Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(46,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.h (of order \(5\), degree \(4\), 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: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 46.1 | ||
Character | \(\chi\) | \(=\) | 225.46 |
Dual form | 225.4.h.d.181.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71061 | + | 5.26471i | −0.604791 | + | 1.86136i | −0.106571 | + | 0.994305i | \(0.533987\pi\) |
−0.498220 | + | 0.867050i | \(0.666013\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −18.3188 | − | 13.3094i | −2.28986 | − | 1.66368i | ||||
\(5\) | −11.1283 | − | 1.07706i | −0.995349 | − | 0.0963350i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.2200 | −1.63173 | −0.815865 | − | 0.578243i | \(-0.803739\pi\) | ||||
−0.815865 | + | 0.578243i | \(0.803739\pi\) | |||||||
\(8\) | 65.5791 | − | 47.6460i | 2.89822 | − | 2.10568i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 24.7066 | − | 56.7450i | 0.781292 | − | 1.79444i | ||||
\(11\) | −6.53575 | + | 20.1150i | −0.179146 | + | 0.551354i | −0.999799 | − | 0.0200732i | \(-0.993610\pi\) |
0.820653 | + | 0.571427i | \(0.193610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85672 | − | 5.71440i | −0.0396125 | − | 0.121915i | 0.929295 | − | 0.369339i | \(-0.120416\pi\) |
−0.968907 | + | 0.247424i | \(0.920416\pi\) | |||||||
\(14\) | 51.6946 | − | 159.100i | 0.986855 | − | 3.03723i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 82.6849 | + | 254.478i | 1.29195 | + | 3.97622i | ||||
\(17\) | 17.3999 | − | 12.6418i | 0.248241 | − | 0.180358i | −0.456706 | − | 0.889618i | \(-0.650971\pi\) |
0.704947 | + | 0.709260i | \(0.250971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −85.2864 | + | 61.9642i | −1.02979 | + | 0.748187i | −0.968267 | − | 0.249918i | \(-0.919596\pi\) |
−0.0615244 | + | 0.998106i | \(0.519596\pi\) | |||||||
\(20\) | 189.523 | + | 167.842i | 2.11893 | + | 1.87653i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −94.7194 | − | 68.8177i | −0.917920 | − | 0.666908i | ||||
\(23\) | 1.91808 | − | 5.90324i | 0.0173890 | − | 0.0535178i | −0.941985 | − | 0.335654i | \(-0.891043\pi\) |
0.959374 | + | 0.282136i | \(0.0910429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 122.680 | + | 23.9717i | 0.981439 | + | 0.191774i | ||||
\(26\) | 33.2608 | 0.250884 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 553.596 | + | 402.211i | 3.73642 | + | 2.71467i | ||||
\(29\) | 187.176 | + | 135.991i | 1.19854 | + | 0.870791i | 0.994140 | − | 0.108097i | \(-0.0344757\pi\) |
0.204400 | + | 0.978887i | \(0.434476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 142.099 | − | 103.241i | 0.823280 | − | 0.598148i | −0.0943701 | − | 0.995537i | \(-0.530084\pi\) |
0.917650 | + | 0.397389i | \(0.130084\pi\) | |||||||
\(32\) | −832.711 | −4.60012 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.7909 | + | 113.231i | 0.185576 | + | 0.571144i | ||||
\(35\) | 336.299 | + | 32.5487i | 1.62414 | + | 0.157193i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −90.6084 | − | 278.864i | −0.402592 | − | 1.23905i | −0.922889 | − | 0.385066i | \(-0.874179\pi\) |
0.520296 | − | 0.853986i | \(-0.325821\pi\) | |||||||
\(38\) | −180.332 | − | 555.004i | −0.769834 | − | 2.36930i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −781.104 | + | 459.589i | −3.08759 | + | 1.81668i | ||||
\(41\) | 18.2039 | + | 56.0257i | 0.0693406 | + | 0.213408i | 0.979722 | − | 0.200362i | \(-0.0642117\pi\) |
−0.910381 | + | 0.413770i | \(0.864212\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −379.656 | −1.34644 | −0.673220 | − | 0.739442i | \(-0.735089\pi\) | ||||
−0.673220 | + | 0.739442i | \(0.735089\pi\) | |||||||
\(44\) | 387.446 | − | 281.496i | 1.32749 | − | 0.964480i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27.7978 | + | 20.1962i | 0.0890990 | + | 0.0647342i | ||||
\(47\) | −131.812 | − | 95.7671i | −0.409080 | − | 0.297214i | 0.364149 | − | 0.931341i | \(-0.381360\pi\) |
−0.773229 | + | 0.634127i | \(0.781360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 570.251 | 1.66254 | ||||||||
\(50\) | −336.061 | + | 604.868i | −0.950525 | + | 1.71082i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −42.0424 | + | 129.393i | −0.112120 | + | 0.345069i | ||||
\(53\) | 214.314 | + | 155.708i | 0.555440 | + | 0.403551i | 0.829787 | − | 0.558080i | \(-0.188462\pi\) |
−0.274347 | + | 0.961631i | \(0.588462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 94.3971 | − | 216.807i | 0.231427 | − | 0.531532i | ||||
\(56\) | −1981.80 | + | 1439.87i | −4.72910 | + | 3.43589i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1036.14 | + | 752.798i | −2.34572 | + | 1.70426i | ||||
\(59\) | −141.788 | − | 436.378i | −0.312868 | − | 0.962908i | −0.976623 | − | 0.214958i | \(-0.931038\pi\) |
0.663755 | − | 0.747950i | \(-0.268962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 185.460 | − | 570.786i | 0.389273 | − | 1.19806i | −0.544059 | − | 0.839047i | \(-0.683113\pi\) |
0.933333 | − | 0.359013i | \(-0.116887\pi\) | |||||||
\(62\) | 300.457 | + | 924.713i | 0.615454 | + | 1.89417i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 762.963 | − | 2348.16i | 1.49016 | − | 4.58625i | ||||
\(65\) | 14.5075 | + | 65.5916i | 0.0276836 | + | 0.125164i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −269.638 | + | 195.903i | −0.491665 | + | 0.357215i | −0.805824 | − | 0.592155i | \(-0.798277\pi\) |
0.314160 | + | 0.949370i | \(0.398277\pi\) | |||||||
\(68\) | −487.002 | −0.868494 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −746.635 | + | 1714.84i | −1.27486 | + | 2.92803i | ||||
\(71\) | 715.330 | + | 519.718i | 1.19569 | + | 0.868721i | 0.993854 | − | 0.110698i | \(-0.0353087\pi\) |
0.201838 | + | 0.979419i | \(0.435309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 100.853 | − | 310.394i | 0.161698 | − | 0.497656i | −0.837080 | − | 0.547081i | \(-0.815739\pi\) |
0.998778 | + | 0.0494250i | \(0.0157389\pi\) | |||||||
\(74\) | 1623.13 | 2.54980 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2387.05 | 3.60281 | ||||||||
\(77\) | 197.511 | − | 607.876i | 0.292317 | − | 0.899661i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −63.7800 | − | 46.3389i | −0.0908330 | − | 0.0659940i | 0.541442 | − | 0.840738i | \(-0.317879\pi\) |
−0.632275 | + | 0.774744i | \(0.717879\pi\) | |||||||
\(80\) | −646.058 | − | 2920.97i | −0.902894 | − | 4.08218i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −326.099 | −0.439165 | ||||||||
\(83\) | 1062.34 | − | 771.834i | 1.40490 | − | 1.02072i | 0.410862 | − | 0.911698i | \(-0.365228\pi\) |
0.994039 | − | 0.109023i | \(-0.0347722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −207.248 | + | 121.941i | −0.264462 | + | 0.155605i | ||||
\(86\) | 649.442 | − | 1998.78i | 0.814315 | − | 2.50620i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 529.790 | + | 1630.53i | 0.641770 | + | 1.97517i | ||||
\(89\) | −348.484 | + | 1072.52i | −0.415047 | + | 1.27738i | 0.497161 | + | 0.867658i | \(0.334376\pi\) |
−0.912209 | + | 0.409726i | \(0.865624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56.1102 | + | 172.690i | 0.0646368 | + | 0.198932i | ||||
\(92\) | −113.706 | + | 82.6120i | −0.128855 | + | 0.0936184i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 729.664 | − | 530.132i | 0.800629 | − | 0.581691i | ||||
\(95\) | 1015.83 | − | 597.700i | 1.09708 | − | 0.645502i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 40.0395 | + | 29.0904i | 0.0419113 | + | 0.0304503i | 0.608544 | − | 0.793520i | \(-0.291754\pi\) |
−0.566632 | + | 0.823971i | \(0.691754\pi\) | |||||||
\(98\) | −975.476 | + | 3002.21i | −1.00549 | + | 3.09458i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1928.30 | − | 2071.93i | −1.92830 | − | 2.07193i | ||||
\(101\) | 790.998 | 0.779279 | 0.389640 | − | 0.920967i | \(-0.372600\pi\) | ||||
0.389640 | + | 0.920967i | \(0.372600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 46.4033 | + | 33.7140i | 0.0443908 | + | 0.0322518i | 0.609759 | − | 0.792587i | \(-0.291266\pi\) |
−0.565369 | + | 0.824838i | \(0.691266\pi\) | |||||||
\(104\) | −394.031 | − | 286.280i | −0.371518 | − | 0.269924i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1186.37 | + | 861.946i | −1.08708 | + | 0.789808i | ||||
\(107\) | 470.946 | 0.425496 | 0.212748 | − | 0.977107i | \(-0.431759\pi\) | ||||
0.212748 | + | 0.977107i | \(0.431759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −71.2432 | − | 219.264i | −0.0626042 | − | 0.192676i | 0.914863 | − | 0.403765i | \(-0.132299\pi\) |
−0.977467 | + | 0.211090i | \(0.932299\pi\) | |||||||
\(110\) | 979.949 | + | 867.845i | 0.849404 | + | 0.752234i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2498.74 | − | 7690.33i | −2.10811 | − | 6.48811i | ||||
\(113\) | 54.7705 | + | 168.566i | 0.0455962 | + | 0.140331i | 0.971263 | − | 0.238009i | \(-0.0764949\pi\) |
−0.925667 | + | 0.378340i | \(0.876495\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.7032 | + | 63.6274i | −0.0224638 | + | 0.0515938i | ||||
\(116\) | −1618.88 | − | 4982.40i | −1.29577 | − | 3.98797i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2539.95 | 1.98153 | ||||||||
\(119\) | −525.827 | + | 382.036i | −0.405063 | + | 0.294295i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 714.905 | + | 519.409i | 0.537119 | + | 0.390240i | ||||
\(122\) | 2687.77 | + | 1952.78i | 1.99459 | + | 1.44915i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3977.16 | −2.88032 | ||||||||
\(125\) | −1339.40 | − | 398.899i | −0.958400 | − | 0.285429i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −250.813 | + | 771.924i | −0.175245 | + | 0.539348i | −0.999645 | − | 0.0266600i | \(-0.991513\pi\) |
0.824400 | + | 0.566008i | \(0.191513\pi\) | |||||||
\(128\) | 5667.82 | + | 4117.91i | 3.91382 | + | 2.84356i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −370.137 | − | 35.8238i | −0.249717 | − | 0.0241689i | ||||
\(131\) | −1053.96 | + | 765.747i | −0.702938 | + | 0.510714i | −0.880888 | − | 0.473325i | \(-0.843054\pi\) |
0.177950 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2577.36 | − | 1872.56i | 1.68034 | − | 1.22084i | ||||
\(134\) | −570.130 | − | 1754.68i | −0.367550 | − | 1.13120i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 538.741 | − | 1658.08i | 0.339682 | − | 1.04543i | ||||
\(137\) | −343.611 | − | 1057.53i | −0.214282 | − | 0.659493i | −0.999204 | − | 0.0398976i | \(-0.987297\pi\) |
0.784922 | − | 0.619595i | \(-0.212703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.34441 | − | 22.6038i | 0.00448162 | − | 0.0137930i | −0.948791 | − | 0.315905i | \(-0.897692\pi\) |
0.953272 | + | 0.302112i | \(0.0976918\pi\) | |||||||
\(140\) | −5727.40 | − | 5072.20i | −3.45753 | − | 3.06199i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3959.81 | + | 2876.97i | −2.34014 | + | 1.70021i | ||||
\(143\) | 127.080 | 0.0743146 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1936.49 | − | 1714.96i | −1.10908 | − | 0.982202i | ||||
\(146\) | 1461.62 | + | 1061.93i | 0.828521 | + | 0.601956i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2051.68 | + | 6314.41i | −1.13950 | + | 3.50703i | ||||
\(149\) | −2190.65 | −1.20446 | −0.602232 | − | 0.798321i | \(-0.705722\pi\) | ||||
−0.602232 | + | 0.798321i | \(0.705722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 891.600 | 0.480513 | 0.240256 | − | 0.970709i | \(-0.422769\pi\) | ||||
0.240256 | + | 0.970709i | \(0.422769\pi\) | |||||||
\(152\) | −2640.66 | + | 8127.11i | −1.40912 | + | 4.33681i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2862.42 | + | 2079.67i | 1.49780 | + | 1.08821i | ||||
\(155\) | −1692.52 | + | 995.850i | −0.877074 | + | 0.516055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2339.90 | 1.18946 | 0.594728 | − | 0.803927i | \(-0.297260\pi\) | ||||
0.594728 | + | 0.803927i | \(0.297260\pi\) | |||||||
\(158\) | 353.063 | − | 256.515i | 0.177773 | − | 0.129160i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9266.69 | + | 896.878i | 4.57873 | + | 0.443153i | ||||
\(161\) | −57.9644 | + | 178.396i | −0.0283741 | + | 0.0873266i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −687.964 | − | 2117.34i | −0.330586 | − | 1.01744i | −0.968856 | − | 0.247626i | \(-0.920350\pi\) |
0.638270 | − | 0.769813i | \(-0.279650\pi\) | |||||||
\(164\) | 412.196 | − | 1268.61i | 0.196263 | − | 0.604035i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2246.24 | + | 6913.21i | 1.05025 | + | 3.23234i | ||||
\(167\) | 501.922 | − | 364.668i | 0.232574 | − | 0.168975i | −0.465394 | − | 0.885103i | \(-0.654087\pi\) |
0.697969 | + | 0.716128i | \(0.254087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1748.20 | − | 1270.14i | 0.795723 | − | 0.578127i | ||||
\(170\) | −287.466 | − | 1299.70i | −0.129692 | − | 0.586366i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6954.85 | + | 5052.99i | 3.08315 | + | 2.24004i | ||||
\(173\) | −774.704 | + | 2384.29i | −0.340461 | + | 1.04783i | 0.623509 | + | 0.781816i | \(0.285707\pi\) |
−0.963969 | + | 0.266013i | \(0.914293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3707.39 | − | 724.427i | −1.60144 | − | 0.312923i | ||||
\(176\) | −5659.23 | −2.42375 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5050.40 | − | 3669.33i | −2.12665 | − | 1.54510i | ||||
\(179\) | 1412.93 | + | 1026.56i | 0.589987 | + | 0.428651i | 0.842311 | − | 0.538992i | \(-0.181195\pi\) |
−0.252324 | + | 0.967643i | \(0.581195\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 275.217 | − | 199.957i | 0.113020 | − | 0.0821142i | −0.529839 | − | 0.848098i | \(-0.677748\pi\) |
0.642860 | + | 0.765984i | \(0.277748\pi\) | |||||||
\(182\) | −1005.14 | −0.409374 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −155.480 | − | 478.518i | −0.0622942 | − | 0.191722i | ||||
\(185\) | 707.968 | + | 3200.88i | 0.281356 | + | 1.27207i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 140.568 | + | 432.623i | 0.0549697 | + | 0.169179i | ||||
\(188\) | 1140.04 | + | 3508.68i | 0.442266 | + | 1.36115i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1409.02 | + | 6370.50i | 0.538006 | + | 2.43245i | ||||
\(191\) | −754.426 | − | 2321.89i | −0.285803 | − | 0.879611i | −0.986157 | − | 0.165815i | \(-0.946974\pi\) |
0.700354 | − | 0.713796i | \(-0.253026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2643.56 | −0.985946 | −0.492973 | − | 0.870045i | \(-0.664090\pi\) | ||||
−0.492973 | + | 0.870045i | \(0.664090\pi\) | |||||||
\(194\) | −221.644 | + | 161.034i | −0.0820264 | + | 0.0595957i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10446.3 | − | 7589.71i | −3.80698 | − | 2.76593i | ||||
\(197\) | −2093.75 | − | 1521.20i | −0.757225 | − | 0.550156i | 0.140833 | − | 0.990033i | \(-0.455022\pi\) |
−0.898058 | + | 0.439877i | \(0.855022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 772.004 | 0.275005 | 0.137502 | − | 0.990501i | \(-0.456093\pi\) | ||||
0.137502 | + | 0.990501i | \(0.456093\pi\) | |||||||
\(200\) | 9187.40 | − | 4273.16i | 3.24824 | − | 1.51079i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1353.09 | + | 4164.37i | −0.471301 | + | 1.45052i | ||||
\(203\) | −5656.46 | − | 4109.66i | −1.95569 | − | 1.42089i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −142.236 | − | 643.080i | −0.0484594 | − | 0.219096i | ||||
\(206\) | −256.872 | + | 186.628i | −0.0868792 | + | 0.0631215i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1300.67 | − | 944.990i | 0.433582 | − | 0.315016i | ||||
\(209\) | −688.997 | − | 2120.52i | −0.228033 | − | 0.701814i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1842.83 | − | 5671.63i | 0.601257 | − | 1.85048i | 0.0805394 | − | 0.996751i | \(-0.474336\pi\) |
0.520718 | − | 0.853729i | \(-0.325664\pi\) | |||||||
\(212\) | −1853.60 | − | 5704.80i | −0.600499 | − | 1.84815i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −805.603 | + | 2479.39i | −0.257336 | + | 0.791998i | ||||
\(215\) | 4224.94 | + | 408.911i | 1.34018 | + | 0.129709i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4294.23 | + | 3119.94i | −1.34337 | + | 0.976016i | ||||
\(218\) | 1276.23 | 0.396501 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4614.82 | + | 2715.28i | −1.41423 | + | 0.832110i | ||||
\(221\) | −104.547 | − | 75.9580i | −0.0318217 | − | 0.0231198i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1435.00 | − | 4416.46i | 0.430917 | − | 1.32623i | −0.466297 | − | 0.884628i | \(-0.654412\pi\) |
0.897213 | − | 0.441597i | \(-0.145588\pi\) | |||||||
\(224\) | 25164.6 | 7.50615 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −981.143 | −0.288782 | ||||||||
\(227\) | −418.007 | + | 1286.49i | −0.122221 | + | 0.376156i | −0.993384 | − | 0.114836i | \(-0.963366\pi\) |
0.871164 | + | 0.490992i | \(0.163366\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2577.13 | + | 1872.40i | 0.743675 | + | 0.540312i | 0.893860 | − | 0.448346i | \(-0.147987\pi\) |
−0.150185 | + | 0.988658i | \(0.547987\pi\) | |||||||
\(230\) | −287.590 | − | 254.690i | −0.0824484 | − | 0.0730165i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18754.3 | 5.30723 | ||||||||
\(233\) | 1720.35 | − | 1249.91i | 0.483708 | − | 0.351434i | −0.319052 | − | 0.947737i | \(-0.603364\pi\) |
0.802759 | + | 0.596303i | \(0.203364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1363.70 | + | 1207.70i | 0.378545 | + | 0.335240i | ||||
\(236\) | −3210.55 | + | 9881.05i | −0.885546 | + | 2.72543i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1111.82 | − | 3421.84i | −0.302810 | − | 0.931953i | ||||
\(239\) | −1449.47 | + | 4461.01i | −0.392295 | + | 1.20736i | 0.538754 | + | 0.842463i | \(0.318895\pi\) |
−0.931049 | + | 0.364895i | \(0.881105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1069.17 | − | 3290.58i | −0.285774 | − | 0.879522i | −0.986166 | − | 0.165763i | \(-0.946991\pi\) |
0.700391 | − | 0.713759i | \(-0.253009\pi\) | |||||||
\(242\) | −3957.46 | + | 2875.26i | −1.05122 | + | 0.763756i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10994.2 | + | 7987.78i | −2.88456 | + | 2.09576i | ||||
\(245\) | −6345.95 | − | 614.194i | −1.65481 | − | 0.160161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 512.442 | + | 372.311i | 0.132008 | + | 0.0959091i | ||||
\(248\) | 4399.70 | − | 13540.9i | 1.12654 | − | 3.46712i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4391.28 | − | 6369.22i | 1.11092 | − | 1.61130i | ||||
\(251\) | −5528.48 | −1.39026 | −0.695128 | − | 0.718886i | \(-0.744652\pi\) | ||||
−0.695128 | + | 0.718886i | \(0.744652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 106.207 | + | 77.1642i | 0.0263921 | + | 0.0191750i | ||||
\(254\) | −3634.91 | − | 2640.92i | −0.897932 | − | 0.652386i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15395.3 | + | 11185.4i | −3.75862 | + | 2.73080i | ||||
\(257\) | −2290.19 | −0.555869 | −0.277934 | − | 0.960600i | \(-0.589650\pi\) | ||||
−0.277934 | + | 0.960600i | \(0.589650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2738.19 | + | 8427.28i | 0.656922 | + | 2.02180i | ||||
\(260\) | 607.226 | − | 1394.65i | 0.144841 | − | 0.332663i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2228.52 | − | 6858.68i | −0.525491 | − | 1.61729i | ||||
\(263\) | −651.760 | − | 2005.91i | −0.152811 | − | 0.470304i | 0.845122 | − | 0.534574i | \(-0.179528\pi\) |
−0.997933 | + | 0.0642705i | \(0.979528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2217.26 | − | 1963.61i | −0.513981 | − | 0.455182i | ||||
\(266\) | 5449.64 | + | 16772.3i | 1.25616 | + | 3.86606i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7546.82 | 1.72013 | ||||||||
\(269\) | 6952.97 | − | 5051.63i | 1.57595 | − | 1.14499i | 0.654787 | − | 0.755814i | \(-0.272758\pi\) |
0.921162 | − | 0.389180i | \(-0.127242\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3304.58 | + | 2400.92i | 0.740734 | + | 0.538175i | 0.892941 | − | 0.450174i | \(-0.148638\pi\) |
−0.152207 | + | 0.988349i | \(0.548638\pi\) | |||||||
\(272\) | 4655.77 | + | 3382.61i | 1.03786 | + | 0.754048i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6155.35 | 1.35715 | ||||||||
\(275\) | −1284.00 | + | 2311.03i | −0.281556 | + | 0.506765i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1157.41 | + | 3562.16i | −0.251055 | + | 0.772669i | 0.743526 | + | 0.668707i | \(0.233152\pi\) |
−0.994581 | + | 0.103962i | \(0.966848\pi\) | |||||||
\(278\) | 106.439 | + | 77.3324i | 0.0229632 | + | 0.0166838i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23605.0 | − | 13888.8i | 5.03810 | − | 2.96434i | ||||
\(281\) | 3085.22 | − | 2241.55i | 0.654978 | − | 0.475870i | −0.209985 | − | 0.977705i | \(-0.567342\pi\) |
0.864963 | + | 0.501835i | \(0.167342\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2689.86 | + | 1954.30i | −0.565003 | + | 0.410499i | −0.833287 | − | 0.552841i | \(-0.813544\pi\) |
0.268284 | + | 0.963340i | \(0.413544\pi\) | |||||||
\(284\) | −6186.88 | − | 19041.3i | −1.29269 | − | 3.97849i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −217.384 | + | 669.040i | −0.0449448 | + | 0.138326i | ||||
\(287\) | −550.121 | − | 1693.10i | −0.113145 | − | 0.348225i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1375.26 | + | 4232.61i | −0.279922 | + | 0.861512i | ||||
\(290\) | 12341.3 | − | 7261.42i | 2.49899 | − | 1.47036i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5978.68 | + | 4343.77i | −1.19820 | + | 0.870547i | ||||
\(293\) | 6316.24 | 1.25938 | 0.629691 | − | 0.776846i | \(-0.283182\pi\) | ||||
0.629691 | + | 0.776846i | \(0.283182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1107.86 | + | 5008.88i | 0.218651 | + | 0.988570i | ||||
\(296\) | −19228.8 | − | 13970.5i | −3.77584 | − | 2.74331i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3747.34 | − | 11533.1i | 0.728449 | − | 2.24193i | ||||
\(299\) | −37.2948 | −0.00721343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11473.2 | 2.19703 | ||||||||
\(302\) | −1525.18 | + | 4694.02i | −0.290610 | + | 0.894405i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22820.4 | − | 16580.0i | −4.30539 | − | 3.12805i | ||||
\(305\) | −2678.63 | + | 6152.15i | −0.502878 | + | 1.15499i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8592.04 | −1.59731 | −0.798655 | − | 0.601790i | \(-0.794455\pi\) | ||||
−0.798655 | + | 0.601790i | \(0.794455\pi\) | |||||||
\(308\) | −11708.6 | + | 8506.82i | −2.16611 | + | 1.57377i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2347.62 | − | 10614.1i | −0.430116 | − | 1.94465i | ||||
\(311\) | 140.125 | − | 431.260i | 0.0255490 | − | 0.0786319i | −0.937469 | − | 0.348069i | \(-0.886838\pi\) |
0.963018 | + | 0.269437i | \(0.0868376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1961.96 | − | 6038.28i | −0.354302 | − | 1.09043i | −0.956413 | − | 0.292016i | \(-0.905674\pi\) |
0.602112 | − | 0.798412i | \(-0.294326\pi\) | |||||||
\(314\) | −4002.65 | + | 12318.9i | −0.719372 | + | 2.21400i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 551.632 | + | 1697.75i | 0.0982017 | + | 0.302234i | ||||
\(317\) | 5897.27 | − | 4284.62i | 1.04487 | − | 0.759143i | 0.0736400 | − | 0.997285i | \(-0.476538\pi\) |
0.971230 | + | 0.238142i | \(0.0765384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3958.79 | + | 2876.23i | −0.694827 | + | 0.504822i | ||||
\(320\) | −11019.6 | + | 25309.4i | −1.92505 | + | 4.42136i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −840.049 | − | 610.332i | −0.145385 | − | 0.105629i | ||||
\(323\) | −700.639 | + | 2156.35i | −0.120695 | + | 0.371462i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −90.7984 | − | 745.551i | −0.0154972 | − | 0.127248i | ||||
\(326\) | 12324.0 | 2.09375 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3863.19 | + | 2806.77i | 0.650333 | + | 0.472494i | ||||
\(329\) | 3983.37 | + | 2894.09i | 0.667508 | + | 0.484973i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3531.10 | + | 2565.49i | −0.586365 | + | 0.426019i | −0.841013 | − | 0.541015i | \(-0.818040\pi\) |
0.254648 | + | 0.967034i | \(0.418040\pi\) | |||||||
\(332\) | −29733.5 | −4.91517 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1061.28 | + | 3266.28i | 0.173864 | + | 0.535098i | ||||
\(335\) | 3211.62 | − | 1889.66i | 0.523790 | − | 0.308189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 663.043 | + | 2040.64i | 0.107176 | + | 0.329853i | 0.990235 | − | 0.139408i | \(-0.0445201\pi\) |
−0.883059 | + | 0.469262i | \(0.844520\pi\) | |||||||
\(338\) | 3696.45 | + | 11376.5i | 0.594853 | + | 1.83077i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5419.52 | + | 524.529i | 0.864455 | + | 0.0836664i | ||||
\(341\) | 1147.96 | + | 3533.07i | 0.182304 | + | 0.561075i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6867.55 | −1.08109 | ||||||||
\(344\) | −24897.5 | + | 18089.1i | −3.90227 | + | 2.83517i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11227.4 | − | 8157.18i | −1.74448 | − | 1.26744i | ||||
\(347\) | 6185.75 | + | 4494.21i | 0.956970 | + | 0.695279i | 0.952445 | − | 0.304710i | \(-0.0985597\pi\) |
0.00452493 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7655.39 | 1.17416 | 0.587082 | − | 0.809527i | \(-0.300276\pi\) | ||||
0.587082 | + | 0.809527i | \(0.300276\pi\) | |||||||
\(350\) | 10155.8 | − | 18279.1i | 1.55100 | − | 2.79160i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5442.39 | − | 16750.0i | 0.824093 | − | 2.53630i | ||||
\(353\) | −5076.69 | − | 3688.43i | −0.765453 | − | 0.556134i | 0.135125 | − | 0.990829i | \(-0.456856\pi\) |
−0.900578 | + | 0.434694i | \(0.856856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7400.67 | − | 6554.05i | −1.10644 | − | 0.979867i | ||||
\(356\) | 20658.5 | − | 15009.3i | 3.07555 | − | 2.23452i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7821.50 | + | 5682.65i | −1.15469 | + | 0.838931i | ||||
\(359\) | 2156.39 | + | 6636.67i | 0.317019 | + | 0.975683i | 0.974916 | + | 0.222575i | \(0.0714462\pi\) |
−0.657897 | + | 0.753108i | \(0.728554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1314.66 | − | 4046.10i | 0.191669 | − | 0.589897i | ||||
\(362\) | 581.926 | + | 1790.98i | 0.0844899 | + | 0.260033i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1270.52 | − | 3910.27i | 0.182949 | − | 0.563060i | ||||
\(365\) | −1456.64 | + | 3345.55i | −0.208888 | + | 0.479764i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1972.27 | + | 1432.94i | −0.280522 | + | 0.203811i | −0.719145 | − | 0.694860i | \(-0.755466\pi\) |
0.438623 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(368\) | 1660.84 | 0.235264 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18062.8 | − | 1748.21i | −2.53794 | − | 0.245635i | ||||
\(371\) | −6476.59 | − | 4705.52i | −0.906328 | − | 0.658486i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 697.469 | − | 2146.59i | 0.0968193 | − | 0.297979i | −0.890904 | − | 0.454191i | \(-0.849928\pi\) |
0.987724 | + | 0.156212i | \(0.0499283\pi\) | |||||||
\(374\) | −2518.09 | −0.348148 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13207.0 | −1.81144 | ||||||||
\(377\) | 429.575 | − | 1322.10i | 0.0586850 | − | 0.180614i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7532.09 | + | 5472.38i | 1.02084 | + | 0.741682i | 0.966454 | − | 0.256838i | \(-0.0826807\pi\) |
0.0543834 | + | 0.998520i | \(0.482681\pi\) | |||||||
\(380\) | −26564.0 | − | 2571.00i | −3.58606 | − | 0.347077i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13514.6 | 1.81012 | ||||||||
\(383\) | 5295.40 | − | 3847.33i | 0.706481 | − | 0.513289i | −0.175555 | − | 0.984470i | \(-0.556172\pi\) |
0.882037 | + | 0.471181i | \(0.156172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2852.68 | + | 6551.92i | −0.377627 | + | 0.867316i | ||||
\(386\) | 4522.09 | − | 13917.6i | 0.596291 | − | 1.83520i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −346.301 | − | 1065.80i | −0.0453112 | − | 0.139454i | ||||
\(389\) | 1760.54 | − | 5418.39i | 0.229468 | − | 0.706230i | −0.768339 | − | 0.640043i | \(-0.778917\pi\) |
0.997807 | − | 0.0661869i | \(-0.0210833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.2531 | − | 126.964i | −0.00533570 | − | 0.0164216i | ||||
\(392\) | 37396.6 | − | 27170.2i | 4.81840 | − | 3.50077i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11590.2 | − | 8420.80i | 1.48200 | − | 1.07674i | ||||
\(395\) | 659.856 | + | 584.369i | 0.0840530 | + | 0.0744375i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7305.74 | + | 5307.93i | 0.923589 | + | 0.671026i | 0.944415 | − | 0.328757i | \(-0.106630\pi\) |
−0.0208261 | + | 0.999783i | \(0.506630\pi\) | |||||||
\(398\) | −1320.60 | + | 4064.38i | −0.166320 | + | 0.511881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4043.50 | + | 33201.4i | 0.505437 | + | 4.15018i | ||||
\(401\) | 1291.00 | 0.160772 | 0.0803859 | − | 0.996764i | \(-0.474385\pi\) | ||||
0.0803859 | + | 0.996764i | \(0.474385\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −853.797 | − | 620.320i | −0.105535 | − | 0.0766758i | ||||
\(404\) | −14490.2 | − | 10527.7i | −1.78444 | − | 1.29647i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31312.1 | − | 22749.6i | 3.82758 | − | 2.78090i | ||||
\(407\) | 6201.53 | 0.755279 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1299.63 | − | 3999.85i | −0.157121 | − | 0.483570i | 0.841248 | − | 0.540649i | \(-0.181821\pi\) |
−0.998370 | + | 0.0570792i | \(0.981821\pi\) | |||||||
\(410\) | 3628.94 | + | 351.227i | 0.437123 | + | 0.0423070i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −401.341 | − | 1235.20i | −0.0479919 | − | 0.147704i | ||||
\(413\) | 4284.83 | + | 13187.4i | 0.510515 | + | 1.57121i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12653.4 | + | 7445.03i | −1.49670 | + | 0.880632i | ||||
\(416\) | 1546.11 | + | 4758.45i | 0.182222 | + | 0.560822i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12342.5 | 1.44424 | ||||||||
\(419\) | −4482.54 | + | 3256.76i | −0.522641 | + | 0.379721i | −0.817598 | − | 0.575790i | \(-0.804695\pi\) |
0.294957 | + | 0.955510i | \(0.404695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5750.48 | + | 4177.97i | 0.665704 | + | 0.483662i | 0.868584 | − | 0.495541i | \(-0.165030\pi\) |
−0.202881 | + | 0.979203i | \(0.565030\pi\) | |||||||
\(422\) | 26707.1 | + | 19403.9i | 3.08077 | + | 2.23831i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21473.4 | 2.45953 | ||||||||
\(425\) | 2437.67 | − | 1133.79i | 0.278222 | − | 0.129404i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5604.60 | + | 17249.2i | −0.635188 | + | 1.95491i | ||||
\(428\) | −8627.18 | − | 6268.01i | −0.974323 | − | 0.707887i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9380.00 | + | 21543.6i | −1.05196 | + | 2.41610i | ||||
\(431\) | −4596.49 | + | 3339.54i | −0.513701 | + | 0.373225i | −0.814226 | − | 0.580549i | \(-0.802838\pi\) |
0.300525 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12267.7 | − | 8913.00i | 1.36154 | − | 0.989218i | 0.363196 | − | 0.931713i | \(-0.381685\pi\) |
0.998345 | − | 0.0575050i | \(-0.0183145\pi\) | |||||||
\(434\) | −9079.84 | − | 27944.9i | −1.00425 | − | 3.09078i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1613.18 | + | 4964.87i | −0.177196 | + | 0.545353i | ||||
\(437\) | 202.203 | + | 622.318i | 0.0221343 | + | 0.0681224i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 583.950 | − | 1797.21i | 0.0634861 | − | 0.195390i | −0.914282 | − | 0.405077i | \(-0.867245\pi\) |
0.977769 | + | 0.209687i | \(0.0672446\pi\) | |||||||
\(440\) | −4139.51 | − | 18715.7i | −0.448508 | − | 2.02780i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 578.736 | − | 420.476i | 0.0622798 | − | 0.0452489i | ||||
\(443\) | 14518.3 | 1.55707 | 0.778536 | − | 0.627600i | \(-0.215963\pi\) | ||||
0.778536 | + | 0.627600i | \(0.215963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5033.22 | − | 11560.1i | 0.536174 | − | 1.23146i | ||||
\(446\) | 20796.7 | + | 15109.7i | 2.20796 | + | 1.60418i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −23056.8 | + | 70961.5i | −2.43154 | + | 7.48351i | ||||
\(449\) | 15727.5 | 1.65307 | 0.826535 | − | 0.562885i | \(-0.190309\pi\) | ||||
0.826535 | + | 0.562885i | \(0.190309\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1245.93 | −0.130086 | ||||||||
\(452\) | 1240.19 | − | 3816.90i | 0.129056 | − | 0.397194i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6057.96 | − | 4401.37i | −0.626243 | − | 0.454992i | ||||
\(455\) | −438.417 | − | 1982.18i | −0.0451721 | − | 0.204233i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3024.30 | −0.309564 | −0.154782 | − | 0.987949i | \(-0.549468\pi\) | ||||
−0.154782 | + | 0.987949i | \(0.549468\pi\) | |||||||
\(458\) | −14266.1 | + | 10364.9i | −1.45548 | + | 1.05747i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1354.33 | − | 796.867i | 0.137274 | − | 0.0807698i | ||||
\(461\) | 1738.63 | − | 5350.95i | 0.175653 | − | 0.540604i | −0.824010 | − | 0.566576i | \(-0.808268\pi\) |
0.999663 | + | 0.0259714i | \(0.00826790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1365.98 | − | 4204.05i | −0.137111 | − | 0.421985i | 0.858801 | − | 0.512309i | \(-0.171210\pi\) |
−0.995912 | + | 0.0903241i | \(0.971210\pi\) | |||||||
\(464\) | −19130.1 | + | 58876.5i | −1.91400 | + | 5.89068i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3637.55 | + | 11195.2i | 0.361602 | + | 1.11290i | ||||
\(467\) | −4026.97 | + | 2925.76i | −0.399028 | + | 0.289911i | −0.769145 | − | 0.639075i | \(-0.779318\pi\) |
0.370117 | + | 0.928985i | \(0.379318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8148.47 | − | 5920.21i | 0.802263 | − | 0.582878i | ||||
\(470\) | −8690.94 | + | 5113.60i | −0.852942 | + | 0.501857i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −30090.0 | − | 21861.7i | −2.93433 | − | 2.13192i | ||||
\(473\) | 2481.34 | − | 7636.76i | 0.241209 | − | 0.742365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11948.3 | + | 5557.30i | −1.15416 | + | 0.536813i | ||||
\(476\) | 14717.2 | 1.41715 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21006.4 | − | 15262.1i | −2.01007 | − | 1.46040i | ||||
\(479\) | 5836.76 | + | 4240.66i | 0.556761 | + | 0.404511i | 0.830272 | − | 0.557358i | \(-0.188185\pi\) |
−0.273511 | + | 0.961869i | \(0.588185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1425.31 | + | 1035.55i | −0.135111 | + | 0.0981639i | ||||
\(482\) | 19152.9 | 1.80994 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6183.20 | − | 19029.9i | −0.580692 | − | 1.78718i | ||||
\(485\) | −414.241 | − | 366.852i | −0.0387829 | − | 0.0343462i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4846.33 | + | 14915.5i | 0.450941 | + | 1.38785i | 0.875835 | + | 0.482610i | \(0.160311\pi\) |
−0.424894 | + | 0.905243i | \(0.639689\pi\) | |||||||
\(488\) | −15033.4 | − | 46268.0i | −1.39453 | − | 4.29192i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 14089.0 | − | 32358.9i | 1.29893 | − | 2.98332i | ||||
\(491\) | −4177.42 | − | 12856.8i | −0.383960 | − | 1.18171i | −0.937232 | − | 0.348707i | \(-0.886621\pi\) |
0.553271 | − | 0.833001i | \(-0.313379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4976.02 | 0.454581 | ||||||||
\(494\) | −2836.69 | + | 2060.98i | −0.258358 | + | 0.187708i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38021.9 | + | 27624.5i | 3.44200 | + | 2.50076i | ||||
\(497\) | −21617.3 | − | 15705.9i | −1.95104 | − | 1.41752i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19053.5 | −1.70932 | −0.854660 | − | 0.519188i | \(-0.826234\pi\) | ||||
−0.854660 | + | 0.519188i | \(0.826234\pi\) | |||||||
\(500\) | 19227.2 | + | 25134.1i | 1.71974 | + | 2.24806i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9457.05 | − | 29105.8i | 0.840815 | − | 2.58776i | ||||
\(503\) | 12244.1 | + | 8895.89i | 1.08537 | + | 0.788565i | 0.978611 | − | 0.205720i | \(-0.0659537\pi\) |
0.106756 | + | 0.994285i | \(0.465954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8802.49 | − | 851.950i | −0.775655 | − | 0.0750719i | ||||
\(506\) | −587.926 | + | 427.153i | −0.0516532 | + | 0.0375282i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14868.5 | − | 10802.6i | 1.29859 | − | 0.943478i | ||||
\(509\) | −2000.14 | − | 6155.78i | −0.174174 | − | 0.536052i | 0.825421 | − | 0.564518i | \(-0.190938\pi\) |
−0.999595 | + | 0.0284660i | \(0.990938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3047.79 | + | 9380.13i | −0.263848 | + | 0.812040i | ||||
\(512\) | −15233.0 | − | 46882.2i | −1.31486 | − | 4.04672i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3917.62 | − | 12057.2i | 0.336185 | − | 1.03467i | ||||
\(515\) | −480.080 | − | 425.160i | −0.0410774 | − | 0.0363782i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2787.84 | − | 2025.49i | 0.237155 | − | 0.172303i | ||||
\(518\) | −49051.1 | −4.16059 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4076.57 | + | 3610.22i | 0.343787 | + | 0.304459i | ||||
\(521\) | 12414.6 | + | 9019.77i | 1.04395 | + | 0.758471i | 0.971052 | − | 0.238869i | \(-0.0767766\pi\) |
0.0728937 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1899.57 | + | 5846.27i | −0.158819 | + | 0.488795i | −0.998528 | − | 0.0542423i | \(-0.982726\pi\) |
0.839709 | + | 0.543037i | \(0.182726\pi\) | |||||||
\(524\) | 29499.0 | 2.45929 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11675.5 | 0.967821 | ||||||||
\(527\) | 1167.36 | − | 3592.77i | 0.0964915 | − | 0.296970i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9812.14 | + | 7128.94i | 0.806455 | + | 0.585924i | ||||
\(530\) | 14130.7 | − | 8314.24i | 1.15811 | − | 0.681411i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −72136.9 | −5.87882 | ||||||||
\(533\) | 286.354 | − | 208.048i | 0.0232709 | − | 0.0169073i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5240.84 | − | 507.236i | −0.423517 | − | 0.0409901i | ||||
\(536\) | −8348.60 | + | 25694.4i | −0.672770 | + | 2.07057i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14701.6 | + | 45246.7i | 1.17812 | + | 3.62588i | ||||
\(539\) | −3727.02 | + | 11470.6i | −0.297837 | + | 0.916648i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3280.78 | − | 10097.2i | −0.260724 | − | 0.802425i | −0.992648 | − | 0.121039i | \(-0.961377\pi\) |
0.731924 | − | 0.681386i | \(-0.238623\pi\) | |||||||
\(542\) | −18293.0 | + | 13290.6i | −1.44972 | + | 1.05329i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14489.1 | + | 10527.0i | −1.14194 | + | 0.829669i | ||||
\(545\) | 556.658 | + | 2516.78i | 0.0437516 | + | 0.197811i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16829.3 | − | 12227.2i | −1.31548 | − | 0.955754i | −0.999977 | − | 0.00683023i | \(-0.997826\pi\) |
−0.315506 | − | 0.948924i | \(-0.602174\pi\) | |||||||
\(548\) | −7780.50 | + | 23945.9i | −0.606508 | + | 1.86664i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9970.49 | − | 10713.1i | −0.772987 | − | 0.830563i | ||||
\(551\) | −24390.1 | −1.88576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1927.43 | + | 1400.36i | 0.148215 | + | 0.107684i | ||||
\(554\) | −16773.8 | − | 12186.9i | −1.28637 | − | 0.934606i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −435.384 | + | 316.325i | −0.0332094 | + | 0.0241280i | ||||
\(557\) | −8938.79 | −0.679980 | −0.339990 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339990 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 704.915 | + | 2169.51i | 0.0533358 | + | 0.164151i | ||||
\(560\) | 19523.9 | + | 88271.9i | 1.47328 | + | 6.66102i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6523.48 | + | 20077.2i | 0.489638 | + | 1.50695i | ||||
\(563\) | −3016.21 | − | 9282.93i | −0.225787 | − | 0.694900i | −0.998211 | − | 0.0597931i | \(-0.980956\pi\) |
0.772424 | − | 0.635107i | \(-0.219044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −427.949 | − | 1934.85i | −0.0318654 | − | 0.144071i | ||||
\(566\) | −5687.52 | − | 17504.4i | −0.422375 | − | 1.29994i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 71673.2 | 5.29462 | ||||||||
\(569\) | −11079.9 | + | 8050.05i | −0.816336 | + | 0.593103i | −0.915661 | − | 0.401952i | \(-0.868332\pi\) |
0.0993244 | + | 0.995055i | \(0.468332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9324.33 | + | 6774.52i | 0.683382 | + | 0.496506i | 0.874478 | − | 0.485065i | \(-0.161204\pi\) |
−0.191096 | + | 0.981571i | \(0.561204\pi\) | |||||||
\(572\) | −2327.96 | − | 1691.36i | −0.170170 | − | 0.123635i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9854.71 | 0.716599 | ||||||||
\(575\) | 376.820 | − | 678.229i | 0.0273296 | − | 0.0491897i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4919.30 | − | 15140.0i | 0.354927 | − | 1.09235i | −0.601125 | − | 0.799155i | \(-0.705280\pi\) |
0.956052 | − | 0.293198i | \(-0.0947195\pi\) | |||||||
\(578\) | −19930.9 | − | 14480.7i | −1.43429 | − | 1.04207i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12649.1 | + | 57189.5i | 0.905562 | + | 4.09425i | ||||
\(581\) | −32103.9 | + | 23324.9i | −2.29242 | + | 1.66554i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4532.78 | + | 3293.26i | −0.322004 | + | 0.233950i | ||||
\(584\) | −8175.19 | − | 25160.6i | −0.579267 | − | 1.78280i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10804.6 | + | 33253.2i | −0.761663 | + | 2.34416i | ||||
\(587\) | −5556.96 | − | 17102.6i | −0.390733 | − | 1.20255i | −0.932235 | − | 0.361853i | \(-0.882144\pi\) |
0.541502 | − | 0.840700i | \(-0.317856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5721.86 | + | 17610.1i | −0.400280 | + | 1.23194i | ||||
\(590\) | −28265.4 | − | 2735.67i | −1.97232 | − | 0.190891i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 63472.7 | − | 46115.6i | 4.40661 | − | 3.20159i | ||||
\(593\) | 230.646 | 0.0159721 | 0.00798607 | − | 0.999968i | \(-0.497458\pi\) | ||||
0.00798607 | + | 0.999968i | \(0.497458\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6263.05 | − | 3685.08i | 0.431530 | − | 0.253905i | ||||
\(596\) | 40130.2 | + | 29156.3i | 2.75805 | + | 2.00384i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 63.7968 | − | 196.346i | 0.00436262 | − | 0.0134268i | ||||
\(599\) | 11209.1 | 0.764597 | 0.382298 | − | 0.924039i | \(-0.375133\pi\) | ||||
0.382298 | + | 0.924039i | \(0.375133\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8219.09 | 0.557843 | 0.278922 | − | 0.960314i | \(-0.410023\pi\) | ||||
0.278922 | + | 0.960314i | \(0.410023\pi\) | |||||||
\(602\) | −19626.2 | + | 60403.1i | −1.32874 | + | 4.08945i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16333.1 | − | 11866.7i | −1.10030 | − | 0.799418i | ||||
\(605\) | −7396.28 | − | 6550.16i | −0.497027 | − | 0.440168i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9305.08 | 0.622210 | 0.311105 | − | 0.950376i | \(-0.399301\pi\) | ||||
0.311105 | + | 0.950376i | \(0.399301\pi\) | |||||||
\(608\) | 71018.9 | − | 51598.3i | 4.73717 | − | 3.44175i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −27807.2 | − | 24626.1i | −1.84570 | − | 1.63456i | ||||
\(611\) | −302.513 | + | 931.040i | −0.0200301 | + | 0.0616463i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2405.39 | − | 7403.03i | −0.158487 | − | 0.487774i | 0.840010 | − | 0.542571i | \(-0.182549\pi\) |
−0.998498 | + | 0.0547965i | \(0.982549\pi\) | |||||||
\(614\) | 14697.6 | − | 45234.6i | 0.966038 | − | 2.97316i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16010.3 | − | 49274.6i | −1.04720 | − | 3.22294i | ||||
\(617\) | −745.708 | + | 541.789i | −0.0486565 | + | 0.0353510i | −0.611848 | − | 0.790976i | \(-0.709573\pi\) |
0.563191 | + | 0.826327i | \(0.309573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6014.72 | − | 4369.95i | 0.390553 | − | 0.283753i | −0.375129 | − | 0.926972i | \(-0.622402\pi\) |
0.765682 | + | 0.643219i | \(0.222402\pi\) | |||||||
\(620\) | 44259.2 | + | 4283.63i | 2.86692 | + | 0.277475i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2030.76 | + | 1475.43i | 0.130910 | + | 0.0951117i | ||||
\(623\) | 10531.2 | − | 32411.7i | 0.677245 | − | 2.08435i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14475.7 | + | 5881.70i | 0.926446 | + | 0.376429i | ||||
\(626\) | 35145.9 | 2.24395 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42864.3 | − | 31142.7i | −2.72368 | − | 1.97887i | ||||
\(629\) | −5101.92 | − | 3706.76i | −0.323413 | − | 0.234973i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5821.33 | − | 4229.44i | 0.367264 | − | 0.266833i | −0.388812 | − | 0.921317i | \(-0.627114\pi\) |
0.756075 | + | 0.654485i | \(0.227114\pi\) | |||||||
\(632\) | −6390.50 | −0.402216 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12469.4 | + | 38376.7i | 0.781106 | + | 2.40400i | ||||
\(635\) | 3622.54 | − | 8320.09i | 0.226388 | − | 0.519957i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1058.80 | − | 3258.65i | −0.0658573 | − | 0.202688i | ||||
\(638\) | −8370.58 | − | 25762.0i | −0.519427 | − | 1.59863i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58638.2 | − | 51930.1i | −3.62169 | − | 3.20737i | ||||
\(641\) | −467.168 | − | 1437.79i | −0.0287863 | − | 0.0885951i | 0.935631 | − | 0.352979i | \(-0.114831\pi\) |
−0.964417 | + | 0.264384i | \(0.914831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22396.8 | −1.37363 | −0.686813 | − | 0.726834i | \(-0.740991\pi\) | ||||
−0.686813 | + | 0.726834i | \(0.740991\pi\) | |||||||
\(644\) | 3436.19 | − | 2496.54i | 0.210256 | − | 0.152760i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10154.0 | − | 7377.32i | −0.618428 | − | 0.449314i | ||||
\(647\) | 1561.70 | + | 1134.64i | 0.0948944 | + | 0.0689448i | 0.634221 | − | 0.773152i | \(-0.281321\pi\) |
−0.539326 | + | 0.842097i | \(0.681321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9704.42 | 0.586952 | ||||||||
\(650\) | 4080.43 | + | 797.319i | 0.246227 | + | 0.0481130i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15577.8 | + | 47943.5i | −0.935696 | + | 2.87978i | ||||
\(653\) | 23581.3 | + | 17132.8i | 1.41318 | + | 1.02674i | 0.992850 | + | 0.119368i | \(0.0380868\pi\) |
0.420333 | + | 0.907370i | \(0.361913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12553.6 | − | 7386.31i | 0.748868 | − | 0.440622i | ||||
\(656\) | −12752.1 | + | 9264.95i | −0.758973 | + | 0.551426i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22050.5 | + | 16020.6i | −1.30641 | + | 0.949162i | ||||
\(659\) | 5189.79 | + | 15972.5i | 0.306776 | + | 0.944161i | 0.979008 | + | 0.203820i | \(0.0653358\pi\) |
−0.672232 | + | 0.740341i | \(0.734664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7008.62 | − | 21570.3i | 0.412411 | − | 1.26927i | −0.502135 | − | 0.864789i | \(-0.667452\pi\) |
0.914546 | − | 0.404482i | \(-0.132548\pi\) | |||||||
\(662\) | −7466.26 | − | 22978.8i | −0.438345 | − | 1.34909i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32892.4 | − | 101232.i | 1.92240 | − | 5.91654i | ||||
\(665\) | −30698.6 | + | 18062.5i | −1.79013 | + | 1.05329i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1161.81 | − | 844.102i | 0.0674442 | − | 0.0490011i | ||||
\(668\) | −14048.2 | −0.813682 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4454.71 | + | 20140.7i | 0.256866 | + | 1.16135i | ||||
\(671\) | 10269.2 | + | 7461.03i | 0.590818 | + | 0.429255i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1787.87 | − | 5502.51i | 0.102403 | − | 0.315165i | −0.886709 | − | 0.462328i | \(-0.847014\pi\) |
0.989112 | + | 0.147163i | \(0.0470142\pi\) | |||||||
\(674\) | −11877.6 | −0.678793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48929.9 | −2.78391 | ||||||||
\(677\) | 2989.08 | − | 9199.45i | 0.169690 | − | 0.522251i | −0.829662 | − | 0.558267i | \(-0.811467\pi\) |
0.999351 | + | 0.0360158i | \(0.0114667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1209.99 | − | 879.113i | −0.0683878 | − | 0.0496867i | ||||
\(680\) | −7781.14 | + | 17871.4i | −0.438813 | + | 1.00785i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20564.3 | −1.15462 | ||||||||
\(683\) | −23680.4 | + | 17204.8i | −1.32666 | + | 0.963872i | −0.326832 | + | 0.945082i | \(0.605981\pi\) |
−0.999823 | + | 0.0187892i | \(0.994019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2684.80 | + | 12138.6i | 0.149753 | + | 0.677068i | ||||
\(686\) | 11747.7 | − | 36155.6i | 0.653831 | − | 2.01229i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −31391.8 | − | 96613.9i | −1.73954 | − | 5.35374i | ||||
\(689\) | 491.859 | − | 1513.79i | 0.0271964 | − | 0.0837020i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6623.67 | − | 20385.6i | −0.364654 | − | 1.12229i | −0.950197 | − | 0.311650i | \(-0.899119\pi\) |
0.585543 | − | 0.810642i | \(-0.300881\pi\) | |||||||
\(692\) | 45925.3 | − | 33366.7i | 2.52286 | − | 1.83296i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34242.1 | + | 24878.4i | −1.87293 | + | 1.36076i | ||||
\(695\) | −106.077 | + | 243.632i | −0.00578952 | + | 0.0132971i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1025.01 | + | 744.714i | 0.0557031 | + | 0.0404707i | ||||
\(698\) | −13095.4 | + | 40303.4i | −0.710124 | + | 2.18554i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 58273.4 | + | 62613.9i | 3.14647 | + | 3.38083i | ||||
\(701\) | −16727.9 | −0.901292 | −0.450646 | − | 0.892703i | \(-0.648806\pi\) | ||||
−0.450646 | + | 0.892703i | \(0.648806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25007.2 | + | 18168.8i | 1.34163 | + | 0.974751i | ||||
\(704\) | 42246.6 | + | 30694.0i | 2.26169 | + | 1.64321i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28102.7 | − | 20417.8i | 1.49810 | − | 1.08844i | ||||
\(707\) | −23904.0 | −1.27157 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5241.61 | − | 16132.0i | −0.277648 | − | 0.854514i | −0.988506 | − | 0.151178i | \(-0.951693\pi\) |
0.710858 | − | 0.703335i | \(-0.248307\pi\) | |||||||
\(710\) | 47164.8 | − | 27751.0i | 2.49305 | − | 1.46687i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28248.2 | + | 86939.0i | 1.48686 | + | 4.57609i | ||||
\(713\) | −336.898 | − | 1036.87i | −0.0176956 | − | 0.0544614i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1414.19 | − | 136.873i | −0.0739689 | − | 0.00715909i | ||||
\(716\) | −12220.4 | − | 37610.7i | −0.637848 | − | 1.96310i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38628.9 | −2.00782 | ||||||||
\(719\) | 6363.32 | − | 4623.22i | 0.330058 | − | 0.239801i | −0.410397 | − | 0.911907i | \(-0.634610\pi\) |
0.740455 | + | 0.672106i | \(0.234610\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1402.31 | − | 1018.84i | −0.0724338 | − | 0.0526262i | ||||
\(722\) | 19052.7 | + | 13842.6i | 0.982088 | + | 0.713529i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7702.96 | −0.395412 | ||||||||
\(725\) | 19702.8 | + | 21170.3i | 1.00930 | + | 1.08448i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2605.34 | − | 8018.41i | 0.132912 | − | 0.409060i | −0.862348 | − | 0.506316i | \(-0.831007\pi\) |
0.995259 | + | 0.0972567i | \(0.0310068\pi\) | |||||||
\(728\) | 11907.6 | + | 8651.40i | 0.606217 | + | 0.440443i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15121.6 | − | 13391.7i | −0.766679 | − | 0.678972i | ||||
\(731\) | −6605.98 | + | 4799.53i | −0.334242 | + | 0.242841i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17055.7 | + | 12391.7i | −0.859435 | + | 0.624416i | −0.927731 | − | 0.373249i | \(-0.878244\pi\) |
0.0682959 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(734\) | −4170.22 | − | 12834.6i | −0.209708 | − | 0.645414i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1597.21 | + | 4915.69i | −0.0799915 | + | 0.246189i | ||||
\(737\) | −2178.31 | − | 6704.14i | −0.108872 | − | 0.335075i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1688.56 | + | 5196.84i | −0.0840522 | + | 0.258686i | −0.984246 | − | 0.176803i | \(-0.943424\pi\) |
0.900194 | + | 0.435489i | \(0.143424\pi\) | |||||||
\(740\) | 29632.7 | − | 68059.1i | 1.47205 | − | 3.38095i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35852.1 | − | 26048.1i | 1.77382 | − | 1.28875i | ||||
\(743\) | −12400.7 | −0.612300 | −0.306150 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306150 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24378.3 | + | 2359.46i | 1.19886 | + | 0.116032i | ||||
\(746\) | 10108.1 | + | 7343.95i | 0.496090 | + | 0.360430i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3182.92 | − | 9796.03i | 0.155587 | − | 0.478848i | ||||
\(749\) | −14232.0 | −0.694293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29073.8 | −1.41267 | −0.706336 | − | 0.707876i | \(-0.749653\pi\) | ||||
−0.706336 | + | 0.707876i | \(0.749653\pi\) | |||||||
\(752\) | 13471.7 | − | 41461.7i | 0.653276 | − | 2.01058i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6225.62 | + | 4523.18i | 0.300694 | + | 0.218467i | ||||
\(755\) | −9922.03 | − | 960.305i | −0.478278 | − | 0.0462902i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17652.4 | −0.847539 | −0.423770 | − | 0.905770i | \(-0.639293\pi\) | ||||
−0.423770 | + | 0.905770i | \(0.639293\pi\) | |||||||
\(758\) | −41695.0 | + | 30293.2i | −1.99793 | + | 1.45158i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 38139.5 | − | 87597.1i | 1.82035 | − | 4.18090i | ||||
\(761\) | 9492.07 | − | 29213.6i | 0.452151 | − | 1.39158i | −0.422296 | − | 0.906458i | \(-0.638776\pi\) |
0.874447 | − | 0.485121i | \(-0.161224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2152.97 | + | 6626.17i | 0.102153 | + | 0.314395i | ||||
\(764\) | −17082.7 | + | 52575.2i | −0.808942 | + | 2.48967i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11196.7 | + | 34460.0i | 0.528139 | + | 1.62545i | ||||
\(767\) | −2230.38 | + | 1620.47i | −0.104999 | + | 0.0762863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1813.75 | + | 1317.77i | −0.0850527 | + | 0.0617944i | −0.629499 | − | 0.777001i | \(-0.716740\pi\) |
0.544446 | + | 0.838796i | \(0.316740\pi\) | |||||||
\(770\) | −29614.1 | − | 26226.3i | −1.38600 | − | 1.22744i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 48426.9 | + | 35184.2i | 2.25767 | + | 1.64030i | ||||
\(773\) | 10264.5 | − | 31590.8i | 0.477604 | − | 1.46991i | −0.364810 | − | 0.931082i | \(-0.618866\pi\) |
0.842414 | − | 0.538831i | \(-0.181134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19907.5 | − | 9259.21i | 0.922708 | − | 0.429162i | ||||
\(776\) | 4011.79 | 0.185586 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25514.6 | + | 18537.5i | 1.17576 | + | 0.854243i | ||||
\(779\) | −5024.13 | − | 3650.24i | −0.231076 | − | 0.167886i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15129.3 | + | 10992.1i | −0.693176 | + | 0.503622i | ||||
\(782\) | 738.996 | 0.0337934 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 47151.2 | + | 145116.i | 2.14792 | + | 6.61062i | ||||
\(785\) | −26039.2 | − | 2520.21i | −1.18392 | − | 0.114586i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −715.273 | − | 2201.38i | −0.0323973 | − | 0.0997088i | 0.933550 | − | 0.358447i | \(-0.116693\pi\) |
−0.965948 | + | 0.258738i | \(0.916693\pi\) | |||||||
\(788\) | 18108.8 | + | 55733.1i | 0.818653 | + | 2.51956i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4205.29 | + | 2474.32i | −0.189389 | + | 0.111433i | ||||
\(791\) | −1655.17 | − | 5094.08i | −0.0744007 | − | 0.228982i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3606.05 | −0.161481 | ||||||||
\(794\) | −40442.0 | + | 29382.8i | −1.80760 | + | 1.31330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14142.2 | − | 10274.9i | −0.629721 | − | 0.457519i | ||||
\(797\) | 23009.0 | + | 16717.0i | 1.02261 | + | 0.742970i | 0.966817 | − | 0.255472i | \(-0.0822308\pi\) |
0.0557946 | + | 0.998442i | \(0.482231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3504.19 | −0.155156 | ||||||||
\(800\) | −102157. | − | 19961.5i | −4.51474 | − | 0.882183i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2208.40 | + | 6796.74i | −0.0972334 | + | 0.299254i | ||||
\(803\) | 5584.42 | + | 4057.32i | 0.245417 | + | 0.178306i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 837.191 | − | 1922.82i | 0.0366548 | − | 0.0841870i | ||||
\(806\) | 4726.32 | − | 3433.87i | 0.206548 | − | 0.150066i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 51872.9 | − | 37687.9i | 2.25852 | − | 1.64091i | ||||
\(809\) | 9126.05 | + | 28087.1i | 0.396607 | + | 1.22063i | 0.927703 | + | 0.373319i | \(0.121780\pi\) |
−0.531096 | + | 0.847311i | \(0.678220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4761.77 | + | 14655.2i | −0.206175 | + | 0.634543i | 0.793488 | + | 0.608586i | \(0.208263\pi\) |
−0.999663 | + | 0.0259564i | \(0.991737\pi\) | |||||||
\(812\) | 48922.6 | + | 150568.i | 2.11435 | + | 6.50728i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10608.4 | + | 32649.3i | −0.456786 | + | 1.40584i | ||||
\(815\) | 5375.41 | + | 24303.4i | 0.231033 | + | 1.04455i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32379.4 | − | 23525.0i | 1.38655 | − | 1.00739i | ||||
\(818\) | 23281.2 | 0.995121 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5953.42 | + | 13673.5i | −0.253540 | + | 0.582318i | ||||
\(821\) | −12992.6 | − | 9439.64i | −0.552306 | − | 0.401274i | 0.276329 | − | 0.961063i | \(-0.410882\pi\) |
−0.828635 | + | 0.559789i | \(0.810882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4778.17 | − | 14705.7i | 0.202377 | − | 0.622854i | −0.797433 | − | 0.603407i | \(-0.793810\pi\) |
0.999811 | − | 0.0194468i | \(-0.00619048\pi\) | |||||||
\(824\) | 4649.42 | 0.196566 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −76757.3 | −3.23333 | ||||||||
\(827\) | 7301.12 | − | 22470.5i | 0.306995 | − | 0.944833i | −0.671930 | − | 0.740614i | \(-0.734535\pi\) |
0.978925 | − | 0.204219i | \(-0.0654654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33429.1 | − | 24287.7i | −1.40053 | − | 1.01755i | −0.994615 | − | 0.103637i | \(-0.966952\pi\) |
−0.405917 | − | 0.913910i | \(-0.633048\pi\) | |||||||
\(830\) | −17551.0 | − | 79351.9i | −0.733980 | − | 3.31849i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14834.9 | −0.618160 | ||||||||
\(833\) | 9922.34 | − | 7209.00i | 0.412711 | − | 0.299852i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5978.33 | + | 3517.55i | −0.247771 | + | 0.145784i | ||||
\(836\) | −15601.2 | + | 48015.6i | −0.645429 | + | 1.98643i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9478.00 | − | 29170.3i | −0.390707 | − | 1.20247i | ||||
\(839\) | 7593.13 | − | 23369.2i | 0.312448 | − | 0.961616i | −0.664344 | − | 0.747427i | \(-0.731289\pi\) |
0.976792 | − | 0.214189i | \(-0.0687110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9004.56 | + | 27713.2i | 0.369206 | + | 1.13630i | ||||
\(842\) | −31832.6 | + | 23127.7i | −1.30288 | + | 0.946597i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −109245. | + | 79370.8i | −4.45539 | + | 3.23703i | ||||
\(845\) | −20822.6 | + | 12251.7i | −0.847716 | + | 0.498782i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21604.5 | − | 15696.6i | −0.876433 | − | 0.636766i | ||||
\(848\) | −21903.8 | + | 67413.0i | −0.887004 | + | 2.72992i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1799.17 | + | 14773.1i | 0.0726011 | + | 0.596132i | ||||
\(851\) | −1819.99 | −0.0733121 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10526.6 | + | 7648.06i | 0.422539 | + | 0.306992i | 0.778658 | − | 0.627448i | \(-0.215901\pi\) |
−0.356120 | + | 0.934440i | \(0.615901\pi\) | |||||||
\(854\) | −81224.6 | − | 59013.1i | −3.25462 | − | 2.36462i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30884.2 | − | 22438.7i | 1.23318 | − | 0.895956i | ||||
\(857\) | 46342.7 | 1.84718 | 0.923592 | − | 0.383377i | \(-0.125239\pi\) | ||||
0.923592 | + | 0.383377i | \(0.125239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7665.49 | − | 23591.9i | −0.304474 | − | 0.937074i | −0.979873 | − | 0.199622i | \(-0.936029\pi\) |
0.675399 | − | 0.737452i | \(-0.263971\pi\) | |||||||
\(860\) | −71953.6 | − | 63722.2i | −2.85302 | − | 2.52664i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9718.93 | − | 29911.8i | −0.384023 | − | 1.18190i | ||||
\(863\) | 9182.33 | + | 28260.3i | 0.362190 | + | 1.11471i | 0.951722 | + | 0.306961i | \(0.0993122\pi\) |
−0.589532 | + | 0.807745i | \(0.700688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11189.2 | − | 25698.8i | 0.439820 | − | 1.01016i | ||||
\(866\) | 25939.1 | + | 79832.4i | 1.01784 | + | 3.13258i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 120190. | 4.69990 | ||||||||
\(869\) | 1348.96 | − | 980.074i | 0.0526584 | − | 0.0382586i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1620.11 | + | 1177.08i | 0.0630258 | + | 0.0457909i | ||||
\(872\) | −15119.1 | − | 10984.7i | −0.587154 | − | 0.426592i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3622.21 | −0.140187 | ||||||||
\(875\) | 40476.9 | + | 12054.7i | 1.56385 | + | 0.465743i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6997.55 | − | 21536.2i | 0.269430 | − | 0.829221i | −0.721209 | − | 0.692717i | \(-0.756413\pi\) |
0.990640 | − | 0.136504i | \(-0.0435866\pi\) | |||||||
\(878\) | 8462.90 | + | 6148.65i | 0.325295 | + | 0.236341i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 62977.8 | + | 6095.31i | 2.41248 | + | 0.233492i | ||||
\(881\) | 3906.80 | − | 2838.45i | 0.149402 | − | 0.108547i | −0.510573 | − | 0.859834i | \(-0.670567\pi\) |
0.659975 | + | 0.751287i | \(0.270567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26636.5 | − | 19352.6i | 1.01516 | − | 0.737560i | 0.0498783 | − | 0.998755i | \(-0.484117\pi\) |
0.965286 | + | 0.261195i | \(0.0841167\pi\) | |||||||
\(884\) | 904.227 | + | 2782.92i | 0.0344032 | + | 0.105882i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24835.0 | + | 76434.4i | −0.941703 | + | 2.89826i | ||||
\(887\) | 101.793 | + | 313.285i | 0.00385328 | + | 0.0118592i | 0.952965 | − | 0.303081i | \(-0.0980154\pi\) |
−0.949111 | + | 0.314941i | \(0.898015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7579.59 | − | 23327.6i | 0.285952 | − | 0.880070i | ||||
\(890\) | 52250.5 | + | 46273.1i | 1.96791 | + | 1.74279i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −85068.0 | + | 61805.5i | −3.19315 | + | 2.31996i | ||||
\(893\) | 17175.9 | 0.643639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14618.0 | − | 12945.7i | −0.545949 | − | 0.483493i | ||||
\(896\) | −171282. | − | 124444.i | −6.38630 | − | 4.63992i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26903.6 | + | 82800.9i | −0.999762 | + | 3.07695i | ||||
\(899\) | 40637.3 | 1.50760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5697.49 | 0.210667 | ||||||||
\(902\) | 2131.30 | − | 6559.47i | 0.0786746 | − | 0.242136i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11623.3 | + | 8444.83i | 0.427639 | + | 0.310698i | ||||
\(905\) | −3278.07 | + | 1928.76i | −0.120405 | + | 0.0708444i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41937.4 | 1.53529 | 0.767646 | − | 0.640874i | \(-0.221428\pi\) | ||||
0.767646 | + | 0.640874i | \(0.221428\pi\) | |||||||
\(908\) | 24779.9 | − | 18003.6i | 0.905671 | − | 0.658008i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11185.6 | + | 1082.60i | 0.407470 | + | 0.0394371i | ||||
\(911\) | 14872.0 | − | 45771.2i | 0.540867 | − | 1.66462i | −0.189751 | − | 0.981832i | \(-0.560768\pi\) |
0.730618 | − | 0.682786i | \(-0.239232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8582.25 | + | 26413.4i | 0.311096 | + | 0.957456i | ||||
\(914\) | 5173.39 | − | 15922.1i | 0.187222 | − | 0.576209i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22289.6 | − | 68600.2i | −0.804004 | − | 2.47447i | ||||
\(917\) | 31850.7 | − | 23140.9i | 1.14700 | − | 0.833348i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11669.3 | − | 8478.28i | 0.418864 | − | 0.304323i | −0.358316 | − | 0.933600i | \(-0.616649\pi\) |
0.777181 | + | 0.629277i | \(0.216649\pi\) | |||||||
\(920\) | 1214.84 | + | 5492.57i | 0.0435349 | + | 0.196831i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25197.1 | + | 18306.7i | 0.900023 | + | 0.653905i | ||||
\(923\) | 1641.71 | − | 5052.66i | 0.0585455 | − | 0.180185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4430.98 | − | 36383.0i | −0.157502 | − | 1.29326i | ||||
\(926\) | 24469.8 | 0.868388 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −155863. | − | 113241.i | −5.51343 | − | 4.00574i | ||||
\(929\) | 25185.6 | + | 18298.4i | 0.889466 | + | 0.646235i | 0.935739 | − | 0.352694i | \(-0.114734\pi\) |
−0.0462726 | + | 0.998929i | \(0.514734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48634.7 | + | 35335.2i | −1.71207 | + | 1.24389i | ||||
\(932\) | −48150.4 | −1.69229 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8514.73 | − | 26205.7i | −0.298298 | − | 0.918068i | ||||
\(935\) | −1098.33 | − | 4965.78i | −0.0384161 | − | 0.173688i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1847.93 | − | 5687.35i | −0.0644282 | − | 0.198290i | 0.913660 | − | 0.406478i | \(-0.133243\pi\) |
−0.978089 | + | 0.208188i | \(0.933243\pi\) | |||||||
\(938\) | 17229.4 | + | 53026.5i | 0.599742 | + | 1.84582i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8907.70 | − | 40273.7i | −0.309082 | − | 1.39743i | ||||
\(941\) | −799.362 | − | 2460.18i | −0.0276923 | − | 0.0852281i | 0.936255 | − | 0.351321i | \(-0.114267\pi\) |
−0.963947 | + | 0.266093i | \(0.914267\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 365.649 | 0.0126269 | ||||||||
\(944\) | 99324.8 | − | 72163.7i | 3.42452 | − | 2.48806i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35960.7 | + | 26127.0i | 1.23592 | + | 0.897952i | ||||
\(947\) | −26622.7 | − | 19342.5i | −0.913539 | − | 0.663725i | 0.0283684 | − | 0.999598i | \(-0.490969\pi\) |
−0.941907 | + | 0.335873i | \(0.890969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1960.98 | −0.0670769 | ||||||||
\(950\) | −8818.68 | − | 72410.7i | −0.301174 | − | 2.47296i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16280.8 | + | 50107.1i | −0.554268 | + | 1.70586i | ||||
\(953\) | −41562.9 | − | 30197.2i | −1.41276 | − | 1.02643i | −0.992915 | − | 0.118829i | \(-0.962086\pi\) |
−0.419841 | − | 0.907598i | \(-0.637914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5894.71 | + | 26651.3i | 0.199736 | + | 0.903053i | ||||
\(956\) | 85926.0 | − | 62428.9i | 2.90695 | − | 2.11202i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32310.2 | + | 23474.8i | −1.08966 | + | 0.791686i | ||||
\(959\) | 10383.9 | + | 31958.5i | 0.349650 | + | 1.07611i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 327.466 | − | 1007.84i | 0.0109921 | − | 0.0338302i | ||||
\(962\) | −3013.71 | − | 9275.23i | −0.101004 | − | 0.310858i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24209.7 | + | 74509.7i | −0.808860 | + | 2.48941i | ||||
\(965\) | 29418.4 | + | 2847.27i | 0.981360 | + | 0.0949811i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15375.5 | − | 11170.9i | 0.511315 | − | 0.371492i | −0.302007 | − | 0.953306i | \(-0.597657\pi\) |
0.813322 | + | 0.581814i | \(0.197657\pi\) | |||||||
\(968\) | 71630.6 | 2.37840 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2639.97 | − | 1553.32i | 0.0873861 | − | 0.0514165i | ||||
\(971\) | 27125.9 | + | 19708.1i | 0.896510 | + | 0.651353i | 0.937567 | − | 0.347804i | \(-0.113073\pi\) |
−0.0410573 | + | 0.999157i | \(0.513073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −221.949 | + | 683.087i | −0.00731279 | + | 0.0225064i | ||||
\(974\) | −86815.8 | −2.85601 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 160587. | 5.26667 | ||||||||
\(977\) | −3924.47 | + | 12078.3i | −0.128511 | + | 0.395515i | −0.994524 | − | 0.104505i | \(-0.966674\pi\) |
0.866014 | + | 0.500020i | \(0.166674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19296.2 | − | 14019.5i | −0.629937 | − | 0.457676i | ||||
\(980\) | 108076. | + | 95712.2i | 3.52281 | + | 3.11981i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 74833.2 | 2.43179 | ||||||||
\(983\) | −33720.8 | + | 24499.6i | −1.09413 | + | 0.794930i | −0.980091 | − | 0.198547i | \(-0.936378\pi\) |
−0.114036 | + | 0.993477i | \(0.536378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21661.5 | + | 19183.5i | 0.700704 | + | 0.620544i | ||||
\(986\) | −8512.02 | + | 26197.3i | −0.274927 | + | 0.846138i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4432.10 | − | 13640.6i | −0.142716 | − | 0.439236i | ||||
\(989\) | −728.209 | + | 2241.20i | −0.0234133 | + | 0.0720586i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2227.57 | − | 6855.76i | −0.0714037 | − | 0.219758i | 0.908986 | − | 0.416827i | \(-0.136858\pi\) |
−0.980390 | + | 0.197069i | \(0.936858\pi\) | |||||||
\(992\) | −118327. | + | 85969.7i | −3.78719 | + | 2.75155i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 119666. | − | 86942.3i | 3.81848 | − | 2.77429i | ||||
\(995\) | −8591.12 | − | 831.493i | −0.273726 | − | 0.0264926i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34106.5 | + | 24779.8i | 1.08341 | + | 0.787147i | 0.978275 | − | 0.207311i | \(-0.0664710\pi\) |
0.105140 | + | 0.994457i | \(0.466471\pi\) | |||||||
\(998\) | 32593.0 | − | 100311.i | 1.03378 | − | 3.18165i | ||||
\(999\) | 0 | 0 |
(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.h.d.46.1 | ✓ | 64 | |
3.2 | odd | 2 | inner | 225.4.h.d.46.16 | yes | 64 | |
25.6 | even | 5 | inner | 225.4.h.d.181.1 | yes | 64 | |
75.56 | odd | 10 | inner | 225.4.h.d.181.16 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.h.d.46.1 | ✓ | 64 | 1.1 | even | 1 | trivial | |
225.4.h.d.46.16 | yes | 64 | 3.2 | odd | 2 | inner | |
225.4.h.d.181.1 | yes | 64 | 25.6 | even | 5 | inner | |
225.4.h.d.181.16 | yes | 64 | 75.56 | odd | 10 | inner |