Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(19,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.u (of order \(8\), 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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 91.7 | ||
Character | \(\chi\) | \(=\) | 288.91 |
Dual form | 288.3.u.a.19.7 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.98676 | − | 0.229757i | 0.993380 | − | 0.114878i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.89442 | − | 0.912943i | 0.973606 | − | 0.228236i | ||||
\(5\) | −4.18866 | − | 1.73500i | −0.837732 | − | 0.347000i | −0.0777729 | − | 0.996971i | \(-0.524781\pi\) |
−0.759959 | + | 0.649971i | \(0.774781\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.93197 | − | 3.93197i | 0.561710 | − | 0.561710i | −0.368083 | − | 0.929793i | \(-0.619986\pi\) |
0.929793 | + | 0.368083i | \(0.119986\pi\) | |||||||
\(8\) | 7.52753 | − | 2.70857i | 0.940941 | − | 0.338571i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.72048 | − | 2.48465i | −0.872048 | − | 0.248465i | ||||
\(11\) | 14.2355 | + | 5.89652i | 1.29413 | + | 0.536048i | 0.920215 | − | 0.391414i | \(-0.128014\pi\) |
0.373919 | + | 0.927462i | \(0.378014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.454935 | − | 0.188440i | 0.0349950 | − | 0.0144954i | −0.365117 | − | 0.930962i | \(-0.618971\pi\) |
0.400112 | + | 0.916466i | \(0.368971\pi\) | |||||||
\(14\) | 6.90848 | − | 8.71527i | 0.493463 | − | 0.622520i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.3331 | − | 7.11077i | 0.895817 | − | 0.444423i | ||||
\(17\) | − | 26.5635i | − | 1.56256i | −0.624181 | − | 0.781280i | \(-0.714567\pi\) | ||
0.624181 | − | 0.781280i | \(-0.285433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.25040 | − | 17.5040i | −0.381600 | − | 0.921264i | −0.991657 | − | 0.128906i | \(-0.958853\pi\) |
0.610057 | − | 0.792358i | \(-0.291147\pi\) | |||||||
\(20\) | −17.8964 | − | 2.93282i | −0.894818 | − | 0.146641i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 29.6372 | + | 8.44428i | 1.34715 | + | 0.383831i | ||||
\(23\) | −0.775848 | − | 0.775848i | −0.0337325 | − | 0.0337325i | 0.690039 | − | 0.723772i | \(-0.257593\pi\) |
−0.723772 | + | 0.690039i | \(0.757593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.14303 | − | 3.14303i | −0.125721 | − | 0.125721i | ||||
\(26\) | 0.860551 | − | 0.478910i | 0.0330981 | − | 0.0184196i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.7231 | − | 18.9024i | 0.418682 | − | 0.675086i | ||||
\(29\) | 17.9907 | + | 43.4334i | 0.620369 | + | 1.49770i | 0.851271 | + | 0.524727i | \(0.175833\pi\) |
−0.230901 | + | 0.972977i | \(0.574167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.6852i | 1.28017i | 0.768306 | + | 0.640083i | \(0.221100\pi\) | ||||
−0.768306 | + | 0.640083i | \(0.778900\pi\) | |||||||
\(32\) | 26.8426 | − | 17.4205i | 0.838832 | − | 0.544391i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.10315 | − | 52.7753i | −0.179504 | − | 1.55222i | ||||
\(35\) | −23.2916 | + | 9.64771i | −0.665475 | + | 0.275649i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.4715 | + | 15.1070i | 0.985717 | + | 0.408297i | 0.816540 | − | 0.577288i | \(-0.195889\pi\) |
0.169177 | + | 0.985586i | \(0.445889\pi\) | |||||||
\(38\) | −18.4265 | − | 33.1104i | −0.484907 | − | 0.871327i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −36.2296 | − | 1.71499i | −0.905740 | − | 0.0428746i | ||||
\(41\) | −38.9661 | + | 38.9661i | −0.950392 | + | 0.950392i | −0.998826 | − | 0.0484342i | \(-0.984577\pi\) |
0.0484342 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.2899 | − | 5.91907i | −0.332324 | − | 0.137653i | 0.210282 | − | 0.977641i | \(-0.432562\pi\) |
−0.542605 | + | 0.839988i | \(0.682562\pi\) | |||||||
\(44\) | 60.8221 | + | 9.96739i | 1.38232 | + | 0.226532i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.71968 | − | 1.36317i | −0.0373843 | − | 0.0296341i | ||||
\(47\) | −62.1759 | −1.32289 | −0.661446 | − | 0.749993i | \(-0.730057\pi\) | ||||
−0.661446 | + | 0.749993i | \(0.730057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.0792i | 0.368964i | ||||||||
\(50\) | −6.96658 | − | 5.52232i | −0.139332 | − | 0.110446i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.59968 | − | 1.14920i | 0.0307630 | − | 0.0220999i | ||||
\(53\) | −11.4986 | + | 27.7600i | −0.216954 | + | 0.523773i | −0.994462 | − | 0.105100i | \(-0.966484\pi\) |
0.777508 | + | 0.628874i | \(0.216484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49.3970 | − | 49.3970i | −0.898128 | − | 0.898128i | ||||
\(56\) | 18.9480 | − | 40.2480i | 0.338357 | − | 0.718715i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 45.7223 | + | 82.1583i | 0.788316 | + | 1.41652i | ||||
\(59\) | 5.30584 | − | 12.8094i | 0.0899295 | − | 0.217109i | −0.872515 | − | 0.488587i | \(-0.837512\pi\) |
0.962445 | + | 0.271478i | \(0.0875124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1407 | + | 34.1386i | 0.231814 | + | 0.559650i | 0.996391 | − | 0.0848835i | \(-0.0270518\pi\) |
−0.764576 | + | 0.644533i | \(0.777052\pi\) | |||||||
\(62\) | 9.11794 | + | 78.8449i | 0.147064 | + | 1.27169i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 49.3273 | − | 40.7776i | 0.770739 | − | 0.637151i | ||||
\(65\) | −2.23251 | −0.0343463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.1257 | − | 10.8216i | 0.389937 | − | 0.161517i | −0.179097 | − | 0.983831i | \(-0.557318\pi\) |
0.569033 | + | 0.822314i | \(0.307318\pi\) | |||||||
\(68\) | −24.2510 | − | 103.450i | −0.356632 | − | 1.52132i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −44.0583 | + | 24.5191i | −0.629404 | + | 0.350273i | ||||
\(71\) | −17.7859 | + | 17.7859i | −0.250505 | + | 0.250505i | −0.821178 | − | 0.570672i | \(-0.806683\pi\) |
0.570672 | + | 0.821178i | \(0.306683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8313 | − | 12.8313i | 0.175771 | − | 0.175771i | −0.613738 | − | 0.789510i | \(-0.710335\pi\) |
0.789510 | + | 0.613738i | \(0.210335\pi\) | |||||||
\(74\) | 75.9311 | + | 21.6344i | 1.02610 | + | 0.292357i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −44.2163 | − | 61.5488i | −0.581793 | − | 0.809853i | ||||
\(77\) | 79.1584 | − | 32.7885i | 1.02803 | − | 0.425824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −144.157 | −1.82477 | −0.912383 | − | 0.409337i | \(-0.865760\pi\) | ||||
−0.912383 | + | 0.409337i | \(0.865760\pi\) | |||||||
\(80\) | −72.3735 | + | 4.91674i | −0.904669 | + | 0.0614592i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −68.4635 | + | 86.3689i | −0.834921 | + | 1.05328i | ||||
\(83\) | 10.9897 | + | 26.5314i | 0.132406 | + | 0.319655i | 0.976153 | − | 0.217086i | \(-0.0696552\pi\) |
−0.843747 | + | 0.536741i | \(0.819655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −46.0877 | + | 111.266i | −0.542208 | + | 1.30901i | ||||
\(86\) | −29.7506 | − | 8.47657i | −0.345937 | − | 0.0985648i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 123.129 | + | 5.82851i | 1.39919 | + | 0.0662330i | ||||
\(89\) | 5.92267 | + | 5.92267i | 0.0665469 | + | 0.0665469i | 0.739597 | − | 0.673050i | \(-0.235016\pi\) |
−0.673050 | + | 0.739597i | \(0.735016\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04785 | − | 2.52973i | 0.0115148 | − | 0.0277993i | ||||
\(92\) | −3.72978 | − | 2.31318i | −0.0405411 | − | 0.0251432i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −123.529 | + | 14.2853i | −1.31413 | + | 0.151972i | ||||
\(95\) | 85.8978i | 0.904187i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.9192 | 0.689889 | 0.344944 | − | 0.938623i | \(-0.387898\pi\) | ||||
0.344944 | + | 0.938623i | \(0.387898\pi\) | |||||||
\(98\) | 4.15383 | + | 35.9191i | 0.0423860 | + | 0.366521i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.1097 | − | 9.37089i | −0.151097 | − | 0.0937089i | ||||
\(101\) | −23.3697 | − | 9.68007i | −0.231384 | − | 0.0958422i | 0.263979 | − | 0.964528i | \(-0.414965\pi\) |
−0.495363 | + | 0.868686i | \(0.664965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5454 | + | 15.5454i | −0.150927 | + | 0.150927i | −0.778532 | − | 0.627605i | \(-0.784035\pi\) |
0.627605 | + | 0.778532i | \(0.284035\pi\) | |||||||
\(104\) | 2.91413 | − | 2.65071i | 0.0280205 | − | 0.0254876i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.4668 | + | 57.7943i | −0.155347 | + | 0.545229i | ||||
\(107\) | −107.060 | − | 44.3456i | −1.00056 | − | 0.414444i | −0.178556 | − | 0.983930i | \(-0.557143\pi\) |
−0.822001 | + | 0.569485i | \(0.807143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 82.3132 | − | 34.0952i | 0.755167 | − | 0.312800i | 0.0283190 | − | 0.999599i | \(-0.490985\pi\) |
0.726848 | + | 0.686799i | \(0.240985\pi\) | |||||||
\(110\) | −109.489 | − | 86.7907i | −0.995358 | − | 0.789006i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 28.3979 | − | 84.3165i | 0.253552 | − | 0.752826i | ||||
\(113\) | 9.91566i | 0.0877492i | 0.999037 | + | 0.0438746i | \(0.0139702\pi\) | ||||
−0.999037 | + | 0.0438746i | \(0.986030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.90367 | + | 4.59586i | 0.0165536 | + | 0.0399640i | ||||
\(116\) | 109.716 | + | 152.724i | 0.945825 | + | 1.31658i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.59837 | − | 26.6683i | 0.0643930 | − | 0.226003i | ||||
\(119\) | −104.447 | − | 104.447i | −0.877705 | − | 0.877705i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 82.3196 | + | 82.3196i | 0.680327 | + | 0.680327i | ||||
\(122\) | 35.9377 | + | 64.5763i | 0.294571 | + | 0.529314i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 36.2303 | + | 154.551i | 0.292180 | + | 1.24638i | ||||
\(125\) | 51.0869 | + | 123.335i | 0.408695 | + | 0.986678i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 59.4093i | − | 0.467790i | −0.972262 | − | 0.233895i | \(-0.924853\pi\) | ||
0.972262 | − | 0.233895i | \(-0.0751471\pi\) | |||||||
\(128\) | 88.6326 | − | 92.3486i | 0.692442 | − | 0.721474i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.43546 | + | 0.512935i | −0.0341190 | + | 0.00394565i | ||||
\(131\) | 176.426 | − | 73.0781i | 1.34676 | − | 0.557848i | 0.411375 | − | 0.911466i | \(-0.365049\pi\) |
0.935390 | + | 0.353618i | \(0.115049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −97.3336 | − | 40.3169i | −0.731832 | − | 0.303135i | ||||
\(134\) | 49.4192 | − | 27.5026i | 0.368800 | − | 0.205243i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −71.9491 | − | 199.958i | −0.529038 | − | 1.47028i | ||||
\(137\) | 138.710 | − | 138.710i | 1.01248 | − | 1.01248i | 0.0125608 | − | 0.999921i | \(-0.496002\pi\) |
0.999921 | − | 0.0125608i | \(-0.00399832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −63.7662 | − | 26.4128i | −0.458750 | − | 0.190020i | 0.141327 | − | 0.989963i | \(-0.454863\pi\) |
−0.600077 | + | 0.799943i | \(0.704863\pi\) | |||||||
\(140\) | −81.8997 | + | 58.8362i | −0.584998 | + | 0.420259i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −31.2498 | + | 39.4227i | −0.220069 | + | 0.277624i | ||||
\(143\) | 7.58736 | 0.0530584 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 213.142i | − | 1.46994i | ||||||
\(146\) | 22.5446 | − | 28.4408i | 0.154415 | − | 0.194800i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 155.827 | + | 25.5366i | 1.05289 | + | 0.172545i | ||||
\(149\) | −41.3888 | + | 99.9214i | −0.277777 | + | 0.670613i | −0.999773 | − | 0.0212835i | \(-0.993225\pi\) |
0.721996 | + | 0.691897i | \(0.243225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 159.036 | + | 159.036i | 1.05322 | + | 1.05322i | 0.998502 | + | 0.0547164i | \(0.0174255\pi\) |
0.0547164 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(152\) | −101.988 | − | 112.124i | −0.670976 | − | 0.737656i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 149.735 | − | 83.3300i | 0.972307 | − | 0.541104i | ||||
\(155\) | 68.8537 | − | 166.228i | 0.444218 | − | 1.07244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31.5775 | + | 76.2349i | 0.201131 | + | 0.485573i | 0.991973 | − | 0.126447i | \(-0.0403573\pi\) |
−0.790843 | + | 0.612020i | \(0.790357\pi\) | |||||||
\(158\) | −286.404 | + | 33.1210i | −1.81269 | + | 0.209626i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −142.659 | + | 26.3967i | −0.891619 | + | 0.164979i | ||||
\(161\) | −6.10122 | −0.0378958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −192.658 | + | 79.8016i | −1.18195 | + | 0.489581i | −0.885126 | − | 0.465351i | \(-0.845928\pi\) |
−0.296826 | + | 0.954932i | \(0.595928\pi\) | |||||||
\(164\) | −116.177 | + | 187.324i | −0.708394 | + | 1.14222i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.9296 | + | 50.1865i | 0.168251 | + | 0.302329i | ||||
\(167\) | −76.7432 | + | 76.7432i | −0.459540 | + | 0.459540i | −0.898504 | − | 0.438964i | \(-0.855345\pi\) |
0.438964 | + | 0.898504i | \(0.355345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −119.330 | + | 119.330i | −0.706092 | + | 0.706092i | ||||
\(170\) | −66.0011 | + | 231.647i | −0.388242 | + | 1.36263i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −61.0547 | − | 10.0055i | −0.354969 | − | 0.0581716i | ||||
\(173\) | −46.0052 | + | 19.0560i | −0.265926 | + | 0.110150i | −0.511663 | − | 0.859187i | \(-0.670970\pi\) |
0.245737 | + | 0.969337i | \(0.420970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.7166 | −0.141238 | ||||||||
\(176\) | 245.967 | − | 16.7099i | 1.39754 | − | 0.0949426i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.1277 | + | 10.4062i | 0.0737511 | + | 0.0584615i | ||||
\(179\) | 29.4799 | + | 71.1707i | 0.164692 | + | 0.397602i | 0.984583 | − | 0.174918i | \(-0.0559660\pi\) |
−0.819891 | + | 0.572520i | \(0.805966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 46.7381 | − | 112.836i | 0.258222 | − | 0.623402i | −0.740599 | − | 0.671947i | \(-0.765458\pi\) |
0.998821 | + | 0.0485445i | \(0.0154583\pi\) | |||||||
\(182\) | 1.50060 | − | 5.26672i | 0.00824506 | − | 0.0289380i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.94165 | − | 3.73878i | −0.0431611 | − | 0.0203194i | ||||
\(185\) | −126.556 | − | 126.556i | −0.684087 | − | 0.684087i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 156.632 | − | 378.144i | 0.837606 | − | 2.02216i | ||||
\(188\) | −242.139 | + | 56.7630i | −1.28797 | + | 0.301931i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.7356 | + | 170.658i | 0.103872 | + | 0.898201i | ||||
\(191\) | − | 227.376i | − | 1.19045i | −0.803559 | − | 0.595226i | \(-0.797063\pi\) | ||
0.803559 | − | 0.595226i | \(-0.202937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −46.4565 | −0.240707 | −0.120354 | − | 0.992731i | \(-0.538403\pi\) | ||||
−0.120354 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(194\) | 132.952 | − | 15.3751i | 0.685321 | − | 0.0792533i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.5053 | + | 70.4082i | 0.0842107 | + | 0.359225i | ||||
\(197\) | 186.490 | + | 77.2467i | 0.946650 | + | 0.392115i | 0.801971 | − | 0.597363i | \(-0.203785\pi\) |
0.144680 | + | 0.989479i | \(0.453785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 54.5057 | − | 54.5057i | 0.273898 | − | 0.273898i | −0.556769 | − | 0.830667i | \(-0.687959\pi\) |
0.830667 | + | 0.556769i | \(0.187959\pi\) | |||||||
\(200\) | −32.1724 | − | 15.1461i | −0.160862 | − | 0.0757307i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −48.6541 | − | 13.8626i | −0.240862 | − | 0.0686267i | ||||
\(203\) | 241.518 | + | 100.040i | 1.18974 | + | 0.492808i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 230.822 | − | 95.6095i | 1.12596 | − | 0.466388i | ||||
\(206\) | −27.3134 | + | 34.4567i | −0.132589 | + | 0.167266i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.18066 | − | 5.93587i | 0.0249070 | − | 0.0285378i | ||||
\(209\) | − | 291.930i | − | 1.39679i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 35.0586 | + | 84.6390i | 0.166155 | + | 0.401133i | 0.984923 | − | 0.172991i | \(-0.0553430\pi\) |
−0.818769 | + | 0.574123i | \(0.805343\pi\) | |||||||
\(212\) | −19.4370 | + | 118.607i | −0.0916839 | + | 0.559465i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −222.890 | − | 63.5062i | −1.04154 | − | 0.296758i | ||||
\(215\) | 49.5860 | + | 49.5860i | 0.230632 | + | 0.230632i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 156.041 | + | 156.041i | 0.719082 | + | 0.719082i | ||||
\(218\) | 155.703 | − | 86.6510i | 0.714233 | − | 0.397482i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −237.470 | − | 147.276i | −1.07941 | − | 0.669438i | ||||
\(221\) | −5.00564 | − | 12.0847i | −0.0226499 | − | 0.0546818i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 428.136i | − | 1.91989i | −0.280181 | − | 0.959947i | \(-0.590394\pi\) | ||
0.280181 | − | 0.959947i | \(-0.409606\pi\) | |||||||
\(224\) | 37.0474 | − | 174.041i | 0.165390 | − | 0.776970i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.27819 | + | 19.7000i | 0.0100805 | + | 0.0871683i | ||||
\(227\) | 112.195 | − | 46.4728i | 0.494252 | − | 0.204726i | −0.121613 | − | 0.992578i | \(-0.538807\pi\) |
0.615865 | + | 0.787852i | \(0.288807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 128.033 | + | 53.0331i | 0.559097 | + | 0.231586i | 0.644293 | − | 0.764779i | \(-0.277152\pi\) |
−0.0851960 | + | 0.996364i | \(0.527152\pi\) | |||||||
\(230\) | 4.83806 | + | 8.69348i | 0.0210350 | + | 0.0377977i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 253.068 | + | 278.217i | 1.09081 | + | 1.19921i | ||||
\(233\) | 90.6042 | − | 90.6042i | 0.388859 | − | 0.388859i | −0.485421 | − | 0.874280i | \(-0.661334\pi\) |
0.874280 | + | 0.485421i | \(0.161334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 260.434 | + | 107.875i | 1.10823 | + | 0.459043i | ||||
\(236\) | 8.96891 | − | 54.7293i | 0.0380039 | − | 0.231904i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −231.508 | − | 183.514i | −0.972724 | − | 0.771065i | ||||
\(239\) | −283.775 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702323\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 309.483i | − | 1.28416i | −0.766636 | − | 0.642082i | \(-0.778071\pi\) | ||
0.766636 | − | 0.642082i | \(-0.221929\pi\) | |||||||
\(242\) | 182.463 | + | 144.636i | 0.753978 | + | 0.597668i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 86.2364 | + | 120.041i | 0.353428 | + | 0.491970i | ||||
\(245\) | 31.3674 | − | 75.7277i | 0.128030 | − | 0.309093i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.59693 | − | 6.59693i | −0.0267082 | − | 0.0267082i | ||||
\(248\) | 107.490 | + | 298.731i | 0.433427 | + | 1.20456i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 129.834 | + | 233.299i | 0.519337 | + | 0.933195i | ||||
\(251\) | 33.9351 | − | 81.9265i | 0.135199 | − | 0.326400i | −0.841751 | − | 0.539866i | \(-0.818475\pi\) |
0.976951 | + | 0.213465i | \(0.0684750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.46975 | − | 15.6194i | −0.0255721 | − | 0.0617366i | ||||
\(254\) | −13.6497 | − | 118.032i | −0.0537389 | − | 0.464693i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 154.874 | − | 203.838i | 0.604976 | − | 0.796244i | ||||
\(257\) | −193.069 | −0.751241 | −0.375621 | − | 0.926774i | \(-0.622570\pi\) | ||||
−0.375621 | + | 0.926774i | \(0.622570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 202.805 | − | 84.0047i | 0.783032 | − | 0.324342i | ||||
\(260\) | −8.69435 | + | 2.03816i | −0.0334398 | + | 0.00783906i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 333.726 | − | 185.724i | 1.27376 | − | 0.708869i | ||||
\(263\) | 14.4799 | − | 14.4799i | 0.0550568 | − | 0.0550568i | −0.679042 | − | 0.734099i | \(-0.737605\pi\) |
0.734099 | + | 0.679042i | \(0.237605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 96.3271 | − | 96.3271i | 0.363498 | − | 0.363498i | ||||
\(266\) | −202.642 | − | 57.7369i | −0.761810 | − | 0.217056i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 91.8652 | − | 65.9954i | 0.342781 | − | 0.246251i | ||||
\(269\) | 125.951 | − | 52.1707i | 0.468220 | − | 0.193943i | −0.136083 | − | 0.990697i | \(-0.543451\pi\) |
0.604303 | + | 0.796754i | \(0.293451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −490.650 | −1.81052 | −0.905258 | − | 0.424863i | \(-0.860322\pi\) | ||||
−0.905258 | + | 0.424863i | \(0.860322\pi\) | |||||||
\(272\) | −188.887 | − | 380.737i | −0.694438 | − | 1.39977i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 243.714 | − | 307.453i | 0.889466 | − | 1.12209i | ||||
\(275\) | −26.2096 | − | 63.2755i | −0.0953076 | − | 0.230093i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −183.667 | + | 443.412i | −0.663059 | + | 1.60076i | 0.129926 | + | 0.991524i | \(0.458526\pi\) |
−0.792985 | + | 0.609241i | \(0.791474\pi\) | |||||||
\(278\) | −132.757 | − | 37.8252i | −0.477542 | − | 0.136062i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −149.197 | + | 135.710i | −0.532846 | + | 0.484680i | ||||
\(281\) | 164.474 | + | 164.474i | 0.585316 | + | 0.585316i | 0.936359 | − | 0.351043i | \(-0.114173\pi\) |
−0.351043 | + | 0.936359i | \(0.614173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −98.6436 | + | 238.147i | −0.348564 | + | 0.841508i | 0.648226 | + | 0.761448i | \(0.275511\pi\) |
−0.996790 | + | 0.0800601i | \(0.974489\pi\) | |||||||
\(284\) | −53.0282 | + | 85.5032i | −0.186719 | + | 0.301068i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0743 | − | 1.74325i | 0.0527072 | − | 0.00609527i | ||||
\(287\) | 306.427i | 1.06769i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −416.621 | −1.44159 | ||||||||
\(290\) | −48.9707 | − | 423.461i | −0.168865 | − | 1.46021i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.2563 | − | 61.6848i | 0.131015 | − | 0.211249i | ||||
\(293\) | 60.5536 | + | 25.0821i | 0.206668 | + | 0.0856045i | 0.483616 | − | 0.875280i | \(-0.339323\pi\) |
−0.276948 | + | 0.960885i | \(0.589323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −44.4487 | + | 44.4487i | −0.150674 | + | 0.150674i | ||||
\(296\) | 315.459 | + | 14.9327i | 1.06574 | + | 0.0504484i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −59.2719 | + | 208.029i | −0.198899 | + | 0.698084i | ||||
\(299\) | −0.499162 | − | 0.206759i | −0.00166944 | − | 0.000691503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −79.4611 | + | 32.9139i | −0.263990 | + | 0.109348i | ||||
\(302\) | 352.506 | + | 279.427i | 1.16724 | + | 0.925254i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −228.388 | − | 199.330i | −0.751275 | − | 0.655692i | ||||
\(305\) | − | 167.529i | − | 0.549276i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 166.166 | + | 401.160i | 0.541257 | + | 1.30671i | 0.923836 | + | 0.382787i | \(0.125036\pi\) |
−0.382580 | + | 0.923923i | \(0.624964\pi\) | |||||||
\(308\) | 278.342 | − | 199.959i | 0.903708 | − | 0.649218i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 98.6038 | − | 346.074i | 0.318077 | − | 1.11637i | ||||
\(311\) | 261.640 | + | 261.640i | 0.841288 | + | 0.841288i | 0.989026 | − | 0.147739i | \(-0.0471995\pi\) |
−0.147739 | + | 0.989026i | \(0.547199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −301.723 | − | 301.723i | −0.963972 | − | 0.963972i | 0.0354015 | − | 0.999373i | \(-0.488729\pi\) |
−0.999373 | + | 0.0354015i | \(0.988729\pi\) | |||||||
\(314\) | 80.2525 | + | 144.205i | 0.255581 | + | 0.459252i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −561.407 | + | 131.607i | −1.77660 | + | 0.416477i | ||||
\(317\) | −11.4511 | − | 27.6454i | −0.0361233 | − | 0.0872094i | 0.904788 | − | 0.425862i | \(-0.140029\pi\) |
−0.940912 | + | 0.338652i | \(0.890029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 724.378i | 2.27078i | ||||||||
\(320\) | −277.364 | + | 85.2207i | −0.866764 | + | 0.266315i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.1217 | + | 1.40180i | −0.0376449 | + | 0.00435341i | ||||
\(323\) | −464.968 | + | 192.596i | −1.43953 | + | 0.596273i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.02215 | − | 0.837602i | −0.00622200 | − | 0.00257724i | ||||
\(326\) | −364.430 | + | 202.811i | −1.11788 | + | 0.622120i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −187.776 | + | 398.860i | −0.572488 | + | 1.21604i | ||||
\(329\) | −244.474 | + | 244.474i | −0.743081 | + | 0.743081i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −117.333 | − | 48.6009i | −0.354480 | − | 0.146830i | 0.198335 | − | 0.980134i | \(-0.436447\pi\) |
−0.552815 | + | 0.833304i | \(0.686447\pi\) | |||||||
\(332\) | 67.0201 | + | 93.2916i | 0.201868 | + | 0.280999i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −134.838 | + | 170.103i | −0.403707 | + | 0.509289i | ||||
\(335\) | −128.207 | −0.382709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 148.325i | − | 0.440134i | −0.975485 | − | 0.220067i | \(-0.929372\pi\) | ||
0.975485 | − | 0.220067i | \(-0.0706276\pi\) | |||||||
\(338\) | −209.662 | + | 264.496i | −0.620303 | + | 0.782532i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −77.9059 | + | 475.390i | −0.229135 | + | 1.39821i | ||||
\(341\) | −234.004 | + | 564.937i | −0.686230 | + | 1.65671i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 263.753 | + | 263.753i | 0.768961 | + | 0.768961i | ||||
\(344\) | −123.600 | − | 5.85080i | −0.359302 | − | 0.0170081i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −87.0230 | + | 48.4296i | −0.251512 | + | 0.139970i | ||||
\(347\) | 215.625 | − | 520.565i | 0.621398 | − | 1.50019i | −0.228664 | − | 0.973505i | \(-0.573436\pi\) |
0.850062 | − | 0.526682i | \(-0.176564\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −92.9006 | − | 224.282i | −0.266191 | − | 0.642641i | 0.733107 | − | 0.680113i | \(-0.238070\pi\) |
−0.999298 | + | 0.0374720i | \(0.988070\pi\) | |||||||
\(350\) | −49.1060 | + | 5.67881i | −0.140303 | + | 0.0162252i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 484.838 | − | 89.7111i | 1.37738 | − | 0.254861i | ||||
\(353\) | −453.234 | −1.28395 | −0.641975 | − | 0.766726i | \(-0.721885\pi\) | ||||
−0.641975 | + | 0.766726i | \(0.721885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 105.357 | − | 43.6405i | 0.296782 | − | 0.122931i | ||||
\(356\) | 28.4725 | + | 17.6583i | 0.0799788 | + | 0.0496021i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 74.9214 | + | 134.626i | 0.209278 | + | 0.376050i | ||||
\(359\) | −175.857 | + | 175.857i | −0.489852 | + | 0.489852i | −0.908259 | − | 0.418407i | \(-0.862588\pi\) |
0.418407 | + | 0.908259i | \(0.362588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44333 | − | 1.44333i | 0.00399816 | − | 0.00399816i | ||||
\(362\) | 66.9326 | − | 234.916i | 0.184897 | − | 0.648939i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.77127 | − | 10.8085i | 0.00486612 | − | 0.0296936i | ||||
\(365\) | −76.0082 | + | 31.4836i | −0.208242 | + | 0.0862566i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 115.194 | 0.313879 | 0.156939 | − | 0.987608i | \(-0.449837\pi\) | ||||
0.156939 | + | 0.987608i | \(0.449837\pi\) | |||||||
\(368\) | −16.6372 | − | 5.60340i | −0.0452097 | − | 0.0152266i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −280.514 | − | 222.359i | −0.758145 | − | 0.600971i | ||||
\(371\) | 63.9394 | + | 154.363i | 0.172343 | + | 0.416074i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −95.1961 | + | 229.824i | −0.255217 | + | 0.616149i | −0.998610 | − | 0.0527059i | \(-0.983215\pi\) |
0.743393 | + | 0.668855i | \(0.233215\pi\) | |||||||
\(374\) | 224.310 | − | 787.269i | 0.599758 | − | 2.10500i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −468.031 | + | 168.408i | −1.24476 | + | 0.447893i | ||||
\(377\) | 16.3692 | + | 16.3692i | 0.0434197 | + | 0.0434197i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 264.738 | − | 639.134i | 0.698517 | − | 1.68637i | −0.0283560 | − | 0.999598i | \(-0.509027\pi\) |
0.726873 | − | 0.686772i | \(-0.240973\pi\) | |||||||
\(380\) | 78.4198 | + | 334.522i | 0.206368 | + | 0.880322i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −52.2412 | − | 451.742i | −0.136757 | − | 1.18257i | ||||
\(383\) | − | 217.725i | − | 0.568473i | −0.958754 | − | 0.284236i | \(-0.908260\pi\) | ||
0.958754 | − | 0.284236i | \(-0.0917401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −388.455 | −1.00897 | ||||||||
\(386\) | −92.2979 | + | 10.6737i | −0.239114 | + | 0.0276521i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 260.612 | − | 61.0934i | 0.671680 | − | 0.157457i | ||||
\(389\) | −452.405 | − | 187.392i | −1.16299 | − | 0.481728i | −0.284123 | − | 0.958788i | \(-0.591703\pi\) |
−0.878871 | + | 0.477060i | \(0.841703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6092 | + | 20.6092i | −0.0527091 | + | 0.0527091i | ||||
\(392\) | 48.9688 | + | 136.092i | 0.124920 | + | 0.347173i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 388.259 | + | 110.623i | 0.985429 | + | 0.280770i | ||||
\(395\) | 603.823 | + | 250.112i | 1.52866 | + | 0.633194i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −281.846 | + | 116.745i | −0.709940 | + | 0.294067i | −0.708280 | − | 0.705932i | \(-0.750529\pi\) |
−0.00166042 | + | 0.999999i | \(0.500529\pi\) | |||||||
\(398\) | 95.7667 | − | 120.813i | 0.240620 | − | 0.303550i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −67.3987 | − | 22.6999i | −0.168497 | − | 0.0567498i | ||||
\(401\) | − | 173.814i | − | 0.433452i | −0.976232 | − | 0.216726i | \(-0.930462\pi\) | ||
0.976232 | − | 0.216726i | \(-0.0695378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.47829 | + | 18.0542i | 0.0185565 | + | 0.0447995i | ||||
\(404\) | −99.8490 | − | 16.3630i | −0.247151 | − | 0.0405026i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 502.823 | + | 143.265i | 1.23848 | + | 0.352869i | ||||
\(407\) | 430.110 | + | 430.110i | 1.05678 | + | 1.05678i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 322.065 | + | 322.065i | 0.787446 | + | 0.787446i | 0.981075 | − | 0.193629i | \(-0.0620258\pi\) |
−0.193629 | + | 0.981075i | \(0.562026\pi\) | |||||||
\(410\) | 436.620 | − | 242.986i | 1.06493 | − | 0.592648i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −46.3484 | + | 74.7326i | −0.112496 | + | 0.181390i | ||||
\(413\) | −29.5039 | − | 71.2287i | −0.0714380 | − | 0.172467i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 130.198i | − | 0.313730i | ||||||
\(416\) | 8.92892 | − | 12.9834i | 0.0214638 | − | 0.0312102i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −67.0729 | − | 579.994i | −0.160461 | − | 1.38755i | ||||
\(419\) | −13.9903 | + | 5.79496i | −0.0333896 | + | 0.0138304i | −0.399316 | − | 0.916813i | \(-0.630752\pi\) |
0.365926 | + | 0.930644i | \(0.380752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −507.883 | − | 210.372i | −1.20637 | − | 0.499696i | −0.313320 | − | 0.949648i | \(-0.601441\pi\) |
−0.893053 | + | 0.449952i | \(0.851441\pi\) | |||||||
\(422\) | 89.0994 | + | 160.102i | 0.211136 | + | 0.379389i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.3659 | + | 240.109i | −0.0268064 | + | 0.566294i | ||||
\(425\) | −83.4900 | + | 83.4900i | −0.196447 | + | 0.196447i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 189.833 | + | 78.6313i | 0.444573 | + | 0.184148i | ||||
\(428\) | −457.421 | − | 74.9610i | −1.06874 | − | 0.175143i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 109.908 | + | 87.1227i | 0.255600 | + | 0.202611i | ||||
\(431\) | −654.734 | −1.51910 | −0.759552 | − | 0.650447i | \(-0.774582\pi\) | ||||
−0.759552 | + | 0.650447i | \(0.774582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 366.488i | 0.846392i | 0.906038 | + | 0.423196i | \(0.139092\pi\) | ||||
−0.906038 | + | 0.423196i | \(0.860908\pi\) | |||||||
\(434\) | 345.867 | + | 274.164i | 0.796929 | + | 0.631715i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 289.435 | − | 207.929i | 0.663843 | − | 0.476900i | ||||
\(437\) | −7.95524 | + | 19.2057i | −0.0182042 | + | 0.0439489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 124.489 | + | 124.489i | 0.283573 | + | 0.283573i | 0.834532 | − | 0.550959i | \(-0.185738\pi\) |
−0.550959 | + | 0.834532i | \(0.685738\pi\) | |||||||
\(440\) | −505.633 | − | 238.042i | −1.14917 | − | 0.541005i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.7215 | − | 22.8593i | −0.0287818 | − | 0.0517178i | ||||
\(443\) | −147.480 | + | 356.047i | −0.332911 | + | 0.803718i | 0.665448 | + | 0.746445i | \(0.268241\pi\) |
−0.998359 | + | 0.0572735i | \(0.981759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5322 | − | 35.0839i | −0.0326567 | − | 0.0788402i | ||||
\(446\) | −98.3673 | − | 850.604i | −0.220554 | − | 1.90718i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 33.6171 | − | 354.290i | 0.0750381 | − | 0.790826i | ||||
\(449\) | 689.326 | 1.53525 | 0.767623 | − | 0.640901i | \(-0.221439\pi\) | ||||
0.767623 | + | 0.640901i | \(0.221439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −784.465 | + | 324.936i | −1.73939 | + | 0.720479i | ||||
\(452\) | 9.05244 | + | 38.6158i | 0.0200275 | + | 0.0854332i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 212.228 | − | 118.108i | 0.467462 | − | 0.260150i | ||||
\(455\) | −8.77817 | + | 8.77817i | −0.0192927 | + | 0.0192927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 86.4503 | − | 86.4503i | 0.189169 | − | 0.189169i | −0.606168 | − | 0.795337i | \(-0.707294\pi\) |
0.795337 | + | 0.606168i | \(0.207294\pi\) | |||||||
\(458\) | 266.556 | + | 75.9475i | 0.582000 | + | 0.165824i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.6094 | + | 16.1603i | 0.0252379 | + | 0.0351310i | ||||
\(461\) | 3.31579 | − | 1.37344i | 0.00719259 | − | 0.00297927i | −0.379084 | − | 0.925362i | \(-0.623761\pi\) |
0.386277 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 113.007 | 0.244075 | 0.122038 | − | 0.992525i | \(-0.461057\pi\) | ||||
0.122038 | + | 0.992525i | \(0.461057\pi\) | |||||||
\(464\) | 566.707 | + | 494.606i | 1.22135 | + | 1.06596i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 159.192 | − | 200.826i | 0.341613 | − | 0.430956i | ||||
\(467\) | 150.402 | + | 363.102i | 0.322059 | + | 0.777520i | 0.999134 | + | 0.0416055i | \(0.0132473\pi\) |
−0.677075 | + | 0.735914i | \(0.736753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60.1753 | − | 145.276i | 0.128306 | − | 0.309757i | ||||
\(470\) | 542.204 | + | 154.485i | 1.15363 | + | 0.328692i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.24464 | − | 110.795i | 0.0111115 | − | 0.234734i | ||||
\(473\) | −168.522 | − | 168.522i | −0.356282 | − | 0.356282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.2275 | + | 77.8040i | −0.0678473 | + | 0.163798i | ||||
\(476\) | −502.115 | − | 311.407i | −1.05486 | − | 0.654215i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −563.793 | + | 65.1993i | −1.17948 | + | 0.136400i | ||||
\(479\) | − | 205.624i | − | 0.429278i | −0.976693 | − | 0.214639i | \(-0.931142\pi\) | ||
0.976693 | − | 0.214639i | \(-0.0688575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.4390 | 0.0404136 | ||||||||
\(482\) | −71.1059 | − | 614.869i | −0.147523 | − | 1.27566i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 395.740 | + | 245.434i | 0.817646 | + | 0.507096i | ||||
\(485\) | −280.302 | − | 116.105i | −0.577942 | − | 0.239391i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 573.249 | − | 573.249i | 1.17710 | − | 1.17710i | 0.196623 | − | 0.980479i | \(-0.437002\pi\) |
0.980479 | − | 0.196623i | \(-0.0629975\pi\) | |||||||
\(488\) | 198.911 | + | 218.678i | 0.407605 | + | 0.448112i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 44.9206 | − | 157.660i | 0.0916747 | − | 0.321754i | ||||
\(491\) | −421.115 | − | 174.432i | −0.857669 | − | 0.355258i | −0.0898735 | − | 0.995953i | \(-0.528646\pi\) |
−0.767795 | + | 0.640695i | \(0.778646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1153.74 | − | 477.897i | 2.34025 | − | 0.969364i | ||||
\(494\) | −14.6222 | − | 11.5908i | −0.0295996 | − | 0.0234632i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 282.192 | + | 568.810i | 0.568936 | + | 1.14679i | ||||
\(497\) | 139.867i | 0.281423i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 115.301 | + | 278.361i | 0.231064 | + | 0.557837i | 0.996303 | − | 0.0859086i | \(-0.0273793\pi\) |
−0.765239 | + | 0.643746i | \(0.777379\pi\) | |||||||
\(500\) | 311.552 | + | 433.678i | 0.623103 | + | 0.867356i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 48.5976 | − | 170.565i | 0.0968080 | − | 0.339771i | ||||
\(503\) | −526.474 | − | 526.474i | −1.04667 | − | 1.04667i | −0.998856 | − | 0.0478110i | \(-0.984775\pi\) |
−0.0478110 | − | 0.998856i | \(-0.515225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 81.0930 | + | 81.0930i | 0.160580 | + | 0.160580i | ||||
\(506\) | −16.4425 | − | 29.5454i | −0.0324950 | − | 0.0583902i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −54.2373 | − | 231.365i | −0.106766 | − | 0.455443i | ||||
\(509\) | 98.1719 | + | 237.008i | 0.192872 | + | 0.465634i | 0.990500 | − | 0.137516i | \(-0.0439119\pi\) |
−0.797628 | + | 0.603150i | \(0.793912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 100.905i | − | 0.197465i | ||||||
\(512\) | 260.864 | − | 440.561i | 0.509499 | − | 0.860471i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −383.582 | + | 44.3589i | −0.746268 | + | 0.0863014i | ||||
\(515\) | 92.0858 | − | 38.1432i | 0.178807 | − | 0.0740644i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −885.103 | − | 366.622i | −1.71200 | − | 0.709133i | ||||
\(518\) | 383.624 | − | 213.493i | 0.740588 | − | 0.412149i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8053 | + | 6.04691i | −0.0323179 | + | 0.0116287i | ||||
\(521\) | 42.3980 | − | 42.3980i | 0.0813781 | − | 0.0813781i | −0.665246 | − | 0.746624i | \(-0.731673\pi\) |
0.746624 | + | 0.665246i | \(0.231673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 160.929 | + | 66.6589i | 0.307703 | + | 0.127455i | 0.531192 | − | 0.847252i | \(-0.321744\pi\) |
−0.223488 | + | 0.974707i | \(0.571744\pi\) | |||||||
\(524\) | 620.362 | − | 445.664i | 1.18390 | − | 0.850504i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.4413 | − | 32.0950i | 0.0483674 | − | 0.0610171i | ||||
\(527\) | 1054.18 | 2.00034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 527.796i | − | 0.997724i | ||||||
\(530\) | 169.247 | − | 213.511i | 0.319334 | − | 0.402850i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −415.865 | − | 68.1511i | −0.781702 | − | 0.128103i | ||||
\(533\) | −10.3843 | + | 25.0698i | −0.0194827 | + | 0.0470353i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 371.497 | + | 371.497i | 0.694386 | + | 0.694386i | ||||
\(536\) | 167.351 | − | 152.224i | 0.312222 | − | 0.283999i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 238.248 | − | 132.589i | 0.442841 | − | 0.246448i | ||||
\(539\) | −106.605 | + | 257.366i | −0.197782 | + | 0.477488i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6178 | − | 71.5038i | −0.0547465 | − | 0.132170i | 0.894140 | − | 0.447788i | \(-0.147788\pi\) |
−0.948886 | + | 0.315618i | \(0.897788\pi\) | |||||||
\(542\) | −974.803 | + | 112.730i | −1.79853 | + | 0.207989i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −462.750 | − | 713.034i | −0.850644 | − | 1.31072i | ||||
\(545\) | −403.937 | −0.741169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 157.659 | − | 65.3046i | 0.288225 | − | 0.119387i | −0.233886 | − | 0.972264i | \(-0.575144\pi\) |
0.522112 | + | 0.852877i | \(0.325144\pi\) | |||||||
\(548\) | 413.561 | − | 666.830i | 0.754674 | − | 1.21684i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −66.6101 | − | 119.691i | −0.121109 | − | 0.217621i | ||||
\(551\) | 629.819 | − | 629.819i | 1.14305 | − | 1.14305i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −566.819 | + | 566.819i | −1.02499 | + | 1.02499i | ||||
\(554\) | −263.026 | + | 923.151i | −0.474775 | + | 1.66634i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −272.446 | − | 44.6479i | −0.490011 | − | 0.0803019i | ||||
\(557\) | 890.709 | − | 368.944i | 1.59912 | − | 0.662376i | 0.607827 | − | 0.794069i | \(-0.292041\pi\) |
0.991291 | + | 0.131693i | \(0.0420413\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.61638 | −0.0136250 | ||||||||
\(560\) | −265.238 | + | 303.903i | −0.473639 | + | 0.542684i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 364.559 | + | 288.981i | 0.648681 | + | 0.514201i | ||||
\(563\) | −106.191 | − | 256.369i | −0.188617 | − | 0.455362i | 0.801077 | − | 0.598562i | \(-0.204261\pi\) |
−0.989694 | + | 0.143200i | \(0.954261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2037 | − | 41.5333i | 0.0304490 | − | 0.0735103i | ||||
\(566\) | −141.265 | + | 495.804i | −0.249585 | + | 0.875979i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −85.7094 | + | 182.058i | −0.150897 | + | 0.320525i | ||||
\(569\) | 351.714 | + | 351.714i | 0.618126 | + | 0.618126i | 0.945050 | − | 0.326925i | \(-0.106012\pi\) |
−0.326925 | + | 0.945050i | \(0.606012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 179.708 | − | 433.854i | 0.314725 | − | 0.759814i | −0.684792 | − | 0.728739i | \(-0.740107\pi\) |
0.999517 | − | 0.0310755i | \(-0.00989322\pi\) | |||||||
\(572\) | 29.5484 | − | 6.92683i | 0.0516580 | − | 0.0121098i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 70.4037 | + | 608.796i | 0.122654 | + | 1.06062i | ||||
\(575\) | 4.87703i | 0.00848179i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 662.602 | 1.14836 | 0.574179 | − | 0.818730i | \(-0.305321\pi\) | ||||
0.574179 | + | 0.818730i | \(0.305321\pi\) | |||||||
\(578\) | −827.725 | + | 95.7214i | −1.43205 | + | 0.165608i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −194.586 | − | 830.064i | −0.335493 | − | 1.43114i | ||||
\(581\) | 147.532 | + | 61.1096i | 0.253927 | + | 0.105180i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −327.375 | + | 327.375i | −0.561535 | + | 0.561535i | ||||
\(584\) | 61.8335 | − | 131.342i | 0.105879 | − | 0.224901i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 126.068 | + | 35.9195i | 0.215133 | + | 0.0612961i | ||||
\(587\) | −650.448 | − | 269.424i | −1.10809 | − | 0.458985i | −0.247809 | − | 0.968809i | \(-0.579711\pi\) |
−0.860279 | + | 0.509824i | \(0.829711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 694.650 | − | 287.733i | 1.17937 | − | 0.488512i | ||||
\(590\) | −78.0965 | + | 98.5213i | −0.132367 | + | 0.166985i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 630.172 | − | 42.8111i | 1.06448 | − | 0.0723160i | ||||
\(593\) | 430.692i | 0.726293i | 0.931732 | + | 0.363147i | \(0.118298\pi\) | ||||
−0.931732 | + | 0.363147i | \(0.881702\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 256.277 | + | 618.708i | 0.430718 | + | 1.03985i | ||||
\(596\) | −69.9630 | + | 426.922i | −0.117388 | + | 0.716312i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.03922 | − | 0.296095i | −0.00173782 | − | 0.000495143i | ||||
\(599\) | 16.0528 | + | 16.0528i | 0.0267993 | + | 0.0267993i | 0.720379 | − | 0.693580i | \(-0.243968\pi\) |
−0.693580 | + | 0.720379i | \(0.743968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 201.233 | + | 201.233i | 0.334831 | + | 0.334831i | 0.854418 | − | 0.519587i | \(-0.173914\pi\) |
−0.519587 | + | 0.854418i | \(0.673914\pi\) | |||||||
\(602\) | −150.308 | + | 83.6487i | −0.249681 | + | 0.138951i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 764.544 | + | 474.163i | 1.26580 | + | 0.785038i | ||||
\(605\) | −201.984 | − | 487.633i | −0.333858 | − | 0.806005i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 713.329i | − | 1.17517i | −0.809162 | − | 0.587586i | \(-0.800079\pi\) | ||
0.809162 | − | 0.587586i | \(-0.199921\pi\) | |||||||
\(608\) | −499.549 | − | 343.548i | −0.821626 | − | 0.565046i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −38.4910 | − | 332.840i | −0.0630999 | − | 0.545639i | ||||
\(611\) | −28.2860 | + | 11.7164i | −0.0462946 | + | 0.0191759i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −349.658 | − | 144.833i | −0.570404 | − | 0.236269i | 0.0787907 | − | 0.996891i | \(-0.474894\pi\) |
−0.649195 | + | 0.760622i | \(0.724894\pi\) | |||||||
\(614\) | 422.301 | + | 758.830i | 0.687786 | + | 1.23588i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 507.057 | − | 461.222i | 0.823144 | − | 0.748737i | ||||
\(617\) | −185.331 | + | 185.331i | −0.300374 | + | 0.300374i | −0.841160 | − | 0.540786i | \(-0.818127\pi\) |
0.540786 | + | 0.841160i | \(0.318127\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −740.280 | − | 306.634i | −1.19593 | − | 0.495370i | −0.306248 | − | 0.951952i | \(-0.599074\pi\) |
−0.889681 | + | 0.456582i | \(0.849074\pi\) | |||||||
\(620\) | 116.389 | − | 710.220i | 0.187725 | − | 1.14552i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 579.930 | + | 459.703i | 0.932364 | + | 0.739072i | ||||
\(623\) | 46.5755 | 0.0747601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 494.120i | − | 0.790591i | ||||||
\(626\) | −668.774 | − | 530.128i | −1.06833 | − | 0.846850i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 192.574 | + | 268.063i | 0.306647 | + | 0.426851i | ||||
\(629\) | 401.295 | − | 968.812i | 0.637989 | − | 1.54024i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0415 | + | 25.0415i | 0.0396854 | + | 0.0396854i | 0.726671 | − | 0.686986i | \(-0.241066\pi\) |
−0.686986 | + | 0.726671i | \(0.741066\pi\) | |||||||
\(632\) | −1085.14 | + | 390.458i | −1.71700 | + | 0.617813i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.1023 | − | 52.2937i | −0.0459026 | − | 0.0824822i | ||||
\(635\) | −103.075 | + | 248.845i | −0.162323 | + | 0.391882i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.40686 | + | 8.22488i | 0.00534828 | + | 0.0129119i | ||||
\(638\) | 166.431 | + | 1439.16i | 0.260863 | + | 2.25574i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −531.476 | + | 233.039i | −0.830432 | + | 0.364124i | ||||
\(641\) | 150.813 | 0.235278 | 0.117639 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117639 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −635.355 | + | 263.173i | −0.988110 | + | 0.409289i | −0.817424 | − | 0.576037i | \(-0.804598\pi\) |
−0.170686 | + | 0.985325i | \(0.554598\pi\) | |||||||
\(644\) | −23.7607 | + | 5.57007i | −0.0368955 | + | 0.00864917i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −879.530 | + | 489.472i | −1.36150 | + | 0.757696i | ||||
\(647\) | 460.454 | − | 460.454i | 0.711675 | − | 0.711675i | −0.255211 | − | 0.966885i | \(-0.582145\pi\) |
0.966885 | + | 0.255211i | \(0.0821448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 151.062 | − | 151.062i | 0.232762 | − | 0.232762i | ||||
\(650\) | −4.20997 | − | 1.19951i | −0.00647688 | − | 0.00184540i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −677.438 | + | 486.667i | −1.03902 | + | 0.746422i | ||||
\(653\) | −308.661 | + | 127.852i | −0.472682 | + | 0.195791i | −0.606291 | − | 0.795243i | \(-0.707343\pi\) |
0.133609 | + | 0.991034i | \(0.457343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −865.779 | −1.32180 | ||||||||
\(656\) | −281.425 | + | 835.583i | −0.429001 | + | 1.27375i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −429.541 | + | 541.880i | −0.652798 | + | 0.823526i | ||||
\(659\) | 187.311 | + | 452.209i | 0.284235 | + | 0.686205i | 0.999925 | − | 0.0122131i | \(-0.00388764\pi\) |
−0.715690 | + | 0.698418i | \(0.753888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −279.659 | + | 675.156i | −0.423084 | + | 1.02142i | 0.558348 | + | 0.829607i | \(0.311436\pi\) |
−0.981432 | + | 0.191809i | \(0.938564\pi\) | |||||||
\(662\) | −244.279 | − | 69.6002i | −0.369001 | − | 0.105136i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 154.587 | + | 169.950i | 0.232812 | + | 0.255948i | ||||
\(665\) | 337.747 | + | 337.747i | 0.507891 | + | 0.507891i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.7397 | − | 47.6558i | 0.0295947 | − | 0.0714479i | ||||
\(668\) | −228.808 | + | 368.933i | −0.342527 | + | 0.552294i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −254.717 | + | 29.4565i | −0.380175 | + | 0.0439649i | ||||
\(671\) | 569.360i | 0.848525i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 74.6107 | 0.110863 | 0.0554314 | − | 0.998462i | \(-0.482347\pi\) | ||||
0.0554314 | + | 0.998462i | \(0.482347\pi\) | |||||||
\(674\) | −34.0787 | − | 294.686i | −0.0505619 | − | 0.437220i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −355.779 | + | 573.661i | −0.526300 | + | 0.848611i | ||||
\(677\) | 250.770 | + | 103.872i | 0.370413 | + | 0.153430i | 0.560122 | − | 0.828410i | \(-0.310754\pi\) |
−0.189709 | + | 0.981840i | \(0.560754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 263.124 | − | 263.124i | 0.387517 | − | 0.387517i | ||||
\(680\) | −45.5560 | + | 962.386i | −0.0669942 | + | 1.41527i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −335.112 | + | 1176.16i | −0.491367 | + | 1.72457i | ||||
\(683\) | −1198.32 | − | 496.359i | −1.75449 | − | 0.726734i | −0.997291 | − | 0.0735510i | \(-0.976567\pi\) |
−0.757200 | − | 0.653183i | \(-0.773433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −821.671 | + | 340.347i | −1.19952 | + | 0.496857i | ||||
\(686\) | 584.614 | + | 463.415i | 0.852207 | + | 0.675533i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −246.907 | + | 16.7738i | −0.358877 | + | 0.0243805i | ||||
\(689\) | 14.7958i | 0.0214743i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.819 | − | 815.567i | −0.488884 | − | 1.18027i | −0.955282 | − | 0.295696i | \(-0.904449\pi\) |
0.466398 | − | 0.884575i | \(-0.345551\pi\) | |||||||
\(692\) | −161.767 | + | 116.212i | −0.233767 | + | 0.167937i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 308.792 | − | 1083.78i | 0.444945 | − | 1.56164i | ||||
\(695\) | 221.269 | + | 221.269i | 0.318372 | + | 0.318372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1035.08 | + | 1035.08i | 1.48504 | + | 1.48504i | ||||
\(698\) | −236.101 | − | 424.250i | −0.338254 | − | 0.607807i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −96.2570 | + | 22.5649i | −0.137510 | + | 0.0322355i | ||||
\(701\) | −487.432 | − | 1176.77i | −0.695338 | − | 1.67870i | −0.733737 | − | 0.679433i | \(-0.762226\pi\) |
0.0383989 | − | 0.999262i | \(-0.487774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 747.930i | − | 1.06391i | ||||||
\(704\) | 942.644 | − | 289.629i | 1.33898 | − | 0.411405i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −900.467 | + | 104.134i | −1.27545 | + | 0.147498i | ||||
\(707\) | −129.951 | + | 53.8274i | −0.183806 | + | 0.0761349i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 949.384 | + | 393.248i | 1.33905 | + | 0.554651i | 0.933222 | − | 0.359300i | \(-0.116985\pi\) |
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(710\) | 199.293 | − | 110.910i | 0.280695 | − | 0.156211i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 60.6250 | + | 28.5411i | 0.0851475 | + | 0.0400858i | ||||
\(713\) | 30.7896 | − | 30.7896i | 0.0431832 | − | 0.0431832i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7809 | − | 13.1641i | −0.0444487 | − | 0.0184113i | ||||
\(716\) | 179.782 | + | 250.255i | 0.251092 | + | 0.349519i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −308.981 | + | 389.790i | −0.430336 | + | 0.542882i | ||||
\(719\) | −349.072 | −0.485496 | −0.242748 | − | 0.970089i | \(-0.578049\pi\) | ||||
−0.242748 | + | 0.970089i | \(0.578049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 122.248i | 0.169554i | ||||||||
\(722\) | 2.53594 | − | 3.19917i | 0.00351239 | − | 0.00443099i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 79.0054 | − | 482.100i | 0.109123 | − | 0.665884i | ||||
\(725\) | 79.9673 | − | 193.058i | 0.110300 | − | 0.266287i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −256.931 | − | 256.931i | −0.353413 | − | 0.353413i | 0.507965 | − | 0.861378i | \(-0.330398\pi\) |
−0.861378 | + | 0.507965i | \(0.830398\pi\) | |||||||
\(728\) | 1.03576 | − | 21.8808i | 0.00142275 | − | 0.0300561i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −143.776 | + | 80.0138i | −0.196954 | + | 0.109608i | ||||
\(731\) | −157.231 | + | 379.590i | −0.215091 | + | 0.519275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 473.293 | + | 1142.63i | 0.645694 | + | 1.55884i | 0.818887 | + | 0.573955i | \(0.194591\pi\) |
−0.173194 | + | 0.984888i | \(0.555409\pi\) | |||||||
\(734\) | 228.862 | − | 26.4665i | 0.311801 | − | 0.0360579i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.3414 | − | 7.31011i | −0.0466596 | − | 0.00993222i | ||||
\(737\) | 435.722 | 0.591211 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −137.009 | + | 56.7511i | −0.185398 | + | 0.0767945i | −0.473451 | − | 0.880820i | \(-0.656992\pi\) |
0.288053 | + | 0.957614i | \(0.406992\pi\) | |||||||
\(740\) | −608.402 | − | 377.325i | −0.822165 | − | 0.509898i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 162.498 | + | 291.992i | 0.219000 | + | 0.393521i | ||||
\(743\) | 644.593 | − | 644.593i | 0.867555 | − | 0.867555i | −0.124647 | − | 0.992201i | \(-0.539780\pi\) |
0.992201 | + | 0.124647i | \(0.0397797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 346.727 | − | 346.727i | 0.465405 | − | 0.465405i | ||||
\(746\) | −136.328 | + | 478.476i | −0.182746 | + | 0.641389i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 264.769 | − | 1615.65i | 0.353969 | − | 2.15996i | ||||
\(749\) | −595.321 | + | 246.590i | −0.794821 | + | 0.329225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5402 | −0.0246873 | −0.0123437 | − | 0.999924i | \(-0.503929\pi\) | ||||
−0.0123437 | + | 0.999924i | \(0.503929\pi\) | |||||||
\(752\) | −891.171 | + | 442.119i | −1.18507 | + | 0.587924i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 36.2826 | + | 28.7608i | 0.0481202 | + | 0.0381442i | ||||
\(755\) | −390.220 | − | 942.075i | −0.516848 | − | 1.24778i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 100.854 | − | 243.482i | 0.133228 | − | 0.321641i | −0.843161 | − | 0.537661i | \(-0.819308\pi\) |
0.976389 | + | 0.216021i | \(0.0693079\pi\) | |||||||
\(758\) | 379.125 | − | 1330.63i | 0.500165 | − | 1.75545i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 232.660 | + | 646.598i | 0.306132 | + | 0.850787i | ||||
\(761\) | 272.267 | + | 272.267i | 0.357775 | + | 0.357775i | 0.862992 | − | 0.505217i | \(-0.168588\pi\) |
−0.505217 | + | 0.862992i | \(0.668588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 189.591 | − | 457.714i | 0.248482 | − | 0.599888i | ||||
\(764\) | −207.582 | − | 885.499i | −0.271704 | − | 1.15903i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −50.0238 | − | 432.567i | −0.0653053 | − | 0.564709i | ||||
\(767\) | − | 6.82730i | − | 0.00890130i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −341.927 | −0.444638 | −0.222319 | − | 0.974974i | \(-0.571363\pi\) | ||||
−0.222319 | + | 0.974974i | \(0.571363\pi\) | |||||||
\(770\) | −771.767 | + | 89.2503i | −1.00229 | + | 0.115909i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −180.921 | + | 42.4121i | −0.234354 | + | 0.0549380i | ||||
\(773\) | 366.728 | + | 151.904i | 0.474421 | + | 0.196512i | 0.607065 | − | 0.794652i | \(-0.292347\pi\) |
−0.132644 | + | 0.991164i | \(0.542347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 124.732 | − | 124.732i | 0.160944 | − | 0.160944i | ||||
\(776\) | 503.736 | − | 181.255i | 0.649144 | − | 0.233576i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −941.874 | − | 268.360i | −1.21063 | − | 0.344936i | ||||
\(779\) | 964.582 | + | 399.543i | 1.23823 | + | 0.512892i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −358.065 | + | 148.315i | −0.458470 | + | 0.189904i | ||||
\(782\) | −36.2105 | + | 45.6807i | −0.0463050 | + | 0.0584153i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 128.557 | + | 259.131i | 0.163976 | + | 0.330524i | ||||
\(785\) | − | 374.109i | − | 0.476572i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 167.684 | + | 404.824i | 0.213067 | + | 0.514389i | 0.993892 | − | 0.110361i | \(-0.0352008\pi\) |
−0.780825 | + | 0.624750i | \(0.785201\pi\) | |||||||
\(788\) | 796.793 | + | 130.577i | 1.01116 | + | 0.165706i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1257.11 | + | 358.179i | 1.59128 | + | 0.453391i | ||||
\(791\) | 38.9881 | + | 38.9881i | 0.0492896 | + | 0.0492896i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8662 | + | 12.8662i | 0.0162247 | + | 0.0162247i | ||||
\(794\) | −533.138 | + | 296.699i | −0.671458 | + | 0.373677i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 162.508 | − | 262.029i | 0.204155 | − | 0.329182i | ||||
\(797\) | 230.548 | + | 556.591i | 0.289269 | + | 0.698358i | 0.999987 | − | 0.00511971i | \(-0.00162966\pi\) |
−0.710718 | + | 0.703477i | \(0.751630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1651.61i | 2.06710i | ||||||||
\(800\) | −139.120 | − | 29.6140i | −0.173901 | − | 0.0370175i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39.9350 | − | 345.327i | −0.0497943 | − | 0.430582i | ||||
\(803\) | 258.320 | − | 106.999i | 0.321693 | − | 0.133250i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.5559 | + | 10.5856i | 0.0317465 | + | 0.0131498i | ||||
\(806\) | 19.0056 | + | 34.1511i | 0.0235802 | + | 0.0423711i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −202.136 | − | 9.56840i | −0.250168 | − | 0.0118421i | ||||
\(809\) | −195.031 | + | 195.031i | −0.241077 | + | 0.241077i | −0.817296 | − | 0.576219i | \(-0.804528\pi\) |
0.576219 | + | 0.817296i | \(0.304528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −889.956 | − | 368.632i | −1.09736 | − | 0.454540i | −0.240791 | − | 0.970577i | \(-0.577407\pi\) |
−0.856566 | + | 0.516037i | \(0.827407\pi\) | |||||||
\(812\) | 1031.90 | + | 169.106i | 1.27082 | + | 0.208259i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 953.347 | + | 755.705i | 1.17119 | + | 0.928385i | ||||
\(815\) | 945.435 | 1.16004 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 293.046i | 0.358686i | ||||||||
\(818\) | 713.863 | + | 565.870i | 0.872693 | + | 0.691772i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 811.631 | − | 583.071i | 0.989794 | − | 0.711062i | ||||
\(821\) | −328.443 | + | 792.932i | −0.400052 | + | 0.965812i | 0.587600 | + | 0.809151i | \(0.300073\pi\) |
−0.987653 | + | 0.156660i | \(0.949927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −319.915 | − | 319.915i | −0.388718 | − | 0.388718i | 0.485512 | − | 0.874230i | \(-0.338633\pi\) |
−0.874230 | + | 0.485512i | \(0.838633\pi\) | |||||||
\(824\) | −74.9128 | + | 159.125i | −0.0909136 | + | 0.193112i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −74.9824 | − | 134.736i | −0.0907777 | − | 0.163118i | ||||
\(827\) | 352.335 | − | 850.612i | 0.426040 | − | 1.02855i | −0.554492 | − | 0.832189i | \(-0.687087\pi\) |
0.980532 | − | 0.196362i | \(-0.0629127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −459.660 | − | 1109.72i | −0.554475 | − | 1.33862i | −0.914086 | − | 0.405519i | \(-0.867091\pi\) |
0.359611 | − | 0.933102i | \(-0.382909\pi\) | |||||||
\(830\) | −29.9139 | − | 258.672i | −0.0360408 | − | 0.311653i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.7566 | − | 27.8464i | 0.0177363 | − | 0.0334693i | ||||
\(833\) | 480.248 | 0.576528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 454.600 | − | 188.302i | 0.544432 | − | 0.225511i | ||||
\(836\) | −266.515 | − | 1136.90i | −0.318798 | − | 1.35993i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.4638 | + | 14.7275i | −0.0315798 | + | 0.0175746i | ||||
\(839\) | −439.790 | + | 439.790i | −0.524184 | + | 0.524184i | −0.918832 | − | 0.394648i | \(-0.870866\pi\) |
0.394648 | + | 0.918832i | \(0.370866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −968.120 | + | 968.120i | −1.15115 | + | 1.15115i | ||||
\(842\) | −1057.38 | − | 301.269i | −1.25579 | − | 0.357801i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 213.804 | + | 297.613i | 0.253322 | + | 0.352623i | ||||
\(845\) | 706.868 | − | 292.794i | 0.836530 | − | 0.346502i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 647.356 | 0.764293 | ||||||||
\(848\) | 32.5853 | + | 479.649i | 0.0384260 | + | 0.565624i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −146.692 | + | 185.057i | −0.172579 | + | 0.217714i | ||||
\(851\) | −16.5756 | − | 40.0171i | −0.0194778 | − | 0.0470236i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 639.942 | − | 1544.96i | 0.750225 | − | 1.81120i | 0.192248 | − | 0.981346i | \(-0.438422\pi\) |
0.557977 | − | 0.829857i | \(-0.311578\pi\) | |||||||
\(854\) | 395.218 | + | 112.606i | 0.462785 | + | 0.131857i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −926.007 | − | 43.8340i | −1.08178 | − | 0.0512080i | ||||
\(857\) | 628.373 | + | 628.373i | 0.733224 | + | 0.733224i | 0.971257 | − | 0.238033i | \(-0.0765026\pi\) |
−0.238033 | + | 0.971257i | \(0.576503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −467.557 | + | 1128.78i | −0.544304 | + | 1.31407i | 0.377357 | + | 0.926068i | \(0.376833\pi\) |
−0.921660 | + | 0.387998i | \(0.873167\pi\) | |||||||
\(860\) | 238.378 | + | 147.840i | 0.277184 | + | 0.171906i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1300.80 | + | 150.430i | −1.50905 | + | 0.174512i | ||||
\(863\) | − | 709.297i | − | 0.821896i | −0.911659 | − | 0.410948i | \(-0.865198\pi\) | ||
0.911659 | − | 0.410948i | \(-0.134802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 225.762 | 0.260997 | ||||||||
\(866\) | 84.2030 | + | 728.123i | 0.0972321 | + | 0.840788i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 750.146 | + | 465.233i | 0.864223 | + | 0.535982i | ||||
\(869\) | −2052.14 | − | 850.023i | −2.36149 | − | 0.978162i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.84629 | − | 9.84629i | 0.0113046 | − | 0.0113046i | ||||
\(872\) | 527.265 | − | 479.604i | 0.604662 | − | 0.550004i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.3925 | + | 39.9848i | −0.0130349 | + | 0.0457492i | ||||
\(875\) | 685.820 | + | 284.076i | 0.783795 | + | 0.324658i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 927.972 | − | 384.378i | 1.05812 | − | 0.438288i | 0.215337 | − | 0.976540i | \(-0.430915\pi\) |
0.842784 | + | 0.538252i | \(0.180915\pi\) | |||||||
\(878\) | 275.931 | + | 218.727i | 0.314272 | + | 0.249119i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1059.26 | − | 356.760i | −1.20371 | − | 0.405409i | ||||
\(881\) | − | 660.780i | − | 0.750034i | −0.927018 | − | 0.375017i | \(-0.877637\pi\) | ||
0.927018 | − | 0.375017i | \(-0.122363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −476.753 | − | 1150.98i | −0.539924 | − | 1.30349i | −0.924775 | − | 0.380514i | \(-0.875747\pi\) |
0.384851 | − | 0.922979i | \(-0.374253\pi\) | |||||||
\(884\) | −30.5267 | − | 42.4930i | −0.0345325 | − | 0.0480690i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −211.202 | + | 741.264i | −0.238377 | + | 0.836641i | ||||
\(887\) | −248.725 | − | 248.725i | −0.280411 | − | 0.280411i | 0.552862 | − | 0.833273i | \(-0.313536\pi\) |
−0.833273 | + | 0.552862i | \(0.813536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −233.595 | − | 233.595i | −0.262762 | − | 0.262762i | ||||
\(890\) | −36.9328 | − | 66.3644i | −0.0414975 | − | 0.0745667i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −390.864 | − | 1667.34i | −0.438189 | − | 1.86922i | ||||
\(893\) | 450.800 | + | 1088.33i | 0.504815 | + | 1.21873i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 349.257i | − | 0.390232i | ||||||
\(896\) | −14.6115 | − | 711.613i | −0.0163075 | − | 0.794210i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1369.52 | − | 158.377i | 1.52508 | − | 0.176367i | ||||
\(899\) | −1723.66 | + | 713.964i | −1.91731 | + | 0.794176i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 737.403 | + | 305.442i | 0.818427 | + | 0.339004i | ||||
\(902\) | −1483.89 | + | 825.806i | −1.64511 | + | 0.915527i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.8573 | + | 74.6404i | 0.0297094 | + | 0.0825668i | ||||
\(905\) | −391.540 | + | 391.540i | −0.432641 | + | 0.432641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 301.032 | + | 124.692i | 0.331899 | + | 0.137477i | 0.542409 | − | 0.840115i | \(-0.317512\pi\) |
−0.210510 | + | 0.977592i | \(0.567512\pi\) | |||||||
\(908\) | 394.509 | − | 283.413i | 0.434481 | − | 0.312129i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.4233 | + | 19.4570i | −0.0169486 | + | 0.0213813i | ||||
\(911\) | −1283.61 | −1.40901 | −0.704507 | − | 0.709697i | \(-0.748832\pi\) | ||||
−0.704507 | + | 0.709697i | \(0.748832\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 442.488i | 0.484652i | ||||||||
\(914\) | 151.893 | − | 191.618i | 0.166185 | − | 0.209648i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 547.032 | + | 89.6463i | 0.597196 | + | 0.0978672i | ||||
\(917\) | 406.361 | − | 981.043i | 0.443142 | − | 1.06984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 299.609 | + | 299.609i | 0.326017 | + | 0.326017i | 0.851070 | − | 0.525053i | \(-0.175954\pi\) |
−0.525053 | + | 0.851070i | \(0.675954\pi\) | |||||||
\(920\) | 26.7781 | + | 29.4392i | 0.0291066 | + | 0.0319992i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.27211 | − | 3.49053i | 0.00680272 | − | 0.00378582i | ||||
\(923\) | −4.73985 | + | 11.4430i | −0.00513526 | + | 0.0123976i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −67.1494 | − | 162.113i | −0.0725940 | − | 0.175257i | ||||
\(926\) | 224.517 | − | 25.9641i | 0.242459 | − | 0.0280390i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1239.55 | + | 852.459i | 1.33572 | + | 0.918598i | ||||
\(929\) | −166.333 | −0.179045 | −0.0895225 | − | 0.995985i | \(-0.528534\pi\) | ||||
−0.0895225 | + | 0.995985i | \(0.528534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 316.459 | − | 131.082i | 0.339913 | − | 0.140797i | ||||
\(932\) | 270.135 | − | 435.568i | 0.289844 | − | 0.467347i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 382.237 | + | 686.840i | 0.409247 | + | 0.735374i | ||||
\(935\) | −1312.16 | + | 1312.16i | −1.40338 | + | 1.40338i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 919.394 | − | 919.394i | 0.981211 | − | 0.981211i | −0.0186162 | − | 0.999827i | \(-0.505926\pi\) |
0.999827 | + | 0.0186162i | \(0.00592605\pi\) | |||||||
\(938\) | 86.1756 | − | 302.454i | 0.0918717 | − | 0.322446i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1112.72 | + | 182.350i | 1.18375 | + | 0.193990i | ||||
\(941\) | −540.855 | + | 224.029i | −0.574766 | + | 0.238076i | −0.651082 | − | 0.759008i | \(-0.725684\pi\) |
0.0763153 | + | 0.997084i | \(0.475684\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.4635 | 0.0641182 | ||||||||
\(944\) | −15.0360 | − | 221.327i | −0.0159279 | − | 0.234457i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −373.531 | − | 296.093i | −0.394853 | − | 0.312995i | ||||
\(947\) | 149.824 | + | 361.708i | 0.158209 | + | 0.381951i | 0.983030 | − | 0.183443i | \(-0.0587241\pi\) |
−0.824821 | + | 0.565394i | \(0.808724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.41948 | − | 8.25535i | 0.00360324 | − | 0.00869900i | ||||
\(950\) | −46.1522 | + | 161.982i | −0.0485813 | + | 0.170508i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1069.13 | − | 503.326i | −1.12303 | − | 0.528703i | ||||
\(953\) | 400.363 | + | 400.363i | 0.420108 | + | 0.420108i | 0.885241 | − | 0.465133i | \(-0.153994\pi\) |
−0.465133 | + | 0.885241i | \(0.653994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −394.498 | + | 952.401i | −0.413086 | + | 0.997279i | ||||
\(956\) | −1105.14 | + | 259.071i | −1.15601 | + | 0.270995i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −47.2436 | − | 408.526i | −0.0493148 | − | 0.426436i | ||||
\(959\) | − | 1090.81i | − | 1.13744i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −613.912 | −0.638827 | ||||||||
\(962\) | 38.6205 | − | 4.46623i | 0.0401461 | − | 0.00464265i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −282.541 | − | 1205.26i | −0.293092 | − | 1.25027i | ||||
\(965\) | 194.590 | + | 80.6020i | 0.201648 | + | 0.0835254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −450.402 | + | 450.402i | −0.465772 | + | 0.465772i | −0.900542 | − | 0.434770i | \(-0.856830\pi\) |
0.434770 | + | 0.900542i | \(0.356830\pi\) | |||||||
\(968\) | 842.631 | + | 396.695i | 0.870487 | + | 0.409809i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −583.568 | − | 166.271i | −0.601616 | − | 0.171413i | ||||
\(971\) | −1287.15 | − | 533.155i | −1.32559 | − | 0.549079i | −0.396198 | − | 0.918165i | \(-0.629671\pi\) |
−0.929395 | + | 0.369086i | \(0.879671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −354.581 | + | 146.872i | −0.364421 | + | 0.150948i | ||||
\(974\) | 1007.20 | − | 1270.62i | 1.03409 | − | 1.30453i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 445.431 | + | 388.760i | 0.456385 | + | 0.398320i | ||||
\(977\) | 1408.92i | 1.44208i | 0.692891 | + | 0.721042i | \(0.256336\pi\) | ||||
−0.692891 | + | 0.721042i | \(0.743664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.3888 | + | 119.235i | 0.0504482 | + | 0.121793i | ||||
\(980\) | 53.0230 | − | 323.553i | 0.0541051 | − | 0.330156i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −876.732 | − | 249.800i | −0.892802 | − | 0.254378i | ||||
\(983\) | 748.725 | + | 748.725i | 0.761674 | + | 0.761674i | 0.976625 | − | 0.214951i | \(-0.0689592\pi\) |
−0.214951 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −647.120 | − | 647.120i | −0.656975 | − | 0.656975i | ||||
\(986\) | 2182.41 | − | 1214.55i | 2.21340 | − | 1.23179i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.7138 | − | 19.6686i | −0.0320990 | − | 0.0199075i | ||||
\(989\) | 6.49449 | + | 15.6791i | 0.00656673 | + | 0.0158535i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1179.74i | − | 1.19045i | −0.803559 | − | 0.595225i | \(-0.797063\pi\) | ||
0.803559 | − | 0.595225i | \(-0.202937\pi\) | |||||||
\(992\) | 691.336 | + | 1065.25i | 0.696911 | + | 1.07384i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.1354 | + | 277.882i | 0.0323294 | + | 0.279559i | ||||
\(995\) | −322.873 | + | 133.738i | −0.324496 | + | 0.134411i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1523.14 | + | 630.907i | 1.52773 | + | 0.632805i | 0.979121 | − | 0.203276i | \(-0.0651588\pi\) |
0.548606 | + | 0.836081i | \(0.315159\pi\) | |||||||
\(998\) | 293.030 | + | 526.545i | 0.293618 | + | 0.527600i | ||||
\(999\) | 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 | 288.3.u.a.91.7 | 28 | ||
3.2 | odd | 2 | 32.3.h.a.27.1 | yes | 28 | ||
12.11 | even | 2 | 128.3.h.a.15.3 | 28 | |||
24.5 | odd | 2 | 256.3.h.b.31.3 | 28 | |||
24.11 | even | 2 | 256.3.h.a.31.5 | 28 | |||
32.19 | odd | 8 | inner | 288.3.u.a.19.7 | 28 | ||
96.29 | odd | 8 | 256.3.h.a.223.5 | 28 | |||
96.35 | even | 8 | 256.3.h.b.223.3 | 28 | |||
96.77 | odd | 8 | 128.3.h.a.111.3 | 28 | |||
96.83 | even | 8 | 32.3.h.a.19.1 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.1 | ✓ | 28 | 96.83 | even | 8 | ||
32.3.h.a.27.1 | yes | 28 | 3.2 | odd | 2 | ||
128.3.h.a.15.3 | 28 | 12.11 | even | 2 | |||
128.3.h.a.111.3 | 28 | 96.77 | odd | 8 | |||
256.3.h.a.31.5 | 28 | 24.11 | even | 2 | |||
256.3.h.a.223.5 | 28 | 96.29 | odd | 8 | |||
256.3.h.b.31.3 | 28 | 24.5 | odd | 2 | |||
256.3.h.b.223.3 | 28 | 96.35 | even | 8 | |||
288.3.u.a.19.7 | 28 | 32.19 | odd | 8 | inner | ||
288.3.u.a.91.7 | 28 | 1.1 | even | 1 | trivial |