Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.22 |
Dual form | 169.4.c.a.146.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50000 | + | 4.33013i | −0.883883 | + | 1.53093i | −0.0368954 | + | 0.999319i | \(0.511747\pi\) |
−0.846988 | + | 0.531612i | \(0.821586\pi\) | |||||||
\(3\) | 3.50000 | − | 6.06218i | 0.673575 | − | 1.16667i | −0.303308 | − | 0.952893i | \(-0.598091\pi\) |
0.976883 | − | 0.213774i | \(-0.0685756\pi\) | |||||||
\(4\) | −8.50000 | − | 14.7224i | −1.06250 | − | 1.84030i | ||||
\(5\) | 7.00000 | 0.626099 | 0.313050 | − | 0.949737i | \(-0.398649\pi\) | ||||
0.313050 | + | 0.949737i | \(0.398649\pi\) | |||||||
\(6\) | 17.5000 | + | 30.3109i | 1.19072 | + | 2.06239i | ||||
\(7\) | −6.50000 | − | 11.2583i | −0.350967 | − | 0.607893i | 0.635452 | − | 0.772140i | \(-0.280814\pi\) |
−0.986419 | + | 0.164248i | \(0.947480\pi\) | |||||||
\(8\) | 45.0000 | 1.98874 | ||||||||
\(9\) | −11.0000 | − | 19.0526i | −0.407407 | − | 0.705650i | ||||
\(10\) | −17.5000 | + | 30.3109i | −0.553399 | + | 0.958514i | ||||
\(11\) | −13.0000 | + | 22.5167i | −0.356332 | + | 0.617184i | −0.987345 | − | 0.158588i | \(-0.949306\pi\) |
0.631013 | + | 0.775772i | \(0.282639\pi\) | |||||||
\(12\) | −119.000 | −2.86270 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 65.0000 | 1.24086 | ||||||||
\(15\) | 24.5000 | − | 42.4352i | 0.421725 | − | 0.730449i | ||||
\(16\) | −44.5000 | + | 77.0763i | −0.695312 | + | 1.20432i | ||||
\(17\) | −38.5000 | − | 66.6840i | −0.549272 | − | 0.951367i | −0.998325 | − | 0.0578615i | \(-0.981572\pi\) |
0.449053 | − | 0.893505i | \(-0.351762\pi\) | |||||||
\(18\) | 110.000 | 1.44040 | ||||||||
\(19\) | −63.0000 | − | 109.119i | −0.760694 | − | 1.31756i | −0.942493 | − | 0.334225i | \(-0.891525\pi\) |
0.181799 | − | 0.983336i | \(-0.441808\pi\) | |||||||
\(20\) | −59.5000 | − | 103.057i | −0.665230 | − | 1.15221i | ||||
\(21\) | −91.0000 | −0.945611 | ||||||||
\(22\) | −65.0000 | − | 112.583i | −0.629911 | − | 1.09104i | ||||
\(23\) | 48.0000 | − | 83.1384i | 0.435161 | − | 0.753720i | −0.562148 | − | 0.827037i | \(-0.690025\pi\) |
0.997309 | + | 0.0733164i | \(0.0233583\pi\) | |||||||
\(24\) | 157.500 | − | 272.798i | 1.33956 | − | 2.32019i | ||||
\(25\) | −76.0000 | −0.608000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | −110.500 | + | 191.392i | −0.745805 | + | 1.29177i | ||||
\(29\) | 41.0000 | − | 71.0141i | 0.262535 | − | 0.454724i | −0.704380 | − | 0.709823i | \(-0.748775\pi\) |
0.966915 | + | 0.255099i | \(0.0821082\pi\) | |||||||
\(30\) | 122.500 | + | 212.176i | 0.745511 | + | 1.29126i | ||||
\(31\) | −196.000 | −1.13557 | −0.567785 | − | 0.823177i | \(-0.692199\pi\) | ||||
−0.567785 | + | 0.823177i | \(0.692199\pi\) | |||||||
\(32\) | −42.5000 | − | 73.6122i | −0.234782 | − | 0.406654i | ||||
\(33\) | 91.0000 | + | 157.617i | 0.480032 | + | 0.831440i | ||||
\(34\) | 385.000 | 1.94197 | ||||||||
\(35\) | −45.5000 | − | 78.8083i | −0.219740 | − | 0.380601i | ||||
\(36\) | −187.000 | + | 323.894i | −0.865741 | + | 1.49951i | ||||
\(37\) | −65.5000 | + | 113.449i | −0.291031 | + | 0.504080i | −0.974054 | − | 0.226317i | \(-0.927331\pi\) |
0.683023 | + | 0.730397i | \(0.260665\pi\) | |||||||
\(38\) | 630.000 | 2.68946 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 315.000 | 1.24515 | ||||||||
\(41\) | 168.000 | − | 290.985i | 0.639932 | − | 1.10839i | −0.345516 | − | 0.938413i | \(-0.612296\pi\) |
0.985447 | − | 0.169981i | \(-0.0543706\pi\) | |||||||
\(42\) | 227.500 | − | 394.042i | 0.835810 | − | 1.44767i | ||||
\(43\) | 100.500 | + | 174.071i | 0.356421 | + | 0.617339i | 0.987360 | − | 0.158493i | \(-0.0506635\pi\) |
−0.630939 | + | 0.775832i | \(0.717330\pi\) | |||||||
\(44\) | 442.000 | 1.51441 | ||||||||
\(45\) | −77.0000 | − | 133.368i | −0.255077 | − | 0.441807i | ||||
\(46\) | 240.000 | + | 415.692i | 0.769262 | + | 1.33240i | ||||
\(47\) | 105.000 | 0.325869 | 0.162934 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162934 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(48\) | 311.500 | + | 539.534i | 0.936691 | + | 1.62240i | ||||
\(49\) | 87.0000 | − | 150.688i | 0.253644 | − | 0.439325i | ||||
\(50\) | 190.000 | − | 329.090i | 0.537401 | − | 0.930806i | ||||
\(51\) | −539.000 | −1.47990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.000 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689126\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689126\pi\) | |||||||
\(54\) | −87.5000 | + | 151.554i | −0.220504 | + | 0.381925i | ||||
\(55\) | −91.0000 | + | 157.617i | −0.223099 | + | 0.386419i | ||||
\(56\) | −292.500 | − | 506.625i | −0.697981 | − | 1.20894i | ||||
\(57\) | −882.000 | −2.04954 | ||||||||
\(58\) | 205.000 | + | 355.070i | 0.464100 | + | 0.803845i | ||||
\(59\) | −147.000 | − | 254.611i | −0.324369 | − | 0.561824i | 0.657015 | − | 0.753877i | \(-0.271819\pi\) |
−0.981384 | + | 0.192054i | \(0.938485\pi\) | |||||||
\(60\) | −833.000 | −1.79233 | ||||||||
\(61\) | 28.0000 | + | 48.4974i | 0.0587710 | + | 0.101794i | 0.893914 | − | 0.448239i | \(-0.147948\pi\) |
−0.835143 | + | 0.550033i | \(0.814615\pi\) | |||||||
\(62\) | 490.000 | − | 848.705i | 1.00371 | − | 1.73848i | ||||
\(63\) | −143.000 | + | 247.683i | −0.285973 | + | 0.495320i | ||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −910.000 | −1.69717 | ||||||||
\(67\) | 239.000 | − | 413.960i | 0.435798 | − | 0.754825i | −0.561562 | − | 0.827435i | \(-0.689799\pi\) |
0.997360 | + | 0.0726096i | \(0.0231327\pi\) | |||||||
\(68\) | −654.500 | + | 1133.63i | −1.16720 | + | 2.02165i | ||||
\(69\) | −336.000 | − | 581.969i | −0.586227 | − | 1.01537i | ||||
\(70\) | 455.000 | 0.776899 | ||||||||
\(71\) | 4.50000 | + | 7.79423i | 0.00752186 | + | 0.0130282i | 0.869762 | − | 0.493472i | \(-0.164272\pi\) |
−0.862240 | + | 0.506500i | \(0.830939\pi\) | |||||||
\(72\) | −495.000 | − | 857.365i | −0.810227 | − | 1.40335i | ||||
\(73\) | −98.0000 | −0.157124 | −0.0785619 | − | 0.996909i | \(-0.525033\pi\) | ||||
−0.0785619 | + | 0.996909i | \(0.525033\pi\) | |||||||
\(74\) | −327.500 | − | 567.247i | −0.514474 | − | 0.891096i | ||||
\(75\) | −266.000 | + | 460.726i | −0.409534 | + | 0.709333i | ||||
\(76\) | −1071.00 | + | 1855.03i | −1.61648 | + | 2.79982i | ||||
\(77\) | 338.000 | 0.500243 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1304.00 | 1.85711 | 0.928554 | − | 0.371198i | \(-0.121053\pi\) | ||||
0.928554 | + | 0.371198i | \(0.121053\pi\) | |||||||
\(80\) | −311.500 | + | 539.534i | −0.435334 | + | 0.754021i | ||||
\(81\) | 419.500 | − | 726.595i | 0.575446 | − | 0.996701i | ||||
\(82\) | 840.000 | + | 1454.92i | 1.13125 | + | 1.95938i | ||||
\(83\) | 308.000 | 0.407318 | 0.203659 | − | 0.979042i | \(-0.434717\pi\) | ||||
0.203659 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(84\) | 773.500 | + | 1339.74i | 1.00471 | + | 1.74021i | ||||
\(85\) | −269.500 | − | 466.788i | −0.343899 | − | 0.595650i | ||||
\(86\) | −1005.00 | −1.26014 | ||||||||
\(87\) | −287.000 | − | 497.099i | −0.353674 | − | 0.612581i | ||||
\(88\) | −585.000 | + | 1013.25i | −0.708650 | + | 1.22742i | ||||
\(89\) | −595.000 | + | 1030.57i | −0.708650 | + | 1.22742i | 0.256708 | + | 0.966489i | \(0.417362\pi\) |
−0.965358 | + | 0.260929i | \(0.915971\pi\) | |||||||
\(90\) | 770.000 | 0.901835 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1632.00 | −1.84943 | ||||||||
\(93\) | −686.000 | + | 1188.19i | −0.764891 | + | 1.32483i | ||||
\(94\) | −262.500 | + | 454.663i | −0.288030 | + | 0.498882i | ||||
\(95\) | −441.000 | − | 763.834i | −0.476270 | − | 0.824924i | ||||
\(96\) | −595.000 | −0.632572 | ||||||||
\(97\) | 35.0000 | + | 60.6218i | 0.0366362 | + | 0.0634558i | 0.883762 | − | 0.467936i | \(-0.155002\pi\) |
−0.847126 | + | 0.531392i | \(0.821669\pi\) | |||||||
\(98\) | 435.000 | + | 753.442i | 0.448384 | + | 0.776624i | ||||
\(99\) | 572.000 | 0.580689 | ||||||||
\(100\) | 646.000 | + | 1118.90i | 0.646000 | + | 1.11890i | ||||
\(101\) | −210.000 | + | 363.731i | −0.206889 | + | 0.358342i | −0.950733 | − | 0.310011i | \(-0.899667\pi\) |
0.743844 | + | 0.668353i | \(0.233001\pi\) | |||||||
\(102\) | 1347.50 | − | 2333.94i | 1.30806 | − | 2.26563i | ||||
\(103\) | 588.000 | 0.562499 | 0.281249 | − | 0.959635i | \(-0.409251\pi\) | ||||
0.281249 | + | 0.959635i | \(0.409251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −637.000 | −0.592046 | ||||||||
\(106\) | 1080.00 | − | 1870.61i | 0.989612 | − | 1.71406i | ||||
\(107\) | 342.000 | − | 592.361i | 0.308994 | − | 0.535194i | −0.669148 | − | 0.743129i | \(-0.733341\pi\) |
0.978143 | + | 0.207935i | \(0.0666743\pi\) | |||||||
\(108\) | −297.500 | − | 515.285i | −0.265064 | − | 0.459105i | ||||
\(109\) | −373.000 | −0.327770 | −0.163885 | − | 0.986479i | \(-0.552403\pi\) | ||||
−0.163885 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(110\) | −455.000 | − | 788.083i | −0.394387 | − | 0.683098i | ||||
\(111\) | 458.500 | + | 794.145i | 0.392062 | + | 0.679071i | ||||
\(112\) | 1157.00 | 0.976127 | ||||||||
\(113\) | 867.000 | + | 1501.69i | 0.721774 | + | 1.25015i | 0.960288 | + | 0.279011i | \(0.0900065\pi\) |
−0.238514 | + | 0.971139i | \(0.576660\pi\) | |||||||
\(114\) | 2205.00 | − | 3819.17i | 1.81155 | − | 3.13770i | ||||
\(115\) | 336.000 | − | 581.969i | 0.272454 | − | 0.471903i | ||||
\(116\) | −1394.00 | −1.11577 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1470.00 | 1.14682 | ||||||||
\(119\) | −500.500 | + | 866.891i | −0.385553 | + | 0.667797i | ||||
\(120\) | 1102.50 | − | 1909.59i | 0.838700 | − | 1.45267i | ||||
\(121\) | 327.500 | + | 567.247i | 0.246056 | + | 0.426181i | ||||
\(122\) | −280.000 | −0.207787 | ||||||||
\(123\) | −1176.00 | − | 2036.89i | −0.862084 | − | 1.49317i | ||||
\(124\) | 1666.00 | + | 2885.60i | 1.20654 | + | 2.08979i | ||||
\(125\) | −1407.00 | −1.00677 | ||||||||
\(126\) | −715.000 | − | 1238.42i | −0.505534 | − | 0.875610i | ||||
\(127\) | −946.000 | + | 1638.52i | −0.660976 | + | 1.14484i | 0.319384 | + | 0.947625i | \(0.396524\pi\) |
−0.980360 | + | 0.197218i | \(0.936809\pi\) | |||||||
\(128\) | 1057.50 | − | 1831.64i | 0.730240 | − | 1.26481i | ||||
\(129\) | 1407.00 | 0.960306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1435.00 | 0.957073 | 0.478536 | − | 0.878068i | \(-0.341167\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341167\pi\) | |||||||
\(132\) | 1547.00 | − | 2679.48i | 1.02007 | − | 1.76681i | ||||
\(133\) | −819.000 | + | 1418.55i | −0.533957 | + | 0.924841i | ||||
\(134\) | 1195.00 | + | 2069.80i | 0.770390 | + | 1.33435i | ||||
\(135\) | 245.000 | 0.156194 | ||||||||
\(136\) | −1732.50 | − | 3000.78i | −1.09236 | − | 1.89202i | ||||
\(137\) | −888.000 | − | 1538.06i | −0.553773 | − | 0.959164i | −0.997998 | − | 0.0632482i | \(-0.979854\pi\) |
0.444224 | − | 0.895916i | \(-0.353479\pi\) | |||||||
\(138\) | 3360.00 | 2.07262 | ||||||||
\(139\) | 934.500 | + | 1618.60i | 0.570239 | + | 0.987683i | 0.996541 | + | 0.0831023i | \(0.0264828\pi\) |
−0.426302 | + | 0.904581i | \(0.640184\pi\) | |||||||
\(140\) | −773.500 | + | 1339.74i | −0.466948 | + | 0.808777i | ||||
\(141\) | 367.500 | − | 636.529i | 0.219497 | − | 0.380180i | ||||
\(142\) | −45.0000 | −0.0265938 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1958.00 | 1.13310 | ||||||||
\(145\) | 287.000 | − | 497.099i | 0.164373 | − | 0.284702i | ||||
\(146\) | 245.000 | − | 424.352i | 0.138879 | − | 0.240546i | ||||
\(147\) | −609.000 | − | 1054.82i | −0.341697 | − | 0.591837i | ||||
\(148\) | 2227.00 | 1.23688 | ||||||||
\(149\) | 1233.00 | + | 2135.62i | 0.677928 | + | 1.17421i | 0.975604 | + | 0.219539i | \(0.0704553\pi\) |
−0.297676 | + | 0.954667i | \(0.596211\pi\) | |||||||
\(150\) | −1330.00 | − | 2303.63i | −0.723960 | − | 1.25394i | ||||
\(151\) | 3323.00 | 1.79087 | 0.895437 | − | 0.445189i | \(-0.146863\pi\) | ||||
0.895437 | + | 0.445189i | \(0.146863\pi\) | |||||||
\(152\) | −2835.00 | − | 4910.36i | −1.51282 | − | 2.62028i | ||||
\(153\) | −847.000 | + | 1467.05i | −0.447555 | + | 0.775188i | ||||
\(154\) | −845.000 | + | 1463.58i | −0.442156 | + | 0.765837i | ||||
\(155\) | −1372.00 | −0.710979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2730.00 | −1.38776 | −0.693878 | − | 0.720092i | \(-0.744099\pi\) | ||||
−0.693878 | + | 0.720092i | \(0.744099\pi\) | |||||||
\(158\) | −3260.00 | + | 5646.49i | −1.64147 | + | 2.84310i | ||||
\(159\) | −1512.00 | + | 2618.86i | −0.754147 | + | 1.30622i | ||||
\(160\) | −297.500 | − | 515.285i | −0.146997 | − | 0.254605i | ||||
\(161\) | −1248.00 | −0.610908 | ||||||||
\(162\) | 2097.50 | + | 3632.98i | 1.01725 | + | 1.76194i | ||||
\(163\) | −272.000 | − | 471.118i | −0.130704 | − | 0.226385i | 0.793244 | − | 0.608903i | \(-0.208390\pi\) |
−0.923948 | + | 0.382518i | \(0.875057\pi\) | |||||||
\(164\) | −5712.00 | −2.71971 | ||||||||
\(165\) | 637.000 | + | 1103.32i | 0.300548 | + | 0.520564i | ||||
\(166\) | −770.000 | + | 1333.68i | −0.360022 | + | 0.623576i | ||||
\(167\) | 812.000 | − | 1406.43i | 0.376254 | − | 0.651691i | −0.614260 | − | 0.789104i | \(-0.710545\pi\) |
0.990514 | + | 0.137413i | \(0.0438786\pi\) | |||||||
\(168\) | −4095.00 | −1.88057 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2695.00 | 1.21587 | ||||||||
\(171\) | −1386.00 | + | 2400.62i | −0.619825 | + | 1.07357i | ||||
\(172\) | 1708.50 | − | 2959.21i | 0.757395 | − | 1.31185i | ||||
\(173\) | 168.000 | + | 290.985i | 0.0738312 | + | 0.127879i | 0.900577 | − | 0.434696i | \(-0.143144\pi\) |
−0.826746 | + | 0.562575i | \(0.809811\pi\) | |||||||
\(174\) | 2870.00 | 1.25043 | ||||||||
\(175\) | 494.000 | + | 855.633i | 0.213388 | + | 0.369599i | ||||
\(176\) | −1157.00 | − | 2003.98i | −0.495524 | − | 0.858272i | ||||
\(177\) | −2058.00 | −0.873948 | ||||||||
\(178\) | −2975.00 | − | 5152.85i | −1.25273 | − | 2.16979i | ||||
\(179\) | 1514.50 | − | 2623.19i | 0.632397 | − | 1.09534i | −0.354663 | − | 0.934994i | \(-0.615405\pi\) |
0.987060 | − | 0.160350i | \(-0.0512621\pi\) | |||||||
\(180\) | −1309.00 | + | 2267.25i | −0.542039 | + | 0.938840i | ||||
\(181\) | −28.0000 | −0.0114985 | −0.00574924 | − | 0.999983i | \(-0.501830\pi\) | ||||
−0.00574924 | + | 0.999983i | \(0.501830\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 392.000 | 0.158347 | ||||||||
\(184\) | 2160.00 | − | 3741.23i | 0.865420 | − | 1.49895i | ||||
\(185\) | −458.500 | + | 794.145i | −0.182214 | + | 0.315604i | ||||
\(186\) | −3430.00 | − | 5940.93i | −1.35215 | − | 2.34199i | ||||
\(187\) | 2002.00 | 0.782892 | ||||||||
\(188\) | −892.500 | − | 1545.86i | −0.346235 | − | 0.599697i | ||||
\(189\) | −227.500 | − | 394.042i | −0.0875566 | − | 0.151652i | ||||
\(190\) | 4410.00 | 1.68387 | ||||||||
\(191\) | −211.000 | − | 365.463i | −0.0799342 | − | 0.138450i | 0.823287 | − | 0.567625i | \(-0.192138\pi\) |
−0.903221 | + | 0.429175i | \(0.858804\pi\) | |||||||
\(192\) | −1004.50 | + | 1739.85i | −0.377571 | + | 0.653971i | ||||
\(193\) | 246.000 | − | 426.084i | 0.0917485 | − | 0.158913i | −0.816498 | − | 0.577348i | \(-0.804088\pi\) |
0.908247 | + | 0.418435i | \(0.137421\pi\) | |||||||
\(194\) | −350.000 | −0.129529 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2958.00 | −1.07799 | ||||||||
\(197\) | 1495.50 | − | 2590.28i | 0.540863 | − | 0.936802i | −0.457992 | − | 0.888956i | \(-0.651431\pi\) |
0.998855 | − | 0.0478455i | \(-0.0152355\pi\) | |||||||
\(198\) | −1430.00 | + | 2476.83i | −0.513261 | + | 0.888994i | ||||
\(199\) | 35.0000 | + | 60.6218i | 0.0124678 | + | 0.0215948i | 0.872192 | − | 0.489164i | \(-0.162698\pi\) |
−0.859724 | + | 0.510759i | \(0.829365\pi\) | |||||||
\(200\) | −3420.00 | −1.20915 | ||||||||
\(201\) | −1673.00 | − | 2897.72i | −0.587086 | − | 1.01686i | ||||
\(202\) | −1050.00 | − | 1818.65i | −0.365731 | − | 0.633465i | ||||
\(203\) | −1066.00 | −0.368564 | ||||||||
\(204\) | 4581.50 | + | 7935.39i | 1.57240 | + | 2.72347i | ||||
\(205\) | 1176.00 | − | 2036.89i | 0.400661 | − | 0.693964i | ||||
\(206\) | −1470.00 | + | 2546.11i | −0.497183 | + | 0.861147i | ||||
\(207\) | −2112.00 | −0.709150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3276.00 | 1.08424 | ||||||||
\(210\) | 1592.50 | − | 2758.29i | 0.523300 | − | 0.906382i | ||||
\(211\) | −1425.50 | + | 2469.04i | −0.465097 | + | 0.805572i | −0.999206 | − | 0.0398440i | \(-0.987314\pi\) |
0.534109 | + | 0.845416i | \(0.320647\pi\) | |||||||
\(212\) | 3672.00 | + | 6360.09i | 1.18959 | + | 2.06044i | ||||
\(213\) | 63.0000 | 0.0202661 | ||||||||
\(214\) | 1710.00 | + | 2961.81i | 0.546230 | + | 0.946098i | ||||
\(215\) | 703.500 | + | 1218.50i | 0.223155 | + | 0.386516i | ||||
\(216\) | 1575.00 | 0.496135 | ||||||||
\(217\) | 1274.00 | + | 2206.63i | 0.398547 | + | 0.690304i | ||||
\(218\) | 932.500 | − | 1615.14i | 0.289710 | − | 0.501793i | ||||
\(219\) | −343.000 | + | 594.093i | −0.105835 | + | 0.183311i | ||||
\(220\) | 3094.00 | 0.948170 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4585.00 | −1.38615 | ||||||||
\(223\) | 108.500 | − | 187.928i | 0.0325816 | − | 0.0564330i | −0.849275 | − | 0.527951i | \(-0.822960\pi\) |
0.881856 | + | 0.471518i | \(0.156294\pi\) | |||||||
\(224\) | −552.500 | + | 956.958i | −0.164801 | + | 0.285444i | ||||
\(225\) | 836.000 | + | 1447.99i | 0.247704 | + | 0.429035i | ||||
\(226\) | −8670.00 | −2.55186 | ||||||||
\(227\) | −1288.00 | − | 2230.88i | −0.376597 | − | 0.652285i | 0.613968 | − | 0.789331i | \(-0.289573\pi\) |
−0.990565 | + | 0.137046i | \(0.956239\pi\) | |||||||
\(228\) | 7497.00 | + | 12985.2i | 2.17764 | + | 3.77178i | ||||
\(229\) | −455.000 | −0.131298 | −0.0656490 | − | 0.997843i | \(-0.520912\pi\) | ||||
−0.0656490 | + | 0.997843i | \(0.520912\pi\) | |||||||
\(230\) | 1680.00 | + | 2909.85i | 0.481634 | + | 0.834215i | ||||
\(231\) | 1183.00 | − | 2049.02i | 0.336951 | − | 0.583616i | ||||
\(232\) | 1845.00 | − | 3195.63i | 0.522113 | − | 0.904326i | ||||
\(233\) | 3061.00 | 0.860656 | 0.430328 | − | 0.902673i | \(-0.358398\pi\) | ||||
0.430328 | + | 0.902673i | \(0.358398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 735.000 | 0.204026 | ||||||||
\(236\) | −2499.00 | + | 4328.39i | −0.689284 | + | 1.19388i | ||||
\(237\) | 4564.00 | − | 7905.08i | 1.25090 | − | 2.16662i | ||||
\(238\) | −2502.50 | − | 4334.46i | −0.681567 | − | 1.18051i | ||||
\(239\) | 3477.00 | 0.941039 | 0.470520 | − | 0.882389i | \(-0.344066\pi\) | ||||
0.470520 | + | 0.882389i | \(0.344066\pi\) | |||||||
\(240\) | 2180.50 | + | 3776.74i | 0.586461 | + | 1.01578i | ||||
\(241\) | −805.000 | − | 1394.30i | −0.215164 | − | 0.372676i | 0.738159 | − | 0.674627i | \(-0.235695\pi\) |
−0.953323 | + | 0.301951i | \(0.902362\pi\) | |||||||
\(242\) | −3275.00 | −0.869938 | ||||||||
\(243\) | −2464.00 | − | 4267.77i | −0.650476 | − | 1.12666i | ||||
\(244\) | 476.000 | − | 824.456i | 0.124888 | − | 0.216313i | ||||
\(245\) | 609.000 | − | 1054.82i | 0.158806 | − | 0.275061i | ||||
\(246\) | 11760.0 | 3.04793 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8820.00 | −2.25835 | ||||||||
\(249\) | 1078.00 | − | 1867.15i | 0.274359 | − | 0.475204i | ||||
\(250\) | 3517.50 | − | 6092.49i | 0.889865 | − | 1.54129i | ||||
\(251\) | −504.000 | − | 872.954i | −0.126742 | − | 0.219523i | 0.795671 | − | 0.605730i | \(-0.207119\pi\) |
−0.922412 | + | 0.386206i | \(0.873785\pi\) | |||||||
\(252\) | 4862.00 | 1.21539 | ||||||||
\(253\) | 1248.00 | + | 2161.60i | 0.310123 | + | 0.537149i | ||||
\(254\) | −4730.00 | − | 8192.60i | −1.16845 | − | 2.02382i | ||||
\(255\) | −3773.00 | −0.926566 | ||||||||
\(256\) | 4139.50 | + | 7169.82i | 1.01062 | + | 1.75045i | ||||
\(257\) | −3020.50 | + | 5231.66i | −0.733127 | + | 1.26981i | 0.222413 | + | 0.974952i | \(0.428607\pi\) |
−0.955540 | + | 0.294861i | \(0.904727\pi\) | |||||||
\(258\) | −3517.50 | + | 6092.49i | −0.848798 | + | 1.47016i | ||||
\(259\) | 1703.00 | 0.408569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1804.00 | −0.427834 | ||||||||
\(262\) | −3587.50 | + | 6213.73i | −0.845941 | + | 1.46521i | ||||
\(263\) | 1854.00 | − | 3211.22i | 0.434686 | − | 0.752899i | −0.562584 | − | 0.826740i | \(-0.690193\pi\) |
0.997270 | + | 0.0738414i | \(0.0235259\pi\) | |||||||
\(264\) | 4095.00 | + | 7092.75i | 0.954658 | + | 1.65352i | ||||
\(265\) | −3024.00 | −0.700992 | ||||||||
\(266\) | −4095.00 | − | 7092.75i | −0.943912 | − | 1.63490i | ||||
\(267\) | 4165.00 | + | 7213.99i | 0.954659 | + | 1.65352i | ||||
\(268\) | −8126.00 | −1.85214 | ||||||||
\(269\) | −4172.00 | − | 7226.12i | −0.945618 | − | 1.63786i | −0.754508 | − | 0.656290i | \(-0.772125\pi\) |
−0.191110 | − | 0.981569i | \(-0.561209\pi\) | |||||||
\(270\) | −612.500 | + | 1060.88i | −0.138058 | + | 0.239123i | ||||
\(271\) | −808.500 | + | 1400.36i | −0.181228 | + | 0.313897i | −0.942299 | − | 0.334772i | \(-0.891341\pi\) |
0.761071 | + | 0.648669i | \(0.224674\pi\) | |||||||
\(272\) | 6853.00 | 1.52766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8880.00 | 1.95788 | ||||||||
\(275\) | 988.000 | − | 1711.27i | 0.216650 | − | 0.375248i | ||||
\(276\) | −5712.00 | + | 9893.47i | −1.24573 | + | 2.15767i | ||||
\(277\) | 1910.00 | + | 3308.22i | 0.414299 | + | 0.717587i | 0.995355 | − | 0.0962771i | \(-0.0306935\pi\) |
−0.581056 | + | 0.813864i | \(0.697360\pi\) | |||||||
\(278\) | −9345.00 | −2.01610 | ||||||||
\(279\) | 2156.00 | + | 3734.30i | 0.462639 | + | 0.801315i | ||||
\(280\) | −2047.50 | − | 3546.37i | −0.437005 | − | 0.756916i | ||||
\(281\) | 6214.00 | 1.31920 | 0.659602 | − | 0.751615i | \(-0.270725\pi\) | ||||
0.659602 | + | 0.751615i | \(0.270725\pi\) | |||||||
\(282\) | 1837.50 | + | 3182.64i | 0.388020 | + | 0.672070i | ||||
\(283\) | 2646.00 | − | 4583.01i | 0.555789 | − | 0.962655i | −0.442052 | − | 0.896989i | \(-0.645749\pi\) |
0.997842 | − | 0.0656661i | \(-0.0209172\pi\) | |||||||
\(284\) | 76.5000 | − | 132.502i | 0.0159839 | − | 0.0276850i | ||||
\(285\) | −6174.00 | −1.28321 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4368.00 | −0.898379 | ||||||||
\(288\) | −935.000 | + | 1619.47i | −0.191303 | + | 0.331347i | ||||
\(289\) | −508.000 | + | 879.882i | −0.103399 | + | 0.179093i | ||||
\(290\) | 1435.00 | + | 2485.49i | 0.290573 | + | 0.503287i | ||||
\(291\) | 490.000 | 0.0987090 | ||||||||
\(292\) | 833.000 | + | 1442.80i | 0.166944 | + | 0.289155i | ||||
\(293\) | −451.500 | − | 782.021i | −0.0900236 | − | 0.155925i | 0.817497 | − | 0.575933i | \(-0.195361\pi\) |
−0.907521 | + | 0.420007i | \(0.862028\pi\) | |||||||
\(294\) | 6090.00 | 1.20808 | ||||||||
\(295\) | −1029.00 | − | 1782.28i | −0.203087 | − | 0.351757i | ||||
\(296\) | −2947.50 | + | 5105.22i | −0.578784 | + | 1.00248i | ||||
\(297\) | −455.000 | + | 788.083i | −0.0888949 | + | 0.153970i | ||||
\(298\) | −12330.0 | −2.39684 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9044.00 | 1.74052 | ||||||||
\(301\) | 1306.50 | − | 2262.92i | 0.250184 | − | 0.433332i | ||||
\(302\) | −8307.50 | + | 14389.0i | −1.58292 | + | 2.74170i | ||||
\(303\) | 1470.00 | + | 2546.11i | 0.278711 | + | 0.482741i | ||||
\(304\) | 11214.0 | 2.11568 | ||||||||
\(305\) | 196.000 | + | 339.482i | 0.0367965 | + | 0.0637334i | ||||
\(306\) | −4235.00 | − | 7335.24i | −0.791173 | − | 1.37035i | ||||
\(307\) | −2114.00 | −0.393004 | −0.196502 | − | 0.980503i | \(-0.562958\pi\) | ||||
−0.196502 | + | 0.980503i | \(0.562958\pi\) | |||||||
\(308\) | −2873.00 | − | 4976.18i | −0.531508 | − | 0.920598i | ||||
\(309\) | 2058.00 | − | 3564.56i | 0.378885 | − | 0.656248i | ||||
\(310\) | 3430.00 | − | 5940.93i | 0.628422 | − | 1.08846i | ||||
\(311\) | 3402.00 | 0.620288 | 0.310144 | − | 0.950690i | \(-0.399623\pi\) | ||||
0.310144 | + | 0.950690i | \(0.399623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10689.0 | −1.93028 | −0.965141 | − | 0.261732i | \(-0.915706\pi\) | ||||
−0.965141 | + | 0.261732i | \(0.915706\pi\) | |||||||
\(314\) | 6825.00 | − | 11821.2i | 1.22661 | − | 2.12456i | ||||
\(315\) | −1001.00 | + | 1733.78i | −0.179047 | + | 0.310119i | ||||
\(316\) | −11084.0 | − | 19198.1i | −1.97318 | − | 3.41764i | ||||
\(317\) | 7054.00 | 1.24982 | 0.624909 | − | 0.780698i | \(-0.285136\pi\) | ||||
0.624909 | + | 0.780698i | \(0.285136\pi\) | |||||||
\(318\) | −7560.00 | − | 13094.3i | −1.33316 | − | 2.30909i | ||||
\(319\) | 1066.00 | + | 1846.37i | 0.187099 | + | 0.324065i | ||||
\(320\) | −2009.00 | −0.350958 | ||||||||
\(321\) | −2394.00 | − | 4146.53i | −0.416262 | − | 0.720987i | ||||
\(322\) | 3120.00 | − | 5404.00i | 0.539971 | − | 0.935258i | ||||
\(323\) | −4851.00 | + | 8402.18i | −0.835656 | + | 1.44740i | ||||
\(324\) | −14263.0 | −2.44564 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2720.00 | 0.462107 | ||||||||
\(327\) | −1305.50 | + | 2261.19i | −0.220778 | + | 0.382398i | ||||
\(328\) | 7560.00 | − | 13094.3i | 1.27266 | − | 2.20430i | ||||
\(329\) | −682.500 | − | 1182.12i | −0.114369 | − | 0.198093i | ||||
\(330\) | −6370.00 | −1.06260 | ||||||||
\(331\) | 4852.00 | + | 8403.91i | 0.805710 | + | 1.39553i | 0.915811 | + | 0.401610i | \(0.131549\pi\) |
−0.110101 | + | 0.993920i | \(0.535117\pi\) | |||||||
\(332\) | −2618.00 | − | 4534.51i | −0.432775 | − | 0.749589i | ||||
\(333\) | 2882.00 | 0.474272 | ||||||||
\(334\) | 4060.00 | + | 7032.13i | 0.665130 | + | 1.15204i | ||||
\(335\) | 1673.00 | − | 2897.72i | 0.272853 | − | 0.472595i | ||||
\(336\) | 4049.50 | − | 7013.94i | 0.657495 | − | 1.13881i | ||||
\(337\) | −10449.0 | −1.68900 | −0.844500 | − | 0.535555i | \(-0.820103\pi\) | ||||
−0.844500 | + | 0.535555i | \(0.820103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12138.0 | 1.94468 | ||||||||
\(340\) | −4581.50 | + | 7935.39i | −0.730784 | + | 1.26576i | ||||
\(341\) | 2548.00 | − | 4413.27i | 0.404639 | − | 0.700855i | ||||
\(342\) | −6930.00 | − | 12003.1i | −1.09571 | − | 1.89782i | ||||
\(343\) | −6721.00 | −1.05802 | ||||||||
\(344\) | 4522.50 | + | 7833.20i | 0.708828 | + | 1.22773i | ||||
\(345\) | −2352.00 | − | 4073.78i | −0.367036 | − | 0.635725i | ||||
\(346\) | −1680.00 | −0.261033 | ||||||||
\(347\) | 310.500 | + | 537.802i | 0.0480361 | + | 0.0832009i | 0.889044 | − | 0.457822i | \(-0.151370\pi\) |
−0.841008 | + | 0.541023i | \(0.818037\pi\) | |||||||
\(348\) | −4879.00 | + | 8450.68i | −0.751557 | + | 1.30173i | ||||
\(349\) | 6240.50 | − | 10808.9i | 0.957153 | − | 1.65784i | 0.227790 | − | 0.973710i | \(-0.426850\pi\) |
0.729363 | − | 0.684127i | \(-0.239817\pi\) | |||||||
\(350\) | −4940.00 | −0.754440 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2210.00 | 0.334640 | ||||||||
\(353\) | −700.000 | + | 1212.44i | −0.105545 | + | 0.182809i | −0.913961 | − | 0.405803i | \(-0.866992\pi\) |
0.808416 | + | 0.588612i | \(0.200325\pi\) | |||||||
\(354\) | 5145.00 | − | 8911.40i | 0.772468 | − | 1.33795i | ||||
\(355\) | 31.5000 | + | 54.5596i | 0.00470943 | + | 0.00815697i | ||||
\(356\) | 20230.0 | 3.01176 | ||||||||
\(357\) | 3503.50 | + | 6068.24i | 0.519397 | + | 0.899623i | ||||
\(358\) | 7572.50 | + | 13116.0i | 1.11793 | + | 1.93631i | ||||
\(359\) | 4968.00 | 0.730365 | 0.365182 | − | 0.930936i | \(-0.381007\pi\) | ||||
0.365182 | + | 0.930936i | \(0.381007\pi\) | |||||||
\(360\) | −3465.00 | − | 6001.56i | −0.507282 | − | 0.878638i | ||||
\(361\) | −4508.50 | + | 7808.95i | −0.657312 | + | 1.13850i | ||||
\(362\) | 70.0000 | − | 121.244i | 0.0101633 | − | 0.0176034i | ||||
\(363\) | 4585.00 | 0.662948 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −686.000 | −0.0983750 | ||||||||
\(366\) | −980.000 | + | 1697.41i | −0.139960 | + | 0.242418i | ||||
\(367\) | −4361.00 | + | 7553.47i | −0.620279 | + | 1.07435i | 0.369155 | + | 0.929368i | \(0.379647\pi\) |
−0.989434 | + | 0.144987i | \(0.953686\pi\) | |||||||
\(368\) | 4272.00 | + | 7399.32i | 0.605145 | + | 1.04814i | ||||
\(369\) | −7392.00 | −1.04285 | ||||||||
\(370\) | −2292.50 | − | 3970.73i | −0.322112 | − | 0.557914i | ||||
\(371\) | 2808.00 | + | 4863.60i | 0.392949 | + | 0.680608i | ||||
\(372\) | 23324.0 | 3.25079 | ||||||||
\(373\) | −5006.00 | − | 8670.65i | −0.694908 | − | 1.20362i | −0.970212 | − | 0.242259i | \(-0.922112\pi\) |
0.275303 | − | 0.961357i | \(-0.411222\pi\) | |||||||
\(374\) | −5005.00 | + | 8668.91i | −0.691985 | + | 1.19855i | ||||
\(375\) | −4924.50 | + | 8529.48i | −0.678134 | + | 1.17456i | ||||
\(376\) | 4725.00 | 0.648067 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2275.00 | 0.309559 | ||||||||
\(379\) | −1686.00 | + | 2920.24i | −0.228507 | + | 0.395785i | −0.957366 | − | 0.288879i | \(-0.906718\pi\) |
0.728859 | + | 0.684664i | \(0.240051\pi\) | |||||||
\(380\) | −7497.00 | + | 12985.2i | −1.01207 | + | 1.75296i | ||||
\(381\) | 6622.00 | + | 11469.6i | 0.890434 | + | 1.54228i | ||||
\(382\) | 2110.00 | 0.282610 | ||||||||
\(383\) | −423.500 | − | 733.524i | −0.0565009 | − | 0.0978624i | 0.836392 | − | 0.548132i | \(-0.184661\pi\) |
−0.892892 | + | 0.450270i | \(0.851328\pi\) | |||||||
\(384\) | −7402.50 | − | 12821.5i | −0.983743 | − | 1.70389i | ||||
\(385\) | 2366.00 | 0.313201 | ||||||||
\(386\) | 1230.00 | + | 2130.42i | 0.162190 | + | 0.280921i | ||||
\(387\) | 2211.00 | − | 3829.56i | 0.290417 | − | 0.503017i | ||||
\(388\) | 595.000 | − | 1030.57i | 0.0778519 | − | 0.134843i | ||||
\(389\) | 11314.0 | 1.47466 | 0.737330 | − | 0.675533i | \(-0.236086\pi\) | ||||
0.737330 | + | 0.675533i | \(0.236086\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7392.00 | −0.956086 | ||||||||
\(392\) | 3915.00 | − | 6780.98i | 0.504432 | − | 0.873702i | ||||
\(393\) | 5022.50 | − | 8699.23i | 0.644661 | − | 1.11658i | ||||
\(394\) | 7477.50 | + | 12951.4i | 0.956119 | + | 1.65605i | ||||
\(395\) | 9128.00 | 1.16273 | ||||||||
\(396\) | −4862.00 | − | 8421.23i | −0.616982 | − | 1.06864i | ||||
\(397\) | 931.000 | + | 1612.54i | 0.117697 | + | 0.203856i | 0.918854 | − | 0.394597i | \(-0.129116\pi\) |
−0.801158 | + | 0.598453i | \(0.795782\pi\) | |||||||
\(398\) | −350.000 | −0.0440802 | ||||||||
\(399\) | 5733.00 | + | 9929.85i | 0.719321 | + | 1.24590i | ||||
\(400\) | 3382.00 | − | 5857.80i | 0.422750 | − | 0.732224i | ||||
\(401\) | 3410.00 | − | 5906.29i | 0.424657 | − | 0.735527i | −0.571732 | − | 0.820441i | \(-0.693728\pi\) |
0.996388 | + | 0.0849139i | \(0.0270615\pi\) | |||||||
\(402\) | 16730.0 | 2.07566 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7140.00 | 0.879278 | ||||||||
\(405\) | 2936.50 | − | 5086.17i | 0.360286 | − | 0.624034i | ||||
\(406\) | 2665.00 | − | 4615.92i | 0.325768 | − | 0.564246i | ||||
\(407\) | −1703.00 | − | 2949.68i | −0.207407 | − | 0.359239i | ||||
\(408\) | −24255.0 | −2.94314 | ||||||||
\(409\) | −6496.00 | − | 11251.4i | −0.785346 | − | 1.36026i | −0.928792 | − | 0.370601i | \(-0.879152\pi\) |
0.143446 | − | 0.989658i | \(-0.454182\pi\) | |||||||
\(410\) | 5880.00 | + | 10184.5i | 0.708274 | + | 1.22677i | ||||
\(411\) | −12432.0 | −1.49203 | ||||||||
\(412\) | −4998.00 | − | 8656.79i | −0.597655 | − | 1.03517i | ||||
\(413\) | −1911.00 | + | 3309.95i | −0.227686 | + | 0.394363i | ||||
\(414\) | 5280.00 | − | 9145.23i | 0.626806 | − | 1.08566i | ||||
\(415\) | 2156.00 | 0.255021 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13083.0 | 1.53640 | ||||||||
\(418\) | −8190.00 | + | 14185.5i | −0.958340 | + | 1.65989i | ||||
\(419\) | 3671.50 | − | 6359.22i | 0.428078 | − | 0.741452i | −0.568625 | − | 0.822597i | \(-0.692524\pi\) |
0.996702 | + | 0.0811449i | \(0.0258577\pi\) | |||||||
\(420\) | 5414.50 | + | 9378.19i | 0.629049 | + | 1.08954i | ||||
\(421\) | 5059.00 | 0.585655 | 0.292827 | − | 0.956165i | \(-0.405404\pi\) | ||||
0.292827 | + | 0.956165i | \(0.405404\pi\) | |||||||
\(422\) | −7127.50 | − | 12345.2i | −0.822183 | − | 1.42406i | ||||
\(423\) | −1155.00 | − | 2000.52i | −0.132761 | − | 0.229949i | ||||
\(424\) | −19440.0 | −2.22663 | ||||||||
\(425\) | 2926.00 | + | 5067.98i | 0.333957 | + | 0.578431i | ||||
\(426\) | −157.500 | + | 272.798i | −0.0179129 | + | 0.0310261i | ||||
\(427\) | 364.000 | − | 630.466i | 0.0412534 | − | 0.0714530i | ||||
\(428\) | −11628.0 | −1.31323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7035.00 | −0.788972 | ||||||||
\(431\) | 1621.50 | − | 2808.52i | 0.181218 | − | 0.313879i | −0.761078 | − | 0.648661i | \(-0.775329\pi\) |
0.942296 | + | 0.334782i | \(0.108663\pi\) | |||||||
\(432\) | −1557.50 | + | 2697.67i | −0.173461 | + | 0.300444i | ||||
\(433\) | −5799.50 | − | 10045.0i | −0.643663 | − | 1.11486i | −0.984609 | − | 0.174774i | \(-0.944080\pi\) |
0.340945 | − | 0.940083i | \(-0.389253\pi\) | |||||||
\(434\) | −12740.0 | −1.40908 | ||||||||
\(435\) | −2009.00 | − | 3479.69i | −0.221435 | − | 0.383536i | ||||
\(436\) | 3170.50 | + | 5491.47i | 0.348256 | + | 0.603196i | ||||
\(437\) | −12096.0 | −1.32410 | ||||||||
\(438\) | −1715.00 | − | 2970.47i | −0.187091 | − | 0.324051i | ||||
\(439\) | 8687.00 | − | 15046.3i | 0.944437 | − | 1.63581i | 0.187563 | − | 0.982253i | \(-0.439941\pi\) |
0.756874 | − | 0.653560i | \(-0.226725\pi\) | |||||||
\(440\) | −4095.00 | + | 7092.75i | −0.443685 | + | 0.768485i | ||||
\(441\) | −3828.00 | −0.413346 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 989.000 | 0.106070 | 0.0530348 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530348 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(444\) | 7794.50 | − | 13500.5i | 0.833132 | − | 1.44303i | ||||
\(445\) | −4165.00 | + | 7213.99i | −0.443685 | + | 0.768485i | ||||
\(446\) | 542.500 | + | 939.638i | 0.0575967 | + | 0.0997604i | ||||
\(447\) | 17262.0 | 1.82654 | ||||||||
\(448\) | 1865.50 | + | 3231.14i | 0.196733 | + | 0.340752i | ||||
\(449\) | −7237.00 | − | 12534.9i | −0.760657 | − | 1.31750i | −0.942512 | − | 0.334172i | \(-0.891543\pi\) |
0.181855 | − | 0.983325i | \(-0.441790\pi\) | |||||||
\(450\) | −8360.00 | −0.875765 | ||||||||
\(451\) | 4368.00 | + | 7565.60i | 0.456056 | + | 0.789912i | ||||
\(452\) | 14739.0 | − | 25528.7i | 1.53377 | − | 2.65657i | ||||
\(453\) | 11630.5 | − | 20144.6i | 1.20629 | − | 2.08935i | ||||
\(454\) | 12880.0 | 1.33147 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39690.0 | −4.07600 | ||||||||
\(457\) | −797.000 | + | 1380.44i | −0.0815801 | + | 0.141301i | −0.903929 | − | 0.427683i | \(-0.859330\pi\) |
0.822349 | + | 0.568984i | \(0.192663\pi\) | |||||||
\(458\) | 1137.50 | − | 1970.21i | 0.116052 | − | 0.201008i | ||||
\(459\) | −1347.50 | − | 2333.94i | −0.137028 | − | 0.237340i | ||||
\(460\) | −11424.0 | −1.15793 | ||||||||
\(461\) | −2957.50 | − | 5122.54i | −0.298795 | − | 0.517528i | 0.677066 | − | 0.735923i | \(-0.263251\pi\) |
−0.975861 | + | 0.218395i | \(0.929918\pi\) | |||||||
\(462\) | 5915.00 | + | 10245.1i | 0.595651 | + | 1.03170i | ||||
\(463\) | 11072.0 | 1.11136 | 0.555680 | − | 0.831396i | \(-0.312458\pi\) | ||||
0.555680 | + | 0.831396i | \(0.312458\pi\) | |||||||
\(464\) | 3649.00 | + | 6320.25i | 0.365087 | + | 0.632350i | ||||
\(465\) | −4802.00 | + | 8317.31i | −0.478898 | + | 0.829475i | ||||
\(466\) | −7652.50 | + | 13254.5i | −0.760719 | + | 1.31760i | ||||
\(467\) | 1260.00 | 0.124852 | 0.0624260 | − | 0.998050i | \(-0.480116\pi\) | ||||
0.0624260 | + | 0.998050i | \(0.480116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6214.00 | −0.611804 | ||||||||
\(470\) | −1837.50 | + | 3182.64i | −0.180335 | + | 0.312350i | ||||
\(471\) | −9555.00 | + | 16549.7i | −0.934758 | + | 1.61905i | ||||
\(472\) | −6615.00 | − | 11457.5i | −0.645085 | − | 1.11732i | ||||
\(473\) | −5226.00 | −0.508016 | ||||||||
\(474\) | 22820.0 | + | 39525.4i | 2.21130 | + | 3.83009i | ||||
\(475\) | 4788.00 | + | 8293.06i | 0.462502 | + | 0.801077i | ||||
\(476\) | 17017.0 | 1.63860 | ||||||||
\(477\) | 4752.00 | + | 8230.71i | 0.456141 | + | 0.790059i | ||||
\(478\) | −8692.50 | + | 15055.9i | −0.831769 | + | 1.44067i | ||||
\(479\) | −6016.50 | + | 10420.9i | −0.573906 | + | 0.994034i | 0.422254 | + | 0.906478i | \(0.361239\pi\) |
−0.996160 | + | 0.0875564i | \(0.972094\pi\) | |||||||
\(480\) | −4165.00 | −0.396053 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8050.00 | 0.760721 | ||||||||
\(483\) | −4368.00 | + | 7565.60i | −0.411493 | + | 0.712726i | ||||
\(484\) | 5567.50 | − | 9643.19i | 0.522868 | − | 0.905634i | ||||
\(485\) | 245.000 | + | 424.352i | 0.0229379 | + | 0.0397296i | ||||
\(486\) | 24640.0 | 2.29978 | ||||||||
\(487\) | −1140.00 | − | 1974.54i | −0.106075 | − | 0.183727i | 0.808102 | − | 0.589042i | \(-0.200495\pi\) |
−0.914177 | + | 0.405316i | \(0.867162\pi\) | |||||||
\(488\) | 1260.00 | + | 2182.38i | 0.116880 | + | 0.202442i | ||||
\(489\) | −3808.00 | −0.352155 | ||||||||
\(490\) | 3045.00 | + | 5274.09i | 0.280733 | + | 0.486243i | ||||
\(491\) | −8383.50 | + | 14520.6i | −0.770554 | + | 1.33464i | 0.166706 | + | 0.986007i | \(0.446687\pi\) |
−0.937260 | + | 0.348632i | \(0.886646\pi\) | |||||||
\(492\) | −19992.0 | + | 34627.2i | −1.83193 | + | 3.17299i | ||||
\(493\) | −6314.00 | −0.576812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4004.00 | 0.363569 | ||||||||
\(496\) | 8722.00 | − | 15106.9i | 0.789575 | − | 1.36758i | ||||
\(497\) | 58.5000 | − | 101.325i | 0.00527985 | − | 0.00914496i | ||||
\(498\) | 5390.00 | + | 9335.75i | 0.485003 | + | 0.840050i | ||||
\(499\) | −12840.0 | −1.15190 | −0.575949 | − | 0.817485i | \(-0.695367\pi\) | ||||
−0.575949 | + | 0.817485i | \(0.695367\pi\) | |||||||
\(500\) | 11959.5 | + | 20714.5i | 1.06969 | + | 1.85276i | ||||
\(501\) | −5684.00 | − | 9844.98i | −0.506871 | − | 0.877926i | ||||
\(502\) | 5040.00 | 0.448100 | ||||||||
\(503\) | 1099.00 | + | 1903.52i | 0.0974195 | + | 0.168735i | 0.910616 | − | 0.413254i | \(-0.135608\pi\) |
−0.813196 | + | 0.581989i | \(0.802274\pi\) | |||||||
\(504\) | −6435.00 | + | 11145.7i | −0.568726 | + | 0.985062i | ||||
\(505\) | −1470.00 | + | 2546.11i | −0.129533 | + | 0.224358i | ||||
\(506\) | −12480.0 | −1.09645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32164.0 | 2.80915 | ||||||||
\(509\) | −8533.00 | + | 14779.6i | −0.743062 | + | 1.28702i | 0.208033 | + | 0.978122i | \(0.433294\pi\) |
−0.951095 | + | 0.308899i | \(0.900039\pi\) | |||||||
\(510\) | 9432.50 | − | 16337.6i | 0.818977 | − | 1.41851i | ||||
\(511\) | 637.000 | + | 1103.32i | 0.0551452 | + | 0.0955144i | ||||
\(512\) | −24475.0 | −2.11260 | ||||||||
\(513\) | −2205.00 | − | 3819.17i | −0.189772 | − | 0.328695i | ||||
\(514\) | −15102.5 | − | 26158.3i | −1.29600 | − | 2.24473i | ||||
\(515\) | 4116.00 | 0.352180 | ||||||||
\(516\) | −11959.5 | − | 20714.5i | −1.02032 | − | 1.76725i | ||||
\(517\) | −1365.00 | + | 2364.25i | −0.116117 | + | 0.201121i | ||||
\(518\) | −4257.50 | + | 7374.21i | −0.361127 | + | 0.625490i | ||||
\(519\) | 2352.00 | 0.198924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2583.00 | 0.217204 | 0.108602 | − | 0.994085i | \(-0.465363\pi\) | ||||
0.108602 | + | 0.994085i | \(0.465363\pi\) | |||||||
\(522\) | 4510.00 | − | 7811.55i | 0.378156 | − | 0.654985i | ||||
\(523\) | −9310.00 | + | 16125.4i | −0.778390 | + | 1.34821i | 0.154480 | + | 0.987996i | \(0.450630\pi\) |
−0.932869 | + | 0.360215i | \(0.882703\pi\) | |||||||
\(524\) | −12197.5 | − | 21126.7i | −1.01689 | − | 1.76130i | ||||
\(525\) | 6916.00 | 0.574931 | ||||||||
\(526\) | 9270.00 | + | 16056.1i | 0.768424 | + | 1.33095i | ||||
\(527\) | 7546.00 | + | 13070.1i | 0.623736 | + | 1.08034i | ||||
\(528\) | −16198.0 | −1.33509 | ||||||||
\(529\) | 1475.50 | + | 2555.64i | 0.121271 | + | 0.210047i | ||||
\(530\) | 7560.00 | − | 13094.3i | 0.619595 | − | 1.07317i | ||||
\(531\) | −3234.00 | + | 5601.45i | −0.264301 | + | 0.457782i | ||||
\(532\) | 27846.0 | 2.26932 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −41650.0 | −3.37523 | ||||||||
\(535\) | 2394.00 | − | 4146.53i | 0.193461 | − | 0.335084i | ||||
\(536\) | 10755.0 | − | 18628.2i | 0.866689 | − | 1.50115i | ||||
\(537\) | −10601.5 | − | 18362.3i | −0.851934 | − | 1.47559i | ||||
\(538\) | 41720.0 | 3.34327 | ||||||||
\(539\) | 2262.00 | + | 3917.90i | 0.180763 | + | 0.313091i | ||||
\(540\) | −2082.50 | − | 3607.00i | −0.165957 | − | 0.287445i | ||||
\(541\) | 16833.0 | 1.33772 | 0.668861 | − | 0.743388i | \(-0.266782\pi\) | ||||
0.668861 | + | 0.743388i | \(0.266782\pi\) | |||||||
\(542\) | −4042.50 | − | 7001.82i | −0.320369 | − | 0.554896i | ||||
\(543\) | −98.0000 | + | 169.741i | −0.00774509 | + | 0.0134149i | ||||
\(544\) | −3272.50 | + | 5668.14i | −0.257918 | + | 0.446727i | ||||
\(545\) | −2611.00 | −0.205216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8615.00 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(548\) | −15096.0 | + | 26147.0i | −1.17677 | + | 2.03822i | ||||
\(549\) | 616.000 | − | 1066.94i | 0.0478875 | − | 0.0829436i | ||||
\(550\) | 4940.00 | + | 8556.33i | 0.382986 | + | 0.663351i | ||||
\(551\) | −10332.0 | −0.798835 | ||||||||
\(552\) | −15120.0 | − | 26188.6i | −1.16585 | − | 2.01931i | ||||
\(553\) | −8476.00 | − | 14680.9i | −0.651783 | − | 1.12892i | ||||
\(554\) | −19100.0 | −1.46477 | ||||||||
\(555\) | 3209.50 | + | 5559.02i | 0.245470 | + | 0.425166i | ||||
\(556\) | 15886.5 | − | 27516.2i | 1.21176 | − | 2.09883i | ||||
\(557\) | 4267.50 | − | 7391.53i | 0.324632 | − | 0.562278i | −0.656806 | − | 0.754059i | \(-0.728093\pi\) |
0.981438 | + | 0.191781i | \(0.0614264\pi\) | |||||||
\(558\) | −21560.0 | −1.63568 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8099.00 | 0.611152 | ||||||||
\(561\) | 7007.00 | − | 12136.5i | 0.527336 | − | 0.913374i | ||||
\(562\) | −15535.0 | + | 26907.4i | −1.16602 | + | 2.01961i | ||||
\(563\) | 2320.50 | + | 4019.22i | 0.173708 | + | 0.300871i | 0.939713 | − | 0.341963i | \(-0.111092\pi\) |
−0.766006 | + | 0.642834i | \(0.777759\pi\) | |||||||
\(564\) | −12495.0 | −0.932862 | ||||||||
\(565\) | 6069.00 | + | 10511.8i | 0.451902 | + | 0.782718i | ||||
\(566\) | 13230.0 | + | 22915.0i | 0.982506 | + | 1.70175i | ||||
\(567\) | −10907.0 | −0.807850 | ||||||||
\(568\) | 202.500 | + | 350.740i | 0.0149590 | + | 0.0259097i | ||||
\(569\) | 2396.50 | − | 4150.86i | 0.176567 | − | 0.305823i | −0.764136 | − | 0.645056i | \(-0.776834\pi\) |
0.940702 | + | 0.339233i | \(0.110168\pi\) | |||||||
\(570\) | 15435.0 | − | 26734.2i | 1.13421 | − | 1.96451i | ||||
\(571\) | −5563.00 | −0.407713 | −0.203857 | − | 0.979001i | \(-0.565348\pi\) | ||||
−0.203857 | + | 0.979001i | \(0.565348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2954.00 | −0.215367 | ||||||||
\(574\) | 10920.0 | − | 18914.0i | 0.794063 | − | 1.37536i | ||||
\(575\) | −3648.00 | + | 6318.52i | −0.264578 | + | 0.458262i | ||||
\(576\) | 3157.00 | + | 5468.08i | 0.228371 | + | 0.395550i | ||||
\(577\) | −24038.0 | −1.73434 | −0.867171 | − | 0.498011i | \(-0.834064\pi\) | ||||
−0.867171 | + | 0.498011i | \(0.834064\pi\) | |||||||
\(578\) | −2540.00 | − | 4399.41i | −0.182786 | − | 0.316594i | ||||
\(579\) | −1722.00 | − | 2982.59i | −0.123599 | − | 0.214080i | ||||
\(580\) | −9758.00 | −0.698584 | ||||||||
\(581\) | −2002.00 | − | 3467.57i | −0.142955 | − | 0.247606i | ||||
\(582\) | −1225.00 | + | 2121.76i | −0.0872472 | + | 0.151117i | ||||
\(583\) | 5616.00 | − | 9727.20i | 0.398955 | − | 0.691011i | ||||
\(584\) | −4410.00 | −0.312478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4515.00 | 0.318281 | ||||||||
\(587\) | −10612.0 | + | 18380.5i | −0.746174 | + | 1.29241i | 0.203470 | + | 0.979081i | \(0.434778\pi\) |
−0.949644 | + | 0.313330i | \(0.898555\pi\) | |||||||
\(588\) | −10353.0 | + | 17931.9i | −0.726106 | + | 1.25765i | ||||
\(589\) | 12348.0 | + | 21387.4i | 0.863821 | + | 1.49618i | ||||
\(590\) | 10290.0 | 0.718021 | ||||||||
\(591\) | −10468.5 | − | 18132.0i | −0.728624 | − | 1.26201i | ||||
\(592\) | −5829.50 | − | 10097.0i | −0.404714 | − | 0.700986i | ||||
\(593\) | −4354.00 | −0.301513 | −0.150757 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150757 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(594\) | −2275.00 | − | 3940.42i | −0.157145 | − | 0.272184i | ||||
\(595\) | −3503.50 | + | 6068.24i | −0.241394 | + | 0.418107i | ||||
\(596\) | 20961.0 | − | 36305.5i | 1.44060 | − | 2.49519i | ||||
\(597\) | 490.000 | 0.0335919 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7310.00 | 0.498629 | 0.249314 | − | 0.968423i | \(-0.419795\pi\) | ||||
0.249314 | + | 0.968423i | \(0.419795\pi\) | |||||||
\(600\) | −11970.0 | + | 20732.6i | −0.814455 | + | 1.41068i | ||||
\(601\) | 3797.50 | − | 6577.46i | 0.257743 | − | 0.446423i | −0.707894 | − | 0.706318i | \(-0.750355\pi\) |
0.965637 | + | 0.259895i | \(0.0836880\pi\) | |||||||
\(602\) | 6532.50 | + | 11314.6i | 0.442267 | + | 0.766029i | ||||
\(603\) | −10516.0 | −0.710190 | ||||||||
\(604\) | −28245.5 | − | 48922.6i | −1.90280 | − | 3.29575i | ||||
\(605\) | 2292.50 | + | 3970.73i | 0.154055 | + | 0.266831i | ||||
\(606\) | −14700.0 | −0.985391 | ||||||||
\(607\) | 413.000 | + | 715.337i | 0.0276164 | + | 0.0478330i | 0.879503 | − | 0.475893i | \(-0.157875\pi\) |
−0.851887 | + | 0.523726i | \(0.824542\pi\) | |||||||
\(608\) | −5355.00 | + | 9275.13i | −0.357194 | + | 0.618678i | ||||
\(609\) | −3731.00 | + | 6462.28i | −0.248256 | + | 0.429992i | ||||
\(610\) | −1960.00 | −0.130095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 28798.0 | 1.90211 | ||||||||
\(613\) | 7295.00 | − | 12635.3i | 0.480656 | − | 0.832521i | −0.519097 | − | 0.854715i | \(-0.673732\pi\) |
0.999754 | + | 0.0221940i | \(0.00706516\pi\) | |||||||
\(614\) | 5285.00 | − | 9153.89i | 0.347370 | − | 0.601663i | ||||
\(615\) | −8232.00 | − | 14258.2i | −0.539750 | − | 0.934875i | ||||
\(616\) | 15210.0 | 0.994851 | ||||||||
\(617\) | 2444.00 | + | 4233.13i | 0.159468 | + | 0.276207i | 0.934677 | − | 0.355498i | \(-0.115689\pi\) |
−0.775209 | + | 0.631705i | \(0.782355\pi\) | |||||||
\(618\) | 10290.0 | + | 17822.8i | 0.669781 | + | 1.16009i | ||||
\(619\) | 11004.0 | 0.714520 | 0.357260 | − | 0.934005i | \(-0.383711\pi\) | ||||
0.357260 | + | 0.934005i | \(0.383711\pi\) | |||||||
\(620\) | 11662.0 | + | 20199.2i | 0.755415 | + | 1.30842i | ||||
\(621\) | 1680.00 | − | 2909.85i | 0.108561 | − | 0.188032i | ||||
\(622\) | −8505.00 | + | 14731.1i | −0.548263 | + | 0.949619i | ||||
\(623\) | 15470.0 | 0.994851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | 26722.5 | − | 46284.7i | 1.70614 | − | 2.95513i | ||||
\(627\) | 11466.0 | − | 19859.7i | 0.730316 | − | 1.26494i | ||||
\(628\) | 23205.0 | + | 40192.2i | 1.47449 | + | 2.55389i | ||||
\(629\) | 10087.0 | 0.639420 | ||||||||
\(630\) | −5005.00 | − | 8668.91i | −0.316514 | − | 0.548219i | ||||
\(631\) | −2487.50 | − | 4308.48i | −0.156935 | − | 0.271819i | 0.776827 | − | 0.629714i | \(-0.216828\pi\) |
−0.933762 | + | 0.357895i | \(0.883495\pi\) | |||||||
\(632\) | 58680.0 | 3.69330 | ||||||||
\(633\) | 9978.50 | + | 17283.3i | 0.626556 | + | 1.08523i | ||||
\(634\) | −17635.0 | + | 30544.7i | −1.10469 | + | 1.91338i | ||||
\(635\) | −6622.00 | + | 11469.6i | −0.413836 | + | 0.716786i | ||||
\(636\) | 51408.0 | 3.20513 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10660.0 | −0.661494 | ||||||||
\(639\) | 99.0000 | − | 171.473i | 0.00612892 | − | 0.0106156i | ||||
\(640\) | 7402.50 | − | 12821.5i | 0.457202 | − | 0.791898i | ||||
\(641\) | −1975.00 | − | 3420.80i | −0.121697 | − | 0.210785i | 0.798740 | − | 0.601676i | \(-0.205500\pi\) |
−0.920437 | + | 0.390891i | \(0.872167\pi\) | |||||||
\(642\) | 23940.0 | 1.47171 | ||||||||
\(643\) | −1841.00 | − | 3188.71i | −0.112911 | − | 0.195568i | 0.804032 | − | 0.594587i | \(-0.202684\pi\) |
−0.916943 | + | 0.399019i | \(0.869351\pi\) | |||||||
\(644\) | 10608.0 | + | 18373.6i | 0.649090 | + | 1.12426i | ||||
\(645\) | 9849.00 | 0.601247 | ||||||||
\(646\) | −24255.0 | − | 42010.9i | −1.47724 | − | 2.55866i | ||||
\(647\) | −5201.00 | + | 9008.40i | −0.316032 | + | 0.547383i | −0.979656 | − | 0.200683i | \(-0.935684\pi\) |
0.663625 | + | 0.748066i | \(0.269017\pi\) | |||||||
\(648\) | 18877.5 | − | 32696.8i | 1.14441 | − | 1.98218i | ||||
\(649\) | 7644.00 | 0.462332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17836.0 | 1.07381 | ||||||||
\(652\) | −4624.00 | + | 8009.00i | −0.277745 | + | 0.481069i | ||||
\(653\) | 15840.0 | − | 27435.7i | 0.949260 | − | 1.64417i | 0.202273 | − | 0.979329i | \(-0.435167\pi\) |
0.746987 | − | 0.664838i | \(-0.231500\pi\) | |||||||
\(654\) | −6527.50 | − | 11306.0i | −0.390284 | − | 0.675991i | ||||
\(655\) | 10045.0 | 0.599222 | ||||||||
\(656\) | 14952.0 | + | 25897.6i | 0.889905 | + | 1.54136i | ||||
\(657\) | 1078.00 | + | 1867.15i | 0.0640134 | + | 0.110874i | ||||
\(658\) | 6825.00 | 0.404356 | ||||||||
\(659\) | −10970.0 | − | 19000.6i | −0.648453 | − | 1.12315i | −0.983492 | − | 0.180949i | \(-0.942083\pi\) |
0.335039 | − | 0.942204i | \(-0.391250\pi\) | |||||||
\(660\) | 10829.0 | − | 18756.4i | 0.638664 | − | 1.10620i | ||||
\(661\) | −15687.0 | + | 27170.7i | −0.923077 | + | 1.59882i | −0.128451 | + | 0.991716i | \(0.541000\pi\) |
−0.794626 | + | 0.607100i | \(0.792333\pi\) | |||||||
\(662\) | −48520.0 | −2.84862 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13860.0 | 0.810049 | ||||||||
\(665\) | −5733.00 | + | 9929.85i | −0.334310 | + | 0.579042i | ||||
\(666\) | −7205.00 | + | 12479.4i | −0.419201 | + | 0.726078i | ||||
\(667\) | −3936.00 | − | 6817.35i | −0.228490 | − | 0.395756i | ||||
\(668\) | −27608.0 | −1.59908 | ||||||||
\(669\) | −759.500 | − | 1315.49i | −0.0438923 | − | 0.0760237i | ||||
\(670\) | 8365.00 | + | 14488.6i | 0.482341 | + | 0.835438i | ||||
\(671\) | −1456.00 | −0.0837679 | ||||||||
\(672\) | 3867.50 | + | 6698.71i | 0.222012 | + | 0.384536i | ||||
\(673\) | −9006.50 | + | 15599.7i | −0.515862 | + | 0.893499i | 0.483969 | + | 0.875085i | \(0.339195\pi\) |
−0.999830 | + | 0.0184136i | \(0.994138\pi\) | |||||||
\(674\) | 26122.5 | − | 45245.5i | 1.49288 | − | 2.58574i | ||||
\(675\) | −2660.00 | −0.151679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10640.0 | −0.604030 | −0.302015 | − | 0.953303i | \(-0.597659\pi\) | ||||
−0.302015 | + | 0.953303i | \(0.597659\pi\) | |||||||
\(678\) | −30345.0 | + | 52559.1i | −1.71887 | + | 2.97717i | ||||
\(679\) | 455.000 | − | 788.083i | 0.0257162 | − | 0.0445418i | ||||
\(680\) | −12127.5 | − | 21005.4i | −0.683924 | − | 1.18459i | ||||
\(681\) | −18032.0 | −1.01467 | ||||||||
\(682\) | 12740.0 | + | 22066.3i | 0.715308 | + | 1.23895i | ||||
\(683\) | −4668.00 | − | 8085.21i | −0.261517 | − | 0.452961i | 0.705128 | − | 0.709080i | \(-0.250889\pi\) |
−0.966645 | + | 0.256119i | \(0.917556\pi\) | |||||||
\(684\) | 47124.0 | 2.63426 | ||||||||
\(685\) | −6216.00 | − | 10766.4i | −0.346717 | − | 0.600531i | ||||
\(686\) | 16802.5 | − | 29102.8i | 0.935164 | − | 1.61975i | ||||
\(687\) | −1592.50 | + | 2758.29i | −0.0884391 | + | 0.153181i | ||||
\(688\) | −17889.0 | −0.991296 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 23520.0 | 1.29767 | ||||||||
\(691\) | 2100.00 | − | 3637.31i | 0.115612 | − | 0.200246i | −0.802412 | − | 0.596770i | \(-0.796450\pi\) |
0.918024 | + | 0.396524i | \(0.129784\pi\) | |||||||
\(692\) | 2856.00 | − | 4946.74i | 0.156891 | − | 0.271744i | ||||
\(693\) | −3718.00 | − | 6439.76i | −0.203803 | − | 0.352996i | ||||
\(694\) | −3105.00 | −0.169833 | ||||||||
\(695\) | 6541.50 | + | 11330.2i | 0.357026 | + | 0.618388i | ||||
\(696\) | −12915.0 | − | 22369.4i | −0.703365 | − | 1.21826i | ||||
\(697\) | −25872.0 | −1.40599 | ||||||||
\(698\) | 31202.5 | + | 54044.3i | 1.69202 | + | 2.93067i | ||||
\(699\) | 10713.5 | − | 18556.3i | 0.579716 | − | 1.00410i | ||||
\(700\) | 8398.00 | − | 14545.8i | 0.453449 | − | 0.785397i | ||||
\(701\) | 9872.00 | 0.531898 | 0.265949 | − | 0.963987i | \(-0.414315\pi\) | ||||
0.265949 | + | 0.963987i | \(0.414315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16506.0 | 0.885541 | ||||||||
\(704\) | 3731.00 | − | 6462.28i | 0.199741 | − | 0.345961i | ||||
\(705\) | 2572.50 | − | 4455.70i | 0.137427 | − | 0.238030i | ||||
\(706\) | −3500.00 | − | 6062.18i | −0.186578 | − | 0.323163i | ||||
\(707\) | 5460.00 | 0.290445 | ||||||||
\(708\) | 17493.0 | + | 30298.8i | 0.928569 | + | 1.60833i | ||||
\(709\) | 14225.0 | + | 24638.4i | 0.753499 | + | 1.30510i | 0.946117 | + | 0.323825i | \(0.104969\pi\) |
−0.192617 | + | 0.981274i | \(0.561698\pi\) | |||||||
\(710\) | −315.000 | −0.0166503 | ||||||||
\(711\) | −14344.0 | − | 24844.5i | −0.756599 | − | 1.31047i | ||||
\(712\) | −26775.0 | + | 46375.7i | −1.40932 | + | 2.44101i | ||||
\(713\) | −9408.00 | + | 16295.1i | −0.494155 | + | 0.855901i | ||||
\(714\) | −35035.0 | −1.83635 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51493.0 | −2.68769 | ||||||||
\(717\) | 12169.5 | − | 21078.2i | 0.633861 | − | 1.09788i | ||||
\(718\) | −12420.0 | + | 21512.1i | −0.645557 | + | 1.11814i | ||||
\(719\) | −16359.0 | − | 28334.6i | −0.848523 | − | 1.46968i | −0.882527 | − | 0.470263i | \(-0.844159\pi\) |
0.0340039 | − | 0.999422i | \(-0.489174\pi\) | |||||||
\(720\) | 13706.0 | 0.709434 | ||||||||
\(721\) | −3822.00 | − | 6619.90i | −0.197418 | − | 0.341939i | ||||
\(722\) | −22542.5 | − | 39044.8i | −1.16197 | − | 2.01260i | ||||
\(723\) | −11270.0 | −0.579718 | ||||||||
\(724\) | 238.000 | + | 412.228i | 0.0122171 | + | 0.0211607i | ||||
\(725\) | −3116.00 | + | 5397.07i | −0.159621 | + | 0.276472i | ||||
\(726\) | −11462.5 | + | 19853.6i | −0.585969 | + | 1.01493i | ||||
\(727\) | −22834.0 | −1.16488 | −0.582439 | − | 0.812874i | \(-0.697901\pi\) | ||||
−0.582439 | + | 0.812874i | \(0.697901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 1715.00 | − | 2970.47i | 0.0869521 | − | 0.150605i | ||||
\(731\) | 7738.50 | − | 13403.5i | 0.391544 | − | 0.678174i | ||||
\(732\) | −3332.00 | − | 5771.19i | −0.168244 | − | 0.291406i | ||||
\(733\) | −7875.00 | −0.396821 | −0.198410 | − | 0.980119i | \(-0.563578\pi\) | ||||
−0.198410 | + | 0.980119i | \(0.563578\pi\) | |||||||
\(734\) | −21805.0 | − | 37767.4i | −1.09651 | − | 1.89921i | ||||
\(735\) | −4263.00 | − | 7383.73i | −0.213936 | − | 0.370548i | ||||
\(736\) | −8160.00 | −0.408671 | ||||||||
\(737\) | 6214.00 | + | 10763.0i | 0.310578 | + | 0.537936i | ||||
\(738\) | 18480.0 | − | 32008.3i | 0.921759 | − | 1.59653i | ||||
\(739\) | −1070.00 | + | 1853.29i | −0.0532620 | + | 0.0922524i | −0.891427 | − | 0.453164i | \(-0.850295\pi\) |
0.838165 | + | 0.545416i | \(0.183629\pi\) | |||||||
\(740\) | 15589.0 | 0.774410 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28080.0 | −1.38928 | ||||||||
\(743\) | 15985.5 | − | 27687.7i | 0.789302 | − | 1.36711i | −0.137094 | − | 0.990558i | \(-0.543776\pi\) |
0.926395 | − | 0.376552i | \(-0.122891\pi\) | |||||||
\(744\) | −30870.0 | + | 53468.4i | −1.52117 | + | 2.63474i | ||||
\(745\) | 8631.00 | + | 14949.3i | 0.424450 | + | 0.735169i | ||||
\(746\) | 50060.0 | 2.45687 | ||||||||
\(747\) | −3388.00 | − | 5868.19i | −0.165944 | − | 0.287424i | ||||
\(748\) | −17017.0 | − | 29474.3i | −0.831822 | − | 1.44076i | ||||
\(749\) | −8892.00 | −0.433787 | ||||||||
\(750\) | −24622.5 | − | 42647.4i | −1.19878 | − | 2.07635i | ||||
\(751\) | 3716.00 | − | 6436.30i | 0.180558 | − | 0.312735i | −0.761513 | − | 0.648150i | \(-0.775543\pi\) |
0.942071 | + | 0.335415i | \(0.108876\pi\) | |||||||
\(752\) | −4672.50 | + | 8093.01i | −0.226581 | + | 0.392449i | ||||
\(753\) | −7056.00 | −0.341481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23261.0 | 1.12126 | ||||||||
\(756\) | −3867.50 | + | 6698.71i | −0.186058 | + | 0.322261i | ||||
\(757\) | −10088.0 | + | 17472.9i | −0.484352 | + | 0.838923i | −0.999838 | − | 0.0179753i | \(-0.994278\pi\) |
0.515486 | + | 0.856898i | \(0.327611\pi\) | |||||||
\(758\) | −8430.00 | − | 14601.2i | −0.403946 | − | 0.699656i | ||||
\(759\) | 17472.0 | 0.835564 | ||||||||
\(760\) | −19845.0 | − | 34372.5i | −0.947176 | − | 1.64056i | ||||
\(761\) | −4739.00 | − | 8208.19i | −0.225741 | − | 0.390994i | 0.730801 | − | 0.682591i | \(-0.239147\pi\) |
−0.956541 | + | 0.291597i | \(0.905814\pi\) | |||||||
\(762\) | −66220.0 | −3.14816 | ||||||||
\(763\) | 2424.50 | + | 4199.36i | 0.115036 | + | 0.199249i | ||||
\(764\) | −3587.00 | + | 6212.87i | −0.169860 | + | 0.294206i | ||||
\(765\) | −5929.00 | + | 10269.3i | −0.280214 | + | 0.485344i | ||||
\(766\) | 4235.00 | 0.199761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 57953.0 | 2.72292 | ||||||||
\(769\) | −6048.00 | + | 10475.4i | −0.283610 | + | 0.491228i | −0.972271 | − | 0.233856i | \(-0.924866\pi\) |
0.688661 | + | 0.725084i | \(0.258199\pi\) | |||||||
\(770\) | −5915.00 | + | 10245.1i | −0.276834 | + | 0.479490i | ||||
\(771\) | 21143.5 | + | 36621.6i | 0.987632 | + | 1.71063i | ||||
\(772\) | −8364.00 | −0.389931 | ||||||||
\(773\) | 8970.50 | + | 15537.4i | 0.417395 | + | 0.722950i | 0.995677 | − | 0.0928877i | \(-0.0296098\pi\) |
−0.578281 | + | 0.815837i | \(0.696276\pi\) | |||||||
\(774\) | 11055.0 | + | 19147.8i | 0.513390 | + | 0.889217i | ||||
\(775\) | 14896.0 | 0.690426 | ||||||||
\(776\) | 1575.00 | + | 2727.98i | 0.0728598 | + | 0.126197i | ||||
\(777\) | 5960.50 | − | 10323.9i | 0.275202 | − | 0.476663i | ||||
\(778\) | −28285.0 | + | 48991.1i | −1.30343 | + | 2.25760i | ||||
\(779\) | −42336.0 | −1.94717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −234.000 | −0.0107211 | ||||||||
\(782\) | 18480.0 | − | 32008.3i | 0.845068 | − | 1.46370i | ||||
\(783\) | 1435.00 | − | 2485.49i | 0.0654952 | − | 0.113441i | ||||
\(784\) | 7743.00 | + | 13411.3i | 0.352724 | + | 0.610936i | ||||
\(785\) | −19110.0 | −0.868873 | ||||||||
\(786\) | 25112.5 | + | 43496.1i | 1.13961 | + | 1.97386i | ||||
\(787\) | 3332.00 | + | 5771.19i | 0.150919 | + | 0.261399i | 0.931565 | − | 0.363574i | \(-0.118444\pi\) |
−0.780647 | + | 0.624972i | \(0.785110\pi\) | |||||||
\(788\) | −50847.0 | −2.29867 | ||||||||
\(789\) | −12978.0 | − | 22478.6i | −0.585588 | − | 1.01427i | ||||
\(790\) | −22820.0 | + | 39525.4i | −1.02772 | + | 1.78006i | ||||
\(791\) | 11271.0 | − | 19521.9i | 0.506638 | − | 0.877523i | ||||
\(792\) | 25740.0 | 1.15484 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9310.00 | −0.416120 | ||||||||
\(795\) | −10584.0 | + | 18332.0i | −0.472171 | + | 0.817824i | ||||
\(796\) | 595.000 | − | 1030.57i | 0.0264940 | − | 0.0458889i | ||||
\(797\) | 721.000 | + | 1248.81i | 0.0320441 | + | 0.0555020i | 0.881603 | − | 0.471992i | \(-0.156465\pi\) |
−0.849559 | + | 0.527494i | \(0.823132\pi\) | |||||||
\(798\) | −57330.0 | −2.54318 | ||||||||
\(799\) | −4042.50 | − | 7001.82i | −0.178990 | − | 0.310021i | ||||
\(800\) | 3230.00 | + | 5594.52i | 0.142747 | + | 0.247245i | ||||
\(801\) | 26180.0 | 1.15484 | ||||||||
\(802\) | 17050.0 | + | 29531.5i | 0.750694 | + | 1.30024i | ||||
\(803\) | 1274.00 | − | 2206.63i | 0.0559881 | − | 0.0969743i | ||||
\(804\) | −28441.0 | + | 49261.3i | −1.24756 | + | 2.16083i | ||||
\(805\) | −8736.00 | −0.382489 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58408.0 | −2.54778 | ||||||||
\(808\) | −9450.00 | + | 16367.9i | −0.411448 | + | 0.712649i | ||||
\(809\) | −15103.5 | + | 26160.0i | −0.656379 | + | 1.13688i | 0.325167 | + | 0.945657i | \(0.394580\pi\) |
−0.981546 | + | 0.191226i | \(0.938754\pi\) | |||||||
\(810\) | 14682.5 | + | 25430.8i | 0.636902 | + | 1.10315i | ||||
\(811\) | −21140.0 | −0.915322 | −0.457661 | − | 0.889127i | \(-0.651313\pi\) | ||||
−0.457661 | + | 0.889127i | \(0.651313\pi\) | |||||||
\(812\) | 9061.00 | + | 15694.1i | 0.391599 | + | 0.678270i | ||||
\(813\) | 5659.50 | + | 9802.54i | 0.244142 | + | 0.422866i | ||||
\(814\) | 17030.0 | 0.733294 | ||||||||
\(815\) | −1904.00 | − | 3297.82i | −0.0818334 | − | 0.141740i | ||||
\(816\) | 23985.5 | − | 41544.1i | 1.02900 | − | 1.78227i | ||||
\(817\) | 12663.0 | − | 21933.0i | 0.542255 | − | 0.939213i | ||||
\(818\) | 64960.0 | 2.77662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39984.0 | −1.70281 | ||||||||
\(821\) | 284.500 | − | 492.768i | 0.0120939 | − | 0.0209473i | −0.859915 | − | 0.510437i | \(-0.829484\pi\) |
0.872009 | + | 0.489490i | \(0.162817\pi\) | |||||||
\(822\) | 31080.0 | − | 53832.1i | 1.31878 | − | 2.28420i | ||||
\(823\) | 4269.00 | + | 7394.12i | 0.180812 | + | 0.313175i | 0.942157 | − | 0.335171i | \(-0.108794\pi\) |
−0.761346 | + | 0.648346i | \(0.775461\pi\) | |||||||
\(824\) | 26460.0 | 1.11866 | ||||||||
\(825\) | −6916.00 | − | 11978.9i | −0.291860 | − | 0.505516i | ||||
\(826\) | −9555.00 | − | 16549.7i | −0.402495 | − | 0.697142i | ||||
\(827\) | 32702.0 | 1.37504 | 0.687521 | − | 0.726164i | \(-0.258699\pi\) | ||||
0.687521 | + | 0.726164i | \(0.258699\pi\) | |||||||
\(828\) | 17952.0 | + | 31093.8i | 0.753472 | + | 1.30505i | ||||
\(829\) | 10577.0 | − | 18319.9i | 0.443130 | − | 0.767523i | −0.554790 | − | 0.831990i | \(-0.687202\pi\) |
0.997920 | + | 0.0644673i | \(0.0205348\pi\) | |||||||
\(830\) | −5390.00 | + | 9335.75i | −0.225409 | + | 0.390420i | ||||
\(831\) | 26740.0 | 1.11625 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13398.0 | −0.557279 | ||||||||
\(834\) | −32707.5 | + | 56651.1i | −1.35800 | + | 2.35212i | ||||
\(835\) | 5684.00 | − | 9844.98i | 0.235572 | − | 0.408023i | ||||
\(836\) | −27846.0 | − | 48230.7i | −1.15200 | − | 1.99533i | ||||
\(837\) | −6860.00 | −0.283293 | ||||||||
\(838\) | 18357.5 | + | 31796.1i | 0.756741 | + | 1.31071i | ||||
\(839\) | −1092.00 | − | 1891.40i | −0.0449345 | − | 0.0778288i | 0.842683 | − | 0.538409i | \(-0.180975\pi\) |
−0.887618 | + | 0.460581i | \(0.847641\pi\) | |||||||
\(840\) | −28665.0 | −1.17742 | ||||||||
\(841\) | 8832.50 | + | 15298.3i | 0.362151 | + | 0.627264i | ||||
\(842\) | −12647.5 | + | 21906.1i | −0.517650 | + | 0.896597i | ||||
\(843\) | 21749.0 | − | 37670.4i | 0.888583 | − | 1.53907i | ||||
\(844\) | 48467.0 | 1.97666 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11550.0 | 0.469382 | ||||||||
\(847\) | 4257.50 | − | 7374.21i | 0.172715 | − | 0.299151i | ||||
\(848\) | 19224.0 | − | 33296.9i | 0.778485 | − | 1.34837i | ||||
\(849\) | −18522.0 | − | 32081.0i | −0.748732 | − | 1.29684i | ||||
\(850\) | −29260.0 | −1.18072 | ||||||||
\(851\) | 6288.00 | + | 10891.1i | 0.253290 | + | 0.438711i | ||||
\(852\) | −535.500 | − | 927.513i | −0.0215328 | − | 0.0372959i | ||||
\(853\) | −36687.0 | −1.47261 | −0.736307 | − | 0.676648i | \(-0.763432\pi\) | ||||
−0.736307 | + | 0.676648i | \(0.763432\pi\) | |||||||
\(854\) | 1820.00 | + | 3152.33i | 0.0729264 | + | 0.126312i | ||||
\(855\) | −9702.00 | + | 16804.4i | −0.388072 | + | 0.672160i | ||||
\(856\) | 15390.0 | − | 26656.3i | 0.614509 | − | 1.06436i | ||||
\(857\) | 36806.0 | 1.46706 | 0.733529 | − | 0.679658i | \(-0.237872\pi\) | ||||
0.733529 | + | 0.679658i | \(0.237872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4900.00 | 0.194628 | 0.0973142 | − | 0.995254i | \(-0.468975\pi\) | ||||
0.0973142 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(860\) | 11959.5 | − | 20714.5i | 0.474204 | − | 0.821346i | ||||
\(861\) | −15288.0 | + | 26479.6i | −0.605126 | + | 1.04811i | ||||
\(862\) | 8107.50 | + | 14042.6i | 0.320351 | + | 0.554864i | ||||
\(863\) | 13697.0 | 0.540268 | 0.270134 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270134 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(864\) | −1487.50 | − | 2576.43i | −0.0585715 | − | 0.101449i | ||||
\(865\) | 1176.00 | + | 2036.89i | 0.0462257 | + | 0.0800652i | ||||
\(866\) | 57995.0 | 2.27569 | ||||||||
\(867\) | 3556.00 | + | 6159.17i | 0.139294 | + | 0.241265i | ||||
\(868\) | 21658.0 | − | 37512.8i | 0.846913 | − | 1.46690i | ||||
\(869\) | −16952.0 | + | 29361.7i | −0.661746 | + | 1.14618i | ||||
\(870\) | 20090.0 | 0.782891 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16785.0 | −0.651848 | ||||||||
\(873\) | 770.000 | − | 1333.68i | 0.0298517 | − | 0.0517047i | ||||
\(874\) | 30240.0 | − | 52377.2i | 1.17035 | − | 2.02710i | ||||
\(875\) | 9145.50 | + | 15840.5i | 0.353342 | + | 0.612006i | ||||
\(876\) | 11662.0 | 0.449797 | ||||||||
\(877\) | 3119.50 | + | 5403.13i | 0.120112 | + | 0.208040i | 0.919812 | − | 0.392360i | \(-0.128341\pi\) |
−0.799700 | + | 0.600400i | \(0.795008\pi\) | |||||||
\(878\) | 43435.0 | + | 75231.6i | 1.66954 | + | 2.89174i | ||||
\(879\) | −6321.00 | −0.242551 | ||||||||
\(880\) | −8099.00 | − | 14027.9i | −0.310247 | − | 0.537363i | ||||
\(881\) | −66.5000 | + | 115.181i | −0.00254307 | + | 0.00440472i | −0.867294 | − | 0.497796i | \(-0.834143\pi\) |
0.864751 | + | 0.502201i | \(0.167476\pi\) | |||||||
\(882\) | 9570.00 | − | 16575.7i | 0.365350 | − | 0.632805i | ||||
\(883\) | −26003.0 | −0.991020 | −0.495510 | − | 0.868602i | \(-0.665019\pi\) | ||||
−0.495510 | + | 0.868602i | \(0.665019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14406.0 | −0.547178 | ||||||||
\(886\) | −2472.50 | + | 4282.50i | −0.0937531 | + | 0.162385i | ||||
\(887\) | 15624.0 | − | 27061.6i | 0.591435 | − | 1.02439i | −0.402605 | − | 0.915374i | \(-0.631895\pi\) |
0.994039 | − | 0.109021i | \(-0.0347716\pi\) | |||||||
\(888\) | 20632.5 | + | 35736.5i | 0.779709 | + | 1.35050i | ||||
\(889\) | 24596.0 | 0.927923 | ||||||||
\(890\) | −20825.0 | − | 36070.0i | −0.784332 | − | 1.35850i | ||||
\(891\) | 10907.0 | + | 18891.5i | 0.410099 | + | 0.710312i | ||||
\(892\) | −3689.00 | −0.138472 | ||||||||
\(893\) | −6615.00 | − | 11457.5i | −0.247886 | − | 0.429352i | ||||
\(894\) | −43155.0 | + | 74746.7i | −1.61445 | + | 2.79631i | ||||
\(895\) | 10601.5 | − | 18362.3i | 0.395943 | − | 0.685794i | ||||
\(896\) | −27495.0 | −1.02516 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72370.0 | 2.68933 | ||||||||
\(899\) | −8036.00 | + | 13918.8i | −0.298126 | + | 0.516370i | ||||
\(900\) | 14212.0 | − | 24615.9i | 0.526370 | − | 0.911700i | ||||
\(901\) | 16632.0 | + | 28807.5i | 0.614975 | + | 1.06517i | ||||
\(902\) | −43680.0 | −1.61240 | ||||||||
\(903\) | −9145.50 | − | 15840.5i | −0.337036 | − | 0.583763i | ||||
\(904\) | 39015.0 | + | 67576.0i | 1.43542 | + | 2.48622i | ||||
\(905\) | −196.000 | −0.00719918 | ||||||||
\(906\) | 58152.5 | + | 100723.i | 2.13244 | + | 3.69349i | ||||
\(907\) | 19126.5 | − | 33128.1i | 0.700204 | − | 1.21279i | −0.268191 | − | 0.963366i | \(-0.586426\pi\) |
0.968395 | − | 0.249423i | \(-0.0802410\pi\) | |||||||
\(908\) | −21896.0 | + | 37925.0i | −0.800269 | + | 1.38611i | ||||
\(909\) | 9240.00 | 0.337152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36374.0 | 1.32286 | 0.661429 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661429 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(912\) | 39249.0 | − | 67981.3i | 1.42507 | − | 2.46829i | ||||
\(913\) | −4004.00 | + | 6935.13i | −0.145140 | + | 0.251390i | ||||
\(914\) | −3985.00 | − | 6902.22i | −0.144215 | − | 0.249787i | ||||
\(915\) | 2744.00 | 0.0991408 | ||||||||
\(916\) | 3867.50 | + | 6698.71i | 0.139504 | + | 0.241628i | ||||
\(917\) | −9327.50 | − | 16155.7i | −0.335901 | − | 0.581798i | ||||
\(918\) | 13475.0 | 0.484468 | ||||||||
\(919\) | 13824.0 | + | 23943.9i | 0.496204 | + | 0.859451i | 0.999990 | − | 0.00437745i | \(-0.00139339\pi\) |
−0.503786 | + | 0.863828i | \(0.668060\pi\) | |||||||
\(920\) | 15120.0 | − | 26188.6i | 0.541839 | − | 0.938492i | ||||
\(921\) | −7399.00 | + | 12815.4i | −0.264718 | + | 0.458505i | ||||
\(922\) | 29575.0 | 1.05640 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −40222.0 | −1.43204 | ||||||||
\(925\) | 4978.00 | − | 8622.15i | 0.176947 | − | 0.306481i | ||||
\(926\) | −27680.0 | + | 47943.2i | −0.982312 | + | 1.70141i | ||||
\(927\) | −6468.00 | − | 11202.9i | −0.229166 | − | 0.396927i | ||||
\(928\) | −6970.00 | −0.246553 | ||||||||
\(929\) | 378.000 | + | 654.715i | 0.0133496 | + | 0.0231222i | 0.872623 | − | 0.488394i | \(-0.162417\pi\) |
−0.859273 | + | 0.511517i | \(0.829084\pi\) | |||||||
\(930\) | −24010.0 | − | 41586.5i | −0.846579 | − | 1.46632i | ||||
\(931\) | −21924.0 | −0.771783 | ||||||||
\(932\) | −26018.5 | − | 45065.4i | −0.914447 | − | 1.58387i | ||||
\(933\) | 11907.0 | − | 20623.5i | 0.417811 | − | 0.723670i | ||||
\(934\) | −3150.00 | + | 5455.96i | −0.110355 | + | 0.191140i | ||||
\(935\) | 14014.0 | 0.490168 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20846.0 | 0.726797 | 0.363399 | − | 0.931634i | \(-0.381616\pi\) | ||||
0.363399 | + | 0.931634i | \(0.381616\pi\) | |||||||
\(938\) | 15535.0 | − | 26907.4i | 0.540763 | − | 0.936629i | ||||
\(939\) | −37411.5 | + | 64798.6i | −1.30019 | + | 2.25199i | ||||
\(940\) | −6247.50 | − | 10821.0i | −0.216778 | − | 0.375470i | ||||
\(941\) | 41321.0 | 1.43148 | 0.715742 | − | 0.698365i | \(-0.246089\pi\) | ||||
0.715742 | + | 0.698365i | \(0.246089\pi\) | |||||||
\(942\) | −47775.0 | − | 82748.7i | −1.65243 | − | 2.86210i | ||||
\(943\) | −16128.0 | − | 27934.5i | −0.556946 | − | 0.964659i | ||||
\(944\) | 26166.0 | 0.902151 | ||||||||
\(945\) | −1592.50 | − | 2758.29i | −0.0548191 | − | 0.0949494i | ||||
\(946\) | 13065.0 | − | 22629.2i | 0.449027 | − | 0.777738i | ||||
\(947\) | 27483.0 | − | 47602.0i | 0.943060 | − | 1.63343i | 0.183469 | − | 0.983025i | \(-0.441267\pi\) |
0.759590 | − | 0.650402i | \(-0.225399\pi\) | |||||||
\(948\) | −155176. | −5.31633 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −47880.0 | −1.63519 | ||||||||
\(951\) | 24689.0 | − | 42762.6i | 0.841846 | − | 1.45812i | ||||
\(952\) | −22522.5 | + | 39010.1i | −0.766763 | + | 1.32807i | ||||
\(953\) | 22276.5 | + | 38584.0i | 0.757195 | + | 1.31150i | 0.944276 | + | 0.329155i | \(0.106764\pi\) |
−0.187081 | + | 0.982344i | \(0.559903\pi\) | |||||||
\(954\) | −47520.0 | −1.61270 | ||||||||
\(955\) | −1477.00 | − | 2558.24i | −0.0500467 | − | 0.0866834i | ||||
\(956\) | −29554.5 | − | 51189.9i | −0.999854 | − | 1.73180i | ||||
\(957\) | 14924.0 | 0.504101 | ||||||||
\(958\) | −30082.5 | − | 52104.4i | −1.01453 | − | 1.75722i | ||||
\(959\) | −11544.0 | + | 19994.8i | −0.388712 | + | 0.673270i | ||||
\(960\) | −7031.50 | + | 12178.9i | −0.236397 | + | 0.409451i | ||||
\(961\) | 8625.00 | 0.289517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15048.0 | −0.503546 | ||||||||
\(964\) | −13685.0 | + | 23703.1i | −0.457224 | + | 0.791936i | ||||
\(965\) | 1722.00 | − | 2982.59i | 0.0574437 | − | 0.0994954i | ||||
\(966\) | −21840.0 | − | 37828.0i | −0.727423 | − | 1.25993i | ||||
\(967\) | 27907.0 | 0.928054 | 0.464027 | − | 0.885821i | \(-0.346404\pi\) | ||||
0.464027 | + | 0.885821i | \(0.346404\pi\) | |||||||
\(968\) | 14737.5 | + | 25526.1i | 0.489340 | + | 0.847562i | ||||
\(969\) | 33957.0 | + | 58815.2i | 1.12575 | + | 1.94986i | ||||
\(970\) | −2450.00 | −0.0810977 | ||||||||
\(971\) | 8221.50 | + | 14240.1i | 0.271720 | + | 0.470634i | 0.969302 | − | 0.245871i | \(-0.0790741\pi\) |
−0.697582 | + | 0.716505i | \(0.745741\pi\) | |||||||
\(972\) | −41888.0 | + | 72552.1i | −1.38226 | + | 2.39415i | ||||
\(973\) | 12148.5 | − | 21041.8i | 0.400270 | − | 0.693289i | ||||
\(974\) | 11400.0 | 0.375030 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4984.00 | −0.163457 | ||||||||
\(977\) | −22707.0 | + | 39329.7i | −0.743563 | + | 1.28789i | 0.207300 | + | 0.978277i | \(0.433532\pi\) |
−0.950863 | + | 0.309612i | \(0.899801\pi\) | |||||||
\(978\) | 9520.00 | − | 16489.1i | 0.311264 | − | 0.539125i | ||||
\(979\) | −15470.0 | − | 26794.8i | −0.505029 | − | 0.874736i | ||||
\(980\) | −20706.0 | −0.674927 | ||||||||
\(981\) | 4103.00 | + | 7106.60i | 0.133536 | + | 0.231291i | ||||
\(982\) | −41917.5 | − | 72603.2i | −1.36216 | − | 2.35933i | ||||
\(983\) | 8981.00 | 0.291403 | 0.145702 | − | 0.989329i | \(-0.453456\pi\) | ||||
0.145702 | + | 0.989329i | \(0.453456\pi\) | |||||||
\(984\) | −52920.0 | − | 91660.1i | −1.71446 | − | 2.96953i | ||||
\(985\) | 10468.5 | − | 18132.0i | 0.338634 | − | 0.586531i | ||||
\(986\) | 15785.0 | − | 27340.4i | 0.509834 | − | 0.883059i | ||||
\(987\) | −9555.00 | −0.308145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19296.0 | 0.620402 | ||||||||
\(990\) | −10010.0 | + | 17337.8i | −0.321352 | + | 0.556598i | ||||
\(991\) | 8707.00 | − | 15081.0i | 0.279099 | − | 0.483413i | −0.692062 | − | 0.721838i | \(-0.743298\pi\) |
0.971161 | + | 0.238424i | \(0.0766309\pi\) | |||||||
\(992\) | 8330.00 | + | 14428.0i | 0.266611 | + | 0.461783i | ||||
\(993\) | 67928.0 | 2.17083 | ||||||||
\(994\) | 292.500 | + | 506.625i | 0.00933354 | + | 0.0161662i | ||||
\(995\) | 245.000 | + | 424.352i | 0.00780605 | + | 0.0135205i | ||||
\(996\) | −36652.0 | −1.16603 | ||||||||
\(997\) | 11851.0 | + | 20526.5i | 0.376454 | + | 0.652038i | 0.990544 | − | 0.137199i | \(-0.0438099\pi\) |
−0.614089 | + | 0.789237i | \(0.710477\pi\) | |||||||
\(998\) | 32100.0 | − | 55598.8i | 1.01814 | − | 1.76348i | ||||
\(999\) | −2292.50 | + | 3970.73i | −0.0726041 | + | 0.125754i |
(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 | 169.4.c.a.22.1 | 2 | ||
13.2 | odd | 12 | 169.4.e.e.23.1 | 4 | |||
13.3 | even | 3 | inner | 169.4.c.a.146.1 | 2 | ||
13.4 | even | 6 | 13.4.a.a.1.1 | ✓ | 1 | ||
13.5 | odd | 4 | 169.4.e.e.147.2 | 4 | |||
13.6 | odd | 12 | 169.4.b.a.168.1 | 2 | |||
13.7 | odd | 12 | 169.4.b.a.168.2 | 2 | |||
13.8 | odd | 4 | 169.4.e.e.147.1 | 4 | |||
13.9 | even | 3 | 169.4.a.e.1.1 | 1 | |||
13.10 | even | 6 | 169.4.c.e.146.1 | 2 | |||
13.11 | odd | 12 | 169.4.e.e.23.2 | 4 | |||
13.12 | even | 2 | 169.4.c.e.22.1 | 2 | |||
39.17 | odd | 6 | 117.4.a.b.1.1 | 1 | |||
39.35 | odd | 6 | 1521.4.a.a.1.1 | 1 | |||
52.43 | odd | 6 | 208.4.a.g.1.1 | 1 | |||
65.4 | even | 6 | 325.4.a.d.1.1 | 1 | |||
65.17 | odd | 12 | 325.4.b.b.274.1 | 2 | |||
65.43 | odd | 12 | 325.4.b.b.274.2 | 2 | |||
91.69 | odd | 6 | 637.4.a.a.1.1 | 1 | |||
104.43 | odd | 6 | 832.4.a.a.1.1 | 1 | |||
104.69 | even | 6 | 832.4.a.r.1.1 | 1 | |||
143.43 | odd | 6 | 1573.4.a.a.1.1 | 1 | |||
156.95 | even | 6 | 1872.4.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.a.1.1 | ✓ | 1 | 13.4 | even | 6 | ||
117.4.a.b.1.1 | 1 | 39.17 | odd | 6 | |||
169.4.a.e.1.1 | 1 | 13.9 | even | 3 | |||
169.4.b.a.168.1 | 2 | 13.6 | odd | 12 | |||
169.4.b.a.168.2 | 2 | 13.7 | odd | 12 | |||
169.4.c.a.22.1 | 2 | 1.1 | even | 1 | trivial | ||
169.4.c.a.146.1 | 2 | 13.3 | even | 3 | inner | ||
169.4.c.e.22.1 | 2 | 13.12 | even | 2 | |||
169.4.c.e.146.1 | 2 | 13.10 | even | 6 | |||
169.4.e.e.23.1 | 4 | 13.2 | odd | 12 | |||
169.4.e.e.23.2 | 4 | 13.11 | odd | 12 | |||
169.4.e.e.147.1 | 4 | 13.8 | odd | 4 | |||
169.4.e.e.147.2 | 4 | 13.5 | odd | 4 | |||
208.4.a.g.1.1 | 1 | 52.43 | odd | 6 | |||
325.4.a.d.1.1 | 1 | 65.4 | even | 6 | |||
325.4.b.b.274.1 | 2 | 65.17 | odd | 12 | |||
325.4.b.b.274.2 | 2 | 65.43 | odd | 12 | |||
637.4.a.a.1.1 | 1 | 91.69 | odd | 6 | |||
832.4.a.a.1.1 | 1 | 104.43 | odd | 6 | |||
832.4.a.r.1.1 | 1 | 104.69 | even | 6 | |||
1521.4.a.a.1.1 | 1 | 39.35 | odd | 6 | |||
1573.4.a.a.1.1 | 1 | 143.43 | odd | 6 | |||
1872.4.a.k.1.1 | 1 | 156.95 | even | 6 |