Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(62,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.62");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.k (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: | \(2.86104277578\) |
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 | 83.9 | ||
Character | \(\chi\) | \(=\) | 105.83 |
Dual form | 105.3.k.d.62.9 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67168 | + | 1.67168i | 0.835842 | + | 0.835842i | 0.988309 | − | 0.152466i | \(-0.0487215\pi\) |
−0.152466 | + | 0.988309i | \(0.548722\pi\) | |||||||
\(3\) | −1.56503 | − | 2.55943i | −0.521678 | − | 0.853143i | ||||
\(4\) | 1.58906i | 0.397265i | ||||||||
\(5\) | 0.529219 | − | 4.97191i | 0.105844 | − | 0.994383i | ||||
\(6\) | 1.66231 | − | 6.89480i | 0.277052 | − | 1.14913i | ||||
\(7\) | 6.78135 | + | 1.73590i | 0.968764 | + | 0.247985i | ||||
\(8\) | 4.03033 | − | 4.03033i | 0.503791 | − | 0.503791i | ||||
\(9\) | −4.10134 | + | 8.01118i | −0.455705 | + | 0.890131i | ||||
\(10\) | 9.19616 | − | 7.42678i | 0.919616 | − | 0.742678i | ||||
\(11\) | − | 4.41779i | − | 0.401617i | −0.979630 | − | 0.200809i | \(-0.935643\pi\) | ||
0.979630 | − | 0.200809i | \(-0.0643570\pi\) | |||||||
\(12\) | 4.06708 | − | 2.48693i | 0.338924 | − | 0.207244i | ||||
\(13\) | 1.62244 | − | 1.62244i | 0.124803 | − | 0.124803i | −0.641946 | − | 0.766750i | \(-0.721873\pi\) |
0.766750 | + | 0.641946i | \(0.221873\pi\) | |||||||
\(14\) | 8.43440 | + | 14.2381i | 0.602457 | + | 1.01701i | ||||
\(15\) | −13.5535 | + | 6.42671i | −0.903567 | + | 0.428447i | ||||
\(16\) | 19.8311 | 1.23945 | ||||||||
\(17\) | −13.9255 | + | 13.9255i | −0.819145 | + | 0.819145i | −0.985984 | − | 0.166839i | \(-0.946644\pi\) |
0.166839 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(18\) | −20.2483 | + | 6.53602i | −1.12491 | + | 0.363112i | ||||
\(19\) | −0.694013 | −0.0365270 | −0.0182635 | − | 0.999833i | \(-0.505814\pi\) | ||||
−0.0182635 | + | 0.999833i | \(0.505814\pi\) | |||||||
\(20\) | 7.90067 | + | 0.840961i | 0.395034 | + | 0.0420481i | ||||
\(21\) | −6.17013 | − | 20.0731i | −0.293816 | − | 0.955862i | ||||
\(22\) | 7.38515 | − | 7.38515i | 0.335689 | − | 0.335689i | ||||
\(23\) | −23.1818 | + | 23.1818i | −1.00790 | + | 1.00790i | −0.00793606 | + | 0.999969i | \(0.502526\pi\) |
−0.999969 | + | 0.00793606i | \(0.997474\pi\) | |||||||
\(24\) | −16.6229 | − | 4.00774i | −0.692623 | − | 0.166989i | ||||
\(25\) | −24.4399 | − | 5.26247i | −0.977594 | − | 0.210499i | ||||
\(26\) | 5.42443 | 0.208632 | ||||||||
\(27\) | 26.9228 | − | 2.04067i | 0.997140 | − | 0.0755805i | ||||
\(28\) | −2.75844 | + | 10.7760i | −0.0985158 | + | 0.384856i | ||||
\(29\) | 49.1234 | 1.69391 | 0.846956 | − | 0.531663i | \(-0.178433\pi\) | ||||
0.846956 | + | 0.531663i | \(0.178433\pi\) | |||||||
\(30\) | −33.4006 | − | 11.9137i | −1.11335 | − | 0.397125i | ||||
\(31\) | 33.8768i | 1.09280i | 0.837524 | + | 0.546401i | \(0.184002\pi\) | ||||
−0.837524 | + | 0.546401i | \(0.815998\pi\) | |||||||
\(32\) | 17.0301 | + | 17.0301i | 0.532190 | + | 0.532190i | ||||
\(33\) | −11.3070 | + | 6.91399i | −0.342637 | + | 0.209515i | ||||
\(34\) | −46.5580 | −1.36935 | ||||||||
\(35\) | 12.2195 | − | 32.7976i | 0.349130 | − | 0.937074i | ||||
\(36\) | −12.7302 | − | 6.51728i | −0.353618 | − | 0.181036i | ||||
\(37\) | 2.02579 | − | 2.02579i | 0.0547510 | − | 0.0547510i | −0.679201 | − | 0.733952i | \(-0.737674\pi\) |
0.733952 | + | 0.679201i | \(0.237674\pi\) | |||||||
\(38\) | −1.16017 | − | 1.16017i | −0.0305308 | − | 0.0305308i | ||||
\(39\) | −6.69171 | − | 1.61335i | −0.171582 | − | 0.0413679i | ||||
\(40\) | −17.9055 | − | 22.1714i | −0.447638 | − | 0.554285i | ||||
\(41\) | 32.5085 | 0.792891 | 0.396446 | − | 0.918058i | \(-0.370244\pi\) | ||||
0.396446 | + | 0.918058i | \(0.370244\pi\) | |||||||
\(42\) | 23.2414 | − | 43.8704i | 0.553366 | − | 1.04453i | ||||
\(43\) | −30.4591 | − | 30.4591i | −0.708351 | − | 0.708351i | 0.257838 | − | 0.966188i | \(-0.416990\pi\) |
−0.966188 | + | 0.257838i | \(0.916990\pi\) | |||||||
\(44\) | 7.02014 | 0.159549 | ||||||||
\(45\) | 37.6604 | + | 24.6312i | 0.836897 | + | 0.547360i | ||||
\(46\) | −77.5053 | −1.68490 | ||||||||
\(47\) | −18.7790 | + | 18.7790i | −0.399554 | + | 0.399554i | −0.878076 | − | 0.478522i | \(-0.841173\pi\) |
0.478522 | + | 0.878076i | \(0.341173\pi\) | |||||||
\(48\) | −31.0364 | − | 50.7563i | −0.646591 | − | 1.05742i | ||||
\(49\) | 42.9733 | + | 23.5434i | 0.877007 | + | 0.480478i | ||||
\(50\) | −32.0585 | − | 49.6529i | −0.641171 | − | 0.993058i | ||||
\(51\) | 57.4350 | + | 13.8474i | 1.12618 | + | 0.271518i | ||||
\(52\) | 2.57816 | + | 2.57816i | 0.0495800 | + | 0.0495800i | ||||
\(53\) | −33.8448 | + | 33.8448i | −0.638581 | + | 0.638581i | −0.950205 | − | 0.311624i | \(-0.899127\pi\) |
0.311624 | + | 0.950205i | \(0.399127\pi\) | |||||||
\(54\) | 48.4178 | + | 41.5950i | 0.896625 | + | 0.770278i | ||||
\(55\) | −21.9649 | − | 2.33798i | −0.399361 | − | 0.0425087i | ||||
\(56\) | 34.3273 | − | 20.3348i | 0.612988 | − | 0.363122i | ||||
\(57\) | 1.08615 | + | 1.77628i | 0.0190553 | + | 0.0311627i | ||||
\(58\) | 82.1189 | + | 82.1189i | 1.41584 | + | 1.41584i | ||||
\(59\) | 23.1041i | 0.391596i | 0.980644 | + | 0.195798i | \(0.0627296\pi\) | ||||
−0.980644 | + | 0.195798i | \(0.937270\pi\) | |||||||
\(60\) | −10.2124 | − | 21.5373i | −0.170207 | − | 0.358955i | ||||
\(61\) | − | 12.9880i | − | 0.212919i | −0.994317 | − | 0.106459i | \(-0.966049\pi\) | ||
0.994317 | − | 0.106459i | \(-0.0339514\pi\) | |||||||
\(62\) | −56.6314 | + | 56.6314i | −0.913410 | + | 0.913410i | ||||
\(63\) | −41.7192 | + | 47.2071i | −0.662209 | + | 0.749319i | ||||
\(64\) | − | 22.3867i | − | 0.349792i | ||||||
\(65\) | −7.20802 | − | 8.92528i | −0.110893 | − | 0.137312i | ||||
\(66\) | −30.4598 | − | 7.34376i | −0.461512 | − | 0.111269i | ||||
\(67\) | −56.3395 | + | 56.3395i | −0.840888 | + | 0.840888i | −0.988974 | − | 0.148086i | \(-0.952689\pi\) |
0.148086 | + | 0.988974i | \(0.452689\pi\) | |||||||
\(68\) | −22.1284 | − | 22.1284i | −0.325418 | − | 0.325418i | ||||
\(69\) | 95.6125 | + | 23.0519i | 1.38569 | + | 0.334085i | ||||
\(70\) | 75.2545 | − | 34.4000i | 1.07506 | − | 0.491429i | ||||
\(71\) | 92.7547i | 1.30640i | 0.757184 | + | 0.653202i | \(0.226575\pi\) | ||||
−0.757184 | + | 0.653202i | \(0.773425\pi\) | |||||||
\(72\) | 15.7579 | + | 48.8175i | 0.218860 | + | 0.678020i | ||||
\(73\) | 95.4460 | − | 95.4460i | 1.30748 | − | 1.30748i | 0.384251 | − | 0.923229i | \(-0.374460\pi\) |
0.923229 | − | 0.384251i | \(-0.125540\pi\) | |||||||
\(74\) | 6.77295 | 0.0915263 | ||||||||
\(75\) | 24.7803 | + | 70.7880i | 0.330404 | + | 0.943840i | ||||
\(76\) | − | 1.10283i | − | 0.0145109i | ||||||
\(77\) | 7.66883 | − | 29.9586i | 0.0995952 | − | 0.389072i | ||||
\(78\) | −8.48941 | − | 13.8834i | −0.108839 | − | 0.177993i | ||||
\(79\) | − | 100.280i | − | 1.26937i | −0.772770 | − | 0.634687i | \(-0.781129\pi\) | ||
0.772770 | − | 0.634687i | \(-0.218871\pi\) | |||||||
\(80\) | 10.4950 | − | 98.5987i | 0.131188 | − | 1.23248i | ||||
\(81\) | −47.3580 | − | 65.7132i | −0.584667 | − | 0.811274i | ||||
\(82\) | 54.3440 | + | 54.3440i | 0.662732 | + | 0.662732i | ||||
\(83\) | 5.62594 | + | 5.62594i | 0.0677824 | + | 0.0677824i | 0.740185 | − | 0.672403i | \(-0.234738\pi\) |
−0.672403 | + | 0.740185i | \(0.734738\pi\) | |||||||
\(84\) | 31.8974 | − | 9.80471i | 0.379731 | − | 0.116723i | ||||
\(85\) | 61.8666 | + | 76.6059i | 0.727842 | + | 0.901245i | ||||
\(86\) | − | 101.836i | − | 1.18414i | ||||||
\(87\) | −76.8798 | − | 125.728i | −0.883676 | − | 1.44515i | ||||
\(88\) | −17.8052 | − | 17.8052i | −0.202331 | − | 0.202331i | ||||
\(89\) | − | 158.669i | − | 1.78280i | −0.453220 | − | 0.891399i | \(-0.649725\pi\) | ||
0.453220 | − | 0.891399i | \(-0.350275\pi\) | |||||||
\(90\) | 21.7807 | + | 104.132i | 0.242008 | + | 1.15702i | ||||
\(91\) | 13.8188 | − | 8.18596i | 0.151854 | − | 0.0899556i | ||||
\(92\) | −36.8373 | − | 36.8373i | −0.400405 | − | 0.400405i | ||||
\(93\) | 86.7053 | − | 53.0184i | 0.932315 | − | 0.570090i | ||||
\(94\) | −62.7852 | −0.667928 | ||||||||
\(95\) | −0.367285 | + | 3.45057i | −0.00386616 | + | 0.0363218i | ||||
\(96\) | 16.9346 | − | 70.2399i | 0.176402 | − | 0.731665i | ||||
\(97\) | −37.1038 | − | 37.1038i | −0.382514 | − | 0.382514i | 0.489493 | − | 0.872007i | \(-0.337182\pi\) |
−0.872007 | + | 0.489493i | \(0.837182\pi\) | |||||||
\(98\) | 32.4807 | + | 111.195i | 0.331435 | + | 1.13464i | ||||
\(99\) | 35.3917 | + | 18.1189i | 0.357492 | + | 0.183019i | ||||
\(100\) | 8.36238 | − | 38.8364i | 0.0836238 | − | 0.388364i | ||||
\(101\) | −17.6626 | −0.174877 | −0.0874384 | − | 0.996170i | \(-0.527868\pi\) | ||||
−0.0874384 | + | 0.996170i | \(0.527868\pi\) | |||||||
\(102\) | 72.8648 | + | 119.162i | 0.714361 | + | 1.16825i | ||||
\(103\) | −96.5666 | + | 96.5666i | −0.937540 | + | 0.937540i | −0.998161 | − | 0.0606213i | \(-0.980692\pi\) |
0.0606213 | + | 0.998161i | \(0.480692\pi\) | |||||||
\(104\) | − | 13.0780i | − | 0.125750i | ||||||
\(105\) | −103.067 | + | 20.0543i | −0.981591 | + | 0.190993i | ||||
\(106\) | −113.156 | −1.06751 | ||||||||
\(107\) | 7.22790 | + | 7.22790i | 0.0675504 | + | 0.0675504i | 0.740075 | − | 0.672524i | \(-0.234790\pi\) |
−0.672524 | + | 0.740075i | \(0.734790\pi\) | |||||||
\(108\) | 3.24275 | + | 42.7819i | 0.0300255 | + | 0.396129i | ||||
\(109\) | − | 125.106i | − | 1.14776i | −0.818940 | − | 0.573880i | \(-0.805438\pi\) | ||
0.818940 | − | 0.573880i | \(-0.194562\pi\) | |||||||
\(110\) | −32.8100 | − | 40.6267i | −0.298273 | − | 0.369334i | ||||
\(111\) | −8.35527 | − | 2.01443i | −0.0752727 | − | 0.0181480i | ||||
\(112\) | 134.482 | + | 34.4248i | 1.20073 | + | 0.307364i | ||||
\(113\) | −71.6887 | + | 71.6887i | −0.634414 | + | 0.634414i | −0.949172 | − | 0.314758i | \(-0.898077\pi\) |
0.314758 | + | 0.949172i | \(0.398077\pi\) | |||||||
\(114\) | −1.15367 | + | 4.78508i | −0.0101199 | + | 0.0419744i | ||||
\(115\) | 102.990 | + | 127.526i | 0.895562 | + | 1.10892i | ||||
\(116\) | 78.0601i | 0.672932i | ||||||||
\(117\) | 6.34349 | + | 19.6519i | 0.0542179 | + | 0.167965i | ||||
\(118\) | −38.6228 | + | 38.6228i | −0.327312 | + | 0.327312i | ||||
\(119\) | −118.607 | + | 70.2603i | −0.996694 | + | 0.590422i | ||||
\(120\) | −28.7233 | + | 80.5269i | −0.239361 | + | 0.671057i | ||||
\(121\) | 101.483 | 0.838703 | ||||||||
\(122\) | 21.7119 | − | 21.7119i | 0.177966 | − | 0.177966i | ||||
\(123\) | −50.8769 | − | 83.2032i | −0.413634 | − | 0.676449i | ||||
\(124\) | −53.8323 | −0.434132 | ||||||||
\(125\) | −39.0986 | + | 118.728i | −0.312789 | + | 0.949823i | ||||
\(126\) | −148.657 | + | 9.17401i | −1.17982 | + | 0.0728096i | ||||
\(127\) | 4.25412 | − | 4.25412i | 0.0334970 | − | 0.0334970i | −0.690160 | − | 0.723657i | \(-0.742460\pi\) |
0.723657 | + | 0.690160i | \(0.242460\pi\) | |||||||
\(128\) | 105.544 | − | 105.544i | 0.824561 | − | 0.824561i | ||||
\(129\) | −30.2883 | + | 125.627i | −0.234793 | + | 0.973855i | ||||
\(130\) | 2.87071 | − | 26.9698i | 0.0220824 | − | 0.207460i | ||||
\(131\) | −115.412 | −0.881007 | −0.440504 | − | 0.897751i | \(-0.645200\pi\) | ||||
−0.440504 | + | 0.897751i | \(0.645200\pi\) | |||||||
\(132\) | −10.9867 | − | 17.9675i | −0.0832329 | − | 0.136118i | ||||
\(133\) | −4.70634 | − | 1.20473i | −0.0353860 | − | 0.00905815i | ||||
\(134\) | −188.364 | −1.40570 | ||||||||
\(135\) | 4.10200 | − | 134.938i | 0.0303852 | − | 0.999538i | ||||
\(136\) | 112.249i | 0.825357i | ||||||||
\(137\) | −134.388 | − | 134.388i | −0.980935 | − | 0.980935i | 0.0188868 | − | 0.999822i | \(-0.493988\pi\) |
−0.999822 | + | 0.0188868i | \(0.993988\pi\) | |||||||
\(138\) | 121.298 | + | 198.369i | 0.878974 | + | 1.43746i | ||||
\(139\) | −228.384 | −1.64305 | −0.821524 | − | 0.570174i | \(-0.806876\pi\) | ||||
−0.821524 | + | 0.570174i | \(0.806876\pi\) | |||||||
\(140\) | 52.1174 | + | 19.4176i | 0.372267 | + | 0.138697i | ||||
\(141\) | 77.4534 | + | 18.6738i | 0.549315 | + | 0.132438i | ||||
\(142\) | −155.057 | + | 155.057i | −1.09195 | + | 1.09195i | ||||
\(143\) | −7.16762 | − | 7.16762i | −0.0501232 | − | 0.0501232i | ||||
\(144\) | −81.3342 | + | 158.871i | −0.564821 | + | 1.10327i | ||||
\(145\) | 25.9971 | − | 244.237i | 0.179290 | − | 1.68440i | ||||
\(146\) | 319.111 | 2.18569 | ||||||||
\(147\) | −6.99698 | − | 146.833i | −0.0475985 | − | 0.998867i | ||||
\(148\) | 3.21909 | + | 3.21909i | 0.0217506 | + | 0.0217506i | ||||
\(149\) | 67.7175 | 0.454480 | 0.227240 | − | 0.973839i | \(-0.427030\pi\) | ||||
0.227240 | + | 0.973839i | \(0.427030\pi\) | |||||||
\(150\) | −76.9104 | + | 159.760i | −0.512736 | + | 1.06507i | ||||
\(151\) | 108.833 | 0.720749 | 0.360375 | − | 0.932808i | \(-0.382649\pi\) | ||||
0.360375 | + | 0.932808i | \(0.382649\pi\) | |||||||
\(152\) | −2.79710 | + | 2.79710i | −0.0184020 | + | 0.0184020i | ||||
\(153\) | −54.4463 | − | 168.673i | −0.355858 | − | 1.10243i | ||||
\(154\) | 62.9012 | − | 37.2614i | 0.408449 | − | 0.241957i | ||||
\(155\) | 168.433 | + | 17.9283i | 1.08666 | + | 0.115666i | ||||
\(156\) | 2.56371 | − | 10.6335i | 0.0164340 | − | 0.0681636i | ||||
\(157\) | −12.8504 | − | 12.8504i | −0.0818495 | − | 0.0818495i | 0.664997 | − | 0.746846i | \(-0.268433\pi\) |
−0.746846 | + | 0.664997i | \(0.768433\pi\) | |||||||
\(158\) | 167.637 | − | 167.637i | 1.06100 | − | 1.06100i | ||||
\(159\) | 139.592 | + | 33.6551i | 0.877935 | + | 0.211667i | ||||
\(160\) | 93.6847 | − | 75.6594i | 0.585529 | − | 0.472871i | ||||
\(161\) | −197.445 | + | 116.963i | −1.22637 | + | 0.726476i | ||||
\(162\) | 30.6841 | − | 189.019i | 0.189408 | − | 1.16679i | ||||
\(163\) | −140.352 | − | 140.352i | −0.861054 | − | 0.861054i | 0.130407 | − | 0.991461i | \(-0.458372\pi\) |
−0.991461 | + | 0.130407i | \(0.958372\pi\) | |||||||
\(164\) | 51.6580i | 0.314988i | ||||||||
\(165\) | 28.3919 | + | 59.8765i | 0.172072 | + | 0.362888i | ||||
\(166\) | 18.8096i | 0.113311i | ||||||||
\(167\) | 70.3795 | − | 70.3795i | 0.421434 | − | 0.421434i | −0.464263 | − | 0.885697i | \(-0.653681\pi\) |
0.885697 | + | 0.464263i | \(0.153681\pi\) | |||||||
\(168\) | −105.769 | − | 56.0336i | −0.629577 | − | 0.333533i | ||||
\(169\) | 163.735i | 0.968848i | ||||||||
\(170\) | −24.6394 | + | 231.482i | −0.144938 | + | 1.36166i | ||||
\(171\) | 2.84638 | − | 5.55986i | 0.0166455 | − | 0.0325138i | ||||
\(172\) | 48.4013 | − | 48.4013i | 0.281403 | − | 0.281403i | ||||
\(173\) | −74.9815 | − | 74.9815i | −0.433419 | − | 0.433419i | 0.456371 | − | 0.889790i | \(-0.349149\pi\) |
−0.889790 | + | 0.456371i | \(0.849149\pi\) | |||||||
\(174\) | 81.6586 | − | 338.696i | 0.469302 | − | 1.94653i | ||||
\(175\) | −156.600 | − | 78.1117i | −0.894857 | − | 0.446352i | ||||
\(176\) | − | 87.6098i | − | 0.497783i | ||||||
\(177\) | 59.1334 | − | 36.1587i | 0.334087 | − | 0.204287i | ||||
\(178\) | 265.245 | − | 265.245i | 1.49014 | − | 1.49014i | ||||
\(179\) | 110.262 | 0.615991 | 0.307996 | − | 0.951388i | \(-0.400342\pi\) | ||||
0.307996 | + | 0.951388i | \(0.400342\pi\) | |||||||
\(180\) | −39.1404 | + | 59.8446i | −0.217447 | + | 0.332470i | ||||
\(181\) | 58.1797i | 0.321435i | 0.987000 | + | 0.160717i | \(0.0513808\pi\) | ||||
−0.987000 | + | 0.160717i | \(0.948619\pi\) | |||||||
\(182\) | 36.7849 | + | 9.41625i | 0.202115 | + | 0.0517376i | ||||
\(183\) | −33.2420 | + | 20.3267i | −0.181650 | + | 0.111075i | ||||
\(184\) | 186.861i | 1.01555i | ||||||||
\(185\) | −8.99995 | − | 11.1441i | −0.0486484 | − | 0.0602385i | ||||
\(186\) | 233.574 | + | 56.3140i | 1.25577 | + | 0.302763i | ||||
\(187\) | 61.5198 | + | 61.5198i | 0.328983 | + | 0.328983i | ||||
\(188\) | −29.8410 | − | 29.8410i | −0.158729 | − | 0.158729i | ||||
\(189\) | 186.115 | + | 32.8966i | 0.984736 | + | 0.174056i | ||||
\(190\) | −6.38225 | + | 5.15428i | −0.0335908 | + | 0.0271278i | ||||
\(191\) | − | 12.6214i | − | 0.0660807i | −0.999454 | − | 0.0330403i | \(-0.989481\pi\) | ||
0.999454 | − | 0.0330403i | \(-0.0105190\pi\) | |||||||
\(192\) | −57.2971 | + | 35.0359i | −0.298423 | + | 0.182479i | ||||
\(193\) | 211.567 | + | 211.567i | 1.09620 | + | 1.09620i | 0.994851 | + | 0.101353i | \(0.0323171\pi\) |
0.101353 | + | 0.994851i | \(0.467683\pi\) | |||||||
\(194\) | − | 124.052i | − | 0.639442i | ||||||
\(195\) | −11.5628 | + | 32.4168i | −0.0592965 | + | 0.166240i | ||||
\(196\) | −37.4119 | + | 68.2872i | −0.190877 | + | 0.348404i | ||||
\(197\) | 102.520 | + | 102.520i | 0.520407 | + | 0.520407i | 0.917694 | − | 0.397288i | \(-0.130048\pi\) |
−0.397288 | + | 0.917694i | \(0.630048\pi\) | |||||||
\(198\) | 28.8748 | + | 89.4528i | 0.145832 | + | 0.451782i | ||||
\(199\) | −235.953 | −1.18570 | −0.592848 | − | 0.805314i | \(-0.701996\pi\) | ||||
−0.592848 | + | 0.805314i | \(0.701996\pi\) | |||||||
\(200\) | −119.710 | + | 77.2912i | −0.598551 | + | 0.386456i | ||||
\(201\) | 232.370 | + | 56.0237i | 1.15607 | + | 0.278725i | ||||
\(202\) | −29.5262 | − | 29.5262i | −0.146169 | − | 0.146169i | ||||
\(203\) | 333.123 | + | 85.2732i | 1.64100 | + | 0.420065i | ||||
\(204\) | −22.0044 | + | 91.2677i | −0.107865 | + | 0.447391i | ||||
\(205\) | 17.2041 | − | 161.630i | 0.0839227 | − | 0.788437i | ||||
\(206\) | −322.858 | −1.56727 | ||||||||
\(207\) | −90.6371 | − | 280.790i | −0.437860 | − | 1.35647i | ||||
\(208\) | 32.1749 | − | 32.1749i | 0.154687 | − | 0.154687i | ||||
\(209\) | 3.06600i | 0.0146699i | ||||||||
\(210\) | −205.820 | − | 138.771i | −0.980096 | − | 0.660815i | ||||
\(211\) | −89.6482 | −0.424873 | −0.212437 | − | 0.977175i | \(-0.568140\pi\) | ||||
−0.212437 | + | 0.977175i | \(0.568140\pi\) | |||||||
\(212\) | −53.7814 | − | 53.7814i | −0.253686 | − | 0.253686i | ||||
\(213\) | 237.399 | − | 145.164i | 1.11455 | − | 0.681522i | ||||
\(214\) | 24.1655i | 0.112923i | ||||||||
\(215\) | −167.559 | + | 135.320i | −0.779346 | + | 0.629397i | ||||
\(216\) | 100.283 | − | 116.732i | 0.464274 | − | 0.540427i | ||||
\(217\) | −58.8067 | + | 229.731i | −0.270999 | + | 1.05867i | ||||
\(218\) | 209.137 | − | 209.137i | 0.959346 | − | 0.959346i | ||||
\(219\) | −393.663 | − | 94.9110i | −1.79755 | − | 0.433384i | ||||
\(220\) | 3.71519 | − | 34.9035i | 0.0168872 | − | 0.158652i | ||||
\(221\) | 45.1866i | 0.204464i | ||||||||
\(222\) | −10.5999 | − | 17.3349i | −0.0477473 | − | 0.0780850i | ||||
\(223\) | 85.1659 | − | 85.1659i | 0.381910 | − | 0.381910i | −0.489880 | − | 0.871790i | \(-0.662959\pi\) |
0.871790 | + | 0.489880i | \(0.162959\pi\) | |||||||
\(224\) | 85.9244 | + | 145.049i | 0.383591 | + | 0.647541i | ||||
\(225\) | 142.395 | − | 174.209i | 0.632866 | − | 0.774262i | ||||
\(226\) | −239.682 | −1.06054 | ||||||||
\(227\) | 129.989 | − | 129.989i | 0.572639 | − | 0.572639i | −0.360226 | − | 0.932865i | \(-0.617300\pi\) |
0.932865 | + | 0.360226i | \(0.117300\pi\) | |||||||
\(228\) | −2.82261 | + | 1.72596i | −0.0123799 | + | 0.00757001i | ||||
\(229\) | 109.923 | 0.480011 | 0.240006 | − | 0.970771i | \(-0.422851\pi\) | ||||
0.240006 | + | 0.970771i | \(0.422851\pi\) | |||||||
\(230\) | −41.0173 | + | 385.350i | −0.178336 | + | 1.67543i | ||||
\(231\) | −88.6788 | + | 27.2584i | −0.383891 | + | 0.118002i | ||||
\(232\) | 197.984 | − | 197.984i | 0.853378 | − | 0.853378i | ||||
\(233\) | −218.319 | + | 218.319i | −0.936990 | + | 0.936990i | −0.998129 | − | 0.0611395i | \(-0.980527\pi\) |
0.0611395 | + | 0.998129i | \(0.480527\pi\) | |||||||
\(234\) | −22.2474 | + | 43.4561i | −0.0950745 | + | 0.185710i | ||||
\(235\) | 83.4295 | + | 103.306i | 0.355019 | + | 0.439600i | ||||
\(236\) | −36.7139 | −0.155567 | ||||||||
\(237\) | −256.661 | + | 156.942i | −1.08296 | + | 0.662204i | ||||
\(238\) | −315.726 | − | 80.8198i | −1.32658 | − | 0.339579i | ||||
\(239\) | 20.1742 | 0.0844109 | 0.0422054 | − | 0.999109i | \(-0.486562\pi\) | ||||
0.0422054 | + | 0.999109i | \(0.486562\pi\) | |||||||
\(240\) | −268.781 | + | 127.449i | −1.11992 | + | 0.531037i | ||||
\(241\) | 257.604i | 1.06890i | 0.845201 | + | 0.534449i | \(0.179481\pi\) | ||||
−0.845201 | + | 0.534449i | \(0.820519\pi\) | |||||||
\(242\) | 169.648 | + | 169.648i | 0.701024 | + | 0.701024i | ||||
\(243\) | −94.0713 | + | 224.053i | −0.387125 | + | 0.922027i | ||||
\(244\) | 20.6388 | 0.0845852 | ||||||||
\(245\) | 139.798 | − | 201.200i | 0.570605 | − | 0.821225i | ||||
\(246\) | 54.0394 | − | 224.140i | 0.219672 | − | 0.911137i | ||||
\(247\) | −1.12600 | + | 1.12600i | −0.00455869 | + | 0.00455869i | ||||
\(248\) | 136.535 | + | 136.535i | 0.550544 | + | 0.550544i | ||||
\(249\) | 5.59441 | − | 23.2040i | 0.0224675 | − | 0.0931887i | ||||
\(250\) | −263.836 | + | 133.115i | −1.05534 | + | 0.532460i | ||||
\(251\) | 191.569 | 0.763223 | 0.381612 | − | 0.924323i | \(-0.375369\pi\) | ||||
0.381612 | + | 0.924323i | \(0.375369\pi\) | |||||||
\(252\) | −75.0149 | − | 66.2943i | −0.297678 | − | 0.263073i | ||||
\(253\) | 102.412 | + | 102.412i | 0.404792 | + | 0.404792i | ||||
\(254\) | 14.2231 | 0.0559964 | ||||||||
\(255\) | 99.2439 | − | 278.234i | 0.389192 | − | 1.09111i | ||||
\(256\) | 263.325 | 1.02861 | ||||||||
\(257\) | 205.696 | − | 205.696i | 0.800374 | − | 0.800374i | −0.182779 | − | 0.983154i | \(-0.558509\pi\) |
0.983154 | + | 0.182779i | \(0.0585094\pi\) | |||||||
\(258\) | −260.642 | + | 159.377i | −1.01024 | + | 0.617739i | ||||
\(259\) | 17.2541 | − | 10.2210i | 0.0666182 | − | 0.0394633i | ||||
\(260\) | 14.1828 | − | 11.4540i | 0.0545493 | − | 0.0440538i | ||||
\(261\) | −201.472 | + | 393.537i | −0.771923 | + | 1.50780i | ||||
\(262\) | −192.932 | − | 192.932i | −0.736383 | − | 0.736383i | ||||
\(263\) | −4.82449 | + | 4.82449i | −0.0183441 | + | 0.0183441i | −0.716219 | − | 0.697875i | \(-0.754129\pi\) |
0.697875 | + | 0.716219i | \(0.254129\pi\) | |||||||
\(264\) | −17.7054 | + | 73.4367i | −0.0670657 | + | 0.278169i | ||||
\(265\) | 150.362 | + | 186.185i | 0.567404 | + | 0.702584i | ||||
\(266\) | −5.85358 | − | 9.88145i | −0.0220059 | − | 0.0371483i | ||||
\(267\) | −406.102 | + | 248.322i | −1.52098 | + | 0.930046i | ||||
\(268\) | −89.5269 | − | 89.5269i | −0.334056 | − | 0.334056i | ||||
\(269\) | 106.984i | 0.397708i | 0.980029 | + | 0.198854i | \(0.0637220\pi\) | ||||
−0.980029 | + | 0.198854i | \(0.936278\pi\) | |||||||
\(270\) | 232.430 | − | 218.716i | 0.860854 | − | 0.810059i | ||||
\(271\) | − | 187.036i | − | 0.690171i | −0.938571 | − | 0.345085i | \(-0.887850\pi\) | ||
0.938571 | − | 0.345085i | \(-0.112150\pi\) | |||||||
\(272\) | −276.158 | + | 276.158i | −1.01529 | + | 1.01529i | ||||
\(273\) | −42.5782 | − | 22.5568i | −0.155964 | − | 0.0826256i | ||||
\(274\) | − | 449.309i | − | 1.63981i | ||||||
\(275\) | −23.2485 | + | 107.970i | −0.0845399 | + | 0.392619i | ||||
\(276\) | −36.6308 | + | 151.934i | −0.132720 | + | 0.550485i | ||||
\(277\) | 95.7717 | − | 95.7717i | 0.345746 | − | 0.345746i | −0.512776 | − | 0.858522i | \(-0.671383\pi\) |
0.858522 | + | 0.512776i | \(0.171383\pi\) | |||||||
\(278\) | −381.786 | − | 381.786i | −1.37333 | − | 1.37333i | ||||
\(279\) | −271.393 | − | 138.941i | −0.972736 | − | 0.497995i | ||||
\(280\) | −82.9364 | − | 181.434i | −0.296201 | − | 0.647979i | ||||
\(281\) | − | 140.834i | − | 0.501189i | −0.968092 | − | 0.250594i | \(-0.919374\pi\) | ||
0.968092 | − | 0.250594i | \(-0.0806261\pi\) | |||||||
\(282\) | 98.2610 | + | 160.694i | 0.348443 | + | 0.569838i | ||||
\(283\) | −204.752 | + | 204.752i | −0.723504 | + | 0.723504i | −0.969317 | − | 0.245813i | \(-0.920945\pi\) |
0.245813 | + | 0.969317i | \(0.420945\pi\) | |||||||
\(284\) | −147.393 | −0.518989 | ||||||||
\(285\) | 9.40630 | − | 4.46022i | 0.0330046 | − | 0.0156499i | ||||
\(286\) | − | 23.9640i | − | 0.0837902i | ||||||
\(287\) | 220.452 | + | 56.4314i | 0.768124 | + | 0.196625i | ||||
\(288\) | −206.277 | + | 66.5848i | −0.716240 | + | 0.231197i | ||||
\(289\) | − | 98.8373i | − | 0.341998i | ||||||
\(290\) | 451.747 | − | 364.829i | 1.55775 | − | 1.25803i | ||||
\(291\) | −36.8958 | + | 153.033i | −0.126790 | + | 0.525888i | ||||
\(292\) | 151.669 | + | 151.669i | 0.519416 | + | 0.519416i | ||||
\(293\) | −158.208 | − | 158.208i | −0.539959 | − | 0.539959i | 0.383558 | − | 0.923517i | \(-0.374699\pi\) |
−0.923517 | + | 0.383558i | \(0.874699\pi\) | |||||||
\(294\) | 233.762 | − | 257.156i | 0.795110 | − | 0.874680i | ||||
\(295\) | 114.872 | + | 12.2272i | 0.389396 | + | 0.0414480i | ||||
\(296\) | − | 16.3292i | − | 0.0551661i | ||||||
\(297\) | −9.01527 | − | 118.939i | −0.0303544 | − | 0.400469i | ||||
\(298\) | 113.202 | + | 113.202i | 0.379873 | + | 0.379873i | ||||
\(299\) | 75.2224i | 0.251580i | ||||||||
\(300\) | −112.486 | + | 39.3774i | −0.374955 | + | 0.131258i | ||||
\(301\) | −153.680 | − | 259.427i | −0.510564 | − | 0.861885i | ||||
\(302\) | 181.935 | + | 181.935i | 0.602433 | + | 0.602433i | ||||
\(303\) | 27.6425 | + | 45.2060i | 0.0912293 | + | 0.149195i | ||||
\(304\) | −13.7631 | −0.0452732 | ||||||||
\(305\) | −64.5754 | − | 6.87352i | −0.211723 | − | 0.0225361i | ||||
\(306\) | 190.950 | − | 372.984i | 0.624020 | − | 1.21890i | ||||
\(307\) | 390.484 | + | 390.484i | 1.27194 | + | 1.27194i | 0.945071 | + | 0.326865i | \(0.105992\pi\) |
0.326865 | + | 0.945071i | \(0.394008\pi\) | |||||||
\(308\) | 47.6060 | + | 12.1862i | 0.154565 | + | 0.0395657i | ||||
\(309\) | 398.285 | + | 96.0253i | 1.28895 | + | 0.310761i | ||||
\(310\) | 251.596 | + | 311.537i | 0.811600 | + | 1.00496i | ||||
\(311\) | −314.164 | −1.01017 | −0.505087 | − | 0.863068i | \(-0.668540\pi\) | ||||
−0.505087 | + | 0.863068i | \(0.668540\pi\) | |||||||
\(312\) | −33.4721 | + | 20.4675i | −0.107282 | + | 0.0656009i | ||||
\(313\) | −138.521 | + | 138.521i | −0.442558 | + | 0.442558i | −0.892871 | − | 0.450313i | \(-0.851312\pi\) |
0.450313 | + | 0.892871i | \(0.351312\pi\) | |||||||
\(314\) | − | 42.9635i | − | 0.136827i | ||||||
\(315\) | 212.631 | + | 232.407i | 0.675019 | + | 0.737800i | ||||
\(316\) | 159.352 | 0.504278 | ||||||||
\(317\) | −171.788 | − | 171.788i | −0.541917 | − | 0.541917i | 0.382174 | − | 0.924090i | \(-0.375176\pi\) |
−0.924090 | + | 0.382174i | \(0.875176\pi\) | |||||||
\(318\) | 177.092 | + | 289.614i | 0.556895 | + | 0.910736i | ||||
\(319\) | − | 217.017i | − | 0.680304i | ||||||
\(320\) | −111.305 | − | 11.8475i | −0.347827 | − | 0.0370234i | ||||
\(321\) | 7.18738 | − | 29.8112i | 0.0223906 | − | 0.0928697i | ||||
\(322\) | −525.591 | − | 134.541i | −1.63227 | − | 0.417830i | ||||
\(323\) | 9.66445 | − | 9.66445i | 0.0299209 | − | 0.0299209i | ||||
\(324\) | 104.422 | − | 75.2547i | 0.322291 | − | 0.232268i | ||||
\(325\) | −48.1904 | + | 31.1142i | −0.148278 | + | 0.0957361i | ||||
\(326\) | − | 469.248i | − | 1.43941i | ||||||
\(327\) | −320.199 | + | 195.795i | −0.979203 | + | 0.598761i | ||||
\(328\) | 131.020 | − | 131.020i | 0.399452 | − | 0.399452i | ||||
\(329\) | −159.946 | + | 94.7486i | −0.486157 | + | 0.287990i | ||||
\(330\) | −52.6324 | + | 147.557i | −0.159492 | + | 0.447142i | ||||
\(331\) | −97.1798 | −0.293595 | −0.146797 | − | 0.989167i | \(-0.546897\pi\) | ||||
−0.146797 | + | 0.989167i | \(0.546897\pi\) | |||||||
\(332\) | −8.93996 | + | 8.93996i | −0.0269276 | + | 0.0269276i | ||||
\(333\) | 7.92049 | + | 24.5374i | 0.0237853 | + | 0.0736858i | ||||
\(334\) | 235.305 | 0.704505 | ||||||||
\(335\) | 250.299 | + | 309.931i | 0.747162 | + | 0.925168i | ||||
\(336\) | −122.361 | − | 398.072i | −0.364169 | − | 1.18474i | ||||
\(337\) | −142.405 | + | 142.405i | −0.422566 | + | 0.422566i | −0.886086 | − | 0.463520i | \(-0.846586\pi\) |
0.463520 | + | 0.886086i | \(0.346586\pi\) | |||||||
\(338\) | −273.714 | + | 273.714i | −0.809804 | + | 0.809804i | ||||
\(339\) | 295.677 | + | 71.2869i | 0.872205 | + | 0.210286i | ||||
\(340\) | −121.731 | + | 98.3097i | −0.358033 | + | 0.289146i | ||||
\(341\) | 149.661 | 0.438888 | ||||||||
\(342\) | 14.0526 | − | 4.53608i | 0.0410894 | − | 0.0132634i | ||||
\(343\) | 250.548 | + | 234.253i | 0.730461 | + | 0.682955i | ||||
\(344\) | −245.520 | −0.713722 | ||||||||
\(345\) | 165.212 | − | 463.177i | 0.478875 | − | 1.34254i | ||||
\(346\) | − | 250.691i | − | 0.724540i | ||||||
\(347\) | −42.5261 | − | 42.5261i | −0.122554 | − | 0.122554i | 0.643170 | − | 0.765723i | \(-0.277619\pi\) |
−0.765723 | + | 0.643170i | \(0.777619\pi\) | |||||||
\(348\) | 199.789 | − | 122.167i | 0.574107 | − | 0.351054i | ||||
\(349\) | 323.576 | 0.927152 | 0.463576 | − | 0.886057i | \(-0.346566\pi\) | ||||
0.463576 | + | 0.886057i | \(0.346566\pi\) | |||||||
\(350\) | −131.208 | − | 392.364i | −0.374879 | − | 1.12104i | ||||
\(351\) | 40.3698 | − | 46.9916i | 0.115014 | − | 0.133879i | ||||
\(352\) | 75.2353 | − | 75.2353i | 0.213737 | − | 0.213737i | ||||
\(353\) | −121.979 | − | 121.979i | −0.345550 | − | 0.345550i | 0.512899 | − | 0.858449i | \(-0.328572\pi\) |
−0.858449 | + | 0.512899i | \(0.828572\pi\) | |||||||
\(354\) | 159.298 | + | 38.4063i | 0.449995 | + | 0.108492i | ||||
\(355\) | 461.168 | + | 49.0876i | 1.29907 | + | 0.138275i | ||||
\(356\) | 252.135 | 0.708243 | ||||||||
\(357\) | 365.449 | + | 193.605i | 1.02367 | + | 0.542312i | ||||
\(358\) | 184.324 | + | 184.324i | 0.514872 | + | 0.514872i | ||||
\(359\) | 456.029 | 1.27028 | 0.635138 | − | 0.772399i | \(-0.280943\pi\) | ||||
0.635138 | + | 0.772399i | \(0.280943\pi\) | |||||||
\(360\) | 251.056 | − | 52.5120i | 0.697377 | − | 0.145867i | ||||
\(361\) | −360.518 | −0.998666 | ||||||||
\(362\) | −97.2581 | + | 97.2581i | −0.268669 | + | 0.268669i | ||||
\(363\) | −158.824 | − | 259.739i | −0.437533 | − | 0.715534i | ||||
\(364\) | 13.0080 | + | 21.9588i | 0.0357362 | + | 0.0603264i | ||||
\(365\) | −424.037 | − | 525.061i | −1.16175 | − | 1.43852i | ||||
\(366\) | −89.5499 | − | 21.5902i | −0.244672 | − | 0.0589896i | ||||
\(367\) | −52.7521 | − | 52.7521i | −0.143739 | − | 0.143739i | 0.631576 | − | 0.775314i | \(-0.282409\pi\) |
−0.775314 | + | 0.631576i | \(0.782409\pi\) | |||||||
\(368\) | −459.721 | + | 459.721i | −1.24924 | + | 1.24924i | ||||
\(369\) | −133.329 | + | 260.432i | −0.361324 | + | 0.705777i | ||||
\(370\) | 3.58438 | − | 33.6745i | 0.00968750 | − | 0.0910122i | ||||
\(371\) | −288.264 | + | 170.762i | −0.776993 | + | 0.460276i | ||||
\(372\) | 84.2494 | + | 137.780i | 0.226477 | + | 0.370376i | ||||
\(373\) | −269.362 | − | 269.362i | −0.722150 | − | 0.722150i | 0.246893 | − | 0.969043i | \(-0.420591\pi\) |
−0.969043 | + | 0.246893i | \(0.920591\pi\) | |||||||
\(374\) | 205.683i | 0.549956i | ||||||||
\(375\) | 365.066 | − | 85.7431i | 0.973509 | − | 0.228648i | ||||
\(376\) | 151.371i | 0.402583i | ||||||||
\(377\) | 79.7000 | − | 79.7000i | 0.211406 | − | 0.211406i | ||||
\(378\) | 256.133 | + | 366.118i | 0.677600 | + | 0.968567i | ||||
\(379\) | 253.497i | 0.668856i | 0.942421 | + | 0.334428i | \(0.108543\pi\) | ||||
−0.942421 | + | 0.334428i | \(0.891457\pi\) | |||||||
\(380\) | −5.48317 | − | 0.583638i | −0.0144294 | − | 0.00153589i | ||||
\(381\) | −17.5459 | − | 4.23027i | −0.0460523 | − | 0.0111031i | ||||
\(382\) | 21.0990 | − | 21.0990i | 0.0552330 | − | 0.0552330i | ||||
\(383\) | 162.755 | + | 162.755i | 0.424948 | + | 0.424948i | 0.886903 | − | 0.461955i | \(-0.152852\pi\) |
−0.461955 | + | 0.886903i | \(0.652852\pi\) | |||||||
\(384\) | −435.311 | − | 104.952i | −1.13362 | − | 0.273313i | ||||
\(385\) | −144.893 | − | 53.9834i | −0.376345 | − | 0.140217i | ||||
\(386\) | 707.348i | 1.83251i | ||||||||
\(387\) | 368.936 | − | 119.090i | 0.953324 | − | 0.307726i | ||||
\(388\) | 58.9602 | − | 58.9602i | 0.151959 | − | 0.151959i | ||||
\(389\) | 309.463 | 0.795534 | 0.397767 | − | 0.917486i | \(-0.369785\pi\) | ||||
0.397767 | + | 0.917486i | \(0.369785\pi\) | |||||||
\(390\) | −73.5200 | + | 34.8613i | −0.188513 | + | 0.0893878i | ||||
\(391\) | − | 645.635i | − | 1.65124i | ||||||
\(392\) | 268.085 | − | 78.3089i | 0.683889 | − | 0.199768i | ||||
\(393\) | 180.624 | + | 295.389i | 0.459602 | + | 0.751625i | ||||
\(394\) | 342.763i | 0.869956i | ||||||||
\(395\) | −498.586 | − | 53.0704i | −1.26224 | − | 0.134355i | ||||
\(396\) | −28.7920 | + | 56.2396i | −0.0727070 | + | 0.142019i | ||||
\(397\) | −463.385 | − | 463.385i | −1.16722 | − | 1.16722i | −0.982859 | − | 0.184357i | \(-0.940980\pi\) |
−0.184357 | − | 0.982859i | \(-0.559020\pi\) | |||||||
\(398\) | −394.440 | − | 394.440i | −0.991055 | − | 0.991055i | ||||
\(399\) | 4.28215 | + | 13.9310i | 0.0107322 | + | 0.0349148i | ||||
\(400\) | −484.670 | − | 104.361i | −1.21167 | − | 0.260902i | ||||
\(401\) | − | 516.485i | − | 1.28799i | −0.765028 | − | 0.643997i | \(-0.777275\pi\) | ||
0.765028 | − | 0.643997i | \(-0.222725\pi\) | |||||||
\(402\) | 294.796 | + | 482.104i | 0.733323 | + | 1.19926i | ||||
\(403\) | 54.9633 | + | 54.9633i | 0.136385 | + | 0.136385i | ||||
\(404\) | − | 28.0669i | − | 0.0694724i | ||||||
\(405\) | −351.783 | + | 200.683i | −0.868600 | + | 0.495514i | ||||
\(406\) | 414.327 | + | 699.427i | 1.02051 | + | 1.72273i | ||||
\(407\) | −8.94950 | − | 8.94950i | −0.0219889 | − | 0.0219889i | ||||
\(408\) | 287.292 | − | 175.673i | 0.704147 | − | 0.430570i | ||||
\(409\) | 119.076 | 0.291139 | 0.145570 | − | 0.989348i | \(-0.453499\pi\) | ||||
0.145570 | + | 0.989348i | \(0.453499\pi\) | |||||||
\(410\) | 298.954 | − | 241.434i | 0.729155 | − | 0.588863i | ||||
\(411\) | −133.635 | + | 554.278i | −0.325145 | + | 1.34861i | ||||
\(412\) | −153.450 | − | 153.450i | −0.372452 | − | 0.372452i | ||||
\(413\) | −40.1064 | + | 156.677i | −0.0971099 | + | 0.379364i | ||||
\(414\) | 317.876 | − | 620.909i | 0.767816 | − | 1.49978i | ||||
\(415\) | 30.9491 | − | 24.9943i | 0.0745760 | − | 0.0602273i | ||||
\(416\) | 55.2607 | 0.132838 | ||||||||
\(417\) | 357.428 | + | 584.532i | 0.857142 | + | 1.40175i | ||||
\(418\) | −5.12539 | + | 5.12539i | −0.0122617 | + | 0.0122617i | ||||
\(419\) | − | 732.322i | − | 1.74778i | −0.486120 | − | 0.873892i | \(-0.661588\pi\) | ||
0.486120 | − | 0.873892i | \(-0.338412\pi\) | |||||||
\(420\) | −31.8675 | − | 163.780i | −0.0758749 | − | 0.389952i | ||||
\(421\) | 307.320 | 0.729976 | 0.364988 | − | 0.931012i | \(-0.381073\pi\) | ||||
0.364988 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(422\) | −149.864 | − | 149.864i | −0.355127 | − | 0.355127i | ||||
\(423\) | −73.4229 | − | 227.461i | −0.173577 | − | 0.537734i | ||||
\(424\) | 272.812i | 0.643424i | ||||||||
\(425\) | 413.619 | − | 267.054i | 0.973220 | − | 0.628363i | ||||
\(426\) | 639.525 | + | 154.187i | 1.50123 | + | 0.361942i | ||||
\(427\) | 22.5459 | − | 88.0764i | 0.0528007 | − | 0.206268i | ||||
\(428\) | −11.4856 | + | 11.4856i | −0.0268354 | + | 0.0268354i | ||||
\(429\) | −7.12744 | + | 29.5626i | −0.0166141 | + | 0.0689104i | ||||
\(430\) | −506.320 | − | 53.8936i | −1.17749 | − | 0.125334i | ||||
\(431\) | − | 205.822i | − | 0.477546i | −0.971075 | − | 0.238773i | \(-0.923255\pi\) | ||
0.971075 | − | 0.238773i | \(-0.0767452\pi\) | |||||||
\(432\) | 533.909 | − | 40.4689i | 1.23590 | − | 0.0936779i | ||||
\(433\) | −291.861 | + | 291.861i | −0.674043 | + | 0.674043i | −0.958646 | − | 0.284603i | \(-0.908138\pi\) |
0.284603 | + | 0.958646i | \(0.408138\pi\) | |||||||
\(434\) | −482.343 | + | 285.731i | −1.11139 | + | 0.658366i | ||||
\(435\) | −665.795 | + | 315.702i | −1.53056 | + | 0.725752i | ||||
\(436\) | 198.801 | 0.455965 | ||||||||
\(437\) | 16.0885 | − | 16.0885i | 0.0368157 | − | 0.0368157i | ||||
\(438\) | −499.420 | − | 816.742i | −1.14023 | − | 1.86471i | ||||
\(439\) | −116.671 | −0.265765 | −0.132882 | − | 0.991132i | \(-0.542423\pi\) | ||||
−0.132882 | + | 0.991132i | \(0.542423\pi\) | |||||||
\(440\) | −97.9486 | + | 79.1029i | −0.222610 | + | 0.179779i | ||||
\(441\) | −364.859 | + | 247.707i | −0.827345 | + | 0.561695i | ||||
\(442\) | −75.5377 | + | 75.5377i | −0.170900 | + | 0.170900i | ||||
\(443\) | 282.021 | − | 282.021i | 0.636617 | − | 0.636617i | −0.313102 | − | 0.949719i | \(-0.601368\pi\) |
0.949719 | + | 0.313102i | \(0.101368\pi\) | |||||||
\(444\) | 3.20105 | − | 13.2770i | 0.00720957 | − | 0.0299032i | ||||
\(445\) | −788.888 | − | 83.9707i | −1.77278 | − | 0.188698i | ||||
\(446\) | 284.741 | 0.638433 | ||||||||
\(447\) | −105.980 | − | 173.318i | −0.237092 | − | 0.387736i | ||||
\(448\) | 38.8610 | − | 151.812i | 0.0867433 | − | 0.338866i | ||||
\(449\) | −407.834 | −0.908317 | −0.454158 | − | 0.890921i | \(-0.650060\pi\) | ||||
−0.454158 | + | 0.890921i | \(0.650060\pi\) | |||||||
\(450\) | 529.261 | − | 53.1832i | 1.17614 | − | 0.118185i | ||||
\(451\) | − | 143.616i | − | 0.318439i | ||||||
\(452\) | −113.918 | − | 113.918i | −0.252030 | − | 0.252030i | ||||
\(453\) | −170.327 | − | 278.550i | −0.375999 | − | 0.614902i | ||||
\(454\) | 434.602 | 0.957272 | ||||||||
\(455\) | −33.3867 | − | 73.0378i | −0.0733775 | − | 0.160523i | ||||
\(456\) | 11.5365 | + | 2.78142i | 0.0252994 | + | 0.00609961i | ||||
\(457\) | 461.473 | − | 461.473i | 1.00979 | − | 1.00979i | 0.00983627 | − | 0.999952i | \(-0.496869\pi\) |
0.999952 | − | 0.00983627i | \(-0.00313103\pi\) | |||||||
\(458\) | 183.756 | + | 183.756i | 0.401214 | + | 0.401214i | ||||
\(459\) | −346.495 | + | 403.330i | −0.754891 | + | 0.878714i | ||||
\(460\) | −202.647 | + | 163.657i | −0.440537 | + | 0.355776i | ||||
\(461\) | 788.797 | 1.71106 | 0.855528 | − | 0.517757i | \(-0.173233\pi\) | ||||
0.855528 | + | 0.517757i | \(0.173233\pi\) | |||||||
\(462\) | −193.810 | − | 102.676i | −0.419503 | − | 0.222242i | ||||
\(463\) | −548.664 | − | 548.664i | −1.18502 | − | 1.18502i | −0.978427 | − | 0.206592i | \(-0.933763\pi\) |
−0.206592 | − | 0.978427i | \(-0.566237\pi\) | |||||||
\(464\) | 974.173 | 2.09951 | ||||||||
\(465\) | −217.717 | − | 459.150i | −0.468208 | − | 0.987419i | ||||
\(466\) | −729.920 | −1.56635 | ||||||||
\(467\) | −299.104 | + | 299.104i | −0.640480 | + | 0.640480i | −0.950673 | − | 0.310194i | \(-0.899606\pi\) |
0.310194 | + | 0.950673i | \(0.399606\pi\) | |||||||
\(468\) | −31.2280 | + | 10.0802i | −0.0667266 | + | 0.0215389i | ||||
\(469\) | −479.857 | + | 284.258i | −1.02315 | + | 0.606094i | ||||
\(470\) | −33.2272 | + | 312.163i | −0.0706961 | + | 0.664176i | ||||
\(471\) | −12.7783 | + | 53.0009i | −0.0271302 | + | 0.112528i | ||||
\(472\) | 93.1173 | + | 93.1173i | 0.197283 | + | 0.197283i | ||||
\(473\) | −134.562 | + | 134.562i | −0.284486 | + | 0.284486i | ||||
\(474\) | −691.414 | − | 166.698i | −1.45868 | − | 0.351683i | ||||
\(475\) | 16.9616 | + | 3.65222i | 0.0357086 | + | 0.00768888i | ||||
\(476\) | −111.648 | − | 188.473i | −0.234554 | − | 0.395952i | ||||
\(477\) | −132.328 | − | 409.946i | −0.277417 | − | 0.859426i | ||||
\(478\) | 33.7249 | + | 33.7249i | 0.0705542 | + | 0.0705542i | ||||
\(479\) | 568.767i | 1.18740i | 0.804685 | + | 0.593702i | \(0.202334\pi\) | ||||
−0.804685 | + | 0.593702i | \(0.797666\pi\) | |||||||
\(480\) | −340.264 | − | 121.370i | −0.708884 | − | 0.252854i | ||||
\(481\) | − | 6.57345i | − | 0.0136662i | ||||||
\(482\) | −430.633 | + | 430.633i | −0.893430 | + | 0.893430i | ||||
\(483\) | 608.366 | + | 322.296i | 1.25956 | + | 0.667279i | ||||
\(484\) | 161.263i | 0.333188i | ||||||||
\(485\) | −204.113 | + | 164.841i | −0.420852 | + | 0.339878i | ||||
\(486\) | −531.803 | + | 217.288i | −1.09424 | + | 0.447094i | ||||
\(487\) | 382.818 | − | 382.818i | 0.786073 | − | 0.786073i | −0.194775 | − | 0.980848i | \(-0.562398\pi\) |
0.980848 | + | 0.194775i | \(0.0623976\pi\) | |||||||
\(488\) | −52.3461 | − | 52.3461i | −0.107267 | − | 0.107267i | ||||
\(489\) | −139.565 | + | 578.875i | −0.285409 | + | 1.18379i | ||||
\(490\) | 570.042 | − | 102.644i | 1.16335 | − | 0.209479i | ||||
\(491\) | − | 1.38553i | − | 0.00282185i | −0.999999 | − | 0.00141093i | \(-0.999551\pi\) | ||
0.999999 | − | 0.00141093i | \(-0.000449112\pi\) | |||||||
\(492\) | 132.215 | − | 80.8465i | 0.268730 | − | 0.164322i | ||||
\(493\) | −684.067 | + | 684.067i | −1.38756 | + | 1.38756i | ||||
\(494\) | −3.76462 | −0.00762070 | ||||||||
\(495\) | 108.815 | − | 166.376i | 0.219829 | − | 0.336113i | ||||
\(496\) | 671.816i | 1.35447i | ||||||||
\(497\) | −161.012 | + | 629.002i | −0.323969 | + | 1.26560i | ||||
\(498\) | 48.1418 | − | 29.4377i | 0.0966703 | − | 0.0591118i | ||||
\(499\) | 356.741i | 0.714913i | 0.933930 | + | 0.357456i | \(0.116356\pi\) | ||||
−0.933930 | + | 0.357456i | \(0.883644\pi\) | |||||||
\(500\) | −188.666 | − | 62.1300i | −0.377331 | − | 0.124260i | ||||
\(501\) | −290.277 | − | 69.9849i | −0.579396 | − | 0.139691i | ||||
\(502\) | 320.243 | + | 320.243i | 0.637934 | + | 0.637934i | ||||
\(503\) | 279.707 | + | 279.707i | 0.556078 | + | 0.556078i | 0.928188 | − | 0.372111i | \(-0.121366\pi\) |
−0.372111 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(504\) | 22.1180 | + | 358.402i | 0.0438849 | + | 0.711116i | ||||
\(505\) | −9.34737 | + | 87.8167i | −0.0185096 | + | 0.173894i | ||||
\(506\) | 342.402i | 0.676685i | ||||||||
\(507\) | 419.069 | − | 256.251i | 0.826566 | − | 0.505427i | ||||
\(508\) | 6.76005 | + | 6.76005i | 0.0133072 | + | 0.0133072i | ||||
\(509\) | − | 493.836i | − | 0.970208i | −0.874457 | − | 0.485104i | \(-0.838782\pi\) | ||
0.874457 | − | 0.485104i | \(-0.161218\pi\) | |||||||
\(510\) | 631.024 | − | 299.215i | 1.23730 | − | 0.586696i | ||||
\(511\) | 812.937 | − | 481.568i | 1.59087 | − | 0.942403i | ||||
\(512\) | 18.0214 | + | 18.0214i | 0.0351981 | + | 0.0351981i | ||||
\(513\) | −18.6847 | + | 1.41625i | −0.0364225 | + | 0.00276073i | ||||
\(514\) | 687.719 | 1.33797 | ||||||||
\(515\) | 429.016 | + | 531.226i | 0.833040 | + | 1.03151i | ||||
\(516\) | −199.629 | − | 48.1300i | −0.386879 | − | 0.0932752i | ||||
\(517\) | 82.9618 | + | 82.9618i | 0.160468 | + | 0.160468i | ||||
\(518\) | 45.9297 | + | 11.7571i | 0.0886674 | + | 0.0226972i | ||||
\(519\) | −74.5612 | + | 309.258i | −0.143663 | + | 0.595873i | ||||
\(520\) | −65.0226 | − | 6.92112i | −0.125043 | − | 0.0133098i | ||||
\(521\) | −16.2593 | −0.0312079 | −0.0156039 | − | 0.999878i | \(-0.504967\pi\) | ||||
−0.0156039 | + | 0.999878i | \(0.504967\pi\) | |||||||
\(522\) | −994.667 | + | 321.072i | −1.90549 | + | 0.615080i | ||||
\(523\) | 629.367 | − | 629.367i | 1.20338 | − | 1.20338i | 0.230246 | − | 0.973132i | \(-0.426047\pi\) |
0.973132 | − | 0.230246i | \(-0.0739530\pi\) | |||||||
\(524\) | − | 183.397i | − | 0.349993i | ||||||
\(525\) | 45.1631 | + | 523.054i | 0.0860249 | + | 0.996293i | ||||
\(526\) | −16.1301 | −0.0306655 | ||||||||
\(527\) | −471.751 | − | 471.751i | −0.895163 | − | 0.895163i | ||||
\(528\) | −224.231 | + | 137.112i | −0.424680 | + | 0.259682i | ||||
\(529\) | − | 545.792i | − | 1.03174i | ||||||
\(530\) | −59.8842 | + | 562.600i | −0.112989 | + | 1.06151i | ||||
\(531\) | −185.091 | − | 94.7580i | −0.348571 | − | 0.178452i | ||||
\(532\) | 1.91439 | − | 7.47866i | 0.00359849 | − | 0.0140576i | ||||
\(533\) | 52.7433 | − | 52.7433i | 0.0989555 | − | 0.0989555i | ||||
\(534\) | −1093.99 | − | 263.758i | −2.04867 | − | 0.493928i | ||||
\(535\) | 39.7616 | − | 32.1113i | 0.0743208 | − | 0.0600212i | ||||
\(536\) | 454.134i | 0.847265i | ||||||||
\(537\) | −172.564 | − | 282.209i | −0.321349 | − | 0.525528i | ||||
\(538\) | −178.843 | + | 178.843i | −0.332421 | + | 0.332421i | ||||
\(539\) | 104.010 | − | 189.847i | 0.192968 | − | 0.352221i | ||||
\(540\) | 214.424 | + | 6.51832i | 0.397082 | + | 0.0120710i | ||||
\(541\) | 577.099 | 1.06673 | 0.533364 | − | 0.845886i | \(-0.320928\pi\) | ||||
0.533364 | + | 0.845886i | \(0.320928\pi\) | |||||||
\(542\) | 312.666 | − | 312.666i | 0.576874 | − | 0.576874i | ||||
\(543\) | 148.907 | − | 91.0532i | 0.274230 | − | 0.167685i | ||||
\(544\) | −474.303 | −0.871881 | ||||||||
\(545\) | −622.015 | − | 66.2084i | −1.14131 | − | 0.121483i | ||||
\(546\) | −33.4695 | − | 108.885i | −0.0612994 | − | 0.199423i | ||||
\(547\) | −289.511 | + | 289.511i | −0.529270 | + | 0.529270i | −0.920355 | − | 0.391084i | \(-0.872100\pi\) |
0.391084 | + | 0.920355i | \(0.372100\pi\) | |||||||
\(548\) | 213.551 | − | 213.551i | 0.389691 | − | 0.389691i | ||||
\(549\) | 104.050 | + | 53.2684i | 0.189526 | + | 0.0970280i | ||||
\(550\) | −219.356 | + | 141.628i | −0.398829 | + | 0.257505i | ||||
\(551\) | −34.0923 | −0.0618735 | ||||||||
\(552\) | 478.257 | − | 292.443i | 0.866407 | − | 0.529788i | ||||
\(553\) | 174.077 | − | 680.037i | 0.314786 | − | 1.22972i | ||||
\(554\) | 320.200 | 0.577979 | ||||||||
\(555\) | −14.4373 | + | 40.4756i | −0.0260132 | + | 0.0729290i | ||||
\(556\) | − | 362.915i | − | 0.652726i | ||||||
\(557\) | 12.4652 | + | 12.4652i | 0.0223792 | + | 0.0223792i | 0.718208 | − | 0.695829i | \(-0.244963\pi\) |
−0.695829 | + | 0.718208i | \(0.744963\pi\) | |||||||
\(558\) | −221.420 | − | 685.949i | −0.396809 | − | 1.22930i | ||||
\(559\) | −98.8363 | −0.176809 | ||||||||
\(560\) | 242.327 | − | 650.413i | 0.432728 | − | 1.16145i | ||||
\(561\) | 61.1750 | − | 253.736i | 0.109046 | − | 0.452292i | ||||
\(562\) | 235.430 | − | 235.430i | 0.418915 | − | 0.418915i | ||||
\(563\) | 689.690 | + | 689.690i | 1.22503 | + | 1.22503i | 0.965823 | + | 0.259204i | \(0.0834602\pi\) |
0.259204 | + | 0.965823i | \(0.416540\pi\) | |||||||
\(564\) | −29.6737 | + | 123.078i | −0.0526130 | + | 0.218223i | ||||
\(565\) | 318.491 | + | 394.369i | 0.563701 | + | 0.697999i | ||||
\(566\) | −684.560 | −1.20947 | ||||||||
\(567\) | −207.080 | − | 527.832i | −0.365220 | − | 0.930921i | ||||
\(568\) | 373.832 | + | 373.832i | 0.658155 | + | 0.658155i | ||||
\(569\) | 44.3368 | 0.0779205 | 0.0389602 | − | 0.999241i | \(-0.487595\pi\) | ||||
0.0389602 | + | 0.999241i | \(0.487595\pi\) | |||||||
\(570\) | 23.1805 | + | 8.26829i | 0.0406675 | + | 0.0145058i | ||||
\(571\) | 89.1696 | 0.156164 | 0.0780819 | − | 0.996947i | \(-0.475120\pi\) | ||||
0.0780819 | + | 0.996947i | \(0.475120\pi\) | |||||||
\(572\) | 11.3898 | − | 11.3898i | 0.0199122 | − | 0.0199122i | ||||
\(573\) | −32.3036 | + | 19.7529i | −0.0563762 | + | 0.0344728i | ||||
\(574\) | 274.190 | + | 462.861i | 0.477683 | + | 0.806378i | ||||
\(575\) | 688.553 | − | 444.566i | 1.19748 | − | 0.773159i | ||||
\(576\) | 179.344 | + | 91.8155i | 0.311361 | + | 0.159402i | ||||
\(577\) | 146.556 | + | 146.556i | 0.253997 | + | 0.253997i | 0.822607 | − | 0.568610i | \(-0.192519\pi\) |
−0.568610 | + | 0.822607i | \(0.692519\pi\) | |||||||
\(578\) | 165.225 | − | 165.225i | 0.285856 | − | 0.285856i | ||||
\(579\) | 210.381 | − | 872.601i | 0.363353 | − | 1.50708i | ||||
\(580\) | 388.108 | + | 41.3109i | 0.669152 | + | 0.0712257i | ||||
\(581\) | 28.3854 | + | 47.9175i | 0.0488561 | + | 0.0824742i | ||||
\(582\) | −317.502 | + | 194.145i | −0.545535 | + | 0.333583i | ||||
\(583\) | 149.519 | + | 149.519i | 0.256465 | + | 0.256465i | ||||
\(584\) | − | 769.358i | − | 1.31739i | ||||||
\(585\) | 101.065 | − | 21.1391i | 0.172760 | − | 0.0361353i | ||||
\(586\) | − | 528.948i | − | 0.902642i | ||||||
\(587\) | 85.7254 | − | 85.7254i | 0.146040 | − | 0.146040i | −0.630307 | − | 0.776346i | \(-0.717071\pi\) |
0.776346 | + | 0.630307i | \(0.217071\pi\) | |||||||
\(588\) | 233.327 | − | 11.1186i | 0.396815 | − | 0.0189092i | ||||
\(589\) | − | 23.5110i | − | 0.0399167i | ||||||
\(590\) | 171.589 | + | 212.469i | 0.290830 | + | 0.360118i | ||||
\(591\) | 101.945 | − | 422.840i | 0.172496 | − | 0.715465i | ||||
\(592\) | 40.1736 | − | 40.1736i | 0.0678608 | − | 0.0678608i | ||||
\(593\) | 607.214 | + | 607.214i | 1.02397 | + | 1.02397i | 0.999706 | + | 0.0242632i | \(0.00772398\pi\) |
0.0242632 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(594\) | 183.758 | − | 213.900i | 0.309357 | − | 0.360100i | ||||
\(595\) | 286.559 | + | 626.885i | 0.481612 | + | 1.05359i | ||||
\(596\) | 107.607i | 0.180549i | ||||||||
\(597\) | 369.275 | + | 603.906i | 0.618551 | + | 1.01157i | ||||
\(598\) | −125.748 | + | 125.748i | −0.210281 | + | 0.210281i | ||||
\(599\) | −214.278 | −0.357726 | −0.178863 | − | 0.983874i | \(-0.557242\pi\) | ||||
−0.178863 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(600\) | 385.172 | + | 185.426i | 0.641953 | + | 0.309044i | ||||
\(601\) | − | 674.896i | − | 1.12296i | −0.827492 | − | 0.561478i | \(-0.810233\pi\) | ||
0.827492 | − | 0.561478i | \(-0.189767\pi\) | |||||||
\(602\) | 176.777 | − | 690.585i | 0.293649 | − | 1.14715i | ||||
\(603\) | −220.278 | − | 682.414i | −0.365304 | − | 1.13170i | ||||
\(604\) | 172.942i | 0.286328i | ||||||||
\(605\) | 53.7068 | − | 504.565i | 0.0887716 | − | 0.833992i | ||||
\(606\) | −29.3607 | + | 121.780i | −0.0484500 | + | 0.200957i | ||||
\(607\) | −428.929 | − | 428.929i | −0.706638 | − | 0.706638i | 0.259189 | − | 0.965827i | \(-0.416545\pi\) |
−0.965827 | + | 0.259189i | \(0.916545\pi\) | |||||||
\(608\) | −11.8191 | − | 11.8191i | −0.0194393 | − | 0.0194393i | ||||
\(609\) | −303.098 | − | 986.060i | −0.497698 | − | 1.61915i | ||||
\(610\) | −96.4594 | − | 119.440i | −0.158130 | − | 0.195803i | ||||
\(611\) | 60.9358i | 0.0997313i | ||||||||
\(612\) | 268.031 | − | 86.5185i | 0.437959 | − | 0.141370i | ||||
\(613\) | −134.802 | − | 134.802i | −0.219905 | − | 0.219905i | 0.588553 | − | 0.808458i | \(-0.299698\pi\) |
−0.808458 | + | 0.588553i | \(0.799698\pi\) | |||||||
\(614\) | 1305.53i | 2.12628i | ||||||||
\(615\) | −440.604 | + | 208.923i | −0.716430 | + | 0.339712i | ||||
\(616\) | −89.8351 | − | 151.651i | −0.145836 | − | 0.246187i | ||||
\(617\) | 525.987 | + | 525.987i | 0.852491 | + | 0.852491i | 0.990439 | − | 0.137948i | \(-0.0440507\pi\) |
−0.137948 | + | 0.990439i | \(0.544051\pi\) | |||||||
\(618\) | 505.283 | + | 826.331i | 0.817610 | + | 1.33711i | ||||
\(619\) | 957.834 | 1.54739 | 0.773695 | − | 0.633558i | \(-0.218406\pi\) | ||||
0.773695 | + | 0.633558i | \(0.218406\pi\) | |||||||
\(620\) | −28.4891 | + | 267.650i | −0.0459502 | + | 0.431693i | ||||
\(621\) | −576.812 | + | 671.425i | −0.928844 | + | 1.08120i | ||||
\(622\) | −525.184 | − | 525.184i | −0.844347 | − | 0.844347i | ||||
\(623\) | 275.433 | − | 1075.99i | 0.442107 | − | 1.72711i | ||||
\(624\) | −132.704 | − | 31.9945i | −0.212667 | − | 0.0512733i | ||||
\(625\) | 569.613 | + | 257.228i | 0.911381 | + | 0.411564i | ||||
\(626\) | −463.126 | −0.739817 | ||||||||
\(627\) | 7.84721 | − | 4.79840i | 0.0125155 | − | 0.00765295i | ||||
\(628\) | 20.4200 | − | 20.4200i | 0.0325159 | − | 0.0325159i | ||||
\(629\) | 56.4200i | 0.0896980i | ||||||||
\(630\) | −33.0596 | + | 743.963i | −0.0524756 | + | 1.18089i | ||||
\(631\) | −482.882 | −0.765265 | −0.382633 | − | 0.923901i | \(-0.624983\pi\) | ||||
−0.382633 | + | 0.923901i | \(0.624983\pi\) | |||||||
\(632\) | −404.164 | − | 404.164i | −0.639499 | − | 0.639499i | ||||
\(633\) | 140.302 | + | 229.448i | 0.221647 | + | 0.362477i | ||||
\(634\) | − | 574.349i | − | 0.905914i | ||||||
\(635\) | −18.8997 | − | 23.4025i | −0.0297634 | − | 0.0368543i | ||||
\(636\) | −53.4800 | + | 221.819i | −0.0840880 | + | 0.348773i | ||||
\(637\) | 107.920 | − | 31.5239i | 0.169419 | − | 0.0494881i | ||||
\(638\) | 362.784 | − | 362.784i | 0.568627 | − | 0.568627i | ||||
\(639\) | −743.074 | − | 380.419i | −1.16287 | − | 0.595334i | ||||
\(640\) | −468.899 | − | 580.610i | −0.732654 | − | 0.907204i | ||||
\(641\) | 618.098i | 0.964272i | 0.876096 | + | 0.482136i | \(0.160139\pi\) | ||||
−0.876096 | + | 0.482136i | \(0.839861\pi\) | |||||||
\(642\) | 61.8499 | − | 37.8199i | 0.0963395 | − | 0.0589094i | ||||
\(643\) | −235.650 | + | 235.650i | −0.366485 | + | 0.366485i | −0.866193 | − | 0.499709i | \(-0.833440\pi\) |
0.499709 | + | 0.866193i | \(0.333440\pi\) | |||||||
\(644\) | −185.861 | − | 313.752i | −0.288604 | − | 0.487193i | ||||
\(645\) | 608.579 | + | 217.075i | 0.943533 | + | 0.336551i | ||||
\(646\) | 32.3118 | 0.0500183 | ||||||||
\(647\) | −129.060 | + | 129.060i | −0.199474 | + | 0.199474i | −0.799775 | − | 0.600300i | \(-0.795048\pi\) |
0.600300 | + | 0.799775i | \(0.295048\pi\) | |||||||
\(648\) | −455.714 | − | 73.9775i | −0.703263 | − | 0.114163i | ||||
\(649\) | 102.069 | 0.157272 | ||||||||
\(650\) | −132.572 | − | 28.5459i | −0.203957 | − | 0.0439167i | ||||
\(651\) | 680.013 | − | 209.025i | 1.04457 | − | 0.321082i | ||||
\(652\) | 223.027 | − | 223.027i | 0.342066 | − | 0.342066i | ||||
\(653\) | −607.844 | + | 607.844i | −0.930849 | + | 0.930849i | −0.997759 | − | 0.0669099i | \(-0.978686\pi\) |
0.0669099 | + | 0.997759i | \(0.478686\pi\) | |||||||
\(654\) | −862.579 | − | 207.965i | −1.31893 | − | 0.317990i | ||||
\(655\) | −61.0782 | + | 573.818i | −0.0932492 | + | 0.876059i | ||||
\(656\) | 644.681 | 0.982745 | ||||||||
\(657\) | 373.178 | + | 1156.09i | 0.568004 | + | 1.75965i | ||||
\(658\) | −425.768 | − | 108.989i | −0.647064 | − | 0.165636i | ||||
\(659\) | −795.993 | −1.20788 | −0.603940 | − | 0.797030i | \(-0.706403\pi\) | ||||
−0.603940 | + | 0.797030i | \(0.706403\pi\) | |||||||
\(660\) | −95.1474 | + | 45.1164i | −0.144163 | + | 0.0683582i | ||||
\(661\) | − | 353.138i | − | 0.534248i | −0.963662 | − | 0.267124i | \(-0.913927\pi\) | ||
0.963662 | − | 0.267124i | \(-0.0860734\pi\) | |||||||
\(662\) | −162.454 | − | 162.454i | −0.245399 | − | 0.245399i | ||||
\(663\) | 115.652 | − | 70.7185i | 0.174437 | − | 0.106664i | ||||
\(664\) | 45.3488 | 0.0682964 | ||||||||
\(665\) | −8.48052 | + | 22.7620i | −0.0127527 | + | 0.0342285i | ||||
\(666\) | −27.7782 | + | 54.2593i | −0.0417090 | + | 0.0814704i | ||||
\(667\) | −1138.77 | + | 1138.77i | −1.70730 | + | 1.70730i | ||||
\(668\) | 111.837 | + | 111.837i | 0.167421 | + | 0.167421i | ||||
\(669\) | −351.263 | − | 84.6885i | −0.525058 | − | 0.126590i | ||||
\(670\) | −99.6858 | + | 936.529i | −0.148785 | + | 1.39780i | ||||
\(671\) | −57.3785 | −0.0855119 | ||||||||
\(672\) | 236.769 | − | 446.924i | 0.352334 | − | 0.665066i | ||||
\(673\) | 45.1352 | + | 45.1352i | 0.0670657 | + | 0.0670657i | 0.739844 | − | 0.672778i | \(-0.234899\pi\) |
−0.672778 | + | 0.739844i | \(0.734899\pi\) | |||||||
\(674\) | −476.112 | −0.706398 | ||||||||
\(675\) | −668.728 | − | 91.8064i | −0.990708 | − | 0.136009i | ||||
\(676\) | −260.185 | −0.384890 | ||||||||
\(677\) | −812.127 | + | 812.127i | −1.19960 | + | 1.19960i | −0.225309 | + | 0.974287i | \(0.572339\pi\) |
−0.974287 | + | 0.225309i | \(0.927661\pi\) | |||||||
\(678\) | 375.110 | + | 613.449i | 0.553260 | + | 0.904791i | ||||
\(679\) | −187.206 | − | 316.022i | −0.275708 | − | 0.465423i | ||||
\(680\) | 558.090 | + | 59.4041i | 0.820720 | + | 0.0873589i | ||||
\(681\) | −536.135 | − | 129.260i | −0.787276 | − | 0.189810i | ||||
\(682\) | 250.186 | + | 250.186i | 0.366841 | + | 0.366841i | ||||
\(683\) | 654.128 | − | 654.128i | 0.957728 | − | 0.957728i | −0.0414145 | − | 0.999142i | \(-0.513186\pi\) |
0.999142 | + | 0.0414145i | \(0.0131864\pi\) | |||||||
\(684\) | 8.83495 | + | 4.52307i | 0.0129166 | + | 0.00661268i | ||||
\(685\) | −739.287 | + | 597.045i | −1.07925 | + | 0.871599i | ||||
\(686\) | 27.2396 | + | 810.435i | 0.0397078 | + | 1.18139i | ||||
\(687\) | −172.033 | − | 281.339i | −0.250411 | − | 0.409518i | ||||
\(688\) | −604.038 | − | 604.038i | −0.877962 | − | 0.877962i | ||||
\(689\) | 109.823i | 0.159394i | ||||||||
\(690\) | 1050.47 | − | 498.104i | 1.52242 | − | 0.721891i | ||||
\(691\) | 1308.29i | 1.89333i | 0.322219 | + | 0.946665i | \(0.395571\pi\) | ||||
−0.322219 | + | 0.946665i | \(0.604429\pi\) | |||||||
\(692\) | 119.150 | − | 119.150i | 0.172182 | − | 0.172182i | ||||
\(693\) | 208.551 | + | 184.307i | 0.300939 | + | 0.265955i | ||||
\(694\) | − | 142.180i | − | 0.204871i | ||||||
\(695\) | −120.865 | + | 1135.50i | −0.173907 | + | 1.63382i | ||||
\(696\) | −816.576 | − | 196.874i | −1.17324 | − | 0.282865i | ||||
\(697\) | −452.697 | + | 452.697i | −0.649493 | + | 0.649493i | ||||
\(698\) | 540.917 | + | 540.917i | 0.774953 | + | 0.774953i | ||||
\(699\) | 900.447 | + | 217.095i | 1.28819 | + | 0.310579i | ||||
\(700\) | 124.124 | − | 248.847i | 0.177320 | − | 0.355496i | ||||
\(701\) | − | 793.166i | − | 1.13148i | −0.824584 | − | 0.565739i | \(-0.808591\pi\) | ||
0.824584 | − | 0.565739i | \(-0.191409\pi\) | |||||||
\(702\) | 146.041 | − | 11.0695i | 0.208035 | − | 0.0157685i | ||||
\(703\) | −1.40592 | + | 1.40592i | −0.00199989 | + | 0.00199989i | ||||
\(704\) | −98.8997 | −0.140483 | ||||||||
\(705\) | 133.834 | − | 375.209i | 0.189836 | − | 0.532211i | ||||
\(706\) | − | 407.822i | − | 0.577651i | ||||||
\(707\) | −119.776 | − | 30.6604i | −0.169414 | − | 0.0433669i | ||||
\(708\) | 57.4584 | + | 93.9665i | 0.0811560 | + | 0.132721i | ||||
\(709\) | 283.272i | 0.399538i | 0.979843 | + | 0.199769i | \(0.0640192\pi\) | ||||
−0.979843 | + | 0.199769i | \(0.935981\pi\) | |||||||
\(710\) | 688.869 | + | 852.987i | 0.970238 | + | 1.20139i | ||||
\(711\) | 803.365 | + | 411.285i | 1.12991 | + | 0.578459i | ||||
\(712\) | −639.489 | − | 639.489i | −0.898158 | − | 0.898158i | ||||
\(713\) | −785.326 | − | 785.326i | −1.10144 | − | 1.10144i | ||||
\(714\) | 287.269 | + | 934.563i | 0.402337 | + | 1.30891i | ||||
\(715\) | −39.4300 | + | 31.8435i | −0.0551469 | + | 0.0445364i | ||||
\(716\) | 175.214i | 0.244712i | ||||||||
\(717\) | −31.5733 | − | 51.6344i | −0.0440353 | − | 0.0720145i | ||||
\(718\) | 762.337 | + | 762.337i | 1.06175 | + | 1.06175i | ||||
\(719\) | − | 639.857i | − | 0.889927i | −0.895549 | − | 0.444963i | \(-0.853217\pi\) | ||
0.895549 | − | 0.444963i | \(-0.146783\pi\) | |||||||
\(720\) | 746.848 | + | 488.464i | 1.03729 | + | 0.678423i | ||||
\(721\) | −822.481 | + | 487.222i | −1.14075 | + | 0.675758i | ||||
\(722\) | −602.673 | − | 602.673i | −0.834727 | − | 0.834727i | ||||
\(723\) | 659.320 | − | 403.159i | 0.911922 | − | 0.557620i | ||||
\(724\) | −92.4510 | −0.127695 | ||||||||
\(725\) | −1200.57 | − | 258.510i | −1.65596 | − | 0.356566i | ||||
\(726\) | 168.697 | − | 699.706i | 0.232365 | − | 0.963782i | ||||
\(727\) | −65.1910 | − | 65.1910i | −0.0896713 | − | 0.0896713i | 0.660848 | − | 0.750520i | \(-0.270197\pi\) |
−0.750520 | + | 0.660848i | \(0.770197\pi\) | |||||||
\(728\) | 22.7020 | − | 88.6863i | 0.0311841 | − | 0.121822i | ||||
\(729\) | 720.671 | − | 109.881i | 0.988575 | − | 0.150729i | ||||
\(730\) | 168.880 | − | 1586.59i | 0.231342 | − | 2.17342i | ||||
\(731\) | 848.314 | 1.16048 | ||||||||
\(732\) | −32.3004 | − | 52.8235i | −0.0441262 | − | 0.0721632i | ||||
\(733\) | −631.927 | + | 631.927i | −0.862110 | + | 0.862110i | −0.991583 | − | 0.129473i | \(-0.958671\pi\) |
0.129473 | + | 0.991583i | \(0.458671\pi\) | |||||||
\(734\) | − | 176.370i | − | 0.240286i | ||||||
\(735\) | −733.746 | − | 42.9187i | −0.998294 | − | 0.0583928i | ||||
\(736\) | −789.576 | −1.07279 | ||||||||
\(737\) | 248.896 | + | 248.896i | 0.337715 | + | 0.337715i | ||||
\(738\) | −658.243 | + | 212.476i | −0.891928 | + | 0.287908i | ||||
\(739\) | 235.665i | 0.318898i | 0.987206 | + | 0.159449i | \(0.0509717\pi\) | ||||
−0.987206 | + | 0.159449i | \(0.949028\pi\) | |||||||
\(740\) | 17.7087 | − | 14.3015i | 0.0239306 | − | 0.0193263i | ||||
\(741\) | 4.64413 | + | 1.11969i | 0.00626738 | + | 0.00151105i | ||||
\(742\) | −767.348 | − | 196.427i | −1.03416 | − | 0.264726i | ||||
\(743\) | −122.316 | + | 122.316i | −0.164625 | + | 0.164625i | −0.784612 | − | 0.619987i | \(-0.787138\pi\) |
0.619987 | + | 0.784612i | \(0.287138\pi\) | |||||||
\(744\) | 135.770 | − | 563.133i | 0.182486 | − | 0.756899i | ||||
\(745\) | 35.8374 | − | 336.685i | 0.0481039 | − | 0.451927i | ||||
\(746\) | − | 900.577i | − | 1.20721i | ||||||
\(747\) | −68.1443 | + | 21.9965i | −0.0912240 | + | 0.0294465i | ||||
\(748\) | −97.7587 | + | 97.7587i | −0.130693 | + | 0.130693i | ||||
\(749\) | 36.4680 | + | 61.5618i | 0.0486889 | + | 0.0821919i | ||||
\(750\) | 753.611 | + | 466.940i | 1.00481 | + | 0.622586i | ||||
\(751\) | 314.517 | 0.418797 | 0.209399 | − | 0.977830i | \(-0.432849\pi\) | ||||
0.209399 | + | 0.977830i | \(0.432849\pi\) | |||||||
\(752\) | −372.409 | + | 372.409i | −0.495225 | + | 0.495225i | ||||
\(753\) | −299.812 | − | 490.307i | −0.398157 | − | 0.651138i | ||||
\(754\) | 266.467 | 0.353404 | ||||||||
\(755\) | 57.5966 | − | 541.109i | 0.0762869 | − | 0.716700i | ||||
\(756\) | −52.2747 | + | 295.748i | −0.0691464 | + | 0.391201i | ||||
\(757\) | 782.579 | − | 782.579i | 1.03379 | − | 1.03379i | 0.0343817 | − | 0.999409i | \(-0.489054\pi\) |
0.999409 | − | 0.0343817i | \(-0.0109462\pi\) | |||||||
\(758\) | −423.766 | + | 423.766i | −0.559058 | + | 0.559058i | ||||
\(759\) | 101.838 | − | 422.396i | 0.134174 | − | 0.556516i | ||||
\(760\) | 12.4267 | + | 15.3872i | 0.0163509 | + | 0.0202463i | ||||
\(761\) | 78.7855 | 0.103529 | 0.0517644 | − | 0.998659i | \(-0.483515\pi\) | ||||
0.0517644 | + | 0.998659i | \(0.483515\pi\) | |||||||
\(762\) | −22.2596 | − | 36.4029i | −0.0292121 | − | 0.0477729i | ||||
\(763\) | 217.171 | − | 848.386i | 0.284627 | − | 1.11191i | ||||
\(764\) | 20.0562 | 0.0262515 | ||||||||
\(765\) | −867.439 | + | 181.438i | −1.13391 | + | 0.237173i | ||||
\(766\) | 544.150i | 0.710379i | ||||||||
\(767\) | 37.4852 | + | 37.4852i | 0.0488725 | + | 0.0488725i | ||||
\(768\) | −412.113 | − | 673.962i | −0.536605 | − | 0.877554i | ||||
\(769\) | −959.073 | −1.24717 | −0.623584 | − | 0.781756i | \(-0.714324\pi\) | ||||
−0.623584 | + | 0.781756i | \(0.714324\pi\) | |||||||
\(770\) | −151.972 | − | 332.459i | −0.197366 | − | 0.431764i | ||||
\(771\) | −848.386 | − | 204.543i | −1.10037 | − | 0.265296i | ||||
\(772\) | −336.193 | + | 336.193i | −0.435483 | + | 0.435483i | ||||
\(773\) | −313.143 | − | 313.143i | −0.405100 | − | 0.405100i | 0.474926 | − | 0.880026i | \(-0.342475\pi\) |
−0.880026 | + | 0.474926i | \(0.842475\pi\) | |||||||
\(774\) | 815.826 | + | 417.664i | 1.05404 | + | 0.539618i | ||||
\(775\) | 178.276 | − | 827.945i | 0.230033 | − | 1.06832i | ||||
\(776\) | −299.081 | −0.385414 | ||||||||
\(777\) | −53.1632 | − | 28.1644i | −0.0684211 | − | 0.0362477i | ||||
\(778\) | 517.324 | + | 517.324i | 0.664941 | + | 0.664941i | ||||
\(779\) | −22.5613 | −0.0289619 | ||||||||
\(780\) | −51.5122 | − | 18.3740i | −0.0660413 | − | 0.0235564i | ||||
\(781\) | 409.771 | 0.524674 | ||||||||
\(782\) | 1079.30 | − | 1079.30i | 1.38018 | − | 1.38018i | ||||
\(783\) | 1322.54 | − | 100.245i | 1.68907 | − | 0.128027i | ||||
\(784\) | 852.210 | + | 466.893i | 1.08700 | + | 0.595527i | ||||
\(785\) | −70.6916 | + | 57.0903i | −0.0900530 | + | 0.0727265i | ||||
\(786\) | −191.851 | + | 795.742i | −0.244085 | + | 1.01239i | ||||
\(787\) | 617.290 | + | 617.290i | 0.784358 | + | 0.784358i | 0.980563 | − | 0.196205i | \(-0.0628617\pi\) |
−0.196205 | + | 0.980563i | \(0.562862\pi\) | |||||||
\(788\) | −162.911 | + | 162.911i | −0.206739 | + | 0.206739i | ||||
\(789\) | 19.8984 | + | 4.79745i | 0.0252198 | + | 0.00608042i | ||||
\(790\) | −744.762 | − | 922.195i | −0.942736 | − | 1.16734i | ||||
\(791\) | −610.590 | + | 361.702i | −0.771922 | + | 0.457272i | ||||
\(792\) | 215.665 | − | 69.6153i | 0.272305 | − | 0.0878981i | ||||
\(793\) | −21.0724 | − | 21.0724i | −0.0265730 | − | 0.0265730i | ||||
\(794\) | − | 1549.27i | − | 1.95122i | ||||||
\(795\) | 241.205 | − | 676.227i | 0.303402 | − | 0.850599i | ||||
\(796\) | − | 374.944i | − | 0.471035i | ||||||
\(797\) | 843.997 | − | 843.997i | 1.05897 | − | 1.05897i | 0.0608184 | − | 0.998149i | \(-0.480629\pi\) |
0.998149 | − | 0.0608184i | \(-0.0193710\pi\) | |||||||
\(798\) | −16.1298 | + | 30.4466i | −0.0202128 | + | 0.0381537i | ||||
\(799\) | − | 523.013i | − | 0.654585i | ||||||
\(800\) | −326.592 | − | 505.833i | −0.408240 | − | 0.632291i | ||||
\(801\) | 1271.13 | + | 650.756i | 1.58692 | + | 0.812429i | ||||
\(802\) | 863.401 | − | 863.401i | 1.07656 | − | 1.07656i | ||||
\(803\) | −421.661 | − | 421.661i | −0.525107 | − | 0.525107i | ||||
\(804\) | −89.0251 | + | 369.250i | −0.110728 | + | 0.459266i | ||||
\(805\) | 477.036 | + | 1043.58i | 0.592592 | + | 1.29637i | ||||
\(806\) | 183.763i | 0.227993i | ||||||||
\(807\) | 273.817 | − | 167.433i | 0.339302 | − | 0.207476i | ||||
\(808\) | −71.1860 | + | 71.1860i | −0.0881014 | + | 0.0881014i | ||||
\(809\) | 56.0803 | 0.0693205 | 0.0346602 | − | 0.999399i | \(-0.488965\pi\) | ||||
0.0346602 | + | 0.999399i | \(0.488965\pi\) | |||||||
\(810\) | −923.549 | − | 252.591i | −1.14018 | − | 0.311841i | ||||
\(811\) | 882.859i | 1.08861i | 0.838889 | + | 0.544303i | \(0.183206\pi\) | ||||
−0.838889 | + | 0.544303i | \(0.816794\pi\) | |||||||
\(812\) | −135.504 | + | 529.353i | −0.166877 | + | 0.651912i | ||||
\(813\) | −478.706 | + | 292.718i | −0.588814 | + | 0.360047i | ||||
\(814\) | − | 29.9215i | − | 0.0367586i | ||||||
\(815\) | −772.094 | + | 623.540i | −0.947354 | + | 0.765080i | ||||
\(816\) | 1139.00 | + | 274.610i | 1.39584 | + | 0.336532i | ||||
\(817\) | 21.1390 | + | 21.1390i | 0.0258739 | + | 0.0258739i | ||||
\(818\) | 199.057 | + | 199.057i | 0.243346 | + | 0.243346i | ||||
\(819\) | 8.90379 | + | 144.278i | 0.0108715 | + | 0.176164i | ||||
\(820\) | 256.839 | + | 27.3384i | 0.313219 | + | 0.0333395i | ||||
\(821\) | − | 1159.68i | − | 1.41253i | −0.707949 | − | 0.706264i | \(-0.750379\pi\) | ||
0.707949 | − | 0.706264i | \(-0.249621\pi\) | |||||||
\(822\) | −1149.97 | + | 703.184i | −1.39900 | + | 0.855454i | ||||
\(823\) | 704.019 | + | 704.019i | 0.855430 | + | 0.855430i | 0.990796 | − | 0.135366i | \(-0.0432210\pi\) |
−0.135366 | + | 0.990796i | \(0.543221\pi\) | |||||||
\(824\) | 778.391i | 0.944649i | ||||||||
\(825\) | 312.727 | − | 109.474i | 0.379062 | − | 0.132696i | ||||
\(826\) | −328.960 | + | 194.870i | −0.398257 | + | 0.235920i | ||||
\(827\) | 572.404 | + | 572.404i | 0.692145 | + | 0.692145i | 0.962704 | − | 0.270558i | \(-0.0872082\pi\) |
−0.270558 | + | 0.962704i | \(0.587208\pi\) | |||||||
\(828\) | 446.192 | − | 144.028i | 0.538880 | − | 0.173947i | ||||
\(829\) | 463.044 | 0.558557 | 0.279279 | − | 0.960210i | \(-0.409905\pi\) | ||||
0.279279 | + | 0.960210i | \(0.409905\pi\) | |||||||
\(830\) | 93.5197 | + | 9.95441i | 0.112674 | + | 0.0119933i | ||||
\(831\) | −395.007 | − | 95.2349i | −0.475339 | − | 0.114603i | ||||
\(832\) | −36.3212 | − | 36.3212i | −0.0436552 | − | 0.0436552i | ||||
\(833\) | −926.277 | + | 270.570i | −1.11198 | + | 0.324814i | ||||
\(834\) | −379.646 | + | 1574.66i | −0.455210 | + | 1.88808i | ||||
\(835\) | −312.674 | − | 387.167i | −0.374460 | − | 0.463673i | ||||
\(836\) | −4.87206 | −0.00582783 | ||||||||
\(837\) | 69.1316 | + | 912.059i | 0.0825945 | + | 1.08968i | ||||
\(838\) | 1224.21 | − | 1224.21i | 1.46087 | − | 1.46087i | ||||
\(839\) | 401.831i | 0.478940i | 0.970904 | + | 0.239470i | \(0.0769737\pi\) | ||||
−0.970904 | + | 0.239470i | \(0.923026\pi\) | |||||||
\(840\) | −334.569 | + | 496.220i | −0.398297 | + | 0.590738i | ||||
\(841\) | 1572.11 | 1.86934 | ||||||||
\(842\) | 513.742 | + | 513.742i | 0.610145 | + | 0.610145i | ||||
\(843\) | −360.455 | + | 220.410i | −0.427586 | + | 0.261459i | ||||
\(844\) | − | 142.456i | − | 0.168787i | ||||||
\(845\) | 814.078 | + | 86.6519i | 0.963406 | + | 0.102547i | ||||
\(846\) | 257.504 | − | 502.984i | 0.304378 | − | 0.594543i | ||||
\(847\) | 688.192 | + | 176.164i | 0.812506 | + | 0.207986i | ||||
\(848\) | −671.181 | + | 671.181i | −0.791487 | + | 0.791487i | ||||
\(849\) | 844.490 | + | 203.604i | 0.994688 | + | 0.239816i | ||||
\(850\) | 1137.87 | + | 245.010i | 1.33867 | + | 0.288247i | ||||
\(851\) | 93.9227i | 0.110367i | ||||||||
\(852\) | 230.675 | + | 377.241i | 0.270745 | + | 0.442771i | ||||
\(853\) | 615.673 | − | 615.673i | 0.721774 | − | 0.721774i | −0.247192 | − | 0.968966i | \(-0.579508\pi\) |
0.968966 | + | 0.247192i | \(0.0795080\pi\) | |||||||
\(854\) | 184.926 | − | 109.546i | 0.216541 | − | 0.128274i | ||||
\(855\) | −26.1368 | − | 17.0944i | −0.0305693 | − | 0.0199934i | ||||
\(856\) | 58.2616 | 0.0680627 | ||||||||
\(857\) | 90.9145 | − | 90.9145i | 0.106085 | − | 0.106085i | −0.652072 | − | 0.758157i | \(-0.726100\pi\) |
0.758157 | + | 0.652072i | \(0.226100\pi\) | |||||||
\(858\) | −61.3341 | + | 37.5045i | −0.0714850 | + | 0.0437115i | ||||
\(859\) | −974.498 | −1.13446 | −0.567228 | − | 0.823561i | \(-0.691984\pi\) | ||||
−0.567228 | + | 0.823561i | \(0.691984\pi\) | |||||||
\(860\) | −215.032 | − | 266.262i | −0.250038 | − | 0.309607i | ||||
\(861\) | −200.582 | − | 652.547i | −0.232964 | − | 0.757895i | ||||
\(862\) | 344.070 | − | 344.070i | 0.399153 | − | 0.399153i | ||||
\(863\) | 341.306 | − | 341.306i | 0.395488 | − | 0.395488i | −0.481150 | − | 0.876638i | \(-0.659781\pi\) |
0.876638 | + | 0.481150i | \(0.159781\pi\) | |||||||
\(864\) | 493.250 | + | 423.744i | 0.570891 | + | 0.490444i | ||||
\(865\) | −412.483 | + | 333.120i | −0.476859 | + | 0.385110i | ||||
\(866\) | −975.798 | −1.12679 | ||||||||
\(867\) | −252.967 | + | 154.684i | −0.291773 | + | 0.178413i | ||||
\(868\) | −365.056 | − | 93.4474i | −0.420571 | − | 0.107658i | ||||
\(869\) | −443.018 | −0.509802 | ||||||||
\(870\) | −1640.75 | − | 585.244i | −1.88592 | − | 0.672694i | ||||
\(871\) | 182.815i | 0.209891i | ||||||||
\(872\) | −504.218 | − | 504.218i | −0.578232 | − | 0.578232i | ||||
\(873\) | 449.421 | − | 145.070i | 0.514801 | − | 0.166174i | ||||
\(874\) | 53.7897 | 0.0615443 | ||||||||
\(875\) | −471.240 | + | 737.264i | −0.538560 | + | 0.842587i | ||||
\(876\) | 150.819 | − | 625.555i | 0.172168 | − | 0.714104i | ||||
\(877\) | −798.731 | + | 798.731i | −0.910754 | + | 0.910754i | −0.996331 | − | 0.0855778i | \(-0.972726\pi\) |
0.0855778 | + | 0.996331i | \(0.472726\pi\) | |||||||
\(878\) | −195.037 | − | 195.037i | −0.222138 | − | 0.222138i | ||||
\(879\) | −157.321 | + | 652.523i | −0.178978 | + | 0.742347i | ||||
\(880\) | −435.588 | − | 46.3648i | −0.494987 | − | 0.0526873i | ||||
\(881\) | −90.0599 | −0.102225 | −0.0511123 | − | 0.998693i | \(-0.516277\pi\) | ||||
−0.0511123 | + | 0.998693i | \(0.516277\pi\) | |||||||
\(882\) | −1024.02 | − | 195.840i | −1.16102 | − | 0.222041i | ||||
\(883\) | −149.663 | − | 149.663i | −0.169494 | − | 0.169494i | 0.617263 | − | 0.786757i | \(-0.288241\pi\) |
−0.786757 | + | 0.617263i | \(0.788241\pi\) | |||||||
\(884\) | −71.8042 | −0.0812265 | ||||||||
\(885\) | −148.484 | − | 313.142i | −0.167778 | − | 0.353833i | ||||
\(886\) | 942.902 | 1.06422 | ||||||||
\(887\) | 449.819 | − | 449.819i | 0.507124 | − | 0.507124i | −0.406518 | − | 0.913643i | \(-0.633257\pi\) |
0.913643 | + | 0.406518i | \(0.133257\pi\) | |||||||
\(888\) | −41.7933 | + | 25.5557i | −0.0470646 | + | 0.0287789i | ||||
\(889\) | 36.2333 | − | 21.4639i | 0.0407574 | − | 0.0241439i | ||||
\(890\) | −1178.40 | − | 1459.15i | −1.32405 | − | 1.63949i | ||||
\(891\) | −290.307 | + | 209.218i | −0.325822 | + | 0.234812i | ||||
\(892\) | 135.334 | + | 135.334i | 0.151719 | + | 0.151719i | ||||
\(893\) | 13.0329 | − | 13.0329i | 0.0145945 | − | 0.0145945i | ||||
\(894\) | 112.568 | − | 466.898i | 0.125915 | − | 0.522258i | ||||
\(895\) | 58.3530 | − | 548.215i | 0.0651989 | − | 0.612531i | ||||
\(896\) | 898.942 | − | 532.516i | 1.00328 | − | 0.594326i | ||||
\(897\) | 192.526 | − | 117.726i | 0.214633 | − | 0.131244i | ||||
\(898\) | −681.770 | − | 681.770i | −0.759210 | − | 0.759210i | ||||
\(899\) | 1664.15i | 1.85111i | ||||||||
\(900\) | 276.828 | + | 226.274i | 0.307587 | + | 0.251415i | ||||
\(901\) | − | 942.610i | − | 1.04618i | ||||||
\(902\) | 240.081 | − | 240.081i | 0.266165 | − | 0.266165i | ||||
\(903\) | −423.472 | + | 799.345i | −0.468961 | + | 0.885210i | ||||
\(904\) | 577.859i | 0.639224i | ||||||||
\(905\) | 289.264 | + | 30.7898i | 0.319629 | + | 0.0340219i | ||||
\(906\) | 180.915 | − | 750.382i | 0.199685 | − | 0.828237i | ||||
\(907\) | 1098.67 | − | 1098.67i | 1.21133 | − | 1.21133i | 0.240735 | − | 0.970591i | \(-0.422611\pi\) |
0.970591 | − | 0.240735i | \(-0.0773886\pi\) | |||||||
\(908\) | 206.561 | + | 206.561i | 0.227490 | + | 0.227490i | ||||
\(909\) | 72.4402 | − | 141.498i | 0.0796922 | − | 0.155663i | ||||
\(910\) | 66.2841 | − | 177.908i | 0.0728397 | − | 0.195504i | ||||
\(911\) | 1217.82i | 1.33680i | 0.743804 | + | 0.668398i | \(0.233020\pi\) | ||||
−0.743804 | + | 0.668398i | \(0.766980\pi\) | |||||||
\(912\) | 21.5396 | + | 35.2255i | 0.0236180 | + | 0.0386245i | ||||
\(913\) | 24.8542 | − | 24.8542i | 0.0272226 | − | 0.0272226i | ||||
\(914\) | 1542.88 | 1.68805 | ||||||||
\(915\) | 83.4704 | + | 176.033i | 0.0912245 | + | 0.192386i | ||||
\(916\) | 174.674i | 0.190692i | ||||||||
\(917\) | −782.649 | − | 200.343i | −0.853488 | − | 0.218477i | ||||
\(918\) | −1253.47 | + | 95.0097i | −1.36544 | + | 0.103496i | ||||
\(919\) | 80.9089i | 0.0880401i | 0.999031 | + | 0.0440201i | \(0.0140166\pi\) | ||||
−0.999031 | + | 0.0440201i | \(0.985983\pi\) | |||||||
\(920\) | 929.055 | + | 98.8903i | 1.00984 | + | 0.107489i | ||||
\(921\) | 388.295 | − | 1610.54i | 0.421602 | − | 1.74868i | ||||
\(922\) | 1318.62 | + | 1318.62i | 1.43017 | + | 1.43017i | ||||
\(923\) | 150.489 | + | 150.489i | 0.163044 | + | 0.163044i | ||||
\(924\) | −43.3152 | − | 140.916i | −0.0468779 | − | 0.152506i | ||||
\(925\) | −60.1705 | + | 38.8493i | −0.0650492 | + | 0.0419992i | ||||
\(926\) | − | 1834.39i | − | 1.98098i | ||||||
\(927\) | −377.560 | − | 1169.66i | −0.407292 | − | 1.26177i | ||||
\(928\) | 836.576 | + | 836.576i | 0.901482 | + | 0.901482i | ||||
\(929\) | 1204.04i | 1.29607i | 0.761612 | + | 0.648033i | \(0.224408\pi\) | ||||
−0.761612 | + | 0.648033i | \(0.775592\pi\) | |||||||
\(930\) | 403.600 | − | 1131.51i | 0.433979 | − | 1.21667i | ||||
\(931\) | −29.8240 | − | 16.3394i | −0.0320344 | − | 0.0175504i | ||||
\(932\) | −346.921 | − | 346.921i | −0.372233 | − | 0.372233i | ||||
\(933\) | 491.678 | + | 804.081i | 0.526986 | + | 0.861823i | ||||
\(934\) | −1000.02 | −1.07068 | ||||||||
\(935\) | 338.429 | − | 273.314i | 0.361956 | − | 0.292314i | ||||
\(936\) | 104.770 | + | 53.6372i | 0.111934 | + | 0.0573048i | ||||
\(937\) | 498.626 | + | 498.626i | 0.532152 | + | 0.532152i | 0.921212 | − | 0.389061i | \(-0.127200\pi\) |
−0.389061 | + | 0.921212i | \(0.627200\pi\) | |||||||
\(938\) | −1277.36 | − | 326.980i | −1.36179 | − | 0.348593i | ||||
\(939\) | 571.323 | + | 137.744i | 0.608438 | + | 0.146692i | ||||
\(940\) | −164.159 | + | 132.574i | −0.174638 | + | 0.141037i | ||||
\(941\) | −759.571 | −0.807195 | −0.403598 | − | 0.914937i | \(-0.632240\pi\) | ||||
−0.403598 | + | 0.914937i | \(0.632240\pi\) | |||||||
\(942\) | −109.962 | + | 67.2394i | −0.116733 | + | 0.0713794i | ||||
\(943\) | −753.607 | + | 753.607i | −0.799159 | + | 0.799159i | ||||
\(944\) | 458.181i | 0.485361i | ||||||||
\(945\) | 262.055 | − | 907.938i | 0.277307 | − | 0.960781i | ||||
\(946\) | −449.890 | −0.475571 | ||||||||
\(947\) | 911.272 | + | 911.272i | 0.962273 | + | 0.962273i | 0.999314 | − | 0.0370409i | \(-0.0117932\pi\) |
−0.0370409 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(948\) | −249.391 | − | 407.849i | −0.263070 | − | 0.430221i | ||||
\(949\) | − | 309.712i | − | 0.326356i | ||||||
\(950\) | 22.2490 | + | 34.4598i | 0.0234200 | + | 0.0362734i | ||||
\(951\) | −170.825 | + | 708.531i | −0.179626 | + | 0.745038i | ||||
\(952\) | −194.852 | + | 761.196i | −0.204676 | + | 0.799576i | ||||
\(953\) | −335.606 | + | 335.606i | −0.352158 | + | 0.352158i | −0.860912 | − | 0.508754i | \(-0.830106\pi\) |
0.508754 | + | 0.860912i | \(0.330106\pi\) | |||||||
\(954\) | 464.090 | − | 906.511i | 0.486468 | − | 0.950221i | ||||
\(955\) | −62.7525 | − | 6.67949i | −0.0657095 | − | 0.00699423i | ||||
\(956\) | 32.0580i | 0.0335335i | ||||||||
\(957\) | −555.440 | + | 339.639i | −0.580397 | + | 0.354900i | ||||
\(958\) | −950.798 | + | 950.798i | −0.992483 | + | 0.992483i | ||||
\(959\) | −678.048 | − | 1144.62i | −0.707037 | − | 1.19355i | ||||
\(960\) | 143.873 | + | 303.418i | 0.149868 | + | 0.316061i | ||||
\(961\) | −186.641 | −0.194215 | ||||||||
\(962\) | 10.9887 | − | 10.9887i | 0.0114228 | − | 0.0114228i | ||||
\(963\) | −87.5481 | + | 28.2599i | −0.0909118 | + | 0.0293457i | ||||
\(964\) | −409.349 | −0.424636 | ||||||||
\(965\) | 1163.86 | − | 939.929i | 1.20607 | − | 0.974019i | ||||
\(966\) | 478.218 | + | 1555.77i | 0.495050 | + | 1.61053i | ||||
\(967\) | −44.4403 | + | 44.4403i | −0.0459568 | + | 0.0459568i | −0.729712 | − | 0.683755i | \(-0.760346\pi\) |
0.683755 | + | 0.729712i | \(0.260346\pi\) | |||||||
\(968\) | 409.011 | − | 409.011i | 0.422532 | − | 0.422532i | ||||
\(969\) | −39.8607 | − | 9.61028i | −0.0411359 | − | 0.00991773i | ||||
\(970\) | −616.775 | − | 65.6506i | −0.635850 | − | 0.0676810i | ||||
\(971\) | 1113.37 | 1.14663 | 0.573313 | − | 0.819337i | \(-0.305658\pi\) | ||||
0.573313 | + | 0.819337i | \(0.305658\pi\) | |||||||
\(972\) | −356.033 | − | 149.485i | −0.366289 | − | 0.153791i | ||||
\(973\) | −1548.75 | − | 396.450i | −1.59173 | − | 0.407452i | ||||
\(974\) | 1279.90 | 1.31407 | ||||||||
\(975\) | 155.054 | + | 74.6449i | 0.159030 | + | 0.0765589i | ||||
\(976\) | − | 257.567i | − | 0.263901i | ||||||
\(977\) | 537.682 | + | 537.682i | 0.550340 | + | 0.550340i | 0.926539 | − | 0.376199i | \(-0.122769\pi\) |
−0.376199 | + | 0.926539i | \(0.622769\pi\) | |||||||
\(978\) | −1201.01 | + | 734.388i | −1.22802 | + | 0.750908i | ||||
\(979\) | −700.966 | −0.716002 | ||||||||
\(980\) | 319.719 | + | 222.148i | 0.326244 | + | 0.226681i | ||||
\(981\) | 1002.25 | + | 513.102i | 1.02166 | + | 0.523039i | ||||
\(982\) | 2.31617 | − | 2.31617i | 0.00235862 | − | 0.00235862i | ||||
\(983\) | −994.643 | − | 994.643i | −1.01184 | − | 1.01184i | −0.999929 | − | 0.0119152i | \(-0.996207\pi\) |
−0.0119152 | − | 0.999929i | \(-0.503793\pi\) | |||||||
\(984\) | −540.388 | − | 130.286i | −0.549174 | − | 0.132404i | ||||
\(985\) | 563.977 | − | 455.465i | 0.572565 | − | 0.462401i | ||||
\(986\) | −2287.09 | −2.31956 | ||||||||
\(987\) | 492.822 | + | 261.084i | 0.499313 | + | 0.264523i | ||||
\(988\) | −1.78928 | − | 1.78928i | −0.00181101 | − | 0.00181101i | ||||
\(989\) | 1412.19 | 1.42790 | ||||||||
\(990\) | 460.033 | − | 96.2226i | 0.464680 | − | 0.0971946i | ||||
\(991\) | −717.169 | −0.723682 | −0.361841 | − | 0.932240i | \(-0.617852\pi\) | ||||
−0.361841 | + | 0.932240i | \(0.617852\pi\) | |||||||
\(992\) | −576.925 | + | 576.925i | −0.581578 | + | 0.581578i | ||||
\(993\) | 152.090 | + | 248.725i | 0.153162 | + | 0.250478i | ||||
\(994\) | −1320.65 | + | 782.330i | −1.32863 | + | 0.787052i | ||||
\(995\) | −124.871 | + | 1173.14i | −0.125499 | + | 1.17904i | ||||
\(996\) | 36.8725 | + | 8.88985i | 0.0370206 | + | 0.00892555i | ||||
\(997\) | −572.089 | − | 572.089i | −0.573810 | − | 0.573810i | 0.359381 | − | 0.933191i | \(-0.382988\pi\) |
−0.933191 | + | 0.359381i | \(0.882988\pi\) | |||||||
\(998\) | −596.359 | + | 596.359i | −0.597554 | + | 0.597554i | ||||
\(999\) | 50.4058 | − | 58.6737i | 0.0504562 | − | 0.0587325i |
(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 | 105.3.k.d.83.9 | yes | 32 | |
3.2 | odd | 2 | inner | 105.3.k.d.83.8 | yes | 32 | |
5.2 | odd | 4 | inner | 105.3.k.d.62.7 | ✓ | 32 | |
7.6 | odd | 2 | inner | 105.3.k.d.83.10 | yes | 32 | |
15.2 | even | 4 | inner | 105.3.k.d.62.10 | yes | 32 | |
21.20 | even | 2 | inner | 105.3.k.d.83.7 | yes | 32 | |
35.27 | even | 4 | inner | 105.3.k.d.62.8 | yes | 32 | |
105.62 | odd | 4 | inner | 105.3.k.d.62.9 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.k.d.62.7 | ✓ | 32 | 5.2 | odd | 4 | inner | |
105.3.k.d.62.8 | yes | 32 | 35.27 | even | 4 | inner | |
105.3.k.d.62.9 | yes | 32 | 105.62 | odd | 4 | inner | |
105.3.k.d.62.10 | yes | 32 | 15.2 | even | 4 | inner | |
105.3.k.d.83.7 | yes | 32 | 21.20 | even | 2 | inner | |
105.3.k.d.83.8 | yes | 32 | 3.2 | odd | 2 | inner | |
105.3.k.d.83.9 | yes | 32 | 1.1 | even | 1 | trivial | |
105.3.k.d.83.10 | yes | 32 | 7.6 | odd | 2 | inner |