Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.4 | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.b.239.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.13038 | + | 3.15276i | −0.794893 | + | 0.606750i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.18345i | − | 0.105851i | −0.998598 | − | 0.0529256i | \(-0.983145\pi\) | ||
0.998598 | − | 0.0529256i | \(-0.0168546\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.12016 | − | 26.0443i | 0.263709 | − | 0.964602i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.7667 | 1.77526 | 0.887632 | − | 0.460554i | \(-0.152349\pi\) | ||||
0.887632 | + | 0.460554i | \(0.152349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −65.6031 | −1.39962 | −0.699809 | − | 0.714330i | \(-0.746731\pi\) | ||||
−0.699809 | + | 0.714330i | \(0.746731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.73115 | + | 4.88812i | 0.0642252 | + | 0.0841404i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 19.9831i | − | 0.285094i | −0.989788 | − | 0.142547i | \(-0.954471\pi\) | ||
0.989788 | − | 0.142547i | \(-0.0455292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 67.2592i | − | 0.812122i | −0.913846 | − | 0.406061i | \(-0.866902\pi\) | ||
0.913846 | − | 0.406061i | \(-0.133098\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −22.0693 | − | 28.9127i | −0.229330 | − | 0.300441i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 79.6645 | 0.722226 | 0.361113 | − | 0.932522i | \(-0.382397\pi\) | ||||
0.361113 | + | 0.932522i | \(0.382397\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 123.599 | 0.988796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 52.7024 | + | 130.021i | 0.375651 | + | 0.926761i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 100.562i | 0.643927i | 0.946752 | + | 0.321963i | \(0.104343\pi\) | ||||
−0.946752 | + | 0.321963i | \(0.895657\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 278.573i | 1.61398i | 0.590568 | + | 0.806988i | \(0.298904\pi\) | ||||
−0.590568 | + | 0.806988i | \(0.701096\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −267.511 | + | 204.194i | −1.41114 | + | 1.07714i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.28417 | 0.0400080 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −45.5075 | −0.202200 | −0.101100 | − | 0.994876i | \(-0.532236\pi\) | ||||
−0.101100 | + | 0.994876i | \(0.532236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 270.966 | − | 206.831i | 1.11255 | − | 0.849217i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.4833i | 0.0475502i | 0.999717 | + | 0.0237751i | \(0.00756856\pi\) | ||||
−0.999717 | + | 0.0237751i | \(0.992431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 368.590i | 1.30720i | 0.756842 | + | 0.653598i | \(0.226741\pi\) | ||||
−0.756842 | + | 0.653598i | \(0.773259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.8222 | − | 8.42637i | −0.102104 | − | 0.0279140i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 303.707 | 0.942559 | 0.471280 | − | 0.881984i | \(-0.343792\pi\) | ||||
0.471280 | + | 0.881984i | \(0.343792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 63.0019 | + | 82.5377i | 0.172981 | + | 0.226619i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 639.462i | 1.65730i | 0.559768 | + | 0.828650i | \(0.310890\pi\) | ||||
−0.559768 | + | 0.828650i | \(0.689110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 76.6484i | − | 0.187914i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 212.052 | + | 277.806i | 0.492755 | + | 0.645550i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −537.860 | −1.18684 | −0.593419 | − | 0.804894i | \(-0.702222\pi\) | ||||
−0.593419 | + | 0.804894i | \(0.702222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 232.141 | 0.487257 | 0.243628 | − | 0.969869i | \(-0.421662\pi\) | ||||
0.243628 | + | 0.969869i | \(0.421662\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 182.310 | + | 49.8411i | 0.364585 | + | 0.0996728i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.6382i | 0.148151i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 533.654i | 0.973079i | 0.873659 | + | 0.486539i | \(0.161741\pi\) | ||||
−0.873659 | + | 0.486539i | \(0.838259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −329.045 | + | 251.163i | −0.574092 | + | 0.438210i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1015.57 | 1.69755 | 0.848777 | − | 0.528751i | \(-0.177339\pi\) | ||||
0.848777 | + | 0.528751i | \(0.177339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −348.158 | −0.558203 | −0.279101 | − | 0.960262i | \(-0.590037\pi\) | ||||
−0.279101 | + | 0.960262i | \(0.590037\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −510.513 | + | 389.680i | −0.785987 | + | 0.599951i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 453.367i | 0.670987i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 517.278i | 0.736688i | 0.929690 | + | 0.368344i | \(0.120075\pi\) | ||||
−0.929690 | + | 0.368344i | \(0.879925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −627.607 | − | 370.878i | −0.860915 | − | 0.508749i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1086.03 | 1.43623 | 0.718113 | − | 0.695926i | \(-0.245006\pi\) | ||||
0.718113 | + | 0.695926i | \(0.245006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.6490 | −0.0301776 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −317.048 | − | 415.359i | −0.390703 | − | 0.511853i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1432.28i | − | 1.70586i | −0.522023 | − | 0.852931i | \(-0.674823\pi\) | ||
0.522023 | − | 0.852931i | \(-0.325177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 459.222i | − | 0.529006i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −878.276 | − | 1150.62i | −0.979280 | − | 1.28294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −79.5981 | −0.0859641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1765.36 | 1.84789 | 0.923945 | − | 0.382526i | \(-0.124946\pi\) | ||||
0.923945 | + | 0.382526i | \(0.124946\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 461.149 | − | 1686.80i | 0.468154 | − | 1.71242i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 167.647i | 0.165163i | 0.996584 | + | 0.0825817i | \(0.0263165\pi\) | ||||
−0.996584 | + | 0.0825817i | \(0.973683\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 412.022i | 0.394153i | 0.980388 | + | 0.197076i | \(0.0631447\pi\) | ||||
−0.980388 | + | 0.197076i | \(0.936855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −34.2168 | + | 26.1180i | −0.0318021 | + | 0.0242749i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1231.17 | −1.11235 | −0.556176 | − | 0.831065i | \(-0.687732\pi\) | ||||
−0.556176 | + | 0.831065i | \(0.687732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −208.736 | −0.183424 | −0.0917122 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917122 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 187.964 | − | 143.475i | 0.160727 | − | 0.122685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1005.81i | − | 0.837333i | −0.908140 | − | 0.418667i | \(-0.862498\pi\) | ||
0.908140 | − | 0.418667i | \(-0.137502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 94.2792i | − | 0.0764485i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −467.104 | + | 1708.58i | −0.369092 | + | 1.35007i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 139.881 | 0.107755 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2863.73 | 2.15156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −39.3568 | − | 51.5606i | −0.0288510 | − | 0.0377973i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 294.206i | − | 0.210517i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 277.716i | 0.194042i | 0.995282 | + | 0.0970208i | \(0.0309313\pi\) | ||||
−0.995282 | + | 0.0970208i | \(0.969069\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1162.08 | − | 1522.42i | −0.793141 | − | 1.03908i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1504.95 | −1.00373 | −0.501864 | − | 0.864946i | \(-0.667352\pi\) | ||||
−0.501864 | + | 0.864946i | \(0.667352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 470.814 | 0.306953 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 153.874 | − | 62.3709i | 0.0980988 | − | 0.0397632i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1007.55i | 0.628328i | 0.949369 | + | 0.314164i | \(0.101724\pi\) | ||||
−0.949369 | + | 0.314164i | \(0.898276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 212.644i | − | 0.129757i | −0.997893 | − | 0.0648786i | \(-0.979334\pi\) | ||
0.997893 | − | 0.0648786i | \(-0.0206660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1254.43 | + | 957.518i | −0.749234 | + | 0.571898i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4248.90 | −2.48469 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 119.010 | 0.0681605 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 202.389 | − | 154.485i | 0.113556 | − | 0.0866785i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2756.72i | − | 1.51570i | −0.652428 | − | 0.757851i | \(-0.726250\pi\) | ||
0.652428 | − | 0.757851i | \(-0.273750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2341.55i | − | 1.26194i | −0.775808 | − | 0.630969i | \(-0.782657\pi\) | ||
0.775808 | − | 0.630969i | \(-0.217343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −520.444 | − | 142.282i | −0.275003 | − | 0.0751820i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 329.679 | 0.170841 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 605.528 | 0.307811 | 0.153906 | − | 0.988086i | \(-0.450815\pi\) | ||||
0.153906 | + | 0.988086i | \(0.450815\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2016.07 | − | 2641.22i | −1.00557 | − | 1.31738i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 557.651i | 0.272976i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1257.83i | 0.604424i | 0.953241 | + | 0.302212i | \(0.0977250\pi\) | ||||
−0.953241 | + | 0.302212i | \(0.902275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 241.654 | + | 316.587i | 0.114017 | + | 0.149371i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1243.14 | −0.576030 | −0.288015 | − | 0.957626i | \(-0.592995\pi\) | ||||
−0.288015 | + | 0.957626i | \(0.592995\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2106.76 | 0.958928 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1751.72 | − | 478.896i | −0.783374 | − | 0.214164i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3555.74i | 1.56265i | 0.624126 | + | 0.781324i | \(0.285455\pi\) | ||||
−0.624126 | + | 0.781324i | \(0.714545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 865.196i | 0.373730i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2221.57 | − | 1695.75i | 0.943408 | − | 0.720113i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1234.43 | 0.515452 | 0.257726 | − | 0.966218i | \(-0.417027\pi\) | ||||
0.257726 | + | 0.966218i | \(0.417027\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1217.00 | 0.499772 | 0.249886 | − | 0.968275i | \(-0.419607\pi\) | ||||
0.249886 | + | 0.968275i | \(0.419607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −958.833 | + | 731.887i | −0.387317 | + | 0.295643i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 53.8561i | 0.0214031i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1294.24i | − | 0.506117i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −910.147 | + | 368.917i | −0.350283 | + | 0.141983i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2105.27 | 0.797549 | 0.398774 | − | 0.917049i | \(-0.369436\pi\) | ||||
0.398774 | + | 0.917049i | \(0.369436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3241.94 | 1.20912 | 0.604560 | − | 0.796559i | \(-0.293349\pi\) | ||||
0.604560 | + | 0.796559i | \(0.293349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −244.775 | − | 320.676i | −0.0898907 | − | 0.117764i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 989.805i | 0.357973i | 0.983852 | + | 0.178987i | \(0.0572818\pi\) | ||||
−0.983852 | + | 0.178987i | \(0.942718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1106.83i | 0.394277i | 0.980376 | + | 0.197139i | \(0.0631649\pi\) | ||||
−0.980376 | + | 0.197139i | \(0.936835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1682.49 | − | 2204.20i | −0.590415 | − | 0.773493i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −703.934 | −0.243382 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7733 | 0.00503324 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 567.224 | − | 2074.80i | 0.190458 | − | 0.696661i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4356.16i | − | 1.44173i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 346.152i | 0.112939i | 0.998404 | + | 0.0564693i | \(0.0179843\pi\) | ||||
−0.998404 | + | 0.0564693i | \(0.982016\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4194.71 | + | 3201.86i | −1.34937 | + | 1.02999i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 436.209 | 0.138368 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1950.01 | −0.610026 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1438.03 | − | 1097.66i | 0.443712 | − | 0.338690i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1310.95i | 0.399023i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3147.46i | 0.945155i | 0.881289 | + | 0.472578i | \(0.156676\pi\) | ||||
−0.881289 | + | 0.472578i | \(0.843324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 880.047 | − | 3219.06i | 0.260755 | − | 0.953794i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1568.11 | 0.458499 | 0.229250 | − | 0.973368i | \(-0.426373\pi\) | ||||
0.229250 | + | 0.973368i | \(0.426373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2522.74 | −0.727979 | −0.363989 | − | 0.931403i | \(-0.618586\pi\) | ||||
−0.363989 | + | 0.931403i | \(0.618586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1429.36 | − | 1872.58i | −0.407121 | − | 0.533362i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5224.03i | − | 1.46883i | −0.678700 | − | 0.734416i | \(-0.737456\pi\) | ||
0.678700 | − | 0.734416i | \(-0.262544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 359.424i | − | 0.0997711i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1630.86 | − | 2136.56i | −0.446985 | − | 0.585588i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −779.036 | −0.210844 | −0.105422 | − | 0.994428i | \(-0.533619\pi\) | ||||
−0.105422 | + | 0.994428i | \(0.533619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −36.8016 | −0.00983651 | −0.00491826 | − | 0.999988i | \(-0.501566\pi\) | ||||
−0.00491826 | + | 0.999988i | \(0.501566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3761.55 | − | 446.826i | 0.993019 | − | 0.117958i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 57.9892i | 0.0151216i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4412.41i | 1.13666i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4485.70 | + | 3423.98i | −1.14165 | + | 0.871430i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3211.48 | 0.807596 | 0.403798 | − | 0.914848i | \(-0.367690\pi\) | ||||
0.403798 | + | 0.914848i | \(0.367690\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5159.61 | 1.28214 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 97.6795 | − | 74.5597i | 0.0239879 | − | 0.0183102i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2038.32i | 0.494736i | 0.968922 | + | 0.247368i | \(0.0795657\pi\) | ||||
−0.968922 | + | 0.247368i | \(0.920434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 318.553i | − | 0.0764244i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2619.06 | + | 716.017i | 0.621133 | + | 0.169810i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2703.80 | −0.633929 | −0.316965 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316965 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 756.773 | 0.175427 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4515.65 | + | 5915.88i | 1.03503 | + | 1.35598i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5494.29i | 1.24533i | 0.782490 | + | 0.622663i | \(0.213949\pi\) | ||||
−0.782490 | + | 0.622663i | \(0.786051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3364.83i | 0.754240i | 0.926164 | + | 0.377120i | \(0.123086\pi\) | ||||
−0.926164 | + | 0.377120i | \(0.876914\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1447.82 | + | 1896.76i | 0.320974 | + | 0.420503i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8005.13 | 1.75537 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8383.07 | −1.81837 | −0.909187 | − | 0.416388i | \(-0.863296\pi\) | ||||
−0.909187 | + | 0.416388i | \(0.863296\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7255.24 | + | 1983.49i | 1.55684 | + | 0.425621i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1391.23i | − | 0.295352i | −0.989036 | − | 0.147676i | \(-0.952821\pi\) | ||
0.989036 | − | 0.147676i | \(-0.0471793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7260.39i | − | 1.52504i | −0.646967 | − | 0.762518i | \(-0.723963\pi\) | ||
0.646967 | − | 0.762518i | \(-0.276037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 328.771 | − | 250.954i | 0.0683323 | − | 0.0521587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −87.3828 | −0.0179723 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4513.68 | 0.918721 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7291.62 | + | 5565.77i | −1.46887 | + | 1.12121i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3239.83i | 0.645983i | 0.946402 | + | 0.322991i | \(0.104688\pi\) | ||||
−0.946402 | + | 0.322991i | \(0.895312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 636.532i | 0.125628i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3413.36 | + | 8421.03i | 0.666880 | + | 1.64525i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5226.24 | −1.01084 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2580.13 | −0.494074 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −528.551 | − | 692.446i | −0.100213 | − | 0.131287i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 274.728i | − | 0.0515767i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4045.04i | − | 0.751995i | −0.926621 | − | 0.375998i | \(-0.877300\pi\) | ||
0.926621 | − | 0.375998i | \(-0.122700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1299.01 | − | 1701.81i | −0.239152 | − | 0.313309i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8078.51 | 1.47296 | 0.736479 | − | 0.676460i | \(-0.236487\pi\) | ||||
0.736479 | + | 0.676460i | \(0.236487\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4511.14 | −0.814648 | −0.407324 | − | 0.913284i | \(-0.633538\pi\) | ||||
−0.407324 | + | 0.913284i | \(0.633538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 58.9846 | − | 215.755i | 0.0105505 | − | 0.0385918i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7417.92i | − | 1.31430i | −0.753762 | − | 0.657148i | \(-0.771763\pi\) | ||
0.753762 | − | 0.657148i | \(-0.228237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6513.07i | 1.14314i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5085.20 | − | 3881.59i | 0.884200 | − | 0.674919i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1344.04 | −0.231531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8108.50 | −1.38394 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 862.159 | − | 658.095i | 0.145803 | − | 0.111293i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2125.95i | 0.356254i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9617.61i | 1.59707i | 0.601945 | + | 0.798537i | \(0.294392\pi\) | ||||
−0.601945 | + | 0.798537i | \(0.705608\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −324.021 | + | 1185.21i | −0.0533220 | + | 0.195042i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 631.555 | 0.103002 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8057.75 | −1.30247 | −0.651237 | − | 0.758875i | \(-0.725750\pi\) | ||||
−0.651237 | + | 0.758875i | \(0.725750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3171.08 | + | 4154.38i | 0.508052 | + | 0.665590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18042.3i | 2.86523i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 297.240 | + | 389.409i | 0.0463851 | + | 0.0607684i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2229.45 | −0.344908 | −0.172454 | − | 0.985018i | \(-0.555170\pi\) | ||||
−0.172454 | + | 0.985018i | \(0.555170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7212.16 | 1.10618 | 0.553092 | − | 0.833120i | \(-0.313448\pi\) | ||||
0.553092 | + | 0.833120i | \(0.313448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3457.44 | − | 8529.78i | −0.525768 | − | 1.29711i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11385.6i | 1.71669i | 0.513072 | + | 0.858345i | \(0.328507\pi\) | ||||
−0.513072 | + | 0.858345i | \(0.671493\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1201.88i | − | 0.179688i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −577.764 | + | 441.013i | −0.0856541 | + | 0.0653806i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12546.9 | 1.84456 | 0.922281 | − | 0.386520i | \(-0.126323\pi\) | ||||
0.922281 | + | 0.386520i | \(0.126323\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2335.20 | 0.340458 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11828.3 | + | 9028.66i | −1.71026 | + | 1.30546i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 412.029i | 0.0590865i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7402.20i | − | 1.05284i | −0.850225 | − | 0.526419i | \(-0.823534\pi\) | ||
0.850225 | − | 0.526419i | \(-0.176466\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 325.117 | + | 88.8827i | 0.0458670 | + | 0.0125394i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4476.23 | −0.626400 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11298.8 | 1.56845 | 0.784223 | − | 0.620479i | \(-0.213062\pi\) | ||||
0.784223 | + | 0.620479i | \(0.213062\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 927.561 | + | 1215.18i | 0.127731 | + | 0.167338i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6597.17i | − | 0.901251i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3011.81i | 0.408196i | 0.978950 | + | 0.204098i | \(0.0654262\pi\) | ||||
−0.978950 | + | 0.204098i | \(0.934574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −875.572 | − | 1147.07i | −0.117735 | − | 0.154242i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −842.726 | −0.112432 | −0.0562158 | − | 0.998419i | \(-0.517903\pi\) | ||||
−0.0562158 | + | 0.998419i | \(0.517903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 536.539 | 0.0710248 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9599.65 | + | 2624.42i | 1.26092 | + | 0.344720i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8773.64i | − | 1.14355i | −0.820410 | − | 0.571776i | \(-0.806255\pi\) | ||
0.820410 | − | 0.571776i | \(-0.193745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1591.94i | − | 0.205902i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6216.04 | − | 4744.76i | 0.797857 | − | 0.609012i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 612.174 | 0.0779793 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9538.13 | −1.20581 | −0.602903 | − | 0.797814i | \(-0.705990\pi\) | ||||
−0.602903 | + | 0.797814i | \(0.705990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1944.64 | + | 1484.37i | −0.243995 | + | 0.186244i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8679.02i | − | 1.08082i | −0.841401 | − | 0.540411i | \(-0.818269\pi\) | ||
0.841401 | − | 0.540411i | \(-0.181731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 18275.3i | − | 2.25895i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −438.917 | + | 742.743i | −0.0538518 | + | 0.0911289i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2947.37 | −0.358958 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6173.70 | −0.746381 | −0.373190 | − | 0.927755i | \(-0.621736\pi\) | ||||
−0.373190 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3176.57 | − | 4161.57i | −0.381238 | − | 0.499453i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3765.02i | − | 0.448582i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1285.26i | − | 0.152026i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 670.418 | + | 878.303i | 0.0787302 | + | 0.103143i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2444.79 | −0.285050 | −0.142525 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142525 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11214.6 | −1.29826 | −0.649130 | − | 0.760677i | \(-0.724867\pi\) | ||||
−0.649130 | + | 0.760677i | \(0.724867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2162.44 | − | 7909.84i | 0.248562 | − | 0.909195i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2469.89i | − | 0.281900i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1624.99i | 0.184166i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17549.6 | − | 13395.8i | 1.97506 | − | 1.50758i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6301.23 | −0.704222 | −0.352111 | − | 0.935958i | \(-0.614536\pi\) | ||||
−0.352111 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3871.02 | −0.429629 | −0.214815 | − | 0.976655i | \(-0.568915\pi\) | ||||
−0.214815 | + | 0.976655i | \(0.568915\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −491.558 | + | 375.212i | −0.0541803 | + | 0.0413564i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5358.17i | − | 0.586535i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7287.82i | − | 0.792320i | −0.918182 | − | 0.396160i | \(-0.870343\pi\) | ||
0.918182 | − | 0.396160i | \(-0.129657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −348.888 | + | 1276.17i | −0.0376728 | + | 0.137800i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6123.28 | −0.656717 | −0.328359 | − | 0.944553i | \(-0.606495\pi\) | ||||
−0.328359 | + | 0.944553i | \(0.606495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1695.04 | −0.180568 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8691.30 | + | 11386.3i | 0.919651 | + | 1.20482i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18140.7i | − | 1.90671i | −0.301846 | − | 0.953357i | \(-0.597603\pi\) | ||
0.301846 | − | 0.953357i | \(-0.402397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 808.499i | 0.0844141i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7382.36 | + | 9671.51i | 0.765681 | + | 1.00311i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −543.467 | −0.0559959 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7050.08 | −0.721638 | −0.360819 | − | 0.932636i | \(-0.617503\pi\) | ||||
−0.360819 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2598.22 | − | 1053.16i | 0.264214 | − | 0.107096i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12573.3i | − | 1.27027i | −0.772401 | − | 0.635135i | \(-0.780944\pi\) | ||
0.772401 | − | 0.635135i | \(-0.219056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11111.1i | 1.11528i | 0.830082 | + | 0.557641i | \(0.188293\pi\) | ||||
−0.830082 | + | 0.557641i | \(0.811707\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1361.70 | + | 1039.40i | −0.135801 | + | 0.103658i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2093.93 | −0.207485 | −0.103742 | − | 0.994604i | \(-0.533082\pi\) | ||||
−0.103742 | + | 0.994604i | \(0.533082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3735.58 | −0.367789 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2501.06 | + | 1909.09i | −0.244677 | + | 0.186764i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23872.4i | 2.32062i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8313.20i | − | 0.803022i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16654.3 | + | 4553.07i | 1.59863 | + | 0.437046i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18334.9 | −1.74894 | −0.874470 | − | 0.485080i | \(-0.838790\pi\) | ||||
−0.874470 | + | 0.485080i | \(0.838790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2985.44 | 0.283002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1758.14 | − | 2303.31i | −0.165628 | − | 0.216986i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2089.22i | − | 0.195601i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8221.50i | − | 0.764994i | −0.923957 | − | 0.382497i | \(-0.875064\pi\) | ||
0.923957 | − | 0.382497i | \(-0.124936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3965.65 | − | 5195.33i | −0.366734 | − | 0.480452i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2498.42 | −0.229637 | −0.114819 | − | 0.993386i | \(-0.536629\pi\) | ||||
−0.114819 | + | 0.993386i | \(0.536629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2009.53 | 0.183580 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1996.25 | − | 545.748i | −0.181262 | − | 0.0495547i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7109.01i | 0.641615i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19078.0i | − | 1.71152i | −0.517377 | − | 0.855758i | \(-0.673091\pi\) | ||
0.517377 | − | 0.855758i | \(-0.326909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5134.65 | − | 3919.33i | 0.457882 | − | 0.349506i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6062.87 | −0.537436 | −0.268718 | − | 0.963219i | \(-0.586600\pi\) | ||||
−0.268718 | + | 0.963219i | \(0.586600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 198.402 | 0.0174827 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8701.75 | + | 6642.13i | −0.762245 | + | 0.581829i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14287.9i | − | 1.24420i | −0.782936 | − | 0.622102i | \(-0.786279\pi\) | ||
0.782936 | − | 0.622102i | \(-0.213721\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2437.11i | − | 0.210981i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8745.10 | − | 3544.72i | 0.752643 | − | 0.305075i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 487.609 | 0.0417216 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19670.1 | 1.67329 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11210.4 | − | 14686.6i | −0.948136 | − | 1.24214i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21919.6i | 1.84321i | 0.388127 | + | 0.921606i | \(0.373122\pi\) | ||||
−0.388127 | + | 0.921606i | \(0.626878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16921.7i | − | 1.41479i | −0.706818 | − | 0.707395i | \(-0.749870\pi\) | ||
0.706818 | − | 0.707395i | \(-0.250130\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2727.76 | − | 3573.59i | −0.226760 | − | 0.297075i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5566.75 | 0.460135 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5820.57 | −0.478390 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3829.65 | + | 14008.2i | −0.312980 | + | 1.14483i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 818.940i | − | 0.0665520i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1457.03i | 0.117744i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5098.69 | + | 3891.88i | −0.409729 | + | 0.312750i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3173.57 | −0.253609 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13388.4 | −1.06398 | −0.531988 | − | 0.846752i | \(-0.678555\pi\) | ||||
−0.531988 | + | 0.846752i | \(0.678555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5026.67 | + | 3836.91i | −0.397265 | + | 0.303237i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 247.029i | 0.0194157i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8932.60i | 0.698228i | 0.937080 | + | 0.349114i | \(0.113517\pi\) | ||||
−0.937080 | + | 0.349114i | \(0.886483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1652.88 | − | 6045.95i | 0.128494 | − | 0.470009i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6763.71 | 0.522947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3620.95 | −0.278442 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −169.795 | − | 222.446i | −0.0129863 | − | 0.0170132i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4587.92i | − | 0.349006i | −0.984657 | − | 0.174503i | \(-0.944168\pi\) | ||
0.984657 | − | 0.174503i | \(-0.0558319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24180.6i | − | 1.82957i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4080.42 | + | 5345.70i | 0.307087 | + | 0.402309i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 618.373 | 0.0462901 | 0.0231450 | − | 0.999732i | \(-0.492632\pi\) | ||||
0.0231450 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1190.33 | −0.0886328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2596.15 | − | 4393.25i | 0.192289 | − | 0.325395i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9659.94i | 0.711715i | 0.934540 | + | 0.355857i | \(0.115811\pi\) | ||||
−0.934540 | + | 0.355857i | \(0.884189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3186.35i | 0.233528i | 0.993160 | + | 0.116764i | \(0.0372522\pi\) | ||||
−0.993160 | + | 0.116764i | \(0.962748\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8695.56 | + | 6637.41i | −0.633966 | + | 0.483912i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9846.49 | 0.714134 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2641.29 | −0.190569 | −0.0952844 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952844 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13390.5 | + | 10221.1i | −0.961121 | + | 0.733634i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7602.18i | 0.542842i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41415.9i | 2.94214i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2022.03 | + | 552.796i | 0.142907 | + | 0.0390689i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17658.4 | 1.24163 | 0.620816 | − | 0.783956i | \(-0.286801\pi\) | ||||
0.620816 | + | 0.783956i | \(0.286801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18736.6 | 1.31075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3120.62 | − | 4088.28i | −0.217200 | − | 0.284550i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15773.9i | − | 1.09234i | −0.837675 | − | 0.546169i | \(-0.816086\pi\) | ||
0.837675 | − | 0.546169i | \(-0.183914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 165.543i | − | 0.0114061i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3489.58 | − | 4571.64i | −0.239228 | − | 0.313408i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17992.2 | −1.22728 | −0.613639 | − | 0.789587i | \(-0.710295\pi\) | ||||
−0.613639 | + | 0.789587i | \(0.710295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2205.18 | −0.149669 | −0.0748344 | − | 0.997196i | \(-0.523843\pi\) | ||||
−0.0748344 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13898.6 | + | 3799.70i | 0.938634 | + | 0.256610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3389.09i | − | 0.227745i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27712.9i | 1.85310i | 0.376172 | + | 0.926550i | \(0.377240\pi\) | ||||
−0.376172 | + | 0.926550i | \(0.622760\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2907.52 | − | 2219.34i | 0.193462 | − | 0.147672i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19924.1 | −1.31922 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5568.02 | −0.366868 | −0.183434 | − | 0.983032i | \(-0.558721\pi\) | ||||
−0.183434 | + | 0.983032i | \(0.558721\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −61.0196 | + | 46.5769i | −0.00400089 | + | 0.00305392i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23868.9i | 1.55741i | 0.627387 | + | 0.778707i | \(0.284124\pi\) | ||||
−0.627387 | + | 0.778707i | \(0.715876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12735.2i | − | 0.826931i | −0.910520 | − | 0.413465i | \(-0.864318\pi\) | ||
0.910520 | − | 0.413465i | \(-0.135682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4198.51 | + | 10358.1i | 0.271305 | + | 0.669331i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10026.0 | 0.644755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15101.8 | 0.966512 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13733.9 | + | 17992.6i | 0.874769 | + | 1.14602i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 909.380i | 0.0576460i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6147.82i | − | 0.387862i | −0.981015 | − | 0.193931i | \(-0.937876\pi\) | ||
0.981015 | − | 0.193931i | \(-0.0621238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1091.33 | − | 1429.74i | −0.0685255 | − | 0.0897741i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 328.663 | 0.0205395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3214.55 | 0.199945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7231.04 | − | 26449.8i | 0.447661 | − | 1.63746i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3596.56i | 0.221616i | 0.993842 | + | 0.110808i | \(0.0353438\pi\) | ||||
−0.993842 | + | 0.110808i | \(0.964656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22806.1i | − | 1.39873i | −0.714763 | − | 0.699366i | \(-0.753466\pi\) | ||
0.714763 | − | 0.699366i | \(-0.246534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1801.71 | + | 1375.26i | −0.109988 | + | 0.0839550i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11623.0 | −0.706257 | −0.353128 | − | 0.935575i | \(-0.614882\pi\) | ||||
−0.353128 | + | 0.935575i | \(0.614882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34835.4 | −2.10695 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8054.31 | − | 6147.93i | 0.484905 | − | 0.370133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 30428.5i | − | 1.82352i | −0.410725 | − | 0.911759i | \(-0.634724\pi\) | ||
0.410725 | − | 0.911759i | \(-0.365276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1781.04i | 0.106246i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2478.94 | + | 9067.52i | −0.147203 | + | 0.538444i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32213.5 | 1.90419 | 0.952094 | − | 0.305805i | \(-0.0989257\pi\) | ||||
0.952094 | + | 0.305805i | \(0.0989257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1968.85 | 0.115854 | 0.0579269 | − | 0.998321i | \(-0.481551\pi\) | ||||
0.0579269 | + | 0.998321i | \(0.481551\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4133.12 | − | 5414.73i | −0.242107 | − | 0.317180i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 557.187i | − | 0.0324914i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8011.22i | 0.465061i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9923.20 | − | 13000.2i | −0.573473 | − | 0.751297i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15035.0 | 0.865009 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18098.8 | −1.03664 | −0.518320 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518320 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6513.99 | + | 16070.5i | 0.371442 | + | 0.916377i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14654.4i | 0.831928i | 0.909381 | + | 0.415964i | \(0.136556\pi\) | ||||
−0.909381 | + | 0.415964i | \(0.863444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12357.5i | 0.698437i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6476.91 | + | 4943.89i | −0.364458 | + | 0.278194i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25524.0 | 1.42994 | 0.714969 | − | 0.699156i | \(-0.246441\pi\) | ||||
0.714969 | + | 0.699156i | \(0.246441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1192.39 | 0.0665093 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10419.9 | − | 7953.59i | 0.578665 | − | 0.441701i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 41950.7i | − | 2.31958i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1294.40i | 0.0712607i | 0.999365 | + | 0.0356303i | \(0.0113439\pi\) | ||||
−0.999365 | + | 0.0356303i | \(0.988656\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11807.6 | + | 3228.04i | 0.647235 | + | 0.176945i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −251.655 | −0.0137350 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 249.453 | 0.0135563 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16470.1 | + | 21577.3i | 0.891213 | + | 1.16756i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5528.84i | − | 0.297891i | −0.988845 | − | 0.148945i | \(-0.952412\pi\) | ||
0.988845 | − | 0.148945i | \(-0.0475878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3060.80i | 0.164211i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1133.18 | + | 1484.56i | 0.0605361 | + | 0.0793073i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1173.53 | −0.0624259 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16540.4 | −0.876146 | −0.438073 | − | 0.898939i | \(-0.644339\pi\) | ||||
−0.438073 | + | 0.898939i | \(0.644339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13472.1 | + | 3683.10i | 0.710611 | + | 0.194272i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22192.4i | 1.16566i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5028.37i | 0.263007i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3217.72 | − | 2456.12i | 0.167598 | − | 0.127929i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2837.86 | 0.147196 | 0.0735982 | − | 0.997288i | \(-0.476552\pi\) | ||||
0.0735982 | + | 0.997288i | \(0.476552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2884.15 | −0.148976 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 152.005 | − | 116.027i | 0.00781897 | − | 0.00596830i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12429.4i | 0.636712i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26062.3i | 1.32957i | 0.747035 | + | 0.664785i | \(0.231477\pi\) | ||||
−0.747035 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14127.9 | + | 13704.8i | −0.717772 | + | 0.696278i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7365.55 | 0.372674 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24086.8 | 1.21373 | 0.606866 | − | 0.794804i | \(-0.292426\pi\) | ||||
0.606866 | + | 0.794804i | \(0.292426\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −182.826 | − | 239.518i | −0.00917503 | − | 0.0120201i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34563.0i | 1.72747i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4960.92i | − | 0.246942i | −0.992348 | − | 0.123471i | \(-0.960597\pi\) | ||
0.992348 | − | 0.123471i | \(-0.0394026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13911.3 | − | 18224.9i | −0.689668 | − | 0.903522i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24905.0 | −1.22971 | −0.614855 | − | 0.788640i | \(-0.710786\pi\) | ||||
−0.614855 | + | 0.788640i | \(0.710786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3262.45 | −0.160439 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7732.67 | − | 28284.7i | 0.378746 | − | 1.38539i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8618.18i | − | 0.420429i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20503.7i | 0.996258i | 0.867103 | + | 0.498129i | \(0.165979\pi\) | ||||
−0.867103 | + | 0.498129i | \(0.834021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13264.6 | + | 10125.0i | −0.641953 | + | 0.490009i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2771.12 | −0.133578 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18685.3 | −0.897132 | −0.448566 | − | 0.893750i | \(-0.648065\pi\) | ||||
−0.448566 | + | 0.893750i | \(0.648065\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21311.2 | + | 16267.0i | −1.01916 | + | 0.777939i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2699.37i | 0.128583i | 0.997931 | + | 0.0642917i | \(0.0204788\pi\) | ||||
−0.997931 | + | 0.0642917i | \(0.979521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1461.15i | − | 0.0693279i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −168.385 | + | 615.921i | −0.00795812 | + | 0.0291094i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35285.3 | 1.66112 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32139.9 | 1.50714 | 0.753572 | − | 0.657366i | \(-0.228329\pi\) | ||||
0.753572 | + | 0.657366i | \(0.228329\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6426.36 | − | 8419.06i | −0.300181 | − | 0.393262i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3369.87i | 0.156799i | 0.996922 | + | 0.0783997i | \(0.0249810\pi\) | ||||
−0.996922 | + | 0.0783997i | \(0.975019\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34431.5i | 1.59589i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1004.32 | + | 1315.75i | 0.0463705 | + | 0.0607492i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 839.613 | 0.0386165 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65775.3 | 3.01361 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13075.2 | + | 5299.86i | −0.596766 | + | 0.241892i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 716.614i | − | 0.0325822i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30361.1i | 1.37516i | 0.726106 | + | 0.687582i | \(0.241328\pi\) | ||||
−0.726106 | + | 0.687582i | \(0.758672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11167.7 | − | 8524.44i | 0.503906 | − | 0.384636i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7040.67 | 0.316482 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15229.2 | −0.681973 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3125.77 | + | 2385.93i | −0.139446 | + | 0.106440i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22114.2i | 0.982840i | 0.870923 | + | 0.491420i | \(0.163522\pi\) | ||||
−0.870923 | + | 0.491420i | \(0.836478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6069.00i | − | 0.268718i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37302.8 | − | 10198.1i | −1.64548 | − | 0.449852i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22549.1 | −0.990957 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 659.954 | 0.0288948 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17322.2 | − | 22693.5i | −0.755602 | − | 0.989901i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 12832.4i | − | 0.557680i | −0.960338 | − | 0.278840i | \(-0.910050\pi\) | ||
0.960338 | − | 0.278840i | \(-0.0899500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30318.5i | − | 1.31273i | −0.754442 | − | 0.656366i | \(-0.772093\pi\) | ||
0.754442 | − | 0.656366i | \(-0.227907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10608.5 | − | 13898.0i | −0.457635 | − | 0.599540i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1488.59 | 0.0639790 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24791.0 | 1.06160 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11960.1 | − | 3269.73i | −0.510280 | − | 0.139504i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22587.1i | 0.960166i | 0.877223 | + | 0.480083i | \(0.159393\pi\) | ||||
−0.877223 | + | 0.480083i | \(0.840607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34300.2i | − | 1.45277i | −0.687287 | − | 0.726386i | \(-0.741199\pi\) | ||
0.687287 | − | 0.726386i | \(-0.258801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −33064.3 | + | 25238.3i | −1.39533 | + | 1.06507i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21362.8 | 0.898258 | 0.449129 | − | 0.893467i | \(-0.351734\pi\) | ||||
0.449129 | + | 0.893467i | \(0.351734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15387.5 | 0.644669 | 0.322335 | − | 0.946626i | \(-0.395532\pi\) | ||||
0.322335 | + | 0.946626i | \(0.395532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34625.3 | − | 26429.8i | 1.44541 | − | 1.10330i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 979.170i | 0.0407277i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1471.20i | 0.0609735i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36220.4 | + | 14681.5i | −1.49577 | + | 0.606292i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4503.18 | −0.185301 | −0.0926503 | − | 0.995699i | \(-0.529534\pi\) | ||||
−0.0926503 | + | 0.995699i | \(0.529534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14276.3 | 0.585358 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4386.22 | + | 5746.32i | 0.179205 | + | 0.234773i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 2493.26i | − | 0.101504i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20046.1i | 0.813213i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22890.3 | + | 29988.2i | 0.925315 | + | 1.21224i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3625.34 | −0.146034 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25936.4 | −1.04108 | −0.520542 | − | 0.853836i | \(-0.674270\pi\) | ||||
−0.520542 | + | 0.853836i | \(0.674270\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −566.751 | + | 2073.07i | −0.0226695 | + | 0.0829212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7711.24i | 0.307364i | 0.988120 | + | 0.153682i | \(0.0491131\pi\) | ||||
−0.988120 | + | 0.153682i | \(0.950887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37861.9i | 1.50388i | 0.659232 | + | 0.751939i | \(0.270881\pi\) | ||||
−0.659232 | + | 0.751939i | \(0.729119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 360.924 | − | 275.497i | 0.0142860 | − | 0.0109047i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15692.4 | −0.618975 | −0.309487 | − | 0.950904i | \(-0.600157\pi\) | ||||
−0.309487 | + | 0.950904i | \(0.600157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4208.05 | 0.165408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18643.2 | + | 14230.6i | −0.730285 | + | 0.557434i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33502.4i | 1.30782i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35009.4i | − | 1.36194i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12569.6 | − | 45977.5i | 0.487306 | − | 1.78248i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2059.44 | 0.0795678 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17225.9 | −0.663260 | −0.331630 | − | 0.943410i | \(-0.607598\pi\) | ||||
−0.331630 | + | 0.943410i | \(0.607598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10214.4 | − | 13381.7i | −0.391950 | − | 0.513487i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22037.7i | − | 0.842757i | −0.906885 | − | 0.421378i | \(-0.861546\pi\) | ||
0.906885 | − | 0.421378i | \(-0.138454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23676.7i | 0.902359i | 0.892433 | + | 0.451180i | \(0.148997\pi\) | ||||
−0.892433 | + | 0.451180i | \(0.851003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2006.83 | − | 2629.12i | −0.0762249 | − | 0.0998610i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28833.0 | 1.09145 | 0.545726 | − | 0.837964i | \(-0.316254\pi\) | ||||
0.545726 | + | 0.837964i | \(0.316254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1944.01 | −0.0733408 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40648.0 | − | 24020.6i | −1.52835 | − | 0.903164i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20427.1i | − | 0.765473i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1460.89i | − | 0.0545613i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21586.4 | − | 16477.1i | 0.803509 | − | 0.613327i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28013.9 | −1.03928 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12778.4 | 0.472487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10656.9 | − | 8134.54i | 0.392736 | − | 0.299779i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1440.26i | − | 0.0529015i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7587.77i | − | 0.277782i | −0.990308 | − | 0.138891i | \(-0.955646\pi\) | ||
0.990308 | − | 0.138891i | \(-0.0443537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4366.24 | + | 1193.67i | 0.159317 | + | 0.0435551i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37134.3 | −1.35051 | −0.675255 | − | 0.737585i | \(-0.735966\pi\) | ||||
−0.675255 | + | 0.737585i | \(0.735966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 70338.3 | 2.54968 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 866.154 | + | 1134.73i | 0.0312942 | + | 0.0409980i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10534.7i | − | 0.379374i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28222.2i | − | 1.01302i | −0.862234 | − | 0.506510i | \(-0.830935\pi\) | ||
0.862234 | − | 0.506510i | \(-0.169065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12753.1 | + | 16707.6i | 0.456273 | + | 0.597756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −66624.7 | −2.37593 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5624.71 | −0.199934 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10730.8 | + | 2933.66i | 0.380201 | + | 0.103942i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6832.83i | − | 0.241311i | −0.992694 | − | 0.120656i | \(-0.961500\pi\) | ||
0.992694 | − | 0.120656i | \(-0.0384997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3295.70i | 0.116017i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33367.3 | + | 25469.6i | −1.17084 | + | 0.893717i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1531.67 | −0.0535732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23643.3 | 0.824324 | 0.412162 | − | 0.911111i | \(-0.364774\pi\) | ||||
0.412162 | + | 0.911111i | \(0.364774\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18632.7 | − | 14222.6i | 0.647558 | − | 0.494287i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 55969.4i | − | 1.93895i | −0.245195 | − | 0.969474i | \(-0.578852\pi\) | ||
0.245195 | − | 0.969474i | \(-0.421148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 994.472i | 0.0343420i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 436.596 | + | 1077.12i | 0.0150291 | + | 0.0370779i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8062.49 | −0.276659 | −0.138329 | − | 0.990386i | \(-0.544173\pi\) | ||||
−0.138329 | + | 0.990386i | \(0.544173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22840.2 | 0.781270 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23387.0 | + | 30638.9i | 0.797449 | + | 1.04472i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16764.7i | − | 0.569846i | −0.958550 | − | 0.284923i | \(-0.908032\pi\) | ||
0.958550 | − | 0.284923i | \(-0.0919681\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2491.49i | − | 0.0844215i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20534.2 | − | 26901.5i | −0.693600 | − | 0.908674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7052.86 | −0.237486 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −47812.1 | −1.60492 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8766.11 | + | 32064.9i | −0.293338 | + | 1.07298i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 3836.69i | − | 0.127987i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7191.31i | 0.239149i | 0.992825 | + | 0.119574i | \(0.0381530\pi\) | ||||
−0.992825 | + | 0.119574i | \(0.961847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5551.42 | − | 4237.45i | 0.184043 | − | 0.140482i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17045.4 | −0.563350 | −0.281675 | − | 0.959510i | \(-0.590890\pi\) | ||||
−0.281675 | + | 0.959510i | \(0.590890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1488.51 | 0.0490436 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 33491.2 | − | 25564.2i | 1.10008 | − | 0.839702i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 51810.0i | − | 1.69657i | −0.529540 | − | 0.848285i | \(-0.677635\pi\) | ||
0.529540 | − | 0.848285i | \(-0.322365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 92764.3i | − | 3.02836i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1486.23 | + | 5436.37i | −0.0483708 | + | 0.176932i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29478.1 | 0.956464 | 0.478232 | − | 0.878234i | \(-0.341278\pi\) | ||||
0.478232 | + | 0.878234i | \(0.341278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1171.39 | 0.0378919 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6702.63 | − | 8781.00i | −0.216157 | − | 0.283184i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29363.5i | 0.944091i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16755.3i | 0.537085i | 0.963268 | + | 0.268542i | \(0.0865419\pi\) | ||||
−0.963268 | + | 0.268542i | \(0.913458\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30322.1 | − | 39724.4i | −0.969024 | − | 1.26950i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1309.88 | 0.0417348 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5075.52 | 0.161227 | 0.0806136 | − | 0.996745i | \(-0.474312\pi\) | ||||
0.0806136 | + | 0.996745i | \(0.474312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2398.36 | − | 5916.94i | −0.0759567 | − | 0.187391i |
(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 | 336.4.h.b.239.4 | yes | 24 | |
3.2 | odd | 2 | inner | 336.4.h.b.239.22 | yes | 24 | |
4.3 | odd | 2 | inner | 336.4.h.b.239.21 | yes | 24 | |
12.11 | even | 2 | inner | 336.4.h.b.239.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.b.239.3 | ✓ | 24 | 12.11 | even | 2 | inner | |
336.4.h.b.239.4 | yes | 24 | 1.1 | even | 1 | trivial | |
336.4.h.b.239.21 | yes | 24 | 4.3 | odd | 2 | inner | |
336.4.h.b.239.22 | yes | 24 | 3.2 | odd | 2 | inner |