Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.8 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.n.765.8 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.674626 | − | 1.24293i | 0.477032 | − | 0.878886i | ||||
\(3\) | 0.839505 | + | 3.13308i | 0.484689 | + | 1.80888i | 0.581459 | + | 0.813576i | \(0.302482\pi\) |
−0.0967700 | + | 0.995307i | \(0.530851\pi\) | |||||||
\(4\) | −1.08976 | − | 1.67703i | −0.544880 | − | 0.838514i | ||||
\(5\) | −0.734404 | + | 2.74083i | −0.328435 | + | 1.22574i | 0.582378 | + | 0.812918i | \(0.302122\pi\) |
−0.910813 | + | 0.412819i | \(0.864544\pi\) | |||||||
\(6\) | 4.46055 | + | 1.07021i | 1.82101 | + | 0.436910i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.81961 | + | 0.223131i | −0.996883 | + | 0.0788889i | ||||
\(9\) | −6.51332 | + | 3.76047i | −2.17111 | + | 1.25349i | ||||
\(10\) | 2.91122 | + | 2.76185i | 0.920609 | + | 0.873374i | ||||
\(11\) | 4.32748 | − | 1.15955i | 1.30479 | − | 0.349616i | 0.461528 | − | 0.887126i | \(-0.347301\pi\) |
0.843258 | + | 0.537509i | \(0.180635\pi\) | |||||||
\(12\) | 4.33940 | − | 4.82218i | 1.25268 | − | 1.39204i | ||||
\(13\) | −0.558438 | + | 0.558438i | −0.154883 | + | 0.154883i | −0.780295 | − | 0.625412i | \(-0.784931\pi\) |
0.625412 | + | 0.780295i | \(0.284931\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.20377 | −2.37640 | ||||||||
\(16\) | −1.62485 | + | 3.65512i | −0.406211 | + | 0.913779i | ||||
\(17\) | −1.09678 | + | 1.89967i | −0.266007 | + | 0.460738i | −0.967827 | − | 0.251616i | \(-0.919038\pi\) |
0.701820 | + | 0.712355i | \(0.252371\pi\) | |||||||
\(18\) | 0.279952 | + | 10.6325i | 0.0659852 | + | 2.50611i | ||||
\(19\) | −2.55326 | − | 0.684144i | −0.585758 | − | 0.156954i | −0.0462445 | − | 0.998930i | \(-0.514725\pi\) |
−0.539514 | + | 0.841977i | \(0.681392\pi\) | |||||||
\(20\) | 5.39678 | − | 1.75523i | 1.20676 | − | 0.392482i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.47820 | − | 6.16103i | 0.315152 | − | 1.31354i | ||||
\(23\) | 0.647926 | − | 0.374080i | 0.135102 | − | 0.0780011i | −0.430926 | − | 0.902387i | \(-0.641813\pi\) |
0.566028 | + | 0.824386i | \(0.308480\pi\) | |||||||
\(24\) | −3.06617 | − | 8.64674i | −0.625879 | − | 1.76501i | ||||
\(25\) | −2.64268 | − | 1.52575i | −0.528537 | − | 0.305151i | ||||
\(26\) | 0.317364 | + | 1.07084i | 0.0622402 | + | 0.210009i | ||||
\(27\) | −10.3691 | − | 10.3691i | −1.99553 | − | 1.99553i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.07468 | + | 3.07468i | −0.570953 | + | 0.570953i | −0.932395 | − | 0.361442i | \(-0.882285\pi\) |
0.361442 | + | 0.932395i | \(0.382285\pi\) | |||||||
\(30\) | −6.20910 | + | 11.4397i | −1.13362 | + | 2.08859i | ||||
\(31\) | −4.43398 | + | 7.67989i | −0.796367 | + | 1.37935i | 0.125601 | + | 0.992081i | \(0.459914\pi\) |
−0.921968 | + | 0.387267i | \(0.873419\pi\) | |||||||
\(32\) | 3.44690 | + | 4.48541i | 0.609331 | + | 0.792916i | ||||
\(33\) | 7.26589 | + | 12.5849i | 1.26483 | + | 2.19075i | ||||
\(34\) | 1.62125 | + | 2.64479i | 0.278042 | + | 0.453577i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.4044 | + | 6.82502i | 2.23406 | + | 1.13750i | ||||
\(37\) | 1.69807 | − | 6.33730i | 0.279162 | − | 1.04185i | −0.673839 | − | 0.738878i | \(-0.735356\pi\) |
0.953001 | − | 0.302967i | \(-0.0979773\pi\) | |||||||
\(38\) | −2.57284 | + | 2.71199i | −0.417370 | + | 0.439943i | ||||
\(39\) | −2.21844 | − | 1.28082i | −0.355235 | − | 0.205095i | ||||
\(40\) | 1.45917 | − | 7.89195i | 0.230715 | − | 1.24783i | ||||
\(41\) | − | 0.267969i | − | 0.0418497i | −0.999781 | − | 0.0209248i | \(-0.993339\pi\) | ||
0.999781 | − | 0.0209248i | \(-0.00666107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.53661 | + | 4.53661i | 0.691827 | + | 0.691827i | 0.962634 | − | 0.270807i | \(-0.0872904\pi\) |
−0.270807 | + | 0.962634i | \(0.587290\pi\) | |||||||
\(44\) | −6.66051 | − | 5.99369i | −1.00411 | − | 0.903582i | ||||
\(45\) | −5.52341 | − | 20.6136i | −0.823381 | − | 3.07290i | ||||
\(46\) | −0.0278487 | − | 1.05769i | −0.00410607 | − | 0.155948i | ||||
\(47\) | −3.74156 | − | 6.48057i | −0.545763 | − | 0.945289i | −0.998558 | − | 0.0536746i | \(-0.982907\pi\) |
0.452796 | − | 0.891614i | \(-0.350427\pi\) | |||||||
\(48\) | −12.8158 | − | 2.02228i | −1.84981 | − | 0.291890i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.67923 | + | 2.25536i | −0.520322 | + | 0.318956i | ||||
\(51\) | −6.87257 | − | 1.84150i | −0.962352 | − | 0.257861i | ||||
\(52\) | 1.54508 | + | 0.327953i | 0.214264 | + | 0.0454789i | ||||
\(53\) | 4.36564 | − | 1.16977i | 0.599667 | − | 0.160680i | 0.0537996 | − | 0.998552i | \(-0.482867\pi\) |
0.545868 | + | 0.837871i | \(0.316200\pi\) | |||||||
\(54\) | −19.8833 | + | 5.89282i | −2.70578 | + | 0.801912i | ||||
\(55\) | 12.7125i | 1.71415i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.57391i | − | 1.13564i | ||||||
\(58\) | 1.74736 | + | 5.89587i | 0.229439 | + | 0.774166i | ||||
\(59\) | 7.07539 | − | 1.89585i | 0.921137 | − | 0.246818i | 0.233066 | − | 0.972461i | \(-0.425124\pi\) |
0.688071 | + | 0.725643i | \(0.258458\pi\) | |||||||
\(60\) | 10.0299 | + | 15.4350i | 1.29486 | + | 1.99265i | ||||
\(61\) | −5.73728 | − | 1.53730i | −0.734583 | − | 0.196831i | −0.127914 | − | 0.991785i | \(-0.540828\pi\) |
−0.606669 | + | 0.794954i | \(0.707495\pi\) | |||||||
\(62\) | 6.55430 | + | 10.6922i | 0.832396 | + | 1.35791i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.90042 | − | 1.25829i | 0.987553 | − | 0.157286i | ||||
\(65\) | −1.12047 | − | 1.94070i | −0.138977 | − | 0.240715i | ||||
\(66\) | 20.5439 | − | 0.540916i | 2.52878 | − | 0.0665822i | ||||
\(67\) | 1.48228 | + | 5.53193i | 0.181089 | + | 0.675833i | 0.995434 | + | 0.0954519i | \(0.0304296\pi\) |
−0.814345 | + | 0.580381i | \(0.802904\pi\) | |||||||
\(68\) | 4.38103 | − | 0.230862i | 0.531277 | − | 0.0279962i | ||||
\(69\) | 1.71596 | + | 1.71596i | 0.206577 | + | 0.206577i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.37949i | 1.11314i | 0.830801 | + | 0.556570i | \(0.187883\pi\) | ||||
−0.830801 | + | 0.556570i | \(0.812117\pi\) | |||||||
\(72\) | 17.5260 | − | 12.0564i | 2.06546 | − | 1.42086i | ||||
\(73\) | 9.08221 | + | 5.24362i | 1.06299 | + | 0.613719i | 0.926258 | − | 0.376889i | \(-0.123006\pi\) |
0.136734 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(74\) | −6.73127 | − | 6.38590i | −0.782494 | − | 0.742345i | ||||
\(75\) | 2.56176 | − | 9.56061i | 0.295806 | − | 1.10396i | ||||
\(76\) | 1.63511 | + | 5.02744i | 0.187560 | + | 0.576687i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.08859 | + | 1.89330i | −0.349714 | + | 0.214374i | ||||
\(79\) | 5.10952 | + | 8.84995i | 0.574866 | + | 0.995697i | 0.996056 | + | 0.0887248i | \(0.0282792\pi\) |
−0.421190 | + | 0.906972i | \(0.638387\pi\) | |||||||
\(80\) | −8.82477 | − | 7.13776i | −0.986639 | − | 0.798026i | ||||
\(81\) | 12.5009 | − | 21.6521i | 1.38898 | − | 2.40579i | ||||
\(82\) | −0.333067 | − | 0.180778i | −0.0367811 | − | 0.0199636i | ||||
\(83\) | 0.474267 | − | 0.474267i | 0.0520576 | − | 0.0520576i | −0.680599 | − | 0.732656i | \(-0.738280\pi\) |
0.732656 | + | 0.680599i | \(0.238280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.40120 | − | 4.40120i | −0.477378 | − | 0.477378i | ||||
\(86\) | 8.69922 | − | 2.57819i | 0.938061 | − | 0.278013i | ||||
\(87\) | −12.2144 | − | 7.05199i | −1.30952 | − | 0.756053i | ||||
\(88\) | −11.9431 | + | 4.23507i | −1.27314 | + | 0.451460i | ||||
\(89\) | 12.5849 | − | 7.26589i | 1.33400 | − | 0.770183i | 0.348087 | − | 0.937462i | \(-0.386831\pi\) |
0.985910 | + | 0.167279i | \(0.0534981\pi\) | |||||||
\(90\) | −29.3476 | − | 7.04127i | −3.09351 | − | 0.742215i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.33343 | − | 0.678932i | −0.139019 | − | 0.0707835i | ||||
\(93\) | −27.7840 | − | 7.44471i | −2.88107 | − | 0.771980i | ||||
\(94\) | −10.5791 | + | 0.278544i | −1.09115 | + | 0.0287296i | ||||
\(95\) | 3.75025 | − | 6.49562i | 0.384768 | − | 0.666437i | ||||
\(96\) | −11.1594 | + | 14.5649i | −1.13896 | + | 1.48653i | ||||
\(97\) | 16.4976 | 1.67507 | 0.837537 | − | 0.546380i | \(-0.183995\pi\) | ||||
0.837537 | + | 0.546380i | \(0.183995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.8259 | + | 23.8259i | −2.39459 | + | 2.39459i | ||||
\(100\) | 0.321159 | + | 6.09456i | 0.0321159 | + | 0.609456i | ||||
\(101\) | 14.7659 | − | 3.95651i | 1.46926 | − | 0.393688i | 0.566585 | − | 0.824003i | \(-0.308264\pi\) |
0.902679 | + | 0.430316i | \(0.141598\pi\) | |||||||
\(102\) | −6.92527 | + | 7.29981i | −0.685704 | + | 0.722789i | ||||
\(103\) | −1.46459 | + | 0.845581i | −0.144310 | + | 0.0833176i | −0.570417 | − | 0.821355i | \(-0.693218\pi\) |
0.426106 | + | 0.904673i | \(0.359885\pi\) | |||||||
\(104\) | 1.44997 | − | 1.69918i | 0.142182 | − | 0.166619i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.49123 | − | 6.21536i | 0.144841 | − | 0.603689i | ||||
\(107\) | −0.692325 | + | 2.58379i | −0.0669296 | + | 0.249785i | −0.991282 | − | 0.131754i | \(-0.957939\pi\) |
0.924353 | + | 0.381539i | \(0.124606\pi\) | |||||||
\(108\) | −6.08944 | + | 28.6891i | −0.585956 | + | 2.76061i | ||||
\(109\) | −2.03730 | − | 7.60329i | −0.195138 | − | 0.728264i | −0.992231 | − | 0.124408i | \(-0.960297\pi\) |
0.797094 | − | 0.603856i | \(-0.206370\pi\) | |||||||
\(110\) | 15.8008 | + | 8.57617i | 1.50654 | + | 0.817705i | ||||
\(111\) | 21.2808 | 2.01988 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.18060 | 0.675494 | 0.337747 | − | 0.941237i | \(-0.390335\pi\) | ||||
0.337747 | + | 0.941237i | \(0.390335\pi\) | |||||||
\(114\) | −10.6568 | − | 5.78418i | −0.998099 | − | 0.541738i | ||||
\(115\) | 0.549451 | + | 2.05058i | 0.0512366 | + | 0.191218i | ||||
\(116\) | 8.50698 | + | 1.80566i | 0.789853 | + | 0.167651i | ||||
\(117\) | 1.53730 | − | 5.73728i | 0.142123 | − | 0.530412i | ||||
\(118\) | 2.41683 | − | 10.0732i | 0.222488 | − | 0.927315i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 25.9511 | − | 2.05365i | 2.36900 | − | 0.187472i | ||||
\(121\) | 7.85629 | − | 4.53583i | 0.714209 | − | 0.412349i | ||||
\(122\) | −5.78128 | + | 6.09395i | −0.523412 | + | 0.551720i | ||||
\(123\) | 0.839566 | − | 0.224961i | 0.0757011 | − | 0.0202841i | ||||
\(124\) | 17.7114 | − | 0.933318i | 1.59053 | − | 0.0838144i | ||||
\(125\) | −3.90951 | + | 3.90951i | −0.349677 | + | 0.349677i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2378 | 0.908462 | 0.454231 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454231 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(128\) | 3.76586 | − | 10.6686i | 0.332858 | − | 0.942977i | ||||
\(129\) | −10.4050 | + | 18.0221i | −0.916113 | + | 1.58675i | ||||
\(130\) | −3.16806 | + | 0.0834141i | −0.277857 | + | 0.00731590i | ||||
\(131\) | −3.87427 | − | 1.03811i | −0.338496 | − | 0.0906998i | 0.0855668 | − | 0.996332i | \(-0.472730\pi\) |
−0.424063 | + | 0.905633i | \(0.639397\pi\) | |||||||
\(132\) | 13.1871 | − | 25.8996i | 1.14779 | − | 2.25427i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.87579 | + | 1.88961i | 0.680365 | + | 0.163238i | ||||
\(135\) | 36.0351 | − | 20.8048i | 3.10140 | − | 1.79060i | ||||
\(136\) | 2.66861 | − | 5.60106i | 0.228831 | − | 0.480287i | ||||
\(137\) | 0.931953 | + | 0.538063i | 0.0796221 | + | 0.0459698i | 0.539282 | − | 0.842125i | \(-0.318696\pi\) |
−0.459660 | + | 0.888095i | \(0.652029\pi\) | |||||||
\(138\) | 3.29045 | − | 0.975190i | 0.280102 | − | 0.0830137i | ||||
\(139\) | 1.02686 | + | 1.02686i | 0.0870973 | + | 0.0870973i | 0.749313 | − | 0.662216i | \(-0.230384\pi\) |
−0.662216 | + | 0.749313i | \(0.730384\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.1631 | − | 17.1631i | 1.44539 | − | 1.44539i | ||||
\(142\) | 11.6581 | + | 6.32764i | 0.978323 | + | 0.531004i | ||||
\(143\) | −1.76910 | + | 3.06417i | −0.147939 | + | 0.256239i | ||||
\(144\) | −3.16181 | − | 29.9171i | −0.263484 | − | 2.49310i | ||||
\(145\) | −6.16912 | − | 10.6852i | −0.512317 | − | 0.887360i | ||||
\(146\) | 12.6446 | − | 7.75109i | 1.04647 | − | 0.641485i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.4783 | + | 4.05842i | −1.02571 | + | 0.333600i | ||||
\(149\) | 0.151905 | − | 0.566917i | 0.0124445 | − | 0.0464437i | −0.959424 | − | 0.281966i | \(-0.909013\pi\) |
0.971869 | + | 0.235522i | \(0.0756801\pi\) | |||||||
\(150\) | −10.1550 | − | 9.63392i | −0.829149 | − | 0.786606i | ||||
\(151\) | −9.36199 | − | 5.40515i | −0.761868 | − | 0.439865i | 0.0680980 | − | 0.997679i | \(-0.478307\pi\) |
−0.829966 | + | 0.557814i | \(0.811640\pi\) | |||||||
\(152\) | 7.35186 | + | 1.35931i | 0.596315 | + | 0.110255i | ||||
\(153\) | − | 16.4976i | − | 1.33375i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.7929 | − | 17.7929i | −1.42916 | − | 1.42916i | ||||
\(156\) | 0.269602 | + | 5.11617i | 0.0215854 | + | 0.409622i | ||||
\(157\) | 2.35072 | + | 8.77302i | 0.187608 | + | 0.700163i | 0.994057 | + | 0.108859i | \(0.0347199\pi\) |
−0.806449 | + | 0.591304i | \(0.798613\pi\) | |||||||
\(158\) | 14.4469 | − | 0.380383i | 1.14933 | − | 0.0302616i | ||||
\(159\) | 7.32996 | + | 12.6959i | 0.581304 | + | 1.00685i | ||||
\(160\) | −14.8252 | + | 6.15327i | −1.17203 | + | 0.486459i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.4787 | − | 30.1448i | −1.45182 | − | 2.36840i | ||||
\(163\) | 14.4844 | + | 3.88107i | 1.13450 | + | 0.303989i | 0.776739 | − | 0.629823i | \(-0.216872\pi\) |
0.357764 | + | 0.933812i | \(0.383539\pi\) | |||||||
\(164\) | −0.449391 | + | 0.292021i | −0.0350915 | + | 0.0228030i | ||||
\(165\) | −39.8292 | + | 10.6722i | −3.10070 | + | 0.830829i | ||||
\(166\) | −0.269529 | − | 0.909434i | −0.0209195 | − | 0.0705858i | ||||
\(167\) | 17.7426i | 1.37296i | 0.727147 | + | 0.686481i | \(0.240846\pi\) | ||||
−0.727147 | + | 0.686481i | \(0.759154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3763i | 0.952023i | ||||||||
\(170\) | −8.43956 | + | 2.50123i | −0.647285 | + | 0.191836i | ||||
\(171\) | 19.2029 | − | 5.14541i | 1.46848 | − | 0.393479i | ||||
\(172\) | 2.66421 | − | 12.5518i | 0.203144 | − | 0.957069i | ||||
\(173\) | −12.1355 | − | 3.25170i | −0.922646 | − | 0.247222i | −0.233930 | − | 0.972253i | \(-0.575159\pi\) |
−0.688716 | + | 0.725031i | \(0.741825\pi\) | |||||||
\(174\) | −17.0053 | + | 10.4242i | −1.28917 | + | 0.790258i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.79322 | + | 17.7015i | −0.210547 | + | 1.33430i | ||||
\(177\) | 11.8797 | + | 20.5762i | 0.892930 | + | 1.54660i | ||||
\(178\) | −0.540916 | − | 20.5439i | −0.0405434 | − | 1.53983i | ||||
\(179\) | 1.22964 | + | 4.58909i | 0.0919079 | + | 0.343005i | 0.996533 | − | 0.0832043i | \(-0.0265154\pi\) |
−0.904625 | + | 0.426209i | \(0.859849\pi\) | |||||||
\(180\) | −28.5504 | + | 31.7268i | −2.12802 | + | 2.36478i | ||||
\(181\) | −3.35107 | − | 3.35107i | −0.249083 | − | 0.249083i | 0.571511 | − | 0.820594i | \(-0.306357\pi\) |
−0.820594 | + | 0.571511i | \(0.806357\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 19.2659i | − | 1.42418i | ||||||
\(184\) | −1.74343 | + | 1.19933i | −0.128527 | + | 0.0884160i | ||||
\(185\) | 16.1224 | + | 9.30827i | 1.18534 | + | 0.684358i | ||||
\(186\) | −27.9971 | + | 29.5113i | −2.05285 | + | 2.16387i | ||||
\(187\) | −2.54352 | + | 9.49256i | −0.186001 | + | 0.694165i | ||||
\(188\) | −6.79070 | + | 13.3370i | −0.495263 | + | 0.972699i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.54360 | − | 9.04342i | −0.402175 | − | 0.656079i | ||||
\(191\) | −9.91610 | − | 17.1752i | −0.717504 | − | 1.24275i | −0.961986 | − | 0.273099i | \(-0.911951\pi\) |
0.244482 | − | 0.969654i | \(-0.421382\pi\) | |||||||
\(192\) | 10.5748 | + | 23.6963i | 0.763168 | + | 1.71013i | ||||
\(193\) | −1.81712 | + | 3.14734i | −0.130799 | + | 0.226551i | −0.923985 | − | 0.382429i | \(-0.875088\pi\) |
0.793186 | + | 0.608980i | \(0.208421\pi\) | |||||||
\(194\) | 11.1297 | − | 20.5054i | 0.799065 | − | 1.47220i | ||||
\(195\) | 5.13974 | − | 5.13974i | 0.368064 | − | 0.368064i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.84601 | − | 9.84601i | −0.701499 | − | 0.701499i | 0.263233 | − | 0.964732i | \(-0.415211\pi\) |
−0.964732 | + | 0.263233i | \(0.915211\pi\) | |||||||
\(198\) | 13.5404 | + | 45.6875i | 0.962274 | + | 3.24687i | ||||
\(199\) | −6.74009 | − | 3.89139i | −0.477792 | − | 0.275854i | 0.241704 | − | 0.970350i | \(-0.422294\pi\) |
−0.719496 | + | 0.694497i | \(0.755627\pi\) | |||||||
\(200\) | 7.79178 | + | 3.71237i | 0.550962 | + | 0.262504i | ||||
\(201\) | −16.0876 | + | 9.28817i | −1.13473 | + | 0.655137i | ||||
\(202\) | 5.04379 | − | 21.0222i | 0.354880 | − | 1.47912i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.40120 | + | 13.5323i | 0.308146 | + | 0.947449i | ||||
\(205\) | 0.734457 | + | 0.196797i | 0.0512967 | + | 0.0137449i | ||||
\(206\) | 0.0629501 | + | 2.39084i | 0.00438594 | + | 0.166578i | ||||
\(207\) | −2.81343 | + | 4.87301i | −0.195547 | + | 0.338698i | ||||
\(208\) | −1.13378 | − | 2.94853i | −0.0786136 | − | 0.204444i | ||||
\(209\) | −11.8425 | −0.819163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.04029 | − | 3.04029i | 0.209302 | − | 0.209302i | −0.594669 | − | 0.803971i | \(-0.702717\pi\) |
0.803971 | + | 0.594669i | \(0.202717\pi\) | |||||||
\(212\) | −6.71924 | − | 6.04654i | −0.461480 | − | 0.415278i | ||||
\(213\) | −29.3866 | + | 7.87413i | −2.01354 | + | 0.539526i | ||||
\(214\) | 2.74442 | + | 2.60361i | 0.187605 | + | 0.177979i | ||||
\(215\) | −15.7658 | + | 9.10239i | −1.07522 | + | 0.620778i | ||||
\(216\) | 31.5505 | + | 26.9232i | 2.14674 | + | 1.83189i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.8248 | − | 2.59716i | −0.733147 | − | 0.175902i | ||||
\(219\) | −8.80409 | + | 32.8573i | −0.594925 | + | 2.22029i | ||||
\(220\) | 21.3192 | − | 13.8536i | 1.43734 | − | 0.934006i | ||||
\(221\) | −0.448368 | − | 1.67333i | −0.0301605 | − | 0.112560i | ||||
\(222\) | 14.3566 | − | 26.4506i | 0.963550 | − | 1.77525i | ||||
\(223\) | −21.2874 | −1.42551 | −0.712756 | − | 0.701412i | \(-0.752553\pi\) | ||||
−0.712756 | + | 0.701412i | \(0.752553\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.9502 | 1.53001 | ||||||||
\(226\) | 4.84422 | − | 8.92500i | 0.322233 | − | 0.593682i | ||||
\(227\) | −5.69486 | − | 21.2535i | −0.377981 | − | 1.41064i | −0.848940 | − | 0.528490i | \(-0.822759\pi\) |
0.470959 | − | 0.882155i | \(-0.343908\pi\) | |||||||
\(228\) | −14.3787 | + | 9.34350i | −0.952252 | + | 0.618789i | ||||
\(229\) | 3.81953 | − | 14.2547i | 0.252402 | − | 0.941976i | −0.717116 | − | 0.696954i | \(-0.754538\pi\) |
0.969518 | − | 0.245022i | \(-0.0787952\pi\) | |||||||
\(230\) | 2.91941 | + | 0.700444i | 0.192500 | + | 0.0461859i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.98334 | − | 9.35545i | 0.524132 | − | 0.614215i | ||||
\(233\) | −19.6072 | + | 11.3202i | −1.28451 | + | 0.741611i | −0.977669 | − | 0.210150i | \(-0.932605\pi\) |
−0.306839 | + | 0.951761i | \(0.599271\pi\) | |||||||
\(234\) | −6.09395 | − | 5.78128i | −0.398374 | − | 0.377934i | ||||
\(235\) | 20.5100 | − | 5.49563i | 1.33792 | − | 0.358496i | ||||
\(236\) | −10.8899 | − | 9.79961i | −0.708870 | − | 0.637900i | ||||
\(237\) | −23.4381 | + | 23.4381i | −1.52247 | + | 1.52247i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5833 | −1.20205 | −0.601026 | − | 0.799230i | \(-0.705241\pi\) | ||||
−0.601026 | + | 0.799230i | \(0.705241\pi\) | |||||||
\(240\) | 14.9547 | − | 33.6409i | 0.965322 | − | 2.17151i | ||||
\(241\) | 6.25821 | − | 10.8395i | 0.403126 | − | 0.698235i | −0.590975 | − | 0.806690i | \(-0.701257\pi\) |
0.994101 | + | 0.108454i | \(0.0345901\pi\) | |||||||
\(242\) | −0.337674 | − | 12.8248i | −0.0217065 | − | 0.824411i | ||||
\(243\) | 35.8389 | + | 9.60301i | 2.29907 | + | 0.616033i | ||||
\(244\) | 3.67416 | + | 11.2969i | 0.235214 | + | 0.723208i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.286782 | − | 1.19529i | 0.0182845 | − | 0.0762088i | ||||
\(247\) | 1.80789 | − | 1.04379i | 0.115033 | − | 0.0664146i | ||||
\(248\) | 10.7885 | − | 22.6437i | 0.685070 | − | 1.43787i | ||||
\(249\) | 1.88406 | + | 1.08777i | 0.119398 | + | 0.0689343i | ||||
\(250\) | 2.22180 | + | 7.49671i | 0.140519 | + | 0.474134i | ||||
\(251\) | 8.79964 | + | 8.79964i | 0.555429 | + | 0.555429i | 0.928003 | − | 0.372574i | \(-0.121525\pi\) |
−0.372574 | + | 0.928003i | \(0.621525\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.37012 | − | 2.37012i | 0.149008 | − | 0.149008i | ||||
\(254\) | 6.90672 | − | 12.7250i | 0.433366 | − | 0.798434i | ||||
\(255\) | 10.0945 | − | 17.4841i | 0.632141 | − | 1.09490i | ||||
\(256\) | −10.7198 | − | 11.8780i | −0.669985 | − | 0.742375i | ||||
\(257\) | −11.3926 | − | 19.7326i | −0.710653 | − | 1.23089i | −0.964612 | − | 0.263672i | \(-0.915066\pi\) |
0.253959 | − | 0.967215i | \(-0.418267\pi\) | |||||||
\(258\) | 15.3807 | + | 25.0909i | 0.957560 | + | 1.56209i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.03358 | + | 3.99396i | −0.126117 | + | 0.247695i | ||||
\(261\) | 8.46414 | − | 31.5886i | 0.523917 | − | 1.95528i | ||||
\(262\) | −3.90398 | + | 4.11512i | −0.241189 | + | 0.254233i | ||||
\(263\) | −11.0752 | − | 6.39429i | −0.682929 | − | 0.394289i | 0.118029 | − | 0.993010i | \(-0.462342\pi\) |
−0.800958 | + | 0.598721i | \(0.795676\pi\) | |||||||
\(264\) | −23.2951 | − | 33.8633i | −1.43371 | − | 2.08414i | ||||
\(265\) | 12.8246i | 0.787808i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.3297 | + | 33.3297i | 2.03974 | + | 2.03974i | ||||
\(268\) | 7.66188 | − | 8.51429i | 0.468024 | − | 0.520093i | ||||
\(269\) | 4.12636 | + | 15.3998i | 0.251589 | + | 0.938943i | 0.969956 | + | 0.243279i | \(0.0782230\pi\) |
−0.718368 | + | 0.695664i | \(0.755110\pi\) | |||||||
\(270\) | −1.54884 | − | 58.8246i | −0.0942592 | − | 3.57995i | ||||
\(271\) | 15.5305 | + | 26.8997i | 0.943412 | + | 1.63404i | 0.758899 | + | 0.651208i | \(0.225737\pi\) |
0.184513 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(272\) | −5.16143 | − | 7.09552i | −0.312958 | − | 0.430229i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.29750 | − | 0.795363i | 0.0783846 | − | 0.0480496i | ||||
\(275\) | −13.2054 | − | 3.53836i | −0.796313 | − | 0.213371i | ||||
\(276\) | 1.00773 | − | 4.74769i | 0.0606581 | − | 0.285778i | ||||
\(277\) | 13.2974 | − | 3.56302i | 0.798961 | − | 0.214081i | 0.163833 | − | 0.986488i | \(-0.447614\pi\) |
0.635128 | + | 0.772407i | \(0.280947\pi\) | |||||||
\(278\) | 1.96907 | − | 0.583572i | 0.118097 | − | 0.0350003i | ||||
\(279\) | − | 66.6954i | − | 3.99295i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.9241i | − | 1.48685i | −0.668820 | − | 0.743424i | \(-0.733200\pi\) | ||
0.668820 | − | 0.743424i | \(-0.266800\pi\) | |||||||
\(282\) | −9.75388 | − | 32.9112i | −0.580835 | − | 1.95983i | ||||
\(283\) | −8.98079 | + | 2.40640i | −0.533853 | + | 0.143045i | −0.515667 | − | 0.856789i | \(-0.672456\pi\) |
−0.0181859 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(284\) | 15.7297 | − | 10.2214i | 0.933384 | − | 0.606528i | ||||
\(285\) | 23.4996 | + | 6.29671i | 1.39200 | + | 0.372985i | ||||
\(286\) | 2.61507 | + | 4.26603i | 0.154632 | + | 0.252256i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −39.3180 | − | 16.2530i | −2.31684 | − | 0.957715i | ||||
\(289\) | 6.09417 | + | 10.5554i | 0.358480 | + | 0.620906i | ||||
\(290\) | −17.4429 | + | 0.459266i | −1.02428 | + | 0.0269690i | ||||
\(291\) | 13.8498 | + | 51.6882i | 0.811890 | + | 3.03001i | ||||
\(292\) | −1.10374 | − | 20.9454i | −0.0645914 | − | 1.22574i | ||||
\(293\) | −22.3389 | − | 22.3389i | −1.30505 | − | 1.30505i | −0.924939 | − | 0.380115i | \(-0.875885\pi\) |
−0.380115 | − | 0.924939i | \(-0.624115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.7848i | 1.21014i | ||||||||
\(296\) | −3.37386 | + | 18.2476i | −0.196102 | + | 1.06062i | ||||
\(297\) | −56.8955 | − | 32.8487i | −3.30141 | − | 1.90607i | ||||
\(298\) | −0.602161 | − | 0.571265i | −0.0348822 | − | 0.0330925i | ||||
\(299\) | −0.152926 | + | 0.570727i | −0.00884393 | + | 0.0330060i | ||||
\(300\) | −18.8251 | + | 6.12263i | −1.08687 | + | 0.353490i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.0341 | + | 7.98987i | −0.750027 | + | 0.459765i | ||||
\(303\) | 24.7921 | + | 42.9412i | 1.42427 | + | 2.46691i | ||||
\(304\) | 6.64928 | − | 8.22084i | 0.381363 | − | 0.471498i | ||||
\(305\) | 8.42696 | − | 14.5959i | 0.482526 | − | 0.835760i | ||||
\(306\) | −20.5054 | − | 11.1297i | −1.17221 | − | 0.636242i | ||||
\(307\) | −11.3960 | + | 11.3960i | −0.650402 | + | 0.650402i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) |
0.302688 | + | 0.953090i | \(0.402116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.87880 | − | 3.87880i | −0.220657 | − | 0.220657i | ||||
\(310\) | −34.1190 | + | 10.1118i | −1.93783 | + | 0.574314i | ||||
\(311\) | 12.4797 | + | 7.20515i | 0.707658 | + | 0.408566i | 0.810193 | − | 0.586163i | \(-0.199362\pi\) |
−0.102535 | + | 0.994729i | \(0.532695\pi\) | |||||||
\(312\) | 6.54094 | + | 3.11641i | 0.370308 | + | 0.176432i | ||||
\(313\) | −9.04739 | + | 5.22352i | −0.511389 | + | 0.295251i | −0.733404 | − | 0.679793i | \(-0.762070\pi\) |
0.222015 | + | 0.975043i | \(0.428736\pi\) | |||||||
\(314\) | 12.4901 | + | 2.99672i | 0.704859 | + | 0.169114i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.27346 | − | 18.2131i | 0.521673 | − | 1.02457i | ||||
\(317\) | −3.09965 | − | 0.830548i | −0.174094 | − | 0.0466482i | 0.170719 | − | 0.985320i | \(-0.445391\pi\) |
−0.344813 | + | 0.938672i | \(0.612058\pi\) | |||||||
\(318\) | 20.7251 | − | 0.545686i | 1.16221 | − | 0.0306005i | ||||
\(319\) | −9.74039 | + | 16.8708i | −0.545357 | + | 0.944586i | ||||
\(320\) | −2.35334 | + | 22.5778i | −0.131556 | + | 1.26214i | ||||
\(321\) | −8.67643 | −0.484271 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.10001 | − | 4.10001i | 0.228130 | − | 0.228130i | ||||
\(324\) | −49.9341 | + | 2.63133i | −2.77412 | + | 0.146185i | ||||
\(325\) | 2.32781 | − | 0.623736i | 0.129124 | − | 0.0345986i | ||||
\(326\) | 14.5954 | − | 15.3848i | 0.808367 | − | 0.852086i | ||||
\(327\) | 22.1114 | − | 12.7660i | 1.22276 | − | 0.705962i | ||||
\(328\) | 0.0597922 | + | 0.755567i | 0.00330147 | + | 0.0417192i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −13.6050 | + | 56.7047i | −0.748929 | + | 3.12149i | ||||
\(331\) | 4.76739 | − | 17.7921i | 0.262039 | − | 0.977944i | −0.701998 | − | 0.712178i | \(-0.747709\pi\) |
0.964038 | − | 0.265765i | \(-0.0856247\pi\) | |||||||
\(332\) | −1.31220 | − | 0.278522i | −0.0720161 | − | 0.0152859i | ||||
\(333\) | 12.7711 | + | 47.6624i | 0.699853 | + | 2.61189i | ||||
\(334\) | 22.0528 | + | 11.9696i | 1.20668 | + | 0.654948i | ||||
\(335\) | −16.2507 | −0.887869 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3502 | 0.890653 | 0.445326 | − | 0.895368i | \(-0.353088\pi\) | ||||
0.445326 | + | 0.895368i | \(0.353088\pi\) | |||||||
\(338\) | 15.3829 | + | 8.34937i | 0.836719 | + | 0.454146i | ||||
\(339\) | 6.02816 | + | 22.4974i | 0.327404 | + | 1.22189i | ||||
\(340\) | −2.58469 | + | 12.1772i | −0.140174 | + | 0.660401i | ||||
\(341\) | −10.2828 | + | 38.3760i | −0.556846 | + | 2.07818i | ||||
\(342\) | 6.55940 | − | 27.3392i | 0.354692 | − | 1.47833i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.8037 | − | 11.7792i | −0.744248 | − | 0.635093i | ||||
\(345\) | −5.96336 | + | 3.44295i | −0.321056 | + | 0.185362i | ||||
\(346\) | −12.2286 | + | 12.8899i | −0.657412 | + | 0.692968i | ||||
\(347\) | −25.0090 | + | 6.70114i | −1.34255 | + | 0.359736i | −0.857381 | − | 0.514683i | \(-0.827910\pi\) |
−0.485172 | + | 0.874419i | \(0.661243\pi\) | |||||||
\(348\) | 1.48439 | + | 28.1689i | 0.0795715 | + | 1.51001i | ||||
\(349\) | 25.0101 | − | 25.0101i | 1.33876 | − | 1.33876i | 0.441494 | − | 0.897264i | \(-0.354448\pi\) |
0.897264 | − | 0.441494i | \(-0.145552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.5810 | 0.618148 | ||||||||
\(352\) | 20.1174 | + | 15.4137i | 1.07226 | + | 0.821553i | ||||
\(353\) | −3.57361 | + | 6.18968i | −0.190204 | + | 0.329443i | −0.945318 | − | 0.326151i | \(-0.894248\pi\) |
0.755114 | + | 0.655594i | \(0.227582\pi\) | |||||||
\(354\) | 33.5891 | − | 0.884392i | 1.78524 | − | 0.0470049i | ||||
\(355\) | −25.7076 | − | 6.88833i | −1.36442 | − | 0.365595i | ||||
\(356\) | −25.8996 | − | 13.1871i | −1.37268 | − | 0.698917i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.53348 | + | 1.56756i | 0.345305 | + | 0.0828480i | ||||
\(359\) | 18.5075 | − | 10.6853i | 0.976790 | − | 0.563950i | 0.0754905 | − | 0.997147i | \(-0.475948\pi\) |
0.901299 | + | 0.433197i | \(0.142614\pi\) | |||||||
\(360\) | 20.1734 | + | 56.8900i | 1.06323 | + | 2.99837i | ||||
\(361\) | −10.4034 | − | 6.00640i | −0.547547 | − | 0.316126i | ||||
\(362\) | −6.42587 | + | 1.90444i | −0.337736 | + | 0.100095i | ||||
\(363\) | 20.8065 | + | 20.8065i | 1.09206 | + | 1.09206i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0419 | + | 21.0419i | −1.10138 | + | 1.10138i | ||||
\(366\) | −23.9462 | − | 12.9973i | −1.25169 | − | 0.679379i | ||||
\(367\) | 5.90009 | − | 10.2193i | 0.307982 | − | 0.533441i | −0.669939 | − | 0.742416i | \(-0.733680\pi\) |
0.977921 | + | 0.208976i | \(0.0670129\pi\) | |||||||
\(368\) | 0.314527 | + | 2.97607i | 0.0163958 | + | 0.155138i | ||||
\(369\) | 1.00769 | + | 1.74537i | 0.0524581 | + | 0.0908601i | ||||
\(370\) | 22.4461 | − | 13.7594i | 1.16692 | − | 0.715319i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 17.7929 | + | 54.7075i | 0.922521 | + | 2.83645i | ||||
\(373\) | 5.33914 | − | 19.9259i | 0.276450 | − | 1.03173i | −0.678413 | − | 0.734680i | \(-0.737332\pi\) |
0.954863 | − | 0.297045i | \(-0.0960012\pi\) | |||||||
\(374\) | 10.0827 | + | 9.56535i | 0.521363 | + | 0.494613i | ||||
\(375\) | −15.5309 | − | 8.96674i | −0.802010 | − | 0.463041i | ||||
\(376\) | 11.9958 | + | 17.4378i | 0.618635 | + | 0.899288i | ||||
\(377\) | − | 3.43403i | − | 0.176862i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1075 | + | 12.1075i | 0.621921 | + | 0.621921i | 0.946022 | − | 0.324102i | \(-0.105062\pi\) |
−0.324102 | + | 0.946022i | \(0.605062\pi\) | |||||||
\(380\) | −14.9802 | + | 0.789397i | −0.768469 | + | 0.0404952i | ||||
\(381\) | 8.59473 | + | 32.0760i | 0.440321 | + | 1.64330i | ||||
\(382\) | −28.0372 | + | 0.738213i | −1.43451 | + | 0.0377703i | ||||
\(383\) | −6.35291 | − | 11.0036i | −0.324619 | − | 0.562256i | 0.656816 | − | 0.754051i | \(-0.271903\pi\) |
−0.981435 | + | 0.191794i | \(0.938569\pi\) | |||||||
\(384\) | 36.5869 | + | 2.84242i | 1.86707 | + | 0.145052i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.68606 | + | 4.38183i | 0.136717 | + | 0.223029i | ||||
\(387\) | −46.6082 | − | 12.4886i | −2.36923 | − | 0.634833i | ||||
\(388\) | −17.9784 | − | 27.6669i | −0.912715 | − | 1.40457i | ||||
\(389\) | 18.2083 | − | 4.87891i | 0.923199 | − | 0.247371i | 0.234247 | − | 0.972177i | \(-0.424738\pi\) |
0.688952 | + | 0.724807i | \(0.258071\pi\) | |||||||
\(390\) | −2.92095 | − | 9.85574i | −0.147908 | − | 0.499065i | ||||
\(391\) | 1.64113i | 0.0829954i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 13.0099i | − | 0.656261i | ||||||
\(394\) | −18.8803 | + | 5.59555i | −0.951175 | + | 0.281900i | ||||
\(395\) | −28.0087 | + | 7.50490i | −1.40927 | + | 0.377613i | ||||
\(396\) | 65.9211 | + | 13.9922i | 3.31266 | + | 0.703133i | ||||
\(397\) | 1.94725 | + | 0.521765i | 0.0977299 | + | 0.0261866i | 0.307353 | − | 0.951596i | \(-0.400557\pi\) |
−0.209623 | + | 0.977782i | \(0.567224\pi\) | |||||||
\(398\) | −9.38378 | + | 5.75224i | −0.470366 | + | 0.288334i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.87076 | − | 7.18020i | 0.493538 | − | 0.359010i | ||||
\(401\) | 6.75679 | + | 11.7031i | 0.337418 | + | 0.584425i | 0.983946 | − | 0.178465i | \(-0.0571131\pi\) |
−0.646528 | + | 0.762890i | \(0.723780\pi\) | |||||||
\(402\) | 0.691466 | + | 26.2618i | 0.0344872 | + | 1.30982i | ||||
\(403\) | −1.81264 | − | 6.76485i | −0.0902938 | − | 0.336981i | ||||
\(404\) | −22.7265 | − | 20.4512i | −1.13069 | − | 1.01749i | ||||
\(405\) | 50.1641 | + | 50.1641i | 2.49268 | + | 2.49268i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 29.3936i | − | 1.45698i | ||||||
\(408\) | 19.7889 | + | 3.65883i | 0.979695 | + | 0.181139i | ||||
\(409\) | 26.1114 | + | 15.0754i | 1.29113 | + | 0.745432i | 0.978854 | − | 0.204560i | \(-0.0655765\pi\) |
0.312273 | + | 0.949993i | \(0.398910\pi\) | |||||||
\(410\) | 0.740089 | − | 0.780115i | 0.0365504 | − | 0.0385272i | ||||
\(411\) | −0.903414 | + | 3.37159i | −0.0445621 | + | 0.166308i | ||||
\(412\) | 3.01412 | + | 1.53468i | 0.148495 | + | 0.0756081i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.15880 | + | 6.78436i | 0.204394 | + | 0.333433i | ||||
\(415\) | 0.951583 | + | 1.64819i | 0.0467114 | + | 0.0809064i | ||||
\(416\) | −4.42970 | − | 0.579944i | −0.217184 | − | 0.0284341i | ||||
\(417\) | −2.35518 | + | 4.07929i | −0.115334 | + | 0.199764i | ||||
\(418\) | −7.98925 | + | 14.7194i | −0.390767 | + | 0.719950i | ||||
\(419\) | 20.8065 | − | 20.8065i | 1.01646 | − | 1.01646i | 0.0166027 | − | 0.999862i | \(-0.494715\pi\) |
0.999862 | − | 0.0166027i | \(-0.00528504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.7151 | + | 27.7151i | 1.35075 | + | 1.35075i | 0.884823 | + | 0.465928i | \(0.154279\pi\) |
0.465928 | + | 0.884823i | \(0.345721\pi\) | |||||||
\(422\) | −1.72782 | − | 5.82994i | −0.0841088 | − | 0.283797i | ||||
\(423\) | 48.7400 | + | 28.1401i | 2.36982 | + | 1.36822i | ||||
\(424\) | −12.0484 | + | 4.27241i | −0.585123 | + | 0.207487i | ||||
\(425\) | 5.79686 | − | 3.34682i | 0.281189 | − | 0.162345i | ||||
\(426\) | −10.0380 | + | 41.8377i | −0.486342 | + | 2.02704i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.08756 | − | 1.65467i | 0.245917 | − | 0.0799813i | ||||
\(429\) | −11.0854 | − | 2.97033i | −0.535210 | − | 0.143409i | ||||
\(430\) | 0.677636 | + | 25.7365i | 0.0326785 | + | 1.24113i | ||||
\(431\) | 1.17780 | − | 2.04001i | 0.0567328 | − | 0.0982641i | −0.836264 | − | 0.548327i | \(-0.815265\pi\) |
0.892997 | + | 0.450063i | \(0.148598\pi\) | |||||||
\(432\) | 54.7484 | − | 21.0521i | 2.63409 | − | 1.01287i | ||||
\(433\) | −8.53525 | −0.410178 | −0.205089 | − | 0.978743i | \(-0.565748\pi\) | ||||
−0.205089 | + | 0.978743i | \(0.565748\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.2986 | − | 28.2986i | 1.35681 | − | 1.35681i | ||||
\(436\) | −10.5308 | + | 11.7024i | −0.504333 | + | 0.560442i | ||||
\(437\) | −1.91025 | + | 0.511850i | −0.0913796 | + | 0.0244851i | ||||
\(438\) | 34.8999 | + | 33.1093i | 1.66758 | + | 1.58202i | ||||
\(439\) | −0.346478 | + | 0.200039i | −0.0165365 | + | 0.00954735i | −0.508245 | − | 0.861212i | \(-0.669706\pi\) |
0.491709 | + | 0.870760i | \(0.336372\pi\) | |||||||
\(440\) | −2.83655 | − | 35.8443i | −0.135227 | − | 1.70881i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.38232 | − | 0.571582i | −0.113315 | − | 0.0271874i | ||||
\(443\) | 4.16746 | − | 15.5532i | 0.198002 | − | 0.738953i | −0.793468 | − | 0.608613i | \(-0.791726\pi\) |
0.991469 | − | 0.130340i | \(-0.0416070\pi\) | |||||||
\(444\) | −23.1909 | − | 35.6885i | −1.10059 | − | 1.69370i | ||||
\(445\) | 10.6722 | + | 39.8292i | 0.505911 | + | 1.88808i | ||||
\(446\) | −14.3611 | + | 26.4588i | −0.680016 | + | 1.25286i | ||||
\(447\) | 1.90372 | 0.0900429 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.33298 | 0.204486 | 0.102243 | − | 0.994759i | \(-0.467398\pi\) | ||||
0.102243 | + | 0.994759i | \(0.467398\pi\) | |||||||
\(450\) | 15.4828 | − | 28.5255i | 0.729866 | − | 1.34471i | ||||
\(451\) | −0.310722 | − | 1.15963i | −0.0146313 | − | 0.0546048i | ||||
\(452\) | −7.82514 | − | 12.0421i | −0.368063 | − | 0.566411i | ||||
\(453\) | 9.07530 | − | 33.8695i | 0.426395 | − | 1.59133i | ||||
\(454\) | −30.2586 | − | 7.25984i | −1.42010 | − | 0.340721i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.91311 | + | 24.1751i | 0.0895895 | + | 1.13210i | ||||
\(457\) | 9.00399 | − | 5.19846i | 0.421189 | − | 0.243174i | −0.274397 | − | 0.961617i | \(-0.588478\pi\) |
0.695586 | + | 0.718443i | \(0.255145\pi\) | |||||||
\(458\) | −15.1408 | − | 14.3640i | −0.707485 | − | 0.671185i | ||||
\(459\) | 31.0705 | − | 8.32530i | 1.45024 | − | 0.388592i | ||||
\(460\) | 2.84011 | − | 3.15609i | 0.132421 | − | 0.147153i | ||||
\(461\) | 14.6872 | − | 14.6872i | 0.684052 | − | 0.684052i | −0.276859 | − | 0.960911i | \(-0.589293\pi\) |
0.960911 | + | 0.276859i | \(0.0892935\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0456 | 0.792176 | 0.396088 | − | 0.918213i | \(-0.370368\pi\) | ||||
0.396088 | + | 0.918213i | \(0.370368\pi\) | |||||||
\(464\) | −6.24243 | − | 16.2342i | −0.289797 | − | 0.753653i | ||||
\(465\) | 40.8094 | − | 70.6839i | 1.89249 | − | 3.27789i | ||||
\(466\) | 0.842743 | + | 32.0073i | 0.0390393 | + | 1.48271i | ||||
\(467\) | −14.4921 | − | 3.88314i | −0.670614 | − | 0.179690i | −0.0925825 | − | 0.995705i | \(-0.529512\pi\) |
−0.578031 | + | 0.816015i | \(0.696179\pi\) | |||||||
\(468\) | −11.2969 | + | 3.67416i | −0.522198 | + | 0.169838i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.00586 | − | 29.2000i | 0.323156 | − | 1.34690i | ||||
\(471\) | −25.5131 | + | 14.7300i | −1.17558 | + | 0.678722i | ||||
\(472\) | −19.5268 | + | 6.92429i | −0.898795 | + | 0.318716i | ||||
\(473\) | 24.8925 | + | 14.3717i | 1.14456 | + | 0.660812i | ||||
\(474\) | 13.3200 | + | 44.9439i | 0.611809 | + | 2.06434i | ||||
\(475\) | 5.70363 | + | 5.70363i | 0.261700 | + | 0.261700i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.0360 | + | 24.0360i | −1.10053 | + | 1.10053i | ||||
\(478\) | −12.5367 | + | 23.0977i | −0.573417 | + | 1.05647i | ||||
\(479\) | −13.1436 | + | 22.7654i | −0.600547 | + | 1.04018i | 0.392191 | + | 0.919884i | \(0.371717\pi\) |
−0.992738 | + | 0.120294i | \(0.961616\pi\) | |||||||
\(480\) | −31.7245 | − | 41.2827i | −1.44802 | − | 1.88429i | ||||
\(481\) | 2.59072 | + | 4.48726i | 0.118127 | + | 0.204601i | ||||
\(482\) | −9.25085 | − | 15.0911i | −0.421365 | − | 0.687383i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.1682 | − | 8.23225i | −0.734918 | − | 0.374193i | ||||
\(485\) | −12.1159 | + | 45.2171i | −0.550154 | + | 2.05320i | ||||
\(486\) | 36.1138 | − | 38.0669i | 1.63815 | − | 1.72675i | ||||
\(487\) | 17.8122 | + | 10.2839i | 0.807146 | + | 0.466006i | 0.845964 | − | 0.533240i | \(-0.179026\pi\) |
−0.0388179 | + | 0.999246i | \(0.512359\pi\) | |||||||
\(488\) | 16.5199 | + | 3.05442i | 0.747822 | + | 0.138267i | ||||
\(489\) | 48.6388i | 2.19952i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2818 | − | 11.2818i | −0.509139 | − | 0.509139i | 0.405123 | − | 0.914262i | \(-0.367229\pi\) |
−0.914262 | + | 0.405123i | \(0.867229\pi\) | |||||||
\(492\) | −1.29219 | − | 1.16282i | −0.0582565 | − | 0.0524241i | ||||
\(493\) | −2.46864 | − | 9.21311i | −0.111182 | − | 0.414937i | ||||
\(494\) | −0.0777057 | − | 2.95125i | −0.00349614 | − | 0.132783i | ||||
\(495\) | −47.8049 | − | 82.8005i | −2.14867 | − | 3.72161i | ||||
\(496\) | −20.8663 | − | 28.6854i | −0.936926 | − | 1.28801i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.62306 | − | 1.60793i | 0.117542 | − | 0.0720531i | ||||
\(499\) | −12.9636 | − | 3.47358i | −0.580329 | − | 0.155499i | −0.0432996 | − | 0.999062i | \(-0.513787\pi\) |
−0.537030 | + | 0.843563i | \(0.680454\pi\) | |||||||
\(500\) | 10.8168 | + | 2.29593i | 0.483741 | + | 0.102677i | ||||
\(501\) | −55.5889 | + | 14.8950i | −2.48353 | + | 0.665459i | ||||
\(502\) | 16.8738 | − | 5.00089i | 0.753116 | − | 0.223201i | ||||
\(503\) | 24.1272i | 1.07578i | 0.843015 | + | 0.537890i | \(0.180778\pi\) | ||||
−0.843015 | + | 0.537890i | \(0.819222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.3766i | 1.93023i | ||||||||
\(506\) | −1.34696 | − | 4.54485i | −0.0598795 | − | 0.202043i | ||||
\(507\) | −38.7759 | + | 10.3900i | −1.72210 | + | 0.461435i | ||||
\(508\) | −11.1568 | − | 17.1692i | −0.495003 | − | 0.761758i | ||||
\(509\) | 33.1419 | + | 8.88035i | 1.46899 | + | 0.393615i | 0.902585 | − | 0.430512i | \(-0.141667\pi\) |
0.566405 | + | 0.824127i | \(0.308334\pi\) | |||||||
\(510\) | −14.9216 | − | 24.3420i | −0.660740 | − | 1.07788i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.9954 | + | 5.31072i | −0.972067 | + | 0.234703i | ||||
\(513\) | 19.3811 | + | 33.5690i | 0.855695 | + | 1.48211i | ||||
\(514\) | −32.2121 | + | 0.848135i | −1.42081 | + | 0.0374096i | ||||
\(515\) | −1.24200 | − | 4.63519i | −0.0547289 | − | 0.204251i | ||||
\(516\) | 41.5625 | − | 2.19018i | 1.82969 | − | 0.0964172i | ||||
\(517\) | −23.7061 | − | 23.7061i | −1.04259 | − | 1.04259i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 40.7513i | − | 1.78878i | ||||||
\(520\) | 3.59231 | + | 5.22202i | 0.157533 | + | 0.229001i | ||||
\(521\) | −20.4408 | − | 11.8015i | −0.895527 | − | 0.517033i | −0.0197804 | − | 0.999804i | \(-0.506297\pi\) |
−0.875746 | + | 0.482772i | \(0.839630\pi\) | |||||||
\(522\) | −33.5523 | − | 31.8308i | −1.46855 | − | 1.39320i | ||||
\(523\) | 2.60866 | − | 9.73565i | 0.114069 | − | 0.425710i | −0.885147 | − | 0.465312i | \(-0.845942\pi\) |
0.999216 | + | 0.0396015i | \(0.0126089\pi\) | |||||||
\(524\) | 2.48109 | + | 7.62854i | 0.108387 | + | 0.333254i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.4193 | + | 9.45202i | −0.672314 | + | 0.412128i | ||||
\(527\) | −9.72617 | − | 16.8462i | −0.423679 | − | 0.733833i | ||||
\(528\) | −57.8052 | + | 6.10917i | −2.51565 | + | 0.265868i | ||||
\(529\) | −11.2201 | + | 19.4338i | −0.487832 | + | 0.844949i | ||||
\(530\) | 15.9401 | + | 8.65179i | 0.692393 | + | 0.375810i | ||||
\(531\) | −38.9550 | + | 38.9550i | −1.69051 | + | 1.69051i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.149644 | + | 0.149644i | 0.00648180 | + | 0.00648180i | ||||
\(534\) | 63.9116 | − | 18.9415i | 2.76573 | − | 0.819678i | ||||
\(535\) | −6.57330 | − | 3.79509i | −0.284188 | − | 0.164076i | ||||
\(536\) | −5.41379 | − | 15.2672i | −0.233840 | − | 0.659441i | ||||
\(537\) | −13.3457 | + | 7.70514i | −0.575909 | + | 0.332501i | ||||
\(538\) | 21.9247 | + | 5.26031i | 0.945239 | + | 0.226788i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −74.1599 | − | 37.7595i | −3.19133 | − | 1.62491i | ||||
\(541\) | 25.3552 | + | 6.79390i | 1.09010 | + | 0.292092i | 0.758729 | − | 0.651407i | \(-0.225821\pi\) |
0.331375 | + | 0.943499i | \(0.392487\pi\) | |||||||
\(542\) | 43.9117 | − | 1.15618i | 1.88617 | − | 0.0496624i | ||||
\(543\) | 7.68592 | − | 13.3124i | 0.329835 | − | 0.571290i | ||||
\(544\) | −12.3013 | + | 1.62849i | −0.527413 | + | 0.0698208i | ||||
\(545\) | 22.3356 | 0.956750 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.2973 | + | 30.2973i | −1.29542 | + | 1.29542i | −0.364032 | + | 0.931387i | \(0.618600\pi\) |
−0.931387 | + | 0.364032i | \(0.881400\pi\) | |||||||
\(548\) | −0.113258 | − | 2.14927i | −0.00483814 | − | 0.0918123i | ||||
\(549\) | 43.1497 | − | 11.5619i | 1.84159 | − | 0.493451i | ||||
\(550\) | −13.3066 | + | 14.0263i | −0.567396 | + | 0.598083i | ||||
\(551\) | 9.95398 | − | 5.74693i | 0.424054 | − | 0.244827i | ||||
\(552\) | −5.22122 | − | 4.45545i | −0.222230 | − | 0.189637i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.54215 | − | 18.9314i | 0.192978 | − | 0.804319i | ||||
\(555\) | −15.6287 | + | 58.3270i | −0.663401 | + | 2.47585i | ||||
\(556\) | 0.603043 | − | 2.84111i | 0.0255747 | − | 0.120490i | ||||
\(557\) | −9.41584 | − | 35.1404i | −0.398962 | − | 1.48895i | −0.814926 | − | 0.579565i | \(-0.803223\pi\) |
0.415965 | − | 0.909381i | \(-0.363444\pi\) | |||||||
\(558\) | −82.8979 | − | 44.9945i | −3.50935 | − | 1.90477i | ||||
\(559\) | −5.06684 | −0.214304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.8762 | −1.34582 | ||||||||
\(562\) | −30.9790 | − | 16.8145i | −1.30677 | − | 0.709275i | ||||
\(563\) | −7.25375 | − | 27.0714i | −0.305709 | − | 1.14092i | −0.932333 | − | 0.361600i | \(-0.882231\pi\) |
0.626624 | − | 0.779322i | \(-0.284436\pi\) | |||||||
\(564\) | −47.4866 | − | 10.0793i | −1.99955 | − | 0.424416i | ||||
\(565\) | −5.27346 | + | 19.6808i | −0.221856 | + | 0.827979i | ||||
\(566\) | −3.06769 | + | 12.7859i | −0.128945 | + | 0.537433i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.09286 | − | 26.4465i | −0.0878144 | − | 1.10967i | ||||
\(569\) | −4.17102 | + | 2.40814i | −0.174858 | + | 0.100954i | −0.584875 | − | 0.811124i | \(-0.698856\pi\) |
0.410016 | + | 0.912078i | \(0.365523\pi\) | |||||||
\(570\) | 23.6798 | − | 24.9605i | 0.991840 | − | 1.04548i | ||||
\(571\) | 18.1409 | − | 4.86083i | 0.759172 | − | 0.203419i | 0.141589 | − | 0.989926i | \(-0.454779\pi\) |
0.617582 | + | 0.786506i | \(0.288112\pi\) | |||||||
\(572\) | 7.06659 | − | 0.372381i | 0.295469 | − | 0.0155700i | ||||
\(573\) | 45.4866 | − | 45.4866i | 1.90023 | − | 1.90023i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.28302 | −0.0952083 | ||||||||
\(576\) | −46.7263 | + | 37.9049i | −1.94693 | + | 1.57937i | ||||
\(577\) | 6.23120 | − | 10.7928i | 0.259408 | − | 0.449309i | −0.706675 | − | 0.707538i | \(-0.749806\pi\) |
0.966084 | + | 0.258230i | \(0.0831391\pi\) | |||||||
\(578\) | 17.2309 | − | 0.453686i | 0.716712 | − | 0.0188708i | ||||
\(579\) | −11.3863 | − | 3.05096i | −0.473200 | − | 0.126794i | ||||
\(580\) | −11.1966 | + | 21.9901i | −0.464912 | + | 0.913090i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 73.5883 | + | 17.6558i | 3.05033 | + | 0.731857i | ||||
\(583\) | 17.5359 | − | 10.1243i | 0.726261 | − | 0.419307i | ||||
\(584\) | −26.7783 | − | 12.7584i | −1.10809 | − | 0.527948i | ||||
\(585\) | 14.5959 | + | 8.42696i | 0.603467 | + | 0.348412i | ||||
\(586\) | −42.8362 | + | 12.6954i | −1.76955 | + | 0.524440i | ||||
\(587\) | 16.7157 | + | 16.7157i | 0.689932 | + | 0.689932i | 0.962217 | − | 0.272285i | \(-0.0877793\pi\) |
−0.272285 | + | 0.962217i | \(0.587779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5753 | − | 16.5753i | 0.682972 | − | 0.682972i | ||||
\(590\) | 25.8341 | + | 14.0219i | 1.06357 | + | 0.577274i | ||||
\(591\) | 22.5825 | − | 39.1141i | 0.928921 | − | 1.60894i | ||||
\(592\) | 20.4045 | + | 16.5038i | 0.838618 | + | 0.678302i | ||||
\(593\) | 1.44134 | + | 2.49647i | 0.0591886 | + | 0.102518i | 0.894101 | − | 0.447865i | \(-0.147815\pi\) |
−0.834913 | + | 0.550382i | \(0.814482\pi\) | |||||||
\(594\) | −79.2119 | + | 48.5567i | −3.25010 | + | 1.99231i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.11628 | + | 0.363055i | −0.0457245 | + | 0.0148713i | ||||
\(597\) | 6.53369 | − | 24.3841i | 0.267406 | − | 0.997974i | ||||
\(598\) | 0.606207 | + | 0.575104i | 0.0247897 | + | 0.0235177i | ||||
\(599\) | 4.25846 | + | 2.45862i | 0.173996 | + | 0.100457i | 0.584469 | − | 0.811416i | \(-0.301303\pi\) |
−0.410473 | + | 0.911873i | \(0.634636\pi\) | |||||||
\(600\) | −5.08989 | + | 27.5288i | −0.207794 | + | 1.12386i | ||||
\(601\) | − | 18.3142i | − | 0.747051i | −0.927620 | − | 0.373526i | \(-0.878149\pi\) | ||
0.927620 | − | 0.373526i | \(-0.121851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.4572 | − | 30.4572i | −1.24031 | − | 1.24031i | ||||
\(604\) | 1.13774 | + | 21.5906i | 0.0462940 | + | 0.878510i | ||||
\(605\) | 6.66227 | + | 24.8639i | 0.270860 | + | 1.01086i | ||||
\(606\) | 70.0984 | − | 1.84567i | 2.84755 | − | 0.0749753i | ||||
\(607\) | 5.07953 | + | 8.79800i | 0.206172 | + | 0.357100i | 0.950505 | − | 0.310708i | \(-0.100566\pi\) |
−0.744334 | + | 0.667808i | \(0.767233\pi\) | |||||||
\(608\) | −5.73217 | − | 13.8106i | −0.232470 | − | 0.560094i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.4567 | − | 20.3209i | −0.504357 | − | 0.822770i | ||||
\(611\) | 5.70843 | + | 1.52957i | 0.230938 | + | 0.0618798i | ||||
\(612\) | −27.6669 | + | 17.9784i | −1.11837 | + | 0.726734i | ||||
\(613\) | −17.9784 | + | 4.81729i | −0.726140 | + | 0.194569i | −0.602910 | − | 0.797810i | \(-0.705992\pi\) |
−0.123230 | + | 0.992378i | \(0.539325\pi\) | |||||||
\(614\) | 6.47640 | + | 21.8524i | 0.261366 | + | 0.881892i | ||||
\(615\) | 2.46632i | 0.0994517i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2380i | 0.573202i | 0.958050 | + | 0.286601i | \(0.0925253\pi\) | ||||
−0.958050 | + | 0.286601i | \(0.907475\pi\) | |||||||
\(618\) | −7.43783 | + | 2.20435i | −0.299193 | + | 0.0886719i | ||||
\(619\) | −32.0464 | + | 8.58680i | −1.28805 | + | 0.345133i | −0.836920 | − | 0.547325i | \(-0.815646\pi\) |
−0.451132 | + | 0.892457i | \(0.648980\pi\) | |||||||
\(620\) | −10.4492 | + | 49.2293i | −0.419651 | + | 1.97710i | ||||
\(621\) | −10.5973 | − | 2.83953i | −0.425254 | − | 0.113946i | ||||
\(622\) | 17.3746 | − | 10.6506i | 0.696659 | − | 0.427051i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.28616 | − | 6.02753i | 0.331712 | − | 0.241294i | ||||
\(625\) | −15.4729 | − | 26.7999i | −0.618917 | − | 1.07200i | ||||
\(626\) | 0.388869 | + | 14.7692i | 0.0155423 | + | 0.590297i | ||||
\(627\) | −9.94184 | − | 37.1035i | −0.397039 | − | 1.48177i | ||||
\(628\) | 12.1509 | − | 13.5027i | 0.484873 | − | 0.538817i | ||||
\(629\) | 10.1764 | + | 10.1764i | 0.405759 | + | 0.405759i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6875i | 0.982795i | 0.870935 | + | 0.491397i | \(0.163514\pi\) | ||||
−0.870935 | + | 0.491397i | \(0.836486\pi\) | |||||||
\(632\) | −16.3816 | − | 23.8133i | −0.651624 | − | 0.947243i | ||||
\(633\) | 12.0778 | + | 6.97313i | 0.480050 | + | 0.277157i | ||||
\(634\) | −3.12342 | + | 3.29234i | −0.124047 | + | 0.130756i | ||||
\(635\) | −7.51871 | + | 28.0602i | −0.298371 | + | 1.11354i | ||||
\(636\) | 13.3034 | − | 26.1280i | 0.527515 | − | 1.03604i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.3982 | + | 23.4881i | 0.570030 | + | 0.929904i | ||||
\(639\) | −35.2713 | − | 61.0916i | −1.39531 | − | 2.41675i | ||||
\(640\) | 26.4751 | + | 18.1566i | 1.04652 | + | 0.717704i | ||||
\(641\) | 24.6259 | − | 42.6533i | 0.972663 | − | 1.68470i | 0.285223 | − | 0.958461i | \(-0.407932\pi\) |
0.687440 | − | 0.726241i | \(-0.258734\pi\) | |||||||
\(642\) | −5.85335 | + | 10.7842i | −0.231013 | + | 0.425619i | ||||
\(643\) | 9.26033 | − | 9.26033i | 0.365192 | − | 0.365192i | −0.500528 | − | 0.865720i | \(-0.666861\pi\) |
0.865720 | + | 0.500528i | \(0.166861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41.7540 | − | 41.7540i | −1.64406 | − | 1.64406i | ||||
\(646\) | −2.33006 | − | 7.86200i | −0.0916749 | − | 0.309326i | ||||
\(647\) | −18.5542 | − | 10.7123i | −0.729442 | − | 0.421144i | 0.0887760 | − | 0.996052i | \(-0.471704\pi\) |
−0.818218 | + | 0.574908i | \(0.805038\pi\) | |||||||
\(648\) | −30.4163 | + | 63.8399i | −1.19486 | + | 2.50787i | ||||
\(649\) | 28.4203 | − | 16.4085i | 1.11560 | − | 0.644089i | ||||
\(650\) | 0.795142 | − | 3.31410i | 0.0311880 | − | 0.129990i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.27582 | − | 28.5201i | −0.363269 | − | 1.11693i | ||||
\(653\) | −7.07682 | − | 1.89623i | −0.276937 | − | 0.0742051i | 0.117677 | − | 0.993052i | \(-0.462455\pi\) |
−0.394615 | + | 0.918847i | \(0.629122\pi\) | |||||||
\(654\) | −0.950378 | − | 36.0952i | −0.0371627 | − | 1.41144i | ||||
\(655\) | 5.69055 | − | 9.85633i | 0.222348 | − | 0.385119i | ||||
\(656\) | 0.979456 | + | 0.435408i | 0.0382413 | + | 0.0169998i | ||||
\(657\) | −78.8738 | −3.07716 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.05464 | + | 2.05464i | −0.0800374 | + | 0.0800374i | −0.745992 | − | 0.665955i | \(-0.768024\pi\) |
0.665955 | + | 0.745992i | \(0.268024\pi\) | |||||||
\(660\) | 61.3018 | + | 55.1645i | 2.38617 | + | 2.14728i | ||||
\(661\) | −16.9833 | + | 4.55066i | −0.660573 | + | 0.177000i | −0.573505 | − | 0.819202i | \(-0.694417\pi\) |
−0.0870687 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(662\) | −18.8982 | − | 17.9286i | −0.734500 | − | 0.696814i | ||||
\(663\) | 4.86627 | − | 2.80954i | 0.188990 | − | 0.109114i | ||||
\(664\) | −1.23143 | + | 1.44307i | −0.0477886 | + | 0.0560021i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 67.8569 | + | 16.2807i | 2.62940 | + | 0.630864i | ||||
\(667\) | −0.841987 | + | 3.14234i | −0.0326018 | + | 0.121672i | ||||
\(668\) | 29.7548 | − | 19.3352i | 1.15125 | − | 0.748100i | ||||
\(669\) | −17.8709 | − | 66.6952i | −0.690930 | − | 2.57858i | ||||
\(670\) | −10.9631 | + | 20.1985i | −0.423542 | + | 0.780336i | ||||
\(671\) | −26.6106 | −1.02729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.1315 | −1.35422 | −0.677109 | − | 0.735883i | \(-0.736768\pi\) | ||||
−0.677109 | + | 0.735883i | \(0.736768\pi\) | |||||||
\(674\) | 11.0303 | − | 20.3222i | 0.424870 | − | 0.782782i | ||||
\(675\) | 11.5815 | + | 43.2229i | 0.445774 | + | 1.66365i | ||||
\(676\) | 20.7554 | − | 13.4872i | 0.798284 | − | 0.518738i | ||||
\(677\) | −8.04169 | + | 30.0120i | −0.309067 | + | 1.15345i | 0.620320 | + | 0.784349i | \(0.287003\pi\) |
−0.929387 | + | 0.369106i | \(0.879664\pi\) | |||||||
\(678\) | 32.0295 | + | 7.68473i | 1.23008 | + | 0.295130i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.3917 | + | 11.4276i | 0.513550 | + | 0.438230i | ||||
\(681\) | 61.8080 | − | 35.6849i | 2.36849 | − | 1.36745i | ||||
\(682\) | 40.7617 | + | 38.6703i | 1.56085 | + | 1.48076i | ||||
\(683\) | −34.0128 | + | 9.11370i | −1.30146 | + | 0.348726i | −0.842003 | − | 0.539472i | \(-0.818624\pi\) |
−0.459460 | + | 0.888198i | \(0.651957\pi\) | |||||||
\(684\) | −29.5556 | − | 26.5966i | −1.13009 | − | 1.01695i | ||||
\(685\) | −2.15917 | + | 2.15917i | −0.0824977 | + | 0.0824977i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.8675 | 1.82626 | ||||||||
\(688\) | −23.9531 | + | 9.21055i | −0.913205 | + | 0.351149i | ||||
\(689\) | −1.78470 | + | 3.09119i | −0.0679916 | + | 0.117765i | ||||
\(690\) | 0.256313 | + | 9.73475i | 0.00975768 | + | 0.370596i | ||||
\(691\) | −31.2778 | − | 8.38087i | −1.18987 | − | 0.318823i | −0.391033 | − | 0.920377i | \(-0.627882\pi\) |
−0.798833 | + | 0.601553i | \(0.794549\pi\) | |||||||
\(692\) | 7.77161 | + | 23.8952i | 0.295432 | + | 0.908358i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.54265 | + | 35.6052i | −0.324274 | + | 1.35156i | ||||
\(695\) | −3.56859 | + | 2.06033i | −0.135364 | + | 0.0781526i | ||||
\(696\) | 36.0134 | + | 17.1585i | 1.36508 | + | 0.650390i | ||||
\(697\) | 0.509052 | + | 0.293901i | 0.0192817 | + | 0.0111323i | ||||
\(698\) | −14.2134 | − | 47.9583i | −0.537984 | − | 1.81525i | ||||
\(699\) | −51.9274 | − | 51.9274i | −1.96407 | − | 1.96407i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3450 | − | 25.3450i | 0.957266 | − | 0.957266i | −0.0418577 | − | 0.999124i | \(-0.513328\pi\) |
0.999124 | + | 0.0418577i | \(0.0133276\pi\) | |||||||
\(702\) | 7.81284 | − | 14.3944i | 0.294877 | − | 0.543281i | ||||
\(703\) | −8.67125 | + | 15.0191i | −0.327043 | + | 0.566454i | ||||
\(704\) | 32.7299 | − | 14.6061i | 1.23356 | − | 0.550489i | ||||
\(705\) | 34.4365 | + | 59.6457i | 1.29695 | + | 2.24639i | ||||
\(706\) | 5.28250 | + | 8.61747i | 0.198809 | + | 0.324323i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.5608 | − | 42.3456i | 0.810306 | − | 1.59145i | ||||
\(709\) | 6.51377 | − | 24.3097i | 0.244630 | − | 0.912971i | −0.728939 | − | 0.684578i | \(-0.759986\pi\) |
0.973569 | − | 0.228393i | \(-0.0733470\pi\) | |||||||
\(710\) | −25.9047 | + | 27.3057i | −0.972187 | + | 1.02477i | ||||
\(711\) | −66.5599 | − | 38.4284i | −2.49619 | − | 1.44118i | ||||
\(712\) | −33.8633 | + | 23.2951i | −1.26908 | + | 0.873020i | ||||
\(713\) | 6.63466i | 0.248470i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.09914 | − | 7.09914i | −0.265493 | − | 0.265493i | ||||
\(716\) | 6.35602 | − | 7.06316i | 0.237536 | − | 0.263963i | ||||
\(717\) | −15.6007 | − | 58.2228i | −0.582620 | − | 2.17437i | ||||
\(718\) | −0.795479 | − | 30.2122i | −0.0296870 | − | 1.12751i | ||||
\(719\) | 14.7568 | + | 25.5596i | 0.550337 | + | 0.953212i | 0.998250 | + | 0.0591349i | \(0.0188342\pi\) |
−0.447913 | + | 0.894077i | \(0.647832\pi\) | |||||||
\(720\) | 84.3199 | + | 13.3053i | 3.14242 | + | 0.495858i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.4839 | + | 8.87863i | −0.539037 | + | 0.330429i | ||||
\(723\) | 39.2149 | + | 10.5076i | 1.45842 | + | 0.390782i | ||||
\(724\) | −1.96798 | + | 9.27171i | −0.0731393 | + | 0.344580i | ||||
\(725\) | 12.8166 | − | 3.43420i | 0.475996 | − | 0.127543i | ||||
\(726\) | 39.8977 | − | 11.8245i | 1.48074 | − | 0.438847i | ||||
\(727\) | 6.61420i | 0.245307i | 0.992450 | + | 0.122654i | \(0.0391404\pi\) | ||||
−0.992450 | + | 0.122654i | \(0.960860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 45.3428i | 1.67936i | ||||||||
\(730\) | 11.9582 | + | 40.3490i | 0.442594 | + | 1.49338i | ||||
\(731\) | −13.5937 | + | 3.64243i | −0.502782 | + | 0.134720i | ||||
\(732\) | −32.3095 | + | 20.9952i | −1.19419 | + | 0.776006i | ||||
\(733\) | −2.54074 | − | 0.680788i | −0.0938442 | − | 0.0251455i | 0.211591 | − | 0.977358i | \(-0.432135\pi\) |
−0.305436 | + | 0.952213i | \(0.598802\pi\) | |||||||
\(734\) | −8.72149 | − | 14.2276i | −0.321916 | − | 0.525150i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.91124 | + | 1.61680i | 0.144170 | + | 0.0595959i | ||||
\(737\) | 12.8291 | + | 22.2206i | 0.472564 | + | 0.818505i | ||||
\(738\) | 2.84918 | − | 0.0750182i | 0.104880 | − | 0.00276146i | ||||
\(739\) | −5.96130 | − | 22.2479i | −0.219290 | − | 0.818402i | −0.984612 | − | 0.174754i | \(-0.944087\pi\) |
0.765322 | − | 0.643647i | \(-0.222580\pi\) | |||||||
\(740\) | −1.95932 | − | 37.1815i | −0.0720259 | − | 1.36682i | ||||
\(741\) | 4.78800 | + | 4.78800i | 0.175892 | + | 0.175892i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.4705i | − | 1.26460i | −0.774723 | − | 0.632300i | \(-0.782111\pi\) | ||
0.774723 | − | 0.632300i | \(-0.217889\pi\) | |||||||
\(744\) | 80.0013 | + | 14.7917i | 2.93299 | + | 0.542290i | ||||
\(745\) | 1.44227 | + | 0.832692i | 0.0528405 | + | 0.0305075i | ||||
\(746\) | −21.1647 | − | 20.0787i | −0.774893 | − | 0.735135i | ||||
\(747\) | −1.30559 | + | 4.87252i | −0.0477690 | + | 0.178276i | ||||
\(748\) | 18.6911 | − | 6.07905i | 0.683415 | − | 0.222272i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21.6226 | + | 13.2546i | −0.789544 | + | 0.483989i | ||||
\(751\) | −1.35839 | − | 2.35281i | −0.0495685 | − | 0.0858552i | 0.840177 | − | 0.542313i | \(-0.182451\pi\) |
−0.889745 | + | 0.456458i | \(0.849118\pi\) | |||||||
\(752\) | 29.7667 | − | 3.14591i | 1.08548 | − | 0.114719i | ||||
\(753\) | −20.1826 | + | 34.9573i | −0.735495 | + | 1.27392i | ||||
\(754\) | −4.26827 | − | 2.31669i | −0.155441 | − | 0.0843688i | ||||
\(755\) | 21.6901 | − | 21.6901i | 0.789383 | − | 0.789383i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.1791 | − | 20.1791i | −0.733420 | − | 0.733420i | 0.237875 | − | 0.971296i | \(-0.423549\pi\) |
−0.971296 | + | 0.237875i | \(0.923549\pi\) | |||||||
\(758\) | 23.2168 | − | 6.88077i | 0.843273 | − | 0.249921i | ||||
\(759\) | 9.41552 | + | 5.43605i | 0.341762 | + | 0.197316i | ||||
\(760\) | −9.12487 | + | 19.1519i | −0.330994 | + | 0.694714i | ||||
\(761\) | 46.8585 | − | 27.0538i | 1.69862 | − | 0.980699i | 0.751549 | − | 0.659677i | \(-0.229307\pi\) |
0.947072 | − | 0.321022i | \(-0.104026\pi\) | |||||||
\(762\) | 45.6665 | + | 10.9566i | 1.65432 | + | 0.396916i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.9971 | + | 35.3464i | −0.651112 | + | 1.27879i | ||||
\(765\) | 45.2171 | + | 12.1159i | 1.63483 | + | 0.438050i | ||||
\(766\) | −17.9625 | + | 0.472949i | −0.649013 | + | 0.0170883i | ||||
\(767\) | −2.89246 | + | 5.00988i | −0.104441 | + | 0.180896i | ||||
\(768\) | 28.2154 | − | 43.5575i | 1.01814 | − | 1.57174i | ||||
\(769\) | 26.9334 | 0.971244 | 0.485622 | − | 0.874169i | \(-0.338593\pi\) | ||||
0.485622 | + | 0.874169i | \(0.338593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.2596 | − | 52.2596i | 1.88208 | − | 1.88208i | ||||
\(772\) | 7.25840 | − | 0.382489i | 0.261236 | − | 0.0137661i | ||||
\(773\) | 11.5879 | − | 3.10496i | 0.416787 | − | 0.111678i | −0.0443301 | − | 0.999017i | \(-0.514115\pi\) |
0.461117 | + | 0.887339i | \(0.347449\pi\) | |||||||
\(774\) | −46.9656 | + | 49.5057i | −1.68815 | + | 1.77945i | ||||
\(775\) | 23.4352 | − | 13.5303i | 0.841818 | − | 0.486024i | ||||
\(776\) | −46.5167 | + | 3.68113i | −1.66985 | + | 0.132145i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.21966 | − | 25.9232i | 0.222986 | − | 0.929390i | ||||
\(779\) | −0.183329 | + | 0.684194i | −0.00656845 | + | 0.0245138i | ||||
\(780\) | −14.2206 | − | 3.01840i | −0.509178 | − | 0.108076i | ||||
\(781\) | 10.8759 | + | 40.5896i | 0.389172 | + | 1.45241i | ||||
\(782\) | 2.03981 | + | 1.10715i | 0.0729435 | + | 0.0395915i | ||||
\(783\) | 63.7632 | 2.27871 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.7717 | −0.919833 | ||||||||
\(786\) | −16.1704 | − | 8.77680i | −0.576779 | − | 0.313058i | ||||
\(787\) | −3.70513 | − | 13.8277i | −0.132074 | − | 0.492905i | 0.867919 | − | 0.496705i | \(-0.165457\pi\) |
−0.999993 | + | 0.00380017i | \(0.998790\pi\) | |||||||
\(788\) | −5.78224 | + | 27.2418i | −0.205984 | + | 0.970449i | ||||
\(789\) | 10.7361 | − | 40.0676i | 0.382215 | − | 1.42645i | ||||
\(790\) | −9.56729 | + | 39.8759i | −0.340389 | + | 1.41872i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 61.8634 | − | 72.4960i | 2.19822 | − | 2.57603i | ||||
\(793\) | 4.06240 | − | 2.34543i | 0.144260 | − | 0.0832886i | ||||
\(794\) | 1.96219 | − | 2.06831i | 0.0696354 | − | 0.0734015i | ||||
\(795\) | −40.1804 | + | 10.7663i | −1.42505 | + | 0.381841i | ||||
\(796\) | 0.819107 | + | 15.5440i | 0.0290325 | + | 0.550943i | ||||
\(797\) | 3.21815 | − | 3.21815i | 0.113993 | − | 0.113993i | −0.647810 | − | 0.761802i | \(-0.724315\pi\) |
0.761802 | + | 0.647810i | \(0.224315\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4146 | 0.580707 | ||||||||
\(800\) | −2.26543 | − | 17.1126i | −0.0800951 | − | 0.605023i | ||||
\(801\) | −54.6463 | + | 94.6502i | −1.93083 | + | 3.34430i | ||||
\(802\) | 19.1045 | − | 0.503015i | 0.674602 | − | 0.0177621i | ||||
\(803\) | 45.3833 | + | 12.1604i | 1.60154 | + | 0.429132i | ||||
\(804\) | 33.1081 | + | 16.8574i | 1.16763 | + | 0.594516i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.63110 | − | 2.31076i | −0.339241 | − | 0.0813930i | ||||
\(807\) | −44.7847 | + | 25.8564i | −1.57649 | + | 0.910190i | ||||
\(808\) | −40.7513 | + | 14.4506i | −1.43363 | + | 0.508370i | ||||
\(809\) | 0.173970 | + | 0.100441i | 0.00611645 | + | 0.00353133i | 0.503055 | − | 0.864254i | \(-0.332209\pi\) |
−0.496939 | + | 0.867786i | \(0.665543\pi\) | |||||||
\(810\) | 96.1926 | − | 28.5086i | 3.37986 | − | 1.00169i | ||||
\(811\) | −10.7615 | − | 10.7615i | −0.377886 | − | 0.377886i | 0.492453 | − | 0.870339i | \(-0.336100\pi\) |
−0.870339 | + | 0.492453i | \(0.836100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −71.2407 | + | 71.2407i | −2.49852 | + | 2.49852i | ||||
\(814\) | −36.5342 | − | 19.8296i | −1.28052 | − | 0.695029i | ||||
\(815\) | −21.2747 | + | 36.8489i | −0.745222 | + | 1.29076i | ||||
\(816\) | 17.8978 | − | 22.1279i | 0.626547 | − | 0.774631i | ||||
\(817\) | −8.47946 | − | 14.6869i | −0.296659 | − | 0.513828i | ||||
\(818\) | 36.3532 | − | 22.2844i | 1.27106 | − | 0.779157i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.470347 | − | 1.44617i | −0.0164252 | − | 0.0505023i | ||||
\(821\) | −5.97882 | + | 22.3132i | −0.208662 | + | 0.778737i | 0.779640 | + | 0.626228i | \(0.215402\pi\) |
−0.988302 | + | 0.152509i | \(0.951265\pi\) | |||||||
\(822\) | 3.58119 | + | 3.39744i | 0.124908 | + | 0.118499i | ||||
\(823\) | 29.9668 | + | 17.3013i | 1.04458 | + | 0.603087i | 0.921126 | − | 0.389264i | \(-0.127271\pi\) |
0.123451 | + | 0.992351i | \(0.460604\pi\) | |||||||
\(824\) | 3.94090 | − | 2.71101i | 0.137288 | − | 0.0944424i | ||||
\(825\) | − | 44.3439i | − | 1.54385i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9781 | + | 25.9781i | 0.903348 | + | 0.903348i | 0.995724 | − | 0.0923762i | \(-0.0294463\pi\) |
−0.0923762 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(828\) | 11.2381 | − | 0.592205i | 0.390552 | − | 0.0205805i | ||||
\(829\) | 8.51045 | + | 31.7614i | 0.295580 | + | 1.10312i | 0.940756 | + | 0.339086i | \(0.110118\pi\) |
−0.645175 | + | 0.764034i | \(0.723216\pi\) | |||||||
\(830\) | 2.69055 | − | 0.0708414i | 0.0933903 | − | 0.00245894i | ||||
\(831\) | 22.3264 | + | 38.6705i | 0.774494 | + | 1.34146i | ||||
\(832\) | −3.70922 | + | 5.11458i | −0.128594 | + | 0.177316i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.48142 | + | 5.67933i | 0.120552 | + | 0.196659i | ||||
\(835\) | −48.6294 | − | 13.0302i | −1.68289 | − | 0.450929i | ||||
\(836\) | 12.9055 | + | 19.8602i | 0.446345 | + | 0.686879i | ||||
\(837\) | 125.610 | − | 33.6571i | 4.34171 | − | 1.16336i | ||||
\(838\) | −11.8245 | − | 39.8977i | −0.408470 | − | 1.37824i | ||||
\(839\) | − | 0.706396i | − | 0.0243875i | −0.999926 | − | 0.0121938i | \(-0.996119\pi\) | ||
0.999926 | − | 0.0121938i | \(-0.00388149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0927i | 0.348025i | ||||||||
\(842\) | 53.1453 | − | 15.7507i | 1.83151 | − | 0.542803i | ||||
\(843\) | 78.0892 | − | 20.9239i | 2.68953 | − | 0.720659i | ||||
\(844\) | −8.41185 | − | 1.78547i | −0.289548 | − | 0.0614583i | ||||
\(845\) | −33.9213 | − | 9.08920i | −1.16693 | − | 0.312678i | ||||
\(846\) | 67.8574 | − | 41.5965i | 2.33299 | − | 1.43012i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.81785 | + | 17.8576i | −0.0967654 | + | 0.613234i | ||||
\(849\) | −15.0788 | − | 26.1173i | −0.517505 | − | 0.896344i | ||||
\(850\) | −0.249157 | − | 9.46296i | −0.00854602 | − | 0.324577i | ||||
\(851\) | −1.27043 | − | 4.74131i | −0.0435498 | − | 0.162530i | ||||
\(852\) | 45.2295 | + | 40.7013i | 1.54954 | + | 1.39440i | ||||
\(853\) | −40.1092 | − | 40.1092i | −1.37331 | − | 1.37331i | −0.855482 | − | 0.517832i | \(-0.826739\pi\) |
−0.517832 | − | 0.855482i | \(-0.673261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.4108i | 1.92921i | ||||||||
\(856\) | 1.37556 | − | 7.43977i | 0.0470158 | − | 0.254286i | ||||
\(857\) | 12.3231 | + | 7.11472i | 0.420947 | + | 0.243034i | 0.695483 | − | 0.718543i | \(-0.255191\pi\) |
−0.274535 | + | 0.961577i | \(0.588524\pi\) | |||||||
\(858\) | −11.1704 | + | 11.7746i | −0.381353 | + | 0.401978i | ||||
\(859\) | −5.65962 | + | 21.1220i | −0.193104 | + | 0.720673i | 0.799646 | + | 0.600472i | \(0.205021\pi\) |
−0.992750 | + | 0.120201i | \(0.961646\pi\) | |||||||
\(860\) | 32.4459 | + | 16.5203i | 1.10640 | + | 0.563336i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.74102 | − | 2.84018i | −0.0592995 | − | 0.0967368i | ||||
\(863\) | 8.97968 | + | 15.5533i | 0.305672 | + | 0.529439i | 0.977411 | − | 0.211349i | \(-0.0677856\pi\) |
−0.671739 | + | 0.740788i | \(0.734452\pi\) | |||||||
\(864\) | 10.7684 | − | 82.2509i | 0.366349 | − | 2.79823i | ||||
\(865\) | 17.8247 | − | 30.8734i | 0.606059 | − | 1.04973i | ||||
\(866\) | −5.75810 | + | 10.6087i | −0.195668 | + | 0.360500i | ||||
\(867\) | −27.9548 | + | 27.9548i | −0.949395 | + | 0.949395i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.3733 | + | 32.3733i | 1.09819 | + | 1.09819i | ||||
\(870\) | −16.0823 | − | 54.2642i | −0.545240 | − | 1.83973i | ||||
\(871\) | −3.91700 | − | 2.26148i | −0.132722 | − | 0.0766274i | ||||
\(872\) | 7.44092 | + | 20.9838i | 0.251981 | + | 0.710600i | ||||
\(873\) | −107.454 | + | 62.0386i | −3.63677 | + | 2.09969i | ||||
\(874\) | −0.652509 | + | 2.71962i | −0.0220714 | + | 0.0919924i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 64.6970 | − | 21.0419i | 2.18591 | − | 0.710939i | ||||
\(877\) | −16.3939 | − | 4.39274i | −0.553583 | − | 0.148332i | −0.0288266 | − | 0.999584i | \(-0.509177\pi\) |
−0.524757 | + | 0.851252i | \(0.675844\pi\) | |||||||
\(878\) | 0.0148921 | + | 0.565600i | 0.000502584 | + | 0.0190881i | ||||
\(879\) | 51.2359 | − | 88.7432i | 1.72814 | − | 2.99323i | ||||
\(880\) | −46.4656 | − | 20.6558i | −1.56636 | − | 0.696308i | ||||
\(881\) | 2.43251 | 0.0819533 | 0.0409766 | − | 0.999160i | \(-0.486953\pi\) | ||||
0.0409766 | + | 0.999160i | \(0.486953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.6792 | + | 12.6792i | −0.426691 | + | 0.426691i | −0.887499 | − | 0.460809i | \(-0.847559\pi\) |
0.460809 | + | 0.887499i | \(0.347559\pi\) | |||||||
\(884\) | −2.31761 | + | 2.57545i | −0.0779496 | + | 0.0866219i | ||||
\(885\) | −65.1203 | + | 17.4489i | −2.18899 | + | 0.586539i | ||||
\(886\) | −16.5200 | − | 15.6724i | −0.555002 | − | 0.526525i | ||||
\(887\) | −23.8413 | + | 13.7648i | −0.800511 | + | 0.462175i | −0.843650 | − | 0.536894i | \(-0.819598\pi\) |
0.0431388 | + | 0.999069i | \(0.486264\pi\) | |||||||
\(888\) | −60.0036 | + | 4.74841i | −2.01359 | + | 0.159346i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 56.7047 | + | 13.6050i | 1.90075 | + | 0.456040i | ||||
\(891\) | 28.9906 | − | 108.195i | 0.971223 | − | 3.62465i | ||||
\(892\) | 23.1982 | + | 35.6996i | 0.776733 | + | 1.19531i | ||||
\(893\) | 5.11954 | + | 19.1064i | 0.171319 | + | 0.639370i | ||||
\(894\) | 1.28430 | − | 2.36620i | 0.0429534 | − | 0.0791374i | ||||
\(895\) | −13.4810 | −0.450620 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.91651 | −0.0639905 | ||||||||
\(898\) | 2.92314 | − | 5.38559i | 0.0975464 | − | 0.179720i | ||||
\(899\) | −9.98010 | − | 37.2462i | −0.332855 | − | 1.24223i | ||||
\(900\) | −25.0102 | − | 38.4881i | −0.833674 | − | 1.28294i | ||||
\(901\) | −2.56595 | + | 9.57627i | −0.0854843 | + | 0.319032i | ||||
\(902\) | −1.65096 | − | 0.396110i | −0.0549710 | − | 0.0131890i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.2465 | + | 1.60222i | −0.673389 | + | 0.0532890i | ||||
\(905\) | 11.6458 | − | 6.72369i | 0.387118 | − | 0.223503i | ||||
\(906\) | −35.9750 | − | 34.1292i | −1.19519 | − | 1.13387i | ||||
\(907\) | 34.4073 | − | 9.21942i | 1.14248 | − | 0.306126i | 0.362530 | − | 0.931972i | \(-0.381913\pi\) |
0.779946 | + | 0.625846i | \(0.215246\pi\) | |||||||
\(908\) | −29.4367 | + | 32.7117i | −0.976891 | + | 1.08557i | ||||
\(909\) | −81.2968 | + | 81.2968i | −2.69645 | + | 2.69645i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.9979 | −1.15953 | −0.579766 | − | 0.814783i | \(-0.696856\pi\) | ||||
−0.579766 | + | 0.814783i | \(0.696856\pi\) | |||||||
\(912\) | 31.3386 | + | 13.9313i | 1.03773 | + | 0.461311i | ||||
\(913\) | 1.50245 | − | 2.60232i | 0.0497238 | − | 0.0861241i | ||||
\(914\) | −0.387004 | − | 14.6984i | −0.0128010 | − | 0.486179i | ||||
\(915\) | 52.8046 | + | 14.1490i | 1.74567 | + | 0.467750i | ||||
\(916\) | −28.0679 | + | 9.12872i | −0.927389 | + | 0.301622i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.6131 | − | 44.2349i | 0.350286 | − | 1.45997i | ||||
\(919\) | −13.4271 | + | 7.75216i | −0.442920 | + | 0.255720i | −0.704836 | − | 0.709371i | \(-0.748979\pi\) |
0.261915 | + | 0.965091i | \(0.415646\pi\) | |||||||
\(920\) | −2.00679 | − | 5.65924i | −0.0661619 | − | 0.186580i | ||||
\(921\) | −45.2714 | − | 26.1374i | −1.49174 | − | 0.861258i | ||||
\(922\) | −8.34684 | − | 28.1636i | −0.274888 | − | 0.927518i | ||||
\(923\) | −5.23786 | − | 5.23786i | −0.172406 | − | 0.172406i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1566 | + | 14.1566i | −0.465467 | + | 0.465467i | ||||
\(926\) | 11.4994 | − | 21.1865i | 0.377893 | − | 0.696232i | ||||
\(927\) | 6.35957 | − | 11.0151i | 0.208876 | − | 0.361783i | ||||
\(928\) | −24.3893 | − | 3.19308i | −0.800617 | − | 0.104818i | ||||
\(929\) | −14.6486 | − | 25.3721i | −0.480604 | − | 0.832431i | 0.519148 | − | 0.854684i | \(-0.326249\pi\) |
−0.999752 | + | 0.0222533i | \(0.992916\pi\) | |||||||
\(930\) | −60.3242 | − | 98.4085i | −1.97811 | − | 3.22694i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 40.3514 | + | 20.5455i | 1.32175 | + | 0.672989i | ||||
\(933\) | −12.0975 | + | 45.1486i | −0.396055 | + | 1.47810i | ||||
\(934\) | −14.6032 | + | 15.3930i | −0.477832 | + | 0.503675i | ||||
\(935\) | −24.1495 | − | 13.9427i | −0.789774 | − | 0.455976i | ||||
\(936\) | −3.05442 | + | 16.5199i | −0.0998368 | + | 0.539971i | ||||
\(937\) | 50.5492i | 1.65137i | 0.564131 | + | 0.825685i | \(0.309211\pi\) | ||||
−0.564131 | + | 0.825685i | \(0.690789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.9610 | − | 23.9610i | −0.781938 | − | 0.781938i | ||||
\(940\) | −31.5673 | − | 28.4069i | −1.02961 | − | 0.926531i | ||||
\(941\) | −14.1591 | − | 52.8424i | −0.461573 | − | 1.72261i | −0.668010 | − | 0.744153i | \(-0.732854\pi\) |
0.206437 | − | 0.978460i | \(-0.433813\pi\) | |||||||
\(942\) | 1.09659 | + | 41.6483i | 0.0357288 | + | 1.35697i | ||||
\(943\) | −0.100242 | − | 0.173624i | −0.00326432 | − | 0.00565397i | ||||
\(944\) | −4.56688 | + | 28.9418i | −0.148639 | + | 0.941976i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.6562 | − | 21.2442i | 1.12677 | − | 0.690709i | ||||
\(947\) | 18.2814 | + | 4.89848i | 0.594064 | + | 0.159179i | 0.543310 | − | 0.839532i | \(-0.317171\pi\) |
0.0507543 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(948\) | 64.8483 | + | 13.7644i | 2.10617 | + | 0.447048i | ||||
\(949\) | −8.00009 | + | 2.14362i | −0.259694 | + | 0.0695848i | ||||
\(950\) | 10.9370 | − | 3.24141i | 0.354844 | − | 0.105165i | ||||
\(951\) | − | 10.4087i | − | 0.337525i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 23.1169i | − | 0.748830i | −0.927261 | − | 0.374415i | \(-0.877844\pi\) | ||
0.927261 | − | 0.374415i | \(-0.122156\pi\) | |||||||
\(954\) | 13.6598 | + | 46.0904i | 0.442252 | + | 1.49223i | ||||
\(955\) | 54.3567 | − | 14.5648i | 1.75894 | − | 0.471307i | ||||
\(956\) | 20.2513 | + | 31.1646i | 0.654974 | + | 1.00794i | ||||
\(957\) | −61.0347 | − | 16.3542i | −1.97297 | − | 0.528657i | ||||
\(958\) | 19.4288 | + | 31.6948i | 0.627717 | + | 1.02401i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −72.7137 | + | 11.5810i | −2.34682 | + | 0.373775i | ||||
\(961\) | −23.8204 | − | 41.2582i | −0.768401 | − | 1.33091i | ||||
\(962\) | 7.32512 | − | 0.192869i | 0.236171 | − | 0.00621833i | ||||
\(963\) | −5.20694 | − | 19.4326i | −0.167791 | − | 0.626205i | ||||
\(964\) | −24.9981 | + | 1.31730i | −0.805136 | + | 0.0424274i | ||||
\(965\) | −7.29184 | − | 7.29184i | −0.234733 | − | 0.234733i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20.7758i | − | 0.668105i | −0.942555 | − | 0.334052i | \(-0.891584\pi\) | ||
0.942555 | − | 0.334052i | \(-0.108416\pi\) | |||||||
\(968\) | −21.1396 | + | 14.5423i | −0.679453 | + | 0.467407i | ||||
\(969\) | 16.2876 | + | 9.40366i | 0.523233 | + | 0.302089i | ||||
\(970\) | 48.0281 | + | 45.5638i | 1.54209 | + | 1.46297i | ||||
\(971\) | 6.54826 | − | 24.4384i | 0.210144 | − | 0.784267i | −0.777676 | − | 0.628665i | \(-0.783602\pi\) |
0.987820 | − | 0.155602i | \(-0.0497316\pi\) | |||||||
\(972\) | −22.9513 | − | 70.5679i | −0.736164 | − | 2.26347i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.7987 | − | 15.2015i | 0.794601 | − | 0.487089i | ||||
\(975\) | 3.90843 | + | 6.76959i | 0.125170 | + | 0.216800i | ||||
\(976\) | 14.9412 | − | 18.4725i | 0.478256 | − | 0.591292i | ||||
\(977\) | −16.8040 | + | 29.1053i | −0.537607 | + | 0.931162i | 0.461426 | + | 0.887179i | \(0.347338\pi\) |
−0.999032 | + | 0.0439831i | \(0.985995\pi\) | |||||||
\(978\) | 60.4547 | + | 32.8130i | 1.93313 | + | 1.04924i | ||||
\(979\) | 46.0358 | − | 46.0358i | 1.47131 | − | 1.47131i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.8615 | + | 41.8615i | 1.33654 | + | 1.33654i | ||||
\(982\) | −21.6334 | + | 6.41150i | −0.690351 | + | 0.204599i | ||||
\(983\) | −4.11952 | − | 2.37841i | −0.131392 | − | 0.0758594i | 0.432863 | − | 0.901460i | \(-0.357503\pi\) |
−0.564255 | + | 0.825600i | \(0.690837\pi\) | |||||||
\(984\) | −2.31705 | + | 0.821637i | −0.0738650 | + | 0.0261928i | ||||
\(985\) | 34.2172 | − | 19.7553i | 1.09025 | − | 0.629456i | ||||
\(986\) | −13.1167 | − | 3.14704i | −0.417720 | − | 0.100222i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.72063 | − | 1.89441i | −0.118369 | − | 0.0602691i | ||||
\(989\) | 4.63644 | + | 1.24233i | 0.147430 | + | 0.0395038i | ||||
\(990\) | −135.166 | + | 3.55888i | −4.29585 | + | 0.113109i | ||||
\(991\) | −14.5579 | + | 25.2150i | −0.462446 | + | 0.800979i | −0.999082 | − | 0.0428342i | \(-0.986361\pi\) |
0.536637 | + | 0.843813i | \(0.319695\pi\) | |||||||
\(992\) | −49.7309 | + | 6.58356i | −1.57896 | + | 0.209028i | ||||
\(993\) | 59.7464 | 1.89599 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.6156 | − | 15.6156i | 0.495048 | − | 0.495048i | ||||
\(996\) | −0.228966 | − | 4.34503i | −0.00725506 | − | 0.137678i | ||||
\(997\) | 9.97995 | − | 2.67412i | 0.316068 | − | 0.0846902i | −0.0972974 | − | 0.995255i | \(-0.531020\pi\) |
0.413366 | + | 0.910565i | \(0.364353\pi\) | |||||||
\(998\) | −13.0630 | + | 13.7695i | −0.413502 | + | 0.435865i | ||||
\(999\) | −83.3196 | + | 48.1046i | −2.63611 | + | 1.52196i |
(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 | 784.2.x.n.165.8 | 40 | ||
7.2 | even | 3 | inner | 784.2.x.n.373.1 | 40 | ||
7.3 | odd | 6 | 784.2.m.i.197.7 | ✓ | 20 | ||
7.4 | even | 3 | 784.2.m.i.197.8 | yes | 20 | ||
7.5 | odd | 6 | inner | 784.2.x.n.373.2 | 40 | ||
7.6 | odd | 2 | inner | 784.2.x.n.165.7 | 40 | ||
16.13 | even | 4 | inner | 784.2.x.n.557.1 | 40 | ||
112.13 | odd | 4 | inner | 784.2.x.n.557.2 | 40 | ||
112.45 | odd | 12 | 784.2.m.i.589.7 | yes | 20 | ||
112.61 | odd | 12 | inner | 784.2.x.n.765.7 | 40 | ||
112.93 | even | 12 | inner | 784.2.x.n.765.8 | 40 | ||
112.109 | even | 12 | 784.2.m.i.589.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.i.197.7 | ✓ | 20 | 7.3 | odd | 6 | ||
784.2.m.i.197.8 | yes | 20 | 7.4 | even | 3 | ||
784.2.m.i.589.7 | yes | 20 | 112.45 | odd | 12 | ||
784.2.m.i.589.8 | yes | 20 | 112.109 | even | 12 | ||
784.2.x.n.165.7 | 40 | 7.6 | odd | 2 | inner | ||
784.2.x.n.165.8 | 40 | 1.1 | even | 1 | trivial | ||
784.2.x.n.373.1 | 40 | 7.2 | even | 3 | inner | ||
784.2.x.n.373.2 | 40 | 7.5 | odd | 6 | inner | ||
784.2.x.n.557.1 | 40 | 16.13 | even | 4 | inner | ||
784.2.x.n.557.2 | 40 | 112.13 | odd | 4 | inner | ||
784.2.x.n.765.7 | 40 | 112.61 | odd | 12 | inner | ||
784.2.x.n.765.8 | 40 | 112.93 | even | 12 | inner |