Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.d.849.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.15831 | + | 2.15831i | 1.24610 | + | 1.24610i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) |
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.31662 | 0.875602 | 0.437801 | − | 0.899072i | \(-0.355757\pi\) | ||||
0.437801 | + | 0.899072i | \(0.355757\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.31662i | 2.10554i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.15831 | − | 3.15831i | −0.952267 | − | 0.952267i | 0.0466445 | − | 0.998912i | \(-0.485147\pi\) |
−0.998912 | + | 0.0466445i | \(0.985147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.31662 | + | 4.31662i | 1.19722 | + | 1.19722i | 0.974997 | + | 0.222220i | \(0.0713302\pi\) |
0.222220 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.31662i | 0.319328i | 0.987171 | + | 0.159664i | \(0.0510411\pi\) | ||||
−0.987171 | + | 0.159664i | \(0.948959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.158312 | + | 0.158312i | −0.0363194 | + | 0.0363194i | −0.725033 | − | 0.688714i | \(-0.758176\pi\) |
0.688714 | + | 0.725033i | \(0.258176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.00000 | + | 5.00000i | 1.09109 | + | 1.09109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.316625 | −0.0660208 | −0.0330104 | − | 0.999455i | \(-0.510509\pi\) | ||||
−0.0330104 | + | 0.999455i | \(0.510509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.15831 | + | 7.15831i | −1.37762 | + | 1.37762i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | + | 2.00000i | −0.371391 | + | 0.371391i | −0.867984 | − | 0.496593i | \(-0.834584\pi\) |
0.496593 | + | 0.867984i | \(0.334584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.31662 | 0.416078 | 0.208039 | − | 0.978121i | \(-0.433292\pi\) | ||||
0.208039 | + | 0.978121i | \(0.433292\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 13.6332i | − | 2.37324i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.683375 | + | 0.683375i | −0.112346 | + | 0.112346i | −0.761045 | − | 0.648699i | \(-0.775313\pi\) |
0.648699 | + | 0.761045i | \(0.275313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.6332i | 2.98371i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000i | 0.780869i | 0.920631 | + | 0.390434i | \(0.127675\pi\) | ||||
−0.920631 | + | 0.390434i | \(0.872325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.63325 | − | 7.63325i | 1.16406 | − | 1.16406i | 0.180481 | − | 0.983578i | \(-0.442234\pi\) |
0.983578 | − | 0.180481i | \(-0.0577655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.63325 | −0.233321 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.84169 | + | 2.84169i | −0.397916 | + | 0.397916i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.31662 | + | 3.31662i | −0.455573 | + | 0.455573i | −0.897199 | − | 0.441626i | \(-0.854402\pi\) |
0.441626 | + | 0.897199i | \(0.354402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.683375 | −0.0905153 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.31662 | − | 1.31662i | −0.171410 | − | 0.171410i | 0.616189 | − | 0.787599i | \(-0.288676\pi\) |
−0.787599 | + | 0.616189i | \(0.788676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.63325 | − | 9.63325i | 1.23341 | − | 1.23341i | 0.270766 | − | 0.962645i | \(-0.412723\pi\) |
0.962645 | − | 0.270766i | \(-0.0872770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.6332i | 1.84362i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.15831 | − | 9.15831i | −1.11887 | − | 1.11887i | −0.991908 | − | 0.126958i | \(-0.959479\pi\) |
−0.126958 | − | 0.991908i | \(-0.540521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.683375 | − | 0.683375i | −0.0822687 | − | 0.0822687i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.63325i | 1.02458i | 0.858813 | + | 0.512289i | \(0.171202\pi\) | ||||
−0.858813 | + | 0.512289i | \(0.828798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.68338 | 0.782230 | 0.391115 | − | 0.920342i | \(-0.372089\pi\) | ||||
0.391115 | + | 0.920342i | \(0.372089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.31662 | − | 7.31662i | −0.833807 | − | 0.833807i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.31662 | 0.485658 | 0.242829 | − | 0.970069i | \(-0.421925\pi\) | ||||
0.242829 | + | 0.970069i | \(0.421925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.9499 | −1.32776 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.15831 | − | 7.15831i | −0.785727 | − | 0.785727i | 0.195064 | − | 0.980791i | \(-0.437509\pi\) |
−0.980791 | + | 0.195064i | \(0.937509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.63325 | −0.925582 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.94987i | − | 0.418686i | −0.977842 | − | 0.209343i | \(-0.932868\pi\) | ||
0.977842 | − | 0.209343i | \(-0.0671325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | + | 10.0000i | 1.04828 | + | 1.04828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | + | 5.00000i | 0.518476 | + | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.63325i | − | 0.673504i | −0.941593 | − | 0.336752i | \(-0.890672\pi\) | ||
0.941593 | − | 0.336752i | \(-0.109328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9499 | − | 19.9499i | 2.00504 | − | 2.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.31662 | + | 5.31662i | 0.529024 | + | 0.529024i | 0.920281 | − | 0.391257i | \(-0.127960\pi\) |
−0.391257 | + | 0.920281i | \(0.627960\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.63325 | −0.456528 | −0.228264 | − | 0.973599i | \(-0.573305\pi\) | ||||
−0.228264 | + | 0.973599i | \(0.573305\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.84169 | + | 2.84169i | −0.274716 | + | 0.274716i | −0.830995 | − | 0.556279i | \(-0.812229\pi\) |
0.556279 | + | 0.830995i | \(0.312229\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.94987 | − | 5.94987i | 0.569895 | − | 0.569895i | −0.362204 | − | 0.932099i | \(-0.617976\pi\) |
0.932099 | + | 0.362204i | \(0.117976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.94987 | −0.279990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.36675i | − | 0.222645i | −0.993784 | − | 0.111323i | \(-0.964491\pi\) | ||
0.993784 | − | 0.111323i | \(-0.0355087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −27.2665 | + | 27.2665i | −2.52079 | + | 2.52079i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.05013i | 0.279605i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94987i | 0.813625i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.7916 | + | 10.7916i | −0.973042 | + | 0.973042i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.31662i | − | 0.560510i | −0.959926 | − | 0.280255i | \(-0.909581\pi\) | ||
0.959926 | − | 0.280255i | \(-0.0904190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 32.9499 | 2.90107 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | + | 1.00000i | −0.0873704 | + | 0.0873704i | −0.749441 | − | 0.662071i | \(-0.769678\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.366750 | + | 0.366750i | −0.0318013 | + | 0.0318013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6332 | −0.993896 | −0.496948 | − | 0.867780i | \(-0.665546\pi\) | ||||
−0.496948 | + | 0.867780i | \(0.665546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.15831 | − | 9.15831i | −0.776798 | − | 0.776798i | 0.202487 | − | 0.979285i | \(-0.435098\pi\) |
−0.979285 | + | 0.202487i | \(0.935098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.2665 | + | 17.2665i | −1.45410 | + | 1.45410i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 27.2665i | − | 2.28014i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.52506 | − | 3.52506i | −0.290742 | − | 0.290742i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.6332 | − | 16.6332i | −1.36265 | − | 1.36265i | −0.870525 | − | 0.492124i | \(-0.836221\pi\) |
−0.492124 | − | 0.870525i | \(-0.663779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.31662i | − | 0.351282i | −0.984454 | − | 0.175641i | \(-0.943800\pi\) | ||
0.984454 | − | 0.175641i | \(-0.0561998\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.31662 | −0.672359 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3166 | + | 11.3166i | 0.903165 | + | 0.903165i | 0.995709 | − | 0.0925436i | \(-0.0294998\pi\) |
−0.0925436 | + | 0.995709i | \(0.529500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.3166 | −1.13538 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.733501 | −0.0578080 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.15831 | − | 7.15831i | −0.560682 | − | 0.560682i | 0.368819 | − | 0.929501i | \(-0.379762\pi\) |
−0.929501 | + | 0.368819i | \(0.879762\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.2665i | 1.86665i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 1.00000i | −0.0764719 | − | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.9499 | − | 12.9499i | −0.984561 | − | 0.984561i | 0.0153219 | − | 0.999883i | \(-0.495123\pi\) |
−0.999883 | + | 0.0153219i | \(0.995123\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.68338i | − | 0.427189i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.79156 | + | 8.79156i | −0.657112 | + | 0.657112i | −0.954696 | − | 0.297584i | \(-0.903819\pi\) |
0.297584 | + | 0.954696i | \(0.403819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.31662 | − | 3.31662i | −0.246523 | − | 0.246523i | 0.573019 | − | 0.819542i | \(-0.305772\pi\) |
−0.819542 | + | 0.573019i | \(0.805772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 41.5831 | 3.07391 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.15831 | − | 4.15831i | 0.304086 | − | 0.304086i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.5831 | + | 16.5831i | −1.20624 | + | 1.20624i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9499 | 1.51588 | 0.757940 | − | 0.652324i | \(-0.226206\pi\) | ||||
0.757940 | + | 0.652324i | \(0.226206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.68338i | 0.337117i | 0.985692 | + | 0.168558i | \(0.0539112\pi\) | ||||
−0.985692 | + | 0.168558i | \(0.946089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5831 | − | 16.5831i | 1.18150 | − | 1.18150i | 0.202143 | − | 0.979356i | \(-0.435210\pi\) |
0.979356 | − | 0.202143i | \(-0.0647904\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.6332i | − | 0.895547i | −0.894147 | − | 0.447774i | \(-0.852217\pi\) | ||
0.894147 | − | 0.447774i | \(-0.147783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 39.5330i | − | 2.78844i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.63325 | + | 4.63325i | −0.325190 | + | 0.325190i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.00000i | − | 0.139010i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7916 | + | 11.7916i | −0.811765 | + | 0.811765i | −0.984898 | − | 0.173134i | \(-0.944611\pi\) |
0.173134 | + | 0.984898i | \(0.444611\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.6332 | + | 18.6332i | −1.27673 | + | 1.27673i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.36675 | 0.364319 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4248 | + | 14.4248i | 0.974738 | + | 0.974738i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.68338 | + | 5.68338i | −0.382305 | + | 0.382305i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000i | 0.401790i | 0.979613 | + | 0.200895i | \(0.0643850\pi\) | ||||
−0.979613 | + | 0.200895i | \(0.935615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.36675 | + | 4.36675i | 0.289831 | + | 0.289831i | 0.837014 | − | 0.547182i | \(-0.184300\pi\) |
−0.547182 | + | 0.837014i | \(0.684300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | + | 2.00000i | 0.132164 | + | 0.132164i | 0.770094 | − | 0.637930i | \(-0.220209\pi\) |
−0.637930 | + | 0.770094i | \(0.720209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 31.5831i | − | 2.07802i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8997 | 0.779578 | 0.389789 | − | 0.920904i | \(-0.372548\pi\) | ||||
0.389789 | + | 0.920904i | \(0.372548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.31662 | + | 9.31662i | 0.605180 | + | 0.605180i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6332 | −1.20528 | −0.602642 | − | 0.798011i | \(-0.705885\pi\) | ||||
−0.602642 | + | 0.798011i | \(0.705885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5831 | 1.19704 | 0.598522 | − | 0.801106i | \(-0.295755\pi\) | ||||
0.598522 | + | 0.801106i | \(0.295755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.31662 | − | 4.31662i | −0.276912 | − | 0.276912i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.36675 | −0.0869642 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 30.8997i | − | 1.95819i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.10819 | + | 9.10819i | 0.574904 | + | 0.574904i | 0.933495 | − | 0.358591i | \(-0.116743\pi\) |
−0.358591 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | + | 1.00000i | 0.0628695 | + | 0.0628695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.6332i | − | 1.03755i | −0.854910 | − | 0.518777i | \(-0.826388\pi\) | ||
0.854910 | − | 0.518777i | \(-0.173612\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.58312 | + | 1.58312i | −0.0983705 | + | 0.0983705i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6332 | − | 12.6332i | −0.781979 | − | 0.781979i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5831 | 0.960897 | 0.480448 | − | 0.877023i | \(-0.340474\pi\) | ||||
0.480448 | + | 0.877023i | \(0.340474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.52506 | − | 8.52506i | 0.521725 | − | 0.521725i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.31662 | + | 6.31662i | −0.385131 | + | 0.385131i | −0.872947 | − | 0.487815i | \(-0.837794\pi\) |
0.487815 | + | 0.872947i | \(0.337794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.949874 | 0.0577008 | 0.0288504 | − | 0.999584i | \(-0.490815\pi\) | ||||
0.0288504 | + | 0.999584i | \(0.490815\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43.1662i | 2.61254i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3166 | − | 14.3166i | 0.860203 | − | 0.860203i | −0.131159 | − | 0.991361i | \(-0.541870\pi\) |
0.991361 | + | 0.131159i | \(0.0418698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.6332i | 0.876070i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.26650i | 0.433483i | 0.976229 | + | 0.216741i | \(0.0695429\pi\) | ||||
−0.976229 | + | 0.216741i | \(0.930457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.84169 | + | 3.84169i | −0.228365 | + | 0.228365i | −0.812009 | − | 0.583645i | \(-0.801626\pi\) |
0.583645 | + | 0.812009i | \(0.301626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5831i | 0.683730i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2665 | 0.898029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.3166 | − | 14.3166i | 0.839255 | − | 0.839255i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.2665 | − | 18.2665i | 1.06714 | − | 1.06714i | 0.0695627 | − | 0.997578i | \(-0.477840\pi\) |
0.997578 | − | 0.0695627i | \(-0.0221604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 45.2164 | 2.62372 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.36675 | − | 1.36675i | −0.0790412 | − | 0.0790412i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6834 | − | 17.6834i | 1.01925 | − | 1.01925i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.9499i | 1.31844i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1583 | − | 14.1583i | −0.808058 | − | 0.808058i | 0.176282 | − | 0.984340i | \(-0.443593\pi\) |
−0.984340 | + | 0.176282i | \(0.943593\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0000 | − | 10.0000i | −0.568880 | − | 0.568880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 12.9499i | − | 0.734320i | −0.930158 | − | 0.367160i | \(-0.880330\pi\) | ||
0.930158 | − | 0.367160i | \(-0.119670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0000 | 0.904373 | 0.452187 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452187 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.9499 | + | 14.9499i | 0.839669 | + | 0.839669i | 0.988815 | − | 0.149147i | \(-0.0476526\pi\) |
−0.149147 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.6332 | 0.707326 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2665 | −0.684649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.208438 | − | 0.208438i | −0.0115978 | − | 0.0115978i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.6834 | 1.42029 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.5330i | 1.02176i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.15831 | + | 1.15831i | 0.0636666 | + | 0.0636666i | 0.738223 | − | 0.674557i | \(-0.235665\pi\) |
−0.674557 | + | 0.738223i | \(0.735665\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.31662 | − | 4.31662i | −0.236550 | − | 0.236550i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.8997i | 1.24743i | 0.781652 | + | 0.623714i | \(0.214377\pi\) | ||||
−0.781652 | + | 0.623714i | \(0.785623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.10819 | − | 5.10819i | 0.277439 | − | 0.277439i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.31662 | − | 7.31662i | −0.396217 | − | 0.396217i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4248 | − | 14.4248i | 0.774364 | − | 0.774364i | −0.204502 | − | 0.978866i | \(-0.565557\pi\) |
0.978866 | + | 0.204502i | \(0.0655574\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2665 | + | 24.2665i | −1.29896 | + | 1.29896i | −0.369874 | + | 0.929082i | \(0.620599\pi\) |
−0.929082 | + | 0.369874i | \(0.879401\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −61.7995 | −3.29861 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 33.2665i | − | 1.77060i | −0.465023 | − | 0.885299i | \(-0.653954\pi\) | ||
0.465023 | − | 0.885299i | \(-0.346046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.58312 | + | 6.58312i | −0.348416 | + | 0.348416i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.68338i | − | 0.511069i | −0.966800 | − | 0.255534i | \(-0.917749\pi\) | ||
0.966800 | − | 0.255534i | \(-0.0822514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9499i | 0.997362i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.3166 | + | 19.3166i | −1.01386 | + | 1.01386i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.6332i | 1.39024i | 0.718892 | + | 0.695122i | \(0.244650\pi\) | ||||
−0.718892 | + | 0.695122i | \(0.755350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.5831 | −1.64415 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.68338 | + | 7.68338i | −0.398901 | + | 0.398901i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.36675 | − | 2.36675i | 0.122546 | − | 0.122546i | −0.643174 | − | 0.765720i | \(-0.722383\pi\) |
0.765720 | + | 0.643174i | \(0.222383\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.2665 | −0.889270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4248 | − | 11.4248i | −0.586853 | − | 0.586853i | 0.349925 | − | 0.936778i | \(-0.386207\pi\) |
−0.936778 | + | 0.349925i | \(0.886207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6332 | − | 13.6332i | 0.698453 | − | 0.698453i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.9499i | − | 0.866098i | −0.901370 | − | 0.433049i | \(-0.857438\pi\) | ||
0.901370 | − | 0.433049i | \(-0.142562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 48.2164 | + | 48.2164i | 2.45098 | + | 2.45098i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.26650 | + | 4.26650i | 0.216320 | + | 0.216320i | 0.806946 | − | 0.590626i | \(-0.201119\pi\) |
−0.590626 | + | 0.806946i | \(0.701119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.416876i | − | 0.0210823i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.31662 | −0.217745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2665 | − | 25.2665i | −1.26809 | − | 1.26809i | −0.947074 | − | 0.321015i | \(-0.895976\pi\) |
−0.321015 | − | 0.947074i | \(-0.604024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.58312 | −0.0792553 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.68338 | 0.134001 | 0.0670007 | − | 0.997753i | \(-0.478657\pi\) | ||||
0.0670007 | + | 0.997753i | \(0.478657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | + | 10.0000i | 0.498135 | + | 0.498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.31662 | 0.213967 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.6332i | − | 0.970802i | −0.874292 | − | 0.485401i | \(-0.838674\pi\) | ||
0.874292 | − | 0.485401i | \(-0.161326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.1082 | − | 25.1082i | −1.23850 | − | 1.23850i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.05013 | − | 3.05013i | −0.150087 | − | 0.150087i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 39.5330i | − | 1.93594i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.5251 | + | 11.5251i | −0.563036 | + | 0.563036i | −0.930169 | − | 0.367132i | \(-0.880340\pi\) |
0.367132 | + | 0.930169i | \(0.380340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.63325 | + | 4.63325i | 0.225811 | + | 0.225811i | 0.810940 | − | 0.585129i | \(-0.198956\pi\) |
−0.585129 | + | 0.810940i | \(0.698956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −50.5330 | −2.45700 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.3166 | − | 22.3166i | 1.07998 | − | 1.07998i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 58.8496 | − | 58.8496i | 2.84129 | − | 2.84129i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9499 | 0.527437 | 0.263718 | − | 0.964600i | \(-0.415051\pi\) | ||||
0.263718 | + | 0.964600i | \(0.415051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.5831i | − | 0.604706i | −0.953196 | − | 0.302353i | \(-0.902228\pi\) | ||
0.953196 | − | 0.302353i | \(-0.0977722\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0501256 | − | 0.0501256i | 0.00239783 | − | 0.00239783i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.36675i | − | 0.256141i | −0.991765 | − | 0.128071i | \(-0.959122\pi\) | ||
0.991765 | − | 0.128071i | \(-0.0408784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 10.3166i | − | 0.491268i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1082 | − | 19.1082i | 0.907857 | − | 0.907857i | −0.0882417 | − | 0.996099i | \(-0.528125\pi\) |
0.996099 | + | 0.0882417i | \(0.0281248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 71.7995i | − | 3.39600i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6834 | −0.976109 | −0.488054 | − | 0.872813i | \(-0.662293\pi\) | ||||
−0.488054 | + | 0.872813i | \(0.662293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7916 | − | 15.7916i | 0.743596 | − | 0.743596i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.31662 | − | 9.31662i | 0.437733 | − | 0.437733i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | 0.795226 | 0.397613 | − | 0.917553i | \(-0.369839\pi\) | ||||
0.397613 | + | 0.917553i | \(0.369839\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.42481 | − | 9.42481i | −0.439913 | − | 0.439913i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.6834 | + | 19.6834i | −0.916746 | + | 0.916746i | −0.996791 | − | 0.0800451i | \(-0.974494\pi\) |
0.0800451 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6332i | 1.14480i | 0.819973 | + | 0.572402i | \(0.193988\pi\) | ||||
−0.819973 | + | 0.572402i | \(0.806012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.2665 | − | 14.2665i | −0.660175 | − | 0.660175i | 0.295246 | − | 0.955421i | \(-0.404598\pi\) |
−0.955421 | + | 0.295246i | \(0.904598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.2164 | − | 21.2164i | −0.979681 | − | 0.979681i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.8496i | 2.25087i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.2164 | −2.21699 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.9499 | − | 20.9499i | −0.959229 | − | 0.959229i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.2164 | 0.466798 | 0.233399 | − | 0.972381i | \(-0.425015\pi\) | ||||
0.233399 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.89975 | −0.269005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.58312 | − | 1.58312i | −0.0720346 | − | 0.0720346i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.2164 | −1.45986 | −0.729932 | − | 0.683520i | \(-0.760448\pi\) | ||||
−0.729932 | + | 0.683520i | \(0.760448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 30.8997i | − | 1.39733i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.6332 | − | 29.6332i | −1.33733 | − | 1.33733i | −0.898637 | − | 0.438693i | \(-0.855442\pi\) |
−0.438693 | − | 0.898637i | \(-0.644558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.63325 | − | 2.63325i | −0.118596 | − | 0.118596i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0000i | 0.897123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.8997 | − | 22.8997i | 1.02513 | − | 1.02513i | 0.0254576 | − | 0.999676i | \(-0.491896\pi\) |
0.999676 | − | 0.0254576i | \(-0.00810429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.8496 | + | 38.8496i | 1.73567 | + | 1.73567i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.8997 | −1.42234 | −0.711170 | − | 0.703020i | \(-0.751834\pi\) | ||||
−0.711170 | + | 0.703020i | \(0.751834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −52.3747 | + | 52.3747i | −2.32604 | + | 2.32604i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.2665 | − | 20.2665i | 0.898297 | − | 0.898297i | −0.0969887 | − | 0.995285i | \(-0.530921\pi\) |
0.995285 | + | 0.0969887i | \(0.0309211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4829 | 0.684922 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.26650i | − | 0.100068i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.2665 | − | 25.2665i | 1.11122 | − | 1.11122i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 55.8997i | − | 2.45373i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.6332i | − | 0.597284i | −0.954365 | − | 0.298642i | \(-0.903466\pi\) | ||
0.954365 | − | 0.298642i | \(-0.0965336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.47494 | + | 7.47494i | −0.326856 | + | 0.326856i | −0.851390 | − | 0.524534i | \(-0.824240\pi\) |
0.524534 | + | 0.851390i | \(0.324240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.05013i | 0.132866i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8997 | −0.995641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.31662 | − | 8.31662i | 0.360911 | − | 0.360911i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.5831 | + | 21.5831i | −0.934869 | + | 0.934869i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.9499 | −1.63766 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.15831 | + | 5.15831i | 0.222184 | + | 0.222184i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.6834 | − | 11.6834i | 0.502308 | − | 0.502308i | −0.409847 | − | 0.912154i | \(-0.634418\pi\) |
0.912154 | + | 0.409847i | \(0.134418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14.3166i | − | 0.614385i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7414 | − | 15.7414i | −0.673055 | − | 0.673055i | 0.285364 | − | 0.958419i | \(-0.407886\pi\) |
−0.958419 | + | 0.285364i | \(0.907886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 60.8496 | + | 60.8496i | 2.59700 | + | 2.59700i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.633250i | − | 0.0269773i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | 0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3166 | + | 26.3166i | 1.11507 | + | 1.11507i | 0.992454 | + | 0.122617i | \(0.0391287\pi\) |
0.122617 | + | 0.992454i | \(0.460871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.8997 | 2.78726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.9499 | 0.757844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.9499 | + | 17.9499i | 0.756497 | + | 0.756497i | 0.975683 | − | 0.219186i | \(-0.0703402\pi\) |
−0.219186 | + | 0.975683i | \(0.570340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.6834 | −1.16259 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000i | 0.377300i | 0.982044 | + | 0.188650i | \(0.0604111\pi\) | ||||
−0.982044 | + | 0.188650i | \(0.939589\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.73350 | + | 1.73350i | 0.0725448 | + | 0.0725448i | 0.742448 | − | 0.669903i | \(-0.233665\pi\) |
−0.669903 | + | 0.742448i | \(0.733665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 45.2164 | + | 45.2164i | 1.88894 | + | 1.88894i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6332i | 0.650821i | 0.945573 | + | 0.325410i | \(0.105502\pi\) | ||||
−0.945573 | + | 0.325410i | \(0.894498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1082 | + | 10.1082i | −0.420082 | + | 0.420082i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.5831 | − | 16.5831i | −0.687984 | − | 0.687984i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.9499 | 0.867655 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.42481 | + | 9.42481i | −0.389004 | + | 0.389004i | −0.874332 | − | 0.485328i | \(-0.838700\pi\) |
0.485328 | + | 0.874332i | \(0.338700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.366750 | + | 0.366750i | −0.0151117 | + | 0.0151117i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 71.5831 | 2.94454 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.5330i | − | 1.45917i | −0.683893 | − | 0.729583i | \(-0.739714\pi\) | ||
0.683893 | − | 0.729583i | \(-0.260286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.2665 | − | 27.2665i | 1.11594 | − | 1.11594i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.2164i | 1.47976i | 0.672738 | + | 0.739880i | \(0.265118\pi\) | ||||
−0.672738 | + | 0.739880i | \(0.734882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0501i | 0.899443i | 0.893169 | + | 0.449722i | \(0.148477\pi\) | ||||
−0.893169 | + | 0.449722i | \(0.851523\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 57.8496 | − | 57.8496i | 2.35582 | − | 2.35582i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1662i | 0.859112i | 0.903040 | + | 0.429556i | \(0.141330\pi\) | ||||
−0.903040 | + | 0.429556i | \(0.858670\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0000 | −0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.5330 | + | 34.5330i | −1.39706 | + | 1.39706i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.2665 | + | 16.2665i | −0.656998 | + | 0.656998i | −0.954669 | − | 0.297671i | \(-0.903790\pi\) |
0.297671 | + | 0.954669i | \(0.403790\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.733501 | −0.0295296 | −0.0147648 | − | 0.999891i | \(-0.504700\pi\) | ||||
−0.0147648 | + | 0.999891i | \(0.504700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.36675 | − | 8.36675i | −0.336288 | − | 0.336288i | 0.518680 | − | 0.854968i | \(-0.326424\pi\) |
−0.854968 | + | 0.518680i | \(0.826424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.26650 | − | 2.26650i | 0.0909515 | − | 0.0909515i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 9.15038i | − | 0.366602i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.15831 | + | 2.15831i | 0.0861947 | + | 0.0861947i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.899749 | − | 0.899749i | −0.0358753 | − | 0.0358753i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3166i | 0.968030i | 0.875060 | + | 0.484015i | \(0.160822\pi\) | ||||
−0.875060 | + | 0.484015i | \(0.839178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.8997 | −2.02308 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.05013 | − | 7.05013i | −0.279336 | − | 0.279336i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −54.5330 | −2.15729 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8997 | −0.943983 | −0.471992 | − | 0.881603i | \(-0.656465\pi\) | ||||
−0.471992 | + | 0.881603i | \(0.656465\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.26650 | + | 2.26650i | 0.0893820 | + | 0.0893820i | 0.750384 | − | 0.661002i | \(-0.229869\pi\) |
−0.661002 | + | 0.750384i | \(0.729869\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.1662 | 0.832131 | 0.416066 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416066 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.31662i | 0.326456i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.5831 | + | 11.5831i | 0.453978 | + | 0.453978i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.3668 | − | 16.3668i | −0.640480 | − | 0.640480i | 0.310193 | − | 0.950674i | \(-0.399606\pi\) |
−0.950674 | + | 0.310193i | \(0.899606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.2164i | 1.64702i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.1583 | + | 25.1583i | −0.980029 | + | 0.980029i | −0.999804 | − | 0.0197757i | \(-0.993705\pi\) |
0.0197757 | + | 0.999804i | \(0.493705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.5831 | − | 35.5831i | −1.38402 | − | 1.38402i | −0.837339 | − | 0.546684i | \(-0.815890\pi\) |
−0.546684 | − | 0.837339i | \(-0.684110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.5330 | −0.952783 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.633250 | − | 0.633250i | 0.0245195 | − | 0.0245195i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9499 | + | 12.9499i | −0.500671 | + | 0.500671i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.8496 | −2.34907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.6332i | 1.64339i | 0.569927 | + | 0.821696i | \(0.306972\pi\) | ||||
−0.569927 | + | 0.821696i | \(0.693028\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.3668 | + | 11.3668i | −0.436860 | + | 0.436860i | −0.890954 | − | 0.454094i | \(-0.849963\pi\) |
0.454094 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15.3668i | − | 0.589722i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.8496i | 0.722319i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.47494 | − | 5.47494i | 0.209493 | − | 0.209493i | −0.594559 | − | 0.804052i | \(-0.702673\pi\) |
0.804052 | + | 0.594559i | \(0.202673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.63325i | 0.329379i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.6332 | −1.09084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1583 | − | 26.1583i | 0.995109 | − | 0.995109i | −0.00487900 | − | 0.999988i | \(-0.501553\pi\) |
0.999988 | + | 0.00487900i | \(0.00155304\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.2164 | − | 46.2164i | 1.75561 | − | 1.75561i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.58312 | −0.249354 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.6834 | + | 25.6834i | 0.971434 | + | 0.971434i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.2665 | + | 21.2665i | −0.803225 | + | 0.803225i | −0.983598 | − | 0.180374i | \(-0.942269\pi\) |
0.180374 | + | 0.983598i | \(0.442269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.216374i | − | 0.00816068i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.3166 | + | 12.3166i | 0.463214 | + | 0.463214i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0000 | + | 22.0000i | 0.826227 | + | 0.826227i | 0.986993 | − | 0.160765i | \(-0.0513962\pi\) |
−0.160765 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.2665i | 1.02257i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.733501 | −0.0274698 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.2164 | − | 40.2164i | −1.50191 | − | 1.50191i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.94987 | 0.110012 | 0.0550059 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550059 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7335 | −0.399736 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.1082 | + | 40.1082i | 1.49164 | + | 1.49164i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.53300 | 0.0939437 | 0.0469719 | − | 0.998896i | \(-0.485043\pi\) | ||||
0.0469719 | + | 0.998896i | \(0.485043\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2164i | 0.637643i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0501 | + | 10.0501i | 0.371717 | + | 0.371717i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.68338 | − | 5.68338i | −0.209920 | − | 0.209920i | 0.594313 | − | 0.804234i | \(-0.297424\pi\) |
−0.804234 | + | 0.594313i | \(0.797424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.8496i | 2.13092i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.3668 | + | 14.3668i | −0.528489 | + | 0.528489i | −0.920122 | − | 0.391632i | \(-0.871911\pi\) |
0.391632 | + | 0.920122i | \(0.371911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.94987 | − | 2.94987i | −0.108366 | − | 0.108366i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.3166 | −0.745345 | −0.372672 | − | 0.927963i | \(-0.621558\pi\) | ||||
−0.372672 | + | 0.927963i | \(0.621558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.2164 | − | 45.2164i | 1.65438 | − | 1.65438i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.58312 | + | 6.58312i | −0.240542 | + | 0.240542i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.4327 | −1.54839 | −0.774196 | − | 0.632945i | \(-0.781846\pi\) | ||||
−0.774196 | + | 0.632945i | \(0.781846\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.3166i | 1.43278i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.3166 | + | 34.3166i | −1.24726 | + | 1.24726i | −0.290333 | + | 0.956926i | \(0.593766\pi\) |
−0.956926 | + | 0.290333i | \(0.906234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.31662i | 0.156684i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.2665i | 1.16966i | 0.811156 | + | 0.584830i | \(0.198839\pi\) | ||||
−0.811156 | + | 0.584830i | \(0.801161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7836 | − | 13.7836i | 0.499001 | − | 0.499001i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.3668i | − | 0.410430i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.4829 | 1.17136 | 0.585681 | − | 0.810542i | \(-0.300827\pi\) | ||||
0.585681 | + | 0.810542i | \(0.300827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.8997 | − | 35.8997i | 1.29290 | − | 1.29290i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.3668 | − | 17.3668i | 0.624639 | − | 0.624639i | −0.322075 | − | 0.946714i | \(-0.604380\pi\) |
0.946714 | + | 0.322075i | \(0.104380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.83375 | −0.245159 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.791562 | − | 0.791562i | −0.0283607 | − | 0.0283607i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.2665 | − | 27.2665i | 0.975672 | − | 0.975672i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 28.6332i | − | 1.02327i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.00000 | − | 7.00000i | −0.249523 | − | 0.249523i | 0.571252 | − | 0.820775i | \(-0.306458\pi\) |
−0.820775 | + | 0.571252i | \(0.806458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.6332 | + | 33.6332i | 1.19738 | + | 1.19738i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.48287i | − | 0.194949i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 83.1662 | 2.95332 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.6332 | + | 15.6332i | 0.553758 | + | 0.553758i | 0.927523 | − | 0.373765i | \(-0.121933\pi\) |
−0.373765 | + | 0.927523i | \(0.621933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5330 | −0.372631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.9499 | 0.881560 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1082 | − | 21.1082i | −0.744892 | − | 0.744892i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.2665 | −0.959826 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.5330i | 1.35475i | 0.735639 | + | 0.677374i | \(0.236882\pi\) | ||||
−0.735639 | + | 0.677374i | \(0.763118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.6332 | + | 37.6332i | 1.32148 | + | 1.32148i | 0.912577 | + | 0.408905i | \(0.134089\pi\) |
0.408905 | + | 0.912577i | \(0.365911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.05013 | + | 2.05013i | 0.0719010 | + | 0.0719010i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.41688i | 0.0845558i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −63.1662 | + | 63.1662i | −2.20721 | + | 2.20721i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.73350 | − | 1.73350i | −0.0604996 | − | 0.0604996i | 0.676210 | − | 0.736709i | \(-0.263621\pi\) |
−0.736709 | + | 0.676210i | \(0.763621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.89975 | 0.345084 | 0.172542 | − | 0.985002i | \(-0.444802\pi\) | ||||
0.172542 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.84169 | + | 7.84169i | −0.272682 | + | 0.272682i | −0.830179 | − | 0.557497i | \(-0.811762\pi\) |
0.557497 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.733501 | − | 0.733501i | 0.0254755 | − | 0.0254755i | −0.694254 | − | 0.719730i | \(-0.744266\pi\) |
0.719730 | + | 0.694254i | \(0.244266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 61.7995 | 2.14380 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.15038i | − | 0.0745061i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5831 | + | 16.5831i | −0.573197 | + | 0.573197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.63325i | − | 0.0909099i | −0.998966 | − | 0.0454549i | \(-0.985526\pi\) | ||
0.998966 | − | 0.0454549i | \(-0.0144737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000i | 0.724138i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.6834 | + | 15.6834i | −0.540164 | + | 0.540164i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.7335i | 0.712412i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.5831 | −0.569131 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.216374 | − | 0.216374i | 0.00741719 | − | 0.00741719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.3668 | + | 20.3668i | −0.697344 | + | 0.697344i | −0.963837 | − | 0.266493i | \(-0.914135\pi\) |
0.266493 | + | 0.963837i | \(0.414135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.6332 | −0.738978 | −0.369489 | − | 0.929235i | \(-0.620467\pi\) | ||||
−0.369489 | + | 0.929235i | \(0.620467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.4248 | + | 22.4248i | 0.765125 | + | 0.765125i | 0.977244 | − | 0.212119i | \(-0.0680365\pi\) |
−0.212119 | + | 0.977244i | \(0.568036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.0000 | + | 25.0000i | −0.851998 | + | 0.851998i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5330i | 0.698951i | 0.936945 | + | 0.349476i | \(0.113640\pi\) | ||||
−0.936945 | + | 0.349476i | \(0.886360\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.9499 | + | 32.9499i | 1.11904 | + | 1.11904i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6332 | − | 13.6332i | −0.462476 | − | 0.462476i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 79.0660i | − | 2.67905i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.8997 | 1.41809 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.41688 | − | 6.41688i | −0.216683 | − | 0.216683i | 0.590416 | − | 0.807099i | \(-0.298964\pi\) |
−0.807099 | + | 0.590416i | \(0.798964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 78.8496 | 2.65953 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.8997 | 1.27687 | 0.638437 | − | 0.769674i | \(-0.279581\pi\) | ||||
0.638437 | + | 0.769674i | \(0.279581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.1583 | + | 22.1583i | 0.745687 | + | 0.745687i | 0.973666 | − | 0.227979i | \(-0.0732119\pi\) |
−0.227979 | + | 0.973666i | \(0.573212\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.5330 | −1.56243 | −0.781213 | − | 0.624265i | \(-0.785399\pi\) | ||||
−0.781213 | + | 0.624265i | \(0.785399\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.6332i | − | 0.490783i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.7414 | + | 37.7414i | 1.26439 | + | 1.26439i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.26650 | − | 1.26650i | −0.0423818 | − | 0.0423818i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.89975i | − | 0.196987i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.63325 | + | 4.63325i | −0.154528 | + | 0.154528i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.36675 | − | 4.36675i | −0.145478 | − | 0.145478i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 76.3325 | 2.54019 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6332 | − | 13.6332i | 0.452685 | − | 0.452685i | −0.443560 | − | 0.896245i | \(-0.646285\pi\) |
0.896245 | + | 0.443560i | \(0.146285\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.5831 | + | 33.5831i | −1.11388 | + | 1.11388i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.1662 | 1.36390 | 0.681949 | − | 0.731399i | \(-0.261132\pi\) | ||||
0.681949 | + | 0.731399i | \(0.261132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.2164i | 1.49644i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.31662 | + | 2.31662i | −0.0765017 | + | 0.0765017i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.41688i | 0.145699i | 0.997343 | + | 0.0728496i | \(0.0232093\pi\) | ||||
−0.997343 | + | 0.0728496i | \(0.976791\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 61.1161i | − | 2.01384i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.2665 | + | 37.2665i | −1.22664 | + | 1.22664i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 29.2665i | − | 0.961238i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0000 | 0.656179 | 0.328089 | − | 0.944647i | \(-0.393595\pi\) | ||||
0.328089 | + | 0.944647i | \(0.393595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.258564 | − | 0.258564i | 0.00847408 | − | 0.00847408i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.9499 | − | 27.9499i | 0.915038 | − | 0.915038i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.9499 | −1.17443 | −0.587216 | − | 0.809431i | \(-0.699776\pi\) | ||||
−0.587216 | + | 0.809431i | \(0.699776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.5330 | + | 34.5330i | 1.12694 | + | 1.12694i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.94987 | − | 8.94987i | 0.291758 | − | 0.291758i | −0.546017 | − | 0.837774i | \(-0.683856\pi\) |
0.837774 | + | 0.546017i | \(0.183856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.58312i | − | 0.0515536i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.41688 | − | 5.41688i | −0.176025 | − | 0.176025i | 0.613596 | − | 0.789620i | \(-0.289723\pi\) |
−0.789620 | + | 0.613596i | \(0.789723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.8496 | + | 28.8496i | 0.936498 | + | 0.936498i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 64.5330i | 2.09263i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.36675 | 0.0766666 | 0.0383333 | − | 0.999265i | \(-0.487795\pi\) | ||||
0.0383333 | + | 0.999265i | \(0.487795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.2665 | + | 27.2665i | 0.881401 | + | 0.881401i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.9499 | −0.870257 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6332 | −0.826879 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.9499 | − | 17.9499i | −0.578427 | − | 0.578427i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.6332 | 0.856468 | 0.428234 | − | 0.903668i | \(-0.359136\pi\) | ||||
0.428234 | + | 0.903668i | \(0.359136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.899749i | − | 0.0289041i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.4749 | − | 37.4749i | −1.20263 | − | 1.20263i | −0.973364 | − | 0.229264i | \(-0.926368\pi\) |
−0.229264 | − | 0.973364i | \(-0.573632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.2164 | − | 21.2164i | −0.680166 | − | 0.680166i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 56.3826i | − | 1.80384i | −0.431903 | − | 0.901920i | \(-0.642158\pi\) | ||
0.431903 | − | 0.901920i | \(-0.357842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4749 | + | 12.4749i | −0.398701 | + | 0.398701i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.5831 | + | 37.5831i | 1.19994 | + | 1.19994i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.3166 | 0.903160 | 0.451580 | − | 0.892231i | \(-0.350861\pi\) | ||||
0.451580 | + | 0.892231i | \(0.350861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −40.0000 | + | 40.0000i | −1.27321 | + | 1.27321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.41688 | + | 2.41688i | −0.0768522 | + | 0.0768522i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.4829 | −1.57188 | −0.785938 | − | 0.618306i | \(-0.787819\pi\) | ||||
−0.785938 | + | 0.618306i | \(0.787819\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.00000i | 0.158670i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.94987 | + | 2.94987i | −0.0934235 | + | 0.0934235i | −0.752274 | − | 0.658850i | \(-0.771043\pi\) |
0.658850 | + | 0.752274i | \(0.271043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.78363i | − | 0.309540i |
(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 | 1600.2.q.d.49.2 | 4 | ||
4.3 | odd | 2 | 400.2.q.d.149.1 | 4 | |||
5.2 | odd | 4 | 1600.2.l.e.1201.2 | 4 | |||
5.3 | odd | 4 | 1600.2.l.d.1201.1 | 4 | |||
5.4 | even | 2 | 1600.2.q.c.49.1 | 4 | |||
16.3 | odd | 4 | 400.2.q.c.349.2 | 4 | |||
16.13 | even | 4 | 1600.2.q.c.849.1 | 4 | |||
20.3 | even | 4 | 400.2.l.e.101.2 | yes | 4 | ||
20.7 | even | 4 | 400.2.l.d.101.1 | ✓ | 4 | ||
20.19 | odd | 2 | 400.2.q.c.149.2 | 4 | |||
80.3 | even | 4 | 400.2.l.e.301.2 | yes | 4 | ||
80.13 | odd | 4 | 1600.2.l.d.401.1 | 4 | |||
80.19 | odd | 4 | 400.2.q.d.349.1 | 4 | |||
80.29 | even | 4 | inner | 1600.2.q.d.849.2 | 4 | ||
80.67 | even | 4 | 400.2.l.d.301.1 | yes | 4 | ||
80.77 | odd | 4 | 1600.2.l.e.401.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.d.101.1 | ✓ | 4 | 20.7 | even | 4 | ||
400.2.l.d.301.1 | yes | 4 | 80.67 | even | 4 | ||
400.2.l.e.101.2 | yes | 4 | 20.3 | even | 4 | ||
400.2.l.e.301.2 | yes | 4 | 80.3 | even | 4 | ||
400.2.q.c.149.2 | 4 | 20.19 | odd | 2 | |||
400.2.q.c.349.2 | 4 | 16.3 | odd | 4 | |||
400.2.q.d.149.1 | 4 | 4.3 | odd | 2 | |||
400.2.q.d.349.1 | 4 | 80.19 | odd | 4 | |||
1600.2.l.d.401.1 | 4 | 80.13 | odd | 4 | |||
1600.2.l.d.1201.1 | 4 | 5.3 | odd | 4 | |||
1600.2.l.e.401.2 | 4 | 80.77 | odd | 4 | |||
1600.2.l.e.1201.2 | 4 | 5.2 | odd | 4 | |||
1600.2.q.c.49.1 | 4 | 5.4 | even | 2 | |||
1600.2.q.c.849.1 | 4 | 16.13 | even | 4 | |||
1600.2.q.d.49.2 | 4 | 1.1 | even | 1 | trivial | ||
1600.2.q.d.849.2 | 4 | 80.29 | even | 4 | inner |