Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(509,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.509");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.23 | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.e.509.23 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 5.15687 | + | 0.637690i | 0.992441 | + | 0.122723i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.99365 | + | 12.1134i | 0.625531 | + | 1.08345i | 0.988438 | + | 0.151626i | \(0.0484511\pi\) |
−0.362907 | + | 0.931826i | \(0.618216\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 26.1867 | + | 6.57697i | 0.969878 | + | 0.243592i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.5333 | − | 15.8964i | −0.754692 | − | 0.435721i | 0.0726950 | − | 0.997354i | \(-0.476840\pi\) |
−0.827387 | + | 0.561633i | \(0.810173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31.1041i | 0.663593i | 0.943351 | + | 0.331797i | \(0.107655\pi\) | ||||
−0.943351 | + | 0.331797i | \(0.892345\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28.3408 | + | 66.9269i | 0.487838 | + | 1.15203i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.5138 | + | 106.545i | −0.877605 | + | 1.52006i | −0.0236424 | + | 0.999720i | \(0.507526\pi\) |
−0.853962 | + | 0.520335i | \(0.825807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −62.7653 | + | 36.2376i | −0.757860 | + | 0.437551i | −0.828527 | − | 0.559949i | \(-0.810821\pi\) |
0.0706666 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 66.1240 | − | 38.1767i | 0.599470 | − | 0.346104i | −0.169363 | − | 0.985554i | \(-0.554171\pi\) |
0.768833 | + | 0.639449i | \(0.220838\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.3223 | + | 61.1801i | −0.282579 | + | 0.489441i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 130.847 | + | 50.6156i | 0.932652 | + | 0.360777i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 14.1082i | − | 0.0903390i | −0.998979 | − | 0.0451695i | \(-0.985617\pi\) | ||
0.998979 | − | 0.0451695i | \(-0.0143828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 267.941 | + | 154.696i | 1.55238 | + | 0.896265i | 0.997948 | + | 0.0640343i | \(0.0203967\pi\) |
0.554429 | + | 0.832231i | \(0.312937\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −131.849 | − | 99.5333i | −0.695514 | − | 0.525046i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.3602 | + | 101.083i | 0.259307 | + | 0.449133i | 0.966056 | − | 0.258331i | \(-0.0831726\pi\) |
−0.706750 | + | 0.707464i | \(0.749839\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.8347 | + | 160.400i | −0.0814385 | + | 0.658577i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −491.980 | −1.87401 | −0.937004 | − | 0.349319i | \(-0.886413\pi\) | ||||
−0.937004 | + | 0.349319i | \(0.886413\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.6538 | 0.0484230 | 0.0242115 | − | 0.999707i | \(-0.492292\pi\) | ||||
0.0242115 | + | 0.999707i | \(0.492292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 103.471 | + | 363.206i | 0.342769 | + | 1.20319i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −43.4381 | − | 75.2370i | −0.134811 | − | 0.233499i | 0.790714 | − | 0.612185i | \(-0.209709\pi\) |
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −385.161 | + | 510.212i | −1.05752 | + | 1.40086i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −388.989 | − | 224.583i | −1.00815 | − | 0.582053i | −0.0974977 | − | 0.995236i | \(-0.531084\pi\) |
−0.910648 | + | 0.413182i | \(0.864417\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 444.695i | − | 1.09023i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −346.781 | + | 146.848i | −0.805829 | + | 0.341236i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 128.392 | − | 222.381i | 0.283308 | − | 0.490704i | −0.688889 | − | 0.724866i | \(-0.741901\pi\) |
0.972197 | + | 0.234162i | \(0.0752348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 238.010 | − | 137.415i | 0.499575 | − | 0.288430i | −0.228963 | − | 0.973435i | \(-0.573533\pi\) |
0.728538 | + | 0.685005i | \(0.240200\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −376.775 | + | 217.531i | −0.718972 | + | 0.415098i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −515.984 | + | 893.710i | −0.940857 | + | 1.62961i | −0.177016 | + | 0.984208i | \(0.556644\pi\) |
−0.763841 | + | 0.645404i | \(0.776689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 365.338 | − | 154.706i | 0.637414 | − | 0.269919i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 931.763i | − | 1.55746i | −0.627356 | − | 0.778732i | \(-0.715863\pi\) | ||
0.627356 | − | 0.778732i | \(-0.284137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 887.716 | + | 512.523i | 1.42328 | + | 0.821730i | 0.996578 | − | 0.0826631i | \(-0.0263425\pi\) |
0.426700 | + | 0.904393i | \(0.359676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −221.167 | + | 292.973i | −0.340509 | + | 0.451062i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 462.310 | + | 800.745i | 0.658405 | + | 1.14039i | 0.981029 | + | 0.193863i | \(0.0621018\pi\) |
−0.322624 | + | 0.946527i | \(0.604565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 642.487 | + | 344.459i | 0.881326 | + | 0.472508i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 991.698 | 1.31148 | 0.655741 | − | 0.754986i | \(-0.272356\pi\) | ||||
0.655741 | + | 0.754986i | \(0.272356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1720.82 | −2.19588 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.99667 | − | 72.7543i | 0.0110867 | − | 0.0896561i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 125.394 | + | 217.188i | 0.149345 | + | 0.258673i | 0.930985 | − | 0.365056i | \(-0.118950\pi\) |
−0.781641 | + | 0.623729i | \(0.785617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1283.09 | + | 968.611i | 1.43065 | + | 1.08000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −877.917 | − | 506.866i | −0.948131 | − | 0.547404i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1059.27i | − | 1.10879i | −0.832252 | − | 0.554397i | \(-0.812949\pi\) | ||
0.832252 | − | 0.554397i | \(-0.187051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −616.457 | − | 597.359i | −0.625821 | − | 0.606433i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −764.116 | + | 1323.49i | −0.752796 | + | 1.30388i | 0.193666 | + | 0.981067i | \(0.437962\pi\) |
−0.946462 | + | 0.322814i | \(0.895371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 164.739 | − | 95.1120i | 0.157594 | − | 0.0909870i | −0.419129 | − | 0.907927i | \(-0.637664\pi\) |
0.576723 | + | 0.816940i | \(0.304331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 154.050 | − | 88.9408i | 0.139183 | − | 0.0803573i | −0.428792 | − | 0.903403i | \(-0.641061\pi\) |
0.567975 | + | 0.823046i | \(0.307727\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.5195 | + | 167.177i | −0.0848156 | + | 0.146905i | −0.905313 | − | 0.424746i | \(-0.860363\pi\) |
0.820497 | + | 0.571651i | \(0.193697\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 236.497 | + | 558.487i | 0.202228 | + | 0.477561i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 452.079i | − | 0.376354i | −0.982135 | − | 0.188177i | \(-0.939742\pi\) | ||
0.982135 | − | 0.188177i | \(-0.0602579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 924.897 | + | 533.989i | 0.749975 | + | 0.432998i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −204.571 | + | 814.513i | −0.161646 | + | 0.643605i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160.111 | − | 277.320i | −0.120294 | − | 0.208355i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2537.08 | − | 313.731i | −1.85984 | − | 0.229985i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 760.285 | 0.544015 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 729.629 | 0.509796 | 0.254898 | − | 0.966968i | \(-0.417958\pi\) | ||||
0.254898 | + | 0.966968i | \(0.417958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 70.4110 | + | 8.70690i | 0.0480569 | + | 0.00594264i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 287.216 | + | 497.472i | 0.191558 | + | 0.331789i | 0.945767 | − | 0.324846i | \(-0.105313\pi\) |
−0.754208 | + | 0.656635i | \(0.771979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 301.976 | + | 1938.99i | 0.192518 | + | 1.23616i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2102.50 | + | 1213.88i | 1.31116 | + | 0.756998i | 0.982288 | − | 0.187376i | \(-0.0599984\pi\) |
0.328871 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1453.63i | − | 0.887014i | −0.896271 | − | 0.443507i | \(-0.853734\pi\) | ||
0.896271 | − | 0.443507i | \(-0.146266\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −176.027 | − | 415.688i | −0.105136 | − | 0.248278i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 494.442 | − | 856.398i | 0.289142 | − | 0.500808i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 170.898 | − | 98.6680i | 0.0978779 | − | 0.0565098i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1704.20 | + | 983.920i | −0.937003 | + | 0.540979i | −0.889020 | − | 0.457869i | \(-0.848613\pi\) |
−0.0479834 | + | 0.998848i | \(0.515279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1086.40 | + | 1881.71i | −0.585499 | + | 1.01411i | 0.409314 | + | 0.912394i | \(0.365768\pi\) |
−0.994813 | + | 0.101720i | \(0.967565\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2311.59 | + | 2385.49i | −1.22144 | + | 1.26049i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4327.56i | 2.24257i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2857.15 | + | 1649.57i | 1.45239 | + | 0.838538i | 0.998617 | − | 0.0525797i | \(-0.0167444\pi\) |
0.453773 | + | 0.891117i | \(0.350078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1862.75 | − | 1406.20i | −0.929094 | − | 0.701377i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1399.63 | − | 2424.23i | −0.672562 | − | 1.16491i | −0.977175 | − | 0.212436i | \(-0.931860\pi\) |
0.304612 | − | 0.952476i | \(-0.401473\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 283.577 | − | 2293.23i | 0.133797 | − | 1.08199i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1933.50 | −0.895921 | −0.447960 | − | 0.894053i | \(-0.647849\pi\) | ||||
−0.447960 | + | 0.894053i | \(0.647849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1229.54 | 0.559644 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1881.95 | + | 536.137i | −0.841616 | + | 0.239763i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1752.50 | − | 3035.43i | −0.770176 | − | 1.33398i | −0.937466 | − | 0.348076i | \(-0.886835\pi\) |
0.167290 | − | 0.985908i | \(-0.446498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 803.910 | − | 1064.92i | 0.341387 | − | 0.452226i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1598.90 | + | 923.127i | 0.667640 | + | 0.385462i | 0.795182 | − | 0.606371i | \(-0.207375\pi\) |
−0.127542 | + | 0.991833i | \(0.540709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 369.402i | − | 0.151699i | −0.997119 | − | 0.0758493i | \(-0.975833\pi\) | ||
0.997119 | − | 0.0758493i | \(-0.0241668\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1315.02 | − | 556.857i | 0.531196 | − | 0.224940i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −816.302 | + | 1413.88i | −0.324409 | + | 0.561893i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3387.36 | − | 1955.69i | 1.32464 | − | 0.764782i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 206.710 | − | 119.344i | 0.0783088 | − | 0.0452116i | −0.460334 | − | 0.887746i | \(-0.652270\pi\) |
0.538643 | + | 0.842534i | \(0.318937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 841.049 | − | 1456.74i | 0.313679 | − | 0.543308i | −0.665477 | − | 0.746418i | \(-0.731772\pi\) |
0.979156 | + | 0.203111i | \(0.0651051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2081.70 | + | 881.514i | −0.764479 | + | 0.323726i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2988.01i | − | 1.08065i | −0.841458 | − | 0.540323i | \(-0.818302\pi\) | ||
0.841458 | − | 0.540323i | \(-0.181698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1746.98 | − | 1008.62i | −0.622312 | − | 0.359292i | 0.155457 | − | 0.987843i | \(-0.450315\pi\) |
−0.777768 | + | 0.628551i | \(0.783648\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3230.77 | + | 4279.71i | −1.13374 | + | 1.50183i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3440.73 | − | 5959.53i | −1.17225 | − | 2.03040i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1982.66 | − | 564.827i | 0.665721 | − | 0.189653i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2304.18 | 0.762601 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4685.01 | 1.52858 | 0.764288 | − | 0.644875i | \(-0.223091\pi\) | ||||
0.764288 | + | 0.644875i | \(0.223091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 594.176 | − | 4804.99i | 0.191137 | − | 1.54569i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 95.4901 | + | 165.394i | 0.0302901 | + | 0.0524640i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4251.01 | + | 3209.10i | 1.31167 | + | 0.990188i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3313.98 | − | 1913.33i | −1.00870 | − | 0.582373i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.2808i | − | 0.00518927i | −0.999997 | − | 0.00259463i | \(-0.999174\pi\) | ||
0.999997 | − | 0.00259463i | \(-0.000825899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1327.36 | + | 1369.79i | −0.393290 | + | 0.405864i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 731.937 | − | 1267.75i | 0.214011 | − | 0.370677i | −0.738956 | − | 0.673754i | \(-0.764681\pi\) |
0.952966 | + | 0.303077i | \(0.0980140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 100.522 | − | 58.0363i | 0.0290073 | − | 0.0167474i | −0.485426 | − | 0.874278i | \(-0.661336\pi\) |
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3248.11 | − | 1875.30i | 0.913265 | − | 0.527274i | 0.0317846 | − | 0.999495i | \(-0.489881\pi\) |
0.881480 | + | 0.472221i | \(0.156548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 607.582 | − | 1052.36i | 0.168656 | − | 0.292122i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1873.45 | + | 4424.15i | 0.513475 | + | 1.21257i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5423.48i | 1.46785i | 0.679232 | + | 0.733924i | \(0.262313\pi\) | ||||
−0.679232 | + | 0.733924i | \(0.737687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3933.77 | − | 2271.16i | −1.05144 | − | 0.607048i | −0.128386 | − | 0.991724i | \(-0.540980\pi\) |
−0.923051 | + | 0.384677i | \(0.874313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3093.57 | + | 2186.04i | 0.816676 | + | 0.577096i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1127.14 | − | 1952.26i | −0.290356 | − | 0.502911i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5114.06 | + | 632.396i | 1.30157 | + | 0.160950i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1115.63 | 0.280549 | 0.140275 | − | 0.990113i | \(-0.455201\pi\) | ||||
0.140275 | + | 0.990113i | \(0.455201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2427.49 | −0.603220 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8874.07 | − | 1097.35i | −2.17928 | − | 0.269486i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3189.65 | + | 5524.63i | 0.774182 | + | 1.34092i | 0.935253 | + | 0.353979i | \(0.115172\pi\) |
−0.161071 | + | 0.986943i | \(0.551495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 92.7894 | − | 369.448i | 0.0220058 | − | 0.0876178i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 624.597 | + | 360.611i | 0.146442 | + | 0.0845485i | 0.571431 | − | 0.820650i | \(-0.306389\pi\) |
−0.424989 | + | 0.905199i | \(0.639722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6282.62i | − | 1.45637i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 508.140 | + | 1199.97i | 0.116471 | + | 0.275046i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2373.32 | − | 4110.72i | 0.537933 | − | 0.931728i | −0.461082 | − | 0.887358i | \(-0.652539\pi\) |
0.999015 | − | 0.0443703i | \(-0.0141281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7124.62 | − | 4113.40i | 1.59701 | − | 0.922034i | 0.604951 | − | 0.796263i | \(-0.293193\pi\) |
0.992059 | − | 0.125772i | \(-0.0401407\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1945.08 | − | 1122.99i | 0.426519 | − | 0.246251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2551.88 | − | 4419.99i | 0.553529 | − | 0.958741i | −0.444487 | − | 0.895785i | \(-0.646614\pi\) |
0.998016 | − | 0.0629556i | \(-0.0200526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5999.07 | + | 5813.22i | 1.28729 | + | 1.24741i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6818.51i | − | 1.44754i | −0.690042 | − | 0.723769i | \(-0.742408\pi\) | ||
0.690042 | − | 0.723769i | \(-0.257592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2317.66 | − | 1338.10i | −0.486822 | − | 0.281067i | 0.236433 | − | 0.971648i | \(-0.424022\pi\) |
−0.723255 | + | 0.690581i | \(0.757355\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4204.09 | − | 3173.68i | −0.873784 | − | 0.659624i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5111.38 | − | 8853.18i | −1.04038 | − | 1.80199i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 675.489 | − | 5462.55i | 0.136075 | − | 1.10041i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1743.71 | −0.347674 | −0.173837 | − | 0.984774i | \(-0.555617\pi\) | ||||
−0.173837 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3591.71 | 0.708872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2798.06 | − | 3473.62i | −0.546666 | − | 0.678652i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1187.45 | + | 2056.73i | 0.229673 | + | 0.397804i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4784.43 | + | 6337.79i | −0.907123 | + | 1.20164i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3329.12 | + | 1922.07i | 0.625000 | + | 0.360844i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1503.17i | − | 0.279448i | −0.990191 | − | 0.139724i | \(-0.955378\pi\) | ||
0.990191 | − | 0.139724i | \(-0.0446215\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 910.189 | − | 385.428i | 0.167569 | − | 0.0709587i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4370.72 | − | 7570.31i | 0.796916 | − | 1.38030i | −0.124699 | − | 0.992195i | \(-0.539796\pi\) |
0.921615 | − | 0.388105i | \(-0.126870\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3230.92 | + | 1865.37i | −0.583458 | + | 0.336860i | −0.762507 | − | 0.646980i | \(-0.776032\pi\) |
0.179048 | + | 0.983840i | \(0.442698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4312.95 | − | 2490.08i | 0.764163 | − | 0.441190i | −0.0666256 | − | 0.997778i | \(-0.521223\pi\) |
0.830788 | + | 0.556589i | \(0.187890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −224.269 | + | 388.446i | −0.0393626 | + | 0.0681781i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 851.133 | − | 360.421i | 0.147993 | − | 0.0626689i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8916.43i | − | 1.53599i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1902.95 | − | 1098.67i | −0.324790 | − | 0.187517i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −604.346 | + | 800.560i | −0.102203 | + | 0.135386i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3097.27 | − | 5364.63i | −0.514324 | − | 0.890836i | −0.999862 | − | 0.0166199i | \(-0.994709\pi\) |
0.485538 | − | 0.874216i | \(-0.338624\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 863.442 | + | 3030.86i | 0.142091 | + | 0.498769i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14434.4 | −2.35414 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2866.79 | −0.463395 | −0.231697 | − | 0.972788i | \(-0.574428\pi\) | ||||
−0.231697 | + | 0.972788i | \(0.574428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 288.286 | − | 2331.31i | 0.0461875 | − | 0.373509i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4918.21 | − | 8518.59i | −0.781044 | − | 1.35281i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4429.06 | + | 3343.51i | 0.691166 | + | 0.521764i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1253.66 | + | 723.803i | 0.193949 | + | 0.111976i | 0.593830 | − | 0.804591i | \(-0.297615\pi\) |
−0.399881 | + | 0.916567i | \(0.630949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5343.79i | − | 0.819618i | −0.912171 | − | 0.409809i | \(-0.865595\pi\) | ||
0.912171 | − | 0.409809i | \(-0.134405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1574.35 | + | 4069.89i | −0.239409 | + | 0.618902i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2201.40 | + | 3812.93i | −0.331922 | + | 0.574906i | −0.982889 | − | 0.184200i | \(-0.941031\pi\) |
0.650966 | + | 0.759107i | \(0.274364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11286.8 | − | 6516.43i | 1.68744 | − | 0.974243i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4640.81 | + | 2679.37i | −0.682263 | + | 0.393905i | −0.800707 | − | 0.599056i | \(-0.795543\pi\) |
0.118444 | + | 0.992961i | \(0.462209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −803.178 | + | 1391.14i | −0.117098 | + | 0.202820i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −648.828 | − | 1532.21i | −0.0938144 | − | 0.221543i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14337.6i | 2.05607i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7217.32 | + | 4166.92i | 1.02654 | + | 0.592674i | 0.915992 | − | 0.401196i | \(-0.131405\pi\) |
0.110550 | + | 0.993871i | \(0.464739\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12883.3 | − | 3235.74i | −1.81756 | − | 0.456493i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3597.98 | − | 6231.89i | −0.499454 | − | 0.865080i | 0.500546 | − | 0.865710i | \(-0.333133\pi\) |
−1.00000 | 0.000630094i | \(0.999799\pi\) | ||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3920.69 | + | 484.826i | 0.539903 | + | 0.0667635i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 438.823 | 0.0599483 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12312.1 | 1.66869 | 0.834343 | − | 0.551245i | \(-0.185847\pi\) | ||||
0.834343 | + | 0.551245i | \(0.185847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3762.61 | + | 465.277i | 0.505943 | + | 0.0625640i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5365.18 | + | 9292.76i | 0.715791 | + | 1.23979i | 0.962654 | + | 0.270736i | \(0.0872669\pi\) |
−0.246863 | + | 0.969050i | \(0.579400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 357.549 | + | 89.8008i | 0.0469644 | + | 0.0117954i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8674.30 | − | 5008.11i | −1.13060 | − | 0.652754i | −0.186516 | − | 0.982452i | \(-0.559720\pi\) |
−0.944086 | + | 0.329698i | \(0.893053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9393.58i | 1.21497i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1163.90 | + | 2748.56i | 0.149392 | + | 0.352790i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6466.47 | + | 11200.3i | −0.823705 | + | 1.42670i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3240.86 | + | 1871.11i | −0.409708 | + | 0.236545i | −0.690664 | − | 0.723176i | \(-0.742682\pi\) |
0.280956 | + | 0.959721i | \(0.409348\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8343.83 | + | 4817.31i | −1.03908 | + | 0.599913i | −0.919572 | − | 0.392920i | \(-0.871465\pi\) |
−0.119507 | + | 0.992833i | \(0.538131\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4811.67 | + | 8334.06i | −0.594756 | + | 1.03015i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 320.779 | + | 10191.7i | 0.0393571 | + | 1.25044i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3710.86i | − | 0.451942i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4547.71 | + | 2625.62i | 0.549803 | + | 0.317429i | 0.749043 | − | 0.662522i | \(-0.230514\pi\) |
−0.199239 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10068.3 | + | 7600.57i | 1.20835 | + | 0.912186i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6935.59 | + | 12012.8i | 0.820373 | + | 1.42093i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 926.963 | − | 7496.17i | 0.108858 | − | 0.880309i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11867.1 | 1.38364 | 0.691819 | − | 0.722071i | \(-0.256809\pi\) | ||||
0.691819 | + | 0.722071i | \(0.256809\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8108.04 | −0.938626 | −0.469313 | − | 0.883032i | \(-0.655498\pi\) | ||||
−0.469313 | + | 0.883032i | \(0.655498\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −642.669 | − | 2255.90i | −0.0738715 | − | 0.259304i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4345.62 | − | 7526.83i | −0.495985 | − | 0.859071i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3095.89 | − | 4101.04i | 0.348417 | − | 0.461538i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 390.334 | + | 225.360i | 0.0436235 | + | 0.0251860i | 0.521653 | − | 0.853158i | \(-0.325316\pi\) |
−0.478030 | + | 0.878344i | \(0.658649\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8133.13i | − | 0.902664i | −0.892356 | − | 0.451332i | \(-0.850949\pi\) | ||
0.892356 | − | 0.451332i | \(-0.149051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 944.219 | − | 399.838i | 0.104073 | − | 0.0440708i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2766.86 | + | 4792.35i | −0.302876 | + | 0.524597i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8016.30 | + | 4628.21i | −0.871520 | + | 0.503172i | −0.867853 | − | 0.496821i | \(-0.834500\pi\) |
−0.00366672 | + | 0.999993i | \(0.501167\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8854.31 | − | 5112.04i | 0.949618 | − | 0.548262i | 0.0566558 | − | 0.998394i | \(-0.481956\pi\) |
0.892962 | + | 0.450132i | \(0.148623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1753.92 | + | 3037.87i | −0.186840 | + | 0.323616i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9415.78 | + | 3987.20i | −0.996311 | + | 0.421897i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2896.50i | 0.304442i | 0.988346 | + | 0.152221i | \(0.0486425\pi\) | ||||
−0.988346 | + | 0.152221i | \(0.951357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13545.8 | + | 7820.69i | 1.41430 | + | 0.816545i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6802.40 | + | 9010.94i | −0.705529 | + | 0.934594i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3995.15 | + | 6919.80i | 0.408939 | + | 0.708303i | 0.994771 | − | 0.102129i | \(-0.0325655\pi\) |
−0.585832 | + | 0.810432i | \(0.699232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13441.8 | + | 10827.6i | −1.36690 | + | 1.10106i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4639.50 | 0.468727 | 0.234363 | − | 0.972149i | \(-0.424699\pi\) | ||||
0.234363 | + | 0.972149i | \(0.424699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4926.63 | 0.494514 | 0.247257 | − | 0.968950i | \(-0.420471\pi\) | ||||
0.247257 | + | 0.968950i | \(0.420471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2759.64 | + | 22316.7i | −0.275216 | + | 2.22562i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3404.64 | − | 5897.01i | −0.337362 | − | 0.584328i | 0.646574 | − | 0.762852i | \(-0.276201\pi\) |
−0.983936 | + | 0.178523i | \(0.942868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13682.0 | + | 10328.6i | 1.33850 | + | 1.01044i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −375.935 | − | 217.046i | −0.0365444 | − | 0.0210989i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5119.98i | − | 0.494570i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8709.26 | − | 8439.45i | −0.835995 | − | 0.810097i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1116.45 | − | 1933.75i | 0.106497 | − | 0.184458i | −0.807852 | − | 0.589386i | \(-0.799370\pi\) |
0.914349 | + | 0.404927i | \(0.132703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3144.09 | + | 1815.24i | −0.298042 | + | 0.172074i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12831.4 | − | 7408.20i | 1.20133 | − | 0.693586i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 60.8391 | − | 105.376i | 0.00566095 | − | 0.00980505i | −0.863181 | − | 0.504895i | \(-0.831531\pi\) |
0.868842 | + | 0.495089i | \(0.164865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5671.82 | − | 13394.0i | −0.524516 | − | 1.23865i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9638.92i | 0.885944i | 0.896535 | + | 0.442972i | \(0.146076\pi\) | ||||
−0.896535 | + | 0.442972i | \(0.853924\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1503.16 | + | 867.849i | 0.137320 | + | 0.0792819i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2924.74 | − | 11645.1i | 0.265571 | − | 1.05739i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1875.57 | + | 3248.58i | 0.168261 | + | 0.291436i | 0.937808 | − | 0.347153i | \(-0.112852\pi\) |
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9970.82 | − | 1232.97i | −0.889148 | − | 0.109951i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13881.9 | 1.23054 | 0.615272 | − | 0.788315i | \(-0.289046\pi\) | ||||
0.615272 | + | 0.788315i | \(0.289046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21375.9 | −1.88359 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6340.57 | + | 784.064i | 0.555413 | + | 0.0686814i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3096.63 | + | 5363.52i | 0.269658 | + | 0.467061i | 0.968773 | − | 0.247948i | \(-0.0797561\pi\) |
−0.699116 | + | 0.715009i | \(0.746423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10046.9 | + | 1564.69i | −0.864678 | + | 0.134664i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2304.25 | + | 1330.36i | 0.197160 | + | 0.113830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2762.03i | 0.234959i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7101.78 | − | 16770.9i | −0.600643 | − | 1.41842i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2256.61 | − | 3908.57i | 0.189758 | − | 0.328671i | −0.755411 | − | 0.655251i | \(-0.772563\pi\) |
0.945170 | + | 0.326580i | \(0.105896\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 537.821 | − | 310.511i | 0.0449661 | − | 0.0259612i | −0.477348 | − | 0.878714i | \(-0.658402\pi\) |
0.522315 | + | 0.852753i | \(0.325069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32964.2 | + | 19031.9i | −2.72475 | + | 1.57313i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3168.58 | + | 5488.13i | −0.260424 | + | 0.451067i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4824.75 | − | 4979.00i | 0.394306 | − | 0.406912i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15302.6i | − | 1.24358i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2154.74 | + | 1244.04i | 0.174127 | + | 0.100532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7656.67 | + | 5780.06i | 0.615288 | + | 0.464484i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5101.80 | + | 8836.58i | 0.405441 | + | 0.702244i | 0.994373 | − | 0.105938i | \(-0.0337846\pi\) |
−0.588932 | + | 0.808183i | \(0.700451\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 235.564 | − | 1904.96i | 0.0186170 | − | 0.150552i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2700.10 | −0.212219 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6359.52 | −0.497100 | −0.248550 | − | 0.968619i | \(-0.579954\pi\) | ||||
−0.248550 | + | 0.968619i | \(0.579954\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7136.48 | − | 2033.07i | 0.554786 | − | 0.158049i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 511.247 | + | 885.507i | 0.0395279 | + | 0.0684643i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5111.18 | + | 6770.63i | −0.390914 | + | 0.517833i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18905.0 | + | 10914.8i | 1.43812 | + | 0.830298i | 0.997719 | − | 0.0675048i | \(-0.0215038\pi\) |
0.440399 | + | 0.897802i | \(0.354837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 424.689i | 0.0321332i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18715.3 | − | 7925.17i | 1.40849 | − | 0.596436i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −312.001 | + | 540.401i | −0.0233557 | + | 0.0404533i | −0.877467 | − | 0.479637i | \(-0.840768\pi\) |
0.854111 | + | 0.520090i | \(0.174102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5476.19 | − | 3161.68i | 0.407761 | − | 0.235421i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12198.4 | + | 7042.74i | −0.898739 | + | 0.518887i | −0.876791 | − | 0.480872i | \(-0.840320\pi\) |
−0.0219483 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4105.50 | + | 7110.94i | −0.300893 | + | 0.521162i | −0.976338 | − | 0.216248i | \(-0.930618\pi\) |
0.675445 | + | 0.737410i | \(0.263951\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1142.08 | − | 483.625i | 0.0832654 | − | 0.0352595i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5393.96i | 0.391207i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9649.07 | + | 5570.89i | 0.696180 | + | 0.401940i | 0.805923 | − | 0.592020i | \(-0.201669\pi\) |
−0.109743 | + | 0.993960i | \(0.535003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5266.13 | − | 6975.89i | 0.377984 | − | 0.500705i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7140.10 | + | 12367.0i | 0.507226 | + | 0.878541i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11297.2 | + | 3218.38i | −0.798429 | + | 0.227459i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5198.19 | 0.365507 | 0.182753 | − | 0.983159i | \(-0.441499\pi\) | ||||
0.182753 | + | 0.983159i | \(0.441499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22423.2 | −1.56865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1905.43 | − | 15408.8i | 0.132621 | − | 1.07248i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5485.15 | − | 9500.55i | −0.379845 | − | 0.657910i | 0.611195 | − | 0.791480i | \(-0.290689\pi\) |
−0.991039 | + | 0.133570i | \(0.957356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8365.76 | − | 6315.35i | −0.573514 | − | 0.432948i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22359.1 | − | 12909.0i | −1.52515 | − | 0.880547i | −0.999555 | − | 0.0298138i | \(-0.990509\pi\) |
−0.525597 | − | 0.850734i | \(-0.676158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11968.5i | − | 0.812323i | −0.913801 | − | 0.406162i | \(-0.866867\pi\) | ||
0.913801 | − | 0.406162i | \(-0.133133\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19389.8 | + | 20009.7i | −1.30948 | + | 1.35134i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2239.52 | − | 3878.96i | 0.150495 | − | 0.260665i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5412.72 | + | 3125.04i | −0.361937 | + | 0.208964i | −0.669930 | − | 0.742424i | \(-0.733676\pi\) |
0.307993 | + | 0.951389i | \(0.400343\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2340.18 | − | 1351.10i | 0.154948 | − | 0.0894594i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2469.83 | + | 4277.87i | −0.162733 | + | 0.281862i | −0.935848 | − | 0.352404i | \(-0.885364\pi\) |
0.773115 | + | 0.634266i | \(0.218698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13943.1 | − | 32926.7i | −0.914212 | − | 2.15891i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14836.2i | − | 0.968042i | −0.875056 | − | 0.484021i | \(-0.839176\pi\) | ||
0.875056 | − | 0.484021i | \(-0.160824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10534.4 | − | 6082.04i | −0.684028 | − | 0.394924i | 0.117343 | − | 0.993091i | \(-0.462562\pi\) |
−0.801371 | + | 0.598168i | \(0.795896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10584.5 | − | 1648.42i | 0.683964 | − | 0.106520i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9732.46 | + | 16857.1i | 0.622877 | + | 1.07886i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11882.4 | + | 1469.35i | 0.756837 | + | 0.0935891i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14359.8 | −0.910276 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8372.13 | 0.528192 | 0.264096 | − | 0.964496i | \(-0.414926\pi\) | ||||
0.264096 | + | 0.964496i | \(0.414926\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24160.0 | + | 2987.58i | 1.51702 | + | 0.187592i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5102.77 | + | 8838.26i | 0.318893 | + | 0.552340i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6128.18 | − | 24399.8i | 0.379385 | − | 1.51055i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12972.5 | + | 7489.69i | 0.799351 | + | 0.461505i | 0.843244 | − | 0.537531i | \(-0.180643\pi\) |
−0.0438933 | + | 0.999036i | \(0.513976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4861.62i | 0.298170i | 0.988824 | + | 0.149085i | \(0.0476329\pi\) | ||||
−0.988824 | + | 0.149085i | \(0.952367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 386.960 | + | 913.807i | 0.0236226 | + | 0.0557847i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13592.4 | + | 23542.8i | −0.825925 | + | 1.43054i | 0.0752852 | + | 0.997162i | \(0.476013\pi\) |
−0.901210 | + | 0.433382i | \(0.857320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7070.10 | + | 4081.92i | −0.427620 | + | 0.246887i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3755.80 | − | 2168.41i | 0.225078 | − | 0.129949i | −0.383222 | − | 0.923656i | \(-0.625185\pi\) |
0.608299 | + | 0.793708i | \(0.291852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4017.37 | + | 6958.30i | −0.239652 | + | 0.415089i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19875.5 | + | 19259.8i | 1.18024 | + | 1.14368i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15562.8i | − | 0.919939i | −0.887935 | − | 0.459969i | \(-0.847860\pi\) | ||
0.887935 | − | 0.459969i | \(-0.152140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12267.0 | − | 7082.34i | −0.721830 | − | 0.416749i | 0.0935956 | − | 0.995610i | \(-0.470164\pi\) |
−0.815426 | + | 0.578861i | \(0.803497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15869.7 | − | 11980.1i | −0.929603 | − | 0.701761i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −538.606 | − | 932.892i | −0.0312667 | − | 0.0541555i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.0198 | − | 89.1148i | 0.000636845 | − | 0.00515004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8737.62 | −0.502700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21045.6 | 1.20542 | 0.602710 | − | 0.797960i | \(-0.294087\pi\) | ||||
0.602710 | + | 0.797960i | \(0.294087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7718.51 | + | 6217.40i | −0.440127 | + | 0.354530i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9037.10 | + | 15652.7i | 0.513034 | + | 0.888601i | 0.999886 | + | 0.0151166i | \(0.00481194\pi\) |
−0.486852 | + | 0.873485i | \(0.661855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4582.94 | − | 6070.89i | 0.257884 | − | 0.341611i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21428.1 | − | 12371.5i | −1.20047 | − | 0.693092i | −0.239811 | − | 0.970820i | \(-0.577086\pi\) |
−0.960660 | + | 0.277727i | \(0.910419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33957.8i | 1.89410i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 555.388 | − | 235.184i | 0.0308433 | − | 0.0130609i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6985.44 | − | 12099.1i | 0.386247 | − | 0.668999i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20190.9 | + | 11657.2i | −1.11158 | + | 0.641769i | −0.939237 | − | 0.343269i | \(-0.888466\pi\) |
−0.172339 | + | 0.985038i | \(0.555132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17608.3 | − | 10166.2i | 0.961038 | − | 0.554855i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30263.5 | − | 52418.0i | 1.64464 | − | 2.84860i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17945.9 | − | 7599.38i | 0.971070 | − | 0.411209i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 901.167i | 0.0485544i | 0.999705 | + | 0.0242772i | \(0.00772843\pi\) | ||||
−0.999705 | + | 0.0242772i | \(0.992272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7325.99 | − | 4229.66i | −0.393037 | − | 0.226920i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3804.30 | − | 5039.45i | 0.203232 | − | 0.269215i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2917.65 | + | 5053.52i | 0.154548 | + | 0.267685i | 0.932894 | − | 0.360150i | \(-0.117274\pi\) |
−0.778346 | + | 0.627835i | \(0.783941\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6839.90 | + | 24009.5i | 0.360783 | + | 1.26642i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23623.1 | 1.24080 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13831.8 | 0.723469 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3458.50 | + | 27968.2i | −0.180139 | + | 1.45675i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9234.41 | − | 15994.5i | −0.478978 | − | 0.829615i | 0.520731 | − | 0.853721i | \(-0.325659\pi\) |
−0.999709 | + | 0.0241060i | \(0.992326\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18837.7 | − | 14220.6i | −0.968991 | − | 0.731495i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 863.142 | + | 498.335i | 0.0442156 | + | 0.0255279i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32300.3i | 1.64780i | 0.566735 | + | 0.823900i | \(0.308206\pi\) | ||||
−0.566735 | + | 0.823900i | \(0.691794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14559.1 | + | 13245.9i | 0.739680 | + | 0.672959i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −839.898 | + | 1454.75i | −0.0424962 | + | 0.0736056i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5189.33 | − | 2996.06i | 0.261490 | − | 0.150971i | −0.363524 | − | 0.931585i | \(-0.618427\pi\) |
0.625014 | + | 0.780613i | \(0.285093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28413.5 | − | 16404.5i | 1.42011 | − | 0.819903i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 653.898 | − | 1132.58i | 0.0325494 | − | 0.0563772i | −0.849292 | − | 0.527924i | \(-0.822971\pi\) |
0.881841 | + | 0.471546i | \(0.156304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4567.56 | − | 10786.3i | −0.226442 | − | 0.534743i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30175.4i | 1.48995i | 0.667095 | + | 0.744973i | \(0.267538\pi\) | ||||
−0.667095 | + | 0.744973i | \(0.732462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23837.2 | − | 13762.4i | −1.17225 | − | 0.676798i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25969.3 | + | 6522.37i | 1.27198 | + | 0.319466i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −536.353 | − | 928.990i | −0.0260610 | − | 0.0451389i | 0.852701 | − | 0.522400i | \(-0.174963\pi\) |
−0.878762 | + | 0.477261i | \(0.841630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5753.16 | + | 711.425i | 0.278428 | + | 0.0344300i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30391.7 | −1.46499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7773.72 | −0.373237 | −0.186619 | − | 0.982432i | \(-0.559753\pi\) | ||||
−0.186619 | + | 0.982432i | \(0.559753\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12518.2 | − | 1547.98i | −0.598660 | − | 0.0740293i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10431.8 | + | 18068.4i | 0.496916 | + | 0.860683i | 0.999994 | − | 0.00355768i | \(-0.00113245\pi\) |
−0.503078 | + | 0.864241i | \(0.667799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −45062.7 | − | 11317.8i | −2.12973 | − | 0.534897i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6916.95 | + | 3993.50i | 0.325628 | + | 0.188001i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1423.15i | 0.0667364i | 0.999443 | + | 0.0333682i | \(0.0106234\pi\) | ||||
−0.999443 | + | 0.0333682i | \(0.989377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12925.6 | + | 30523.8i | 0.603767 | + | 1.42580i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2664.15 | − | 4614.44i | 0.123962 | − | 0.214709i | −0.797365 | − | 0.603498i | \(-0.793773\pi\) |
0.921327 | + | 0.388789i | \(0.127107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18928.6 | + | 10928.4i | −0.877337 | + | 0.506531i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30879.3 | − | 17828.1i | 1.42024 | − | 0.819974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14811.7 | + | 25654.5i | −0.678621 | + | 1.17541i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 714.096 | − | 1846.02i | 0.0325922 | − | 0.0842548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46146.2i | 2.09813i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9982.43 | + | 5763.36i | 0.452141 | + | 0.261044i | 0.708734 | − | 0.705476i | \(-0.249267\pi\) |
−0.256593 | + | 0.966520i | \(0.582600\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2991.01 | + | 2257.93i | 0.134959 | + | 0.101881i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4274.17 | + | 7403.09i | 0.191400 | + | 0.331515i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4006.36 | − | 32398.7i | 0.178731 | − | 1.44536i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42557.4 | −1.89142 | −0.945709 | − | 0.325013i | \(-0.894631\pi\) | ||||
−0.945709 | + | 0.325013i | \(0.894631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10688.2 | 0.473242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1855.20 | + | 6512.15i | 0.0818357 | + | 0.287260i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16294.5 | − | 28222.9i | −0.716091 | − | 1.24031i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14860.3 | − | 19685.0i | 0.648212 | − | 0.858668i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16963.5 | − | 9793.90i | −0.737214 | − | 0.425630i | 0.0838418 | − | 0.996479i | \(-0.473281\pi\) |
−0.821055 | + | 0.570849i | \(0.806614\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26034.2i | 1.12723i | 0.826038 | + | 0.563615i | \(0.190590\pi\) | ||||
−0.826038 | + | 0.563615i | \(0.809410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39363.8 | − | 16669.0i | 1.69809 | − | 0.719074i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19577.1 | − | 33908.5i | 0.841418 | − | 1.45738i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −856.986 | + | 494.781i | −0.0366979 | + | 0.0211875i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25214.2 | + | 14557.4i | −1.07184 | + | 0.618827i | −0.928683 | − | 0.370874i | \(-0.879058\pi\) |
−0.143156 | + | 0.989700i | \(0.545725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14791.2 | − | 25619.1i | 0.626475 | − | 1.08509i | −0.361779 | − | 0.932264i | \(-0.617831\pi\) |
0.988254 | − | 0.152822i | \(-0.0488361\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10746.7 | − | 4550.78i | 0.453516 | − | 0.192046i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 33550.7i | − | 1.41073i | −0.708845 | − | 0.705364i | \(-0.750784\pi\) | ||
0.708845 | − | 0.705364i | \(-0.249216\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40841.4 | − | 23579.8i | −1.71108 | − | 0.987890i | −0.933116 | − | 0.359576i | \(-0.882921\pi\) |
−0.777960 | − | 0.628314i | \(-0.783745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15978.3 | − | 21166.0i | 0.667005 | − | 0.883563i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13522.2 | − | 23421.2i | −0.560426 | − | 0.970687i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27229.4 | + | 33803.6i | 1.12448 | + | 1.39597i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4790.07 | 0.197106 | 0.0985528 | − | 0.995132i | \(-0.468579\pi\) | ||||
0.0985528 | + | 0.995132i | \(0.468579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24190.0 | 0.991839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4348.10 | − | 35162.2i | 0.177647 | − | 1.43660i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8598.96 | + | 14893.8i | 0.350075 | + | 0.606347i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11098.6 | − | 8378.38i | −0.448649 | − | 0.338687i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7718.02 | + | 4456.00i | 0.310894 | + | 0.179494i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4925.15i | 0.197695i | 0.995103 | + | 0.0988475i | \(0.0315156\pi\) | ||||
−0.995103 | + | 0.0988475i | \(0.968484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19656.1 | − | 19047.2i | −0.786228 | − | 0.761871i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2465.89 | − | 4271.05i | 0.0982885 | − | 0.170241i | −0.812688 | − | 0.582699i | \(-0.801997\pi\) |
0.910976 | + | 0.412459i | \(0.135330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30455.0 | + | 17583.2i | −1.20968 | + | 0.698407i | −0.962688 | − | 0.270612i | \(-0.912774\pi\) |
−0.246987 | + | 0.969019i | \(0.579441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27078.5 | + | 15633.8i | −1.06809 | + | 0.616664i | −0.927660 | − | 0.373426i | \(-0.878183\pi\) |
−0.140433 | + | 0.990090i | \(0.544850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24512.8 | − | 42457.4i | 0.963538 | − | 1.66890i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20713.2 | − | 48914.2i | −0.811369 | − | 1.91605i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29396.2i | − | 1.14752i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27798.0 | − | 16049.2i | −1.08140 | − | 0.624347i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6966.82 | − | 27738.9i | 0.270093 | − | 1.07540i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6398.52 | − | 11082.6i | −0.246366 | − | 0.426718i | 0.716149 | − | 0.697947i | \(-0.245903\pi\) |
−0.962515 | + | 0.271230i | \(0.912570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8992.07 | − | 1111.94i | −0.345045 | − | 0.0426677i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2497.90 | 0.0955235 | 0.0477618 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477618 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8139.20 | −0.310199 | −0.155100 | − | 0.987899i | \(-0.549570\pi\) | ||||
−0.155100 | + | 0.987899i | \(0.549570\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18522.0 | + | 2290.40i | 0.703514 | + | 0.0869953i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2928.50 | − | 5072.31i | −0.110856 | − | 0.192008i | 0.805260 | − | 0.592922i | \(-0.202026\pi\) |
−0.916116 | + | 0.400914i | \(0.868693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12214.2 | − | 19697.3i | −0.459248 | − | 0.740611i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5452.81 | + | 3148.18i | 0.204335 | + | 0.117973i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25824.1i | 0.964475i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4811.98 | + | 11363.5i | 0.179116 | + | 0.422984i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2182.48 | − | 3780.17i | 0.0809677 | − | 0.140240i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47856.3 | − | 27629.9i | 1.76951 | − | 1.02163i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4474.70 | − | 2583.47i | 0.164358 | − | 0.0948922i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11271.2 | − | 19522.3i | 0.412629 | − | 0.714694i | −0.582547 | − | 0.812797i | \(-0.697944\pi\) |
0.995176 | + | 0.0981025i | \(0.0312773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28714.2 | + | 29632.2i | −1.04773 | + | 1.08123i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14306.2i | − | 0.520291i | −0.965569 | − | 0.260146i | \(-0.916229\pi\) | ||
0.965569 | − | 0.260146i | \(-0.0837706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27304.7 | − | 15764.4i | −0.989765 | − | 0.571441i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15942.2 | + | 12034.8i | 0.575991 | + | 0.434818i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10485.9 | − | 18162.0i | −0.376384 | − | 0.651916i | 0.614149 | − | 0.789190i | \(-0.289499\pi\) |
−0.990533 | + | 0.137274i | \(0.956166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 958.557 | − | 7751.66i | 0.0342948 | − | 0.277335i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28981.6 | 1.03352 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8245.67 | −0.293098 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4939.52 | − | 1407.19i | 0.175011 | − | 0.0498577i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10933.3 | − | 18937.1i | −0.386125 | − | 0.668789i | 0.605799 | − | 0.795618i | \(-0.292853\pi\) |
−0.991925 | + | 0.126829i | \(0.959520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27366.8 | − | 36252.0i | 0.960288 | − | 1.27207i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47380.0 | + | 27354.8i | 1.65721 | + | 0.956790i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32284.1i | − | 1.12559i | −0.826597 | − | 0.562794i | \(-0.809726\pi\) | ||
0.826597 | − | 0.562794i | \(-0.190274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17851.0 | + | 7559.17i | −0.620388 | + | 0.262709i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11899.7 | + | 20610.9i | −0.412242 | + | 0.714024i | −0.995135 | − | 0.0985254i | \(-0.968587\pi\) |
0.582893 | + | 0.812549i | \(0.301921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32531.7 | + | 18782.2i | −1.12341 | + | 0.648602i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8449.22 | + | 4878.16i | −0.289929 | + | 0.167391i | −0.637910 | − | 0.770111i | \(-0.720201\pi\) |
0.347981 | + | 0.937502i | \(0.386867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15941.5 | + | 27611.6i | −0.545295 | + | 0.944478i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23829.3 | − | 10090.7i | 0.812531 | − | 0.344074i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36031.4i | 1.22473i | 0.790574 | + | 0.612367i | \(0.209782\pi\) | ||||
−0.790574 | + | 0.612367i | \(0.790218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2891.31 | + | 1669.30i | 0.0979692 | + | 0.0565626i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1404.24 | + | 1860.15i | −0.0474321 | + | 0.0628320i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32966.2 | + | 57099.1i | 1.10658 | + | 1.91666i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4619.02 | − | 1315.88i | 0.154565 | − | 0.0440330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23528.0 | 0.784864 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24872.5 | −0.827142 | −0.413571 | − | 0.910472i | \(-0.635719\pi\) | ||||
−0.413571 | + | 0.910472i | \(0.635719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5685.92 | − | 45980.9i | 0.188502 | − | 1.52438i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12506.4 | + | 21661.8i | 0.413337 | + | 0.715921i | 0.995252 | − | 0.0973288i | \(-0.0310299\pi\) |
−0.581915 | + | 0.813249i | \(0.697697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9112.66 | − | 6879.18i | −0.299322 | − | 0.225959i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2276.88 | − | 1314.56i | −0.0745588 | − | 0.0430465i | 0.462257 | − | 0.886746i | \(-0.347040\pi\) |
−0.536816 | + | 0.843699i | \(0.680373\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7973.21i | − | 0.260291i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3627.05 | + | 3743.00i | −0.118046 | + | 0.121819i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 806.903 | − | 1397.60i | 0.0261813 | − | 0.0453473i | −0.852638 | − | 0.522502i | \(-0.824999\pi\) |
0.878819 | + | 0.477155i | \(0.158332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36194.9 | − | 20897.1i | 1.17083 | − | 0.675977i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 902.846 | − | 521.258i | 0.0290281 | − | 0.0167594i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16663.5 | − | 28862.0i | 0.534140 | − | 0.925157i | −0.465065 | − | 0.885277i | \(-0.653969\pi\) |
0.999204 | − | 0.0398803i | \(-0.0126977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12551.3 | − | 29639.8i | −0.401110 | − | 0.947221i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 28215.7i | − | 0.898993i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41092.8 | − | 23724.9i | −1.30534 | − | 0.753637i | −0.324024 | − | 0.946049i | \(-0.605036\pi\) |
−0.981314 | + | 0.192412i | \(0.938369\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2519.91 | + | 16180.4i | 0.0798063 | + | 0.512437i |
(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 | 588.4.k.e.521.23 | 48 | ||
3.2 | odd | 2 | inner | 588.4.k.e.521.17 | 48 | ||
7.2 | even | 3 | inner | 588.4.k.e.509.8 | 48 | ||
7.3 | odd | 6 | 588.4.f.d.293.16 | yes | 24 | ||
7.4 | even | 3 | 588.4.f.d.293.9 | ✓ | 24 | ||
7.5 | odd | 6 | inner | 588.4.k.e.509.17 | 48 | ||
7.6 | odd | 2 | inner | 588.4.k.e.521.2 | 48 | ||
21.2 | odd | 6 | inner | 588.4.k.e.509.2 | 48 | ||
21.5 | even | 6 | inner | 588.4.k.e.509.23 | 48 | ||
21.11 | odd | 6 | 588.4.f.d.293.15 | yes | 24 | ||
21.17 | even | 6 | 588.4.f.d.293.10 | yes | 24 | ||
21.20 | even | 2 | inner | 588.4.k.e.521.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.f.d.293.9 | ✓ | 24 | 7.4 | even | 3 | ||
588.4.f.d.293.10 | yes | 24 | 21.17 | even | 6 | ||
588.4.f.d.293.15 | yes | 24 | 21.11 | odd | 6 | ||
588.4.f.d.293.16 | yes | 24 | 7.3 | odd | 6 | ||
588.4.k.e.509.2 | 48 | 21.2 | odd | 6 | inner | ||
588.4.k.e.509.8 | 48 | 7.2 | even | 3 | inner | ||
588.4.k.e.509.17 | 48 | 7.5 | odd | 6 | inner | ||
588.4.k.e.509.23 | 48 | 21.5 | even | 6 | inner | ||
588.4.k.e.521.2 | 48 | 7.6 | odd | 2 | inner | ||
588.4.k.e.521.8 | 48 | 21.20 | even | 2 | inner | ||
588.4.k.e.521.17 | 48 | 3.2 | odd | 2 | inner | ||
588.4.k.e.521.23 | 48 | 1.1 | even | 1 | trivial |