Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,2,Mod(257,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.v (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: | \(9.58204824255\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.593 |
Dual form | 1200.2.v.l.257.1 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.67303 | + | 0.448288i | −0.965926 | + | 0.258819i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | − | 2.44949i | 0.925820 | − | 0.925820i | −0.0716124 | − | 0.997433i | \(-0.522814\pi\) |
0.997433 | + | 0.0716124i | \(0.0228145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.59808 | − | 1.50000i | 0.866025 | − | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.12132 | − | 2.12132i | −0.514496 | − | 0.514496i | 0.401405 | − | 0.915901i | \(-0.368522\pi\) |
−0.915901 | + | 0.401405i | \(0.868522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) | ||
0.993399 | − | 0.114708i | \(-0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 5.19615i | −0.654654 | + | 1.13389i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | − | 4.24264i | 0.884652 | − | 0.884652i | −0.109351 | − | 0.994003i | \(-0.534877\pi\) |
0.994003 | + | 0.109351i | \(0.0348774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.707107 | + | 0.707107i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.32937 | − | 8.69333i | −0.405492 | − | 1.51331i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.44949 | − | 2.44949i | 0.402694 | − | 0.402694i | −0.476488 | − | 0.879181i | \(-0.658090\pi\) |
0.879181 | + | 0.476488i | \(0.158090\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.19615i | 0.811503i | 0.913984 | + | 0.405751i | \(0.132990\pi\) | ||||
−0.913984 | + | 0.405751i | \(0.867010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.44949 | − | 2.44949i | −0.373544 | − | 0.373544i | 0.495222 | − | 0.868766i | \(-0.335087\pi\) |
−0.868766 | + | 0.495222i | \(0.835087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | + | 2.59808i | 0.630126 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | \(-0.614802\pi\) |
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.448288 | + | 1.67303i | 0.0593772 | + | 0.221599i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3923 | 1.35296 | 0.676481 | − | 0.736460i | \(-0.263504\pi\) | ||||
0.676481 | + | 0.736460i | \(0.263504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0000 | 1.79252 | 0.896258 | − | 0.443533i | \(-0.146275\pi\) | ||||
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.68973 | − | 10.0382i | 0.338874 | − | 1.26469i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.67423 | − | 3.67423i | 0.448879 | − | 0.448879i | −0.446103 | − | 0.894982i | \(-0.647188\pi\) |
0.894982 | + | 0.446103i | \(0.147188\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.19615 | + | 9.00000i | −0.625543 | + | 1.08347i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12372 | + | 6.12372i | 0.716728 | + | 0.716728i | 0.967934 | − | 0.251206i | \(-0.0808271\pi\) |
−0.251206 | + | 0.967934i | \(0.580827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7279 | + | 12.7279i | 1.45048 | + | 1.45048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0000i | − | 1.57512i | −0.616236 | − | 0.787562i | \(-0.711343\pi\) | ||
0.616236 | − | 0.787562i | \(-0.288657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.12132 | + | 2.12132i | −0.232845 | + | 0.232845i | −0.813879 | − | 0.581034i | \(-0.802648\pi\) |
0.581034 | + | 0.813879i | \(0.302648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.5885 | 1.65237 | 0.826187 | − | 0.563397i | \(-0.190506\pi\) | ||||
0.826187 | + | 0.563397i | \(0.190506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.34607 | + | 0.896575i | −0.346971 | + | 0.0929705i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | + | 4.89898i | −0.497416 | + | 0.497416i | −0.910633 | − | 0.413217i | \(-0.864405\pi\) |
0.413217 | + | 0.910633i | \(0.364405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.79423 | + | 13.5000i | 0.783349 | + | 1.35680i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3923i | 1.03407i | 0.855963 | + | 0.517036i | \(0.172965\pi\) | ||||
−0.855963 | + | 0.517036i | \(0.827035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.79796 | + | 9.79796i | 0.965422 | + | 0.965422i | 0.999422 | − | 0.0340002i | \(-0.0108247\pi\) |
−0.0340002 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.36396 | + | 6.36396i | 0.615227 | + | 0.615227i | 0.944303 | − | 0.329076i | \(-0.106737\pi\) |
−0.329076 | + | 0.944303i | \(0.606737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.957826i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) | ||
0.877862 | − | 0.478913i | \(-0.158969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.36396 | − | 6.36396i | 0.598671 | − | 0.598671i | −0.341288 | − | 0.939959i | \(-0.610863\pi\) |
0.939959 | + | 0.341288i | \(0.110863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3923 | −0.952661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.32937 | − | 8.69333i | −0.210032 | − | 0.783851i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.19615 | + | 3.00000i | 0.457496 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.3923i | − | 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44949 | − | 2.44949i | −0.212398 | − | 0.212398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8492 | − | 14.8492i | −1.26866 | − | 1.26866i | −0.946783 | − | 0.321874i | \(-0.895687\pi\) |
−0.321874 | − | 0.946783i | \(-0.604313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.00000i | − | 0.593732i | −0.954919 | − | 0.296866i | \(-0.904058\pi\) | ||
0.954919 | − | 0.296866i | \(-0.0959415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.24144 | + | 8.36516i | 0.184871 | + | 0.689947i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.7846 | −1.70274 | −0.851371 | − | 0.524564i | \(-0.824228\pi\) | ||||
−0.851371 | + | 0.524564i | \(0.824228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.69333 | − | 2.32937i | −0.702814 | − | 0.188319i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2474 | − | 12.2474i | 0.977453 | − | 0.977453i | −0.0222985 | − | 0.999751i | \(-0.507098\pi\) |
0.999751 | + | 0.0222985i | \(0.00709843\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.19615 | + | 9.00000i | −0.412082 | + | 0.713746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.7846i | − | 1.63806i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.67423 | + | 3.67423i | 0.287788 | + | 0.287788i | 0.836205 | − | 0.548417i | \(-0.184769\pi\) |
−0.548417 | + | 0.836205i | \(0.684769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.48528 | − | 8.48528i | −0.656611 | − | 0.656611i | 0.297966 | − | 0.954577i | \(-0.403692\pi\) |
−0.954577 | + | 0.297966i | \(0.903692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.50000 | − | 2.59808i | −0.114708 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.48528 | + | 8.48528i | −0.645124 | + | 0.645124i | −0.951811 | − | 0.306687i | \(-0.900780\pi\) |
0.306687 | + | 0.951811i | \(0.400780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.3867 | + | 4.65874i | −1.30686 | + | 0.350173i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5885 | −1.16514 | −0.582568 | − | 0.812782i | \(-0.697952\pi\) | ||||
−0.582568 | + | 0.812782i | \(0.697952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.4225 | + | 6.27603i | −1.73144 | + | 0.463937i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0227 | − | 11.0227i | 0.806060 | − | 0.806060i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.0000i | 1.30931i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3923i | 0.751961i | 0.926628 | + | 0.375980i | \(0.122694\pi\) | ||||
−0.926628 | + | 0.375980i | \(0.877306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.12372 | + | 6.12372i | 0.440795 | + | 0.440795i | 0.892279 | − | 0.451484i | \(-0.149105\pi\) |
−0.451484 | + | 0.892279i | \(0.649105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.24264 | − | 4.24264i | −0.302276 | − | 0.302276i | 0.539628 | − | 0.841904i | \(-0.318565\pi\) |
−0.841904 | + | 0.539628i | \(0.818565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000i | 1.13421i | 0.823646 | + | 0.567105i | \(0.191937\pi\) | ||||
−0.823646 | + | 0.567105i | \(0.808063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | + | 7.79423i | −0.317406 | + | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.65874 | − | 17.3867i | 0.323805 | − | 1.20846i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.19615 | 0.359425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0000 | −1.58339 | −0.791693 | − | 0.610920i | \(-0.790800\pi\) | ||||
−0.791693 | + | 0.610920i | \(0.790800\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.89898 | − | 4.89898i | 0.332564 | − | 0.332564i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9904 | − | 7.50000i | −0.877809 | − | 0.506803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796 | + | 9.79796i | 0.656120 | + | 0.656120i | 0.954460 | − | 0.298340i | \(-0.0964329\pi\) |
−0.298340 | + | 0.954460i | \(0.596433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.48528 | − | 8.48528i | −0.563188 | − | 0.563188i | 0.367024 | − | 0.930212i | \(-0.380377\pi\) |
−0.930212 | + | 0.367024i | \(0.880377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0000i | 1.05731i | 0.848837 | + | 0.528655i | \(0.177303\pi\) | ||||
−0.848837 | + | 0.528655i | \(0.822697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −27.0000 | − | 15.5885i | −1.77647 | − | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7279 | + | 12.7279i | −0.833834 | + | 0.833834i | −0.988039 | − | 0.154205i | \(-0.950718\pi\) |
0.154205 | + | 0.988039i | \(0.450718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.27603 | + | 23.4225i | 0.407672 | + | 1.52145i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7846 | 1.34444 | 0.672222 | − | 0.740349i | \(-0.265340\pi\) | ||||
0.672222 | + | 0.740349i | \(0.265340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.03459 | + | 15.0573i | −0.258819 | + | 0.965926i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.59808 | − | 4.50000i | 0.164646 | − | 0.285176i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615i | 0.327978i | 0.986462 | + | 0.163989i | \(0.0524362\pi\) | ||||
−0.986462 | + | 0.163989i | \(0.947564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0454 | + | 22.0454i | 1.38598 | + | 1.38598i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.24264 | + | 4.24264i | 0.264649 | + | 0.264649i | 0.826940 | − | 0.562291i | \(-0.190080\pi\) |
−0.562291 | + | 0.826940i | \(0.690080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7279 | + | 12.7279i | −0.784837 | + | 0.784837i | −0.980643 | − | 0.195805i | \(-0.937268\pi\) |
0.195805 | + | 0.980643i | \(0.437268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.0800 | + | 6.98811i | −1.59607 | + | 0.427666i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7846 | −1.26726 | −0.633630 | − | 0.773636i | \(-0.718436\pi\) | ||||
−0.633630 | + | 0.773636i | \(0.718436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | 0.607457 | 0.303728 | − | 0.952759i | \(-0.401768\pi\) | ||||
0.303728 | + | 0.952759i | \(0.401768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.79796 | − | 9.79796i | 0.588702 | − | 0.588702i | −0.348578 | − | 0.937280i | \(-0.613335\pi\) |
0.937280 | + | 0.348578i | \(0.113335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.19615 | − | 3.00000i | 0.311086 | − | 0.179605i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.7846i | − | 1.23991i | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||
0.784639 | − | 0.619953i | \(-0.212848\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.12372 | + | 6.12372i | 0.364018 | + | 0.364018i | 0.865290 | − | 0.501272i | \(-0.167134\pi\) |
−0.501272 | + | 0.865290i | \(0.667134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.7279 | + | 12.7279i | 0.751305 | + | 0.751305i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 8.00000i | − | 0.470588i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 10.3923i | 0.351726 | − | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.2132 | + | 21.2132i | −1.23929 | + | 1.23929i | −0.278996 | + | 0.960292i | \(0.590002\pi\) |
−0.960292 | + | 0.278996i | \(0.909998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.0919 | − | 19.0919i | −1.10782 | − | 1.10782i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.65874 | − | 17.3867i | −0.267638 | − | 0.998838i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.22474 | + | 1.22474i | −0.0698999 | + | 0.0698999i | −0.741192 | − | 0.671293i | \(-0.765739\pi\) |
0.671293 | + | 0.741192i | \(0.265739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.7846 | − | 12.0000i | −1.18240 | − | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.1769i | − | 1.76788i | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||
0.467600 | − | 0.883940i | \(-0.345119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6969 | − | 14.6969i | −0.830720 | − | 0.830720i | 0.156895 | − | 0.987615i | \(-0.449852\pi\) |
−0.987615 | + | 0.156895i | \(0.949852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.48528 | + | 8.48528i | 0.476581 | + | 0.476581i | 0.904036 | − | 0.427456i | \(-0.140590\pi\) |
−0.427456 | + | 0.904036i | \(0.640590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5000 | − | 7.79423i | −0.753497 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.12132 | + | 2.12132i | −0.118033 | + | 0.118033i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.48288 | + | 16.7303i | 0.247904 | + | 0.925189i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0000 | 0.714545 | 0.357272 | − | 0.934000i | \(-0.383707\pi\) | ||||
0.357272 | + | 0.934000i | \(0.383707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.68973 | − | 10.0382i | 0.147396 | − | 0.550090i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.67423 | + | 3.67423i | −0.200148 | + | 0.200148i | −0.800064 | − | 0.599915i | \(-0.795201\pi\) |
0.599915 | + | 0.800064i | \(0.295201\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.79423 | + | 13.5000i | −0.423324 | + | 0.733219i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3923i | 0.562775i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.89898 | + | 4.89898i | 0.264520 | + | 0.264520i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.36396 | − | 6.36396i | −0.341635 | − | 0.341635i | 0.515347 | − | 0.856982i | \(-0.327663\pi\) |
−0.856982 | + | 0.515347i | \(0.827663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0000i | 1.17763i | 0.808267 | + | 0.588817i | \(0.200406\pi\) | ||||
−0.808267 | + | 0.588817i | \(0.799594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7279 | − | 12.7279i | 0.677439 | − | 0.677439i | −0.281981 | − | 0.959420i | \(-0.590992\pi\) |
0.959420 | + | 0.281981i | \(0.0909915\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.3867 | − | 4.65874i | 0.920200 | − | 0.246567i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3923 | −0.548485 | −0.274242 | − | 0.961661i | \(-0.588427\pi\) | ||||
−0.274242 | + | 0.961661i | \(0.588427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.7685 | − | 7.17260i | 1.40498 | − | 0.376464i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6969 | + | 14.6969i | −0.767174 | + | 0.767174i | −0.977608 | − | 0.210434i | \(-0.932512\pi\) |
0.210434 | + | 0.977608i | \(0.432512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.79423 | + | 13.5000i | 0.405751 | + | 0.702782i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.7846i | − | 1.07908i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.44949 | − | 2.44949i | −0.126830 | − | 0.126830i | 0.640843 | − | 0.767672i | \(-0.278585\pi\) |
−0.767672 | + | 0.640843i | \(0.778585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0000i | 0.565032i | 0.959263 | + | 0.282516i | \(0.0911690\pi\) | ||||
−0.959263 | + | 0.282516i | \(0.908831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.00000 | − | 15.5885i | 0.461084 | − | 0.798621i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.24264 | + | 4.24264i | −0.216789 | + | 0.216789i | −0.807144 | − | 0.590355i | \(-0.798988\pi\) |
0.590355 | + | 0.807144i | \(0.298988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.0382 | − | 2.68973i | −0.510270 | − | 0.136726i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.3923 | 0.526911 | 0.263455 | − | 0.964672i | \(-0.415138\pi\) | ||||
0.263455 | + | 0.964672i | \(0.415138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.65874 | + | 17.3867i | 0.235002 | + | 0.877041i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5959 | + | 19.5959i | −0.983491 | + | 0.983491i | −0.999866 | − | 0.0163750i | \(-0.994787\pi\) |
0.0163750 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.19615 | + | 3.00000i | 0.260133 | + | 0.150188i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.19615i | − | 0.259483i | −0.991548 | − | 0.129742i | \(-0.958585\pi\) | ||
0.991548 | − | 0.129742i | \(-0.0414148\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7279 | + | 12.7279i | 0.630900 | + | 0.630900i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.00000i | − | 0.247234i | −0.992330 | − | 0.123617i | \(-0.960551\pi\) | ||
0.992330 | − | 0.123617i | \(-0.0394494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.5000 | + | 18.1865i | 1.55378 | + | 0.897076i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.4558 | − | 25.4558i | 1.25260 | − | 1.25260i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.13801 | + | 11.7112i | 0.153669 | + | 0.573501i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.9808 | −1.26924 | −0.634622 | − | 0.772823i | \(-0.718844\pi\) | ||||
−0.634622 | + | 0.772823i | \(0.718844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | 0.194948 | 0.0974740 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974740 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.2929 | − | 34.2929i | 1.65955 | − | 1.65955i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3923i | 0.500580i | 0.968171 | + | 0.250290i | \(0.0805259\pi\) | ||||
−0.968171 | + | 0.250290i | \(0.919474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.9217 | + | 15.9217i | 0.765147 | + | 0.765147i | 0.977248 | − | 0.212101i | \(-0.0680304\pi\) |
−0.212101 | + | 0.977248i | \(0.568030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.24264 | − | 4.24264i | −0.202953 | − | 0.202953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000i | 0.190910i | 0.995434 | + | 0.0954548i | \(0.0304305\pi\) | ||||
−0.995434 | + | 0.0954548i | \(0.969569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.50000 | − | 12.9904i | −0.357143 | − | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8492 | − | 14.8492i | 0.705509 | − | 0.705509i | −0.260079 | − | 0.965587i | \(-0.583748\pi\) |
0.965587 | + | 0.260079i | \(0.0837485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.7733 | − | 9.31749i | 1.64472 | − | 0.440702i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9808 | 1.22611 | 0.613054 | − | 0.790041i | \(-0.289941\pi\) | ||||
0.613054 | + | 0.790041i | \(0.289941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | −1.27138 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.4225 | + | 6.27603i | −1.10048 | + | 0.294874i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.3712 | + | 18.3712i | −0.859367 | + | 0.859367i | −0.991264 | − | 0.131896i | \(-0.957893\pi\) |
0.131896 | + | 0.991264i | \(0.457893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.5885 | 0.727607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.4949 | − | 24.4949i | −1.13837 | − | 1.13837i | −0.988742 | − | 0.149633i | \(-0.952191\pi\) |
−0.149633 | − | 0.988742i | \(-0.547809\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.48528 | − | 8.48528i | −0.392652 | − | 0.392652i | 0.482980 | − | 0.875632i | \(-0.339555\pi\) |
−0.875632 | + | 0.482980i | \(0.839555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 18.0000i | − | 0.831163i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0000 | + | 25.9808i | −0.691164 | + | 1.19713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.7279 | − | 12.7279i | 0.585230 | − | 0.585230i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.65874 | − | 17.3867i | 0.213309 | − | 0.796081i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.31749 | + | 34.7733i | 0.423960 | + | 1.58224i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.0454 | + | 22.0454i | −0.998973 | + | 0.998973i | −0.999999 | − | 0.00102669i | \(-0.999673\pi\) |
0.00102669 | + | 0.999999i | \(0.499673\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.79423 | − | 4.50000i | −0.352467 | − | 0.203497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.1769i | 1.40699i | 0.710698 | + | 0.703497i | \(0.248379\pi\) | ||||
−0.710698 | + | 0.703497i | \(0.751621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.0000i | − | 0.895323i | −0.894203 | − | 0.447661i | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | + | 10.3923i | 0.804181 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.48528 | + | 8.48528i | −0.378340 | + | 0.378340i | −0.870503 | − | 0.492163i | \(-0.836206\pi\) |
0.492163 | + | 0.870503i | \(0.336206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.82774 | + | 21.7494i | 0.258819 | + | 0.965926i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3923 | 0.460631 | 0.230315 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230315 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0000 | 1.32712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.67423 | + | 3.67423i | 0.162221 | + | 0.162221i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.3923 | − | 18.0000i | 0.456172 | − | 0.790112i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3731i | 1.59353i | 0.604287 | + | 0.796766i | \(0.293458\pi\) | ||||
−0.604287 | + | 0.796766i | \(0.706542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6186 | − | 30.6186i | −1.33886 | − | 1.33886i | −0.897167 | − | 0.441692i | \(-0.854378\pi\) |
−0.441692 | − | 0.897167i | \(-0.645622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.24264 | − | 4.24264i | −0.184812 | − | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.0000i | − | 0.565217i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0000 | − | 15.5885i | 1.17170 | − | 0.676481i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.0800 | − | 6.98811i | 1.12543 | − | 0.301559i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.9808 | 1.11907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.34607 | − | 0.896575i | 0.143593 | − | 0.0384757i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.57321 | + | 8.57321i | −0.366564 | + | 0.366564i | −0.866223 | − | 0.499658i | \(-0.833459\pi\) |
0.499658 | + | 0.866223i | \(0.333459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.3731 | − | 21.0000i | 1.55236 | − | 0.896258i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.2929 | − | 34.2929i | −1.45828 | − | 1.45828i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.5000 | + | 23.3827i | −0.569970 | + | 0.987218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.06918 | − | 30.1146i | −0.338874 | − | 1.26469i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.9808 | −1.08917 | −0.544585 | − | 0.838706i | \(-0.683313\pi\) | ||||
−0.544585 | + | 0.838706i | \(0.683313\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.65874 | − | 17.3867i | −0.194622 | − | 0.726338i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4722 | − | 13.4722i | 0.560855 | − | 0.560855i | −0.368695 | − | 0.929550i | \(-0.620195\pi\) |
0.929550 | + | 0.368695i | \(0.120195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9904 | − | 7.50000i | −0.539862 | − | 0.311689i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923i | 0.431145i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.0454 | + | 22.0454i | 0.913027 | + | 0.913027i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8492 | + | 14.8492i | 0.612894 | + | 0.612894i | 0.943699 | − | 0.330805i | \(-0.107320\pi\) |
−0.330805 | + | 0.943699i | \(0.607320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.00000i | − | 0.0824086i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 5.19615i | 0.370211 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.3345 | + | 23.3345i | −0.958234 | + | 0.958234i | −0.999162 | − | 0.0409281i | \(-0.986969\pi\) |
0.0409281 | + | 0.999162i | \(0.486969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.17260 | − | 26.7685i | −0.293555 | − | 1.09556i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.3923 | −0.424618 | −0.212309 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212309 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00000 | −0.203954 | −0.101977 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101977 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.03459 | − | 15.0573i | 0.164301 | − | 0.613180i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.89898 | − | 4.89898i | 0.198843 | − | 0.198843i | −0.600661 | − | 0.799504i | \(-0.705096\pi\) |
0.799504 | + | 0.600661i | \(0.205096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.1464 | − | 17.1464i | −0.692538 | − | 0.692538i | 0.270252 | − | 0.962790i | \(-0.412893\pi\) |
−0.962790 | + | 0.270252i | \(0.912893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2132 | − | 21.2132i | −0.854011 | − | 0.854011i | 0.136613 | − | 0.990624i | \(-0.456378\pi\) |
−0.990624 | + | 0.136613i | \(0.956378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.1769i | 1.25109i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.1838 | − | 38.1838i | 1.52980 | − | 1.52980i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.69333 | + | 2.32937i | −0.347178 | + | 0.0930261i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3923 | −0.414368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0000 | 1.35352 | 0.676759 | − | 0.736204i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736204i | \(0.263384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.4797 | − | 10.3106i | 1.52943 | − | 0.409810i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7846i | 0.820943i | 0.911873 | + | 0.410471i | \(0.134636\pi\) | ||||
−0.911873 | + | 0.410471i | \(0.865364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0454 | − | 22.0454i | −0.869386 | − | 0.869386i | 0.123018 | − | 0.992404i | \(-0.460743\pi\) |
−0.992404 | + | 0.123018i | \(0.960743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9411 | − | 33.9411i | −1.33436 | − | 1.33436i | −0.901422 | − | 0.432941i | \(-0.857476\pi\) |
−0.432941 | − | 0.901422i | \(-0.642524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.0000i | 2.11969i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | + | 10.3923i | −0.235159 | + | 0.407307i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.24264 | − | 4.24264i | 0.166027 | − | 0.166027i | −0.619203 | − | 0.785231i | \(-0.712544\pi\) |
0.785231 | + | 0.619203i | \(0.212544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.0955 | + | 6.72432i | 0.979068 | + | 0.262341i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.9808 | 1.01207 | 0.506033 | − | 0.862514i | \(-0.331111\pi\) | ||||
0.506033 | + | 0.862514i | \(0.331111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7846 | − | 12.0000i | −0.803579 | − | 0.463947i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 72.7461i | 2.80833i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.89898 | − | 4.89898i | −0.188842 | − | 0.188842i | 0.606353 | − | 0.795195i | \(-0.292632\pi\) |
−0.795195 | + | 0.606353i | \(0.792632\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.4558 | + | 25.4558i | 0.978348 | + | 0.978348i | 0.999771 | − | 0.0214229i | \(-0.00681965\pi\) |
−0.0214229 | + | 0.999771i | \(0.506820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000i | 0.921035i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | + | 10.3923i | 0.689761 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8492 | − | 14.8492i | 0.568190 | − | 0.568190i | −0.363431 | − | 0.931621i | \(-0.618395\pi\) |
0.931621 | + | 0.363431i | \(0.118395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.17260 | − | 26.7685i | −0.273652 | − | 1.02128i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.0000 | −1.40755 | −0.703773 | − | 0.710425i | \(-0.748503\pi\) | ||||
−0.703773 | + | 0.710425i | \(0.748503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 52.1600 | + | 13.9762i | 1.98139 | + | 0.530913i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0227 | − | 11.0227i | 0.417515 | − | 0.417515i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.5885 | − | 27.0000i | 0.589610 | − | 1.02123i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20.7846i | − | 0.785024i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.44949 | − | 2.44949i | −0.0923843 | − | 0.0923843i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.4558 | + | 25.4558i | 0.957366 | + | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0000i | 1.50223i | 0.660171 | + | 0.751116i | \(0.270484\pi\) | ||||
−0.660171 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.0000 | − | 36.3731i | −0.787562 | − | 1.36410i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.48528 | − | 8.48528i | 0.317776 | − | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.7733 | + | 9.31749i | −1.29863 | + | 0.347968i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.1769 | 1.16270 | 0.581351 | − | 0.813653i | \(-0.302524\pi\) | ||||
0.581351 | + | 0.813653i | \(0.302524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.0000 | 1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.67303 | − | 0.448288i | 0.0622208 | − | 0.0166720i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.89898 | + | 4.89898i | −0.181693 | + | 0.181693i | −0.792093 | − | 0.610400i | \(-0.791009\pi\) |
0.610400 | + | 0.792093i | \(0.291009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3923i | 0.384373i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6969 | − | 14.6969i | −0.542844 | − | 0.542844i | 0.381518 | − | 0.924362i | \(-0.375402\pi\) |
−0.924362 | + | 0.381518i | \(0.875402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.0919 | + | 19.0919i | 0.703259 | + | 0.703259i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000i | 0.735712i | 0.929883 | + | 0.367856i | \(0.119908\pi\) | ||||
−0.929883 | + | 0.367856i | \(0.880092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7279 | + | 12.7279i | −0.466942 | + | 0.466942i | −0.900922 | − | 0.433980i | \(-0.857109\pi\) |
0.433980 | + | 0.900922i | \(0.357109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.32937 | + | 8.69333i | −0.0852272 | + | 0.318072i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.1769 | 1.13918 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.32937 | − | 8.69333i | −0.0848870 | − | 0.316803i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4949 | + | 24.4949i | −0.890282 | + | 0.890282i | −0.994549 | − | 0.104267i | \(-0.966750\pi\) |
0.104267 | + | 0.994549i | \(0.466750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −46.7654 | − | 27.0000i | −1.69748 | − | 0.980038i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.19615i | 0.188360i | 0.995555 | + | 0.0941802i | \(0.0300230\pi\) | ||||
−0.995555 | + | 0.0941802i | \(0.969977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.4949 | − | 24.4949i | −0.886775 | − | 0.886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.0000i | − | 0.468792i | −0.972141 | − | 0.234396i | \(-0.924689\pi\) | ||
0.972141 | − | 0.234396i | \(-0.0753112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | − | 5.19615i | −0.324127 | − | 0.187135i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.48528 | − | 8.48528i | 0.305194 | − | 0.305194i | −0.537848 | − | 0.843042i | \(-0.680762\pi\) |
0.843042 | + | 0.537848i | \(0.180762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.37945 | + | 20.0764i | 0.192987 | + | 0.720237i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.19615 | 0.186171 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1464 | − | 17.1464i | 0.611204 | − | 0.611204i | −0.332056 | − | 0.943260i | \(-0.607742\pi\) |
0.943260 | + | 0.332056i | \(0.107742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.5885 | − | 27.0000i | 0.554964 | − | 0.961225i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 31.1769i | − | 1.10852i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.6985 | − | 29.6985i | −1.05197 | − | 1.05197i | −0.998573 | − | 0.0534012i | \(-0.982994\pi\) |
−0.0534012 | − | 0.998573i | \(-0.517006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.5000 | − | 23.3827i | 1.43100 | − | 0.826187i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.8198 | + | 31.8198i | −1.12290 | + | 1.12290i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.7733 | − | 9.31749i | 1.22408 | − | 0.327991i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7846 | −0.730748 | −0.365374 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365374 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.7303 | + | 4.48288i | −0.586758 | + | 0.157221i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.44949 | + | 2.44949i | −0.0856968 | + | 0.0856968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 31.1769i | − | 1.08808i | −0.839059 | − | 0.544041i | \(-0.816894\pi\) | ||
0.839059 | − | 0.544041i | \(-0.183106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.12132 | + | 2.12132i | 0.0737655 | + | 0.0737655i | 0.743027 | − | 0.669261i | \(-0.233389\pi\) |
−0.669261 | + | 0.743027i | \(0.733389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 44.0000i | − | 1.52818i | −0.645108 | − | 0.764092i | \(-0.723188\pi\) | ||
0.645108 | − | 0.764092i | \(-0.276812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | + | 20.7846i | −0.416275 | + | 0.721010i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6066 | + | 10.6066i | −0.367497 | + | 0.367497i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.34847 | + | 7.34847i | −0.254000 | + | 0.254000i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7846 | −0.717564 | −0.358782 | − | 0.933421i | \(-0.616808\pi\) | ||||
−0.358782 | + | 0.933421i | \(0.616808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.31749 | + | 34.7733i | 0.320911 | + | 1.19766i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.1918 | + | 39.1918i | −1.34665 | + | 1.34665i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9904 | − | 7.50000i | −0.445829 | − | 0.257399i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 20.7846i | − | 0.712487i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.34847 | + | 7.34847i | 0.251607 | + | 0.251607i | 0.821629 | − | 0.570022i | \(-0.193065\pi\) |
−0.570022 | + | 0.821629i | \(0.693065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.0624 | + | 36.0624i | 1.23187 | + | 1.23187i | 0.963245 | + | 0.268625i | \(0.0865692\pi\) |
0.268625 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.00000i | 0.238837i | 0.992844 | + | 0.119418i | \(0.0381030\pi\) | ||||
−0.992844 | + | 0.119418i | \(0.961897\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.0000 | − | 15.5885i | −0.920158 | − | 0.531253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.9411 | − | 33.9411i | 1.15537 | − | 1.15537i | 0.169910 | − | 0.985460i | \(-0.445652\pi\) |
0.985460 | − | 0.169910i | \(-0.0543476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.58630 | + | 13.3843i | 0.121797 | + | 0.454553i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 72.7461 | 2.46774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.37945 | + | 20.0764i | −0.182067 | + | 0.679483i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.2929 | − | 34.2929i | 1.15799 | − | 1.15799i | 0.173080 | − | 0.984908i | \(-0.444628\pi\) |
0.984908 | − | 0.173080i | \(-0.0553718\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.9808 | − | 45.0000i | 0.876309 | − | 1.51781i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.7846i | 0.700251i | 0.936703 | + | 0.350126i | \(0.113861\pi\) | ||||
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.8207 | + | 20.8207i | 0.700671 | + | 0.700671i | 0.964555 | − | 0.263883i | \(-0.0850034\pi\) |
−0.263883 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.9411 | + | 33.9411i | 1.13963 | + | 1.13963i | 0.988516 | + | 0.151115i | \(0.0482865\pi\) |
0.151115 | + | 0.988516i | \(0.451714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000i | 1.20740i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.5000 | + | 23.3827i | 1.35680 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0764 | − | 5.37945i | 0.668100 | − | 0.179017i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1464 | + | 17.1464i | −0.569338 | + | 0.569338i | −0.931943 | − | 0.362605i | \(-0.881887\pi\) |
0.362605 | + | 0.931943i | \(0.381887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5885 | + | 27.0000i | 0.517036 | + | 0.895533i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 41.5692i | − | 1.37725i | −0.725118 | − | 0.688625i | \(-0.758215\pi\) | ||
0.725118 | − | 0.688625i | \(-0.241785\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0227 | − | 11.0227i | −0.364798 | − | 0.364798i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.4558 | − | 25.4558i | −0.840626 | − | 0.840626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0000i | 0.857661i | 0.903385 | + | 0.428830i | \(0.141074\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50000 | − | 2.59808i | 0.0494267 | − | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.1528 | + | 10.7589i | 1.31879 | + | 0.353369i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.5692 | −1.36384 | −0.681921 | − | 0.731426i | \(-0.738855\pi\) | ||||
−0.681921 | + | 0.731426i | \(0.738855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.9762 | + | 52.1600i | 0.457561 | + | 1.70764i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.12372 | + | 6.12372i | −0.200053 | + | 0.200053i | −0.800023 | − | 0.599970i | \(-0.795179\pi\) |
0.599970 | + | 0.800023i | \(0.295179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.1769 | + | 18.0000i | 1.01742 | + | 0.587408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.7846i | − | 0.677559i | −0.940866 | − | 0.338779i | \(-0.889986\pi\) | ||
0.940866 | − | 0.338779i | \(-0.110014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.0454 | + | 22.0454i | 0.717897 | + | 0.717897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9706 | − | 16.9706i | −0.551469 | − | 0.551469i | 0.375396 | − | 0.926865i | \(-0.377507\pi\) |
−0.926865 | + | 0.375396i | \(0.877507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | − | 10.3923i | −0.583690 | − | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.36396 | − | 6.36396i | 0.206149 | − | 0.206149i | −0.596479 | − | 0.802628i | \(-0.703434\pi\) |
0.802628 | + | 0.596479i | \(0.203434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.7461 | −2.34910 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.0800 | + | 6.98811i | 0.840416 | + | 0.225189i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.79796 | + | 9.79796i | −0.315081 | + | 0.315081i | −0.846874 | − | 0.531793i | \(-0.821518\pi\) |
0.531793 | + | 0.846874i | \(0.321518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.59808 | − | 4.50000i | 0.0834622 | − | 0.144561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 5.19615i | − | 0.166752i | −0.996518 | − | 0.0833762i | \(-0.973430\pi\) | ||
0.996518 | − | 0.0833762i | \(-0.0265703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1464 | − | 17.1464i | −0.549689 | − | 0.549689i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.36396 | − | 6.36396i | −0.203601 | − | 0.203601i | 0.597940 | − | 0.801541i | \(-0.295986\pi\) |
−0.801541 | + | 0.597940i | \(0.795986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 81.0000i | 2.58877i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0000 | − | 25.9808i | −0.478913 | − | 0.829502i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2132 | + | 21.2132i | −0.676596 | + | 0.676596i | −0.959228 | − | 0.282632i | \(-0.908792\pi\) |
0.282632 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.7846 | −0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000 | 0.317660 | 0.158830 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158830 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.7494 | + | 5.82774i | −0.690197 | + | 0.184938i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0908 | + | 44.0908i | −1.39637 | + | 1.39637i | −0.586214 | + | 0.810157i | \(0.699382\pi\) |
−0.810157 | + | 0.586214i | \(0.800618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.0000i | 0.569495i |
(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 | 1200.2.v.l.593.1 | 8 | ||
3.2 | odd | 2 | inner | 1200.2.v.l.593.3 | 8 | ||
4.3 | odd | 2 | 150.2.e.b.143.4 | yes | 8 | ||
5.2 | odd | 4 | inner | 1200.2.v.l.257.3 | 8 | ||
5.3 | odd | 4 | inner | 1200.2.v.l.257.2 | 8 | ||
5.4 | even | 2 | inner | 1200.2.v.l.593.4 | 8 | ||
12.11 | even | 2 | 150.2.e.b.143.2 | yes | 8 | ||
15.2 | even | 4 | inner | 1200.2.v.l.257.1 | 8 | ||
15.8 | even | 4 | inner | 1200.2.v.l.257.4 | 8 | ||
15.14 | odd | 2 | inner | 1200.2.v.l.593.2 | 8 | ||
20.3 | even | 4 | 150.2.e.b.107.3 | yes | 8 | ||
20.7 | even | 4 | 150.2.e.b.107.2 | yes | 8 | ||
20.19 | odd | 2 | 150.2.e.b.143.1 | yes | 8 | ||
60.23 | odd | 4 | 150.2.e.b.107.1 | ✓ | 8 | ||
60.47 | odd | 4 | 150.2.e.b.107.4 | yes | 8 | ||
60.59 | even | 2 | 150.2.e.b.143.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.e.b.107.1 | ✓ | 8 | 60.23 | odd | 4 | ||
150.2.e.b.107.2 | yes | 8 | 20.7 | even | 4 | ||
150.2.e.b.107.3 | yes | 8 | 20.3 | even | 4 | ||
150.2.e.b.107.4 | yes | 8 | 60.47 | odd | 4 | ||
150.2.e.b.143.1 | yes | 8 | 20.19 | odd | 2 | ||
150.2.e.b.143.2 | yes | 8 | 12.11 | even | 2 | ||
150.2.e.b.143.3 | yes | 8 | 60.59 | even | 2 | ||
150.2.e.b.143.4 | yes | 8 | 4.3 | odd | 2 | ||
1200.2.v.l.257.1 | 8 | 15.2 | even | 4 | inner | ||
1200.2.v.l.257.2 | 8 | 5.3 | odd | 4 | inner | ||
1200.2.v.l.257.3 | 8 | 5.2 | odd | 4 | inner | ||
1200.2.v.l.257.4 | 8 | 15.8 | even | 4 | inner | ||
1200.2.v.l.593.1 | 8 | 1.1 | even | 1 | trivial | ||
1200.2.v.l.593.2 | 8 | 15.14 | odd | 2 | inner | ||
1200.2.v.l.593.3 | 8 | 3.2 | odd | 2 | inner | ||
1200.2.v.l.593.4 | 8 | 5.4 | even | 2 | inner |