Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), 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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.13 | ||
Root | \(-1.13508 + 1.13508i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.h.369.4 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.51561i | 1.45239i | 0.687491 | + | 0.726193i | \(0.258712\pi\) | ||||
−0.687491 | + | 0.726193i | \(0.741288\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.92655 | − | 1.13508i | −0.861578 | − | 0.507625i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.64022i | 1.75384i | 0.480636 | + | 0.876920i | \(0.340406\pi\) | ||||
−0.480636 | + | 0.876920i | \(0.659594\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.32827 | −1.10942 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64944 | 0.497326 | 0.248663 | − | 0.968590i | \(-0.420009\pi\) | ||||
0.248663 | + | 0.968590i | \(0.420009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.91631i | − | 0.531489i | −0.964043 | − | 0.265745i | \(-0.914382\pi\) | ||
0.964043 | − | 0.265745i | \(-0.0856178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.85542 | − | 4.84643i | 0.737267 | − | 1.25134i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.969195i | 0.235064i | 0.993069 | + | 0.117532i | \(0.0374983\pi\) | ||||
−0.993069 | + | 0.117532i | \(0.962502\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.91039 | −1.12652 | −0.563261 | − | 0.826279i | \(-0.690453\pi\) | ||||
−0.563261 | + | 0.826279i | \(0.690453\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.6730 | −2.54725 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42317 | + | 4.37359i | 0.484634 | + | 0.874717i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.825798i | − | 0.158925i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.48480 | −1.38989 | −0.694946 | − | 0.719062i | \(-0.744572\pi\) | ||||
−0.694946 | + | 0.719062i | \(0.744572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.77655 | −1.39671 | −0.698355 | − | 0.715751i | \(-0.746084\pi\) | ||||
−0.698355 | + | 0.715751i | \(0.746084\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.14935i | 0.722309i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.26704 | − | 8.93961i | 0.890293 | − | 1.51107i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.63254i | 1.25478i | 0.778704 | + | 0.627391i | \(0.215877\pi\) | ||||
−0.778704 | + | 0.627391i | \(0.784123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82068 | 0.771927 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.79719 | 0.905368 | 0.452684 | − | 0.891671i | \(-0.350466\pi\) | ||||
0.452684 | + | 0.891671i | \(0.350466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.77230i | − | 0.575270i | −0.957740 | − | 0.287635i | \(-0.907131\pi\) | ||
0.957740 | − | 0.287635i | \(-0.0928691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.41207 | + | 3.77787i | 0.955855 | + | 0.563171i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.22605i | 0.324702i | 0.986733 | + | 0.162351i | \(0.0519077\pi\) | ||||
−0.986733 | + | 0.162351i | \(0.948092\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.5317 | −2.07595 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.43811 | −0.341404 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.2963i | − | 1.55166i | −0.630941 | − | 0.775831i | \(-0.717331\pi\) | ||
0.630941 | − | 0.775831i | \(-0.282669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.17773 | − | 1.87226i | −0.428485 | − | 0.252455i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.3526i | − | 1.63614i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1233 | 1.31794 | 0.658968 | − | 0.752171i | \(-0.270993\pi\) | ||||
0.658968 | + | 0.752171i | \(0.270993\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.06140 | 0.776083 | 0.388042 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388042 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 15.4439i | − | 1.94575i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.17517 | + | 3.69186i | −0.269797 | + | 0.457919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0618i | − | 1.47358i | −0.676119 | − | 0.736792i | \(-0.736340\pi\) | ||
0.676119 | − | 0.736792i | \(-0.263660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.51561 | −0.302843 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.01159 | −0.357411 | −0.178705 | − | 0.983903i | \(-0.557191\pi\) | ||||
−0.178705 | + | 0.983903i | \(0.557191\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 16.6439i | − | 1.94802i | −0.226495 | − | 0.974012i | \(-0.572727\pi\) | ||
0.226495 | − | 0.974012i | \(-0.427273\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.0022 | + | 6.09574i | −1.27043 | + | 0.703875i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.65379i | 0.872230i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.163787 | −0.0184275 | −0.00921377 | − | 0.999958i | \(-0.502933\pi\) | ||||
−0.00921377 | + | 0.999958i | \(0.502933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.90743 | −0.878603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.66822i | − | 0.622168i | −0.950382 | − | 0.311084i | \(-0.899308\pi\) | ||
0.950382 | − | 0.311084i | \(-0.100692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10012 | − | 1.86720i | 0.119325 | − | 0.202526i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 18.8288i | − | 2.01866i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.90271 | 0.413687 | 0.206843 | − | 0.978374i | \(-0.433681\pi\) | ||||
0.206843 | + | 0.978374i | \(0.433681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.89211 | 0.932147 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 19.5627i | − | 2.02856i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.46010 | + | 5.57371i | 0.970586 | + | 0.571850i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.79123i | 0.181872i | 0.995857 | + | 0.0909362i | \(0.0289859\pi\) | ||||
−0.995857 | + | 0.0909362i | \(0.971014\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.48979 | −0.551745 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.68775 | −0.764960 | −0.382480 | − | 0.923964i | \(-0.624930\pi\) | ||||
−0.382480 | + | 0.923964i | \(0.624930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.30773i | − | 0.227387i | −0.993516 | − | 0.113694i | \(-0.963732\pi\) | ||
0.993516 | − | 0.113694i | \(-0.0362682\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.4885 | + | 13.2498i | 2.19466 | + | 1.29305i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.7032i | 1.03472i | 0.855768 | + | 0.517359i | \(0.173085\pi\) | ||||
−0.855768 | + | 0.517359i | \(0.826915\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.94739 | −0.761222 | −0.380611 | − | 0.924735i | \(-0.624286\pi\) | ||||
−0.380611 | + | 0.924735i | \(0.624286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.2005 | −1.82243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5761i | 1.37120i | 0.727977 | + | 0.685602i | \(0.240461\pi\) | ||||
−0.727977 | + | 0.685602i | \(0.759539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.13508 | − | 1.92655i | 0.105847 | − | 0.179651i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.37800i | 0.589646i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.49728 | −0.412265 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.27934 | −0.752667 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.5834i | 1.31494i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.296037 | − | 11.1764i | 0.0264784 | − | 0.999649i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8047i | 1.93485i | 0.253158 | + | 0.967425i | \(0.418531\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.48962 | 0.835514 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.66922 | 0.320581 | 0.160290 | − | 0.987070i | \(-0.448757\pi\) | ||||
0.160290 | + | 0.987070i | \(0.448757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 22.7853i | − | 1.97574i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.937350 | + | 1.59094i | −0.0806742 | + | 0.136926i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.42421i | 0.292550i | 0.989244 | + | 0.146275i | \(0.0467284\pi\) | ||||
−0.989244 | + | 0.146275i | \(0.953272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.2838 | −1.04190 | −0.520950 | − | 0.853587i | \(-0.674422\pi\) | ||||
−0.520950 | + | 0.853587i | \(0.674422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.59985 | −0.471593 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.16085i | − | 0.264323i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4198 | + | 8.49588i | 1.19750 | + | 0.705544i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 36.5560i | − | 3.01509i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.42737 | −0.116935 | −0.0584675 | − | 0.998289i | \(-0.518621\pi\) | ||||
−0.0584675 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9521 | −1.37954 | −0.689772 | − | 0.724027i | \(-0.742289\pi\) | ||||
−0.689772 | + | 0.724027i | \(0.742289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.22574i | − | 0.260786i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.9819 | + | 8.82704i | 1.20338 | + | 0.709005i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.6335i | − | 1.56693i | −0.621438 | − | 0.783464i | \(-0.713451\pi\) | ||
0.621438 | − | 0.783464i | \(-0.286549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.4169 | 2.25361 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.64022 | −0.365701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4311i | 1.05200i | 0.850483 | + | 0.526002i | \(0.176310\pi\) | ||||
−0.850483 | + | 0.526002i | \(0.823690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.70986 | − | 7.99392i | 0.366662 | − | 0.622326i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.14523i | 0.166003i | 0.996549 | + | 0.0830013i | \(0.0264506\pi\) | ||||
−0.996549 | + | 0.0830013i | \(0.973549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.32775 | 0.717519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.3431 | 1.24979 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.04953i | − | 0.155823i | −0.996960 | − | 0.0779115i | \(-0.975175\pi\) | ||
0.996960 | − | 0.0779115i | \(-0.0248252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.2944 | + | 11.2440i | −1.53411 | + | 0.849970i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.4661i | 1.91415i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.8683 | 1.41028 | 0.705140 | − | 0.709068i | \(-0.250884\pi\) | ||||
0.705140 | + | 0.709068i | \(0.250884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.49843 | −0.334366 | −0.167183 | − | 0.985926i | \(-0.553467\pi\) | ||||
−0.167183 | + | 0.985926i | \(0.553467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.2481i | 1.12717i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.66358 | − | 14.7045i | 0.636959 | − | 1.08109i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.59863i | 0.116904i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.83189 | 0.278729 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0622 | −1.45165 | −0.725823 | − | 0.687881i | \(-0.758541\pi\) | ||||
−0.725823 | + | 0.687881i | \(0.758541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.77197i | 0.343494i | 0.985141 | + | 0.171747i | \(0.0549412\pi\) | ||||
−0.985141 | + | 0.171747i | \(0.945059\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.28727 | − | 5.47188i | −0.665075 | − | 0.391849i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.7807i | − | 1.12433i | −0.827026 | − | 0.562164i | \(-0.809969\pi\) | ||
0.827026 | − | 0.562164i | \(-0.190031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0195 | 0.852039 | 0.426020 | − | 0.904714i | \(-0.359915\pi\) | ||||
0.426020 | + | 0.904714i | \(0.359915\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.3427 | 2.14021 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 34.7312i | − | 2.43765i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1686 | − | 6.58029i | −0.780046 | − | 0.459588i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.32827i | − | 0.231331i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.09942 | −0.560248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0791 | −1.10693 | −0.553467 | − | 0.832871i | \(-0.686696\pi\) | ||||
−0.553467 | + | 0.832871i | \(0.686696\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.57598i | − | 0.519098i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.28188 | + | 7.26752i | −0.292022 | + | 0.495640i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 36.0850i | − | 2.44961i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 41.8696 | 2.82928 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.85728 | 0.124934 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.2248i | 1.22042i | 0.792239 | + | 0.610211i | \(0.208915\pi\) | ||||
−0.792239 | + | 0.610211i | \(0.791085\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.06496 | − | 14.5565i | −0.537664 | − | 0.970432i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5475i | 0.700065i | 0.936737 | + | 0.350033i | \(0.113830\pi\) | ||||
−0.936737 | + | 0.350033i | \(0.886170\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0719 | −1.45855 | −0.729276 | − | 0.684219i | \(-0.760143\pi\) | ||||
−0.729276 | + | 0.684219i | \(0.760143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.2539 | −1.26681 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9562i | 0.783277i | 0.920119 | + | 0.391638i | \(0.128092\pi\) | ||||
−0.920119 | + | 0.391638i | \(0.871908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.52675 | − | 4.28858i | 0.164827 | − | 0.279756i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.412025i | − | 0.0267639i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.163761 | −0.0105928 | −0.00529640 | − | 0.999986i | \(-0.501686\pi\) | ||||
−0.00529640 | + | 0.999986i | \(0.501686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.69099 | −0.431004 | −0.215502 | − | 0.976503i | \(-0.569139\pi\) | ||||
−0.215502 | + | 0.976503i | \(0.569139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 22.3694i | − | 1.43500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.9960 | + | 16.4947i | 1.78860 | + | 1.05381i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.40984i | 0.598734i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.2590 | 0.903628 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.90434 | −0.435798 | −0.217899 | − | 0.975971i | \(-0.569920\pi\) | ||||
−0.217899 | + | 0.975971i | \(0.569920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.64944i | 0.103700i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.69714 | + | 2.76746i | 0.294146 | + | 0.173305i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3210i | 1.57948i | 0.613440 | + | 0.789742i | \(0.289785\pi\) | ||||
−0.613440 | + | 0.789742i | \(0.710215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.4167 | −2.20069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.9114 | 1.54198 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.56021i | 0.589508i | 0.955573 | + | 0.294754i | \(0.0952377\pi\) | ||||
−0.955573 | + | 0.294754i | \(0.904762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.8222 | + | 21.7628i | −0.787662 | + | 1.33688i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.81768i | 0.600832i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.7061 | 1.75024 | 0.875120 | − | 0.483905i | \(-0.160782\pi\) | ||||
0.875120 | + | 0.483905i | \(0.160782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.19440 | −0.194046 | −0.0970229 | − | 0.995282i | \(-0.530932\pi\) | ||||
−0.0970229 | + | 0.995282i | \(0.530932\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.3691i | 1.35384i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.99688 | + | 7.21398i | 0.241021 | + | 0.435020i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.2490i | 1.03639i | 0.855261 | + | 0.518197i | \(0.173397\pi\) | ||||
−0.855261 | + | 0.518197i | \(0.826603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.8825 | 1.54954 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1604 | 0.725430 | 0.362715 | − | 0.931900i | \(-0.381850\pi\) | ||||
0.362715 | + | 0.931900i | \(0.381850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.0741i | − | 0.658287i | −0.944280 | − | 0.329144i | \(-0.893240\pi\) | ||
0.944280 | − | 0.329144i | \(-0.106760\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.0212 | + | 23.7979i | −0.830547 | + | 1.40967i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.9002i | 1.58787i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0607 | 0.944745 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50604 | −0.264149 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.1811i | 1.23741i | 0.785623 | + | 0.618706i | \(0.212343\pi\) | ||||
−0.785623 | + | 0.618706i | \(0.787657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.5029 | − | 11.4908i | −1.13551 | − | 0.669017i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.36211i | − | 0.0790374i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.91631 | 0.110823 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.5043 | 1.00893 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 19.3393i | − | 1.11102i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.6776 | − | 6.88020i | −0.668656 | − | 0.393959i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2792i | 1.15739i | 0.815543 | + | 0.578697i | \(0.196438\pi\) | ||||
−0.815543 | + | 0.578697i | \(0.803562\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.80534 | 0.330254 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.4696 | −1.95459 | −0.977295 | − | 0.211882i | \(-0.932041\pi\) | ||||
−0.977295 | + | 0.211882i | \(0.932041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4447i | 0.929510i | 0.885439 | + | 0.464755i | \(0.153858\pi\) | ||||
−0.885439 | + | 0.464755i | \(0.846142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5301 | + | 29.7534i | −0.987712 | + | 1.67642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.18172i | − | 0.0663720i | −0.999449 | − | 0.0331860i | \(-0.989435\pi\) | ||
0.999449 | − | 0.0331860i | \(-0.0105654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.3458 | −0.691230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.9251 | −1.50281 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.75913i | − | 0.264805i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.38115 | − | 4.64355i | 0.464903 | − | 0.257578i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 19.9925i | − | 1.10559i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3294 | −0.569476 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.6576 | 1.84999 | 0.924996 | − | 0.379977i | \(-0.124068\pi\) | ||||
0.924996 | + | 0.379977i | \(0.124068\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 25.4032i | − | 1.39208i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.6912 | + | 23.2376i | −0.748028 | + | 1.26961i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.29846i | − | 0.288625i | −0.989532 | − | 0.144313i | \(-0.953903\pi\) | ||
0.989532 | − | 0.144313i | \(-0.0460971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.6677 | −1.99152 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8270 | −0.694620 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 34.9487i | − | 1.88705i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.84643 | + | 2.85542i | 0.260923 | + | 0.153731i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.6842i | 1.80826i | 0.427256 | + | 0.904131i | \(0.359480\pi\) | ||||
−0.427256 | + | 0.904131i | \(0.640520\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2892 | −1.03253 | −0.516264 | − | 0.856430i | \(-0.672678\pi\) | ||||
−0.516264 | + | 0.856430i | \(0.672678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.58249 | −0.0844668 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.05334i | 0.322187i | 0.986939 | + | 0.161093i | \(0.0515020\pi\) | ||||
−0.986939 | + | 0.161093i | \(0.948498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.80198 | + | 3.41841i | 0.307937 | + | 0.181431i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 11.3134i | − | 0.598768i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.9564 | 0.842149 | 0.421074 | − | 0.907026i | \(-0.361653\pi\) | ||||
0.421074 | + | 0.907026i | \(0.361653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.11195 | 0.269050 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.8275i | − | 1.09316i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.8923 | + | 32.0653i | −0.988866 | + | 1.67838i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.7786i | − | 0.719237i | −0.933099 | − | 0.359619i | \(-0.882907\pi\) | ||
0.933099 | − | 0.359619i | \(-0.117093\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.2946 | −1.00444 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 52.4172 | 2.72137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.0667i | − | 0.676566i | −0.941044 | − | 0.338283i | \(-0.890154\pi\) | ||
0.941044 | − | 0.338283i | \(-0.109846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.1155 | + | 0.744713i | 1.45188 | + | 0.0384568i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.3432i | 0.738713i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.1458 | −1.85668 | −0.928342 | − | 0.371727i | \(-0.878766\pi\) | ||||
−0.928342 | + | 0.371727i | \(0.878766\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54.8519 | −2.81015 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.4289i | − | 1.04387i | −0.852987 | − | 0.521933i | \(-0.825211\pi\) | ||
0.852987 | − | 0.521933i | \(-0.174789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.68769 | − | 14.7454i | 0.442766 | − | 0.751495i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5552i | 0.638218i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.3561 | −1.89403 | −0.947015 | − | 0.321189i | \(-0.895917\pi\) | ||||
−0.947015 | + | 0.321189i | \(0.895917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.969195 | −0.0490143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.23030i | 0.465607i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.315544 | + | 0.185913i | 0.0158768 | + | 0.00935428i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.73956i | 0.488814i | 0.969673 | + | 0.244407i | \(0.0785934\pi\) | ||||
−0.969673 | + | 0.244407i | \(0.921407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 57.3189 | 2.86953 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8802 | −1.34233 | −0.671166 | − | 0.741307i | \(-0.734206\pi\) | ||||
−0.671166 | + | 0.741307i | \(0.734206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.9023i | 0.742336i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2340 | + | 8.97560i | 0.756985 | + | 0.446001i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.5895i | 0.624036i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8307 | −1.17835 | −0.589175 | − | 0.808005i | \(-0.700547\pi\) | ||||
−0.589175 | + | 0.808005i | \(0.700547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.61395 | −0.424895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 46.9742i | 2.31145i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.43391 | + | 10.9201i | −0.315828 | + | 0.536047i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 30.9012i | − | 1.51324i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8463 | 0.822995 | 0.411497 | − | 0.911411i | \(-0.365006\pi\) | ||||
0.411497 | + | 0.911411i | \(0.365006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4397 | 0.508798 | 0.254399 | − | 0.967099i | \(-0.418122\pi\) | ||||
0.254399 | + | 0.967099i | \(0.418122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7.40888i | − | 0.360232i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.23886 | + | 2.34852i | −0.205615 | + | 0.113920i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.1263i | 1.36113i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.95145 | 0.383899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3189 | −0.737886 | −0.368943 | − | 0.929452i | \(-0.620280\pi\) | ||||
−0.368943 | + | 0.929452i | \(0.620280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.5759i | − | 0.844642i | −0.906446 | − | 0.422321i | \(-0.861216\pi\) | ||
0.906446 | − | 0.422321i | \(-0.138784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.3723 | + | 36.2746i | −1.02472 | + | 1.73923i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.91039i | − | 0.234896i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7104 | 1.27482 | 0.637408 | − | 0.770527i | \(-0.280007\pi\) | ||||
0.637408 | + | 0.770527i | \(0.280007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 48.3654 | 2.30311 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.9540i | 0.710487i | 0.934774 | + | 0.355243i | \(0.115602\pi\) | ||||
−0.934774 | + | 0.355243i | \(0.884398\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.51876 | − | 4.42990i | −0.356423 | − | 0.209998i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.59071i | − | 0.169835i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.46847 | 0.305266 | 0.152633 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152633 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.56213 | 0.450263 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 42.6448i | − | 2.00363i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.1311 | − | 10.0933i | −0.803117 | − | 0.473181i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.1286i | 1.92391i | 0.273202 | + | 0.961957i | \(0.411917\pi\) | ||||
−0.273202 | + | 0.961957i | \(0.588083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.800359 | 0.0373576 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9053 | 0.601060 | 0.300530 | − | 0.953772i | \(-0.402836\pi\) | ||||
0.300530 | + | 0.953772i | \(0.402836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.74237i | − | 0.313344i | −0.987651 | − | 0.156672i | \(-0.949923\pi\) | ||
0.987651 | − | 0.156672i | \(-0.0500766\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.2054 | + | 37.6885i | −1.02975 | + | 1.74776i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 9.30704i | − | 0.430678i | −0.976539 | − | 0.215339i | \(-0.930914\pi\) | ||
0.976539 | − | 0.215339i | \(-0.0690857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 55.9695 | 2.58443 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.3902 | 2.27578 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.22220i | − | 0.286097i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.8987 | − | 21.4760i | −0.545950 | − | 0.985387i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 37.5970i | 1.72145i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6673 | 1.44691 | 0.723457 | − | 0.690370i | \(-0.242552\pi\) | ||||
0.723457 | + | 0.690370i | \(0.242552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6263 | 0.666903 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 11.6730i | − | 0.531139i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.03320 | − | 3.45090i | 0.0923229 | − | 0.156697i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.7582i | 0.759385i | 0.925113 | + | 0.379693i | \(0.123970\pi\) | ||||
−0.925113 | + | 0.379693i | \(0.876030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.7873 | −1.52792 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.5811 | −1.10933 | −0.554666 | − | 0.832073i | \(-0.687154\pi\) | ||||
−0.554666 | + | 0.832073i | \(0.687154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.25423i | − | 0.326714i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.5763 | + | 6.23138i | 0.475372 | + | 0.280080i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13.9745i | − | 0.626841i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.25368 | 0.100888 | 0.0504442 | − | 0.998727i | \(-0.483936\pi\) | ||||
0.0504442 | + | 0.998727i | \(0.483936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.39654 | −0.241100 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.8452i | 0.483566i | 0.970330 | + | 0.241783i | \(0.0777322\pi\) | ||||
−0.970330 | + | 0.241783i | \(0.922268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8108 | + | 8.72624i | 0.659073 | + | 0.388313i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.4649i | 1.04211i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6490 | −0.870926 | −0.435463 | − | 0.900207i | \(-0.643415\pi\) | ||||
−0.435463 | + | 0.900207i | \(0.643415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 77.2316 | 3.41652 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.05499i | 0.179032i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.61947 | + | 4.44595i | −0.115427 | + | 0.195912i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.67174i | 0.161483i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.15581 | 0.226315 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.9000 | 0.871836 | 0.435918 | − | 0.899986i | \(-0.356424\pi\) | ||||
0.435918 | + | 0.899986i | \(0.356424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.4617i | − | 0.894726i | −0.894352 | − | 0.447363i | \(-0.852363\pi\) | ||
0.894352 | − | 0.447363i | \(-0.147637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −28.2856 | − | 51.0527i | −1.23448 | − | 2.22812i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 7.53700i | − | 0.328317i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.6930 | −1.46215 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.1092i | − | 0.481194i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1490 | − | 20.6202i | 0.525249 | − | 0.891491i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 47.4651i | 2.04827i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.9692 | −1.03243 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.86543 | −0.209181 | −0.104591 | − | 0.994515i | \(-0.533353\pi\) | ||||
−0.104591 | + | 0.994515i | \(0.533353\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 11.3163i | − | 0.485628i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.3110 | + | 9.02096i | 0.655852 | + | 0.386415i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 33.3411i | − | 1.42556i | −0.701386 | − | 0.712781i | \(-0.747435\pi\) | ||
0.701386 | − | 0.712781i | \(-0.252565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.1740 | −0.861005 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.7533 | 1.56574 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.760011i | − | 0.0323189i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.9906 | + | 21.7941i | 1.57016 | + | 0.925110i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19.3928i | − | 0.821697i | −0.911704 | − | 0.410849i | \(-0.865232\pi\) | ||
0.911704 | − | 0.410849i | \(-0.134768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.22890 | −0.305750 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.02153 | −0.169789 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7.49245i | − | 0.315769i | −0.987458 | − | 0.157884i | \(-0.949533\pi\) | ||
0.987458 | − | 0.157884i | \(-0.0504674\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5451 | − | 28.0815i | 0.696057 | − | 1.18140i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 36.6922i | − | 1.54093i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.26375 | 0.136823 | 0.0684117 | − | 0.997657i | \(-0.478207\pi\) | ||||
0.0684117 | + | 0.997657i | \(0.478207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9738 | −0.626636 | −0.313318 | − | 0.949648i | \(-0.601441\pi\) | ||||
−0.313318 | + | 0.949648i | \(0.601441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 50.4685i | − | 2.10835i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.37359 | + | 2.42317i | −0.182391 | + | 0.101053i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.5111i | − | 0.895520i | −0.894154 | − | 0.447760i | \(-0.852222\pi\) | ||
0.894154 | − | 0.447760i | \(-0.147778\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0044 | −0.498886 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.3018 | 1.09118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.6326i | − | 0.771681i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.23957 | − | 12.2875i | 0.299319 | − | 0.508026i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.76395i | − | 0.0728059i | −0.999337 | − | 0.0364030i | \(-0.988410\pi\) | ||
0.999337 | − | 0.0364030i | \(-0.0115900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.1859 | 1.57342 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.6980 | 1.63296 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.68465i | 0.356636i | 0.983973 | + | 0.178318i | \(0.0570656\pi\) | ||||
−0.983973 | + | 0.178318i | \(0.942934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.66423 | + | 5.10479i | 0.355199 | + | 0.209276i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.2363i | 1.23749i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3988 | −0.956049 | −0.478024 | − | 0.878347i | \(-0.658647\pi\) | ||||
−0.478024 | + | 0.878347i | \(0.658647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0536 | 0.858794 | 0.429397 | − | 0.903116i | \(-0.358726\pi\) | ||||
0.429397 | + | 0.903116i | \(0.358726\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.1450i | 1.63483i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.9505 | + | 9.39774i | 0.648481 | + | 0.382072i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.0489i | 1.42259i | 0.702892 | + | 0.711296i | \(0.251892\pi\) | ||||
−0.702892 | + | 0.711296i | \(0.748108\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 87.3699 | 3.54041 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.26580 | 0.172576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.5922i | 1.11444i | 0.830365 | + | 0.557219i | \(0.188132\pi\) | ||||
−0.830365 | + | 0.557219i | \(0.811868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.5534 | − | 28.0957i | 0.667498 | − | 1.13293i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.22209i | − | 0.331009i | −0.986209 | − | 0.165504i | \(-0.947075\pi\) | ||
0.986209 | − | 0.165504i | \(-0.0529252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.5042 | −0.783940 | −0.391970 | − | 0.919978i | \(-0.628206\pi\) | ||||
−0.391970 | + | 0.919978i | \(0.628206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.825798 | 0.0331381 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.1095i | 0.725540i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.2565 | + | 21.1959i | −0.530260 | + | 0.847835i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 20.3749i | − | 0.813696i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.39742 | −0.294955 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.59833 | 0.302485 | 0.151242 | − | 0.988497i | \(-0.451673\pi\) | ||||
0.151242 | + | 0.988497i | \(0.451673\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 40.4488i | − | 1.60770i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.7501 | − | 42.0077i | 0.982178 | − | 1.66702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.8472i | 1.10335i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.0234 | 0.396520 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.02749 | −0.0800809 | −0.0400405 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400405 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.7200i | 0.856554i | 0.903647 | + | 0.428277i | \(0.140879\pi\) | ||||
−0.903647 | + | 0.428277i | \(0.859121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.2822 | − | 10.7715i | −0.719861 | − | 0.424128i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3675i | 0.486216i | 0.969999 | + | 0.243108i | \(0.0781670\pi\) | ||||
−0.969999 | + | 0.243108i | \(0.921833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6978 | 0.655444 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 90.7755 | 3.55777 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.8363i | 0.971921i | 0.873981 | + | 0.485960i | \(0.161530\pi\) | ||||
−0.873981 | + | 0.485960i | \(0.838470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.06892 | − | 4.16487i | −0.276205 | − | 0.162735i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 55.3955i | 2.16118i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4867 | −1.14864 | −0.574319 | − | 0.818631i | \(-0.694733\pi\) | ||||
−0.574319 | + | 0.818631i | \(0.694733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3911 | 1.64882 | 0.824411 | − | 0.565992i | \(-0.191507\pi\) | ||||
0.824411 | + | 0.565992i | \(0.191507\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.67218i | 0.181452i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25.8633 | + | 43.8970i | −1.00293 | + | 1.70225i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.48480i | − | 0.289813i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.8464 | −1.77252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.99794 | 0.385966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.5867i | − | 0.793559i | −0.917914 | − | 0.396779i | \(-0.870128\pi\) | ||
0.917914 | − | 0.396779i | \(-0.129872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.61170 | − | 2.00105i | 0.139014 | − | 0.0770203i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.8416i | 0.493545i | 0.969073 | + | 0.246772i | \(0.0793700\pi\) | ||||
−0.969073 | + | 0.246772i | \(0.920630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.31173 | −0.318975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.5335 | −1.01676 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.1531i | 1.80426i | 0.431460 | + | 0.902132i | \(0.357999\pi\) | ||||
−0.431460 | + | 0.902132i | \(0.642001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.88676 | − | 6.59690i | 0.148506 | − | 0.252054i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 55.5242i | − | 2.11838i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.6472 | −0.824691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.9278 | −1.13851 | −0.569253 | − | 0.822163i | \(-0.692767\pi\) | ||||
−0.569253 | + | 0.822163i | \(0.692767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 25.4739i | − | 0.967673i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6653 | + | 13.9432i | 0.897678 | + | 0.528894i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.61860i | 0.212820i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.0771 | −1.13762 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7689 | 0.595585 | 0.297793 | − | 0.954631i | \(-0.403750\pi\) | ||||
0.297793 | + | 0.954631i | \(0.403750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 37.4788i | − | 1.41354i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.7884 | + | 6.35630i | 0.406314 | + | 0.239392i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 35.6729i | − | 1.34162i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.221825 | 0.00833080 | 0.00416540 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416540 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.545129 | 0.0204439 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.77655i | − | 0.291234i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58783 | + | 6.08952i | −0.134177 | + | 0.227735i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.411958i | − | 0.0153848i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.2546 | −1.61312 | −0.806562 | − | 0.591149i | \(-0.798675\pi\) | ||||
−0.806562 | + | 0.591149i | \(0.798675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7084 | 0.398801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.8319i | − | 0.625984i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1369 | − | 32.7354i | −0.673589 | − | 1.21576i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.90379i | − | 0.330223i | −0.986275 | − | 0.165112i | \(-0.947202\pi\) | ||
0.986275 | − | 0.165112i | \(-0.0527985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.5502 | 1.20556 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.65609 | 0.135226 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0655i | 0.519521i | 0.965673 | + | 0.259761i | \(0.0836436\pi\) | ||||
−0.965673 | + | 0.259761i | \(0.916356\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41.4941 | + | 70.4268i | −1.53053 | + | 2.59773i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 19.8953i | − | 0.732852i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.4096 | −1.37614 | −0.688068 | − | 0.725646i | \(-0.741541\pi\) | ||||
−0.688068 | + | 0.725646i | \(0.741541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.6714 | −0.869592 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.48682i | − | 0.274665i | −0.990525 | − | 0.137332i | \(-0.956147\pi\) | ||
0.990525 | − | 0.137332i | \(-0.0438528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.74990 | + | 1.62019i | 0.100749 | + | 0.0593591i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.8654i | 0.690248i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.6653 | −1.81473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.0524 | −1.06014 | −0.530069 | − | 0.847955i | \(-0.677834\pi\) | ||||
−0.530069 | + | 0.847955i | \(0.677834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 17.3686i | − | 0.632947i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.6591 | + | 19.2421i | 1.18858 | + | 0.700291i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 52.0910i | − | 1.89328i | −0.322295 | − | 0.946639i | \(-0.604454\pi\) | ||
0.322295 | − | 0.946639i | \(-0.395546\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.14935 | −0.150612 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.8693 | 0.792762 | 0.396381 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396381 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 36.8777i | − | 1.33506i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.66149 | + | 6.21455i | −0.132381 | + | 0.224687i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 19.3993i | − | 0.700469i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.9646 | −1.47722 | −0.738611 | − | 0.674132i | \(-0.764518\pi\) | ||||
−0.738611 | + | 0.674132i | \(0.764518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.6977 | −2.29402 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.3674i | 1.12821i | 0.825704 | + | 0.564103i | \(0.190778\pi\) | ||||
−0.825704 | + | 0.564103i | \(0.809222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.8439 | − | 34.0114i | −0.676893 | − | 1.22173i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 89.0945i | − | 3.19625i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.4665 | −1.01992 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.96746 | −0.177750 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.18093i | 0.220888i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.2857 | + | 37.8249i | −0.795411 | + | 1.35003i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.8694i | − | 0.636977i | −0.947927 | − | 0.318489i | \(-0.896825\pi\) | ||
0.947927 | − | 0.318489i | \(-0.103175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0497 | −0.856192 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −67.6364 | −2.40487 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.6155i | − | 0.412480i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54.7466 | − | 32.2556i | −1.94166 | − | 1.14399i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0293i | 0.780319i | 0.920747 | + | 0.390159i | \(0.127580\pi\) | ||||
−0.920747 | + | 0.390159i | \(0.872420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.15747 | −0.0763259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9893 | −0.458953 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 27.4532i | − | 0.968803i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.93961 | + | 5.26704i | 0.315080 | + | 0.185639i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.2132i | 2.54202i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0548 | 0.740246 | 0.370123 | − | 0.928983i | \(-0.379316\pi\) | ||||
0.370123 | + | 0.928983i | \(0.379316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0175 | 1.19451 | 0.597257 | − | 0.802050i | \(-0.296257\pi\) | ||||
0.597257 | + | 0.802050i | \(0.296257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.03584i | − | 0.281829i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.2454 | − | 25.8756i | 0.534024 | − | 0.906384i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5235i | 0.648054i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.5954 | −1.03415 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.94320 | −0.102718 | −0.0513591 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513591 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.4173i | 1.44372i | 0.692041 | + | 0.721859i | \(0.256712\pi\) | ||||
−0.692041 | + | 0.721859i | \(0.743288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.1475 | + | 10.0546i | −0.631816 | + | 0.350055i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.4450i | − | 0.815262i | −0.913147 | − | 0.407631i | \(-0.866355\pi\) | ||
0.913147 | − | 0.407631i | \(-0.133645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.16155 | 0.179268 | 0.0896340 | − | 0.995975i | \(-0.471430\pi\) | ||||
0.0896340 | + | 0.995975i | \(0.471430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.3918 | −1.50524 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14.0840i | − | 0.487983i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.43501 | − | 4.13288i | 0.0842670 | − | 0.143024i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.42186i | 0.221972i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.55411 | 0.260797 | 0.130398 | − | 0.991462i | \(-0.458374\pi\) | ||||
0.130398 | + | 0.991462i | \(0.458374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0222 | 0.931801 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.5908i | 1.05360i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.9704 | − | 10.5878i | −0.618199 | − | 0.364231i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 38.4180i | − | 1.32006i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.8581 | 0.956087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.63254 | −0.261640 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.3528i | − | 0.662628i | −0.943521 | − | 0.331314i | \(-0.892508\pi\) | ||
0.943521 | − | 0.331314i | \(-0.107492\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.4858 | − | 18.5508i | −1.07679 | − | 0.634424i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.6628i | − | 0.671667i | −0.941921 | − | 0.335833i | \(-0.890982\pi\) | ||
0.941921 | − | 0.335833i | \(-0.109018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1341 | −0.755205 | −0.377602 | − | 0.925968i | \(-0.623251\pi\) | ||||
−0.377602 | + | 0.925968i | \(0.623251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −67.6704 | −2.30620 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 57.4689i | 1.95626i | 0.207986 | + | 0.978132i | \(0.433309\pi\) | ||||
−0.207986 | + | 0.978132i | \(0.566691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.32639 | + | 3.94852i | −0.0790996 | + | 0.134254i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.4023i | 1.37213i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.270158 | −0.00916449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.1142 | −0.783194 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.96171i | − | 0.201773i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.8611 | + | 1.37368i | 1.75323 | + | 0.0464388i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.5774i | 0.492243i | 0.969239 | + | 0.246121i | \(0.0791562\pi\) | ||||
−0.969239 | + | 0.246121i | \(0.920844\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −53.2832 | −1.79720 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.1713 | 1.01650 | 0.508248 | − | 0.861211i | \(-0.330293\pi\) | ||||
0.508248 | + | 0.861211i | \(0.330293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.92294i | 0.300281i | 0.988665 | + | 0.150140i | \(0.0479726\pi\) | ||||
−0.988665 | + | 0.150140i | \(0.952027\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.9062 | − | 49.0617i | 0.971671 | − | 1.64919i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 31.3040i | − | 1.05109i | −0.850767 | − | 0.525543i | \(-0.823862\pi\) | ||
0.850767 | − | 0.525543i | \(-0.176138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −101.178 | −3.39342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.0429 | −0.436952 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.9308i | − | 0.365784i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.3506 | − | 21.4171i | −1.21507 | − | 0.715893i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.82068i | 0.160958i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.2060 | 1.94128 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9483 | 0.364740 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 44.0340i | 1.46536i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.66645 | + | 5.10610i | 0.288082 | + | 0.169733i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.2883i | 1.83582i | 0.396793 | + | 0.917908i | \(0.370123\pi\) | ||||
−0.396793 | + | 0.917908i | \(0.629877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.5869 | 0.848664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0030 | 0.994044 | 0.497022 | − | 0.867738i | \(-0.334427\pi\) | ||||
0.497022 | + | 0.867738i | \(0.334427\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.34941i | − | 0.309420i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.3079 | − | 29.3762i | 0.572180 | − | 0.971146i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.0260i | 0.562247i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.98146 | 0.197310 | 0.0986551 | − | 0.995122i | \(-0.468546\pi\) | ||||
0.0986551 | + | 0.995122i | \(0.468546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.0144 | −1.68098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.77115i | 0.189960i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.3816 | + | 18.4949i | −1.09758 | + | 0.608110i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.68075i | 0.252269i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 59.4966 | 1.95202 | 0.976009 | − | 0.217728i | \(-0.0698647\pi\) | ||||
0.976009 | + | 0.217728i | \(0.0698647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 71.3563 | 2.33861 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 86.7119i | − | 2.83882i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.81458 | − | 3.07984i | 0.0593432 | − | 0.100722i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 59.7229i | − | 1.95106i | −0.219863 | − | 0.975531i | \(-0.570561\pi\) | ||
0.219863 | − | 0.975531i | \(-0.429439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.3684 | −1.35001 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.6385 | 1.35738 | 0.678688 | − | 0.734426i | \(-0.262549\pi\) | ||||
0.678688 | + | 0.734426i | \(0.262549\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.79719i | 0.188782i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.38231 | − | 4.34951i | −0.240147 | − | 0.141490i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0566i | 0.749239i | 0.927179 | + | 0.374620i | \(0.122227\pi\) | ||||
−0.927179 | + | 0.374620i | \(0.877773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.8950 | −1.03535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97274 | 0.0963978 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.5945i | − | 1.47695i | −0.674280 | − | 0.738476i | \(-0.735546\pi\) | ||
0.674280 | − | 0.738476i | \(-0.264454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.6507 | + | 22.7722i | 1.25071 | + | 0.736892i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 31.0571i | − | 1.00393i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8891 | −0.513085 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4748 | 0.950800 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 35.6232i | − | 1.14794i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.41659 | − | 9.19343i | 0.174366 | − | 0.295947i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.5979i | 1.53064i | 0.643647 | + | 0.765322i | \(0.277420\pi\) | ||||
−0.643647 | + | 0.765322i | \(0.722580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.9721 | 0.384599 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0384 | −0.643064 | −0.321532 | − | 0.946899i | \(-0.604198\pi\) | ||||
−0.321532 | + | 0.946899i | \(0.604198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 56.9996i | − | 1.82732i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.6813 | + | 21.0837i | 0.374102 | + | 0.675218i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.86869i | 0.0597846i | 0.999553 | + | 0.0298923i | \(0.00951644\pi\) | ||||
−0.999553 | + | 0.0298923i | \(0.990484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.43730 | 0.205737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.4511 | 0.844518 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.3038i | − | 0.966542i | −0.875471 | − | 0.483271i | \(-0.839449\pi\) | ||
0.875471 | − | 0.483271i | \(-0.160551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9124 | + | 30.4022i | −0.570737 | + | 0.968696i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 25.9846i | − | 0.827098i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.77230 | 0.119952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.1424 | 0.957505 | 0.478752 | − | 0.877950i | \(-0.341089\pi\) | ||||
0.478752 | + | 0.877950i | \(0.341089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 84.6694i | 2.68690i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.1561 | − | 13.6431i | −0.734099 | − | 0.432516i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9205i | 0.440865i | 0.975402 | + | 0.220433i | \(0.0707469\pi\) | ||||
−0.975402 | + | 0.220433i | \(0.929253\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.30294 | 0.199416 |
(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 | 1840.2.e.h.369.13 | 16 | ||
4.3 | odd | 2 | 920.2.e.c.369.4 | ✓ | 16 | ||
5.2 | odd | 4 | 9200.2.a.dd.1.7 | 8 | |||
5.3 | odd | 4 | 9200.2.a.de.1.2 | 8 | |||
5.4 | even | 2 | inner | 1840.2.e.h.369.4 | 16 | ||
20.3 | even | 4 | 4600.2.a.bj.1.7 | 8 | |||
20.7 | even | 4 | 4600.2.a.bk.1.2 | 8 | |||
20.19 | odd | 2 | 920.2.e.c.369.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.4 | ✓ | 16 | 4.3 | odd | 2 | ||
920.2.e.c.369.13 | yes | 16 | 20.19 | odd | 2 | ||
1840.2.e.h.369.4 | 16 | 5.4 | even | 2 | inner | ||
1840.2.e.h.369.13 | 16 | 1.1 | even | 1 | trivial | ||
4600.2.a.bj.1.7 | 8 | 20.3 | even | 4 | |||
4600.2.a.bk.1.2 | 8 | 20.7 | even | 4 | |||
9200.2.a.dd.1.7 | 8 | 5.2 | odd | 4 | |||
9200.2.a.de.1.2 | 8 | 5.3 | odd | 4 |