Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,4,Mod(3,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.c (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.13923111069\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(-1.40126 + 1.01807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.9 |
Dual form | 121.4.c.f.27.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.226216 | − | 0.696222i | 0.0799795 | − | 0.246152i | −0.903070 | − | 0.429494i | \(-0.858692\pi\) |
0.983049 | + | 0.183343i | \(0.0586918\pi\) | |||||||
\(3\) | −4.79602 | + | 3.48451i | −0.922994 | + | 0.670594i | −0.944267 | − | 0.329179i | \(-0.893228\pi\) |
0.0212735 | + | 0.999774i | \(0.493228\pi\) | |||||||
\(4\) | 6.03859 | + | 4.38729i | 0.754823 | + | 0.548411i | ||||
\(5\) | −3.97285 | − | 12.2272i | −0.355342 | − | 1.09363i | −0.955811 | − | 0.293983i | \(-0.905019\pi\) |
0.600468 | − | 0.799648i | \(-0.294981\pi\) | |||||||
\(6\) | 1.34106 | + | 4.12734i | 0.0912473 | + | 0.280830i | ||||
\(7\) | 13.6952 | + | 9.95015i | 0.739472 | + | 0.537258i | 0.892546 | − | 0.450957i | \(-0.148917\pi\) |
−0.153074 | + | 0.988215i | \(0.548917\pi\) | |||||||
\(8\) | 9.15848 | − | 6.65403i | 0.404752 | − | 0.294069i | ||||
\(9\) | 2.51651 | − | 7.74502i | 0.0932040 | − | 0.286853i | ||||
\(10\) | −9.41154 | −0.297619 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −44.2487 | −1.06446 | ||||||||
\(13\) | −23.0653 | + | 70.9878i | −0.492090 | + | 1.51450i | 0.329352 | + | 0.944207i | \(0.393170\pi\) |
−0.821443 | + | 0.570291i | \(0.806830\pi\) | |||||||
\(14\) | 10.0256 | − | 7.28401i | 0.191389 | − | 0.139052i | ||||
\(15\) | 61.6595 | + | 44.7983i | 1.06136 | + | 0.771124i | ||||
\(16\) | 15.8914 | + | 48.9087i | 0.248303 | + | 0.764198i | ||||
\(17\) | 25.5819 | + | 78.7328i | 0.364971 | + | 1.12327i | 0.949999 | + | 0.312253i | \(0.101084\pi\) |
−0.585028 | + | 0.811013i | \(0.698916\pi\) | |||||||
\(18\) | −4.82297 | − | 3.50410i | −0.0631548 | − | 0.0458846i | ||||
\(19\) | −54.9509 | + | 39.9242i | −0.663505 | + | 0.482065i | −0.867845 | − | 0.496835i | \(-0.834495\pi\) |
0.204340 | + | 0.978900i | \(0.434495\pi\) | |||||||
\(20\) | 29.6537 | − | 91.2648i | 0.331539 | − | 1.02037i | ||||
\(21\) | −100.354 | −1.04281 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.3538 | 0.121064 | 0.0605319 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605319 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(24\) | −20.7382 | + | 63.8257i | −0.176382 | + | 0.542848i | ||||
\(25\) | −32.5930 | + | 23.6802i | −0.260744 | + | 0.189442i | ||||
\(26\) | 44.2055 | + | 32.1172i | 0.333439 | + | 0.242258i | ||||
\(27\) | −34.5433 | − | 106.313i | −0.246217 | − | 0.757779i | ||||
\(28\) | 39.0455 | + | 120.170i | 0.263532 | + | 0.811069i | ||||
\(29\) | 136.720 | + | 99.3327i | 0.875456 | + | 0.636056i | 0.932045 | − | 0.362342i | \(-0.118023\pi\) |
−0.0565897 | + | 0.998398i | \(0.518023\pi\) | |||||||
\(30\) | 45.1379 | − | 32.7946i | 0.274701 | − | 0.199582i | ||||
\(31\) | −20.2398 | + | 62.2918i | −0.117264 | + | 0.360901i | −0.992412 | − | 0.122953i | \(-0.960763\pi\) |
0.875149 | + | 0.483854i | \(0.160763\pi\) | |||||||
\(32\) | 128.210 | 0.708268 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 60.6025 | 0.305684 | ||||||||
\(35\) | 67.2532 | − | 206.984i | 0.324796 | − | 0.999619i | ||||
\(36\) | 49.1758 | − | 35.7283i | 0.227666 | − | 0.165409i | ||||
\(37\) | −33.0535 | − | 24.0148i | −0.146864 | − | 0.106703i | 0.511927 | − | 0.859029i | \(-0.328932\pi\) |
−0.658791 | + | 0.752326i | \(0.728932\pi\) | |||||||
\(38\) | 15.3653 | + | 47.2895i | 0.0655942 | + | 0.201878i | ||||
\(39\) | −136.736 | − | 420.830i | −0.561418 | − | 1.72787i | ||||
\(40\) | −117.745 | − | 85.5469i | −0.465429 | − | 0.338154i | ||||
\(41\) | 222.422 | − | 161.599i | 0.847230 | − | 0.615548i | −0.0771511 | − | 0.997019i | \(-0.524582\pi\) |
0.924381 | + | 0.381471i | \(0.124582\pi\) | |||||||
\(42\) | −22.7017 | + | 69.8685i | −0.0834034 | + | 0.256689i | ||||
\(43\) | 2.28719 | 0.00811146 | 0.00405573 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405573 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −104.697 | −0.346830 | ||||||||
\(46\) | 3.02085 | − | 9.29723i | 0.00968261 | − | 0.0298000i | ||||
\(47\) | −58.1247 | + | 42.2301i | −0.180391 | + | 0.131061i | −0.674316 | − | 0.738443i | \(-0.735562\pi\) |
0.493926 | + | 0.869504i | \(0.335562\pi\) | |||||||
\(48\) | −246.638 | − | 179.193i | −0.741649 | − | 0.538840i | ||||
\(49\) | −17.4397 | − | 53.6738i | −0.0508445 | − | 0.156483i | ||||
\(50\) | 9.11361 | + | 28.0488i | 0.0257772 | + | 0.0793340i | ||||
\(51\) | −397.036 | − | 288.464i | −1.09012 | − | 0.792020i | ||||
\(52\) | −450.726 | + | 327.472i | −1.20201 | + | 0.873311i | ||||
\(53\) | −46.0451 | + | 141.712i | −0.119336 | + | 0.367277i | −0.992827 | − | 0.119563i | \(-0.961851\pi\) |
0.873491 | + | 0.486840i | \(0.161851\pi\) | |||||||
\(54\) | −81.8320 | −0.206221 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 191.636 | 0.457293 | ||||||||
\(57\) | 124.429 | − | 382.954i | 0.289141 | − | 0.889886i | ||||
\(58\) | 100.086 | − | 72.7166i | 0.226585 | − | 0.164623i | ||||
\(59\) | −441.425 | − | 320.714i | −0.974044 | − | 0.707684i | −0.0176741 | − | 0.999844i | \(-0.505626\pi\) |
−0.956370 | + | 0.292160i | \(0.905626\pi\) | |||||||
\(60\) | 175.793 | + | 541.036i | 0.378247 | + | 1.16413i | ||||
\(61\) | −31.3042 | − | 96.3445i | −0.0657065 | − | 0.202224i | 0.912813 | − | 0.408378i | \(-0.133905\pi\) |
−0.978520 | + | 0.206154i | \(0.933905\pi\) | |||||||
\(62\) | 38.7903 | + | 28.1828i | 0.0794576 | + | 0.0577293i | ||||
\(63\) | 111.528 | − | 81.0300i | 0.223035 | − | 0.162045i | ||||
\(64\) | −98.1279 | + | 302.007i | −0.191656 | + | 0.589857i | ||||
\(65\) | 959.615 | 1.83116 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 411.641 | 0.750596 | 0.375298 | − | 0.926904i | \(-0.377540\pi\) | ||||
0.375298 | + | 0.926904i | \(0.377540\pi\) | |||||||
\(68\) | −190.946 | + | 587.670i | −0.340523 | + | 1.04802i | ||||
\(69\) | −64.0452 | + | 46.5316i | −0.111741 | + | 0.0811847i | ||||
\(70\) | −128.893 | − | 93.6462i | −0.220081 | − | 0.159898i | ||||
\(71\) | −145.434 | − | 447.601i | −0.243097 | − | 0.748176i | −0.995944 | − | 0.0899799i | \(-0.971320\pi\) |
0.752846 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(72\) | −28.4882 | − | 87.6775i | −0.0466300 | − | 0.143512i | ||||
\(73\) | 493.986 | + | 358.902i | 0.792009 | + | 0.575428i | 0.908559 | − | 0.417757i | \(-0.137184\pi\) |
−0.116550 | + | 0.993185i | \(0.537184\pi\) | |||||||
\(74\) | −24.1969 | + | 17.5800i | −0.0380112 | + | 0.0276167i | ||||
\(75\) | 73.8027 | − | 227.141i | 0.113627 | − | 0.349707i | ||||
\(76\) | −506.985 | −0.765199 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −323.923 | −0.470219 | ||||||||
\(79\) | 302.288 | − | 930.348i | 0.430507 | − | 1.32497i | −0.467114 | − | 0.884197i | \(-0.654706\pi\) |
0.897621 | − | 0.440768i | \(-0.145294\pi\) | |||||||
\(80\) | 534.881 | − | 388.613i | 0.747518 | − | 0.543104i | ||||
\(81\) | 714.005 | + | 518.755i | 0.979431 | + | 0.711598i | ||||
\(82\) | −62.1932 | − | 191.411i | −0.0837572 | − | 0.257778i | ||||
\(83\) | −8.08200 | − | 24.8738i | −0.0106881 | − | 0.0328947i | 0.945570 | − | 0.325418i | \(-0.105505\pi\) |
−0.956258 | + | 0.292523i | \(0.905505\pi\) | |||||||
\(84\) | −605.995 | − | 440.281i | −0.787137 | − | 0.571888i | ||||
\(85\) | 861.047 | − | 625.587i | 1.09875 | − | 0.798288i | ||||
\(86\) | 0.517399 | − | 1.59239i | 0.000648750 | − | 0.00199665i | ||||
\(87\) | −1001.84 | −1.23458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −352.887 | −0.420292 | −0.210146 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210146 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(90\) | −23.6842 | + | 72.8926i | −0.0277393 | + | 0.0853728i | ||||
\(91\) | −1022.22 | + | 742.689i | −1.17756 | + | 0.855549i | ||||
\(92\) | 80.6382 | + | 58.5871i | 0.0913817 | + | 0.0663927i | ||||
\(93\) | −119.986 | − | 369.278i | −0.133784 | − | 0.411746i | ||||
\(94\) | 16.2527 | + | 50.0208i | 0.0178334 | + | 0.0548857i | ||||
\(95\) | 706.471 | + | 513.281i | 0.762973 | + | 0.554332i | ||||
\(96\) | −614.898 | + | 446.750i | −0.653727 | + | 0.474961i | ||||
\(97\) | 261.918 | − | 806.101i | 0.274162 | − | 0.843785i | −0.715277 | − | 0.698841i | \(-0.753700\pi\) |
0.989440 | − | 0.144944i | \(-0.0463003\pi\) | |||||||
\(98\) | −41.3140 | −0.0425851 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −300.708 | −0.300708 | ||||||||
\(101\) | −399.702 | + | 1230.15i | −0.393780 | + | 1.21193i | 0.536127 | + | 0.844137i | \(0.319887\pi\) |
−0.929908 | + | 0.367793i | \(0.880113\pi\) | |||||||
\(102\) | −290.651 | + | 211.170i | −0.282144 | + | 0.204990i | ||||
\(103\) | 1395.75 | + | 1014.07i | 1.33522 | + | 0.970091i | 0.999605 | + | 0.0280904i | \(0.00894263\pi\) |
0.335611 | + | 0.942001i | \(0.391057\pi\) | |||||||
\(104\) | 261.111 | + | 803.618i | 0.246193 | + | 0.757704i | ||||
\(105\) | 398.691 | + | 1227.04i | 0.370554 | + | 1.14045i | ||||
\(106\) | 88.2470 | + | 64.1152i | 0.0808614 | + | 0.0587493i | ||||
\(107\) | −391.709 | + | 284.593i | −0.353906 | + | 0.257128i | −0.750506 | − | 0.660864i | \(-0.770190\pi\) |
0.396600 | + | 0.917992i | \(0.370190\pi\) | |||||||
\(108\) | 257.835 | − | 793.535i | 0.229724 | − | 0.707018i | ||||
\(109\) | 64.2563 | 0.0564645 | 0.0282323 | − | 0.999601i | \(-0.491012\pi\) | ||||
0.0282323 | + | 0.999601i | \(0.491012\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 242.205 | 0.207109 | ||||||||
\(112\) | −269.013 | + | 827.936i | −0.226958 | + | 0.698505i | ||||
\(113\) | 1622.15 | − | 1178.56i | 1.35043 | − | 0.981145i | 0.351440 | − | 0.936210i | \(-0.385692\pi\) |
0.998990 | − | 0.0449344i | \(-0.0143079\pi\) | |||||||
\(114\) | −238.473 | − | 173.261i | −0.195921 | − | 0.142345i | ||||
\(115\) | −53.0527 | − | 163.280i | −0.0430191 | − | 0.132399i | ||||
\(116\) | 389.792 | + | 1199.66i | 0.311994 | + | 0.960219i | ||||
\(117\) | 491.758 | + | 357.283i | 0.388573 | + | 0.282315i | ||||
\(118\) | −323.145 | + | 234.779i | −0.252101 | + | 0.183162i | ||||
\(119\) | −433.055 | + | 1332.81i | −0.333597 | + | 1.02671i | ||||
\(120\) | 862.797 | 0.656352 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −74.1587 | −0.0550329 | ||||||||
\(123\) | −503.645 | + | 1550.06i | −0.369205 | + | 1.13629i | ||||
\(124\) | −395.512 | + | 287.356i | −0.286436 | + | 0.208108i | ||||
\(125\) | −881.102 | − | 640.158i | −0.630465 | − | 0.458060i | ||||
\(126\) | −31.1853 | − | 95.9786i | −0.0220493 | − | 0.0678608i | ||||
\(127\) | −33.8698 | − | 104.240i | −0.0236650 | − | 0.0728334i | 0.938527 | − | 0.345207i | \(-0.112191\pi\) |
−0.962192 | + | 0.272374i | \(0.912191\pi\) | |||||||
\(128\) | 1017.86 | + | 739.518i | 0.702867 | + | 0.510662i | ||||
\(129\) | −10.9694 | + | 7.96973i | −0.00748683 | + | 0.00543950i | ||||
\(130\) | 217.080 | − | 668.105i | 0.146456 | − | 0.450744i | ||||
\(131\) | −1156.71 | −0.771469 | −0.385734 | − | 0.922610i | \(-0.626052\pi\) | ||||
−0.385734 | + | 0.922610i | \(0.626052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1149.82 | −0.749636 | ||||||||
\(134\) | 93.1198 | − | 286.593i | 0.0600323 | − | 0.184760i | ||||
\(135\) | −1162.68 | + | 844.735i | −0.741240 | + | 0.538542i | ||||
\(136\) | 758.181 | + | 550.851i | 0.478041 | + | 0.347317i | ||||
\(137\) | 61.2853 | + | 188.617i | 0.0382186 | + | 0.117625i | 0.968346 | − | 0.249613i | \(-0.0803035\pi\) |
−0.930127 | + | 0.367238i | \(0.880303\pi\) | |||||||
\(138\) | 17.9082 | + | 55.1158i | 0.0110467 | + | 0.0339983i | ||||
\(139\) | −2346.26 | − | 1704.66i | −1.43171 | − | 1.04020i | −0.989696 | − | 0.143186i | \(-0.954265\pi\) |
−0.442011 | − | 0.897010i | \(-0.645735\pi\) | |||||||
\(140\) | 1314.21 | − | 954.831i | 0.793366 | − | 0.576414i | ||||
\(141\) | 131.616 | − | 405.072i | 0.0786104 | − | 0.241938i | ||||
\(142\) | −344.529 | −0.203607 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 418.789 | 0.242355 | ||||||||
\(145\) | 671.391 | − | 2066.33i | 0.384524 | − | 1.18344i | ||||
\(146\) | 361.623 | − | 262.734i | 0.204987 | − | 0.148932i | ||||
\(147\) | 270.668 | + | 196.652i | 0.151866 | + | 0.110337i | ||||
\(148\) | −94.2367 | − | 290.031i | −0.0523393 | − | 0.161084i | ||||
\(149\) | −1077.96 | − | 3317.61i | −0.592683 | − | 1.82409i | −0.565939 | − | 0.824447i | \(-0.691486\pi\) |
−0.0267432 | − | 0.999642i | \(-0.508514\pi\) | |||||||
\(150\) | −141.445 | − | 102.766i | −0.0769931 | − | 0.0559388i | ||||
\(151\) | −941.148 | + | 683.784i | −0.507216 | + | 0.368514i | −0.811766 | − | 0.583982i | \(-0.801494\pi\) |
0.304551 | + | 0.952496i | \(0.401494\pi\) | |||||||
\(152\) | −237.610 | + | 731.290i | −0.126794 | + | 0.390233i | ||||
\(153\) | 674.164 | 0.356228 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 842.061 | 0.436361 | ||||||||
\(156\) | 1020.61 | − | 3141.12i | 0.523810 | − | 1.61212i | ||||
\(157\) | −276.730 | + | 201.056i | −0.140672 | + | 0.102204i | −0.655895 | − | 0.754852i | \(-0.727709\pi\) |
0.515224 | + | 0.857056i | \(0.327709\pi\) | |||||||
\(158\) | −579.346 | − | 420.919i | −0.291711 | − | 0.211940i | ||||
\(159\) | −272.965 | − | 840.099i | −0.136148 | − | 0.419020i | ||||
\(160\) | −509.360 | − | 1567.65i | −0.251678 | − | 0.774584i | ||||
\(161\) | 182.883 | + | 132.873i | 0.0895232 | + | 0.0650424i | ||||
\(162\) | 522.688 | − | 379.755i | 0.253495 | − | 0.184175i | ||||
\(163\) | −431.045 | + | 1326.62i | −0.207129 | + | 0.637479i | 0.792490 | + | 0.609885i | \(0.208784\pi\) |
−0.999619 | + | 0.0275936i | \(0.991216\pi\) | |||||||
\(164\) | 2052.09 | 0.977082 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.1460 | −0.00895191 | ||||||||
\(167\) | −147.927 | + | 455.273i | −0.0685447 | + | 0.210959i | −0.979462 | − | 0.201631i | \(-0.935376\pi\) |
0.910917 | + | 0.412590i | \(0.135376\pi\) | |||||||
\(168\) | −919.089 | + | 667.757i | −0.422079 | + | 0.306658i | ||||
\(169\) | −2729.85 | − | 1983.35i | −1.24254 | − | 0.902755i | ||||
\(170\) | −240.765 | − | 740.998i | −0.108622 | − | 0.334305i | ||||
\(171\) | 170.929 | + | 526.065i | 0.0764401 | + | 0.235259i | ||||
\(172\) | 13.8114 | + | 10.0346i | 0.00612272 | + | 0.00444841i | ||||
\(173\) | 1463.18 | − | 1063.06i | 0.643024 | − | 0.467184i | −0.217864 | − | 0.975979i | \(-0.569909\pi\) |
0.860888 | + | 0.508795i | \(0.169909\pi\) | |||||||
\(174\) | −226.631 | + | 697.500i | −0.0987407 | + | 0.303893i | ||||
\(175\) | −681.990 | −0.294592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3234.61 | 1.37361 | ||||||||
\(178\) | −79.8288 | + | 245.688i | −0.0336147 | + | 0.103456i | ||||
\(179\) | 3583.82 | − | 2603.80i | 1.49647 | − | 1.08725i | 0.524703 | − | 0.851285i | \(-0.324176\pi\) |
0.971763 | − | 0.235960i | \(-0.0758235\pi\) | |||||||
\(180\) | −632.224 | − | 459.338i | −0.261795 | − | 0.190206i | ||||
\(181\) | 1053.49 | + | 3242.32i | 0.432627 | + | 1.33149i | 0.895499 | + | 0.445064i | \(0.146819\pi\) |
−0.462872 | + | 0.886425i | \(0.653181\pi\) | |||||||
\(182\) | 285.833 | + | 879.703i | 0.116414 | + | 0.358285i | ||||
\(183\) | 485.849 | + | 352.990i | 0.196257 | + | 0.142589i | ||||
\(184\) | 122.301 | − | 88.8567i | 0.0490007 | − | 0.0356011i | ||||
\(185\) | −162.316 | + | 499.558i | −0.0645067 | + | 0.198531i | ||||
\(186\) | −284.242 | −0.112052 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −536.267 | −0.208039 | ||||||||
\(189\) | 584.757 | − | 1799.70i | 0.225052 | − | 0.692638i | ||||
\(190\) | 517.173 | − | 375.748i | 0.197472 | − | 0.143472i | ||||
\(191\) | −2365.37 | − | 1718.54i | −0.896083 | − | 0.651043i | 0.0413737 | − | 0.999144i | \(-0.486827\pi\) |
−0.937457 | + | 0.348101i | \(0.886827\pi\) | |||||||
\(192\) | −581.722 | − | 1790.36i | −0.218657 | − | 0.672958i | ||||
\(193\) | 767.655 | + | 2362.60i | 0.286306 | + | 0.881159i | 0.986004 | + | 0.166720i | \(0.0533177\pi\) |
−0.699698 | + | 0.714438i | \(0.746682\pi\) | |||||||
\(194\) | −501.975 | − | 364.706i | −0.185772 | − | 0.134971i | ||||
\(195\) | −4602.33 | + | 3343.79i | −1.69015 | + | 1.22797i | ||||
\(196\) | 130.171 | − | 400.626i | 0.0474386 | − | 0.146001i | ||||
\(197\) | 5125.67 | 1.85375 | 0.926876 | − | 0.375369i | \(-0.122484\pi\) | ||||
0.926876 | + | 0.375369i | \(0.122484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.69219 | −0.00274013 | −0.00137006 | − | 0.999999i | \(-0.500436\pi\) | ||||
−0.00137006 | + | 0.999999i | \(0.500436\pi\) | |||||||
\(200\) | −140.934 | + | 433.750i | −0.0498276 | + | 0.153354i | ||||
\(201\) | −1974.24 | + | 1434.37i | −0.692796 | + | 0.503346i | ||||
\(202\) | 766.042 | + | 556.562i | 0.266824 | + | 0.193859i | ||||
\(203\) | 884.029 | + | 2720.76i | 0.305649 | + | 0.940690i | ||||
\(204\) | −1131.96 | − | 3483.83i | −0.388497 | − | 1.19567i | ||||
\(205\) | −2859.54 | − | 2077.58i | −0.974240 | − | 0.707826i | ||||
\(206\) | 1021.76 | − | 742.352i | 0.345579 | − | 0.251078i | ||||
\(207\) | 33.6050 | − | 103.426i | 0.0112836 | − | 0.0347274i | ||||
\(208\) | −3838.46 | −1.27956 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 944.484 | 0.310360 | ||||||||
\(211\) | −960.222 | + | 2955.26i | −0.313291 | + | 0.964211i | 0.663161 | + | 0.748477i | \(0.269214\pi\) |
−0.976452 | + | 0.215734i | \(0.930786\pi\) | |||||||
\(212\) | −899.780 | + | 653.729i | −0.291496 | + | 0.211784i | ||||
\(213\) | 2257.18 | + | 1639.94i | 0.726100 | + | 0.527542i | ||||
\(214\) | 109.529 | + | 337.096i | 0.0349872 | + | 0.107680i | ||||
\(215\) | −9.08665 | − | 27.9658i | −0.00288234 | − | 0.00887095i | ||||
\(216\) | −1023.78 | − | 743.818i | −0.322496 | − | 0.234307i | ||||
\(217\) | −897.001 | + | 651.709i | −0.280610 | + | 0.203875i | ||||
\(218\) | 14.5358 | − | 44.7366i | 0.00451600 | − | 0.0138988i | ||||
\(219\) | −3619.76 | −1.11690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6179.13 | −1.88078 | ||||||||
\(222\) | 54.7907 | − | 168.628i | 0.0165645 | − | 0.0509802i | ||||
\(223\) | 9.96586 | − | 7.24062i | 0.00299266 | − | 0.00217430i | −0.586288 | − | 0.810103i | \(-0.699411\pi\) |
0.589281 | + | 0.807928i | \(0.299411\pi\) | |||||||
\(224\) | 1755.87 | + | 1275.71i | 0.523744 | + | 0.380522i | ||||
\(225\) | 101.383 | + | 312.025i | 0.0300394 | + | 0.0924518i | ||||
\(226\) | −453.582 | − | 1395.98i | −0.133504 | − | 0.410882i | ||||
\(227\) | 3734.34 | + | 2713.16i | 1.09188 | + | 0.793298i | 0.979716 | − | 0.200391i | \(-0.0642214\pi\) |
0.112165 | + | 0.993690i | \(0.464221\pi\) | |||||||
\(228\) | 2431.51 | − | 1766.59i | 0.706274 | − | 0.513138i | ||||
\(229\) | 1568.15 | − | 4826.26i | 0.452516 | − | 1.39270i | −0.421512 | − | 0.906823i | \(-0.638500\pi\) |
0.874027 | − | 0.485877i | \(-0.161500\pi\) | |||||||
\(230\) | −125.680 | −0.0360309 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1913.11 | 0.541386 | ||||||||
\(233\) | −65.4135 | + | 201.322i | −0.0183922 | + | 0.0566054i | −0.959831 | − | 0.280577i | \(-0.909474\pi\) |
0.941439 | + | 0.337183i | \(0.109474\pi\) | |||||||
\(234\) | 359.992 | − | 261.549i | 0.100570 | − | 0.0730684i | ||||
\(235\) | 747.275 | + | 542.927i | 0.207433 | + | 0.150709i | ||||
\(236\) | −1258.52 | − | 3873.31i | −0.347129 | − | 1.06835i | ||||
\(237\) | 1792.03 | + | 5515.29i | 0.491159 | + | 1.51163i | ||||
\(238\) | 829.964 | + | 603.004i | 0.226044 | + | 0.164231i | ||||
\(239\) | 3488.88 | − | 2534.82i | 0.944254 | − | 0.686041i | −0.00518659 | − | 0.999987i | \(-0.501651\pi\) |
0.949441 | + | 0.313946i | \(0.101651\pi\) | |||||||
\(240\) | −1211.17 | + | 3727.59i | −0.325753 | + | 1.00256i | ||||
\(241\) | 996.584 | 0.266372 | 0.133186 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133186 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2213.80 | −0.584426 | ||||||||
\(244\) | 233.658 | − | 719.125i | 0.0613050 | − | 0.188677i | ||||
\(245\) | −586.993 | + | 426.475i | −0.153068 | + | 0.111210i | ||||
\(246\) | 965.253 | + | 701.297i | 0.250172 | + | 0.181761i | ||||
\(247\) | −1566.67 | − | 4821.71i | −0.403582 | − | 1.24210i | ||||
\(248\) | 229.125 | + | 705.174i | 0.0586671 | + | 0.180559i | ||||
\(249\) | 125.435 | + | 91.1335i | 0.0319241 | + | 0.0231942i | ||||
\(250\) | −645.012 | + | 468.628i | −0.163176 | + | 0.118555i | ||||
\(251\) | −85.5644 | + | 263.340i | −0.0215170 | + | 0.0662226i | −0.961238 | − | 0.275718i | \(-0.911084\pi\) |
0.939721 | + | 0.341941i | \(0.111084\pi\) | |||||||
\(252\) | 1028.97 | 0.257219 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −80.2364 | −0.0198208 | ||||||||
\(255\) | −1949.73 | + | 6000.65i | −0.478811 | + | 1.47363i | ||||
\(256\) | −1310.09 | + | 951.838i | −0.319847 | + | 0.232382i | ||||
\(257\) | 2617.31 | + | 1901.59i | 0.635267 | + | 0.461548i | 0.858221 | − | 0.513281i | \(-0.171570\pi\) |
−0.222954 | + | 0.974829i | \(0.571570\pi\) | |||||||
\(258\) | 3.06724 | + | 9.44001i | 0.000740148 | + | 0.00227794i | ||||
\(259\) | −213.724 | − | 657.775i | −0.0512748 | − | 0.157808i | ||||
\(260\) | 5794.72 | + | 4210.11i | 1.38220 | + | 1.00423i | ||||
\(261\) | 1113.39 | − | 808.925i | 0.264050 | − | 0.191844i | ||||
\(262\) | −261.667 | + | 805.328i | −0.0617017 | + | 0.189898i | ||||
\(263\) | −207.944 | −0.0487544 | −0.0243772 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243772 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1915.67 | 0.444071 | ||||||||
\(266\) | −260.107 | + | 800.526i | −0.0599555 | + | 0.184524i | ||||
\(267\) | 1692.45 | − | 1229.64i | 0.387927 | − | 0.281845i | ||||
\(268\) | 2485.73 | + | 1805.99i | 0.566567 | + | 0.411635i | ||||
\(269\) | 1555.29 | + | 4786.70i | 0.352520 | + | 1.08495i | 0.957433 | + | 0.288654i | \(0.0932078\pi\) |
−0.604913 | + | 0.796291i | \(0.706792\pi\) | |||||||
\(270\) | 325.106 | + | 1000.57i | 0.0732790 | + | 0.225530i | ||||
\(271\) | 1203.02 | + | 874.043i | 0.269661 | + | 0.195920i | 0.714395 | − | 0.699742i | \(-0.246702\pi\) |
−0.444734 | + | 0.895663i | \(0.646702\pi\) | |||||||
\(272\) | −3444.19 | + | 2502.35i | −0.767774 | + | 0.557821i | ||||
\(273\) | 2314.70 | − | 7123.90i | 0.513157 | − | 1.57933i | ||||
\(274\) | 145.183 | 0.0320102 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −590.890 | −0.128867 | ||||||||
\(277\) | 72.8773 | − | 224.293i | 0.0158078 | − | 0.0486515i | −0.942841 | − | 0.333242i | \(-0.891858\pi\) |
0.958649 | + | 0.284590i | \(0.0918575\pi\) | |||||||
\(278\) | −1717.58 | + | 1247.90i | −0.370553 | + | 0.269223i | ||||
\(279\) | 431.517 | + | 313.515i | 0.0925959 | + | 0.0672748i | ||||
\(280\) | −761.340 | − | 2343.16i | −0.162496 | − | 0.500110i | ||||
\(281\) | 1518.82 | + | 4674.46i | 0.322439 | + | 0.992365i | 0.972583 | + | 0.232555i | \(0.0747084\pi\) |
−0.650144 | + | 0.759811i | \(0.725292\pi\) | |||||||
\(282\) | −252.246 | − | 183.268i | −0.0532662 | − | 0.0387001i | ||||
\(283\) | −4206.53 | + | 3056.22i | −0.883577 | + | 0.641956i | −0.934195 | − | 0.356762i | \(-0.883881\pi\) |
0.0506182 | + | 0.998718i | \(0.483881\pi\) | |||||||
\(284\) | 1085.54 | − | 3340.94i | 0.226813 | − | 0.698058i | ||||
\(285\) | −5176.78 | −1.07595 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4654.04 | 0.957210 | ||||||||
\(288\) | 322.642 | − | 992.991i | 0.0660134 | − | 0.203169i | ||||
\(289\) | −1569.73 | + | 1140.47i | −0.319505 | + | 0.232134i | ||||
\(290\) | −1286.74 | − | 934.874i | −0.260552 | − | 0.189302i | ||||
\(291\) | 1552.70 | + | 4778.73i | 0.312787 | + | 0.962660i | ||||
\(292\) | 1408.37 | + | 4334.52i | 0.282255 | + | 0.868693i | ||||
\(293\) | −7184.81 | − | 5220.07i | −1.43256 | − | 1.04082i | −0.989532 | − | 0.144313i | \(-0.953903\pi\) |
−0.443032 | − | 0.896506i | \(-0.646097\pi\) | |||||||
\(294\) | 198.143 | − | 143.959i | 0.0393058 | − | 0.0285573i | ||||
\(295\) | −2167.71 | + | 6671.52i | −0.427827 | + | 1.31671i | ||||
\(296\) | −462.515 | −0.0908215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2553.64 | −0.496405 | ||||||||
\(299\) | −308.011 | + | 947.959i | −0.0595743 | + | 0.183351i | ||||
\(300\) | 1442.20 | − | 1047.82i | 0.277551 | − | 0.201653i | ||||
\(301\) | 31.3235 | + | 22.7579i | 0.00599819 | + | 0.00435794i | ||||
\(302\) | 263.163 | + | 809.931i | 0.0501434 | + | 0.154325i | ||||
\(303\) | −2369.51 | − | 7292.61i | −0.449257 | − | 1.38267i | ||||
\(304\) | −2825.88 | − | 2053.13i | −0.533143 | − | 0.387351i | ||||
\(305\) | −1053.65 | + | 765.524i | −0.197810 | + | 0.143717i | ||||
\(306\) | 152.507 | − | 469.368i | 0.0284910 | − | 0.0876862i | ||||
\(307\) | 1497.93 | 0.278474 | 0.139237 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139237 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10227.6 | −1.88293 | ||||||||
\(310\) | 190.488 | − | 586.261i | 0.0349000 | − | 0.107411i | ||||
\(311\) | 6055.25 | − | 4399.40i | 1.10406 | − | 0.802145i | 0.122340 | − | 0.992488i | \(-0.460960\pi\) |
0.981718 | + | 0.190343i | \(0.0609601\pi\) | |||||||
\(312\) | −4052.51 | − | 2944.32i | −0.735347 | − | 0.534261i | ||||
\(313\) | −203.445 | − | 626.140i | −0.0367393 | − | 0.113072i | 0.931005 | − | 0.365007i | \(-0.118933\pi\) |
−0.967744 | + | 0.251934i | \(0.918933\pi\) | |||||||
\(314\) | 77.3787 | + | 238.147i | 0.0139068 | + | 0.0428007i | ||||
\(315\) | −1433.85 | − | 1041.75i | −0.256471 | − | 0.186337i | ||||
\(316\) | 5907.10 | − | 4291.76i | 1.05158 | − | 0.764020i | ||||
\(317\) | 72.2196 | − | 222.269i | 0.0127958 | − | 0.0393813i | −0.944455 | − | 0.328641i | \(-0.893409\pi\) |
0.957251 | + | 0.289260i | \(0.0934092\pi\) | |||||||
\(318\) | −646.645 | −0.114032 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4082.53 | 0.713189 | ||||||||
\(321\) | 886.976 | − | 2729.83i | 0.154225 | − | 0.474655i | ||||
\(322\) | 133.880 | − | 97.2695i | 0.0231703 | − | 0.0168342i | ||||
\(323\) | −4549.09 | − | 3305.11i | −0.783647 | − | 0.569353i | ||||
\(324\) | 2035.65 | + | 6265.09i | 0.349049 | + | 1.07426i | ||||
\(325\) | −929.238 | − | 2859.90i | −0.158599 | − | 0.488119i | ||||
\(326\) | 826.113 | + | 600.206i | 0.140350 | + | 0.101970i | ||||
\(327\) | −308.174 | + | 223.902i | −0.0521164 | + | 0.0378648i | ||||
\(328\) | 961.762 | − | 2960.00i | 0.161904 | − | 0.498288i | ||||
\(329\) | −1216.23 | −0.203808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8532.95 | 1.41696 | 0.708480 | − | 0.705731i | \(-0.249381\pi\) | ||||
0.708480 | + | 0.705731i | \(0.249381\pi\) | |||||||
\(332\) | 60.3249 | − | 185.661i | 0.00997216 | − | 0.0306912i | ||||
\(333\) | −269.174 | + | 195.567i | −0.0442963 | + | 0.0321832i | ||||
\(334\) | 283.508 | + | 205.980i | 0.0464457 | + | 0.0337448i | ||||
\(335\) | −1635.39 | − | 5033.20i | −0.266719 | − | 0.820876i | ||||
\(336\) | −1594.76 | − | 4908.17i | −0.258933 | − | 0.796913i | ||||
\(337\) | 9458.37 | + | 6871.90i | 1.52887 | + | 1.11079i | 0.956861 | + | 0.290545i | \(0.0938366\pi\) |
0.572011 | + | 0.820246i | \(0.306163\pi\) | |||||||
\(338\) | −1998.39 | + | 1451.92i | −0.321592 | + | 0.233650i | ||||
\(339\) | −3673.14 | + | 11304.8i | −0.588489 | + | 1.81118i | ||||
\(340\) | 7944.14 | 1.26715 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 404.925 | 0.0640229 | ||||||||
\(343\) | 2089.49 | − | 6430.79i | 0.328927 | − | 1.01233i | ||||
\(344\) | 20.9472 | − | 15.2190i | 0.00328313 | − | 0.00238533i | ||||
\(345\) | 823.391 | + | 598.229i | 0.128492 | + | 0.0933552i | ||||
\(346\) | −409.131 | − | 1259.18i | −0.0635694 | − | 0.195647i | ||||
\(347\) | −1421.11 | − | 4373.71i | −0.219853 | − | 0.676637i | −0.998773 | − | 0.0495148i | \(-0.984232\pi\) |
0.778921 | − | 0.627123i | \(-0.215768\pi\) | |||||||
\(348\) | −6049.67 | − | 4395.34i | −0.931886 | − | 0.677055i | ||||
\(349\) | 5436.81 | − | 3950.08i | 0.833885 | − | 0.605853i | −0.0867706 | − | 0.996228i | \(-0.527655\pi\) |
0.920656 | + | 0.390375i | \(0.127655\pi\) | |||||||
\(350\) | −154.277 | + | 474.816i | −0.0235613 | + | 0.0725142i | ||||
\(351\) | 8343.72 | 1.26882 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5738.70 | 0.865270 | 0.432635 | − | 0.901569i | \(-0.357584\pi\) | ||||
0.432635 | + | 0.901569i | \(0.357584\pi\) | |||||||
\(354\) | 731.721 | − | 2252.01i | 0.109860 | − | 0.338115i | ||||
\(355\) | −4895.11 | + | 3556.50i | −0.731846 | + | 0.531717i | ||||
\(356\) | −2130.94 | − | 1548.22i | −0.317246 | − | 0.230493i | ||||
\(357\) | −2567.24 | − | 7901.14i | −0.380595 | − | 1.17135i | ||||
\(358\) | −1002.10 | − | 3084.15i | −0.147941 | − | 0.455315i | ||||
\(359\) | −3329.32 | − | 2418.89i | −0.489456 | − | 0.355611i | 0.315519 | − | 0.948919i | \(-0.397821\pi\) |
−0.804975 | + | 0.593308i | \(0.797821\pi\) | |||||||
\(360\) | −958.869 | + | 696.659i | −0.140380 | + | 0.101992i | ||||
\(361\) | −693.885 | + | 2135.56i | −0.101164 | + | 0.311351i | ||||
\(362\) | 2495.69 | 0.362349 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9431.18 | −1.35804 | ||||||||
\(365\) | 2425.82 | − | 7465.91i | 0.347872 | − | 1.07064i | ||||
\(366\) | 355.666 | − | 258.407i | 0.0507950 | − | 0.0369047i | ||||
\(367\) | −7817.53 | − | 5679.77i | −1.11191 | − | 0.807851i | −0.128948 | − | 0.991651i | \(-0.541160\pi\) |
−0.982964 | + | 0.183800i | \(0.941160\pi\) | |||||||
\(368\) | 212.211 | + | 653.118i | 0.0300605 | + | 0.0925167i | ||||
\(369\) | −691.859 | − | 2129.32i | −0.0976064 | − | 0.300402i | ||||
\(370\) | 311.085 | + | 226.016i | 0.0437095 | + | 0.0317568i | ||||
\(371\) | −2040.66 | + | 1482.62i | −0.285568 | + | 0.207477i | ||||
\(372\) | 895.586 | − | 2756.33i | 0.124822 | − | 0.384164i | ||||
\(373\) | 141.780 | 0.0196812 | 0.00984062 | − | 0.999952i | \(-0.496868\pi\) | ||||
0.00984062 | + | 0.999952i | \(0.496868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6456.42 | 0.889088 | ||||||||
\(376\) | −251.334 | + | 773.527i | −0.0344723 | + | 0.106095i | ||||
\(377\) | −10204.9 | + | 7414.29i | −1.39411 | + | 1.01288i | ||||
\(378\) | −1120.71 | − | 814.241i | −0.152494 | − | 0.110794i | ||||
\(379\) | −871.345 | − | 2681.73i | −0.118095 | − | 0.363459i | 0.874485 | − | 0.485053i | \(-0.161200\pi\) |
−0.992580 | + | 0.121594i | \(0.961200\pi\) | |||||||
\(380\) | 2014.17 | + | 6198.99i | 0.271908 | + | 0.836845i | ||||
\(381\) | 525.667 | + | 381.920i | 0.0706844 | + | 0.0513552i | ||||
\(382\) | −1731.57 | + | 1258.06i | −0.231923 | + | 0.168502i | ||||
\(383\) | −1958.50 | + | 6027.64i | −0.261291 | + | 0.804172i | 0.731233 | + | 0.682128i | \(0.238945\pi\) |
−0.992525 | + | 0.122045i | \(0.961055\pi\) | |||||||
\(384\) | −7458.53 | −0.991189 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1818.55 | 0.239797 | ||||||||
\(387\) | 5.75573 | − | 17.7143i | 0.000756021 | − | 0.00232679i | ||||
\(388\) | 5118.21 | − | 3718.60i | 0.669685 | − | 0.486555i | ||||
\(389\) | 7123.60 | + | 5175.60i | 0.928486 | + | 0.674584i | 0.945622 | − | 0.325269i | \(-0.105455\pi\) |
−0.0171360 | + | 0.999853i | \(0.505455\pi\) | |||||||
\(390\) | 1286.90 | + | 3960.66i | 0.167089 | + | 0.514246i | ||||
\(391\) | 341.616 | + | 1051.38i | 0.0441848 | + | 0.135987i | ||||
\(392\) | −516.868 | − | 375.526i | −0.0665963 | − | 0.0483851i | ||||
\(393\) | 5547.61 | − | 4030.58i | 0.712061 | − | 0.517343i | ||||
\(394\) | 1159.51 | − | 3568.60i | 0.148262 | − | 0.456304i | ||||
\(395\) | −12576.5 | −1.60200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4315.26 | 0.545534 | 0.272767 | − | 0.962080i | \(-0.412061\pi\) | ||||
0.272767 | + | 0.962080i | \(0.412061\pi\) | |||||||
\(398\) | −1.74010 | + | 5.35547i | −0.000219154 | + | 0.000674486i | ||||
\(399\) | 5514.53 | − | 4006.54i | 0.691910 | − | 0.502702i | ||||
\(400\) | −1676.12 | − | 1217.77i | −0.209515 | − | 0.152221i | ||||
\(401\) | 111.766 | + | 343.979i | 0.0139185 | + | 0.0428367i | 0.957775 | − | 0.287520i | \(-0.0928309\pi\) |
−0.943856 | + | 0.330357i | \(0.892831\pi\) | |||||||
\(402\) | 552.033 | + | 1698.98i | 0.0684899 | + | 0.210790i | ||||
\(403\) | −3955.12 | − | 2873.56i | −0.488880 | − | 0.355192i | ||||
\(404\) | −7810.68 | + | 5674.79i | −0.961870 | + | 0.698840i | ||||
\(405\) | 3506.27 | − | 10791.2i | 0.430193 | − | 1.32400i | ||||
\(406\) | 2094.24 | 0.255998 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5555.70 | −0.674137 | ||||||||
\(409\) | −2849.29 | + | 8769.22i | −0.344470 | + | 1.06017i | 0.617396 | + | 0.786652i | \(0.288188\pi\) |
−0.961867 | + | 0.273519i | \(0.911812\pi\) | |||||||
\(410\) | −2093.33 | + | 1520.89i | −0.252152 | + | 0.183199i | ||||
\(411\) | −951.162 | − | 691.060i | −0.114154 | − | 0.0829378i | ||||
\(412\) | 3979.33 | + | 12247.1i | 0.475843 | + | 1.46449i | ||||
\(413\) | −2854.25 | − | 8784.48i | −0.340069 | − | 1.04662i | ||||
\(414\) | −64.4052 | − | 46.7931i | −0.00764575 | − | 0.00555496i | ||||
\(415\) | −272.028 | + | 197.640i | −0.0321767 | + | 0.0233777i | ||||
\(416\) | −2957.21 | + | 9101.37i | −0.348532 | + | 1.07267i | ||||
\(417\) | 17192.6 | 2.01901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14912.9 | −1.73876 | −0.869380 | − | 0.494144i | \(-0.835481\pi\) | ||||
−0.869380 | + | 0.494144i | \(0.835481\pi\) | |||||||
\(420\) | −2975.87 | + | 9158.78i | −0.345732 | + | 1.06405i | ||||
\(421\) | 10910.4 | − | 7926.88i | 1.26304 | − | 0.917654i | 0.264139 | − | 0.964485i | \(-0.414912\pi\) |
0.998903 | + | 0.0468306i | \(0.0149121\pi\) | |||||||
\(422\) | 1840.30 | + | 1337.05i | 0.212285 | + | 0.154234i | ||||
\(423\) | 180.801 | + | 556.449i | 0.0207822 | + | 0.0639610i | ||||
\(424\) | 521.254 | + | 1604.26i | 0.0597036 | + | 0.183749i | ||||
\(425\) | −2698.20 | − | 1960.36i | −0.307958 | − | 0.223744i | ||||
\(426\) | 1652.37 | − | 1200.52i | 0.187928 | − | 0.136538i | ||||
\(427\) | 529.925 | − | 1630.94i | 0.0600582 | − | 0.184840i | ||||
\(428\) | −3613.96 | −0.408148 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.5260 | −0.00241413 | ||||||||
\(431\) | −125.564 | + | 386.447i | −0.0140330 | + | 0.0431890i | −0.957828 | − | 0.287343i | \(-0.907228\pi\) |
0.943795 | + | 0.330532i | \(0.107228\pi\) | |||||||
\(432\) | 4650.71 | − | 3378.94i | 0.517957 | − | 0.376318i | ||||
\(433\) | 1429.29 | + | 1038.44i | 0.158631 | + | 0.115252i | 0.664269 | − | 0.747494i | \(-0.268743\pi\) |
−0.505638 | + | 0.862746i | \(0.668743\pi\) | |||||||
\(434\) | 250.818 | + | 771.938i | 0.0277411 | + | 0.0853784i | ||||
\(435\) | 3980.14 | + | 12249.6i | 0.438697 | + | 1.35017i | ||||
\(436\) | 388.017 | + | 281.911i | 0.0426207 | + | 0.0309658i | ||||
\(437\) | −733.805 | + | 533.140i | −0.0803264 | + | 0.0583606i | ||||
\(438\) | −818.848 | + | 2520.16i | −0.0893289 | + | 0.274926i | ||||
\(439\) | −7824.19 | −0.850634 | −0.425317 | − | 0.905044i | \(-0.639837\pi\) | ||||
−0.425317 | + | 0.905044i | \(0.639837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −459.591 | −0.0496265 | ||||||||
\(442\) | −1397.82 | + | 4302.04i | −0.150424 | + | 0.462958i | ||||
\(443\) | −9439.52 | + | 6858.21i | −1.01238 | + | 0.735538i | −0.964707 | − | 0.263325i | \(-0.915181\pi\) |
−0.0476744 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(444\) | 1462.58 | + | 1062.62i | 0.156331 | + | 0.113581i | ||||
\(445\) | 1401.97 | + | 4314.81i | 0.149348 | + | 0.459644i | ||||
\(446\) | −2.78664 | − | 8.57640i | −0.000295855 | − | 0.000910547i | ||||
\(447\) | 16730.2 | + | 12155.2i | 1.77027 | + | 1.28617i | ||||
\(448\) | −4348.89 | + | 3159.66i | −0.458629 | + | 0.333214i | ||||
\(449\) | 5245.64 | − | 16144.4i | 0.551352 | − | 1.69689i | −0.154035 | − | 0.988065i | \(-0.549227\pi\) |
0.705387 | − | 0.708822i | \(-0.250773\pi\) | |||||||
\(450\) | 240.173 | 0.0251597 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14966.1 | 1.55741 | ||||||||
\(453\) | 2131.11 | − | 6558.88i | 0.221034 | − | 0.680272i | ||||
\(454\) | 2733.73 | − | 1986.17i | 0.282600 | − | 0.205321i | ||||
\(455\) | 13142.1 | + | 9548.31i | 1.35409 | + | 0.983806i | ||||
\(456\) | −1408.60 | − | 4335.23i | −0.144658 | − | 0.445210i | ||||
\(457\) | 5003.87 | + | 15400.3i | 0.512190 | + | 1.57636i | 0.788337 | + | 0.615244i | \(0.210943\pi\) |
−0.276146 | + | 0.961116i | \(0.589057\pi\) | |||||||
\(458\) | −3005.41 | − | 2183.56i | −0.306623 | − | 0.222775i | ||||
\(459\) | 7486.68 | − | 5439.39i | 0.761325 | − | 0.553135i | ||||
\(460\) | 395.991 | − | 1218.73i | 0.0401373 | − | 0.123530i | ||||
\(461\) | −8586.04 | −0.867444 | −0.433722 | − | 0.901047i | \(-0.642800\pi\) | ||||
−0.433722 | + | 0.901047i | \(0.642800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7917.20 | −0.794694 | −0.397347 | − | 0.917668i | \(-0.630069\pi\) | ||||
−0.397347 | + | 0.917668i | \(0.630069\pi\) | |||||||
\(464\) | −2685.56 | + | 8265.31i | −0.268694 | + | 0.826956i | ||||
\(465\) | −4038.54 | + | 2934.17i | −0.402759 | + | 0.292621i | ||||
\(466\) | 125.367 | + | 91.0846i | 0.0124625 | + | 0.00905454i | ||||
\(467\) | −4683.14 | − | 14413.2i | −0.464047 | − | 1.42819i | −0.860177 | − | 0.509995i | \(-0.829647\pi\) |
0.396130 | − | 0.918194i | \(-0.370353\pi\) | |||||||
\(468\) | 1402.02 | + | 4314.97i | 0.138479 | + | 0.426195i | ||||
\(469\) | 5637.51 | + | 4095.89i | 0.555045 | + | 0.403264i | ||||
\(470\) | 547.043 | − | 397.450i | 0.0536877 | − | 0.0390064i | ||||
\(471\) | 626.619 | − | 1928.53i | 0.0613017 | − | 0.188667i | ||||
\(472\) | −6176.82 | −0.602354 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4245.25 | 0.411373 | ||||||||
\(475\) | 845.603 | − | 2602.50i | 0.0816819 | − | 0.251391i | ||||
\(476\) | −8462.44 | + | 6148.32i | −0.814864 | + | 0.592033i | ||||
\(477\) | 981.691 | + | 713.241i | 0.0942318 | + | 0.0684634i | ||||
\(478\) | −975.555 | − | 3002.45i | −0.0933491 | − | 0.287299i | ||||
\(479\) | −3090.51 | − | 9511.62i | −0.294800 | − | 0.907301i | −0.983289 | − | 0.182054i | \(-0.941725\pi\) |
0.688489 | − | 0.725247i | \(-0.258275\pi\) | |||||||
\(480\) | 7905.38 | + | 5743.60i | 0.751729 | + | 0.546163i | ||||
\(481\) | 2467.15 | − | 1792.49i | 0.233872 | − | 0.169918i | ||||
\(482\) | 225.443 | − | 693.843i | 0.0213043 | − | 0.0655678i | ||||
\(483\) | −1340.11 | −0.126246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10896.9 | −1.02021 | ||||||||
\(486\) | −500.798 | + | 1541.30i | −0.0467421 | + | 0.143857i | ||||
\(487\) | −5699.15 | + | 4140.68i | −0.530294 | + | 0.385281i | −0.820468 | − | 0.571693i | \(-0.806287\pi\) |
0.290174 | + | 0.956974i | \(0.406287\pi\) | |||||||
\(488\) | −927.779 | − | 674.071i | −0.0860626 | − | 0.0625282i | ||||
\(489\) | −2555.33 | − | 7864.48i | −0.236310 | − | 0.727289i | ||||
\(490\) | 164.134 | + | 505.153i | 0.0151323 | + | 0.0465724i | ||||
\(491\) | −10781.3 | − | 7833.07i | −0.990944 | − | 0.719963i | −0.0308160 | − | 0.999525i | \(-0.509811\pi\) |
−0.960128 | + | 0.279562i | \(0.909811\pi\) | |||||||
\(492\) | −9841.87 | + | 7150.54i | −0.901841 | + | 0.655226i | ||||
\(493\) | −4323.20 | + | 13305.4i | −0.394944 | + | 1.21551i | ||||
\(494\) | −3711.38 | −0.338022 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3368.25 | −0.304917 | ||||||||
\(497\) | 2461.94 | − | 7577.09i | 0.222200 | − | 0.683861i | ||||
\(498\) | 91.8245 | − | 66.7144i | 0.00826256 | − | 0.00600310i | ||||
\(499\) | 16236.3 | + | 11796.3i | 1.45658 | + | 1.05827i | 0.984237 | + | 0.176856i | \(0.0565928\pi\) |
0.472346 | + | 0.881413i | \(0.343407\pi\) | |||||||
\(500\) | −2512.05 | − | 7731.30i | −0.224685 | − | 0.691509i | ||||
\(501\) | −876.943 | − | 2698.95i | −0.0782015 | − | 0.240679i | ||||
\(502\) | 163.987 | + | 119.144i | 0.0145799 | + | 0.0105929i | ||||
\(503\) | 6296.05 | − | 4574.35i | 0.558106 | − | 0.405487i | −0.272660 | − | 0.962111i | \(-0.587903\pi\) |
0.830765 | + | 0.556623i | \(0.187903\pi\) | |||||||
\(504\) | 482.253 | − | 1484.22i | 0.0426216 | − | 0.131176i | ||||
\(505\) | 16629.3 | 1.46533 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20003.4 | 1.75224 | ||||||||
\(508\) | 252.808 | − | 778.062i | 0.0220798 | − | 0.0679545i | ||||
\(509\) | 1194.05 | − | 867.531i | 0.103979 | − | 0.0755455i | −0.534581 | − | 0.845117i | \(-0.679530\pi\) |
0.638560 | + | 0.769572i | \(0.279530\pi\) | |||||||
\(510\) | 3736.73 | + | 2714.89i | 0.324441 | + | 0.235720i | ||||
\(511\) | 3194.11 | + | 9830.46i | 0.276515 | + | 0.851025i | ||||
\(512\) | 3476.63 | + | 10700.0i | 0.300091 | + | 0.923586i | ||||
\(513\) | 6142.66 | + | 4462.91i | 0.528665 | + | 0.384098i | ||||
\(514\) | 1916.01 | − | 1392.06i | 0.164419 | − | 0.119458i | ||||
\(515\) | 6854.12 | − | 21094.8i | 0.586463 | − | 1.80495i | ||||
\(516\) | −101.205 | −0.00863431 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −506.305 | −0.0429455 | ||||||||
\(519\) | −3313.17 | + | 10196.9i | −0.280216 | + | 0.862417i | ||||
\(520\) | 8788.62 | − | 6385.31i | 0.741166 | − | 0.538489i | ||||
\(521\) | −6156.16 | − | 4472.71i | −0.517670 | − | 0.376109i | 0.298055 | − | 0.954549i | \(-0.403662\pi\) |
−0.815725 | + | 0.578439i | \(0.803662\pi\) | |||||||
\(522\) | −311.324 | − | 958.158i | −0.0261040 | − | 0.0803399i | ||||
\(523\) | −3848.16 | − | 11843.4i | −0.321737 | − | 0.990204i | −0.972892 | − | 0.231259i | \(-0.925715\pi\) |
0.651155 | − | 0.758944i | \(-0.274285\pi\) | |||||||
\(524\) | −6984.91 | − | 5074.83i | −0.582323 | − | 0.423082i | ||||
\(525\) | 3270.83 | − | 2376.40i | 0.271906 | − | 0.197552i | ||||
\(526\) | −47.0404 | + | 144.775i | −0.00389935 | + | 0.0120010i | ||||
\(527\) | −5422.18 | −0.448186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11988.7 | −0.985344 | ||||||||
\(530\) | 433.356 | − | 1333.73i | 0.0355165 | − | 0.109309i | ||||
\(531\) | −3594.78 | + | 2611.76i | −0.293786 | + | 0.213448i | ||||
\(532\) | −6943.26 | − | 5044.57i | −0.565843 | − | 0.411109i | ||||
\(533\) | 6341.31 | + | 19516.6i | 0.515334 | + | 1.58603i | ||||
\(534\) | −473.241 | − | 1456.49i | −0.0383505 | − | 0.118031i | ||||
\(535\) | 5035.97 | + | 3658.85i | 0.406961 | + | 0.295674i | ||||
\(536\) | 3770.01 | − | 2739.07i | 0.303805 | − | 0.220727i | ||||
\(537\) | −8115.10 | + | 24975.7i | −0.652128 | + | 2.00704i | ||||
\(538\) | 3684.44 | 0.295255 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10727.0 | −0.854847 | ||||||||
\(541\) | −2877.62 | + | 8856.40i | −0.228685 | + | 0.703819i | 0.769212 | + | 0.638994i | \(0.220649\pi\) |
−0.997897 | + | 0.0648254i | \(0.979351\pi\) | |||||||
\(542\) | 880.670 | − | 639.844i | 0.0697933 | − | 0.0507078i | ||||
\(543\) | −16350.5 | − | 11879.3i | −1.29220 | − | 0.938839i | ||||
\(544\) | 3279.86 | + | 10094.4i | 0.258497 | + | 0.795573i | ||||
\(545\) | −255.280 | − | 785.672i | −0.0200642 | − | 0.0617514i | ||||
\(546\) | −4436.19 | − | 3223.08i | −0.347713 | − | 0.252629i | ||||
\(547\) | −8914.20 | + | 6476.54i | −0.696789 | + | 0.506247i | −0.878885 | − | 0.477034i | \(-0.841712\pi\) |
0.182096 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(548\) | −457.439 | + | 1407.85i | −0.0356585 | + | 0.109745i | ||||
\(549\) | −824.968 | −0.0641325 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11478.6 | −0.887490 | ||||||||
\(552\) | −276.935 | + | 852.317i | −0.0213535 | + | 0.0657192i | ||||
\(553\) | 13397.0 | − | 9733.49i | 1.03020 | − | 0.748481i | ||||
\(554\) | −139.672 | − | 101.477i | −0.0107113 | − | 0.00778225i | ||||
\(555\) | −962.244 | − | 2961.48i | −0.0735946 | − | 0.226501i | ||||
\(556\) | −6689.27 | − | 20587.4i | −0.510230 | − | 1.57033i | ||||
\(557\) | −9723.11 | − | 7064.25i | −0.739643 | − | 0.537382i | 0.152956 | − | 0.988233i | \(-0.451121\pi\) |
−0.892599 | + | 0.450851i | \(0.851121\pi\) | |||||||
\(558\) | 315.892 | − | 229.509i | 0.0239656 | − | 0.0174120i | ||||
\(559\) | −52.7548 | + | 162.362i | −0.00399157 | + | 0.0122848i | ||||
\(560\) | 11192.1 | 0.844555 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3598.04 | 0.270061 | ||||||||
\(563\) | 2708.19 | − | 8334.95i | 0.202729 | − | 0.623937i | −0.797070 | − | 0.603887i | \(-0.793618\pi\) |
0.999799 | − | 0.0200493i | \(-0.00638233\pi\) | |||||||
\(564\) | 2571.94 | − | 1868.63i | 0.192018 | − | 0.139510i | ||||
\(565\) | −20855.0 | − | 15152.0i | −1.55288 | − | 1.12823i | ||||
\(566\) | 1176.22 | + | 3620.05i | 0.0873505 | + | 0.268837i | ||||
\(567\) | 4616.76 | + | 14208.9i | 0.341950 | + | 1.05241i | ||||
\(568\) | −4310.31 | − | 3131.62i | −0.318410 | − | 0.231338i | ||||
\(569\) | −8311.16 | + | 6038.41i | −0.612341 | + | 0.444892i | −0.850238 | − | 0.526399i | \(-0.823542\pi\) |
0.237897 | + | 0.971290i | \(0.423542\pi\) | |||||||
\(570\) | −1171.07 | + | 3604.19i | −0.0860540 | + | 0.264847i | ||||
\(571\) | −2602.62 | −0.190747 | −0.0953734 | − | 0.995442i | \(-0.530404\pi\) | ||||
−0.0953734 | + | 0.995442i | \(0.530404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17332.6 | 1.26366 | ||||||||
\(574\) | 1052.82 | − | 3240.24i | 0.0765572 | − | 0.235619i | ||||
\(575\) | −435.242 | + | 316.222i | −0.0315667 | + | 0.0229345i | ||||
\(576\) | 2092.11 | + | 1520.00i | 0.151339 | + | 0.109954i | ||||
\(577\) | −6095.99 | − | 18761.5i | −0.439825 | − | 1.35364i | −0.888060 | − | 0.459728i | \(-0.847947\pi\) |
0.448235 | − | 0.893916i | \(-0.352053\pi\) | |||||||
\(578\) | 438.925 | + | 1350.87i | 0.0315863 | + | 0.0972127i | ||||
\(579\) | −11914.2 | − | 8656.17i | −0.855159 | − | 0.621309i | ||||
\(580\) | 13119.8 | − | 9532.12i | 0.939261 | − | 0.682413i | ||||
\(581\) | 136.814 | − | 421.069i | 0.00976935 | − | 0.0300670i | ||||
\(582\) | 3678.30 | 0.261977 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6912.30 | 0.489783 | ||||||||
\(585\) | 2414.88 | − | 7432.24i | 0.170672 | − | 0.525274i | ||||
\(586\) | −5259.65 | + | 3821.36i | −0.370775 | + | 0.269384i | ||||
\(587\) | 8184.14 | + | 5946.12i | 0.575461 | + | 0.418097i | 0.837085 | − | 0.547073i | \(-0.184258\pi\) |
−0.261624 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(588\) | 771.683 | + | 2374.99i | 0.0541219 | + | 0.166570i | ||||
\(589\) | −1374.75 | − | 4231.05i | −0.0961725 | − | 0.295988i | ||||
\(590\) | 4154.49 | + | 3018.41i | 0.289894 | + | 0.210620i | ||||
\(591\) | −24582.8 | + | 17860.5i | −1.71100 | + | 1.24312i | ||||
\(592\) | 649.265 | − | 1998.23i | 0.0450754 | − | 0.138728i | ||||
\(593\) | −3130.32 | −0.216774 | −0.108387 | − | 0.994109i | \(-0.534569\pi\) | ||||
−0.108387 | + | 0.994109i | \(0.534569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18016.9 | 1.24138 | ||||||||
\(596\) | 8045.98 | − | 24763.0i | 0.552980 | − | 1.70190i | ||||
\(597\) | 36.8919 | − | 26.8035i | 0.00252912 | − | 0.00183751i | ||||
\(598\) | 590.313 | + | 428.887i | 0.0403674 | + | 0.0293286i | ||||
\(599\) | 3114.92 | + | 9586.73i | 0.212474 | + | 0.653928i | 0.999323 | + | 0.0367829i | \(0.0117110\pi\) |
−0.786849 | + | 0.617145i | \(0.788289\pi\) | |||||||
\(600\) | −835.484 | − | 2571.36i | −0.0568475 | − | 0.174959i | ||||
\(601\) | 3864.69 | + | 2807.86i | 0.262303 | + | 0.190574i | 0.711162 | − | 0.703029i | \(-0.248169\pi\) |
−0.448859 | + | 0.893603i | \(0.648169\pi\) | |||||||
\(602\) | 22.9304 | − | 16.6599i | 0.00155245 | − | 0.00112792i | ||||
\(603\) | 1035.90 | − | 3188.17i | 0.0699586 | − | 0.215310i | ||||
\(604\) | −8683.16 | −0.584955 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5613.29 | −0.376278 | ||||||||
\(607\) | 794.591 | − | 2445.50i | 0.0531325 | − | 0.163525i | −0.920969 | − | 0.389635i | \(-0.872601\pi\) |
0.974102 | + | 0.226110i | \(0.0726010\pi\) | |||||||
\(608\) | −7045.27 | + | 5118.69i | −0.469940 | + | 0.341431i | ||||
\(609\) | −13720.3 | − | 9968.41i | −0.912933 | − | 0.663285i | ||||
\(610\) | 294.621 | + | 906.751i | 0.0195555 | + | 0.0601857i | ||||
\(611\) | −1657.15 | − | 5100.20i | −0.109724 | − | 0.337695i | ||||
\(612\) | 4071.00 | + | 2957.75i | 0.268889 | + | 0.195360i | ||||
\(613\) | 10284.1 | − | 7471.84i | 0.677604 | − | 0.492308i | −0.194958 | − | 0.980812i | \(-0.562457\pi\) |
0.872562 | + | 0.488504i | \(0.162457\pi\) | |||||||
\(614\) | 338.857 | − | 1042.89i | 0.0222722 | − | 0.0685468i | ||||
\(615\) | 20953.8 | 1.37388 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16236.1 | 1.05939 | 0.529693 | − | 0.848189i | \(-0.322307\pi\) | ||||
0.529693 | + | 0.848189i | \(0.322307\pi\) | |||||||
\(618\) | −2313.64 | + | 7120.66i | −0.150596 | + | 0.463487i | ||||
\(619\) | −10240.0 | + | 7439.78i | −0.664910 | + | 0.483086i | −0.868318 | − | 0.496009i | \(-0.834798\pi\) |
0.203407 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(620\) | 5084.86 | + | 3694.37i | 0.329376 | + | 0.239305i | ||||
\(621\) | −461.286 | − | 1419.69i | −0.0298080 | − | 0.0917396i | ||||
\(622\) | −1693.16 | − | 5211.01i | −0.109147 | − | 0.335921i | ||||
\(623\) | −4832.86 | − | 3511.28i | −0.310794 | − | 0.225805i | ||||
\(624\) | 18409.3 | − | 13375.2i | 1.18103 | − | 0.858069i | ||||
\(625\) | −5883.02 | + | 18106.1i | −0.376513 | + | 1.15879i | ||||
\(626\) | −481.955 | −0.0307713 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2553.15 | −0.162232 | ||||||||
\(629\) | 1045.18 | − | 3216.74i | 0.0662546 | − | 0.203911i | ||||
\(630\) | −1049.65 | + | 762.617i | −0.0663796 | + | 0.0482276i | ||||
\(631\) | 3195.59 | + | 2321.73i | 0.201608 | + | 0.146477i | 0.684008 | − | 0.729474i | \(-0.260235\pi\) |
−0.482401 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(632\) | −3422.06 | − | 10532.0i | −0.215383 | − | 0.662881i | ||||
\(633\) | −5692.39 | − | 17519.4i | −0.357428 | − | 1.10005i | ||||
\(634\) | −138.411 | − | 100.562i | −0.00867038 | − | 0.00629940i | ||||
\(635\) | −1140.01 | + | 828.263i | −0.0712437 | + | 0.0517616i | ||||
\(636\) | 2037.44 | − | 6270.59i | 0.127028 | − | 0.390951i | ||||
\(637\) | 4212.44 | 0.262014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3832.67 | −0.237274 | ||||||||
\(640\) | 4998.41 | − | 15383.5i | 0.308718 | − | 0.950137i | ||||
\(641\) | 5985.32 | − | 4348.59i | 0.368808 | − | 0.267955i | −0.387908 | − | 0.921698i | \(-0.626802\pi\) |
0.756717 | + | 0.653743i | \(0.226802\pi\) | |||||||
\(642\) | −1699.92 | − | 1235.06i | −0.104502 | − | 0.0759253i | ||||
\(643\) | −3860.14 | − | 11880.3i | −0.236748 | − | 0.728637i | −0.996885 | − | 0.0788729i | \(-0.974868\pi\) |
0.760136 | − | 0.649764i | \(-0.225132\pi\) | |||||||
\(644\) | 521.407 | + | 1604.72i | 0.0319042 | + | 0.0981910i | ||||
\(645\) | 141.027 | + | 102.462i | 0.00860919 | + | 0.00625494i | ||||
\(646\) | −3330.16 | + | 2419.51i | −0.202823 | + | 0.147359i | ||||
\(647\) | −3236.02 | + | 9959.44i | −0.196632 | + | 0.605172i | 0.803321 | + | 0.595546i | \(0.203064\pi\) |
−0.999954 | + | 0.00962607i | \(0.996936\pi\) | |||||||
\(648\) | 9991.02 | 0.605685 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2201.33 | −0.132836 | ||||||||
\(651\) | 2031.14 | − | 6251.22i | 0.122284 | − | 0.376351i | ||||
\(652\) | −8423.18 | + | 6119.80i | −0.505946 | + | 0.367592i | ||||
\(653\) | −5127.50 | − | 3725.34i | −0.307281 | − | 0.223253i | 0.423448 | − | 0.905920i | \(-0.360820\pi\) |
−0.730729 | + | 0.682668i | \(0.760820\pi\) | |||||||
\(654\) | 86.1712 | + | 265.208i | 0.00515223 | + | 0.0158569i | ||||
\(655\) | 4595.44 | + | 14143.3i | 0.274136 | + | 0.843703i | ||||
\(656\) | 11438.2 | + | 8310.32i | 0.680771 | + | 0.494609i | ||||
\(657\) | 4022.82 | − | 2922.75i | 0.238881 | − | 0.173557i | ||||
\(658\) | −275.130 | + | 846.762i | −0.0163004 | + | 0.0501675i | ||||
\(659\) | −15196.7 | −0.898302 | −0.449151 | − | 0.893456i | \(-0.648274\pi\) | ||||
−0.449151 | + | 0.893456i | \(0.648274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2298.17 | 0.135232 | 0.0676161 | − | 0.997711i | \(-0.478461\pi\) | ||||
0.0676161 | + | 0.997711i | \(0.478461\pi\) | |||||||
\(662\) | 1930.29 | − | 5940.83i | 0.113328 | − | 0.348787i | ||||
\(663\) | 29635.2 | − | 21531.2i | 1.73595 | − | 1.26124i | ||||
\(664\) | −239.530 | − | 174.029i | −0.0139994 | − | 0.0101711i | ||||
\(665\) | 4568.04 | + | 14059.0i | 0.266377 | + | 0.819826i | ||||
\(666\) | 75.2662 | + | 231.645i | 0.00437914 | + | 0.0134776i | ||||
\(667\) | 1825.73 | + | 1326.47i | 0.105986 | + | 0.0770033i | ||||
\(668\) | −2890.69 | + | 2100.21i | −0.167431 | + | 0.121646i | ||||
\(669\) | −22.5664 | + | 69.4523i | −0.00130414 | + | 0.00401372i | ||||
\(670\) | −3874.18 | −0.223392 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12866.4 | −0.738589 | ||||||||
\(673\) | −7169.08 | + | 22064.2i | −0.410621 | + | 1.26376i | 0.505489 | + | 0.862833i | \(0.331312\pi\) |
−0.916110 | + | 0.400928i | \(0.868688\pi\) | |||||||
\(674\) | 6924.00 | − | 5030.58i | 0.395701 | − | 0.287494i | ||||
\(675\) | 3643.40 | + | 2647.08i | 0.207755 | + | 0.150943i | ||||
\(676\) | −7782.90 | − | 23953.3i | −0.442814 | − | 1.36284i | ||||
\(677\) | 662.958 | + | 2040.38i | 0.0376360 | + | 0.115832i | 0.968109 | − | 0.250528i | \(-0.0806041\pi\) |
−0.930473 | + | 0.366359i | \(0.880604\pi\) | |||||||
\(678\) | 7039.70 | + | 5114.64i | 0.398758 | + | 0.289715i | ||||
\(679\) | 11607.8 | − | 8433.59i | 0.656065 | − | 0.476659i | ||||
\(680\) | 3723.21 | − | 11458.9i | 0.209968 | − | 0.646217i | ||||
\(681\) | −27364.0 | −1.53978 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29544.6 | −1.65519 | −0.827593 | − | 0.561329i | \(-0.810290\pi\) | ||||
−0.827593 | + | 0.561329i | \(0.810290\pi\) | |||||||
\(684\) | −1275.83 | + | 3926.60i | −0.0713196 | + | 0.219499i | ||||
\(685\) | 2062.77 | − | 1498.69i | 0.115058 | − | 0.0835942i | ||||
\(686\) | −4004.58 | − | 2909.50i | −0.222880 | − | 0.161932i | ||||
\(687\) | 9296.29 | + | 28611.1i | 0.516267 | + | 1.58891i | ||||
\(688\) | 36.3466 | + | 111.863i | 0.00201410 | + | 0.00619876i | ||||
\(689\) | −8997.80 | − | 6537.29i | −0.497517 | − | 0.361467i | ||||
\(690\) | 602.764 | − | 437.934i | 0.0332563 | − | 0.0241621i | ||||
\(691\) | 8591.62 | − | 26442.3i | 0.472997 | − | 1.45573i | −0.375644 | − | 0.926764i | \(-0.622578\pi\) |
0.848641 | − | 0.528970i | \(-0.177422\pi\) | |||||||
\(692\) | 13499.5 | 0.741579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3366.55 | −0.184139 | ||||||||
\(695\) | −11521.8 | + | 35460.5i | −0.628845 | + | 1.93539i | ||||
\(696\) | −9175.30 | + | 6666.24i | −0.499696 | + | 0.363051i | ||||
\(697\) | 18413.1 | + | 13377.9i | 1.00064 | + | 0.727007i | ||||
\(698\) | −1520.23 | − | 4678.80i | −0.0824380 | − | 0.253718i | ||||
\(699\) | −387.785 | − | 1193.48i | −0.0209834 | − | 0.0645801i | ||||
\(700\) | −4118.25 | − | 2992.09i | −0.222365 | − | 0.161557i | ||||
\(701\) | −15935.8 | + | 11578.0i | −0.858613 | + | 0.623819i | −0.927507 | − | 0.373805i | \(-0.878053\pi\) |
0.0688945 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(702\) | 1887.48 | − | 5809.08i | 0.101479 | − | 0.312321i | ||||
\(703\) | 2775.09 | 0.148883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5475.78 | −0.292524 | ||||||||
\(706\) | 1298.19 | − | 3995.41i | 0.0692038 | − | 0.212987i | ||||
\(707\) | −17714.2 | + | 12870.1i | −0.942308 | + | 0.684627i | ||||
\(708\) | 19532.5 | + | 14191.2i | 1.03683 | + | 0.753300i | ||||
\(709\) | 5909.18 | + | 18186.6i | 0.313010 | + | 0.963345i | 0.976566 | + | 0.215218i | \(0.0690464\pi\) |
−0.663556 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(710\) | 1368.76 | + | 4212.62i | 0.0723504 | + | 0.222672i | ||||
\(711\) | −6444.85 | − | 4682.46i | −0.339945 | − | 0.246984i | ||||
\(712\) | −3231.91 | + | 2348.12i | −0.170114 | + | 0.123595i | ||||
\(713\) | −270.279 | + | 831.833i | −0.0141964 | + | 0.0436920i | ||||
\(714\) | −6081.70 | −0.318770 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33064.8 | 1.72582 | ||||||||
\(717\) | −7900.12 | + | 24314.1i | −0.411486 | + | 1.26642i | ||||
\(718\) | −2437.23 | + | 1770.75i | −0.126681 | + | 0.0920389i | ||||
\(719\) | −1486.52 | − | 1080.02i | −0.0771042 | − | 0.0560195i | 0.548565 | − | 0.836108i | \(-0.315174\pi\) |
−0.625670 | + | 0.780088i | \(0.715174\pi\) | |||||||
\(720\) | −1663.79 | − | 5120.61i | −0.0861190 | − | 0.265047i | ||||
\(721\) | 9024.91 | + | 27775.8i | 0.466165 | + | 1.43471i | ||||
\(722\) | 1329.85 | + | 966.196i | 0.0685486 | + | 0.0498034i | ||||
\(723\) | −4779.63 | + | 3472.61i | −0.245860 | + | 0.178627i | ||||
\(724\) | −7863.38 | + | 24201.0i | −0.403647 | + | 1.24230i | ||||
\(725\) | −6808.33 | −0.348765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7555.46 | −0.385442 | −0.192721 | − | 0.981254i | \(-0.561731\pi\) | ||||
−0.192721 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(728\) | −4420.15 | + | 13603.8i | −0.225030 | + | 0.692570i | ||||
\(729\) | −8660.70 | + | 6292.36i | −0.440009 | + | 0.319685i | ||||
\(730\) | −4649.17 | − | 3377.82i | −0.235717 | − | 0.171258i | ||||
\(731\) | 58.5105 | + | 180.077i | 0.00296045 | + | 0.00911133i | ||||
\(732\) | 1385.17 | + | 4263.12i | 0.0699419 | + | 0.215259i | ||||
\(733\) | 9695.77 | + | 7044.39i | 0.488569 | + | 0.354966i | 0.804634 | − | 0.593771i | \(-0.202362\pi\) |
−0.316065 | + | 0.948738i | \(0.602362\pi\) | |||||||
\(734\) | −5722.83 | + | 4157.88i | −0.287784 | + | 0.209087i | ||||
\(735\) | 1329.17 | − | 4090.77i | 0.0667037 | − | 0.205293i | ||||
\(736\) | 1712.10 | 0.0857456 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1638.99 | −0.0817508 | ||||||||
\(739\) | 8387.49 | − | 25814.0i | 0.417508 | − | 1.28496i | −0.492479 | − | 0.870324i | \(-0.663909\pi\) |
0.909988 | − | 0.414635i | \(-0.136091\pi\) | |||||||
\(740\) | −3171.87 | + | 2304.50i | −0.157568 | + | 0.114480i | ||||
\(741\) | 24315.1 | + | 17665.9i | 1.20545 | + | 0.875809i | ||||
\(742\) | 570.605 | + | 1756.14i | 0.0282312 | + | 0.0868868i | ||||
\(743\) | 9030.29 | + | 27792.4i | 0.445881 | + | 1.37228i | 0.881515 | + | 0.472156i | \(0.156524\pi\) |
−0.435634 | + | 0.900124i | \(0.643476\pi\) | |||||||
\(744\) | −3556.07 | − | 2583.64i | −0.175231 | − | 0.127313i | ||||
\(745\) | −36282.4 | + | 26360.7i | −1.78428 | + | 1.29635i | ||||
\(746\) | 32.0730 | − | 98.7104i | 0.00157409 | − | 0.00484457i | ||||
\(747\) | −212.987 | −0.0104321 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8196.29 | −0.399847 | ||||||||
\(750\) | 1460.55 | − | 4495.10i | 0.0711088 | − | 0.218850i | ||||
\(751\) | 7167.40 | − | 5207.42i | 0.348258 | − | 0.253025i | −0.399880 | − | 0.916568i | \(-0.630948\pi\) |
0.748138 | + | 0.663543i | \(0.230948\pi\) | |||||||
\(752\) | −2989.10 | − | 2171.71i | −0.144948 | − | 0.105311i | ||||
\(753\) | −507.243 | − | 1561.13i | −0.0245484 | − | 0.0755523i | ||||
\(754\) | 2853.48 | + | 8782.10i | 0.137822 | + | 0.424172i | ||||
\(755\) | 12099.8 | + | 8791.01i | 0.583253 | + | 0.423758i | ||||
\(756\) | 11426.9 | − | 8302.12i | 0.549725 | − | 0.399398i | ||||
\(757\) | 11042.5 | − | 33985.4i | 0.530182 | − | 1.63173i | −0.223653 | − | 0.974669i | \(-0.571798\pi\) |
0.753835 | − | 0.657064i | \(-0.228202\pi\) | |||||||
\(758\) | −2064.19 | −0.0989112 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9885.59 | 0.471826 | ||||||||
\(761\) | −10628.5 | + | 32711.3i | −0.506287 | + | 1.55819i | 0.292310 | + | 0.956324i | \(0.405576\pi\) |
−0.798597 | + | 0.601867i | \(0.794424\pi\) | |||||||
\(762\) | 384.815 | − | 279.585i | 0.0182945 | − | 0.0132917i | ||||
\(763\) | 880.003 | + | 639.359i | 0.0417539 | + | 0.0303360i | ||||
\(764\) | −6743.74 | − | 20755.1i | −0.319345 | − | 0.982844i | ||||
\(765\) | −2678.35 | − | 8243.12i | −0.126583 | − | 0.389583i | ||||
\(766\) | 3753.53 | + | 2727.10i | 0.177050 | + | 0.128635i | ||||
\(767\) | 32948.4 | − | 23938.4i | 1.55110 | − | 1.12694i | ||||
\(768\) | 2966.54 | − | 9130.06i | 0.139382 | − | 0.428975i | ||||
\(769\) | 11602.7 | 0.544091 | 0.272045 | − | 0.962284i | \(-0.412300\pi\) | ||||
0.272045 | + | 0.962284i | \(0.412300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19178.8 | −0.895859 | ||||||||
\(772\) | −5729.86 | + | 17634.7i | −0.267127 | + | 0.822132i | ||||
\(773\) | 10258.8 | − | 7453.47i | 0.477341 | − | 0.346808i | −0.322955 | − | 0.946414i | \(-0.604676\pi\) |
0.800295 | + | 0.599606i | \(0.204676\pi\) | |||||||
\(774\) | −11.0310 | − | 8.01452i | −0.000512277 | − | 0.000372191i | ||||
\(775\) | −815.405 | − | 2509.56i | −0.0377938 | − | 0.116317i | ||||
\(776\) | −2965.05 | − | 9125.47i | −0.137164 | − | 0.422146i | ||||
\(777\) | 3317.05 | + | 2409.98i | 0.153151 | + | 0.111271i | ||||
\(778\) | 5214.84 | − | 3788.80i | 0.240310 | − | 0.174595i | ||||
\(779\) | −5770.57 | + | 17760.0i | −0.265407 | + | 0.816839i | ||||
\(780\) | −42461.7 | −1.94920 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 809.276 | 0.0370072 | ||||||||
\(783\) | 5837.65 | − | 17966.4i | 0.266437 | − | 0.820010i | ||||
\(784\) | 2347.97 | − | 1705.90i | 0.106959 | − | 0.0777105i | ||||
\(785\) | 3557.75 | + | 2584.86i | 0.161760 | + | 0.117525i | ||||
\(786\) | −1551.22 | − | 4774.15i | −0.0703944 | − | 0.216652i | ||||
\(787\) | 1365.12 | + | 4201.39i | 0.0618312 | + | 0.190297i | 0.977201 | − | 0.212318i | \(-0.0681013\pi\) |
−0.915369 | + | 0.402615i | \(0.868101\pi\) | |||||||
\(788\) | 30951.8 | + | 22487.8i | 1.39925 | + | 1.01662i | ||||
\(789\) | 997.305 | − | 724.584i | 0.0450000 | − | 0.0326944i | ||||
\(790\) | −2845.00 | + | 8756.01i | −0.128127 | + | 0.394335i | ||||
\(791\) | 33942.4 | 1.52573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7561.33 | 0.338601 | ||||||||
\(794\) | 976.182 | − | 3004.38i | 0.0436315 | − | 0.134284i | ||||
\(795\) | −9187.59 | + | 6675.18i | −0.409875 | + | 0.297791i | ||||
\(796\) | −46.4500 | − | 33.7479i | −0.00206831 | − | 0.00150272i | ||||
\(797\) | −8352.75 | − | 25707.1i | −0.371229 | − | 1.14253i | −0.945988 | − | 0.324203i | \(-0.894904\pi\) |
0.574758 | − | 0.818323i | \(-0.305096\pi\) | |||||||
\(798\) | −1541.97 | − | 4745.68i | −0.0684022 | − | 0.210520i | ||||
\(799\) | −4811.83 | − | 3496.00i | −0.213054 | − | 0.154793i | ||||
\(800\) | −4178.76 | + | 3036.05i | −0.184677 | + | 0.134176i | ||||
\(801\) | −888.044 | + | 2733.12i | −0.0391729 | + | 0.120562i | ||||
\(802\) | 264.769 | 0.0116575 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18214.6 | −0.798979 | ||||||||
\(805\) | 898.087 | − | 2764.03i | 0.0393210 | − | 0.121018i | ||||
\(806\) | −2895.35 | + | 2103.59i | −0.126531 | + | 0.0919304i | ||||
\(807\) | −24138.5 | − | 17537.7i | −1.05293 | − | 0.765000i | ||||
\(808\) | 4524.82 | + | 13926.0i | 0.197008 | + | 0.606329i | ||||
\(809\) | −7307.33 | − | 22489.7i | −0.317568 | − | 0.977372i | −0.974685 | − | 0.223584i | \(-0.928224\pi\) |
0.657117 | − | 0.753789i | \(-0.271776\pi\) | |||||||
\(810\) | −6719.89 | − | 4882.29i | −0.291497 | − | 0.211785i | ||||
\(811\) | 27090.8 | − | 19682.6i | 1.17298 | − | 0.852219i | 0.181617 | − | 0.983369i | \(-0.441867\pi\) |
0.991363 | + | 0.131150i | \(0.0418669\pi\) | |||||||
\(812\) | −6598.48 | + | 20308.0i | −0.285174 | + | 0.877676i | ||||
\(813\) | −8815.30 | −0.380278 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17933.3 | 0.770768 | ||||||||
\(816\) | 7798.92 | − | 24002.6i | 0.334580 | − | 1.02973i | ||||
\(817\) | −125.683 | + | 91.3140i | −0.00538200 | + | 0.00391025i | ||||
\(818\) | 5460.76 | + | 3967.48i | 0.233412 | + | 0.169584i | ||||
\(819\) | 3179.71 | + | 9786.13i | 0.135663 | + | 0.417527i | ||||
\(820\) | −8152.65 | − | 25091.3i | −0.347199 | − | 1.06857i | ||||
\(821\) | 2108.05 | + | 1531.59i | 0.0896119 | + | 0.0651068i | 0.631689 | − | 0.775222i | \(-0.282362\pi\) |
−0.542077 | + | 0.840329i | \(0.682362\pi\) | |||||||
\(822\) | −696.299 | + | 505.891i | −0.0295453 | + | 0.0214659i | ||||
\(823\) | 9881.19 | − | 30411.2i | 0.418513 | − | 1.28805i | −0.490557 | − | 0.871409i | \(-0.663207\pi\) |
0.909070 | − | 0.416642i | \(-0.136793\pi\) | |||||||
\(824\) | 19530.6 | 0.825705 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6761.62 | −0.284827 | ||||||||
\(827\) | 11668.2 | − | 35911.0i | 0.490620 | − | 1.50997i | −0.333054 | − | 0.942908i | \(-0.608079\pi\) |
0.823674 | − | 0.567064i | \(-0.191921\pi\) | |||||||
\(828\) | 656.685 | − | 477.110i | 0.0275621 | − | 0.0200250i | ||||
\(829\) | 920.300 | + | 668.637i | 0.0385565 | + | 0.0280129i | 0.606897 | − | 0.794781i | \(-0.292414\pi\) |
−0.568340 | + | 0.822794i | \(0.692414\pi\) | |||||||
\(830\) | 76.0641 | + | 234.101i | 0.00318099 | + | 0.00979009i | ||||
\(831\) | 432.031 | + | 1329.66i | 0.0180349 | + | 0.0555057i | ||||
\(832\) | −19175.4 | − | 13931.8i | −0.799025 | − | 0.580526i | ||||
\(833\) | 3779.75 | − | 2746.15i | 0.157216 | − | 0.114224i | ||||
\(834\) | 3889.25 | − | 11969.9i | 0.161479 | − | 0.496982i | ||||
\(835\) | 6154.40 | 0.255068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7321.60 | 0.302356 | ||||||||
\(838\) | −3373.53 | + | 10382.6i | −0.139065 | + | 0.427998i | ||||
\(839\) | 30234.8 | − | 21966.8i | 1.24412 | − | 0.903909i | 0.246258 | − | 0.969204i | \(-0.420799\pi\) |
0.997866 | + | 0.0652950i | \(0.0207988\pi\) | |||||||
\(840\) | 11816.2 | + | 8584.96i | 0.485354 | + | 0.352630i | ||||
\(841\) | 1288.68 | + | 3966.15i | 0.0528386 | + | 0.162620i | ||||
\(842\) | −3050.75 | − | 9389.25i | −0.124864 | − | 0.384293i | ||||
\(843\) | −23572.5 | − | 17126.4i | −0.963084 | − | 0.699721i | ||||
\(844\) | −18764.0 | + | 13632.8i | −0.765263 | + | 0.555996i | ||||
\(845\) | −13405.5 | + | 41257.9i | −0.545756 | + | 1.67966i | ||||
\(846\) | 428.312 | 0.0174062 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7662.68 | −0.310304 | ||||||||
\(849\) | 9525.15 | − | 29315.4i | 0.385044 | − | 1.18504i | ||||
\(850\) | −1975.22 | + | 1435.08i | −0.0797053 | + | 0.0579093i | ||||
\(851\) | −441.391 | − | 320.689i | −0.0177799 | − | 0.0129179i | ||||
\(852\) | 6435.29 | + | 19805.8i | 0.258767 | + | 0.796402i | ||||
\(853\) | 6950.05 | + | 21390.1i | 0.278974 | + | 0.858595i | 0.988140 | + | 0.153553i | \(0.0490717\pi\) |
−0.709166 | + | 0.705042i | \(0.750928\pi\) | |||||||
\(854\) | −1015.62 | − | 737.890i | −0.0406953 | − | 0.0295668i | ||||
\(855\) | 5753.21 | − | 4179.95i | 0.230124 | − | 0.167195i | ||||
\(856\) | −1693.77 | + | 5212.89i | −0.0676307 | + | 0.208146i | ||||
\(857\) | −43409.5 | −1.73027 | −0.865135 | − | 0.501539i | \(-0.832767\pi\) | ||||
−0.865135 | + | 0.501539i | \(0.832767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29533.2 | 1.17306 | 0.586532 | − | 0.809926i | \(-0.300493\pi\) | ||||
0.586532 | + | 0.809926i | \(0.300493\pi\) | |||||||
\(860\) | 67.8237 | − | 208.740i | 0.00268926 | − | 0.00827670i | ||||
\(861\) | −22320.9 | + | 16217.1i | −0.883499 | + | 0.641900i | ||||
\(862\) | 240.648 | + | 174.841i | 0.00950870 | + | 0.00690847i | ||||
\(863\) | 4434.90 | + | 13649.2i | 0.174931 | + | 0.538384i | 0.999630 | − | 0.0271884i | \(-0.00865540\pi\) |
−0.824699 | + | 0.565572i | \(0.808655\pi\) | |||||||
\(864\) | −4428.81 | − | 13630.5i | −0.174388 | − | 0.536711i | ||||
\(865\) | −18811.2 | − | 13667.1i | −0.739421 | − | 0.537221i | ||||
\(866\) | 1046.31 | − | 760.188i | 0.0410566 | − | 0.0298294i | ||||
\(867\) | 3554.45 | − | 10939.5i | 0.139234 | − | 0.428517i | ||||
\(868\) | −8275.85 | −0.323618 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 9428.82 | 0.367433 | ||||||||
\(871\) | −9494.64 | + | 29221.5i | −0.369361 | + | 1.13678i | ||||
\(872\) | 588.490 | − | 427.563i | 0.0228541 | − | 0.0166045i | ||||
\(873\) | −5584.15 | − | 4057.12i | −0.216489 | − | 0.157288i | ||||
\(874\) | 205.185 | + | 631.496i | 0.00794108 | + | 0.0244401i | ||||
\(875\) | −5697.21 | − | 17534.2i | −0.220115 | − | 0.677445i | ||||
\(876\) | −21858.2 | − | 15880.9i | −0.843061 | − | 0.612519i | ||||
\(877\) | −34988.9 | + | 25420.9i | −1.34720 | + | 0.978796i | −0.348051 | + | 0.937476i | \(0.613156\pi\) |
−0.999146 | + | 0.0413205i | \(0.986844\pi\) | |||||||
\(878\) | −1769.96 | + | 5447.37i | −0.0680333 | + | 0.209385i | ||||
\(879\) | 52647.9 | 2.02021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3816.13 | 0.145935 | 0.0729675 | − | 0.997334i | \(-0.476753\pi\) | ||||
0.0729675 | + | 0.997334i | \(0.476753\pi\) | |||||||
\(882\) | −103.967 | + | 319.977i | −0.00396910 | + | 0.0122156i | ||||
\(883\) | −39470.0 | + | 28676.6i | −1.50427 | + | 1.09292i | −0.535629 | + | 0.844454i | \(0.679925\pi\) |
−0.968641 | + | 0.248463i | \(0.920075\pi\) | |||||||
\(884\) | −37313.2 | − | 27109.6i | −1.41966 | − | 1.03144i | ||||
\(885\) | −12850.6 | − | 39550.1i | −0.488100 | − | 1.50222i | ||||
\(886\) | 2639.46 | + | 8123.44i | 0.100084 | + | 0.308027i | ||||
\(887\) | 33570.3 | + | 24390.2i | 1.27078 | + | 0.923274i | 0.999233 | − | 0.0391521i | \(-0.0124657\pi\) |
0.271544 | + | 0.962426i | \(0.412466\pi\) | |||||||
\(888\) | 2218.23 | − | 1611.64i | 0.0838277 | − | 0.0609044i | ||||
\(889\) | 573.355 | − | 1764.60i | 0.0216307 | − | 0.0665725i | ||||
\(890\) | 3321.21 | 0.125087 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 91.9464 | 0.00345134 | ||||||||
\(893\) | 1508.00 | − | 4641.16i | 0.0565100 | − | 0.173920i | ||||
\(894\) | 12247.3 | − | 8898.20i | 0.458179 | − | 0.332886i | ||||
\(895\) | −46075.1 | − | 33475.5i | −1.72080 | − | 1.25024i | ||||
\(896\) | 6581.48 | + | 20255.7i | 0.245393 | + | 0.755241i | ||||
\(897\) | −1825.95 | − | 5619.70i | −0.0679673 | − | 0.209182i | ||||
\(898\) | −10053.5 | − | 7304.26i | −0.373595 | − | 0.271432i | ||||
\(899\) | −8954.79 | + | 6506.03i | −0.332212 | + | 0.241366i | ||||
\(900\) | −756.733 | + | 2328.99i | −0.0280272 | + | 0.0862587i | ||||
\(901\) | −12335.3 | −0.456104 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −229.528 | −0.00845871 | ||||||||
\(904\) | 7014.24 | − | 21587.6i | 0.258064 | − | 0.794240i | ||||
\(905\) | 35459.0 | − | 25762.5i | 1.30243 | − | 0.946269i | ||||
\(906\) | −4084.34 | − | 2967.45i | −0.149772 | − | 0.108816i | ||||
\(907\) | 6679.49 | + | 20557.4i | 0.244530 | + | 0.752586i | 0.995713 | + | 0.0924926i | \(0.0294835\pi\) |
−0.751183 | + | 0.660094i | \(0.770517\pi\) | |||||||
\(908\) | 10646.7 | + | 32767.3i | 0.389124 | + | 1.19760i | ||||
\(909\) | 8521.72 | + | 6191.39i | 0.310943 | + | 0.225914i | ||||
\(910\) | 9620.70 | − | 6989.85i | 0.350465 | − | 0.254628i | ||||
\(911\) | 1126.78 | − | 3467.89i | 0.0409792 | − | 0.126121i | −0.928474 | − | 0.371397i | \(-0.878879\pi\) |
0.969453 | + | 0.245276i | \(0.0788787\pi\) | |||||||
\(912\) | 20707.1 | 0.751844 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11854.0 | 0.428988 | ||||||||
\(915\) | 2385.86 | − | 7342.94i | 0.0862014 | − | 0.265301i | ||||
\(916\) | 30643.6 | − | 22263.9i | 1.10534 | − | 0.803077i | ||||
\(917\) | −15841.4 | − | 11509.5i | −0.570479 | − | 0.414477i | ||||
\(918\) | −2093.41 | − | 6442.87i | −0.0752647 | − | 0.231641i | ||||
\(919\) | −9666.05 | − | 29749.0i | −0.346957 | − | 1.06782i | −0.960528 | − | 0.278184i | \(-0.910267\pi\) |
0.613571 | − | 0.789640i | \(-0.289733\pi\) | |||||||
\(920\) | −1572.35 | − | 1142.38i | −0.0563465 | − | 0.0409382i | ||||
\(921\) | −7184.11 | + | 5219.56i | −0.257030 | + | 0.186743i | ||||
\(922\) | −1942.30 | + | 5977.79i | −0.0693777 | + | 0.213523i | ||||
\(923\) | 35128.7 | 1.25274 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1645.99 | 0.0585079 | ||||||||
\(926\) | −1791.00 | + | 5512.13i | −0.0635592 | + | 0.195615i | ||||
\(927\) | 11366.4 | − | 8258.18i | 0.402721 | − | 0.292594i | ||||
\(928\) | 17528.9 | + | 12735.5i | 0.620057 | + | 0.450498i | ||||
\(929\) | 2026.51 | + | 6236.96i | 0.0715690 | + | 0.220267i | 0.980443 | − | 0.196805i | \(-0.0630565\pi\) |
−0.908874 | + | 0.417071i | \(0.863056\pi\) | |||||||
\(930\) | 1129.25 | + | 3475.48i | 0.0398168 | + | 0.122543i | ||||
\(931\) | 3101.21 | + | 2253.16i | 0.109171 | + | 0.0793171i | ||||
\(932\) | −1278.26 | + | 928.713i | −0.0449259 | + | 0.0326406i | ||||
\(933\) | −13711.3 | + | 42199.2i | −0.481125 | + | 1.48075i | ||||
\(934\) | −11094.2 | −0.388665 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6881.13 | 0.240296 | ||||||||
\(937\) | 7562.68 | − | 23275.5i | 0.263673 | − | 0.811503i | −0.728323 | − | 0.685234i | \(-0.759700\pi\) |
0.991996 | − | 0.126269i | \(-0.0403002\pi\) | |||||||
\(938\) | 4126.94 | − | 2998.40i | 0.143656 | − | 0.104372i | ||||
\(939\) | 3157.52 | + | 2294.07i | 0.109736 | + | 0.0797276i | ||||
\(940\) | 2130.51 | + | 6557.02i | 0.0739249 | + | 0.227518i | ||||
\(941\) | −4765.30 | − | 14666.1i | −0.165084 | − | 0.508078i | 0.833958 | − | 0.551828i | \(-0.186069\pi\) |
−0.999043 | + | 0.0437502i | \(0.986069\pi\) | |||||||
\(942\) | −1200.94 | − | 872.531i | −0.0415378 | − | 0.0301790i | ||||
\(943\) | 2970.18 | − | 2157.96i | 0.102569 | − | 0.0745206i | ||||
\(944\) | 8670.83 | − | 26686.1i | 0.298953 | − | 0.920082i | ||||
\(945\) | −24328.3 | −0.837461 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33141.2 | −1.13722 | −0.568608 | − | 0.822609i | \(-0.692518\pi\) | ||||
−0.568608 | + | 0.822609i | \(0.692518\pi\) | |||||||
\(948\) | −13375.9 | + | 41166.7i | −0.458257 | + | 1.41037i | ||||
\(949\) | −36871.6 | + | 26788.8i | −1.26122 | + | 0.916333i | ||||
\(950\) | −1620.63 | − | 1177.45i | −0.0553474 | − | 0.0402123i | ||||
\(951\) | 428.133 | + | 1317.66i | 0.0145985 | + | 0.0449295i | ||||
\(952\) | 4902.40 | + | 15088.0i | 0.166899 | + | 0.513662i | ||||
\(953\) | −16775.3 | − | 12188.0i | −0.570205 | − | 0.414279i | 0.264974 | − | 0.964255i | \(-0.414637\pi\) |
−0.835180 | + | 0.549977i | \(0.814637\pi\) | |||||||
\(954\) | 718.648 | − | 522.128i | 0.0243890 | − | 0.0177196i | ||||
\(955\) | −11615.6 | + | 35749.2i | −0.393584 | + | 1.21133i | ||||
\(956\) | 32188.9 | 1.08898 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7321.32 | −0.246911 | ||||||||
\(959\) | −1037.45 | + | 3192.94i | −0.0349333 | + | 0.107513i | ||||
\(960\) | −19579.9 | + | 14225.6i | −0.658269 | + | 0.478261i | ||||
\(961\) | 20630.8 | + | 14989.2i | 0.692518 | + | 0.503144i | ||||
\(962\) | −689.861 | − | 2123.17i | −0.0231206 | − | 0.0711578i | ||||
\(963\) | 1218.44 | + | 3749.98i | 0.0407723 | + | 0.125484i | ||||
\(964\) | 6017.96 | + | 4372.30i | 0.201064 | + | 0.146081i | ||||
\(965\) | 25838.1 | − | 18772.5i | 0.861926 | − | 0.626226i | ||||
\(966\) | −303.154 | + | 933.012i | −0.0100971 | + | 0.0310758i | ||||
\(967\) | 8178.87 | 0.271990 | 0.135995 | − | 0.990710i | \(-0.456577\pi\) | ||||
0.135995 | + | 0.990710i | \(0.456577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33334.2 | 1.10511 | ||||||||
\(970\) | −2465.05 | + | 7586.65i | −0.0815960 | + | 0.251127i | ||||
\(971\) | 16646.4 | − | 12094.3i | 0.550163 | − | 0.399717i | −0.277682 | − | 0.960673i | \(-0.589566\pi\) |
0.827846 | + | 0.560956i | \(0.189566\pi\) | |||||||
\(972\) | −13368.2 | − | 9712.60i | −0.441139 | − | 0.320506i | ||||
\(973\) | −15170.9 | − | 46691.3i | −0.499853 | − | 1.53839i | ||||
\(974\) | 1593.59 | + | 4904.56i | 0.0524249 | + | 0.161347i | ||||
\(975\) | 14422.0 | + | 10478.2i | 0.473716 | + | 0.344175i | ||||
\(976\) | 4214.62 | − | 3062.10i | 0.138224 | − | 0.100426i | ||||
\(977\) | 4493.69 | − | 13830.1i | 0.147150 | − | 0.452882i | −0.850131 | − | 0.526571i | \(-0.823477\pi\) |
0.997281 | + | 0.0736895i | \(0.0234774\pi\) | |||||||
\(978\) | −6053.48 | −0.197923 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5415.68 | −0.176528 | ||||||||
\(981\) | 161.701 | − | 497.666i | 0.00526272 | − | 0.0161970i | ||||
\(982\) | −7892.46 | + | 5734.21i | −0.256475 | + | 0.186340i | ||||
\(983\) | 23692.6 | + | 17213.7i | 0.768746 | + | 0.558527i | 0.901580 | − | 0.432611i | \(-0.142408\pi\) |
−0.132834 | + | 0.991138i | \(0.542408\pi\) | |||||||
\(984\) | 5701.52 | + | 17547.5i | 0.184713 | + | 0.568489i | ||||
\(985\) | −20363.5 | − | 62672.5i | −0.658716 | − | 2.02732i | ||||
\(986\) | 8285.56 | + | 6019.81i | 0.267613 | + | 0.194432i | ||||
\(987\) | 5833.04 | − | 4237.95i | 0.188113 | − | 0.136672i | ||||
\(988\) | 11693.8 | − | 35989.7i | 0.376547 | − | 1.15889i | ||||
\(989\) | 30.5427 | 0.000982004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38085.9 | −1.22083 | −0.610413 | − | 0.792083i | \(-0.708997\pi\) | ||||
−0.610413 | + | 0.792083i | \(0.708997\pi\) | |||||||
\(992\) | −2594.95 | + | 7986.44i | −0.0830542 | + | 0.255615i | ||||
\(993\) | −40924.2 | + | 29733.2i | −1.30784 | + | 0.950205i | ||||
\(994\) | −4718.40 | − | 3428.12i | −0.150562 | − | 0.109390i | ||||
\(995\) | 30.5599 | + | 94.0538i | 0.000973683 | + | 0.00299669i | ||||
\(996\) | 357.618 | + | 1100.64i | 0.0113771 | + | 0.0350150i | ||||
\(997\) | −21684.6 | − | 15754.8i | −0.688825 | − | 0.500460i | 0.187449 | − | 0.982274i | \(-0.439978\pi\) |
−0.876274 | + | 0.481814i | \(0.839978\pi\) | |||||||
\(998\) | 11885.8 | − | 8635.52i | 0.376991 | − | 0.273900i | ||||
\(999\) | −1411.32 | + | 4343.59i | −0.0446968 | + | 0.137563i |
(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 | 121.4.c.f.9.2 | 8 | ||
11.2 | odd | 10 | 121.4.c.c.3.2 | 8 | |||
11.3 | even | 5 | inner | 121.4.c.f.81.1 | 8 | ||
11.4 | even | 5 | 121.4.a.c.1.2 | 2 | |||
11.5 | even | 5 | inner | 121.4.c.f.27.2 | 8 | ||
11.6 | odd | 10 | 121.4.c.c.27.1 | 8 | |||
11.7 | odd | 10 | 11.4.a.a.1.1 | ✓ | 2 | ||
11.8 | odd | 10 | 121.4.c.c.81.2 | 8 | |||
11.9 | even | 5 | inner | 121.4.c.f.3.1 | 8 | ||
11.10 | odd | 2 | 121.4.c.c.9.1 | 8 | |||
33.26 | odd | 10 | 1089.4.a.v.1.1 | 2 | |||
33.29 | even | 10 | 99.4.a.c.1.2 | 2 | |||
44.7 | even | 10 | 176.4.a.i.1.1 | 2 | |||
44.15 | odd | 10 | 1936.4.a.w.1.1 | 2 | |||
55.7 | even | 20 | 275.4.b.c.199.2 | 4 | |||
55.18 | even | 20 | 275.4.b.c.199.3 | 4 | |||
55.29 | odd | 10 | 275.4.a.b.1.2 | 2 | |||
77.62 | even | 10 | 539.4.a.e.1.1 | 2 | |||
88.29 | odd | 10 | 704.4.a.p.1.1 | 2 | |||
88.51 | even | 10 | 704.4.a.n.1.2 | 2 | |||
132.95 | odd | 10 | 1584.4.a.bc.1.2 | 2 | |||
143.51 | odd | 10 | 1859.4.a.a.1.2 | 2 | |||
165.29 | even | 10 | 2475.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.4.a.a.1.1 | ✓ | 2 | 11.7 | odd | 10 | ||
99.4.a.c.1.2 | 2 | 33.29 | even | 10 | |||
121.4.a.c.1.2 | 2 | 11.4 | even | 5 | |||
121.4.c.c.3.2 | 8 | 11.2 | odd | 10 | |||
121.4.c.c.9.1 | 8 | 11.10 | odd | 2 | |||
121.4.c.c.27.1 | 8 | 11.6 | odd | 10 | |||
121.4.c.c.81.2 | 8 | 11.8 | odd | 10 | |||
121.4.c.f.3.1 | 8 | 11.9 | even | 5 | inner | ||
121.4.c.f.9.2 | 8 | 1.1 | even | 1 | trivial | ||
121.4.c.f.27.2 | 8 | 11.5 | even | 5 | inner | ||
121.4.c.f.81.1 | 8 | 11.3 | even | 5 | inner | ||
176.4.a.i.1.1 | 2 | 44.7 | even | 10 | |||
275.4.a.b.1.2 | 2 | 55.29 | odd | 10 | |||
275.4.b.c.199.2 | 4 | 55.7 | even | 20 | |||
275.4.b.c.199.3 | 4 | 55.18 | even | 20 | |||
539.4.a.e.1.1 | 2 | 77.62 | even | 10 | |||
704.4.a.n.1.2 | 2 | 88.51 | even | 10 | |||
704.4.a.p.1.1 | 2 | 88.29 | odd | 10 | |||
1089.4.a.v.1.1 | 2 | 33.26 | odd | 10 | |||
1584.4.a.bc.1.2 | 2 | 132.95 | odd | 10 | |||
1859.4.a.a.1.2 | 2 | 143.51 | odd | 10 | |||
1936.4.a.w.1.1 | 2 | 44.15 | odd | 10 | |||
2475.4.a.q.1.1 | 2 | 165.29 | even | 10 |