Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(143,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.143");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 143.4 | ||
Character | \(\chi\) | \(=\) | 189.143 |
Dual form | 189.4.i.a.152.19 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.10714i | − | 1.45209i | −0.687645 | − | 0.726047i | \(-0.741356\pi\) | ||
0.687645 | − | 0.726047i | \(-0.258644\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.86861 | −1.10858 | ||||||||
\(5\) | 3.80591 | − | 6.59204i | 0.340411 | − | 0.589610i | −0.644098 | − | 0.764943i | \(-0.722767\pi\) |
0.984509 | + | 0.175333i | \(0.0561004\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.1152 | − | 13.0764i | 0.708153 | − | 0.706059i | ||||
\(8\) | 3.56749i | 0.157662i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −27.0744 | − | 15.6314i | −0.856168 | − | 0.494309i | ||||
\(11\) | −6.20961 | + | 3.58512i | −0.170206 | + | 0.0982686i | −0.582683 | − | 0.812699i | \(-0.697997\pi\) |
0.412477 | + | 0.910968i | \(0.364664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.6417 | − | 34.4342i | 1.27243 | − | 0.734640i | 0.296988 | − | 0.954881i | \(-0.404018\pi\) |
0.975445 | + | 0.220241i | \(0.0706844\pi\) | |||||||
\(14\) | −53.7066 | − | 53.8659i | −1.02526 | − | 1.02830i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −56.2967 | −0.879635 | ||||||||
\(17\) | 11.4334 | − | 19.8032i | 0.163118 | − | 0.282529i | −0.772867 | − | 0.634568i | \(-0.781178\pi\) |
0.935985 | + | 0.352039i | \(0.114512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −86.1218 | + | 49.7224i | −1.03988 | + | 0.600374i | −0.919799 | − | 0.392390i | \(-0.871648\pi\) |
−0.120079 | + | 0.992764i | \(0.538315\pi\) | |||||||
\(20\) | −33.7532 | + | 58.4622i | −0.377372 | + | 0.653627i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.7246 | + | 25.5037i | 0.142695 | + | 0.247155i | ||||
\(23\) | −106.045 | − | 61.2248i | −0.961383 | − | 0.555055i | −0.0647848 | − | 0.997899i | \(-0.520636\pi\) |
−0.896598 | + | 0.442844i | \(0.853969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.5300 | + | 58.0757i | 0.268240 | + | 0.464606i | ||||
\(26\) | −141.426 | − | 244.957i | −1.06677 | − | 1.84769i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −116.313 | + | 115.969i | −0.785042 | + | 0.782720i | ||||
\(29\) | −143.427 | − | 82.8076i | −0.918404 | − | 0.530241i | −0.0352788 | − | 0.999378i | \(-0.511232\pi\) |
−0.883126 | + | 0.469136i | \(0.844565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 13.7877i | − | 0.0798820i | −0.999202 | − | 0.0399410i | \(-0.987283\pi\) | ||
0.999202 | − | 0.0399410i | \(-0.0127170\pi\) | |||||||
\(32\) | 259.758i | 1.43498i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −81.3346 | − | 46.9585i | −0.410258 | − | 0.236862i | ||||
\(35\) | −36.2848 | − | 136.223i | −0.175236 | − | 0.657884i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 126.544 | + | 219.181i | 0.562263 | + | 0.973868i | 0.997299 | + | 0.0734549i | \(0.0234025\pi\) |
−0.435035 | + | 0.900413i | \(0.643264\pi\) | |||||||
\(38\) | 204.217 | + | 353.714i | 0.871799 | + | 1.51000i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 23.5171 | + | 13.5776i | 0.0929593 | + | 0.0536701i | ||||
\(41\) | 159.598 | + | 276.433i | 0.607929 | + | 1.05296i | 0.991581 | + | 0.129486i | \(0.0413328\pi\) |
−0.383652 | + | 0.923478i | \(0.625334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 156.693 | − | 271.399i | 0.555707 | − | 0.962512i | −0.442141 | − | 0.896945i | \(-0.645781\pi\) |
0.997848 | − | 0.0655670i | \(-0.0208856\pi\) | |||||||
\(44\) | 55.0706 | − | 31.7950i | 0.188686 | − | 0.108938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −251.459 | + | 435.540i | −0.805992 | + | 1.39602i | ||||
\(47\) | 70.7867 | 0.219687 | 0.109844 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109844 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.01583 | − | 342.998i | 0.00296162 | − | 0.999996i | ||||
\(50\) | 238.525 | − | 137.713i | 0.674651 | − | 0.389510i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −528.939 | + | 305.383i | −1.41059 | + | 0.814404i | ||||
\(53\) | 254.574 | + | 146.979i | 0.659783 | + | 0.380926i | 0.792194 | − | 0.610269i | \(-0.208939\pi\) |
−0.132412 | + | 0.991195i | \(0.542272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 54.5786i | 0.133807i | ||||||||
\(56\) | 46.6500 | + | 46.7883i | 0.111319 | + | 0.111649i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −340.103 | + | 589.075i | −0.769960 | + | 1.33361i | ||||
\(59\) | −461.230 | −1.01775 | −0.508873 | − | 0.860842i | \(-0.669938\pi\) | ||||
−0.508873 | + | 0.860842i | \(0.669938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 662.411i | − | 1.39038i | −0.718827 | − | 0.695189i | \(-0.755321\pi\) | ||
0.718827 | − | 0.695189i | \(-0.244679\pi\) | |||||||
\(62\) | −56.6280 | −0.115996 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 616.491 | 1.20408 | ||||||||
\(65\) | − | 524.214i | − | 1.00032i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 718.278 | 1.30973 | 0.654863 | − | 0.755748i | \(-0.272726\pi\) | ||||
0.654863 | + | 0.755748i | \(0.272726\pi\) | |||||||
\(68\) | −101.398 | + | 175.627i | −0.180829 | + | 0.313204i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −559.489 | + | 149.027i | −0.955310 | + | 0.254459i | ||||
\(71\) | − | 92.9435i | − | 0.155357i | −0.996978 | − | 0.0776787i | \(-0.975249\pi\) | ||
0.996978 | − | 0.0776787i | \(-0.0247508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −882.012 | − | 509.230i | −1.41413 | − | 0.816450i | −0.418358 | − | 0.908282i | \(-0.637394\pi\) |
−0.995774 | + | 0.0918323i | \(0.970728\pi\) | |||||||
\(74\) | 900.207 | − | 519.735i | 1.41415 | − | 0.816459i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 763.780 | − | 440.969i | 1.15278 | − | 0.665560i | ||||
\(77\) | −34.5597 | + | 128.219i | −0.0511486 | + | 0.189765i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 796.225 | 1.13395 | 0.566977 | − | 0.823734i | \(-0.308113\pi\) | ||||
0.566977 | + | 0.823734i | \(0.308113\pi\) | |||||||
\(80\) | −214.260 | + | 371.110i | −0.299438 | + | 0.518641i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1135.35 | − | 655.493i | 1.52900 | − | 0.882770i | ||||
\(83\) | 10.7079 | − | 18.5466i | 0.0141608 | − | 0.0245272i | −0.858858 | − | 0.512213i | \(-0.828826\pi\) |
0.873019 | + | 0.487686i | \(0.162159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −87.0290 | − | 150.739i | −0.111054 | − | 0.192352i | ||||
\(86\) | −1114.68 | − | 643.558i | −1.39766 | − | 0.806938i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.7899 | − | 22.1527i | −0.0154933 | − | 0.0268351i | ||||
\(89\) | −339.721 | − | 588.414i | −0.404611 | − | 0.700806i | 0.589665 | − | 0.807648i | \(-0.299260\pi\) |
−0.994276 | + | 0.106841i | \(0.965926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 331.937 | − | 1231.51i | 0.382379 | − | 1.41865i | ||||
\(92\) | 940.467 | + | 542.979i | 1.06577 | + | 0.615320i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 290.731i | − | 0.319007i | ||||||
\(95\) | 756.957i | 0.817496i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 984.068 | + | 568.152i | 1.03007 | + | 0.594713i | 0.917005 | − | 0.398875i | \(-0.130599\pi\) |
0.113067 | + | 0.993587i | \(0.463933\pi\) | |||||||
\(98\) | −1408.74 | − | 4.17218i | −1.45209 | − | 0.00430054i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −297.365 | − | 515.051i | −0.297365 | − | 0.515051i | ||||
\(101\) | 771.052 | + | 1335.50i | 0.759629 | + | 1.31572i | 0.943040 | + | 0.332679i | \(0.107953\pi\) |
−0.183411 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 362.228 | + | 209.132i | 0.346518 | + | 0.200062i | 0.663151 | − | 0.748486i | \(-0.269219\pi\) |
−0.316632 | + | 0.948548i | \(0.602552\pi\) | |||||||
\(104\) | 122.844 | + | 212.772i | 0.115825 | + | 0.200615i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 603.662 | − | 1045.57i | 0.553140 | − | 0.958066i | ||||
\(107\) | 1368.79 | − | 790.270i | 1.23669 | − | 0.714003i | 0.268273 | − | 0.963343i | \(-0.413547\pi\) |
0.968416 | + | 0.249340i | \(0.0802138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 234.533 | − | 406.222i | 0.206093 | − | 0.356964i | −0.744387 | − | 0.667748i | \(-0.767258\pi\) |
0.950480 | + | 0.310784i | \(0.100592\pi\) | |||||||
\(110\) | 224.162 | 0.194300 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −738.341 | + | 736.157i | −0.622916 | + | 0.621074i | ||||
\(113\) | 1733.74 | − | 1000.97i | 1.44333 | − | 0.833306i | 0.445259 | − | 0.895402i | \(-0.353112\pi\) |
0.998070 | + | 0.0620958i | \(0.0197784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −807.193 | + | 466.033i | −0.654531 | + | 0.377894i | ||||
\(116\) | 1272.00 | + | 734.388i | 1.01812 | + | 0.587813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1894.34i | 1.47786i | ||||||||
\(119\) | −109.004 | − | 409.230i | −0.0839693 | − | 0.315244i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −639.794 | + | 1108.16i | −0.480687 | + | 0.832574i | ||||
\(122\) | −2720.61 | −2.01896 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 122.278i | 0.0885553i | ||||||||
\(125\) | 1461.93 | 1.04607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 522.832 | 0.365306 | 0.182653 | − | 0.983177i | \(-0.441532\pi\) | ||||
0.182653 | + | 0.983177i | \(0.441532\pi\) | |||||||
\(128\) | − | 453.948i | − | 0.313466i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2153.02 | −1.45256 | ||||||||
\(131\) | −1280.94 | + | 2218.65i | −0.854321 | + | 1.47973i | 0.0229522 | + | 0.999737i | \(0.492693\pi\) |
−0.877273 | + | 0.479991i | \(0.840640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −479.312 | + | 1778.28i | −0.312494 | + | 1.15937i | ||||
\(134\) | − | 2950.07i | − | 1.90184i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 70.6479 | + | 40.7886i | 0.0445441 | + | 0.0257176i | ||||
\(137\) | 1.06378 | − | 0.614174i | 0.000663394 | − | 0.000383011i | −0.499668 | − | 0.866217i | \(-0.666545\pi\) |
0.500332 | + | 0.865834i | \(0.333211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1676.23 | + | 967.770i | −1.02285 | + | 0.590541i | −0.914927 | − | 0.403619i | \(-0.867752\pi\) |
−0.107920 | + | 0.994160i | \(0.534419\pi\) | |||||||
\(140\) | 321.796 | + | 1208.11i | 0.194262 | + | 0.729315i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −381.732 | −0.225593 | ||||||||
\(143\) | −246.901 | + | 427.645i | −0.144384 | + | 0.250080i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1091.74 | + | 630.317i | −0.625271 | + | 0.361000i | ||||
\(146\) | −2091.48 | + | 3622.55i | −1.18556 | + | 2.05345i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1122.27 | − | 1943.83i | −0.623311 | − | 1.07961i | ||||
\(149\) | 2102.67 | + | 1213.97i | 1.15609 | + | 0.667468i | 0.950363 | − | 0.311142i | \(-0.100712\pi\) |
0.205725 | + | 0.978610i | \(0.434045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 698.188 | + | 1209.30i | 0.376276 | + | 0.651730i | 0.990517 | − | 0.137389i | \(-0.0438710\pi\) |
−0.614241 | + | 0.789119i | \(0.710538\pi\) | |||||||
\(152\) | −177.384 | − | 307.239i | −0.0946565 | − | 0.163950i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 526.613 | + | 141.942i | 0.275556 | + | 0.0742726i | ||||
\(155\) | −90.8889 | − | 52.4747i | −0.0470992 | − | 0.0271927i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 733.416i | − | 0.372822i | −0.982472 | − | 0.186411i | \(-0.940314\pi\) | ||
0.982472 | − | 0.186411i | \(-0.0596855\pi\) | |||||||
\(158\) | − | 3270.21i | − | 1.64661i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1712.34 | + | 988.618i | 0.846075 | + | 0.488482i | ||||
\(161\) | −2191.39 | + | 583.705i | −1.07271 | + | 0.285729i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1504.67 | − | 2606.16i | −0.723036 | − | 1.25233i | −0.959777 | − | 0.280762i | \(-0.909413\pi\) |
0.236742 | − | 0.971573i | \(-0.423920\pi\) | |||||||
\(164\) | −1415.42 | − | 2451.57i | −0.673935 | − | 1.16729i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −76.1736 | − | 43.9789i | −0.0356158 | − | 0.0205628i | ||||
\(167\) | 40.1692 | + | 69.5751i | 0.0186131 | + | 0.0322388i | 0.875182 | − | 0.483794i | \(-0.160742\pi\) |
−0.856569 | + | 0.516033i | \(0.827408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1272.92 | − | 2204.77i | 0.579392 | − | 1.00354i | ||||
\(170\) | −619.105 | + | 357.440i | −0.279313 | + | 0.161261i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1389.64 | + | 2406.94i | −0.616043 | + | 1.06702i | ||||
\(173\) | 2746.72 | 1.20711 | 0.603553 | − | 0.797323i | \(-0.293751\pi\) | ||||
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1199.17 | + | 323.222i | 0.517994 | + | 0.139619i | ||||
\(176\) | 349.580 | − | 201.830i | 0.149719 | − | 0.0864405i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2416.70 | + | 1395.28i | −1.01764 | + | 0.587533i | ||||
\(179\) | −2491.90 | − | 1438.70i | −1.04052 | − | 0.600745i | −0.120540 | − | 0.992708i | \(-0.538463\pi\) |
−0.919981 | + | 0.391964i | \(0.871796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 320.544i | − | 0.131634i | −0.997832 | − | 0.0658172i | \(-0.979035\pi\) | ||
0.997832 | − | 0.0658172i | \(-0.0209654\pi\) | |||||||
\(182\) | −5057.98 | − | 1363.31i | −2.06001 | − | 0.555250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 218.419 | − | 378.313i | 0.0875113 | − | 0.151574i | ||||
\(185\) | 1926.46 | 0.765603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 163.960i | 0.0641175i | ||||||||
\(188\) | −627.780 | −0.243540 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3108.93 | 1.18708 | ||||||||
\(191\) | − | 945.061i | − | 0.358022i | −0.983847 | − | 0.179011i | \(-0.942710\pi\) | ||
0.983847 | − | 0.179011i | \(-0.0572898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 786.769 | 0.293434 | 0.146717 | − | 0.989178i | \(-0.453129\pi\) | ||||
0.146717 | + | 0.989178i | \(0.453129\pi\) | |||||||
\(194\) | 2333.48 | − | 4041.71i | 0.863578 | − | 1.49576i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.00904 | + | 3041.92i | −0.00328318 | + | 1.10857i | ||||
\(197\) | 5047.70i | 1.82555i | 0.408462 | + | 0.912775i | \(0.366065\pi\) | ||||
−0.408462 | + | 0.912775i | \(0.633935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1052.30 | + | 607.546i | 0.374852 | + | 0.216421i | 0.675576 | − | 0.737290i | \(-0.263895\pi\) |
−0.300724 | + | 0.953711i | \(0.597228\pi\) | |||||||
\(200\) | −207.185 | + | 119.618i | −0.0732509 | + | 0.0422914i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5485.09 | − | 3166.82i | 1.91054 | − | 1.10305i | ||||
\(203\) | −2963.90 | + | 789.471i | −1.02475 | + | 0.272956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2429.67 | 0.827784 | ||||||||
\(206\) | 858.937 | − | 1487.72i | 0.290509 | − | 0.503177i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3357.63 | + | 1938.53i | −1.11928 | + | 0.646215i | ||||
\(209\) | 356.522 | − | 617.514i | 0.117996 | − | 0.204375i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 312.466 | + | 541.206i | 0.101948 | + | 0.176579i | 0.912487 | − | 0.409105i | \(-0.134159\pi\) |
−0.810539 | + | 0.585684i | \(0.800826\pi\) | |||||||
\(212\) | −2257.72 | − | 1303.50i | −0.731419 | − | 0.422285i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3245.75 | − | 5621.80i | −1.03680 | − | 1.79579i | ||||
\(215\) | −1192.72 | − | 2065.85i | −0.378338 | − | 0.655300i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −180.293 | − | 180.828i | −0.0564014 | − | 0.0565687i | ||||
\(218\) | −1668.41 | − | 963.259i | −0.518345 | − | 0.299267i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 484.036i | − | 0.148335i | ||||||
\(221\) | − | 1574.80i | − | 0.479332i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2295.49 | − | 1325.30i | −0.689316 | − | 0.397977i | 0.114040 | − | 0.993476i | \(-0.463621\pi\) |
−0.803356 | + | 0.595499i | \(0.796954\pi\) | |||||||
\(224\) | 3396.70 | + | 3406.78i | 1.01318 | + | 1.01618i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4111.14 | − | 7120.70i | −1.21004 | − | 2.09585i | ||||
\(227\) | −408.886 | − | 708.211i | −0.119554 | − | 0.207073i | 0.800037 | − | 0.599951i | \(-0.204813\pi\) |
−0.919591 | + | 0.392877i | \(0.871480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 608.798 | + | 351.489i | 0.175679 | + | 0.101428i | 0.585261 | − | 0.810845i | \(-0.300992\pi\) |
−0.409582 | + | 0.912273i | \(0.634325\pi\) | |||||||
\(230\) | 1914.06 | + | 3315.25i | 0.548737 | + | 0.950441i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 295.416 | − | 511.675i | 0.0835991 | − | 0.144798i | ||||
\(233\) | −3559.17 | + | 2054.89i | −1.00073 | + | 0.577769i | −0.908463 | − | 0.417966i | \(-0.862743\pi\) |
−0.0922626 | + | 0.995735i | \(0.529410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 269.408 | − | 466.629i | 0.0747841 | − | 0.129530i | ||||
\(236\) | 4090.47 | 1.12825 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1680.77 | + | 447.693i | −0.457764 | + | 0.121931i | ||||
\(239\) | 2082.70 | − | 1202.45i | 0.563677 | − | 0.325439i | −0.190943 | − | 0.981601i | \(-0.561155\pi\) |
0.754620 | + | 0.656162i | \(0.227821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −629.048 | + | 363.181i | −0.168135 | + | 0.0970729i | −0.581706 | − | 0.813399i | \(-0.697615\pi\) |
0.413571 | + | 0.910472i | \(0.364281\pi\) | |||||||
\(242\) | 4551.35 | + | 2627.72i | 1.20897 | + | 0.698002i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5874.66i | 1.54134i | ||||||||
\(245\) | −2257.19 | − | 1312.12i | −0.588599 | − | 0.342156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3424.30 | + | 5931.06i | −0.882117 | + | 1.52787i | ||||
\(248\) | 49.1875 | 0.0125944 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 6004.35i | − | 1.51899i | ||||||
\(251\) | −529.985 | −0.133276 | −0.0666382 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666382 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 877.994 | 0.218178 | ||||||||
\(254\) | − | 2147.35i | − | 0.530458i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3067.50 | 0.748901 | ||||||||
\(257\) | −974.429 | + | 1687.76i | −0.236511 | + | 0.409648i | −0.959711 | − | 0.280990i | \(-0.909337\pi\) |
0.723200 | + | 0.690639i | \(0.242670\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4525.75 | + | 1219.86i | 1.08578 | + | 0.292657i | ||||
\(260\) | 4649.05i | 1.10893i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9112.31 | + | 5260.99i | 2.14870 | + | 1.24055i | ||||
\(263\) | 438.975 | − | 253.443i | 0.102922 | − | 0.0594218i | −0.447656 | − | 0.894206i | \(-0.647741\pi\) |
0.550577 | + | 0.834784i | \(0.314408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1937.78 | − | 1118.78i | 0.449195 | − | 0.259343i | ||||
\(266\) | 7303.65 | + | 1968.60i | 1.68352 | + | 0.453770i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6370.13 | −1.45193 | ||||||||
\(269\) | 3851.69 | − | 6671.33i | 0.873018 | − | 1.51211i | 0.0141598 | − | 0.999900i | \(-0.495493\pi\) |
0.858859 | − | 0.512213i | \(-0.171174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4585.66 | + | 2647.53i | −1.02789 | + | 0.593455i | −0.916380 | − | 0.400308i | \(-0.868903\pi\) |
−0.111513 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(272\) | −643.662 | + | 1114.85i | −0.143484 | + | 0.248522i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.52250 | − | 4.36910i | −0.000556167 | − | 0.000963310i | ||||
\(275\) | −416.417 | − | 240.418i | −0.0913123 | − | 0.0527192i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2108.49 | − | 3652.01i | −0.457353 | − | 0.792158i | 0.541467 | − | 0.840722i | \(-0.317869\pi\) |
−0.998820 | + | 0.0485637i | \(0.984536\pi\) | |||||||
\(278\) | 3974.77 | + | 6884.50i | 0.857521 | + | 1.48527i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 485.976 | − | 129.446i | 0.103724 | − | 0.0276281i | ||||
\(281\) | 7104.37 | + | 4101.71i | 1.50823 | + | 0.870774i | 0.999954 | + | 0.00957745i | \(0.00304864\pi\) |
0.508271 | + | 0.861197i | \(0.330285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1569.02i | 0.329571i | 0.986329 | + | 0.164786i | \(0.0526932\pi\) | ||||
−0.986329 | + | 0.164786i | \(0.947307\pi\) | |||||||
\(284\) | 824.280i | 0.172225i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1756.40 | + | 1014.06i | 0.363140 | + | 0.209659i | ||||
\(287\) | 5707.90 | + | 1538.49i | 1.17396 | + | 0.316426i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2195.06 | + | 3801.95i | 0.446785 | + | 0.773854i | ||||
\(290\) | 2588.80 | + | 4483.94i | 0.524206 | + | 0.907951i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7822.22 | + | 4516.16i | 1.56767 | + | 0.905097i | ||||
\(293\) | 227.022 | + | 393.213i | 0.0452653 | + | 0.0784019i | 0.887770 | − | 0.460287i | \(-0.152253\pi\) |
−0.842505 | + | 0.538688i | \(0.818920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1755.40 | + | 3040.45i | −0.346452 | + | 0.600073i | ||||
\(296\) | −781.927 | + | 451.446i | −0.153542 | + | 0.0886478i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4985.97 | − | 8635.94i | 0.969226 | − | 1.67875i | ||||
\(299\) | −8432.91 | −1.63106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1493.88 | − | 5608.43i | −0.286065 | − | 1.07397i | ||||
\(302\) | 4966.75 | − | 2867.56i | 0.946372 | − | 0.546388i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4848.37 | − | 2799.21i | 0.914714 | − | 0.528110i | ||||
\(305\) | −4366.64 | − | 2521.08i | −0.819780 | − | 0.473300i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 74.2025i | 0.0137947i | 0.999976 | + | 0.00689733i | \(0.00219550\pi\) | ||||
−0.999976 | + | 0.00689733i | \(0.997804\pi\) | |||||||
\(308\) | 306.496 | − | 1137.12i | 0.0567021 | − | 0.210369i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −215.521 | + | 373.294i | −0.0394864 | + | 0.0683924i | ||||
\(311\) | −6425.91 | −1.17164 | −0.585820 | − | 0.810441i | \(-0.699227\pi\) | ||||
−0.585820 | + | 0.810441i | \(0.699227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7714.65i | − | 1.39316i | −0.717481 | − | 0.696578i | \(-0.754705\pi\) | ||
0.717481 | − | 0.696578i | \(-0.245295\pi\) | |||||||
\(314\) | −3012.24 | −0.541372 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7061.41 | −1.25707 | ||||||||
\(317\) | 306.057i | 0.0542267i | 0.999632 | + | 0.0271133i | \(0.00863150\pi\) | ||||
−0.999632 | + | 0.0271133i | \(0.991368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1187.50 | 0.208424 | ||||||||
\(320\) | 2346.31 | − | 4063.93i | 0.409884 | − | 0.709939i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2397.36 | + | 9000.36i | 0.414906 | + | 1.55767i | ||||
\(323\) | 2273.98i | 0.391727i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3999.58 | + | 2309.16i | 0.682636 | + | 0.394120i | ||||
\(326\) | −10703.9 | + | 6179.89i | −1.81851 | + | 1.04992i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −986.172 | + | 569.367i | −0.166013 | + | 0.0958476i | ||||
\(329\) | 928.381 | − | 925.635i | 0.155572 | − | 0.155112i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4099.12 | −0.680688 | −0.340344 | − | 0.940301i | \(-0.610544\pi\) | ||||
−0.340344 | + | 0.940301i | \(0.610544\pi\) | |||||||
\(332\) | −94.9642 | + | 164.483i | −0.0156983 | + | 0.0271903i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 285.755 | − | 164.981i | 0.0468138 | − | 0.0270280i | ||||
\(335\) | 2733.70 | − | 4734.91i | 0.445845 | − | 0.772227i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3390.68 | − | 5872.83i | −0.548078 | − | 0.949298i | −0.998406 | − | 0.0564355i | \(-0.982026\pi\) |
0.450329 | − | 0.892863i | \(-0.351307\pi\) | |||||||
\(338\) | −9055.29 | − | 5228.08i | −1.45723 | − | 0.841331i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 771.826 | + | 1336.84i | 0.123112 | + | 0.213237i | ||||
\(341\) | 49.4305 | + | 85.6161i | 0.00784989 | + | 0.0135964i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4471.86 | − | 4511.77i | −0.703959 | − | 0.710241i | ||||
\(344\) | 968.216 | + | 559.000i | 0.151752 | + | 0.0876141i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 11281.2i | − | 1.75283i | ||||||
\(347\) | − | 9757.99i | − | 1.50961i | −0.655946 | − | 0.754807i | \(-0.727730\pi\) | ||
0.655946 | − | 0.754807i | \(-0.272270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2576.08 | + | 1487.30i | 0.395113 | + | 0.228119i | 0.684373 | − | 0.729132i | \(-0.260076\pi\) |
−0.289260 | + | 0.957251i | \(0.593409\pi\) | |||||||
\(350\) | 1327.52 | − | 4925.18i | 0.202739 | − | 0.752176i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −931.265 | − | 1613.00i | −0.141013 | − | 0.244242i | ||||
\(353\) | −4894.29 | − | 8477.16i | −0.737951 | − | 1.27817i | −0.953416 | − | 0.301657i | \(-0.902460\pi\) |
0.215465 | − | 0.976511i | \(-0.430873\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −612.687 | − | 353.735i | −0.0916002 | − | 0.0528854i | ||||
\(356\) | 3012.85 | + | 5218.41i | 0.448542 | + | 0.776897i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5908.94 | + | 10234.6i | −0.872338 | + | 1.51093i | ||||
\(359\) | −3444.96 | + | 1988.95i | −0.506456 | + | 0.292403i | −0.731376 | − | 0.681975i | \(-0.761121\pi\) |
0.224919 | + | 0.974377i | \(0.427788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1515.14 | − | 2624.30i | 0.220898 | − | 0.382606i | ||||
\(362\) | −1316.52 | −0.191145 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2943.82 | + | 10921.8i | −0.423896 | + | 1.57268i | ||||
\(365\) | −6713.72 | + | 3876.17i | −0.962773 | + | 0.555858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3060.78 | + | 1767.14i | −0.435344 | + | 0.251346i | −0.701621 | − | 0.712551i | \(-0.747540\pi\) |
0.266277 | + | 0.963897i | \(0.414207\pi\) | |||||||
\(368\) | 5969.95 | + | 3446.75i | 0.845667 | + | 0.488246i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 7912.26i | − | 1.11173i | ||||||
\(371\) | 5260.74 | − | 1401.26i | 0.736183 | − | 0.196092i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2362.93 | + | 4092.71i | −0.328010 | + | 0.568129i | −0.982117 | − | 0.188272i | \(-0.939711\pi\) |
0.654107 | + | 0.756402i | \(0.273045\pi\) | |||||||
\(374\) | 673.408 | 0.0931046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 252.531i | 0.0346365i | ||||||||
\(377\) | −11405.6 | −1.55815 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5183.61 | 0.702545 | 0.351272 | − | 0.936273i | \(-0.385749\pi\) | ||||
0.351272 | + | 0.936273i | \(0.385749\pi\) | |||||||
\(380\) | − | 6713.16i | − | 0.906257i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3881.50 | −0.519882 | ||||||||
\(383\) | −3447.20 | + | 5970.73i | −0.459906 | + | 0.796580i | −0.998955 | − | 0.0456938i | \(-0.985450\pi\) |
0.539050 | + | 0.842274i | \(0.318783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 713.692 | + | 715.808i | 0.0944756 | + | 0.0947558i | ||||
\(386\) | − | 3231.37i | − | 0.426094i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8727.32 | − | 5038.72i | −1.14191 | − | 0.659284i | ||||
\(389\) | 2437.14 | − | 1407.08i | 0.317655 | − | 0.183398i | −0.332692 | − | 0.943036i | \(-0.607957\pi\) |
0.650347 | + | 0.759637i | \(0.274624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2424.90 | + | 1400.02i | −0.313638 | + | 0.181079i | ||||
\(392\) | 1223.65 | + | 3.62398i | 0.157662 | + | 0.000466936i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20731.6 | 2.65087 | ||||||||
\(395\) | 3030.36 | − | 5248.75i | 0.386011 | − | 0.668590i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5248.35 | + | 3030.14i | −0.663494 | + | 0.383068i | −0.793607 | − | 0.608431i | \(-0.791799\pi\) |
0.130113 | + | 0.991499i | \(0.458466\pi\) | |||||||
\(398\) | 2495.28 | − | 4321.95i | 0.314264 | − | 0.544320i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1887.63 | − | 3269.47i | −0.235954 | − | 0.408684i | ||||
\(401\) | 10447.9 | + | 6032.11i | 1.30111 | + | 0.751196i | 0.980594 | − | 0.196048i | \(-0.0628108\pi\) |
0.320515 | + | 0.947244i | \(0.396144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −474.767 | − | 822.321i | −0.0586845 | − | 0.101645i | ||||
\(404\) | −6838.15 | − | 11844.0i | −0.842106 | − | 1.45857i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3242.47 | + | 12173.1i | 0.396357 | + | 1.48804i | ||||
\(407\) | −1571.58 | − | 907.352i | −0.191401 | − | 0.110506i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 337.510i | 0.0408039i | 0.999792 | + | 0.0204019i | \(0.00649459\pi\) | ||||
−0.999792 | + | 0.0204019i | \(0.993505\pi\) | |||||||
\(410\) | − | 9979.00i | − | 1.20202i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3212.46 | − | 1854.71i | −0.384142 | − | 0.221784i | ||||
\(413\) | −6049.11 | + | 6031.23i | −0.720720 | + | 0.718589i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −81.5067 | − | 141.174i | −0.00964098 | − | 0.0166987i | ||||
\(416\) | 8944.56 | + | 15492.4i | 1.05419 | + | 1.82591i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2536.22 | − | 1464.28i | −0.296771 | − | 0.171341i | ||||
\(419\) | 4094.25 | + | 7091.45i | 0.477368 | + | 0.826826i | 0.999664 | − | 0.0259386i | \(-0.00825744\pi\) |
−0.522295 | + | 0.852765i | \(0.674924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 958.165 | − | 1659.59i | 0.110922 | − | 0.192122i | −0.805220 | − | 0.592976i | \(-0.797953\pi\) |
0.916142 | + | 0.400853i | \(0.131286\pi\) | |||||||
\(422\) | 2222.81 | − | 1283.34i | 0.256409 | − | 0.148038i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −524.345 | + | 908.193i | −0.0600577 | + | 0.104023i | ||||
\(425\) | 1533.45 | 0.175019 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8661.95 | − | 8687.64i | −0.981688 | − | 0.984600i | ||||
\(428\) | −12139.2 | + | 7008.59i | −1.37096 | + | 0.791526i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8484.72 | + | 4898.66i | −0.951557 | + | 0.549382i | ||||
\(431\) | −8604.78 | − | 4967.97i | −0.961665 | − | 0.555218i | −0.0649800 | − | 0.997887i | \(-0.520698\pi\) |
−0.896685 | + | 0.442669i | \(0.854032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4551.00i | 0.505098i | 0.967584 | + | 0.252549i | \(0.0812688\pi\) | ||||
−0.967584 | + | 0.252549i | \(0.918731\pi\) | |||||||
\(434\) | −742.686 | + | 740.490i | −0.0821430 | + | 0.0819001i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2079.98 | + | 3602.63i | −0.228470 | + | 0.395721i | ||||
\(437\) | 12177.0 | 1.33296 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7418.00i | 0.806474i | 0.915096 | + | 0.403237i | \(0.132115\pi\) | ||||
−0.915096 | + | 0.403237i | \(0.867885\pi\) | |||||||
\(440\) | −194.709 | −0.0210963 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6467.91 | −0.696035 | ||||||||
\(443\) | 6327.38i | 0.678607i | 0.940677 | + | 0.339303i | \(0.110191\pi\) | ||||
−0.940677 | + | 0.339303i | \(0.889809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5171.80 | −0.550936 | ||||||||
\(446\) | −5443.21 | + | 9427.91i | −0.577900 | + | 1.00095i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8085.38 | − | 8061.47i | 0.852675 | − | 0.850154i | ||||
\(449\) | − | 14396.4i | − | 1.51316i | −0.653904 | − | 0.756578i | \(-0.726870\pi\) | ||
0.653904 | − | 0.756578i | \(-0.273130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1982.09 | − | 1144.36i | −0.206946 | − | 0.119481i | ||||
\(452\) | −15375.8 | + | 8877.24i | −1.60004 | + | 0.923783i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2908.72 | + | 1679.35i | −0.300690 | + | 0.173603i | ||||
\(455\) | −6854.83 | − | 6875.16i | −0.706284 | − | 0.708379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5147.23 | 0.526865 | 0.263432 | − | 0.964678i | \(-0.415145\pi\) | ||||
0.263432 | + | 0.964678i | \(0.415145\pi\) | |||||||
\(458\) | 1443.62 | − | 2500.42i | 0.147283 | − | 0.255102i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7158.68 | − | 4133.06i | 0.725598 | − | 0.418924i | ||||
\(461\) | 446.618 | − | 773.565i | 0.0451217 | − | 0.0781530i | −0.842583 | − | 0.538567i | \(-0.818966\pi\) |
0.887704 | + | 0.460414i | \(0.152299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5520.47 | + | 9561.73i | 0.554121 | + | 0.959765i | 0.997971 | + | 0.0636644i | \(0.0202787\pi\) |
−0.443851 | + | 0.896101i | \(0.646388\pi\) | |||||||
\(464\) | 8074.46 | + | 4661.79i | 0.807861 | + | 0.466419i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8439.72 | + | 14618.0i | 0.838975 | + | 1.45315i | ||||
\(467\) | 4900.18 | + | 8487.36i | 0.485553 | + | 0.841003i | 0.999862 | − | 0.0166023i | \(-0.00528493\pi\) |
−0.514309 | + | 0.857605i | \(0.671952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9420.34 | − | 9392.49i | 0.927486 | − | 0.924744i | ||||
\(470\) | −1916.51 | − | 1106.50i | −0.188089 | − | 0.108593i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 1645.44i | − | 0.160460i | ||||||
\(473\) | 2247.05i | 0.218434i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5775.33 | − | 3334.39i | −0.557875 | − | 0.322089i | ||||
\(476\) | 966.711 | + | 3629.30i | 0.0930864 | + | 0.349472i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4938.63 | − | 8553.95i | −0.472568 | − | 0.818512i | ||||
\(479\) | −69.3349 | − | 120.092i | −0.00661377 | − | 0.0114554i | 0.862700 | − | 0.505717i | \(-0.168772\pi\) |
−0.869313 | + | 0.494261i | \(0.835439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15094.6 | + | 8714.89i | 1.43088 | + | 0.826122i | ||||
\(482\) | 1491.64 | + | 2583.59i | 0.140959 | + | 0.244148i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5674.08 | − | 9827.80i | 0.532878 | − | 0.922971i | ||||
\(485\) | 7490.56 | − | 4324.68i | 0.701296 | − | 0.404894i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9148.40 | + | 15845.5i | −0.851239 | + | 1.47439i | 0.0288514 | + | 0.999584i | \(0.490815\pi\) |
−0.880091 | + | 0.474806i | \(0.842518\pi\) | |||||||
\(488\) | 2363.15 | 0.219210 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5389.06 | + | 9270.61i | −0.496843 | + | 0.854701i | ||||
\(491\) | −5097.03 | + | 2942.77i | −0.468484 | + | 0.270479i | −0.715605 | − | 0.698505i | \(-0.753849\pi\) |
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3279.71 | + | 1893.54i | −0.299616 | + | 0.172984i | ||||
\(494\) | 24359.7 | + | 14064.1i | 2.21861 | + | 1.28092i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 776.201i | 0.0702670i | ||||||||
\(497\) | −1215.37 | − | 1218.97i | −0.109691 | − | 0.110017i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −267.363 | + | 463.086i | −0.0239856 | + | 0.0415442i | −0.877769 | − | 0.479084i | \(-0.840969\pi\) |
0.853783 | + | 0.520628i | \(0.174302\pi\) | |||||||
\(500\) | −12965.3 | −1.15965 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2176.72i | 0.193530i | ||||||||
\(503\) | −10504.5 | −0.931155 | −0.465578 | − | 0.885007i | \(-0.654153\pi\) | ||||
−0.465578 | + | 0.885007i | \(0.654153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11738.2 | 1.03434 | ||||||||
\(506\) | − | 3606.04i | − | 0.316815i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4636.79 | −0.404969 | ||||||||
\(509\) | −1408.94 | + | 2440.35i | −0.122691 | + | 0.212508i | −0.920828 | − | 0.389969i | \(-0.872486\pi\) |
0.798137 | + | 0.602476i | \(0.205819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18226.6 | + | 4854.90i | −1.57788 | + | 0.420289i | ||||
\(512\) | − | 16230.2i | − | 1.40094i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6931.87 | + | 4002.12i | 0.594848 | + | 0.343435i | ||||
\(515\) | 2757.22 | − | 1591.88i | 0.235918 | − | 0.136207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −439.558 | + | 253.779i | −0.0373921 | + | 0.0215884i | ||||
\(518\) | 5010.12 | − | 18587.9i | 0.424965 | − | 1.57665i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1870.13 | 0.157713 | ||||||||
\(521\) | −5520.76 | + | 9562.24i | −0.464240 | + | 0.804087i | −0.999167 | − | 0.0408113i | \(-0.987006\pi\) |
0.534927 | + | 0.844898i | \(0.320339\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4094.57 | + | 2364.00i | −0.342338 | + | 0.197649i | −0.661306 | − | 0.750117i | \(-0.729997\pi\) |
0.318967 | + | 0.947766i | \(0.396664\pi\) | |||||||
\(524\) | 11360.1 | − | 19676.3i | 0.947080 | − | 1.64039i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1040.92 | − | 1802.93i | −0.0862860 | − | 0.149452i | ||||
\(527\) | −273.040 | − | 157.640i | −0.0225689 | − | 0.0130302i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1413.46 | + | 2448.19i | 0.116172 | + | 0.201216i | ||||
\(530\) | −4594.97 | − | 7958.72i | −0.376590 | − | 0.652273i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4250.83 | − | 15770.9i | 0.346423 | − | 1.28525i | ||||
\(533\) | 19037.5 | + | 10991.3i | 1.54710 | + | 0.893218i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 12030.8i | − | 0.972218i | ||||||
\(536\) | 2562.45i | 0.206495i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27400.1 | − | 15819.5i | −2.19573 | − | 1.26770i | ||||
\(539\) | 1223.38 | + | 2133.53i | 0.0977641 | + | 0.170496i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11254.7 | + | 19493.8i | 0.894415 | + | 1.54917i | 0.834527 | + | 0.550967i | \(0.185741\pi\) |
0.0598879 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(542\) | 10873.8 | + | 18834.0i | 0.861752 | + | 1.49260i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5144.05 | + | 2969.92i | 0.405421 | + | 0.234070i | ||||
\(545\) | −1785.22 | − | 3092.10i | −0.140313 | − | 0.243029i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1219.31 | + | 2111.91i | −0.0953088 | + | 0.165080i | −0.909737 | − | 0.415184i | \(-0.863717\pi\) |
0.814429 | + | 0.580264i | \(0.197051\pi\) | |||||||
\(548\) | −9.43426 | + | 5.44687i | −0.000735422 | + | 0.000424596i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −987.432 | + | 1710.28i | −0.0765532 | + | 0.132594i | ||||
\(551\) | 16469.6 | 1.27337 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10442.6 | − | 10411.8i | 0.803013 | − | 0.800638i | ||||
\(554\) | −14999.3 | + | 8659.85i | −1.15029 | + | 0.664119i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14865.8 | − | 8582.77i | 1.13390 | − | 0.654660i | ||||
\(557\) | 9826.37 | + | 5673.25i | 0.747498 | + | 0.431568i | 0.824789 | − | 0.565440i | \(-0.191294\pi\) |
−0.0772911 | + | 0.997009i | \(0.524627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21582.3i | − | 1.63298i | ||||||
\(560\) | 2042.71 | + | 7668.92i | 0.154144 | + | 0.578698i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16846.3 | − | 29178.7i | 1.26445 | − | 2.19008i | ||||
\(563\) | −16855.7 | −1.26178 | −0.630891 | − | 0.775871i | \(-0.717311\pi\) | ||||
−0.630891 | + | 0.775871i | \(0.717311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 15238.5i | − | 1.13467i | ||||||
\(566\) | 6444.19 | 0.478568 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 331.576 | 0.0244940 | ||||||||
\(569\) | 11917.1i | 0.878019i | 0.898482 | + | 0.439009i | \(0.144671\pi\) | ||||
−0.898482 | + | 0.439009i | \(0.855329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20409.3 | 1.49580 | 0.747902 | − | 0.663809i | \(-0.231061\pi\) | ||||
0.747902 | + | 0.663809i | \(0.231061\pi\) | |||||||
\(572\) | 2189.67 | − | 3792.62i | 0.160061 | − | 0.277233i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6318.80 | − | 23443.2i | 0.459480 | − | 1.70470i | ||||
\(575\) | − | 8211.49i | − | 0.595552i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3374.84 | − | 1948.46i | −0.243495 | − | 0.140582i | 0.373287 | − | 0.927716i | \(-0.378231\pi\) |
−0.616782 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(578\) | 15615.1 | − | 9015.40i | 1.12371 | − | 0.648774i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9682.23 | − | 5590.04i | 0.693160 | − | 0.400196i | ||||
\(581\) | −102.087 | − | 383.263i | −0.00728964 | − | 0.0273673i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2107.74 | −0.149732 | ||||||||
\(584\) | 1816.67 | − | 3146.57i | 0.128724 | − | 0.222956i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1614.98 | − | 932.410i | 0.113847 | − | 0.0657295i | ||||
\(587\) | 8643.77 | − | 14971.5i | 0.607780 | − | 1.05271i | −0.383826 | − | 0.923406i | \(-0.625394\pi\) |
0.991606 | − | 0.129300i | \(-0.0412730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 685.557 | + | 1187.42i | 0.0479591 | + | 0.0830675i | ||||
\(590\) | 12487.5 | + | 7209.68i | 0.871362 | + | 0.503081i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7124.01 | − | 12339.2i | −0.494586 | − | 0.856649i | ||||
\(593\) | 985.742 | + | 1707.36i | 0.0682623 | + | 0.118234i | 0.898136 | − | 0.439717i | \(-0.144921\pi\) |
−0.829874 | + | 0.557951i | \(0.811588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3112.52 | − | 838.939i | −0.214455 | − | 0.0578036i | ||||
\(596\) | −18647.7 | − | 10766.3i | −1.28161 | − | 0.739939i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34635.1i | 2.36845i | ||||||||
\(599\) | 13995.3i | 0.954646i | 0.878728 | + | 0.477323i | \(0.158393\pi\) | ||||
−0.878728 | + | 0.477323i | \(0.841607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17296.5 | + | 9986.12i | 1.17394 | + | 0.677774i | 0.954605 | − | 0.297875i | \(-0.0962780\pi\) |
0.219335 | + | 0.975650i | \(0.429611\pi\) | |||||||
\(602\) | −23034.6 | + | 6135.56i | −1.55950 | + | 0.415393i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6191.95 | − | 10724.8i | −0.417131 | − | 0.722492i | ||||
\(605\) | 4870.00 | + | 8435.09i | 0.327262 | + | 0.566835i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11256.5 | − | 6498.92i | −0.752694 | − | 0.434568i | 0.0739724 | − | 0.997260i | \(-0.476432\pi\) |
−0.826667 | + | 0.562692i | \(0.809766\pi\) | |||||||
\(608\) | −12915.8 | − | 22370.8i | −0.861522 | − | 1.49220i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10354.4 | + | 17934.4i | −0.687276 | + | 1.19040i | ||||
\(611\) | 4221.84 | − | 2437.48i | 0.279538 | − | 0.161391i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3450.80 | + | 5976.96i | −0.227368 | + | 0.393812i | −0.957027 | − | 0.289998i | \(-0.906345\pi\) |
0.729659 | + | 0.683811i | \(0.239679\pi\) | |||||||
\(614\) | 304.760 | 0.0200311 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −457.420 | − | 123.292i | −0.0299188 | − | 0.00806422i | ||||
\(617\) | 8207.48 | − | 4738.59i | 0.535528 | − | 0.309187i | −0.207737 | − | 0.978185i | \(-0.566610\pi\) |
0.743265 | + | 0.668998i | \(0.233276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13493.9 | + | 7790.69i | −0.876195 | + | 0.505871i | −0.869402 | − | 0.494106i | \(-0.835496\pi\) |
−0.00679306 | + | 0.999977i | \(0.502162\pi\) | |||||||
\(620\) | 806.058 | + | 465.378i | 0.0522130 | + | 0.0301452i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26392.1i | 1.70133i | ||||||||
\(623\) | −12149.8 | − | 3274.83i | −0.781337 | − | 0.210599i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1372.72 | − | 2377.62i | 0.0878540 | − | 0.152168i | ||||
\(626\) | −31685.2 | −2.02299 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6504.38i | 0.413301i | ||||||||
\(629\) | 5787.32 | 0.366861 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7028.73 | 0.443438 | 0.221719 | − | 0.975111i | \(-0.428833\pi\) | ||||
0.221719 | + | 0.975111i | \(0.428833\pi\) | |||||||
\(632\) | 2840.53i | 0.178782i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1257.02 | 0.0787422 | ||||||||
\(635\) | 1989.85 | − | 3446.53i | 0.124354 | − | 0.215388i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11750.3 | − | 20492.0i | −0.730868 | − | 1.27460i | ||||
\(638\) | − | 4877.23i | − | 0.302651i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2992.44 | − | 1727.69i | −0.184823 | − | 0.106707i | ||||
\(641\) | −16662.3 | + | 9620.01i | −1.02671 | + | 0.592773i | −0.916041 | − | 0.401084i | \(-0.868634\pi\) |
−0.110672 | + | 0.993857i | \(0.535300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2402.55 | + | 1387.11i | −0.147352 | + | 0.0850737i | −0.571863 | − | 0.820349i | \(-0.693779\pi\) |
0.424511 | + | 0.905423i | \(0.360446\pi\) | |||||||
\(644\) | 19434.6 | − | 5176.65i | 1.18918 | − | 0.316753i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9339.57 | 0.568824 | ||||||||
\(647\) | 4830.91 | − | 8367.38i | 0.293544 | − | 0.508432i | −0.681101 | − | 0.732189i | \(-0.738499\pi\) |
0.974645 | + | 0.223757i | \(0.0718321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2864.06 | − | 1653.56i | 0.173227 | − | 0.100012i | ||||
\(650\) | 9484.04 | − | 16426.8i | 0.572299 | − | 0.991251i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13344.3 | + | 23113.0i | 0.801540 | + | 1.38831i | ||||
\(653\) | 10293.4 | + | 5942.91i | 0.616865 | + | 0.356147i | 0.775647 | − | 0.631167i | \(-0.217424\pi\) |
−0.158783 | + | 0.987314i | \(0.550757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9750.28 | + | 16888.0i | 0.581641 | + | 1.00743i | ||||
\(656\) | −8984.86 | − | 15562.2i | −0.534756 | − | 0.926224i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3801.71 | − | 3812.99i | −0.225237 | − | 0.225906i | ||||
\(659\) | −20497.2 | − | 11834.1i | −1.21162 | − | 0.699529i | −0.248508 | − | 0.968630i | \(-0.579940\pi\) |
−0.963112 | + | 0.269100i | \(0.913274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9602.52i | − | 0.565045i | −0.959261 | − | 0.282523i | \(-0.908829\pi\) | ||
0.959261 | − | 0.282523i | \(-0.0911712\pi\) | |||||||
\(662\) | 16835.7i | 0.988423i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 66.1650 | + | 38.2004i | 0.00386702 | + | 0.00223262i | ||||
\(665\) | 9898.27 | + | 9927.63i | 0.577201 | + | 0.578913i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10139.8 | + | 17562.6i | 0.588626 | + | 1.01953i | ||||
\(668\) | −356.245 | − | 617.034i | −0.0206340 | − | 0.0357392i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19447.0 | − | 11227.7i | −1.12135 | − | 0.647409i | ||||
\(671\) | 2374.82 | + | 4113.31i | 0.136630 | + | 0.236651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3469.40 | + | 6009.18i | −0.198716 | + | 0.344186i | −0.948112 | − | 0.317936i | \(-0.897010\pi\) |
0.749397 | + | 0.662121i | \(0.230344\pi\) | |||||||
\(674\) | −24120.6 | + | 13926.0i | −1.37847 | + | 0.795860i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11289.1 | + | 19553.2i | −0.642300 | + | 1.11250i | ||||
\(677\) | −8352.99 | −0.474197 | −0.237098 | − | 0.971486i | \(-0.576196\pi\) | ||||
−0.237098 | + | 0.971486i | \(0.576196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20335.6 | − | 5416.65i | 1.14935 | − | 0.306144i | ||||
\(680\) | 537.759 | − | 310.476i | 0.0303267 | − | 0.0175091i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 351.638 | − | 203.018i | 0.0197433 | − | 0.0113988i | ||||
\(683\) | 8631.82 | + | 4983.58i | 0.483583 | + | 0.279197i | 0.721908 | − | 0.691989i | \(-0.243265\pi\) |
−0.238325 | + | 0.971185i | \(0.576598\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.34998i | − | 0.000521524i | ||||||
\(686\) | −18530.5 | + | 18366.6i | −1.03134 | + | 1.02221i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8821.27 | + | 15278.9i | −0.488819 | + | 0.846660i | ||||
\(689\) | 20244.3 | 1.11937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4794.06i | − | 0.263929i | −0.991254 | − | 0.131964i | \(-0.957872\pi\) | ||
0.991254 | − | 0.131964i | \(-0.0421285\pi\) | |||||||
\(692\) | −24359.6 | −1.33817 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40077.4 | −2.19210 | ||||||||
\(695\) | 14733.0i | 0.804107i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7299.00 | 0.396656 | ||||||||
\(698\) | 6108.56 | − | 10580.3i | 0.331250 | − | 0.573741i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10635.0 | − | 2866.53i | −0.574236 | − | 0.154778i | ||||
\(701\) | 13815.7i | 0.744382i | 0.928156 | + | 0.372191i | \(0.121393\pi\) | ||||
−0.928156 | + | 0.372191i | \(0.878607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21796.4 | − | 12584.2i | −1.16937 | − | 0.675136i | ||||
\(704\) | −3828.17 | + | 2210.19i | −0.204942 | + | 0.118324i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34816.9 | + | 20101.5i | −1.85602 | + | 1.07157i | ||||
\(707\) | 27576.0 | + | 7432.75i | 1.46691 | + | 0.395385i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 134.605 | 0.00713001 | 0.00356501 | − | 0.999994i | \(-0.498865\pi\) | ||||
0.00356501 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(710\) | −1452.84 | + | 2516.39i | −0.0767945 | + | 0.133012i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2099.16 | − | 1211.95i | 0.110491 | − | 0.0637919i | ||||
\(713\) | −844.149 | + | 1462.11i | −0.0443389 | + | 0.0767972i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1879.37 | + | 3255.16i | 0.0982999 | + | 0.170260i | ||||
\(716\) | 22099.7 | + | 12759.2i | 1.15350 | + | 0.665971i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8168.88 | + | 14148.9i | 0.424596 | + | 0.735422i | ||||
\(719\) | −279.689 | − | 484.435i | −0.0145071 | − | 0.0251271i | 0.858681 | − | 0.512511i | \(-0.171285\pi\) |
−0.873188 | + | 0.487384i | \(0.837951\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7485.38 | − | 1993.83i | 0.386644 | − | 0.102988i | ||||
\(722\) | −10778.4 | − | 6222.89i | −0.555580 | − | 0.320764i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2842.77i | 0.145927i | ||||||||
\(725\) | − | 11106.2i | − | 0.568928i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6529.04 | + | 3769.54i | 0.333079 | + | 0.192303i | 0.657207 | − | 0.753710i | \(-0.271738\pi\) |
−0.324128 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(728\) | 4393.40 | + | 1184.18i | 0.223668 | + | 0.0602868i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15920.0 | + | 27574.2i | 0.807157 | + | 1.39804i | ||||
\(731\) | −3583.05 | − | 6206.03i | −0.181291 | − | 0.314006i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29593.0 | − | 17085.5i | −1.49119 | − | 0.860939i | −0.491241 | − | 0.871024i | \(-0.663457\pi\) |
−0.999949 | + | 0.0100844i | \(0.996790\pi\) | |||||||
\(734\) | 7257.90 | + | 12571.0i | 0.364978 | + | 0.632161i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15903.7 | − | 27545.9i | 0.796490 | − | 1.37956i | ||||
\(737\) | −4460.23 | + | 2575.11i | −0.222923 | + | 0.128705i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5524.56 | + | 9568.82i | −0.274999 | + | 0.476312i | −0.970135 | − | 0.242566i | \(-0.922011\pi\) |
0.695136 | + | 0.718878i | \(0.255344\pi\) | |||||||
\(740\) | −17085.1 | −0.848729 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5755.19 | − | 21606.6i | −0.284743 | − | 1.06901i | ||||
\(743\) | 5588.14 | − | 3226.32i | 0.275921 | − | 0.159303i | −0.355655 | − | 0.934617i | \(-0.615742\pi\) |
0.631575 | + | 0.775315i | \(0.282409\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16005.1 | − | 9240.57i | 0.787091 | − | 0.454427i | ||||
\(746\) | 16809.3 | + | 9704.87i | 0.824977 | + | 0.476301i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1454.10i | − | 0.0710791i | ||||||
\(749\) | 7618.01 | − | 28263.3i | 0.371637 | − | 1.37880i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 843.892 | − | 1461.66i | 0.0410041 | − | 0.0710211i | −0.844795 | − | 0.535090i | \(-0.820278\pi\) |
0.885799 | + | 0.464069i | \(0.153611\pi\) | |||||||
\(752\) | −3985.06 | −0.193245 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 46844.6i | 2.26257i | ||||||||
\(755\) | 10629.0 | 0.512355 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10839.9 | 0.520453 | 0.260226 | − | 0.965548i | \(-0.416203\pi\) | ||||
0.260226 | + | 0.965548i | \(0.416203\pi\) | |||||||
\(758\) | − | 21289.8i | − | 1.02016i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2700.44 | −0.128889 | ||||||||
\(761\) | −4529.42 | + | 7845.18i | −0.215757 | + | 0.373702i | −0.953507 | − | 0.301372i | \(-0.902555\pi\) |
0.737749 | + | 0.675075i | \(0.235889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2235.99 | − | 8394.52i | −0.106092 | − | 0.398299i | ||||
\(764\) | 8381.38i | 0.396895i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24522.6 | + | 14158.2i | 1.15671 | + | 0.667826i | ||||
\(767\) | −27508.6 | + | 15882.1i | −1.29501 | + | 0.747677i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10991.2 | + | 6345.79i | −0.515415 | + | 0.297575i | −0.735057 | − | 0.678006i | \(-0.762844\pi\) |
0.219642 | + | 0.975581i | \(0.429511\pi\) | |||||||
\(770\) | 2939.93 | − | 2931.23i | 0.137594 | − | 0.137187i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6977.54 | −0.325294 | ||||||||
\(773\) | 10423.9 | − | 18054.8i | 0.485023 | − | 0.840085i | −0.514829 | − | 0.857293i | \(-0.672145\pi\) |
0.999852 | + | 0.0172084i | \(0.00547788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 800.730 | − | 462.302i | 0.0371136 | − | 0.0214276i | ||||
\(776\) | −2026.88 | + | 3510.66i | −0.0937639 | + | 0.162404i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5779.09 | − | 10009.7i | −0.266312 | − | 0.461265i | ||||
\(779\) | −27489.8 | − | 15871.2i | −1.26434 | − | 0.729969i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 333.214 | + | 577.143i | 0.0152667 | + | 0.0264428i | ||||
\(782\) | 5750.06 | + | 9959.40i | 0.262943 | + | 0.455431i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −57.1881 | + | 19309.7i | −0.00260514 | + | 0.879631i | ||||
\(785\) | −4834.71 | − | 2791.32i | −0.219819 | − | 0.126913i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5164.85i | 0.233935i | 0.993136 | + | 0.116968i | \(0.0373173\pi\) | ||||
−0.993136 | + | 0.116968i | \(0.962683\pi\) | |||||||
\(788\) | − | 44766.0i | − | 2.02376i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21557.3 | − | 12446.1i | −0.970855 | − | 0.560524i | ||||
\(791\) | 9649.14 | − | 35799.0i | 0.433734 | − | 1.60918i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22809.6 | − | 39507.3i | −1.02143 | − | 1.76916i | ||||
\(794\) | 12445.2 | + | 21555.7i | 0.556251 | + | 0.963455i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9332.44 | − | 5388.09i | −0.415552 | − | 0.239919i | ||||
\(797\) | −3686.20 | − | 6384.68i | −0.163829 | − | 0.283760i | 0.772410 | − | 0.635125i | \(-0.219051\pi\) |
−0.936239 | + | 0.351364i | \(0.885718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 809.332 | − | 1401.80i | 0.0358349 | − | 0.0620679i | ||||
\(800\) | −15085.7 | + | 8709.70i | −0.666698 | + | 0.384918i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24774.7 | − | 42911.1i | 1.09081 | − | 1.88933i | ||||
\(803\) | 7302.60 | 0.320925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4492.45 | + | 16667.3i | −0.196693 | + | 0.729744i | ||||
\(806\) | −3377.39 | + | 1949.94i | −0.147597 | + | 0.0852154i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4764.39 | + | 2750.72i | −0.207439 | + | 0.119765i | ||||
\(809\) | −15808.7 | − | 9127.15i | −0.687026 | − | 0.396655i | 0.115471 | − | 0.993311i | \(-0.463162\pi\) |
−0.802497 | + | 0.596656i | \(0.796496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32302.9i | − | 1.39865i | −0.714802 | − | 0.699327i | \(-0.753483\pi\) | ||
0.714802 | − | 0.699327i | \(-0.246517\pi\) | |||||||
\(812\) | 26285.6 | − | 7001.51i | 1.13602 | − | 0.302592i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3726.62 | + | 6454.70i | −0.160464 | + | 0.277933i | ||||
\(815\) | −22906.6 | −0.984518 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31164.5i | 1.33453i | ||||||||
\(818\) | 1386.20 | 0.0592510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21547.8 | −0.917661 | ||||||||
\(821\) | − | 17372.0i | − | 0.738475i | −0.929335 | − | 0.369238i | \(-0.879619\pi\) | ||
0.929335 | − | 0.369238i | \(-0.120381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12896.9 | −0.546241 | −0.273120 | − | 0.961980i | \(-0.588056\pi\) | ||||
−0.273120 | + | 0.961980i | \(0.588056\pi\) | |||||||
\(824\) | −746.079 | + | 1292.25i | −0.0315423 | + | 0.0546329i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24771.1 | + | 24844.6i | 1.04346 | + | 1.04655i | ||||
\(827\) | 34437.8i | 1.44803i | 0.689785 | + | 0.724014i | \(0.257705\pi\) | ||||
−0.689785 | + | 0.724014i | \(0.742295\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37770.2 | − | 21806.6i | −1.58240 | − | 0.913601i | −0.994508 | − | 0.104664i | \(-0.966623\pi\) |
−0.587896 | − | 0.808937i | \(-0.700043\pi\) | |||||||
\(830\) | −579.820 | + | 334.759i | −0.0242480 | + | 0.0139996i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 36768.6 | − | 21228.3i | 1.53212 | − | 0.884568i | ||||
\(833\) | −6780.86 | − | 3941.75i | −0.282044 | − | 0.163954i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 611.522 | 0.0253444 | ||||||||
\(836\) | −3161.85 | + | 5476.49i | −0.130807 | + | 0.226565i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29125.6 | − | 16815.7i | 1.20063 | − | 0.693183i | ||||
\(839\) | −15073.9 | + | 26108.8i | −0.620274 | + | 1.07435i | 0.369160 | + | 0.929366i | \(0.379645\pi\) |
−0.989434 | + | 0.144981i | \(0.953688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1519.71 | + | 2632.21i | 0.0623112 | + | 0.107926i | ||||
\(842\) | −6816.17 | − | 3935.32i | −0.278980 | − | 0.161069i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2771.14 | − | 4799.75i | −0.113017 | − | 0.195751i | ||||
\(845\) | −9689.27 | − | 16782.3i | −0.394463 | − | 0.683230i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6099.67 | + | 22899.9i | 0.247446 | + | 0.928983i | ||||
\(848\) | −14331.7 | − | 8274.40i | −0.580368 | − | 0.335076i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 6298.09i | − | 0.254144i | ||||||
\(851\) | − | 30990.6i | − | 1.24835i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23967.5 | + | 13837.6i | 0.962053 | + | 0.555441i | 0.896804 | − | 0.442428i | \(-0.145883\pi\) |
0.0652484 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(854\) | −35681.4 | + | 35575.8i | −1.42973 | + | 1.42550i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2819.28 | + | 4883.14i | 0.112571 | + | 0.194979i | ||||
\(857\) | −8243.26 | − | 14277.8i | −0.328570 | − | 0.569100i | 0.653658 | − | 0.756790i | \(-0.273233\pi\) |
−0.982228 | + | 0.187690i | \(0.939900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17391.0 | + | 10040.7i | 0.690771 | + | 0.398817i | 0.803901 | − | 0.594764i | \(-0.202754\pi\) |
−0.113130 | + | 0.993580i | \(0.536088\pi\) | |||||||
\(860\) | 10577.7 | + | 18321.2i | 0.419416 | + | 0.726450i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20404.2 | + | 35341.0i | −0.806228 | + | 1.39643i | ||||
\(863\) | 23674.1 | − | 13668.3i | 0.933808 | − | 0.539134i | 0.0457940 | − | 0.998951i | \(-0.485418\pi\) |
0.888014 | + | 0.459817i | \(0.152085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10453.8 | − | 18106.5i | 0.410913 | − | 0.711721i | ||||
\(866\) | 18691.6 | 0.733449 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1598.95 | + | 1603.69i | 0.0625252 | + | 0.0627107i | ||||
\(869\) | −4944.25 | + | 2854.56i | −0.193006 | + | 0.111432i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42839.3 | − | 24733.3i | 1.66654 | − | 0.962177i | ||||
\(872\) | 1449.20 | + | 836.694i | 0.0562798 | + | 0.0324932i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 50012.6i | − | 1.93559i | ||||||
\(875\) | 19173.5 | − | 19116.7i | 0.740778 | − | 0.738588i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21668.1 | − | 37530.3i | 0.834300 | − | 1.44505i | −0.0602984 | − | 0.998180i | \(-0.519205\pi\) |
0.894599 | − | 0.446870i | \(-0.147461\pi\) | |||||||
\(878\) | 30466.8 | 1.17108 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 3072.59i | − | 0.117701i | ||||||
\(881\) | −48.3703 | −0.00184976 | −0.000924878 | − | 1.00000i | \(-0.500294\pi\) | ||||
−0.000924878 | 1.00000i | \(0.500294\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36776.7 | 1.40162 | 0.700812 | − | 0.713346i | \(-0.252821\pi\) | ||||
0.700812 | + | 0.713346i | \(0.252821\pi\) | |||||||
\(884\) | 13966.3i | 0.531376i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25987.4 | 0.985400 | ||||||||
\(887\) | −13975.2 | + | 24205.7i | −0.529019 | + | 0.916288i | 0.470408 | + | 0.882449i | \(0.344107\pi\) |
−0.999427 | + | 0.0338392i | \(0.989227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6857.04 | − | 6836.76i | 0.258693 | − | 0.257927i | ||||
\(890\) | 21241.3i | 0.800011i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20357.8 | + | 11753.6i | 0.764159 | + | 0.441188i | ||||
\(893\) | −6096.28 | + | 3519.69i | −0.228448 | + | 0.131895i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18967.9 | + | 10951.1i | −0.708410 | + | 0.409001i | ||||
\(896\) | −5936.00 | − | 5953.61i | −0.221326 | − | 0.221982i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59127.9 | −2.19724 | ||||||||
\(899\) | −1141.73 | + | 1977.53i | −0.0423567 | + | 0.0733640i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5821.30 | − | 3360.93i | 0.215245 | − | 0.124272i | ||||
\(902\) | −4700.04 | + | 8140.71i | −0.173497 | + | 0.300506i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3570.97 | + | 6185.09i | 0.131381 | + | 0.227559i | ||||
\(905\) | −2113.03 | − | 1219.96i | −0.0776129 | − | 0.0448098i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10805.4 | − | 18715.5i | −0.395576 | − | 0.685158i | 0.597598 | − | 0.801796i | \(-0.296122\pi\) |
−0.993175 | + | 0.116637i | \(0.962788\pi\) | |||||||
\(908\) | 3626.25 | + | 6280.85i | 0.132535 | + | 0.229557i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28237.2 | + | 28153.7i | −1.02863 | + | 1.02559i | ||||
\(911\) | 5927.13 | + | 3422.03i | 0.215560 | + | 0.124453i | 0.603892 | − | 0.797066i | \(-0.293616\pi\) |
−0.388333 | + | 0.921519i | \(0.626949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 153.556i | 0.00556624i | ||||||||
\(914\) | − | 21140.4i | − | 0.765057i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5399.19 | − | 3117.22i | −0.194753 | − | 0.112441i | ||||
\(917\) | 12212.2 | + | 45848.0i | 0.439785 | + | 1.65107i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14558.6 | + | 25216.3i | 0.522573 | + | 0.905124i | 0.999655 | + | 0.0262648i | \(0.00836130\pi\) |
−0.477082 | + | 0.878859i | \(0.658305\pi\) | |||||||
\(920\) | −1662.57 | − | 2879.66i | −0.0595797 | − | 0.103195i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3177.14 | − | 1834.32i | −0.113485 | − | 0.0655209i | ||||
\(923\) | −3200.43 | − | 5543.31i | −0.114132 | − | 0.197682i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8486.06 | + | 14698.3i | −0.301643 | + | 0.522461i | ||||
\(926\) | 39271.4 | − | 22673.3i | 1.39367 | − | 0.804635i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21510.0 | − | 37256.4i | 0.760883 | − | 1.31789i | ||||
\(929\) | 22477.8 | 0.793834 | 0.396917 | − | 0.917854i | \(-0.370080\pi\) | ||||
0.396917 | + | 0.917854i | \(0.370080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16967.2 | + | 29590.1i | 0.597292 | + | 1.04165i | ||||
\(932\) | 31564.9 | − | 18224.0i | 1.10938 | − | 0.640501i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34858.8 | − | 20125.7i | 1.22121 | − | 0.705068i | ||||
\(935\) | 1080.83 | + | 624.019i | 0.0378043 | + | 0.0218263i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25912.1i | 0.903426i | 0.892163 | + | 0.451713i | \(0.149187\pi\) | ||||
−0.892163 | + | 0.451713i | \(0.850813\pi\) | |||||||
\(938\) | −38576.3 | − | 38690.7i | −1.34281 | − | 1.34680i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2389.28 | + | 4138.35i | −0.0829038 | + | 0.143594i | ||||
\(941\) | 39812.7 | 1.37923 | 0.689615 | − | 0.724176i | \(-0.257780\pi\) | ||||
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39085.6i | − | 1.34974i | ||||||
\(944\) | 25965.7 | 0.895246 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9228.94 | 0.317187 | ||||||||
\(947\) | 37664.1i | 1.29242i | 0.763161 | + | 0.646209i | \(0.223646\pi\) | ||||
−0.763161 | + | 0.646209i | \(0.776354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −70139.6 | −2.39919 | ||||||||
\(950\) | −13694.8 | + | 23720.1i | −0.467703 | + | 0.810086i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1459.93 | − | 388.870i | 0.0497022 | − | 0.0132388i | ||||
\(953\) | 18055.8i | 0.613730i | 0.951753 | + | 0.306865i | \(0.0992801\pi\) | ||||
−0.951753 | + | 0.306865i | \(0.900720\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6229.88 | − | 3596.82i | −0.211093 | − | 0.121875i | ||||
\(956\) | −18470.7 | + | 10664.0i | −0.624879 | + | 0.360774i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −493.233 | + | 284.768i | −0.0166343 | + | 0.00960381i | ||||
\(959\) | 5.92049 | − | 21.9654i | 0.000199356 | − | 0.000739625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29600.9 | 0.993619 | ||||||||
\(962\) | 35793.3 | − | 61995.8i | 1.19961 | − | 2.07778i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5578.78 | − | 3220.91i | 0.186391 | − | 0.107613i | ||||
\(965\) | 2994.37 | − | 5186.41i | 0.0998884 | − | 0.173012i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15995.7 | − | 27705.3i | −0.531940 | − | 0.921348i | −0.999305 | − | 0.0372829i | \(-0.988130\pi\) |
0.467364 | − | 0.884065i | \(-0.345204\pi\) | |||||||
\(968\) | −3953.34 | − | 2282.46i | −0.131266 | − | 0.0757862i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17762.1 | − | 30764.8i | −0.587944 | − | 1.01835i | ||||
\(971\) | 13431.5 | + | 23264.0i | 0.443910 | + | 0.768874i | 0.997976 | − | 0.0635987i | \(-0.0202578\pi\) |
−0.554066 | + | 0.832473i | \(0.686924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9329.07 | + | 34611.5i | −0.307376 | + | 1.14038i | ||||
\(974\) | 65079.7 | + | 37573.8i | 2.14095 | + | 1.23608i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37291.5i | 1.22303i | ||||||||
\(977\) | 29282.8i | 0.958894i | 0.877571 | + | 0.479447i | \(0.159163\pi\) | ||||
−0.877571 | + | 0.479447i | \(0.840837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4219.07 | + | 2435.88i | 0.137734 | + | 0.0795210i | ||||
\(980\) | 20018.2 | + | 11636.7i | 0.652507 | + | 0.379306i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12086.4 | + | 20934.2i | 0.392761 | + | 0.680283i | ||||
\(983\) | −996.957 | − | 1726.78i | −0.0323479 | − | 0.0560282i | 0.849398 | − | 0.527752i | \(-0.176965\pi\) |
−0.881746 | + | 0.471724i | \(0.843632\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33274.6 | + | 19211.1i | 1.07636 | + | 0.621438i | ||||
\(986\) | 7777.05 | + | 13470.2i | 0.251188 | + | 0.435071i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30368.8 | − | 52600.3i | 0.977894 | − | 1.69376i | ||||
\(989\) | −33232.8 | + | 19187.0i | −1.06849 | + | 0.616896i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8752.81 | + | 15160.3i | −0.280567 | + | 0.485957i | −0.971525 | − | 0.236939i | \(-0.923856\pi\) |
0.690957 | + | 0.722896i | \(0.257189\pi\) | |||||||
\(992\) | 3581.47 | 0.114629 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5006.49 | + | 4991.68i | −0.159755 | + | 0.159282i | ||||
\(995\) | 8009.93 | − | 4624.53i | 0.255208 | − | 0.147344i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26709.1 | + | 15420.5i | −0.848431 | + | 0.489842i | −0.860121 | − | 0.510090i | \(-0.829612\pi\) |
0.0116900 | + | 0.999932i | \(0.496279\pi\) | |||||||
\(998\) | 1901.96 | + | 1098.10i | 0.0603261 | + | 0.0348293i | ||||
\(999\) | 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 | 189.4.i.a.143.4 | 44 | ||
3.2 | odd | 2 | 63.4.i.a.38.19 | yes | 44 | ||
7.5 | odd | 6 | 189.4.s.a.89.4 | 44 | |||
9.4 | even | 3 | 63.4.s.a.59.19 | yes | 44 | ||
9.5 | odd | 6 | 189.4.s.a.17.4 | 44 | |||
21.5 | even | 6 | 63.4.s.a.47.19 | yes | 44 | ||
63.5 | even | 6 | inner | 189.4.i.a.152.19 | 44 | ||
63.40 | odd | 6 | 63.4.i.a.5.4 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.4 | ✓ | 44 | 63.40 | odd | 6 | ||
63.4.i.a.38.19 | yes | 44 | 3.2 | odd | 2 | ||
63.4.s.a.47.19 | yes | 44 | 21.5 | even | 6 | ||
63.4.s.a.59.19 | yes | 44 | 9.4 | even | 3 | ||
189.4.i.a.143.4 | 44 | 1.1 | even | 1 | trivial | ||
189.4.i.a.152.19 | 44 | 63.5 | even | 6 | inner | ||
189.4.s.a.17.4 | 44 | 9.5 | odd | 6 | |||
189.4.s.a.89.4 | 44 | 7.5 | odd | 6 |