Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,3,Mod(11,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.r (of order \(6\), 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: | \(3.43325133094\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.5 | ||
Character | \(\chi\) | \(=\) | 126.11 |
Dual form | 126.3.r.a.23.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 0.146807 | + | 2.99641i | 0.0489357 | + | 0.998802i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.36201 | + | 1.36371i | 0.472402 | + | 0.272742i | 0.717245 | − | 0.696821i | \(-0.245403\pi\) |
−0.244842 | + | 0.969563i | \(0.578736\pi\) | |||||||
\(6\) | 4.23756 | − | 0.207617i | 0.706260 | − | 0.0346028i | ||||
\(7\) | −2.54299 | + | 6.52175i | −0.363285 | + | 0.931678i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −8.95690 | + | 0.879787i | −0.995211 | + | 0.0977541i | ||||
\(10\) | 1.92857 | − | 3.34039i | 0.192857 | − | 0.334039i | ||||
\(11\) | −2.52158 | + | 1.45583i | −0.229234 | + | 0.132348i | −0.610219 | − | 0.792233i | \(-0.708918\pi\) |
0.380984 | + | 0.924581i | \(0.375585\pi\) | |||||||
\(12\) | −0.293614 | − | 5.99281i | −0.0244678 | − | 0.499401i | ||||
\(13\) | 10.4745 | + | 18.1424i | 0.805731 | + | 1.39557i | 0.915796 | + | 0.401643i | \(0.131561\pi\) |
−0.110065 | + | 0.993924i | \(0.535106\pi\) | |||||||
\(14\) | 9.22314 | + | 3.59634i | 0.658796 | + | 0.256881i | ||||
\(15\) | −3.73946 | + | 7.27775i | −0.249298 | + | 0.485183i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 24.7647 | + | 14.2979i | 1.45675 | + | 0.841053i | 0.998850 | − | 0.0479514i | \(-0.0152693\pi\) |
0.457898 | + | 0.889005i | \(0.348603\pi\) | |||||||
\(18\) | 1.24421 | + | 12.6670i | 0.0691226 | + | 0.703720i | ||||
\(19\) | −17.7418 | − | 30.7298i | −0.933782 | − | 1.61736i | −0.776792 | − | 0.629757i | \(-0.783155\pi\) |
−0.156989 | − | 0.987600i | \(-0.550179\pi\) | |||||||
\(20\) | −4.72402 | − | 2.72742i | −0.236201 | − | 0.136371i | ||||
\(21\) | −19.9151 | − | 6.66240i | −0.948339 | − | 0.317257i | ||||
\(22\) | 2.05886 | + | 3.56605i | 0.0935845 | + | 0.162093i | ||||
\(23\) | 13.6186 | + | 7.86269i | 0.592112 | + | 0.341856i | 0.765932 | − | 0.642921i | \(-0.222278\pi\) |
−0.173820 | + | 0.984777i | \(0.555611\pi\) | |||||||
\(24\) | −8.47512 | + | 0.415233i | −0.353130 | + | 0.0173014i | ||||
\(25\) | −8.78060 | − | 15.2084i | −0.351224 | − | 0.608338i | ||||
\(26\) | 25.6572 | − | 14.8132i | 0.986815 | − | 0.569738i | ||||
\(27\) | −3.95113 | − | 26.7093i | −0.146338 | − | 0.989235i | ||||
\(28\) | 5.08599 | − | 13.0435i | 0.181642 | − | 0.465839i | ||||
\(29\) | 18.1582 | + | 10.4836i | 0.626144 | + | 0.361505i | 0.779257 | − | 0.626704i | \(-0.215597\pi\) |
−0.153113 | + | 0.988209i | \(0.548930\pi\) | |||||||
\(30\) | 10.2923 | + | 5.28840i | 0.343076 | + | 0.176280i | ||||
\(31\) | −12.4651 | −0.402101 | −0.201050 | − | 0.979581i | \(-0.564435\pi\) | ||||
−0.201050 | + | 0.979581i | \(0.564435\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −4.73245 | − | 7.34194i | −0.143408 | − | 0.222483i | ||||
\(34\) | 20.2203 | − | 35.0226i | 0.594715 | − | 1.03008i | ||||
\(35\) | −14.9003 | + | 11.9365i | −0.425724 | + | 0.341044i | ||||
\(36\) | 17.9138 | − | 1.75957i | 0.497605 | − | 0.0488771i | ||||
\(37\) | −5.80585 | − | 10.0560i | −0.156915 | − | 0.271785i | 0.776840 | − | 0.629698i | \(-0.216821\pi\) |
−0.933755 | + | 0.357914i | \(0.883488\pi\) | |||||||
\(38\) | −43.4585 | + | 25.0908i | −1.14364 | + | 0.660283i | ||||
\(39\) | −52.8242 | + | 34.0493i | −1.35447 | + | 0.873059i | ||||
\(40\) | −3.85715 | + | 6.68078i | −0.0964287 | + | 0.167019i | ||||
\(41\) | 26.4059 | − | 15.2455i | 0.644047 | − | 0.371841i | −0.142125 | − | 0.989849i | \(-0.545393\pi\) |
0.786172 | + | 0.618008i | \(0.212060\pi\) | |||||||
\(42\) | −9.42206 | + | 28.1642i | −0.224335 | + | 0.670577i | ||||
\(43\) | −12.6505 | + | 21.9113i | −0.294197 | + | 0.509564i | −0.974798 | − | 0.223090i | \(-0.928386\pi\) |
0.680601 | + | 0.732655i | \(0.261719\pi\) | |||||||
\(44\) | 5.04315 | − | 2.91167i | 0.114617 | − | 0.0661742i | ||||
\(45\) | −22.3561 | − | 10.1365i | −0.496802 | − | 0.225256i | ||||
\(46\) | 11.1195 | − | 19.2596i | 0.241729 | − | 0.418687i | ||||
\(47\) | − | 84.6070i | − | 1.80015i | −0.435736 | − | 0.900075i | \(-0.643512\pi\) | ||
0.435736 | − | 0.900075i | \(-0.356488\pi\) | |||||||
\(48\) | 0.587228 | + | 11.9856i | 0.0122339 | + | 0.249700i | ||||
\(49\) | −36.0664 | − | 33.1695i | −0.736048 | − | 0.676929i | ||||
\(50\) | −21.5080 | + | 12.4176i | −0.430160 | + | 0.248353i | ||||
\(51\) | −39.2067 | + | 76.3041i | −0.768759 | + | 1.49616i | ||||
\(52\) | −20.9490 | − | 36.2847i | −0.402866 | − | 0.697784i | ||||
\(53\) | 15.1905 | + | 8.77025i | 0.286614 | + | 0.165476i | 0.636414 | − | 0.771348i | \(-0.280417\pi\) |
−0.349800 | + | 0.936824i | \(0.613750\pi\) | |||||||
\(54\) | −37.7727 | + | 5.58775i | −0.699494 | + | 0.103477i | ||||
\(55\) | −7.94133 | −0.144388 | ||||||||
\(56\) | −18.4463 | − | 7.19267i | −0.329398 | − | 0.128441i | ||||
\(57\) | 89.4743 | − | 57.6731i | 1.56972 | − | 1.01181i | ||||
\(58\) | 14.8261 | − | 25.6795i | 0.255622 | − | 0.442751i | ||||
\(59\) | 43.1446i | 0.731264i | 0.930760 | + | 0.365632i | \(0.119147\pi\) | ||||
−0.930760 | + | 0.365632i | \(0.880853\pi\) | |||||||
\(60\) | 7.47893 | − | 14.5555i | 0.124649 | − | 0.242592i | ||||
\(61\) | 30.2949 | 0.496637 | 0.248319 | − | 0.968678i | \(-0.420122\pi\) | ||||
0.248319 | + | 0.968678i | \(0.420122\pi\) | |||||||
\(62\) | 17.6283i | 0.284328i | ||||||||
\(63\) | 17.0396 | − | 60.6519i | 0.270470 | − | 0.962729i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 57.1367i | 0.879026i | ||||||||
\(66\) | −10.3831 | + | 6.69270i | −0.157319 | + | 0.101405i | ||||
\(67\) | 86.4501 | 1.29030 | 0.645150 | − | 0.764056i | \(-0.276795\pi\) | ||||
0.645150 | + | 0.764056i | \(0.276795\pi\) | |||||||
\(68\) | −49.5294 | − | 28.5958i | −0.728374 | − | 0.420527i | ||||
\(69\) | −21.5605 | + | 41.9611i | −0.312471 | + | 0.608132i | ||||
\(70\) | 16.8808 | + | 21.0723i | 0.241155 | + | 0.301032i | ||||
\(71\) | 1.24828i | 0.0175814i | 0.999961 | + | 0.00879071i | \(0.00279821\pi\) | ||||
−0.999961 | + | 0.00879071i | \(0.997202\pi\) | |||||||
\(72\) | −2.48841 | − | 25.3339i | −0.0345613 | − | 0.351860i | ||||
\(73\) | −6.48414 | + | 11.2309i | −0.0888239 | + | 0.153848i | −0.907014 | − | 0.421100i | \(-0.861644\pi\) |
0.818190 | + | 0.574947i | \(0.194978\pi\) | |||||||
\(74\) | −14.2214 | + | 8.21071i | −0.192181 | + | 0.110956i | ||||
\(75\) | 44.2816 | − | 28.5429i | 0.590422 | − | 0.380573i | ||||
\(76\) | 35.4837 | + | 61.4596i | 0.466891 | + | 0.808679i | ||||
\(77\) | −3.08222 | − | 20.1473i | −0.0400288 | − | 0.261653i | ||||
\(78\) | 48.1530 | + | 74.7047i | 0.617346 | + | 0.957752i | ||||
\(79\) | 103.529 | 1.31049 | 0.655247 | − | 0.755415i | \(-0.272565\pi\) | ||||
0.655247 | + | 0.755415i | \(0.272565\pi\) | |||||||
\(80\) | 9.44805 | + | 5.45483i | 0.118101 | + | 0.0681854i | ||||
\(81\) | 79.4519 | − | 15.7603i | 0.980888 | − | 0.194572i | ||||
\(82\) | −21.5604 | − | 37.3436i | −0.262931 | − | 0.455410i | ||||
\(83\) | 35.2944 | + | 20.3772i | 0.425234 | + | 0.245509i | 0.697314 | − | 0.716766i | \(-0.254378\pi\) |
−0.272080 | + | 0.962275i | \(0.587712\pi\) | |||||||
\(84\) | 39.8303 | + | 13.3248i | 0.474170 | + | 0.158629i | ||||
\(85\) | 38.9964 | + | 67.5437i | 0.458781 | + | 0.794631i | ||||
\(86\) | 30.9872 | + | 17.8905i | 0.360316 | + | 0.208029i | ||||
\(87\) | −28.7475 | + | 55.9484i | −0.330431 | + | 0.643085i | ||||
\(88\) | −4.11772 | − | 7.13210i | −0.0467923 | − | 0.0810466i | ||||
\(89\) | 15.5031 | − | 8.95074i | 0.174193 | − | 0.100570i | −0.410369 | − | 0.911920i | \(-0.634600\pi\) |
0.584561 | + | 0.811350i | \(0.301267\pi\) | |||||||
\(90\) | −14.3352 | + | 31.6163i | −0.159280 | + | 0.351292i | ||||
\(91\) | −144.957 | + | 22.1761i | −1.59293 | + | 0.243693i | ||||
\(92\) | −27.2372 | − | 15.7254i | −0.296056 | − | 0.170928i | ||||
\(93\) | −1.82997 | − | 37.3505i | −0.0196771 | − | 0.401619i | ||||
\(94\) | −119.652 | −1.27290 | ||||||||
\(95\) | − | 96.7788i | − | 1.01872i | ||||||
\(96\) | 16.9502 | − | 0.830466i | 0.176565 | − | 0.00865069i | ||||
\(97\) | −2.62198 | + | 4.54141i | −0.0270307 | + | 0.0468186i | −0.879224 | − | 0.476408i | \(-0.841939\pi\) |
0.852194 | + | 0.523227i | \(0.175272\pi\) | |||||||
\(98\) | −46.9088 | + | 51.0055i | −0.478661 | + | 0.520465i | ||||
\(99\) | 21.3047 | − | 15.2582i | 0.215199 | − | 0.154123i | ||||
\(100\) | 17.5612 | + | 30.4169i | 0.175612 | + | 0.304169i | ||||
\(101\) | 155.079 | − | 89.5347i | 1.53543 | − | 0.886482i | 0.536334 | − | 0.844006i | \(-0.319809\pi\) |
0.999097 | − | 0.0424762i | \(-0.0135247\pi\) | |||||||
\(102\) | 107.910 | + | 55.4467i | 1.05794 | + | 0.543595i | ||||
\(103\) | −76.1322 | + | 131.865i | −0.739148 | + | 1.28024i | 0.213732 | + | 0.976892i | \(0.431438\pi\) |
−0.952880 | + | 0.303349i | \(0.901895\pi\) | |||||||
\(104\) | −51.3144 | + | 29.6264i | −0.493407 | + | 0.284869i | ||||
\(105\) | −37.9542 | − | 42.8951i | −0.361469 | − | 0.408525i | ||||
\(106\) | 12.4030 | − | 21.4826i | 0.117010 | − | 0.202666i | ||||
\(107\) | −129.207 | + | 74.5978i | −1.20754 | + | 0.697175i | −0.962222 | − | 0.272267i | \(-0.912227\pi\) |
−0.245321 | + | 0.969442i | \(0.578893\pi\) | |||||||
\(108\) | 7.90227 | + | 53.4187i | 0.0731692 | + | 0.494617i | ||||
\(109\) | −11.0071 | + | 19.0649i | −0.100983 | + | 0.174907i | −0.912090 | − | 0.409990i | \(-0.865532\pi\) |
0.811107 | + | 0.584898i | \(0.198865\pi\) | |||||||
\(110\) | 11.2307i | 0.102098i | ||||||||
\(111\) | 29.2796 | − | 18.8730i | 0.263780 | − | 0.170027i | ||||
\(112\) | −10.1720 | + | 26.0870i | −0.0908212 | + | 0.232920i | ||||
\(113\) | 13.7209 | − | 7.92175i | 0.121424 | − | 0.0701040i | −0.438058 | − | 0.898947i | \(-0.644334\pi\) |
0.559482 | + | 0.828843i | \(0.311000\pi\) | |||||||
\(114\) | −81.5621 | − | 126.536i | −0.715457 | − | 1.10996i | ||||
\(115\) | 21.4448 | + | 37.1436i | 0.186477 | + | 0.322987i | ||||
\(116\) | −36.3164 | − | 20.9673i | −0.313072 | − | 0.180752i | ||||
\(117\) | −109.780 | − | 153.284i | −0.938294 | − | 1.31012i | ||||
\(118\) | 61.0156 | 0.517082 | ||||||||
\(119\) | −156.224 | + | 125.150i | −1.31281 | + | 1.05168i | ||||
\(120\) | −20.5846 | − | 10.5768i | −0.171538 | − | 0.0881400i | ||||
\(121\) | −56.2611 | + | 97.4471i | −0.464968 | + | 0.805348i | ||||
\(122\) | − | 42.8434i | − | 0.351176i | ||||||
\(123\) | 49.5582 | + | 76.8848i | 0.402912 | + | 0.625079i | ||||
\(124\) | 24.9302 | 0.201050 | ||||||||
\(125\) | − | 116.082i | − | 0.928657i | ||||||
\(126\) | −85.7747 | − | 24.0976i | −0.680752 | − | 0.191251i | ||||
\(127\) | −86.5080 | −0.681166 | −0.340583 | − | 0.940215i | \(-0.610624\pi\) | ||||
−0.340583 | + | 0.940215i | \(0.610624\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −67.5122 | − | 34.6892i | −0.523350 | − | 0.268909i | ||||
\(130\) | 80.8035 | 0.621565 | ||||||||
\(131\) | 87.6284 | + | 50.5923i | 0.668919 | + | 0.386200i | 0.795667 | − | 0.605734i | \(-0.207121\pi\) |
−0.126748 | + | 0.991935i | \(0.540454\pi\) | |||||||
\(132\) | 9.46490 | + | 14.6839i | 0.0717038 | + | 0.111242i | ||||
\(133\) | 245.529 | − | 37.5622i | 1.84608 | − | 0.282422i | ||||
\(134\) | − | 122.259i | − | 0.912380i | ||||||
\(135\) | 27.0911 | − | 68.4760i | 0.200675 | − | 0.507229i | ||||
\(136\) | −40.4406 | + | 70.0452i | −0.297357 | + | 0.515038i | ||||
\(137\) | 35.2605 | − | 20.3576i | 0.257376 | − | 0.148596i | −0.365761 | − | 0.930709i | \(-0.619191\pi\) |
0.623137 | + | 0.782113i | \(0.285858\pi\) | |||||||
\(138\) | 59.3420 | + | 30.4912i | 0.430014 | + | 0.220951i | ||||
\(139\) | −22.3342 | − | 38.6840i | −0.160678 | − | 0.278302i | 0.774434 | − | 0.632655i | \(-0.218035\pi\) |
−0.935112 | + | 0.354352i | \(0.884701\pi\) | |||||||
\(140\) | 29.8007 | − | 23.8731i | 0.212862 | − | 0.170522i | ||||
\(141\) | 253.517 | − | 12.4209i | 1.79799 | − | 0.0880915i | ||||
\(142\) | 1.76534 | 0.0124319 | ||||||||
\(143\) | −52.8245 | − | 30.4983i | −0.369402 | − | 0.213275i | ||||
\(144\) | −35.8276 | + | 3.51915i | −0.248803 | + | 0.0244385i | ||||
\(145\) | 28.5932 | + | 49.5249i | 0.197195 | + | 0.341551i | ||||
\(146\) | 15.8828 | + | 9.16996i | 0.108787 | + | 0.0628080i | ||||
\(147\) | 94.0946 | − | 112.939i | 0.640099 | − | 0.768292i | ||||
\(148\) | 11.6117 | + | 20.1121i | 0.0784574 | + | 0.135892i | ||||
\(149\) | −54.3567 | − | 31.3829i | −0.364810 | − | 0.210623i | 0.306379 | − | 0.951910i | \(-0.400883\pi\) |
−0.671189 | + | 0.741286i | \(0.734216\pi\) | |||||||
\(150\) | −40.3658 | − | 62.6237i | −0.269105 | − | 0.417491i | ||||
\(151\) | −94.8677 | − | 164.316i | −0.628263 | − | 1.08818i | −0.987900 | − | 0.155091i | \(-0.950433\pi\) |
0.359637 | − | 0.933092i | \(-0.382900\pi\) | |||||||
\(152\) | 86.9170 | − | 50.1815i | 0.571822 | − | 0.330142i | ||||
\(153\) | −234.394 | − | 106.277i | −1.53199 | − | 0.694622i | ||||
\(154\) | −28.4925 | + | 4.35892i | −0.185016 | + | 0.0283047i | ||||
\(155\) | −29.4428 | − | 16.9988i | −0.189953 | − | 0.109670i | ||||
\(156\) | 105.648 | − | 68.0986i | 0.677233 | − | 0.436529i | ||||
\(157\) | −86.0225 | −0.547914 | −0.273957 | − | 0.961742i | \(-0.588333\pi\) | ||||
−0.273957 | + | 0.961742i | \(0.588333\pi\) | |||||||
\(158\) | − | 146.412i | − | 0.926659i | ||||||
\(159\) | −24.0492 | + | 46.8045i | −0.151253 | + | 0.294368i | ||||
\(160\) | 7.71430 | − | 13.3616i | 0.0482144 | − | 0.0835097i | ||||
\(161\) | −85.9105 | + | 68.8222i | −0.533606 | + | 0.427467i | ||||
\(162\) | −22.2885 | − | 112.362i | −0.137583 | − | 0.693593i | ||||
\(163\) | 36.5758 | + | 63.3511i | 0.224391 | + | 0.388657i | 0.956137 | − | 0.292921i | \(-0.0946273\pi\) |
−0.731745 | + | 0.681578i | \(0.761294\pi\) | |||||||
\(164\) | −52.8119 | + | 30.4909i | −0.322024 | + | 0.185920i | ||||
\(165\) | −1.16584 | − | 23.7954i | −0.00706571 | − | 0.144215i | ||||
\(166\) | 28.8177 | − | 49.9138i | 0.173601 | − | 0.300686i | ||||
\(167\) | −72.8922 | + | 42.0843i | −0.436480 | + | 0.252002i | −0.702103 | − | 0.712075i | \(-0.747756\pi\) |
0.265623 | + | 0.964077i | \(0.414422\pi\) | |||||||
\(168\) | 18.8441 | − | 56.3285i | 0.112167 | − | 0.335289i | ||||
\(169\) | −134.930 | + | 233.706i | −0.798405 | + | 1.38288i | ||||
\(170\) | 95.5212 | − | 55.1492i | 0.561889 | − | 0.324407i | ||||
\(171\) | 185.948 | + | 259.634i | 1.08741 | + | 1.51833i | ||||
\(172\) | 25.3009 | − | 43.8225i | 0.147099 | − | 0.254782i | ||||
\(173\) | − | 236.832i | − | 1.36897i | −0.729026 | − | 0.684486i | \(-0.760027\pi\) | ||
0.729026 | − | 0.684486i | \(-0.239973\pi\) | |||||||
\(174\) | 79.1229 | + | 40.6551i | 0.454729 | + | 0.233650i | ||||
\(175\) | 121.515 | − | 18.5899i | 0.694369 | − | 0.106228i | ||||
\(176\) | −10.0863 | + | 5.82333i | −0.0573086 | + | 0.0330871i | ||||
\(177\) | −129.279 | + | 6.33393i | −0.730388 | + | 0.0357849i | ||||
\(178\) | −12.6583 | − | 21.9247i | −0.0711138 | − | 0.123173i | ||||
\(179\) | −166.309 | − | 96.0186i | −0.929101 | − | 0.536417i | −0.0425737 | − | 0.999093i | \(-0.513556\pi\) |
−0.886527 | + | 0.462677i | \(0.846889\pi\) | |||||||
\(180\) | 44.7121 | + | 20.2731i | 0.248401 | + | 0.112628i | ||||
\(181\) | −45.1148 | −0.249253 | −0.124626 | − | 0.992204i | \(-0.539773\pi\) | ||||
−0.124626 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(182\) | 31.3618 | + | 205.000i | 0.172317 | + | 1.12637i | ||||
\(183\) | 4.44750 | + | 90.7758i | 0.0243033 | + | 0.496042i | ||||
\(184\) | −22.2391 | + | 38.5192i | −0.120864 | + | 0.209343i | ||||
\(185\) | − | 31.6699i | − | 0.171189i | ||||||
\(186\) | −52.8217 | + | 2.58796i | −0.283987 | + | 0.0139138i | ||||
\(187\) | −83.2615 | −0.445249 | ||||||||
\(188\) | 169.214i | 0.900075i | ||||||||
\(189\) | 184.239 | + | 42.1534i | 0.974811 | + | 0.223034i | ||||
\(190\) | −136.866 | −0.720347 | ||||||||
\(191\) | 87.2707i | 0.456915i | 0.973554 | + | 0.228457i | \(0.0733681\pi\) | ||||
−0.973554 | + | 0.228457i | \(0.926632\pi\) | |||||||
\(192\) | −1.17446 | − | 23.9712i | −0.00611696 | − | 0.124850i | ||||
\(193\) | −158.035 | −0.818832 | −0.409416 | − | 0.912348i | \(-0.634268\pi\) | ||||
−0.409416 | + | 0.912348i | \(0.634268\pi\) | |||||||
\(194\) | 6.42252 | + | 3.70804i | 0.0331058 | + | 0.0191136i | ||||
\(195\) | −171.205 | + | 8.38807i | −0.877973 | + | 0.0430157i | ||||
\(196\) | 72.1327 | + | 66.3391i | 0.368024 | + | 0.338465i | ||||
\(197\) | − | 72.5385i | − | 0.368216i | −0.982906 | − | 0.184108i | \(-0.941060\pi\) | ||
0.982906 | − | 0.184108i | \(-0.0589396\pi\) | |||||||
\(198\) | −21.5783 | − | 30.1294i | −0.108982 | − | 0.152169i | ||||
\(199\) | 156.303 | − | 270.725i | 0.785442 | − | 1.36043i | −0.143292 | − | 0.989680i | \(-0.545769\pi\) |
0.928735 | − | 0.370745i | \(-0.120898\pi\) | |||||||
\(200\) | 43.0160 | − | 24.8353i | 0.215080 | − | 0.124176i | ||||
\(201\) | 12.6915 | + | 259.040i | 0.0631417 | + | 1.28875i | ||||
\(202\) | −126.621 | − | 219.314i | −0.626837 | − | 1.08571i | ||||
\(203\) | −114.548 | + | 91.7632i | −0.564275 | + | 0.452036i | ||||
\(204\) | 78.4134 | − | 152.608i | 0.384379 | − | 0.748080i | ||||
\(205\) | 83.1615 | 0.405666 | ||||||||
\(206\) | 186.485 | + | 107.667i | 0.905267 | + | 0.522656i | ||||
\(207\) | −128.898 | − | 58.4439i | −0.622694 | − | 0.282338i | ||||
\(208\) | 41.8980 | + | 72.5695i | 0.201433 | + | 0.348892i | ||||
\(209\) | 89.4749 | + | 51.6583i | 0.428109 | + | 0.247169i | ||||
\(210\) | −60.6628 | + | 53.6753i | −0.288871 | + | 0.255597i | ||||
\(211\) | 91.2819 | + | 158.105i | 0.432616 | + | 0.749312i | 0.997098 | − | 0.0761331i | \(-0.0242574\pi\) |
−0.564482 | + | 0.825445i | \(0.690924\pi\) | |||||||
\(212\) | −30.3810 | − | 17.5405i | −0.143307 | − | 0.0827382i | ||||
\(213\) | −3.74035 | + | 0.183256i | −0.0175604 | + | 0.000860359i | ||||
\(214\) | 105.497 | + | 182.726i | 0.492977 | + | 0.853862i | ||||
\(215\) | −59.7611 | + | 34.5031i | −0.277959 | + | 0.160480i | ||||
\(216\) | 75.5454 | − | 11.1755i | 0.349747 | − | 0.0517384i | ||||
\(217\) | 31.6987 | − | 81.2943i | 0.146077 | − | 0.374628i | ||||
\(218\) | 26.9619 | + | 15.5664i | 0.123678 | + | 0.0714057i | ||||
\(219\) | −34.6042 | − | 17.7804i | −0.158010 | − | 0.0811888i | ||||
\(220\) | 15.8827 | 0.0721939 | ||||||||
\(221\) | 599.054i | 2.71065i | ||||||||
\(222\) | −26.6904 | − | 41.4076i | −0.120227 | − | 0.186521i | ||||
\(223\) | 125.388 | − | 217.179i | 0.562279 | − | 0.973896i | −0.435018 | − | 0.900422i | \(-0.643258\pi\) |
0.997297 | − | 0.0734742i | \(-0.0234087\pi\) | |||||||
\(224\) | 36.8926 | + | 14.3853i | 0.164699 | + | 0.0642203i | ||||
\(225\) | 92.0271 | + | 128.495i | 0.409009 | + | 0.571091i | ||||
\(226\) | −11.2030 | − | 19.4042i | −0.0495710 | − | 0.0858595i | ||||
\(227\) | 351.333 | − | 202.842i | 1.54772 | − | 0.893578i | 0.549407 | − | 0.835555i | \(-0.314854\pi\) |
0.998315 | − | 0.0580230i | \(-0.0184797\pi\) | |||||||
\(228\) | −178.949 | + | 115.346i | −0.784862 | + | 0.505905i | ||||
\(229\) | −54.8376 | + | 94.9815i | −0.239465 | + | 0.414766i | −0.960561 | − | 0.278069i | \(-0.910306\pi\) |
0.721096 | + | 0.692836i | \(0.243639\pi\) | |||||||
\(230\) | 52.5289 | − | 30.3276i | 0.228387 | − | 0.131859i | ||||
\(231\) | 59.9169 | − | 12.1933i | 0.259380 | − | 0.0527850i | ||||
\(232\) | −29.6522 | + | 51.3591i | −0.127811 | + | 0.221375i | ||||
\(233\) | −59.9074 | + | 34.5876i | −0.257113 | + | 0.148445i | −0.623017 | − | 0.782208i | \(-0.714093\pi\) |
0.365904 | + | 0.930653i | \(0.380760\pi\) | |||||||
\(234\) | −216.776 | + | 155.253i | −0.926394 | + | 0.663474i | ||||
\(235\) | 115.379 | − | 199.843i | 0.490976 | − | 0.850395i | ||||
\(236\) | − | 86.2891i | − | 0.365632i | ||||||
\(237\) | 15.1988 | + | 310.215i | 0.0641299 | + | 1.30892i | ||||
\(238\) | 176.988 | + | 220.934i | 0.743648 | + | 0.928294i | ||||
\(239\) | −206.558 | + | 119.256i | −0.864260 | + | 0.498981i | −0.865437 | − | 0.501018i | \(-0.832959\pi\) |
0.00117636 | + | 0.999999i | \(0.499626\pi\) | |||||||
\(240\) | −14.9579 | + | 29.1110i | −0.0623244 | + | 0.121296i | ||||
\(241\) | −140.911 | − | 244.065i | −0.584693 | − | 1.01272i | −0.994914 | − | 0.100732i | \(-0.967881\pi\) |
0.410220 | − | 0.911987i | \(-0.365452\pi\) | |||||||
\(242\) | 137.811 | + | 79.5652i | 0.569467 | + | 0.328782i | ||||
\(243\) | 58.8884 | + | 235.757i | 0.242339 | + | 0.970192i | ||||
\(244\) | −60.5898 | −0.248319 | ||||||||
\(245\) | −39.9556 | − | 127.531i | −0.163084 | − | 0.520534i | ||||
\(246\) | 108.731 | − | 70.0859i | 0.441998 | − | 0.284902i | ||||
\(247\) | 371.674 | − | 643.758i | 1.50475 | − | 2.60631i | ||||
\(248\) | − | 35.2567i | − | 0.142164i | ||||||
\(249\) | −55.8770 | + | 108.748i | −0.224405 | + | 0.436738i | ||||
\(250\) | −164.165 | −0.656660 | ||||||||
\(251\) | − | 222.540i | − | 0.886615i | −0.896370 | − | 0.443308i | \(-0.853805\pi\) | ||
0.896370 | − | 0.443308i | \(-0.146195\pi\) | |||||||
\(252\) | −34.0792 | + | 121.304i | −0.135235 | + | 0.481364i | ||||
\(253\) | −45.7871 | −0.180977 | ||||||||
\(254\) | 122.341i | 0.481657i | ||||||||
\(255\) | −196.663 | + | 126.765i | −0.771229 | + | 0.497117i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 291.865 | + | 168.508i | 1.13566 | + | 0.655674i | 0.945353 | − | 0.326050i | \(-0.105718\pi\) |
0.190309 | + | 0.981724i | \(0.439051\pi\) | |||||||
\(258\) | −49.0580 | + | 95.4767i | −0.190147 | + | 0.370065i | ||||
\(259\) | 80.3471 | − | 12.2919i | 0.310220 | − | 0.0474589i | ||||
\(260\) | − | 114.273i | − | 0.439513i | ||||||
\(261\) | −171.864 | − | 77.9255i | −0.658484 | − | 0.298565i | ||||
\(262\) | 71.5483 | − | 123.925i | 0.273085 | − | 0.472997i | ||||
\(263\) | −141.259 | + | 81.5557i | −0.537105 | + | 0.310098i | −0.743905 | − | 0.668285i | \(-0.767029\pi\) |
0.206800 | + | 0.978383i | \(0.433695\pi\) | |||||||
\(264\) | 20.7661 | − | 13.3854i | 0.0786596 | − | 0.0507023i | ||||
\(265\) | 23.9201 | + | 41.4309i | 0.0902646 | + | 0.156343i | ||||
\(266\) | −53.1209 | − | 347.231i | −0.199703 | − | 1.30538i | ||||
\(267\) | 29.0960 | + | 45.1396i | 0.108974 | + | 0.169062i | ||||
\(268\) | −172.900 | −0.645150 | ||||||||
\(269\) | 430.483 | + | 248.539i | 1.60031 | + | 0.923938i | 0.991425 | + | 0.130677i | \(0.0417152\pi\) |
0.608882 | + | 0.793261i | \(0.291618\pi\) | |||||||
\(270\) | −96.8396 | − | 38.3126i | −0.358665 | − | 0.141899i | ||||
\(271\) | −86.2128 | − | 149.325i | −0.318129 | − | 0.551015i | 0.661969 | − | 0.749531i | \(-0.269721\pi\) |
−0.980098 | + | 0.198516i | \(0.936388\pi\) | |||||||
\(272\) | 99.0588 | + | 57.1916i | 0.364187 | + | 0.210263i | ||||
\(273\) | −87.7293 | − | 431.093i | −0.321353 | − | 1.57910i | ||||
\(274\) | −28.7901 | − | 49.8659i | −0.105073 | − | 0.181992i | ||||
\(275\) | 44.2819 | + | 25.5662i | 0.161025 | + | 0.0929679i | ||||
\(276\) | 43.1210 | − | 83.9222i | 0.156236 | − | 0.304066i | ||||
\(277\) | −44.6018 | − | 77.2526i | −0.161017 | − | 0.278890i | 0.774216 | − | 0.632921i | \(-0.218144\pi\) |
−0.935234 | + | 0.354031i | \(0.884811\pi\) | |||||||
\(278\) | −54.7075 | + | 31.5854i | −0.196790 | + | 0.113616i | ||||
\(279\) | 111.649 | − | 10.9666i | 0.400175 | − | 0.0393070i | ||||
\(280\) | −33.7616 | − | 42.1445i | −0.120577 | − | 0.150516i | ||||
\(281\) | −406.825 | − | 234.881i | −1.44778 | − | 0.835874i | −0.449428 | − | 0.893317i | \(-0.648372\pi\) |
−0.998349 | + | 0.0574426i | \(0.981705\pi\) | |||||||
\(282\) | −17.5658 | − | 358.527i | −0.0622901 | − | 1.27137i | ||||
\(283\) | −47.4160 | −0.167548 | −0.0837738 | − | 0.996485i | \(-0.526697\pi\) | ||||
−0.0837738 | + | 0.996485i | \(0.526697\pi\) | |||||||
\(284\) | − | 2.49656i | − | 0.00879071i | ||||||
\(285\) | 289.989 | − | 14.2078i | 1.01750 | − | 0.0498520i | ||||
\(286\) | −43.1311 | + | 74.7052i | −0.150808 | + | 0.261207i | ||||
\(287\) | 32.2770 | + | 210.982i | 0.112463 | + | 0.735129i | ||||
\(288\) | 4.97683 | + | 50.6679i | 0.0172806 | + | 0.175930i | ||||
\(289\) | 264.360 | + | 457.886i | 0.914742 | + | 1.58438i | ||||
\(290\) | 70.0388 | − | 40.4369i | 0.241513 | − | 0.139438i | ||||
\(291\) | −13.9928 | − | 7.18981i | −0.0480853 | − | 0.0247073i | ||||
\(292\) | 12.9683 | − | 22.4617i | 0.0444119 | − | 0.0769238i | ||||
\(293\) | 80.5230 | − | 46.4900i | 0.274823 | − | 0.158669i | −0.356255 | − | 0.934389i | \(-0.615946\pi\) |
0.631077 | + | 0.775720i | \(0.282613\pi\) | |||||||
\(294\) | −159.720 | − | 133.070i | −0.543265 | − | 0.452618i | ||||
\(295\) | −58.8366 | + | 101.908i | −0.199446 | + | 0.345451i | ||||
\(296\) | 28.4427 | − | 16.4214i | 0.0960903 | − | 0.0554778i | ||||
\(297\) | 48.8474 | + | 61.5975i | 0.164469 | + | 0.207399i | ||||
\(298\) | −44.3821 | + | 76.8720i | −0.148933 | + | 0.257960i | ||||
\(299\) | 329.431i | 1.10178i | ||||||||
\(300\) | −88.5632 | + | 57.0859i | −0.295211 | + | 0.190286i | ||||
\(301\) | −110.730 | − | 138.223i | −0.367872 | − | 0.459214i | ||||
\(302\) | −232.378 | + | 134.163i | −0.769462 | + | 0.444249i | ||||
\(303\) | 291.049 | + | 451.534i | 0.960557 | + | 1.49021i | ||||
\(304\) | −70.9674 | − | 122.919i | −0.233445 | − | 0.404339i | ||||
\(305\) | 71.5569 | + | 41.3134i | 0.234613 | + | 0.135454i | ||||
\(306\) | −150.299 | + | 331.483i | −0.491172 | + | 1.08328i | ||||
\(307\) | 202.315 | 0.659008 | 0.329504 | − | 0.944154i | \(-0.393119\pi\) | ||||
0.329504 | + | 0.944154i | \(0.393119\pi\) | |||||||
\(308\) | 6.16444 | + | 40.2945i | 0.0200144 | + | 0.130826i | ||||
\(309\) | −406.297 | − | 208.764i | −1.31488 | − | 0.675613i | ||||
\(310\) | −24.0399 | + | 41.6383i | −0.0775481 | + | 0.134317i | ||||
\(311\) | − | 297.017i | − | 0.955037i | −0.878622 | − | 0.477519i | \(-0.841536\pi\) | ||
0.878622 | − | 0.477519i | \(-0.158464\pi\) | |||||||
\(312\) | −96.3059 | − | 149.409i | −0.308673 | − | 0.478876i | ||||
\(313\) | −378.321 | −1.20869 | −0.604347 | − | 0.796721i | \(-0.706566\pi\) | ||||
−0.604347 | + | 0.796721i | \(0.706566\pi\) | |||||||
\(314\) | 121.654i | 0.387434i | ||||||||
\(315\) | 122.959 | − | 120.023i | 0.390347 | − | 0.381027i | ||||
\(316\) | −207.058 | −0.655247 | ||||||||
\(317\) | − | 258.230i | − | 0.814607i | −0.913293 | − | 0.407304i | \(-0.866469\pi\) | ||
0.913293 | − | 0.407304i | \(-0.133531\pi\) | |||||||
\(318\) | 66.1916 | + | 34.0106i | 0.208150 | + | 0.106952i | ||||
\(319\) | −61.0497 | −0.191378 | ||||||||
\(320\) | −18.8961 | − | 10.9097i | −0.0590503 | − | 0.0340927i | ||||
\(321\) | −242.494 | − | 376.205i | −0.755432 | − | 1.17198i | ||||
\(322\) | 97.3293 | + | 121.496i | 0.302265 | + | 0.377316i | ||||
\(323\) | − | 1014.69i | − | 3.14144i | ||||||
\(324\) | −158.904 | + | 31.5206i | −0.490444 | + | 0.0972859i | ||||
\(325\) | 183.945 | − | 318.602i | 0.565984 | − | 0.980313i | ||||
\(326\) | 89.5920 | − | 51.7260i | 0.274822 | − | 0.158669i | ||||
\(327\) | −58.7421 | − | 30.1830i | −0.179640 | − | 0.0923026i | ||||
\(328\) | 43.1207 | + | 74.6873i | 0.131466 | + | 0.227705i | ||||
\(329\) | 551.785 | + | 215.155i | 1.67716 | + | 0.653967i | ||||
\(330\) | −33.6518 | + | 1.64875i | −0.101975 | + | 0.00499621i | ||||
\(331\) | −381.770 | −1.15338 | −0.576692 | − | 0.816961i | \(-0.695657\pi\) | ||||
−0.576692 | + | 0.816961i | \(0.695657\pi\) | |||||||
\(332\) | −70.5888 | − | 40.7544i | −0.212617 | − | 0.122754i | ||||
\(333\) | 60.8496 | + | 84.9629i | 0.182731 | + | 0.255144i | ||||
\(334\) | 59.5162 | + | 103.085i | 0.178192 | + | 0.308638i | ||||
\(335\) | 204.196 | + | 117.893i | 0.609541 | + | 0.351919i | ||||
\(336\) | −79.6605 | − | 26.6496i | −0.237085 | − | 0.0793143i | ||||
\(337\) | −121.433 | − | 210.329i | −0.360337 | − | 0.624122i | 0.627679 | − | 0.778472i | \(-0.284005\pi\) |
−0.988016 | + | 0.154350i | \(0.950672\pi\) | |||||||
\(338\) | 330.511 | + | 190.820i | 0.977842 | + | 0.564558i | ||||
\(339\) | 25.7511 | + | 39.9503i | 0.0759619 | + | 0.117848i | ||||
\(340\) | −77.9927 | − | 135.087i | −0.229390 | − | 0.397316i | ||||
\(341\) | 31.4318 | − | 18.1471i | 0.0921752 | − | 0.0532174i | ||||
\(342\) | 367.179 | − | 262.970i | 1.07362 | − | 0.768917i | ||||
\(343\) | 308.040 | − | 150.866i | 0.898075 | − | 0.439842i | ||||
\(344\) | −61.9744 | − | 35.7809i | −0.180158 | − | 0.104014i | ||||
\(345\) | −108.149 | + | 69.7104i | −0.313475 | + | 0.202059i | ||||
\(346\) | −334.931 | −0.968009 | ||||||||
\(347\) | − | 242.378i | − | 0.698495i | −0.937031 | − | 0.349247i | \(-0.886437\pi\) | ||
0.937031 | − | 0.349247i | \(-0.113563\pi\) | |||||||
\(348\) | 57.4949 | − | 111.897i | 0.165215 | − | 0.321542i | ||||
\(349\) | −2.46388 | + | 4.26756i | −0.00705982 | + | 0.0122280i | −0.869534 | − | 0.493874i | \(-0.835581\pi\) |
0.862474 | + | 0.506102i | \(0.168914\pi\) | |||||||
\(350\) | −26.2900 | − | 171.848i | −0.0751144 | − | 0.490993i | ||||
\(351\) | 443.185 | − | 351.450i | 1.26263 | − | 1.00128i | ||||
\(352\) | 8.23544 | + | 14.2642i | 0.0233961 | + | 0.0405233i | ||||
\(353\) | −530.683 | + | 306.390i | −1.50335 | + | 0.867960i | −0.503359 | + | 0.864078i | \(0.667903\pi\) |
−0.999992 | + | 0.00388263i | \(0.998764\pi\) | |||||||
\(354\) | 8.95753 | + | 182.828i | 0.0253037 | + | 0.516462i | ||||
\(355\) | −1.70229 | + | 2.94845i | −0.00479518 | + | 0.00830550i | ||||
\(356\) | −31.0063 | + | 17.9015i | −0.0870963 | + | 0.0502850i | ||||
\(357\) | −397.934 | − | 449.737i | −1.11466 | − | 1.25977i | ||||
\(358\) | −135.791 | + | 235.196i | −0.379304 | + | 0.656973i | ||||
\(359\) | −461.352 | + | 266.362i | −1.28510 | + | 0.741955i | −0.977777 | − | 0.209649i | \(-0.932768\pi\) |
−0.307327 | + | 0.951604i | \(0.599435\pi\) | |||||||
\(360\) | 28.6704 | − | 63.2325i | 0.0796401 | − | 0.175646i | ||||
\(361\) | −449.046 | + | 777.771i | −1.24390 | + | 2.15449i | ||||
\(362\) | 63.8019i | 0.176248i | ||||||||
\(363\) | −300.251 | − | 154.275i | −0.827136 | − | 0.425000i | ||||
\(364\) | 289.913 | − | 44.3522i | 0.796465 | − | 0.121847i | ||||
\(365\) | −30.6313 | + | 17.6850i | −0.0839212 | + | 0.0484520i | ||||
\(366\) | 128.376 | − | 6.28972i | 0.350755 | − | 0.0171850i | ||||
\(367\) | 185.198 | + | 320.773i | 0.504628 | + | 0.874041i | 0.999986 | + | 0.00535178i | \(0.00170353\pi\) |
−0.495358 | + | 0.868689i | \(0.664963\pi\) | |||||||
\(368\) | 54.4743 | + | 31.4508i | 0.148028 | + | 0.0854641i | ||||
\(369\) | −223.102 | + | 159.784i | −0.604614 | + | 0.433018i | ||||
\(370\) | −44.7881 | −0.121049 | ||||||||
\(371\) | −95.8268 | + | 76.7660i | −0.258293 | + | 0.206917i | ||||
\(372\) | 3.65993 | + | 74.7011i | 0.00983853 | + | 0.200809i | ||||
\(373\) | 209.212 | − | 362.366i | 0.560891 | − | 0.971492i | −0.436528 | − | 0.899691i | \(-0.643792\pi\) |
0.997419 | − | 0.0718011i | \(-0.0228747\pi\) | |||||||
\(374\) | 117.750i | 0.314838i | ||||||||
\(375\) | 347.829 | − | 17.0417i | 0.927544 | − | 0.0454445i | ||||
\(376\) | 239.305 | 0.636449 | ||||||||
\(377\) | 439.243i | 1.16510i | ||||||||
\(378\) | 59.6139 | − | 260.554i | 0.157709 | − | 0.689295i | ||||
\(379\) | 241.600 | 0.637468 | 0.318734 | − | 0.947844i | \(-0.396742\pi\) | ||||
0.318734 | + | 0.947844i | \(0.396742\pi\) | |||||||
\(380\) | 193.558i | 0.509362i | ||||||||
\(381\) | −12.7000 | − | 259.213i | −0.0333333 | − | 0.680350i | ||||
\(382\) | 123.419 | 0.323087 | ||||||||
\(383\) | −145.452 | − | 83.9766i | −0.379770 | − | 0.219260i | 0.297948 | − | 0.954582i | \(-0.403698\pi\) |
−0.677718 | + | 0.735322i | \(0.737031\pi\) | |||||||
\(384\) | −33.9005 | + | 1.66093i | −0.0882825 | + | 0.00432534i | ||||
\(385\) | 20.1948 | − | 51.7913i | 0.0524539 | − | 0.134523i | ||||
\(386\) | 223.495i | 0.579002i | ||||||||
\(387\) | 94.0317 | − | 207.387i | 0.242976 | − | 0.535883i | ||||
\(388\) | 5.24396 | − | 9.08281i | 0.0135154 | − | 0.0234093i | ||||
\(389\) | 436.463 | − | 251.992i | 1.12201 | − | 0.647795i | 0.180099 | − | 0.983648i | \(-0.442358\pi\) |
0.941914 | + | 0.335854i | \(0.109025\pi\) | |||||||
\(390\) | 11.8625 | + | 242.120i | 0.0304167 | + | 0.620820i | ||||
\(391\) | 224.840 | + | 389.435i | 0.575039 | + | 0.995997i | ||||
\(392\) | 93.8176 | − | 102.011i | 0.239331 | − | 0.260232i | ||||
\(393\) | −138.730 | + | 269.997i | −0.353004 | + | 0.687016i | ||||
\(394\) | −102.585 | −0.260368 | ||||||||
\(395\) | 244.537 | + | 141.183i | 0.619080 | + | 0.357426i | ||||
\(396\) | −42.6094 | + | 30.5164i | −0.107599 | + | 0.0770616i | ||||
\(397\) | 170.757 | + | 295.760i | 0.430118 | + | 0.744986i | 0.996883 | − | 0.0788933i | \(-0.0251386\pi\) |
−0.566765 | + | 0.823879i | \(0.691805\pi\) | |||||||
\(398\) | −382.863 | − | 221.046i | −0.961966 | − | 0.555391i | ||||
\(399\) | 148.597 | + | 730.191i | 0.372423 | + | 1.83005i | ||||
\(400\) | −35.1224 | − | 60.8338i | −0.0878060 | − | 0.152084i | ||||
\(401\) | −589.296 | − | 340.230i | −1.46957 | − | 0.848455i | −0.470150 | − | 0.882587i | \(-0.655800\pi\) |
−0.999417 | + | 0.0341316i | \(0.989133\pi\) | |||||||
\(402\) | 366.337 | − | 17.9485i | 0.911287 | − | 0.0446479i | ||||
\(403\) | −130.566 | − | 226.147i | −0.323985 | − | 0.561158i | ||||
\(404\) | −310.157 | + | 179.069i | −0.767716 | + | 0.443241i | ||||
\(405\) | 209.159 | + | 71.1232i | 0.516442 | + | 0.175613i | ||||
\(406\) | 129.773 | + | 161.995i | 0.319638 | + | 0.399002i | ||||
\(407\) | 29.2798 | + | 16.9047i | 0.0719405 | + | 0.0415349i | ||||
\(408\) | −215.821 | − | 110.893i | −0.528972 | − | 0.271797i | ||||
\(409\) | −257.554 | −0.629717 | −0.314858 | − | 0.949139i | \(-0.601957\pi\) | ||||
−0.314858 | + | 0.949139i | \(0.601957\pi\) | |||||||
\(410\) | − | 117.608i | − | 0.286849i | ||||||
\(411\) | 66.1763 | + | 102.666i | 0.161013 | + | 0.249796i | ||||
\(412\) | 152.264 | − | 263.730i | 0.369574 | − | 0.640121i | ||||
\(413\) | −281.378 | − | 109.716i | −0.681303 | − | 0.265657i | ||||
\(414\) | −82.6521 | + | 182.289i | −0.199643 | + | 0.440311i | ||||
\(415\) | 55.5772 | + | 96.2625i | 0.133921 | + | 0.231958i | ||||
\(416\) | 102.629 | − | 59.2527i | 0.246704 | − | 0.142434i | ||||
\(417\) | 112.634 | − | 72.6015i | 0.270106 | − | 0.174104i | ||||
\(418\) | 73.0559 | − | 126.537i | 0.174775 | − | 0.302719i | ||||
\(419\) | 187.674 | − | 108.354i | 0.447909 | − | 0.258600i | −0.259038 | − | 0.965867i | \(-0.583405\pi\) |
0.706947 | + | 0.707267i | \(0.250072\pi\) | |||||||
\(420\) | 75.9084 | + | 85.7902i | 0.180734 | + | 0.204262i | ||||
\(421\) | −395.045 | + | 684.238i | −0.938349 | + | 1.62527i | −0.169799 | + | 0.985479i | \(0.554312\pi\) |
−0.768550 | + | 0.639790i | \(0.779021\pi\) | |||||||
\(422\) | 223.594 | − | 129.092i | 0.529844 | − | 0.305905i | ||||
\(423\) | 74.4361 | + | 757.816i | 0.175972 | + | 1.79153i | ||||
\(424\) | −24.8060 | + | 42.9653i | −0.0585048 | + | 0.101333i | ||||
\(425\) | − | 502.177i | − | 1.18159i | ||||||
\(426\) | 0.259164 | + | 5.28966i | 0.000608365 | + | 0.0124170i | ||||
\(427\) | −77.0397 | + | 197.576i | −0.180421 | + | 0.462706i | ||||
\(428\) | 258.414 | − | 149.196i | 0.603771 | − | 0.348588i | ||||
\(429\) | 83.6301 | − | 162.761i | 0.194942 | − | 0.379397i | ||||
\(430\) | 48.7948 | + | 84.5150i | 0.113476 | + | 0.196547i | ||||
\(431\) | 478.460 | + | 276.239i | 1.11012 | + | 0.640925i | 0.938859 | − | 0.344301i | \(-0.111884\pi\) |
0.171256 | + | 0.985227i | \(0.445218\pi\) | |||||||
\(432\) | −15.8045 | − | 106.837i | −0.0365846 | − | 0.247309i | ||||
\(433\) | −351.734 | −0.812319 | −0.406160 | − | 0.913802i | \(-0.633132\pi\) | ||||
−0.406160 | + | 0.913802i | \(0.633132\pi\) | |||||||
\(434\) | −114.968 | − | 44.8288i | −0.264902 | − | 0.103292i | ||||
\(435\) | −144.199 | + | 92.9475i | −0.331492 | + | 0.213672i | ||||
\(436\) | 22.0143 | − | 38.1298i | 0.0504914 | − | 0.0874537i | ||||
\(437\) | − | 557.995i | − | 1.27688i | ||||||
\(438\) | −25.1452 | + | 48.9377i | −0.0574092 | + | 0.111730i | ||||
\(439\) | 47.2343 | 0.107595 | 0.0537976 | − | 0.998552i | \(-0.482867\pi\) | ||||
0.0537976 | + | 0.998552i | \(0.482867\pi\) | |||||||
\(440\) | − | 22.4615i | − | 0.0510488i | ||||||
\(441\) | 352.225 | + | 265.365i | 0.798696 | + | 0.601735i | ||||
\(442\) | 847.190 | 1.91672 | ||||||||
\(443\) | 512.244i | 1.15631i | 0.815928 | + | 0.578154i | \(0.196227\pi\) | ||||
−0.815928 | + | 0.578154i | \(0.803773\pi\) | |||||||
\(444\) | −58.5592 | + | 37.7460i | −0.131890 | + | 0.0850134i | ||||
\(445\) | 48.8248 | 0.109719 | ||||||||
\(446\) | −307.137 | − | 177.326i | −0.688648 | − | 0.397591i | ||||
\(447\) | 86.0559 | − | 167.482i | 0.192519 | − | 0.374680i | ||||
\(448\) | 20.3440 | − | 52.1740i | 0.0454106 | − | 0.116460i | ||||
\(449\) | 560.296i | 1.24787i | 0.781475 | + | 0.623937i | \(0.214468\pi\) | ||||
−0.781475 | + | 0.623937i | \(0.785532\pi\) | |||||||
\(450\) | 181.720 | − | 130.146i | 0.403822 | − | 0.289213i | ||||
\(451\) | −44.3897 | + | 76.8853i | −0.0984251 | + | 0.170477i | ||||
\(452\) | −27.4417 | + | 15.8435i | −0.0607118 | + | 0.0350520i | ||||
\(453\) | 478.429 | − | 308.385i | 1.05614 | − | 0.680761i | ||||
\(454\) | −286.862 | − | 496.860i | −0.631855 | − | 1.09440i | ||||
\(455\) | −372.631 | − | 145.298i | −0.818969 | − | 0.319337i | ||||
\(456\) | 163.124 | + | 253.071i | 0.357729 | + | 0.554981i | ||||
\(457\) | 669.482 | 1.46495 | 0.732475 | − | 0.680794i | \(-0.238365\pi\) | ||||
0.732475 | + | 0.680794i | \(0.238365\pi\) | |||||||
\(458\) | 134.324 | + | 77.5520i | 0.293284 | + | 0.169328i | ||||
\(459\) | 284.039 | − | 717.942i | 0.618821 | − | 1.56414i | ||||
\(460\) | −42.8897 | − | 74.2871i | −0.0932385 | − | 0.161494i | ||||
\(461\) | 80.8290 | + | 46.6667i | 0.175334 | + | 0.101229i | 0.585099 | − | 0.810962i | \(-0.301056\pi\) |
−0.409765 | + | 0.912191i | \(0.634389\pi\) | |||||||
\(462\) | −17.2440 | − | 84.7353i | −0.0373246 | − | 0.183410i | ||||
\(463\) | −208.033 | − | 360.324i | −0.449316 | − | 0.778238i | 0.549026 | − | 0.835805i | \(-0.314999\pi\) |
−0.998342 | + | 0.0575676i | \(0.981666\pi\) | |||||||
\(464\) | 72.6327 | + | 41.9345i | 0.156536 | + | 0.0903761i | ||||
\(465\) | 46.6129 | − | 90.7180i | 0.100243 | − | 0.195092i | ||||
\(466\) | 48.9142 | + | 84.7219i | 0.104966 | + | 0.181807i | ||||
\(467\) | −646.848 | + | 373.458i | −1.38511 | + | 0.799696i | −0.992760 | − | 0.120119i | \(-0.961672\pi\) |
−0.392354 | + | 0.919814i | \(0.628339\pi\) | |||||||
\(468\) | 219.561 | + | 306.568i | 0.469147 | + | 0.655060i | ||||
\(469\) | −219.842 | + | 563.806i | −0.468746 | + | 1.20214i | ||||
\(470\) | −282.620 | − | 163.171i | −0.601320 | − | 0.347172i | ||||
\(471\) | −12.6287 | − | 257.758i | −0.0268126 | − | 0.547258i | ||||
\(472\) | −122.031 | −0.258541 | ||||||||
\(473\) | − | 73.6679i | − | 0.155746i | ||||||
\(474\) | 438.710 | − | 21.4943i | 0.925549 | − | 0.0453467i | ||||
\(475\) | −311.568 | + | 539.652i | −0.655933 | + | 1.13611i | ||||
\(476\) | 312.448 | − | 250.299i | 0.656403 | − | 0.525839i | ||||
\(477\) | −143.776 | − | 65.1898i | −0.301417 | − | 0.136666i | ||||
\(478\) | 168.654 | + | 292.117i | 0.352833 | + | 0.611124i | ||||
\(479\) | −9.52571 | + | 5.49967i | −0.0198867 | + | 0.0114816i | −0.509910 | − | 0.860228i | \(-0.670321\pi\) |
0.490024 | + | 0.871709i | \(0.336988\pi\) | |||||||
\(480\) | 41.1692 | + | 21.1536i | 0.0857691 | + | 0.0440700i | ||||
\(481\) | 121.627 | − | 210.664i | 0.252862 | − | 0.437970i | ||||
\(482\) | −345.160 | + | 199.278i | −0.716100 | + | 0.413441i | ||||
\(483\) | −218.831 | − | 247.319i | −0.453067 | − | 0.512048i | ||||
\(484\) | 112.522 | − | 194.894i | 0.232484 | − | 0.402674i | ||||
\(485\) | −12.3863 | + | 7.15124i | −0.0255388 | + | 0.0147448i | ||||
\(486\) | 333.410 | − | 83.2808i | 0.686029 | − | 0.171360i | ||||
\(487\) | −207.376 | + | 359.187i | −0.425824 | + | 0.737549i | −0.996497 | − | 0.0836282i | \(-0.973349\pi\) |
0.570673 | + | 0.821178i | \(0.306683\pi\) | |||||||
\(488\) | 85.6869i | 0.175588i | ||||||||
\(489\) | −184.456 | + | 118.896i | −0.377211 | + | 0.243142i | ||||
\(490\) | −180.356 | + | 56.5058i | −0.368073 | + | 0.115318i | ||||
\(491\) | 49.0458 | − | 28.3166i | 0.0998896 | − | 0.0576713i | −0.449223 | − | 0.893420i | \(-0.648299\pi\) |
0.549113 | + | 0.835748i | \(0.314966\pi\) | |||||||
\(492\) | −99.1164 | − | 153.770i | −0.201456 | − | 0.312540i | ||||
\(493\) | 299.788 | + | 519.248i | 0.608089 | + | 1.05324i | ||||
\(494\) | −910.412 | − | 525.627i | −1.84294 | − | 1.06402i | ||||
\(495\) | 71.1296 | − | 6.98668i | 0.143696 | − | 0.0141145i | ||||
\(496\) | −49.8605 | −0.100525 | ||||||||
\(497\) | −8.14097 | − | 3.17437i | −0.0163802 | − | 0.00638706i | ||||
\(498\) | 153.793 | + | 79.0220i | 0.308821 | + | 0.158679i | ||||
\(499\) | 223.211 | − | 386.613i | 0.447317 | − | 0.774775i | −0.550894 | − | 0.834575i | \(-0.685713\pi\) |
0.998210 | + | 0.0598003i | \(0.0190464\pi\) | |||||||
\(500\) | 232.164i | 0.464328i | ||||||||
\(501\) | −136.803 | − | 212.236i | −0.273059 | − | 0.423625i | ||||
\(502\) | −314.720 | −0.626932 | ||||||||
\(503\) | − | 198.013i | − | 0.393663i | −0.980437 | − | 0.196832i | \(-0.936935\pi\) | ||
0.980437 | − | 0.196832i | \(-0.0630652\pi\) | |||||||
\(504\) | 171.549 | + | 48.1952i | 0.340376 | + | 0.0956255i | ||||
\(505\) | 488.397 | 0.967122 | ||||||||
\(506\) | 64.7527i | 0.127970i | ||||||||
\(507\) | −720.088 | − | 369.997i | −1.42029 | − | 0.729776i | ||||
\(508\) | 173.016 | 0.340583 | ||||||||
\(509\) | 592.816 | + | 342.262i | 1.16467 | + | 0.672421i | 0.952418 | − | 0.304794i | \(-0.0985878\pi\) |
0.212249 | + | 0.977216i | \(0.431921\pi\) | |||||||
\(510\) | 179.272 | + | 278.124i | 0.351515 | + | 0.545341i | ||||
\(511\) | −56.7557 | − | 70.8480i | −0.111068 | − | 0.138646i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −750.672 | + | 595.290i | −1.46330 | + | 1.16041i | ||||
\(514\) | 238.307 | − | 412.759i | 0.463632 | − | 0.803034i | ||||
\(515\) | −359.650 | + | 207.644i | −0.698350 | + | 0.403193i | ||||
\(516\) | 135.024 | + | 69.3784i | 0.261675 | + | 0.134454i | ||||
\(517\) | 123.174 | + | 213.343i | 0.238247 | + | 0.412656i | ||||
\(518\) | −17.3833 | − | 113.628i | −0.0335585 | − | 0.219359i | ||||
\(519\) | 709.645 | − | 34.7686i | 1.36733 | − | 0.0669916i | ||||
\(520\) | −161.607 | −0.310783 | ||||||||
\(521\) | −818.004 | − | 472.275i | −1.57006 | − | 0.906477i | −0.996160 | − | 0.0875552i | \(-0.972095\pi\) |
−0.573905 | − | 0.818922i | \(-0.694572\pi\) | |||||||
\(522\) | −110.203 | + | 243.053i | −0.211117 | + | 0.465618i | ||||
\(523\) | −129.056 | − | 223.531i | −0.246761 | − | 0.427402i | 0.715864 | − | 0.698239i | \(-0.246033\pi\) |
−0.962625 | + | 0.270837i | \(0.912700\pi\) | |||||||
\(524\) | −175.257 | − | 101.185i | −0.334459 | − | 0.193100i | ||||
\(525\) | 73.5420 | + | 361.378i | 0.140080 | + | 0.688339i | ||||
\(526\) | 115.337 | + | 199.770i | 0.219272 | + | 0.379791i | ||||
\(527\) | −308.695 | − | 178.225i | −0.585759 | − | 0.338188i | ||||
\(528\) | −18.9298 | − | 29.3678i | −0.0358519 | − | 0.0556208i | ||||
\(529\) | −140.856 | − | 243.970i | −0.266269 | − | 0.461191i | ||||
\(530\) | 58.5921 | − | 33.8282i | 0.110551 | − | 0.0638267i | ||||
\(531\) | −37.9580 | − | 386.441i | −0.0714841 | − | 0.727762i | ||||
\(532\) | −491.059 | + | 75.1244i | −0.923042 | + | 0.141211i | ||||
\(533\) | 553.178 | + | 319.378i | 1.03786 | + | 0.599207i | ||||
\(534\) | 63.8371 | − | 41.1480i | 0.119545 | − | 0.0770561i | ||||
\(535\) | −406.918 | −0.760595 | ||||||||
\(536\) | 244.518i | 0.456190i | ||||||||
\(537\) | 263.295 | − | 512.426i | 0.490308 | − | 0.954238i | ||||
\(538\) | 351.488 | − | 608.794i | 0.653323 | − | 1.13159i | ||||
\(539\) | 139.233 | + | 31.1329i | 0.258318 | + | 0.0577605i | ||||
\(540\) | −54.1822 | + | 136.952i | −0.100337 | + | 0.253615i | ||||
\(541\) | −388.642 | − | 673.147i | −0.718377 | − | 1.24426i | −0.961643 | − | 0.274305i | \(-0.911552\pi\) |
0.243266 | − | 0.969960i | \(-0.421781\pi\) | |||||||
\(542\) | −211.177 | + | 121.923i | −0.389626 | + | 0.224951i | ||||
\(543\) | −6.62317 | − | 135.182i | −0.0121974 | − | 0.248954i | ||||
\(544\) | 80.8812 | − | 140.090i | 0.148679 | − | 0.257519i | ||||
\(545\) | −51.9979 | + | 30.0210i | −0.0954091 | + | 0.0550845i | ||||
\(546\) | −609.658 | + | 124.068i | −1.11659 | + | 0.227231i | ||||
\(547\) | 201.360 | − | 348.766i | 0.368118 | − | 0.637598i | −0.621154 | − | 0.783689i | \(-0.713336\pi\) |
0.989271 | + | 0.146090i | \(0.0466691\pi\) | |||||||
\(548\) | −70.5210 | + | 40.7153i | −0.128688 | + | 0.0742980i | ||||
\(549\) | −271.348 | + | 26.6530i | −0.494259 | + | 0.0485483i | ||||
\(550\) | 36.1560 | − | 62.6241i | 0.0657382 | − | 0.113862i | ||||
\(551\) | − | 743.996i | − | 1.35026i | ||||||
\(552\) | −118.684 | − | 60.9824i | −0.215007 | − | 0.110475i | ||||
\(553\) | −263.274 | + | 675.190i | −0.476083 | + | 1.22096i | ||||
\(554\) | −109.252 | + | 63.0765i | −0.197205 | + | 0.113857i | ||||
\(555\) | 94.8960 | − | 4.64937i | 0.170984 | − | 0.00837725i | ||||
\(556\) | 44.6685 | + | 77.3681i | 0.0803390 | + | 0.139151i | ||||
\(557\) | 155.838 | + | 89.9733i | 0.279782 | + | 0.161532i | 0.633325 | − | 0.773886i | \(-0.281690\pi\) |
−0.353543 | + | 0.935418i | \(0.615023\pi\) | |||||||
\(558\) | −15.5092 | − | 157.895i | −0.0277942 | − | 0.282966i | ||||
\(559\) | −530.030 | −0.948175 | ||||||||
\(560\) | −59.6014 | + | 47.7462i | −0.106431 | + | 0.0852610i | ||||
\(561\) | −12.2234 | − | 249.485i | −0.0217885 | − | 0.444715i | ||||
\(562\) | −332.171 | + | 575.338i | −0.591052 | + | 1.02373i | ||||
\(563\) | 9.40822i | 0.0167109i | 0.999965 | + | 0.00835544i | \(0.00265965\pi\) | ||||
−0.999965 | + | 0.00835544i | \(0.997340\pi\) | |||||||
\(564\) | −507.034 | + | 24.8418i | −0.898996 | + | 0.0440458i | ||||
\(565\) | 43.2118 | 0.0764811 | ||||||||
\(566\) | 67.0563i | 0.118474i | ||||||||
\(567\) | −99.2610 | + | 558.244i | −0.175064 | + | 0.984557i | ||||
\(568\) | −3.53067 | −0.00621597 | ||||||||
\(569\) | − | 33.0375i | − | 0.0580624i | −0.999579 | − | 0.0290312i | \(-0.990758\pi\) | ||
0.999579 | − | 0.0290312i | \(-0.00924221\pi\) | |||||||
\(570\) | −20.0929 | − | 410.106i | −0.0352507 | − | 0.719484i | ||||
\(571\) | −410.353 | −0.718657 | −0.359329 | − | 0.933211i | \(-0.616994\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616994\pi\) | |||||||
\(572\) | 105.649 | + | 60.9965i | 0.184701 | + | 0.106637i | ||||
\(573\) | −261.498 | + | 12.8120i | −0.456367 | + | 0.0223594i | ||||
\(574\) | 298.374 | − | 45.6465i | 0.519815 | − | 0.0795236i | ||||
\(575\) | − | 276.157i | − | 0.480272i | ||||||
\(576\) | 71.6552 | − | 7.03830i | 0.124401 | − | 0.0122193i | ||||
\(577\) | 205.506 | − | 355.947i | 0.356163 | − | 0.616892i | −0.631154 | − | 0.775658i | \(-0.717418\pi\) |
0.987316 | + | 0.158766i | \(0.0507516\pi\) | |||||||
\(578\) | 647.548 | − | 373.862i | 1.12033 | − | 0.646820i | ||||
\(579\) | −23.2006 | − | 473.536i | −0.0400701 | − | 0.817851i | ||||
\(580\) | −57.1865 | − | 99.0499i | −0.0985973 | − | 0.170776i | ||||
\(581\) | −222.648 | + | 178.362i | −0.383216 | + | 0.306991i | ||||
\(582\) | −10.1679 | + | 19.7888i | −0.0174707 | + | 0.0340014i | ||||
\(583\) | −51.0721 | −0.0876022 | ||||||||
\(584\) | −31.7657 | − | 18.3399i | −0.0543933 | − | 0.0314040i | ||||
\(585\) | −50.2681 | − | 511.767i | −0.0859284 | − | 0.874816i | ||||
\(586\) | −65.7468 | − | 113.877i | −0.112196 | − | 0.194329i | ||||
\(587\) | 474.540 | + | 273.976i | 0.808416 | + | 0.466739i | 0.846406 | − | 0.532539i | \(-0.178762\pi\) |
−0.0379895 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(588\) | −188.189 | + | 225.878i | −0.320050 | + | 0.384146i | ||||
\(589\) | 221.154 | + | 383.050i | 0.375474 | + | 0.650340i | ||||
\(590\) | 144.120 | + | 83.2075i | 0.244271 | + | 0.141030i | ||||
\(591\) | 217.355 | − | 10.6492i | 0.367775 | − | 0.0180189i | ||||
\(592\) | −23.2234 | − | 40.2241i | −0.0392287 | − | 0.0679461i | ||||
\(593\) | 347.401 | − | 200.572i | 0.585837 | − | 0.338233i | −0.177613 | − | 0.984100i | \(-0.556837\pi\) |
0.763450 | + | 0.645867i | \(0.223504\pi\) | |||||||
\(594\) | 87.1120 | − | 69.0807i | 0.146653 | − | 0.116297i | ||||
\(595\) | −539.670 | + | 82.5612i | −0.907009 | + | 0.138758i | ||||
\(596\) | 108.713 | + | 62.7657i | 0.182405 | + | 0.105312i | ||||
\(597\) | 834.147 | + | 428.603i | 1.39723 | + | 0.717928i | ||||
\(598\) | 465.886 | 0.779074 | ||||||||
\(599\) | 245.708i | 0.410197i | 0.978741 | + | 0.205098i | \(0.0657515\pi\) | ||||
−0.978741 | + | 0.205098i | \(0.934249\pi\) | |||||||
\(600\) | 80.7316 | + | 125.247i | 0.134553 | + | 0.208746i | ||||
\(601\) | 243.356 | − | 421.505i | 0.404919 | − | 0.701340i | −0.589393 | − | 0.807846i | \(-0.700633\pi\) |
0.994312 | + | 0.106507i | \(0.0339665\pi\) | |||||||
\(602\) | −195.477 | + | 156.595i | −0.324713 | + | 0.260125i | ||||
\(603\) | −774.324 | + | 76.0577i | −1.28412 | + | 0.126132i | ||||
\(604\) | 189.735 | + | 328.631i | 0.314132 | + | 0.544092i | ||||
\(605\) | −265.779 | + | 153.447i | −0.439304 | + | 0.253632i | ||||
\(606\) | 638.566 | − | 411.605i | 1.05374 | − | 0.679217i | ||||
\(607\) | 265.813 | − | 460.402i | 0.437913 | − | 0.758487i | −0.559616 | − | 0.828752i | \(-0.689051\pi\) |
0.997528 | + | 0.0702653i | \(0.0223846\pi\) | |||||||
\(608\) | −173.834 | + | 100.363i | −0.285911 | + | 0.165071i | ||||
\(609\) | −291.776 | − | 329.760i | −0.479107 | − | 0.541478i | ||||
\(610\) | 58.4259 | − | 101.197i | 0.0957802 | − | 0.165896i | ||||
\(611\) | 1534.97 | − | 886.216i | 2.51223 | − | 1.45044i | ||||
\(612\) | 468.788 | + | 212.554i | 0.765993 | + | 0.347311i | ||||
\(613\) | 417.393 | − | 722.946i | 0.680902 | − | 1.17936i | −0.293803 | − | 0.955866i | \(-0.594921\pi\) |
0.974706 | − | 0.223492i | \(-0.0717456\pi\) | |||||||
\(614\) | − | 286.117i | − | 0.465989i | ||||||
\(615\) | 12.2087 | + | 249.186i | 0.0198515 | + | 0.405180i | ||||
\(616\) | 56.9851 | − | 8.71783i | 0.0925082 | − | 0.0141523i | ||||
\(617\) | 739.602 | − | 427.009i | 1.19871 | − | 0.692073i | 0.238439 | − | 0.971157i | \(-0.423364\pi\) |
0.960267 | + | 0.279084i | \(0.0900308\pi\) | |||||||
\(618\) | −295.237 | + | 574.591i | −0.477730 | + | 0.929759i | ||||
\(619\) | 383.189 | + | 663.703i | 0.619045 | + | 1.07222i | 0.989660 | + | 0.143431i | \(0.0458136\pi\) |
−0.370615 | + | 0.928787i | \(0.620853\pi\) | |||||||
\(620\) | 58.8855 | + | 33.9976i | 0.0949766 | + | 0.0548348i | ||||
\(621\) | 156.198 | − | 394.810i | 0.251527 | − | 0.635765i | ||||
\(622\) | −420.045 | −0.675313 | ||||||||
\(623\) | 18.9501 | + | 123.869i | 0.0304174 | + | 0.198827i | ||||
\(624\) | −211.297 | + | 136.197i | −0.338617 | + | 0.218265i | ||||
\(625\) | −61.2128 | + | 106.024i | −0.0979405 | + | 0.169638i | ||||
\(626\) | 535.027i | 0.854676i | ||||||||
\(627\) | −141.654 | + | 275.687i | −0.225923 | + | 0.439692i | ||||
\(628\) | 172.045 | 0.273957 | ||||||||
\(629\) | − | 332.046i | − | 0.527895i | ||||||
\(630\) | −169.739 | − | 173.891i | −0.269427 | − | 0.276017i | ||||
\(631\) | 414.115 | 0.656283 | 0.328142 | − | 0.944629i | \(-0.393578\pi\) | ||||
0.328142 | + | 0.944629i | \(0.393578\pi\) | |||||||
\(632\) | 292.824i | 0.463330i | ||||||||
\(633\) | −460.346 | + | 296.729i | −0.727244 | + | 0.468765i | ||||
\(634\) | −365.193 | −0.576014 | ||||||||
\(635\) | −204.333 | − | 117.972i | −0.321784 | − | 0.185782i | ||||
\(636\) | 48.0983 | − | 93.6090i | 0.0756263 | − | 0.147184i | ||||
\(637\) | 223.997 | − | 1001.76i | 0.351643 | − | 1.57263i | ||||
\(638\) | 86.3373i | 0.135325i | ||||||||
\(639\) | −1.09822 | − | 11.1807i | −0.00171866 | − | 0.0174972i | ||||
\(640\) | −15.4286 | + | 26.7231i | −0.0241072 | + | 0.0417549i | ||||
\(641\) | 443.256 | − | 255.914i | 0.691507 | − | 0.399242i | −0.112669 | − | 0.993633i | \(-0.535940\pi\) |
0.804176 | + | 0.594391i | \(0.202607\pi\) | |||||||
\(642\) | −532.035 | + | 342.938i | −0.828715 | + | 0.534171i | ||||
\(643\) | 474.057 | + | 821.091i | 0.737258 | + | 1.27697i | 0.953725 | + | 0.300679i | \(0.0972132\pi\) |
−0.216467 | + | 0.976290i | \(0.569453\pi\) | |||||||
\(644\) | 171.821 | − | 137.644i | 0.266803 | − | 0.213733i | ||||
\(645\) | −112.159 | − | 174.003i | −0.173889 | − | 0.269773i | ||||
\(646\) | −1434.98 | −2.22133 | ||||||||
\(647\) | −118.963 | − | 68.6832i | −0.183868 | − | 0.106156i | 0.405241 | − | 0.914210i | \(-0.367188\pi\) |
−0.589109 | + | 0.808054i | \(0.700521\pi\) | |||||||
\(648\) | 44.5769 | + | 224.724i | 0.0687915 | + | 0.346796i | ||||
\(649\) | −62.8113 | − | 108.792i | −0.0967817 | − | 0.167631i | ||||
\(650\) | −450.571 | − | 260.137i | −0.693186 | − | 0.400211i | ||||
\(651\) | 248.244 | + | 83.0476i | 0.381328 | + | 0.127569i | ||||
\(652\) | −73.1516 | − | 126.702i | −0.112196 | − | 0.194329i | ||||
\(653\) | 126.996 | + | 73.3211i | 0.194481 | + | 0.112283i | 0.594078 | − | 0.804407i | \(-0.297517\pi\) |
−0.399598 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(654\) | −42.6852 | + | 83.0739i | −0.0652678 | + | 0.127024i | ||||
\(655\) | 137.986 | + | 238.999i | 0.210666 | + | 0.364884i | ||||
\(656\) | 105.624 | − | 60.9819i | 0.161012 | − | 0.0929602i | ||||
\(657\) | 48.1970 | − | 106.298i | 0.0733593 | − | 0.161794i | ||||
\(658\) | 304.275 | − | 780.343i | 0.462424 | − | 1.18593i | ||||
\(659\) | 736.802 | + | 425.393i | 1.11806 | + | 0.645513i | 0.940905 | − | 0.338670i | \(-0.109977\pi\) |
0.177155 | + | 0.984183i | \(0.443310\pi\) | |||||||
\(660\) | 2.33169 | + | 47.5909i | 0.00353286 | + | 0.0721074i | ||||
\(661\) | −280.785 | −0.424788 | −0.212394 | − | 0.977184i | \(-0.568126\pi\) | ||||
−0.212394 | + | 0.977184i | \(0.568126\pi\) | |||||||
\(662\) | 539.905i | 0.815566i | ||||||||
\(663\) | −1795.01 | + | 87.9453i | −2.70740 | + | 0.132648i | ||||
\(664\) | −57.6355 | + | 99.8276i | −0.0868004 | + | 0.150343i | ||||
\(665\) | 631.167 | + | 246.108i | 0.949123 | + | 0.370087i | ||||
\(666\) | 120.156 | − | 86.0543i | 0.180414 | − | 0.129211i | ||||
\(667\) | 164.859 | + | 285.544i | 0.247165 | + | 0.428103i | ||||
\(668\) | 145.784 | − | 84.1686i | 0.218240 | − | 0.126001i | ||||
\(669\) | 669.164 | + | 343.831i | 1.00024 | + | 0.513947i | ||||
\(670\) | 166.725 | − | 288.777i | 0.248844 | − | 0.431010i | ||||
\(671\) | −76.3909 | + | 44.1043i | −0.113846 | + | 0.0657292i | ||||
\(672\) | −37.6883 | + | 112.657i | −0.0560837 | + | 0.167644i | ||||
\(673\) | −182.652 | + | 316.362i | −0.271400 | + | 0.470078i | −0.969220 | − | 0.246194i | \(-0.920820\pi\) |
0.697821 | + | 0.716272i | \(0.254153\pi\) | |||||||
\(674\) | −297.450 | + | 171.733i | −0.441321 | + | 0.254797i | ||||
\(675\) | −371.514 | + | 294.615i | −0.550391 | + | 0.436466i | ||||
\(676\) | 269.861 | − | 467.413i | 0.399202 | − | 0.691439i | ||||
\(677\) | 942.705i | 1.39247i | 0.717812 | + | 0.696237i | \(0.245144\pi\) | ||||
−0.717812 | + | 0.696237i | \(0.754856\pi\) | |||||||
\(678\) | 56.4983 | − | 36.4175i | 0.0833308 | − | 0.0537132i | ||||
\(679\) | −22.9502 | − | 28.6487i | −0.0338000 | − | 0.0421925i | ||||
\(680\) | −191.042 | + | 110.298i | −0.280945 | + | 0.162203i | ||||
\(681\) | 659.376 | + | 1022.96i | 0.968246 | + | 1.50214i | ||||
\(682\) | −25.6639 | − | 44.4512i | −0.0376304 | − | 0.0651777i | ||||
\(683\) | 730.079 | + | 421.511i | 1.06893 | + | 0.617147i | 0.927889 | − | 0.372857i | \(-0.121622\pi\) |
0.141041 | + | 0.990004i | \(0.454955\pi\) | |||||||
\(684\) | −371.895 | − | 519.269i | −0.543706 | − | 0.759165i | ||||
\(685\) | 111.048 | 0.162113 | ||||||||
\(686\) | −213.356 | − | 435.634i | −0.311015 | − | 0.635035i | ||||
\(687\) | −292.654 | − | 150.372i | −0.425988 | − | 0.218882i | ||||
\(688\) | −50.6019 | + | 87.6450i | −0.0735493 | + | 0.127391i | ||||
\(689\) | 367.456i | 0.533318i | ||||||||
\(690\) | 98.5854 | + | 152.946i | 0.142877 | + | 0.221660i | ||||
\(691\) | −749.201 | −1.08423 | −0.542113 | − | 0.840305i | \(-0.682376\pi\) | ||||
−0.542113 | + | 0.840305i | \(0.682376\pi\) | |||||||
\(692\) | 473.664i | 0.684486i | ||||||||
\(693\) | 45.3324 | + | 177.745i | 0.0654147 | + | 0.256487i | ||||
\(694\) | −342.774 | −0.493910 | ||||||||
\(695\) | − | 121.830i | − | 0.175294i | ||||||
\(696\) | −158.246 | − | 81.3101i | −0.227365 | − | 0.116825i | ||||
\(697\) | 871.914 | 1.25095 | ||||||||
\(698\) | 6.03525 | + | 3.48445i | 0.00864648 | + | 0.00499205i | ||||
\(699\) | −112.433 | − | 174.429i | −0.160849 | − | 0.249541i | ||||
\(700\) | −243.029 | + | 37.1797i | −0.347185 | + | 0.0531139i | ||||
\(701\) | 849.790i | 1.21225i | 0.795368 | + | 0.606127i | \(0.207278\pi\) | ||||
−0.795368 | + | 0.606127i | \(0.792722\pi\) | |||||||
\(702\) | −497.025 | − | 626.758i | −0.708013 | − | 0.892817i | ||||
\(703\) | −206.013 | + | 356.825i | −0.293048 | + | 0.507575i | ||||
\(704\) | 20.1726 | − | 11.6467i | 0.0286543 | − | 0.0165436i | ||||
\(705\) | 615.749 | + | 316.385i | 0.873402 | + | 0.448773i | ||||
\(706\) | 433.301 | + | 750.499i | 0.613741 | + | 1.06303i | ||||
\(707\) | 189.558 | + | 1239.07i | 0.268117 | + | 1.75257i | ||||
\(708\) | 258.557 | − | 12.6679i | 0.365194 | − | 0.0178925i | ||||
\(709\) | −875.721 | −1.23515 | −0.617575 | − | 0.786512i | \(-0.711885\pi\) | ||||
−0.617575 | + | 0.786512i | \(0.711885\pi\) | |||||||
\(710\) | 4.16974 | + | 2.40740i | 0.00587288 | + | 0.00339071i | ||||
\(711\) | −927.299 | + | 91.0835i | −1.30422 | + | 0.128106i | ||||
\(712\) | 25.3165 | + | 43.8495i | 0.0355569 | + | 0.0615863i | ||||
\(713\) | −169.757 | − | 98.0094i | −0.238089 | − | 0.137461i | ||||
\(714\) | −636.024 | + | 562.763i | −0.890791 | + | 0.788184i | ||||
\(715\) | −83.1815 | − | 144.075i | −0.116338 | − | 0.201503i | ||||
\(716\) | 332.618 | + | 192.037i | 0.464550 | + | 0.268208i | ||||
\(717\) | −387.665 | − | 601.425i | −0.540676 | − | 0.838807i | ||||
\(718\) | 376.693 | + | 652.451i | 0.524641 | + | 0.908706i | ||||
\(719\) | 32.2621 | − | 18.6266i | 0.0448708 | − | 0.0259062i | −0.477397 | − | 0.878688i | \(-0.658420\pi\) |
0.522268 | + | 0.852782i | \(0.325086\pi\) | |||||||
\(720\) | −89.4243 | − | 40.5461i | −0.124200 | − | 0.0563140i | ||||
\(721\) | −666.385 | − | 831.847i | −0.924252 | − | 1.15374i | ||||
\(722\) | 1099.93 | + | 635.048i | 1.52346 | + | 0.879567i | ||||
\(723\) | 710.632 | − | 458.057i | 0.982893 | − | 0.633551i | ||||
\(724\) | 90.2296 | 0.124626 | ||||||||
\(725\) | − | 368.210i | − | 0.507876i | ||||||
\(726\) | −218.178 | + | 424.618i | −0.300521 | + | 0.584874i | ||||
\(727\) | 92.7399 | − | 160.630i | 0.127565 | − | 0.220949i | −0.795168 | − | 0.606390i | \(-0.792617\pi\) |
0.922733 | + | 0.385440i | \(0.125950\pi\) | |||||||
\(728\) | −62.7235 | − | 409.999i | −0.0861587 | − | 0.563186i | ||||
\(729\) | −697.777 | + | 211.064i | −0.957170 | + | 0.289526i | ||||
\(730\) | 25.0103 | + | 43.3191i | 0.0342607 | + | 0.0593413i | ||||
\(731\) | −626.570 | + | 361.751i | −0.857142 | + | 0.494871i | ||||
\(732\) | −8.89500 | − | 181.552i | −0.0121516 | − | 0.248021i | ||||
\(733\) | 315.666 | − | 546.749i | 0.430649 | − | 0.745906i | −0.566280 | − | 0.824213i | \(-0.691618\pi\) |
0.996929 | + | 0.0783065i | \(0.0249513\pi\) | |||||||
\(734\) | 453.641 | − | 261.910i | 0.618040 | − | 0.356826i | ||||
\(735\) | 376.268 | − | 138.446i | 0.511930 | − | 0.188361i | ||||
\(736\) | 44.4781 | − | 77.0384i | 0.0604322 | − | 0.104672i | ||||
\(737\) | −217.991 | + | 125.857i | −0.295781 | + | 0.170769i | ||||
\(738\) | 225.968 | + | 315.514i | 0.306190 | + | 0.427526i | ||||
\(739\) | 245.760 | − | 425.669i | 0.332558 | − | 0.576007i | −0.650455 | − | 0.759545i | \(-0.725422\pi\) |
0.983013 | + | 0.183538i | \(0.0587550\pi\) | |||||||
\(740\) | 63.3399i | 0.0855944i | ||||||||
\(741\) | 1983.53 | + | 1019.18i | 2.67682 | + | 1.37541i | ||||
\(742\) | 108.564 | + | 135.520i | 0.146312 | + | 0.182641i | ||||
\(743\) | −487.432 | + | 281.419i | −0.656032 | + | 0.378760i | −0.790764 | − | 0.612122i | \(-0.790316\pi\) |
0.134731 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(744\) | 105.643 | − | 5.17593i | 0.141994 | − | 0.00695689i | ||||
\(745\) | −85.5942 | − | 148.253i | −0.114891 | − | 0.198998i | ||||
\(746\) | −512.464 | − | 295.871i | −0.686948 | − | 0.396610i | ||||
\(747\) | −334.056 | − | 151.465i | −0.447196 | − | 0.202765i | ||||
\(748\) | 166.523 | 0.222624 | ||||||||
\(749\) | −157.935 | − | 1032.36i | −0.210861 | − | 1.37831i | ||||
\(750\) | −24.1006 | − | 491.905i | −0.0321341 | − | 0.655873i | ||||
\(751\) | 32.3457 | − | 56.0244i | 0.0430702 | − | 0.0745997i | −0.843687 | − | 0.536836i | \(-0.819619\pi\) |
0.886757 | + | 0.462236i | \(0.152953\pi\) | |||||||
\(752\) | − | 338.428i | − | 0.450037i | ||||||
\(753\) | 666.821 | − | 32.6705i | 0.885553 | − | 0.0433871i | ||||
\(754\) | 621.184 | 0.823851 | ||||||||
\(755\) | − | 517.488i | − | 0.685414i | ||||||
\(756\) | −368.478 | − | 84.3068i | −0.487405 | − | 0.111517i | ||||
\(757\) | −629.889 | −0.832086 | −0.416043 | − | 0.909345i | \(-0.636583\pi\) | ||||
−0.416043 | + | 0.909345i | \(0.636583\pi\) | |||||||
\(758\) | − | 341.674i | − | 0.450758i | ||||||
\(759\) | −6.72187 | − | 137.197i | −0.00885622 | − | 0.180760i | ||||
\(760\) | 273.732 | 0.360174 | ||||||||
\(761\) | 412.140 | + | 237.949i | 0.541577 | + | 0.312680i | 0.745718 | − | 0.666262i | \(-0.232107\pi\) |
−0.204141 | + | 0.978942i | \(0.565440\pi\) | |||||||
\(762\) | −366.583 | + | 17.9605i | −0.481080 | + | 0.0235702i | ||||
\(763\) | −96.3454 | − | 120.268i | −0.126272 | − | 0.157625i | ||||
\(764\) | − | 174.541i | − | 0.228457i | ||||||
\(765\) | −408.710 | − | 570.673i | −0.534262 | − | 0.745978i | ||||
\(766\) | −118.761 | + | 205.700i | −0.155040 | + | 0.268538i | ||||
\(767\) | −782.745 | + | 451.918i | −1.02053 | + | 0.589202i | ||||
\(768\) | 2.34891 | + | 47.9425i | 0.00305848 | + | 0.0624251i | ||||
\(769\) | 424.359 | + | 735.011i | 0.551832 | + | 0.955801i | 0.998142 | + | 0.0609226i | \(0.0194043\pi\) |
−0.446311 | + | 0.894878i | \(0.647262\pi\) | |||||||
\(770\) | −73.2440 | − | 28.5597i | −0.0951221 | − | 0.0370905i | ||||
\(771\) | −462.071 | + | 899.284i | −0.599314 | + | 1.16639i | ||||
\(772\) | 316.069 | 0.409416 | ||||||||
\(773\) | −45.6733 | − | 26.3695i | −0.0590857 | − | 0.0341132i | 0.470166 | − | 0.882578i | \(-0.344194\pi\) |
−0.529252 | + | 0.848465i | \(0.677527\pi\) | |||||||
\(774\) | −293.289 | − | 132.981i | −0.378926 | − | 0.171810i | ||||
\(775\) | 109.451 | + | 189.575i | 0.141227 | + | 0.244613i | ||||
\(776\) | −12.8450 | − | 7.41609i | −0.0165529 | − | 0.00955681i | ||||
\(777\) | 48.6269 | + | 238.948i | 0.0625829 | + | 0.307526i | ||||
\(778\) | −356.371 | − | 617.252i | −0.458060 | − | 0.793383i | ||||
\(779\) | −936.980 | − | 540.966i | −1.20280 | − | 0.694436i | ||||
\(780\) | 342.409 | − | 16.7761i | 0.438986 | − | 0.0215079i | ||||
\(781\) | −1.81729 | − | 3.14764i | −0.00232687 | − | 0.00403026i | ||||
\(782\) | 550.744 | − | 317.972i | 0.704276 | − | 0.406614i | ||||
\(783\) | 208.265 | − | 526.415i | 0.265984 | − | 0.672305i | ||||
\(784\) | −144.265 | − | 132.678i | −0.184012 | − | 0.169232i | ||||
\(785\) | −203.186 | − | 117.310i | −0.258836 | − | 0.149439i | ||||
\(786\) | 381.834 | + | 196.195i | 0.485794 | + | 0.249611i | ||||
\(787\) | −312.691 | −0.397320 | −0.198660 | − | 0.980068i | \(-0.563659\pi\) | ||||
−0.198660 | + | 0.980068i | \(0.563659\pi\) | |||||||
\(788\) | 145.077i | 0.184108i | ||||||||
\(789\) | −265.112 | − | 411.295i | −0.336010 | − | 0.521287i | ||||
\(790\) | 199.663 | − | 345.827i | 0.252739 | − | 0.437756i | ||||
\(791\) | 16.7715 | + | 109.629i | 0.0212030 | + | 0.138595i | ||||
\(792\) | 43.1567 | + | 60.2587i | 0.0544908 | + | 0.0760843i | ||||
\(793\) | 317.324 | + | 549.621i | 0.400156 | + | 0.693091i | ||||
\(794\) | 418.267 | − | 241.487i | 0.526785 | − | 0.304139i | ||||
\(795\) | −120.632 | + | 77.7568i | −0.151738 | + | 0.0978072i | ||||
\(796\) | −312.606 | + | 541.449i | −0.392721 | + | 0.680213i | ||||
\(797\) | 406.221 | − | 234.532i | 0.509688 | − | 0.294269i | −0.223017 | − | 0.974814i | \(-0.571591\pi\) |
0.732705 | + | 0.680546i | \(0.238257\pi\) | |||||||
\(798\) | 1032.65 | − | 210.148i | 1.29404 | − | 0.263343i | ||||
\(799\) | 1209.70 | − | 2095.27i | 1.51402 | − | 2.62236i | ||||
\(800\) | −86.0319 | + | 49.6706i | −0.107540 | + | 0.0620882i | ||||
\(801\) | −130.985 | + | 93.8103i | −0.163527 | + | 0.117116i | ||||
\(802\) | −481.159 | + | 833.391i | −0.599948 | + | 1.03914i | ||||
\(803\) | − | 37.7593i | − | 0.0470228i | ||||||
\(804\) | −25.3830 | − | 518.079i | −0.0315709 | − | 0.644377i | ||||
\(805\) | −296.775 | + | 45.4020i | −0.368665 | + | 0.0564000i | ||||
\(806\) | −319.820 | + | 184.648i | −0.396799 | + | 0.229092i | ||||
\(807\) | −681.527 | + | 1326.39i | −0.844519 | + | 1.64360i | ||||
\(808\) | 253.242 | + | 438.629i | 0.313419 | + | 0.542857i | ||||
\(809\) | −476.849 | − | 275.309i | −0.589430 | − | 0.340308i | 0.175442 | − | 0.984490i | \(-0.443865\pi\) |
−0.764872 | + | 0.644182i | \(0.777198\pi\) | |||||||
\(810\) | 100.583 | − | 295.795i | 0.124177 | − | 0.365180i | ||||
\(811\) | −848.334 | −1.04604 | −0.523018 | − | 0.852322i | \(-0.675194\pi\) | ||||
−0.523018 | + | 0.852322i | \(0.675194\pi\) | |||||||
\(812\) | 229.095 | − | 183.526i | 0.282137 | − | 0.226018i | ||||
\(813\) | 434.782 | − | 280.251i | 0.534787 | − | 0.344712i | ||||
\(814\) | 23.9069 | − | 41.4079i | 0.0293696 | − | 0.0508696i | ||||
\(815\) | 199.515i | 0.244803i | ||||||||
\(816\) | −156.827 | + | 305.217i | −0.192190 | + | 0.374040i | ||||
\(817\) | 897.771 | 1.09886 | ||||||||
\(818\) | 364.237i | 0.445277i | ||||||||
\(819\) | 1278.85 | − | 326.160i | 1.56148 | − | 0.398242i | ||||
\(820\) | −166.323 | −0.202833 | ||||||||
\(821\) | − | 1379.51i | − | 1.68028i | −0.542373 | − | 0.840138i | \(-0.682474\pi\) | ||
0.542373 | − | 0.840138i | \(-0.317526\pi\) | |||||||
\(822\) | 145.192 | − | 93.5874i | 0.176632 | − | 0.113853i | ||||
\(823\) | −103.993 | −0.126359 | −0.0631794 | − | 0.998002i | \(-0.520124\pi\) | ||||
−0.0631794 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(824\) | −372.970 | − | 215.334i | −0.452634 | − | 0.261328i | ||||
\(825\) | −70.1057 | + | 136.440i | −0.0849767 | + | 0.165382i | ||||
\(826\) | −155.162 | + | 397.929i | −0.187848 | + | 0.481754i | ||||
\(827\) | 445.099i | 0.538209i | 0.963111 | + | 0.269104i | \(0.0867277\pi\) | ||||
−0.963111 | + | 0.269104i | \(0.913272\pi\) | |||||||
\(828\) | 257.796 | + | 116.888i | 0.311347 | + | 0.141169i | ||||
\(829\) | 370.808 | − | 642.258i | 0.447295 | − | 0.774738i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) |
0.998209 | + | 0.0598243i | \(0.0190541\pi\) | |||||||
\(830\) | 136.136 | − | 78.5980i | 0.164019 | − | 0.0946964i | ||||
\(831\) | 224.932 | − | 144.986i | 0.270677 | − | 0.174472i | ||||
\(832\) | −83.7960 | − | 145.139i | −0.100716 | − | 0.174446i | ||||
\(833\) | −418.918 | − | 1337.11i | −0.502903 | − | 1.60517i | ||||
\(834\) | −102.674 | − | 159.289i | −0.123110 | − | 0.190994i | ||||
\(835\) | −229.563 | −0.274926 | ||||||||
\(836\) | −178.950 | − | 103.317i | −0.214055 | − | 0.123585i | ||||
\(837\) | 49.2513 | + | 332.935i | 0.0588427 | + | 0.397772i | ||||
\(838\) | −153.235 | − | 265.411i | −0.182858 | − | 0.316720i | ||||
\(839\) | 290.739 | + | 167.858i | 0.346531 | + | 0.200069i | 0.663156 | − | 0.748481i | \(-0.269217\pi\) |
−0.316626 | + | 0.948551i | \(0.602550\pi\) | |||||||
\(840\) | 121.326 | − | 107.351i | 0.144435 | − | 0.127798i | ||||
\(841\) | −200.687 | − | 347.600i | −0.238629 | − | 0.413317i | ||||
\(842\) | 967.659 | + | 558.678i | 1.14924 | + | 0.663513i | ||||
\(843\) | 644.073 | − | 1253.50i | 0.764025 | − | 1.48695i | ||||
\(844\) | −182.564 | − | 316.210i | −0.216308 | − | 0.374656i | ||||
\(845\) | −637.415 | + | 368.012i | −0.754337 | + | 0.435517i | ||||
\(846\) | 1071.71 | − | 105.269i | 1.26680 | − | 0.124431i | ||||
\(847\) | −492.454 | − | 614.728i | −0.581409 | − | 0.725771i | ||||
\(848\) | 60.7621 | + | 35.0810i | 0.0716534 | + | 0.0413691i | ||||
\(849\) | −6.96100 | − | 142.077i | −0.00819905 | − | 0.167347i | ||||
\(850\) | −710.185 | −0.835512 | ||||||||
\(851\) | − | 182.599i | − | 0.214569i | ||||||
\(852\) | 7.48071 | − | 0.366513i | 0.00878018 | − | 0.000430179i | ||||
\(853\) | 346.509 | − | 600.172i | 0.406224 | − | 0.703601i | −0.588239 | − | 0.808687i | \(-0.700179\pi\) |
0.994463 | + | 0.105086i | \(0.0335119\pi\) | |||||||
\(854\) | 279.414 | + | 108.951i | 0.327183 | + | 0.127577i | ||||
\(855\) | 85.1448 | + | 866.838i | 0.0995845 | + | 1.01385i | ||||
\(856\) | −210.994 | − | 365.453i | −0.246489 | − | 0.426931i | ||||
\(857\) | −735.467 | + | 424.622i | −0.858188 | + | 0.495475i | −0.863405 | − | 0.504511i | \(-0.831673\pi\) |
0.00521719 | + | 0.999986i | \(0.498339\pi\) | |||||||
\(858\) | −230.179 | − | 118.271i | −0.268274 | − | 0.137845i | ||||
\(859\) | −730.939 | + | 1266.02i | −0.850919 | + | 1.47383i | 0.0294619 | + | 0.999566i | \(0.490621\pi\) |
−0.880380 | + | 0.474268i | \(0.842713\pi\) | |||||||
\(860\) | 119.522 | − | 69.0062i | 0.138979 | − | 0.0802398i | ||||
\(861\) | −627.449 | + | 127.689i | −0.728745 | + | 0.148303i | ||||
\(862\) | 390.661 | − | 676.644i | 0.453203 | − | 0.784970i | ||||
\(863\) | 262.264 | − | 151.418i | 0.303898 | − | 0.175455i | −0.340295 | − | 0.940319i | \(-0.610527\pi\) |
0.644193 | + | 0.764863i | \(0.277194\pi\) | |||||||
\(864\) | −151.091 | + | 22.3510i | −0.174874 | + | 0.0258692i | ||||
\(865\) | 322.970 | − | 559.400i | 0.373376 | − | 0.646706i | ||||
\(866\) | 497.427i | 0.574396i | ||||||||
\(867\) | −1333.20 | + | 859.352i | −1.53772 | + | 0.991179i | ||||
\(868\) | −63.3974 | + | 162.589i | −0.0730385 | + | 0.187314i | ||||
\(869\) | −261.056 | + | 150.721i | −0.300410 | + | 0.173442i | ||||
\(870\) | 131.448 | + | 203.928i | 0.151089 | + | 0.234400i | ||||
\(871\) | 905.522 | + | 1568.41i | 1.03963 | + | 1.80070i | ||||
\(872\) | −53.9237 | − | 31.1329i | −0.0618391 | − | 0.0357028i | ||||
\(873\) | 19.4893 | − | 42.9837i | 0.0223246 | − | 0.0492368i | ||||
\(874\) | −789.124 | −0.902888 | ||||||||
\(875\) | 757.058 | + | 295.196i | 0.865209 | + | 0.337367i | ||||
\(876\) | 69.2083 | + | 35.5607i | 0.0790049 | + | 0.0405944i | ||||
\(877\) | 155.891 | − | 270.011i | 0.177754 | − | 0.307880i | −0.763357 | − | 0.645977i | \(-0.776450\pi\) |
0.941111 | + | 0.338098i | \(0.109783\pi\) | |||||||
\(878\) | − | 66.7994i | − | 0.0760813i | ||||||
\(879\) | 151.124 | + | 234.455i | 0.171927 | + | 0.266729i | ||||
\(880\) | −31.7653 | −0.0360969 | ||||||||
\(881\) | − | 1088.82i | − | 1.23589i | −0.786220 | − | 0.617947i | \(-0.787965\pi\) | ||
0.786220 | − | 0.617947i | \(-0.212035\pi\) | |||||||
\(882\) | 375.283 | − | 498.121i | 0.425491 | − | 0.564763i | ||||
\(883\) | 877.900 | 0.994224 | 0.497112 | − | 0.867686i | \(-0.334394\pi\) | ||||
0.497112 | + | 0.867686i | \(0.334394\pi\) | |||||||
\(884\) | − | 1198.11i | − | 1.35533i | ||||||
\(885\) | −313.995 | − | 161.338i | −0.354797 | − | 0.182302i | ||||
\(886\) | 724.422 | 0.817633 | ||||||||
\(887\) | −1311.60 | − | 757.255i | −1.47870 | − | 0.853726i | −0.478987 | − | 0.877822i | \(-0.658996\pi\) |
−0.999710 | + | 0.0240962i | \(0.992329\pi\) | |||||||
\(888\) | 53.3808 | + | 82.8152i | 0.0601136 | + | 0.0932604i | ||||
\(889\) | 219.989 | − | 564.184i | 0.247457 | − | 0.634627i | ||||
\(890\) | − | 69.0487i | − | 0.0775828i | ||||||
\(891\) | −177.400 | + | 155.410i | −0.199102 | + | 0.174422i | ||||
\(892\) | −250.776 | + | 434.358i | −0.281140 | + | 0.486948i | ||||
\(893\) | −2599.96 | + | 1501.08i | −2.91148 | + | 1.68095i | ||||
\(894\) | −236.855 | − | 121.701i | −0.264939 | − | 0.136131i | ||||
\(895\) | −261.883 | − | 453.594i | −0.292606 | − | 0.506809i | ||||
\(896\) | −73.7851 | − | 28.7707i | −0.0823495 | − | 0.0321102i | ||||
\(897\) | −987.110 | + | 48.3628i | −1.10046 | + | 0.0539162i | ||||
\(898\) | 792.378 | 0.882380 | ||||||||
\(899\) | −226.344 | − | 130.680i | −0.251773 | − | 0.145361i | ||||
\(900\) | −184.054 | − | 256.991i | −0.204505 | − | 0.285545i | ||||
\(901\) | 250.793 | + | 434.385i | 0.278349 | + | 0.482115i | ||||
\(902\) | 108.732 | + | 62.7766i | 0.120546 | + | 0.0695971i | ||||
\(903\) | 397.917 | − | 352.083i | 0.440662 | − | 0.389904i | ||||
\(904\) | 22.4061 | + | 38.8085i | 0.0247855 | + | 0.0429297i | ||||
\(905\) | −106.562 | − | 61.5234i | −0.117748 | − | 0.0679817i | ||||
\(906\) | −436.122 | − | 676.601i | −0.481371 | − | 0.746800i | ||||
\(907\) | 183.872 | + | 318.475i | 0.202725 | + | 0.351131i | 0.949406 | − | 0.314052i | \(-0.101687\pi\) |
−0.746680 | + | 0.665183i | \(0.768353\pi\) | |||||||
\(908\) | −702.666 | + | 405.684i | −0.773861 | + | 0.446789i | ||||
\(909\) | −1310.25 | + | 938.389i | −1.44142 | + | 1.03233i | ||||
\(910\) | −205.483 | + | 526.980i | −0.225805 | + | 0.579099i | ||||
\(911\) | −742.768 | − | 428.837i | −0.815333 | − | 0.470733i | 0.0334717 | − | 0.999440i | \(-0.489344\pi\) |
−0.848804 | + | 0.528707i | \(0.822677\pi\) | |||||||
\(912\) | 357.897 | − | 230.693i | 0.392431 | − | 0.252952i | ||||
\(913\) | −118.663 | −0.129971 | ||||||||
\(914\) | − | 946.791i | − | 1.03588i | ||||||
\(915\) | −113.287 | + | 220.479i | −0.123810 | + | 0.240960i | ||||
\(916\) | 109.675 | − | 189.963i | 0.119733 | − | 0.207383i | ||||
\(917\) | −552.788 | + | 442.834i | −0.602823 | + | 0.482916i | ||||
\(918\) | −1015.32 | − | 401.692i | −1.10602 | − | 0.437573i | ||||
\(919\) | −52.7068 | − | 91.2909i | −0.0573524 | − | 0.0993372i | 0.835924 | − | 0.548846i | \(-0.184933\pi\) |
−0.893276 | + | 0.449508i | \(0.851599\pi\) | |||||||
\(920\) | −105.058 | + | 60.6552i | −0.114193 | + | 0.0659295i | ||||
\(921\) | 29.7013 | + | 606.219i | 0.0322490 | + | 0.658218i | ||||
\(922\) | 65.9966 | − | 114.310i | 0.0715798 | − | 0.123980i | ||||
\(923\) | −22.6468 | + | 13.0751i | −0.0245360 | + | 0.0141659i | ||||
\(924\) | −119.834 | + | 24.3867i | −0.129690 | + | 0.0263925i | ||||
\(925\) | −101.958 | + | 176.596i | −0.110225 | + | 0.190914i | ||||
\(926\) | −509.575 | + | 294.203i | −0.550297 | + | 0.317714i | ||||
\(927\) | 565.895 | − | 1248.08i | 0.610459 | − | 1.34636i | ||||
\(928\) | 59.3044 | − | 102.718i | 0.0639056 | − | 0.110688i | ||||
\(929\) | 515.060i | 0.554424i | 0.960809 | + | 0.277212i | \(0.0894105\pi\) | ||||
−0.960809 | + | 0.277212i | \(0.910590\pi\) | |||||||
\(930\) | −128.295 | − | 65.9205i | −0.137951 | − | 0.0708823i | ||||
\(931\) | −379.409 | + | 1696.80i | −0.407528 | + | 1.82256i | ||||
\(932\) | 119.815 | − | 69.1752i | 0.128557 | − | 0.0742223i | ||||
\(933\) | 889.982 | − | 43.6041i | 0.953893 | − | 0.0467354i | ||||
\(934\) | 528.149 | + | 914.781i | 0.565470 | + | 0.979423i | ||||
\(935\) | −196.665 | − | 113.544i | −0.210337 | − | 0.121438i | ||||
\(936\) | 433.553 | − | 310.506i | 0.463197 | − | 0.331737i | ||||
\(937\) | 86.9061 | 0.0927493 | 0.0463746 | − | 0.998924i | \(-0.485233\pi\) | ||||
0.0463746 | + | 0.998924i | \(0.485233\pi\) | |||||||
\(938\) | 797.342 | + | 310.904i | 0.850044 | + | 0.331454i | ||||
\(939\) | −55.5403 | − | 1133.60i | −0.0591483 | − | 1.20725i | ||||
\(940\) | −230.759 | + | 399.686i | −0.245488 | + | 0.425197i | ||||
\(941\) | − | 677.244i | − | 0.719707i | −0.933009 | − | 0.359853i | \(-0.882827\pi\) | ||
0.933009 | − | 0.359853i | \(-0.117173\pi\) | |||||||
\(942\) | −364.525 | + | 17.8597i | −0.386970 | + | 0.0189593i | ||||
\(943\) | 479.482 | 0.508465 | ||||||||
\(944\) | 172.578i | 0.182816i | ||||||||
\(945\) | 377.690 | + | 350.815i | 0.399672 | + | 0.371233i | ||||
\(946\) | −104.182 | −0.110129 | ||||||||
\(947\) | 947.519i | 1.00055i | 0.865867 | + | 0.500274i | \(0.166767\pi\) | ||||
−0.865867 | + | 0.500274i | \(0.833233\pi\) | |||||||
\(948\) | −30.3976 | − | 620.430i | −0.0320650 | − | 0.654462i | ||||
\(949\) | −271.673 | −0.286273 | ||||||||
\(950\) | 763.183 | + | 440.624i | 0.803350 | + | 0.463815i | ||||
\(951\) | 773.763 | − | 37.9101i | 0.813631 | − | 0.0398634i | ||||
\(952\) | −353.977 | − | 441.868i | −0.371824 | − | 0.464147i | ||||
\(953\) | 1873.88i | 1.96630i | 0.182805 | + | 0.983149i | \(0.441482\pi\) | ||||
−0.182805 | + | 0.983149i | \(0.558518\pi\) | |||||||
\(954\) | −92.1923 | + | 203.330i | −0.0966376 | + | 0.213134i | ||||
\(955\) | −119.012 | + | 206.134i | −0.124620 | + | 0.215848i | ||||
\(956\) | 413.116 | − | 238.513i | 0.432130 | − | 0.249490i | ||||
\(957\) | −8.96252 | − | 182.930i | −0.00936523 | − | 0.191149i | ||||
\(958\) | 7.77771 | + | 13.4714i | 0.00811870 | + | 0.0140620i | ||||
\(959\) | 43.1002 | + | 281.729i | 0.0449429 | + | 0.293774i | ||||
\(960\) | 29.9157 | − | 58.2220i | 0.0311622 | − | 0.0606479i | ||||
\(961\) | −805.621 | −0.838315 | ||||||||
\(962\) | −297.924 | − | 172.006i | −0.309692 | − | 0.178801i | ||||
\(963\) | 1091.66 | − | 781.839i | 1.13361 | − | 0.811878i | ||||
\(964\) | 281.822 | + | 488.130i | 0.292347 | + | 0.506359i | ||||
\(965\) | −373.280 | − | 215.513i | −0.386818 | − | 0.223330i | ||||
\(966\) | −349.762 | + | 309.474i | −0.362073 | + | 0.320367i | ||||
\(967\) | −801.055 | − | 1387.47i | −0.828392 | − | 1.43482i | −0.899299 | − | 0.437334i | \(-0.855923\pi\) |
0.0709071 | − | 0.997483i | \(-0.477411\pi\) | |||||||
\(968\) | −275.622 | − | 159.130i | −0.284733 | − | 0.164391i | ||||
\(969\) | 3040.41 | − | 148.963i | 3.13768 | − | 0.153729i | ||||
\(970\) | 10.1134 | + | 17.5169i | 0.0104262 | + | 0.0180586i | ||||
\(971\) | 1566.15 | − | 904.219i | 1.61293 | − | 0.931225i | 0.624242 | − | 0.781231i | \(-0.285408\pi\) |
0.988687 | − | 0.149994i | \(-0.0479253\pi\) | |||||||
\(972\) | −117.777 | − | 471.513i | −0.121170 | − | 0.485096i | ||||
\(973\) | 309.083 | − | 47.2850i | 0.317660 | − | 0.0485971i | ||||
\(974\) | 507.966 | + | 293.275i | 0.521526 | + | 0.301103i | ||||
\(975\) | 981.665 | + | 504.400i | 1.00684 | + | 0.517334i | ||||
\(976\) | 121.180 | 0.124159 | ||||||||
\(977\) | 36.3348i | 0.0371902i | 0.999827 | + | 0.0185951i | \(0.00591934\pi\) | ||||
−0.999827 | + | 0.0185951i | \(0.994081\pi\) | |||||||
\(978\) | 168.145 | + | 260.860i | 0.171927 | + | 0.266728i | ||||
\(979\) | −26.0616 | + | 45.1400i | −0.0266206 | + | 0.0461082i | ||||
\(980\) | 79.9112 | + | 255.062i | 0.0815421 | + | 0.260267i | ||||
\(981\) | 81.8167 | − | 180.446i | 0.0834013 | − | 0.183941i | ||||
\(982\) | −40.0457 | − | 69.3613i | −0.0407798 | − | 0.0706326i | ||||
\(983\) | 677.386 | − | 391.089i | 0.689101 | − | 0.397853i | −0.114174 | − | 0.993461i | \(-0.536422\pi\) |
0.803275 | + | 0.595608i | \(0.203089\pi\) | |||||||
\(984\) | −217.463 | + | 140.172i | −0.220999 | + | 0.142451i | ||||
\(985\) | 98.9214 | − | 171.337i | 0.100428 | − | 0.173946i | ||||
\(986\) | 734.328 | − | 423.964i | 0.744754 | − | 0.429984i | ||||
\(987\) | −563.686 | + | 1684.96i | −0.571111 | + | 1.70715i | ||||
\(988\) | −743.348 | + | 1287.52i | −0.752377 | + | 1.30315i | ||||
\(989\) | −344.563 | + | 198.934i | −0.348395 | + | 0.201146i | ||||
\(990\) | −9.88065 | − | 100.593i | −0.00998046 | − | 0.101609i | ||||
\(991\) | −716.282 | + | 1240.64i | −0.722787 | + | 1.25190i | 0.237091 | + | 0.971488i | \(0.423806\pi\) |
−0.959878 | + | 0.280417i | \(0.909527\pi\) | |||||||
\(992\) | 70.5133i | 0.0710820i | ||||||||
\(993\) | −56.0466 | − | 1143.94i | −0.0564417 | − | 1.15200i | ||||
\(994\) | −4.48924 | + | 11.5131i | −0.00451634 | + | 0.0115826i | ||||
\(995\) | 738.379 | − | 426.303i | 0.742090 | − | 0.428446i | ||||
\(996\) | 111.754 | − | 217.496i | 0.112203 | − | 0.218369i | ||||
\(997\) | 213.563 | + | 369.901i | 0.214205 | + | 0.371014i | 0.953026 | − | 0.302887i | \(-0.0979505\pi\) |
−0.738821 | + | 0.673902i | \(0.764617\pi\) | |||||||
\(998\) | −546.753 | − | 315.668i | −0.547849 | − | 0.316301i | ||||
\(999\) | −245.650 | + | 194.803i | −0.245896 | + | 0.194998i |
(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 | 126.3.r.a.11.5 | yes | 32 | |
3.2 | odd | 2 | 378.3.r.a.305.11 | 32 | |||
7.2 | even | 3 | 126.3.i.a.65.2 | ✓ | 32 | ||
9.4 | even | 3 | 378.3.i.a.179.11 | 32 | |||
9.5 | odd | 6 | 126.3.i.a.95.2 | yes | 32 | ||
21.2 | odd | 6 | 378.3.i.a.359.14 | 32 | |||
63.23 | odd | 6 | inner | 126.3.r.a.23.13 | yes | 32 | |
63.58 | even | 3 | 378.3.r.a.233.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.i.a.65.2 | ✓ | 32 | 7.2 | even | 3 | ||
126.3.i.a.95.2 | yes | 32 | 9.5 | odd | 6 | ||
126.3.r.a.11.5 | yes | 32 | 1.1 | even | 1 | trivial | |
126.3.r.a.23.13 | yes | 32 | 63.23 | odd | 6 | inner | |
378.3.i.a.179.11 | 32 | 9.4 | even | 3 | |||
378.3.i.a.359.14 | 32 | 21.2 | odd | 6 | |||
378.3.r.a.233.3 | 32 | 63.58 | even | 3 | |||
378.3.r.a.305.11 | 32 | 3.2 | odd | 2 |