Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
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, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.9 | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.f.76.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48830 | − | 2.57780i | 0.526192 | − | 0.911391i | −0.473342 | − | 0.880879i | \(-0.656953\pi\) |
0.999534 | − | 0.0305128i | \(-0.00971403\pi\) | |||||||
\(3\) | −5.14295 | − | 0.741698i | −0.989760 | − | 0.142740i | ||||
\(4\) | −0.430049 | − | 0.744867i | −0.0537561 | − | 0.0931084i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −9.56618 | + | 12.1536i | −0.650896 | + | 0.826950i | ||||
\(7\) | −12.4826 | + | 21.6204i | −0.673995 | + | 1.16739i | 0.302767 | + | 0.953065i | \(0.402090\pi\) |
−0.976762 | + | 0.214329i | \(0.931244\pi\) | |||||||
\(8\) | 21.2526 | 0.939240 | ||||||||
\(9\) | 25.8998 | + | 7.62902i | 0.959251 | + | 0.282556i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 31.6260 | − | 54.7779i | 0.866873 | − | 1.50147i | 0.00169771 | − | 0.999999i | \(-0.499460\pi\) |
0.865175 | − | 0.501470i | \(-0.167207\pi\) | |||||||
\(12\) | 1.65925 | + | 4.14978i | 0.0399154 | + | 0.0998281i | ||||
\(13\) | −45.2407 | − | 78.3591i | −0.965193 | − | 1.67176i | −0.709097 | − | 0.705111i | \(-0.750897\pi\) |
−0.256096 | − | 0.966651i | \(-0.582436\pi\) | |||||||
\(14\) | 37.1555 | + | 64.3552i | 0.709301 | + | 1.22855i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 35.0705 | − | 60.7439i | 0.547977 | − | 0.949123i | ||||
\(17\) | 10.2256 | 0.145886 | 0.0729431 | − | 0.997336i | \(-0.476761\pi\) | ||||
0.0729431 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(18\) | 58.2126 | − | 55.4103i | 0.762270 | − | 0.725574i | ||||
\(19\) | 24.7438 | 0.298770 | 0.149385 | − | 0.988779i | \(-0.452271\pi\) | ||||
0.149385 | + | 0.988779i | \(0.452271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 80.2329 | − | 101.934i | 0.833727 | − | 1.05923i | ||||
\(22\) | −94.1377 | − | 163.051i | −0.912283 | − | 1.58012i | ||||
\(23\) | −1.34587 | − | 2.33111i | −0.0122014 | − | 0.0211335i | 0.859860 | − | 0.510530i | \(-0.170551\pi\) |
−0.872062 | + | 0.489396i | \(0.837217\pi\) | |||||||
\(24\) | −109.301 | − | 15.7630i | −0.929622 | − | 0.134067i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −269.326 | −2.03151 | ||||||||
\(27\) | −127.543 | − | 58.4454i | −0.909096 | − | 0.416586i | ||||
\(28\) | 21.4725 | 0.144925 | ||||||||
\(29\) | 54.8481 | − | 94.9997i | 0.351208 | − | 0.608310i | −0.635253 | − | 0.772304i | \(-0.719104\pi\) |
0.986461 | + | 0.163994i | \(0.0524376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.7253 | + | 60.1459i | 0.201189 | + | 0.348469i | 0.948912 | − | 0.315542i | \(-0.102186\pi\) |
−0.747723 | + | 0.664011i | \(0.768853\pi\) | |||||||
\(32\) | −19.3803 | − | 33.5677i | −0.107062 | − | 0.185437i | ||||
\(33\) | −203.279 | + | 258.263i | −1.07232 | + | 1.36236i | ||||
\(34\) | 15.2187 | − | 26.3595i | 0.0767642 | − | 0.132959i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.45557 | − | 22.5727i | −0.0252573 | − | 0.104503i | ||||
\(37\) | 23.0916 | 0.102601 | 0.0513005 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513005 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(38\) | 36.8262 | − | 63.7848i | 0.157210 | − | 0.272296i | ||||
\(39\) | 174.551 | + | 436.552i | 0.716682 | + | 1.79242i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −133.285 | − | 230.856i | −0.507698 | − | 0.879359i | −0.999960 | − | 0.00891175i | \(-0.997163\pi\) |
0.492262 | − | 0.870447i | \(-0.336170\pi\) | |||||||
\(42\) | −143.357 | − | 358.533i | −0.526676 | − | 1.31721i | ||||
\(43\) | 235.348 | − | 407.635i | 0.834657 | − | 1.44567i | −0.0596515 | − | 0.998219i | \(-0.518999\pi\) |
0.894309 | − | 0.447450i | \(-0.147668\pi\) | |||||||
\(44\) | −54.4030 | −0.186399 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.01221 | −0.0256812 | ||||||||
\(47\) | 218.609 | − | 378.643i | 0.678456 | − | 1.17512i | −0.296989 | − | 0.954881i | \(-0.595983\pi\) |
0.975446 | − | 0.220240i | \(-0.0706841\pi\) | |||||||
\(48\) | −225.419 | + | 286.391i | −0.677843 | + | 0.861187i | ||||
\(49\) | −140.129 | − | 242.710i | −0.408538 | − | 0.707608i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.5896 | − | 7.58429i | −0.144392 | − | 0.0208238i | ||||
\(52\) | −38.9114 | + | 67.3966i | −0.103770 | + | 0.179735i | ||||
\(53\) | 114.841 | 0.297634 | 0.148817 | − | 0.988865i | \(-0.452453\pi\) | ||||
0.148817 | + | 0.988865i | \(0.452453\pi\) | |||||||
\(54\) | −340.482 | + | 241.796i | −0.858032 | + | 0.609338i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −265.286 | + | 459.490i | −0.633043 | + | 1.09646i | ||||
\(57\) | −127.256 | − | 18.3524i | −0.295710 | − | 0.0426463i | ||||
\(58\) | −163.260 | − | 282.775i | −0.369606 | − | 0.640176i | ||||
\(59\) | 237.113 | + | 410.692i | 0.523212 | + | 0.906229i | 0.999635 | + | 0.0270133i | \(0.00859965\pi\) |
−0.476423 | + | 0.879216i | \(0.658067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 166.782 | − | 288.875i | 0.350070 | − | 0.606338i | −0.636192 | − | 0.771531i | \(-0.719491\pi\) |
0.986261 | + | 0.165193i | \(0.0528246\pi\) | |||||||
\(62\) | 206.726 | 0.423455 | ||||||||
\(63\) | −488.238 | + | 464.734i | −0.976384 | + | 0.929381i | ||||
\(64\) | 445.754 | 0.870613 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 363.210 | + | 908.386i | 0.677396 | + | 1.69416i | ||||
\(67\) | −38.0819 | − | 65.9599i | −0.0694395 | − | 0.120273i | 0.829215 | − | 0.558929i | \(-0.188788\pi\) |
−0.898655 | + | 0.438657i | \(0.855454\pi\) | |||||||
\(68\) | −4.39750 | − | 7.61669i | −0.00784228 | − | 0.0135832i | ||||
\(69\) | 5.19275 | + | 12.9870i | 0.00905991 | + | 0.0226588i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −658.251 | −1.10028 | −0.550141 | − | 0.835072i | \(-0.685426\pi\) | ||||
−0.550141 | + | 0.835072i | \(0.685426\pi\) | |||||||
\(72\) | 550.437 | + | 162.136i | 0.900967 | + | 0.265388i | ||||
\(73\) | −549.827 | −0.881540 | −0.440770 | − | 0.897620i | \(-0.645294\pi\) | ||||
−0.440770 | + | 0.897620i | \(0.645294\pi\) | |||||||
\(74\) | 34.3671 | − | 59.5256i | 0.0539878 | − | 0.0935097i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.6411 | − | 18.4309i | −0.0160607 | − | 0.0278180i | ||||
\(77\) | 789.547 | + | 1367.54i | 1.16854 | + | 2.02396i | ||||
\(78\) | 1385.13 | + | 199.758i | 2.01070 | + | 0.289977i | ||||
\(79\) | 85.7122 | − | 148.458i | 0.122068 | − | 0.211428i | −0.798515 | − | 0.601975i | \(-0.794381\pi\) |
0.920583 | + | 0.390547i | \(0.127714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 612.596 | + | 395.180i | 0.840324 | + | 0.542085i | ||||
\(82\) | −793.470 | −1.06859 | ||||||||
\(83\) | −166.418 | + | 288.244i | −0.220081 | + | 0.381191i | −0.954832 | − | 0.297145i | \(-0.903965\pi\) |
0.734752 | + | 0.678336i | \(0.237299\pi\) | |||||||
\(84\) | −110.432 | − | 15.9261i | −0.143441 | − | 0.0206866i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −700.536 | − | 1213.36i | −0.878380 | − | 1.52140i | ||||
\(87\) | −352.542 | + | 447.897i | −0.434442 | + | 0.551950i | ||||
\(88\) | 672.134 | − | 1164.17i | 0.814202 | − | 1.41024i | ||||
\(89\) | −621.568 | −0.740293 | −0.370146 | − | 0.928973i | \(-0.620692\pi\) | ||||
−0.370146 | + | 0.928973i | \(0.620692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2258.88 | 2.60214 | ||||||||
\(92\) | −1.15758 | + | 2.00499i | −0.00131181 | + | 0.00227211i | ||||
\(93\) | −133.980 | − | 335.083i | −0.149388 | − | 0.373618i | ||||
\(94\) | −650.711 | − | 1127.06i | −0.713997 | − | 1.23668i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 74.7748 | + | 187.011i | 0.0794965 | + | 0.198820i | ||||
\(97\) | −759.010 | + | 1314.64i | −0.794492 | + | 1.37610i | 0.128669 | + | 0.991688i | \(0.458930\pi\) |
−0.923161 | + | 0.384413i | \(0.874404\pi\) | |||||||
\(98\) | −834.211 | −0.859878 | ||||||||
\(99\) | 1237.01 | − | 1177.46i | 1.25580 | − | 1.19534i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −42.5888 | + | 73.7660i | −0.0419579 | + | 0.0726732i | −0.886242 | − | 0.463223i | \(-0.846693\pi\) |
0.844284 | + | 0.535896i | \(0.180026\pi\) | |||||||
\(102\) | −97.8196 | + | 124.278i | −0.0949567 | + | 0.120641i | ||||
\(103\) | 692.546 | + | 1199.52i | 0.662510 | + | 1.14750i | 0.979954 | + | 0.199224i | \(0.0638422\pi\) |
−0.317444 | + | 0.948277i | \(0.602824\pi\) | |||||||
\(104\) | −961.481 | − | 1665.33i | −0.906547 | − | 1.57019i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 170.917 | − | 296.038i | 0.156613 | − | 0.271262i | ||||
\(107\) | 1051.56 | 0.950077 | 0.475039 | − | 0.879965i | \(-0.342434\pi\) | ||||
0.475039 | + | 0.879965i | \(0.342434\pi\) | |||||||
\(108\) | 11.3155 | + | 120.137i | 0.0100818 | + | 0.107039i | ||||
\(109\) | 89.9209 | 0.0790170 | 0.0395085 | − | 0.999219i | \(-0.487421\pi\) | ||||
0.0395085 | + | 0.999219i | \(0.487421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −118.759 | − | 17.1270i | −0.101550 | − | 0.0146452i | ||||
\(112\) | 875.539 | + | 1516.48i | 0.738667 | + | 1.27941i | ||||
\(113\) | 216.322 | + | 374.680i | 0.180087 | + | 0.311920i | 0.941910 | − | 0.335865i | \(-0.109029\pi\) |
−0.761823 | + | 0.647785i | \(0.775695\pi\) | |||||||
\(114\) | −236.704 | + | 300.728i | −0.194468 | + | 0.247068i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −94.3495 | −0.0755184 | ||||||||
\(117\) | −573.919 | − | 2374.63i | −0.453495 | − | 1.87636i | ||||
\(118\) | 1411.58 | 1.10124 | ||||||||
\(119\) | −127.641 | + | 221.081i | −0.0983266 | + | 0.170307i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1334.91 | − | 2312.13i | −1.00294 | − | 1.73714i | ||||
\(122\) | −496.442 | − | 859.863i | −0.368408 | − | 0.638101i | ||||
\(123\) | 514.252 | + | 1286.14i | 0.376980 | + | 0.942823i | ||||
\(124\) | 29.8672 | − | 51.7314i | 0.0216302 | − | 0.0374647i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 471.351 | + | 1950.24i | 0.333264 | + | 1.37890i | ||||
\(127\) | 2059.97 | 1.43931 | 0.719657 | − | 0.694330i | \(-0.244299\pi\) | ||||
0.719657 | + | 0.694330i | \(0.244299\pi\) | |||||||
\(128\) | 818.456 | − | 1417.61i | 0.565171 | − | 0.978906i | ||||
\(129\) | −1512.73 | + | 1921.89i | −1.03247 | + | 1.31173i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 936.224 | + | 1621.59i | 0.624414 | + | 1.08152i | 0.988654 | + | 0.150212i | \(0.0479956\pi\) |
−0.364240 | + | 0.931305i | \(0.618671\pi\) | |||||||
\(132\) | 279.792 | + | 40.3506i | 0.184490 | + | 0.0266066i | ||||
\(133\) | −308.866 | + | 534.972i | −0.201369 | + | 0.348782i | ||||
\(134\) | −226.709 | −0.146154 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 217.320 | 0.137022 | ||||||||
\(137\) | −1120.99 | + | 1941.61i | −0.699071 | + | 1.21083i | 0.269717 | + | 0.962940i | \(0.413070\pi\) |
−0.968789 | + | 0.247888i | \(0.920264\pi\) | |||||||
\(138\) | 41.2064 | + | 5.94264i | 0.0254182 | + | 0.00366573i | ||||
\(139\) | 132.227 | + | 229.023i | 0.0806857 | + | 0.139752i | 0.903545 | − | 0.428494i | \(-0.140956\pi\) |
−0.822859 | + | 0.568246i | \(0.807622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1405.13 | + | 1785.20i | −0.839246 | + | 1.06625i | ||||
\(142\) | −979.673 | + | 1696.84i | −0.578960 | + | 1.00279i | ||||
\(143\) | −5723.13 | −3.34680 | ||||||||
\(144\) | 1371.73 | − | 1305.70i | 0.793828 | − | 0.755613i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −818.305 | + | 1417.35i | −0.463859 | + | 0.803428i | ||||
\(147\) | 540.656 | + | 1352.18i | 0.303351 | + | 0.758677i | ||||
\(148\) | −9.93053 | − | 17.2002i | −0.00551543 | − | 0.00955301i | ||||
\(149\) | −22.1989 | − | 38.4496i | −0.0122054 | − | 0.0211404i | 0.859858 | − | 0.510533i | \(-0.170552\pi\) |
−0.872064 | + | 0.489393i | \(0.837219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 609.223 | − | 1055.20i | 0.328330 | − | 0.568685i | −0.653850 | − | 0.756624i | \(-0.726847\pi\) |
0.982181 | + | 0.187939i | \(0.0601808\pi\) | |||||||
\(152\) | 525.870 | 0.280616 | ||||||||
\(153\) | 264.840 | + | 78.0111i | 0.139941 | + | 0.0412211i | ||||
\(154\) | 4700.32 | 2.45950 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 250.107 | − | 317.756i | 0.128363 | − | 0.163082i | ||||
\(157\) | −1793.39 | − | 3106.25i | −0.911645 | − | 1.57902i | −0.811741 | − | 0.584018i | \(-0.801480\pi\) |
−0.0999041 | − | 0.994997i | \(-0.531854\pi\) | |||||||
\(158\) | −255.130 | − | 441.899i | −0.128463 | − | 0.222504i | ||||
\(159\) | −590.621 | − | 85.1773i | −0.294587 | − | 0.0424843i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.1996 | 0.0328948 | ||||||||
\(162\) | 1930.42 | − | 991.008i | 0.936223 | − | 0.480623i | ||||
\(163\) | 1138.29 | 0.546981 | 0.273490 | − | 0.961875i | \(-0.411822\pi\) | ||||
0.273490 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(164\) | −114.638 | + | 198.559i | −0.0545838 | + | 0.0945419i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 495.357 | + | 857.984i | 0.231609 | + | 0.401159i | ||||
\(167\) | −112.979 | − | 195.685i | −0.0523506 | − | 0.0906738i | 0.838663 | − | 0.544651i | \(-0.183338\pi\) |
−0.891013 | + | 0.453977i | \(0.850005\pi\) | |||||||
\(168\) | 1705.16 | − | 2166.37i | 0.783069 | − | 0.994874i | ||||
\(169\) | −2994.94 | + | 5187.38i | −1.36319 | + | 2.36112i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 640.860 | + | 188.771i | 0.286595 | + | 0.0844193i | ||||
\(172\) | −404.845 | −0.179472 | ||||||||
\(173\) | 318.937 | − | 552.415i | 0.140164 | − | 0.242771i | −0.787395 | − | 0.616449i | \(-0.788570\pi\) |
0.927558 | + | 0.373679i | \(0.121904\pi\) | |||||||
\(174\) | 629.905 | + | 1575.39i | 0.274443 | + | 0.686378i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2218.28 | − | 3842.18i | −0.950052 | − | 1.64554i | ||||
\(177\) | −914.850 | − | 2288.03i | −0.388499 | − | 0.971633i | ||||
\(178\) | −925.077 | + | 1602.28i | −0.389536 | + | 0.674697i | ||||
\(179\) | −3726.05 | −1.55586 | −0.777928 | − | 0.628353i | \(-0.783729\pi\) | ||||
−0.777928 | + | 0.628353i | \(0.783729\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2524.11 | −1.03655 | −0.518275 | − | 0.855214i | \(-0.673426\pi\) | ||||
−0.518275 | + | 0.855214i | \(0.673426\pi\) | |||||||
\(182\) | 3361.88 | − | 5822.94i | 1.36922 | − | 2.37157i | ||||
\(183\) | −1072.01 | + | 1361.97i | −0.433034 | + | 0.550161i | ||||
\(184\) | −28.6032 | − | 49.5422i | −0.0114601 | − | 0.0198494i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1063.18 | − | 153.328i | −0.419119 | − | 0.0604439i | ||||
\(187\) | 323.394 | − | 560.135i | 0.126465 | − | 0.219044i | ||||
\(188\) | −376.051 | −0.145885 | ||||||||
\(189\) | 2855.67 | − | 2027.98i | 1.09905 | − | 0.780496i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 109.186 | − | 189.115i | 0.0413634 | − | 0.0716435i | −0.844603 | − | 0.535394i | \(-0.820163\pi\) |
0.885966 | + | 0.463750i | \(0.153497\pi\) | |||||||
\(192\) | −2292.49 | − | 330.614i | −0.861698 | − | 0.124271i | ||||
\(193\) | 942.571 | + | 1632.58i | 0.351543 | + | 0.608890i | 0.986520 | − | 0.163641i | \(-0.0523239\pi\) |
−0.634977 | + | 0.772531i | \(0.718991\pi\) | |||||||
\(194\) | 2259.26 | + | 3913.16i | 0.836111 | + | 1.44819i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −120.524 | + | 208.754i | −0.0439229 | + | 0.0760766i | ||||
\(197\) | −3145.83 | −1.13772 | −0.568861 | − | 0.822433i | \(-0.692616\pi\) | ||||
−0.568861 | + | 0.822433i | \(0.692616\pi\) | |||||||
\(198\) | −1194.22 | − | 4941.17i | −0.428635 | − | 1.77350i | ||||
\(199\) | −1725.22 | −0.614562 | −0.307281 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307281 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 146.931 | + | 367.473i | 0.0515608 | + | 0.128953i | ||||
\(202\) | 126.769 | + | 219.571i | 0.0441558 | + | 0.0764801i | ||||
\(203\) | 1369.29 | + | 2371.68i | 0.473425 | + | 0.819996i | ||||
\(204\) | 16.9668 | + | 42.4339i | 0.00582311 | + | 0.0145635i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4122.85 | 1.39443 | ||||||||
\(207\) | −17.0736 | − | 70.6430i | −0.00573283 | − | 0.0237199i | ||||
\(208\) | −6346.45 | −2.11561 | ||||||||
\(209\) | 782.549 | − | 1355.41i | 0.258995 | − | 0.448593i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −291.383 | − | 504.690i | −0.0950694 | − | 0.164665i | 0.814568 | − | 0.580068i | \(-0.196974\pi\) |
−0.909638 | + | 0.415403i | \(0.863641\pi\) | |||||||
\(212\) | −49.3873 | − | 85.5413i | −0.0159997 | − | 0.0277123i | ||||
\(213\) | 3385.35 | + | 488.224i | 1.08902 | + | 0.157054i | ||||
\(214\) | 1565.03 | − | 2710.72i | 0.499923 | − | 0.865892i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2710.61 | − | 1242.12i | −0.853859 | − | 0.391274i | ||||
\(217\) | −1733.84 | −0.542400 | ||||||||
\(218\) | 133.829 | − | 231.798i | 0.0415781 | − | 0.0720155i | ||||
\(219\) | 2827.73 | + | 407.806i | 0.872513 | + | 0.125831i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −462.612 | − | 801.267i | −0.140808 | − | 0.243887i | ||||
\(222\) | −220.898 | + | 280.647i | −0.0667826 | + | 0.0848459i | ||||
\(223\) | 2832.72 | − | 4906.42i | 0.850642 | − | 1.47336i | −0.0299878 | − | 0.999550i | \(-0.509547\pi\) |
0.880630 | − | 0.473805i | \(-0.157120\pi\) | |||||||
\(224\) | 967.663 | 0.288637 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1287.80 | 0.379041 | ||||||||
\(227\) | −1854.97 | + | 3212.91i | −0.542374 | + | 0.939419i | 0.456393 | + | 0.889778i | \(0.349141\pi\) |
−0.998767 | + | 0.0496409i | \(0.984192\pi\) | |||||||
\(228\) | 41.0563 | + | 102.681i | 0.0119255 | + | 0.0298256i | ||||
\(229\) | −1787.15 | − | 3095.43i | −0.515712 | − | 0.893239i | −0.999834 | − | 0.0182383i | \(-0.994194\pi\) |
0.484122 | − | 0.875001i | \(-0.339139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3046.30 | − | 7618.77i | −0.867670 | − | 2.17004i | ||||
\(232\) | 1165.66 | − | 2018.99i | 0.329869 | − | 0.571349i | ||||
\(233\) | 4505.75 | 1.26687 | 0.633436 | − | 0.773795i | \(-0.281644\pi\) | ||||
0.633436 | + | 0.773795i | \(0.281644\pi\) | |||||||
\(234\) | −6975.48 | − | 2054.69i | −1.94872 | − | 0.574015i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 203.941 | − | 353.235i | 0.0562517 | − | 0.0974308i | ||||
\(237\) | −550.924 | + | 699.939i | −0.150997 | + | 0.191839i | ||||
\(238\) | 379.936 | + | 658.069i | 0.103477 | + | 0.179228i | ||||
\(239\) | 1145.81 | + | 1984.59i | 0.310109 | + | 0.537124i | 0.978386 | − | 0.206789i | \(-0.0663012\pi\) |
−0.668277 | + | 0.743913i | \(0.732968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1128.08 | − | 1953.89i | 0.301518 | − | 0.522245i | −0.674962 | − | 0.737853i | \(-0.735840\pi\) |
0.976480 | + | 0.215608i | \(0.0691733\pi\) | |||||||
\(242\) | −7946.96 | −2.11095 | ||||||||
\(243\) | −2857.44 | − | 2486.75i | −0.754342 | − | 0.656482i | ||||
\(244\) | −286.898 | −0.0752736 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4080.77 | + | 588.515i | 1.05764 | + | 0.152530i | ||||
\(247\) | −1119.43 | − | 1938.91i | −0.288370 | − | 0.499472i | ||||
\(248\) | 738.001 | + | 1278.26i | 0.188964 | + | 0.327296i | ||||
\(249\) | 1069.67 | − | 1358.99i | 0.272238 | − | 0.345873i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3797.01 | 0.954841 | 0.477421 | − | 0.878675i | \(-0.341572\pi\) | ||||
0.477421 | + | 0.878675i | \(0.341572\pi\) | |||||||
\(252\) | 556.132 | + | 163.814i | 0.139020 | + | 0.0409496i | ||||
\(253\) | −170.258 | −0.0423084 | ||||||||
\(254\) | 3065.85 | − | 5310.20i | 0.757355 | − | 1.31178i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −653.194 | − | 1131.37i | −0.159471 | − | 0.276212i | ||||
\(257\) | 2021.09 | + | 3500.63i | 0.490553 | + | 0.849662i | 0.999941 | − | 0.0108747i | \(-0.00346159\pi\) |
−0.509388 | + | 0.860537i | \(0.670128\pi\) | |||||||
\(258\) | 2702.87 | + | 6759.85i | 0.652222 | + | 1.63120i | ||||
\(259\) | −288.242 | + | 499.250i | −0.0691525 | + | 0.119776i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2145.31 | − | 2042.03i | 0.508779 | − | 0.484286i | ||||
\(262\) | 5573.51 | 1.31425 | ||||||||
\(263\) | 3230.95 | − | 5596.18i | 0.757525 | − | 1.31207i | −0.186584 | − | 0.982439i | \(-0.559742\pi\) |
0.944109 | − | 0.329633i | \(-0.106925\pi\) | |||||||
\(264\) | −4320.21 | + | 5488.75i | −1.00716 | + | 1.27958i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 919.369 | + | 1592.39i | 0.211918 | + | 0.367052i | ||||
\(267\) | 3196.69 | + | 461.016i | 0.732712 | + | 0.105669i | ||||
\(268\) | −32.7542 | + | 56.7320i | −0.00746560 | + | 0.0129308i | ||||
\(269\) | 4397.95 | 0.996832 | 0.498416 | − | 0.866938i | \(-0.333915\pi\) | ||||
0.498416 | + | 0.866938i | \(0.333915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2614.32 | −0.586009 | −0.293005 | − | 0.956111i | \(-0.594655\pi\) | ||||
−0.293005 | + | 0.956111i | \(0.594655\pi\) | |||||||
\(272\) | 358.616 | − | 621.141i | 0.0799423 | − | 0.138464i | ||||
\(273\) | −11617.3 | − | 1675.40i | −2.57549 | − | 0.371429i | ||||
\(274\) | 3336.73 | + | 5779.39i | 0.735692 | + | 1.27426i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.44047 | − | 9.45297i | 0.00162269 | − | 0.00206160i | ||||
\(277\) | 830.494 | − | 1438.46i | 0.180143 | − | 0.312016i | −0.761786 | − | 0.647828i | \(-0.775677\pi\) |
0.941929 | + | 0.335812i | \(0.109011\pi\) | |||||||
\(278\) | 787.170 | 0.169825 | ||||||||
\(279\) | 440.522 | + | 1822.69i | 0.0945282 | + | 0.391116i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2504.38 | + | 4337.71i | −0.531668 | + | 0.920876i | 0.467649 | + | 0.883914i | \(0.345101\pi\) |
−0.999317 | + | 0.0369615i | \(0.988232\pi\) | |||||||
\(282\) | 2510.63 | + | 6279.06i | 0.530162 | + | 1.32593i | ||||
\(283\) | −136.204 | − | 235.913i | −0.0286096 | − | 0.0495532i | 0.851366 | − | 0.524572i | \(-0.175775\pi\) |
−0.879976 | + | 0.475019i | \(0.842441\pi\) | |||||||
\(284\) | 283.080 | + | 490.310i | 0.0591469 | + | 0.102446i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8517.71 | + | 14753.1i | −1.76106 | + | 3.05024i | ||||
\(287\) | 6654.95 | 1.36874 | ||||||||
\(288\) | −245.857 | − | 1017.25i | −0.0503030 | − | 0.208132i | ||||
\(289\) | −4808.44 | −0.978717 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4878.61 | − | 6198.18i | 0.982781 | − | 1.24860i | ||||
\(292\) | 236.453 | + | 409.548i | 0.0473882 | + | 0.0820787i | ||||
\(293\) | 2448.54 | + | 4240.99i | 0.488209 | + | 0.845602i | 0.999908 | − | 0.0135624i | \(-0.00431717\pi\) |
−0.511699 | + | 0.859165i | \(0.670984\pi\) | |||||||
\(294\) | 4290.30 | + | 618.732i | 0.851073 | + | 0.122739i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 490.756 | 0.0963669 | ||||||||
\(297\) | −7235.18 | + | 5138.12i | −1.41356 | + | 1.00385i | ||||
\(298\) | −132.154 | −0.0256896 | ||||||||
\(299\) | −121.776 | + | 210.922i | −0.0235535 | + | 0.0407958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5875.50 | + | 10176.7i | 1.12511 | + | 1.94875i | ||||
\(302\) | −1813.41 | − | 3140.91i | −0.345529 | − | 0.598475i | ||||
\(303\) | 273.744 | − | 347.786i | 0.0519016 | − | 0.0659399i | ||||
\(304\) | 867.779 | − | 1503.04i | 0.163719 | − | 0.283569i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 595.258 | − | 566.602i | 0.111205 | − | 0.105851i | ||||
\(307\) | 2095.63 | 0.389590 | 0.194795 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194795 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(308\) | 679.088 | − | 1176.22i | 0.125632 | − | 0.217601i | ||||
\(309\) | −2672.04 | − | 6682.75i | −0.491932 | − | 1.23032i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2525.57 | + | 4374.41i | 0.460488 | + | 0.797589i | 0.998985 | − | 0.0450384i | \(-0.0143410\pi\) |
−0.538497 | + | 0.842627i | \(0.681008\pi\) | |||||||
\(312\) | 3709.67 | + | 9277.85i | 0.673136 | + | 1.68351i | ||||
\(313\) | −2961.90 | + | 5130.16i | −0.534876 | + | 0.926433i | 0.464293 | + | 0.885682i | \(0.346308\pi\) |
−0.999169 | + | 0.0407513i | \(0.987025\pi\) | |||||||
\(314\) | −10676.4 | −1.91880 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −147.442 | −0.0262476 | ||||||||
\(317\) | 2355.68 | − | 4080.15i | 0.417376 | − | 0.722916i | −0.578299 | − | 0.815825i | \(-0.696283\pi\) |
0.995675 | + | 0.0929092i | \(0.0296166\pi\) | |||||||
\(318\) | −1098.59 | + | 1395.74i | −0.193729 | + | 0.246129i | ||||
\(319\) | −3469.25 | − | 6008.92i | −0.608906 | − | 1.05466i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5408.12 | − | 779.941i | −0.940349 | − | 0.135614i | ||||
\(322\) | 100.013 | − | 173.227i | 0.0173090 | − | 0.0299801i | ||||
\(323\) | 253.020 | 0.0435864 | ||||||||
\(324\) | 30.9100 | − | 626.249i | 0.00530006 | − | 0.107382i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1694.11 | − | 2934.29i | 0.287817 | − | 0.498514i | ||||
\(327\) | −462.458 | − | 66.6941i | −0.0782079 | − | 0.0112789i | ||||
\(328\) | −2832.65 | − | 4906.29i | −0.476850 | − | 0.825929i | ||||
\(329\) | 5457.61 | + | 9452.86i | 0.914552 | + | 1.58405i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3180.59 | + | 5508.94i | −0.528159 | + | 0.914799i | 0.471302 | + | 0.881972i | \(0.343784\pi\) |
−0.999461 | + | 0.0328269i | \(0.989549\pi\) | |||||||
\(332\) | 286.271 | 0.0473228 | ||||||||
\(333\) | 598.067 | + | 176.166i | 0.0984201 | + | 0.0289906i | ||||
\(334\) | −672.582 | −0.110186 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3378.08 | − | 8448.55i | −0.548481 | − | 1.37174i | ||||
\(337\) | 1310.07 | + | 2269.11i | 0.211763 | + | 0.366785i | 0.952266 | − | 0.305268i | \(-0.0987460\pi\) |
−0.740503 | + | 0.672053i | \(0.765413\pi\) | |||||||
\(338\) | 8914.70 | + | 15440.7i | 1.43460 | + | 2.48481i | ||||
\(339\) | −834.631 | − | 2087.41i | −0.133720 | − | 0.334432i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4392.89 | 0.697620 | ||||||||
\(342\) | 1440.40 | − | 1371.06i | 0.227743 | − | 0.216780i | ||||
\(343\) | −1566.39 | −0.246580 | ||||||||
\(344\) | 5001.76 | − | 8663.29i | 0.783944 | − | 1.35783i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −949.344 | − | 1644.31i | −0.147506 | − | 0.255488i | ||||
\(347\) | 3841.31 | + | 6653.34i | 0.594272 | + | 1.02931i | 0.993649 | + | 0.112522i | \(0.0358929\pi\) |
−0.399378 | + | 0.916786i | \(0.630774\pi\) | |||||||
\(348\) | 485.234 | + | 69.9788i | 0.0747451 | + | 0.0107795i | ||||
\(349\) | 1840.37 | − | 3187.62i | 0.282272 | − | 0.488910i | −0.689672 | − | 0.724122i | \(-0.742245\pi\) |
0.971944 | + | 0.235212i | \(0.0755785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1190.38 | + | 12638.2i | 0.181019 | + | 1.92188i | ||||
\(352\) | −2451.69 | −0.371237 | ||||||||
\(353\) | 5064.30 | − | 8771.63i | 0.763585 | − | 1.32257i | −0.177406 | − | 0.984138i | \(-0.556771\pi\) |
0.940991 | − | 0.338431i | \(-0.109896\pi\) | |||||||
\(354\) | −7259.67 | − | 1046.96i | −1.08996 | − | 0.157191i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 267.305 | + | 462.985i | 0.0397953 | + | 0.0689275i | ||||
\(357\) | 820.428 | − | 1042.34i | 0.121629 | − | 0.154528i | ||||
\(358\) | −5545.47 | + | 9605.03i | −0.818679 | + | 1.41799i | ||||
\(359\) | 7181.79 | 1.05582 | 0.527911 | − | 0.849300i | \(-0.322975\pi\) | ||||
0.527911 | + | 0.849300i | \(0.322975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6246.74 | −0.910737 | ||||||||
\(362\) | −3756.62 | + | 6506.66i | −0.545424 | + | 0.944702i | ||||
\(363\) | 5150.47 | + | 12881.3i | 0.744709 | + | 1.86251i | ||||
\(364\) | −971.428 | − | 1682.56i | −0.139881 | − | 0.242281i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1915.42 | + | 4790.44i | 0.273553 | + | 0.684153i | ||||
\(367\) | 4640.66 | − | 8037.87i | 0.660056 | − | 1.14325i | −0.320544 | − | 0.947234i | \(-0.603866\pi\) |
0.980600 | − | 0.196018i | \(-0.0628010\pi\) | |||||||
\(368\) | −188.801 | −0.0267444 | ||||||||
\(369\) | −1690.84 | − | 6995.96i | −0.238541 | − | 0.986979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1433.51 | + | 2482.91i | −0.200604 | + | 0.347456i | ||||
\(372\) | −191.974 | + | 243.899i | −0.0267564 | + | 0.0339935i | ||||
\(373\) | −1833.25 | − | 3175.29i | −0.254483 | − | 0.440778i | 0.710272 | − | 0.703928i | \(-0.248572\pi\) |
−0.964755 | + | 0.263149i | \(0.915239\pi\) | |||||||
\(374\) | −962.613 | − | 1667.29i | −0.133090 | − | 0.230518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4646.01 | − | 8047.13i | 0.637233 | − | 1.10372i | ||||
\(377\) | −9925.46 | −1.35593 | ||||||||
\(378\) | −977.642 | − | 10379.6i | −0.133028 | − | 1.41235i | ||||
\(379\) | −6530.29 | −0.885062 | −0.442531 | − | 0.896753i | \(-0.645919\pi\) | ||||
−0.442531 | + | 0.896753i | \(0.645919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10594.3 | − | 1527.88i | −1.42458 | − | 0.205447i | ||||
\(382\) | −325.002 | − | 562.919i | −0.0435302 | − | 0.0753965i | ||||
\(383\) | 1657.53 | + | 2870.93i | 0.221138 | + | 0.383022i | 0.955154 | − | 0.296110i | \(-0.0956896\pi\) |
−0.734016 | + | 0.679132i | \(0.762356\pi\) | |||||||
\(384\) | −5260.71 | + | 6683.63i | −0.699113 | + | 0.888210i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5611.30 | 0.739916 | ||||||||
\(387\) | 9205.32 | − | 8762.18i | 1.20913 | − | 1.15092i | ||||
\(388\) | 1305.65 | 0.170835 | ||||||||
\(389\) | −2338.24 | + | 4049.95i | −0.304765 | + | 0.527868i | −0.977209 | − | 0.212280i | \(-0.931911\pi\) |
0.672444 | + | 0.740148i | \(0.265245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7623 | − | 23.8370i | −0.00178002 | − | 0.00308309i | ||||
\(392\) | −2978.09 | − | 5158.21i | −0.383715 | − | 0.664614i | ||||
\(393\) | −3612.22 | − | 9034.13i | −0.463645 | − | 1.15957i | ||||
\(394\) | −4681.93 | + | 8109.34i | −0.598661 | + | 1.03691i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1409.02 | − | 415.041i | −0.178803 | − | 0.0526682i | ||||
\(397\) | −3995.97 | −0.505169 | −0.252584 | − | 0.967575i | \(-0.581280\pi\) | ||||
−0.252584 | + | 0.967575i | \(0.581280\pi\) | |||||||
\(398\) | −2567.64 | + | 4447.29i | −0.323378 | + | 0.560107i | ||||
\(399\) | 1985.27 | − | 2522.25i | 0.249092 | − | 0.316467i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2543.18 | − | 4404.92i | −0.316710 | − | 0.548557i | 0.663090 | − | 0.748540i | \(-0.269245\pi\) |
−0.979799 | + | 0.199983i | \(0.935911\pi\) | |||||||
\(402\) | 1165.95 | + | 168.149i | 0.144658 | + | 0.0208620i | ||||
\(403\) | 3141.99 | − | 5442.09i | 0.388371 | − | 0.672679i | ||||
\(404\) | 73.2611 | 0.00902197 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8151.63 | 0.996450 | ||||||||
\(407\) | 730.296 | − | 1264.91i | 0.0889420 | − | 0.154052i | ||||
\(408\) | −1117.66 | − | 161.186i | −0.135619 | − | 0.0195585i | ||||
\(409\) | 3737.95 | + | 6474.31i | 0.451906 | + | 0.782724i | 0.998504 | − | 0.0546708i | \(-0.0174109\pi\) |
−0.546599 | + | 0.837395i | \(0.684078\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7205.29 | − | 9154.18i | 0.864746 | − | 1.09864i | ||||
\(412\) | 595.657 | − | 1031.71i | 0.0712280 | − | 0.123371i | ||||
\(413\) | −11839.1 | −1.41057 | ||||||||
\(414\) | −207.514 | − | 61.1253i | −0.0246347 | − | 0.00725639i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1753.56 | + | 3037.25i | −0.206671 | + | 0.357965i | ||||
\(417\) | −510.168 | − | 1275.93i | −0.0599114 | − | 0.149838i | ||||
\(418\) | −2329.33 | − | 4034.52i | −0.272563 | − | 0.472092i | ||||
\(419\) | −4320.40 | − | 7483.15i | −0.503736 | − | 0.872497i | −0.999991 | − | 0.00431947i | \(-0.998625\pi\) |
0.496255 | − | 0.868177i | \(-0.334708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1344.32 | − | 2328.42i | 0.155625 | − | 0.269550i | −0.777662 | − | 0.628683i | \(-0.783594\pi\) |
0.933286 | + | 0.359133i | \(0.116928\pi\) | |||||||
\(422\) | −1734.66 | −0.200099 | ||||||||
\(423\) | 8550.60 | − | 8138.98i | 0.982848 | − | 0.935534i | ||||
\(424\) | 2440.67 | 0.279550 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6296.95 | − | 8000.15i | 0.716169 | − | 0.909879i | ||||
\(427\) | 4163.73 | + | 7211.80i | 0.471890 | + | 0.817338i | ||||
\(428\) | −452.223 | − | 783.273i | −0.0510725 | − | 0.0884602i | ||||
\(429\) | 29433.7 | + | 4244.83i | 3.31253 | + | 0.477721i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11019.7 | 1.23156 | 0.615779 | − | 0.787919i | \(-0.288842\pi\) | ||||
0.615779 | + | 0.787919i | \(0.288842\pi\) | |||||||
\(432\) | −8023.19 | + | 5697.73i | −0.893555 | + | 0.634565i | ||||
\(433\) | 13547.6 | 1.50360 | 0.751798 | − | 0.659394i | \(-0.229187\pi\) | ||||
0.751798 | + | 0.659394i | \(0.229187\pi\) | |||||||
\(434\) | −2580.47 | + | 4469.50i | −0.285407 | + | 0.494339i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −38.6704 | − | 66.9791i | −0.00424765 | − | 0.00735715i | ||||
\(437\) | −33.3020 | − | 57.6807i | −0.00364542 | − | 0.00631406i | ||||
\(438\) | 5259.74 | − | 6682.40i | 0.573790 | − | 0.728990i | ||||
\(439\) | 5105.54 | − | 8843.06i | 0.555067 | − | 0.961404i | −0.442832 | − | 0.896605i | \(-0.646026\pi\) |
0.997898 | − | 0.0647988i | \(-0.0206406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1777.66 | − | 7355.17i | −0.191951 | − | 0.794209i | ||||
\(442\) | −2754.01 | −0.296369 | ||||||||
\(443\) | 4916.42 | − | 8515.50i | 0.527283 | − | 0.913281i | −0.472211 | − | 0.881485i | \(-0.656544\pi\) |
0.999494 | − | 0.0317956i | \(-0.0101226\pi\) | |||||||
\(444\) | 38.3148 | + | 95.8250i | 0.00409536 | + | 0.0102425i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8431.86 | − | 14604.4i | −0.895202 | − | 1.55054i | ||||
\(447\) | 85.6498 | + | 214.209i | 0.00906285 | + | 0.0226661i | ||||
\(448\) | −5564.15 | + | 9637.38i | −0.586788 | + | 1.01635i | ||||
\(449\) | 4038.48 | 0.424471 | 0.212235 | − | 0.977219i | \(-0.431926\pi\) | ||||
0.212235 | + | 0.977219i | \(0.431926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16861.1 | −1.76044 | ||||||||
\(452\) | 186.058 | − | 322.262i | 0.0193616 | − | 0.0335352i | ||||
\(453\) | −3915.84 | + | 4975.00i | −0.406142 | + | 0.515996i | ||||
\(454\) | 5521.50 | + | 9563.51i | 0.570786 | + | 0.988630i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2704.52 | − | 390.037i | −0.277743 | − | 0.0400551i | ||||
\(457\) | −2944.34 | + | 5099.74i | −0.301379 | + | 0.522004i | −0.976449 | − | 0.215750i | \(-0.930780\pi\) |
0.675069 | + | 0.737754i | \(0.264114\pi\) | |||||||
\(458\) | −10639.2 | −1.08545 | ||||||||
\(459\) | −1304.20 | − | 597.638i | −0.132625 | − | 0.0607742i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1176.55 | + | 2037.84i | −0.118866 | + | 0.205882i | −0.919319 | − | 0.393514i | \(-0.871259\pi\) |
0.800452 | + | 0.599396i | \(0.204593\pi\) | |||||||
\(462\) | −24173.5 | − | 3486.22i | −2.43431 | − | 0.351068i | ||||
\(463\) | 6788.85 | + | 11758.6i | 0.681435 | + | 1.18028i | 0.974543 | + | 0.224201i | \(0.0719771\pi\) |
−0.293108 | + | 0.956079i | \(0.594690\pi\) | |||||||
\(464\) | −3847.10 | − | 6663.38i | −0.384908 | − | 0.666680i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6705.88 | − | 11614.9i | 0.666618 | − | 1.15462i | ||||
\(467\) | 491.494 | 0.0487015 | 0.0243508 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243508 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(468\) | −1521.97 | + | 1448.70i | −0.150327 | + | 0.143090i | ||||
\(469\) | 1901.44 | 0.187208 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6919.42 | + | 17305.4i | 0.676921 | + | 1.69297i | ||||
\(472\) | 5039.26 | + | 8728.26i | 0.491421 | + | 0.851167i | ||||
\(473\) | −14886.3 | − | 25783.8i | −1.44708 | − | 2.50642i | ||||
\(474\) | 984.366 | + | 2461.89i | 0.0953870 | + | 0.238562i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 219.568 | 0.0211426 | ||||||||
\(477\) | 2974.36 | + | 876.125i | 0.285506 | + | 0.0840985i | ||||
\(478\) | 6821.19 | 0.652707 | ||||||||
\(479\) | −6102.77 | + | 10570.3i | −0.582135 | + | 1.00829i | 0.413091 | + | 0.910690i | \(0.364449\pi\) |
−0.995226 | + | 0.0975976i | \(0.968884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1044.68 | − | 1809.44i | −0.0990297 | − | 0.171525i | ||||
\(482\) | −3357.83 | − | 5815.93i | −0.317313 | − | 0.549602i | ||||
\(483\) | −345.604 | − | 49.8418i | −0.0325580 | − | 0.00469540i | ||||
\(484\) | −1148.15 | + | 1988.66i | −0.107828 | + | 0.186764i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10663.1 | + | 3664.91i | −0.995240 | + | 0.342065i | ||||
\(487\) | −7900.12 | −0.735089 | −0.367545 | − | 0.930006i | \(-0.619801\pi\) | ||||
−0.367545 | + | 0.930006i | \(0.619801\pi\) | |||||||
\(488\) | 3544.55 | − | 6139.33i | 0.328799 | − | 0.569497i | ||||
\(489\) | −5854.17 | − | 844.268i | −0.541380 | − | 0.0780759i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4723.85 | + | 8181.95i | 0.434184 | + | 0.752029i | 0.997229 | − | 0.0743974i | \(-0.0237033\pi\) |
−0.563044 | + | 0.826427i | \(0.690370\pi\) | |||||||
\(492\) | 736.849 | − | 936.152i | 0.0675197 | − | 0.0857825i | ||||
\(493\) | 560.853 | − | 971.426i | 0.0512364 | − | 0.0887441i | ||||
\(494\) | −6664.16 | −0.606953 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4871.33 | 0.440986 | ||||||||
\(497\) | 8216.66 | − | 14231.7i | 0.741585 | − | 1.28446i | ||||
\(498\) | −1911.23 | − | 4779.97i | −0.171976 | − | 0.430111i | ||||
\(499\) | 9371.20 | + | 16231.4i | 0.840707 | + | 1.45615i | 0.889298 | + | 0.457328i | \(0.151193\pi\) |
−0.0485916 | + | 0.998819i | \(0.515473\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 435.904 | + | 1090.19i | 0.0388717 | + | 0.0972179i | ||||
\(502\) | 5651.07 | − | 9787.95i | 0.502430 | − | 0.870234i | ||||
\(503\) | −10305.9 | −0.913553 | −0.456777 | − | 0.889581i | \(-0.650996\pi\) | ||||
−0.456777 | + | 0.889581i | \(0.650996\pi\) | |||||||
\(504\) | −10376.3 | + | 9876.80i | −0.917059 | + | 0.872912i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −253.394 | + | 438.892i | −0.0222624 | + | 0.0385595i | ||||
\(507\) | 19250.3 | − | 24457.1i | 1.68626 | − | 2.14236i | ||||
\(508\) | −885.889 | − | 1534.40i | −0.0773720 | − | 0.134012i | ||||
\(509\) | 5844.86 | + | 10123.6i | 0.508976 | + | 0.881572i | 0.999946 | + | 0.0103957i | \(0.00330910\pi\) |
−0.490970 | + | 0.871176i | \(0.663358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6863.25 | − | 11887.5i | 0.594153 | − | 1.02910i | ||||
\(512\) | 9206.71 | 0.794693 | ||||||||
\(513\) | −3155.89 | − | 1446.16i | −0.271610 | − | 0.124463i | ||||
\(514\) | 12031.9 | 1.03250 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2082.10 | + | 300.273i | 0.177634 | + | 0.0256178i | ||||
\(517\) | −13827.5 | − | 23949.9i | −1.17627 | − | 2.03736i | ||||
\(518\) | 857.980 | + | 1486.06i | 0.0727750 | + | 0.126050i | ||||
\(519\) | −2050.00 | + | 2604.48i | −0.173381 | + | 0.220278i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18320.4 | −1.54056 | −0.770278 | − | 0.637708i | \(-0.779883\pi\) | ||||
−0.770278 | + | 0.637708i | \(0.779883\pi\) | |||||||
\(522\) | −2071.11 | − | 8569.33i | −0.173659 | − | 0.718524i | ||||
\(523\) | −4497.23 | −0.376004 | −0.188002 | − | 0.982169i | \(-0.560201\pi\) | ||||
−0.188002 | + | 0.982169i | \(0.560201\pi\) | |||||||
\(524\) | 805.245 | − | 1394.72i | 0.0671322 | − | 0.116276i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9617.23 | − | 16657.5i | −0.797208 | − | 1.38080i | ||||
\(527\) | 355.086 | + | 615.027i | 0.0293506 | + | 0.0508368i | ||||
\(528\) | 8558.76 | + | 21405.4i | 0.705440 | + | 1.76430i | ||||
\(529\) | 6079.88 | − | 10530.7i | 0.499702 | − | 0.865510i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3008.00 | + | 12445.8i | 0.245830 | + | 1.01714i | ||||
\(532\) | 531.311 | 0.0432993 | ||||||||
\(533\) | −12059.8 | + | 20888.2i | −0.980053 | + | 1.69750i | ||||
\(534\) | 5946.03 | − | 7554.31i | 0.481854 | − | 0.612185i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −809.339 | − | 1401.82i | −0.0652204 | − | 0.112965i | ||||
\(537\) | 19162.9 | + | 2763.61i | 1.53992 | + | 0.222083i | ||||
\(538\) | 6545.45 | − | 11337.1i | 0.524525 | − | 0.908504i | ||||
\(539\) | −17726.8 | −1.41660 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 85.5785 | 0.00680094 | 0.00340047 | − | 0.999994i | \(-0.498918\pi\) | ||||
0.00340047 | + | 0.999994i | \(0.498918\pi\) | |||||||
\(542\) | −3890.88 | + | 6739.20i | −0.308353 | + | 0.534084i | ||||
\(543\) | 12981.3 | + | 1872.13i | 1.02594 | + | 0.147957i | ||||
\(544\) | −198.175 | − | 343.249i | −0.0156189 | − | 0.0270527i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −21608.8 | + | 27453.6i | −1.69372 | + | 2.15184i | ||||
\(547\) | −9158.66 | + | 15863.3i | −0.715897 | + | 1.23997i | 0.246715 | + | 0.969088i | \(0.420649\pi\) |
−0.962612 | + | 0.270883i | \(0.912684\pi\) | |||||||
\(548\) | 1928.33 | 0.150318 | ||||||||
\(549\) | 6523.45 | − | 6209.41i | 0.507129 | − | 0.482716i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1357.15 | − | 2350.66i | 0.104930 | − | 0.181745i | ||||
\(552\) | 110.359 | + | 276.008i | 0.00850943 | + | 0.0212820i | ||||
\(553\) | 2139.82 | + | 3706.27i | 0.164547 | + | 0.285003i | ||||
\(554\) | −2472.04 | − | 4281.70i | −0.189579 | − | 0.328361i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 113.728 | − | 196.983i | 0.00867471 | − | 0.0150250i | ||||
\(557\) | −21598.8 | −1.64304 | −0.821519 | − | 0.570181i | \(-0.806873\pi\) | ||||
−0.821519 | + | 0.570181i | \(0.806873\pi\) | |||||||
\(558\) | 5354.15 | + | 1577.12i | 0.406200 | + | 0.119650i | ||||
\(559\) | −42589.2 | −3.22242 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2078.65 | + | 2640.88i | −0.156436 | + | 0.198749i | ||||
\(562\) | 7454.51 | + | 12911.6i | 0.559519 | + | 0.969115i | ||||
\(563\) | 5576.22 | + | 9658.30i | 0.417424 | + | 0.723000i | 0.995680 | − | 0.0928559i | \(-0.0295996\pi\) |
−0.578255 | + | 0.815856i | \(0.696266\pi\) | |||||||
\(564\) | 1934.01 | + | 278.916i | 0.144391 | + | 0.0208236i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −810.849 | −0.0602165 | ||||||||
\(567\) | −16190.7 | + | 8311.73i | −1.19920 | + | 0.615626i | ||||
\(568\) | −13989.5 | −1.03343 | ||||||||
\(569\) | 10090.5 | − | 17477.2i | 0.743436 | − | 1.28767i | −0.207487 | − | 0.978238i | \(-0.566528\pi\) |
0.950922 | − | 0.309430i | \(-0.100138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4075.42 | − | 7058.83i | −0.298688 | − | 0.517343i | 0.677148 | − | 0.735847i | \(-0.263216\pi\) |
−0.975836 | + | 0.218504i | \(0.929882\pi\) | |||||||
\(572\) | 2461.23 | + | 4262.97i | 0.179911 | + | 0.311615i | ||||
\(573\) | −701.803 | + | 891.627i | −0.0511662 | + | 0.0650057i | ||||
\(574\) | 9904.53 | − | 17155.2i | 0.720222 | − | 1.24746i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11544.9 | + | 3400.66i | 0.835136 | + | 0.245997i | ||||
\(577\) | −11901.4 | −0.858689 | −0.429345 | − | 0.903141i | \(-0.641255\pi\) | ||||
−0.429345 | + | 0.903141i | \(0.641255\pi\) | |||||||
\(578\) | −7156.38 | + | 12395.2i | −0.514993 | + | 0.891994i | ||||
\(579\) | −3636.71 | − | 9095.37i | −0.261030 | − | 0.652834i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4154.63 | − | 7196.04i | −0.296666 | − | 0.513841i | ||||
\(582\) | −8716.88 | − | 21800.8i | −0.620836 | − | 1.55270i | ||||
\(583\) | 3631.96 | − | 6290.75i | 0.258011 | − | 0.446889i | ||||
\(584\) | −11685.2 | −0.827977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14576.6 | 1.02757 | ||||||||
\(587\) | 1613.51 | − | 2794.68i | 0.113452 | − | 0.196505i | −0.803708 | − | 0.595024i | \(-0.797142\pi\) |
0.917160 | + | 0.398519i | \(0.130476\pi\) | |||||||
\(588\) | 774.682 | − | 984.219i | 0.0543323 | − | 0.0690281i | ||||
\(589\) | 859.237 | + | 1488.24i | 0.0601090 | + | 0.104112i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16178.8 | + | 2333.26i | 1.12607 | + | 0.162398i | ||||
\(592\) | 809.834 | − | 1402.67i | 0.0562230 | − | 0.0973810i | ||||
\(593\) | 7574.79 | 0.524552 | 0.262276 | − | 0.964993i | \(-0.415527\pi\) | ||||
0.262276 | + | 0.964993i | \(0.415527\pi\) | |||||||
\(594\) | 2476.97 | + | 26297.9i | 0.171096 | + | 1.81653i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.0932 | + | 33.0705i | −0.00131223 | + | 0.00227285i | ||||
\(597\) | 8872.73 | + | 1279.59i | 0.608269 | + | 0.0877225i | ||||
\(598\) | 362.478 | + | 627.830i | 0.0247873 | + | 0.0429329i | ||||
\(599\) | 4937.32 | + | 8551.69i | 0.336784 | + | 0.583326i | 0.983826 | − | 0.179128i | \(-0.0573276\pi\) |
−0.647042 | + | 0.762454i | \(0.723994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 175.136 | − | 303.345i | 0.0118868 | − | 0.0205885i | −0.860021 | − | 0.510259i | \(-0.829550\pi\) |
0.871908 | + | 0.489670i | \(0.162883\pi\) | |||||||
\(602\) | 34977.9 | 2.36809 | ||||||||
\(603\) | −483.104 | − | 1998.87i | −0.0326261 | − | 0.134992i | ||||
\(604\) | −1047.98 | −0.0705991 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −489.113 | − | 1223.27i | −0.0327869 | − | 0.0819997i | ||||
\(607\) | 9468.84 | + | 16400.5i | 0.633160 | + | 1.09667i | 0.986902 | + | 0.161323i | \(0.0515760\pi\) |
−0.353741 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(608\) | −479.543 | − | 830.593i | −0.0319869 | − | 0.0554029i | ||||
\(609\) | −5283.11 | − | 13213.0i | −0.351531 | − | 0.879176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39560.1 | −2.61936 | ||||||||
\(612\) | −55.7863 | − | 230.819i | −0.00368469 | − | 0.0152456i | ||||
\(613\) | 4729.36 | 0.311610 | 0.155805 | − | 0.987788i | \(-0.450203\pi\) | ||||
0.155805 | + | 0.987788i | \(0.450203\pi\) | |||||||
\(614\) | 3118.92 | − | 5402.13i | 0.204999 | − | 0.355069i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16779.9 | + | 29063.7i | 1.09754 | + | 1.90099i | ||||
\(617\) | 11066.2 | + | 19167.2i | 0.722053 | + | 1.25063i | 0.960175 | + | 0.279398i | \(0.0901348\pi\) |
−0.238122 | + | 0.971235i | \(0.576532\pi\) | |||||||
\(618\) | −21203.6 | − | 3057.91i | −1.38015 | − | 0.199041i | ||||
\(619\) | −2433.31 | + | 4214.61i | −0.158001 | + | 0.273666i | −0.934148 | − | 0.356886i | \(-0.883838\pi\) |
0.776146 | + | 0.630553i | \(0.217172\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.4128 | + | 375.977i | 0.00228835 | + | 0.0242954i | ||||
\(622\) | 15035.2 | 0.969221 | ||||||||
\(623\) | 7758.76 | − | 13438.6i | 0.498954 | − | 0.864213i | ||||
\(624\) | 32639.5 | + | 4707.15i | 2.09395 | + | 0.301982i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8816.36 | + | 15270.4i | 0.562895 | + | 0.974963i | ||||
\(627\) | −5029.91 | + | 6390.41i | −0.320376 | + | 0.407031i | ||||
\(628\) | −1542.49 | + | 2671.68i | −0.0980130 | + | 0.169764i | ||||
\(629\) | 236.125 | 0.0149681 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24104.7 | 1.52075 | 0.760375 | − | 0.649484i | \(-0.225015\pi\) | ||||
0.760375 | + | 0.649484i | \(0.225015\pi\) | |||||||
\(632\) | 1821.61 | − | 3155.11i | 0.114651 | − | 0.198582i | ||||
\(633\) | 1124.24 | + | 2811.71i | 0.0705916 | + | 0.176549i | ||||
\(634\) | −7011.89 | − | 12145.0i | −0.439239 | − | 0.760785i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 190.550 | + | 476.565i | 0.0118802 | + | 0.0297123i | ||||
\(637\) | −12679.0 | + | 21960.7i | −0.788636 | + | 1.36596i | ||||
\(638\) | −20653.1 | −1.28161 | ||||||||
\(639\) | −17048.6 | − | 5021.81i | −1.05545 | − | 0.310892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1638.33 | − | 2837.68i | 0.100952 | − | 0.174854i | −0.811125 | − | 0.584873i | \(-0.801144\pi\) |
0.912077 | + | 0.410019i | \(0.134478\pi\) | |||||||
\(642\) | −10059.4 | + | 12780.3i | −0.618401 | + | 0.785667i | ||||
\(643\) | −4751.07 | − | 8229.10i | −0.291390 | − | 0.504703i | 0.682748 | − | 0.730654i | \(-0.260785\pi\) |
−0.974139 | + | 0.225951i | \(0.927451\pi\) | |||||||
\(644\) | −28.8991 | − | 50.0548i | −0.00176830 | − | 0.00306279i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 376.569 | − | 652.236i | 0.0229348 | − | 0.0397243i | ||||
\(647\) | 15190.4 | 0.923024 | 0.461512 | − | 0.887134i | \(-0.347307\pi\) | ||||
0.461512 | + | 0.887134i | \(0.347307\pi\) | |||||||
\(648\) | 13019.2 | + | 8398.59i | 0.789266 | + | 0.509148i | ||||
\(649\) | 29995.8 | 1.81423 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8917.05 | + | 1285.99i | 0.536846 | + | 0.0774221i | ||||
\(652\) | −489.521 | − | 847.876i | −0.0294036 | − | 0.0509285i | ||||
\(653\) | −3355.41 | − | 5811.73i | −0.201083 | − | 0.348286i | 0.747795 | − | 0.663930i | \(-0.231113\pi\) |
−0.948878 | + | 0.315644i | \(0.897779\pi\) | |||||||
\(654\) | −860.199 | + | 1092.87i | −0.0514319 | + | 0.0653432i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18697.5 | −1.11283 | ||||||||
\(657\) | −14240.4 | − | 4194.64i | −0.845617 | − | 0.249085i | ||||
\(658\) | 32490.1 | 1.92492 | ||||||||
\(659\) | −10490.6 | + | 18170.2i | −0.620113 | + | 1.07407i | 0.369351 | + | 0.929290i | \(0.379580\pi\) |
−0.989464 | + | 0.144778i | \(0.953753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9666.37 | + | 16742.6i | 0.568802 | + | 0.985194i | 0.996685 | + | 0.0813598i | \(0.0259263\pi\) |
−0.427883 | + | 0.903834i | \(0.640740\pi\) | |||||||
\(662\) | 9467.30 | + | 16397.9i | 0.555827 | + | 0.962720i | ||||
\(663\) | 1784.89 | + | 4463.99i | 0.104554 | + | 0.261489i | ||||
\(664\) | −3536.80 | + | 6125.92i | −0.206709 | + | 0.358030i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1344.22 | − | 1279.51i | 0.0782096 | − | 0.0744446i | ||||
\(667\) | −295.274 | −0.0171410 | ||||||||
\(668\) | −97.1727 | + | 168.308i | −0.00562833 | + | 0.00974855i | ||||
\(669\) | −18207.6 | + | 23132.4i | −1.05224 | + | 1.33685i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10549.3 | − | 18271.9i | −0.606932 | − | 1.05124i | ||||
\(672\) | −4976.64 | − | 717.713i | −0.285681 | − | 0.0412000i | ||||
\(673\) | 1657.53 | − | 2870.92i | 0.0949374 | − | 0.164436i | −0.814645 | − | 0.579960i | \(-0.803068\pi\) |
0.909582 | + | 0.415523i | \(0.136402\pi\) | |||||||
\(674\) | 7799.11 | 0.445713 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5151.88 | 0.293120 | ||||||||
\(677\) | −9420.59 | + | 16316.9i | −0.534804 | + | 0.926308i | 0.464368 | + | 0.885642i | \(0.346281\pi\) |
−0.999173 | + | 0.0406661i | \(0.987052\pi\) | |||||||
\(678\) | −6623.10 | − | 955.160i | −0.375160 | − | 0.0541043i | ||||
\(679\) | −18948.8 | − | 32820.2i | −1.07097 | − | 1.85497i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11923.0 | − | 15148.0i | 0.670913 | − | 0.852381i | ||||
\(682\) | 6537.92 | − | 11324.0i | 0.367082 | − | 0.635804i | ||||
\(683\) | 20540.7 | 1.15076 | 0.575379 | − | 0.817887i | \(-0.304854\pi\) | ||||
0.575379 | + | 0.817887i | \(0.304854\pi\) | |||||||
\(684\) | −134.992 | − | 558.536i | −0.00754611 | − | 0.0312225i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2331.25 | + | 4037.84i | −0.129748 | + | 0.224731i | ||||
\(687\) | 6895.32 | + | 17245.1i | 0.382930 | + | 0.957705i | ||||
\(688\) | −16507.6 | − | 28591.9i | −0.914746 | − | 1.58439i | ||||
\(689\) | −5195.48 | − | 8998.84i | −0.287275 | − | 0.497574i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12816.9 | − | 22199.5i | 0.705611 | − | 1.22215i | −0.260860 | − | 0.965377i | \(-0.584006\pi\) |
0.966471 | − | 0.256777i | \(-0.0826607\pi\) | |||||||
\(692\) | −548.634 | −0.0301386 | ||||||||
\(693\) | 10016.1 | + | 41442.3i | 0.549035 | + | 2.27167i | ||||
\(694\) | 22868.0 | 1.25080 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7492.42 | + | 9518.97i | −0.408045 | + | 0.518413i | ||||
\(697\) | −1362.92 | − | 2360.64i | −0.0740661 | − | 0.128286i | ||||
\(698\) | −5478.04 | − | 9488.25i | −0.297059 | − | 0.514521i | ||||
\(699\) | −23172.8 | − | 3341.90i | −1.25390 | − | 0.180833i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35929.9 | 1.93588 | 0.967941 | − | 0.251178i | \(-0.0808179\pi\) | ||||
0.967941 | + | 0.251178i | \(0.0808179\pi\) | |||||||
\(702\) | 34350.6 | + | 15740.9i | 1.84683 | + | 0.846298i | ||||
\(703\) | 571.375 | 0.0306541 | ||||||||
\(704\) | 14097.4 | − | 24417.4i | 0.754711 | − | 1.30720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15074.4 | − | 26109.6i | −0.803585 | − | 1.39185i | ||||
\(707\) | −1063.23 | − | 1841.58i | −0.0565588 | − | 0.0979626i | ||||
\(708\) | −1310.85 | + | 1665.41i | −0.0695829 | + | 0.0884038i | ||||
\(709\) | 5590.21 | − | 9682.53i | 0.296114 | − | 0.512884i | −0.679129 | − | 0.734019i | \(-0.737643\pi\) |
0.975243 | + | 0.221134i | \(0.0709759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3352.52 | − | 3191.13i | 0.176834 | − | 0.168322i | ||||
\(712\) | −13209.9 | −0.695313 | ||||||||
\(713\) | 93.4714 | − | 161.897i | 0.00490958 | − | 0.00850364i | ||||
\(714\) | −1465.90 | − | 3666.21i | −0.0768348 | − | 0.192163i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1602.39 | + | 2775.41i | 0.0836368 | + | 0.144863i | ||||
\(717\) | −4420.85 | − | 11056.5i | −0.230264 | − | 0.575889i | ||||
\(718\) | 10688.6 | − | 18513.2i | 0.555565 | − | 0.962267i | ||||
\(719\) | 33908.0 | 1.75877 | 0.879385 | − | 0.476111i | \(-0.157954\pi\) | ||||
0.879385 | + | 0.476111i | \(0.157954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34579.0 | −1.78611 | ||||||||
\(722\) | −9297.00 | + | 16102.9i | −0.479222 | + | 0.830037i | ||||
\(723\) | −7250.84 | + | 9212.05i | −0.372976 | + | 0.473858i | ||||
\(724\) | 1085.49 | + | 1880.12i | 0.0557209 | + | 0.0965115i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 40870.8 | + | 5894.25i | 2.08934 | + | 0.301317i | ||||
\(727\) | −1790.58 | + | 3101.37i | −0.0913465 | + | 0.158217i | −0.908078 | − | 0.418801i | \(-0.862450\pi\) |
0.816731 | + | 0.577018i | \(0.195784\pi\) | |||||||
\(728\) | 48006.9 | 2.44403 | ||||||||
\(729\) | 12851.3 | + | 14908.6i | 0.652912 | + | 0.757434i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2406.57 | − | 4168.30i | 0.121765 | − | 0.210903i | ||||
\(732\) | 1475.50 | + | 212.792i | 0.0745028 | + | 0.0107445i | ||||
\(733\) | −5008.11 | − | 8674.31i | −0.252359 | − | 0.437098i | 0.711816 | − | 0.702366i | \(-0.247873\pi\) |
−0.964175 | + | 0.265268i | \(0.914540\pi\) | |||||||
\(734\) | −13813.4 | − | 23925.4i | −0.694633 | − | 1.20314i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.1667 | + | 90.3554i | −0.00261262 | + | 0.00452520i | ||||
\(737\) | −4817.52 | −0.240781 | ||||||||
\(738\) | −20550.7 | − | 6053.40i | −1.02504 | − | 0.301936i | ||||
\(739\) | 7686.38 | 0.382609 | 0.191304 | − | 0.981531i | \(-0.438728\pi\) | ||||
0.191304 | + | 0.981531i | \(0.438728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4319.07 | + | 10802.0i | 0.214123 | + | 0.535520i | ||||
\(742\) | 4266.97 | + | 7390.61i | 0.211113 | + | 0.365658i | ||||
\(743\) | −5342.39 | − | 9253.29i | −0.263786 | − | 0.456891i | 0.703459 | − | 0.710736i | \(-0.251638\pi\) |
−0.967245 | + | 0.253845i | \(0.918305\pi\) | |||||||
\(744\) | −2847.42 | − | 7121.37i | −0.140311 | − | 0.350917i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10913.7 | −0.535629 | ||||||||
\(747\) | −6509.19 | + | 6195.84i | −0.318820 | + | 0.303472i | ||||
\(748\) | −556.302 | −0.0271931 | ||||||||
\(749\) | −13126.2 | + | 22735.2i | −0.640347 | + | 1.10911i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −949.678 | − | 1644.89i | −0.0461441 | − | 0.0799240i | 0.842031 | − | 0.539429i | \(-0.181360\pi\) |
−0.888175 | + | 0.459505i | \(0.848027\pi\) | |||||||
\(752\) | −15333.5 | − | 26558.4i | −0.743557 | − | 1.28788i | ||||
\(753\) | −19527.8 | − | 2816.23i | −0.945064 | − | 0.136294i | ||||
\(754\) | −14772.0 | + | 25585.9i | −0.713482 | + | 1.23579i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2738.65 | − | 1254.97i | −0.131751 | − | 0.0603740i | ||||
\(757\) | −3716.63 | −0.178445 | −0.0892227 | − | 0.996012i | \(-0.528438\pi\) | ||||
−0.0892227 | + | 0.996012i | \(0.528438\pi\) | |||||||
\(758\) | −9719.01 | + | 16833.8i | −0.465713 | + | 0.806638i | ||||
\(759\) | 875.628 | + | 126.280i | 0.0418752 | + | 0.00603909i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6324.33 | + | 10954.1i | 0.301257 | + | 0.521793i | 0.976421 | − | 0.215875i | \(-0.0692604\pi\) |
−0.675164 | + | 0.737668i | \(0.735927\pi\) | |||||||
\(762\) | −19706.0 | + | 25036.1i | −0.936843 | + | 1.19024i | ||||
\(763\) | −1122.44 | + | 1944.13i | −0.0532571 | + | 0.0922440i | ||||
\(764\) | −187.821 | −0.00889415 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9867.58 | 0.465444 | ||||||||
\(767\) | 21454.3 | − | 37160.0i | 1.01000 | − | 1.74937i | ||||
\(768\) | 2520.21 | + | 6303.02i | 0.118412 | + | 0.296147i | ||||
\(769\) | −7749.61 | − | 13422.7i | −0.363404 | − | 0.629435i | 0.625114 | − | 0.780533i | \(-0.285052\pi\) |
−0.988519 | + | 0.151098i | \(0.951719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7797.94 | − | 19502.6i | −0.364249 | − | 0.910983i | ||||
\(772\) | 810.704 | − | 1404.18i | 0.0377952 | − | 0.0654631i | ||||
\(773\) | 14179.9 | 0.659789 | 0.329895 | − | 0.944018i | \(-0.392987\pi\) | ||||
0.329895 | + | 0.944018i | \(0.392987\pi\) | |||||||
\(774\) | −8886.94 | − | 36770.2i | −0.412706 | − | 1.70760i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16130.9 | + | 27939.5i | −0.746219 | + | 1.29249i | ||||
\(777\) | 1852.71 | − | 2353.83i | 0.0855412 | − | 0.108678i | ||||
\(778\) | 6959.99 | + | 12055.1i | 0.320730 | + | 0.555520i | ||||
\(779\) | −3297.98 | − | 5712.27i | −0.151685 | − | 0.262726i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20817.9 | + | 36057.6i | −0.953805 | + | 1.65204i | ||||
\(782\) | −81.9295 | −0.00374654 | ||||||||
\(783\) | −12547.8 | + | 8910.89i | −0.572696 | + | 0.406704i | ||||
\(784\) | −19657.5 | −0.895477 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −28664.3 | − | 4133.86i | −1.30079 | − | 0.187595i | ||||
\(787\) | −8560.74 | − | 14827.6i | −0.387748 | − | 0.671598i | 0.604399 | − | 0.796682i | \(-0.293413\pi\) |
−0.992146 | + | 0.125084i | \(0.960080\pi\) | |||||||
\(788\) | 1352.86 | + | 2343.23i | 0.0611596 | + | 0.105932i | ||||
\(789\) | −20767.3 | + | 26384.4i | −0.937053 | + | 1.19051i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10801.0 | −0.485511 | ||||||||
\(792\) | 26289.6 | − | 25024.0i | 1.17950 | − | 1.12271i | ||||
\(793\) | −30181.3 | −1.35154 | ||||||||
\(794\) | −5947.18 | + | 10300.8i | −0.265816 | + | 0.460406i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 741.931 | + | 1285.06i | 0.0330365 | + | 0.0572209i | ||||
\(797\) | −3411.17 | − | 5908.31i | −0.151606 | − | 0.262589i | 0.780212 | − | 0.625515i | \(-0.215111\pi\) |
−0.931818 | + | 0.362926i | \(0.881778\pi\) | |||||||
\(798\) | −3547.19 | − | 8871.49i | −0.157355 | − | 0.393543i | ||||
\(799\) | 2235.41 | − | 3871.84i | 0.0989775 | − | 0.171434i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16098.5 | − | 4741.95i | −0.710126 | − | 0.209174i | ||||
\(802\) | −15140.0 | −0.666600 | ||||||||
\(803\) | −17388.8 | + | 30118.4i | −0.764183 | + | 1.32360i | ||||
\(804\) | 210.531 | − | 267.476i | 0.00923490 | − | 0.0117328i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9352.42 | − | 16198.9i | −0.408716 | − | 0.707917i | ||||
\(807\) | −22618.4 | − | 3261.95i | −0.986625 | − | 0.142288i | ||||
\(808\) | −905.122 | + | 1567.72i | −0.0394085 | + | 0.0682575i | ||||
\(809\) | 7352.18 | 0.319517 | 0.159758 | − | 0.987156i | \(-0.448928\pi\) | ||||
0.159758 | + | 0.987156i | \(0.448928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11737.3 | 0.508201 | 0.254101 | − | 0.967178i | \(-0.418221\pi\) | ||||
0.254101 | + | 0.967178i | \(0.418221\pi\) | |||||||
\(812\) | 1177.72 | − | 2039.88i | 0.0508990 | − | 0.0881597i | ||||
\(813\) | 13445.3 | + | 1939.03i | 0.580009 | + | 0.0836468i | ||||
\(814\) | −2173.79 | − | 3765.12i | −0.0936012 | − | 0.162122i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2305.04 | + | 2928.51i | −0.0988880 | + | 0.125635i | ||||
\(817\) | 5823.42 | − | 10086.5i | 0.249370 | − | 0.431922i | ||||
\(818\) | 22252.7 | 0.951157 | ||||||||
\(819\) | 58504.4 | + | 17233.0i | 2.49610 | + | 0.735251i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20571.2 | − | 35630.4i | 0.874471 | − | 1.51463i | 0.0171458 | − | 0.999853i | \(-0.494542\pi\) |
0.857325 | − | 0.514775i | \(-0.172125\pi\) | |||||||
\(822\) | −12874.1 | − | 32198.0i | −0.546271 | − | 1.36622i | ||||
\(823\) | 13613.4 | + | 23579.0i | 0.576588 | + | 0.998679i | 0.995867 | + | 0.0908220i | \(0.0289494\pi\) |
−0.419279 | + | 0.907857i | \(0.637717\pi\) | |||||||
\(824\) | 14718.4 | + | 25493.0i | 0.622256 | + | 1.07778i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17620.1 | + | 30518.9i | −0.742230 | + | 1.28558i | ||||
\(827\) | 16572.1 | 0.696820 | 0.348410 | − | 0.937342i | \(-0.386722\pi\) | ||||
0.348410 | + | 0.937342i | \(0.386722\pi\) | |||||||
\(828\) | −45.2772 | + | 43.0975i | −0.00190035 | + | 0.00180887i | ||||
\(829\) | −2162.45 | −0.0905972 | −0.0452986 | − | 0.998973i | \(-0.514424\pi\) | ||||
−0.0452986 | + | 0.998973i | \(0.514424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5338.08 | + | 6781.93i | −0.222835 | + | 0.283108i | ||||
\(832\) | −20166.2 | − | 34928.9i | −0.840309 | − | 1.45546i | ||||
\(833\) | −1432.89 | − | 2481.85i | −0.0596001 | − | 0.103230i | ||||
\(834\) | −4048.37 | − | 583.842i | −0.168086 | − | 0.0242408i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1346.14 | −0.0556904 | ||||||||
\(837\) | −913.698 | − | 9700.71i | −0.0377324 | − | 0.400604i | ||||
\(838\) | −25720.1 | −1.06025 | ||||||||
\(839\) | −22804.3 | + | 39498.2i | −0.938369 | + | 1.62530i | −0.169857 | + | 0.985469i | \(0.554331\pi\) |
−0.768513 | + | 0.639835i | \(0.779003\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6177.87 | + | 10700.4i | 0.253306 | + | 0.438738i | ||||
\(842\) | −4001.48 | − | 6930.76i | −0.163777 | − | 0.283670i | ||||
\(843\) | 16097.2 | − | 20451.1i | 0.657669 | − | 0.835556i | ||||
\(844\) | −250.618 | + | 434.083i | −0.0102211 | + | 0.0177035i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8254.86 | − | 34155.0i | −0.335471 | − | 1.38803i | ||||
\(847\) | 66652.4 | 2.70390 | ||||||||
\(848\) | 4027.53 | − | 6975.89i | 0.163097 | − | 0.282492i | ||||
\(849\) | 525.515 | + | 1314.31i | 0.0212434 | + | 0.0531295i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.0783 | − | 53.8292i | −0.00125188 | − | 0.00216832i | ||||
\(852\) | −1092.21 | − | 2731.60i | −0.0439182 | − | 0.109839i | ||||
\(853\) | −9760.04 | + | 16904.9i | −0.391767 | + | 0.678560i | −0.992683 | − | 0.120752i | \(-0.961469\pi\) |
0.600916 | + | 0.799312i | \(0.294803\pi\) | |||||||
\(854\) | 24787.5 | 0.993220 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22348.4 | 0.892351 | ||||||||
\(857\) | −13592.8 | + | 23543.5i | −0.541800 | + | 0.938425i | 0.457001 | + | 0.889466i | \(0.348924\pi\) |
−0.998801 | + | 0.0489585i | \(0.984410\pi\) | |||||||
\(858\) | 54748.5 | − | 69556.8i | 2.17842 | − | 2.76764i | ||||
\(859\) | 9414.91 | + | 16307.1i | 0.373961 | + | 0.647719i | 0.990171 | − | 0.139863i | \(-0.0446661\pi\) |
−0.616210 | + | 0.787582i | \(0.711333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34226.0 | − | 4935.96i | −1.35473 | − | 0.195374i | ||||
\(862\) | 16400.6 | − | 28406.7i | 0.648036 | − | 1.12243i | ||||
\(863\) | −33858.8 | −1.33553 | −0.667767 | − | 0.744370i | \(-0.732750\pi\) | ||||
−0.667767 | + | 0.744370i | \(0.732750\pi\) | |||||||
\(864\) | 509.938 | + | 5414.00i | 0.0200792 | + | 0.213181i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20162.9 | − | 34923.1i | 0.791180 | − | 1.37036i | ||||
\(867\) | 24729.5 | + | 3566.41i | 0.968695 | + | 0.139702i | ||||
\(868\) | 745.637 | + | 1291.48i | 0.0291573 | + | 0.0505020i | ||||
\(869\) | −5421.47 | − | 9390.27i | −0.211635 | − | 0.366563i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3445.70 | + | 5968.14i | −0.134045 | + | 0.232173i | ||||
\(872\) | 1911.05 | 0.0742160 | ||||||||
\(873\) | −29687.6 | + | 28258.5i | −1.15094 | + | 1.09554i | ||||
\(874\) | −198.253 | −0.00767277 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −912.302 | − | 2281.66i | −0.0351870 | − | 0.0880024i | ||||
\(877\) | −14223.6 | − | 24636.1i | −0.547661 | − | 0.948576i | −0.998434 | − | 0.0559378i | \(-0.982185\pi\) |
0.450774 | − | 0.892638i | \(-0.351148\pi\) | |||||||
\(878\) | −15197.1 | − | 26322.2i | −0.584143 | − | 1.01177i | ||||
\(879\) | −9447.16 | − | 23627.3i | −0.362508 | − | 0.906630i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15935.0 | −0.609378 | −0.304689 | − | 0.952452i | \(-0.598553\pi\) | ||||
−0.304689 | + | 0.952452i | \(0.598553\pi\) | |||||||
\(882\) | −21605.9 | − | 6364.21i | −0.824838 | − | 0.242964i | ||||
\(883\) | −22277.5 | −0.849036 | −0.424518 | − | 0.905419i | \(-0.639556\pi\) | ||||
−0.424518 | + | 0.905419i | \(0.639556\pi\) | |||||||
\(884\) | −397.892 | + | 689.169i | −0.0151386 | + | 0.0262209i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14634.2 | − | 25347.2i | −0.554904 | − | 0.961122i | ||||
\(887\) | −19273.3 | − | 33382.3i | −0.729576 | − | 1.26366i | −0.957062 | − | 0.289882i | \(-0.906384\pi\) |
0.227486 | − | 0.973781i | \(-0.426949\pi\) | |||||||
\(888\) | −2523.93 | − | 363.993i | −0.0953802 | − | 0.0137554i | ||||
\(889\) | −25713.7 | + | 44537.4i | −0.970090 | + | 1.68024i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41021.1 | − | 21058.7i | 1.54238 | − | 0.791801i | ||||
\(892\) | −4872.84 | −0.182909 | ||||||||
\(893\) | 5409.23 | − | 9369.07i | 0.202702 | − | 0.351091i | ||||
\(894\) | 679.662 | + | 98.0185i | 0.0254265 | + | 0.00366692i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20432.8 | + | 35390.7i | 0.761845 | + | 1.31955i | ||||
\(897\) | 782.728 | − | 994.441i | 0.0291355 | − | 0.0370161i | ||||
\(898\) | 6010.45 | − | 10410.4i | 0.223353 | − | 0.386859i | ||||
\(899\) | 7618.46 | 0.282636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1174.32 | 0.0434208 | ||||||||
\(902\) | −25094.3 | + | 43464.6i | −0.926329 | + | 1.60445i | ||||
\(903\) | −22669.4 | − | 56695.8i | −0.835425 | − | 2.08939i | ||||
\(904\) | 4597.39 | + | 7962.92i | 0.169145 | + | 0.292968i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6996.65 | + | 17498.6i | 0.256565 | + | 0.641667i | ||||
\(907\) | −20997.9 | + | 36369.4i | −0.768714 | + | 1.33145i | 0.169546 | + | 0.985522i | \(0.445770\pi\) |
−0.938260 | + | 0.345930i | \(0.887564\pi\) | |||||||
\(908\) | 3190.92 | 0.116624 | ||||||||
\(909\) | −1665.80 | + | 1585.61i | −0.0607824 | + | 0.0578563i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21274.1 | + | 36847.8i | −0.773701 | + | 1.34009i | 0.161820 | + | 0.986820i | \(0.448264\pi\) |
−0.935521 | + | 0.353270i | \(0.885070\pi\) | |||||||
\(912\) | −5577.74 | + | 7086.41i | −0.202519 | + | 0.257297i | ||||
\(913\) | 10526.2 | + | 18232.0i | 0.381564 | + | 0.660888i | ||||
\(914\) | 8764.09 | + | 15179.9i | 0.317167 | + | 0.549349i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1537.12 | + | 2662.37i | −0.0554453 | + | 0.0960342i | ||||
\(917\) | −46745.9 | −1.68341 | ||||||||
\(918\) | −3481.63 | + | 2472.50i | −0.125175 | + | 0.0888940i | ||||
\(919\) | 27133.7 | 0.973947 | 0.486974 | − | 0.873417i | \(-0.338101\pi\) | ||||
0.486974 | + | 0.873417i | \(0.338101\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10777.7 | − | 1554.32i | −0.385600 | − | 0.0556099i | ||||
\(922\) | 3502.10 | + | 6065.82i | 0.125093 | + | 0.216667i | ||||
\(923\) | 29779.7 | + | 51580.0i | 1.06198 | + | 1.83941i | ||||
\(924\) | −4364.91 | + | 5545.53i | −0.155406 | + | 0.197440i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 40415.2 | 1.43426 | ||||||||
\(927\) | 8785.58 | + | 36350.8i | 0.311280 | + | 1.28794i | ||||
\(928\) | −4251.89 | −0.150404 | ||||||||
\(929\) | 12532.6 | − | 21707.0i | 0.442605 | − | 0.766614i | −0.555277 | − | 0.831665i | \(-0.687388\pi\) |
0.997882 | + | 0.0650513i | \(0.0207211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3467.32 | − | 6005.57i | −0.122059 | − | 0.211412i | ||||
\(932\) | −1937.69 | − | 3356.18i | −0.0681022 | − | 0.117956i | ||||
\(933\) | −9744.37 | − | 24370.6i | −0.341925 | − | 0.855152i | ||||
\(934\) | 731.488 | − | 1266.97i | 0.0256264 | − | 0.0443861i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12197.3 | − | 50466.9i | −0.425940 | − | 1.76235i | ||||
\(937\) | 6703.82 | 0.233729 | 0.116865 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116865 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(938\) | 2829.91 | − | 4901.54i | 0.0985071 | − | 0.170619i | ||||
\(939\) | 19037.9 | − | 24187.3i | 0.661638 | − | 0.840598i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26885.4 | + | 46566.9i | 0.931391 | + | 1.61322i | 0.780946 | + | 0.624599i | \(0.214738\pi\) |
0.150446 | + | 0.988618i | \(0.451929\pi\) | |||||||
\(942\) | 54908.1 | + | 7918.65i | 1.89915 | + | 0.273889i | ||||
\(943\) | −358.768 | + | 621.405i | −0.0123893 | + | 0.0214589i | ||||
\(944\) | 33262.7 | 1.14683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −88620.6 | −3.04578 | ||||||||
\(947\) | 4382.86 | − | 7591.33i | 0.150395 | − | 0.260491i | −0.780978 | − | 0.624559i | \(-0.785279\pi\) |
0.931373 | + | 0.364067i | \(0.118612\pi\) | |||||||
\(948\) | 758.286 | + | 109.357i | 0.0259789 | + | 0.00374658i | ||||
\(949\) | 24874.5 | + | 43084.0i | 0.850856 | + | 1.47372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15141.4 | + | 19236.8i | −0.516291 | + | 0.655937i | ||||
\(952\) | −2712.71 | + | 4698.55i | −0.0923522 | + | 0.159959i | ||||
\(953\) | −18136.4 | −0.616471 | −0.308236 | − | 0.951310i | \(-0.599739\pi\) | ||||
−0.308236 | + | 0.951310i | \(0.599739\pi\) | |||||||
\(954\) | 6685.20 | − | 6363.37i | 0.226878 | − | 0.215956i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 985.505 | − | 1706.95i | 0.0333405 | − | 0.0577474i | ||||
\(957\) | 13385.4 | + | 33476.7i | 0.452129 | + | 1.13077i | ||||
\(958\) | 18165.5 | + | 31463.5i | 0.612630 | + | 1.06111i | ||||
\(959\) | −27985.7 | − | 48472.6i | −0.942341 | − | 1.63218i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12483.8 | − | 21622.6i | 0.419046 | − | 0.725810i | ||||
\(962\) | −6219.17 | −0.208435 | ||||||||
\(963\) | 27235.2 | + | 8022.38i | 0.911362 | + | 0.268450i | ||||
\(964\) | −1940.52 | −0.0648338 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −642.843 | + | 816.720i | −0.0214111 | + | 0.0272024i | ||||
\(967\) | 9276.92 | + | 16068.1i | 0.308506 | + | 0.534348i | 0.978036 | − | 0.208437i | \(-0.0668376\pi\) |
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(968\) | −28370.3 | − | 49138.8i | −0.941999 | − | 1.63159i | ||||
\(969\) | −1301.27 | − | 187.664i | −0.0431401 | − | 0.00622151i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44276.7 | 1.46334 | 0.731672 | − | 0.681657i | \(-0.238740\pi\) | ||||
0.731672 | + | 0.681657i | \(0.238740\pi\) | |||||||
\(972\) | −623.456 | + | 3197.84i | −0.0205734 | + | 0.105525i | ||||
\(973\) | −6602.11 | −0.217527 | ||||||||
\(974\) | −11757.7 | + | 20365.0i | −0.386798 | + | 0.669954i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11698.3 | − | 20262.0i | −0.383660 | − | 0.664519i | ||||
\(977\) | −20059.1 | − | 34743.4i | −0.656856 | − | 1.13771i | −0.981425 | − | 0.191846i | \(-0.938553\pi\) |
0.324569 | − | 0.945862i | \(-0.394781\pi\) | |||||||
\(978\) | −10889.1 | + | 13834.4i | −0.356028 | + | 0.452326i | ||||
\(979\) | −19657.7 | + | 34048.2i | −0.641740 | + | 1.11153i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2328.93 | + | 686.008i | 0.0757972 | + | 0.0223268i | ||||
\(982\) | 28122.0 | 0.913857 | ||||||||
\(983\) | −4487.23 | + | 7772.11i | −0.145596 | + | 0.252179i | −0.929595 | − | 0.368583i | \(-0.879843\pi\) |
0.783999 | + | 0.620762i | \(0.213176\pi\) | |||||||
\(984\) | 10929.2 | + | 27333.8i | 0.354074 | + | 0.885537i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1669.43 | − | 2891.54i | −0.0539204 | − | 0.0933929i | ||||
\(987\) | −21057.0 | − | 52663.4i | −0.679080 | − | 1.69837i | ||||
\(988\) | −962.818 | + | 1667.65i | −0.0310034 | + | 0.0536994i | ||||
\(989\) | −1266.99 | −0.0407361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 715.965 | 0.0229499 | 0.0114750 | − | 0.999934i | \(-0.496347\pi\) | ||||
0.0114750 | + | 0.999934i | \(0.496347\pi\) | |||||||
\(992\) | 1345.97 | − | 2331.29i | 0.0430793 | − | 0.0746155i | ||||
\(993\) | 20443.5 | − | 25973.1i | 0.653330 | − | 0.830042i | ||||
\(994\) | −24457.6 | − | 42361.9i | −0.780432 | − | 1.35175i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1472.28 | − | 212.326i | −0.0468382 | − | 0.00675484i | ||||
\(997\) | 15885.1 | − | 27513.9i | 0.504601 | − | 0.873995i | −0.495385 | − | 0.868674i | \(-0.664973\pi\) |
0.999986 | − | 0.00532109i | \(-0.00169376\pi\) | |||||||
\(998\) | 55788.5 | 1.76949 | ||||||||
\(999\) | −2945.16 | − | 1349.60i | −0.0932742 | − | 0.0427422i |
(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.e.f.151.9 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.124.18 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.124.7 | 48 | |||
5.4 | even | 2 | 225.4.e.e.151.4 | yes | 24 | ||
9.2 | odd | 6 | 2025.4.a.bj.1.9 | 12 | |||
9.4 | even | 3 | inner | 225.4.e.f.76.9 | yes | 24 | |
9.7 | even | 3 | 2025.4.a.bf.1.4 | 12 | |||
45.4 | even | 6 | 225.4.e.e.76.4 | ✓ | 24 | ||
45.13 | odd | 12 | 225.4.k.e.49.18 | 48 | |||
45.22 | odd | 12 | 225.4.k.e.49.7 | 48 | |||
45.29 | odd | 6 | 2025.4.a.be.1.4 | 12 | |||
45.34 | even | 6 | 2025.4.a.bi.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.4 | ✓ | 24 | 45.4 | even | 6 | ||
225.4.e.e.151.4 | yes | 24 | 5.4 | even | 2 | ||
225.4.e.f.76.9 | yes | 24 | 9.4 | even | 3 | inner | |
225.4.e.f.151.9 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.k.e.49.7 | 48 | 45.22 | odd | 12 | |||
225.4.k.e.49.18 | 48 | 45.13 | odd | 12 | |||
225.4.k.e.124.7 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.124.18 | 48 | 5.2 | odd | 4 | |||
2025.4.a.be.1.4 | 12 | 45.29 | odd | 6 | |||
2025.4.a.bf.1.4 | 12 | 9.7 | even | 3 | |||
2025.4.a.bi.1.9 | 12 | 45.34 | even | 6 | |||
2025.4.a.bj.1.9 | 12 | 9.2 | odd | 6 |