Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
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([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.e.147.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.33013 | + | 2.50000i | −1.53093 | + | 0.883883i | −0.531612 | + | 0.846988i | \(0.678414\pi\) |
−0.999319 | + | 0.0368954i | \(0.988253\pi\) | |||||||
\(3\) | 3.50000 | + | 6.06218i | 0.673575 | + | 1.16667i | 0.976883 | + | 0.213774i | \(0.0685756\pi\) |
−0.303308 | + | 0.952893i | \(0.598091\pi\) | |||||||
\(4\) | 8.50000 | − | 14.7224i | 1.06250 | − | 1.84030i | ||||
\(5\) | − | 7.00000i | − | 0.626099i | −0.949737 | − | 0.313050i | \(-0.898649\pi\) | ||
0.949737 | − | 0.313050i | \(-0.101351\pi\) | |||||||
\(6\) | −30.3109 | − | 17.5000i | −2.06239 | − | 1.19072i | ||||
\(7\) | −11.2583 | − | 6.50000i | −0.607893 | − | 0.350967i | 0.164248 | − | 0.986419i | \(-0.447480\pi\) |
−0.772140 | + | 0.635452i | \(0.780814\pi\) | |||||||
\(8\) | 45.0000i | 1.98874i | ||||||||
\(9\) | −11.0000 | + | 19.0526i | −0.407407 | + | 0.705650i | ||||
\(10\) | 17.5000 | + | 30.3109i | 0.553399 | + | 0.958514i | ||||
\(11\) | 22.5167 | − | 13.0000i | 0.617184 | − | 0.356332i | −0.158588 | − | 0.987345i | \(-0.550694\pi\) |
0.775772 | + | 0.631013i | \(0.217361\pi\) | |||||||
\(12\) | 119.000 | 2.86270 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 65.0000 | 1.24086 | ||||||||
\(15\) | 42.4352 | − | 24.5000i | 0.730449 | − | 0.421725i | ||||
\(16\) | −44.5000 | − | 77.0763i | −0.695312 | − | 1.20432i | ||||
\(17\) | 38.5000 | − | 66.6840i | 0.549272 | − | 0.951367i | −0.449053 | − | 0.893505i | \(-0.648238\pi\) |
0.998325 | − | 0.0578615i | \(-0.0184282\pi\) | |||||||
\(18\) | − | 110.000i | − | 1.44040i | ||||||
\(19\) | 109.119 | + | 63.0000i | 1.31756 | + | 0.760694i | 0.983336 | − | 0.181799i | \(-0.0581920\pi\) |
0.334225 | + | 0.942493i | \(0.391525\pi\) | |||||||
\(20\) | −103.057 | − | 59.5000i | −1.15221 | − | 0.665230i | ||||
\(21\) | − | 91.0000i | − | 0.945611i | ||||||
\(22\) | −65.0000 | + | 112.583i | −0.629911 | + | 1.09104i | ||||
\(23\) | −48.0000 | − | 83.1384i | −0.435161 | − | 0.753720i | 0.562148 | − | 0.827037i | \(-0.309975\pi\) |
−0.997309 | + | 0.0733164i | \(0.976642\pi\) | |||||||
\(24\) | −272.798 | + | 157.500i | −2.32019 | + | 1.33956i | ||||
\(25\) | 76.0000 | 0.608000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | −191.392 | + | 110.500i | −1.29177 | + | 0.745805i | ||||
\(29\) | 41.0000 | + | 71.0141i | 0.262535 | + | 0.454724i | 0.966915 | − | 0.255099i | \(-0.0821082\pi\) |
−0.704380 | + | 0.709823i | \(0.748775\pi\) | |||||||
\(30\) | −122.500 | + | 212.176i | −0.745511 | + | 1.29126i | ||||
\(31\) | 196.000i | 1.13557i | 0.823177 | + | 0.567785i | \(0.192199\pi\) | ||||
−0.823177 | + | 0.567785i | \(0.807801\pi\) | |||||||
\(32\) | 73.6122 | + | 42.5000i | 0.406654 | + | 0.234782i | ||||
\(33\) | 157.617 | + | 91.0000i | 0.831440 | + | 0.480032i | ||||
\(34\) | 385.000i | 1.94197i | ||||||||
\(35\) | −45.5000 | + | 78.8083i | −0.219740 | + | 0.380601i | ||||
\(36\) | 187.000 | + | 323.894i | 0.865741 | + | 1.49951i | ||||
\(37\) | 113.449 | − | 65.5000i | 0.504080 | − | 0.291031i | −0.226317 | − | 0.974054i | \(-0.572669\pi\) |
0.730397 | + | 0.683023i | \(0.239335\pi\) | |||||||
\(38\) | −630.000 | −2.68946 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 315.000 | 1.24515 | ||||||||
\(41\) | 290.985 | − | 168.000i | 1.10839 | − | 0.639932i | 0.169981 | − | 0.985447i | \(-0.445629\pi\) |
0.938413 | + | 0.345516i | \(0.112296\pi\) | |||||||
\(42\) | 227.500 | + | 394.042i | 0.835810 | + | 1.44767i | ||||
\(43\) | −100.500 | + | 174.071i | −0.356421 | + | 0.617339i | −0.987360 | − | 0.158493i | \(-0.949336\pi\) |
0.630939 | + | 0.775832i | \(0.282670\pi\) | |||||||
\(44\) | − | 442.000i | − | 1.51441i | ||||||
\(45\) | 133.368 | + | 77.0000i | 0.441807 | + | 0.255077i | ||||
\(46\) | 415.692 | + | 240.000i | 1.33240 | + | 0.769262i | ||||
\(47\) | 105.000i | 0.325869i | 0.986637 | + | 0.162934i | \(0.0520959\pi\) | ||||
−0.986637 | + | 0.162934i | \(0.947904\pi\) | |||||||
\(48\) | 311.500 | − | 539.534i | 0.936691 | − | 1.62240i | ||||
\(49\) | −87.0000 | − | 150.688i | −0.253644 | − | 0.439325i | ||||
\(50\) | −329.090 | + | 190.000i | −0.930806 | + | 0.537401i | ||||
\(51\) | 539.000 | 1.47990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.000 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689126\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689126\pi\) | |||||||
\(54\) | −151.554 | + | 87.5000i | −0.381925 | + | 0.220504i | ||||
\(55\) | −91.0000 | − | 157.617i | −0.223099 | − | 0.386419i | ||||
\(56\) | 292.500 | − | 506.625i | 0.697981 | − | 1.20894i | ||||
\(57\) | 882.000i | 2.04954i | ||||||||
\(58\) | −355.070 | − | 205.000i | −0.803845 | − | 0.464100i | ||||
\(59\) | −254.611 | − | 147.000i | −0.561824 | − | 0.324369i | 0.192054 | − | 0.981384i | \(-0.438485\pi\) |
−0.753877 | + | 0.657015i | \(0.771819\pi\) | |||||||
\(60\) | − | 833.000i | − | 1.79233i | ||||||
\(61\) | 28.0000 | − | 48.4974i | 0.0587710 | − | 0.101794i | −0.835143 | − | 0.550033i | \(-0.814615\pi\) |
0.893914 | + | 0.448239i | \(0.147948\pi\) | |||||||
\(62\) | −490.000 | − | 848.705i | −1.00371 | − | 1.73848i | ||||
\(63\) | 247.683 | − | 143.000i | 0.495320 | − | 0.285973i | ||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −910.000 | −1.69717 | ||||||||
\(67\) | 413.960 | − | 239.000i | 0.754825 | − | 0.435798i | −0.0726096 | − | 0.997360i | \(-0.523133\pi\) |
0.827435 | + | 0.561562i | \(0.189799\pi\) | |||||||
\(68\) | −654.500 | − | 1133.63i | −1.16720 | − | 2.02165i | ||||
\(69\) | 336.000 | − | 581.969i | 0.586227 | − | 1.01537i | ||||
\(70\) | − | 455.000i | − | 0.776899i | ||||||
\(71\) | −7.79423 | − | 4.50000i | −0.0130282 | − | 0.00752186i | 0.493472 | − | 0.869762i | \(-0.335728\pi\) |
−0.506500 | + | 0.862240i | \(0.669061\pi\) | |||||||
\(72\) | −857.365 | − | 495.000i | −1.40335 | − | 0.810227i | ||||
\(73\) | − | 98.0000i | − | 0.157124i | −0.996909 | − | 0.0785619i | \(-0.974967\pi\) | ||
0.996909 | − | 0.0785619i | \(-0.0250328\pi\) | |||||||
\(74\) | −327.500 | + | 567.247i | −0.514474 | + | 0.891096i | ||||
\(75\) | 266.000 | + | 460.726i | 0.409534 | + | 0.709333i | ||||
\(76\) | 1855.03 | − | 1071.00i | 2.79982 | − | 1.61648i | ||||
\(77\) | −338.000 | −0.500243 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1304.00 | 1.85711 | 0.928554 | − | 0.371198i | \(-0.121053\pi\) | ||||
0.928554 | + | 0.371198i | \(0.121053\pi\) | |||||||
\(80\) | −539.534 | + | 311.500i | −0.754021 | + | 0.435334i | ||||
\(81\) | 419.500 | + | 726.595i | 0.575446 | + | 0.996701i | ||||
\(82\) | −840.000 | + | 1454.92i | −1.13125 | + | 1.95938i | ||||
\(83\) | − | 308.000i | − | 0.407318i | −0.979042 | − | 0.203659i | \(-0.934717\pi\) | ||
0.979042 | − | 0.203659i | \(-0.0652834\pi\) | |||||||
\(84\) | −1339.74 | − | 773.500i | −1.74021 | − | 1.00471i | ||||
\(85\) | −466.788 | − | 269.500i | −0.595650 | − | 0.343899i | ||||
\(86\) | − | 1005.00i | − | 1.26014i | ||||||
\(87\) | −287.000 | + | 497.099i | −0.353674 | + | 0.612581i | ||||
\(88\) | 585.000 | + | 1013.25i | 0.708650 | + | 1.22742i | ||||
\(89\) | 1030.57 | − | 595.000i | 1.22742 | − | 0.708650i | 0.260929 | − | 0.965358i | \(-0.415971\pi\) |
0.966489 | + | 0.256708i | \(0.0826378\pi\) | |||||||
\(90\) | −770.000 | −0.901835 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1632.00 | −1.84943 | ||||||||
\(93\) | −1188.19 | + | 686.000i | −1.32483 | + | 0.764891i | ||||
\(94\) | −262.500 | − | 454.663i | −0.288030 | − | 0.498882i | ||||
\(95\) | 441.000 | − | 763.834i | 0.476270 | − | 0.824924i | ||||
\(96\) | 595.000i | 0.632572i | ||||||||
\(97\) | −60.6218 | − | 35.0000i | −0.0634558 | − | 0.0366362i | 0.467936 | − | 0.883762i | \(-0.344998\pi\) |
−0.531392 | + | 0.847126i | \(0.678331\pi\) | |||||||
\(98\) | 753.442 | + | 435.000i | 0.776624 | + | 0.448384i | ||||
\(99\) | 572.000i | 0.580689i | ||||||||
\(100\) | 646.000 | − | 1118.90i | 0.646000 | − | 1.11890i | ||||
\(101\) | 210.000 | + | 363.731i | 0.206889 | + | 0.358342i | 0.950733 | − | 0.310011i | \(-0.100333\pi\) |
−0.743844 | + | 0.668353i | \(0.766999\pi\) | |||||||
\(102\) | −2333.94 | + | 1347.50i | −2.26563 | + | 1.30806i | ||||
\(103\) | −588.000 | −0.562499 | −0.281249 | − | 0.959635i | \(-0.590749\pi\) | ||||
−0.281249 | + | 0.959635i | \(0.590749\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −637.000 | −0.592046 | ||||||||
\(106\) | 1870.61 | − | 1080.00i | 1.71406 | − | 0.989612i | ||||
\(107\) | 342.000 | + | 592.361i | 0.308994 | + | 0.535194i | 0.978143 | − | 0.207935i | \(-0.0666743\pi\) |
−0.669148 | + | 0.743129i | \(0.733341\pi\) | |||||||
\(108\) | 297.500 | − | 515.285i | 0.265064 | − | 0.459105i | ||||
\(109\) | 373.000i | 0.327770i | 0.986479 | + | 0.163885i | \(0.0524026\pi\) | ||||
−0.986479 | + | 0.163885i | \(0.947597\pi\) | |||||||
\(110\) | 788.083 | + | 455.000i | 0.683098 | + | 0.394387i | ||||
\(111\) | 794.145 | + | 458.500i | 0.679071 | + | 0.392062i | ||||
\(112\) | 1157.00i | 0.976127i | ||||||||
\(113\) | 867.000 | − | 1501.69i | 0.721774 | − | 1.25015i | −0.238514 | − | 0.971139i | \(-0.576660\pi\) |
0.960288 | − | 0.279011i | \(-0.0900065\pi\) | |||||||
\(114\) | −2205.00 | − | 3819.17i | −1.81155 | − | 3.13770i | ||||
\(115\) | −581.969 | + | 336.000i | −0.471903 | + | 0.272454i | ||||
\(116\) | 1394.00 | 1.11577 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1470.00 | 1.14682 | ||||||||
\(119\) | −866.891 | + | 500.500i | −0.667797 | + | 0.385553i | ||||
\(120\) | 1102.50 | + | 1909.59i | 0.838700 | + | 1.45267i | ||||
\(121\) | −327.500 | + | 567.247i | −0.246056 | + | 0.426181i | ||||
\(122\) | 280.000i | 0.207787i | ||||||||
\(123\) | 2036.89 | + | 1176.00i | 1.49317 | + | 0.862084i | ||||
\(124\) | 2885.60 | + | 1666.00i | 2.08979 | + | 1.20654i | ||||
\(125\) | − | 1407.00i | − | 1.00677i | ||||||
\(126\) | −715.000 | + | 1238.42i | −0.505534 | + | 0.875610i | ||||
\(127\) | 946.000 | + | 1638.52i | 0.660976 | + | 1.14484i | 0.980360 | + | 0.197218i | \(0.0631907\pi\) |
−0.319384 | + | 0.947625i | \(0.603476\pi\) | |||||||
\(128\) | −1831.64 | + | 1057.50i | −1.26481 | + | 0.730240i | ||||
\(129\) | −1407.00 | −0.960306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1435.00 | 0.957073 | 0.478536 | − | 0.878068i | \(-0.341167\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341167\pi\) | |||||||
\(132\) | 2679.48 | − | 1547.00i | 1.76681 | − | 1.02007i | ||||
\(133\) | −819.000 | − | 1418.55i | −0.533957 | − | 0.924841i | ||||
\(134\) | −1195.00 | + | 2069.80i | −0.770390 | + | 1.33435i | ||||
\(135\) | − | 245.000i | − | 0.156194i | ||||||
\(136\) | 3000.78 | + | 1732.50i | 1.89202 | + | 1.09236i | ||||
\(137\) | −1538.06 | − | 888.000i | −0.959164 | − | 0.553773i | −0.0632482 | − | 0.997998i | \(-0.520146\pi\) |
−0.895916 | + | 0.444224i | \(0.853479\pi\) | |||||||
\(138\) | 3360.00i | 2.07262i | ||||||||
\(139\) | 934.500 | − | 1618.60i | 0.570239 | − | 0.987683i | −0.426302 | − | 0.904581i | \(-0.640184\pi\) |
0.996541 | − | 0.0831023i | \(-0.0264828\pi\) | |||||||
\(140\) | 773.500 | + | 1339.74i | 0.466948 | + | 0.808777i | ||||
\(141\) | −636.529 | + | 367.500i | −0.380180 | + | 0.219497i | ||||
\(142\) | 45.0000 | 0.0265938 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1958.00 | 1.13310 | ||||||||
\(145\) | 497.099 | − | 287.000i | 0.284702 | − | 0.164373i | ||||
\(146\) | 245.000 | + | 424.352i | 0.138879 | + | 0.240546i | ||||
\(147\) | 609.000 | − | 1054.82i | 0.341697 | − | 0.591837i | ||||
\(148\) | − | 2227.00i | − | 1.23688i | ||||||
\(149\) | −2135.62 | − | 1233.00i | −1.17421 | − | 0.677928i | −0.219539 | − | 0.975604i | \(-0.570455\pi\) |
−0.954667 | + | 0.297676i | \(0.903789\pi\) | |||||||
\(150\) | −2303.63 | − | 1330.00i | −1.25394 | − | 0.723960i | ||||
\(151\) | 3323.00i | 1.79087i | 0.445189 | + | 0.895437i | \(0.353137\pi\) | ||||
−0.445189 | + | 0.895437i | \(0.646863\pi\) | |||||||
\(152\) | −2835.00 | + | 4910.36i | −1.51282 | + | 2.62028i | ||||
\(153\) | 847.000 | + | 1467.05i | 0.447555 | + | 0.775188i | ||||
\(154\) | 1463.58 | − | 845.000i | 0.765837 | − | 0.442156i | ||||
\(155\) | 1372.00 | 0.710979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2730.00 | −1.38776 | −0.693878 | − | 0.720092i | \(-0.744099\pi\) | ||||
−0.693878 | + | 0.720092i | \(0.744099\pi\) | |||||||
\(158\) | −5646.49 | + | 3260.00i | −2.84310 | + | 1.64147i | ||||
\(159\) | −1512.00 | − | 2618.86i | −0.754147 | − | 1.30622i | ||||
\(160\) | 297.500 | − | 515.285i | 0.146997 | − | 0.254605i | ||||
\(161\) | 1248.00i | 0.610908i | ||||||||
\(162\) | −3632.98 | − | 2097.50i | −1.76194 | − | 1.01725i | ||||
\(163\) | −471.118 | − | 272.000i | −0.226385 | − | 0.130704i | 0.382518 | − | 0.923948i | \(-0.375057\pi\) |
−0.608903 | + | 0.793244i | \(0.708390\pi\) | |||||||
\(164\) | − | 5712.00i | − | 2.71971i | ||||||
\(165\) | 637.000 | − | 1103.32i | 0.300548 | − | 0.520564i | ||||
\(166\) | 770.000 | + | 1333.68i | 0.360022 | + | 0.623576i | ||||
\(167\) | −1406.43 | + | 812.000i | −0.651691 | + | 0.376254i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.137413 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(168\) | 4095.00 | 1.88057 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2695.00 | 1.21587 | ||||||||
\(171\) | −2400.62 | + | 1386.00i | −1.07357 | + | 0.619825i | ||||
\(172\) | 1708.50 | + | 2959.21i | 0.757395 | + | 1.31185i | ||||
\(173\) | −168.000 | + | 290.985i | −0.0738312 | + | 0.127879i | −0.900577 | − | 0.434696i | \(-0.856856\pi\) |
0.826746 | + | 0.562575i | \(0.190189\pi\) | |||||||
\(174\) | − | 2870.00i | − | 1.25043i | ||||||
\(175\) | −855.633 | − | 494.000i | −0.369599 | − | 0.213388i | ||||
\(176\) | −2003.98 | − | 1157.00i | −0.858272 | − | 0.495524i | ||||
\(177\) | − | 2058.00i | − | 0.873948i | ||||||
\(178\) | −2975.00 | + | 5152.85i | −1.25273 | + | 2.16979i | ||||
\(179\) | −1514.50 | − | 2623.19i | −0.632397 | − | 1.09534i | −0.987060 | − | 0.160350i | \(-0.948738\pi\) |
0.354663 | − | 0.934994i | \(-0.384595\pi\) | |||||||
\(180\) | 2267.25 | − | 1309.00i | 0.938840 | − | 0.542039i | ||||
\(181\) | 28.0000 | 0.0114985 | 0.00574924 | − | 0.999983i | \(-0.498170\pi\) | ||||
0.00574924 | + | 0.999983i | \(0.498170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 392.000 | 0.158347 | ||||||||
\(184\) | 3741.23 | − | 2160.00i | 1.49895 | − | 0.865420i | ||||
\(185\) | −458.500 | − | 794.145i | −0.182214 | − | 0.315604i | ||||
\(186\) | 3430.00 | − | 5940.93i | 1.35215 | − | 2.34199i | ||||
\(187\) | − | 2002.00i | − | 0.782892i | ||||||
\(188\) | 1545.86 | + | 892.500i | 0.599697 | + | 0.346235i | ||||
\(189\) | −394.042 | − | 227.500i | −0.151652 | − | 0.0875566i | ||||
\(190\) | 4410.00i | 1.68387i | ||||||||
\(191\) | −211.000 | + | 365.463i | −0.0799342 | + | 0.138450i | −0.903221 | − | 0.429175i | \(-0.858804\pi\) |
0.823287 | + | 0.567625i | \(0.192138\pi\) | |||||||
\(192\) | 1004.50 | + | 1739.85i | 0.377571 | + | 0.653971i | ||||
\(193\) | −426.084 | + | 246.000i | −0.158913 | + | 0.0917485i | −0.577348 | − | 0.816498i | \(-0.695912\pi\) |
0.418435 | + | 0.908247i | \(0.362579\pi\) | |||||||
\(194\) | 350.000 | 0.129529 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2958.00 | −1.07799 | ||||||||
\(197\) | 2590.28 | − | 1495.50i | 0.936802 | − | 0.540863i | 0.0478455 | − | 0.998855i | \(-0.484765\pi\) |
0.888956 | + | 0.457992i | \(0.151431\pi\) | |||||||
\(198\) | −1430.00 | − | 2476.83i | −0.513261 | − | 0.888994i | ||||
\(199\) | −35.0000 | + | 60.6218i | −0.0124678 | + | 0.0215948i | −0.872192 | − | 0.489164i | \(-0.837302\pi\) |
0.859724 | + | 0.510759i | \(0.170635\pi\) | |||||||
\(200\) | 3420.00i | 1.20915i | ||||||||
\(201\) | 2897.72 | + | 1673.00i | 1.01686 | + | 0.587086i | ||||
\(202\) | −1818.65 | − | 1050.00i | −0.633465 | − | 0.365731i | ||||
\(203\) | − | 1066.00i | − | 0.368564i | ||||||
\(204\) | 4581.50 | − | 7935.39i | 1.57240 | − | 2.72347i | ||||
\(205\) | −1176.00 | − | 2036.89i | −0.400661 | − | 0.693964i | ||||
\(206\) | 2546.11 | − | 1470.00i | 0.861147 | − | 0.497183i | ||||
\(207\) | 2112.00 | 0.709150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3276.00 | 1.08424 | ||||||||
\(210\) | 2758.29 | − | 1592.50i | 0.906382 | − | 0.523300i | ||||
\(211\) | −1425.50 | − | 2469.04i | −0.465097 | − | 0.805572i | 0.534109 | − | 0.845416i | \(-0.320647\pi\) |
−0.999206 | + | 0.0398440i | \(0.987314\pi\) | |||||||
\(212\) | −3672.00 | + | 6360.09i | −1.18959 | + | 2.06044i | ||||
\(213\) | − | 63.0000i | − | 0.0202661i | ||||||
\(214\) | −2961.81 | − | 1710.00i | −0.946098 | − | 0.546230i | ||||
\(215\) | 1218.50 | + | 703.500i | 0.386516 | + | 0.223155i | ||||
\(216\) | 1575.00i | 0.496135i | ||||||||
\(217\) | 1274.00 | − | 2206.63i | 0.398547 | − | 0.690304i | ||||
\(218\) | −932.500 | − | 1615.14i | −0.289710 | − | 0.501793i | ||||
\(219\) | 594.093 | − | 343.000i | 0.183311 | − | 0.105835i | ||||
\(220\) | −3094.00 | −0.948170 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4585.00 | −1.38615 | ||||||||
\(223\) | 187.928 | − | 108.500i | 0.0564330 | − | 0.0325816i | −0.471518 | − | 0.881856i | \(-0.656294\pi\) |
0.527951 | + | 0.849275i | \(0.322960\pi\) | |||||||
\(224\) | −552.500 | − | 956.958i | −0.164801 | − | 0.285444i | ||||
\(225\) | −836.000 | + | 1447.99i | −0.247704 | + | 0.429035i | ||||
\(226\) | 8670.00i | 2.55186i | ||||||||
\(227\) | 2230.88 | + | 1288.00i | 0.652285 | + | 0.376597i | 0.789331 | − | 0.613968i | \(-0.210427\pi\) |
−0.137046 | + | 0.990565i | \(0.543761\pi\) | |||||||
\(228\) | 12985.2 | + | 7497.00i | 3.77178 | + | 2.17764i | ||||
\(229\) | − | 455.000i | − | 0.131298i | −0.997843 | − | 0.0656490i | \(-0.979088\pi\) | ||
0.997843 | − | 0.0656490i | \(-0.0209118\pi\) | |||||||
\(230\) | 1680.00 | − | 2909.85i | 0.481634 | − | 0.834215i | ||||
\(231\) | −1183.00 | − | 2049.02i | −0.336951 | − | 0.583616i | ||||
\(232\) | −3195.63 | + | 1845.00i | −0.904326 | + | 0.522113i | ||||
\(233\) | −3061.00 | −0.860656 | −0.430328 | − | 0.902673i | \(-0.641602\pi\) | ||||
−0.430328 | + | 0.902673i | \(0.641602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 735.000 | 0.204026 | ||||||||
\(236\) | −4328.39 | + | 2499.00i | −1.19388 | + | 0.689284i | ||||
\(237\) | 4564.00 | + | 7905.08i | 1.25090 | + | 2.16662i | ||||
\(238\) | 2502.50 | − | 4334.46i | 0.681567 | − | 1.18051i | ||||
\(239\) | − | 3477.00i | − | 0.941039i | −0.882389 | − | 0.470520i | \(-0.844066\pi\) | ||
0.882389 | − | 0.470520i | \(-0.155934\pi\) | |||||||
\(240\) | −3776.74 | − | 2180.50i | −1.01578 | − | 0.586461i | ||||
\(241\) | −1394.30 | − | 805.000i | −0.372676 | − | 0.215164i | 0.301951 | − | 0.953323i | \(-0.402362\pi\) |
−0.674627 | + | 0.738159i | \(0.735695\pi\) | |||||||
\(242\) | − | 3275.00i | − | 0.869938i | ||||||
\(243\) | −2464.00 | + | 4267.77i | −0.650476 | + | 1.12666i | ||||
\(244\) | −476.000 | − | 824.456i | −0.124888 | − | 0.216313i | ||||
\(245\) | −1054.82 | + | 609.000i | −0.275061 | + | 0.158806i | ||||
\(246\) | −11760.0 | −3.04793 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8820.00 | −2.25835 | ||||||||
\(249\) | 1867.15 | − | 1078.00i | 0.475204 | − | 0.274359i | ||||
\(250\) | 3517.50 | + | 6092.49i | 0.889865 | + | 1.54129i | ||||
\(251\) | 504.000 | − | 872.954i | 0.126742 | − | 0.219523i | −0.795671 | − | 0.605730i | \(-0.792881\pi\) |
0.922412 | + | 0.386206i | \(0.126215\pi\) | |||||||
\(252\) | − | 4862.00i | − | 1.21539i | ||||||
\(253\) | −2161.60 | − | 1248.00i | −0.537149 | − | 0.310123i | ||||
\(254\) | −8192.60 | − | 4730.00i | −2.02382 | − | 1.16845i | ||||
\(255\) | − | 3773.00i | − | 0.926566i | ||||||
\(256\) | 4139.50 | − | 7169.82i | 1.01062 | − | 1.75045i | ||||
\(257\) | 3020.50 | + | 5231.66i | 0.733127 | + | 1.26981i | 0.955540 | + | 0.294861i | \(0.0952732\pi\) |
−0.222413 | + | 0.974952i | \(0.571393\pi\) | |||||||
\(258\) | 6092.49 | − | 3517.50i | 1.47016 | − | 0.848798i | ||||
\(259\) | −1703.00 | −0.408569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1804.00 | −0.427834 | ||||||||
\(262\) | −6213.73 | + | 3587.50i | −1.46521 | + | 0.845941i | ||||
\(263\) | 1854.00 | + | 3211.22i | 0.434686 | + | 0.752899i | 0.997270 | − | 0.0738414i | \(-0.0235259\pi\) |
−0.562584 | + | 0.826740i | \(0.690193\pi\) | |||||||
\(264\) | −4095.00 | + | 7092.75i | −0.954658 | + | 1.65352i | ||||
\(265\) | 3024.00i | 0.700992i | ||||||||
\(266\) | 7092.75 | + | 4095.00i | 1.63490 | + | 0.943912i | ||||
\(267\) | 7213.99 | + | 4165.00i | 1.65352 | + | 0.954659i | ||||
\(268\) | − | 8126.00i | − | 1.85214i | ||||||
\(269\) | −4172.00 | + | 7226.12i | −0.945618 | + | 1.63786i | −0.191110 | + | 0.981569i | \(0.561209\pi\) |
−0.754508 | + | 0.656290i | \(0.772125\pi\) | |||||||
\(270\) | 612.500 | + | 1060.88i | 0.138058 | + | 0.239123i | ||||
\(271\) | 1400.36 | − | 808.500i | 0.313897 | − | 0.181228i | −0.334772 | − | 0.942299i | \(-0.608659\pi\) |
0.648669 | + | 0.761071i | \(0.275326\pi\) | |||||||
\(272\) | −6853.00 | −1.52766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8880.00 | 1.95788 | ||||||||
\(275\) | 1711.27 | − | 988.000i | 0.375248 | − | 0.216650i | ||||
\(276\) | −5712.00 | − | 9893.47i | −1.24573 | − | 2.15767i | ||||
\(277\) | −1910.00 | + | 3308.22i | −0.414299 | + | 0.717587i | −0.995355 | − | 0.0962771i | \(-0.969306\pi\) |
0.581056 | + | 0.813864i | \(0.302640\pi\) | |||||||
\(278\) | 9345.00i | 2.01610i | ||||||||
\(279\) | −3734.30 | − | 2156.00i | −0.801315 | − | 0.462639i | ||||
\(280\) | −3546.37 | − | 2047.50i | −0.756916 | − | 0.437005i | ||||
\(281\) | 6214.00i | 1.31920i | 0.751615 | + | 0.659602i | \(0.229275\pi\) | ||||
−0.751615 | + | 0.659602i | \(0.770725\pi\) | |||||||
\(282\) | 1837.50 | − | 3182.64i | 0.388020 | − | 0.672070i | ||||
\(283\) | −2646.00 | − | 4583.01i | −0.555789 | − | 0.962655i | −0.997842 | − | 0.0656661i | \(-0.979083\pi\) |
0.442052 | − | 0.896989i | \(-0.354251\pi\) | |||||||
\(284\) | −132.502 | + | 76.5000i | −0.0276850 | + | 0.0159839i | ||||
\(285\) | 6174.00 | 1.28321 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4368.00 | −0.898379 | ||||||||
\(288\) | −1619.47 | + | 935.000i | −0.331347 | + | 0.191303i | ||||
\(289\) | −508.000 | − | 879.882i | −0.103399 | − | 0.179093i | ||||
\(290\) | −1435.00 | + | 2485.49i | −0.290573 | + | 0.503287i | ||||
\(291\) | − | 490.000i | − | 0.0987090i | ||||||
\(292\) | −1442.80 | − | 833.000i | −0.289155 | − | 0.166944i | ||||
\(293\) | −782.021 | − | 451.500i | −0.155925 | − | 0.0900236i | 0.420007 | − | 0.907521i | \(-0.362028\pi\) |
−0.575933 | + | 0.817497i | \(0.695361\pi\) | |||||||
\(294\) | 6090.00i | 1.20808i | ||||||||
\(295\) | −1029.00 | + | 1782.28i | −0.203087 | + | 0.351757i | ||||
\(296\) | 2947.50 | + | 5105.22i | 0.578784 | + | 1.00248i | ||||
\(297\) | 788.083 | − | 455.000i | 0.153970 | − | 0.0888949i | ||||
\(298\) | 12330.0 | 2.39684 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9044.00 | 1.74052 | ||||||||
\(301\) | 2262.92 | − | 1306.50i | 0.433332 | − | 0.250184i | ||||
\(302\) | −8307.50 | − | 14389.0i | −1.58292 | − | 2.74170i | ||||
\(303\) | −1470.00 | + | 2546.11i | −0.278711 | + | 0.482741i | ||||
\(304\) | − | 11214.0i | − | 2.11568i | ||||||
\(305\) | −339.482 | − | 196.000i | −0.0637334 | − | 0.0367965i | ||||
\(306\) | −7335.24 | − | 4235.00i | −1.37035 | − | 0.791173i | ||||
\(307\) | − | 2114.00i | − | 0.393004i | −0.980503 | − | 0.196502i | \(-0.937042\pi\) | ||
0.980503 | − | 0.196502i | \(-0.0629583\pi\) | |||||||
\(308\) | −2873.00 | + | 4976.18i | −0.531508 | + | 0.920598i | ||||
\(309\) | −2058.00 | − | 3564.56i | −0.378885 | − | 0.656248i | ||||
\(310\) | −5940.93 | + | 3430.00i | −1.08846 | + | 0.628422i | ||||
\(311\) | −3402.00 | −0.620288 | −0.310144 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310144 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10689.0 | −1.93028 | −0.965141 | − | 0.261732i | \(-0.915706\pi\) | ||||
−0.965141 | + | 0.261732i | \(0.915706\pi\) | |||||||
\(314\) | 11821.2 | − | 6825.00i | 2.12456 | − | 1.22661i | ||||
\(315\) | −1001.00 | − | 1733.78i | −0.179047 | − | 0.310119i | ||||
\(316\) | 11084.0 | − | 19198.1i | 1.97318 | − | 3.41764i | ||||
\(317\) | − | 7054.00i | − | 1.24982i | −0.780698 | − | 0.624909i | \(-0.785136\pi\) | ||
0.780698 | − | 0.624909i | \(-0.214864\pi\) | |||||||
\(318\) | 13094.3 | + | 7560.00i | 2.30909 | + | 1.33316i | ||||
\(319\) | 1846.37 | + | 1066.00i | 0.324065 | + | 0.187099i | ||||
\(320\) | − | 2009.00i | − | 0.350958i | ||||||
\(321\) | −2394.00 | + | 4146.53i | −0.416262 | + | 0.720987i | ||||
\(322\) | −3120.00 | − | 5404.00i | −0.539971 | − | 0.935258i | ||||
\(323\) | 8402.18 | − | 4851.00i | 1.44740 | − | 0.835656i | ||||
\(324\) | 14263.0 | 2.44564 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2720.00 | 0.462107 | ||||||||
\(327\) | −2261.19 | + | 1305.50i | −0.382398 | + | 0.220778i | ||||
\(328\) | 7560.00 | + | 13094.3i | 1.27266 | + | 2.20430i | ||||
\(329\) | 682.500 | − | 1182.12i | 0.114369 | − | 0.198093i | ||||
\(330\) | 6370.00i | 1.06260i | ||||||||
\(331\) | −8403.91 | − | 4852.00i | −1.39553 | − | 0.805710i | −0.401610 | − | 0.915811i | \(-0.631549\pi\) |
−0.993920 | + | 0.110101i | \(0.964883\pi\) | |||||||
\(332\) | −4534.51 | − | 2618.00i | −0.749589 | − | 0.432775i | ||||
\(333\) | 2882.00i | 0.474272i | ||||||||
\(334\) | 4060.00 | − | 7032.13i | 0.665130 | − | 1.15204i | ||||
\(335\) | −1673.00 | − | 2897.72i | −0.272853 | − | 0.472595i | ||||
\(336\) | −7013.94 | + | 4049.50i | −1.13881 | + | 0.657495i | ||||
\(337\) | 10449.0 | 1.68900 | 0.844500 | − | 0.535555i | \(-0.179897\pi\) | ||||
0.844500 | + | 0.535555i | \(0.179897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12138.0 | 1.94468 | ||||||||
\(340\) | −7935.39 | + | 4581.50i | −1.26576 | + | 0.730784i | ||||
\(341\) | 2548.00 | + | 4413.27i | 0.404639 | + | 0.700855i | ||||
\(342\) | 6930.00 | − | 12003.1i | 1.09571 | − | 1.89782i | ||||
\(343\) | 6721.00i | 1.05802i | ||||||||
\(344\) | −7833.20 | − | 4522.50i | −1.22773 | − | 0.708828i | ||||
\(345\) | −4073.78 | − | 2352.00i | −0.635725 | − | 0.367036i | ||||
\(346\) | − | 1680.00i | − | 0.261033i | ||||||
\(347\) | 310.500 | − | 537.802i | 0.0480361 | − | 0.0832009i | −0.841008 | − | 0.541023i | \(-0.818037\pi\) |
0.889044 | + | 0.457822i | \(0.151370\pi\) | |||||||
\(348\) | 4879.00 | + | 8450.68i | 0.751557 | + | 1.30173i | ||||
\(349\) | −10808.9 | + | 6240.50i | −1.65784 | + | 0.957153i | −0.684127 | + | 0.729363i | \(0.739817\pi\) |
−0.973710 | + | 0.227790i | \(0.926850\pi\) | |||||||
\(350\) | 4940.00 | 0.754440 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2210.00 | 0.334640 | ||||||||
\(353\) | −1212.44 | + | 700.000i | −0.182809 | + | 0.105545i | −0.588612 | − | 0.808416i | \(-0.700325\pi\) |
0.405803 | + | 0.913961i | \(0.366992\pi\) | |||||||
\(354\) | 5145.00 | + | 8911.40i | 0.772468 | + | 1.33795i | ||||
\(355\) | −31.5000 | + | 54.5596i | −0.00470943 | + | 0.00815697i | ||||
\(356\) | − | 20230.0i | − | 3.01176i | ||||||
\(357\) | −6068.24 | − | 3503.50i | −0.899623 | − | 0.519397i | ||||
\(358\) | 13116.0 | + | 7572.50i | 1.93631 | + | 1.11793i | ||||
\(359\) | 4968.00i | 0.730365i | 0.930936 | + | 0.365182i | \(0.118993\pi\) | ||||
−0.930936 | + | 0.365182i | \(0.881007\pi\) | |||||||
\(360\) | −3465.00 | + | 6001.56i | −0.507282 | + | 0.878638i | ||||
\(361\) | 4508.50 | + | 7808.95i | 0.657312 | + | 1.13850i | ||||
\(362\) | −121.244 | + | 70.0000i | −0.0176034 | + | 0.0101633i | ||||
\(363\) | −4585.00 | −0.662948 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −686.000 | −0.0983750 | ||||||||
\(366\) | −1697.41 | + | 980.000i | −0.242418 | + | 0.139960i | ||||
\(367\) | −4361.00 | − | 7553.47i | −0.620279 | − | 1.07435i | −0.989434 | − | 0.144987i | \(-0.953686\pi\) |
0.369155 | − | 0.929368i | \(-0.379647\pi\) | |||||||
\(368\) | −4272.00 | + | 7399.32i | −0.605145 | + | 1.04814i | ||||
\(369\) | 7392.00i | 1.04285i | ||||||||
\(370\) | 3970.73 | + | 2292.50i | 0.557914 | + | 0.322112i | ||||
\(371\) | 4863.60 | + | 2808.00i | 0.680608 | + | 0.392949i | ||||
\(372\) | 23324.0i | 3.25079i | ||||||||
\(373\) | −5006.00 | + | 8670.65i | −0.694908 | + | 1.20362i | 0.275303 | + | 0.961357i | \(0.411222\pi\) |
−0.970212 | + | 0.242259i | \(0.922112\pi\) | |||||||
\(374\) | 5005.00 | + | 8668.91i | 0.691985 | + | 1.19855i | ||||
\(375\) | 8529.48 | − | 4924.50i | 1.17456 | − | 0.678134i | ||||
\(376\) | −4725.00 | −0.648067 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2275.00 | 0.309559 | ||||||||
\(379\) | −2920.24 | + | 1686.00i | −0.395785 | + | 0.228507i | −0.684664 | − | 0.728859i | \(-0.740051\pi\) |
0.288879 | + | 0.957366i | \(0.406718\pi\) | |||||||
\(380\) | −7497.00 | − | 12985.2i | −1.01207 | − | 1.75296i | ||||
\(381\) | −6622.00 | + | 11469.6i | −0.890434 | + | 1.54228i | ||||
\(382\) | − | 2110.00i | − | 0.282610i | ||||||
\(383\) | 733.524 | + | 423.500i | 0.0978624 | + | 0.0565009i | 0.548132 | − | 0.836392i | \(-0.315339\pi\) |
−0.450270 | + | 0.892892i | \(0.648672\pi\) | |||||||
\(384\) | −12821.5 | − | 7402.50i | −1.70389 | − | 0.983743i | ||||
\(385\) | 2366.00i | 0.313201i | ||||||||
\(386\) | 1230.00 | − | 2130.42i | 0.162190 | − | 0.280921i | ||||
\(387\) | −2211.00 | − | 3829.56i | −0.290417 | − | 0.503017i | ||||
\(388\) | −1030.57 | + | 595.000i | −0.134843 | + | 0.0778519i | ||||
\(389\) | −11314.0 | −1.47466 | −0.737330 | − | 0.675533i | \(-0.763914\pi\) | ||||
−0.737330 | + | 0.675533i | \(0.763914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7392.00 | −0.956086 | ||||||||
\(392\) | 6780.98 | − | 3915.00i | 0.873702 | − | 0.504432i | ||||
\(393\) | 5022.50 | + | 8699.23i | 0.644661 | + | 1.11658i | ||||
\(394\) | −7477.50 | + | 12951.4i | −0.956119 | + | 1.65605i | ||||
\(395\) | − | 9128.00i | − | 1.16273i | ||||||
\(396\) | 8421.23 | + | 4862.00i | 1.06864 | + | 0.616982i | ||||
\(397\) | 1612.54 | + | 931.000i | 0.203856 | + | 0.117697i | 0.598453 | − | 0.801158i | \(-0.295782\pi\) |
−0.394597 | + | 0.918854i | \(0.629116\pi\) | |||||||
\(398\) | − | 350.000i | − | 0.0440802i | ||||||
\(399\) | 5733.00 | − | 9929.85i | 0.719321 | − | 1.24590i | ||||
\(400\) | −3382.00 | − | 5857.80i | −0.422750 | − | 0.732224i | ||||
\(401\) | −5906.29 | + | 3410.00i | −0.735527 | + | 0.424657i | −0.820441 | − | 0.571732i | \(-0.806272\pi\) |
0.0849139 | + | 0.996388i | \(0.472938\pi\) | |||||||
\(402\) | −16730.0 | −2.07566 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7140.00 | 0.879278 | ||||||||
\(405\) | 5086.17 | − | 2936.50i | 0.624034 | − | 0.360286i | ||||
\(406\) | 2665.00 | + | 4615.92i | 0.325768 | + | 0.564246i | ||||
\(407\) | 1703.00 | − | 2949.68i | 0.207407 | − | 0.359239i | ||||
\(408\) | 24255.0i | 2.94314i | ||||||||
\(409\) | 11251.4 | + | 6496.00i | 1.36026 | + | 0.785346i | 0.989658 | − | 0.143446i | \(-0.0458184\pi\) |
0.370601 | + | 0.928792i | \(0.379152\pi\) | |||||||
\(410\) | 10184.5 | + | 5880.00i | 1.22677 | + | 0.708274i | ||||
\(411\) | − | 12432.0i | − | 1.49203i | ||||||
\(412\) | −4998.00 | + | 8656.79i | −0.597655 | + | 1.03517i | ||||
\(413\) | 1911.00 | + | 3309.95i | 0.227686 | + | 0.394363i | ||||
\(414\) | −9145.23 | + | 5280.00i | −1.08566 | + | 0.626806i | ||||
\(415\) | −2156.00 | −0.255021 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13083.0 | 1.53640 | ||||||||
\(418\) | −14185.5 | + | 8190.00i | −1.65989 | + | 0.958340i | ||||
\(419\) | 3671.50 | + | 6359.22i | 0.428078 | + | 0.741452i | 0.996702 | − | 0.0811449i | \(-0.0258577\pi\) |
−0.568625 | + | 0.822597i | \(0.692524\pi\) | |||||||
\(420\) | −5414.50 | + | 9378.19i | −0.629049 | + | 1.08954i | ||||
\(421\) | − | 5059.00i | − | 0.585655i | −0.956165 | − | 0.292827i | \(-0.905404\pi\) | ||
0.956165 | − | 0.292827i | \(-0.0945961\pi\) | |||||||
\(422\) | 12345.2 | + | 7127.50i | 1.42406 | + | 0.822183i | ||||
\(423\) | −2000.52 | − | 1155.00i | −0.229949 | − | 0.132761i | ||||
\(424\) | − | 19440.0i | − | 2.22663i | ||||||
\(425\) | 2926.00 | − | 5067.98i | 0.333957 | − | 0.578431i | ||||
\(426\) | 157.500 | + | 272.798i | 0.0179129 | + | 0.0310261i | ||||
\(427\) | −630.466 | + | 364.000i | −0.0714530 | + | 0.0412534i | ||||
\(428\) | 11628.0 | 1.31323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7035.00 | −0.788972 | ||||||||
\(431\) | 2808.52 | − | 1621.50i | 0.313879 | − | 0.181218i | −0.334782 | − | 0.942296i | \(-0.608663\pi\) |
0.648661 | + | 0.761078i | \(0.275329\pi\) | |||||||
\(432\) | −1557.50 | − | 2697.67i | −0.173461 | − | 0.300444i | ||||
\(433\) | 5799.50 | − | 10045.0i | 0.643663 | − | 1.11486i | −0.340945 | − | 0.940083i | \(-0.610747\pi\) |
0.984609 | − | 0.174774i | \(-0.0559196\pi\) | |||||||
\(434\) | 12740.0i | 1.40908i | ||||||||
\(435\) | 3479.69 | + | 2009.00i | 0.383536 | + | 0.221435i | ||||
\(436\) | 5491.47 | + | 3170.50i | 0.603196 | + | 0.348256i | ||||
\(437\) | − | 12096.0i | − | 1.32410i | ||||||
\(438\) | −1715.00 | + | 2970.47i | −0.187091 | + | 0.324051i | ||||
\(439\) | −8687.00 | − | 15046.3i | −0.944437 | − | 1.63581i | −0.756874 | − | 0.653560i | \(-0.773275\pi\) |
−0.187563 | − | 0.982253i | \(-0.560059\pi\) | |||||||
\(440\) | 7092.75 | − | 4095.00i | 0.768485 | − | 0.443685i | ||||
\(441\) | 3828.00 | 0.413346 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 989.000 | 0.106070 | 0.0530348 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530348 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(444\) | 13500.5 | − | 7794.50i | 1.44303 | − | 0.833132i | ||||
\(445\) | −4165.00 | − | 7213.99i | −0.443685 | − | 0.768485i | ||||
\(446\) | −542.500 | + | 939.638i | −0.0575967 | + | 0.0997604i | ||||
\(447\) | − | 17262.0i | − | 1.82654i | ||||||
\(448\) | −3231.14 | − | 1865.50i | −0.340752 | − | 0.196733i | ||||
\(449\) | −12534.9 | − | 7237.00i | −1.31750 | − | 0.760657i | −0.334172 | − | 0.942512i | \(-0.608457\pi\) |
−0.983325 | + | 0.181855i | \(0.941790\pi\) | |||||||
\(450\) | − | 8360.00i | − | 0.875765i | ||||||
\(451\) | 4368.00 | − | 7565.60i | 0.456056 | − | 0.789912i | ||||
\(452\) | −14739.0 | − | 25528.7i | −1.53377 | − | 2.65657i | ||||
\(453\) | −20144.6 | + | 11630.5i | −2.08935 | + | 1.20629i | ||||
\(454\) | −12880.0 | −1.33147 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39690.0 | −4.07600 | ||||||||
\(457\) | −1380.44 | + | 797.000i | −0.141301 | + | 0.0815801i | −0.568984 | − | 0.822349i | \(-0.692663\pi\) |
0.427683 | + | 0.903929i | \(0.359330\pi\) | |||||||
\(458\) | 1137.50 | + | 1970.21i | 0.116052 | + | 0.201008i | ||||
\(459\) | 1347.50 | − | 2333.94i | 0.137028 | − | 0.237340i | ||||
\(460\) | 11424.0i | 1.15793i | ||||||||
\(461\) | 5122.54 | + | 2957.50i | 0.517528 | + | 0.298795i | 0.735923 | − | 0.677066i | \(-0.236749\pi\) |
−0.218395 | + | 0.975861i | \(0.570082\pi\) | |||||||
\(462\) | 10245.1 | + | 5915.00i | 1.03170 | + | 0.595651i | ||||
\(463\) | 11072.0i | 1.11136i | 0.831396 | + | 0.555680i | \(0.187542\pi\) | ||||
−0.831396 | + | 0.555680i | \(0.812458\pi\) | |||||||
\(464\) | 3649.00 | − | 6320.25i | 0.365087 | − | 0.632350i | ||||
\(465\) | 4802.00 | + | 8317.31i | 0.478898 | + | 0.829475i | ||||
\(466\) | 13254.5 | − | 7652.50i | 1.31760 | − | 0.760719i | ||||
\(467\) | −1260.00 | −0.124852 | −0.0624260 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624260 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6214.00 | −0.611804 | ||||||||
\(470\) | −3182.64 | + | 1837.50i | −0.312350 | + | 0.180335i | ||||
\(471\) | −9555.00 | − | 16549.7i | −0.934758 | − | 1.61905i | ||||
\(472\) | 6615.00 | − | 11457.5i | 0.645085 | − | 1.11732i | ||||
\(473\) | 5226.00i | 0.508016i | ||||||||
\(474\) | −39525.4 | − | 22820.0i | −3.83009 | − | 2.21130i | ||||
\(475\) | 8293.06 | + | 4788.00i | 0.801077 | + | 0.462502i | ||||
\(476\) | 17017.0i | 1.63860i | ||||||||
\(477\) | 4752.00 | − | 8230.71i | 0.456141 | − | 0.790059i | ||||
\(478\) | 8692.50 | + | 15055.9i | 0.831769 | + | 1.44067i | ||||
\(479\) | 10420.9 | − | 6016.50i | 0.994034 | − | 0.573906i | 0.0875564 | − | 0.996160i | \(-0.472094\pi\) |
0.906478 | + | 0.422254i | \(0.138761\pi\) | |||||||
\(480\) | 4165.00 | 0.396053 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8050.00 | 0.760721 | ||||||||
\(483\) | −7565.60 | + | 4368.00i | −0.712726 | + | 0.411493i | ||||
\(484\) | 5567.50 | + | 9643.19i | 0.522868 | + | 0.905634i | ||||
\(485\) | −245.000 | + | 424.352i | −0.0229379 | + | 0.0397296i | ||||
\(486\) | − | 24640.0i | − | 2.29978i | ||||||
\(487\) | 1974.54 | + | 1140.00i | 0.183727 | + | 0.106075i | 0.589042 | − | 0.808102i | \(-0.299505\pi\) |
−0.405316 | + | 0.914177i | \(0.632838\pi\) | |||||||
\(488\) | 2182.38 | + | 1260.00i | 0.202442 | + | 0.116880i | ||||
\(489\) | − | 3808.00i | − | 0.352155i | ||||||
\(490\) | 3045.00 | − | 5274.09i | 0.280733 | − | 0.486243i | ||||
\(491\) | 8383.50 | + | 14520.6i | 0.770554 | + | 1.33464i | 0.937260 | + | 0.348632i | \(0.113354\pi\) |
−0.166706 | + | 0.986007i | \(0.553313\pi\) | |||||||
\(492\) | 34627.2 | − | 19992.0i | 3.17299 | − | 1.83193i | ||||
\(493\) | 6314.00 | 0.576812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4004.00 | 0.363569 | ||||||||
\(496\) | 15106.9 | − | 8722.00i | 1.36758 | − | 0.789575i | ||||
\(497\) | 58.5000 | + | 101.325i | 0.00527985 | + | 0.00914496i | ||||
\(498\) | −5390.00 | + | 9335.75i | −0.485003 | + | 0.840050i | ||||
\(499\) | 12840.0i | 1.15190i | 0.817485 | + | 0.575949i | \(0.195367\pi\) | ||||
−0.817485 | + | 0.575949i | \(0.804633\pi\) | |||||||
\(500\) | −20714.5 | − | 11959.5i | −1.85276 | − | 1.06969i | ||||
\(501\) | −9844.98 | − | 5684.00i | −0.877926 | − | 0.506871i | ||||
\(502\) | 5040.00i | 0.448100i | ||||||||
\(503\) | 1099.00 | − | 1903.52i | 0.0974195 | − | 0.168735i | −0.813196 | − | 0.581989i | \(-0.802274\pi\) |
0.910616 | + | 0.413254i | \(0.135608\pi\) | |||||||
\(504\) | 6435.00 | + | 11145.7i | 0.568726 | + | 0.985062i | ||||
\(505\) | 2546.11 | − | 1470.00i | 0.224358 | − | 0.129533i | ||||
\(506\) | 12480.0 | 1.09645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32164.0 | 2.80915 | ||||||||
\(509\) | −14779.6 | + | 8533.00i | −1.28702 | + | 0.743062i | −0.978122 | − | 0.208033i | \(-0.933294\pi\) |
−0.308899 | + | 0.951095i | \(0.599961\pi\) | |||||||
\(510\) | 9432.50 | + | 16337.6i | 0.818977 | + | 1.41851i | ||||
\(511\) | −637.000 | + | 1103.32i | −0.0551452 | + | 0.0955144i | ||||
\(512\) | 24475.0i | 2.11260i | ||||||||
\(513\) | 3819.17 | + | 2205.00i | 0.328695 | + | 0.189772i | ||||
\(514\) | −26158.3 | − | 15102.5i | −2.24473 | − | 1.29600i | ||||
\(515\) | 4116.00i | 0.352180i | ||||||||
\(516\) | −11959.5 | + | 20714.5i | −1.02032 | + | 1.76725i | ||||
\(517\) | 1365.00 | + | 2364.25i | 0.116117 | + | 0.201121i | ||||
\(518\) | 7374.21 | − | 4257.50i | 0.625490 | − | 0.361127i | ||||
\(519\) | −2352.00 | −0.198924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2583.00 | 0.217204 | 0.108602 | − | 0.994085i | \(-0.465363\pi\) | ||||
0.108602 | + | 0.994085i | \(0.465363\pi\) | |||||||
\(522\) | 7811.55 | − | 4510.00i | 0.654985 | − | 0.378156i | ||||
\(523\) | −9310.00 | − | 16125.4i | −0.778390 | − | 1.34821i | −0.932869 | − | 0.360215i | \(-0.882703\pi\) |
0.154480 | − | 0.987996i | \(-0.450630\pi\) | |||||||
\(524\) | 12197.5 | − | 21126.7i | 1.01689 | − | 1.76130i | ||||
\(525\) | − | 6916.00i | − | 0.574931i | ||||||
\(526\) | −16056.1 | − | 9270.00i | −1.33095 | − | 0.768424i | ||||
\(527\) | 13070.1 | + | 7546.00i | 1.08034 | + | 0.623736i | ||||
\(528\) | − | 16198.0i | − | 1.33509i | ||||||
\(529\) | 1475.50 | − | 2555.64i | 0.121271 | − | 0.210047i | ||||
\(530\) | −7560.00 | − | 13094.3i | −0.619595 | − | 1.07317i | ||||
\(531\) | 5601.45 | − | 3234.00i | 0.457782 | − | 0.264301i | ||||
\(532\) | −27846.0 | −2.26932 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −41650.0 | −3.37523 | ||||||||
\(535\) | 4146.53 | − | 2394.00i | 0.335084 | − | 0.193461i | ||||
\(536\) | 10755.0 | + | 18628.2i | 0.866689 | + | 1.50115i | ||||
\(537\) | 10601.5 | − | 18362.3i | 0.851934 | − | 1.47559i | ||||
\(538\) | − | 41720.0i | − | 3.34327i | ||||||
\(539\) | −3917.90 | − | 2262.00i | −0.313091 | − | 0.180763i | ||||
\(540\) | −3607.00 | − | 2082.50i | −0.287445 | − | 0.165957i | ||||
\(541\) | 16833.0i | 1.33772i | 0.743388 | + | 0.668861i | \(0.233218\pi\) | ||||
−0.743388 | + | 0.668861i | \(0.766782\pi\) | |||||||
\(542\) | −4042.50 | + | 7001.82i | −0.320369 | + | 0.554896i | ||||
\(543\) | 98.0000 | + | 169.741i | 0.00774509 | + | 0.0134149i | ||||
\(544\) | 5668.14 | − | 3272.50i | 0.446727 | − | 0.257918i | ||||
\(545\) | 2611.00 | 0.205216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8615.00 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(548\) | −26147.0 | + | 15096.0i | −2.03822 | + | 1.17677i | ||||
\(549\) | 616.000 | + | 1066.94i | 0.0478875 | + | 0.0829436i | ||||
\(550\) | −4940.00 | + | 8556.33i | −0.382986 | + | 0.663351i | ||||
\(551\) | 10332.0i | 0.798835i | ||||||||
\(552\) | 26188.6 | + | 15120.0i | 2.01931 | + | 1.16585i | ||||
\(553\) | −14680.9 | − | 8476.00i | −1.12892 | − | 0.651783i | ||||
\(554\) | − | 19100.0i | − | 1.46477i | ||||||
\(555\) | 3209.50 | − | 5559.02i | 0.245470 | − | 0.425166i | ||||
\(556\) | −15886.5 | − | 27516.2i | −1.21176 | − | 2.09883i | ||||
\(557\) | −7391.53 | + | 4267.50i | −0.562278 | + | 0.324632i | −0.754059 | − | 0.656806i | \(-0.771907\pi\) |
0.191781 | + | 0.981438i | \(0.438574\pi\) | |||||||
\(558\) | 21560.0 | 1.63568 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8099.00 | 0.611152 | ||||||||
\(561\) | 12136.5 | − | 7007.00i | 0.913374 | − | 0.527336i | ||||
\(562\) | −15535.0 | − | 26907.4i | −1.16602 | − | 2.01961i | ||||
\(563\) | −2320.50 | + | 4019.22i | −0.173708 | + | 0.300871i | −0.939713 | − | 0.341963i | \(-0.888908\pi\) |
0.766006 | + | 0.642834i | \(0.222241\pi\) | |||||||
\(564\) | 12495.0i | 0.932862i | ||||||||
\(565\) | −10511.8 | − | 6069.00i | −0.782718 | − | 0.451902i | ||||
\(566\) | 22915.0 | + | 13230.0i | 1.70175 | + | 0.982506i | ||||
\(567\) | − | 10907.0i | − | 0.807850i | ||||||
\(568\) | 202.500 | − | 350.740i | 0.0149590 | − | 0.0259097i | ||||
\(569\) | −2396.50 | − | 4150.86i | −0.176567 | − | 0.305823i | 0.764136 | − | 0.645056i | \(-0.223166\pi\) |
−0.940702 | + | 0.339233i | \(0.889832\pi\) | |||||||
\(570\) | −26734.2 | + | 15435.0i | −1.96451 | + | 1.13421i | ||||
\(571\) | 5563.00 | 0.407713 | 0.203857 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203857 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2954.00 | −0.215367 | ||||||||
\(574\) | 18914.0 | − | 10920.0i | 1.37536 | − | 0.794063i | ||||
\(575\) | −3648.00 | − | 6318.52i | −0.264578 | − | 0.458262i | ||||
\(576\) | −3157.00 | + | 5468.08i | −0.228371 | + | 0.395550i | ||||
\(577\) | 24038.0i | 1.73434i | 0.498011 | + | 0.867171i | \(0.334064\pi\) | ||||
−0.498011 | + | 0.867171i | \(0.665936\pi\) | |||||||
\(578\) | 4399.41 | + | 2540.00i | 0.316594 | + | 0.182786i | ||||
\(579\) | −2982.59 | − | 1722.00i | −0.214080 | − | 0.123599i | ||||
\(580\) | − | 9758.00i | − | 0.698584i | ||||||
\(581\) | −2002.00 | + | 3467.57i | −0.142955 | + | 0.247606i | ||||
\(582\) | 1225.00 | + | 2121.76i | 0.0872472 | + | 0.151117i | ||||
\(583\) | −9727.20 | + | 5616.00i | −0.691011 | + | 0.398955i | ||||
\(584\) | 4410.00 | 0.312478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4515.00 | 0.318281 | ||||||||
\(587\) | −18380.5 | + | 10612.0i | −1.29241 | + | 0.746174i | −0.979081 | − | 0.203470i | \(-0.934778\pi\) |
−0.313330 | + | 0.949644i | \(0.601445\pi\) | |||||||
\(588\) | −10353.0 | − | 17931.9i | −0.726106 | − | 1.25765i | ||||
\(589\) | −12348.0 | + | 21387.4i | −0.863821 | + | 1.49618i | ||||
\(590\) | − | 10290.0i | − | 0.718021i | ||||||
\(591\) | 18132.0 | + | 10468.5i | 1.26201 | + | 0.728624i | ||||
\(592\) | −10097.0 | − | 5829.50i | −0.700986 | − | 0.404714i | ||||
\(593\) | − | 4354.00i | − | 0.301513i | −0.988571 | − | 0.150757i | \(-0.951829\pi\) | ||
0.988571 | − | 0.150757i | \(-0.0481710\pi\) | |||||||
\(594\) | −2275.00 | + | 3940.42i | −0.157145 | + | 0.272184i | ||||
\(595\) | 3503.50 | + | 6068.24i | 0.241394 | + | 0.418107i | ||||
\(596\) | −36305.5 | + | 20961.0i | −2.49519 | + | 1.44060i | ||||
\(597\) | −490.000 | −0.0335919 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7310.00 | 0.498629 | 0.249314 | − | 0.968423i | \(-0.419795\pi\) | ||||
0.249314 | + | 0.968423i | \(0.419795\pi\) | |||||||
\(600\) | −20732.6 | + | 11970.0i | −1.41068 | + | 0.814455i | ||||
\(601\) | 3797.50 | + | 6577.46i | 0.257743 | + | 0.446423i | 0.965637 | − | 0.259895i | \(-0.0836880\pi\) |
−0.707894 | + | 0.706318i | \(0.750355\pi\) | |||||||
\(602\) | −6532.50 | + | 11314.6i | −0.442267 | + | 0.766029i | ||||
\(603\) | 10516.0i | 0.710190i | ||||||||
\(604\) | 48922.6 | + | 28245.5i | 3.29575 | + | 1.90280i | ||||
\(605\) | 3970.73 | + | 2292.50i | 0.266831 | + | 0.154055i | ||||
\(606\) | − | 14700.0i | − | 0.985391i | ||||||
\(607\) | 413.000 | − | 715.337i | 0.0276164 | − | 0.0478330i | −0.851887 | − | 0.523726i | \(-0.824542\pi\) |
0.879503 | + | 0.475893i | \(0.157875\pi\) | |||||||
\(608\) | 5355.00 | + | 9275.13i | 0.357194 | + | 0.618678i | ||||
\(609\) | 6462.28 | − | 3731.00i | 0.429992 | − | 0.248256i | ||||
\(610\) | 1960.00 | 0.130095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 28798.0 | 1.90211 | ||||||||
\(613\) | 12635.3 | − | 7295.00i | 0.832521 | − | 0.480656i | −0.0221940 | − | 0.999754i | \(-0.507065\pi\) |
0.854715 | + | 0.519097i | \(0.173732\pi\) | |||||||
\(614\) | 5285.00 | + | 9153.89i | 0.347370 | + | 0.601663i | ||||
\(615\) | 8232.00 | − | 14258.2i | 0.539750 | − | 0.934875i | ||||
\(616\) | − | 15210.0i | − | 0.994851i | ||||||
\(617\) | −4233.13 | − | 2444.00i | −0.276207 | − | 0.159468i | 0.355498 | − | 0.934677i | \(-0.384311\pi\) |
−0.631705 | + | 0.775209i | \(0.717645\pi\) | |||||||
\(618\) | 17822.8 | + | 10290.0i | 1.16009 | + | 0.669781i | ||||
\(619\) | 11004.0i | 0.714520i | 0.934005 | + | 0.357260i | \(0.116289\pi\) | ||||
−0.934005 | + | 0.357260i | \(0.883711\pi\) | |||||||
\(620\) | 11662.0 | − | 20199.2i | 0.755415 | − | 1.30842i | ||||
\(621\) | −1680.00 | − | 2909.85i | −0.108561 | − | 0.188032i | ||||
\(622\) | 14731.1 | − | 8505.00i | 0.949619 | − | 0.548263i | ||||
\(623\) | −15470.0 | −0.994851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | 46284.7 | − | 26722.5i | 2.95513 | − | 1.70614i | ||||
\(627\) | 11466.0 | + | 19859.7i | 0.730316 | + | 1.26494i | ||||
\(628\) | −23205.0 | + | 40192.2i | −1.47449 | + | 2.55389i | ||||
\(629\) | − | 10087.0i | − | 0.639420i | ||||||
\(630\) | 8668.91 | + | 5005.00i | 0.548219 | + | 0.316514i | ||||
\(631\) | −4308.48 | − | 2487.50i | −0.271819 | − | 0.156935i | 0.357895 | − | 0.933762i | \(-0.383495\pi\) |
−0.629714 | + | 0.776827i | \(0.716828\pi\) | |||||||
\(632\) | 58680.0i | 3.69330i | ||||||||
\(633\) | 9978.50 | − | 17283.3i | 0.626556 | − | 1.08523i | ||||
\(634\) | 17635.0 | + | 30544.7i | 1.10469 | + | 1.91338i | ||||
\(635\) | 11469.6 | − | 6622.00i | 0.716786 | − | 0.413836i | ||||
\(636\) | −51408.0 | −3.20513 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10660.0 | −0.661494 | ||||||||
\(639\) | 171.473 | − | 99.0000i | 0.0106156 | − | 0.00612892i | ||||
\(640\) | 7402.50 | + | 12821.5i | 0.457202 | + | 0.791898i | ||||
\(641\) | 1975.00 | − | 3420.80i | 0.121697 | − | 0.210785i | −0.798740 | − | 0.601676i | \(-0.794500\pi\) |
0.920437 | + | 0.390891i | \(0.127833\pi\) | |||||||
\(642\) | − | 23940.0i | − | 1.47171i | ||||||
\(643\) | 3188.71 | + | 1841.00i | 0.195568 | + | 0.112911i | 0.594587 | − | 0.804032i | \(-0.297316\pi\) |
−0.399019 | + | 0.916943i | \(0.630649\pi\) | |||||||
\(644\) | 18373.6 | + | 10608.0i | 1.12426 | + | 0.649090i | ||||
\(645\) | 9849.00i | 0.601247i | ||||||||
\(646\) | −24255.0 | + | 42010.9i | −1.47724 | + | 2.55866i | ||||
\(647\) | 5201.00 | + | 9008.40i | 0.316032 | + | 0.547383i | 0.979656 | − | 0.200683i | \(-0.0643161\pi\) |
−0.663625 | + | 0.748066i | \(0.730983\pi\) | |||||||
\(648\) | −32696.8 | + | 18877.5i | −1.98218 | + | 1.14441i | ||||
\(649\) | −7644.00 | −0.462332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17836.0 | 1.07381 | ||||||||
\(652\) | −8009.00 | + | 4624.00i | −0.481069 | + | 0.277745i | ||||
\(653\) | 15840.0 | + | 27435.7i | 0.949260 | + | 1.64417i | 0.746987 | + | 0.664838i | \(0.231500\pi\) |
0.202273 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(654\) | 6527.50 | − | 11306.0i | 0.390284 | − | 0.675991i | ||||
\(655\) | − | 10045.0i | − | 0.599222i | ||||||
\(656\) | −25897.6 | − | 14952.0i | −1.54136 | − | 0.889905i | ||||
\(657\) | 1867.15 | + | 1078.00i | 0.110874 | + | 0.0640134i | ||||
\(658\) | 6825.00i | 0.404356i | ||||||||
\(659\) | −10970.0 | + | 19000.6i | −0.648453 | + | 1.12315i | 0.335039 | + | 0.942204i | \(0.391250\pi\) |
−0.983492 | + | 0.180949i | \(0.942083\pi\) | |||||||
\(660\) | −10829.0 | − | 18756.4i | −0.638664 | − | 1.10620i | ||||
\(661\) | 27170.7 | − | 15687.0i | 1.59882 | − | 0.923077i | 0.607100 | − | 0.794626i | \(-0.292333\pi\) |
0.991716 | − | 0.128451i | \(-0.0410004\pi\) | |||||||
\(662\) | 48520.0 | 2.84862 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13860.0 | 0.810049 | ||||||||
\(665\) | −9929.85 | + | 5733.00i | −0.579042 | + | 0.334310i | ||||
\(666\) | −7205.00 | − | 12479.4i | −0.419201 | − | 0.726078i | ||||
\(667\) | 3936.00 | − | 6817.35i | 0.228490 | − | 0.395756i | ||||
\(668\) | 27608.0i | 1.59908i | ||||||||
\(669\) | 1315.49 | + | 759.500i | 0.0760237 | + | 0.0438923i | ||||
\(670\) | 14488.6 | + | 8365.00i | 0.835438 | + | 0.482341i | ||||
\(671\) | − | 1456.00i | − | 0.0837679i | ||||||
\(672\) | 3867.50 | − | 6698.71i | 0.222012 | − | 0.384536i | ||||
\(673\) | 9006.50 | + | 15599.7i | 0.515862 | + | 0.893499i | 0.999830 | + | 0.0184136i | \(0.00586157\pi\) |
−0.483969 | + | 0.875085i | \(0.660805\pi\) | |||||||
\(674\) | −45245.5 | + | 26122.5i | −2.58574 | + | 1.49288i | ||||
\(675\) | 2660.00 | 0.151679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10640.0 | −0.604030 | −0.302015 | − | 0.953303i | \(-0.597659\pi\) | ||||
−0.302015 | + | 0.953303i | \(0.597659\pi\) | |||||||
\(678\) | −52559.1 | + | 30345.0i | −2.97717 | + | 1.71887i | ||||
\(679\) | 455.000 | + | 788.083i | 0.0257162 | + | 0.0445418i | ||||
\(680\) | 12127.5 | − | 21005.4i | 0.683924 | − | 1.18459i | ||||
\(681\) | 18032.0i | 1.01467i | ||||||||
\(682\) | −22066.3 | − | 12740.0i | −1.23895 | − | 0.715308i | ||||
\(683\) | −8085.21 | − | 4668.00i | −0.452961 | − | 0.261517i | 0.256119 | − | 0.966645i | \(-0.417556\pi\) |
−0.709080 | + | 0.705128i | \(0.750889\pi\) | |||||||
\(684\) | 47124.0i | 2.63426i | ||||||||
\(685\) | −6216.00 | + | 10766.4i | −0.346717 | + | 0.600531i | ||||
\(686\) | −16802.5 | − | 29102.8i | −0.935164 | − | 1.61975i | ||||
\(687\) | 2758.29 | − | 1592.50i | 0.153181 | − | 0.0884391i | ||||
\(688\) | 17889.0 | 0.991296 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 23520.0 | 1.29767 | ||||||||
\(691\) | 3637.31 | − | 2100.00i | 0.200246 | − | 0.115612i | −0.396524 | − | 0.918024i | \(-0.629784\pi\) |
0.596770 | + | 0.802412i | \(0.296450\pi\) | |||||||
\(692\) | 2856.00 | + | 4946.74i | 0.156891 | + | 0.271744i | ||||
\(693\) | 3718.00 | − | 6439.76i | 0.203803 | − | 0.352996i | ||||
\(694\) | 3105.00i | 0.169833i | ||||||||
\(695\) | −11330.2 | − | 6541.50i | −0.618388 | − | 0.357026i | ||||
\(696\) | −22369.4 | − | 12915.0i | −1.21826 | − | 0.703365i | ||||
\(697\) | − | 25872.0i | − | 1.40599i | ||||||
\(698\) | 31202.5 | − | 54044.3i | 1.69202 | − | 2.93067i | ||||
\(699\) | −10713.5 | − | 18556.3i | −0.579716 | − | 1.00410i | ||||
\(700\) | −14545.8 | + | 8398.00i | −0.785397 | + | 0.453449i | ||||
\(701\) | −9872.00 | −0.531898 | −0.265949 | − | 0.963987i | \(-0.585685\pi\) | ||||
−0.265949 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16506.0 | 0.885541 | ||||||||
\(704\) | 6462.28 | − | 3731.00i | 0.345961 | − | 0.199741i | ||||
\(705\) | 2572.50 | + | 4455.70i | 0.137427 | + | 0.238030i | ||||
\(706\) | 3500.00 | − | 6062.18i | 0.186578 | − | 0.323163i | ||||
\(707\) | − | 5460.00i | − | 0.290445i | ||||||
\(708\) | −30298.8 | − | 17493.0i | −1.60833 | − | 0.928569i | ||||
\(709\) | 24638.4 | + | 14225.0i | 1.30510 | + | 0.753499i | 0.981274 | − | 0.192617i | \(-0.0616976\pi\) |
0.323825 | + | 0.946117i | \(0.395031\pi\) | |||||||
\(710\) | − | 315.000i | − | 0.0166503i | ||||||
\(711\) | −14344.0 | + | 24844.5i | −0.756599 | + | 1.31047i | ||||
\(712\) | 26775.0 | + | 46375.7i | 1.40932 | + | 2.44101i | ||||
\(713\) | 16295.1 | − | 9408.00i | 0.855901 | − | 0.494155i | ||||
\(714\) | 35035.0 | 1.83635 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51493.0 | −2.68769 | ||||||||
\(717\) | 21078.2 | − | 12169.5i | 1.09788 | − | 0.633861i | ||||
\(718\) | −12420.0 | − | 21512.1i | −0.645557 | − | 1.11814i | ||||
\(719\) | 16359.0 | − | 28334.6i | 0.848523 | − | 1.46968i | −0.0340039 | − | 0.999422i | \(-0.510826\pi\) |
0.882527 | − | 0.470263i | \(-0.155841\pi\) | |||||||
\(720\) | − | 13706.0i | − | 0.709434i | ||||||
\(721\) | 6619.90 | + | 3822.00i | 0.341939 | + | 0.197418i | ||||
\(722\) | −39044.8 | − | 22542.5i | −2.01260 | − | 1.16197i | ||||
\(723\) | − | 11270.0i | − | 0.579718i | ||||||
\(724\) | 238.000 | − | 412.228i | 0.0122171 | − | 0.0211607i | ||||
\(725\) | 3116.00 | + | 5397.07i | 0.159621 | + | 0.276472i | ||||
\(726\) | 19853.6 | − | 11462.5i | 1.01493 | − | 0.585969i | ||||
\(727\) | 22834.0 | 1.16488 | 0.582439 | − | 0.812874i | \(-0.302099\pi\) | ||||
0.582439 | + | 0.812874i | \(0.302099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 2970.47 | − | 1715.00i | 0.150605 | − | 0.0869521i | ||||
\(731\) | 7738.50 | + | 13403.5i | 0.391544 | + | 0.678174i | ||||
\(732\) | 3332.00 | − | 5771.19i | 0.168244 | − | 0.291406i | ||||
\(733\) | 7875.00i | 0.396821i | 0.980119 | + | 0.198410i | \(0.0635779\pi\) | ||||
−0.980119 | + | 0.198410i | \(0.936422\pi\) | |||||||
\(734\) | 37767.4 | + | 21805.0i | 1.89921 | + | 1.09651i | ||||
\(735\) | −7383.73 | − | 4263.00i | −0.370548 | − | 0.213936i | ||||
\(736\) | − | 8160.00i | − | 0.408671i | ||||||
\(737\) | 6214.00 | − | 10763.0i | 0.310578 | − | 0.537936i | ||||
\(738\) | −18480.0 | − | 32008.3i | −0.921759 | − | 1.59653i | ||||
\(739\) | 1853.29 | − | 1070.00i | 0.0922524 | − | 0.0532620i | −0.453164 | − | 0.891427i | \(-0.649705\pi\) |
0.545416 | + | 0.838165i | \(0.316371\pi\) | |||||||
\(740\) | −15589.0 | −0.774410 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28080.0 | −1.38928 | ||||||||
\(743\) | 27687.7 | − | 15985.5i | 1.36711 | − | 0.789302i | 0.376552 | − | 0.926395i | \(-0.377109\pi\) |
0.990558 | + | 0.137094i | \(0.0437761\pi\) | |||||||
\(744\) | −30870.0 | − | 53468.4i | −1.52117 | − | 2.63474i | ||||
\(745\) | −8631.00 | + | 14949.3i | −0.424450 | + | 0.735169i | ||||
\(746\) | − | 50060.0i | − | 2.45687i | ||||||
\(747\) | 5868.19 | + | 3388.00i | 0.287424 | + | 0.165944i | ||||
\(748\) | −29474.3 | − | 17017.0i | −1.44076 | − | 0.831822i | ||||
\(749\) | − | 8892.00i | − | 0.433787i | ||||||
\(750\) | −24622.5 | + | 42647.4i | −1.19878 | + | 2.07635i | ||||
\(751\) | −3716.00 | − | 6436.30i | −0.180558 | − | 0.312735i | 0.761513 | − | 0.648150i | \(-0.224457\pi\) |
−0.942071 | + | 0.335415i | \(0.891124\pi\) | |||||||
\(752\) | 8093.01 | − | 4672.50i | 0.392449 | − | 0.226581i | ||||
\(753\) | 7056.00 | 0.341481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23261.0 | 1.12126 | ||||||||
\(756\) | −6698.71 | + | 3867.50i | −0.322261 | + | 0.186058i | ||||
\(757\) | −10088.0 | − | 17472.9i | −0.484352 | − | 0.838923i | 0.515486 | − | 0.856898i | \(-0.327611\pi\) |
−0.999838 | + | 0.0179753i | \(0.994278\pi\) | |||||||
\(758\) | 8430.00 | − | 14601.2i | 0.403946 | − | 0.699656i | ||||
\(759\) | − | 17472.0i | − | 0.835564i | ||||||
\(760\) | 34372.5 | + | 19845.0i | 1.64056 | + | 0.947176i | ||||
\(761\) | −8208.19 | − | 4739.00i | −0.390994 | − | 0.225741i | 0.291597 | − | 0.956541i | \(-0.405814\pi\) |
−0.682591 | + | 0.730801i | \(0.739147\pi\) | |||||||
\(762\) | − | 66220.0i | − | 3.14816i | ||||||
\(763\) | 2424.50 | − | 4199.36i | 0.115036 | − | 0.199249i | ||||
\(764\) | 3587.00 | + | 6212.87i | 0.169860 | + | 0.294206i | ||||
\(765\) | 10269.3 | − | 5929.00i | 0.485344 | − | 0.280214i | ||||
\(766\) | −4235.00 | −0.199761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 57953.0 | 2.72292 | ||||||||
\(769\) | −10475.4 | + | 6048.00i | −0.491228 | + | 0.283610i | −0.725084 | − | 0.688661i | \(-0.758199\pi\) |
0.233856 | + | 0.972271i | \(0.424866\pi\) | |||||||
\(770\) | −5915.00 | − | 10245.1i | −0.276834 | − | 0.479490i | ||||
\(771\) | −21143.5 | + | 36621.6i | −0.987632 | + | 1.71063i | ||||
\(772\) | 8364.00i | 0.389931i | ||||||||
\(773\) | −15537.4 | − | 8970.50i | −0.722950 | − | 0.417395i | 0.0928877 | − | 0.995677i | \(-0.470390\pi\) |
−0.815837 | + | 0.578281i | \(0.803724\pi\) | |||||||
\(774\) | 19147.8 | + | 11055.0i | 0.889217 | + | 0.513390i | ||||
\(775\) | 14896.0i | 0.690426i | ||||||||
\(776\) | 1575.00 | − | 2727.98i | 0.0728598 | − | 0.126197i | ||||
\(777\) | −5960.50 | − | 10323.9i | −0.275202 | − | 0.476663i | ||||
\(778\) | 48991.1 | − | 28285.0i | 2.25760 | − | 1.30343i | ||||
\(779\) | 42336.0 | 1.94717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −234.000 | −0.0107211 | ||||||||
\(782\) | 32008.3 | − | 18480.0i | 1.46370 | − | 0.845068i | ||||
\(783\) | 1435.00 | + | 2485.49i | 0.0654952 | + | 0.113441i | ||||
\(784\) | −7743.00 | + | 13411.3i | −0.352724 | + | 0.610936i | ||||
\(785\) | 19110.0i | 0.868873i | ||||||||
\(786\) | −43496.1 | − | 25112.5i | −1.97386 | − | 1.13961i | ||||
\(787\) | 5771.19 | + | 3332.00i | 0.261399 | + | 0.150919i | 0.624972 | − | 0.780647i | \(-0.285110\pi\) |
−0.363574 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(788\) | − | 50847.0i | − | 2.29867i | ||||||
\(789\) | −12978.0 | + | 22478.6i | −0.585588 | + | 1.01427i | ||||
\(790\) | 22820.0 | + | 39525.4i | 1.02772 | + | 1.78006i | ||||
\(791\) | −19521.9 | + | 11271.0i | −0.877523 | + | 0.506638i | ||||
\(792\) | −25740.0 | −1.15484 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9310.00 | −0.416120 | ||||||||
\(795\) | −18332.0 | + | 10584.0i | −0.817824 | + | 0.472171i | ||||
\(796\) | 595.000 | + | 1030.57i | 0.0264940 | + | 0.0458889i | ||||
\(797\) | −721.000 | + | 1248.81i | −0.0320441 | + | 0.0555020i | −0.881603 | − | 0.471992i | \(-0.843535\pi\) |
0.849559 | + | 0.527494i | \(0.176868\pi\) | |||||||
\(798\) | 57330.0i | 2.54318i | ||||||||
\(799\) | 7001.82 | + | 4042.50i | 0.310021 | + | 0.178990i | ||||
\(800\) | 5594.52 | + | 3230.00i | 0.247245 | + | 0.142747i | ||||
\(801\) | 26180.0i | 1.15484i | ||||||||
\(802\) | 17050.0 | − | 29531.5i | 0.750694 | − | 1.30024i | ||||
\(803\) | −1274.00 | − | 2206.63i | −0.0559881 | − | 0.0969743i | ||||
\(804\) | 49261.3 | − | 28441.0i | 2.16083 | − | 1.24756i | ||||
\(805\) | 8736.00 | 0.382489 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58408.0 | −2.54778 | ||||||||
\(808\) | −16367.9 | + | 9450.00i | −0.712649 | + | 0.411448i | ||||
\(809\) | −15103.5 | − | 26160.0i | −0.656379 | − | 1.13688i | −0.981546 | − | 0.191226i | \(-0.938754\pi\) |
0.325167 | − | 0.945657i | \(-0.394580\pi\) | |||||||
\(810\) | −14682.5 | + | 25430.8i | −0.636902 | + | 1.10315i | ||||
\(811\) | 21140.0i | 0.915322i | 0.889127 | + | 0.457661i | \(0.151313\pi\) | ||||
−0.889127 | + | 0.457661i | \(0.848687\pi\) | |||||||
\(812\) | −15694.1 | − | 9061.00i | −0.678270 | − | 0.391599i | ||||
\(813\) | 9802.54 | + | 5659.50i | 0.422866 | + | 0.244142i | ||||
\(814\) | 17030.0i | 0.733294i | ||||||||
\(815\) | −1904.00 | + | 3297.82i | −0.0818334 | + | 0.141740i | ||||
\(816\) | −23985.5 | − | 41544.1i | −1.02900 | − | 1.78227i | ||||
\(817\) | −21933.0 | + | 12663.0i | −0.939213 | + | 0.542255i | ||||
\(818\) | −64960.0 | −2.77662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39984.0 | −1.70281 | ||||||||
\(821\) | 492.768 | − | 284.500i | 0.0209473 | − | 0.0120939i | −0.489490 | − | 0.872009i | \(-0.662817\pi\) |
0.510437 | + | 0.859915i | \(0.329484\pi\) | |||||||
\(822\) | 31080.0 | + | 53832.1i | 1.31878 | + | 2.28420i | ||||
\(823\) | −4269.00 | + | 7394.12i | −0.180812 | + | 0.313175i | −0.942157 | − | 0.335171i | \(-0.891206\pi\) |
0.761346 | + | 0.648346i | \(0.224539\pi\) | |||||||
\(824\) | − | 26460.0i | − | 1.11866i | ||||||
\(825\) | 11978.9 | + | 6916.00i | 0.505516 | + | 0.291860i | ||||
\(826\) | −16549.7 | − | 9555.00i | −0.697142 | − | 0.402495i | ||||
\(827\) | 32702.0i | 1.37504i | 0.726164 | + | 0.687521i | \(0.241301\pi\) | ||||
−0.726164 | + | 0.687521i | \(0.758699\pi\) | |||||||
\(828\) | 17952.0 | − | 31093.8i | 0.753472 | − | 1.30505i | ||||
\(829\) | −10577.0 | − | 18319.9i | −0.443130 | − | 0.767523i | 0.554790 | − | 0.831990i | \(-0.312798\pi\) |
−0.997920 | + | 0.0644673i | \(0.979465\pi\) | |||||||
\(830\) | 9335.75 | − | 5390.00i | 0.390420 | − | 0.225409i | ||||
\(831\) | −26740.0 | −1.11625 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13398.0 | −0.557279 | ||||||||
\(834\) | −56651.1 | + | 32707.5i | −2.35212 | + | 1.35800i | ||||
\(835\) | 5684.00 | + | 9844.98i | 0.235572 | + | 0.408023i | ||||
\(836\) | 27846.0 | − | 48230.7i | 1.15200 | − | 1.99533i | ||||
\(837\) | 6860.00i | 0.283293i | ||||||||
\(838\) | −31796.1 | − | 18357.5i | −1.31071 | − | 0.756741i | ||||
\(839\) | −1891.40 | − | 1092.00i | −0.0778288 | − | 0.0449345i | 0.460581 | − | 0.887618i | \(-0.347641\pi\) |
−0.538409 | + | 0.842683i | \(0.680975\pi\) | |||||||
\(840\) | − | 28665.0i | − | 1.17742i | ||||||
\(841\) | 8832.50 | − | 15298.3i | 0.362151 | − | 0.627264i | ||||
\(842\) | 12647.5 | + | 21906.1i | 0.517650 | + | 0.896597i | ||||
\(843\) | −37670.4 | + | 21749.0i | −1.53907 | + | 0.888583i | ||||
\(844\) | −48467.0 | −1.97666 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11550.0 | 0.469382 | ||||||||
\(847\) | 7374.21 | − | 4257.50i | 0.299151 | − | 0.172715i | ||||
\(848\) | 19224.0 | + | 33296.9i | 0.778485 | + | 1.34837i | ||||
\(849\) | 18522.0 | − | 32081.0i | 0.748732 | − | 1.29684i | ||||
\(850\) | 29260.0i | 1.18072i | ||||||||
\(851\) | −10891.1 | − | 6288.00i | −0.438711 | − | 0.253290i | ||||
\(852\) | −927.513 | − | 535.500i | −0.0372959 | − | 0.0215328i | ||||
\(853\) | − | 36687.0i | − | 1.47261i | −0.676648 | − | 0.736307i | \(-0.736568\pi\) | ||
0.676648 | − | 0.736307i | \(-0.263432\pi\) | |||||||
\(854\) | 1820.00 | − | 3152.33i | 0.0729264 | − | 0.126312i | ||||
\(855\) | 9702.00 | + | 16804.4i | 0.388072 | + | 0.672160i | ||||
\(856\) | −26656.3 | + | 15390.0i | −1.06436 | + | 0.614509i | ||||
\(857\) | −36806.0 | −1.46706 | −0.733529 | − | 0.679658i | \(-0.762128\pi\) | ||||
−0.733529 | + | 0.679658i | \(0.762128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4900.00 | 0.194628 | 0.0973142 | − | 0.995254i | \(-0.468975\pi\) | ||||
0.0973142 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(860\) | 20714.5 | − | 11959.5i | 0.821346 | − | 0.474204i | ||||
\(861\) | −15288.0 | − | 26479.6i | −0.605126 | − | 1.04811i | ||||
\(862\) | −8107.50 | + | 14042.6i | −0.320351 | + | 0.554864i | ||||
\(863\) | − | 13697.0i | − | 0.540268i | −0.962823 | − | 0.270134i | \(-0.912932\pi\) | ||
0.962823 | − | 0.270134i | \(-0.0870680\pi\) | |||||||
\(864\) | 2576.43 | + | 1487.50i | 0.101449 | + | 0.0585715i | ||||
\(865\) | 2036.89 | + | 1176.00i | 0.0800652 | + | 0.0462257i | ||||
\(866\) | 57995.0i | 2.27569i | ||||||||
\(867\) | 3556.00 | − | 6159.17i | 0.139294 | − | 0.241265i | ||||
\(868\) | −21658.0 | − | 37512.8i | −0.846913 | − | 1.46690i | ||||
\(869\) | 29361.7 | − | 16952.0i | 1.14618 | − | 0.661746i | ||||
\(870\) | −20090.0 | −0.782891 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16785.0 | −0.651848 | ||||||||
\(873\) | 1333.68 | − | 770.000i | 0.0517047 | − | 0.0298517i | ||||
\(874\) | 30240.0 | + | 52377.2i | 1.17035 | + | 2.02710i | ||||
\(875\) | −9145.50 | + | 15840.5i | −0.353342 | + | 0.612006i | ||||
\(876\) | − | 11662.0i | − | 0.449797i | ||||||
\(877\) | −5403.13 | − | 3119.50i | −0.208040 | − | 0.120112i | 0.392360 | − | 0.919812i | \(-0.371659\pi\) |
−0.600400 | + | 0.799700i | \(0.704992\pi\) | |||||||
\(878\) | 75231.6 | + | 43435.0i | 2.89174 | + | 1.66954i | ||||
\(879\) | − | 6321.00i | − | 0.242551i | ||||||
\(880\) | −8099.00 | + | 14027.9i | −0.310247 | + | 0.537363i | ||||
\(881\) | 66.5000 | + | 115.181i | 0.00254307 | + | 0.00440472i | 0.867294 | − | 0.497796i | \(-0.165857\pi\) |
−0.864751 | + | 0.502201i | \(0.832524\pi\) | |||||||
\(882\) | −16575.7 | + | 9570.00i | −0.632805 | + | 0.365350i | ||||
\(883\) | 26003.0 | 0.991020 | 0.495510 | − | 0.868602i | \(-0.334981\pi\) | ||||
0.495510 | + | 0.868602i | \(0.334981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14406.0 | −0.547178 | ||||||||
\(886\) | −4282.50 | + | 2472.50i | −0.162385 | + | 0.0937531i | ||||
\(887\) | 15624.0 | + | 27061.6i | 0.591435 | + | 1.02439i | 0.994039 | + | 0.109021i | \(0.0347716\pi\) |
−0.402605 | + | 0.915374i | \(0.631895\pi\) | |||||||
\(888\) | −20632.5 | + | 35736.5i | −0.779709 | + | 1.35050i | ||||
\(889\) | − | 24596.0i | − | 0.927923i | ||||||
\(890\) | 36070.0 | + | 20825.0i | 1.35850 | + | 0.784332i | ||||
\(891\) | 18891.5 | + | 10907.0i | 0.710312 | + | 0.410099i | ||||
\(892\) | − | 3689.00i | − | 0.138472i | ||||||
\(893\) | −6615.00 | + | 11457.5i | −0.247886 | + | 0.429352i | ||||
\(894\) | 43155.0 | + | 74746.7i | 1.61445 | + | 2.79631i | ||||
\(895\) | −18362.3 | + | 10601.5i | −0.685794 | + | 0.395943i | ||||
\(896\) | 27495.0 | 1.02516 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72370.0 | 2.68933 | ||||||||
\(899\) | −13918.8 | + | 8036.00i | −0.516370 | + | 0.298126i | ||||
\(900\) | 14212.0 | + | 24615.9i | 0.526370 | + | 0.911700i | ||||
\(901\) | −16632.0 | + | 28807.5i | −0.614975 | + | 1.06517i | ||||
\(902\) | 43680.0i | 1.61240i | ||||||||
\(903\) | 15840.5 | + | 9145.50i | 0.583763 | + | 0.337036i | ||||
\(904\) | 67576.0 | + | 39015.0i | 2.48622 | + | 1.43542i | ||||
\(905\) | − | 196.000i | − | 0.00719918i | ||||||
\(906\) | 58152.5 | − | 100723.i | 2.13244 | − | 3.69349i | ||||
\(907\) | −19126.5 | − | 33128.1i | −0.700204 | − | 1.21279i | −0.968395 | − | 0.249423i | \(-0.919759\pi\) |
0.268191 | − | 0.963366i | \(-0.413574\pi\) | |||||||
\(908\) | 37925.0 | − | 21896.0i | 1.38611 | − | 0.800269i | ||||
\(909\) | −9240.00 | −0.337152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36374.0 | 1.32286 | 0.661429 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661429 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(912\) | 67981.3 | − | 39249.0i | 2.46829 | − | 1.42507i | ||||
\(913\) | −4004.00 | − | 6935.13i | −0.145140 | − | 0.251390i | ||||
\(914\) | 3985.00 | − | 6902.22i | 0.144215 | − | 0.249787i | ||||
\(915\) | − | 2744.00i | − | 0.0991408i | ||||||
\(916\) | −6698.71 | − | 3867.50i | −0.241628 | − | 0.139504i | ||||
\(917\) | −16155.7 | − | 9327.50i | −0.581798 | − | 0.335901i | ||||
\(918\) | 13475.0i | 0.484468i | ||||||||
\(919\) | 13824.0 | − | 23943.9i | 0.496204 | − | 0.859451i | −0.503786 | − | 0.863828i | \(-0.668060\pi\) |
0.999990 | + | 0.00437745i | \(0.00139339\pi\) | |||||||
\(920\) | −15120.0 | − | 26188.6i | −0.541839 | − | 0.938492i | ||||
\(921\) | 12815.4 | − | 7399.00i | 0.458505 | − | 0.264718i | ||||
\(922\) | −29575.0 | −1.05640 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −40222.0 | −1.43204 | ||||||||
\(925\) | 8622.15 | − | 4978.00i | 0.306481 | − | 0.176947i | ||||
\(926\) | −27680.0 | − | 47943.2i | −0.982312 | − | 1.70141i | ||||
\(927\) | 6468.00 | − | 11202.9i | 0.229166 | − | 0.396927i | ||||
\(928\) | 6970.00i | 0.246553i | ||||||||
\(929\) | −654.715 | − | 378.000i | −0.0231222 | − | 0.0133496i | 0.488394 | − | 0.872623i | \(-0.337583\pi\) |
−0.511517 | + | 0.859273i | \(0.670916\pi\) | |||||||
\(930\) | −41586.5 | − | 24010.0i | −1.46632 | − | 0.846579i | ||||
\(931\) | − | 21924.0i | − | 0.771783i | ||||||
\(932\) | −26018.5 | + | 45065.4i | −0.914447 | + | 1.58387i | ||||
\(933\) | −11907.0 | − | 20623.5i | −0.417811 | − | 0.723670i | ||||
\(934\) | 5455.96 | − | 3150.00i | 0.191140 | − | 0.110355i | ||||
\(935\) | −14014.0 | −0.490168 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20846.0 | 0.726797 | 0.363399 | − | 0.931634i | \(-0.381616\pi\) | ||||
0.363399 | + | 0.931634i | \(0.381616\pi\) | |||||||
\(938\) | 26907.4 | − | 15535.0i | 0.936629 | − | 0.540763i | ||||
\(939\) | −37411.5 | − | 64798.6i | −1.30019 | − | 2.25199i | ||||
\(940\) | 6247.50 | − | 10821.0i | 0.216778 | − | 0.375470i | ||||
\(941\) | − | 41321.0i | − | 1.43148i | −0.698365 | − | 0.715742i | \(-0.746089\pi\) | ||
0.698365 | − | 0.715742i | \(-0.253911\pi\) | |||||||
\(942\) | 82748.7 | + | 47775.0i | 2.86210 | + | 1.65243i | ||||
\(943\) | −27934.5 | − | 16128.0i | −0.964659 | − | 0.556946i | ||||
\(944\) | 26166.0i | 0.902151i | ||||||||
\(945\) | −1592.50 | + | 2758.29i | −0.0548191 | + | 0.0949494i | ||||
\(946\) | −13065.0 | − | 22629.2i | −0.449027 | − | 0.777738i | ||||
\(947\) | −47602.0 | + | 27483.0i | −1.63343 | + | 0.943060i | −0.650402 | + | 0.759590i | \(0.725399\pi\) |
−0.983025 | + | 0.183469i | \(0.941267\pi\) | |||||||
\(948\) | 155176. | 5.31633 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −47880.0 | −1.63519 | ||||||||
\(951\) | 42762.6 | − | 24689.0i | 1.45812 | − | 0.841846i | ||||
\(952\) | −22522.5 | − | 39010.1i | −0.766763 | − | 1.32807i | ||||
\(953\) | −22276.5 | + | 38584.0i | −0.757195 | + | 1.31150i | 0.187081 | + | 0.982344i | \(0.440097\pi\) |
−0.944276 | + | 0.329155i | \(0.893236\pi\) | |||||||
\(954\) | 47520.0i | 1.61270i | ||||||||
\(955\) | 2558.24 | + | 1477.00i | 0.0866834 | + | 0.0500467i | ||||
\(956\) | −51189.9 | − | 29554.5i | −1.73180 | − | 0.999854i | ||||
\(957\) | 14924.0i | 0.504101i | ||||||||
\(958\) | −30082.5 | + | 52104.4i | −1.01453 | + | 1.75722i | ||||
\(959\) | 11544.0 | + | 19994.8i | 0.388712 | + | 0.673270i | ||||
\(960\) | 12178.9 | − | 7031.50i | 0.409451 | − | 0.236397i | ||||
\(961\) | −8625.00 | −0.289517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15048.0 | −0.503546 | ||||||||
\(964\) | −23703.1 | + | 13685.0i | −0.791936 | + | 0.457224i | ||||
\(965\) | 1722.00 | + | 2982.59i | 0.0574437 | + | 0.0994954i | ||||
\(966\) | 21840.0 | − | 37828.0i | 0.727423 | − | 1.25993i | ||||
\(967\) | − | 27907.0i | − | 0.928054i | −0.885821 | − | 0.464027i | \(-0.846404\pi\) | ||
0.885821 | − | 0.464027i | \(-0.153596\pi\) | |||||||
\(968\) | −25526.1 | − | 14737.5i | −0.847562 | − | 0.489340i | ||||
\(969\) | 58815.2 | + | 33957.0i | 1.94986 | + | 1.12575i | ||||
\(970\) | − | 2450.00i | − | 0.0810977i | ||||||
\(971\) | 8221.50 | − | 14240.1i | 0.271720 | − | 0.470634i | −0.697582 | − | 0.716505i | \(-0.745741\pi\) |
0.969302 | + | 0.245871i | \(0.0790741\pi\) | |||||||
\(972\) | 41888.0 | + | 72552.1i | 1.38226 | + | 2.39415i | ||||
\(973\) | −21041.8 | + | 12148.5i | −0.693289 | + | 0.400270i | ||||
\(974\) | −11400.0 | −0.375030 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4984.00 | −0.163457 | ||||||||
\(977\) | −39329.7 | + | 22707.0i | −1.28789 | + | 0.743563i | −0.978277 | − | 0.207300i | \(-0.933532\pi\) |
−0.309612 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(978\) | 9520.00 | + | 16489.1i | 0.311264 | + | 0.539125i | ||||
\(979\) | 15470.0 | − | 26794.8i | 0.505029 | − | 0.874736i | ||||
\(980\) | 20706.0i | 0.674927i | ||||||||
\(981\) | −7106.60 | − | 4103.00i | −0.231291 | − | 0.133536i | ||||
\(982\) | −72603.2 | − | 41917.5i | −2.35933 | − | 1.36216i | ||||
\(983\) | 8981.00i | 0.291403i | 0.989329 | + | 0.145702i | \(0.0465440\pi\) | ||||
−0.989329 | + | 0.145702i | \(0.953456\pi\) | |||||||
\(984\) | −52920.0 | + | 91660.1i | −1.71446 | + | 2.96953i | ||||
\(985\) | −10468.5 | − | 18132.0i | −0.338634 | − | 0.586531i | ||||
\(986\) | −27340.4 | + | 15785.0i | −0.883059 | + | 0.509834i | ||||
\(987\) | 9555.00 | 0.308145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19296.0 | 0.620402 | ||||||||
\(990\) | −17337.8 | + | 10010.0i | −0.556598 | + | 0.321352i | ||||
\(991\) | 8707.00 | + | 15081.0i | 0.279099 | + | 0.483413i | 0.971161 | − | 0.238424i | \(-0.0766309\pi\) |
−0.692062 | + | 0.721838i | \(0.743298\pi\) | |||||||
\(992\) | −8330.00 | + | 14428.0i | −0.266611 | + | 0.461783i | ||||
\(993\) | − | 67928.0i | − | 2.17083i | ||||||
\(994\) | −506.625 | − | 292.500i | −0.0161662 | − | 0.00933354i | ||||
\(995\) | 424.352 | + | 245.000i | 0.0135205 | + | 0.00780605i | ||||
\(996\) | − | 36652.0i | − | 1.16603i | ||||||
\(997\) | 11851.0 | − | 20526.5i | 0.376454 | − | 0.652038i | −0.614089 | − | 0.789237i | \(-0.710477\pi\) |
0.990544 | + | 0.137199i | \(0.0438099\pi\) | |||||||
\(998\) | −32100.0 | − | 55598.8i | −1.01814 | − | 1.76348i | ||||
\(999\) | 3970.73 | − | 2292.50i | 0.125754 | − | 0.0726041i |
(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.e.e.23.1 | 4 | ||
13.2 | odd | 12 | 13.4.a.a.1.1 | ✓ | 1 | ||
13.3 | even | 3 | 169.4.b.a.168.1 | 2 | |||
13.4 | even | 6 | inner | 169.4.e.e.147.1 | 4 | ||
13.5 | odd | 4 | 169.4.c.e.146.1 | 2 | |||
13.6 | odd | 12 | 169.4.c.e.22.1 | 2 | |||
13.7 | odd | 12 | 169.4.c.a.22.1 | 2 | |||
13.8 | odd | 4 | 169.4.c.a.146.1 | 2 | |||
13.9 | even | 3 | inner | 169.4.e.e.147.2 | 4 | ||
13.10 | even | 6 | 169.4.b.a.168.2 | 2 | |||
13.11 | odd | 12 | 169.4.a.e.1.1 | 1 | |||
13.12 | even | 2 | inner | 169.4.e.e.23.2 | 4 | ||
39.2 | even | 12 | 117.4.a.b.1.1 | 1 | |||
39.11 | even | 12 | 1521.4.a.a.1.1 | 1 | |||
52.15 | even | 12 | 208.4.a.g.1.1 | 1 | |||
65.2 | even | 12 | 325.4.b.b.274.1 | 2 | |||
65.28 | even | 12 | 325.4.b.b.274.2 | 2 | |||
65.54 | odd | 12 | 325.4.a.d.1.1 | 1 | |||
91.41 | even | 12 | 637.4.a.a.1.1 | 1 | |||
104.67 | even | 12 | 832.4.a.a.1.1 | 1 | |||
104.93 | odd | 12 | 832.4.a.r.1.1 | 1 | |||
143.54 | even | 12 | 1573.4.a.a.1.1 | 1 | |||
156.119 | odd | 12 | 1872.4.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.a.1.1 | ✓ | 1 | 13.2 | odd | 12 | ||
117.4.a.b.1.1 | 1 | 39.2 | even | 12 | |||
169.4.a.e.1.1 | 1 | 13.11 | odd | 12 | |||
169.4.b.a.168.1 | 2 | 13.3 | even | 3 | |||
169.4.b.a.168.2 | 2 | 13.10 | even | 6 | |||
169.4.c.a.22.1 | 2 | 13.7 | odd | 12 | |||
169.4.c.a.146.1 | 2 | 13.8 | odd | 4 | |||
169.4.c.e.22.1 | 2 | 13.6 | odd | 12 | |||
169.4.c.e.146.1 | 2 | 13.5 | odd | 4 | |||
169.4.e.e.23.1 | 4 | 1.1 | even | 1 | trivial | ||
169.4.e.e.23.2 | 4 | 13.12 | even | 2 | inner | ||
169.4.e.e.147.1 | 4 | 13.4 | even | 6 | inner | ||
169.4.e.e.147.2 | 4 | 13.9 | even | 3 | inner | ||
208.4.a.g.1.1 | 1 | 52.15 | even | 12 | |||
325.4.a.d.1.1 | 1 | 65.54 | odd | 12 | |||
325.4.b.b.274.1 | 2 | 65.2 | even | 12 | |||
325.4.b.b.274.2 | 2 | 65.28 | even | 12 | |||
637.4.a.a.1.1 | 1 | 91.41 | even | 12 | |||
832.4.a.a.1.1 | 1 | 104.67 | even | 12 | |||
832.4.a.r.1.1 | 1 | 104.93 | odd | 12 | |||
1521.4.a.a.1.1 | 1 | 39.11 | even | 12 | |||
1573.4.a.a.1.1 | 1 | 143.54 | even | 12 | |||
1872.4.a.k.1.1 | 1 | 156.119 | odd | 12 |