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 | 91.6 | ||
Character | \(\chi\) | \(=\) | 288.91 |
Dual form | 288.3.u.a.19.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.62478 | + | 1.16623i | 0.812389 | + | 0.583116i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.27980 | + | 3.78974i | 0.319951 | + | 0.947434i | ||||
\(5\) | 4.51028 | + | 1.86822i | 0.902055 | + | 0.373644i | 0.785010 | − | 0.619483i | \(-0.212658\pi\) |
0.117045 | + | 0.993127i | \(0.462658\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.85317 | + | 3.85317i | −0.550453 | + | 0.550453i | −0.926571 | − | 0.376119i | \(-0.877258\pi\) |
0.376119 | + | 0.926571i | \(0.377258\pi\) | |||||||
\(8\) | −2.34032 | + | 7.65003i | −0.292539 | + | 0.956253i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.14942 | + | 8.29547i | 0.514942 | + | 0.829547i | ||||
\(11\) | 4.56441 | + | 1.89064i | 0.414946 | + | 0.171876i | 0.580382 | − | 0.814344i | \(-0.302903\pi\) |
−0.165436 | + | 0.986221i | \(0.552903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.58307 | + | 2.31258i | −0.429467 | + | 0.177891i | −0.586937 | − | 0.809633i | \(-0.699666\pi\) |
0.157470 | + | 0.987524i | \(0.449666\pi\) | |||||||
\(14\) | −10.7542 | + | 1.76685i | −0.768159 | + | 0.126204i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.7242 | + | 9.70024i | −0.795263 | + | 0.606265i | ||||
\(17\) | − | 25.0539i | − | 1.47376i | −0.676025 | − | 0.736879i | \(-0.736299\pi\) | ||
0.676025 | − | 0.736879i | \(-0.263701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.43433 | + | 15.5338i | 0.338649 | + | 0.817571i | 0.997846 | + | 0.0656005i | \(0.0208963\pi\) |
−0.659197 | + | 0.751970i | \(0.729104\pi\) | |||||||
\(20\) | −1.30778 | + | 19.4837i | −0.0653891 | + | 0.974186i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.21122 | + | 8.39503i | 0.236874 | + | 0.381592i | ||||
\(23\) | 26.9024 | + | 26.9024i | 1.16967 | + | 1.16967i | 0.982287 | + | 0.187381i | \(0.0600000\pi\) |
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.825315 | − | 0.825315i | −0.0330126 | − | 0.0330126i | ||||
\(26\) | −11.7682 | − | 2.75372i | −0.452625 | − | 0.105912i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −19.5338 | − | 9.67119i | −0.697636 | − | 0.345400i | ||||
\(29\) | 0.210028 | + | 0.507052i | 0.00724234 | + | 0.0174846i | 0.927459 | − | 0.373924i | \(-0.121988\pi\) |
−0.920217 | + | 0.391409i | \(0.871988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 15.8372i | − | 0.510877i | −0.966825 | − | 0.255438i | \(-0.917780\pi\) | ||
0.966825 | − | 0.255438i | \(-0.0822198\pi\) | |||||||
\(32\) | −31.9867 | + | 0.921357i | −0.999585 | + | 0.0287924i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 29.2186 | − | 40.7070i | 0.859372 | − | 1.19726i | ||||
\(35\) | −24.5774 | + | 10.1803i | −0.702212 | + | 0.290866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.18606 | − | 0.905498i | −0.0590828 | − | 0.0244729i | 0.352946 | − | 0.935644i | \(-0.385180\pi\) |
−0.412029 | + | 0.911171i | \(0.635180\pi\) | |||||||
\(38\) | −7.66172 | + | 32.7430i | −0.201624 | + | 0.861657i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −24.8474 | + | 30.1315i | −0.621185 | + | 0.753288i | ||||
\(41\) | 31.1517 | − | 31.1517i | 0.759798 | − | 0.759798i | −0.216488 | − | 0.976285i | \(-0.569460\pi\) |
0.976285 | + | 0.216488i | \(0.0694601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9078 | + | 5.34659i | 0.300182 | + | 0.124339i | 0.527691 | − | 0.849437i | \(-0.323058\pi\) |
−0.227509 | + | 0.973776i | \(0.573058\pi\) | |||||||
\(44\) | −1.32348 | + | 19.7175i | −0.0300790 | + | 0.448126i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.3360 | + | 75.0848i | 0.268173 | + | 1.63228i | ||||
\(47\) | −15.0033 | −0.319220 | −0.159610 | − | 0.987180i | \(-0.551024\pi\) | ||||
−0.159610 | + | 0.987180i | \(0.551024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.3062i | 0.394004i | ||||||||
\(50\) | −0.378444 | − | 2.30346i | −0.00756888 | − | 0.0460692i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.9093 | − | 18.1987i | −0.305948 | − | 0.349975i | ||||
\(53\) | 15.4409 | − | 37.2776i | 0.291338 | − | 0.703352i | −0.708660 | − | 0.705550i | \(-0.750700\pi\) |
0.999998 | + | 0.00219873i | \(0.000699877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.0546 | + | 17.0546i | 0.310084 | + | 0.310084i | ||||
\(56\) | −20.4592 | − | 38.4945i | −0.365343 | − | 0.687401i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.250092 | + | 1.06879i | −0.00431193 | + | 0.0184274i | ||||
\(59\) | 14.7242 | − | 35.5473i | 0.249562 | − | 0.602496i | −0.748605 | − | 0.663016i | \(-0.769276\pi\) |
0.998167 | + | 0.0605202i | \(0.0192760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.4603 | − | 37.3243i | −0.253447 | − | 0.611875i | 0.745031 | − | 0.667030i | \(-0.232435\pi\) |
−0.998478 | + | 0.0551552i | \(0.982435\pi\) | |||||||
\(62\) | 18.4698 | − | 25.7319i | 0.297900 | − | 0.415030i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −53.0458 | − | 35.8070i | −0.828841 | − | 0.559484i | ||||
\(65\) | −29.5016 | −0.453870 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.3598 | − | 25.4161i | 0.915818 | − | 0.379344i | 0.125537 | − | 0.992089i | \(-0.459935\pi\) |
0.790281 | + | 0.612745i | \(0.209935\pi\) | |||||||
\(68\) | 94.9476 | − | 32.0641i | 1.39629 | − | 0.471530i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −51.8054 | − | 12.1223i | −0.740077 | − | 0.173175i | ||||
\(71\) | 51.7789 | − | 51.7789i | 0.729281 | − | 0.729281i | −0.241196 | − | 0.970477i | \(-0.577540\pi\) |
0.970477 | + | 0.241196i | \(0.0775395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 64.9440 | − | 64.9440i | 0.889643 | − | 0.889643i | −0.104845 | − | 0.994489i | \(-0.533435\pi\) |
0.994489 | + | 0.104845i | \(0.0334347\pi\) | |||||||
\(74\) | −2.49585 | − | 4.02069i | −0.0337277 | − | 0.0543337i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −50.6345 | + | 44.2647i | −0.666243 | + | 0.582430i | ||||
\(77\) | −24.8724 | + | 10.3025i | −0.323018 | + | 0.133798i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38.1202 | −0.482535 | −0.241267 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(80\) | −75.5118 | + | 19.9792i | −0.943898 | + | 0.249740i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 86.9447 | − | 14.2845i | 1.06030 | − | 0.174201i | ||||
\(83\) | −15.9782 | − | 38.5748i | −0.192509 | − | 0.464757i | 0.797923 | − | 0.602759i | \(-0.205932\pi\) |
−0.990432 | + | 0.138002i | \(0.955932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46.8061 | − | 113.000i | 0.550660 | − | 1.32941i | ||||
\(86\) | 14.7370 | + | 23.7405i | 0.171360 | + | 0.276053i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −25.1456 | + | 30.4932i | −0.285745 | + | 0.346513i | ||||
\(89\) | −23.7666 | − | 23.7666i | −0.267040 | − | 0.267040i | 0.560866 | − | 0.827906i | \(-0.310468\pi\) |
−0.827906 | + | 0.560866i | \(0.810468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6017 | − | 30.4233i | 0.138481 | − | 0.334322i | ||||
\(92\) | −67.5231 | + | 136.383i | −0.733947 | + | 1.48242i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.3771 | − | 17.4974i | −0.259331 | − | 0.186142i | ||||
\(95\) | 82.0827i | 0.864028i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −118.710 | −1.22382 | −0.611908 | − | 0.790929i | \(-0.709598\pi\) | ||||
−0.611908 | + | 0.790929i | \(0.709598\pi\) | |||||||
\(98\) | −22.5155 | + | 31.3682i | −0.229750 | + | 0.320084i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.07148 | − | 4.18397i | 0.0207148 | − | 0.0418397i | ||||
\(101\) | 182.236 | + | 75.4846i | 1.80432 | + | 0.747372i | 0.984652 | + | 0.174529i | \(0.0558402\pi\) |
0.819665 | + | 0.572844i | \(0.194160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −80.3171 | + | 80.3171i | −0.779777 | + | 0.779777i | −0.979793 | − | 0.200016i | \(-0.935901\pi\) |
0.200016 | + | 0.979793i | \(0.435901\pi\) | |||||||
\(104\) | −4.62518 | − | 48.1228i | −0.0444728 | − | 0.462719i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 68.5624 | − | 42.5602i | 0.646815 | − | 0.401511i | ||||
\(107\) | −22.6854 | − | 9.39659i | −0.212013 | − | 0.0878186i | 0.274150 | − | 0.961687i | \(-0.411604\pi\) |
−0.486162 | + | 0.873868i | \(0.661604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 181.428 | − | 75.1501i | 1.66448 | − | 0.689450i | 0.666074 | − | 0.745886i | \(-0.267974\pi\) |
0.998406 | + | 0.0564360i | \(0.0179737\pi\) | |||||||
\(110\) | 7.82031 | + | 47.5996i | 0.0710937 | + | 0.432724i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.6518 | − | 86.4052i | 0.104034 | − | 0.771475i | ||||
\(113\) | − | 32.7876i | − | 0.290156i | −0.989420 | − | 0.145078i | \(-0.953657\pi\) | ||
0.989420 | − | 0.145078i | \(-0.0463433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 71.0777 | + | 171.597i | 0.618067 | + | 1.49214i | ||||
\(116\) | −1.65280 | + | 1.44488i | −0.0142483 | + | 0.0124558i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 65.3799 | − | 40.5846i | 0.554067 | − | 0.343937i | ||||
\(119\) | 96.5368 | + | 96.5368i | 0.811234 | + | 0.811234i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −68.3006 | − | 68.3006i | −0.564468 | − | 0.564468i | ||||
\(122\) | 18.4094 | − | 78.6740i | 0.150897 | − | 0.644869i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 60.0187 | − | 20.2685i | 0.484022 | − | 0.163456i | ||||
\(125\) | −48.8860 | − | 118.021i | −0.391088 | − | 0.944169i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 130.165i | 1.02492i | 0.858710 | + | 0.512462i | \(0.171266\pi\) | ||||
−0.858710 | + | 0.512462i | \(0.828734\pi\) | |||||||
\(128\) | −44.4285 | − | 120.042i | −0.347097 | − | 0.937829i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −47.9335 | − | 34.4057i | −0.368719 | − | 0.264659i | ||||
\(131\) | −24.3356 | + | 10.0801i | −0.185768 | + | 0.0769476i | −0.473628 | − | 0.880725i | \(-0.657056\pi\) |
0.287861 | + | 0.957672i | \(0.407056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −84.6471 | − | 35.0620i | −0.636444 | − | 0.263624i | ||||
\(134\) | 129.337 | + | 30.2643i | 0.965202 | + | 0.225853i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 191.663 | + | 58.6340i | 1.40929 | + | 0.431132i | ||||
\(137\) | −147.886 | + | 147.886i | −1.07946 | + | 1.07946i | −0.0829047 | + | 0.996557i | \(0.526420\pi\) |
−0.996557 | + | 0.0829047i | \(0.973580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −206.929 | − | 85.7129i | −1.48870 | − | 0.616639i | −0.517666 | − | 0.855583i | \(-0.673199\pi\) |
−0.971033 | + | 0.238944i | \(0.923199\pi\) | |||||||
\(140\) | −70.0349 | − | 80.1131i | −0.500249 | − | 0.572237i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 144.516 | − | 23.7430i | 1.01772 | − | 0.167204i | ||||
\(143\) | −29.8556 | −0.208781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.67932i | 0.0184781i | ||||||||
\(146\) | 181.259 | − | 29.7797i | 1.24150 | − | 0.203971i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.633863 | − | 9.44347i | 0.00428286 | − | 0.0638072i | ||||
\(149\) | 20.4247 | − | 49.3095i | 0.137078 | − | 0.330936i | −0.840402 | − | 0.541964i | \(-0.817681\pi\) |
0.977480 | + | 0.211028i | \(0.0676810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 180.137 | + | 180.137i | 1.19296 | + | 1.19296i | 0.976232 | + | 0.216726i | \(0.0695379\pi\) |
0.216726 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(152\) | −133.893 | + | 12.8687i | −0.880873 | + | 0.0846624i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −52.4272 | − | 12.2677i | −0.340436 | − | 0.0796607i | ||||
\(155\) | 29.5873 | − | 71.4300i | 0.190886 | − | 0.460839i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −60.3999 | − | 145.818i | −0.384713 | − | 0.928779i | −0.991040 | − | 0.133564i | \(-0.957358\pi\) |
0.606327 | − | 0.795215i | \(-0.292642\pi\) | |||||||
\(158\) | −61.9369 | − | 44.4571i | −0.392006 | − | 0.281374i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −145.990 | − | 55.6026i | −0.912439 | − | 0.347516i | ||||
\(161\) | −207.319 | −1.28769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −152.162 | + | 63.0277i | −0.933512 | + | 0.386673i | −0.797010 | − | 0.603966i | \(-0.793586\pi\) |
−0.136502 | + | 0.990640i | \(0.543586\pi\) | |||||||
\(164\) | 157.925 | + | 78.1887i | 0.962956 | + | 0.476760i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.0262 | − | 81.3099i | 0.114615 | − | 0.489818i | ||||
\(167\) | −94.8188 | + | 94.8188i | −0.567777 | + | 0.567777i | −0.931505 | − | 0.363728i | \(-0.881504\pi\) |
0.363728 | + | 0.931505i | \(0.381504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −93.6785 | + | 93.6785i | −0.554310 | + | 0.554310i | ||||
\(170\) | 207.834 | − | 129.013i | 1.22255 | − | 0.758900i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.74270 | + | 55.7598i | −0.0217599 | + | 0.324185i | ||||
\(173\) | 107.416 | − | 44.4930i | 0.620900 | − | 0.257185i | −0.0499813 | − | 0.998750i | \(-0.515916\pi\) |
0.670881 | + | 0.741565i | \(0.265916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.36016 | 0.0363437 | ||||||||
\(176\) | −76.4181 | + | 20.2190i | −0.434194 | + | 0.114881i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.8981 | − | 66.3328i | −0.0612250 | − | 0.372656i | ||||
\(179\) | −54.7154 | − | 132.095i | −0.305673 | − | 0.737959i | −0.999835 | − | 0.0181410i | \(-0.994225\pi\) |
0.694163 | − | 0.719818i | \(-0.255775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −128.496 | + | 310.218i | −0.709925 | + | 1.71391i | −0.00973575 | + | 0.999953i | \(0.503099\pi\) |
−0.700189 | + | 0.713957i | \(0.746901\pi\) | |||||||
\(182\) | 55.9556 | − | 34.7345i | 0.307448 | − | 0.190849i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −268.764 | + | 142.844i | −1.46067 | + | 0.776325i | ||||
\(185\) | −8.16809 | − | 8.16809i | −0.0441518 | − | 0.0441518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 47.3678 | − | 114.356i | 0.253304 | − | 0.611530i | ||||
\(188\) | −19.2013 | − | 56.8587i | −0.102135 | − | 0.302440i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −95.7274 | + | 133.366i | −0.503829 | + | 0.701927i | ||||
\(191\) | 312.806i | 1.63773i | 0.573986 | + | 0.818865i | \(0.305396\pi\) | ||||
−0.573986 | + | 0.818865i | \(0.694604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −70.6708 | −0.366170 | −0.183085 | − | 0.983097i | \(-0.558608\pi\) | ||||
−0.183085 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(194\) | −192.878 | − | 138.444i | −0.994215 | − | 0.713627i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −73.1653 | + | 24.7081i | −0.373292 | + | 0.126062i | ||||
\(197\) | −81.5762 | − | 33.7900i | −0.414092 | − | 0.171523i | 0.165904 | − | 0.986142i | \(-0.446946\pi\) |
−0.579996 | + | 0.814619i | \(0.696946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.666 | − | 102.666i | 0.515910 | − | 0.515910i | −0.400421 | − | 0.916331i | \(-0.631136\pi\) |
0.916331 | + | 0.400421i | \(0.131136\pi\) | |||||||
\(200\) | 8.24518 | − | 4.38218i | 0.0412259 | − | 0.0219109i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 208.060 | + | 335.175i | 1.03000 | + | 1.65928i | ||||
\(203\) | −2.76303 | − | 1.14449i | −0.0136110 | − | 0.00563786i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 198.701 | − | 82.3046i | 0.969273 | − | 0.401486i | ||||
\(206\) | −224.166 | + | 36.8290i | −1.08818 | + | 0.178782i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 48.6075 | − | 83.5828i | 0.233690 | − | 0.401841i | ||||
\(209\) | 83.0678i | 0.397454i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.35160 | + | 20.1625i | 0.0395810 | + | 0.0955571i | 0.942434 | − | 0.334393i | \(-0.108531\pi\) |
−0.902853 | + | 0.429950i | \(0.858531\pi\) | |||||||
\(212\) | 161.034 | + | 10.8089i | 0.759593 | + | 0.0509852i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.9001 | − | 41.7238i | −0.121028 | − | 0.194971i | ||||
\(215\) | 48.2292 | + | 48.2292i | 0.224322 | + | 0.224322i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 61.0233 | + | 61.0233i | 0.281213 | + | 0.281213i | ||||
\(218\) | 382.423 | + | 89.4854i | 1.75423 | + | 0.410484i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −42.8059 | + | 86.4591i | −0.194572 | + | 0.392996i | ||||
\(221\) | 57.9391 | + | 139.877i | 0.262168 | + | 0.632930i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 131.685i | 0.590516i | 0.955418 | + | 0.295258i | \(0.0954056\pi\) | ||||
−0.955418 | + | 0.295258i | \(0.904594\pi\) | |||||||
\(224\) | 119.700 | − | 126.800i | 0.534376 | − | 0.566073i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 38.2380 | − | 53.2726i | 0.169194 | − | 0.235719i | ||||
\(227\) | −60.7552 | + | 25.1656i | −0.267644 | + | 0.110862i | −0.512470 | − | 0.858705i | \(-0.671269\pi\) |
0.244825 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 123.210 | + | 51.0352i | 0.538035 | + | 0.222861i | 0.635118 | − | 0.772415i | \(-0.280951\pi\) |
−0.0970835 | + | 0.995276i | \(0.530951\pi\) | |||||||
\(230\) | −84.6362 | + | 361.699i | −0.367983 | + | 1.57261i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.37050 | + | 0.420057i | −0.0188383 | + | 0.00181059i | ||||
\(233\) | −110.005 | + | 110.005i | −0.472124 | + | 0.472124i | −0.902601 | − | 0.430477i | \(-0.858345\pi\) |
0.430477 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −67.6692 | − | 28.0295i | −0.287954 | − | 0.119274i | ||||
\(236\) | 153.559 | + | 10.3071i | 0.650673 | + | 0.0436743i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 44.2665 | + | 269.435i | 0.185994 | + | 1.13208i | ||||
\(239\) | −277.831 | −1.16247 | −0.581236 | − | 0.813735i | \(-0.697431\pi\) | ||||
−0.581236 | + | 0.813735i | \(0.697431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 52.0006i | − | 0.215770i | −0.994163 | − | 0.107885i | \(-0.965592\pi\) | ||
0.994163 | − | 0.107885i | \(-0.0344079\pi\) | |||||||
\(242\) | −31.3189 | − | 190.628i | −0.129417 | − | 0.787718i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 121.663 | − | 106.358i | 0.498620 | − | 0.435894i | ||||
\(245\) | −36.0681 | + | 87.0762i | −0.147217 | + | 0.355413i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −71.8466 | − | 71.8466i | −0.290877 | − | 0.290877i | ||||
\(248\) | 121.155 | + | 37.0640i | 0.488528 | + | 0.149452i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 58.2113 | − | 248.771i | 0.232845 | − | 0.995082i | ||||
\(251\) | −28.7912 | + | 69.5080i | −0.114706 | + | 0.276924i | −0.970798 | − | 0.239899i | \(-0.922886\pi\) |
0.856092 | + | 0.516823i | \(0.172886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 71.9307 | + | 173.656i | 0.284311 | + | 0.686388i | ||||
\(254\) | −151.803 | + | 211.490i | −0.597650 | + | 0.832637i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 67.8107 | − | 246.856i | 0.264885 | − | 0.964280i | ||||
\(257\) | −241.501 | −0.939692 | −0.469846 | − | 0.882748i | \(-0.655691\pi\) | ||||
−0.469846 | + | 0.882748i | \(0.655691\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9123 | − | 4.93424i | 0.0459935 | − | 0.0190511i | ||||
\(260\) | −37.7562 | − | 111.803i | −0.145216 | − | 0.430012i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −51.2957 | − | 12.0030i | −0.195785 | − | 0.0458129i | ||||
\(263\) | 118.637 | − | 118.637i | 0.451090 | − | 0.451090i | −0.444626 | − | 0.895716i | \(-0.646664\pi\) |
0.895716 | + | 0.444626i | \(0.146664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 139.285 | − | 139.285i | 0.525606 | − | 0.525606i | ||||
\(266\) | −96.6423 | − | 155.686i | −0.363317 | − | 0.585286i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 174.849 | + | 200.010i | 0.652420 | + | 0.746305i | ||||
\(269\) | 231.194 | − | 95.7638i | 0.859459 | − | 0.355999i | 0.0909629 | − | 0.995854i | \(-0.471006\pi\) |
0.768496 | + | 0.639855i | \(0.221006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.13724 | −0.00788650 | −0.00394325 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394325 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(272\) | 243.029 | + | 318.791i | 0.893488 | + | 1.17202i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −412.752 | + | 67.8126i | −1.50639 | + | 0.247491i | ||||
\(275\) | −2.20670 | − | 5.32745i | −0.00802437 | − | 0.0193725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −177.679 | + | 428.955i | −0.641441 | + | 1.54857i | 0.183296 | + | 0.983058i | \(0.441323\pi\) |
−0.824737 | + | 0.565517i | \(0.808677\pi\) | |||||||
\(278\) | −236.253 | − | 380.592i | −0.849830 | − | 1.36904i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −20.3606 | − | 211.843i | −0.0727166 | − | 0.756582i | ||||
\(281\) | 261.664 | + | 261.664i | 0.931188 | + | 0.931188i | 0.997780 | − | 0.0665922i | \(-0.0212126\pi\) |
−0.0665922 | + | 0.997780i | \(0.521213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 160.904 | − | 388.456i | 0.568564 | − | 1.37264i | −0.334201 | − | 0.942502i | \(-0.608466\pi\) |
0.902765 | − | 0.430134i | \(-0.141534\pi\) | |||||||
\(284\) | 262.495 | + | 129.962i | 0.924280 | + | 0.457611i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −48.5088 | − | 34.8186i | −0.169611 | − | 0.121743i | ||||
\(287\) | 240.066i | 0.836465i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −338.697 | −1.17196 | ||||||||
\(290\) | −3.12471 | + | 4.35331i | −0.0107749 | + | 0.0150114i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 329.236 | + | 163.005i | 1.12752 | + | 0.558236i | ||||
\(293\) | 141.895 | + | 58.7749i | 0.484284 | + | 0.200597i | 0.611448 | − | 0.791285i | \(-0.290587\pi\) |
−0.127164 | + | 0.991882i | \(0.540587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 132.820 | − | 132.820i | 0.450238 | − | 0.450238i | ||||
\(296\) | 12.0432 | − | 14.6043i | 0.0406864 | − | 0.0493389i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 90.6919 | − | 56.2971i | 0.304335 | − | 0.188916i | ||||
\(299\) | −212.412 | − | 87.9838i | −0.710407 | − | 0.294260i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −70.3373 | + | 29.1347i | −0.233679 | + | 0.0967929i | ||||
\(302\) | 82.6009 | + | 502.764i | 0.273513 | + | 1.66478i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −232.554 | − | 135.241i | −0.764979 | − | 0.444872i | ||||
\(305\) | − | 197.226i | − | 0.646643i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −36.1806 | − | 87.3476i | −0.117852 | − | 0.284520i | 0.853935 | − | 0.520379i | \(-0.174209\pi\) |
−0.971787 | + | 0.235860i | \(0.924209\pi\) | |||||||
\(308\) | −70.8755 | − | 81.0746i | −0.230115 | − | 0.263229i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 131.377 | − | 81.5523i | 0.423796 | − | 0.263072i | ||||
\(311\) | −221.462 | − | 221.462i | −0.712098 | − | 0.712098i | 0.254876 | − | 0.966974i | \(-0.417965\pi\) |
−0.966974 | + | 0.254876i | \(0.917965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 280.384 | + | 280.384i | 0.895795 | + | 0.895795i | 0.995061 | − | 0.0992662i | \(-0.0316495\pi\) |
−0.0992662 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(314\) | 71.9216 | − | 307.363i | 0.229050 | − | 0.978862i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.7864 | − | 144.466i | −0.154387 | − | 0.457170i | ||||
\(317\) | −155.972 | − | 376.549i | −0.492024 | − | 1.18785i | −0.953688 | − | 0.300796i | \(-0.902748\pi\) |
0.461665 | − | 0.887055i | \(-0.347252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.71148i | 0.00849994i | ||||||||
\(320\) | −172.356 | − | 260.600i | −0.538613 | − | 0.814376i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −336.847 | − | 241.782i | −1.04611 | − | 0.750875i | ||||
\(323\) | 389.183 | − | 161.205i | 1.20490 | − | 0.499086i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.51640 | + | 2.69918i | 0.0200505 | + | 0.00830517i | ||||
\(326\) | −320.735 | − | 75.0507i | −0.983850 | − | 0.230217i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 165.407 | + | 311.216i | 0.504288 | + | 0.948830i | ||||
\(329\) | 57.8104 | − | 57.8104i | 0.175715 | − | 0.175715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −418.148 | − | 173.202i | −1.26329 | − | 0.523270i | −0.352370 | − | 0.935861i | \(-0.614624\pi\) |
−0.910917 | + | 0.412591i | \(0.864624\pi\) | |||||||
\(332\) | 125.739 | − | 109.921i | 0.378733 | − | 0.331089i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −264.640 | + | 43.4787i | −0.792336 | + | 0.130176i | ||||
\(335\) | 324.232 | 0.967857 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 38.1203i | 0.113116i | 0.998399 | + | 0.0565582i | \(0.0180127\pi\) | ||||
−0.998399 | + | 0.0565582i | \(0.981987\pi\) | |||||||
\(338\) | −261.457 | + | 42.9558i | −0.773543 | + | 0.127088i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 488.142 | + | 32.7650i | 1.43571 | + | 0.0963676i | ||||
\(341\) | 29.9424 | − | 72.2873i | 0.0878076 | − | 0.211986i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −263.195 | − | 263.195i | −0.767333 | − | 0.767333i | ||||
\(344\) | −71.1100 | + | 86.2324i | −0.206715 | + | 0.250676i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 226.416 | + | 52.9803i | 0.654381 | + | 0.153122i | ||||
\(347\) | 201.452 | − | 486.348i | 0.580553 | − | 1.40158i | −0.311760 | − | 0.950161i | \(-0.600918\pi\) |
0.892313 | − | 0.451418i | \(-0.149082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −53.2160 | − | 128.475i | −0.152481 | − | 0.368122i | 0.829118 | − | 0.559073i | \(-0.188843\pi\) |
−0.981600 | + | 0.190951i | \(0.938843\pi\) | |||||||
\(350\) | 10.3338 | + | 7.41742i | 0.0295253 | + | 0.0211926i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −147.742 | − | 56.2699i | −0.419723 | − | 0.159858i | ||||
\(353\) | 223.875 | 0.634208 | 0.317104 | − | 0.948391i | \(-0.397290\pi\) | ||||
0.317104 | + | 0.948391i | \(0.397290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 330.272 | − | 136.803i | 0.930343 | − | 0.385361i | ||||
\(356\) | 59.6525 | − | 120.486i | 0.167563 | − | 0.338443i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 65.1527 | − | 278.435i | 0.181991 | − | 0.777752i | ||||
\(359\) | 44.5652 | − | 44.5652i | 0.124137 | − | 0.124137i | −0.642309 | − | 0.766446i | \(-0.722023\pi\) |
0.766446 | + | 0.642309i | \(0.222023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.3658 | − | 55.3658i | 0.153368 | − | 0.153368i | ||||
\(362\) | −570.564 | + | 354.178i | −1.57614 | + | 0.978393i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 131.424 | + | 8.82141i | 0.361055 | + | 0.0242346i | ||||
\(365\) | 414.245 | − | 171.586i | 1.13492 | − | 0.470098i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −294.972 | −0.803739 | −0.401869 | − | 0.915697i | \(-0.631639\pi\) | ||||
−0.401869 | + | 0.915697i | \(0.631639\pi\) | |||||||
\(368\) | −603.271 | − | 81.3518i | −1.63932 | − | 0.221065i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.74544 | − | 22.7972i | −0.0101228 | − | 0.0616141i | ||||
\(371\) | 84.1406 | + | 203.133i | 0.226794 | + | 0.547529i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 96.5187 | − | 233.017i | 0.258763 | − | 0.624710i | −0.740094 | − | 0.672504i | \(-0.765219\pi\) |
0.998857 | + | 0.0477936i | \(0.0152190\pi\) | |||||||
\(374\) | 210.328 | − | 130.561i | 0.562374 | − | 0.349094i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 35.1125 | − | 114.776i | 0.0933844 | − | 0.305255i | ||||
\(377\) | −2.34520 | − | 2.34520i | −0.00622069 | − | 0.00622069i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −70.2002 | + | 169.478i | −0.185225 | + | 0.447172i | −0.989029 | − | 0.147722i | \(-0.952806\pi\) |
0.803804 | + | 0.594894i | \(0.202806\pi\) | |||||||
\(380\) | −311.072 | + | 105.050i | −0.818609 | + | 0.276447i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −364.805 | + | 508.241i | −0.954987 | + | 1.33047i | ||||
\(383\) | − | 519.043i | − | 1.35520i | −0.735429 | − | 0.677602i | \(-0.763019\pi\) | ||
0.735429 | − | 0.677602i | \(-0.236981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −131.429 | −0.341373 | ||||||||
\(386\) | −114.824 | − | 82.4186i | −0.297473 | − | 0.213520i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −151.926 | − | 449.880i | −0.391561 | − | 1.15949i | ||||
\(389\) | −52.0121 | − | 21.5441i | −0.133707 | − | 0.0553834i | 0.314827 | − | 0.949149i | \(-0.398054\pi\) |
−0.448534 | + | 0.893766i | \(0.648054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 674.009 | − | 674.009i | 1.72381 | − | 1.72381i | ||||
\(392\) | −147.693 | − | 45.1826i | −0.376767 | − | 0.115262i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −93.1362 | − | 150.038i | −0.236386 | − | 0.380807i | ||||
\(395\) | −171.933 | − | 71.2169i | −0.435273 | − | 0.180296i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 138.533 | − | 57.3823i | 0.348950 | − | 0.144540i | −0.201322 | − | 0.979525i | \(-0.564524\pi\) |
0.550272 | + | 0.834985i | \(0.314524\pi\) | |||||||
\(398\) | 286.542 | − | 47.0770i | 0.719955 | − | 0.118284i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.5072 | + | 2.49572i | 0.0462681 | + | 0.00623930i | ||||
\(401\) | − | 11.3014i | − | 0.0281830i | −0.999901 | − | 0.0140915i | \(-0.995514\pi\) | ||
0.999901 | − | 0.0140915i | \(-0.00448560\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.6248 | + | 88.4200i | 0.0908803 | + | 0.219404i | ||||
\(404\) | −52.8404 | + | 787.232i | −0.130793 | + | 1.94859i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.15458 | − | 5.08187i | −0.00776989 | − | 0.0125169i | ||||
\(407\) | −8.26612 | − | 8.26612i | −0.0203099 | − | 0.0203099i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 188.958 | + | 188.958i | 0.462001 | + | 0.462001i | 0.899311 | − | 0.437310i | \(-0.144069\pi\) |
−0.437310 | + | 0.899311i | \(0.644069\pi\) | |||||||
\(410\) | 418.831 | + | 98.0048i | 1.02154 | + | 0.239036i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −407.171 | − | 201.590i | −0.988278 | − | 0.489297i | ||||
\(413\) | 80.2350 | + | 193.704i | 0.194274 | + | 0.469018i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 203.834i | − | 0.491166i | ||||||
\(416\) | 176.453 | − | 79.1159i | 0.424167 | − | 0.190183i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −96.8763 | + | 134.967i | −0.231762 | + | 0.322887i | ||||
\(419\) | 238.026 | − | 98.5936i | 0.568081 | − | 0.235307i | −0.0801080 | − | 0.996786i | \(-0.525527\pi\) |
0.648189 | + | 0.761479i | \(0.275527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 324.923 | + | 134.588i | 0.771790 | + | 0.319686i | 0.733597 | − | 0.679585i | \(-0.237840\pi\) |
0.0381925 | + | 0.999270i | \(0.487840\pi\) | |||||||
\(422\) | −9.94472 | + | 42.4995i | −0.0235657 | + | 0.100710i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 249.038 | + | 205.365i | 0.587355 | + | 0.484351i | ||||
\(425\) | −20.6773 | + | 20.6773i | −0.0486526 | + | 0.0486526i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 203.388 | + | 84.2461i | 0.476318 | + | 0.197298i | ||||
\(428\) | 6.57776 | − | 97.9973i | 0.0153686 | − | 0.228966i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.1153 | + | 134.608i | 0.0514309 | + | 0.313042i | ||||
\(431\) | 16.1400 | 0.0374479 | 0.0187239 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187239 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 732.781i | − | 1.69233i | −0.532918 | − | 0.846167i | \(-0.678905\pi\) | ||
0.532918 | − | 0.846167i | \(-0.321095\pi\) | |||||||
\(434\) | 27.9819 | + | 170.317i | 0.0644745 | + | 0.392435i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 516.992 | + | 591.388i | 1.18576 | + | 1.35639i | ||||
\(437\) | −244.799 | + | 590.996i | −0.560180 | + | 1.35239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 460.630 | + | 460.630i | 1.04927 | + | 1.04927i | 0.998722 | + | 0.0505487i | \(0.0160970\pi\) |
0.0505487 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(440\) | −170.381 | + | 90.5551i | −0.387231 | + | 0.205807i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −68.9914 | + | 294.840i | −0.156089 | + | 0.667059i | ||||
\(443\) | 55.5453 | − | 134.098i | 0.125384 | − | 0.302705i | −0.848705 | − | 0.528866i | \(-0.822618\pi\) |
0.974090 | + | 0.226161i | \(0.0726175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −62.7927 | − | 151.595i | −0.141107 | − | 0.340663i | ||||
\(446\) | −153.575 | + | 213.959i | −0.344339 | + | 0.479728i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 342.365 | − | 66.4243i | 0.764207 | − | 0.148269i | ||||
\(449\) | −731.262 | −1.62865 | −0.814323 | − | 0.580412i | \(-0.802892\pi\) | ||||
−0.814323 | + | 0.580412i | \(0.802892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 201.086 | − | 83.2924i | 0.445866 | − | 0.184684i | ||||
\(452\) | 124.256 | − | 41.9617i | 0.274903 | − | 0.0928356i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −128.063 | − | 29.9662i | −0.282077 | − | 0.0660047i | ||||
\(455\) | 113.675 | − | 113.675i | 0.249834 | − | 0.249834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −332.873 | + | 332.873i | −0.728388 | + | 0.728388i | −0.970298 | − | 0.241911i | \(-0.922226\pi\) |
0.241911 | + | 0.970298i | \(0.422226\pi\) | |||||||
\(458\) | 140.670 | + | 226.612i | 0.307139 | + | 0.494787i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −559.341 | + | 488.976i | −1.21596 | + | 1.06299i | ||||
\(461\) | 132.650 | − | 54.9455i | 0.287744 | − | 0.119188i | −0.234143 | − | 0.972202i | \(-0.575228\pi\) |
0.521887 | + | 0.853015i | \(0.325228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −873.591 | −1.88680 | −0.943402 | − | 0.331650i | \(-0.892395\pi\) | ||||
−0.943402 | + | 0.331650i | \(0.892395\pi\) | |||||||
\(464\) | −7.59097 | − | 4.41452i | −0.0163598 | − | 0.00951404i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −307.025 | + | 50.4422i | −0.658852 | + | 0.108245i | ||||
\(467\) | 135.550 | + | 327.247i | 0.290258 | + | 0.700744i | 0.999993 | − | 0.00372448i | \(-0.00118554\pi\) |
−0.709735 | + | 0.704468i | \(0.751186\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −138.497 | + | 334.362i | −0.295303 | + | 0.712925i | ||||
\(470\) | −77.2585 | − | 124.460i | −0.164380 | − | 0.264808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 237.478 | + | 195.832i | 0.503132 | + | 0.414899i | ||||
\(473\) | 48.8081 | + | 48.8081i | 0.103188 | + | 0.103188i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.50997 | − | 18.1307i | 0.0158105 | − | 0.0381698i | ||||
\(476\) | −242.301 | + | 489.397i | −0.509035 | + | 1.02815i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −451.413 | − | 324.015i | −0.944379 | − | 0.677856i | ||||
\(479\) | − | 296.032i | − | 0.618021i | −0.951059 | − | 0.309011i | \(-0.900002\pi\) | ||
0.951059 | − | 0.309011i | \(-0.0999979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2990 | 0.0297276 | ||||||||
\(482\) | 60.6448 | − | 84.4895i | 0.125819 | − | 0.175289i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 171.430 | − | 346.253i | 0.354194 | − | 0.715398i | ||||
\(485\) | −535.416 | − | 221.777i | −1.10395 | − | 0.457271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −232.632 | + | 232.632i | −0.477683 | + | 0.477683i | −0.904390 | − | 0.426707i | \(-0.859674\pi\) |
0.426707 | + | 0.904390i | \(0.359674\pi\) | |||||||
\(488\) | 321.714 | − | 30.9206i | 0.659250 | − | 0.0633618i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −160.154 | + | 99.4156i | −0.326844 | + | 0.202889i | ||||
\(491\) | −217.435 | − | 90.0644i | −0.442840 | − | 0.183430i | 0.150110 | − | 0.988669i | \(-0.452037\pi\) |
−0.592951 | + | 0.805239i | \(0.702037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.7036 | − | 5.26201i | 0.0257680 | − | 0.0106735i | ||||
\(494\) | −32.9449 | − | 200.524i | −0.0666901 | − | 0.405920i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 153.624 | + | 201.515i | 0.309727 | + | 0.406281i | ||||
\(497\) | 399.026i | 0.802869i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 64.7699 | + | 156.368i | 0.129799 | + | 0.313364i | 0.975396 | − | 0.220458i | \(-0.0707553\pi\) |
−0.845597 | + | 0.533822i | \(0.820755\pi\) | |||||||
\(500\) | 384.705 | − | 336.309i | 0.769409 | − | 0.672618i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −127.842 | + | 79.3579i | −0.254665 | + | 0.158083i | ||||
\(503\) | 612.203 | + | 612.203i | 1.21710 | + | 1.21710i | 0.968642 | + | 0.248460i | \(0.0799246\pi\) |
0.248460 | + | 0.968642i | \(0.420075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 680.913 | + | 680.913i | 1.34834 | + | 1.34834i | ||||
\(506\) | −85.6520 | + | 366.041i | −0.169273 | + | 0.723400i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −493.292 | + | 166.586i | −0.971048 | + | 0.327925i | ||||
\(509\) | 273.870 | + | 661.182i | 0.538056 | + | 1.29898i | 0.926078 | + | 0.377332i | \(0.123158\pi\) |
−0.388022 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 500.480i | 0.979413i | ||||||||
\(512\) | 398.068 | − | 322.003i | 0.777477 | − | 0.628911i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −392.385 | − | 281.646i | −0.763395 | − | 0.547950i | ||||
\(515\) | −512.302 | + | 212.202i | −0.994761 | + | 0.412043i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −68.4813 | − | 28.3659i | −0.132459 | − | 0.0548663i | ||||
\(518\) | 25.1093 | + | 5.87548i | 0.0484736 | + | 0.0113426i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 69.0430 | − | 225.688i | 0.132775 | − | 0.434015i | ||||
\(521\) | 527.816 | − | 527.816i | 1.01308 | − | 1.01308i | 0.0131690 | − | 0.999913i | \(-0.495808\pi\) |
0.999913 | − | 0.0131690i | \(-0.00419195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.01268 | + | 2.07632i | 0.00958447 | + | 0.00397002i | 0.387471 | − | 0.921882i | \(-0.373349\pi\) |
−0.377886 | + | 0.925852i | \(0.623349\pi\) | |||||||
\(524\) | −69.3458 | − | 79.3249i | −0.132339 | − | 0.151383i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 331.116 | − | 54.4002i | 0.629498 | − | 0.103423i | ||||
\(527\) | −396.783 | −0.752908 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 918.476i | 1.73625i | ||||||||
\(530\) | 388.747 | − | 63.8687i | 0.733485 | − | 0.120507i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.5439 | − | 365.663i | 0.0461352 | − | 0.687336i | ||||
\(533\) | −101.881 | + | 245.963i | −0.191147 | + | 0.461469i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −84.7624 | − | 84.7624i | −0.158434 | − | 0.158434i | ||||
\(536\) | 50.8322 | + | 528.886i | 0.0948363 | + | 0.986727i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 487.322 | + | 114.031i | 0.905804 | + | 0.211954i | ||||
\(539\) | −36.5010 | + | 88.1213i | −0.0677199 | + | 0.163490i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −229.279 | − | 553.528i | −0.423806 | − | 1.02316i | −0.981215 | − | 0.192919i | \(-0.938204\pi\) |
0.557409 | − | 0.830238i | \(-0.311796\pi\) | |||||||
\(542\) | −3.47254 | − | 2.49252i | −0.00640691 | − | 0.00459875i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.0836 | + | 801.392i | 0.0424330 | + | 1.47315i | ||||
\(545\) | 958.688 | 1.75906 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −391.381 | + | 162.115i | −0.715504 | + | 0.296371i | −0.710580 | − | 0.703617i | \(-0.751567\pi\) |
−0.00492387 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(548\) | −749.716 | − | 371.185i | −1.36809 | − | 0.677344i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.62764 | − | 11.2294i | 0.00477753 | − | 0.0204172i | ||||
\(551\) | −6.52508 | + | 6.52508i | −0.0118423 | + | 0.0118423i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 146.884 | − | 146.884i | 0.265613 | − | 0.265613i | ||||
\(554\) | −788.950 | + | 489.742i | −1.42410 | + | 0.884010i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 60.0003 | − | 893.903i | 0.107914 | − | 1.60774i | ||||
\(557\) | −364.486 | + | 150.975i | −0.654374 | + | 0.271050i | −0.685069 | − | 0.728478i | \(-0.740228\pi\) |
0.0306953 | + | 0.999529i | \(0.490228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −84.4296 | −0.151037 | ||||||||
\(560\) | 213.977 | − | 367.943i | 0.382101 | − | 0.657041i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 119.985 | + | 730.306i | 0.213496 | + | 1.29948i | ||||
\(563\) | −114.762 | − | 277.059i | −0.203840 | − | 0.492113i | 0.788591 | − | 0.614918i | \(-0.210811\pi\) |
−0.992431 | + | 0.122805i | \(0.960811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.2544 | − | 147.881i | 0.108415 | − | 0.261736i | ||||
\(566\) | 714.463 | − | 443.503i | 1.26230 | − | 0.783575i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 274.931 | + | 517.289i | 0.484034 | + | 0.910721i | ||||
\(569\) | −172.424 | − | 172.424i | −0.303029 | − | 0.303029i | 0.539169 | − | 0.842198i | \(-0.318739\pi\) |
−0.842198 | + | 0.539169i | \(0.818739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 295.206 | − | 712.690i | 0.516998 | − | 1.24814i | −0.422740 | − | 0.906251i | \(-0.638932\pi\) |
0.939739 | − | 0.341894i | \(-0.111068\pi\) | |||||||
\(572\) | −38.2094 | − | 113.145i | −0.0667996 | − | 0.197806i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −279.972 | + | 390.053i | −0.487757 | + | 0.679535i | ||||
\(575\) | − | 44.4059i | − | 0.0772276i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −756.330 | −1.31080 | −0.655398 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(578\) | −550.307 | − | 394.999i | −0.952088 | − | 0.683389i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.1539 | + | 3.42901i | −0.0175068 | + | 0.00591209i | ||||
\(581\) | 210.202 | + | 87.0686i | 0.361794 | + | 0.149860i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 140.957 | − | 140.957i | 0.241779 | − | 0.241779i | ||||
\(584\) | 344.834 | + | 648.813i | 0.590469 | + | 1.11098i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 162.003 | + | 260.979i | 0.276455 | + | 0.445356i | ||||
\(587\) | −736.720 | − | 305.159i | −1.25506 | − | 0.519863i | −0.346670 | − | 0.937987i | \(-0.612688\pi\) |
−0.908390 | + | 0.418125i | \(0.862688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 246.012 | − | 101.902i | 0.417678 | − | 0.173008i | ||||
\(590\) | 370.702 | − | 60.9040i | 0.628309 | − | 0.103227i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 36.5995 | − | 9.68362i | 0.0618234 | − | 0.0163575i | ||||
\(593\) | 76.7003i | 0.129343i | 0.997907 | + | 0.0646714i | \(0.0205999\pi\) | ||||
−0.997907 | + | 0.0646714i | \(0.979400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 255.056 | + | 615.759i | 0.428665 | + | 1.03489i | ||||
\(596\) | 213.010 | + | 14.2976i | 0.357399 | + | 0.0239892i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −242.512 | − | 390.676i | −0.405539 | − | 0.653304i | ||||
\(599\) | −34.1251 | − | 34.1251i | −0.0569702 | − | 0.0569702i | 0.678048 | − | 0.735018i | \(-0.262826\pi\) |
−0.735018 | + | 0.678048i | \(0.762826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 212.552 | + | 212.552i | 0.353664 | + | 0.353664i | 0.861471 | − | 0.507807i | \(-0.169544\pi\) |
−0.507807 | + | 0.861471i | \(0.669544\pi\) | |||||||
\(602\) | −148.260 | − | 34.6923i | −0.246280 | − | 0.0576284i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −452.131 | + | 913.211i | −0.748561 | + | 1.51194i | ||||
\(605\) | −180.454 | − | 435.655i | −0.298271 | − | 0.720091i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 56.8377i | − | 0.0936371i | −0.998903 | − | 0.0468186i | \(-0.985092\pi\) | ||
0.998903 | − | 0.0468186i | \(-0.0149083\pi\) | |||||||
\(608\) | −220.125 | − | 490.949i | −0.362048 | − | 0.807481i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 230.012 | − | 320.449i | 0.377068 | − | 0.525326i | ||||
\(611\) | 83.7646 | − | 34.6964i | 0.137094 | − | 0.0567863i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.45320 | − | 3.08722i | −0.0121586 | − | 0.00503624i | 0.376596 | − | 0.926378i | \(-0.377095\pi\) |
−0.388754 | + | 0.921341i | \(0.627095\pi\) | |||||||
\(614\) | 43.0822 | − | 184.115i | 0.0701665 | − | 0.299862i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.6050 | − | 214.386i | −0.0334497 | − | 0.348028i | ||||
\(617\) | 325.733 | − | 325.733i | 0.527931 | − | 0.527931i | −0.392024 | − | 0.919955i | \(-0.628225\pi\) |
0.919955 | + | 0.392024i | \(0.128225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 76.1643 | + | 31.5483i | 0.123044 | + | 0.0509665i | 0.443356 | − | 0.896346i | \(-0.353788\pi\) |
−0.320312 | + | 0.947312i | \(0.603788\pi\) | |||||||
\(620\) | 308.567 | + | 20.7116i | 0.497689 | + | 0.0334058i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −101.551 | − | 618.104i | −0.163265 | − | 0.993736i | ||||
\(623\) | 183.153 | 0.293986 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 594.458i | − | 0.951133i | ||||||
\(626\) | 128.569 | + | 782.554i | 0.205381 | + | 1.25009i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 475.313 | − | 415.519i | 0.756868 | − | 0.661654i | ||||
\(629\) | −22.6862 | + | 54.7694i | −0.0360671 | + | 0.0870738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 70.1301 | + | 70.1301i | 0.111141 | + | 0.111141i | 0.760490 | − | 0.649349i | \(-0.224959\pi\) |
−0.649349 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(632\) | 89.2134 | − | 291.621i | 0.141160 | − | 0.461425i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 185.724 | − | 793.707i | 0.292940 | − | 1.25190i | ||||
\(635\) | −243.177 | + | 587.082i | −0.382956 | + | 0.924538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.6471 | − | 107.788i | −0.0700897 | − | 0.169211i | ||||
\(638\) | −3.16222 | + | 4.40555i | −0.00495645 | + | 0.00690526i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.8802 | − | 624.425i | 0.0373128 | − | 0.975664i | ||||
\(641\) | −458.396 | −0.715126 | −0.357563 | − | 0.933889i | \(-0.616392\pi\) | ||||
−0.357563 | + | 0.933889i | \(0.616392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −882.443 | + | 365.520i | −1.37238 | + | 0.568460i | −0.942434 | − | 0.334393i | \(-0.891469\pi\) |
−0.429950 | + | 0.902853i | \(0.641469\pi\) | |||||||
\(644\) | −265.327 | − | 785.684i | −0.411999 | − | 1.22001i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 820.338 | + | 191.956i | 1.26987 | + | 0.297145i | ||||
\(647\) | 130.433 | − | 130.433i | 0.201597 | − | 0.201597i | −0.599087 | − | 0.800684i | \(-0.704470\pi\) |
0.800684 | + | 0.599087i | \(0.204470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 134.414 | − | 134.414i | 0.207110 | − | 0.207110i | ||||
\(650\) | 7.43982 | + | 11.9852i | 0.0114459 | + | 0.0184388i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −433.597 | − | 495.992i | −0.665026 | − | 0.760724i | ||||
\(653\) | −989.811 | + | 409.993i | −1.51579 | + | 0.627861i | −0.976743 | − | 0.214415i | \(-0.931216\pi\) |
−0.539047 | + | 0.842275i | \(0.681216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −128.592 | −0.196324 | ||||||||
\(656\) | −94.2016 | + | 698.560i | −0.143600 | + | 1.06488i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 161.349 | − | 26.5087i | 0.245212 | − | 0.0402867i | ||||
\(659\) | 457.745 | + | 1105.09i | 0.694605 | + | 1.67693i | 0.735289 | + | 0.677753i | \(0.237046\pi\) |
−0.0406841 | + | 0.999172i | \(0.512954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −96.2729 | + | 232.423i | −0.145647 | + | 0.351624i | −0.979821 | − | 0.199879i | \(-0.935945\pi\) |
0.834173 | + | 0.551502i | \(0.185945\pi\) | |||||||
\(662\) | −477.403 | − | 769.073i | −0.721152 | − | 1.16174i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 332.493 | − | 31.9565i | 0.500742 | − | 0.0481273i | ||||
\(665\) | −316.278 | − | 316.278i | −0.475607 | − | 0.475607i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.99066 | + | 19.2912i | −0.0119800 | + | 0.0289223i | ||||
\(668\) | −480.688 | − | 237.989i | −0.719592 | − | 0.356271i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 526.805 | + | 378.130i | 0.786277 | + | 0.564373i | ||||
\(671\) | − | 199.593i | − | 0.297456i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −135.640 | −0.201545 | −0.100772 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100772 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(674\) | −44.4571 | + | 61.9369i | −0.0659601 | + | 0.0918946i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −474.907 | − | 235.127i | −0.702525 | − | 0.347820i | ||||
\(677\) | 348.196 | + | 144.228i | 0.514322 | + | 0.213039i | 0.624721 | − | 0.780848i | \(-0.285213\pi\) |
−0.110399 | + | 0.993887i | \(0.535213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 457.411 | − | 457.411i | 0.673653 | − | 0.673653i | ||||
\(680\) | 754.911 | + | 622.523i | 1.11016 | + | 0.915476i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 132.954 | − | 82.5310i | 0.194947 | − | 0.121013i | ||||
\(683\) | 812.940 | + | 336.731i | 1.19025 | + | 0.493017i | 0.887836 | − | 0.460159i | \(-0.152208\pi\) |
0.302413 | + | 0.953177i | \(0.402208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −943.292 | + | 390.724i | −1.37707 | + | 0.570400i | ||||
\(686\) | −120.687 | − | 734.581i | −0.175928 | − | 1.07082i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −216.105 | + | 57.1778i | −0.314106 | + | 0.0831073i | ||||
\(689\) | 243.832i | 0.353892i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −78.3893 | − | 189.249i | −0.113443 | − | 0.273876i | 0.856953 | − | 0.515395i | \(-0.172355\pi\) |
−0.970396 | + | 0.241518i | \(0.922355\pi\) | |||||||
\(692\) | 306.088 | + | 350.135i | 0.442323 | + | 0.505975i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 894.509 | − | 555.267i | 1.28892 | − | 0.800097i | ||||
\(695\) | −773.177 | − | 773.177i | −1.11249 | − | 1.11249i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −780.471 | − | 780.471i | −1.11976 | − | 1.11976i | ||||
\(698\) | 63.3672 | − | 270.805i | 0.0907840 | − | 0.387973i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.13975 | + | 24.1033i | 0.0116282 | + | 0.0344333i | ||||
\(701\) | −432.140 | − | 1043.28i | −0.616463 | − | 1.48827i | −0.855785 | − | 0.517332i | \(-0.826925\pi\) |
0.239322 | − | 0.970940i | \(-0.423075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 39.7843i | − | 0.0565921i | ||||||
\(704\) | −174.425 | − | 263.728i | −0.247762 | − | 0.374614i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 363.748 | + | 261.091i | 0.515223 | + | 0.369817i | ||||
\(707\) | −993.041 | + | 411.331i | −1.40458 | + | 0.581798i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 367.507 | + | 152.226i | 0.518345 | + | 0.214706i | 0.626490 | − | 0.779430i | \(-0.284491\pi\) |
−0.108145 | + | 0.994135i | \(0.534491\pi\) | |||||||
\(710\) | 696.162 | + | 162.899i | 0.980510 | + | 0.229435i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 237.436 | − | 126.194i | 0.333478 | − | 0.177238i | ||||
\(713\) | 426.058 | − | 426.058i | 0.597556 | − | 0.597556i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −134.657 | − | 55.7768i | −0.188332 | − | 0.0780096i | ||||
\(716\) | 430.579 | − | 376.412i | 0.601367 | − | 0.525715i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 124.382 | − | 20.4352i | 0.173234 | − | 0.0284612i | ||||
\(719\) | 100.566 | 0.139869 | 0.0699344 | − | 0.997552i | \(-0.477721\pi\) | ||||
0.0699344 | + | 0.997552i | \(0.477721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 618.950i | − | 0.858461i | ||||||
\(722\) | 154.527 | − | 25.3877i | 0.214026 | − | 0.0351631i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1340.09 | − | 89.9495i | −1.85096 | − | 0.124240i | ||||
\(725\) | 0.245139 | − | 0.591817i | 0.000338122 | − | 0.000816300i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −332.402 | − | 332.402i | −0.457224 | − | 0.457224i | 0.440519 | − | 0.897743i | \(-0.354794\pi\) |
−0.897743 | + | 0.440519i | \(0.854794\pi\) | |||||||
\(728\) | 203.247 | + | 167.604i | 0.279185 | + | 0.230225i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 873.164 | + | 204.317i | 1.19612 | + | 0.279886i | ||||
\(731\) | 133.953 | − | 323.391i | 0.183246 | − | 0.442395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −166.189 | − | 401.215i | −0.226724 | − | 0.547360i | 0.769051 | − | 0.639187i | \(-0.220729\pi\) |
−0.995775 | + | 0.0918276i | \(0.970729\pi\) | |||||||
\(734\) | −479.264 | − | 344.006i | −0.652948 | − | 0.468673i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −885.306 | − | 835.733i | −1.20286 | − | 1.13551i | ||||
\(737\) | 328.124 | 0.445215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1011.25 | − | 418.874i | 1.36840 | − | 0.566812i | 0.427049 | − | 0.904229i | \(-0.359553\pi\) |
0.941355 | + | 0.337417i | \(0.109553\pi\) | |||||||
\(740\) | 20.5014 | − | 41.4085i | 0.0277045 | − | 0.0559574i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −100.191 | + | 428.174i | −0.135028 | + | 0.577054i | ||||
\(743\) | −458.897 | + | 458.897i | −0.617627 | + | 0.617627i | −0.944922 | − | 0.327295i | \(-0.893863\pi\) |
0.327295 | + | 0.944922i | \(0.393863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 184.242 | − | 184.242i | 0.247304 | − | 0.247304i | ||||
\(746\) | 428.573 | − | 266.037i | 0.574495 | − | 0.356618i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 494.001 | + | 33.1582i | 0.660429 | + | 0.0443292i | ||||
\(749\) | 123.617 | − | 51.2039i | 0.165043 | − | 0.0683630i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −636.920 | −0.848096 | −0.424048 | − | 0.905640i | \(-0.639391\pi\) | ||||
−0.424048 | + | 0.905640i | \(0.639391\pi\) | |||||||
\(752\) | 190.905 | − | 145.536i | 0.253864 | − | 0.193532i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.07538 | − | 6.54548i | −0.00142623 | − | 0.00868100i | ||||
\(755\) | 475.932 | + | 1149.00i | 0.630373 | + | 1.52186i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −414.804 | + | 1001.43i | −0.547958 | + | 1.32289i | 0.371038 | + | 0.928618i | \(0.379002\pi\) |
−0.918995 | + | 0.394269i | \(0.870998\pi\) | |||||||
\(758\) | −311.711 | + | 193.495i | −0.411228 | + | 0.255270i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −627.935 | − | 192.099i | −0.826230 | − | 0.252762i | ||||
\(761\) | 520.779 | + | 520.779i | 0.684334 | + | 0.684334i | 0.960974 | − | 0.276639i | \(-0.0892207\pi\) |
−0.276639 | + | 0.960974i | \(0.589221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −409.508 | + | 988.640i | −0.536708 | + | 1.29573i | ||||
\(764\) | −1185.45 | + | 400.331i | −1.55164 | + | 0.523993i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 605.325 | − | 843.330i | 0.790241 | − | 1.10095i | ||||
\(767\) | 232.514i | 0.303147i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 973.035 | 1.26533 | 0.632663 | − | 0.774427i | \(-0.281962\pi\) | ||||
0.632663 | + | 0.774427i | \(0.281962\pi\) | |||||||
\(770\) | −213.542 | − | 153.276i | −0.277328 | − | 0.199060i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −90.4448 | − | 267.824i | −0.117157 | − | 0.346922i | ||||
\(773\) | −959.578 | − | 397.470i | −1.24137 | − | 0.514192i | −0.337227 | − | 0.941423i | \(-0.609489\pi\) |
−0.904142 | + | 0.427232i | \(0.859489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.0707 | + | 13.0707i | −0.0168654 | + | 0.0168654i | ||||
\(776\) | 277.819 | − | 908.136i | 0.358015 | − | 1.17028i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −59.3827 | − | 95.6626i | −0.0763273 | − | 0.122960i | ||||
\(779\) | 684.346 | + | 283.465i | 0.878493 | + | 0.363884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 334.236 | − | 138.445i | 0.427958 | − | 0.177266i | ||||
\(782\) | 1881.17 | − | 309.064i | 2.40558 | − | 0.395222i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −187.275 | − | 245.656i | −0.238871 | − | 0.313336i | ||||
\(785\) | − | 770.521i | − | 0.981556i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 412.612 | + | 996.133i | 0.524284 | + | 1.26573i | 0.935219 | + | 0.354070i | \(0.115202\pi\) |
−0.410935 | + | 0.911665i | \(0.634798\pi\) | |||||||
\(788\) | 23.6535 | − | 352.397i | 0.0300171 | − | 0.447204i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −196.297 | − | 316.225i | −0.248477 | − | 0.400285i | ||||
\(791\) | 126.336 | + | 126.336i | 0.159717 | + | 0.159717i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 172.631 | + | 172.631i | 0.217694 | + | 0.217694i | ||||
\(794\) | 292.006 | + | 68.3283i | 0.367766 | + | 0.0860558i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 520.470 | + | 257.685i | 0.653856 | + | 0.323725i | ||||
\(797\) | 46.5600 | + | 112.406i | 0.0584191 | + | 0.141036i | 0.950394 | − | 0.311049i | \(-0.100680\pi\) |
−0.891975 | + | 0.452085i | \(0.850680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 375.892i | 0.470453i | ||||||||
\(800\) | 27.1595 | + | 25.6387i | 0.0339494 | + | 0.0320484i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.1800 | − | 18.3622i | 0.0164339 | − | 0.0228955i | ||||
\(803\) | 419.216 | − | 173.645i | 0.522063 | − | 0.216245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −935.065 | − | 387.317i | −1.16157 | − | 0.481139i | ||||
\(806\) | −43.6112 | + | 186.376i | −0.0541082 | + | 0.231236i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1003.95 | + | 1217.45i | −1.24251 | + | 1.50675i | ||||
\(809\) | 80.8371 | − | 80.8371i | 0.0999222 | − | 0.0999222i | −0.655378 | − | 0.755301i | \(-0.727491\pi\) |
0.755301 | + | 0.655378i | \(0.227491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1277.99 | + | 529.360i | 1.57582 | + | 0.652725i | 0.987744 | − | 0.156082i | \(-0.0498865\pi\) |
0.588074 | + | 0.808807i | \(0.299886\pi\) | |||||||
\(812\) | 0.801157 | − | 11.9359i | 0.000986647 | − | 0.0146994i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.79039 | − | 23.0708i | −0.00465650 | − | 0.0283425i | ||||
\(815\) | −804.044 | −0.986557 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 234.910i | 0.287527i | ||||||||
\(818\) | 86.6459 | + | 527.384i | 0.105924 | + | 0.644724i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 566.211 | + | 647.690i | 0.690501 | + | 0.789866i | ||||
\(821\) | −83.7084 | + | 202.090i | −0.101959 | + | 0.246151i | −0.966625 | − | 0.256197i | \(-0.917530\pi\) |
0.864666 | + | 0.502348i | \(0.167530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 588.539 | + | 588.539i | 0.715114 | + | 0.715114i | 0.967601 | − | 0.252486i | \(-0.0812482\pi\) |
−0.252486 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(824\) | −426.460 | − | 802.395i | −0.517549 | − | 0.973780i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −95.5403 | + | 408.299i | −0.115666 | + | 0.494309i | ||||
\(827\) | −281.470 | + | 679.529i | −0.340351 | + | 0.821679i | 0.657329 | + | 0.753603i | \(0.271686\pi\) |
−0.997680 | + | 0.0680759i | \(0.978314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.83745 | + | 16.5071i | 0.00824783 | + | 0.0199120i | 0.927950 | − | 0.372705i | \(-0.121570\pi\) |
−0.919702 | + | 0.392617i | \(0.871570\pi\) | |||||||
\(830\) | 237.718 | − | 331.185i | 0.286407 | − | 0.399018i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 378.965 | + | 77.2398i | 0.455487 | + | 0.0928363i | ||||
\(833\) | 483.695 | 0.580666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −604.801 | + | 250.517i | −0.724313 | + | 0.300020i | ||||
\(836\) | −314.805 | + | 106.311i | −0.376561 | + | 0.127166i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 501.723 | + | 117.401i | 0.598714 | + | 0.140097i | ||||
\(839\) | 358.991 | − | 358.991i | 0.427879 | − | 0.427879i | −0.460026 | − | 0.887905i | \(-0.652160\pi\) |
0.887905 | + | 0.460026i | \(0.152160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 594.464 | − | 594.464i | 0.706854 | − | 0.706854i | ||||
\(842\) | 370.968 | + | 597.611i | 0.440579 | + | 0.709752i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −65.7223 | + | 57.4545i | −0.0778700 | + | 0.0680740i | ||||
\(845\) | −597.527 | + | 247.504i | −0.707133 | + | 0.292904i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 526.348 | 0.621426 | ||||||||
\(848\) | 165.129 | + | 624.109i | 0.194727 | + | 0.735977i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −57.7107 | + | 9.48150i | −0.0678949 | + | 0.0111547i | ||||
\(851\) | −34.4503 | − | 83.1704i | −0.0404821 | − | 0.0977325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 545.396 | − | 1316.70i | 0.639386 | − | 1.54361i | −0.188114 | − | 0.982147i | \(-0.560237\pi\) |
0.827499 | − | 0.561467i | \(-0.189763\pi\) | |||||||
\(854\) | 232.210 | + | 374.079i | 0.271908 | + | 0.438031i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 124.975 | − | 151.553i | 0.145999 | − | 0.177048i | ||||
\(857\) | −157.052 | − | 157.052i | −0.183258 | − | 0.183258i | 0.609516 | − | 0.792774i | \(-0.291364\pi\) |
−0.792774 | + | 0.609516i | \(0.791364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.7307 | − | 42.8057i | 0.0206411 | − | 0.0498321i | −0.913223 | − | 0.407460i | \(-0.866414\pi\) |
0.933864 | + | 0.357628i | \(0.116414\pi\) | |||||||
\(860\) | −121.052 | + | 244.500i | −0.140758 | + | 0.284302i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.2240 | + | 18.8230i | 0.0304222 | + | 0.0218365i | ||||
\(863\) | 186.088i | 0.215629i | 0.994171 | + | 0.107815i | \(0.0343853\pi\) | ||||
−0.994171 | + | 0.107815i | \(0.965615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 567.597 | 0.656181 | ||||||||
\(866\) | 854.592 | − | 1190.61i | 0.986827 | − | 1.37483i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −153.164 | + | 309.360i | −0.176457 | + | 0.356406i | ||||
\(869\) | −173.996 | − | 72.0716i | −0.200226 | − | 0.0829363i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −283.799 | + | 283.799i | −0.325831 | + | 0.325831i | ||||
\(872\) | 150.301 | + | 1563.81i | 0.172363 | + | 1.79336i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1086.98 | + | 674.745i | −1.24369 | + | 0.772020i | ||||
\(875\) | 643.121 | + | 266.390i | 0.734996 | + | 0.304445i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −216.654 | + | 89.7412i | −0.247040 | + | 0.102328i | −0.502768 | − | 0.864421i | \(-0.667685\pi\) |
0.255728 | + | 0.966749i | \(0.417685\pi\) | |||||||
\(878\) | 211.220 | + | 1285.62i | 0.240569 | + | 1.46426i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −382.440 | − | 51.5725i | −0.434591 | − | 0.0586051i | ||||
\(881\) | 47.9671i | 0.0544462i | 0.999629 | + | 0.0272231i | \(0.00866645\pi\) | ||||
−0.999629 | + | 0.0272231i | \(0.991334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 115.380 | + | 278.551i | 0.130668 | + | 0.315460i | 0.975650 | − | 0.219335i | \(-0.0703888\pi\) |
−0.844982 | + | 0.534795i | \(0.820389\pi\) | |||||||
\(884\) | −455.948 | + | 398.590i | −0.515778 | + | 0.450893i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 246.639 | − | 153.101i | 0.278373 | − | 0.172800i | ||||
\(887\) | −233.227 | − | 233.227i | −0.262939 | − | 0.262939i | 0.563308 | − | 0.826247i | \(-0.309528\pi\) |
−0.826247 | + | 0.563308i | \(0.809528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −501.549 | − | 501.549i | −0.564172 | − | 0.564172i | ||||
\(890\) | 74.7708 | − | 319.539i | 0.0840122 | − | 0.359033i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −499.052 | + | 168.531i | −0.559475 | + | 0.188936i | ||||
\(893\) | −96.5364 | − | 233.059i | −0.108103 | − | 0.260985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 698.004i | − | 0.779892i | ||||||
\(896\) | 633.733 | + | 291.352i | 0.707291 | + | 0.325170i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1188.14 | − | 852.821i | −1.32309 | − | 0.949690i | ||||
\(899\) | 8.03028 | − | 3.32625i | 0.00893246 | − | 0.00369994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −933.949 | − | 386.854i | −1.03657 | − | 0.429361i | ||||
\(902\) | 423.858 | + | 99.1810i | 0.469909 | + | 0.109957i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 250.826 | + | 76.7333i | 0.277462 | + | 0.0848820i | ||||
\(905\) | −1159.11 | + | 1159.11i | −1.28078 | + | 1.28078i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −827.946 | − | 342.947i | −0.912841 | − | 0.378111i | −0.123697 | − | 0.992320i | \(-0.539475\pi\) |
−0.789143 | + | 0.614209i | \(0.789475\pi\) | |||||||
\(908\) | −173.126 | − | 198.039i | −0.190667 | − | 0.218105i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 317.267 | − | 52.1249i | 0.348645 | − | 0.0572801i | ||||
\(911\) | −1321.92 | −1.45107 | −0.725534 | − | 0.688186i | \(-0.758407\pi\) | ||||
−0.725534 | + | 0.688186i | \(0.758407\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 206.280i | − | 0.225937i | ||||||
\(914\) | −929.052 | + | 152.637i | −1.01647 | + | 0.166999i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.7255 | + | 532.248i | −0.0390016 | + | 0.581057i | ||||
\(917\) | 54.9287 | − | 132.610i | 0.0599004 | − | 0.144612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −717.026 | − | 717.026i | −0.780224 | − | 0.780224i | 0.199645 | − | 0.979868i | \(-0.436021\pi\) |
−0.979868 | + | 0.199645i | \(0.936021\pi\) | |||||||
\(920\) | −1479.06 | + | 142.156i | −1.60768 | + | 0.154517i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 279.606 | + | 65.4267i | 0.303260 | + | 0.0709617i | ||||
\(923\) | −169.342 | + | 408.828i | −0.183469 | + | 0.442934i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.05687 | + | 2.55151i | 0.00114256 | + | 0.00275839i | ||||
\(926\) | −1419.39 | − | 1018.81i | −1.53282 | − | 1.10023i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.18528 | − | 16.0254i | −0.00774276 | − | 0.0172688i | ||||
\(929\) | 430.578 | 0.463485 | 0.231743 | − | 0.972777i | \(-0.425557\pi\) | ||||
0.231743 | + | 0.972777i | \(0.425557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −299.899 | + | 124.222i | −0.322126 | + | 0.133429i | ||||
\(932\) | −557.674 | − | 276.105i | −0.598363 | − | 0.296250i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −161.407 | + | 689.787i | −0.172813 | + | 0.738530i | ||||
\(935\) | 427.284 | − | 427.284i | 0.456988 | − | 0.456988i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 752.850 | − | 752.850i | 0.803469 | − | 0.803469i | −0.180167 | − | 0.983636i | \(-0.557664\pi\) |
0.983636 | + | 0.180167i | \(0.0576639\pi\) | |||||||
\(938\) | −614.971 | + | 381.744i | −0.655619 | + | 0.406976i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.6211 | − | 292.321i | 0.0208735 | − | 0.310979i | ||||
\(941\) | 1482.20 | − | 613.948i | 1.57513 | − | 0.652442i | 0.587501 | − | 0.809223i | \(-0.300112\pi\) |
0.987633 | + | 0.156781i | \(0.0501118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1676.11 | 1.77742 | ||||||||
\(944\) | 157.464 | + | 595.139i | 0.166805 | + | 0.630444i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.3807 | + | 136.224i | 0.0236582 | + | 0.144000i | ||||
\(947\) | −528.730 | − | 1276.47i | −0.558321 | − | 1.34791i | −0.911094 | − | 0.412198i | \(-0.864761\pi\) |
0.352773 | − | 0.935709i | \(-0.385239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −212.398 | + | 512.775i | −0.223813 | + | 0.540332i | ||||
\(950\) | 33.3466 | − | 20.6999i | 0.0351017 | − | 0.0217894i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −964.436 | + | 512.583i | −1.01306 | + | 0.538427i | ||||
\(953\) | 538.112 | + | 538.112i | 0.564650 | + | 0.564650i | 0.930625 | − | 0.365975i | \(-0.119264\pi\) |
−0.365975 | + | 0.930625i | \(0.619264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −584.391 | + | 1410.84i | −0.611927 | + | 1.47732i | ||||
\(956\) | −355.569 | − | 1052.91i | −0.371934 | − | 1.10137i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 345.242 | − | 480.987i | 0.360378 | − | 0.502074i | ||||
\(959\) | − | 1139.66i | − | 1.18839i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 710.184 | 0.739005 | ||||||||
\(962\) | 23.2327 | + | 16.6759i | 0.0241504 | + | 0.0173347i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 197.069 | − | 66.5506i | 0.204428 | − | 0.0690359i | ||||
\(965\) | −318.745 | − | 132.028i | −0.330306 | − | 0.136817i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −380.769 | + | 380.769i | −0.393763 | + | 0.393763i | −0.876026 | − | 0.482263i | \(-0.839815\pi\) |
0.482263 | + | 0.876026i | \(0.339815\pi\) | |||||||
\(968\) | 682.347 | − | 362.657i | 0.704904 | − | 0.374645i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −611.289 | − | 984.757i | −0.630195 | − | 1.01521i | ||||
\(971\) | 1000.67 | + | 414.490i | 1.03055 | + | 0.426869i | 0.832912 | − | 0.553405i | \(-0.186672\pi\) |
0.197642 | + | 0.980274i | \(0.436672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1127.60 | − | 467.067i | 1.15889 | − | 0.480028i | ||||
\(974\) | −649.277 | + | 106.672i | −0.666609 | + | 0.109520i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 558.775 | + | 324.954i | 0.572515 | + | 0.332945i | ||||
\(977\) | − | 920.476i | − | 0.942145i | −0.882095 | − | 0.471072i | \(-0.843867\pi\) | ||
0.882095 | − | 0.471072i | \(-0.156133\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63.5463 | − | 153.414i | −0.0649094 | − | 0.156705i | ||||
\(980\) | −376.156 | − | 25.2483i | −0.383833 | − | 0.0257635i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −248.247 | − | 399.914i | −0.252797 | − | 0.407244i | ||||
\(983\) | −465.265 | − | 465.265i | −0.473312 | − | 0.473312i | 0.429673 | − | 0.902985i | \(-0.358629\pi\) |
−0.902985 | + | 0.429673i | \(0.858629\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −304.804 | − | 304.804i | −0.309446 | − | 0.309446i | ||||
\(986\) | 26.7773 | + | 6.26578i | 0.0271575 | + | 0.00635474i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 180.330 | − | 364.229i | 0.182520 | − | 0.368653i | ||||
\(989\) | 203.415 | + | 491.087i | 0.205677 | + | 0.496549i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 365.984i | 0.369307i | 0.982804 | + | 0.184654i | \(0.0591164\pi\) | ||||
−0.982804 | + | 0.184654i | \(0.940884\pi\) | |||||||
\(992\) | 14.5917 | + | 506.580i | 0.0147094 | + | 0.510665i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −465.357 | + | 648.329i | −0.468166 | + | 0.652242i | ||||
\(995\) | 654.855 | − | 271.250i | 0.658146 | − | 0.272613i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −77.3922 | − | 32.0569i | −0.0776251 | − | 0.0321534i | 0.343533 | − | 0.939141i | \(-0.388376\pi\) |
−0.421158 | + | 0.906987i | \(0.638376\pi\) | |||||||
\(998\) | −77.1252 | + | 329.601i | −0.0772798 | + | 0.330261i | ||||
\(999\) | 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.91.6 | 28 | ||
3.2 | odd | 2 | 32.3.h.a.27.2 | yes | 28 | ||
12.11 | even | 2 | 128.3.h.a.15.7 | 28 | |||
24.5 | odd | 2 | 256.3.h.b.31.7 | 28 | |||
24.11 | even | 2 | 256.3.h.a.31.1 | 28 | |||
32.19 | odd | 8 | inner | 288.3.u.a.19.6 | 28 | ||
96.29 | odd | 8 | 256.3.h.a.223.1 | 28 | |||
96.35 | even | 8 | 256.3.h.b.223.7 | 28 | |||
96.77 | odd | 8 | 128.3.h.a.111.7 | 28 | |||
96.83 | even | 8 | 32.3.h.a.19.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.2 | ✓ | 28 | 96.83 | even | 8 | ||
32.3.h.a.27.2 | yes | 28 | 3.2 | odd | 2 | ||
128.3.h.a.15.7 | 28 | 12.11 | even | 2 | |||
128.3.h.a.111.7 | 28 | 96.77 | odd | 8 | |||
256.3.h.a.31.1 | 28 | 24.11 | even | 2 | |||
256.3.h.a.223.1 | 28 | 96.29 | odd | 8 | |||
256.3.h.b.31.7 | 28 | 24.5 | odd | 2 | |||
256.3.h.b.223.7 | 28 | 96.35 | even | 8 | |||
288.3.u.a.19.6 | 28 | 32.19 | odd | 8 | inner | ||
288.3.u.a.91.6 | 28 | 1.1 | even | 1 | trivial |