.496 | −0.342990 | −0.171495 | − | 0.985185i | \(-0.554860\pi\) | ||||
−0.171495 | + | 0.985185i | \(0.554860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −100.725 | − | 69.0165i | −0.341442 | − | 0.233954i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 305.331i | 1.02118i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80.2547 | −0.266627 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 115.052 | − | 167.912i | 0.377221 | − | 0.550530i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 214.703i | − | 0.699360i | −0.936869 | − | 0.349680i | \(-0.886290\pi\) | ||
0.936869 | − | 0.349680i | \(-0.113710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 347.773i | 1.11824i | 0.829087 | + | 0.559120i | \(0.188861\pi\) | ||||
−0.829087 | + | 0.559120i | \(0.811139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 254.365i | − | 0.812668i | −0.913725 | − | 0.406334i | \(-0.866807\pi\) | ||
0.913725 | − | 0.406334i | \(-0.133193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 417.859 | 1.31817 | 0.659083 | − | 0.752070i | \(-0.270944\pi\) | ||||
0.659083 | + | 0.752070i | \(0.270944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.5269 | 0.145852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −513.564 | −1.58998 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 362.980 | − | 140.517i | 1.11686 | − | 0.432360i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 570.675i | − | 1.73457i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 38.0345 | 0.114908 | 0.0574540 | − | 0.998348i | \(-0.481702\pi\) | ||||
0.0574540 | + | 0.998348i | \(0.481702\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −242.983 | − | 166.491i | −0.725322 | − | 0.496987i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 342.230i | − | 1.01552i | −0.861499 | − | 0.507760i | \(-0.830474\pi\) | ||
0.861499 | − | 0.507760i | \(-0.169526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 196.999i | − | 0.577711i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 311.143i | 0.907122i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −590.327 | −1.70123 | −0.850615 | − | 0.525788i | \(-0.823770\pi\) | ||||
−0.850615 | + | 0.525788i | \(0.823770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 45.5246 | 0.130443 | 0.0652215 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652215 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 215.450 | 0.610339 | 0.305170 | − | 0.952298i | \(-0.401287\pi\) | ||||
0.305170 | + | 0.952298i | \(0.401287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 139.992 | + | 95.9219i | 0.394344 | + | 0.270203i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 69.0790i | 0.192421i | 0.995361 | + | 0.0962104i | \(0.0306722\pi\) | ||||
−0.995361 | + | 0.0962104i | \(0.969328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 373.756 | 1.03534 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 329.234 | + | 225.590i | 0.902012 | + | 0.618055i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 234.990i | − | 0.640299i | −0.947367 | − | 0.320150i | \(-0.896267\pi\) | ||
0.947367 | − | 0.320150i | \(-0.103733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 356.240i | − | 0.960216i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 138.314i | 0.370814i | 0.982662 | + | 0.185407i | \(0.0593604\pi\) | ||||
−0.982662 | + | 0.185407i | \(0.940640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −108.544 | −0.287916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −412.330 | −1.08794 | −0.543971 | − | 0.839104i | \(-0.683080\pi\) | ||||
−0.543971 | + | 0.839104i | \(0.683080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 448.998 | 1.17232 | 0.586159 | − | 0.810196i | \(-0.300639\pi\) | ||||
0.586159 | + | 0.810196i | \(0.300639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 141.981 | − | 207.212i | 0.368781 | − | 0.538213i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 361.573i | 0.929494i | 0.885444 | + | 0.464747i | \(0.153855\pi\) | ||||
−0.885444 | + | 0.464747i | \(0.846145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 371.560 | 0.950282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 243.195 | − | 354.928i | 0.615684 | − | 0.898552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 673.227i | − | 1.69579i | −0.530168 | − | 0.847893i | \(-0.677871\pi\) | ||
0.530168 | − | 0.847893i | \(-0.322129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 138.781i | − | 0.346086i | −0.984914 | − | 0.173043i | \(-0.944640\pi\) | ||
0.984914 | − | 0.173043i | \(-0.0553600\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 459.587i | 1.14041i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 348.448 | 0.856137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −635.790 | −1.55450 | −0.777249 | − | 0.629193i | \(-0.783386\pi\) | ||||
−0.777249 | + | 0.629193i | \(0.783386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 183.831 | 0.445111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 432.620 | − | 631.382i | 1.04246 | − | 1.52140i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 785.128i | − | 1.87381i | −0.349578 | − | 0.936907i | \(-0.613675\pi\) | ||
0.349578 | − | 0.936907i | \(-0.386325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −116.223 | −0.276064 | −0.138032 | − | 0.990428i | \(-0.544078\pi\) | ||||
−0.138032 | + | 0.990428i | \(0.544078\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −170.996 | − | 441.713i | −0.402344 | − | 1.03932i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 306.451i | 0.717684i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 606.430i | − | 1.40703i | −0.710680 | − | 0.703515i | \(-0.751613\pi\) | ||
0.710680 | − | 0.703515i | \(-0.248387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 638.451i | − | 1.47448i | −0.675629 | − | 0.737242i | \(-0.736128\pi\) | ||
0.675629 | − | 0.737242i | \(-0.263872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −531.591 | −1.21646 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −752.450 | −1.71401 | −0.857005 | − | 0.515309i | \(-0.827677\pi\) | ||||
−0.857005 | + | 0.515309i | \(0.827677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 308.710 | 0.696862 | 0.348431 | − | 0.937334i | \(-0.386715\pi\) | ||||
0.348431 | + | 0.937334i | \(0.386715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 343.647 | + | 235.465i | 0.772240 | + | 0.529136i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 516.232i | − | 1.14974i | −0.818246 | − | 0.574869i | \(-0.805053\pi\) | ||
0.818246 | − | 0.574869i | \(-0.194947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 406.117 | 0.900480 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −331.232 | + | 483.413i | −0.727983 | + | 1.06245i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 481.476i | − | 1.05356i | −0.850002 | − | 0.526779i | \(-0.823400\pi\) | ||
0.850002 | − | 0.526779i | \(-0.176600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 68.6414i | 0.148897i | 0.997225 | + | 0.0744484i | \(0.0237196\pi\) | ||||
−0.997225 | + | 0.0744484i | \(0.976280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 219.016i | 0.473037i | 0.971627 | + | 0.236518i | \(0.0760064\pi\) | ||||
−0.971627 | + | 0.236518i | \(0.923994\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −87.1086 | −0.186528 | −0.0932640 | − | 0.995641i | \(-0.529730\pi\) | ||||
−0.0932640 | + | 0.995641i | \(0.529730\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 443.461 | 0.945546 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 71.1486 | 0.150420 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 244.644 | + | 631.959i | 0.515041 | + | 1.33044i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 702.080i | − | 1.46572i | −0.680379 | − | 0.732860i | \(-0.738185\pi\) | ||
0.680379 | − | 0.732860i | \(-0.261815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −812.907 | −1.69003 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 66.8912 | + | 45.8336i | 0.137920 | + | 0.0945022i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 272.680i | − | 0.559918i | −0.960012 | − | 0.279959i | \(-0.909679\pi\) | ||
0.960012 | − | 0.279959i | \(-0.0903208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 764.337i | − | 1.55669i | −0.627834 | − | 0.778347i | \(-0.716058\pi\) | ||
0.627834 | − | 0.778347i | \(-0.283942\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 132.088i | 0.267928i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −255.496 | −0.514076 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −873.142 | −1.74978 | −0.874891 | − | 0.484319i | \(-0.839067\pi\) | ||||
−0.874891 | + | 0.484319i | \(0.839067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −966.017 | −1.92051 | −0.960255 | − | 0.279123i | \(-0.909956\pi\) | ||||
−0.960255 | + | 0.279123i | \(0.909956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 523.999 | + | 359.042i | 1.03762 | + | 0.710974i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 987.379i | − | 1.93984i | −0.243424 | − | 0.969920i | \(-0.578271\pi\) | ||
0.243424 | − | 0.969920i | \(-0.421729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −600.877 | −1.17588 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −541.356 | − | 370.935i | −1.05118 | − | 0.720261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 505.923i | 0.978575i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 952.317i | 1.82786i | 0.405868 | + | 0.913932i | \(0.366969\pi\) | ||||
−0.405868 | + | 0.913932i | \(0.633031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 660.769i | 1.26342i | 0.775205 | + | 0.631710i | \(0.217647\pi\) | ||||
−0.775205 | + | 0.631710i | \(0.782353\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 559.275 | 1.06124 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −144.397 | −0.272962 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −947.444 | −1.77757 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 372.836 | − | 544.131i | 0.696890 | − | 1.01707i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 51.1692i | 0.0949336i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 520.946 | 0.962931 | 0.481466 | − | 0.876465i | \(-0.340105\pi\) | ||||
0.481466 | + | 0.876465i | \(0.340105\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −569.692 | + | 831.430i | −1.04531 | + | 1.52556i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 788.066i | 1.44071i | 0.693608 | + | 0.720353i | \(0.256020\pi\) | ||||
−0.693608 | + | 0.720353i | \(0.743980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 188.979i | − | 0.342974i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 647.769i | 1.17137i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −142.413 | −0.255678 | −0.127839 | − | 0.991795i | \(-0.540804\pi\) | ||||
−0.127839 | + | 0.991795i | \(0.540804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −165.985 | −0.296932 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −832.795 | −1.47921 | −0.739605 | − | 0.673041i | \(-0.764988\pi\) | ||||
−0.739605 | + | 0.673041i | \(0.764988\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 95.2345 | − | 138.989i | 0.168557 | − | 0.245998i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1017.03i | 1.78740i | 0.448666 | + | 0.893699i | \(0.351899\pi\) | ||||
−0.448666 | + | 0.893699i | \(0.648101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 356.274 | 0.623948 | 0.311974 | − | 0.950091i | \(-0.399010\pi\) | ||||
0.311974 | + | 0.950091i | \(0.399010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −176.999 | − | 457.218i | −0.307824 | − | 0.795162i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 269.258i | − | 0.466651i | −0.972399 | − | 0.233326i | \(-0.925039\pi\) | ||
0.972399 | − | 0.233326i | \(-0.0749608\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1152.32i | 1.98334i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 315.819i | 0.541714i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −716.019 | −1.21979 | −0.609897 | − | 0.792481i | \(-0.708789\pi\) | ||||
−0.609897 | + | 0.792481i | \(0.708789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −800.155 | −1.35850 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 680.538 | 1.14762 | 0.573809 | − | 0.818989i | \(-0.305465\pi\) | ||||
0.573809 | + | 0.818989i | \(0.305465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 588.268 | + | 403.079i | 0.988687 | + | 0.677444i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1006.72i | − | 1.68066i | −0.542073 | − | 0.840332i | \(-0.682360\pi\) | ||
0.542073 | − | 0.840332i | \(-0.317640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 165.880 | 0.276007 | 0.138004 | − | 0.990432i | \(-0.455931\pi\) | ||||
0.138004 | + | 0.990432i | \(0.455931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 216.098 | − | 315.381i | 0.357186 | − | 0.521291i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 201.754i | − | 0.332379i | −0.986094 | − | 0.166190i | \(-0.946854\pi\) | ||
0.986094 | − | 0.166190i | \(-0.0531464\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1180.29i | − | 1.93173i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 741.425i | − | 1.20950i | −0.796415 | − | 0.604751i | \(-0.793273\pi\) | ||
0.796415 | − | 0.604751i | \(-0.206727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 695.522 | 1.12726 | 0.563632 | − | 0.826026i | \(-0.309404\pi\) | ||||
0.563632 | + | 0.826026i | \(0.309404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −465.817 | −0.752532 | −0.376266 | − | 0.926512i | \(-0.622792\pi\) | ||||
−0.376266 | + | 0.926512i | \(0.622792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −627.181 | −1.00671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −462.086 | + | 420.834i | −0.739338 | + | 0.673334i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 989.233i | 1.57271i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 340.458 | 0.539554 | 0.269777 | − | 0.962923i | \(-0.413050\pi\) | ||||
0.269777 | + | 0.962923i | \(0.413050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 487.040 | + | 333.718i | 0.766992 | + | 0.525540i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 119.374i | − | 0.187401i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1060.95i | − | 1.65515i | −0.561359 | − | 0.827573i | \(-0.689721\pi\) | ||
0.561359 | − | 0.827573i | \(-0.310279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 969.459i | − | 1.50771i | −0.657039 | − | 0.753856i | \(-0.728191\pi\) | ||
0.657039 | − | 0.753856i | \(-0.271809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 761.354 | 1.17674 | 0.588372 | − | 0.808590i | \(-0.299769\pi\) | ||||
0.588372 | + | 0.808590i | \(0.299769\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −162.973 | −0.251113 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −363.354 | −0.556438 | −0.278219 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278219 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −115.751 | − | 79.3123i | −0.176720 | − | 0.121088i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 283.185i | − | 0.429720i | −0.976645 | − | 0.214860i | \(-0.931070\pi\) | ||
0.976645 | − | 0.214860i | \(-0.0689295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −703.455 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678602\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −841.636 | − | 576.685i | −1.26562 | − | 0.867196i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 136.725i | 0.204985i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 271.679i | − | 0.404887i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 450.802i | 0.669839i | 0.942247 | + | 0.334920i | \(0.108709\pi\) | ||||
−0.942247 | + | 0.334920i | \(0.891291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −292.845 | −0.432563 | −0.216281 | − | 0.976331i | \(-0.569393\pi\) | ||||
−0.216281 | + | 0.976331i | \(0.569393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −122.081 | −0.179796 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −161.354 | −0.236243 | −0.118121 | − | 0.992999i | \(-0.537687\pi\) | ||||
−0.118121 | + | 0.992999i | \(0.537687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 304.583 | − | 444.520i | 0.444647 | − | 0.648934i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 736.786i | − | 1.06936i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 611.834 | 0.885432 | 0.442716 | − | 0.896662i | \(-0.354015\pi\) | ||||
0.442716 | + | 0.896662i | \(0.354015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 483.120 | − | 705.083i | 0.695136 | − | 1.01451i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1152.95i | 1.65416i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 702.946i | − | 1.00278i | −0.865222 | − | 0.501388i | \(-0.832823\pi\) | ||
0.865222 | − | 0.501388i | \(-0.167177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1415.30i | − | 2.01322i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −956.336 | −1.35267 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −361.678 | −0.510124 | −0.255062 | − | 0.966925i | \(-0.582096\pi\) | ||||
−0.255062 | + | 0.966925i | \(0.582096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 578.907 | 0.811932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 293.649 | − | 428.562i | 0.410698 | − | 0.599387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 271.814i | 0.378044i | 0.981973 | + | 0.189022i | \(0.0605318\pi\) | ||||
−0.981973 | + | 0.189022i | \(0.939468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 988.014 | 1.37034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 162.539 | − | 62.9224i | 0.224192 | − | 0.0867896i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 754.003i | 1.03714i | 0.855034 | + | 0.518572i | \(0.173536\pi\) | ||||
−0.855034 | + | 0.518572i | \(0.826464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 201.989i | 0.276318i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.9221i | − | 0.0230860i | −0.999933 | − | 0.0115430i | \(-0.996326\pi\) | ||
0.999933 | − | 0.0115430i | \(-0.00367434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −393.144 | −0.533438 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −874.635 | −1.18354 | −0.591769 | − | 0.806107i | \(-0.701570\pi\) | ||||
−0.591769 | + | 0.806107i | \(0.701570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 272.840 | 0.367213 | 0.183607 | − | 0.983000i | \(-0.441223\pi\) | ||||
0.183607 | + | 0.983000i | \(0.441223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 336.969 | + | 230.890i | 0.452307 | + | 0.309919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 993.079i | 1.32587i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1277.28 | 1.70077 | 0.850386 | − | 0.526160i | \(-0.176369\pi\) | ||||
0.850386 | + | 0.526160i | \(0.176369\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.0378 | − | 38.0006i | 0.0344872 | − | 0.0503319i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1087.23i | 1.43624i | 0.695921 | + | 0.718118i | \(0.254996\pi\) | ||||
−0.695921 | + | 0.718118i | \(0.745004\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1017.04i | 1.33645i | 0.743958 | + | 0.668226i | \(0.232946\pi\) | ||||
−0.743958 | + | 0.668226i | \(0.767054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1517.42i | − | 1.98876i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 380.205 | 0.495704 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −205.301 | −0.266971 | −0.133486 | − | 0.991051i | \(-0.542617\pi\) | ||||
−0.133486 | + | 0.991051i | \(0.542617\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 254.726 | 0.329530 | 0.164765 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164765 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −266.420 | − | 688.208i | −0.343768 | − | 0.888010i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1649.53i | − | 2.11750i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 226.506 | 0.290020 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1189.40 | + | 814.972i | 1.51516 | + | 1.03818i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 66.9905i | 0.0851214i | 0.999094 | + | 0.0425607i | \(0.0135516\pi\) | ||||
−0.999094 | + | 0.0425607i | \(0.986448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 253.665i | 0.320688i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 633.811i | 0.799257i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 642.644 | 0.806329 | 0.403164 | − | 0.915128i | \(-0.367910\pi\) | ||||
0.403164 | + | 0.915128i | \(0.367910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1436.30 | −1.79762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 532.698 | 0.663385 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 608.918 | + | 417.228i | 0.756420 | + | 0.518296i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 479.966i | 0.593283i | 0.954989 | + | 0.296642i | \(0.0958667\pi\) | ||||
−0.954989 | + | 0.296642i | \(0.904133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −478.009 | −0.589407 | −0.294703 | − | 0.955589i | \(-0.595221\pi\) | ||||
−0.294703 | + | 0.955589i | \(0.595221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 285.042 | + | 195.309i | 0.349745 | + | 0.239643i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 288.985i | − | 0.353715i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 894.509i | − | 1.08954i | −0.838587 | − | 0.544768i | \(-0.816618\pi\) | ||
0.838587 | − | 0.544768i | \(-0.183382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 376.036i | 0.456909i | 0.973555 | + | 0.228455i | \(0.0733672\pi\) | ||||
−0.973555 | + | 0.228455i | \(0.926633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −363.894 | −0.440017 | −0.220008 | − | 0.975498i | \(-0.570608\pi\) | ||||
−0.220008 | + | 0.975498i | \(0.570608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −398.314 | −0.480475 | −0.240238 | − | 0.970714i | \(-0.577225\pi\) | ||||
−0.240238 | + | 0.970714i | \(0.577225\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −145.268 | −0.174391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 551.743 | − | 805.234i | 0.660770 | − | 0.964352i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1499.60i | 1.78736i | 0.448702 | + | 0.893682i | \(0.351887\pi\) | ||||
−0.448702 | + | 0.893682i | \(0.648113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 792.395 | 0.942205 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −207.438 | + | 302.743i | −0.245489 | + | 0.358276i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 575.593i | 0.679567i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1023.96i | 1.20324i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1524.29i | − | 1.78697i | −0.449093 | − | 0.893485i | \(-0.648253\pi\) | ||
0.449093 | − | 0.893485i | \(-0.351747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −931.475 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −102.105 | −0.118865 | −0.0594325 | − | 0.998232i | \(-0.518929\pi\) | ||||
−0.0594325 | + | 0.998232i | \(0.518929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 971.646 | 1.12589 | 0.562947 | − | 0.826493i | \(-0.309668\pi\) | ||||
0.562947 | + | 0.826493i | \(0.309668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −167.815 | + | 244.915i | −0.194006 | + | 0.283139i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 574.270i | − | 0.660840i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 917.179 | 1.05302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 215.772 | − | 915.899i | 0.246596 | − | 1.04674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 771.593i | − | 0.879810i | −0.898044 | − | 0.439905i | \(-0.855012\pi\) | ||
0.898044 | − | 0.439905i | \(-0.144988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 279.972i | − | 0.317789i | −0.987296 | − | 0.158895i | \(-0.949207\pi\) | ||
0.987296 | − | 0.158895i | \(-0.0507930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 75.4516i | − | 0.0854492i | −0.999087 | − | 0.0427246i | \(-0.986396\pi\) | ||
0.999087 | − | 0.0427246i | \(-0.0136038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −669.288 | −0.754553 | −0.377276 | − | 0.926101i | \(-0.623139\pi\) | ||||
−0.377276 | + | 0.926101i | \(0.623139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −888.884 | −0.999869 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2054.92 | 2.30114 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 338.888 | + | 232.205i | 0.378646 | + | 0.259447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 205.800i | 0.228921i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −896.601 | −0.995117 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −684.276 | + | 998.658i | −0.756106 | + | 1.10349i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 459.134i | 0.506212i | 0.967439 | + | 0.253106i | \(0.0814521\pi\) | ||||
−0.967439 | + | 0.253106i | \(0.918548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 670.249i | 0.735729i | 0.929879 | + | 0.367864i | \(0.119911\pi\) | ||||
−0.929879 | + | 0.367864i | \(0.880089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1021.57i | − | 1.11892i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 211.255 | 0.230376 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.6103 | −0.0246032 | −0.0123016 | − | 0.999924i | \(-0.503916\pi\) | ||||
−0.0123016 | + | 0.999924i | \(0.503916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −528.424 | −0.572507 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1217.29 | − | 471.237i | 1.31598 | − | 0.509445i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 944.272i | 1.01644i | 0.861228 | + | 0.508220i | \(0.169696\pi\) | ||||
−0.861228 | + | 0.508220i | \(0.830304\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 207.835 | 0.223238 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −521.520 | − | 357.343i | −0.557776 | − | 0.382185i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1037.45i | − | 1.10721i | −0.832781 | − | 0.553603i | \(-0.813253\pi\) | ||
0.832781 | − | 0.553603i | \(-0.186747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 410.283i | − | 0.436007i | −0.975948 | − | 0.218004i | \(-0.930046\pi\) | ||
0.975948 | − | 0.218004i | \(-0.0699544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1193.42i | 1.26556i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −753.302 | −0.795462 | −0.397731 | − | 0.917502i | \(-0.630202\pi\) | ||||
−0.397731 | + | 0.917502i | \(0.630202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1242.75 | −1.30954 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −661.356 | −0.693973 | −0.346986 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346986 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −113.021 | − | 77.4418i | −0.118347 | − | 0.0810909i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 811.282i | 0.845966i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −89.6241 | −0.0932613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −576.221 | − | 394.824i | −0.597120 | − | 0.409144i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1584.38i | − | 1.63845i | −0.573470 | − | 0.819227i | \(-0.694403\pi\) | ||
0.573470 | − | 0.819227i | \(-0.305597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 982.405i | 1.01175i | 0.862608 | + | 0.505873i | \(0.168829\pi\) | ||||
−0.862608 | + | 0.505873i | \(0.831171\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1286.83i | 1.32254i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1891.35 | 1.93588 | 0.967939 | − | 0.251185i | \(-0.0808201\pi\) | ||||
0.967939 | + | 0.251185i | \(0.0808201\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 556.017 | 0.567944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1431.06 | −1.45581 | −0.727906 | − | 0.685677i | \(-0.759506\pi\) | ||||
−0.727906 | + | 0.685677i | \(0.759506\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 354.095 | − | 516.780i | 0.359488 | − | 0.524650i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 209.079i | 0.211404i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 159.789 | 0.161240 | 0.0806200 | − | 0.996745i | \(-0.474310\pi\) | ||||
0.0806200 | + | 0.996745i | \(0.474310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −685.764 | + | 1000.83i | −0.689210 | + | 1.00586i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 651.900i | 0.653861i | 0.945048 | + | 0.326931i | \(0.106014\pi\) | ||||
−0.945048 | + | 0.326931i | \(0.893986\pi\) | |||||||
\(998\) | 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 | 1620.3.b.a.809.17 | yes | 24 | |
3.2 | odd | 2 | inner | 1620.3.b.a.809.8 | yes | 24 | |
5.4 | even | 2 | inner | 1620.3.b.a.809.7 | ✓ | 24 | |
9.2 | odd | 6 | 1620.3.t.f.1349.10 | 48 | |||
9.4 | even | 3 | 1620.3.t.f.269.2 | 48 | |||
9.5 | odd | 6 | 1620.3.t.f.269.23 | 48 | |||
9.7 | even | 3 | 1620.3.t.f.1349.15 | 48 | |||
15.14 | odd | 2 | inner | 1620.3.b.a.809.18 | yes | 24 | |
45.4 | even | 6 | 1620.3.t.f.269.10 | 48 | |||
45.14 | odd | 6 | 1620.3.t.f.269.15 | 48 | |||
45.29 | odd | 6 | 1620.3.t.f.1349.2 | 48 | |||
45.34 | even | 6 | 1620.3.t.f.1349.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.3.b.a.809.7 | ✓ | 24 | 5.4 | even | 2 | inner | |
1620.3.b.a.809.8 | yes | 24 | 3.2 | odd | 2 | inner | |
1620.3.b.a.809.17 | yes | 24 | 1.1 | even | 1 | trivial | |
1620.3.b.a.809.18 | yes | 24 | 15.14 | odd | 2 | inner | |
1620.3.t.f.269.2 | 48 | 9.4 | even | 3 | |||
1620.3.t.f.269.10 | 48 | 45.4 | even | 6 | |||
1620.3.t.f.269.15 | 48 | 45.14 | odd | 6 | |||
1620.3.t.f.269.23 | 48 | 9.5 | odd | 6 | |||
1620.3.t.f.1349.2 | 48 | 45.29 | odd | 6 | |||
1620.3.t.f.1349.10 | 48 | 9.2 | odd | 6 | |||
1620.3.t.f.1349.15 | 48 | 9.7 | even | 3 | |||
1620.3.t.f.1349.23 | 48 | 45.34 | even | 6 |