Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(401,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.l (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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.681615360000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.6 | ||
Root | \(-2.22255 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.401 |
Dual form | 1200.3.l.x.401.5 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.291610 | + | 2.98579i | 0.0972033 | + | 0.995265i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.46268 | 0.637525 | 0.318763 | − | 0.947835i | \(-0.396733\pi\) | ||||
0.318763 | + | 0.947835i | \(0.396733\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.82993 | + | 1.74137i | −0.981103 | + | 0.193486i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 17.8696i | − | 1.62451i | −0.583305 | − | 0.812253i | \(-0.698241\pi\) | ||
0.583305 | − | 0.812253i | \(-0.301759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.0107 | 0.846980 | 0.423490 | − | 0.905901i | \(-0.360805\pi\) | ||||
0.423490 | + | 0.905901i | \(0.360805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.794055i | 0.0467091i | 0.999727 | + | 0.0233546i | \(0.00743466\pi\) | ||||
−0.999727 | + | 0.0233546i | \(0.992565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.5852 | −1.39922 | −0.699611 | − | 0.714524i | \(-0.746643\pi\) | ||||
−0.699611 | + | 0.714524i | \(0.746643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30136 | + | 13.3246i | 0.0619696 | + | 0.634506i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 14.9276i | − | 0.649027i | −0.945881 | − | 0.324514i | \(-0.894799\pi\) | ||
0.945881 | − | 0.324514i | \(-0.105201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.77428 | − | 25.8565i | −0.287936 | − | 0.957650i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.58545i | − | 0.192602i | −0.995352 | − | 0.0963008i | \(-0.969299\pi\) | ||
0.995352 | − | 0.0963008i | \(-0.0307011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −53.1074 | −1.71314 | −0.856571 | − | 0.516030i | \(-0.827409\pi\) | ||||
−0.856571 | + | 0.516030i | \(0.827409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 53.3549 | − | 5.21095i | 1.61681 | − | 0.157907i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −51.7565 | −1.39882 | −0.699412 | − | 0.714719i | \(-0.746555\pi\) | ||||
−0.699412 | + | 0.714719i | \(0.746555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.21084 | + | 32.8758i | 0.0823293 | + | 0.842969i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 67.8236i | − | 1.65423i | −0.562030 | − | 0.827117i | \(-0.689980\pi\) | ||
0.562030 | − | 0.827117i | \(-0.310020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −40.8243 | −0.949403 | −0.474701 | − | 0.880147i | \(-0.657444\pi\) | ||||
−0.474701 | + | 0.880147i | \(0.657444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.3483i | − | 0.262729i | −0.991334 | − | 0.131365i | \(-0.958064\pi\) | ||
0.991334 | − | 0.131365i | \(-0.0419359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −29.0845 | −0.593562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.37088 | + | 0.231554i | −0.0464879 | + | 0.00454028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.0351i | 0.698775i | 0.936978 | + | 0.349387i | \(0.113610\pi\) | ||||
−0.936978 | + | 0.349387i | \(0.886390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.75251 | − | 79.3779i | −0.136009 | − | 1.39260i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 61.0932i | − | 1.03548i | −0.855539 | − | 0.517739i | \(-0.826774\pi\) | ||
0.855539 | − | 0.517739i | \(-0.173226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 97.8289 | 1.60375 | 0.801876 | − | 0.597490i | \(-0.203835\pi\) | ||||
0.801876 | + | 0.597490i | \(0.203835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −39.4051 | + | 7.77119i | −0.625478 | + | 0.123352i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.02541 | 0.0451553 | 0.0225777 | − | 0.999745i | \(-0.492813\pi\) | ||||
0.0225777 | + | 0.999745i | \(0.492813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 44.5708 | − | 4.35305i | 0.645954 | − | 0.0630876i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 57.0787i | − | 0.803926i | −0.915656 | − | 0.401963i | \(-0.868328\pi\) | ||
0.915656 | − | 0.401963i | \(-0.131672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31.4690 | 0.431082 | 0.215541 | − | 0.976495i | \(-0.430848\pi\) | ||||
0.215541 | + | 0.976495i | \(0.430848\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 79.7461i | − | 1.03566i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.16053 | 0.0273485 | 0.0136743 | − | 0.999907i | \(-0.495647\pi\) | ||||
0.0136743 | + | 0.999907i | \(0.495647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 74.9352 | − | 30.7524i | 0.925126 | − | 0.379660i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0710i | 0.157482i | 0.996895 | + | 0.0787411i | \(0.0250900\pi\) | ||||
−0.996895 | + | 0.0787411i | \(0.974910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.6770 | − | 1.62877i | 0.191690 | − | 0.0187215i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 173.692i | 1.95160i | 0.218667 | + | 0.975800i | \(0.429829\pi\) | ||||
−0.218667 | + | 0.975800i | \(0.570171\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.1374 | 0.539971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.4866 | − | 158.568i | −0.166523 | − | 1.70503i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.6381 | 0.944722 | 0.472361 | − | 0.881405i | \(-0.343402\pi\) | ||||
0.472361 | + | 0.881405i | \(0.343402\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.1176 | + | 157.787i | 0.314319 | + | 1.59381i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 116.353i | − | 1.15201i | −0.817446 | − | 0.576005i | \(-0.804611\pi\) | ||
0.817446 | − | 0.576005i | \(-0.195389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −182.071 | −1.76768 | −0.883842 | − | 0.467786i | \(-0.845052\pi\) | ||||
−0.883842 | + | 0.467786i | \(0.845052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 102.828i | − | 0.961013i | −0.876991 | − | 0.480506i | \(-0.840453\pi\) | ||
0.876991 | − | 0.480506i | \(-0.159547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75.4257 | 0.691979 | 0.345990 | − | 0.938238i | \(-0.387543\pi\) | ||||
0.345990 | + | 0.938238i | \(0.387543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0927 | − | 154.534i | −0.135970 | − | 1.39220i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 141.923i | 1.25596i | 0.778230 | + | 0.627980i | \(0.216118\pi\) | ||||
−0.778230 | + | 0.627980i | \(0.783882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −97.2241 | + | 19.1738i | −0.830975 | + | 0.163879i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.54361i | 0.0297782i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −198.322 | −1.63902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 202.507 | − | 19.7780i | 1.64640 | − | 0.160797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 112.920 | 0.889132 | 0.444566 | − | 0.895746i | \(-0.353358\pi\) | ||||
0.444566 | + | 0.895746i | \(0.353358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.9048 | − | 121.893i | −0.0922851 | − | 0.944907i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 107.233i | − | 0.818570i | −0.912407 | − | 0.409285i | \(-0.865778\pi\) | ||
0.912407 | − | 0.409285i | \(-0.134222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −118.641 | −0.892039 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 67.7434i | 0.494477i | 0.968955 | + | 0.247239i | \(0.0795232\pi\) | ||||
−0.968955 | + | 0.247239i | \(0.920477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 141.204 | 1.01586 | 0.507928 | − | 0.861399i | \(-0.330411\pi\) | ||||
0.507928 | + | 0.861399i | \(0.330411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.8694 | − | 3.60088i | 0.261485 | − | 0.0255382i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 196.757i | − | 1.37593i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.48134 | − | 86.8404i | −0.0576962 | − | 0.590751i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 55.0831i | − | 0.369685i | −0.982768 | − | 0.184843i | \(-0.940822\pi\) | ||
0.982768 | − | 0.184843i | \(-0.0591775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −56.1302 | −0.371723 | −0.185862 | − | 0.982576i | \(-0.559508\pi\) | ||||
−0.185862 | + | 0.982576i | \(0.559508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.38275 | − | 7.01145i | −0.00903756 | − | 0.0458265i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 274.266 | 1.74692 | 0.873460 | − | 0.486896i | \(-0.161871\pi\) | ||||
0.873460 | + | 0.486896i | \(0.161871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −110.579 | + | 10.7998i | −0.695466 | + | 0.0679232i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 66.6172i | − | 0.413771i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 260.316 | 1.59703 | 0.798516 | − | 0.601974i | \(-0.205619\pi\) | ||||
0.798516 | + | 0.601974i | \(0.205619\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 179.949i | − | 1.07754i | −0.842453 | − | 0.538769i | \(-0.818889\pi\) | ||
0.842453 | − | 0.538769i | \(-0.181111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −47.7635 | −0.282624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 234.745 | − | 46.2948i | 1.37278 | − | 0.270730i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 111.265i | − | 0.643148i | −0.946884 | − | 0.321574i | \(-0.895788\pi\) | ||
0.946884 | − | 0.321574i | \(-0.104212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 182.412 | − | 17.8154i | 1.03057 | − | 0.100652i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 77.8475i | − | 0.434902i | −0.976071 | − | 0.217451i | \(-0.930226\pi\) | ||
0.976071 | − | 0.217451i | \(-0.0697743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −238.852 | −1.31963 | −0.659813 | − | 0.751430i | \(-0.729364\pi\) | ||||
−0.659813 | + | 0.751430i | \(0.729364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.5279 | + | 292.097i | 0.155890 | + | 1.59616i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.1894 | 0.0758793 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.6941 | − | 115.389i | −0.183567 | − | 0.610526i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 177.248i | 0.928002i | 0.885835 | + | 0.464001i | \(0.153587\pi\) | ||||
−0.885835 | + | 0.464001i | \(0.846413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −284.254 | −1.47282 | −0.736409 | − | 0.676536i | \(-0.763480\pi\) | ||||
−0.736409 | + | 0.676536i | \(0.763480\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 244.341i | − | 1.24031i | −0.784479 | − | 0.620156i | \(-0.787069\pi\) | ||
0.784479 | − | 0.620156i | \(-0.212931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −74.0122 | −0.371921 | −0.185960 | − | 0.982557i | \(-0.559540\pi\) | ||||
−0.185960 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.882239 | + | 9.03324i | 0.00438925 | + | 0.0449415i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 24.9260i | − | 0.122788i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.9946 | + | 131.810i | 0.125578 | + | 0.636763i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 475.066i | 2.27304i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31.0682 | 0.147243 | 0.0736214 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736214 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 170.425 | − | 16.6447i | 0.800119 | − | 0.0781443i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −237.001 | −1.09217 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.17668 | + | 93.9600i | 0.0419026 | + | 0.429041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.74314i | 0.0395617i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 100.432 | 0.450366 | 0.225183 | − | 0.974316i | \(-0.427702\pi\) | ||||
0.225183 | + | 0.974316i | \(0.427702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 349.117i | 1.53796i | 0.639273 | + | 0.768980i | \(0.279236\pi\) | ||||
−0.639273 | + | 0.768980i | \(0.720764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −165.007 | −0.720555 | −0.360278 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360278 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 238.105 | − | 23.2548i | 1.03076 | − | 0.100670i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 124.800i | 0.535620i | 0.963472 | + | 0.267810i | \(0.0863000\pi\) | ||||
−0.963472 | + | 0.267810i | \(0.913700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.630033 | + | 6.45091i | 0.00265837 | + | 0.0272190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 61.8321i | − | 0.258712i | −0.991598 | − | 0.129356i | \(-0.958709\pi\) | ||
0.991598 | − | 0.129356i | \(-0.0412910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.25555 | 0.00935913 | 0.00467956 | − | 0.999989i | \(-0.498510\pi\) | ||||
0.00467956 | + | 0.999989i | \(0.498510\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 113.672 | + | 214.773i | 0.467787 | + | 0.883841i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −292.723 | −1.18511 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.0274 | + | 3.81164i | −0.156736 | + | 0.0153078i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 108.993i | 0.434234i | 0.976146 | + | 0.217117i | \(0.0696654\pi\) | ||||
−0.976146 | + | 0.217117i | \(0.930335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −266.750 | −1.05435 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.4664i | 0.122437i | 0.998124 | + | 0.0612187i | \(0.0194987\pi\) | ||||
−0.998124 | + | 0.0612187i | \(0.980501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −230.972 | −0.891785 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.72636 | + | 49.3191i | 0.0372657 | + | 0.188962i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 235.190i | − | 0.894260i | −0.894469 | − | 0.447130i | \(-0.852446\pi\) | ||
0.894469 | − | 0.447130i | \(-0.147554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −518.609 | + | 50.6504i | −1.94236 | + | 0.189702i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 221.066i | − | 0.821808i | −0.911679 | − | 0.410904i | \(-0.865213\pi\) | ||
0.911679 | − | 0.410904i | \(-0.134787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −268.830 | −0.991991 | −0.495995 | − | 0.868325i | \(-0.665197\pi\) | ||||
−0.495995 | + | 0.868325i | \(0.665197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.3290 | + | 146.714i | 0.0524870 | + | 0.537414i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −144.697 | −0.522370 | −0.261185 | − | 0.965289i | \(-0.584113\pi\) | ||||
−0.261185 | + | 0.965289i | \(0.584113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 468.934 | − | 92.4798i | 1.68077 | − | 0.331469i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 189.426i | − | 0.674112i | −0.941485 | − | 0.337056i | \(-0.890569\pi\) | ||
0.941485 | − | 0.337056i | \(-0.109431\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −420.621 | −1.48629 | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||||
−0.743146 | + | 0.669129i | \(0.766667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 302.675i | − | 1.05462i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 288.369 | 0.997818 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.7226 | + | 273.612i | 0.0918302 | + | 0.940249i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 283.828i | − | 0.968696i | −0.874875 | − | 0.484348i | \(-0.839057\pi\) | ||
0.874875 | − | 0.484348i | \(-0.160943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −462.045 | + | 138.923i | −1.55571 | + | 0.467754i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 164.364i | − | 0.549713i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −182.186 | −0.605268 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 347.406 | − | 33.9297i | 1.14656 | − | 0.111979i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 167.979 | 0.547162 | 0.273581 | − | 0.961849i | \(-0.411792\pi\) | ||||
0.273581 | + | 0.961849i | \(0.411792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −53.0938 | − | 543.628i | −0.171825 | − | 1.75931i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 192.970i | 0.620482i | 0.950658 | + | 0.310241i | \(0.100410\pi\) | ||||
−0.950658 | + | 0.310241i | \(0.899590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −161.056 | −0.514555 | −0.257278 | − | 0.966338i | \(-0.582825\pi\) | ||||
−0.257278 | + | 0.966338i | \(0.582825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 514.761i | 1.62385i | 0.583761 | + | 0.811926i | \(0.301581\pi\) | ||||
−0.583761 | + | 0.811926i | \(0.698419\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −99.8096 | −0.312883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 307.024 | − | 29.9858i | 0.956462 | − | 0.0934136i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.1101i | − | 0.0653564i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.9949 | + | 225.206i | 0.0672627 | + | 0.688702i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 55.1064i | − | 0.167497i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −63.7466 | −0.192588 | −0.0962939 | − | 0.995353i | \(-0.530699\pi\) | ||||
−0.0962939 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 457.006 | − | 90.1274i | 1.37239 | − | 0.270653i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 64.2444 | 0.190636 | 0.0953181 | − | 0.995447i | \(-0.469613\pi\) | ||||
0.0953181 | + | 0.995447i | \(0.469613\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −423.754 | + | 41.3863i | −1.25001 | + | 0.122083i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 949.006i | 2.78301i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −348.466 | −1.01594 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 66.1416i | − | 0.190610i | −0.995448 | − | 0.0953049i | \(-0.969617\pi\) | ||
0.995448 | − | 0.0953049i | \(-0.0303826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −188.752 | −0.540837 | −0.270419 | − | 0.962743i | \(-0.587162\pi\) | ||||
−0.270419 | + | 0.962743i | \(0.587162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −85.6006 | − | 284.700i | −0.243876 | − | 0.811110i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 435.927i | 1.23492i | 0.786602 | + | 0.617461i | \(0.211839\pi\) | ||||
−0.786602 | + | 0.617461i | \(0.788161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5805 | + | 1.03335i | −0.0296372 | + | 0.00289454i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 188.255i | 0.524386i | 0.965015 | + | 0.262193i | \(0.0844457\pi\) | ||||
−0.965015 | + | 0.262193i | \(0.915554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 345.773 | 0.957820 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −57.8326 | − | 592.148i | −0.159318 | − | 1.63126i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 276.868 | 0.754409 | 0.377205 | − | 0.926130i | \(-0.376885\pi\) | ||||
0.377205 | + | 0.926130i | \(0.376885\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 118.106 | + | 598.877i | 0.320071 | + | 1.62297i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 165.275i | 0.445486i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 510.098 | 1.36756 | 0.683778 | − | 0.729691i | \(-0.260336\pi\) | ||||
0.683778 | + | 0.729691i | \(0.260336\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 61.4999i | − | 0.163130i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 298.461 | 0.787497 | 0.393748 | − | 0.919218i | \(-0.371178\pi\) | ||||
0.393748 | + | 0.919218i | \(0.371178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.9285 | + | 337.155i | 0.0864266 | + | 0.884922i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 500.548i | 1.30691i | 0.756963 | + | 0.653457i | \(0.226682\pi\) | ||||
−0.756963 | + | 0.653457i | \(0.773318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 360.476 | − | 71.0904i | 0.931462 | − | 0.183696i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 465.726i | − | 1.19724i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) | ||
0.801033 | − | 0.598620i | \(-0.204284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.8534 | 0.0303155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 320.175 | − | 31.2701i | 0.814694 | − | 0.0795678i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 344.998 | 0.869013 | 0.434507 | − | 0.900669i | \(-0.356923\pi\) | ||||
0.434507 | + | 0.900669i | \(0.356923\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.5969 | − | 354.238i | −0.0867091 | − | 0.887815i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 428.755i | 1.06922i | 0.845100 | + | 0.534608i | \(0.179541\pi\) | ||||
−0.845100 | + | 0.534608i | \(0.820459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −584.752 | −1.45100 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 924.866i | 2.27240i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −349.445 | −0.854389 | −0.427194 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427194 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −202.268 | + | 19.7547i | −0.492136 | + | 0.0480648i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 272.639i | − | 0.660143i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.1765 | + | 421.606i | 0.0987447 | + | 1.01105i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 225.745i | − | 0.538770i | −0.963033 | − | 0.269385i | \(-0.913180\pi\) | ||
0.963033 | − | 0.269385i | \(-0.0868205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −138.931 | −0.330003 | −0.165002 | − | 0.986293i | \(-0.552763\pi\) | ||||
−0.165002 | + | 0.986293i | \(0.552763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.5030 | + | 109.034i | 0.0508345 | + | 0.257765i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 436.579 | 1.02243 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 587.477 | − | 57.3764i | 1.36941 | − | 0.133745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 289.802i | 0.672394i | 0.941792 | + | 0.336197i | \(0.109141\pi\) | ||||
−0.941792 | + | 0.336197i | \(0.890859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −53.8425 | −0.124348 | −0.0621738 | − | 0.998065i | \(-0.519803\pi\) | ||||
−0.0621738 | + | 0.998065i | \(0.519803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 396.854i | 0.908133i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −333.179 | −0.758949 | −0.379474 | − | 0.925202i | \(-0.623895\pi\) | ||||
−0.379474 | + | 0.925202i | \(0.623895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 256.814 | − | 50.6471i | 0.582345 | − | 0.114846i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 652.015i | 1.47182i | 0.677081 | + | 0.735909i | \(0.263245\pi\) | ||||
−0.677081 | + | 0.735909i | \(0.736755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 164.467 | − | 16.0628i | 0.367935 | − | 0.0359346i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 115.054i | 0.256245i | 0.991758 | + | 0.128122i | \(0.0408950\pi\) | ||||
−0.991758 | + | 0.128122i | \(0.959105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1211.98 | −2.68731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.3681 | − | 167.593i | −0.0361327 | − | 0.369963i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 138.318 | 0.302666 | 0.151333 | − | 0.988483i | \(-0.451643\pi\) | ||||
0.151333 | + | 0.988483i | \(0.451643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.5315 | − | 6.17321i | 0.0447310 | − | 0.0134493i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 300.475i | − | 0.651789i | −0.945406 | − | 0.325894i | \(-0.894335\pi\) | ||
0.945406 | − | 0.325894i | \(-0.105665\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −91.5721 | −0.197780 | −0.0988899 | − | 0.995098i | \(-0.531529\pi\) | ||||
−0.0988899 | + | 0.995098i | \(0.531529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 308.136i | 0.659821i | 0.944012 | + | 0.329910i | \(0.107019\pi\) | ||||
−0.944012 | + | 0.329910i | \(0.892981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5014 | 0.0287877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 79.9788 | + | 818.903i | 0.169806 | + | 1.73865i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 729.513i | 1.54231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −64.4919 | − | 327.017i | −0.135203 | − | 0.685570i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 218.332i | 0.455808i | 0.973684 | + | 0.227904i | \(0.0731873\pi\) | ||||
−0.973684 | + | 0.227904i | \(0.926813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −569.877 | −1.18478 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 198.905 | − | 19.4262i | 0.411812 | − | 0.0402200i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −538.368 | −1.10548 | −0.552739 | − | 0.833354i | \(-0.686417\pi\) | ||||
−0.552739 | + | 0.833354i | \(0.686417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 75.9108 | + | 777.250i | 0.155237 | + | 1.58947i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 418.223i | − | 0.851777i | −0.904776 | − | 0.425889i | \(-0.859962\pi\) | ||
0.904776 | − | 0.425889i | \(-0.140038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.43515 | 0.00899625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 254.724i | − | 0.512523i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 732.199 | 1.46733 | 0.733667 | − | 0.679510i | \(-0.237807\pi\) | ||||
0.733667 | + | 0.679510i | \(0.237807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 537.291 | − | 52.4749i | 1.07244 | − | 0.104740i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 338.339i | − | 0.672641i | −0.941748 | − | 0.336321i | \(-0.890817\pi\) | ||
0.941748 | − | 0.336321i | \(-0.109183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.9283 | − | 142.612i | −0.0274720 | − | 0.281286i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 864.760i | − | 1.69894i | −0.527637 | − | 0.849470i | \(-0.676922\pi\) | ||
0.527637 | − | 0.849470i | \(-0.323078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 140.436 | 0.274826 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 206.681 | + | 687.401i | 0.402887 | + | 1.33996i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −220.659 | −0.426806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 332.213 | − | 32.4459i | 0.640103 | − | 0.0625162i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 294.647i | − | 0.565541i | −0.959188 | − | 0.282770i | \(-0.908747\pi\) | ||
0.959188 | − | 0.282770i | \(-0.0912534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −613.850 | −1.17371 | −0.586855 | − | 0.809692i | \(-0.699634\pi\) | ||||
−0.586855 | + | 0.809692i | \(0.699634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 42.1702i | − | 0.0800193i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 306.166 | 0.578763 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 106.386 | + | 539.448i | 0.200351 | + | 1.01591i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 746.788i | − | 1.40110i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 232.437 | − | 22.7011i | 0.432843 | − | 0.0422740i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 519.728i | 0.964245i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 188.436 | 0.348311 | 0.174156 | − | 0.984718i | \(-0.444280\pi\) | ||||
0.174156 | + | 0.984718i | \(0.444280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −69.6517 | − | 713.163i | −0.128272 | − | 1.31338i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 637.744 | 1.16589 | 0.582947 | − | 0.812510i | \(-0.301899\pi\) | ||||
0.582947 | + | 0.812510i | \(0.301899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −863.822 | + | 170.357i | −1.57345 | + | 0.310304i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 148.490i | 0.269492i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.64176 | 0.0174354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 77.2307i | 0.138655i | 0.997594 | + | 0.0693274i | \(0.0220853\pi\) | ||||
−0.997594 | + | 0.0693274i | \(0.977915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −449.506 | −0.804125 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13778 | + | 42.3667i | 0.00737572 | + | 0.0755200i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 257.584i | − | 0.457521i | −0.973483 | − | 0.228760i | \(-0.926533\pi\) | ||
0.973483 | − | 0.228760i | \(-0.0734672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 334.412 | − | 137.238i | 0.589791 | − | 0.242042i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 307.483i | − | 0.540392i | −0.962805 | − | 0.270196i | \(-0.912911\pi\) | ||
0.962805 | − | 0.270196i | \(-0.0870886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 384.100 | 0.672679 | 0.336340 | − | 0.941741i | \(-0.390811\pi\) | ||||
0.336340 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −529.227 | + | 51.6874i | −0.923608 | + | 0.0902049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 235.337 | 0.407863 | 0.203932 | − | 0.978985i | \(-0.434628\pi\) | ||||
0.203932 | + | 0.978985i | \(0.434628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −82.8913 | − | 848.724i | −0.143163 | − | 1.46584i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 58.3317i | 0.100399i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 661.801 | 1.13516 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 230.275i | 0.392292i | 0.980575 | + | 0.196146i | \(0.0628426\pi\) | ||||
−0.980575 | + | 0.196146i | \(0.937157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1411.87 | 2.39706 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 729.553 | − | 71.2524i | 1.23444 | − | 0.120562i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1042.09i | − | 1.75731i | −0.477455 | − | 0.878656i | \(-0.658441\pi\) | ||
0.477455 | − | 0.878656i | \(-0.341559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.5827 | − | 220.985i | −0.0361519 | − | 0.370160i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 136.181i | − | 0.227348i | −0.993518 | − | 0.113674i | \(-0.963738\pi\) | ||
0.993518 | − | 0.113674i | \(-0.0362619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 136.625 | 0.227329 | 0.113665 | − | 0.993519i | \(-0.463741\pi\) | ||||
0.113665 | + | 0.993519i | \(0.463741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.7141 | + | 5.26837i | −0.0443020 | + | 0.00873693i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −426.666 | −0.702910 | −0.351455 | − | 0.936205i | \(-0.614313\pi\) | ||||
−0.351455 | + | 0.936205i | \(0.614313\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 74.4240 | − | 7.26868i | 0.122207 | − | 0.0119354i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 135.964i | − | 0.222527i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −665.317 | −1.08535 | −0.542673 | − | 0.839944i | \(-0.682588\pi\) | ||||
−0.542673 | + | 0.839944i | \(0.682588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 826.628i | 1.33975i | 0.742473 | + | 0.669877i | \(0.233653\pi\) | ||||
−0.742473 | + | 0.669877i | \(0.766347\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.8176 | −0.0320155 | −0.0160078 | − | 0.999872i | \(-0.505096\pi\) | ||||
−0.0160078 | + | 0.999872i | \(0.505096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −385.977 | + | 116.052i | −0.621541 | + | 0.186879i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 775.133i | 1.24419i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1418.45 | + | 138.534i | −2.26228 | + | 0.220948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 41.0975i | − | 0.0653378i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 728.156 | 1.15397 | 0.576986 | − | 0.816754i | \(-0.304229\pi\) | ||||
0.576986 | + | 0.816754i | \(0.304229\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.05981 | + | 92.7633i | 0.0143125 | + | 0.146546i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −320.242 | −0.502735 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 99.3955 | + | 504.001i | 0.155548 | + | 0.788734i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 438.969i | − | 0.684819i | −0.939551 | − | 0.342410i | \(-0.888757\pi\) | ||
0.939551 | − | 0.342410i | \(-0.111243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 483.535 | 0.751998 | 0.375999 | − | 0.926620i | \(-0.377300\pi\) | ||||
0.375999 | + | 0.926620i | \(0.377300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 575.687i | − | 0.889780i | −0.895585 | − | 0.444890i | \(-0.853243\pi\) | ||
0.895585 | − | 0.444890i | \(-0.146757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1091.71 | −1.68214 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −69.1119 | − | 707.636i | −0.106163 | − | 1.08700i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 407.885i | − | 0.624633i | −0.949978 | − | 0.312317i | \(-0.898895\pi\) | ||
0.949978 | − | 0.312317i | \(-0.101105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −277.869 | + | 54.7993i | −0.422936 | + | 0.0834084i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 187.060i | − | 0.283854i | −0.989877 | − | 0.141927i | \(-0.954670\pi\) | ||
0.989877 | − | 0.141927i | \(-0.0453298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 483.965 | 0.732171 | 0.366085 | − | 0.930581i | \(-0.380698\pi\) | ||||
0.366085 | + | 0.930581i | \(0.380698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.1052 | + | 2.54959i | −0.0393744 | + | 0.00384553i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −83.3775 | −0.125004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.2869 | + | 299.868i | 0.0437771 | + | 0.448233i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1748.16i | − | 2.60531i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −480.449 | −0.713891 | −0.356945 | − | 0.934125i | \(-0.616182\pi\) | ||||
−0.356945 | + | 0.934125i | \(0.616182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1245.12i | − | 1.83918i | −0.392881 | − | 0.919589i | \(-0.628522\pi\) | ||
0.392881 | − | 0.919589i | \(-0.371478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 408.951 | 0.602284 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1042.39 | + | 101.806i | −1.53068 | + | 0.149495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 118.409i | 0.173366i | 0.996236 | + | 0.0866832i | \(0.0276268\pi\) | ||||
−0.996236 | + | 0.0866832i | \(0.972373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.1177 | − | 492.677i | −0.0700404 | − | 0.717143i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 407.784i | 0.591848i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 481.257 | 0.696465 | 0.348232 | − | 0.937408i | \(-0.386782\pi\) | ||||
0.348232 | + | 0.937408i | \(0.386782\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 138.868 | + | 704.152i | 0.200387 | + | 1.01609i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 53.8556 | 0.0772678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −372.626 | + | 36.3928i | −0.533084 | + | 0.0520641i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 644.879i | 0.919941i | 0.887934 | + | 0.459971i | \(0.152140\pi\) | ||||
−0.887934 | + | 0.459971i | \(0.847860\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1375.96 | 1.95726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 519.246i | − | 0.734436i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −534.801 | −0.754303 | −0.377151 | − | 0.926152i | \(-0.623096\pi\) | ||||
−0.377151 | + | 0.926152i | \(0.623096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.0774 | + | 3.76230i | −0.0268317 | + | 0.00529156i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 792.767i | 1.11188i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 184.618 | − | 18.0309i | 0.257487 | − | 0.0251476i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 891.507i | 1.23993i | 0.784631 | + | 0.619963i | \(0.212852\pi\) | ||||
−0.784631 | + | 0.619963i | \(0.787148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −812.526 | −1.12694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.657741 | + | 6.73461i | 0.000909739 | + | 0.00931481i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −720.024 | −0.990405 | −0.495202 | − | 0.868778i | \(-0.664906\pi\) | ||||
−0.495202 | + | 0.868778i | \(0.664906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −608.121 | + | 402.032i | −0.834185 | + | 0.551484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 32.4167i | − | 0.0443458i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −953.335 | −1.30059 | −0.650296 | − | 0.759681i | \(-0.725355\pi\) | ||||
−0.650296 | + | 0.759681i | \(0.725355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 54.0627i | − | 0.0733552i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −615.723 | −0.833185 | −0.416592 | − | 0.909093i | \(-0.636776\pi\) | ||||
−0.416592 | + | 0.909093i | \(0.636776\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −85.3609 | − | 874.010i | −0.115197 | − | 1.17950i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 377.743i | 0.508403i | 0.967151 | + | 0.254201i | \(0.0818126\pi\) | ||||
−0.967151 | + | 0.254201i | \(0.918187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.7615 | − | 115.416i | −0.0304706 | − | 0.154506i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 458.890i | − | 0.612670i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −735.578 | −0.979465 | −0.489733 | − | 0.871873i | \(-0.662906\pi\) | ||||
−0.489733 | + | 0.871873i | \(0.662906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −325.430 | + | 31.7834i | −0.432178 | + | 0.0422090i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −921.601 | −1.21744 | −0.608719 | − | 0.793386i | \(-0.708316\pi\) | ||||
−0.608719 | + | 0.793386i | \(0.708316\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −77.7871 | − | 796.462i | −0.102486 | − | 1.04936i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 240.158i | 0.315582i | 0.987473 | + | 0.157791i | \(0.0504372\pi\) | ||||
−0.987473 | + | 0.157791i | \(0.949563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 336.601 | 0.441154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 672.682i | − | 0.877029i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.79672 | −0.00623760 | −0.00311880 | − | 0.999995i | \(-0.500993\pi\) | ||||
−0.00311880 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −93.9522 | + | 9.17592i | −0.121858 | + | 0.0119013i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 140.044i | − | 0.181170i | −0.995889 | − | 0.0905850i | \(-0.971126\pi\) | ||
0.995889 | − | 0.0905850i | \(-0.0288737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −67.3539 | − | 689.636i | −0.0866845 | − | 0.887562i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1803.10i | 2.31464i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1019.97 | −1.30598 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −144.420 | + | 43.4228i | −0.184445 | + | 0.0554570i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 649.685 | 0.825520 | 0.412760 | − | 0.910840i | \(-0.364565\pi\) | ||||
0.412760 | + | 0.910840i | \(0.364565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 702.230 | − | 68.5838i | 0.890025 | − | 0.0869250i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 633.358i | 0.800706i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1077.17 | 1.35835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 547.802i | − | 0.687329i | −0.939092 | − | 0.343665i | \(-0.888332\pi\) | ||
0.939092 | − | 0.343665i | \(-0.111668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.80522 | 0.0122719 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −302.463 | − | 1533.69i | −0.377607 | − | 1.91472i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 562.338i | − | 0.700296i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 660.059 | − | 64.4652i | 0.817916 | − | 0.0798825i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 719.685i | 0.889598i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 775.519 | 0.956251 | 0.478125 | − | 0.878292i | \(-0.341316\pi\) | ||||
0.478125 | + | 0.878292i | \(0.341316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −78.3934 | − | 802.669i | −0.0964248 | − | 0.987293i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1085.32 | 1.32842 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −433.879 | + | 85.5666i | −0.529767 | + | 0.104477i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1383.11i | − | 1.68466i | −0.538960 | − | 0.842331i | \(-0.681183\pi\) | ||
0.538960 | − | 0.842331i | \(-0.318817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 536.474 | 0.651852 | 0.325926 | − | 0.945395i | \(-0.394324\pi\) | ||||
0.325926 | + | 0.945395i | \(0.394324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1652.28i | − | 1.99792i | −0.0455686 | − | 0.998961i | \(-0.514510\pi\) | ||
0.0455686 | − | 0.998961i | \(-0.485490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −999.416 | −1.20557 | −0.602784 | − | 0.797904i | \(-0.705942\pi\) | ||||
−0.602784 | + | 0.797904i | \(0.705942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.1950 | − | 432.034i | −0.0507761 | − | 0.519897i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 23.0947i | − | 0.0277247i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 412.872 | + | 1373.17i | 0.493276 | + | 1.64059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1394.04i | − | 1.66155i | −0.556611 | − | 0.830773i | \(-0.687899\pi\) | ||
0.556611 | − | 0.830773i | \(-0.312101\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 809.803 | 0.962905 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 565.586 | − | 55.2384i | 0.670920 | − | 0.0655260i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −885.045 | −1.04492 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −122.657 | − | 1255.89i | −0.144473 | − | 1.47925i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 772.602i | 0.907875i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1293.04 | 1.51587 | 0.757935 | − | 0.652330i | \(-0.226208\pi\) | ||||
0.757935 | + | 0.652330i | \(0.226208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1513.48i | − | 1.76602i | −0.469357 | − | 0.883008i | \(-0.655514\pi\) | ||
0.469357 | − | 0.883008i | \(-0.344486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −767.814 | −0.893846 | −0.446923 | − | 0.894572i | \(-0.647480\pi\) | ||||
−0.446923 | + | 0.894572i | \(0.647480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 903.724 | − | 88.2629i | 1.04962 | − | 0.102512i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.2279i | 0.0338677i | 0.999857 | + | 0.0169339i | \(0.00539048\pi\) | ||||
−0.999857 | + | 0.0169339i | \(0.994610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 84.0914 | + | 861.012i | 0.0969913 | + | 0.993093i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 38.6078i | − | 0.0444279i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3120 | 0.0382457 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −809.157 | + | 159.576i | −0.926870 | + | 0.182791i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1070.98 | 1.22119 | 0.610595 | − | 0.791943i | \(-0.290930\pi\) | ||||
0.610595 | + | 0.791943i | \(0.290930\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 847.452 | − | 82.7671i | 0.964109 | − | 0.0941605i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 489.535i | − | 0.555659i | −0.960630 | − | 0.277829i | \(-0.910385\pi\) | ||
0.960630 | − | 0.277829i | \(-0.0896150\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −742.175 | −0.840515 | −0.420257 | − | 0.907405i | \(-0.638060\pi\) | ||||
−0.420257 | + | 0.907405i | \(0.638060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1441.82i | 1.62550i | 0.582612 | + | 0.812751i | \(0.302031\pi\) | ||||
−0.582612 | + | 0.812751i | \(0.697969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 503.924 | 0.566844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −549.533 | − | 1339.06i | −0.616759 | − | 1.50287i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 328.282i | 0.367617i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 490.758 | − | 47.9303i | 0.547110 | − | 0.0534340i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 296.629i | 0.329954i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.4079 | −0.0326392 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.1272 | − | 543.969i | −0.0588341 | − | 0.602402i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −352.397 | −0.388531 | −0.194265 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 202.614 | + | 1027.39i | 0.222898 | + | 1.13024i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 184.505i | − | 0.202531i | −0.994859 | − | 0.101265i | \(-0.967711\pi\) | ||
0.994859 | − | 0.101265i | \(-0.0322891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 233.574 | 0.255831 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 478.545i | − | 0.521859i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −666.062 | −0.724769 | −0.362384 | − | 0.932029i | \(-0.618037\pi\) | ||||
−0.362384 | + | 0.932029i | \(0.618037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.9843 | + | 501.550i | 0.0531860 | + | 0.544571i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 628.479i | − | 0.680909i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1607.68 | − | 317.055i | 1.73428 | − | 0.342022i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 957.310i | 1.03047i | 0.857048 | + | 0.515237i | \(0.172296\pi\) | ||||
−0.857048 | + | 0.515237i | \(0.827704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 773.218 | 0.830524 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −576.169 | + | 56.2720i | −0.617544 | + | 0.0603130i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1108.63 | −1.18317 | −0.591585 | − | 0.806243i | \(-0.701498\pi\) | ||||
−0.591585 | + | 0.806243i | \(0.701498\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.9655 | − | 480.879i | −0.0500165 | − | 0.512119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4523i | 0.0536157i | 0.999641 | + | 0.0268078i | \(0.00853422\pi\) | ||||
−0.999641 | + | 0.0268078i | \(0.991466\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1012.45 | −1.07364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 883.676i | 0.933132i | 0.884486 | + | 0.466566i | \(0.154509\pi\) | ||||
−0.884486 | + | 0.466566i | \(0.845491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 346.497 | 0.365118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1536.97 | + | 150.109i | −1.61616 | + | 0.157844i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1238.78i | − | 1.29988i | −0.759987 | − | 0.649938i | \(-0.774795\pi\) | ||
0.759987 | − | 0.649938i | \(-0.225205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.1055 | − | 298.011i | −0.0304132 | − | 0.311401i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 302.317i | 0.315242i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1859.39 | 1.93485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 179.063 | + | 907.967i | 0.185943 | + | 0.942852i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1221.47 | 1.26315 | 0.631575 | − | 0.775314i | \(-0.282409\pi\) | ||||
0.631575 | + | 0.775314i | \(0.282409\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.0304 | − | 6.15592i | 0.0650469 | − | 0.00635286i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1142.08i | − | 1.17619i | −0.808792 | − | 0.588095i | \(-0.799878\pi\) | ||
0.808792 | − | 0.588095i | \(-0.200122\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 630.148 | 0.647634 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 364.738i | 0.373324i | 0.982424 | + | 0.186662i | \(0.0597669\pi\) | ||||
−0.982424 | + | 0.186662i | \(0.940233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3103.81 | 3.17039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −666.004 | + | 131.344i | −0.678903 | + | 0.133888i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 40.0459i | − | 0.0407384i | −0.999793 | − | 0.0203692i | \(-0.993516\pi\) | ||
0.999793 | − | 0.0203692i | \(-0.00648417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 164.536 | − | 16.0696i | 0.166703 | − | 0.0162812i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 609.410i | 0.616188i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 910.307 | 0.918574 | 0.459287 | − | 0.888288i | \(-0.348105\pi\) | ||||
0.459287 | + | 0.888288i | \(0.348105\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.5891 | − | 190.334i | −0.0187202 | − | 0.191676i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −358.437 | −0.359516 | −0.179758 | − | 0.983711i | \(-0.557531\pi\) | ||||
−0.179758 | + | 0.983711i | \(0.557531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 402.369 | + | 1338.24i | 0.402772 | + | 1.33958i |
(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 | 1200.3.l.x.401.6 | 8 | ||
3.2 | odd | 2 | inner | 1200.3.l.x.401.5 | 8 | ||
4.3 | odd | 2 | 600.3.l.f.401.3 | 8 | |||
5.2 | odd | 4 | 1200.3.c.m.449.15 | 16 | |||
5.3 | odd | 4 | 1200.3.c.m.449.2 | 16 | |||
5.4 | even | 2 | 240.3.l.d.161.3 | 8 | |||
12.11 | even | 2 | 600.3.l.f.401.4 | 8 | |||
15.2 | even | 4 | 1200.3.c.m.449.1 | 16 | |||
15.8 | even | 4 | 1200.3.c.m.449.16 | 16 | |||
15.14 | odd | 2 | 240.3.l.d.161.4 | 8 | |||
20.3 | even | 4 | 600.3.c.d.449.15 | 16 | |||
20.7 | even | 4 | 600.3.c.d.449.2 | 16 | |||
20.19 | odd | 2 | 120.3.l.a.41.6 | yes | 8 | ||
40.19 | odd | 2 | 960.3.l.h.641.3 | 8 | |||
40.29 | even | 2 | 960.3.l.g.641.6 | 8 | |||
60.23 | odd | 4 | 600.3.c.d.449.1 | 16 | |||
60.47 | odd | 4 | 600.3.c.d.449.16 | 16 | |||
60.59 | even | 2 | 120.3.l.a.41.5 | ✓ | 8 | ||
120.29 | odd | 2 | 960.3.l.g.641.5 | 8 | |||
120.59 | even | 2 | 960.3.l.h.641.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.5 | ✓ | 8 | 60.59 | even | 2 | ||
120.3.l.a.41.6 | yes | 8 | 20.19 | odd | 2 | ||
240.3.l.d.161.3 | 8 | 5.4 | even | 2 | |||
240.3.l.d.161.4 | 8 | 15.14 | odd | 2 | |||
600.3.c.d.449.1 | 16 | 60.23 | odd | 4 | |||
600.3.c.d.449.2 | 16 | 20.7 | even | 4 | |||
600.3.c.d.449.15 | 16 | 20.3 | even | 4 | |||
600.3.c.d.449.16 | 16 | 60.47 | odd | 4 | |||
600.3.l.f.401.3 | 8 | 4.3 | odd | 2 | |||
600.3.l.f.401.4 | 8 | 12.11 | even | 2 | |||
960.3.l.g.641.5 | 8 | 120.29 | odd | 2 | |||
960.3.l.g.641.6 | 8 | 40.29 | even | 2 | |||
960.3.l.h.641.3 | 8 | 40.19 | odd | 2 | |||
960.3.l.h.641.4 | 8 | 120.59 | even | 2 | |||
1200.3.c.m.449.1 | 16 | 15.2 | even | 4 | |||
1200.3.c.m.449.2 | 16 | 5.3 | odd | 4 | |||
1200.3.c.m.449.15 | 16 | 5.2 | odd | 4 | |||
1200.3.c.m.449.16 | 16 | 15.8 | even | 4 | |||
1200.3.l.x.401.5 | 8 | 3.2 | odd | 2 | inner | ||
1200.3.l.x.401.6 | 8 | 1.1 | even | 1 | trivial |