Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (of order \(4\), degree \(2\), 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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 657.2 | ||
Character | \(\chi\) | \(=\) | 1400.657 |
Dual form | 1400.2.x.c.993.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −2.09284 | − | 2.09284i | −1.20830 | − | 1.20830i | −0.971577 | − | 0.236725i | \(-0.923926\pi\) |
−0.236725 | − | 0.971577i | \(-0.576074\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59595 | − | 0.510946i | 0.981175 | − | 0.193119i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.75996i | 1.91999i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.94864 | −1.19056 | −0.595279 | − | 0.803519i | \(-0.702959\pi\) | ||||
−0.595279 | + | 0.803519i | \(0.702959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.69798 | + | 1.69798i | 0.470934 | + | 0.470934i | 0.902217 | − | 0.431283i | \(-0.141939\pi\) |
−0.431283 | + | 0.902217i | \(0.641939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.66927 | − | 2.66927i | 0.647392 | − | 0.647392i | −0.304970 | − | 0.952362i | \(-0.598646\pi\) |
0.952362 | + | 0.304970i | \(0.0986464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.36102 | 1.22990 | 0.614952 | − | 0.788565i | \(-0.289176\pi\) | ||||
0.614952 | + | 0.788565i | \(0.289176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.50223 | − | 4.36357i | −1.41890 | − | 0.952209i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.55527 | − | 3.55527i | 0.741325 | − | 0.741325i | −0.231508 | − | 0.972833i | \(-0.574366\pi\) |
0.972833 | + | 0.231508i | \(0.0743660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.77616 | − | 5.77616i | 1.11162 | − | 1.11162i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.24449i | 1.34527i | 0.739975 | + | 0.672634i | \(0.234837\pi\) | ||||
−0.739975 | + | 0.672634i | \(0.765163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.174160i | 0.0312801i | 0.999878 | + | 0.0156401i | \(0.00497859\pi\) | ||||
−0.999878 | + | 0.0156401i | \(0.995021\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.26386 | + | 8.26386i | 1.43855 | + | 1.43855i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.85737 | + | 4.85737i | 0.798547 | + | 0.798547i | 0.982866 | − | 0.184320i | \(-0.0590081\pi\) |
−0.184320 | + | 0.982866i | \(0.559008\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 7.10719i | − | 1.13806i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.732583i | 0.114410i | 0.998362 | + | 0.0572051i | \(0.0182189\pi\) | ||||
−0.998362 | + | 0.0572051i | \(0.981781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.20187 | − | 8.20187i | 1.25077 | − | 1.25077i | 0.295400 | − | 0.955374i | \(-0.404547\pi\) |
0.955374 | − | 0.295400i | \(-0.0954529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.31716 | − | 2.31716i | 0.337993 | − | 0.337993i | −0.517619 | − | 0.855612i | \(-0.673181\pi\) |
0.855612 | + | 0.517619i | \(0.173181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.47787 | − | 2.65278i | 0.925410 | − | 0.378968i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.1727 | −1.56449 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.53449 | + | 4.53449i | −0.622860 | + | 0.622860i | −0.946262 | − | 0.323402i | \(-0.895173\pi\) |
0.323402 | + | 0.946262i | \(0.395173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.2198 | − | 11.2198i | −1.48609 | − | 1.48609i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1904 | −1.71724 | −0.858620 | − | 0.512613i | \(-0.828678\pi\) | ||||
−0.858620 | + | 0.512613i | \(0.828678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.3556i | − | 1.71001i | −0.518622 | − | 0.855004i | \(-0.673555\pi\) | ||
0.518622 | − | 0.855004i | \(-0.326445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.94303 | + | 14.9525i | 0.370787 | + | 1.88384i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55658 | − | 6.55658i | −0.801014 | − | 0.801014i | 0.182240 | − | 0.983254i | \(-0.441665\pi\) |
−0.983254 | + | 0.182240i | \(0.941665\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.8812 | −1.79149 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3312 | 1.93816 | 0.969081 | − | 0.246742i | \(-0.0793599\pi\) | ||||
0.969081 | + | 0.246742i | \(0.0793599\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.02549 | − | 7.02549i | −0.822271 | − | 0.822271i | 0.164162 | − | 0.986433i | \(-0.447508\pi\) |
−0.986433 | + | 0.164162i | \(0.947508\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.2504 | + | 2.01754i | −1.16815 | + | 0.229920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.63234i | 0.746197i | 0.927792 | + | 0.373098i | \(0.121705\pi\) | ||||
−0.927792 | + | 0.373098i | \(0.878295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.89727 | −0.766363 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4642 | − | 10.4642i | −1.14860 | − | 1.14860i | −0.986829 | − | 0.161766i | \(-0.948281\pi\) |
−0.161766 | − | 0.986829i | \(-0.551719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.1616 | − | 15.1616i | 1.62549 | − | 1.62549i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.43554 | 0.364166 | 0.182083 | − | 0.983283i | \(-0.441716\pi\) | ||||
0.182083 | + | 0.983283i | \(0.441716\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.27543 | + | 3.54028i | 0.553015 | + | 0.371122i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.364490 | − | 0.364490i | 0.0377958 | − | 0.0377958i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.40892 | + | 1.40892i | −0.143054 | + | 0.143054i | −0.775007 | − | 0.631953i | \(-0.782254\pi\) |
0.631953 | + | 0.775007i | \(0.282254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 22.7440i | − | 2.28586i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.1783i | − | 1.21178i | −0.795547 | − | 0.605891i | \(-0.792817\pi\) | ||
0.795547 | − | 0.605891i | \(-0.207183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.52421 | + | 9.52421i | 0.938449 | + | 0.938449i | 0.998213 | − | 0.0597638i | \(-0.0190348\pi\) |
−0.0597638 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.98949 | − | 8.98949i | −0.869046 | − | 0.869046i | 0.123321 | − | 0.992367i | \(-0.460646\pi\) |
−0.992367 | + | 0.123321i | \(0.960646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.86269i | 0.369979i | 0.982741 | + | 0.184989i | \(0.0592251\pi\) | ||||
−0.982741 | + | 0.184989i | \(0.940775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 20.3314i | − | 1.92977i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.94525 | − | 2.94525i | 0.277066 | − | 0.277066i | −0.554870 | − | 0.831937i | \(-0.687232\pi\) |
0.831937 | + | 0.554870i | \(0.187232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.78028 | + | 9.78028i | −0.904187 | + | 0.904187i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.56542 | − | 8.29312i | 0.510181 | − | 0.760229i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.59172 | 0.417429 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.53318 | − | 1.53318i | 0.138242 | − | 0.138242i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.73709 | − | 1.73709i | −0.154142 | − | 0.154142i | 0.625823 | − | 0.779965i | \(-0.284763\pi\) |
−0.779965 | + | 0.625823i | \(0.784763\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −34.3304 | −3.02262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.70296i | − | 0.236158i | −0.993004 | − | 0.118079i | \(-0.962326\pi\) | ||
0.993004 | − | 0.118079i | \(-0.0376737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.9169 | − | 2.73919i | 1.20675 | − | 0.237518i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.26814 | + | 3.26814i | 0.279216 | + | 0.279216i | 0.832796 | − | 0.553580i | \(-0.186739\pi\) |
−0.553580 | + | 0.832796i | \(0.686739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.4638 | 1.82054 | 0.910269 | − | 0.414017i | \(-0.135874\pi\) | ||||
0.910269 | + | 0.414017i | \(0.135874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.69891 | −0.816795 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.70469 | − | 6.70469i | −0.560674 | − | 0.560674i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.1090 | − | 8.00531i | −1.57608 | − | 0.660267i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.09645i | 0.171747i | 0.996306 | + | 0.0858737i | \(0.0273682\pi\) | ||||
−0.996306 | + | 0.0858737i | \(0.972632\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.78039 | 0.144886 | 0.0724432 | − | 0.997373i | \(-0.476920\pi\) | ||||
0.0724432 | + | 0.997373i | \(0.476920\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.3749 | + | 15.3749i | 1.24298 | + | 1.24298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.64528 | − | 4.64528i | 0.370734 | − | 0.370734i | −0.497011 | − | 0.867744i | \(-0.665569\pi\) |
0.867744 | + | 0.497011i | \(0.165569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.9799 | 1.50521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.41274 | − | 11.0458i | 0.584205 | − | 0.870534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.67419 | − | 1.67419i | 0.131132 | − | 0.131132i | −0.638494 | − | 0.769627i | \(-0.720442\pi\) |
0.769627 | + | 0.638494i | \(0.220442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.65522 | + | 1.65522i | −0.128084 | + | 0.128084i | −0.768243 | − | 0.640158i | \(-0.778869\pi\) |
0.640158 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.23375i | − | 0.556443i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.8793i | 2.36140i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.949313 | − | 0.949313i | −0.0721750 | − | 0.0721750i | 0.670098 | − | 0.742273i | \(-0.266252\pi\) |
−0.742273 | + | 0.670098i | \(0.766252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.6053 | + | 27.6053i | 2.07494 | + | 2.07494i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6926i | 1.24767i | 0.781558 | + | 0.623833i | \(0.214425\pi\) | ||||
−0.781558 | + | 0.623833i | \(0.785575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6406i | 1.38554i | 0.721158 | + | 0.692771i | \(0.243610\pi\) | ||||
−0.721158 | + | 0.692771i | \(0.756390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.9511 | + | 27.9511i | −2.06621 | + | 2.06621i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5400 | + | 10.5400i | −0.770758 | + | 0.770758i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.0433 | − | 17.9459i | 0.876020 | − | 1.30537i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.33648 | −0.313777 | −0.156888 | − | 0.987616i | \(-0.550146\pi\) | ||||
−0.156888 | + | 0.987616i | \(0.550146\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8884 | − | 11.8884i | 0.855747 | − | 0.855747i | −0.135087 | − | 0.990834i | \(-0.543131\pi\) |
0.990834 | + | 0.135087i | \(0.0431313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.85131 | + | 2.85131i | 0.203148 | + | 0.203148i | 0.801347 | − | 0.598200i | \(-0.204117\pi\) |
−0.598200 | + | 0.801347i | \(0.704117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.34228 | −0.307816 | −0.153908 | − | 0.988085i | \(-0.549186\pi\) | ||||
−0.153908 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.4438i | 1.93573i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.70154 | + | 18.8063i | 0.259797 | + | 1.31994i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.4782 | + | 20.4782i | 1.42333 | + | 1.42333i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1687 | −1.46427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8362 | −1.29674 | −0.648369 | − | 0.761326i | \(-0.724549\pi\) | ||||
−0.648369 | + | 0.761326i | \(0.724549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.1787 | − | 34.1787i | −2.34189 | − | 2.34189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0889865 | + | 0.452111i | 0.00604080 | + | 0.0306913i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.4065i | 1.98710i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.06470 | 0.609758 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9232 | − | 13.9232i | −0.932366 | − | 0.932366i | 0.0654872 | − | 0.997853i | \(-0.479140\pi\) |
−0.997853 | + | 0.0654872i | \(0.979140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.91799 | − | 6.91799i | 0.459163 | − | 0.459163i | −0.439218 | − | 0.898381i | \(-0.644744\pi\) |
0.898381 | + | 0.439218i | \(0.144744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.64658 | 0.108809 | 0.0544047 | − | 0.998519i | \(-0.482674\pi\) | ||||
0.0544047 | + | 0.998519i | \(0.482674\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.6749 | + | 17.2302i | 1.68929 | + | 1.13366i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.73081 | − | 4.73081i | 0.309926 | − | 0.309926i | −0.534955 | − | 0.844881i | \(-0.679671\pi\) |
0.844881 | + | 0.534955i | \(0.179671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8804 | − | 13.8804i | 0.901631 | − | 0.901631i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.18344i | 0.335289i | 0.985848 | + | 0.167644i | \(0.0536160\pi\) | ||||
−0.985848 | + | 0.167644i | \(0.946384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.65109i | − | 0.557265i | −0.960398 | − | 0.278633i | \(-0.910119\pi\) | ||
0.960398 | − | 0.278633i | \(-0.0898812\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.89359 | − | 2.89359i | −0.185624 | − | 0.185624i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.10289 | + | 9.10289i | 0.579203 | + | 0.579203i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.7998i | 2.77570i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0974i | 0.700459i | 0.936664 | + | 0.350230i | \(0.113896\pi\) | ||||
−0.936664 | + | 0.350230i | \(0.886104\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0385 | + | 14.0385i | −0.882591 | + | 0.882591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62391 | − | 1.62391i | 0.101297 | − | 0.101297i | −0.654642 | − | 0.755939i | \(-0.727181\pi\) |
0.755939 | + | 0.654642i | \(0.227181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.0913 | + | 10.1276i | 0.937729 | + | 0.629300i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −41.7280 | −2.58290 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.7161 | − | 20.7161i | 1.27741 | − | 1.27741i | 0.335301 | − | 0.942111i | \(-0.391162\pi\) |
0.942111 | − | 0.335301i | \(-0.108838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.19003 | − | 7.19003i | −0.440023 | − | 0.440023i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.0977 | 1.89606 | 0.948031 | − | 0.318179i | \(-0.103071\pi\) | ||||
0.948031 | + | 0.318179i | \(0.103071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.24962i | − | 0.561875i | −0.959726 | − | 0.280937i | \(-0.909355\pi\) | ||
0.959726 | − | 0.280937i | \(-0.0906453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.63139 | − | 18.4499i | −0.219782 | − | 1.11664i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3476 | + | 14.3476i | 0.862066 | + | 0.862066i | 0.991578 | − | 0.129512i | \(-0.0413410\pi\) |
−0.129512 | + | 0.991578i | \(0.541341\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00316 | −0.0600574 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3108 | 0.734402 | 0.367201 | − | 0.930142i | \(-0.380316\pi\) | ||||
0.367201 | + | 0.930142i | \(0.380316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.14401 | + | 7.14401i | 0.424667 | + | 0.424667i | 0.886807 | − | 0.462140i | \(-0.152918\pi\) |
−0.462140 | + | 0.886807i | \(0.652918\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.374310 | + | 1.90174i | 0.0220948 | + | 0.112256i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.75003i | 0.161766i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.89727 | 0.345704 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8037 | − | 10.8037i | −0.631156 | − | 0.631156i | 0.317202 | − | 0.948358i | \(-0.397257\pi\) |
−0.948358 | + | 0.317202i | \(0.897257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.8079 | + | 22.8079i | −1.32345 | + | 1.32345i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0735 | 0.698230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.1009 | − | 25.4823i | 0.985680 | − | 1.46878i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.4872 | + | 25.4872i | −1.46420 | + | 1.46420i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5142 | + | 21.5142i | −1.22788 | + | 1.22788i | −0.263113 | + | 0.964765i | \(0.584749\pi\) |
−0.964765 | + | 0.263113i | \(0.915251\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 39.8653i | − | 2.26786i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8682i | 0.899802i | 0.893078 | + | 0.449901i | \(0.148541\pi\) | ||||
−0.893078 | + | 0.449901i | \(0.851459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6132 | + | 16.6132i | 0.939036 | + | 0.939036i | 0.998246 | − | 0.0592093i | \(-0.0188579\pi\) |
−0.0592093 | + | 0.998246i | \(0.518858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.53714 | + | 9.53714i | 0.535659 | + | 0.535659i | 0.922251 | − | 0.386592i | \(-0.126348\pi\) |
−0.386592 | + | 0.922251i | \(0.626348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.6059i | − | 1.60162i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 37.6271i | 2.10014i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3100 | − | 14.3100i | 0.796230 | − | 0.796230i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.08400 | − | 8.08400i | 0.447046 | − | 0.447046i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.83129 | − | 7.19917i | 0.266357 | − | 0.396903i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9177 | 0.710021 | 0.355011 | − | 0.934862i | \(-0.384477\pi\) | ||||
0.355011 | + | 0.934862i | \(0.384477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.9783 | + | 27.9783i | −1.53320 | + | 1.53320i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.12871 | + | 7.12871i | 0.388326 | + | 0.388326i | 0.874090 | − | 0.485764i | \(-0.161459\pi\) |
−0.485764 | + | 0.874090i | \(0.661459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3279 | −0.669559 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.687696i | − | 0.0372408i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4608 | − | 10.1963i | 0.834803 | − | 0.550549i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.28294 | + | 1.28294i | 0.0688717 | + | 0.0688717i | 0.740704 | − | 0.671832i | \(-0.234492\pi\) |
−0.671832 | + | 0.740704i | \(0.734492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4635 | 0.774213 | 0.387106 | − | 0.922035i | \(-0.373475\pi\) | ||||
0.387106 | + | 0.922035i | \(0.373475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.6156 | 1.04700 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.19731 | − | 1.19731i | −0.0637263 | − | 0.0637263i | 0.674525 | − | 0.738252i | \(-0.264348\pi\) |
−0.738252 | + | 0.674525i | \(0.764348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.0037 | + | 5.70864i | −1.53504 | + | 0.302133i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1832i | 1.43467i | 0.696726 | + | 0.717337i | \(0.254639\pi\) | ||||
−0.696726 | + | 0.717337i | \(0.745361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.74058 | 0.512662 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.60974 | − | 9.60974i | −0.504380 | − | 0.504380i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0535 | + | 18.0535i | −0.942383 | + | 0.942383i | −0.998428 | − | 0.0560450i | \(-0.982151\pi\) |
0.0560450 | + | 0.998428i | \(0.482151\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.21965 | −0.219666 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.45441 | + | 14.0882i | −0.490849 | + | 0.731421i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.4769 | − | 23.4769i | 1.21559 | − | 1.21559i | 0.246430 | − | 0.969161i | \(-0.420743\pi\) |
0.969161 | − | 0.246430i | \(-0.0792574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3010 | + | 12.3010i | −0.633533 | + | 0.633533i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 32.9476i | − | 1.69241i | −0.532861 | − | 0.846203i | \(-0.678883\pi\) | ||
0.532861 | − | 0.846203i | \(-0.321117\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.27092i | 0.372501i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.6328 | − | 12.6328i | −0.645506 | − | 0.645506i | 0.306398 | − | 0.951904i | \(-0.400876\pi\) |
−0.951904 | + | 0.306398i | \(0.900876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 47.2425 | + | 47.2425i | 2.40147 | + | 2.40147i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.77597i | − | 0.191449i | −0.995408 | − | 0.0957246i | \(-0.969483\pi\) | ||
0.995408 | − | 0.0957246i | \(-0.0305168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.9799i | − | 0.959856i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | + | 5.65685i | −0.285351 | + | 0.285351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0271 | + | 16.0271i | −0.804375 | + | 0.804375i | −0.983776 | − | 0.179401i | \(-0.942584\pi\) |
0.179401 | + | 0.983776i | \(0.442584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.8586 | − | 23.3932i | −1.74511 | − | 1.17113i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.52985 | 0.176272 | 0.0881362 | − | 0.996108i | \(-0.471909\pi\) | ||||
0.0881362 | + | 0.996108i | \(0.471909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.295720 | + | 0.295720i | −0.0147309 | + | 0.0147309i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.1800 | − | 19.1800i | −0.950717 | − | 0.950717i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.07318 | 0.250852 | 0.125426 | − | 0.992103i | \(-0.459970\pi\) | ||||
0.125426 | + | 0.992103i | \(0.459970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 13.6794i | − | 0.674754i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.2415 | + | 6.73957i | −1.68491 | + | 0.331632i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44.9204 | − | 44.9204i | −2.19976 | − | 2.19976i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.44663 | −0.461498 | −0.230749 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230749 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4827 | 1.48564 | 0.742818 | − | 0.669493i | \(-0.233489\pi\) | ||||
0.742818 | + | 0.669493i | \(0.233489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.3468 | + | 13.3468i | 0.648942 | + | 0.648942i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.82398 | − | 34.6704i | −0.330236 | − | 1.67782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.0637i | 1.35493i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.4845 | −0.553191 | −0.276595 | − | 0.960987i | \(-0.589206\pi\) | ||||
−0.276595 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8641 | + | 26.8641i | 1.29101 | + | 1.29101i | 0.934164 | + | 0.356845i | \(0.116148\pi\) |
0.356845 | + | 0.934164i | \(0.383852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.0599 | − | 19.0599i | 0.911758 | − | 0.911758i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5387 | −0.646166 | −0.323083 | − | 0.946371i | \(-0.604719\pi\) | ||||
−0.323083 | + | 0.946371i | \(0.604719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.2799 | + | 37.3123i | 0.727614 | + | 1.77677i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.27325 | + | 7.27325i | −0.345563 | + | 0.345563i | −0.858454 | − | 0.512891i | \(-0.828574\pi\) |
0.512891 | + | 0.858454i | \(0.328574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.38752 | − | 4.38752i | 0.207523 | − | 0.207523i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.85641i | − | 0.229188i | −0.993412 | − | 0.114594i | \(-0.963443\pi\) | ||
0.993412 | − | 0.114594i | \(-0.0365567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.89270i | − | 0.136212i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.72608 | − | 3.72608i | −0.175066 | − | 0.175066i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5716 | − | 14.5716i | −0.681629 | − | 0.681629i | 0.278738 | − | 0.960367i | \(-0.410084\pi\) |
−0.960367 | + | 0.278738i | \(0.910084\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 30.8362i | − | 1.43931i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.19256i | − | 0.334991i | −0.985873 | − | 0.167495i | \(-0.946432\pi\) | ||
0.985873 | − | 0.167495i | \(-0.0535680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.74846 | − | 3.74846i | 0.174206 | − | 0.174206i | −0.614619 | − | 0.788824i | \(-0.710690\pi\) |
0.788824 | + | 0.614619i | \(0.210690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.4030 | + | 17.4030i | −0.805314 | + | 0.805314i | −0.983921 | − | 0.178607i | \(-0.942841\pi\) |
0.178607 | + | 0.983921i | \(0.442841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.3706 | − | 13.6705i | −0.940626 | − | 0.631244i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.4437 | −0.895917 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.3862 | + | 32.3862i | −1.48912 | + | 1.48912i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.1185 | − | 26.1185i | −1.19588 | − | 1.19588i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.8582 | −1.36426 | −0.682129 | − | 0.731232i | \(-0.738946\pi\) | ||||
−0.682129 | + | 0.731232i | \(0.738946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4954i | 0.752125i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38.6308 | + | 7.60350i | −1.75776 | + | 0.345971i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7577 | + | 18.7577i | 0.849993 | + | 0.849993i | 0.990132 | − | 0.140139i | \(-0.0447550\pi\) |
−0.140139 | + | 0.990132i | \(0.544755\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.00761 | −0.316895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.7440 | 0.936163 | 0.468081 | − | 0.883685i | \(-0.344945\pi\) | ||||
0.468081 | + | 0.883685i | \(0.344945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3375 | + | 19.3375i | 0.870917 | + | 0.870917i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.3950 | − | 8.34438i | 1.90168 | − | 0.374297i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.19553i | 0.0535192i | 0.999642 | + | 0.0267596i | \(0.00851886\pi\) | ||||
−0.999642 | + | 0.0267596i | \(0.991481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.92820 | 0.309529 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.8461 | − | 12.8461i | −0.572779 | − | 0.572779i | 0.360125 | − | 0.932904i | \(-0.382734\pi\) |
−0.932904 | + | 0.360125i | \(0.882734\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.1391 | + | 15.1391i | −0.672351 | + | 0.672351i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.4311 | −0.816943 | −0.408471 | − | 0.912771i | \(-0.633938\pi\) | ||||
−0.408471 | + | 0.912771i | \(0.633938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.8274 | − | 14.6481i | −0.965589 | − | 0.647996i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.9661 | − | 30.9661i | 1.36719 | − | 1.36719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.14963 | + | 9.14963i | −0.402400 | + | 0.402400i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.97352i | 0.174418i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.4435i | − | 1.33375i | −0.745168 | − | 0.666877i | \(-0.767631\pi\) | ||
0.745168 | − | 0.666877i | \(-0.232369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.5460 | − | 12.5460i | −0.548599 | − | 0.548599i | 0.377436 | − | 0.926036i | \(-0.376806\pi\) |
−0.926036 | + | 0.377436i | \(0.876806\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.464880 | + | 0.464880i | 0.0202505 | + | 0.0202505i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 2.27988i | − | 0.0991254i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 75.9760i | − | 3.29708i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.24391 | + | 1.24391i | −0.0538796 | + | 0.0538796i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.9350 | − | 34.9350i | 1.50756 | − | 1.50756i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.5787 | + | 10.4748i | −1.10175 | + | 0.451183i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0700 | −0.862875 | −0.431438 | − | 0.902143i | \(-0.641994\pi\) | ||||
−0.431438 | + | 0.902143i | \(0.641994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39.0117 | − | 39.0117i | 1.67415 | − | 1.67415i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3298 | − | 12.3298i | −0.527185 | − | 0.527185i | 0.392547 | − | 0.919732i | \(-0.371594\pi\) |
−0.919732 | + | 0.392547i | \(0.871594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 76.9277 | 3.28319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.8379i | 1.65455i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.38877 | + | 17.2172i | 0.144105 | + | 0.732150i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.8455 | − | 10.8455i | −0.459541 | − | 0.459541i | 0.438964 | − | 0.898505i | \(-0.355346\pi\) |
−0.898505 | + | 0.438964i | \(0.855346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.8532 | 1.17806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.1169 | 1.86262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8745 | + | 29.8745i | 1.25906 | + | 1.25906i | 0.951542 | + | 0.307517i | \(0.0994982\pi\) |
0.307517 | + | 0.951542i | \(0.400502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9049 | + | 3.52413i | −0.751937 | + | 0.148000i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.2736i | 0.682225i | 0.940023 | + | 0.341112i | \(0.110804\pi\) | ||||
−0.940023 | + | 0.341112i | \(0.889196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0495 | −1.00644 | −0.503221 | − | 0.864158i | \(-0.667852\pi\) | ||||
−0.503221 | + | 0.864158i | \(0.667852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.07557 | + | 9.07557i | 0.379137 | + | 0.379137i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1701 | + | 11.1701i | −0.465017 | + | 0.465017i | −0.900296 | − | 0.435278i | \(-0.856650\pi\) |
0.435278 | + | 0.900296i | \(0.356650\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.7611 | −2.06800 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.5111 | − | 21.8179i | −1.34879 | − | 0.905157i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.9050 | − | 17.9050i | 0.741551 | − | 0.741551i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.4617 | − | 15.4617i | 0.638171 | − | 0.638171i | −0.311933 | − | 0.950104i | \(-0.600977\pi\) |
0.950104 | + | 0.311933i | \(0.100977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.933678i | 0.0384715i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 11.9347i | − | 0.490928i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.5438 | − | 32.5438i | −1.33641 | − | 1.33641i | −0.899508 | − | 0.436904i | \(-0.856075\pi\) |
−0.436904 | − | 0.899508i | \(-0.643925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.08770 | + | 9.08770i | 0.371935 | + | 0.371935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 21.7804i | − | 0.889923i | −0.895550 | − | 0.444961i | \(-0.853217\pi\) | ||
0.895550 | − | 0.444961i | \(-0.146783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.8736i | 0.810660i | 0.914170 | + | 0.405330i | \(0.132843\pi\) | ||||
−0.914170 | + | 0.405330i | \(0.867157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.7657 | − | 37.7657i | 1.53794 | − | 1.53794i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.80167 | + | 6.80167i | −0.276071 | + | 0.276071i | −0.831538 | − | 0.555467i | \(-0.812539\pi\) |
0.555467 | + | 0.831538i | \(0.312539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.6119 | − | 47.1054i | 1.28098 | − | 1.90881i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.86898 | 0.318345 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0751 | + | 13.0751i | −0.528098 | + | 0.528098i | −0.920005 | − | 0.391907i | \(-0.871815\pi\) |
0.391907 | + | 0.920005i | \(0.371815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.6256 | − | 21.6256i | −0.870614 | − | 0.870614i | 0.121925 | − | 0.992539i | \(-0.461093\pi\) |
−0.992539 | + | 0.121925i | \(0.961093\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.9528 | 1.72642 | 0.863210 | − | 0.504845i | \(-0.168451\pi\) | ||||
0.863210 | + | 0.504845i | \(0.168451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 41.0716i | − | 1.64815i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.91847 | − | 1.75537i | 0.357311 | − | 0.0703276i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 44.3028 | + | 44.3028i | 1.76928 | + | 1.76928i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.9312 | 1.03395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.7175 | −0.904370 | −0.452185 | − | 0.891924i | \(-0.649355\pi\) | ||||
−0.452185 | + | 0.891924i | \(0.649355\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.4212 | + | 39.4212i | 1.56685 | + | 1.56685i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5036 | + | 6.49492i | 0.614276 | + | 0.257338i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 94.0674i | 3.72125i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0435 | −1.02866 | −0.514328 | − | 0.857594i | \(-0.671959\pi\) | ||||
−0.514328 | + | 0.857594i | \(0.671959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7907 | + | 12.7907i | 0.504416 | + | 0.504416i | 0.912807 | − | 0.408391i | \(-0.133910\pi\) |
−0.408391 | + | 0.912807i | \(0.633910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.81311 | − | 1.81311i | 0.0712805 | − | 0.0712805i | −0.670568 | − | 0.741848i | \(-0.733949\pi\) |
0.741848 | + | 0.670568i | \(0.233949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.0840 | 2.04447 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.759961 | − | 1.13243i | 0.0297852 | − | 0.0443834i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.4676 | + | 21.4676i | −0.840092 | + | 0.840092i | −0.988871 | − | 0.148778i | \(-0.952466\pi\) |
0.148778 | + | 0.988871i | \(0.452466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.4665 | − | 40.4665i | 1.57875 | − | 1.57875i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.6423i | 1.07679i | 0.842692 | + | 0.538396i | \(0.180969\pi\) | ||||
−0.842692 | + | 0.538396i | \(0.819031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 7.38292i | − | 0.287162i | −0.989639 | − | 0.143581i | \(-0.954138\pi\) | ||
0.989639 | − | 0.143581i | \(-0.0458618\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.9710 | − | 18.9710i | −0.736772 | − | 0.736772i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.7561 | + | 25.7561i | 0.997281 | + | 0.997281i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 58.2781i | 2.25316i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.7363i | 2.03586i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4963 | − | 12.4963i | 0.481697 | − | 0.481697i | −0.423976 | − | 0.905673i | \(-0.639366\pi\) |
0.905673 | + | 0.423976i | \(0.139366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0753 | − | 27.0753i | 1.04059 | − | 1.04059i | 0.0414483 | − | 0.999141i | \(-0.486803\pi\) |
0.999141 | − | 0.0414483i | \(-0.0131972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.93759 | + | 4.37735i | −0.112734 | + | 0.167987i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.9565 | −1.10962 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.7113 | + | 17.7113i | −0.677704 | + | 0.677704i | −0.959480 | − | 0.281776i | \(-0.909076\pi\) |
0.281776 | + | 0.959480i | \(0.409076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.44604 | − | 3.44604i | −0.131474 | − | 0.131474i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.3989 | −0.586652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.75386i | − | 0.104762i | −0.998627 | − | 0.0523810i | \(-0.983319\pi\) | ||
0.998627 | − | 0.0523810i | \(-0.0166810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.6209 | − | 59.0422i | −0.441443 | − | 2.24283i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.95546 | + | 1.95546i | 0.0740683 | + | 0.0740683i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.8017 | −0.748968 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.66352 | −0.0628301 | −0.0314151 | − | 0.999506i | \(-0.510001\pi\) | ||||
−0.0314151 | + | 0.999506i | \(0.510001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0405 | + | 26.0405i | 0.982135 | + | 0.982135i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.22244 | − | 31.6141i | −0.234019 | − | 1.18897i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.7442i | − | 1.07951i | −0.841822 | − | 0.539756i | \(-0.818516\pi\) | ||
0.841822 | − | 0.539756i | \(-0.181484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.2020 | −1.43269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.619187 | + | 0.619187i | 0.0231887 | + | 0.0231887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.8481 | − | 10.8481i | 0.405130 | − | 0.405130i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.1059 | −1.57029 | −0.785143 | − | 0.619314i | \(-0.787411\pi\) | ||||
−0.785143 | + | 0.619314i | \(0.787411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.5907 | + | 19.8580i | 1.10202 | + | 0.739550i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.1053 | + | 18.1053i | −0.673345 | + | 0.673345i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.6639 | + | 15.6639i | −0.580943 | + | 0.580943i | −0.935162 | − | 0.354219i | \(-0.884747\pi\) |
0.354219 | + | 0.935162i | \(0.384747\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.8035i | 1.21494i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 43.7860i | − | 1.61948i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.73703 | − | 3.73703i | −0.138031 | − | 0.138031i | 0.634715 | − | 0.772746i | \(-0.281117\pi\) |
−0.772746 | + | 0.634715i | \(0.781117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.8895 | + | 25.8895i | 0.953654 | + | 0.953654i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.2445i | 0.523993i | 0.965069 | + | 0.261997i | \(0.0843809\pi\) | ||||
−0.965069 | + | 0.261997i | \(0.915619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 38.1018i | − | 1.39970i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.30083 | + | 4.30083i | −0.157782 | + | 0.157782i | −0.781583 | − | 0.623801i | \(-0.785588\pi\) |
0.623801 | + | 0.781583i | \(0.285588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 60.2734 | − | 60.2734i | 2.20529 | − | 2.20529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.9294 | − | 18.7431i | −1.02052 | − | 0.684857i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.2906 | −1.03234 | −0.516170 | − | 0.856486i | \(-0.672643\pi\) | ||||
−0.516170 | + | 0.856486i | \(0.672643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.2250 | − | 23.2250i | 0.846366 | − | 0.846366i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1132 | + | 15.1132i | 0.549299 | + | 0.549299i | 0.926238 | − | 0.376939i | \(-0.123023\pi\) |
−0.376939 | + | 0.926238i | \(0.623023\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 58.7605 | 2.13287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.7113i | 0.859533i | 0.902940 | + | 0.429766i | \(0.141404\pi\) | ||||
−0.902940 | + | 0.429766i | \(0.858596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.97363 | + | 10.0273i | 0.0714501 | + | 0.363014i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.3969 | − | 22.3969i | −0.808706 | − | 0.808706i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.3228 | −0.985286 | −0.492643 | − | 0.870232i | \(-0.663969\pi\) | ||||
−0.492643 | + | 0.870232i | \(0.663969\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.79718 | −0.244794 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.79374 | − | 7.79374i | −0.280321 | − | 0.280321i | 0.552916 | − | 0.833237i | \(-0.313515\pi\) |
−0.833237 | + | 0.552916i | \(0.813515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3882 | − | 52.7792i | −0.372676 | − | 1.89344i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.92739i | 0.140713i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.4861 | −2.30750 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.8453 | + | 41.8453i | 1.49543 | + | 1.49543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.99375 | − | 6.99375i | 0.249300 | − | 0.249300i | −0.571383 | − | 0.820683i | \(-0.693593\pi\) |
0.820683 | + | 0.571383i | \(0.193593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −86.7112 | −3.08700 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.14086 | − | 9.15059i | 0.218344 | − | 0.325357i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6775 | − | 22.6775i | 0.805300 | − | 0.805300i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.1365 | + | 14.1365i | −0.500740 | + | 0.500740i | −0.911668 | − | 0.410928i | \(-0.865205\pi\) |
0.410928 | + | 0.911668i | \(0.365205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.3703i | − | 0.437628i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.7886i | 0.699195i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.7411 | + | 27.7411i | 0.978962 | + | 0.978962i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −65.0826 | − | 65.0826i | −2.29101 | − | 2.29101i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.37370i | 0.259246i | 0.991563 | + | 0.129623i | \(0.0413766\pi\) | ||||
−0.991563 | + | 0.129623i | \(0.958623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8396i | 0.907351i | 0.891167 | + | 0.453675i | \(0.149887\pi\) | ||||
−0.891167 | + | 0.453675i | \(0.850113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.3580 | + | 19.3580i | −0.678914 | + | 0.678914i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.9704 | − | 43.9704i | 1.53833 | − | 1.53833i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.3919 | + | 30.3863i | −0.712550 | + | 1.06178i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6580 | −0.686070 | −0.343035 | − | 0.939323i | \(-0.611455\pi\) | ||||
−0.343035 | + | 0.939323i | \(0.611455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.50942 | + | 2.50942i | −0.0874728 | + | 0.0874728i | −0.749489 | − | 0.662016i | \(-0.769701\pi\) |
0.662016 | + | 0.749489i | \(0.269701\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.3351 | + | 24.3351i | 0.846213 | + | 0.846213i | 0.989658 | − | 0.143445i | \(-0.0458181\pi\) |
−0.143445 | + | 0.989658i | \(0.545818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.2235 | 1.11917 | 0.559584 | − | 0.828773i | \(-0.310961\pi\) | ||||
0.559584 | + | 0.828773i | \(0.310961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 60.0546i | − | 2.08327i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2102 | − | 24.3721i | 0.353762 | − | 0.844444i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00598 | + | 1.00598i | 0.0347717 | + | 0.0347717i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.6243 | 0.642984 | 0.321492 | − | 0.946912i | \(-0.395816\pi\) | ||||
0.321492 | + | 0.946912i | \(0.395816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4827 | −0.809748 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.7646 | − | 25.7646i | −0.887379 | − | 0.887379i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.9199 | − | 2.34612i | 0.409571 | − | 0.0806136i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 29.9025i | − | 1.02625i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.5385 | 1.18397 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.641601 | − | 0.641601i | −0.0219680 | − | 0.0219680i | 0.696037 | − | 0.718005i | \(-0.254945\pi\) |
−0.718005 | + | 0.696037i | \(0.754945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0372 | + | 22.0372i | −0.752778 | + | 0.752778i | −0.974997 | − | 0.222219i | \(-0.928670\pi\) |
0.222219 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.584800 | 0.0199531 | 0.00997656 | − | 0.999950i | \(-0.496824\pi\) | ||||
0.00997656 | + | 0.999950i | \(0.496824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.19668 | − | 4.76342i | 0.108942 | − | 0.162337i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.85864 | − | 1.85864i | 0.0632688 | − | 0.0632688i | −0.674764 | − | 0.738033i | \(-0.735755\pi\) |
0.738033 | + | 0.674764i | \(0.235755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.75537 | − | 5.75537i | 0.195463 | − | 0.195463i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26.1887i | − | 0.888391i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 22.2658i | − | 0.754449i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.11530 | − | 8.11530i | −0.274661 | − | 0.274661i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.60420 | + | 2.60420i | 0.0879377 | + | 0.0879377i | 0.749707 | − | 0.661770i | \(-0.230194\pi\) |
−0.661770 | + | 0.749707i | \(0.730194\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.2206i | 1.52525i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.41484i | − | 0.317194i | −0.987343 | − | 0.158597i | \(-0.949303\pi\) | ||
0.987343 | − | 0.158597i | \(-0.0506971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5450 | + | 21.5450i | −0.725046 | + | 0.725046i | −0.969628 | − | 0.244583i | \(-0.921349\pi\) |
0.244583 | + | 0.969628i | \(0.421349\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6835 | + | 11.6835i | −0.392293 | + | 0.392293i | −0.875504 | − | 0.483211i | \(-0.839470\pi\) |
0.483211 | + | 0.875504i | \(0.339470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.39697 | − | 3.62184i | −0.181008 | − | 0.121473i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.2348 | 0.912400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.4224 | − | 12.4224i | 0.415699 | − | 0.415699i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.2680 | − | 25.2680i | −0.843673 | − | 0.843673i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.26170 | −0.0420802 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.2075i | 0.806470i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −89.1199 | + | 17.5410i | −2.96572 | + | 0.583727i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.07325 | + | 9.07325i | 0.301272 | + | 0.301272i | 0.841512 | − | 0.540239i | \(-0.181666\pi\) |
−0.540239 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 70.1464 | 2.32661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.95674 | −0.230487 | −0.115243 | − | 0.993337i | \(-0.536765\pi\) | ||||
−0.115243 | + | 0.993337i | \(0.536765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.3193 | + | 41.3193i | 1.36747 | + | 1.36747i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.38106 | − | 7.01673i | −0.0456067 | − | 0.231713i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.8965i | − | 0.491390i | −0.969347 | − | 0.245695i | \(-0.920984\pi\) | ||
0.969347 | − | 0.245695i | \(-0.0790161\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 90.0514 | 2.96729 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.7301 | + | 27.7301i | 0.912746 | + | 0.912746i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −54.8591 | + | 54.8591i | −1.80181 | + | 1.80181i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.87543 | −0.0943397 | −0.0471699 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471699 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.7280 | − | 14.2216i | 1.13816 | − | 0.466094i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.2096 | − | 33.2096i | 1.08723 | − | 1.08723i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.5847 | + | 25.5847i | −0.835816 | + | 0.835816i | −0.988305 | − | 0.152489i | \(-0.951271\pi\) |
0.152489 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 69.5377i | − | 2.26928i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.0907i | 1.20912i | 0.796558 | + | 0.604562i | \(0.206652\pi\) | ||||
−0.796558 | + | 0.604562i | \(0.793348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.60453 | + | 2.60453i | 0.0848151 | + | 0.0848151i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.321147 | + | 0.321147i | 0.0104359 | + | 0.0104359i | 0.712305 | − | 0.701870i | \(-0.247651\pi\) |
−0.701870 | + | 0.712305i | \(0.747651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 23.8582i | − | 0.774471i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 39.9194i | − | 1.29448i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.73528 | + | 4.73528i | −0.153391 | + | 0.153391i | −0.779630 | − | 0.626240i | \(-0.784593\pi\) |
0.626240 | + | 0.779630i | \(0.284593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59.8675 | + | 59.8675i | −1.93524 | + | 1.93524i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.1537 | + | 6.81406i | 0.327882 | + | 0.220038i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9697 | 0.999022 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.7791 | − | 51.7791i | 1.66856 | − | 1.66856i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.63821 | + | 6.63821i | 0.213470 | + | 0.213470i | 0.805740 | − | 0.592269i | \(-0.201768\pi\) |
−0.592269 | + | 0.805740i | \(0.701768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −59.8971 | −1.92417 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.9800i | − | 0.512823i | −0.966568 | − | 0.256412i | \(-0.917460\pi\) | ||
0.966568 | − | 0.256412i | \(-0.0825402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.7189 | − | 10.9669i | 1.78627 | − | 0.351581i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.8732 | + | 22.8732i | 0.731780 | + | 0.731780i | 0.970972 | − | 0.239193i | \(-0.0768827\pi\) |
−0.239193 | + | 0.970972i | \(0.576883\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5657 | −0.433561 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.2490 | −0.710354 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0432 | + | 12.0432i | 0.384119 | + | 0.384119i | 0.872584 | − | 0.488465i | \(-0.162443\pi\) |
−0.488465 | + | 0.872584i | \(0.662443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.1778 | + | 4.95562i | −0.801419 | + | 0.157739i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 58.3197i | − | 1.85446i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0158 | −0.699354 | −0.349677 | − | 0.936870i | \(-0.613709\pi\) | ||||
−0.349677 | + | 0.936870i | \(0.613709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.0347 | − | 27.0347i | −0.857920 | − | 0.857920i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1156 | − | 34.1156i | 1.08045 | − | 1.08045i | 0.0839845 | − | 0.996467i | \(-0.473235\pi\) |
0.996467 | − | 0.0839845i | \(-0.0267646\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 56.1139 | 1.77536 |
(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 | 1400.2.x.c.657.2 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.993.1 | yes | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.993.16 | yes | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.657.15 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.657.16 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.993.2 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.993.15 | yes | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.657.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.1 | ✓ | 32 | 35.34 | odd | 2 | inner | |
1400.2.x.c.657.2 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.657.15 | yes | 32 | 5.4 | even | 2 | inner | |
1400.2.x.c.657.16 | yes | 32 | 7.6 | odd | 2 | inner | |
1400.2.x.c.993.1 | yes | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.993.2 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.993.15 | yes | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.993.16 | yes | 32 | 5.3 | odd | 4 | inner |