Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.78 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.7 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.58466i | 1.79233i | 0.443722 | + | 0.896164i | \(0.353658\pi\) | ||||
−0.443722 | + | 0.896164i | \(0.646342\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.84977 | −2.21244 | ||||||||
\(5\) | 7.20639i | 1.44128i | 0.693311 | + | 0.720639i | \(0.256151\pi\) | ||||
−0.693311 | + | 0.720639i | \(0.743849\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.70987 | 0.672839 | 0.336420 | − | 0.941712i | \(-0.390784\pi\) | ||||
0.336420 | + | 0.941712i | \(0.390784\pi\) | |||||||
\(8\) | − 17.3848i | − 2.17310i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −25.8324 | −2.58324 | ||||||||
\(11\) | − 15.5657i | − 1.41506i | −0.706683 | − | 0.707531i | \(-0.749809\pi\) | ||||
0.706683 | − | 0.707531i | \(-0.250191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.78351 | −0.752578 | −0.376289 | − | 0.926502i | \(-0.622800\pi\) | ||||
−0.376289 | + | 0.926502i | \(0.622800\pi\) | |||||||
\(14\) | 16.8833i | 1.20595i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 26.9194 | 1.68246 | ||||||||
\(17\) | − 23.5044i | − 1.38261i | −0.722562 | − | 0.691306i | \(-0.757036\pi\) | ||||
0.722562 | − | 0.691306i | \(-0.242964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.7089 | 1.35310 | 0.676550 | − | 0.736397i | \(-0.263474\pi\) | ||||
0.676550 | + | 0.736397i | \(0.263474\pi\) | |||||||
\(20\) | − 63.7749i | − 3.18874i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 55.7976 | 2.53626 | ||||||||
\(23\) | 5.95651i | 0.258979i | 0.991581 | + | 0.129489i | \(0.0413338\pi\) | ||||
−0.991581 | + | 0.129489i | \(0.958666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.9320 | −1.07728 | ||||||||
\(26\) | − 35.0705i | − 1.34887i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −41.6813 | −1.48862 | ||||||||
\(29\) | − 53.9788i | − 1.86134i | −0.365861 | − | 0.930669i | \(-0.619226\pi\) | ||||
0.365861 | − | 0.930669i | \(-0.380774\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8286 | 0.349310 | 0.174655 | − | 0.984630i | \(-0.444119\pi\) | ||||
0.174655 | + | 0.984630i | \(0.444119\pi\) | |||||||
\(32\) | 26.9577i | 0.842427i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 84.2553 | 2.47810 | ||||||||
\(35\) | 33.9412i | 0.969748i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −62.1323 | −1.67925 | −0.839625 | − | 0.543166i | \(-0.817225\pi\) | ||||
−0.839625 | + | 0.543166i | \(0.817225\pi\) | |||||||
\(38\) | 92.1576i | 2.42520i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 125.281 | 3.13204 | ||||||||
\(41\) | − 33.5546i | − 0.818405i | −0.912444 | − | 0.409202i | \(-0.865807\pi\) | ||||
0.912444 | − | 0.409202i | \(-0.134193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 77.7688 | 1.80858 | 0.904288 | − | 0.426922i | \(-0.140402\pi\) | ||||
0.904288 | + | 0.426922i | \(0.140402\pi\) | |||||||
\(44\) | 137.753i | 3.13074i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.3520 | −0.464175 | ||||||||
\(47\) | − 59.3622i | − 1.26303i | −0.775365 | − | 0.631513i | \(-0.782434\pi\) | ||||
0.775365 | − | 0.631513i | \(-0.217566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.8171 | −0.547287 | ||||||||
\(50\) | − 96.5421i | − 1.93084i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 86.5819 | 1.66504 | ||||||||
\(53\) | − 88.7794i | − 1.67508i | −0.546374 | − | 0.837542i | \(-0.683992\pi\) | ||||
0.546374 | − | 0.837542i | \(-0.316008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 112.172 | 2.03950 | ||||||||
\(56\) | − 81.8801i | − 1.46214i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 193.496 | 3.33613 | ||||||||
\(59\) | 14.4209i | 0.244421i | 0.992504 | + | 0.122211i | \(0.0389983\pi\) | ||||
−0.992504 | + | 0.122211i | \(0.961002\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.6267 | −1.28896 | −0.644481 | − | 0.764620i | \(-0.722927\pi\) | ||||
−0.644481 | + | 0.764620i | \(0.722927\pi\) | |||||||
\(62\) | 38.8169i | 0.626079i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.0435 | 0.172555 | ||||||||
\(65\) | − 70.5038i | − 1.08467i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18.8207 | −0.280906 | −0.140453 | − | 0.990087i | \(-0.544856\pi\) | ||||
−0.140453 | + | 0.990087i | \(0.544856\pi\) | |||||||
\(68\) | 208.009i | 3.05895i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −121.668 | −1.73811 | ||||||||
\(71\) | 75.8330i | 1.06807i | 0.845462 | + | 0.534035i | \(0.179325\pi\) | ||||
−0.845462 | + | 0.534035i | \(0.820675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.6238 | −0.624984 | −0.312492 | − | 0.949920i | \(-0.601164\pi\) | ||||
−0.312492 | + | 0.949920i | \(0.601164\pi\) | |||||||
\(74\) | − 222.723i | − 3.00977i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −227.518 | −2.99366 | ||||||||
\(77\) | − 73.3124i | − 0.952109i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.3446 | −0.713222 | −0.356611 | − | 0.934253i | \(-0.616068\pi\) | ||||
−0.356611 | + | 0.934253i | \(0.616068\pi\) | |||||||
\(80\) | 193.991i | 2.42489i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 120.282 | 1.46685 | ||||||||
\(83\) | − 128.210i | − 1.54470i | −0.635199 | − | 0.772348i | \(-0.719082\pi\) | ||||
0.635199 | − | 0.772348i | \(-0.280918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 169.382 | 1.99273 | ||||||||
\(86\) | 278.775i | 3.24156i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −270.606 | −3.07506 | ||||||||
\(89\) | 70.1992i | 0.788756i | 0.918948 | + | 0.394378i | \(0.129040\pi\) | ||||
−0.918948 | + | 0.394378i | \(0.870960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −46.0791 | −0.506364 | ||||||||
\(92\) | − 52.7137i | − 0.572975i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 212.793 | 2.26376 | ||||||||
\(95\) | 185.268i | 1.95019i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.59545 | −0.0473758 | −0.0236879 | − | 0.999719i | \(-0.507541\pi\) | ||||
−0.0236879 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(98\) | − 96.1301i | − 0.980919i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 238.342 | 2.38342 | ||||||||
\(101\) | 119.961i | 1.18774i | 0.804562 | + | 0.593868i | \(0.202400\pi\) | ||||
−0.804562 | + | 0.593868i | \(0.797600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −158.473 | −1.53858 | −0.769289 | − | 0.638901i | \(-0.779389\pi\) | ||||
−0.769289 | + | 0.638901i | \(0.779389\pi\) | |||||||
\(104\) | 170.084i | 1.63542i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 318.244 | 3.00230 | ||||||||
\(107\) | 158.986i | 1.48585i | 0.669372 | + | 0.742927i | \(0.266563\pi\) | ||||
−0.669372 | + | 0.742927i | \(0.733437\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 58.4012 | 0.535790 | 0.267895 | − | 0.963448i | \(-0.413672\pi\) | ||||
0.267895 | + | 0.963448i | \(0.413672\pi\) | |||||||
\(110\) | 402.099i | 3.65545i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 126.787 | 1.13203 | ||||||||
\(113\) | 80.9446i | 0.716324i | 0.933659 | + | 0.358162i | \(0.116596\pi\) | ||||
−0.933659 | + | 0.358162i | \(0.883404\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.9249 | −0.373260 | ||||||||
\(116\) | 477.700i | 4.11811i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −51.6938 | −0.438083 | ||||||||
\(119\) | − 110.703i | − 0.930276i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −121.290 | −1.00240 | ||||||||
\(122\) | − 281.850i | − 2.31025i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −95.8308 | −0.772829 | ||||||||
\(125\) | − 13.9230i | − 0.111384i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2694 | 0.0887357 | ||||||||
\(128\) | 147.418i | 1.15170i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 252.732 | 1.94409 | ||||||||
\(131\) | − 17.1308i | − 0.130770i | −0.997860 | − | 0.0653848i | \(-0.979173\pi\) | ||||
0.997860 | − | 0.0653848i | \(-0.0208275\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 121.086 | 0.910419 | ||||||||
\(134\) | − 67.4659i | − 0.503477i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −408.619 | −3.00455 | ||||||||
\(137\) | 28.8275i | 0.210420i | 0.994450 | + | 0.105210i | \(0.0335515\pi\) | ||||
−0.994450 | + | 0.105210i | \(0.966449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25.6315 | 0.184399 | 0.0921997 | − | 0.995741i | \(-0.470610\pi\) | ||||
0.0921997 | + | 0.995741i | \(0.470610\pi\) | |||||||
\(140\) | − 300.372i | − 2.14551i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −271.836 | −1.91433 | ||||||||
\(143\) | 152.287i | 1.06494i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 388.992 | 2.68271 | ||||||||
\(146\) | − 163.546i | − 1.12018i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 549.856 | 3.71525 | ||||||||
\(149\) | − 60.3128i | − 0.404784i | −0.979305 | − | 0.202392i | \(-0.935128\pi\) | ||||
0.979305 | − | 0.202392i | \(-0.0648715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 31.2208 | 0.206760 | 0.103380 | − | 0.994642i | \(-0.467034\pi\) | ||||
0.103380 | + | 0.994642i | \(0.467034\pi\) | |||||||
\(152\) | − 446.943i | − 2.94042i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 262.800 | 1.70649 | ||||||||
\(155\) | 78.0352i | 0.503453i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −58.7863 | −0.374435 | −0.187218 | − | 0.982318i | \(-0.559947\pi\) | ||||
−0.187218 | + | 0.982318i | \(0.559947\pi\) | |||||||
\(158\) | − 201.976i | − 1.27833i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −194.267 | −1.21417 | ||||||||
\(161\) | 28.0544i | 0.174251i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −97.1285 | −0.595881 | −0.297940 | − | 0.954585i | \(-0.596300\pi\) | ||||
−0.297940 | + | 0.954585i | \(0.596300\pi\) | |||||||
\(164\) | 296.950i | 1.81067i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 459.588 | 2.76860 | ||||||||
\(167\) | − 147.196i | − 0.881415i | −0.897651 | − | 0.440707i | \(-0.854728\pi\) | ||||
0.897651 | − | 0.440707i | \(-0.145272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −73.2829 | −0.433627 | ||||||||
\(170\) | 607.176i | 3.57162i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −688.236 | −4.00137 | ||||||||
\(173\) | 37.9424i | 0.219320i | 0.993969 | + | 0.109660i | \(0.0349763\pi\) | ||||
−0.993969 | + | 0.109660i | \(0.965024\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −126.846 | −0.724837 | ||||||||
\(176\) | − 419.018i | − 2.38079i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −251.640 | −1.41371 | ||||||||
\(179\) | − 220.858i | − 1.23384i | −0.787024 | − | 0.616922i | \(-0.788379\pi\) | ||||
0.787024 | − | 0.616922i | \(-0.211621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 136.292 | 0.752996 | 0.376498 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376498 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(182\) | − 165.178i | − 0.907571i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 103.553 | 0.562785 | ||||||||
\(185\) | − 447.749i | − 2.42027i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −365.862 | −1.95648 | ||||||||
\(188\) | 525.342i | 2.79437i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −664.124 | −3.49539 | ||||||||
\(191\) | − 202.812i | − 1.06185i | −0.847420 | − | 0.530923i | \(-0.821845\pi\) | ||||
0.847420 | − | 0.530923i | \(-0.178155\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 193.960 | 1.00497 | 0.502486 | − | 0.864585i | \(-0.332419\pi\) | ||||
0.502486 | + | 0.864585i | \(0.332419\pi\) | |||||||
\(194\) | − 16.4731i | − 0.0849130i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 237.325 | 1.21084 | ||||||||
\(197\) | − 266.715i | − 1.35388i | −0.736036 | − | 0.676942i | \(-0.763305\pi\) | ||||
0.736036 | − | 0.676942i | \(-0.236695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 160.272 | 0.805388 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(200\) | 468.207i | 2.34104i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −430.020 | −2.12881 | ||||||||
\(203\) | − 254.233i | − 1.25238i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 241.807 | 1.17955 | ||||||||
\(206\) | − 568.073i | − 2.75764i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −263.366 | −1.26618 | ||||||||
\(209\) | − 400.176i | − 1.91472i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −210.891 | −0.999483 | −0.499741 | − | 0.866175i | \(-0.666572\pi\) | ||||
−0.499741 | + | 0.866175i | \(0.666572\pi\) | |||||||
\(212\) | 785.677i | 3.70603i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −569.912 | −2.66314 | ||||||||
\(215\) | 560.432i | 2.60666i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 51.0014 | 0.235030 | ||||||||
\(218\) | 209.348i | 0.960313i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −992.699 | −4.51227 | ||||||||
\(221\) | 229.956i | 1.04052i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 392.407 | 1.75967 | 0.879835 | − | 0.475279i | \(-0.157653\pi\) | ||||
0.879835 | + | 0.475279i | \(0.157653\pi\) | |||||||
\(224\) | 126.967i | 0.566818i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −290.159 | −1.28389 | ||||||||
\(227\) | 22.0499i | 0.0971360i | 0.998820 | + | 0.0485680i | \(0.0154658\pi\) | ||||
−0.998820 | + | 0.0485680i | \(0.984534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −263.211 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(230\) | − 153.871i | − 0.669005i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −938.410 | −4.04487 | ||||||||
\(233\) | − 129.088i | − 0.554025i | −0.960866 | − | 0.277013i | \(-0.910656\pi\) | ||||
0.960866 | − | 0.277013i | \(-0.0893444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 427.787 | 1.82037 | ||||||||
\(236\) | − 127.621i | − 0.540768i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 396.832 | 1.66736 | ||||||||
\(239\) | − 289.053i | − 1.20943i | −0.796443 | − | 0.604713i | \(-0.793288\pi\) | ||||
0.796443 | − | 0.604713i | \(-0.206712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −104.175 | −0.432260 | −0.216130 | − | 0.976365i | \(-0.569344\pi\) | ||||
−0.216130 | + | 0.976365i | \(0.569344\pi\) | |||||||
\(242\) | − 434.784i | − 1.79663i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 695.829 | 2.85176 | ||||||||
\(245\) | − 193.254i | − 0.788793i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −251.523 | −1.01831 | ||||||||
\(248\) | − 188.253i | − 0.759085i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 49.9091 | 0.199636 | ||||||||
\(251\) | 440.383i | 1.75451i | 0.480023 | + | 0.877256i | \(0.340628\pi\) | ||||
−0.480023 | + | 0.877256i | \(0.659372\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 92.7170 | 0.366470 | ||||||||
\(254\) | 40.3970i | 0.159043i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −484.269 | −1.89167 | ||||||||
\(257\) | 104.246i | 0.405628i | 0.979217 | + | 0.202814i | \(0.0650087\pi\) | ||||
−0.979217 | + | 0.202814i | \(0.934991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −292.635 | −1.12987 | ||||||||
\(260\) | 623.942i | 2.39978i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 61.4082 | 0.234382 | ||||||||
\(263\) | − 106.847i | − 0.406262i | −0.979152 | − | 0.203131i | \(-0.934888\pi\) | ||||
0.979152 | − | 0.203131i | \(-0.0651118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 639.779 | 2.41426 | ||||||||
\(266\) | 434.051i | 1.63177i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 166.559 | 0.621490 | ||||||||
\(269\) | − 280.299i | − 1.04200i | −0.853556 | − | 0.521001i | \(-0.825559\pi\) | ||||
0.853556 | − | 0.521001i | \(-0.174441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.5309 | 0.0942100 | 0.0471050 | − | 0.998890i | \(-0.485000\pi\) | ||||
0.0471050 | + | 0.998890i | \(0.485000\pi\) | |||||||
\(272\) | − 632.724i | − 2.32619i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −103.337 | −0.377142 | ||||||||
\(275\) | 419.215i | 1.52442i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 281.436 | 1.01602 | 0.508008 | − | 0.861352i | \(-0.330382\pi\) | ||||
0.508008 | + | 0.861352i | \(0.330382\pi\) | |||||||
\(278\) | 91.8802i | 0.330504i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 590.060 | 2.10736 | ||||||||
\(281\) | − 521.602i | − 1.85623i | −0.372289 | − | 0.928117i | \(-0.621427\pi\) | ||||
0.372289 | − | 0.928117i | \(-0.378573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 219.479 | 0.775543 | 0.387771 | − | 0.921756i | \(-0.373245\pi\) | ||||
0.387771 | + | 0.921756i | \(0.373245\pi\) | |||||||
\(284\) | − 671.105i | − 2.36305i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −545.897 | −1.90873 | ||||||||
\(287\) | − 158.038i | − 0.550655i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −263.457 | −0.911616 | ||||||||
\(290\) | 1394.40i | 4.80829i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 403.760 | 1.38274 | ||||||||
\(293\) | 122.921i | 0.419524i | 0.977752 | + | 0.209762i | \(0.0672689\pi\) | ||||
−0.977752 | + | 0.209762i | \(0.932731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −103.922 | −0.352279 | ||||||||
\(296\) | 1080.16i | 3.64917i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 216.201 | 0.725506 | ||||||||
\(299\) | − 58.2755i | − 0.194901i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 366.281 | 1.21688 | ||||||||
\(302\) | 111.916i | 0.370582i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 692.068 | 2.27654 | ||||||||
\(305\) | − 566.615i | − 1.85775i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 358.046 | 1.16627 | 0.583136 | − | 0.812375i | \(-0.301825\pi\) | ||||
0.583136 | + | 0.812375i | \(0.301825\pi\) | |||||||
\(308\) | 648.798i | 2.10649i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −279.730 | −0.902353 | ||||||||
\(311\) | 101.682i | 0.326953i | 0.986547 | + | 0.163476i | \(0.0522707\pi\) | ||||
−0.986547 | + | 0.163476i | \(0.947729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −113.540 | −0.362747 | −0.181374 | − | 0.983414i | \(-0.558054\pi\) | ||||
−0.181374 | + | 0.983414i | \(0.558054\pi\) | |||||||
\(314\) | − 210.729i | − 0.671111i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 498.637 | 1.57796 | ||||||||
\(317\) | 563.141i | 1.77647i | 0.459389 | + | 0.888235i | \(0.348068\pi\) | ||||
−0.459389 | + | 0.888235i | \(0.651932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −840.217 | −2.63391 | ||||||||
\(320\) | 79.5838i | 0.248699i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −100.565 | −0.312315 | ||||||||
\(323\) | − 604.272i | − 1.87081i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 263.490 | 0.810738 | ||||||||
\(326\) | − 348.173i | − 1.06801i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −583.339 | −1.77847 | ||||||||
\(329\) | − 279.589i | − 0.849814i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 248.907 | 0.751985 | 0.375993 | − | 0.926623i | \(-0.377302\pi\) | ||||
0.375993 | + | 0.926623i | \(0.377302\pi\) | |||||||
\(332\) | 1134.63i | 3.41755i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 527.648 | 1.57979 | ||||||||
\(335\) | − 135.630i | − 0.404864i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 81.4574 | 0.241713 | 0.120857 | − | 0.992670i | \(-0.461436\pi\) | ||||
0.120857 | + | 0.992670i | \(0.461436\pi\) | |||||||
\(338\) | − 262.694i | − 0.777201i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1498.99 | −4.40880 | ||||||||
\(341\) | − 168.555i | − 0.494295i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −357.089 | −1.04108 | ||||||||
\(344\) | − 1351.99i | − 3.93021i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −136.011 | −0.393094 | ||||||||
\(347\) | − 94.2754i | − 0.271687i | −0.990730 | − | 0.135844i | \(-0.956626\pi\) | ||||
0.990730 | − | 0.135844i | \(-0.0433745\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −544.452 | −1.56003 | −0.780017 | − | 0.625759i | \(-0.784789\pi\) | ||||
−0.780017 | + | 0.625759i | \(0.784789\pi\) | |||||||
\(350\) | − 454.701i | − 1.29915i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 419.614 | 1.19209 | ||||||||
\(353\) | 420.122i | 1.19015i | 0.803671 | + | 0.595073i | \(0.202877\pi\) | ||||
−0.803671 | + | 0.595073i | \(0.797123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −546.482 | −1.53939 | ||||||||
\(356\) | − 621.247i | − 1.74508i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 791.701 | 2.21145 | ||||||||
\(359\) | − 381.254i | − 1.06199i | −0.847375 | − | 0.530995i | \(-0.821818\pi\) | ||||
0.847375 | − | 0.530995i | \(-0.178182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 299.947 | 0.830879 | ||||||||
\(362\) | 488.561i | 1.34962i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 407.790 | 1.12030 | ||||||||
\(365\) | − 328.783i | − 0.900775i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.78670 | 0.0266668 | 0.0133334 | − | 0.999911i | \(-0.495756\pi\) | ||||
0.0133334 | + | 0.999911i | \(0.495756\pi\) | |||||||
\(368\) | 160.345i | 0.435721i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1605.03 | 4.33791 | ||||||||
\(371\) | − 418.140i | − 1.12706i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 254.878 | 0.683319 | 0.341659 | − | 0.939824i | \(-0.389011\pi\) | ||||
0.341659 | + | 0.939824i | \(0.389011\pi\) | |||||||
\(374\) | − 1311.49i | − 3.50666i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1032.00 | −2.74468 | ||||||||
\(377\) | 528.102i | 1.40080i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −99.9256 | −0.263656 | −0.131828 | − | 0.991273i | \(-0.542085\pi\) | ||||
−0.131828 | + | 0.991273i | \(0.542085\pi\) | |||||||
\(380\) | − 1639.58i | − 4.31469i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 727.013 | 1.90318 | ||||||||
\(383\) | 10.5938i | 0.0276600i | 0.999904 | + | 0.0138300i | \(0.00440236\pi\) | ||||
−0.999904 | + | 0.0138300i | \(0.995598\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 528.317 | 1.37225 | ||||||||
\(386\) | 695.279i | 1.80124i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 40.6687 | 0.104816 | ||||||||
\(389\) | 62.8874i | 0.161664i | 0.996728 | + | 0.0808322i | \(0.0257578\pi\) | ||||
−0.996728 | + | 0.0808322i | \(0.974242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 140.004 | 0.358067 | ||||||||
\(392\) | 466.209i | 1.18931i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 956.082 | 2.42661 | ||||||||
\(395\) | − 406.041i | − 1.02795i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 461.795 | 1.16321 | 0.581605 | − | 0.813471i | \(-0.302425\pi\) | ||||
0.581605 | + | 0.813471i | \(0.302425\pi\) | |||||||
\(398\) | 574.521i | 1.44352i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −724.994 | −1.81248 | ||||||||
\(401\) | − 496.739i | − 1.23875i | −0.785095 | − | 0.619376i | \(-0.787386\pi\) | ||||
0.785095 | − | 0.619376i | \(-0.212614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −105.942 | −0.262883 | ||||||||
\(404\) | − 1061.63i | − 2.62780i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 911.340 | 2.24468 | ||||||||
\(407\) | 967.130i | 2.37624i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 364.666 | 0.891605 | 0.445802 | − | 0.895131i | \(-0.352918\pi\) | ||||
0.445802 | + | 0.895131i | \(0.352918\pi\) | |||||||
\(410\) | 866.797i | 2.11414i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1402.45 | 3.40401 | ||||||||
\(413\) | 67.9204i | 0.164456i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 923.930 | 2.22634 | ||||||||
\(416\) | − 263.741i | − 0.633992i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1434.50 | 3.43181 | ||||||||
\(419\) | − 430.068i | − 1.02642i | −0.858264 | − | 0.513208i | \(-0.828457\pi\) | ||||
0.858264 | − | 0.513208i | \(-0.171543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −522.669 | −1.24149 | −0.620747 | − | 0.784011i | \(-0.713171\pi\) | ||||
−0.620747 | + | 0.784011i | \(0.713171\pi\) | |||||||
\(422\) | − 755.971i | − 1.79140i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1543.41 | −3.64012 | ||||||||
\(425\) | 633.021i | 1.48946i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −370.322 | −0.867265 | ||||||||
\(428\) | − 1406.99i | − 3.28737i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2008.96 | −4.67199 | ||||||||
\(431\) | − 110.538i | − 0.256469i | −0.991744 | − | 0.128235i | \(-0.959069\pi\) | ||||
0.991744 | − | 0.128235i | \(-0.0409310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −73.8530 | −0.170561 | −0.0852806 | − | 0.996357i | \(-0.527179\pi\) | ||||
−0.0852806 | + | 0.996357i | \(0.527179\pi\) | |||||||
\(434\) | 182.823i | 0.421250i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −516.837 | −1.18541 | ||||||||
\(437\) | 153.135i | 0.350424i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 330.242 | 0.752260 | 0.376130 | − | 0.926567i | \(-0.377255\pi\) | ||||
0.376130 | + | 0.926567i | \(0.377255\pi\) | |||||||
\(440\) | − 1950.09i | − 4.43202i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −824.312 | −1.86496 | ||||||||
\(443\) | − 425.440i | − 0.960360i | −0.877170 | − | 0.480180i | \(-0.840571\pi\) | ||||
0.877170 | − | 0.480180i | \(-0.159429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −505.883 | −1.13682 | ||||||||
\(446\) | 1406.64i | 3.15391i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 52.0135 | 0.116102 | ||||||||
\(449\) | 149.718i | 0.333447i | 0.986004 | + | 0.166724i | \(0.0533187\pi\) | ||||
−0.986004 | + | 0.166724i | \(0.946681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −522.300 | −1.15809 | ||||||||
\(452\) | − 716.341i | − 1.58483i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −79.0412 | −0.174100 | ||||||||
\(455\) | − 332.064i | − 0.729811i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −424.824 | −0.929593 | −0.464797 | − | 0.885418i | \(-0.653873\pi\) | ||||
−0.464797 | + | 0.885418i | \(0.653873\pi\) | |||||||
\(458\) | − 943.520i | − 2.06009i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 379.876 | 0.825816 | ||||||||
\(461\) | 28.8882i | 0.0626642i | 0.999509 | + | 0.0313321i | \(0.00997495\pi\) | ||||
−0.999509 | + | 0.0313321i | \(0.990025\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 514.451 | 1.11113 | 0.555563 | − | 0.831474i | \(-0.312503\pi\) | ||||
0.555563 | + | 0.831474i | \(0.312503\pi\) | |||||||
\(464\) | − 1453.08i | − 3.13163i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 462.736 | 0.992995 | ||||||||
\(467\) | − 424.921i | − 0.909894i | −0.890518 | − | 0.454947i | \(-0.849658\pi\) | ||||
0.890518 | − | 0.454947i | \(-0.150342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −88.6433 | −0.189005 | ||||||||
\(470\) | 1533.47i | 3.26270i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 250.703 | 0.531151 | ||||||||
\(473\) | − 1210.52i | − 2.55925i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −692.393 | −1.45767 | ||||||||
\(476\) | 979.695i | 2.05818i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1036.16 | 2.16769 | ||||||||
\(479\) | 400.532i | 0.836183i | 0.908405 | + | 0.418091i | \(0.137301\pi\) | ||||
−0.908405 | + | 0.418091i | \(0.862699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 607.872 | 1.26377 | ||||||||
\(482\) | − 373.431i | − 0.774753i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1073.39 | 2.21775 | ||||||||
\(485\) | − 33.1166i | − 0.0682817i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −823.321 | −1.69060 | −0.845299 | − | 0.534293i | \(-0.820578\pi\) | ||||
−0.845299 | + | 0.534293i | \(0.820578\pi\) | |||||||
\(488\) | 1366.91i | 2.80104i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 692.751 | 1.41378 | ||||||||
\(491\) | 258.140i | 0.525744i | 0.964831 | + | 0.262872i | \(0.0846698\pi\) | ||||
−0.964831 | + | 0.262872i | \(0.915330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1268.74 | −2.57351 | ||||||||
\(494\) | − 901.625i | − 1.82515i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 291.500 | 0.587701 | ||||||||
\(497\) | 357.164i | 0.718640i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −49.8261 | −0.0998520 | −0.0499260 | − | 0.998753i | \(-0.515899\pi\) | ||||
−0.0499260 | + | 0.998753i | \(0.515899\pi\) | |||||||
\(500\) | 123.215i | 0.246430i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1578.62 | −3.14466 | ||||||||
\(503\) | 879.672i | 1.74885i | 0.485160 | + | 0.874426i | \(0.338762\pi\) | ||||
−0.485160 | + | 0.874426i | \(0.661238\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −864.488 | −1.71186 | ||||||||
\(506\) | 332.359i | 0.656836i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −99.7319 | −0.196323 | ||||||||
\(509\) | 116.561i | 0.229001i | 0.993423 | + | 0.114500i | \(0.0365267\pi\) | ||||
−0.993423 | + | 0.114500i | \(0.963473\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −214.882 | −0.420513 | ||||||||
\(512\) | − 1146.27i | − 2.23880i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −373.688 | −0.727019 | ||||||||
\(515\) | − 1142.02i | − 2.21752i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −924.013 | −1.78726 | ||||||||
\(518\) | − 1049.00i | − 2.02509i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1225.69 | −2.35710 | ||||||||
\(521\) | 909.374i | 1.74544i | 0.488222 | + | 0.872719i | \(0.337646\pi\) | ||||
−0.488222 | + | 0.872719i | \(0.662354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 942.453 | 1.80201 | 0.901007 | − | 0.433804i | \(-0.142829\pi\) | ||||
0.901007 | + | 0.433804i | \(0.142829\pi\) | |||||||
\(524\) | 151.604i | 0.289320i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 383.010 | 0.728156 | ||||||||
\(527\) | − 254.520i | − 0.482960i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 493.520 | 0.932930 | ||||||||
\(530\) | 2293.39i | 4.32715i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1071.58 | −2.01425 | ||||||||
\(533\) | 328.282i | 0.615913i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1145.72 | −2.14153 | ||||||||
\(536\) | 327.194i | 0.610437i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1004.77 | 1.86761 | ||||||||
\(539\) | 417.426i | 0.774445i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 697.261 | 1.28884 | 0.644419 | − | 0.764673i | \(-0.277099\pi\) | ||||
0.644419 | + | 0.764673i | \(0.277099\pi\) | |||||||
\(542\) | 91.5196i | 0.168855i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 633.624 | 1.16475 | ||||||||
\(545\) | 420.861i | 0.772223i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 951.659 | 1.73978 | 0.869890 | − | 0.493246i | \(-0.164190\pi\) | ||||
0.869890 | + | 0.493246i | \(0.164190\pi\) | |||||||
\(548\) | − 255.117i | − 0.465542i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1502.74 | −2.73226 | ||||||||
\(551\) | − 1387.74i | − 2.51858i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −265.376 | −0.479884 | ||||||||
\(554\) | 1008.85i | 1.82103i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −226.833 | −0.407973 | ||||||||
\(557\) | 840.713i | 1.50936i | 0.656093 | + | 0.754680i | \(0.272208\pi\) | ||||
−0.656093 | + | 0.754680i | \(0.727792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −760.852 | −1.36109 | ||||||||
\(560\) | 913.676i | 1.63156i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1869.76 | 3.32698 | ||||||||
\(563\) | 838.241i | 1.48888i | 0.667688 | + | 0.744442i | \(0.267284\pi\) | ||||
−0.667688 | + | 0.744442i | \(0.732716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −583.318 | −1.03242 | ||||||||
\(566\) | 786.756i | 1.39003i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1318.34 | 2.32102 | ||||||||
\(569\) | − 940.180i | − 1.65234i | −0.563423 | − | 0.826168i | \(-0.690516\pi\) | ||||
0.563423 | − | 0.826168i | \(-0.309484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 612.707 | 1.07304 | 0.536521 | − | 0.843887i | \(-0.319738\pi\) | ||||
0.536521 | + | 0.843887i | \(0.319738\pi\) | |||||||
\(572\) | − 1347.70i | − 2.35613i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 566.512 | 0.986954 | ||||||||
\(575\) | − 160.421i | − 0.278993i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −68.6703 | −0.119013 | −0.0595064 | − | 0.998228i | \(-0.518953\pi\) | ||||
−0.0595064 | + | 0.998228i | \(0.518953\pi\) | |||||||
\(578\) | − 944.404i | − 1.63392i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3442.49 | −5.93533 | ||||||||
\(581\) | − 603.852i | − 1.03933i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1381.91 | −2.37035 | ||||||||
\(584\) | 793.160i | 1.35815i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −440.628 | −0.751925 | ||||||||
\(587\) | − 613.626i | − 1.04536i | −0.852529 | − | 0.522680i | \(-0.824932\pi\) | ||||
0.852529 | − | 0.522680i | \(-0.175068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 278.392 | 0.472652 | ||||||||
\(590\) | − 372.526i | − 0.631400i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1672.56 | −2.82527 | ||||||||
\(593\) | 10.5482i | 0.0177878i | 0.999960 | + | 0.00889392i | \(0.00283106\pi\) | ||||
−0.999960 | + | 0.00889392i | \(0.997169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 797.767 | 1.34079 | ||||||||
\(596\) | 533.755i | 0.895562i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 208.898 | 0.349328 | ||||||||
\(599\) | − 12.8106i | − 0.0213866i | −0.999943 | − | 0.0106933i | \(-0.996596\pi\) | ||||
0.999943 | − | 0.0106933i | \(-0.00340385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1099.50 | 1.82946 | 0.914728 | − | 0.404071i | \(-0.132405\pi\) | ||||
0.914728 | + | 0.404071i | \(0.132405\pi\) | |||||||
\(602\) | 1312.99i | 2.18105i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −276.297 | −0.457445 | ||||||||
\(605\) | − 874.064i | − 1.44473i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 169.097 | 0.278579 | 0.139289 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139289 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(608\) | 693.052i | 1.13989i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2031.12 | 3.32970 | ||||||||
\(611\) | 580.771i | 0.950526i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −52.3964 | −0.0854754 | −0.0427377 | − | 0.999086i | \(-0.513608\pi\) | ||||
−0.0427377 | + | 0.999086i | \(0.513608\pi\) | |||||||
\(614\) | 1283.47i | 2.09034i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1274.52 | −2.06902 | ||||||||
\(617\) | − 425.530i | − 0.689677i | −0.938662 | − | 0.344838i | \(-0.887934\pi\) | ||||
0.938662 | − | 0.344838i | \(-0.112066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 167.798 | 0.271079 | 0.135539 | − | 0.990772i | \(-0.456723\pi\) | ||||
0.135539 | + | 0.990772i | \(0.456723\pi\) | |||||||
\(620\) | − 690.594i | − 1.11386i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −364.496 | −0.586007 | ||||||||
\(623\) | 330.630i | 0.530706i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −572.966 | −0.916746 | ||||||||
\(626\) | − 407.002i | − 0.650163i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 520.246 | 0.828416 | ||||||||
\(629\) | 1460.38i | 2.32175i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −930.073 | −1.47397 | −0.736983 | − | 0.675911i | \(-0.763750\pi\) | ||||
−0.736983 | + | 0.675911i | \(0.763750\pi\) | |||||||
\(632\) | 979.538i | 1.54990i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2018.67 | −3.18402 | ||||||||
\(635\) | 81.2119i | 0.127893i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 262.365 | 0.411876 | ||||||||
\(638\) | − 3011.89i | − 4.72083i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1062.35 | −1.65992 | ||||||||
\(641\) | − 23.8249i | − 0.0371683i | −0.999827 | − | 0.0185841i | \(-0.994084\pi\) | ||||
0.999827 | − | 0.0185841i | \(-0.00591585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 762.785 | 1.18629 | 0.593146 | − | 0.805095i | \(-0.297886\pi\) | ||||
0.593146 | + | 0.805095i | \(0.297886\pi\) | |||||||
\(644\) | − 248.275i | − 0.385520i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2166.11 | 3.35311 | ||||||||
\(647\) | 1067.19i | 1.64944i | 0.565539 | + | 0.824722i | \(0.308668\pi\) | ||||
−0.565539 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 224.470 | 0.345871 | ||||||||
\(650\) | 944.521i | 1.45311i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 859.565 | 1.31835 | ||||||||
\(653\) | 437.847i | 0.670516i | 0.942126 | + | 0.335258i | \(0.108824\pi\) | ||||
−0.942126 | + | 0.335258i | \(0.891176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 123.451 | 0.188475 | ||||||||
\(656\) | − 903.269i | − 1.37693i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1002.23 | 1.52315 | ||||||||
\(659\) | 528.030i | 0.801260i | 0.916240 | + | 0.400630i | \(0.131209\pi\) | ||||
−0.916240 | + | 0.400630i | \(0.868791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1149.03 | −1.73831 | −0.869157 | − | 0.494536i | \(-0.835338\pi\) | ||||
−0.869157 | + | 0.494536i | \(0.835338\pi\) | |||||||
\(662\) | 892.247i | 1.34780i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2228.90 | −3.35678 | ||||||||
\(665\) | 872.590i | 1.31217i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 321.525 | 0.482047 | ||||||||
\(668\) | 1302.65i | 1.95008i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 486.185 | 0.725650 | ||||||||
\(671\) | 1223.88i | 1.82396i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 932.678 | 1.38585 | 0.692926 | − | 0.721009i | \(-0.256321\pi\) | ||||
0.692926 | + | 0.721009i | \(0.256321\pi\) | |||||||
\(674\) | 291.997i | 0.433230i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 648.537 | 0.959374 | ||||||||
\(677\) | 216.494i | 0.319785i | 0.987134 | + | 0.159892i | \(0.0511147\pi\) | ||||
−0.987134 | + | 0.159892i | \(0.948885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.6440 | −0.0318763 | ||||||||
\(680\) | − 2944.67i | − 4.33039i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 604.211 | 0.885940 | ||||||||
\(683\) | − 230.195i | − 0.337036i | −0.985699 | − | 0.168518i | \(-0.946102\pi\) | ||||
0.985699 | − | 0.168518i | \(-0.0538981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −207.742 | −0.303273 | ||||||||
\(686\) | − 1280.04i | − 1.86595i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2093.49 | 3.04286 | ||||||||
\(689\) | 868.574i | 1.26063i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7096 | −0.0198402 | −0.00992011 | − | 0.999951i | \(-0.503158\pi\) | ||||
−0.00992011 | + | 0.999951i | \(0.503158\pi\) | |||||||
\(692\) | − 335.782i | − 0.485234i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 337.945 | 0.486953 | ||||||||
\(695\) | 184.711i | 0.265771i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −788.681 | −1.13154 | ||||||||
\(698\) | − 1951.67i | − 2.79609i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1122.56 | 1.60366 | ||||||||
\(701\) | 310.382i | 0.442770i | 0.975186 | + | 0.221385i | \(0.0710578\pi\) | ||||
−0.975186 | + | 0.221385i | \(0.928942\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1597.35 | −2.27219 | ||||||||
\(704\) | − 171.900i | − 0.244175i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1505.99 | −2.13313 | ||||||||
\(707\) | 565.003i | 0.799155i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1053.71 | −1.48619 | −0.743093 | − | 0.669188i | \(-0.766642\pi\) | ||||
−0.743093 | + | 0.669188i | \(0.766642\pi\) | |||||||
\(710\) | − 1958.95i | − 2.75909i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1220.40 | 1.71404 | ||||||||
\(713\) | 64.5007i | 0.0904638i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1097.44 | −1.53488 | ||||||||
\(716\) | 1954.54i | 2.72981i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1366.67 | 1.90343 | ||||||||
\(719\) | − 1131.63i | − 1.57390i | −0.617017 | − | 0.786950i | \(-0.711659\pi\) | ||||
0.617017 | − | 0.786950i | \(-0.288341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −746.390 | −1.03522 | ||||||||
\(722\) | 1075.21i | 1.48921i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1206.16 | −1.66596 | ||||||||
\(725\) | 1453.76i | 2.00519i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 70.7147 | 0.0972692 | 0.0486346 | − | 0.998817i | \(-0.484513\pi\) | ||||
0.0486346 | + | 0.998817i | \(0.484513\pi\) | |||||||
\(728\) | 801.075i | 1.10038i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1178.57 | 1.61448 | ||||||||
\(731\) | − 1827.91i | − 2.50056i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 980.186 | 1.33722 | 0.668612 | − | 0.743611i | \(-0.266889\pi\) | ||||
0.668612 | + | 0.743611i | \(0.266889\pi\) | |||||||
\(734\) | 35.0820i | 0.0477956i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −160.574 | −0.218171 | ||||||||
\(737\) | 292.957i | 0.397500i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −483.337 | −0.654042 | −0.327021 | − | 0.945017i | \(-0.606045\pi\) | ||||
−0.327021 | + | 0.945017i | \(0.606045\pi\) | |||||||
\(740\) | 3962.48i | 5.35470i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1498.89 | 2.02007 | ||||||||
\(743\) | 530.012i | 0.713341i | 0.934230 | + | 0.356671i | \(0.116088\pi\) | ||||
−0.934230 | + | 0.356671i | \(0.883912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 434.638 | 0.583406 | ||||||||
\(746\) | 913.650i | 1.22473i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3237.79 | 4.32860 | ||||||||
\(749\) | 748.806i | 0.999741i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 263.871 | 0.351360 | 0.175680 | − | 0.984447i | \(-0.443788\pi\) | ||||
0.175680 | + | 0.984447i | \(0.443788\pi\) | |||||||
\(752\) | − 1597.99i | − 2.12499i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1893.07 | −2.51070 | ||||||||
\(755\) | 224.989i | 0.297999i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1216.09 | −1.60646 | −0.803232 | − | 0.595667i | \(-0.796888\pi\) | ||||
−0.803232 | + | 0.595667i | \(0.796888\pi\) | |||||||
\(758\) | − 358.199i | − 0.472558i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3220.85 | 4.23796 | ||||||||
\(761\) | − 599.778i | − 0.788145i | −0.919079 | − | 0.394073i | \(-0.871066\pi\) | ||||
0.919079 | − | 0.394073i | \(-0.128934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 275.062 | 0.360501 | ||||||||
\(764\) | 1794.84i | 2.34927i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.9750 | −0.0495758 | ||||||||
\(767\) | − 141.087i | − 0.183946i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 378.397 | 0.492063 | 0.246032 | − | 0.969262i | \(-0.420873\pi\) | ||||
0.246032 | + | 0.969262i | \(0.420873\pi\) | |||||||
\(770\) | 1893.84i | 2.45953i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1716.50 | −2.22344 | ||||||||
\(773\) | 868.664i | 1.12376i | 0.827220 | + | 0.561879i | \(0.189921\pi\) | ||||
−0.827220 | + | 0.561879i | \(0.810079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −291.637 | −0.376305 | ||||||||
\(776\) | 79.8909i | 0.102952i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −225.430 | −0.289756 | ||||||||
\(779\) | − 862.652i | − 1.10738i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1180.39 | 1.51139 | ||||||||
\(782\) | 501.867i | 0.641774i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −721.899 | −0.920790 | ||||||||
\(785\) | − 423.637i | − 0.539665i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 56.4537 | 0.0717328 | 0.0358664 | − | 0.999357i | \(-0.488581\pi\) | ||||
0.0358664 | + | 0.999357i | \(0.488581\pi\) | |||||||
\(788\) | 2360.37i | 2.99539i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1455.52 | 1.84243 | ||||||||
\(791\) | 381.239i | 0.481971i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 769.245 | 0.970045 | ||||||||
\(794\) | 1655.38i | 2.08486i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1418.37 | −1.78187 | ||||||||
\(797\) | − 457.708i | − 0.574289i | −0.957887 | − | 0.287145i | \(-0.907294\pi\) | ||||
0.957887 | − | 0.287145i | \(-0.0927060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1395.27 | −1.74628 | ||||||||
\(800\) | − 726.025i | − 0.907531i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1780.64 | 2.22025 | ||||||||
\(803\) | 710.165i | 0.884390i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −202.171 | −0.251144 | ||||||||
\(806\) | − 379.765i | − 0.471173i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2085.50 | 2.58107 | ||||||||
\(809\) | − 1039.81i | − 1.28530i | −0.766159 | − | 0.642651i | \(-0.777834\pi\) | ||||
0.766159 | − | 0.642651i | \(-0.222166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −855.629 | −1.05503 | −0.527515 | − | 0.849546i | \(-0.676876\pi\) | ||||
−0.527515 | + | 0.849546i | \(0.676876\pi\) | |||||||
\(812\) | 2249.91i | 2.77082i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3466.83 | −4.25901 | ||||||||
\(815\) | − 699.946i | − 0.858829i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1999.35 | 2.44719 | ||||||||
\(818\) | 1307.20i | 1.59805i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2139.94 | −2.60968 | ||||||||
\(821\) | 701.585i | 0.854549i | 0.904122 | + | 0.427275i | \(0.140526\pi\) | ||||
−0.904122 | + | 0.427275i | \(0.859474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −507.346 | −0.616460 | −0.308230 | − | 0.951312i | \(-0.599737\pi\) | ||||
−0.308230 | + | 0.951312i | \(0.599737\pi\) | |||||||
\(824\) | 2755.03i | 3.34348i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −243.471 | −0.294760 | ||||||||
\(827\) | 1126.11i | 1.36168i | 0.732434 | + | 0.680838i | \(0.238384\pi\) | ||||
−0.732434 | + | 0.680838i | \(0.761616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1160.25 | −1.39957 | −0.699786 | − | 0.714352i | \(-0.746721\pi\) | ||||
−0.699786 | + | 0.714352i | \(0.746721\pi\) | |||||||
\(830\) | 3311.97i | 3.99033i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −108.044 | −0.129861 | ||||||||
\(833\) | 630.320i | 0.756686i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1060.75 | 1.27036 | ||||||||
\(836\) | 3541.47i | 4.23621i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1541.65 | 1.83967 | ||||||||
\(839\) | − 607.665i | − 0.724272i | −0.932125 | − | 0.362136i | \(-0.882048\pi\) | ||||
0.932125 | − | 0.362136i | \(-0.117952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2072.71 | −2.46458 | ||||||||
\(842\) | − 1873.59i | − 2.22517i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1866.34 | 2.21130 | ||||||||
\(845\) | − 528.105i | − 0.624976i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −571.261 | −0.674453 | ||||||||
\(848\) | − 2389.89i | − 2.81826i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2269.17 | −2.66961 | ||||||||
\(851\) | − 370.091i | − 0.434890i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −273.450 | −0.320574 | −0.160287 | − | 0.987070i | \(-0.551242\pi\) | ||||
−0.160287 | + | 0.987070i | \(0.551242\pi\) | |||||||
\(854\) | − 1327.48i | − 1.55442i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2763.94 | 3.22890 | ||||||||
\(857\) | − 1326.64i | − 1.54800i | −0.633184 | − | 0.774001i | \(-0.718253\pi\) | ||||
0.633184 | − | 0.774001i | \(-0.281747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 251.982 | 0.293343 | 0.146672 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146672 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(860\) | − 4959.70i | − 5.76709i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 396.242 | 0.459677 | ||||||||
\(863\) | 456.453i | 0.528915i | 0.964397 | + | 0.264457i | \(0.0851929\pi\) | ||||
−0.964397 | + | 0.264457i | \(0.914807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −273.428 | −0.316101 | ||||||||
\(866\) | − 264.738i | − 0.305702i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −451.351 | −0.519990 | ||||||||
\(869\) | 877.041i | 1.00925i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 184.133 | 0.211404 | ||||||||
\(872\) | − 1015.29i | − 1.16432i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −548.937 | −0.628075 | ||||||||
\(875\) | − 65.5755i | − 0.0749434i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 537.509 | 0.612896 | 0.306448 | − | 0.951887i | \(-0.400860\pi\) | ||||
0.306448 | + | 0.951887i | \(0.400860\pi\) | |||||||
\(878\) | 1183.81i | 1.34830i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3019.61 | 3.43137 | ||||||||
\(881\) | − 1228.12i | − 1.39401i | −0.717067 | − | 0.697004i | \(-0.754516\pi\) | ||||
0.717067 | − | 0.697004i | \(-0.245484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.2818 | −0.0648718 | −0.0324359 | − | 0.999474i | \(-0.510326\pi\) | ||||
−0.0324359 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(884\) | − 2035.06i | − 2.30210i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1525.06 | 1.72128 | ||||||||
\(887\) | − 1335.11i | − 1.50520i | −0.658481 | − | 0.752598i | \(-0.728801\pi\) | ||||
0.658481 | − | 0.752598i | \(-0.271199\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 53.0776 | 0.0597048 | ||||||||
\(890\) | − 1813.42i | − 2.03755i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3472.71 | −3.89317 | ||||||||
\(893\) | − 1526.14i | − 1.70900i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1591.59 | 1.77831 | ||||||||
\(896\) | 694.320i | 0.774910i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −536.687 | −0.597647 | ||||||||
\(899\) | − 584.516i | − 0.650184i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2086.71 | −2.31599 | ||||||||
\(902\) | − 1872.27i | − 2.07568i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1407.20 | 1.55664 | ||||||||
\(905\) | 982.175i | 1.08528i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1726.30 | −1.90331 | −0.951654 | − | 0.307173i | \(-0.900617\pi\) | ||||
−0.951654 | + | 0.307173i | \(0.900617\pi\) | |||||||
\(908\) | − 195.136i | − 0.214908i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1190.34 | 1.30806 | ||||||||
\(911\) | − 1710.32i | − 1.87741i | −0.344721 | − | 0.938705i | \(-0.612026\pi\) | ||||
0.344721 | − | 0.938705i | \(-0.387974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1995.67 | −2.18584 | ||||||||
\(914\) | − 1522.85i | − 1.66614i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2329.35 | 2.54296 | ||||||||
\(917\) | − 80.6840i | − 0.0879870i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −307.462 | −0.334561 | −0.167280 | − | 0.985909i | \(-0.553499\pi\) | ||||
−0.167280 | + | 0.985909i | \(0.553499\pi\) | |||||||
\(920\) | 746.240i | 0.811130i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −103.554 | −0.112315 | ||||||||
\(923\) | − 741.913i | − 0.803807i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1673.35 | 1.80902 | ||||||||
\(926\) | 1844.13i | 1.99150i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1455.14 | 1.56804 | ||||||||
\(929\) | − 1510.66i | − 1.62612i | −0.582180 | − | 0.813060i | \(-0.697800\pi\) | ||||
0.582180 | − | 0.813060i | \(-0.302200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −689.438 | −0.740535 | ||||||||
\(932\) | 1142.40i | 1.22575i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1523.20 | 1.63083 | ||||||||
\(935\) | − 2636.54i | − 2.81983i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −452.031 | −0.482423 | −0.241212 | − | 0.970473i | \(-0.577545\pi\) | ||||
−0.241212 | + | 0.970473i | \(0.577545\pi\) | |||||||
\(938\) | − 317.756i | − 0.338759i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3785.82 | −4.02747 | ||||||||
\(941\) | 706.234i | 0.750515i | 0.926921 | + | 0.375257i | \(0.122446\pi\) | ||||
−0.926921 | + | 0.375257i | \(0.877554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 199.868 | 0.211949 | ||||||||
\(944\) | 388.200i | 0.411229i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4339.31 | 4.58701 | ||||||||
\(947\) | 663.862i | 0.701016i | 0.936560 | + | 0.350508i | \(0.113991\pi\) | ||||
−0.936560 | + | 0.350508i | \(0.886009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 446.361 | 0.470349 | ||||||||
\(950\) | − 2481.99i | − 2.61262i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1924.54 | −2.02158 | ||||||||
\(953\) | − 59.7064i | − 0.0626510i | −0.999509 | − | 0.0313255i | \(-0.990027\pi\) | ||||
0.999509 | − | 0.0313255i | \(-0.00997285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1461.55 | 1.53041 | ||||||||
\(956\) | 2558.05i | 2.67579i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1435.77 | −1.49871 | ||||||||
\(959\) | 135.774i | 0.141579i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −843.741 | −0.877982 | ||||||||
\(962\) | 2179.01i | 2.26509i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 921.923 | 0.956351 | ||||||||
\(965\) | 1397.75i | 1.44844i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1441.18 | 1.49036 | 0.745182 | − | 0.666861i | \(-0.232363\pi\) | ||||
0.745182 | + | 0.666861i | \(0.232363\pi\) | |||||||
\(968\) | 2108.60i | 2.17831i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 118.712 | 0.122383 | ||||||||
\(971\) | 942.274i | 0.970416i | 0.874399 | + | 0.485208i | \(0.161256\pi\) | ||||
−0.874399 | + | 0.485208i | \(0.838744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 120.721 | 0.124071 | ||||||||
\(974\) | − 2951.33i | − 3.03011i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2116.58 | −2.16863 | ||||||||
\(977\) | − 1642.03i | − 1.68068i | −0.542058 | − | 0.840341i | \(-0.682355\pi\) | ||||
0.542058 | − | 0.840341i | \(-0.317645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1092.70 | 1.11614 | ||||||||
\(980\) | 1710.26i | 1.74516i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −925.345 | −0.942307 | ||||||||
\(983\) | − 704.163i | − 0.716341i | −0.933656 | − | 0.358170i | \(-0.883401\pi\) | ||||
0.933656 | − | 0.358170i | \(-0.116599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1922.05 | 1.95132 | ||||||||
\(986\) | − 4548.00i | − 4.61258i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2225.92 | 2.25296 | ||||||||
\(989\) | 463.230i | 0.468383i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1524.19 | −1.53803 | −0.769015 | − | 0.639230i | \(-0.779253\pi\) | ||||
−0.769015 | + | 0.639230i | \(0.779253\pi\) | |||||||
\(992\) | 291.914i | 0.294268i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1280.31 | −1.28804 | ||||||||
\(995\) | 1154.98i | 1.16079i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −165.044 | −0.165540 | −0.0827702 | − | 0.996569i | \(-0.526377\pi\) | ||||
−0.0827702 | + | 0.996569i | \(0.526377\pi\) | |||||||
\(998\) | − 178.610i | − 0.178968i | ||||||||
\(999\) | 0 | 0 |
(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 | 1143.3.b.a.890.78 | yes | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.7 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.7 | ✓ | 84 | 3.2 | odd | 2 | inner | |
1143.3.b.a.890.78 | yes | 84 | 1.1 | even | 1 | trivial |