Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.1 | ||
Character | \(\chi\) | \(=\) | 225.124 |
Dual form | 225.4.k.d.49.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.66357 | − | 2.69252i | −1.64882 | − | 0.951948i | −0.977541 | − | 0.210745i | \(-0.932411\pi\) |
−0.671281 | − | 0.741203i | \(-0.734256\pi\) | |||||||
\(3\) | 3.19791 | + | 4.09553i | 0.615438 | + | 0.788185i | ||||
\(4\) | 10.4993 | + | 18.1853i | 1.31241 | + | 2.27316i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.88642 | − | 27.7102i | −0.264437 | − | 1.88544i | ||||
\(7\) | −10.8861 | − | 6.28510i | −0.587795 | − | 0.339363i | 0.176430 | − | 0.984313i | \(-0.443545\pi\) |
−0.764225 | + | 0.644950i | \(0.776878\pi\) | |||||||
\(8\) | − | 69.9976i | − | 3.09349i | ||||||
\(9\) | −6.54673 | + | 26.1943i | −0.242471 | + | 0.970159i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.41534 | + | 11.1117i | −0.175845 | + | 0.304573i | −0.940454 | − | 0.339922i | \(-0.889599\pi\) |
0.764608 | + | 0.644495i | \(0.222933\pi\) | |||||||
\(12\) | −40.9026 | + | 101.155i | −0.983964 | + | 2.43341i | ||||
\(13\) | −51.8442 | + | 29.9322i | −1.10608 | + | 0.638593i | −0.937810 | − | 0.347148i | \(-0.887150\pi\) |
−0.168266 | + | 0.985742i | \(0.553817\pi\) | |||||||
\(14\) | 33.8455 | + | 58.6220i | 0.646113 | + | 1.11910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −104.475 | + | 180.957i | −1.63243 | + | 2.82745i | ||||
\(17\) | − | 110.011i | − | 1.56950i | −0.619810 | − | 0.784752i | \(-0.712790\pi\) | ||
0.619810 | − | 0.784752i | \(-0.287210\pi\) | |||||||
\(18\) | 101.060 | − | 104.532i | 1.32333 | − | 1.36880i | ||||
\(19\) | 12.0872 | 0.145947 | 0.0729733 | − | 0.997334i | \(-0.476751\pi\) | ||||
0.0729733 | + | 0.997334i | \(0.476751\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.07201 | − | 64.6836i | −0.0942702 | − | 0.672148i | ||||
\(22\) | 59.8368 | − | 34.5468i | 0.579875 | − | 0.334791i | ||||
\(23\) | 58.6485 | − | 33.8608i | 0.531699 | − | 0.306976i | −0.210009 | − | 0.977699i | \(-0.567349\pi\) |
0.741708 | + | 0.670723i | \(0.234016\pi\) | |||||||
\(24\) | 286.677 | − | 223.846i | 2.43824 | − | 1.90385i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 322.372 | 2.43163 | ||||||||
\(27\) | −128.215 | + | 56.9547i | −0.913891 | + | 0.405960i | ||||
\(28\) | − | 263.956i | − | 1.78154i | ||||||
\(29\) | 99.9790 | − | 173.169i | 0.640194 | − | 1.10885i | −0.345195 | − | 0.938531i | \(-0.612187\pi\) |
0.985389 | − | 0.170318i | \(-0.0544794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.3143 | − | 66.3624i | −0.221982 | − | 0.384485i | 0.733427 | − | 0.679768i | \(-0.237919\pi\) |
−0.955410 | + | 0.295283i | \(0.904586\pi\) | |||||||
\(32\) | 489.500 | − | 282.613i | 2.70413 | − | 1.56123i | ||||
\(33\) | −66.0240 | + | 9.26000i | −0.348282 | + | 0.0488473i | ||||
\(34\) | −296.206 | + | 513.044i | −1.49409 | + | 2.58783i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −545.086 | + | 155.967i | −2.52355 | + | 0.722069i | ||||
\(37\) | − | 22.4815i | − | 0.0998900i | −0.998752 | − | 0.0499450i | \(-0.984095\pi\) | ||
0.998752 | − | 0.0499450i | \(-0.0159046\pi\) | |||||||
\(38\) | −56.3694 | − | 32.5449i | −0.240640 | − | 0.138934i | ||||
\(39\) | −288.381 | − | 116.609i | −1.18405 | − | 0.478778i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.8807 | − | 76.0037i | −0.167147 | − | 0.289507i | 0.770269 | − | 0.637719i | \(-0.220122\pi\) |
−0.937416 | + | 0.348213i | \(0.886789\pi\) | |||||||
\(42\) | −131.854 | + | 326.083i | −0.484415 | + | 1.19799i | ||||
\(43\) | 103.412 | + | 59.7050i | 0.366749 | + | 0.211743i | 0.672037 | − | 0.740517i | \(-0.265419\pi\) |
−0.305288 | + | 0.952260i | \(0.598753\pi\) | |||||||
\(44\) | −269.426 | −0.923124 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −364.682 | −1.16890 | ||||||||
\(47\) | −210.579 | − | 121.578i | −0.653533 | − | 0.377317i | 0.136276 | − | 0.990671i | \(-0.456487\pi\) |
−0.789808 | + | 0.613354i | \(0.789820\pi\) | |||||||
\(48\) | −1075.22 | + | 150.801i | −3.23321 | + | 0.453465i | ||||
\(49\) | −92.4951 | − | 160.206i | −0.269665 | − | 0.467073i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 450.553 | − | 351.805i | 1.23706 | − | 0.965932i | ||||
\(52\) | −1088.65 | − | 628.534i | −2.90325 | − | 1.67619i | ||||
\(53\) | 293.518i | 0.760712i | 0.924840 | + | 0.380356i | \(0.124199\pi\) | ||||
−0.924840 | + | 0.380356i | \(0.875801\pi\) | |||||||
\(54\) | 751.293 | + | 79.6094i | 1.89330 | + | 0.200620i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −439.942 | + | 762.002i | −1.04982 | + | 1.81834i | ||||
\(57\) | 38.6537 | + | 49.5034i | 0.0898212 | + | 0.115033i | ||||
\(58\) | −932.519 | + | 538.390i | −2.11113 | + | 1.21886i | ||||
\(59\) | −290.692 | − | 503.493i | −0.641438 | − | 1.11100i | −0.985112 | − | 0.171914i | \(-0.945005\pi\) |
0.343674 | − | 0.939089i | \(-0.388328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 386.847 | − | 670.038i | 0.811977 | − | 1.40639i | −0.0995008 | − | 0.995037i | \(-0.531725\pi\) |
0.911478 | − | 0.411349i | \(-0.134942\pi\) | |||||||
\(62\) | 412.648i | 0.845263i | ||||||||
\(63\) | 235.902 | − | 244.007i | 0.471760 | − | 0.487968i | ||||
\(64\) | −1372.15 | −2.67998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 332.840 | + | 134.586i | 0.620755 | + | 0.251006i | ||||
\(67\) | −200.431 | + | 115.719i | −0.365471 | + | 0.211005i | −0.671478 | − | 0.741024i | \(-0.734340\pi\) |
0.306007 | + | 0.952029i | \(0.401007\pi\) | |||||||
\(68\) | 2000.58 | − | 1155.03i | 3.56773 | − | 2.05983i | ||||
\(69\) | 326.231 | + | 131.913i | 0.569182 | + | 0.230152i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −744.342 | −1.24418 | −0.622092 | − | 0.782944i | \(-0.713717\pi\) | ||||
−0.622092 | + | 0.782944i | \(0.713717\pi\) | |||||||
\(72\) | 1833.54 | + | 458.255i | 3.00117 | + | 0.750082i | ||||
\(73\) | 264.839i | 0.424616i | 0.977203 | + | 0.212308i | \(0.0680981\pi\) | ||||
−0.977203 | + | 0.212308i | \(0.931902\pi\) | |||||||
\(74\) | −60.5317 | + | 104.844i | −0.0950901 | + | 0.164701i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 126.907 | + | 219.809i | 0.191542 | + | 0.331760i | ||||
\(77\) | 139.676 | − | 80.6421i | 0.206722 | − | 0.119351i | ||||
\(78\) | 1030.92 | + | 1320.28i | 1.49652 | + | 1.91657i | ||||
\(79\) | 279.858 | − | 484.729i | 0.398564 | − | 0.690333i | −0.594985 | − | 0.803737i | \(-0.702842\pi\) |
0.993549 | + | 0.113404i | \(0.0361755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −643.281 | − | 342.974i | −0.882415 | − | 0.470471i | ||||
\(82\) | 472.598i | 0.636460i | ||||||||
\(83\) | −1057.32 | − | 610.443i | −1.39826 | − | 0.807288i | −0.404052 | − | 0.914736i | \(-0.632399\pi\) |
−0.994211 | + | 0.107448i | \(0.965732\pi\) | |||||||
\(84\) | 1081.04 | − | 844.108i | 1.40418 | − | 1.09643i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −321.513 | − | 556.878i | −0.403136 | − | 0.698252i | ||||
\(87\) | 1028.94 | − | 144.311i | 1.26798 | − | 0.177837i | ||||
\(88\) | 777.792 | + | 449.059i | 0.942193 | + | 0.543975i | ||||
\(89\) | 255.905 | 0.304785 | 0.152392 | − | 0.988320i | \(-0.451302\pi\) | ||||
0.152392 | + | 0.988320i | \(0.451302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 752.509 | 0.866861 | ||||||||
\(92\) | 1231.53 | + | 711.027i | 1.39561 | + | 0.805757i | ||||
\(93\) | 149.263 | − | 369.138i | 0.166429 | − | 0.411590i | ||||
\(94\) | 654.699 | + | 1133.97i | 0.718373 | + | 1.24426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2722.83 | + | 1100.99i | 2.89476 | + | 1.17051i | ||||
\(97\) | −908.909 | − | 524.759i | −0.951400 | − | 0.549291i | −0.0578842 | − | 0.998323i | \(-0.518435\pi\) |
−0.893515 | + | 0.449032i | \(0.851769\pi\) | |||||||
\(98\) | 996.177i | 1.02683i | ||||||||
\(99\) | −249.064 | − | 240.791i | −0.252847 | − | 0.244448i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.3635 | + | 76.8398i | −0.0437062 | + | 0.0757014i | −0.887051 | − | 0.461671i | \(-0.847250\pi\) |
0.843345 | + | 0.537373i | \(0.180583\pi\) | |||||||
\(102\) | −3048.43 | + | 427.548i | −2.95921 | + | 0.415035i | ||||
\(103\) | 1337.20 | − | 772.035i | 1.27921 | − | 0.738552i | 0.302507 | − | 0.953147i | \(-0.402176\pi\) |
0.976703 | + | 0.214595i | \(0.0688430\pi\) | |||||||
\(104\) | 2095.19 | + | 3628.97i | 1.97548 | + | 3.42163i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 790.301 | − | 1368.84i | 0.724158 | − | 1.25428i | ||||
\(107\) | − | 585.772i | − | 0.529240i | −0.964353 | − | 0.264620i | \(-0.914753\pi\) | ||
0.964353 | − | 0.264620i | \(-0.0852466\pi\) | |||||||
\(108\) | −2381.90 | − | 1733.65i | −2.12221 | − | 1.54463i | ||||
\(109\) | −1367.04 | −1.20127 | −0.600634 | − | 0.799524i | \(-0.705085\pi\) | ||||
−0.600634 | + | 0.799524i | \(0.705085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 92.0735 | − | 71.8937i | 0.0787318 | − | 0.0614761i | ||||
\(112\) | 2274.66 | − | 1313.28i | 1.91907 | − | 1.10797i | ||||
\(113\) | −147.596 | + | 85.2146i | −0.122873 | + | 0.0709408i | −0.560177 | − | 0.828373i | \(-0.689267\pi\) |
0.437304 | + | 0.899314i | \(0.355933\pi\) | |||||||
\(114\) | −46.9758 | − | 334.938i | −0.0385937 | − | 0.275174i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4198.83 | 3.36079 | ||||||||
\(117\) | −444.644 | − | 1553.98i | −0.351345 | − | 1.22791i | ||||
\(118\) | 3130.77i | 2.44246i | ||||||||
\(119\) | −691.429 | + | 1197.59i | −0.532632 | + | 0.922546i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 583.187 | + | 1010.11i | 0.438157 | + | 0.758910i | ||||
\(122\) | −3608.17 | + | 2083.18i | −2.67761 | + | 1.54592i | ||||
\(123\) | 170.949 | − | 422.768i | 0.125316 | − | 0.309916i | ||||
\(124\) | 804.545 | − | 1393.51i | 0.582664 | − | 1.00920i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1757.14 | + | 502.775i | −1.24237 | + | 0.355482i | ||||
\(127\) | 1809.74i | 1.26447i | 0.774775 | + | 0.632237i | \(0.217863\pi\) | ||||
−0.774775 | + | 0.632237i | \(0.782137\pi\) | |||||||
\(128\) | 2483.13 | + | 1433.63i | 1.71468 | + | 0.989973i | ||||
\(129\) | 86.1791 | + | 614.459i | 0.0588190 | + | 0.419381i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 619.147 | + | 1072.39i | 0.412940 | + | 0.715232i | 0.995210 | − | 0.0977630i | \(-0.0311687\pi\) |
−0.582270 | + | 0.812995i | \(0.697835\pi\) | |||||||
\(132\) | −861.600 | − | 1103.44i | −0.568126 | − | 0.727593i | ||||
\(133\) | −131.582 | − | 75.9691i | −0.0857867 | − | 0.0495290i | ||||
\(134\) | 1246.30 | 0.803462 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7700.50 | −4.85524 | ||||||||
\(137\) | −438.367 | − | 253.091i | −0.273374 | − | 0.157832i | 0.357046 | − | 0.934087i | \(-0.383784\pi\) |
−0.630420 | + | 0.776254i | \(0.717117\pi\) | |||||||
\(138\) | −1166.22 | − | 1493.57i | −0.719387 | − | 0.921311i | ||||
\(139\) | −106.840 | − | 185.052i | −0.0651946 | − | 0.112920i | 0.831586 | − | 0.555396i | \(-0.187433\pi\) |
−0.896780 | + | 0.442476i | \(0.854100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −175.487 | − | 1251.23i | −0.104813 | − | 0.747320i | ||||
\(142\) | 3471.29 | + | 2004.15i | 2.05144 | + | 1.18440i | ||||
\(143\) | − | 768.103i | − | 0.449175i | ||||||
\(144\) | −4056.06 | − | 3921.33i | −2.34726 | − | 2.26929i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 713.082 | − | 1235.09i | 0.404213 | − | 0.700117i | ||||
\(147\) | 360.338 | − | 891.141i | 0.202178 | − | 0.500001i | ||||
\(148\) | 408.832 | − | 236.039i | 0.227066 | − | 0.131097i | ||||
\(149\) | −452.655 | − | 784.022i | −0.248879 | − | 0.431071i | 0.714336 | − | 0.699803i | \(-0.246729\pi\) |
−0.963215 | + | 0.268732i | \(0.913395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −679.335 | + | 1176.64i | −0.366116 | + | 0.634131i | −0.988955 | − | 0.148219i | \(-0.952646\pi\) |
0.622839 | + | 0.782350i | \(0.285979\pi\) | |||||||
\(152\) | − | 846.073i | − | 0.451484i | ||||||
\(153\) | 2881.66 | + | 720.211i | 1.52267 | + | 0.380560i | ||||
\(154\) | −868.521 | −0.454464 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −907.235 | − | 6468.60i | −0.465622 | − | 3.31989i | ||||
\(157\) | 1646.61 | − | 950.670i | 0.837030 | − | 0.483259i | −0.0192236 | − | 0.999815i | \(-0.506119\pi\) |
0.856254 | + | 0.516556i | \(0.172786\pi\) | |||||||
\(158\) | −2610.28 | + | 1507.05i | −1.31432 | + | 0.758824i | ||||
\(159\) | −1202.11 | + | 938.643i | −0.599582 | + | 0.468172i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −851.273 | −0.416706 | ||||||||
\(162\) | 2076.53 | + | 3331.53i | 1.00708 | + | 1.61574i | ||||
\(163\) | 2325.15i | 1.11730i | 0.829404 | + | 0.558649i | \(0.188680\pi\) | ||||
−0.829404 | + | 0.558649i | \(0.811320\pi\) | |||||||
\(164\) | 921.432 | − | 1595.97i | 0.438730 | − | 0.759903i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3287.26 | + | 5693.69i | 1.53699 | + | 2.66215i | ||||
\(167\) | 1702.43 | − | 982.901i | 0.788853 | − | 0.455444i | −0.0507059 | − | 0.998714i | \(-0.516147\pi\) |
0.839558 | + | 0.543269i | \(0.182814\pi\) | |||||||
\(168\) | −4527.70 | + | 635.019i | −2.07928 | + | 0.291624i | ||||
\(169\) | 693.379 | − | 1200.97i | 0.315603 | − | 0.546640i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −79.1314 | + | 316.615i | −0.0353879 | + | 0.141591i | ||||
\(172\) | 2507.44i | 1.11157i | ||||||||
\(173\) | −1990.04 | − | 1148.95i | −0.874567 | − | 0.504932i | −0.00570381 | − | 0.999984i | \(-0.501816\pi\) |
−0.868863 | + | 0.495052i | \(0.835149\pi\) | |||||||
\(174\) | −5187.10 | − | 2097.43i | −2.25996 | − | 0.913828i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1340.49 | − | 2321.80i | −0.574110 | − | 0.994387i | ||||
\(177\) | 1132.46 | − | 2800.66i | 0.480911 | − | 1.18933i | ||||
\(178\) | −1193.43 | − | 689.027i | −0.502536 | − | 0.290139i | ||||
\(179\) | 873.696 | 0.364822 | 0.182411 | − | 0.983222i | \(-0.441610\pi\) | ||||
0.182411 | + | 0.983222i | \(0.441610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1494.20 | 0.613609 | 0.306805 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306805 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(182\) | −3509.38 | − | 2026.14i | −1.42930 | − | 0.825206i | ||||
\(183\) | 3981.26 | − | 558.380i | 1.60821 | − | 0.225555i | ||||
\(184\) | −2370.17 | − | 4105.26i | −0.949627 | − | 1.64480i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1690.01 | + | 1319.61i | −0.666224 | + | 0.520207i | ||||
\(187\) | 1222.41 | + | 705.758i | 0.478028 | + | 0.275990i | ||||
\(188\) | − | 5105.91i | − | 1.98078i | ||||||
\(189\) | 1753.73 | + | 185.831i | 0.674948 | + | 0.0715196i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2525.13 | + | 4373.65i | −0.956607 | + | 1.65689i | −0.225959 | + | 0.974137i | \(0.572551\pi\) |
−0.730648 | + | 0.682754i | \(0.760782\pi\) | |||||||
\(192\) | −4388.02 | − | 5619.68i | −1.64936 | − | 2.11232i | ||||
\(193\) | −4470.08 | + | 2580.80i | −1.66717 | + | 0.962539i | −0.698011 | + | 0.716087i | \(0.745931\pi\) |
−0.969155 | + | 0.246452i | \(0.920735\pi\) | |||||||
\(194\) | 2825.84 | + | 4894.50i | 1.04579 | + | 1.81137i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1942.26 | − | 3364.10i | 0.707822 | − | 1.22598i | ||||
\(197\) | 374.025i | 0.135270i | 0.997710 | + | 0.0676350i | \(0.0215453\pi\) | ||||
−0.997710 | + | 0.0676350i | \(0.978455\pi\) | |||||||
\(198\) | 513.194 | + | 1793.55i | 0.184197 | + | 0.643748i | ||||
\(199\) | −603.342 | −0.214924 | −0.107462 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107462 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1114.89 | − | 450.813i | −0.391236 | − | 0.158198i | ||||
\(202\) | 413.785 | − | 238.899i | 0.144128 | − | 0.0832121i | ||||
\(203\) | −2176.76 | + | 1256.76i | −0.752606 | + | 0.434517i | ||||
\(204\) | 11128.2 | + | 4499.73i | 3.81925 | + | 1.54433i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8314.87 | −2.81225 | ||||||||
\(207\) | 503.002 | + | 1757.93i | 0.168894 | + | 0.590265i | ||||
\(208\) | − | 12508.7i | − | 4.16983i | ||||||
\(209\) | −77.5434 | + | 134.309i | −0.0256640 | + | 0.0444514i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1205.91 | − | 2088.69i | −0.393450 | − | 0.681476i | 0.599452 | − | 0.800411i | \(-0.295385\pi\) |
−0.992902 | + | 0.118935i | \(0.962052\pi\) | |||||||
\(212\) | −5337.70 | + | 3081.72i | −1.72922 | + | 0.998366i | ||||
\(213\) | −2380.34 | − | 3048.47i | −0.765719 | − | 0.980648i | ||||
\(214\) | −1577.20 | + | 2731.79i | −0.503809 | + | 0.872623i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3986.69 | + | 8974.76i | 1.25583 | + | 2.82711i | ||||
\(217\) | 963.237i | 0.301331i | ||||||||
\(218\) | 6375.27 | + | 3680.76i | 1.98068 | + | 1.14354i | ||||
\(219\) | −1084.65 | + | 846.930i | −0.334676 | + | 0.261325i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3292.87 | + | 5703.42i | 1.00227 | + | 1.73599i | ||||
\(222\) | −622.966 | + | 87.3724i | −0.188337 | + | 0.0264146i | ||||
\(223\) | 4746.93 | + | 2740.64i | 1.42546 | + | 0.822990i | 0.996758 | − | 0.0804554i | \(-0.0256375\pi\) |
0.428703 | + | 0.903446i | \(0.358971\pi\) | |||||||
\(224\) | −7105.00 | −2.11930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 917.766 | 0.270128 | ||||||||
\(227\) | 4739.30 | + | 2736.24i | 1.38572 | + | 0.800046i | 0.992830 | − | 0.119539i | \(-0.0381415\pi\) |
0.392891 | + | 0.919585i | \(0.371475\pi\) | |||||||
\(228\) | −494.397 | + | 1222.68i | −0.143606 | + | 0.355148i | ||||
\(229\) | 1637.99 | + | 2837.08i | 0.472670 | + | 0.818689i | 0.999511 | − | 0.0312750i | \(-0.00995677\pi\) |
−0.526840 | + | 0.849964i | \(0.676623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 776.945 | + | 314.162i | 0.221295 | + | 0.0894820i | ||||
\(232\) | −12121.4 | − | 6998.29i | −3.43021 | − | 1.98043i | ||||
\(233\) | − | 3446.21i | − | 0.968965i | −0.874801 | − | 0.484483i | \(-0.839008\pi\) | ||
0.874801 | − | 0.484483i | \(-0.160992\pi\) | |||||||
\(234\) | −2110.48 | + | 8444.31i | −0.589601 | + | 2.35907i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6104.11 | − | 10572.6i | 1.68366 | − | 2.91618i | ||||
\(237\) | 2880.18 | − | 403.952i | 0.789401 | − | 0.110715i | ||||
\(238\) | 6449.06 | − | 3723.37i | 1.75643 | − | 1.01408i | ||||
\(239\) | −862.406 | − | 1493.73i | −0.233408 | − | 0.404274i | 0.725401 | − | 0.688326i | \(-0.241654\pi\) |
−0.958809 | + | 0.284053i | \(0.908321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2787.86 | − | 4828.71i | 0.745152 | − | 1.29064i | −0.204972 | − | 0.978768i | \(-0.565710\pi\) |
0.950124 | − | 0.311873i | \(-0.100956\pi\) | |||||||
\(242\) | − | 6280.96i | − | 1.66841i | ||||||
\(243\) | −652.496 | − | 3731.37i | −0.172254 | − | 0.985053i | ||||
\(244\) | 16246.4 | 4.26259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1935.54 | + | 1511.33i | −0.501649 | + | 0.391702i | ||||
\(247\) | −626.649 | + | 361.796i | −0.161428 | + | 0.0932006i | ||||
\(248\) | −4645.21 | + | 2681.91i | −1.18940 | + | 0.686700i | ||||
\(249\) | −881.123 | − | 6282.42i | −0.224253 | − | 1.59893i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1356.38 | −0.341090 | −0.170545 | − | 0.985350i | \(-0.554553\pi\) | ||||
−0.170545 | + | 0.985350i | \(0.554553\pi\) | |||||||
\(252\) | 6914.14 | + | 1728.05i | 1.72837 | + | 0.431971i | ||||
\(253\) | 868.913i | 0.215921i | ||||||||
\(254\) | 4872.75 | − | 8439.84i | 1.20371 | − | 2.08489i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2231.56 | − | 3865.18i | −0.544815 | − | 0.943647i | ||||
\(257\) | −3540.16 | + | 2043.91i | −0.859256 | + | 0.496092i | −0.863763 | − | 0.503898i | \(-0.831899\pi\) |
0.00450688 | + | 0.999990i | \(0.498565\pi\) | |||||||
\(258\) | 1252.54 | − | 3097.61i | 0.302246 | − | 0.747476i | ||||
\(259\) | −141.298 | + | 244.736i | −0.0338990 | + | 0.0587148i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3881.49 | + | 3752.57i | 0.920530 | + | 0.889954i | ||||
\(262\) | − | 6668.25i | − | 1.57239i | ||||||
\(263\) | −372.616 | − | 215.130i | −0.0873631 | − | 0.0504391i | 0.455682 | − | 0.890143i | \(-0.349395\pi\) |
−0.543045 | + | 0.839704i | \(0.682729\pi\) | |||||||
\(264\) | 648.178 | + | 4621.52i | 0.151108 | + | 1.07741i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 409.096 | + | 708.575i | 0.0942980 | + | 0.163329i | ||||
\(267\) | 818.360 | + | 1048.06i | 0.187576 | + | 0.240227i | ||||
\(268\) | −4208.76 | − | 2429.93i | −0.959295 | − | 0.553849i | ||||
\(269\) | −3467.85 | −0.786017 | −0.393008 | − | 0.919535i | \(-0.628566\pi\) | ||||
−0.393008 | + | 0.919535i | \(0.628566\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −55.4415 | −0.0124274 | −0.00621371 | − | 0.999981i | \(-0.501978\pi\) | ||||
−0.00621371 | + | 0.999981i | \(0.501978\pi\) | |||||||
\(272\) | 19907.2 | + | 11493.4i | 4.43769 | + | 2.56210i | ||||
\(273\) | 2406.46 | + | 3081.92i | 0.533499 | + | 0.683247i | ||||
\(274\) | 1362.90 | + | 2360.62i | 0.300497 | + | 0.520475i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1026.31 | + | 7317.59i | 0.223828 | + | 1.59589i | ||||
\(277\) | 1362.72 | + | 786.769i | 0.295589 | + | 0.170658i | 0.640460 | − | 0.767992i | \(-0.278744\pi\) |
−0.344871 | + | 0.938650i | \(0.612077\pi\) | |||||||
\(278\) | 1150.67i | 0.248247i | ||||||||
\(279\) | 1989.15 | − | 569.160i | 0.426836 | − | 0.122132i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4073.23 | + | 7055.04i | −0.864727 | + | 1.49775i | 0.00259078 | + | 0.999997i | \(0.499175\pi\) |
−0.867318 | + | 0.497755i | \(0.834158\pi\) | |||||||
\(282\) | −2550.55 | + | 6307.68i | −0.538592 | + | 1.33198i | ||||
\(283\) | −2683.21 | + | 1549.15i | −0.563605 | + | 0.325398i | −0.754591 | − | 0.656195i | \(-0.772165\pi\) |
0.190986 | + | 0.981593i | \(0.438832\pi\) | |||||||
\(284\) | −7815.05 | − | 13536.1i | −1.63288 | − | 2.82823i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2068.13 | + | 3582.10i | −0.427591 | + | 0.740609i | ||||
\(287\) | 1103.18i | 0.226894i | ||||||||
\(288\) | 4198.22 | + | 14672.3i | 0.858967 | + | 3.00199i | ||||
\(289\) | −7189.39 | −1.46334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −757.445 | − | 5400.60i | −0.152585 | − | 1.08793i | ||||
\(292\) | −4816.16 | + | 2780.61i | −0.965221 | + | 0.557271i | ||||
\(293\) | −105.794 | + | 61.0799i | −0.0210939 | + | 0.0121786i | −0.510510 | − | 0.859872i | \(-0.670543\pi\) |
0.489416 | + | 0.872050i | \(0.337210\pi\) | |||||||
\(294\) | −4079.87 | + | 3185.69i | −0.809330 | + | 0.631949i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1573.65 | −0.309008 | ||||||||
\(297\) | 189.682 | − | 1790.07i | 0.0370588 | − | 0.349733i | ||||
\(298\) | 4875.12i | 0.947679i | ||||||||
\(299\) | −2027.06 | + | 3510.97i | −0.392066 | + | 0.679078i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −750.504 | − | 1299.91i | −0.143715 | − | 0.248922i | ||||
\(302\) | 6336.25 | − | 3658.24i | 1.20732 | − | 0.697046i | ||||
\(303\) | −456.570 | + | 64.0349i | −0.0865652 | + | 0.0121410i | ||||
\(304\) | −1262.81 | + | 2187.25i | −0.238247 | + | 0.412657i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11499.6 | − | 11117.7i | −2.14833 | − | 2.07697i | ||||
\(307\) | − | 1928.53i | − | 0.358525i | −0.983801 | − | 0.179263i | \(-0.942629\pi\) | ||
0.983801 | − | 0.179263i | \(-0.0573712\pi\) | |||||||
\(308\) | 2933.00 | + | 1693.37i | 0.542608 | + | 0.313275i | ||||
\(309\) | 7438.15 | + | 3007.66i | 1.36939 | + | 0.553721i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3969.65 | − | 6875.63i | −0.723788 | − | 1.25364i | −0.959471 | − | 0.281807i | \(-0.909066\pi\) |
0.235683 | − | 0.971830i | \(-0.424267\pi\) | |||||||
\(312\) | −8162.33 | + | 20186.0i | −1.48109 | + | 3.66285i | ||||
\(313\) | −5853.37 | − | 3379.44i | −1.05703 | − | 0.610279i | −0.132424 | − | 0.991193i | \(-0.542276\pi\) |
−0.924611 | + | 0.380914i | \(0.875609\pi\) | |||||||
\(314\) | −10238.8 | −1.84015 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11753.2 | 2.09232 | ||||||||
\(317\) | −7295.60 | − | 4212.12i | −1.29262 | − | 0.746297i | −0.313505 | − | 0.949587i | \(-0.601503\pi\) |
−0.979119 | + | 0.203290i | \(0.934837\pi\) | |||||||
\(318\) | 8133.44 | − | 1140.73i | 1.43428 | − | 0.201161i | ||||
\(319\) | 1282.80 | + | 2221.87i | 0.225150 | + | 0.389972i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2399.05 | − | 1873.25i | 0.417139 | − | 0.325715i | ||||
\(322\) | 3969.97 | + | 2292.06i | 0.687074 | + | 0.396683i | ||||
\(323\) | − | 1329.72i | − | 0.229064i | ||||||
\(324\) | −516.912 | − | 15299.2i | −0.0886337 | − | 2.62332i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6260.49 | − | 10843.5i | 1.06361 | − | 1.84222i | ||||
\(327\) | −4371.66 | − | 5598.73i | −0.739307 | − | 0.946822i | ||||
\(328\) | −5320.08 | + | 3071.55i | −0.895586 | + | 0.517067i | ||||
\(329\) | 1528.25 | + | 2647.01i | 0.256095 | + | 0.443570i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128.837 | + | 223.153i | −0.0213944 | + | 0.0370562i | −0.876524 | − | 0.481357i | \(-0.840144\pi\) |
0.855130 | + | 0.518414i | \(0.173477\pi\) | |||||||
\(332\) | − | 25636.9i | − | 4.23797i | ||||||
\(333\) | 588.886 | + | 147.180i | 0.0969091 | + | 0.0242205i | ||||
\(334\) | −10585.9 | −1.73424 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12652.7 | + | 5116.20i | 2.05435 | + | 0.830690i | ||||
\(337\) | −9612.47 | + | 5549.76i | −1.55378 | + | 0.897077i | −0.555954 | + | 0.831213i | \(0.687647\pi\) |
−0.997829 | + | 0.0658636i | \(0.979020\pi\) | |||||||
\(338\) | −6467.25 | + | 3733.87i | −1.04075 | + | 0.600874i | ||||
\(339\) | −820.997 | − | 331.975i | −0.131535 | − | 0.0531870i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 983.198 | 0.156138 | ||||||||
\(342\) | 1221.53 | − | 1263.49i | 0.193136 | − | 0.199772i | ||||
\(343\) | 6636.94i | 1.04478i | ||||||||
\(344\) | 4179.21 | − | 7238.60i | 0.655023 | − | 1.13453i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6187.14 | + | 10716.4i | 0.961337 | + | 1.66508i | ||||
\(347\) | 8562.02 | − | 4943.28i | 1.32459 | − | 0.764753i | 0.340134 | − | 0.940377i | \(-0.389528\pi\) |
0.984457 | + | 0.175624i | \(0.0561943\pi\) | |||||||
\(348\) | 13427.5 | + | 17196.4i | 2.06836 | + | 2.64892i | ||||
\(349\) | 3029.60 | − | 5247.42i | 0.464673 | − | 0.804837i | −0.534514 | − | 0.845160i | \(-0.679505\pi\) |
0.999187 | + | 0.0403230i | \(0.0128387\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4942.43 | − | 6790.54i | 0.751589 | − | 1.03263i | ||||
\(352\) | 7252.23i | 1.09814i | ||||||||
\(353\) | −7877.96 | − | 4548.34i | −1.18782 | − | 0.685790i | −0.230012 | − | 0.973188i | \(-0.573877\pi\) |
−0.957811 | + | 0.287398i | \(0.907210\pi\) | |||||||
\(354\) | −12822.2 | + | 10011.9i | −1.92511 | + | 1.50318i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2686.81 | + | 4653.70i | 0.400002 | + | 0.692824i | ||||
\(357\) | −7115.90 | + | 998.020i | −1.05494 | + | 0.147957i | ||||
\(358\) | −4074.55 | − | 2352.44i | −0.601527 | − | 0.347291i | ||||
\(359\) | 8804.63 | 1.29440 | 0.647201 | − | 0.762319i | \(-0.275939\pi\) | ||||
0.647201 | + | 0.762319i | \(0.275939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6712.90 | −0.978700 | ||||||||
\(362\) | −6968.33 | − | 4023.17i | −1.01173 | − | 0.584124i | ||||
\(363\) | −2271.95 | + | 5618.70i | −0.328503 | + | 0.812411i | ||||
\(364\) | 7900.80 | + | 13684.6i | 1.13768 | + | 1.97051i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20070.3 | − | 8115.56i | −2.86638 | − | 1.15904i | ||||
\(367\) | −7493.17 | − | 4326.18i | −1.06578 | − | 0.615326i | −0.138752 | − | 0.990327i | \(-0.544309\pi\) |
−0.927025 | + | 0.375001i | \(0.877642\pi\) | |||||||
\(368\) | 14150.5i | 2.00447i | ||||||||
\(369\) | 2278.14 | − | 651.849i | 0.321396 | − | 0.0919619i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1844.79 | − | 3195.27i | 0.258158 | − | 0.447143i | ||||
\(372\) | 8280.04 | − | 1161.29i | 1.15403 | − | 0.161855i | ||||
\(373\) | 10321.8 | − | 5959.31i | 1.43283 | − | 0.827243i | 0.435491 | − | 0.900193i | \(-0.356575\pi\) |
0.997336 | + | 0.0729500i | \(0.0232413\pi\) | |||||||
\(374\) | −3800.53 | − | 6582.70i | −0.525456 | − | 0.910116i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8510.14 | + | 14740.0i | −1.16723 | + | 2.02170i | ||||
\(377\) | 11970.4i | 1.63529i | ||||||||
\(378\) | −7678.30 | − | 5588.59i | −1.04479 | − | 0.760439i | ||||
\(379\) | −5052.23 | −0.684738 | −0.342369 | − | 0.939566i | \(-0.611229\pi\) | ||||
−0.342369 | + | 0.939566i | \(0.611229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7411.83 | + | 5787.38i | −0.996640 | + | 0.778206i | ||||
\(382\) | 23552.2 | − | 13597.9i | 3.15455 | − | 1.82128i | ||||
\(383\) | 4616.24 | − | 2665.19i | 0.615871 | − | 0.355573i | −0.159388 | − | 0.987216i | \(-0.550952\pi\) |
0.775260 | + | 0.631642i | \(0.217619\pi\) | |||||||
\(384\) | 2069.33 | + | 14754.4i | 0.275000 | + | 1.96076i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27795.4 | 3.66515 | ||||||||
\(387\) | −2240.94 | + | 2317.93i | −0.294350 | + | 0.304463i | ||||
\(388\) | − | 22038.4i | − | 2.88358i | ||||||
\(389\) | 1669.76 | − | 2892.11i | 0.217635 | − | 0.376955i | −0.736449 | − | 0.676493i | \(-0.763499\pi\) |
0.954085 | + | 0.299537i | \(0.0968324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3725.05 | − | 6451.98i | −0.481800 | − | 0.834503i | ||||
\(392\) | −11214.0 | + | 6474.43i | −1.44488 | + | 0.834205i | ||||
\(393\) | −2412.04 | + | 5965.15i | −0.309597 | + | 0.765654i | ||||
\(394\) | 1007.07 | − | 1744.29i | 0.128770 | − | 0.223036i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1763.86 | − | 7057.42i | 0.223831 | − | 0.895577i | ||||
\(397\) | 9041.65i | 1.14304i | 0.820588 | + | 0.571520i | \(0.193646\pi\) | ||||
−0.820588 | + | 0.571520i | \(0.806354\pi\) | |||||||
\(398\) | 2813.73 | + | 1624.51i | 0.354371 | + | 0.204596i | ||||
\(399\) | −109.655 | − | 781.842i | −0.0137584 | − | 0.0980978i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 835.978 | + | 1447.96i | 0.104107 | + | 0.180318i | 0.913373 | − | 0.407124i | \(-0.133468\pi\) |
−0.809266 | + | 0.587442i | \(0.800135\pi\) | |||||||
\(402\) | 3985.56 | + | 5104.26i | 0.494482 | + | 0.633277i | ||||
\(403\) | 3972.75 | + | 2293.67i | 0.491059 | + | 0.283513i | ||||
\(404\) | −1863.14 | −0.229442 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13535.3 | 1.65455 | ||||||||
\(407\) | 249.807 | + | 144.226i | 0.0304238 | + | 0.0175652i | ||||
\(408\) | −24625.5 | − | 31537.6i | −2.98810 | − | 3.82683i | ||||
\(409\) | 236.363 | + | 409.393i | 0.0285755 | + | 0.0494943i | 0.879960 | − | 0.475049i | \(-0.157570\pi\) |
−0.851384 | + | 0.524543i | \(0.824236\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −365.316 | − | 2604.71i | −0.0438436 | − | 0.312605i | ||||
\(412\) | 28079.4 | + | 16211.6i | 3.35770 | + | 1.93857i | ||||
\(413\) | 7308.11i | 0.870722i | ||||||||
\(414\) | 2387.48 | − | 9552.59i | 0.283425 | − | 1.13402i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16918.5 | + | 29303.7i | −1.99398 | + | 3.45368i | ||||
\(417\) | 416.222 | − | 1029.35i | 0.0488789 | − | 0.120881i | ||||
\(418\) | 723.258 | − | 417.573i | 0.0846309 | − | 0.0488617i | ||||
\(419\) | 6269.65 | + | 10859.3i | 0.731008 | + | 1.26614i | 0.956453 | + | 0.291887i | \(0.0942830\pi\) |
−0.225445 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3375.88 | − | 5847.19i | 0.390808 | − | 0.676900i | −0.601748 | − | 0.798686i | \(-0.705529\pi\) |
0.992556 | + | 0.121786i | \(0.0388623\pi\) | |||||||
\(422\) | 12987.7i | 1.49818i | ||||||||
\(423\) | 4563.24 | − | 4720.02i | 0.524521 | − | 0.542542i | ||||
\(424\) | 20545.5 | 2.35325 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2892.82 | + | 20625.9i | 0.329009 | + | 2.34584i | ||||
\(427\) | −8422.51 | + | 4862.74i | −0.954552 | + | 0.551111i | ||||
\(428\) | 10652.4 | − | 6150.18i | 1.20305 | − | 0.694580i | ||||
\(429\) | 3145.79 | − | 2456.32i | 0.354033 | − | 0.276439i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7535.06 | 0.842114 | 0.421057 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421057 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(432\) | 3089.01 | − | 29151.8i | 0.344028 | − | 3.24668i | ||||
\(433\) | 5135.13i | 0.569928i | 0.958538 | + | 0.284964i | \(0.0919816\pi\) | ||||
−0.958538 | + | 0.284964i | \(0.908018\pi\) | |||||||
\(434\) | 2593.53 | − | 4492.13i | 0.286851 | − | 0.496841i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14352.9 | − | 24859.9i | −1.57656 | − | 2.73068i | ||||
\(437\) | 708.895 | − | 409.281i | 0.0775996 | − | 0.0448022i | ||||
\(438\) | 7338.74 | − | 1029.27i | 0.800590 | − | 0.112284i | ||||
\(439\) | 8486.60 | − | 14699.2i | 0.922650 | − | 1.59808i | 0.127353 | − | 0.991857i | \(-0.459352\pi\) |
0.795297 | − | 0.606220i | \(-0.207315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4802.02 | − | 1374.02i | 0.518521 | − | 0.148366i | ||||
\(442\) | − | 35464.4i | − | 3.81645i | ||||||
\(443\) | 9831.39 | + | 5676.15i | 1.05441 | + | 0.608763i | 0.923880 | − | 0.382681i | \(-0.124999\pi\) |
0.130529 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(444\) | 2274.11 | + | 919.550i | 0.243073 | + | 0.0982881i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14758.4 | − | 25562.3i | −1.56689 | − | 2.71393i | ||||
\(447\) | 1763.43 | − | 4361.09i | 0.186594 | − | 0.461460i | ||||
\(448\) | 14937.4 | + | 8624.10i | 1.57528 | + | 0.909488i | ||||
\(449\) | −11059.8 | −1.16246 | −0.581230 | − | 0.813740i | \(-0.697428\pi\) | ||||
−0.581230 | + | 0.813740i | \(0.697428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1126.04 | 0.117568 | ||||||||
\(452\) | −3099.30 | − | 1789.38i | −0.322520 | − | 0.186207i | ||||
\(453\) | −6991.42 | + | 980.562i | −0.725134 | + | 0.101702i | ||||
\(454\) | −14734.7 | − | 25521.3i | −1.52320 | − | 2.63827i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3465.12 | − | 2705.67i | 0.355853 | − | 0.277861i | ||||
\(457\) | −308.897 | − | 178.342i | −0.0316184 | − | 0.0182549i | 0.484107 | − | 0.875009i | \(-0.339144\pi\) |
−0.515726 | + | 0.856754i | \(0.672478\pi\) | |||||||
\(458\) | − | 17641.3i | − | 1.79983i | ||||||
\(459\) | 6265.63 | + | 14105.1i | 0.637156 | + | 1.43435i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5159.88 | + | 8937.17i | −0.521300 | + | 0.902918i | 0.478393 | + | 0.878146i | \(0.341219\pi\) |
−0.999693 | + | 0.0247726i | \(0.992114\pi\) | |||||||
\(462\) | −2777.45 | − | 3557.05i | −0.279694 | − | 0.358201i | ||||
\(463\) | 15734.4 | − | 9084.27i | 1.57935 | − | 0.911839i | 0.584403 | − | 0.811464i | \(-0.301329\pi\) |
0.994950 | − | 0.100376i | \(-0.0320044\pi\) | |||||||
\(464\) | 20890.7 | + | 36183.7i | 2.09014 | + | 3.62023i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9278.98 | + | 16071.7i | −0.922404 | + | 1.59765i | ||||
\(467\) | 3817.15i | 0.378237i | 0.981954 | + | 0.189118i | \(0.0605630\pi\) | ||||
−0.981954 | + | 0.189118i | \(0.939437\pi\) | |||||||
\(468\) | 23591.1 | − | 24401.6i | 2.33013 | − | 2.41018i | ||||
\(469\) | 2909.22 | 0.286429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9159.21 | + | 3703.58i | 0.896038 | + | 0.362318i | ||||
\(472\) | −35243.3 | + | 20347.7i | −3.43687 | + | 1.98428i | ||||
\(473\) | −1326.85 | + | 766.056i | −0.128982 | + | 0.0744679i | ||||
\(474\) | −14519.6 | − | 5871.08i | −1.40698 | − | 0.568919i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −29038.0 | −2.79613 | ||||||||
\(477\) | −7688.48 | − | 1921.58i | −0.738012 | − | 0.184451i | ||||
\(478\) | 9288.17i | 0.888768i | ||||||||
\(479\) | 1453.28 | − | 2517.16i | 0.138627 | − | 0.240109i | −0.788350 | − | 0.615227i | \(-0.789064\pi\) |
0.926977 | + | 0.375118i | \(0.122398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 672.921 | + | 1165.53i | 0.0637891 | + | 0.110486i | ||||
\(482\) | −26002.7 | + | 15012.7i | −2.45725 | + | 1.41869i | ||||
\(483\) | −2722.29 | − | 3486.41i | −0.256457 | − | 0.328442i | ||||
\(484\) | −12246.1 | + | 21210.8i | −1.15008 | + | 1.99200i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7003.82 | + | 19158.4i | −0.653703 | + | 1.78815i | ||||
\(487\) | 10411.1i | 0.968734i | 0.874865 | + | 0.484367i | \(0.160950\pi\) | ||||
−0.874865 | + | 0.484367i | \(0.839050\pi\) | |||||||
\(488\) | −46901.0 | − | 27078.3i | −4.35064 | − | 2.51184i | ||||
\(489\) | −9522.70 | + | 7435.61i | −0.880637 | + | 0.687628i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7316.26 | − | 12672.1i | −0.672460 | − | 1.16474i | −0.977204 | − | 0.212301i | \(-0.931904\pi\) |
0.304744 | − | 0.952434i | \(-0.401429\pi\) | |||||||
\(492\) | 9482.99 | − | 1330.01i | 0.868956 | − | 0.121873i | ||||
\(493\) | −19050.4 | − | 10998.8i | −1.74034 | − | 1.00479i | ||||
\(494\) | 3896.57 | 0.354888 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16011.6 | 1.44948 | ||||||||
\(497\) | 8102.99 | + | 4678.26i | 0.731325 | + | 0.422231i | ||||
\(498\) | −12806.3 | + | 31671.0i | −1.15234 | + | 2.84982i | ||||
\(499\) | 4083.42 | + | 7072.69i | 0.366330 | + | 0.634503i | 0.988989 | − | 0.147991i | \(-0.0472807\pi\) |
−0.622658 | + | 0.782494i | \(0.713947\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9469.74 | + | 3829.14i | 0.844464 | + | 0.341464i | ||||
\(502\) | 6325.56 | + | 3652.06i | 0.562397 | + | 0.324700i | ||||
\(503\) | 8080.38i | 0.716275i | 0.933669 | + | 0.358137i | \(0.116588\pi\) | ||||
−0.933669 | + | 0.358137i | \(0.883412\pi\) | |||||||
\(504\) | −17079.9 | − | 16512.6i | −1.50952 | − | 1.45938i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2339.56 | − | 4052.24i | 0.205546 | − | 0.356016i | ||||
\(507\) | 7135.96 | − | 1000.83i | 0.625087 | − | 0.0876698i | ||||
\(508\) | −32910.6 | + | 19000.9i | −2.87435 | + | 1.65951i | ||||
\(509\) | 58.0903 | + | 100.615i | 0.00505856 | + | 0.00876169i | 0.868544 | − | 0.495613i | \(-0.165056\pi\) |
−0.863485 | + | 0.504374i | \(0.831723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1664.54 | − | 2883.06i | 0.144099 | − | 0.249587i | ||||
\(512\) | 1095.90i | 0.0945947i | ||||||||
\(513\) | −1549.76 | + | 688.421i | −0.133379 | + | 0.0592486i | ||||
\(514\) | 22013.0 | 1.88901 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10269.3 | + | 8018.57i | −0.876124 | + | 0.684104i | ||||
\(517\) | 2701.87 | − | 1559.92i | 0.229841 | − | 0.132699i | ||||
\(518\) | 1317.91 | − | 760.895i | 0.111787 | − | 0.0645402i | ||||
\(519\) | −1658.41 | − | 11824.5i | −0.140263 | − | 1.00007i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14479.3 | −1.21756 | −0.608780 | − | 0.793339i | \(-0.708341\pi\) | ||||
−0.608780 | + | 0.793339i | \(0.708341\pi\) | |||||||
\(522\) | −7997.79 | − | 27951.3i | −0.670601 | − | 2.34367i | ||||
\(523\) | − | 6841.05i | − | 0.571966i | −0.958235 | − | 0.285983i | \(-0.907680\pi\) | ||
0.958235 | − | 0.285983i | \(-0.0923201\pi\) | |||||||
\(524\) | −13001.2 | + | 22518.7i | −1.08389 | + | 1.87736i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1158.48 | + | 2006.55i | 0.0960308 | + | 0.166330i | ||||
\(527\) | −7300.58 | + | 4214.99i | −0.603450 | + | 0.348402i | ||||
\(528\) | 5222.22 | − | 12914.9i | 0.430432 | − | 1.06449i | ||||
\(529\) | −3790.40 | + | 6565.16i | −0.311531 | + | 0.539588i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15091.7 | − | 4318.23i | 1.23338 | − | 0.352910i | ||||
\(532\) | − | 3190.48i | − | 0.260009i | ||||||
\(533\) | 4549.92 | + | 2626.90i | 0.369754 | + | 0.213478i | ||||
\(534\) | −994.552 | − | 7091.17i | −0.0805964 | − | 0.574654i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8100.05 | + | 14029.7i | 0.652741 | + | 1.13058i | ||||
\(537\) | 2794.00 | + | 3578.25i | 0.224525 | + | 0.287547i | ||||
\(538\) | 16172.6 | + | 9337.24i | 1.29600 | + | 0.748247i | ||||
\(539\) | 2373.55 | 0.189677 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12746.0 | −1.01293 | −0.506465 | − | 0.862261i | \(-0.669048\pi\) | ||||
−0.506465 | + | 0.862261i | \(0.669048\pi\) | |||||||
\(542\) | 258.555 | + | 149.277i | 0.0204906 | + | 0.0118303i | ||||
\(543\) | 4778.33 | + | 6119.56i | 0.377639 | + | 0.483638i | ||||
\(544\) | −31090.5 | − | 53850.3i | −2.45036 | − | 4.24414i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2924.56 | − | 20852.2i | −0.229230 | − | 1.63442i | ||||
\(547\) | −4313.28 | − | 2490.27i | −0.337152 | − | 0.194655i | 0.321860 | − | 0.946787i | \(-0.395692\pi\) |
−0.659012 | + | 0.752132i | \(0.729025\pi\) | |||||||
\(548\) | − | 10629.1i | − | 0.828563i | ||||||
\(549\) | 15018.6 | + | 14519.7i | 1.16754 | + | 1.12876i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1208.46 | − | 2093.12i | 0.0934342 | − | 0.161833i | ||||
\(552\) | 9233.61 | − | 22835.4i | 0.711972 | − | 1.76076i | ||||
\(553\) | −6093.14 | + | 3517.88i | −0.468547 | + | 0.270516i | ||||
\(554\) | −4236.77 | − | 7338.31i | −0.324916 | − | 0.562771i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2243.48 | − | 3885.83i | 0.171124 | − | 0.296395i | ||||
\(557\) | − | 635.610i | − | 0.0483513i | −0.999708 | − | 0.0241756i | \(-0.992304\pi\) | ||
0.999708 | − | 0.0241756i | \(-0.00769610\pi\) | |||||||
\(558\) | −10809.0 | − | 2701.49i | −0.820039 | − | 0.204952i | ||||
\(559\) | −7148.42 | −0.540869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1018.70 | + | 7263.36i | 0.0766660 | + | 0.546630i | ||||
\(562\) | 37991.6 | − | 21934.4i | 2.85156 | − | 1.64635i | ||||
\(563\) | 6527.82 | − | 3768.84i | 0.488659 | − | 0.282127i | −0.235359 | − | 0.971908i | \(-0.575627\pi\) |
0.724018 | + | 0.689781i | \(0.242293\pi\) | |||||||
\(564\) | 20911.4 | − | 16328.2i | 1.56122 | − | 1.21905i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16684.5 | 1.23905 | ||||||||
\(567\) | 4847.20 | + | 7776.73i | 0.359018 | + | 0.576000i | ||||
\(568\) | 52102.2i | 3.84887i | ||||||||
\(569\) | −1129.18 | + | 1955.79i | −0.0831943 | + | 0.144097i | −0.904620 | − | 0.426218i | \(-0.859846\pi\) |
0.821426 | + | 0.570315i | \(0.193179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5688.66 | − | 9853.06i | −0.416923 | − | 0.722132i | 0.578705 | − | 0.815537i | \(-0.303558\pi\) |
−0.995628 | + | 0.0934047i | \(0.970225\pi\) | |||||||
\(572\) | 13968.2 | − | 8064.52i | 1.02105 | − | 0.589501i | ||||
\(573\) | −25987.5 | + | 3644.81i | −1.89467 | + | 0.265731i | ||||
\(574\) | 2970.33 | − | 5144.76i | 0.215991 | − | 0.374108i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8983.10 | − | 35942.5i | 0.649819 | − | 2.60001i | ||||
\(577\) | − | 25027.9i | − | 1.80576i | −0.429890 | − | 0.902881i | \(-0.641447\pi\) | ||
0.429890 | − | 0.902881i | \(-0.358553\pi\) | |||||||
\(578\) | 33528.3 | + | 19357.5i | 2.41279 | + | 1.39302i | ||||
\(579\) | −24864.6 | − | 10054.2i | −1.78470 | − | 0.721652i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7673.39 | + | 13290.7i | 0.547928 | + | 0.949039i | ||||
\(582\) | −11008.8 | + | 27225.5i | −0.784071 | + | 1.93906i | ||||
\(583\) | −3261.48 | − | 1883.02i | −0.231692 | − | 0.133768i | ||||
\(584\) | 18538.1 | 1.31355 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 657.835 | 0.0463736 | ||||||||
\(587\) | −128.396 | − | 74.1295i | −0.00902806 | − | 0.00521235i | 0.495479 | − | 0.868620i | \(-0.334992\pi\) |
−0.504507 | + | 0.863407i | \(0.668326\pi\) | |||||||
\(588\) | 19988.9 | − | 2803.49i | 1.40192 | − | 0.196622i | ||||
\(589\) | −463.112 | − | 802.133i | −0.0323976 | − | 0.0561143i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1531.83 | + | 1196.10i | −0.106618 | + | 0.0832503i | ||||
\(592\) | 4068.17 | + | 2348.76i | 0.282434 | + | 0.163063i | ||||
\(593\) | 27452.6i | 1.90109i | 0.310590 | + | 0.950544i | \(0.399473\pi\) | ||||
−0.310590 | + | 0.950544i | \(0.600527\pi\) | |||||||
\(594\) | −5704.40 | + | 7837.42i | −0.394031 | + | 0.541369i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9505.10 | − | 16463.3i | 0.653262 | − | 1.13148i | ||||
\(597\) | −1929.43 | − | 2471.01i | −0.132272 | − | 0.169400i | ||||
\(598\) | 18906.7 | − | 10915.8i | 1.29289 | − | 0.746453i | ||||
\(599\) | −1906.00 | − | 3301.29i | −0.130012 | − | 0.225187i | 0.793669 | − | 0.608350i | \(-0.208168\pi\) |
−0.923681 | + | 0.383163i | \(0.874835\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11584.3 | + | 20064.6i | −0.786247 | + | 1.36182i | 0.142004 | + | 0.989866i | \(0.454646\pi\) |
−0.928251 | + | 0.371954i | \(0.878688\pi\) | |||||||
\(602\) | 8082.97i | 0.547238i | ||||||||
\(603\) | −1719.01 | − | 6007.73i | −0.116092 | − | 0.405728i | ||||
\(604\) | −28530.1 | −1.92197 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2301.66 | + | 930.691i | 0.154288 | + | 0.0623873i | ||||
\(607\) | 6367.69 | − | 3676.39i | 0.425794 | − | 0.245832i | −0.271759 | − | 0.962365i | \(-0.587605\pi\) |
0.697553 | + | 0.716533i | \(0.254272\pi\) | |||||||
\(608\) | 5916.67 | − | 3415.99i | 0.394659 | − | 0.227856i | ||||
\(609\) | −12108.2 | − | 4896.01i | −0.805662 | − | 0.325774i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14556.4 | 0.963809 | ||||||||
\(612\) | 17158.1 | + | 59965.4i | 1.13329 | + | 3.96072i | ||||
\(613\) | − | 19902.6i | − | 1.31135i | −0.755043 | − | 0.655676i | \(-0.772384\pi\) | ||
0.755043 | − | 0.655676i | \(-0.227616\pi\) | |||||||
\(614\) | −5192.61 | + | 8993.86i | −0.341297 | + | 0.591144i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5644.76 | − | 9777.01i | −0.369211 | − | 0.639492i | ||||
\(617\) | 21724.4 | − | 12542.6i | 1.41749 | − | 0.818390i | 0.421414 | − | 0.906868i | \(-0.361534\pi\) |
0.996078 | + | 0.0884785i | \(0.0282005\pi\) | |||||||
\(618\) | −26590.2 | − | 34053.8i | −1.73077 | − | 2.21658i | ||||
\(619\) | −1565.52 | + | 2711.56i | −0.101654 | + | 0.176069i | −0.912366 | − | 0.409375i | \(-0.865747\pi\) |
0.810712 | + | 0.585445i | \(0.199080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5591.11 | + | 7681.78i | −0.361294 | + | 0.496391i | ||||
\(622\) | 42753.3i | 2.75603i | ||||||||
\(623\) | −2785.81 | − | 1608.39i | −0.179151 | − | 0.103433i | ||||
\(624\) | 51229.9 | − | 40001.8i | 3.28660 | − | 2.56627i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18198.4 | + | 31520.6i | 1.16191 | + | 2.01248i | ||||
\(627\) | −798.043 | + | 111.927i | −0.0508306 | + | 0.00712910i | ||||
\(628\) | 34576.4 | + | 19962.7i | 2.19705 | + | 1.26847i | ||||
\(629\) | −2473.21 | −0.156778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22527.2 | −1.42123 | −0.710614 | − | 0.703582i | \(-0.751583\pi\) | ||||
−0.710614 | + | 0.703582i | \(0.751583\pi\) | |||||||
\(632\) | −33929.9 | − | 19589.4i | −2.13553 | − | 1.23295i | ||||
\(633\) | 4697.92 | − | 11618.3i | 0.294985 | − | 0.729518i | ||||
\(634\) | 22682.4 | + | 39287.0i | 1.42087 | + | 2.46102i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −29690.8 | − | 12005.6i | −1.85113 | − | 0.748513i | ||||
\(637\) | 9590.66 | + | 5537.17i | 0.596540 | + | 0.344412i | ||||
\(638\) | − | 13815.8i | − | 0.857325i | ||||||
\(639\) | 4873.00 | − | 19497.5i | 0.301679 | − | 1.20706i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3462.88 | − | 5997.88i | 0.213378 | − | 0.369582i | −0.739391 | − | 0.673276i | \(-0.764887\pi\) |
0.952770 | + | 0.303694i | \(0.0982200\pi\) | |||||||
\(642\) | −16231.9 | + | 2276.55i | −0.997852 | + | 0.139951i | ||||
\(643\) | 12959.7 | − | 7482.26i | 0.794835 | − | 0.458898i | −0.0468271 | − | 0.998903i | \(-0.514911\pi\) |
0.841662 | + | 0.540005i | \(0.181578\pi\) | |||||||
\(644\) | −8937.75 | − | 15480.6i | −0.546889 | − | 0.947240i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3580.29 | + | 6201.25i | −0.218057 | + | 0.377685i | ||||
\(647\) | − | 2371.74i | − | 0.144115i | −0.997400 | − | 0.0720577i | \(-0.977043\pi\) | ||
0.997400 | − | 0.0720577i | \(-0.0229566\pi\) | |||||||
\(648\) | −24007.3 | + | 45028.1i | −1.45540 | + | 2.72974i | ||||
\(649\) | 7459.55 | 0.451176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3944.97 | + | 3080.35i | −0.237505 | + | 0.185451i | ||||
\(652\) | −42283.4 | + | 24412.4i | −2.53980 | + | 1.46635i | ||||
\(653\) | 13831.9 | − | 7985.85i | 0.828919 | − | 0.478577i | −0.0245632 | − | 0.999698i | \(-0.507820\pi\) |
0.853482 | + | 0.521122i | \(0.174486\pi\) | |||||||
\(654\) | 5312.87 | + | 37880.9i | 0.317660 | + | 2.26492i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18337.8 | 1.09142 | ||||||||
\(657\) | −6937.25 | − | 1733.83i | −0.411945 | − | 0.102957i | ||||
\(658\) | − | 16459.4i | − | 0.975158i | ||||||
\(659\) | −3421.46 | + | 5926.15i | −0.202248 | + | 0.350304i | −0.949252 | − | 0.314515i | \(-0.898158\pi\) |
0.747005 | + | 0.664819i | \(0.231491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6695.50 | + | 11597.0i | 0.393986 | + | 0.682404i | 0.992971 | − | 0.118356i | \(-0.0377624\pi\) |
−0.598985 | + | 0.800760i | \(0.704429\pi\) | |||||||
\(662\) | 1201.68 | − | 693.793i | 0.0705511 | − | 0.0407327i | ||||
\(663\) | −12828.2 | + | 31725.1i | −0.751443 | + | 1.85837i | ||||
\(664\) | −42729.6 | + | 74009.8i | −2.49733 | + | 4.32551i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2350.03 | − | 2271.97i | −0.136729 | − | 0.132188i | ||||
\(667\) | − | 13541.5i | − | 0.786098i | ||||||
\(668\) | 35748.7 | + | 20639.5i | 2.07060 | + | 1.19546i | ||||
\(669\) | 3955.88 | + | 28205.5i | 0.228615 | + | 1.63003i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4963.51 | + | 8597.05i | 0.285565 | + | 0.494613i | ||||
\(672\) | −22721.2 | − | 29098.7i | −1.30430 | − | 1.67040i | ||||
\(673\) | −27628.1 | − | 15951.1i | −1.58244 | − | 0.913624i | −0.994502 | − | 0.104720i | \(-0.966605\pi\) |
−0.587941 | − | 0.808904i | \(-0.700061\pi\) | |||||||
\(674\) | 59771.3 | 3.41588 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29119.9 | 1.65680 | ||||||||
\(677\) | 10271.7 | + | 5930.38i | 0.583123 | + | 0.336666i | 0.762373 | − | 0.647137i | \(-0.224034\pi\) |
−0.179251 | + | 0.983803i | \(0.557367\pi\) | |||||||
\(678\) | 2934.93 | + | 3758.74i | 0.166247 | + | 0.212911i | ||||
\(679\) | 6596.33 | + | 11425.2i | 0.372818 | + | 0.645741i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3949.53 | + | 28160.2i | 0.222241 | + | 1.58458i | ||||
\(682\) | −4585.22 | − | 2647.28i | −0.257444 | − | 0.148636i | ||||
\(683\) | − | 7639.34i | − | 0.427981i | −0.976836 | − | 0.213991i | \(-0.931354\pi\) | ||
0.976836 | − | 0.213991i | \(-0.0686462\pi\) | |||||||
\(684\) | −6588.55 | + | 1885.20i | −0.368303 | + | 0.105384i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17870.1 | − | 30951.9i | 0.994580 | − | 1.72266i | ||||
\(687\) | −6381.21 | + | 15781.2i | −0.354379 | + | 0.876405i | ||||
\(688\) | −21608.0 | + | 12475.4i | −1.19738 | + | 0.691309i | ||||
\(689\) | −8785.64 | − | 15217.2i | −0.485786 | − | 0.841406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7863.00 | − | 13619.1i | 0.432883 | − | 0.749776i | −0.564237 | − | 0.825613i | \(-0.690829\pi\) |
0.997120 | + | 0.0758369i | \(0.0241628\pi\) | |||||||
\(692\) | − | 48252.6i | − | 2.65071i | ||||||
\(693\) | 1197.94 | + | 4186.66i | 0.0656652 | + | 0.229492i | ||||
\(694\) | −53239.5 | −2.91202 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10101.4 | − | 72023.4i | −0.550135 | − | 3.92247i | ||||
\(697\) | −8361.23 | + | 4827.36i | −0.454382 | + | 0.262338i | ||||
\(698\) | −28257.5 | + | 16314.5i | −1.53232 | + | 0.884688i | ||||
\(699\) | 14114.1 | − | 11020.7i | 0.763724 | − | 0.596338i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6338.17 | −0.341497 | −0.170748 | − | 0.985315i | \(-0.554619\pi\) | ||||
−0.170748 | + | 0.985315i | \(0.554619\pi\) | |||||||
\(702\) | −41333.0 | + | 18360.6i | −2.22224 | + | 0.987146i | ||||
\(703\) | − | 271.737i | − | 0.0145786i | ||||||
\(704\) | 8802.82 | − | 15246.9i | 0.471262 | − | 0.816250i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24493.0 | + | 42423.1i | 1.30567 | + | 2.26149i | ||||
\(707\) | 965.892 | − | 557.658i | 0.0513806 | − | 0.0296646i | ||||
\(708\) | 62820.9 | − | 8810.76i | 3.33468 | − | 0.467696i | ||||
\(709\) | 17191.8 | − | 29777.1i | 0.910651 | − | 1.57729i | 0.0975047 | − | 0.995235i | \(-0.468914\pi\) |
0.813147 | − | 0.582059i | \(-0.197753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10865.0 | + | 10504.1i | 0.573092 | + | 0.554056i | ||||
\(712\) | − | 17912.7i | − | 0.942847i | ||||||
\(713\) | −4494.16 | − | 2594.70i | −0.236055 | − | 0.136287i | ||||
\(714\) | 35872.7 | + | 14505.3i | 1.88025 | + | 0.760292i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9173.18 | + | 15888.4i | 0.478796 | + | 0.829299i | ||||
\(717\) | 3359.72 | − | 8308.83i | 0.174995 | − | 0.432774i | ||||
\(718\) | −41061.0 | − | 23706.6i | −2.13424 | − | 1.23220i | ||||
\(719\) | 988.886 | 0.0512924 | 0.0256462 | − | 0.999671i | \(-0.491836\pi\) | ||||
0.0256462 | + | 0.999671i | \(0.491836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19409.3 | −1.00255 | ||||||||
\(722\) | 31306.1 | + | 18074.6i | 1.61370 | + | 0.931671i | ||||
\(723\) | 28691.4 | − | 4024.03i | 1.47586 | − | 0.206992i | ||||
\(724\) | 15688.1 | + | 27172.5i | 0.805307 | + | 1.39483i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25723.8 | − | 20085.9i | 1.31502 | − | 1.02680i | ||||
\(727\) | 11857.5 | + | 6845.92i | 0.604910 | + | 0.349245i | 0.770971 | − | 0.636871i | \(-0.219771\pi\) |
−0.166061 | + | 0.986116i | \(0.553105\pi\) | |||||||
\(728\) | − | 52673.8i | − | 2.68162i | ||||||
\(729\) | 13195.3 | − | 14604.9i | 0.670392 | − | 0.742007i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6568.20 | − | 11376.5i | 0.332331 | − | 0.575614i | ||||
\(732\) | 51954.7 | + | 66537.8i | 2.62336 | + | 3.35971i | ||||
\(733\) | 2166.74 | − | 1250.97i | 0.109182 | − | 0.0630363i | −0.444415 | − | 0.895821i | \(-0.646588\pi\) |
0.553597 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(734\) | 23296.6 | + | 40350.9i | 1.17152 | + | 2.02913i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19139.0 | − | 33149.7i | 0.958521 | − | 1.66021i | ||||
\(737\) | − | 2969.51i | − | 0.148417i | ||||||
\(738\) | −12379.4 | − | 3093.97i | −0.617468 | − | 0.154323i | ||||
\(739\) | −26453.1 | −1.31677 | −0.658384 | − | 0.752682i | \(-0.728760\pi\) | ||||
−0.658384 | + | 0.752682i | \(0.728760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3485.72 | − | 1409.47i | −0.172808 | − | 0.0698760i | ||||
\(742\) | −17206.6 | + | 9934.24i | −0.851313 | + | 0.491506i | ||||
\(743\) | 18085.0 | − | 10441.4i | 0.892967 | − | 0.515555i | 0.0180555 | − | 0.999837i | \(-0.494252\pi\) |
0.874912 | + | 0.484282i | \(0.160919\pi\) | |||||||
\(744\) | −25838.8 | − | 10448.1i | −1.27325 | − | 0.514845i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −64182.2 | −3.14997 | ||||||||
\(747\) | 22912.1 | − | 23699.3i | 1.12224 | − | 1.16079i | ||||
\(748\) | 29639.8i | 1.44885i | ||||||||
\(749\) | −3681.64 | + | 6376.78i | −0.179605 | + | 0.311085i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8847.65 | + | 15324.6i | 0.429901 | + | 0.744610i | 0.996864 | − | 0.0791332i | \(-0.0252152\pi\) |
−0.566963 | + | 0.823743i | \(0.691882\pi\) | |||||||
\(752\) | 44000.6 | − | 25403.7i | 2.13369 | − | 1.23189i | ||||
\(753\) | −4337.57 | − | 5555.08i | −0.209920 | − | 0.268842i | ||||
\(754\) | 32230.4 | − | 55824.8i | 1.55672 | − | 2.69631i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15033.5 | + | 33843.2i | 0.723233 | + | 1.62813i | ||||
\(757\) | 7755.61i | 0.372368i | 0.982515 | + | 0.186184i | \(0.0596120\pi\) | ||||
−0.982515 | + | 0.186184i | \(0.940388\pi\) | |||||||
\(758\) | 23561.4 | + | 13603.2i | 1.12901 | + | 0.651835i | ||||
\(759\) | −3558.66 | + | 2778.71i | −0.170186 | + | 0.132886i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8527.15 | − | 14769.5i | −0.406188 | − | 0.703538i | 0.588271 | − | 0.808664i | \(-0.299809\pi\) |
−0.994459 | + | 0.105126i | \(0.966476\pi\) | |||||||
\(762\) | 50148.2 | − | 7033.40i | 2.38409 | − | 0.334374i | ||||
\(763\) | 14881.7 | + | 8591.95i | 0.706099 | + | 0.407667i | ||||
\(764\) | −106048. | −5.02184 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28704.2 | −1.35395 | ||||||||
\(767\) | 30141.3 | + | 17402.1i | 1.41896 | + | 0.819236i | ||||
\(768\) | 8693.61 | − | 21499.9i | 0.408468 | − | 1.01017i | ||||
\(769\) | −5024.16 | − | 8702.11i | −0.235599 | − | 0.408070i | 0.723847 | − | 0.689960i | \(-0.242372\pi\) |
−0.959447 | + | 0.281890i | \(0.909039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19692.0 | − | 7962.57i | −0.919831 | − | 0.371939i | ||||
\(772\) | −93865.1 | − | 54193.0i | −4.37601 | − | 2.52649i | ||||
\(773\) | − | 7293.24i | − | 0.339352i | −0.985500 | − | 0.169676i | \(-0.945728\pi\) | ||
0.985500 | − | 0.169676i | \(-0.0542722\pi\) | |||||||
\(774\) | 16691.9 | − | 4776.09i | 0.775164 | − | 0.221800i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36731.9 | + | 63621.5i | −1.69922 | + | 2.94314i | ||||
\(777\) | −1454.18 | + | 203.952i | −0.0671409 | + | 0.00941665i | ||||
\(778\) | −15574.1 | + | 8991.70i | −0.717684 | + | 0.414355i | ||||
\(779\) | −530.394 | − | 918.670i | −0.0243945 | − | 0.0422526i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4775.21 | − | 8270.90i | 0.218784 | − | 0.378945i | ||||
\(782\) | 40119.0i | 1.83460i | ||||||||
\(783\) | −2956.07 | + | 27897.1i | −0.134919 | + | 1.27326i | ||||
\(784\) | 38653.8 | 1.76083 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27310.0 | − | 21324.5i | 1.23933 | − | 0.967708i | ||||
\(787\) | 24643.8 | − | 14228.1i | 1.11621 | − | 0.644445i | 0.175780 | − | 0.984429i | \(-0.443755\pi\) |
0.940431 | + | 0.339985i | \(0.110422\pi\) | |||||||
\(788\) | −6801.75 | + | 3926.99i | −0.307490 | + | 0.177530i | ||||
\(789\) | −310.522 | − | 2214.03i | −0.0140112 | − | 0.0999004i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2142.33 | 0.0962989 | ||||||||
\(792\) | −16854.8 | + | 17433.9i | −0.756197 | + | 0.782178i | ||||
\(793\) | 46316.7i | 2.07409i | ||||||||
\(794\) | 24344.8 | − | 42166.4i | 1.08812 | − | 1.88467i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6334.66 | − | 10971.9i | −0.282068 | − | 0.488556i | ||||
\(797\) | 3534.65 | − | 2040.73i | 0.157094 | − | 0.0906981i | −0.419392 | − | 0.907805i | \(-0.637757\pi\) |
0.576486 | + | 0.817107i | \(0.304424\pi\) | |||||||
\(798\) | −1593.74 | + | 3941.42i | −0.0706988 | + | 0.174843i | ||||
\(799\) | −13374.9 | + | 23165.9i | −0.592201 | + | 1.02572i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1675.34 | + | 6703.24i | −0.0739015 | + | 0.295689i | ||||
\(802\) | − | 9003.54i | − | 0.396416i | ||||||
\(803\) | −2942.81 | − | 1699.03i | −0.129327 | − | 0.0746668i | ||||
\(804\) | −3507.40 | − | 25007.8i | −0.153851 | − | 1.09696i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12351.5 | − | 21393.4i | −0.539779 | − | 0.934925i | ||||
\(807\) | −11089.9 | − | 14202.7i | −0.483745 | − | 0.619527i | ||||
\(808\) | 5378.60 | + | 3105.34i | 0.234181 | + | 0.135205i | ||||
\(809\) | −14209.7 | −0.617536 | −0.308768 | − | 0.951137i | \(-0.599917\pi\) | ||||
−0.308768 | + | 0.951137i | \(0.599917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4901.79 | 0.212238 | 0.106119 | − | 0.994353i | \(-0.466158\pi\) | ||||
0.106119 | + | 0.994353i | \(0.466158\pi\) | |||||||
\(812\) | −45708.9 | − | 26390.0i | −1.97545 | − | 1.14053i | ||||
\(813\) | −177.297 | − | 227.062i | −0.00764831 | − | 0.00979511i | ||||
\(814\) | −776.663 | − | 1345.22i | −0.0334423 | − | 0.0579237i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16589.8 | + | 118286.i | 0.711714 | + | 5.07454i | ||||
\(817\) | 1249.96 | + | 721.665i | 0.0535258 | + | 0.0309031i | ||||
\(818\) | − | 2545.64i | − | 0.108810i | ||||||
\(819\) | −4926.47 | + | 19711.4i | −0.210189 | + | 0.840992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7259.82 | − | 12574.4i | 0.308611 | − | 0.534530i | −0.669448 | − | 0.742859i | \(-0.733469\pi\) |
0.978059 | + | 0.208329i | \(0.0668026\pi\) | |||||||
\(822\) | −5309.54 | + | 13130.9i | −0.225294 | + | 0.557167i | ||||
\(823\) | 33260.9 | − | 19203.2i | 1.40875 | − | 0.813344i | 0.413485 | − | 0.910511i | \(-0.364312\pi\) |
0.995268 | + | 0.0971672i | \(0.0309782\pi\) | |||||||
\(824\) | −54040.6 | − | 93601.1i | −2.28470 | − | 3.95722i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19677.2 | − | 34081.9i | 0.828882 | − | 1.43567i | ||||
\(827\) | − | 10446.4i | − | 0.439248i | −0.975585 | − | 0.219624i | \(-0.929517\pi\) | ||
0.975585 | − | 0.219624i | \(-0.0704830\pi\) | |||||||
\(828\) | −26687.4 | + | 27604.3i | −1.12011 | + | 1.15859i | ||||
\(829\) | 6474.00 | 0.271232 | 0.135616 | − | 0.990761i | \(-0.456699\pi\) | ||||
0.135616 | + | 0.990761i | \(0.456699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1135.63 | + | 8097.09i | 0.0474064 | + | 0.338008i | ||||
\(832\) | 71138.0 | − | 41071.6i | 2.96426 | − | 1.71142i | ||||
\(833\) | −17624.4 | + | 10175.5i | −0.733073 | + | 0.423240i | ||||
\(834\) | −4712.61 | + | 3679.75i | −0.195665 | + | 0.152781i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3256.60 | −0.134727 | ||||||||
\(837\) | 8692.13 | + | 6326.49i | 0.358953 | + | 0.261261i | ||||
\(838\) | − | 67524.5i | − | 2.78353i | ||||||
\(839\) | 7919.71 | − | 13717.3i | 0.325886 | − | 0.564452i | −0.655805 | − | 0.754930i | \(-0.727671\pi\) |
0.981691 | + | 0.190478i | \(0.0610039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7797.09 | − | 13505.0i | −0.319697 | − | 0.553731i | ||||
\(842\) | −31487.3 | + | 18179.2i | −1.28875 | + | 0.744058i | ||||
\(843\) | −41919.9 | + | 5879.36i | −1.71269 | + | 0.240209i | ||||
\(844\) | 25322.3 | − | 43859.5i | 1.03274 | − | 1.78875i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −33989.7 | + | 9725.57i | −1.38131 | + | 0.395239i | ||||
\(847\) | − | 14661.5i | − | 0.594778i | ||||||
\(848\) | −53114.0 | − | 30665.4i | −2.15087 | − | 1.24181i | ||||
\(849\) | −14925.3 | − | 6035.12i | −0.603338 | − | 0.243963i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −761.239 | − | 1318.51i | −0.0306639 | − | 0.0531114i | ||||
\(852\) | 30445.5 | − | 75293.9i | 1.22423 | − | 3.02761i | ||||
\(853\) | −16316.2 | − | 9420.17i | −0.654931 | − | 0.378125i | 0.135412 | − | 0.990789i | \(-0.456764\pi\) |
−0.790343 | + | 0.612665i | \(0.790098\pi\) | |||||||
\(854\) | 52372.0 | 2.09852 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41002.6 | −1.63720 | ||||||||
\(857\) | −7842.91 | − | 4528.11i | −0.312612 | − | 0.180487i | 0.335483 | − | 0.942046i | \(-0.391101\pi\) |
−0.648095 | + | 0.761560i | \(0.724434\pi\) | |||||||
\(858\) | −21284.3 | + | 2985.17i | −0.846893 | + | 0.118778i | ||||
\(859\) | 11027.7 | + | 19100.6i | 0.438022 | + | 0.758676i | 0.997537 | − | 0.0701440i | \(-0.0223459\pi\) |
−0.559515 | + | 0.828820i | \(0.689013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4518.10 | + | 3527.87i | −0.178835 | + | 0.139639i | ||||
\(862\) | −35140.3 | − | 20288.3i | −1.38850 | − | 0.801649i | ||||
\(863\) | − | 13105.6i | − | 0.516941i | −0.966019 | − | 0.258471i | \(-0.916781\pi\) | ||
0.966019 | − | 0.258471i | \(-0.0832185\pi\) | |||||||
\(864\) | −46665.2 | + | 64114.6i | −1.83748 | + | 2.52456i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13826.4 | − | 23948.1i | 0.542542 | − | 0.939710i | ||||
\(867\) | −22991.0 | − | 29444.4i | −0.900596 | − | 1.15338i | ||||
\(868\) | −17516.7 | + | 10113.3i | −0.684973 | + | 0.395470i | ||||
\(869\) | 3590.78 | + | 6219.41i | 0.140171 | + | 0.242784i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6927.46 | − | 11998.7i | 0.269492 | − | 0.466775i | ||||
\(872\) | 95689.2i | 3.71611i | ||||||||
\(873\) | 19696.1 | − | 20372.8i | 0.763586 | − | 0.789821i | ||||
\(874\) | −4407.98 | −0.170597 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26789.7 | − | 10832.6i | −1.03327 | − | 0.417807i | ||||
\(877\) | −31802.4 | + | 18361.1i | −1.22450 | + | 0.706967i | −0.965875 | − | 0.259010i | \(-0.916604\pi\) |
−0.258628 | + | 0.965977i | \(0.583270\pi\) | |||||||
\(878\) | −79155.8 | + | 45700.6i | −3.04257 | + | 1.75663i | ||||
\(879\) | −588.473 | − | 237.952i | −0.0225810 | − | 0.00913076i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36054.4 | 1.37878 | 0.689390 | − | 0.724390i | \(-0.257879\pi\) | ||||
0.689390 | + | 0.724390i | \(0.257879\pi\) | |||||||
\(882\) | −26094.1 | − | 6521.70i | −0.996186 | − | 0.248976i | ||||
\(883\) | − | 13524.6i | − | 0.515446i | −0.966219 | − | 0.257723i | \(-0.917028\pi\) | ||
0.966219 | − | 0.257723i | \(-0.0829721\pi\) | |||||||
\(884\) | −69145.6 | + | 119764.i | −2.63079 | + | 4.55666i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30566.3 | − | 52942.3i | −1.15902 | − | 2.00749i | ||||
\(887\) | −34407.4 | + | 19865.1i | −1.30246 | + | 0.751978i | −0.980826 | − | 0.194884i | \(-0.937567\pi\) |
−0.321639 | + | 0.946863i | \(0.604234\pi\) | |||||||
\(888\) | −5032.39 | − | 6444.92i | −0.190176 | − | 0.243556i | ||||
\(889\) | 11374.4 | − | 19701.0i | 0.429116 | − | 0.743251i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7937.89 | − | 4947.65i | 0.298462 | − | 0.186030i | ||||
\(892\) | 115099.i | 4.32040i | ||||||||
\(893\) | −2545.30 | − | 1469.53i | −0.0953810 | − | 0.0550682i | ||||
\(894\) | −19966.2 | + | 15590.2i | −0.746946 | + | 0.583238i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18021.1 | − | 31213.4i | −0.671921 | − | 1.16380i | ||||
\(897\) | −20861.6 | + | 2925.88i | −0.776532 | + | 0.108910i | ||||
\(898\) | 51578.2 | + | 29778.7i | 1.91669 | + | 1.10660i | ||||
\(899\) | −15322.5 | −0.568447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32290.1 | 1.19394 | ||||||||
\(902\) | −5251.37 | − | 3031.88i | −0.193849 | − | 0.111919i | ||||
\(903\) | 2923.78 | − | 7230.71i | 0.107749 | − | 0.266471i | ||||
\(904\) | 5964.81 | + | 10331.4i | 0.219454 | + | 0.380106i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35245.2 | + | 14251.6i | 1.29243 | + | 0.522602i | ||||
\(907\) | −19938.0 | − | 11511.2i | −0.729912 | − | 0.421415i | 0.0884783 | − | 0.996078i | \(-0.471800\pi\) |
−0.818390 | + | 0.574663i | \(0.805133\pi\) | |||||||
\(908\) | 114914.i | 4.19995i | ||||||||
\(909\) | −1722.33 | − | 1665.12i | −0.0628449 | − | 0.0607574i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15940.1 | + | 27609.1i | −0.579714 | + | 1.00409i | 0.415798 | + | 0.909457i | \(0.363502\pi\) |
−0.995512 | + | 0.0946365i | \(0.969831\pi\) | |||||||
\(912\) | −12996.3 | + | 1822.76i | −0.471877 | + | 0.0661817i | ||||
\(913\) | 13566.1 | − | 7832.41i | 0.491756 | − | 0.283916i | ||||
\(914\) | 960.376 | + | 1663.42i | 0.0347554 | + | 0.0601981i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34395.5 | + | 59574.7i | −1.24067 | + | 2.14891i | ||||
\(917\) | − | 15565.6i | − | 0.560547i | ||||||
\(918\) | 8757.89 | − | 82650.4i | 0.314873 | − | 2.97153i | ||||
\(919\) | −38459.6 | −1.38049 | −0.690243 | − | 0.723578i | \(-0.742496\pi\) | ||||
−0.690243 | + | 0.723578i | \(0.742496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7898.37 | − | 6167.28i | 0.282584 | − | 0.220650i | ||||
\(922\) | 48126.9 | − | 27786.1i | 1.71906 | − | 0.992501i | ||||
\(923\) | 38589.8 | − | 22279.8i | 1.37616 | − | 0.794528i | ||||
\(924\) | 2444.23 | + | 17427.4i | 0.0870231 | + | 0.620477i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −97838.1 | −3.47209 | ||||||||
\(927\) | 11468.6 | + | 40081.4i | 0.406341 | + | 1.42011i | ||||
\(928\) | − | 113021.i | − | 3.99796i | ||||||
\(929\) | −18600.5 | + | 32217.1i | −0.656903 | + | 1.13779i | 0.324509 | + | 0.945882i | \(0.394801\pi\) |
−0.981413 | + | 0.191908i | \(0.938533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1118.00 | − | 1936.44i | −0.0393567 | − | 0.0681678i | ||||
\(932\) | 62670.3 | − | 36182.7i | 2.20261 | − | 1.27168i | ||||
\(933\) | 15464.8 | − | 38245.5i | 0.542651 | − | 1.34201i | ||||
\(934\) | 10277.7 | − | 17801.5i | 0.360062 | − | 0.623645i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −108775. | + | 31124.0i | −3.79852 | + | 1.08688i | ||||
\(937\) | − | 23593.7i | − | 0.822595i | −0.911501 | − | 0.411298i | \(-0.865076\pi\) | ||
0.911501 | − | 0.411298i | \(-0.134924\pi\) | |||||||
\(938\) | −13567.4 | − | 7833.12i | −0.472271 | − | 0.272666i | ||||
\(939\) | −4877.94 | − | 34779.8i | −0.169527 | − | 1.20873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18285.8 | − | 31672.0i | −0.633477 | − | 1.09721i | −0.986836 | − | 0.161726i | \(-0.948294\pi\) |
0.353359 | − | 0.935488i | \(-0.385039\pi\) | |||||||
\(942\) | −32742.7 | − | 41933.2i | −1.13250 | − | 1.45038i | ||||
\(943\) | −5147.08 | − | 2971.67i | −0.177744 | − | 0.102620i | ||||
\(944\) | 121481. | 4.18841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8250.48 | 0.283558 | ||||||||
\(947\) | −28502.4 | − | 16455.9i | −0.978039 | − | 0.564671i | −0.0763615 | − | 0.997080i | \(-0.524330\pi\) |
−0.901678 | + | 0.432409i | \(0.857664\pi\) | |||||||
\(948\) | 37585.8 | + | 48135.8i | 1.28769 | + | 1.64913i | ||||
\(949\) | −7927.21 | − | 13730.3i | −0.271157 | − | 0.469658i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6079.83 | − | 43349.3i | −0.207310 | − | 1.47813i | ||||
\(952\) | 83828.5 | + | 48398.4i | 2.85388 | + | 1.64769i | ||||
\(953\) | 21564.5i | 0.732993i | 0.930419 | + | 0.366497i | \(0.119443\pi\) | ||||
−0.930419 | + | 0.366497i | \(0.880557\pi\) | |||||||
\(954\) | 30681.9 | + | 29662.8i | 1.04126 | + | 1.00668i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18109.3 | − | 31366.2i | 0.612653 | − | 1.06115i | ||||
\(957\) | −4997.47 | + | 12359.1i | −0.168804 | + | 0.417464i | ||||
\(958\) | −13555.0 | + | 7825.98i | −0.457142 | + | 0.263931i | ||||
\(959\) | 3181.41 | + | 5510.36i | 0.107125 | + | 0.185546i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11959.5 | − | 20714.5i | 0.401448 | − | 0.695328i | ||||
\(962\) | − | 7247.40i | − | 0.242895i | ||||||
\(963\) | 15343.9 | + | 3834.89i | 0.513447 | + | 0.128326i | ||||
\(964\) | 117082. | 3.91178 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3308.40 | + | 23589.0i | 0.110193 | + | 0.785675i | ||||
\(967\) | 25776.2 | − | 14881.9i | 0.857193 | − | 0.494901i | −0.00587841 | − | 0.999983i | \(-0.501871\pi\) |
0.863071 | + | 0.505082i | \(0.168538\pi\) | |||||||
\(968\) | 70705.2 | − | 40821.7i | 2.34768 | − | 1.35543i | ||||
\(969\) | 5445.91 | − | 4252.33i | 0.180545 | − | 0.140975i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29812.3 | 0.985297 | 0.492648 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492648 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(972\) | 61005.4 | − | 51042.6i | 2.01311 | − | 1.68435i | ||||
\(973\) | 2686.00i | 0.0884986i | ||||||||
\(974\) | 28032.1 | − | 48553.1i | 0.922184 | − | 1.59727i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 80831.9 | + | 140005.i | 2.65099 | + | 4.59165i | ||||
\(977\) | −4988.07 | + | 2879.87i | −0.163339 | + | 0.0943041i | −0.579441 | − | 0.815014i | \(-0.696729\pi\) |
0.416102 | + | 0.909318i | \(0.363396\pi\) | |||||||
\(978\) | 64430.3 | − | 9036.49i | 2.10660 | − | 0.295455i | ||||
\(979\) | −1641.72 | + | 2843.54i | −0.0535950 | + | 0.0928292i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8949.61 | − | 35808.5i | 0.291273 | − | 1.16542i | ||||
\(982\) | 78796.5i | 2.56059i | ||||||||
\(983\) | −15286.6 | − | 8825.70i | −0.495998 | − | 0.286364i | 0.231062 | − | 0.972939i | \(-0.425780\pi\) |
−0.727059 | + | 0.686575i | \(0.759113\pi\) | |||||||
\(984\) | −29592.7 | − | 11966.0i | −0.958722 | − | 0.387665i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59228.7 | + | 102587.i | 1.91301 | + | 3.31343i | ||||
\(987\) | −5953.70 | + | 14723.9i | −0.192005 | + | 0.474841i | ||||
\(988\) | −13158.7 | − | 7597.20i | −0.423720 | − | 0.244635i | ||||
\(989\) | 8086.63 | 0.260000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5186.45 | −0.166249 | −0.0831246 | − | 0.996539i | \(-0.526490\pi\) | ||||
−0.0831246 | + | 0.996539i | \(0.526490\pi\) | |||||||
\(992\) | −37509.7 | − | 21656.2i | −1.20054 | − | 0.693131i | ||||
\(993\) | −1325.94 | + | 185.966i | −0.0423740 | + | 0.00594305i | ||||
\(994\) | −25192.6 | − | 43634.8i | −0.803884 | − | 1.39237i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 104996. | − | 81984.4i | 3.34030 | − | 2.60821i | ||||
\(997\) | 13951.9 | + | 8055.12i | 0.443190 | + | 0.255876i | 0.704950 | − | 0.709257i | \(-0.250970\pi\) |
−0.261760 | + | 0.965133i | \(0.584303\pi\) | |||||||
\(998\) | − | 43978.6i | − | 1.39491i | ||||||
\(999\) | 1280.42 | + | 2882.47i | 0.0405514 | + | 0.0912885i |
(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 | 225.4.k.d.124.1 | 28 | ||
5.2 | odd | 4 | 225.4.e.d.151.7 | 14 | |||
5.3 | odd | 4 | 45.4.e.c.16.1 | ✓ | 14 | ||
5.4 | even | 2 | inner | 225.4.k.d.124.14 | 28 | ||
9.4 | even | 3 | inner | 225.4.k.d.49.14 | 28 | ||
15.8 | even | 4 | 135.4.e.c.46.7 | 14 | |||
45.2 | even | 12 | 2025.4.a.ba.1.7 | 7 | |||
45.4 | even | 6 | inner | 225.4.k.d.49.1 | 28 | ||
45.7 | odd | 12 | 2025.4.a.bb.1.1 | 7 | |||
45.13 | odd | 12 | 45.4.e.c.31.1 | yes | 14 | ||
45.22 | odd | 12 | 225.4.e.d.76.7 | 14 | |||
45.23 | even | 12 | 135.4.e.c.91.7 | 14 | |||
45.38 | even | 12 | 405.4.a.n.1.1 | 7 | |||
45.43 | odd | 12 | 405.4.a.m.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.1 | ✓ | 14 | 5.3 | odd | 4 | ||
45.4.e.c.31.1 | yes | 14 | 45.13 | odd | 12 | ||
135.4.e.c.46.7 | 14 | 15.8 | even | 4 | |||
135.4.e.c.91.7 | 14 | 45.23 | even | 12 | |||
225.4.e.d.76.7 | 14 | 45.22 | odd | 12 | |||
225.4.e.d.151.7 | 14 | 5.2 | odd | 4 | |||
225.4.k.d.49.1 | 28 | 45.4 | even | 6 | inner | ||
225.4.k.d.49.14 | 28 | 9.4 | even | 3 | inner | ||
225.4.k.d.124.1 | 28 | 1.1 | even | 1 | trivial | ||
225.4.k.d.124.14 | 28 | 5.4 | even | 2 | inner | ||
405.4.a.m.1.7 | 7 | 45.43 | odd | 12 | |||
405.4.a.n.1.1 | 7 | 45.38 | even | 12 | |||
2025.4.a.ba.1.7 | 7 | 45.2 | even | 12 | |||
2025.4.a.bb.1.1 | 7 | 45.7 | odd | 12 |