Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(538,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1617.538");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.c (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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 231) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 538.20 | ||
Character | \(\chi\) | \(=\) | 1617.538 |
Dual form | 1617.2.c.a.538.13 |
$q$-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 \(\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(442\) | \(1079\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.615506i | 0.435229i | 0.976035 | + | 0.217614i | \(0.0698275\pi\) | ||||
−0.976035 | + | 0.217614i | \(0.930172\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.62115 | 0.810576 | ||||||||
\(5\) | − | 3.28584i | − | 1.46947i | −0.678354 | − | 0.734735i | \(-0.737306\pi\) | ||
0.678354 | − | 0.734735i | \(-0.262694\pi\) | |||||||
\(6\) | −0.615506 | −0.251279 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.22884i | 0.788015i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.02245 | 0.639556 | ||||||||
\(11\) | −0.0656613 | + | 3.31597i | −0.0197976 | + | 0.999804i | ||||
\(12\) | 1.62115i | 0.467986i | ||||||||
\(13\) | −0.142630 | −0.0395583 | −0.0197792 | − | 0.999804i | \(-0.506296\pi\) | ||||
−0.0197792 | + | 0.999804i | \(0.506296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.28584 | 0.848399 | ||||||||
\(16\) | 1.87044 | 0.467609 | ||||||||
\(17\) | 7.26368 | 1.76170 | 0.880851 | − | 0.473394i | \(-0.156971\pi\) | ||||
0.880851 | + | 0.473394i | \(0.156971\pi\) | |||||||
\(18\) | − | 0.615506i | − | 0.145076i | ||||||
\(19\) | 0.869142 | 0.199395 | 0.0996974 | − | 0.995018i | \(-0.468213\pi\) | ||||
0.0996974 | + | 0.995018i | \(0.468213\pi\) | |||||||
\(20\) | − | 5.32684i | − | 1.19112i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.04100 | − | 0.0404149i | −0.435143 | − | 0.00861650i | ||||
\(23\) | −3.56308 | −0.742954 | −0.371477 | − | 0.928442i | \(-0.621149\pi\) | ||||
−0.371477 | + | 0.928442i | \(0.621149\pi\) | |||||||
\(24\) | −2.22884 | −0.454961 | ||||||||
\(25\) | −5.79672 | −1.15934 | ||||||||
\(26\) | − | 0.0877894i | − | 0.0172169i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70637i | 0.688256i | 0.938923 | + | 0.344128i | \(0.111825\pi\) | ||||
−0.938923 | + | 0.344128i | \(0.888175\pi\) | |||||||
\(30\) | 2.02245i | 0.369248i | ||||||||
\(31\) | − | 4.82080i | − | 0.865841i | −0.901432 | − | 0.432921i | \(-0.857483\pi\) | ||
0.901432 | − | 0.432921i | \(-0.142517\pi\) | |||||||
\(32\) | 5.60895i | 0.991532i | ||||||||
\(33\) | −3.31597 | − | 0.0656613i | −0.577237 | − | 0.0114302i | ||||
\(34\) | 4.47084i | 0.766743i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.62115 | −0.270192 | ||||||||
\(37\) | 9.39271 | 1.54415 | 0.772076 | − | 0.635531i | \(-0.219219\pi\) | ||||
0.772076 | + | 0.635531i | \(0.219219\pi\) | |||||||
\(38\) | 0.534962i | 0.0867824i | ||||||||
\(39\) | − | 0.142630i | − | 0.0228390i | ||||||
\(40\) | 7.32361 | 1.15796 | ||||||||
\(41\) | 3.19487 | 0.498954 | 0.249477 | − | 0.968381i | \(-0.419741\pi\) | ||||
0.249477 | + | 0.968381i | \(0.419741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.66641i | − | 1.47411i | −0.675831 | − | 0.737057i | \(-0.736215\pi\) | ||
0.675831 | − | 0.737057i | \(-0.263785\pi\) | |||||||
\(44\) | −0.106447 | + | 5.37570i | −0.0160475 | + | 0.810417i | ||||
\(45\) | 3.28584i | 0.489824i | ||||||||
\(46\) | − | 2.19310i | − | 0.323355i | ||||||
\(47\) | 8.76297i | 1.27821i | 0.769119 | + | 0.639106i | \(0.220695\pi\) | ||||
−0.769119 | + | 0.639106i | \(0.779305\pi\) | |||||||
\(48\) | 1.87044i | 0.269974i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 3.56792i | − | 0.504580i | ||||||
\(51\) | 7.26368i | 1.01712i | ||||||||
\(52\) | −0.231224 | −0.0320650 | ||||||||
\(53\) | −6.62537 | −0.910065 | −0.455032 | − | 0.890475i | \(-0.650372\pi\) | ||||
−0.455032 | + | 0.890475i | \(0.650372\pi\) | |||||||
\(54\) | 0.615506 | 0.0837598 | ||||||||
\(55\) | 10.8958 | + | 0.215752i | 1.46918 | + | 0.0290920i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.869142i | 0.115121i | ||||||||
\(58\) | −2.28130 | −0.299549 | ||||||||
\(59\) | − | 1.54704i | − | 0.201408i | −0.994916 | − | 0.100704i | \(-0.967890\pi\) | ||
0.994916 | − | 0.100704i | \(-0.0321095\pi\) | |||||||
\(60\) | 5.32684 | 0.687692 | ||||||||
\(61\) | 15.2529 | 1.95293 | 0.976467 | − | 0.215669i | \(-0.0691932\pi\) | ||||
0.976467 | + | 0.215669i | \(0.0691932\pi\) | |||||||
\(62\) | 2.96723 | 0.376839 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.288529 | 0.0360662 | ||||||||
\(65\) | 0.468657i | 0.0581298i | ||||||||
\(66\) | 0.0404149 | − | 2.04100i | 0.00497474 | − | 0.251230i | ||||
\(67\) | 13.0157 | 1.59012 | 0.795061 | − | 0.606530i | \(-0.207439\pi\) | ||||
0.795061 | + | 0.606530i | \(0.207439\pi\) | |||||||
\(68\) | 11.7755 | 1.42799 | ||||||||
\(69\) | − | 3.56308i | − | 0.428945i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.66532 | 0.316315 | 0.158158 | − | 0.987414i | \(-0.449445\pi\) | ||||
0.158158 | + | 0.987414i | \(0.449445\pi\) | |||||||
\(72\) | − | 2.22884i | − | 0.262672i | ||||||
\(73\) | −5.48838 | −0.642366 | −0.321183 | − | 0.947017i | \(-0.604080\pi\) | ||||
−0.321183 | + | 0.947017i | \(0.604080\pi\) | |||||||
\(74\) | 5.78127i | 0.672059i | ||||||||
\(75\) | − | 5.79672i | − | 0.669348i | ||||||
\(76\) | 1.40901 | 0.161625 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0877894 | 0.00994019 | ||||||||
\(79\) | 7.05347i | 0.793577i | 0.917910 | + | 0.396789i | \(0.129875\pi\) | ||||
−0.917910 | + | 0.396789i | \(0.870125\pi\) | |||||||
\(80\) | − | 6.14595i | − | 0.687138i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.96646i | 0.217159i | ||||||||
\(83\) | −6.31032 | −0.692648 | −0.346324 | − | 0.938115i | \(-0.612570\pi\) | ||||
−0.346324 | + | 0.938115i | \(0.612570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 23.8673i | − | 2.58877i | ||||||
\(86\) | 5.94974 | 0.641577 | ||||||||
\(87\) | −3.70637 | −0.397365 | ||||||||
\(88\) | −7.39078 | − | 0.146349i | −0.787860 | − | 0.0156008i | ||||
\(89\) | − | 7.87864i | − | 0.835134i | −0.908646 | − | 0.417567i | \(-0.862883\pi\) | ||
0.908646 | − | 0.417567i | \(-0.137117\pi\) | |||||||
\(90\) | −2.02245 | −0.213185 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.77630 | −0.602221 | ||||||||
\(93\) | 4.82080 | 0.499894 | ||||||||
\(94\) | −5.39367 | −0.556314 | ||||||||
\(95\) | − | 2.85586i | − | 0.293005i | ||||||
\(96\) | −5.60895 | −0.572461 | ||||||||
\(97\) | − | 8.07193i | − | 0.819580i | −0.912180 | − | 0.409790i | \(-0.865602\pi\) | ||
0.912180 | − | 0.409790i | \(-0.134398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0656613 | − | 3.31597i | 0.00659921 | − | 0.333268i | ||||
\(100\) | −9.39737 | −0.939737 | ||||||||
\(101\) | −6.89607 | −0.686185 | −0.343092 | − | 0.939302i | \(-0.611474\pi\) | ||||
−0.343092 | + | 0.939302i | \(0.611474\pi\) | |||||||
\(102\) | −4.47084 | −0.442679 | ||||||||
\(103\) | − | 3.46014i | − | 0.340938i | −0.985363 | − | 0.170469i | \(-0.945472\pi\) | ||
0.985363 | − | 0.170469i | \(-0.0545282\pi\) | |||||||
\(104\) | − | 0.317899i | − | 0.0311725i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.07796i | − | 0.396086i | ||||||
\(107\) | 2.12139i | 0.205082i | 0.994729 | + | 0.102541i | \(0.0326973\pi\) | ||||
−0.994729 | + | 0.102541i | \(0.967303\pi\) | |||||||
\(108\) | − | 1.62115i | − | 0.155995i | ||||||
\(109\) | 3.22456i | 0.308857i | 0.988004 | + | 0.154428i | \(0.0493536\pi\) | ||||
−0.988004 | + | 0.154428i | \(0.950646\pi\) | |||||||
\(110\) | −0.132797 | + | 6.70641i | −0.0126617 | + | 0.639431i | ||||
\(111\) | 9.39271i | 0.891516i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8894 | 1.11846 | 0.559228 | − | 0.829014i | \(-0.311098\pi\) | ||||
0.559228 | + | 0.829014i | \(0.311098\pi\) | |||||||
\(114\) | −0.534962 | −0.0501038 | ||||||||
\(115\) | 11.7077i | 1.09175i | ||||||||
\(116\) | 6.00859i | 0.557884i | ||||||||
\(117\) | 0.142630 | 0.0131861 | ||||||||
\(118\) | 0.952216 | 0.0876586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.32361i | 0.668551i | ||||||||
\(121\) | −10.9914 | − | 0.435462i | −0.999216 | − | 0.0395875i | ||||
\(122\) | 9.38825i | 0.849973i | ||||||||
\(123\) | 3.19487i | 0.288071i | ||||||||
\(124\) | − | 7.81525i | − | 0.701830i | ||||||
\(125\) | 2.61791i | 0.234153i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6821i | 1.39156i | 0.718254 | + | 0.695781i | \(0.244942\pi\) | ||||
−0.718254 | + | 0.695781i | \(0.755058\pi\) | |||||||
\(128\) | 11.3955i | 1.00723i | ||||||||
\(129\) | 9.66641 | 0.851080 | ||||||||
\(130\) | −0.288462 | −0.0252998 | ||||||||
\(131\) | −10.0286 | −0.876200 | −0.438100 | − | 0.898926i | \(-0.644348\pi\) | ||||
−0.438100 | + | 0.898926i | \(0.644348\pi\) | |||||||
\(132\) | −5.37570 | − | 0.106447i | −0.467895 | − | 0.00926502i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.01125i | 0.692067i | ||||||||
\(135\) | −3.28584 | −0.282800 | ||||||||
\(136\) | 16.1896i | 1.38825i | ||||||||
\(137\) | 14.6785 | 1.25407 | 0.627033 | − | 0.778993i | \(-0.284269\pi\) | ||||
0.627033 | + | 0.778993i | \(0.284269\pi\) | |||||||
\(138\) | 2.19310 | 0.186689 | ||||||||
\(139\) | −4.45534 | −0.377897 | −0.188948 | − | 0.981987i | \(-0.560508\pi\) | ||||
−0.188948 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.76297 | −0.737976 | ||||||||
\(142\) | 1.64052i | 0.137669i | ||||||||
\(143\) | 0.00936524 | − | 0.472956i | 0.000783161 | − | 0.0395506i | ||||
\(144\) | −1.87044 | −0.155870 | ||||||||
\(145\) | 12.1785 | 1.01137 | ||||||||
\(146\) | − | 3.37813i | − | 0.279576i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.2270 | 1.25165 | ||||||||
\(149\) | 5.01591i | 0.410920i | 0.978666 | + | 0.205460i | \(0.0658690\pi\) | ||||
−0.978666 | + | 0.205460i | \(0.934131\pi\) | |||||||
\(150\) | 3.56792 | 0.291320 | ||||||||
\(151\) | 14.7324i | 1.19890i | 0.800411 | + | 0.599452i | \(0.204615\pi\) | ||||
−0.800411 | + | 0.599452i | \(0.795385\pi\) | |||||||
\(152\) | 1.93718i | 0.157126i | ||||||||
\(153\) | −7.26368 | −0.587234 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.8404 | −1.27233 | ||||||||
\(156\) | − | 0.231224i | − | 0.0185127i | ||||||
\(157\) | − | 10.3667i | − | 0.827354i | −0.910424 | − | 0.413677i | \(-0.864244\pi\) | ||
0.910424 | − | 0.413677i | \(-0.135756\pi\) | |||||||
\(158\) | −4.34146 | −0.345388 | ||||||||
\(159\) | − | 6.62537i | − | 0.525426i | ||||||
\(160\) | 18.4301 | 1.45703 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.615506i | 0.0483588i | ||||||||
\(163\) | −6.22238 | −0.487374 | −0.243687 | − | 0.969854i | \(-0.578357\pi\) | ||||
−0.243687 | + | 0.969854i | \(0.578357\pi\) | |||||||
\(164\) | 5.17936 | 0.404440 | ||||||||
\(165\) | −0.215752 | + | 10.8958i | −0.0167963 | + | 0.848233i | ||||
\(166\) | − | 3.88404i | − | 0.301460i | ||||||
\(167\) | −21.3050 | −1.64863 | −0.824316 | − | 0.566129i | \(-0.808440\pi\) | ||||
−0.824316 | + | 0.566129i | \(0.808440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9797 | −0.998435 | ||||||||
\(170\) | 14.6905 | 1.12671 | ||||||||
\(171\) | −0.869142 | −0.0664650 | ||||||||
\(172\) | − | 15.6707i | − | 1.19488i | ||||||
\(173\) | −1.49705 | −0.113818 | −0.0569091 | − | 0.998379i | \(-0.518125\pi\) | ||||
−0.0569091 | + | 0.998379i | \(0.518125\pi\) | |||||||
\(174\) | − | 2.28130i | − | 0.172945i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.122815 | + | 6.20232i | −0.00925755 | + | 0.467518i | ||||
\(177\) | 1.54704 | 0.116283 | ||||||||
\(178\) | 4.84935 | 0.363474 | ||||||||
\(179\) | −15.3266 | −1.14556 | −0.572780 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572780 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(180\) | 5.32684i | 0.397039i | ||||||||
\(181\) | 14.5930i | 1.08469i | 0.840156 | + | 0.542345i | \(0.182463\pi\) | ||||
−0.840156 | + | 0.542345i | \(0.817537\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.2529i | 1.12753i | ||||||||
\(184\) | − | 7.94155i | − | 0.585459i | ||||||
\(185\) | − | 30.8629i | − | 2.26909i | ||||||
\(186\) | 2.96723i | 0.217568i | ||||||||
\(187\) | −0.476943 | + | 24.0862i | −0.0348775 | + | 1.76136i | ||||
\(188\) | 14.2061i | 1.03609i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.75780 | 0.127524 | ||||||||
\(191\) | −8.97161 | −0.649163 | −0.324582 | − | 0.945858i | \(-0.605223\pi\) | ||||
−0.324582 | + | 0.945858i | \(0.605223\pi\) | |||||||
\(192\) | 0.288529i | 0.0208228i | ||||||||
\(193\) | 2.11199i | 0.152025i | 0.997107 | + | 0.0760123i | \(0.0242188\pi\) | ||||
−0.997107 | + | 0.0760123i | \(0.975781\pi\) | |||||||
\(194\) | 4.96832 | 0.356705 | ||||||||
\(195\) | −0.468657 | −0.0335613 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.47897i | − | 0.675348i | −0.941263 | − | 0.337674i | \(-0.890360\pi\) | ||
0.941263 | − | 0.337674i | \(-0.109640\pi\) | |||||||
\(198\) | 2.04100 | + | 0.0404149i | 0.145048 | + | 0.00287217i | ||||
\(199\) | 1.33263i | 0.0944675i | 0.998884 | + | 0.0472337i | \(0.0150406\pi\) | ||||
−0.998884 | + | 0.0472337i | \(0.984959\pi\) | |||||||
\(200\) | − | 12.9200i | − | 0.913581i | ||||||
\(201\) | 13.0157i | 0.918057i | ||||||||
\(202\) | − | 4.24458i | − | 0.298647i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 11.7755i | 0.824452i | ||||||||
\(205\) | − | 10.4978i | − | 0.733199i | ||||||
\(206\) | 2.12974 | 0.148386 | ||||||||
\(207\) | 3.56308 | 0.247651 | ||||||||
\(208\) | −0.266780 | −0.0184978 | ||||||||
\(209\) | −0.0570690 | + | 2.88205i | −0.00394754 | + | 0.199356i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.34281i | − | 0.367814i | −0.982944 | − | 0.183907i | \(-0.941125\pi\) | ||
0.982944 | − | 0.183907i | \(-0.0588745\pi\) | |||||||
\(212\) | −10.7407 | −0.737676 | ||||||||
\(213\) | 2.66532i | 0.182625i | ||||||||
\(214\) | −1.30573 | −0.0892577 | ||||||||
\(215\) | −31.7623 | −2.16617 | ||||||||
\(216\) | 2.22884 | 0.151654 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.98474 | −0.134423 | ||||||||
\(219\) | − | 5.48838i | − | 0.370870i | ||||||
\(220\) | 17.6637 | + | 0.349767i | 1.19088 | + | 0.0235813i | ||||
\(221\) | −1.03602 | −0.0696900 | ||||||||
\(222\) | −5.78127 | −0.388014 | ||||||||
\(223\) | − | 24.5309i | − | 1.64271i | −0.570415 | − | 0.821356i | \(-0.693218\pi\) | ||
0.570415 | − | 0.821356i | \(-0.306782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.79672 | 0.386448 | ||||||||
\(226\) | 7.31797i | 0.486784i | ||||||||
\(227\) | −13.1568 | −0.873249 | −0.436625 | − | 0.899644i | \(-0.643826\pi\) | ||||
−0.436625 | + | 0.899644i | \(0.643826\pi\) | |||||||
\(228\) | 1.40901i | 0.0933140i | ||||||||
\(229\) | − | 14.0607i | − | 0.929160i | −0.885531 | − | 0.464580i | \(-0.846205\pi\) | ||
0.885531 | − | 0.464580i | \(-0.153795\pi\) | |||||||
\(230\) | −7.20617 | −0.475161 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.26092 | −0.542356 | ||||||||
\(233\) | − | 25.8509i | − | 1.69355i | −0.531953 | − | 0.846774i | \(-0.678542\pi\) | ||
0.531953 | − | 0.846774i | \(-0.321458\pi\) | |||||||
\(234\) | 0.0877894i | 0.00573897i | ||||||||
\(235\) | 28.7937 | 1.87829 | ||||||||
\(236\) | − | 2.50799i | − | 0.163257i | ||||||
\(237\) | −7.05347 | −0.458172 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.49156i | 0.484589i | 0.970203 | + | 0.242294i | \(0.0779000\pi\) | ||||
−0.970203 | + | 0.242294i | \(0.922100\pi\) | |||||||
\(240\) | 6.14595 | 0.396719 | ||||||||
\(241\) | −18.1572 | −1.16961 | −0.584803 | − | 0.811176i | \(-0.698828\pi\) | ||||
−0.584803 | + | 0.811176i | \(0.698828\pi\) | |||||||
\(242\) | 0.268030 | − | 6.76526i | 0.0172296 | − | 0.434888i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 24.7273 | 1.58300 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.96646 | −0.125377 | ||||||||
\(247\) | −0.123965 | −0.00788772 | ||||||||
\(248\) | 10.7448 | 0.682296 | ||||||||
\(249\) | − | 6.31032i | − | 0.399900i | ||||||
\(250\) | −1.61134 | −0.101910 | ||||||||
\(251\) | 3.07493i | 0.194088i | 0.995280 | + | 0.0970441i | \(0.0309388\pi\) | ||||
−0.995280 | + | 0.0970441i | \(0.969061\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.233957 | − | 11.8151i | 0.0147087 | − | 0.742809i | ||||
\(254\) | −9.65244 | −0.605648 | ||||||||
\(255\) | 23.8673 | 1.49463 | ||||||||
\(256\) | −6.43694 | −0.402309 | ||||||||
\(257\) | 3.48778i | 0.217562i | 0.994066 | + | 0.108781i | \(0.0346947\pi\) | ||||
−0.994066 | + | 0.108781i | \(0.965305\pi\) | |||||||
\(258\) | 5.94974i | 0.370415i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.759765i | 0.0471186i | ||||||||
\(261\) | − | 3.70637i | − | 0.229419i | ||||||
\(262\) | − | 6.17265i | − | 0.381348i | ||||||
\(263\) | 6.46276i | 0.398511i | 0.979948 | + | 0.199255i | \(0.0638523\pi\) | ||||
−0.979948 | + | 0.199255i | \(0.936148\pi\) | |||||||
\(264\) | 0.146349 | − | 7.39078i | 0.00900714 | − | 0.454871i | ||||
\(265\) | 21.7699i | 1.33731i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.87864 | 0.482165 | ||||||||
\(268\) | 21.1004 | 1.28891 | ||||||||
\(269\) | 16.5450i | 1.00877i | 0.863479 | + | 0.504384i | \(0.168280\pi\) | ||||
−0.863479 | + | 0.504384i | \(0.831720\pi\) | |||||||
\(270\) | − | 2.02245i | − | 0.123083i | ||||||
\(271\) | −4.03699 | −0.245230 | −0.122615 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122615 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(272\) | 13.5863 | 0.823788 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.03469i | 0.545806i | ||||||||
\(275\) | 0.380620 | − | 19.2218i | 0.0229523 | − | 1.15912i | ||||
\(276\) | − | 5.77630i | − | 0.347692i | ||||||
\(277\) | − | 2.44867i | − | 0.147126i | −0.997291 | − | 0.0735632i | \(-0.976563\pi\) | ||
0.997291 | − | 0.0735632i | \(-0.0234371\pi\) | |||||||
\(278\) | − | 2.74229i | − | 0.164472i | ||||||
\(279\) | 4.82080i | 0.288614i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.1901i | − | 0.846509i | −0.906011 | − | 0.423254i | \(-0.860888\pi\) | ||
0.906011 | − | 0.423254i | \(-0.139112\pi\) | |||||||
\(282\) | − | 5.39367i | − | 0.321188i | ||||||
\(283\) | −26.6806 | −1.58599 | −0.792997 | − | 0.609225i | \(-0.791481\pi\) | ||||
−0.792997 | + | 0.609225i | \(0.791481\pi\) | |||||||
\(284\) | 4.32089 | 0.256398 | ||||||||
\(285\) | 2.85586 | 0.169166 | ||||||||
\(286\) | 0.291107 | + | 0.00576437i | 0.0172135 | + | 0.000340854i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 5.60895i | − | 0.330511i | ||||||
\(289\) | 35.7611 | 2.10359 | ||||||||
\(290\) | 7.49597i | 0.440178i | ||||||||
\(291\) | 8.07193 | 0.473185 | ||||||||
\(292\) | −8.89749 | −0.520686 | ||||||||
\(293\) | −18.4082 | −1.07542 | −0.537708 | − | 0.843131i | \(-0.680710\pi\) | ||||
−0.537708 | + | 0.843131i | \(0.680710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.08334 | −0.295963 | ||||||||
\(296\) | 20.9349i | 1.21681i | ||||||||
\(297\) | 3.31597 | + | 0.0656613i | 0.192412 | + | 0.00381005i | ||||
\(298\) | −3.08733 | −0.178844 | ||||||||
\(299\) | 0.508201 | 0.0293900 | ||||||||
\(300\) | − | 9.39737i | − | 0.542557i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.06787 | −0.521798 | ||||||||
\(303\) | − | 6.89607i | − | 0.396169i | ||||||
\(304\) | 1.62568 | 0.0932389 | ||||||||
\(305\) | − | 50.1185i | − | 2.86978i | ||||||
\(306\) | − | 4.47084i | − | 0.255581i | ||||||
\(307\) | 24.2462 | 1.38380 | 0.691902 | − | 0.721991i | \(-0.256773\pi\) | ||||
0.691902 | + | 0.721991i | \(0.256773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.46014 | 0.196841 | ||||||||
\(310\) | − | 9.74984i | − | 0.553754i | ||||||
\(311\) | 12.5362i | 0.710861i | 0.934703 | + | 0.355431i | \(0.115666\pi\) | ||||
−0.934703 | + | 0.355431i | \(0.884334\pi\) | |||||||
\(312\) | 0.317899 | 0.0179975 | ||||||||
\(313\) | 9.56160i | 0.540453i | 0.962797 | + | 0.270227i | \(0.0870986\pi\) | ||||
−0.962797 | + | 0.270227i | \(0.912901\pi\) | |||||||
\(314\) | 6.38078 | 0.360088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4347i | 0.643255i | ||||||||
\(317\) | −13.8291 | −0.776718 | −0.388359 | − | 0.921508i | \(-0.626958\pi\) | ||||
−0.388359 | + | 0.921508i | \(0.626958\pi\) | |||||||
\(318\) | 4.07796 | 0.228681 | ||||||||
\(319\) | −12.2902 | − | 0.243365i | −0.688121 | − | 0.0136258i | ||||
\(320\) | − | 0.948060i | − | 0.0529982i | ||||||
\(321\) | −2.12139 | −0.118404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.31317 | 0.351274 | ||||||||
\(324\) | 1.62115 | 0.0900640 | ||||||||
\(325\) | 0.826784 | 0.0458617 | ||||||||
\(326\) | − | 3.82991i | − | 0.212119i | ||||||
\(327\) | −3.22456 | −0.178318 | ||||||||
\(328\) | 7.12085i | 0.393183i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.70641 | − | 0.132797i | −0.369175 | − | 0.00731023i | ||||
\(331\) | −18.2492 | −1.00307 | −0.501533 | − | 0.865139i | \(-0.667230\pi\) | ||||
−0.501533 | + | 0.865139i | \(0.667230\pi\) | |||||||
\(332\) | −10.2300 | −0.561443 | ||||||||
\(333\) | −9.39271 | −0.514717 | ||||||||
\(334\) | − | 13.1134i | − | 0.717532i | ||||||
\(335\) | − | 42.7675i | − | 2.33664i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 31.5515i | − | 1.71872i | −0.511370 | − | 0.859360i | \(-0.670862\pi\) | ||
0.511370 | − | 0.859360i | \(-0.329138\pi\) | |||||||
\(338\) | − | 7.98906i | − | 0.434548i | ||||||
\(339\) | 11.8894i | 0.645741i | ||||||||
\(340\) | − | 38.6925i | − | 2.09839i | ||||||
\(341\) | 15.9856 | + | 0.316540i | 0.865671 | + | 0.0171416i | ||||
\(342\) | − | 0.534962i | − | 0.0289275i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 21.5449 | 1.16162 | ||||||||
\(345\) | −11.7077 | −0.630322 | ||||||||
\(346\) | − | 0.921441i | − | 0.0495370i | ||||||
\(347\) | 16.2883i | 0.874401i | 0.899364 | + | 0.437200i | \(0.144030\pi\) | ||||
−0.899364 | + | 0.437200i | \(0.855970\pi\) | |||||||
\(348\) | −6.00859 | −0.322094 | ||||||||
\(349\) | −16.8476 | −0.901829 | −0.450915 | − | 0.892567i | \(-0.648902\pi\) | ||||
−0.450915 | + | 0.892567i | \(0.648902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.142630i | 0.00761300i | ||||||||
\(352\) | −18.5991 | − | 0.368291i | −0.991337 | − | 0.0196300i | ||||
\(353\) | 10.0756i | 0.536272i | 0.963381 | + | 0.268136i | \(0.0864076\pi\) | ||||
−0.963381 | + | 0.268136i | \(0.913592\pi\) | |||||||
\(354\) | 0.952216i | 0.0506097i | ||||||||
\(355\) | − | 8.75780i | − | 0.464816i | ||||||
\(356\) | − | 12.7725i | − | 0.676939i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 9.43359i | − | 0.498581i | ||||||
\(359\) | − | 13.4533i | − | 0.710036i | −0.934859 | − | 0.355018i | \(-0.884475\pi\) | ||
0.934859 | − | 0.355018i | \(-0.115525\pi\) | |||||||
\(360\) | −7.32361 | −0.385988 | ||||||||
\(361\) | −18.2446 | −0.960242 | ||||||||
\(362\) | −8.98209 | −0.472088 | ||||||||
\(363\) | 0.435462 | − | 10.9914i | 0.0228558 | − | 0.576898i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0339i | 0.943938i | ||||||||
\(366\) | −9.38825 | −0.490732 | ||||||||
\(367\) | − | 18.3475i | − | 0.957729i | −0.877889 | − | 0.478865i | \(-0.841048\pi\) | ||
0.877889 | − | 0.478865i | \(-0.158952\pi\) | |||||||
\(368\) | −6.66452 | −0.347412 | ||||||||
\(369\) | −3.19487 | −0.166318 | ||||||||
\(370\) | 18.9963 | 0.987571 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.81525 | 0.405202 | ||||||||
\(373\) | − | 24.1790i | − | 1.25194i | −0.779847 | − | 0.625970i | \(-0.784703\pi\) | ||
0.779847 | − | 0.625970i | \(-0.215297\pi\) | |||||||
\(374\) | −14.8252 | − | 0.293561i | −0.766593 | − | 0.0151797i | ||||
\(375\) | −2.61791 | −0.135188 | ||||||||
\(376\) | −19.5313 | −1.00725 | ||||||||
\(377\) | − | 0.528638i | − | 0.0272263i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5684 | 0.902427 | 0.451214 | − | 0.892416i | \(-0.350991\pi\) | ||||
0.451214 | + | 0.892416i | \(0.350991\pi\) | |||||||
\(380\) | − | 4.62978i | − | 0.237503i | ||||||
\(381\) | −15.6821 | −0.803419 | ||||||||
\(382\) | − | 5.52209i | − | 0.282534i | ||||||
\(383\) | − | 11.3567i | − | 0.580298i | −0.956981 | − | 0.290149i | \(-0.906295\pi\) | ||
0.956981 | − | 0.290149i | \(-0.0937049\pi\) | |||||||
\(384\) | −11.3955 | −0.581524 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.29995 | −0.0661655 | ||||||||
\(387\) | 9.66641i | 0.491371i | ||||||||
\(388\) | − | 13.0858i | − | 0.664332i | ||||||
\(389\) | 0.196302 | 0.00995292 | 0.00497646 | − | 0.999988i | \(-0.498416\pi\) | ||||
0.00497646 | + | 0.999988i | \(0.498416\pi\) | |||||||
\(390\) | − | 0.288462i | − | 0.0146068i | ||||||
\(391\) | −25.8811 | −1.30886 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.0286i | − | 0.505874i | ||||||
\(394\) | 5.83437 | 0.293931 | ||||||||
\(395\) | 23.1766 | 1.16614 | ||||||||
\(396\) | 0.106447 | − | 5.37570i | 0.00534916 | − | 0.270139i | ||||
\(397\) | 11.6923i | 0.586818i | 0.955987 | + | 0.293409i | \(0.0947898\pi\) | ||||
−0.955987 | + | 0.293409i | \(0.905210\pi\) | |||||||
\(398\) | −0.820241 | −0.0411150 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.8424 | −0.542120 | ||||||||
\(401\) | 28.2224 | 1.40936 | 0.704680 | − | 0.709525i | \(-0.251091\pi\) | ||||
0.704680 | + | 0.709525i | \(0.251091\pi\) | |||||||
\(402\) | −8.01125 | −0.399565 | ||||||||
\(403\) | 0.687588i | 0.0342512i | ||||||||
\(404\) | −11.1796 | −0.556205 | ||||||||
\(405\) | − | 3.28584i | − | 0.163275i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.616737 | + | 31.1460i | −0.0305705 | + | 1.54385i | ||||
\(408\) | −16.1896 | −0.801505 | ||||||||
\(409\) | −20.5708 | −1.01716 | −0.508581 | − | 0.861014i | \(-0.669830\pi\) | ||||
−0.508581 | + | 0.861014i | \(0.669830\pi\) | |||||||
\(410\) | 6.46147 | 0.319109 | ||||||||
\(411\) | 14.6785i | 0.724036i | ||||||||
\(412\) | − | 5.60941i | − | 0.276356i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.19310i | 0.107785i | ||||||||
\(415\) | 20.7347i | 1.01783i | ||||||||
\(416\) | − | 0.800002i | − | 0.0392233i | ||||||
\(417\) | − | 4.45534i | − | 0.218179i | ||||||
\(418\) | −1.77392 | − | 0.0351263i | −0.0867654 | − | 0.00171808i | ||||
\(419\) | 24.6522i | 1.20434i | 0.798368 | + | 0.602170i | \(0.205697\pi\) | ||||
−0.798368 | + | 0.602170i | \(0.794303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5775 | 1.39278 | 0.696391 | − | 0.717663i | \(-0.254788\pi\) | ||||
0.696391 | + | 0.717663i | \(0.254788\pi\) | |||||||
\(422\) | 3.28853 | 0.160083 | ||||||||
\(423\) | − | 8.76297i | − | 0.426070i | ||||||
\(424\) | − | 14.7669i | − | 0.717144i | ||||||
\(425\) | −42.1056 | −2.04242 | ||||||||
\(426\) | −1.64052 | −0.0794835 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.43909i | 0.166235i | ||||||||
\(429\) | 0.472956 | + | 0.00936524i | 0.0228345 | + | 0.000452158i | ||||
\(430\) | − | 19.5499i | − | 0.942779i | ||||||
\(431\) | 18.9985i | 0.915128i | 0.889177 | + | 0.457564i | \(0.151278\pi\) | ||||
−0.889177 | + | 0.457564i | \(0.848722\pi\) | |||||||
\(432\) | − | 1.87044i | − | 0.0899914i | ||||||
\(433\) | 13.5205i | 0.649755i | 0.945756 | + | 0.324878i | \(0.105323\pi\) | ||||
−0.945756 | + | 0.324878i | \(0.894677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.1785i | 0.583916i | ||||||||
\(436\) | 5.22750i | 0.250352i | ||||||||
\(437\) | −3.09683 | −0.148141 | ||||||||
\(438\) | 3.37813 | 0.161413 | ||||||||
\(439\) | −2.40989 | −0.115018 | −0.0575089 | − | 0.998345i | \(-0.518316\pi\) | ||||
−0.0575089 | + | 0.998345i | \(0.518316\pi\) | |||||||
\(440\) | −0.480878 | + | 24.2849i | −0.0229250 | + | 1.15774i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.637674i | − | 0.0303311i | ||||||
\(443\) | 23.7193 | 1.12694 | 0.563470 | − | 0.826136i | \(-0.309466\pi\) | ||||
0.563470 | + | 0.826136i | \(0.309466\pi\) | |||||||
\(444\) | 15.2270i | 0.722642i | ||||||||
\(445\) | −25.8879 | −1.22720 | ||||||||
\(446\) | 15.0989 | 0.714956 | ||||||||
\(447\) | −5.01591 | −0.237245 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.0666558 | −0.00314568 | −0.00157284 | − | 0.999999i | \(-0.500501\pi\) | ||||
−0.00157284 | + | 0.999999i | \(0.500501\pi\) | |||||||
\(450\) | 3.56792i | 0.168193i | ||||||||
\(451\) | −0.209779 | + | 10.5941i | −0.00987811 | + | 0.498856i | ||||
\(452\) | 19.2744 | 0.906594 | ||||||||
\(453\) | −14.7324 | −0.692188 | ||||||||
\(454\) | − | 8.09811i | − | 0.380063i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.93718 | −0.0907168 | ||||||||
\(457\) | − | 31.1211i | − | 1.45578i | −0.685692 | − | 0.727892i | \(-0.740500\pi\) | ||
0.685692 | − | 0.727892i | \(-0.259500\pi\) | |||||||
\(458\) | 8.65448 | 0.404397 | ||||||||
\(459\) | − | 7.26368i | − | 0.339040i | ||||||
\(460\) | 18.9800i | 0.884946i | ||||||||
\(461\) | 3.58542 | 0.166990 | 0.0834948 | − | 0.996508i | \(-0.473392\pi\) | ||||
0.0834948 | + | 0.996508i | \(0.473392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7914 | −0.966260 | −0.483130 | − | 0.875549i | \(-0.660500\pi\) | ||||
−0.483130 | + | 0.875549i | \(0.660500\pi\) | |||||||
\(464\) | 6.93254i | 0.321835i | ||||||||
\(465\) | − | 15.8404i | − | 0.734579i | ||||||
\(466\) | 15.9114 | 0.737081 | ||||||||
\(467\) | − | 38.8763i | − | 1.79898i | −0.436939 | − | 0.899491i | \(-0.643937\pi\) | ||
0.436939 | − | 0.899491i | \(-0.356063\pi\) | |||||||
\(468\) | 0.231224 | 0.0106883 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.7227i | 0.817488i | ||||||||
\(471\) | 10.3667 | 0.477673 | ||||||||
\(472\) | 3.44812 | 0.158713 | ||||||||
\(473\) | 32.0536 | + | 0.634709i | 1.47383 | + | 0.0291840i | ||||
\(474\) | − | 4.34146i | − | 0.199410i | ||||||
\(475\) | −5.03818 | −0.231167 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.62537 | 0.303355 | ||||||||
\(478\) | −4.61110 | −0.210907 | ||||||||
\(479\) | 16.1591 | 0.738329 | 0.369164 | − | 0.929364i | \(-0.379644\pi\) | ||||
0.369164 | + | 0.929364i | \(0.379644\pi\) | |||||||
\(480\) | 18.4301i | 0.841215i | ||||||||
\(481\) | −1.33968 | −0.0610840 | ||||||||
\(482\) | − | 11.1758i | − | 0.509046i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.8187 | − | 0.705951i | −0.809941 | − | 0.0320887i | ||||
\(485\) | −26.5230 | −1.20435 | ||||||||
\(486\) | −0.615506 | −0.0279199 | ||||||||
\(487\) | −0.0472275 | −0.00214008 | −0.00107004 | − | 0.999999i | \(-0.500341\pi\) | ||||
−0.00107004 | + | 0.999999i | \(0.500341\pi\) | |||||||
\(488\) | 33.9963i | 1.53894i | ||||||||
\(489\) | − | 6.22238i | − | 0.281386i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.2054i | − | 1.36315i | −0.731748 | − | 0.681576i | \(-0.761295\pi\) | ||
0.731748 | − | 0.681576i | \(-0.238705\pi\) | |||||||
\(492\) | 5.17936i | 0.233504i | ||||||||
\(493\) | 26.9219i | 1.21250i | ||||||||
\(494\) | − | 0.0763015i | − | 0.00343296i | ||||||
\(495\) | −10.8958 | − | 0.215752i | −0.489728 | − | 0.00969734i | ||||
\(496\) | − | 9.01700i | − | 0.404875i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.88404 | 0.174048 | ||||||||
\(499\) | 1.50934 | 0.0675673 | 0.0337836 | − | 0.999429i | \(-0.489244\pi\) | ||||
0.0337836 | + | 0.999429i | \(0.489244\pi\) | |||||||
\(500\) | 4.24402i | 0.189798i | ||||||||
\(501\) | − | 21.3050i | − | 0.951839i | ||||||
\(502\) | −1.89264 | −0.0844727 | ||||||||
\(503\) | −37.3354 | −1.66471 | −0.832353 | − | 0.554247i | \(-0.813006\pi\) | ||||
−0.832353 | + | 0.554247i | \(0.813006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6594i | 1.00833i | ||||||||
\(506\) | 7.27227 | + | 0.144002i | 0.323292 | + | 0.00640166i | ||||
\(507\) | − | 12.9797i | − | 0.576447i | ||||||
\(508\) | 25.4231i | 1.12797i | ||||||||
\(509\) | 10.8665i | 0.481650i | 0.970569 | + | 0.240825i | \(0.0774180\pi\) | ||||
−0.970569 | + | 0.240825i | \(0.922582\pi\) | |||||||
\(510\) | 14.6905i | 0.650505i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.8290i | 0.832132i | ||||||||
\(513\) | − | 0.869142i | − | 0.0383736i | ||||||
\(514\) | −2.14675 | −0.0946891 | ||||||||
\(515\) | −11.3695 | −0.500998 | ||||||||
\(516\) | 15.6707 | 0.689865 | ||||||||
\(517\) | −29.0578 | − | 0.575388i | −1.27796 | − | 0.0253055i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.49705i | − | 0.0657130i | ||||||
\(520\) | −1.04456 | −0.0458071 | ||||||||
\(521\) | − | 17.8174i | − | 0.780593i | −0.920689 | − | 0.390297i | \(-0.872372\pi\) | ||
0.920689 | − | 0.390297i | \(-0.127628\pi\) | |||||||
\(522\) | 2.28130 | 0.0998496 | ||||||||
\(523\) | 32.3763 | 1.41572 | 0.707858 | − | 0.706355i | \(-0.249662\pi\) | ||||
0.707858 | + | 0.706355i | \(0.249662\pi\) | |||||||
\(524\) | −16.2578 | −0.710227 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.97787 | −0.173443 | ||||||||
\(527\) | − | 35.0168i | − | 1.52535i | ||||||
\(528\) | −6.20232 | − | 0.122815i | −0.269921 | − | 0.00534485i | ||||
\(529\) | −10.3044 | −0.448019 | ||||||||
\(530\) | −13.3995 | −0.582037 | ||||||||
\(531\) | 1.54704i | 0.0671360i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.455682 | −0.0197378 | ||||||||
\(534\) | 4.84935i | 0.209852i | ||||||||
\(535\) | 6.97053 | 0.301362 | ||||||||
\(536\) | 29.0100i | 1.25304i | ||||||||
\(537\) | − | 15.3266i | − | 0.661390i | ||||||
\(538\) | −10.1836 | −0.439045 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.32684 | −0.229231 | ||||||||
\(541\) | 24.7892i | 1.06577i | 0.846187 | + | 0.532886i | \(0.178893\pi\) | ||||
−0.846187 | + | 0.532886i | \(0.821107\pi\) | |||||||
\(542\) | − | 2.48479i | − | 0.106731i | ||||||
\(543\) | −14.5930 | −0.626246 | ||||||||
\(544\) | 40.7416i | 1.74678i | ||||||||
\(545\) | 10.5954 | 0.453856 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2233i | 0.650903i | 0.945559 | + | 0.325452i | \(0.105516\pi\) | ||||
−0.945559 | + | 0.325452i | \(0.894484\pi\) | |||||||
\(548\) | 23.7960 | 1.01652 | ||||||||
\(549\) | −15.2529 | −0.650978 | ||||||||
\(550\) | 11.8311 | + | 0.234274i | 0.504481 | + | 0.00998949i | ||||
\(551\) | 3.22136i | 0.137235i | ||||||||
\(552\) | 7.94155 | 0.338015 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.50717 | 0.0640337 | ||||||||
\(555\) | 30.8629 | 1.31006 | ||||||||
\(556\) | −7.22278 | −0.306314 | ||||||||
\(557\) | 22.0992i | 0.936375i | 0.883629 | + | 0.468187i | \(0.155093\pi\) | ||||
−0.883629 | + | 0.468187i | \(0.844907\pi\) | |||||||
\(558\) | −2.96723 | −0.125613 | ||||||||
\(559\) | 1.37872i | 0.0583135i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0862 | − | 0.476943i | −1.01692 | − | 0.0201365i | ||||
\(562\) | 8.73408 | 0.368425 | ||||||||
\(563\) | 25.9110 | 1.09202 | 0.546009 | − | 0.837779i | \(-0.316146\pi\) | ||||
0.546009 | + | 0.837779i | \(0.316146\pi\) | |||||||
\(564\) | −14.2061 | −0.598185 | ||||||||
\(565\) | − | 39.0665i | − | 1.64354i | ||||||
\(566\) | − | 16.4221i | − | 0.690270i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.94058i | 0.249261i | ||||||||
\(569\) | 29.6107i | 1.24134i | 0.784070 | + | 0.620672i | \(0.213140\pi\) | ||||
−0.784070 | + | 0.620672i | \(0.786860\pi\) | |||||||
\(570\) | 1.75780i | 0.0736261i | ||||||||
\(571\) | 8.32745i | 0.348493i | 0.984702 | + | 0.174246i | \(0.0557489\pi\) | ||||
−0.984702 | + | 0.174246i | \(0.944251\pi\) | |||||||
\(572\) | 0.0151825 | − | 0.766733i | 0.000634811 | − | 0.0320587i | ||||
\(573\) | − | 8.97161i | − | 0.374795i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.6542 | 0.861340 | ||||||||
\(576\) | −0.288529 | −0.0120221 | ||||||||
\(577\) | − | 28.5782i | − | 1.18973i | −0.803827 | − | 0.594864i | \(-0.797206\pi\) | ||
0.803827 | − | 0.594864i | \(-0.202794\pi\) | |||||||
\(578\) | 22.0112i | 0.915544i | ||||||||
\(579\) | −2.11199 | −0.0877714 | ||||||||
\(580\) | 19.7433 | 0.819794 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.96832i | 0.205944i | ||||||||
\(583\) | 0.435030 | − | 21.9696i | 0.0180171 | − | 0.909886i | ||||
\(584\) | − | 12.2327i | − | 0.506194i | ||||||
\(585\) | − | 0.468657i | − | 0.0193766i | ||||||
\(586\) | − | 11.3303i | − | 0.468052i | ||||||
\(587\) | 26.8088i | 1.10652i | 0.833009 | + | 0.553260i | \(0.186616\pi\) | ||||
−0.833009 | + | 0.553260i | \(0.813384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.18996i | − | 0.172644i | ||||||
\(590\) | − | 3.12883i | − | 0.128812i | ||||||
\(591\) | 9.47897 | 0.389913 | ||||||||
\(592\) | 17.5685 | 0.722060 | ||||||||
\(593\) | 24.3666 | 1.00062 | 0.500308 | − | 0.865848i | \(-0.333220\pi\) | ||||
0.500308 | + | 0.865848i | \(0.333220\pi\) | |||||||
\(594\) | −0.0404149 | + | 2.04100i | −0.00165825 | + | 0.0837434i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.13156i | 0.333082i | ||||||||
\(597\) | −1.33263 | −0.0545408 | ||||||||
\(598\) | 0.312801i | 0.0127914i | ||||||||
\(599\) | −37.3795 | −1.52728 | −0.763642 | − | 0.645640i | \(-0.776591\pi\) | ||||
−0.763642 | + | 0.645640i | \(0.776591\pi\) | |||||||
\(600\) | 12.9200 | 0.527456 | ||||||||
\(601\) | −0.423296 | −0.0172666 | −0.00863329 | − | 0.999963i | \(-0.502748\pi\) | ||||
−0.00863329 | + | 0.999963i | \(0.502748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0157 | −0.530041 | ||||||||
\(604\) | 23.8834i | 0.971803i | ||||||||
\(605\) | −1.43086 | + | 36.1159i | −0.0581727 | + | 1.46832i | ||||
\(606\) | 4.24458 | 0.172424 | ||||||||
\(607\) | −31.5129 | −1.27907 | −0.639534 | − | 0.768763i | \(-0.720873\pi\) | ||||
−0.639534 | + | 0.768763i | \(0.720873\pi\) | |||||||
\(608\) | 4.87497i | 0.197706i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.8483 | 1.24901 | ||||||||
\(611\) | − | 1.24986i | − | 0.0505639i | ||||||
\(612\) | −11.7755 | −0.475998 | ||||||||
\(613\) | − | 28.0471i | − | 1.13281i | −0.824127 | − | 0.566405i | \(-0.808334\pi\) | ||
0.824127 | − | 0.566405i | \(-0.191666\pi\) | |||||||
\(614\) | 14.9237i | 0.602271i | ||||||||
\(615\) | 10.4978 | 0.423313 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.4810 | −1.66996 | −0.834981 | − | 0.550279i | \(-0.814521\pi\) | ||||
−0.834981 | + | 0.550279i | \(0.814521\pi\) | |||||||
\(618\) | 2.12974i | 0.0856707i | ||||||||
\(619\) | 10.7333i | 0.431409i | 0.976459 | + | 0.215704i | \(0.0692047\pi\) | ||||
−0.976459 | + | 0.215704i | \(0.930795\pi\) | |||||||
\(620\) | −25.6796 | −1.03132 | ||||||||
\(621\) | 3.56308i | 0.142982i | ||||||||
\(622\) | −7.71610 | −0.309387 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.266780i | − | 0.0106797i | ||||||
\(625\) | −20.3816 | −0.815264 | ||||||||
\(626\) | −5.88522 | −0.235221 | ||||||||
\(627\) | −2.88205 | − | 0.0570690i | −0.115098 | − | 0.00227912i | ||||
\(628\) | − | 16.8060i | − | 0.670633i | ||||||
\(629\) | 68.2256 | 2.72033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.36006 | 0.133762 | 0.0668809 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668809 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(632\) | −15.7211 | −0.625351 | ||||||||
\(633\) | 5.34281 | 0.212358 | ||||||||
\(634\) | − | 8.51189i | − | 0.338050i | ||||||
\(635\) | 51.5289 | 2.04486 | ||||||||
\(636\) | − | 10.7407i | − | 0.425898i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.149793 | − | 7.56472i | 0.00593036 | − | 0.299490i | ||||
\(639\) | −2.66532 | −0.105438 | ||||||||
\(640\) | 37.4437 | 1.48009 | ||||||||
\(641\) | 33.6673 | 1.32978 | 0.664890 | − | 0.746941i | \(-0.268478\pi\) | ||||
0.664890 | + | 0.746941i | \(0.268478\pi\) | |||||||
\(642\) | − | 1.30573i | − | 0.0515330i | ||||||
\(643\) | − | 37.8334i | − | 1.49200i | −0.665944 | − | 0.746002i | \(-0.731971\pi\) | ||
0.665944 | − | 0.746002i | \(-0.268029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 31.7623i | − | 1.25064i | ||||||
\(646\) | 3.88580i | 0.152885i | ||||||||
\(647\) | − | 5.02324i | − | 0.197484i | −0.995113 | − | 0.0987421i | \(-0.968518\pi\) | ||
0.995113 | − | 0.0987421i | \(-0.0314819\pi\) | |||||||
\(648\) | 2.22884i | 0.0875572i | ||||||||
\(649\) | 5.12996 | + | 0.101581i | 0.201369 | + | 0.00398740i | ||||
\(650\) | 0.508891i | 0.0199603i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0874 | −0.395054 | ||||||||
\(653\) | −31.7175 | −1.24120 | −0.620601 | − | 0.784126i | \(-0.713111\pi\) | ||||
−0.620601 | + | 0.784126i | \(0.713111\pi\) | |||||||
\(654\) | − | 1.98474i | − | 0.0776093i | ||||||
\(655\) | 32.9522i | 1.28755i | ||||||||
\(656\) | 5.97580 | 0.233316 | ||||||||
\(657\) | 5.48838 | 0.214122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.15699i | − | 0.122979i | −0.998108 | − | 0.0614894i | \(-0.980415\pi\) | ||
0.998108 | − | 0.0614894i | \(-0.0195851\pi\) | |||||||
\(660\) | −0.349767 | + | 17.6637i | −0.0136147 | + | 0.687557i | ||||
\(661\) | 44.4762i | 1.72992i | 0.501837 | + | 0.864962i | \(0.332658\pi\) | ||||
−0.501837 | + | 0.864962i | \(0.667342\pi\) | |||||||
\(662\) | − | 11.2325i | − | 0.436563i | ||||||
\(663\) | − | 1.03602i | − | 0.0402355i | ||||||
\(664\) | − | 14.0647i | − | 0.545816i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 5.78127i | − | 0.224020i | ||||||
\(667\) | − | 13.2061i | − | 0.511343i | ||||||
\(668\) | −34.5387 | −1.33634 | ||||||||
\(669\) | 24.5309 | 0.948421 | ||||||||
\(670\) | 26.3237 | 1.01697 | ||||||||
\(671\) | −1.00152 | + | 50.5782i | −0.0386634 | + | 1.95255i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 29.7473i | − | 1.14667i | −0.819319 | − | 0.573337i | \(-0.805648\pi\) | ||
0.819319 | − | 0.573337i | \(-0.194352\pi\) | |||||||
\(674\) | 19.4202 | 0.748037 | ||||||||
\(675\) | 5.79672i | 0.223116i | ||||||||
\(676\) | −21.0420 | −0.809307 | ||||||||
\(677\) | −14.3360 | −0.550978 | −0.275489 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275489 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(678\) | −7.31797 | −0.281045 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 53.1964 | 2.03999 | ||||||||
\(681\) | − | 13.1568i | − | 0.504171i | ||||||
\(682\) | −0.194832 | + | 9.83927i | −0.00746052 | + | 0.376765i | ||||
\(683\) | 14.2841 | 0.546567 | 0.273284 | − | 0.961933i | \(-0.411890\pi\) | ||||
0.273284 | + | 0.961933i | \(0.411890\pi\) | |||||||
\(684\) | −1.40901 | −0.0538749 | ||||||||
\(685\) | − | 48.2311i | − | 1.84281i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0607 | 0.536451 | ||||||||
\(688\) | − | 18.0804i | − | 0.689309i | ||||||
\(689\) | 0.944973 | 0.0360006 | ||||||||
\(690\) | − | 7.20617i | − | 0.274334i | ||||||
\(691\) | − | 20.5745i | − | 0.782691i | −0.920244 | − | 0.391345i | \(-0.872010\pi\) | ||
0.920244 | − | 0.391345i | \(-0.127990\pi\) | |||||||
\(692\) | −2.42694 | −0.0922583 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0255 | −0.380564 | ||||||||
\(695\) | 14.6395i | 0.555308i | ||||||||
\(696\) | − | 8.26092i | − | 0.313129i | ||||||
\(697\) | 23.2065 | 0.879009 | ||||||||
\(698\) | − | 10.3698i | − | 0.392502i | ||||||
\(699\) | 25.8509 | 0.977770 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.46334i | − | 0.281886i | −0.990018 | − | 0.140943i | \(-0.954987\pi\) | ||
0.990018 | − | 0.140943i | \(-0.0450135\pi\) | |||||||
\(702\) | −0.0877894 | −0.00331340 | ||||||||
\(703\) | 8.16360 | 0.307896 | ||||||||
\(704\) | −0.0189452 | + | 0.956756i | −0.000714024 | + | 0.0360591i | ||||
\(705\) | 28.7937i | 1.08443i | ||||||||
\(706\) | −6.20162 | −0.233401 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.50799 | 0.0942562 | ||||||||
\(709\) | −35.0131 | −1.31495 | −0.657473 | − | 0.753478i | \(-0.728374\pi\) | ||||
−0.657473 | + | 0.753478i | \(0.728374\pi\) | |||||||
\(710\) | 5.39049 | 0.202301 | ||||||||
\(711\) | − | 7.05347i | − | 0.264526i | ||||||
\(712\) | 17.5602 | 0.658098 | ||||||||
\(713\) | 17.1769i | 0.643280i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.55406 | − | 0.0307727i | −0.0581184 | − | 0.00115083i | ||||
\(716\) | −24.8467 | −0.928564 | ||||||||
\(717\) | −7.49156 | −0.279777 | ||||||||
\(718\) | 8.28057 | 0.309028 | ||||||||
\(719\) | 27.2316i | 1.01557i | 0.861484 | + | 0.507784i | \(0.169535\pi\) | ||||
−0.861484 | + | 0.507784i | \(0.830465\pi\) | |||||||
\(720\) | 6.14595i | 0.229046i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 11.2297i | − | 0.417925i | ||||||
\(723\) | − | 18.1572i | − | 0.675272i | ||||||
\(724\) | 23.6575i | 0.879224i | ||||||||
\(725\) | − | 21.4848i | − | 0.797926i | ||||||
\(726\) | 6.76526 | + | 0.268030i | 0.251082 | + | 0.00994752i | ||||
\(727\) | 31.0062i | 1.14996i | 0.818168 | + | 0.574979i | \(0.194990\pi\) | ||||
−0.818168 | + | 0.574979i | \(0.805010\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −11.1000 | −0.410829 | ||||||||
\(731\) | − | 70.2137i | − | 2.59695i | ||||||
\(732\) | 24.7273i | 0.913946i | ||||||||
\(733\) | 29.6380 | 1.09471 | 0.547353 | − | 0.836902i | \(-0.315636\pi\) | ||||
0.547353 | + | 0.836902i | \(0.315636\pi\) | |||||||
\(734\) | 11.2930 | 0.416831 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 19.9852i | − | 0.736663i | ||||||
\(737\) | −0.854628 | + | 43.1598i | −0.0314806 | + | 1.58981i | ||||
\(738\) | − | 1.96646i | − | 0.0723864i | ||||||
\(739\) | 30.9252i | 1.13760i | 0.822476 | + | 0.568800i | \(0.192592\pi\) | ||||
−0.822476 | + | 0.568800i | \(0.807408\pi\) | |||||||
\(740\) | − | 50.0335i | − | 1.83927i | ||||||
\(741\) | − | 0.123965i | − | 0.00455398i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.4931i | − | 1.26543i | −0.774385 | − | 0.632715i | \(-0.781941\pi\) | ||
0.774385 | − | 0.632715i | \(-0.218059\pi\) | |||||||
\(744\) | 10.7448i | 0.393924i | ||||||||
\(745\) | 16.4815 | 0.603834 | ||||||||
\(746\) | 14.8823 | 0.544881 | ||||||||
\(747\) | 6.31032 | 0.230883 | ||||||||
\(748\) | −0.773197 | + | 39.0474i | −0.0282709 | + | 1.42771i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 1.61134i | − | 0.0588377i | ||||||
\(751\) | 33.8376 | 1.23475 | 0.617376 | − | 0.786669i | \(-0.288196\pi\) | ||||
0.617376 | + | 0.786669i | \(0.288196\pi\) | |||||||
\(752\) | 16.3906i | 0.597703i | ||||||||
\(753\) | −3.07493 | −0.112057 | ||||||||
\(754\) | 0.325380 | 0.0118496 | ||||||||
\(755\) | 48.4082 | 1.76175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.9449 | 0.761257 | 0.380628 | − | 0.924728i | \(-0.375708\pi\) | ||||
0.380628 | + | 0.924728i | \(0.375708\pi\) | |||||||
\(758\) | 10.8135i | 0.392762i | ||||||||
\(759\) | 11.8151 | + | 0.233957i | 0.428861 | + | 0.00849209i | ||||
\(760\) | 6.36526 | 0.230892 | ||||||||
\(761\) | 25.8678 | 0.937708 | 0.468854 | − | 0.883276i | \(-0.344667\pi\) | ||||
0.468854 | + | 0.883276i | \(0.344667\pi\) | |||||||
\(762\) | − | 9.65244i | − | 0.349671i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.5443 | −0.526196 | ||||||||
\(765\) | 23.8673i | 0.862923i | ||||||||
\(766\) | 6.99010 | 0.252562 | ||||||||
\(767\) | 0.220654i | 0.00796737i | ||||||||
\(768\) | − | 6.43694i | − | 0.232273i | ||||||
\(769\) | 2.66035 | 0.0959346 | 0.0479673 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479673 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.48778 | −0.125609 | ||||||||
\(772\) | 3.42386i | 0.123227i | ||||||||
\(773\) | 33.2866i | 1.19724i | 0.801035 | + | 0.598618i | \(0.204283\pi\) | ||||
−0.801035 | + | 0.598618i | \(0.795717\pi\) | |||||||
\(774\) | −5.94974 | −0.213859 | ||||||||
\(775\) | 27.9448i | 1.00381i | ||||||||
\(776\) | 17.9911 | 0.645841 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.120825i | 0.00433180i | ||||||||
\(779\) | 2.77679 | 0.0994889 | ||||||||
\(780\) | −0.759765 | −0.0272039 | ||||||||
\(781\) | −0.175008 | + | 8.83813i | −0.00626229 | + | 0.316253i | ||||
\(782\) | − | 15.9300i | − | 0.569655i | ||||||
\(783\) | 3.70637 | 0.132455 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.0633 | −1.21577 | ||||||||
\(786\) | 6.17265 | 0.220171 | ||||||||
\(787\) | 14.9131 | 0.531595 | 0.265797 | − | 0.964029i | \(-0.414365\pi\) | ||||
0.265797 | + | 0.964029i | \(0.414365\pi\) | |||||||
\(788\) | − | 15.3668i | − | 0.547421i | ||||||
\(789\) | −6.46276 | −0.230080 | ||||||||
\(790\) | 14.2653i | 0.507537i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.39078 | + | 0.146349i | 0.262620 | + | 0.00520027i | ||||
\(793\) | −2.17551 | −0.0772547 | ||||||||
\(794\) | −7.19667 | −0.255400 | ||||||||
\(795\) | −21.7699 | −0.772098 | ||||||||
\(796\) | 2.16039i | 0.0765730i | ||||||||
\(797\) | − | 37.8391i | − | 1.34033i | −0.742212 | − | 0.670165i | \(-0.766223\pi\) | ||
0.742212 | − | 0.670165i | \(-0.233777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.6515i | 2.25183i | ||||||||
\(800\) | − | 32.5135i | − | 1.14953i | ||||||
\(801\) | 7.87864i | 0.278378i | ||||||||
\(802\) | 17.3711i | 0.613394i | ||||||||
\(803\) | 0.360374 | − | 18.1993i | 0.0127173 | − | 0.642240i | ||||
\(804\) | 21.1004i | 0.744155i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.423215 | −0.0149071 | ||||||||
\(807\) | −16.5450 | −0.582413 | ||||||||
\(808\) | − | 15.3703i | − | 0.540724i | ||||||
\(809\) | − | 41.5952i | − | 1.46241i | −0.682158 | − | 0.731204i | \(-0.738959\pi\) | ||
0.682158 | − | 0.731204i | \(-0.261041\pi\) | |||||||
\(810\) | 2.02245 | 0.0710618 | ||||||||
\(811\) | −10.1870 | −0.357713 | −0.178857 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178857 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.03699i | − | 0.141583i | ||||||
\(814\) | −19.1705 | − | 0.379606i | −0.671927 | − | 0.0133052i | ||||
\(815\) | 20.4457i | 0.716182i | ||||||||
\(816\) | 13.5863i | 0.475614i | ||||||||
\(817\) | − | 8.40149i | − | 0.293931i | ||||||
\(818\) | − | 12.6615i | − | 0.442698i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 17.0185i | − | 0.594313i | ||||||
\(821\) | 35.9322i | 1.25404i | 0.779003 | + | 0.627021i | \(0.215726\pi\) | ||||
−0.779003 | + | 0.627021i | \(0.784274\pi\) | |||||||
\(822\) | −9.03469 | −0.315121 | ||||||||
\(823\) | 4.64415 | 0.161885 | 0.0809425 | − | 0.996719i | \(-0.474207\pi\) | ||||
0.0809425 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(824\) | 7.71211 | 0.268664 | ||||||||
\(825\) | 19.2218 | + | 0.380620i | 0.669217 | + | 0.0132515i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.9418i | − | 1.00641i | −0.864168 | − | 0.503203i | \(-0.832155\pi\) | ||
0.864168 | − | 0.503203i | \(-0.167845\pi\) | |||||||
\(828\) | 5.77630 | 0.200740 | ||||||||
\(829\) | − | 6.60597i | − | 0.229435i | −0.993398 | − | 0.114717i | \(-0.963404\pi\) | ||
0.993398 | − | 0.114717i | \(-0.0365963\pi\) | |||||||
\(830\) | −12.7623 | −0.442987 | ||||||||
\(831\) | 2.44867 | 0.0849435 | ||||||||
\(832\) | −0.0411528 | −0.00142672 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.74229 | 0.0949577 | ||||||||
\(835\) | 70.0049i | 2.42262i | ||||||||
\(836\) | −0.0925175 | + | 4.67225i | −0.00319978 | + | 0.161593i | ||||
\(837\) | −4.82080 | −0.166631 | ||||||||
\(838\) | −15.1736 | −0.524164 | ||||||||
\(839\) | − | 10.2775i | − | 0.354817i | −0.984137 | − | 0.177409i | \(-0.943229\pi\) | ||
0.984137 | − | 0.177409i | \(-0.0567714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.2628 | 0.526304 | ||||||||
\(842\) | 17.5896i | 0.606179i | ||||||||
\(843\) | 14.1901 | 0.488732 | ||||||||
\(844\) | − | 8.66150i | − | 0.298141i | ||||||
\(845\) | 42.6490i | 1.46717i | ||||||||
\(846\) | 5.39367 | 0.185438 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.3923 | −0.425555 | ||||||||
\(849\) | − | 26.6806i | − | 0.915674i | ||||||
\(850\) | − | 25.9162i | − | 0.888920i | ||||||
\(851\) | −33.4670 | −1.14723 | ||||||||
\(852\) | 4.32089i | 0.148031i | ||||||||
\(853\) | −11.9462 | −0.409031 | −0.204516 | − | 0.978863i | \(-0.565562\pi\) | ||||
−0.204516 | + | 0.978863i | \(0.565562\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.85586i | 0.0976683i | ||||||||
\(856\) | −4.72824 | −0.161608 | ||||||||
\(857\) | −42.2024 | −1.44160 | −0.720802 | − | 0.693141i | \(-0.756227\pi\) | ||||
−0.720802 | + | 0.693141i | \(0.756227\pi\) | |||||||
\(858\) | −0.00576437 | + | 0.291107i | −0.000196792 | + | 0.00993824i | ||||
\(859\) | 40.8408i | 1.39347i | 0.717329 | + | 0.696735i | \(0.245365\pi\) | ||||
−0.717329 | + | 0.696735i | \(0.754635\pi\) | |||||||
\(860\) | −51.4914 | −1.75584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.6937 | −0.398290 | ||||||||
\(863\) | −5.24851 | −0.178661 | −0.0893307 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893307 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(864\) | 5.60895 | 0.190820 | ||||||||
\(865\) | 4.91905i | 0.167253i | ||||||||
\(866\) | −8.32198 | −0.282792 | ||||||||
\(867\) | 35.7611i | 1.21451i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.3891 | − | 0.463140i | −0.793422 | − | 0.0157109i | ||||
\(870\) | −7.49597 | −0.254137 | ||||||||
\(871\) | −1.85642 | −0.0629025 | ||||||||
\(872\) | −7.18703 | −0.243384 | ||||||||
\(873\) | 8.07193i | 0.273193i | ||||||||
\(874\) | − | 1.90612i | − | 0.0644753i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 8.89749i | − | 0.300618i | ||||||
\(877\) | 9.72659i | 0.328444i | 0.986423 | + | 0.164222i | \(0.0525113\pi\) | ||||
−0.986423 | + | 0.164222i | \(0.947489\pi\) | |||||||
\(878\) | − | 1.48330i | − | 0.0500590i | ||||||
\(879\) | − | 18.4082i | − | 0.620892i | ||||||
\(880\) | 20.3798 | + | 0.403551i | 0.687004 | + | 0.0136037i | ||||
\(881\) | − | 16.1119i | − | 0.542824i | −0.962463 | − | 0.271412i | \(-0.912509\pi\) | ||
0.962463 | − | 0.271412i | \(-0.0874906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.01412 | −0.135086 | −0.0675430 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675430 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(884\) | −1.67954 | −0.0564890 | ||||||||
\(885\) | − | 5.08334i | − | 0.170875i | ||||||
\(886\) | 14.5994i | 0.490477i | ||||||||
\(887\) | 28.2123 | 0.947276 | 0.473638 | − | 0.880720i | \(-0.342941\pi\) | ||||
0.473638 | + | 0.880720i | \(0.342941\pi\) | |||||||
\(888\) | −20.9349 | −0.702528 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 15.9342i | − | 0.534115i | ||||||
\(891\) | −0.0656613 | + | 3.31597i | −0.00219974 | + | 0.111089i | ||||
\(892\) | − | 39.7684i | − | 1.33154i | ||||||
\(893\) | 7.61627i | 0.254869i | ||||||||
\(894\) | − | 3.08733i | − | 0.103256i | ||||||
\(895\) | 50.3606i | 1.68337i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.508201i | 0.0169683i | ||||||||
\(898\) | − | 0.0410271i | − | 0.00136909i | ||||||
\(899\) | 17.8677 | 0.595920 | ||||||||
\(900\) | 9.39737 | 0.313246 | ||||||||
\(901\) | −48.1246 | −1.60326 | ||||||||
\(902\) | −6.52073 | − | 0.129120i | −0.217117 | − | 0.00429924i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4995i | 0.881360i | ||||||||
\(905\) | 47.9503 | 1.59392 | ||||||||
\(906\) | − | 9.06787i | − | 0.301260i | ||||||
\(907\) | −7.21757 | −0.239655 | −0.119828 | − | 0.992795i | \(-0.538234\pi\) | ||||
−0.119828 | + | 0.992795i | \(0.538234\pi\) | |||||||
\(908\) | −21.3292 | −0.707835 | ||||||||
\(909\) | 6.89607 | 0.228728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0138 | −0.497431 | −0.248715 | − | 0.968577i | \(-0.580008\pi\) | ||||
−0.248715 | + | 0.968577i | \(0.580008\pi\) | |||||||
\(912\) | 1.62568i | 0.0538315i | ||||||||
\(913\) | 0.414344 | − | 20.9249i | 0.0137128 | − | 0.692512i | ||||
\(914\) | 19.1552 | 0.633599 | ||||||||
\(915\) | 50.1185 | 1.65687 | ||||||||
\(916\) | − | 22.7946i | − | 0.753155i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.47084 | 0.147560 | ||||||||
\(919\) | 18.7654i | 0.619013i | 0.950897 | + | 0.309507i | \(0.100164\pi\) | ||||
−0.950897 | + | 0.309507i | \(0.899836\pi\) | |||||||
\(920\) | −26.0946 | −0.860315 | ||||||||
\(921\) | 24.2462i | 0.798940i | ||||||||
\(922\) | 2.20685i | 0.0726787i | ||||||||
\(923\) | −0.380153 | −0.0125129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54.4469 | −1.79020 | ||||||||
\(926\) | − | 12.7973i | − | 0.420544i | ||||||
\(927\) | 3.46014i | 0.113646i | ||||||||
\(928\) | −20.7889 | −0.682428 | ||||||||
\(929\) | − | 1.14582i | − | 0.0375933i | −0.999823 | − | 0.0187966i | \(-0.994016\pi\) | ||
0.999823 | − | 0.0187966i | \(-0.00598351\pi\) | |||||||
\(930\) | 9.74984 | 0.319710 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 41.9082i | − | 1.37275i | ||||||
\(933\) | −12.5362 | −0.410416 | ||||||||
\(934\) | 23.9286 | 0.782969 | ||||||||
\(935\) | 79.1433 | + | 1.56716i | 2.58826 | + | 0.0512515i | ||||
\(936\) | 0.317899i | 0.0103908i | ||||||||
\(937\) | −46.7125 | −1.52603 | −0.763015 | − | 0.646380i | \(-0.776282\pi\) | ||||
−0.763015 | + | 0.646380i | \(0.776282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.56160 | −0.312031 | ||||||||
\(940\) | 46.6790 | 1.52250 | ||||||||
\(941\) | −5.32897 | −0.173719 | −0.0868597 | − | 0.996221i | \(-0.527683\pi\) | ||||
−0.0868597 | + | 0.996221i | \(0.527683\pi\) | |||||||
\(942\) | 6.38078i | 0.207897i | ||||||||
\(943\) | −11.3836 | −0.370700 | ||||||||
\(944\) | − | 2.89365i | − | 0.0941803i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.390668 | + | 19.7292i | −0.0127017 | + | 0.641451i | ||||
\(947\) | 30.7126 | 0.998025 | 0.499012 | − | 0.866595i | \(-0.333696\pi\) | ||||
0.499012 | + | 0.866595i | \(0.333696\pi\) | |||||||
\(948\) | −11.4347 | −0.371383 | ||||||||
\(949\) | 0.782805 | 0.0254109 | ||||||||
\(950\) | − | 3.10103i | − | 0.100611i | ||||||
\(951\) | − | 13.8291i | − | 0.448439i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.1207i | − | 0.425021i | −0.977159 | − | 0.212510i | \(-0.931836\pi\) | ||
0.977159 | − | 0.212510i | \(-0.0681640\pi\) | |||||||
\(954\) | 4.07796i | 0.132029i | ||||||||
\(955\) | 29.4793i | 0.953926i | ||||||||
\(956\) | 12.1450i | 0.392796i | ||||||||
\(957\) | 0.243365 | − | 12.2902i | 0.00786688 | − | 0.397287i | ||||
\(958\) | 9.94604i | 0.321342i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.948060 | 0.0305985 | ||||||||
\(961\) | 7.75989 | 0.250319 | ||||||||
\(962\) | − | 0.824580i | − | 0.0265855i | ||||||
\(963\) | − | 2.12139i | − | 0.0683608i | ||||||
\(964\) | −29.4355 | −0.948054 | ||||||||
\(965\) | 6.93966 | 0.223396 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7216i | 0.827150i | 0.910470 | + | 0.413575i | \(0.135720\pi\) | ||||
−0.910470 | + | 0.413575i | \(0.864280\pi\) | |||||||
\(968\) | 0.970577 | − | 24.4980i | 0.0311955 | − | 0.787397i | ||||
\(969\) | 6.31317i | 0.202808i | ||||||||
\(970\) | − | 16.3251i | − | 0.524167i | ||||||
\(971\) | 14.4915i | 0.465055i | 0.972590 | + | 0.232528i | \(0.0746996\pi\) | ||||
−0.972590 | + | 0.232528i | \(0.925300\pi\) | |||||||
\(972\) | 1.62115i | 0.0519985i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 0.0290688i | − | 0.000931425i | ||||||
\(975\) | 0.826784i | 0.0264783i | ||||||||
\(976\) | 28.5296 | 0.913210 | ||||||||
\(977\) | −46.0408 | −1.47298 | −0.736488 | − | 0.676451i | \(-0.763517\pi\) | ||||
−0.736488 | + | 0.676451i | \(0.763517\pi\) | |||||||
\(978\) | 3.82991 | 0.122467 | ||||||||
\(979\) | 26.1254 | + | 0.517321i | 0.834970 | + | 0.0165337i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.22456i | − | 0.102952i | ||||||
\(982\) | 18.5916 | 0.593283 | ||||||||
\(983\) | − | 7.22848i | − | 0.230553i | −0.993333 | − | 0.115276i | \(-0.963225\pi\) | ||
0.993333 | − | 0.115276i | \(-0.0367753\pi\) | |||||||
\(984\) | −7.12085 | −0.227004 | ||||||||
\(985\) | −31.1463 | −0.992405 | ||||||||
\(986\) | −16.5706 | −0.527716 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.200967 | −0.00639360 | ||||||||
\(989\) | 34.4422i | 1.09520i | ||||||||
\(990\) | 0.132797 | − | 6.70641i | 0.00422056 | − | 0.213144i | ||||
\(991\) | −18.2014 | −0.578187 | −0.289093 | − | 0.957301i | \(-0.593354\pi\) | ||||
−0.289093 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(992\) | 27.0396 | 0.858509 | ||||||||
\(993\) | − | 18.2492i | − | 0.579120i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.37880 | 0.138817 | ||||||||
\(996\) | − | 10.2300i | − | 0.324150i | ||||||
\(997\) | −1.43859 | −0.0455605 | −0.0227802 | − | 0.999740i | \(-0.507252\pi\) | ||||
−0.0227802 | + | 0.999740i | \(0.507252\pi\) | |||||||
\(998\) | 0.929007i | 0.0294072i | ||||||||
\(999\) | − | 9.39271i | − | 0.297172i |
(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 | 1617.2.c.a.538.20 | 32 | ||
7.4 | even | 3 | 231.2.p.a.208.7 | yes | 32 | ||
7.5 | odd | 6 | 231.2.p.a.10.10 | yes | 32 | ||
7.6 | odd | 2 | inner | 1617.2.c.a.538.19 | 32 | ||
11.10 | odd | 2 | inner | 1617.2.c.a.538.14 | 32 | ||
21.5 | even | 6 | 693.2.bg.b.10.7 | 32 | |||
21.11 | odd | 6 | 693.2.bg.b.208.10 | 32 | |||
77.32 | odd | 6 | 231.2.p.a.208.10 | yes | 32 | ||
77.54 | even | 6 | 231.2.p.a.10.7 | ✓ | 32 | ||
77.76 | even | 2 | inner | 1617.2.c.a.538.13 | 32 | ||
231.32 | even | 6 | 693.2.bg.b.208.7 | 32 | |||
231.131 | odd | 6 | 693.2.bg.b.10.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.p.a.10.7 | ✓ | 32 | 77.54 | even | 6 | ||
231.2.p.a.10.10 | yes | 32 | 7.5 | odd | 6 | ||
231.2.p.a.208.7 | yes | 32 | 7.4 | even | 3 | ||
231.2.p.a.208.10 | yes | 32 | 77.32 | odd | 6 | ||
693.2.bg.b.10.7 | 32 | 21.5 | even | 6 | |||
693.2.bg.b.10.10 | 32 | 231.131 | odd | 6 | |||
693.2.bg.b.208.7 | 32 | 231.32 | even | 6 | |||
693.2.bg.b.208.10 | 32 | 21.11 | odd | 6 | |||
1617.2.c.a.538.13 | 32 | 77.76 | even | 2 | inner | ||
1617.2.c.a.538.14 | 32 | 11.10 | odd | 2 | inner | ||
1617.2.c.a.538.19 | 32 | 7.6 | odd | 2 | inner | ||
1617.2.c.a.538.20 | 32 | 1.1 | even | 1 | trivial |