Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 49.18 | ||
Character | \(\chi\) | \(=\) | 576.49 |
Dual form | 576.2.bb.e.529.18 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71859 | + | 0.215523i | 0.992228 | + | 0.124432i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73721 | − | 0.733432i | 1.22412 | − | 0.328001i | 0.411830 | − | 0.911261i | \(-0.364890\pi\) |
0.812286 | + | 0.583260i | \(0.198223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14487 | − | 0.660988i | 0.432718 | − | 0.249830i | −0.267786 | − | 0.963479i | \(-0.586292\pi\) |
0.700504 | + | 0.713648i | \(0.252959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.90710 | + | 0.740791i | 0.969033 | + | 0.246930i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.343957 | − | 1.28367i | 0.103707 | − | 0.387040i | −0.894488 | − | 0.447092i | \(-0.852460\pi\) |
0.998195 | + | 0.0600515i | \(0.0191265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.902174 | − | 3.36696i | −0.250218 | − | 0.933827i | −0.970689 | − | 0.240341i | \(-0.922741\pi\) |
0.720470 | − | 0.693486i | \(-0.243926\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.86220 | − | 0.670538i | 1.25542 | − | 0.173132i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.60772 | −1.84514 | −0.922572 | − | 0.385825i | \(-0.873917\pi\) | ||||
−0.922572 | + | 0.385825i | \(0.873917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32297 | + | 4.32297i | −0.991757 | + | 0.991757i | −0.999966 | − | 0.00820954i | \(-0.997387\pi\) |
0.00820954 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.11001 | − | 0.889223i | 0.460442 | − | 0.194044i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46087 | + | 1.99814i | 0.721642 | + | 0.416640i | 0.815357 | − | 0.578959i | \(-0.196541\pi\) |
−0.0937148 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.62424 | − | 1.51511i | 0.524849 | − | 0.303021i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.83645 | + | 1.89966i | 0.930776 | + | 0.365590i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54658 | − | 0.950303i | −0.658583 | − | 0.176467i | −0.0859765 | − | 0.996297i | \(-0.527401\pi\) |
−0.572606 | + | 0.819830i | \(0.694068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.569129 | + | 0.985760i | −0.102219 | + | 0.177048i | −0.912598 | − | 0.408857i | \(-0.865927\pi\) |
0.810380 | + | 0.585905i | \(0.199261\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.867781 | − | 2.13197i | 0.151061 | − | 0.371128i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.64894 | − | 2.64894i | 0.447753 | − | 0.447753i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.26014 | + | 2.26014i | 0.371565 | + | 0.371565i | 0.868047 | − | 0.496482i | \(-0.165375\pi\) |
−0.496482 | + | 0.868047i | \(0.665375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.824810 | − | 5.98086i | −0.132075 | − | 0.957704i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.42311 | − | 0.821634i | −0.222253 | − | 0.128318i | 0.384740 | − | 0.923025i | \(-0.374291\pi\) |
−0.606993 | + | 0.794707i | \(0.707624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65438 | + | 6.17424i | −0.252291 | + | 0.941563i | 0.717287 | + | 0.696778i | \(0.245384\pi\) |
−0.969578 | + | 0.244784i | \(0.921283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.50065 | − | 0.104463i | 1.26720 | − | 0.0155724i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.58731 | − | 7.94546i | −0.669129 | − | 1.15896i | −0.978148 | − | 0.207909i | \(-0.933334\pi\) |
0.309020 | − | 0.951056i | \(-0.399999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.62619 | + | 4.54869i | −0.375170 | + | 0.649813i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0746 | − | 1.63964i | −1.83080 | − | 0.229595i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.72215 | + | 7.72215i | 1.06072 | + | 1.06072i | 0.998033 | + | 0.0626852i | \(0.0199664\pi\) |
0.0626852 | + | 0.998033i | \(0.480034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.76593i | − | 0.507798i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.36111 | + | 6.49771i | −1.10746 | + | 0.860642i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.80982 | − | 1.28879i | 0.626185 | − | 0.167786i | 0.0682473 | − | 0.997668i | \(-0.478259\pi\) |
0.557938 | + | 0.829883i | \(0.311593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.92979 | + | 2.66068i | 1.27138 | + | 0.340665i | 0.830559 | − | 0.556931i | \(-0.188021\pi\) |
0.440820 | + | 0.897596i | \(0.354688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.81789 | − | 1.07345i | 0.481009 | − | 0.135242i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.93887 | − | 8.55438i | −0.612592 | − | 1.06104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.73189 | + | 13.9276i | 0.455923 | + | 1.70153i | 0.685359 | + | 0.728205i | \(0.259645\pi\) |
−0.229436 | + | 0.973324i | \(0.573688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.51718 | + | 4.17987i | 0.664190 | + | 0.503198i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.87498i | − | 0.934588i | −0.884102 | − | 0.467294i | \(-0.845229\pi\) | ||
0.884102 | − | 0.467294i | \(-0.154771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.577222i | 0.0675588i | 0.999429 | + | 0.0337794i | \(0.0107544\pi\) | ||||
−0.999429 | + | 0.0337794i | \(0.989246\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.83654 | − | 2.03826i | 0.558475 | − | 0.235358i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.454704 | − | 1.69698i | −0.0518183 | − | 0.193389i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.716890 | − | 1.24169i | −0.0806564 | − | 0.139701i | 0.822876 | − | 0.568221i | \(-0.192368\pi\) |
−0.903532 | + | 0.428521i | \(0.859035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.90246 | + | 4.30711i | 0.878051 | + | 0.478567i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.30414 | − | 0.885341i | −0.362676 | − | 0.0971788i | 0.0728790 | − | 0.997341i | \(-0.476781\pi\) |
−0.435555 | + | 0.900162i | \(0.643448\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.8239 | + | 5.57975i | −2.25867 | + | 0.605208i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.89030 | − | 2.39755i | −0.631506 | − | 0.257044i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.2114i | − | 1.71841i | −0.511635 | − | 0.859203i | \(-0.670960\pi\) | ||
0.511635 | − | 0.859203i | \(-0.329040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25839 | − | 3.25839i | −0.341572 | − | 0.341572i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.19055 | + | 1.57146i | −0.123455 | + | 0.162952i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.66225 | + | 15.0035i | −0.888728 | + | 1.53932i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.648931 | − | 1.12398i | −0.0658889 | − | 0.114123i | 0.831199 | − | 0.555975i | \(-0.187655\pi\) |
−0.897088 | + | 0.441852i | \(0.854322\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95085 | − | 3.47695i | 0.196068 | − | 0.349446i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.60956 | − | 9.73900i | 0.259661 | − | 0.969067i | −0.705777 | − | 0.708434i | \(-0.749402\pi\) |
0.965438 | − | 0.260633i | \(-0.0839313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.04850 | − | 4.64680i | −0.793042 | − | 0.457863i | 0.0479901 | − | 0.998848i | \(-0.484718\pi\) |
−0.841033 | + | 0.540985i | \(0.818052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.12335 | − | 3.98154i | 0.499988 | − | 0.388558i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.89502 | − | 1.89502i | −0.183199 | − | 0.183199i | 0.609549 | − | 0.792748i | \(-0.291350\pi\) |
−0.792748 | + | 0.609549i | \(0.791350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.63272 | + | 8.63272i | −0.826864 | + | 0.826864i | −0.987082 | − | 0.160217i | \(-0.948780\pi\) |
0.160217 | + | 0.987082i | \(0.448780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.39715 | + | 4.37137i | 0.322443 | + | 0.414912i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.70180 | + | 2.94761i | −0.160092 | + | 0.277288i | −0.934902 | − | 0.354907i | \(-0.884512\pi\) |
0.774809 | + | 0.632195i | \(0.217846\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9386 | + | 2.93099i | 1.02003 | + | 0.273317i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.128497 | − | 10.4564i | −0.0118796 | − | 0.966695i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.70982 | + | 5.02862i | −0.798428 | + | 0.460972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.99679 | + | 4.61695i | 0.726981 | + | 0.419722i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.26866 | − | 1.71877i | −0.204559 | − | 0.154976i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.94700 | + | 3.94700i | −0.353031 | + | 0.353031i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.24504 | 0.465422 | 0.232711 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232711 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.17390 | + | 10.2544i | −0.367491 | + | 0.902852i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.68026 | − | 6.27080i | −0.146805 | − | 0.547883i | −0.999668 | − | 0.0257490i | \(-0.991803\pi\) |
0.852864 | − | 0.522134i | \(-0.174864\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.09178 | + | 7.80665i | −0.181381 | + | 0.676922i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.6316 | + | 1.65256i | 1.25929 | + | 0.142229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.16622 | + | 3.56007i | −0.526816 | + | 0.304157i | −0.739719 | − | 0.672916i | \(-0.765042\pi\) |
0.212903 | + | 0.977073i | \(0.431708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.07133 | + | 1.09091i | −0.345326 | + | 0.0925298i | −0.427313 | − | 0.904104i | \(-0.640540\pi\) |
0.0819876 | + | 0.996633i | \(0.473873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.17128 | − | 14.6437i | −0.519716 | − | 1.23322i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.63236 | −0.387378 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4047 | −0.864063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.49369 | + | 7.25133i | −0.453112 | + | 0.598080i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.40971 | + | 2.25338i | −0.688950 | + | 0.184604i | −0.586276 | − | 0.810111i | \(-0.699407\pi\) |
−0.102674 | + | 0.994715i | \(0.532740\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.8103 | + | 10.2828i | −1.44938 | + | 0.836803i | −0.998445 | − | 0.0557515i | \(-0.982245\pi\) |
−0.450940 | + | 0.892554i | \(0.648911\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.1164 | − | 5.63573i | −1.78801 | − | 0.455622i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.834834 | + | 3.11564i | −0.0670555 | + | 0.250255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.38710 | − | 8.90879i | −0.190512 | − | 0.710999i | −0.993383 | − | 0.114847i | \(-0.963362\pi\) |
0.802872 | − | 0.596152i | \(-0.203304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.6069 | + | 14.9355i | 0.920487 | + | 1.18446i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28298 | 0.416357 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4053 | − | 10.4053i | 0.815004 | − | 0.815004i | −0.170375 | − | 0.985379i | \(-0.554498\pi\) |
0.985379 | + | 0.170375i | \(0.0544981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.811644 | − | 6.47209i | 0.0631864 | − | 0.503851i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.95392 | + | 3.43750i | 0.460728 | + | 0.266001i | 0.712350 | − | 0.701824i | \(-0.247631\pi\) |
−0.251622 | + | 0.967826i | \(0.580964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.735830 | − | 0.424832i | 0.0566023 | − | 0.0326794i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.7697 | + | 9.36488i | −1.20594 | + | 0.716150i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.07494 | − | 0.823927i | −0.233783 | − | 0.0626420i | 0.140025 | − | 0.990148i | \(-0.455282\pi\) |
−0.373808 | + | 0.927506i | \(0.621948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00294 | − | 3.46919i | 0.151408 | − | 0.262246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.54387 | − | 1.17827i | 0.642197 | − | 0.0885642i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.73648 | − | 3.73648i | 0.279278 | − | 0.279278i | −0.553543 | − | 0.832821i | \(-0.686725\pi\) |
0.832821 | + | 0.553543i | \(0.186725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.169132 | + | 0.169132i | 0.0125715 | + | 0.0125715i | 0.713365 | − | 0.700793i | \(-0.247170\pi\) |
−0.700793 | + | 0.713365i | \(0.747170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.4918 | + | 6.71271i | 1.21911 | + | 0.496218i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.84414 | + | 4.52882i | 0.576713 | + | 0.332965i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.61673 | + | 9.76578i | −0.191354 | + | 0.714145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.79274 | − | 1.02198i | 0.494099 | − | 0.0743383i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0451 | − | 19.1306i | −0.799194 | − | 1.38424i | −0.920142 | − | 0.391586i | \(-0.871927\pi\) |
0.120947 | − | 0.992659i | \(-0.461407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.90683 | − | 13.6950i | 0.569146 | − | 0.985790i | −0.427505 | − | 0.904013i | \(-0.640607\pi\) |
0.996651 | − | 0.0817767i | \(-0.0260594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.64423 | − | 15.7659i | −0.475803 | − | 1.12902i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.19611 | + | 1.19611i | 0.0852196 | + | 0.0852196i | 0.748432 | − | 0.663212i | \(-0.230807\pi\) |
−0.663212 | + | 0.748432i | \(0.730807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.39170i | − | 0.453095i | −0.974000 | − | 0.226548i | \(-0.927256\pi\) | ||
0.974000 | − | 0.226548i | \(-0.0727439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.41187 | + | 24.7402i | 0.240655 | + | 1.74504i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.68849 | + | 1.25628i | −0.329068 | + | 0.0881734i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.49796 | − | 1.20523i | −0.314151 | − | 0.0841766i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.58090 | + | 8.37256i | 0.596414 | + | 0.581933i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.06233 | + | 7.03617i | 0.280997 | + | 0.486702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.539586 | − | 2.01376i | −0.0371466 | − | 0.138633i | 0.944862 | − | 0.327468i | \(-0.106195\pi\) |
−0.982009 | + | 0.188835i | \(0.939529\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.69724 | − | 13.5339i | 0.116293 | − | 0.927324i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.1135i | 1.23533i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.50475i | 0.102149i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.124405 | + | 0.992008i | −0.00840649 | + | 0.0670337i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.86349 | + | 25.6149i | 0.461688 | + | 1.72304i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6496 | − | 23.6417i | −0.914042 | − | 1.58317i | −0.808297 | − | 0.588775i | \(-0.799611\pi\) |
−0.105745 | − | 0.994393i | \(-0.533723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.75131 | − | 2.46055i | 0.583421 | − | 0.164037i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.80787 | − | 0.752368i | −0.186365 | − | 0.0499364i | 0.164429 | − | 0.986389i | \(-0.447422\pi\) |
−0.350794 | + | 0.936452i | \(0.614088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.48583 | + | 1.73787i | −0.428596 | + | 0.114842i | −0.466667 | − | 0.884433i | \(-0.654545\pi\) |
0.0380710 | + | 0.999275i | \(0.487879\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.415712 | − | 3.01441i | −0.0273518 | − | 0.198333i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.8159i | − | 0.774086i | −0.922062 | − | 0.387043i | \(-0.873497\pi\) | ||
0.922062 | − | 0.387043i | \(-0.126503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3839 | − | 18.3839i | −1.19923 | − | 1.19923i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.964426 | − | 2.28846i | −0.0626462 | − | 0.148651i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.75364 | − | 3.03739i | 0.113433 | − | 0.196472i | −0.803719 | − | 0.595009i | \(-0.797148\pi\) |
0.917152 | + | 0.398537i | \(0.130482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.35635 | − | 7.54543i | −0.280617 | − | 0.486044i | 0.690920 | − | 0.722932i | \(-0.257206\pi\) |
−0.971537 | + | 0.236888i | \(0.923873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6528 | + | 9.10531i | 0.811678 | + | 0.584106i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.85226 | + | 14.3768i | −0.246112 | + | 0.918502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.4553 | + | 10.6552i | 1.17428 | + | 0.677973i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.48765 | − | 2.23366i | −0.347766 | − | 0.141552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.70213 | + | 9.70213i | 0.612393 | + | 0.612393i | 0.943569 | − | 0.331176i | \(-0.107445\pi\) |
−0.331176 | + | 0.943569i | \(0.607445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.75533 | − | 3.75533i | 0.236096 | − | 0.236096i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.9903 | + | 5.10127i | −2.31642 | + | 0.319454i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.26857 | + | 16.0536i | −0.578158 | + | 1.00140i | 0.417533 | + | 0.908662i | \(0.362895\pi\) |
−0.995691 | + | 0.0927366i | \(0.970439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.08149 | + | 1.09363i | 0.253611 | + | 0.0679550i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.60628 | − | 5.38990i | −0.594614 | − | 0.333626i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.42692 | + | 1.97853i | −0.211313 | + | 0.122002i | −0.601922 | − | 0.798555i | \(-0.705598\pi\) |
0.390608 | + | 0.920557i | \(0.372265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.8008 | + | 15.4734i | 1.64636 | + | 0.950525i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.49393 | − | 27.8608i | 0.213825 | − | 1.70505i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6742 | − | 17.6742i | 1.07762 | − | 1.07762i | 0.0808951 | − | 0.996723i | \(-0.474222\pi\) |
0.996723 | − | 0.0808951i | \(-0.0257779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9563 | 1.63748 | 0.818738 | − | 0.574167i | \(-0.194674\pi\) | ||||
0.818738 | + | 0.574167i | \(0.194674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.89758 | − | 6.30209i | −0.296415 | − | 0.381420i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.04226 | − | 3.88979i | −0.0628509 | − | 0.234563i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.47723 | − | 9.24514i | 0.148842 | − | 0.555487i | −0.850712 | − | 0.525632i | \(-0.823829\pi\) |
0.999554 | − | 0.0298548i | \(-0.00950449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.38476 | + | 2.44410i | −0.142772 | + | 0.146324i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.51476 | − | 4.91600i | 0.507948 | − | 0.293264i | −0.224042 | − | 0.974580i | \(-0.571925\pi\) |
0.731990 | + | 0.681316i | \(0.238592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.0988 | − | 8.06496i | 1.78919 | − | 0.479412i | 0.796982 | − | 0.604003i | \(-0.206428\pi\) |
0.992208 | + | 0.124591i | \(0.0397617\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.1204 | + | 23.9179i | −1.07336 | + | 1.41677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.17236 | −0.128231 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8774 | 2.40456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.873002 | − | 2.07152i | −0.0511763 | − | 0.121435i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.6204 | − | 8.20472i | 1.78886 | − | 0.479325i | 0.796711 | − | 0.604360i | \(-0.206571\pi\) |
0.992152 | + | 0.125035i | \(0.0399044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2202 | − | 7.05535i | 0.711489 | − | 0.410778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.10207 | − | 5.55499i | 0.238026 | − | 0.322333i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.60533 | − | 13.4553i | 0.208502 | − | 0.778139i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18706 | + | 8.16220i | 0.126060 | + | 0.470462i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.58374 | − | 16.1749i | 0.378226 | − | 0.929225i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.1313 | 1.66805 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2513 | + | 17.2513i | −0.984581 | + | 0.984581i | −0.999883 | − | 0.0153018i | \(-0.995129\pi\) |
0.0153018 | + | 0.999883i | \(0.495129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8306 | − | 9.72059i | −0.729906 | − | 0.552985i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.53625 | + | 4.92841i | 0.484046 | + | 0.279464i | 0.722101 | − | 0.691787i | \(-0.243176\pi\) |
−0.238055 | + | 0.971252i | \(0.576510\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.45774 | + | 4.88308i | −0.478060 | + | 0.276008i | −0.719608 | − | 0.694381i | \(-0.755678\pi\) |
0.241548 | + | 0.970389i | \(0.422345\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.66305 | − | 5.73843i | 0.544451 | − | 0.323324i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8098 | − | 3.43237i | −0.719469 | − | 0.192781i | −0.119534 | − | 0.992830i | \(-0.538140\pi\) |
−0.599935 | + | 0.800049i | \(0.704807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43974 | + | 4.22576i | −0.136599 | + | 0.236597i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.84834 | − | 3.66519i | −0.158979 | − | 0.204571i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.8879 | − | 32.8879i | 1.82993 | − | 1.82993i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.46883 | − | 7.46883i | −0.414296 | − | 0.414296i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.6966 | + | 12.9756i | −0.923327 | + | 0.717550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5037 | − | 6.06432i | −0.579089 | − | 0.334337i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.274151 | + | 1.02314i | −0.0150687 | + | 0.0562371i | −0.973051 | − | 0.230591i | \(-0.925934\pi\) |
0.957982 | + | 0.286828i | \(0.0926008\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.89617 | + | 8.24476i | 0.268308 | + | 0.451810i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.4299 | + | 35.3857i | 1.11621 | + | 1.93332i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.50387 | + | 4.33683i | −0.136395 | + | 0.236242i | −0.926129 | − | 0.377206i | \(-0.876885\pi\) |
0.789735 | + | 0.613448i | \(0.210218\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.55998 | + | 4.69895i | −0.193351 | + | 0.255212i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.06963 | + | 1.06963i | 0.0579238 | + | 0.0579238i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1974i | 0.874575i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.1673 | + | 7.39470i | 0.978094 | + | 0.398117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.88711 | + | 1.57745i | −0.316036 | + | 0.0846817i | −0.413350 | − | 0.910572i | \(-0.635642\pi\) |
0.0973140 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.42227 | − | 1.45289i | −0.290247 | − | 0.0777715i | 0.110758 | − | 0.993847i | \(-0.464672\pi\) |
−0.401005 | + | 0.916076i | \(0.631339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.03276 | − | 17.9980i | 0.108501 | − | 0.960661i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.06146 | − | 8.76671i | −0.269395 | − | 0.466605i | 0.699311 | − | 0.714817i | \(-0.253490\pi\) |
−0.968706 | + | 0.248212i | \(0.920157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.77576 | − | 21.5554i | −0.306546 | − | 1.14404i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0524 | + | 6.76496i | −0.849582 | + | 0.358040i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.28081i | 0.278710i | 0.990242 | + | 0.139355i | \(0.0445030\pi\) | ||||
−0.990242 | + | 0.139355i | \(0.955497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.3761i | − | 0.967163i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.7481 | + | 9.65813i | 0.669104 | + | 0.506920i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.423353 | + | 1.57998i | 0.0221593 | + | 0.0826997i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.01941 | − | 8.69388i | −0.262011 | − | 0.453817i | 0.704765 | − | 0.709441i | \(-0.251052\pi\) |
−0.966776 | + | 0.255624i | \(0.917719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.52847 | − | 3.44280i | −0.183685 | − | 0.179225i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.9451 | + | 3.73657i | 0.723992 | + | 0.193993i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1865 | − | 6.74869i | 1.30411 | − | 0.349434i | 0.461105 | − | 0.887346i | \(-0.347453\pi\) |
0.843001 | + | 0.537912i | \(0.180787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.63395 | + | 5.93261i | −0.394215 | + | 0.306359i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.7985i | 0.659157i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.3259 | + | 11.3259i | 0.581771 | + | 0.581771i | 0.935390 | − | 0.353619i | \(-0.115049\pi\) |
−0.353619 | + | 0.935390i | \(0.615049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.01407 | + | 1.13043i | 0.461805 | + | 0.0579135i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.50076 | + | 4.33145i | −0.127783 | + | 0.221327i | −0.922817 | − | 0.385238i | \(-0.874119\pi\) |
0.795034 | + | 0.606564i | \(0.207453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.48924 | − | 4.31148i | −0.126863 | − | 0.219733i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.38328 | + | 16.7236i | −0.476979 | + | 0.850107i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.45749 | + | 12.9035i | −0.175302 | + | 0.654235i | 0.821198 | + | 0.570643i | \(0.193306\pi\) |
−0.996500 | + | 0.0835921i | \(0.973361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.3294 | − | 15.2013i | −1.33153 | − | 0.768761i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.53617 | − | 11.1391i | −0.0774895 | − | 0.561892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.87297 | − | 2.87297i | −0.144555 | − | 0.144555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7165 | + | 18.7165i | −0.939356 | + | 0.939356i | −0.998263 | − | 0.0589078i | \(-0.981238\pi\) |
0.0589078 | + | 0.998263i | \(0.481238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.27743 | + | 12.9656i | −0.264202 | + | 0.649092i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.66124 | − | 11.5376i | 0.332647 | − | 0.576161i | −0.650383 | − | 0.759606i | \(-0.725392\pi\) |
0.983030 | + | 0.183445i | \(0.0587250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.83247 | + | 1.02691i | 0.190909 | + | 0.0511538i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.7896 | + | 5.99352i | 1.23181 | + | 0.297820i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.67866 | − | 2.12388i | 0.182345 | − | 0.105277i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6037 | − | 6.12206i | −0.524320 | − | 0.302717i | 0.214380 | − | 0.976750i | \(-0.431227\pi\) |
−0.738701 | + | 0.674034i | \(0.764560\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3645 | + | 4.78934i | −0.560568 | + | 0.236241i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.65472 | − | 4.65472i | 0.229044 | − | 0.229044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.69344 | −0.475832 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.23206 | + | 0.997361i | −0.354156 | + | 0.0488410i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.58573 | + | 32.0424i | 0.419440 | + | 1.56537i | 0.775772 | + | 0.631013i | \(0.217361\pi\) |
−0.356332 | + | 0.934360i | \(0.615973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.61930 | − | 24.7035i | 0.322605 | − | 1.20398i | −0.594093 | − | 0.804396i | \(-0.702489\pi\) |
0.916698 | − | 0.399581i | \(-0.130844\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.44985 | − | 26.4965i | −0.362224 | − | 1.28830i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.9645 | + | 11.5265i | −0.968421 | + | 0.559118i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1269 | − | 3.51736i | 0.635258 | − | 0.170217i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.96113 | − | 0.998381i | −0.384367 | − | 0.0482023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3041 | 0.496332 | 0.248166 | − | 0.968717i | \(-0.420172\pi\) | ||||
0.248166 | + | 0.968717i | \(0.420172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7692 | −0.565591 | −0.282795 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.8814 | − | 2.24245i | −0.857347 | − | 0.107517i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.5991 | + | 6.32337i | −1.12890 | + | 0.302488i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9893 | − | 13.8502i | 1.14494 | − | 0.661034i | 0.197294 | − | 0.980344i | \(-0.436785\pi\) |
0.947650 | + | 0.319310i | \(0.103451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0042 | + | 11.2780i | −0.524011 | + | 0.537050i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.50677 | + | 24.2836i | −0.309146 | + | 1.15375i | 0.620172 | + | 0.784466i | \(0.287063\pi\) |
−0.929317 | + | 0.369282i | \(0.879604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.8900 | − | 44.3739i | −0.563638 | − | 2.10353i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9385 | + | 2.06014i | −0.706567 | + | 0.0974413i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0988 | −0.948522 | −0.474261 | − | 0.880384i | \(-0.657285\pi\) | ||||
−0.474261 | + | 0.880384i | \(0.657285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54419 | + | 1.54419i | −0.0727133 | + | 0.0727133i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.8248 | + | 13.8334i | −1.54225 | + | 0.649949i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3087 | − | 6.52907i | −0.530159 | − | 0.306088i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.8270 | + | 12.0245i | −0.974244 | + | 0.562480i | −0.900527 | − | 0.434799i | \(-0.856819\pi\) |
−0.0737167 | + | 0.997279i | \(0.523486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −36.7944 | − | 14.4521i | −1.71742 | − | 0.674566i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.90967 | − | 1.04759i | −0.182092 | − | 0.0487913i | 0.166621 | − | 0.986021i | \(-0.446714\pi\) |
−0.348713 | + | 0.937230i | \(0.613381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.16489 | + | 8.94585i | −0.240033 | + | 0.415749i | −0.960723 | − | 0.277508i | \(-0.910492\pi\) |
0.720691 | + | 0.693257i | \(0.243825\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.10623 | + | 5.17459i | −0.0976741 | + | 0.239966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8966 | + | 11.8966i | −0.550509 | + | 0.550509i | −0.926588 | − | 0.376079i | \(-0.877272\pi\) |
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4785 | + | 13.4785i | 0.622380 | + | 0.622380i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.18240 | − | 15.8250i | −0.100560 | − | 0.729179i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.35663 | + | 4.24735i | 0.338258 | + | 0.195293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.79476 | + | 17.8943i | −0.219999 | + | 0.821046i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.7286 | + | 28.1695i | 0.765948 | + | 1.28980i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.47878 | + | 12.9536i | 0.341714 | + | 0.591866i | 0.984751 | − | 0.173969i | \(-0.0556593\pi\) |
−0.643037 | + | 0.765835i | \(0.722326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.57077 | − | 9.64886i | 0.254005 | − | 0.439950i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.07927 | + | 1.13860i | 0.413121 | + | 0.0518082i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.60062 | − | 2.60062i | −0.118088 | − | 0.118088i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0362i | 1.22513i | 0.790420 | + | 0.612565i | \(0.209862\pi\) | ||||
−0.790420 | + | 0.612565i | \(0.790138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.1250 | − | 15.6398i | 0.910082 | − | 0.707257i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.41853 | + | 1.45189i | −0.244535 | + | 0.0655229i | −0.379005 | − | 0.925395i | \(-0.623734\pi\) |
0.134470 | + | 0.990918i | \(0.457067\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.9814 | + | 7.22964i | 1.21518 | + | 0.325607i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.78977 | − | 10.9479i | 0.125391 | − | 0.492073i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.20527 | − | 9.01579i | −0.233488 | − | 0.404413i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68146 | − | 21.2035i | −0.254337 | − | 0.949198i | −0.968458 | − | 0.249176i | \(-0.919840\pi\) |
0.714121 | − | 0.700022i | \(-0.246826\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.49148 | + | 7.19085i | 0.424048 | + | 0.321264i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.1955i | − | 1.03423i | −0.855915 | − | 0.517117i | \(-0.827005\pi\) | ||
0.855915 | − | 0.517117i | \(-0.172995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 28.5716i | − | 1.27142i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.35615 | − | 0.571523i | 0.0602288 | − | 0.0253822i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.37049 | − | 12.5788i | −0.149394 | − | 0.557547i | −0.999520 | − | 0.0309681i | \(-0.990141\pi\) |
0.850126 | − | 0.526579i | \(-0.176526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.381537 | + | 0.660842i | 0.0168782 | + | 0.0292339i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.1200 | + | 12.6957i | −1.28568 | + | 0.560527i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.4385 | − | 6.81623i | −1.12095 | − | 0.300359i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7772 | + | 3.15568i | −0.517959 | + | 0.138787i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.10698 | − | 2.07871i | −0.224171 | − | 0.0912453i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.4547i | 0.939949i | 0.882680 | + | 0.469974i | \(0.155737\pi\) | ||||
−0.882680 | + | 0.469974i | \(0.844263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.07495 | − | 2.07495i | −0.0907314 | − | 0.0907314i | 0.660284 | − | 0.751016i | \(-0.270436\pi\) |
−0.751016 | + | 0.660284i | \(0.770436\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.18992 | − | 5.53043i | 0.182863 | − | 0.241368i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.32977 | − | 7.49939i | 0.188608 | − | 0.326678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.51490 | − | 6.08799i | −0.152822 | − | 0.264695i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.9374 | − | 0.183562i | 0.648226 | − | 0.00796593i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.48251 | + | 5.53282i | −0.0642148 | + | 0.239653i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.57693 | − | 3.79719i | −0.284346 | − | 0.164167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.22677 | − | 5.61618i | 0.311858 | − | 0.242356i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.93571 | + | 4.93571i | 0.212596 | + | 0.212596i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7947 | − | 22.7947i | 0.980022 | − | 0.980022i | −0.0197819 | − | 0.999804i | \(-0.506297\pi\) |
0.999804 | + | 0.0197819i | \(0.00629719\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.254217 | + | 0.327121i | 0.0109095 | + | 0.0140381i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.2980 | + | 29.9610i | −0.740965 | + | 1.28339i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3804 | − | 3.58528i | −0.572106 | − | 0.153295i | −0.0388438 | − | 0.999245i | \(-0.512367\pi\) |
−0.533262 | + | 0.845950i | \(0.679034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.8959 | + | 15.0908i | 1.14789 | + | 0.644058i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.4399 | − | 11.2236i | 0.828166 | − | 0.478142i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.64148 | − | 0.947711i | −0.0698030 | − | 0.0403008i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.5048 | + | 9.47377i | 0.530799 | + | 0.402139i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.62660 | + | 8.62660i | −0.365521 | + | 0.365521i | −0.865841 | − | 0.500320i | \(-0.833216\pi\) |
0.500320 | + | 0.865841i | \(0.333216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2810 | 0.942384 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.60184 | + | 16.2194i | −0.278730 | + | 0.684784i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.46409 | + | 20.3923i | 0.230284 | + | 0.859432i | 0.980218 | + | 0.197920i | \(0.0634185\pi\) |
−0.749934 | + | 0.661513i | \(0.769915\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.49631 | + | 9.31636i | −0.105021 | + | 0.391942i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.8942 | − | 0.292376i | 0.499509 | − | 0.0122786i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.4776 | − | 12.4001i | 0.900389 | − | 0.519840i | 0.0230625 | − | 0.999734i | \(-0.492658\pi\) |
0.877326 | + | 0.479894i | \(0.159325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7063 | + | 4.74438i | −0.740985 | + | 0.198546i | −0.609516 | − | 0.792774i | \(-0.708636\pi\) |
−0.131469 | + | 0.991320i | \(0.541969\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8589 | − | 35.2582i | −0.620738 | − | 1.47293i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.1096 | 0.505004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4462 | −0.976078 | −0.488039 | − | 0.872822i | \(-0.662288\pi\) | ||||
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.5402 | − | 21.8320i | 0.687387 | − | 0.907308i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.36800 | + | 1.17040i | −0.181215 | + | 0.0485564i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5688 | − | 7.25657i | 0.520545 | − | 0.300537i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.02079 | − | 28.5271i | −0.331619 | − | 1.17945i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.33159 | + | 16.1657i | −0.178784 | + | 0.667230i | 0.817092 | + | 0.576507i | \(0.195585\pi\) |
−0.995876 | + | 0.0907235i | \(0.971082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.80108 | − | 6.72173i | −0.0742123 | − | 0.276964i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.79784 | + | 2.31342i | 0.0739532 | + | 0.0951613i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.18675 | 0.254059 | 0.127030 | − | 0.991899i | \(-0.459456\pi\) | ||||
0.127030 | + | 0.991899i | \(0.459456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1524 | + | 20.1524i | −0.826168 | + | 0.826168i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.37756 | − | 10.9847i | 0.0563797 | − | 0.449574i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.98730 | − | 4.61147i | −0.326352 | − | 0.188420i | 0.327868 | − | 0.944723i | \(-0.393670\pi\) |
−0.654220 | + | 0.756304i | \(0.727003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0097 | + | 8.66586i | −0.612259 | + | 0.353488i | −0.773849 | − | 0.633370i | \(-0.781671\pi\) |
0.161590 | + | 0.986858i | \(0.448338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.531535 | + | 43.2535i | 0.0216458 | + | 1.76142i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.2751 | + | 6.77243i | 1.02758 | + | 0.275339i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8418 | + | 20.5106i | −0.480643 | + | 0.832498i | −0.999753 | − | 0.0222090i | \(-0.992930\pi\) |
0.519110 | + | 0.854707i | \(0.326263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.32835 | + | 1.14855i | −0.337482 | + | 0.0465415i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6135 | + | 22.6135i | −0.914844 | + | 0.914844i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4110 | + | 15.4110i | 0.622445 | + | 0.622445i | 0.946156 | − | 0.323711i | \(-0.104930\pi\) |
−0.323711 | + | 0.946156i | \(0.604930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.47040 | − | 3.04070i | −0.301236 | − | 0.122613i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.9979 | − | 6.92700i | −0.483018 | − | 0.278870i | 0.238655 | − | 0.971104i | \(-0.423293\pi\) |
−0.721673 | + | 0.692234i | \(0.756627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3518 | − | 38.6333i | 0.416072 | − | 1.55280i | −0.366606 | − | 0.930376i | \(-0.619480\pi\) |
0.782678 | − | 0.622427i | \(-0.213853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9426 | + | 16.2384i | 0.519367 | + | 0.651624i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7156 | − | 18.5599i | −0.429310 | − | 0.743586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.4844 | + | 26.8198i | −0.619377 | + | 1.07279i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.46503 | + | 12.9678i | 0.218252 | + | 0.517884i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.1945 | − | 17.1945i | −0.685591 | − | 0.685591i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.7956i | − | 0.668624i | −0.942462 | − | 0.334312i | \(-0.891496\pi\) | ||
0.942462 | − | 0.334312i | \(-0.108504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.493315 | − | 3.57712i | −0.0196075 | − | 0.142178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.3567 | − | 3.84688i | 0.569730 | − | 0.152659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6845 | + | 4.73856i | 0.700687 | + | 0.187749i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.83371 | − | 22.8933i | 0.230778 | − | 0.905647i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0246 | + | 34.6837i | 0.790925 | + | 1.36992i | 0.925395 | + | 0.379005i | \(0.123734\pi\) |
−0.134470 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.289008 | + | 1.07859i | 0.0113974 | + | 0.0425356i | 0.971390 | − | 0.237489i | \(-0.0763242\pi\) |
−0.959993 | + | 0.280024i | \(0.909658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.90388 | + | 31.1297i | −0.153715 | + | 1.22573i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.9272i | − | 1.25519i | −0.778541 | − | 0.627594i | \(-0.784040\pi\) | ||
0.778541 | − | 0.627594i | \(-0.215960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.61750i | − | 0.259759i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.324308 | + | 2.58605i | −0.0127106 | + | 0.101355i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.36682 | − | 12.5651i | −0.131754 | − | 0.491712i | 0.868236 | − | 0.496151i | \(-0.165254\pi\) |
−0.999990 | + | 0.00443888i | \(0.998587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.19841 | − | 15.9321i | −0.359412 | − | 0.622519i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.427601 | + | 1.67804i | −0.0166823 | + | 0.0654667i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.4883 | − | 4.15007i | −0.603337 | − | 0.161664i | −0.0557954 | − | 0.998442i | \(-0.517769\pi\) |
−0.547541 | + | 0.836779i | \(0.684436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9923 | − | 5.89283i | 0.855403 | − | 0.229204i | 0.195637 | − | 0.980676i | \(-0.437322\pi\) |
0.659765 | + | 0.751472i | \(0.270656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.27493 | + | 45.5007i | 0.243698 | + | 1.76710i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.9026i | 0.888124i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3754 | − | 10.3754i | −0.401738 | − | 0.401738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.3627 | − | 43.5722i | −0.709941 | − | 1.68460i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.83085 | − | 11.8314i | 0.263702 | − | 0.456745i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3212 | + | 28.2692i | 0.629136 | + | 1.08970i | 0.987725 | + | 0.156201i | \(0.0499246\pi\) |
−0.358589 | + | 0.933496i | \(0.616742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.5702 | − | 2.34257i | 0.599298 | − | 0.0901656i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.84993 | − | 14.3681i | 0.147965 | − | 0.552212i | −0.851641 | − | 0.524126i | \(-0.824392\pi\) |
0.999606 | − | 0.0280861i | \(-0.00894127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.48588 | − | 0.857871i | −0.0570227 | − | 0.0329221i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.66343 | − | 1.89817i | −0.178703 | − | 0.0727381i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.4912 | − | 21.4912i | −0.822338 | − | 0.822338i | 0.164105 | − | 0.986443i | \(-0.447526\pi\) |
−0.986443 | + | 0.164105i | \(0.947526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2671 | + | 14.2671i | −0.545120 | + | 0.545120i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.5210 | + | 1.58885i | −0.439555 | + | 0.0606183i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.0334 | − | 32.9669i | 0.725116 | − | 1.25594i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.83775 | + | 2.36807i | 0.336204 | + | 0.0900855i | 0.422971 | − | 0.906143i | \(-0.360987\pi\) |
−0.0867676 | + | 0.996229i | \(0.527654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0647636 | − | 5.27012i | −0.00246017 | − | 0.200195i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3440 | + | 5.97209i | −0.392369 | + | 0.226534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8266 | + | 6.25077i | 0.410088 | + | 0.236765i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.54660 | − | 20.3067i | 0.0963212 | − | 0.768070i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.05144 | + | 4.05144i | −0.153021 | + | 0.153021i | −0.779466 | − | 0.626445i | \(-0.784509\pi\) |
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5411 | −0.737005 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.6322 | − | 35.5565i | −1.04069 | − | 1.33913i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.44978 | − | 12.8747i | −0.129742 | − | 0.484204i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00775 | + | 3.76098i | −0.0378469 | + | 0.141247i | −0.982264 | − | 0.187503i | \(-0.939961\pi\) |
0.944417 | + | 0.328750i | \(0.106627\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.16424 | − | 4.14078i | −0.0436623 | − | 0.155291i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.93936 | + | 2.27439i | −0.147530 | + | 0.0851767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6797 | + | 3.39752i | −0.474195 | + | 0.127060i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.66841 | − | 4.84208i | 0.136999 | − | 0.180831i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.0063 | 1.38010 | 0.690050 | − | 0.723761i | \(-0.257588\pi\) | ||||
0.690050 | + | 0.723761i | \(0.257588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2859 | −0.457552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.86057 | − | 13.9064i | −0.217957 | − | 0.517184i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.7469 | + | 2.87962i | −0.399129 | + | 0.106946i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.4066 | + | 16.4006i | −1.05354 | + | 0.608264i | −0.923640 | − | 0.383262i | \(-0.874801\pi\) |
−0.129905 | + | 0.991526i | \(0.541467\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.7826 | + | 18.3753i | 0.732688 | + | 0.680565i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.5861 | − | 46.9719i | 0.465513 | − | 1.73732i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.9743 | + | 40.9566i | 0.405345 | + | 1.51277i | 0.803419 | + | 0.595413i | \(0.203012\pi\) |
−0.398075 | + | 0.917353i | \(0.630322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.71899 | + | 23.8776i | −0.358490 | + | 0.880740i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.1620 | 0.705842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3761 | − | 15.3761i | 0.565620 | − | 0.565620i | −0.365278 | − | 0.930898i | \(-0.619026\pi\) |
0.930898 | + | 0.365278i | \(0.119026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.4207 | + | 22.2894i | 1.08080 | + | 0.818823i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.4824 | − | 23.3725i | −1.48516 | − | 0.857456i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
−0.999857 | + | 0.0168926i | \(0.994623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3664 | + | 12.3359i | −0.782805 | + | 0.451952i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.94961 | − | 5.02145i | −0.327449 | − | 0.183725i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.42213 | − | 0.916958i | −0.125042 | − | 0.0335049i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7074 | + | 44.5265i | −0.938077 | + | 1.62480i | −0.169023 | + | 0.985612i | \(0.554061\pi\) |
−0.769054 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.5829 | + | 18.7650i | 0.531432 | + | 0.683835i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.2088 | + | 41.2088i | −1.49974 | + | 1.49974i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4143 | + | 25.4143i | 0.923698 | + | 0.923698i | 0.997289 | − | 0.0735910i | \(-0.0234459\pi\) |
−0.0735910 | + | 0.997289i | \(0.523446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.26324 | − | 5.64452i | 0.263639 | − | 0.204883i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.2336 | + | 11.6819i | 0.733467 | + | 0.423467i | 0.819689 | − | 0.572808i | \(-0.194146\pi\) |
−0.0862220 | + | 0.996276i | \(0.527479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.17717 | + | 15.5894i | −0.151224 | + | 0.564375i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −64.6706 | + | 0.794725i | −2.33817 | + | 0.0287334i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.67859 | − | 15.0318i | −0.313366 | − | 0.542765i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7645 | + | 22.1087i | −0.460299 | + | 0.797261i | −0.998976 | − | 0.0452513i | \(-0.985591\pi\) |
0.538677 | + | 0.842513i | \(0.318924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3888 | + | 25.5920i | −0.698270 | + | 0.921674i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2256 | − | 19.2256i | −0.691496 | − | 0.691496i | 0.271065 | − | 0.962561i | \(-0.412624\pi\) |
−0.962561 | + | 0.271065i | \(0.912624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.44916i | 0.123898i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.77870 | + | 2.75916i | 0.243185 | + | 0.0989843i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.70397 | − | 2.60017i | 0.347681 | − | 0.0931608i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1088 | − | 2.70866i | −0.361723 | − | 0.0969234i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.3476 | − | 11.3334i | −0.548479 | − | 0.405022i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.0680 | − | 22.6344i | −0.466416 | − | 0.807857i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.16260 | − | 19.2671i | −0.184027 | − | 0.686797i | −0.994837 | − | 0.101488i | \(-0.967640\pi\) |
0.810810 | − | 0.585309i | \(-0.199027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.31589 | + | 2.66171i | −0.224852 | + | 0.0947593i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.49949i | 0.159983i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.8336i | − | 1.27249i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 42.7246 | + | 32.3687i | 1.51529 | + | 1.14800i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.02171 | − | 11.2772i | −0.107035 | − | 0.399458i | 0.891534 | − | 0.452955i | \(-0.149630\pi\) |
−0.998568 | + | 0.0534965i | \(0.982963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.8990 | + | 60.4469i | 1.23464 | + | 2.13846i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0093 | − | 47.1282i | 0.424326 | − | 1.66519i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.740961 | + | 0.198540i | 0.0261479 | + | 0.00700632i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.4606 | − | 3.87471i | 0.509669 | − | 0.136565i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.1840 | − | 26.5656i | 1.20333 | − | 0.935152i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 13.1110i | − | 0.460958i | −0.973077 | − | 0.230479i | \(-0.925971\pi\) | ||
0.973077 | − | 0.230479i | \(-0.0740292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.1945 | + | 34.1945i | 1.20073 | + | 1.20073i | 0.973944 | + | 0.226789i | \(0.0728227\pi\) |
0.226789 | + | 0.973944i | \(0.427177\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.3267 | + | 5.80969i | 1.62475 | + | 0.203755i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.8498 | − | 36.1129i | 0.730337 | − | 1.26498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.5392 | − | 33.8429i | −0.683590 | − | 1.18401i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.05868 | − | 11.8862i | −0.246650 | − | 0.415339i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.39631 | − | 23.8714i | 0.223233 | − | 0.833116i | −0.759872 | − | 0.650073i | \(-0.774738\pi\) |
0.983105 | − | 0.183044i | \(-0.0585949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2152 | + | 9.36184i | 0.565226 | + | 0.326333i | 0.755240 | − | 0.655448i | \(-0.227520\pi\) |
−0.190014 | + | 0.981781i | \(0.560853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.952888 | − | 6.90958i | −0.0331753 | − | 0.240561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.1212 | + | 24.1212i | 0.838775 | + | 0.838775i | 0.988698 | − | 0.149923i | \(-0.0479025\pi\) |
−0.149923 | + | 0.988698i | \(0.547902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8683 | + | 20.8683i | −0.724787 | + | 0.724787i | −0.969576 | − | 0.244789i | \(-0.921281\pi\) |
0.244789 | + | 0.969576i | \(0.421281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.24988 | − | 15.3547i | 0.216806 | − | 0.532649i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.9793 | − | 34.6052i | 0.692242 | − | 1.19900i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.8183 | + | 5.04234i | 0.651233 | + | 0.174497i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.62517 | + | 3.68643i | −0.159869 | + | 0.127422i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.01977 | − | 2.89816i | 0.173302 | − | 0.100056i | −0.410840 | − | 0.911707i | \(-0.634765\pi\) |
0.584142 | + | 0.811652i | \(0.301431\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4396 | − | 7.75936i | −0.463435 | − | 0.267564i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.6929 | − | 6.61346i | 0.540492 | − | 0.227780i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.70253 | − | 1.70253i | 0.0585689 | − | 0.0585689i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2070 | 0.419437 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.4657 | − | 7.37337i | 1.83494 | − | 0.253053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.30600 | + | 12.3381i | 0.113328 | + | 0.422946i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.461332 | + | 1.72171i | −0.0157957 | + | 0.0589504i | −0.973374 | − | 0.229223i | \(-0.926381\pi\) |
0.957578 | + | 0.288174i | \(0.0930481\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.2964 | + | 37.1996i | −1.24131 | + | 1.27220i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.6918 | − | 7.32760i | 0.433543 | − | 0.250306i | −0.267312 | − | 0.963610i | \(-0.586135\pi\) |
0.700855 | + | 0.713304i | \(0.252802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.3859 | − | 13.7688i | 1.75327 | − | 0.469786i | 0.767947 | − | 0.640513i | \(-0.221278\pi\) |
0.985318 | + | 0.170727i | \(0.0546116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.73340 | − | 0.468194i | −0.127234 | − | 0.0159560i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.9467 | −0.815157 | −0.407578 | − | 0.913170i | \(-0.633627\pi\) | ||||
−0.407578 | + | 0.913170i | \(0.633627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.02103 | −0.306724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 70.2515 | + | 8.81003i | 2.38587 | + | 0.299204i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.84049 | + | 0.493159i | −0.0624345 | + | 0.0167293i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.5269 | − | 25.1303i | 1.47485 | − | 0.851507i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.05387 | − | 3.74825i | −0.0356681 | − | 0.126859i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.90986 | + | 7.12771i | −0.0645652 | + | 0.240961i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6447 | + | 39.7266i | 0.359446 | + | 1.34147i | 0.874796 | + | 0.484492i | \(0.160996\pi\) |
−0.515349 | + | 0.856980i | \(0.672338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.3922 | − | 7.50114i | 1.83460 | − | 0.253007i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2335 | −1.38919 | −0.694597 | − | 0.719399i | \(-0.744417\pi\) | ||||
−0.694597 | + | 0.719399i | \(0.744417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.9719 | − | 11.9719i | 0.402885 | − | 0.402885i | −0.476364 | − | 0.879248i | \(-0.658045\pi\) |
0.879248 | + | 0.476364i | \(0.158045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.5221 | − | 9.49151i | 0.757074 | − | 0.319054i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.7452 | + | 15.4413i | 0.898016 | + | 0.518470i | 0.876556 | − | 0.481300i | \(-0.159835\pi\) |
0.0214599 | + | 0.999770i | \(0.493169\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.00486 | − | 3.46691i | 0.201397 | − | 0.116276i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.24700 | − | 8.66266i | 0.276285 | − | 0.290210i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 54.1788 | + | 14.5172i | 1.81302 | + | 0.485798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.48706 | − | 12.9680i | 0.250265 | − | 0.433471i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.09601 | − | 22.3471i | 0.303707 | − | 0.746147i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.95523 | − | 2.95523i | 0.0985624 | − | 0.0985624i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.7480 | − | 58.7480i | −1.95718 | − | 1.95718i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.99951 | + | 14.4988i | 0.0665395 | + | 0.482491i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.586997 | + | 0.338903i | 0.0195125 | + | 0.0112655i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.16365 | + | 26.7351i | −0.237865 | + | 0.887725i | 0.738971 | + | 0.673737i | \(0.235312\pi\) |
−0.976836 | + | 0.213988i | \(0.931355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.8008 | − | 26.3791i | 0.490912 | − | 0.874940i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.83009 | + | 8.36596i | 0.160028 | + | 0.277177i | 0.934878 | − | 0.354968i | \(-0.115508\pi\) |
−0.774850 | + | 0.632145i | \(0.782175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.27297 | + | 3.93689i | −0.0752242 | + | 0.130292i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50.0647 | + | 6.27846i | 1.65509 | + | 0.207560i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.06859 | − | 6.06859i | −0.200403 | − | 0.200403i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.5574i | − | 0.414229i | −0.978317 | − | 0.207115i | \(-0.933593\pi\) | ||
0.978317 | − | 0.207115i | \(-0.0664073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.3659 | + | 25.9298i | −1.09944 | + | 0.854415i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.5147 | + | 7.10460i | −0.872743 | + | 0.233851i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.35553 | + | 2.50681i | 0.307608 | + | 0.0824233i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.9555 | − | 19.4710i | −0.655424 | − | 0.639511i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.50031 | + | 7.79477i | 0.147650 | + | 0.255738i | 0.930359 | − | 0.366651i | \(-0.119496\pi\) |
−0.782708 | + | 0.622389i | \(0.786162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.31092 | − | 31.0168i | −0.272379 | − | 1.01653i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.6081 | + | 10.3097i | 0.445510 | + | 0.337523i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.6501i | 0.936960i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.2265i | 1.93485i | 0.253166 | + | 0.967423i | \(0.418528\pi\) | ||||
−0.253166 | + | 0.967423i | \(0.581472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.5878 | + | 6.56917i | −0.508689 | + | 0.214377i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.95446 | − | 11.0262i | −0.0963126 | − | 0.359443i | 0.900903 | − | 0.434021i | \(-0.142906\pi\) |
−0.997215 | + | 0.0745778i | \(0.976239\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.28347 | − | 5.68714i | −0.106925 | − | 0.185199i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.8436 | − | 7.77939i | 0.580452 | − | 0.253064i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.32058 | − | 2.22949i | −0.270382 | − | 0.0724488i | 0.121080 | − | 0.992643i | \(-0.461364\pi\) |
−0.391463 | + | 0.920194i | \(0.628031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.94348 | − | 0.520755i | 0.0630882 | − | 0.0169044i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2750 | − | 8.65964i | −0.689889 | − | 0.280808i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.5260i | 1.40995i | 0.709234 | + | 0.704973i | \(0.249041\pi\) | ||||
−0.709234 | + | 0.704973i | \(0.750959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.2637 | − | 44.2637i | −1.43234 | − | 1.43234i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.10367 | + | 6.73653i | −0.164978 | + | 0.217761i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.70633 | + | 8.15160i | −0.151975 | + | 0.263229i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8522 | + | 25.7247i | 0.479103 | + | 0.829830i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.10520 | − | 6.91283i | −0.132288 | − | 0.222763i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5982 | − | 43.2852i | 0.373361 | − | 1.39340i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.2267 | + | 15.1420i | 0.843393 | + | 0.486933i | 0.858416 | − | 0.512954i | \(-0.171449\pi\) |
−0.0150229 | + | 0.999887i | \(0.504782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.6090 | − | 49.4328i | 2.04341 | − | 1.58801i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.06755 | − | 9.06755i | −0.290992 | − | 0.290992i | 0.546480 | − | 0.837472i | \(-0.315967\pi\) |
−0.837472 | + | 0.546480i | \(0.815967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.94005 | + | 3.94005i | −0.126312 | + | 0.126312i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.2261 | − | 14.4456i | −0.359524 | − | 0.462628i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.4475 | − | 18.0956i | 0.334246 | − | 0.578931i | −0.649094 | − | 0.760708i | \(-0.724852\pi\) |
0.983340 | + | 0.181778i | \(0.0581851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.8100 | − | 5.57603i | −0.665092 | − | 0.178211i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.4912 | + | 18.7011i | −1.00544 | + | 0.597081i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.14158 | − | 0.659092i | 0.0364108 | − | 0.0210218i | −0.481684 | − | 0.876345i | \(-0.659975\pi\) |
0.518095 | + | 0.855323i | \(0.326641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.15128 | + | 2.39674i | 0.132271 | + | 0.0763665i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.7446 | − | 12.6859i | −0.532986 | − | 0.403796i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0626 | + | 18.0626i | −0.574357 | + | 0.574357i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.51185 | −0.0797914 | −0.0398957 | − | 0.999204i | \(-0.512703\pi\) | ||||
−0.0398957 | + | 0.999204i | \(0.512703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.691664 | + | 1.69928i | −0.0219493 | + | 0.0539250i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.68788 | − | 17.4954i | −0.148616 | − | 0.554641i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9030 | − | 44.4227i | 0.376973 | − | 1.40688i | −0.473468 | − | 0.880811i | \(-0.656998\pi\) |
0.850441 | − | 0.526071i | \(-0.176335\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.63757 | + | 15.2246i | 0.210003 | + | 0.481685i |
(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 | 576.2.bb.e.49.18 | 72 | ||
3.2 | odd | 2 | 1728.2.bc.e.1009.5 | 72 | |||
4.3 | odd | 2 | 144.2.x.e.85.17 | yes | 72 | ||
9.2 | odd | 6 | 1728.2.bc.e.1585.14 | 72 | |||
9.7 | even | 3 | inner | 576.2.bb.e.241.11 | 72 | ||
12.11 | even | 2 | 432.2.y.e.37.2 | 72 | |||
16.3 | odd | 4 | 144.2.x.e.13.7 | ✓ | 72 | ||
16.13 | even | 4 | inner | 576.2.bb.e.337.11 | 72 | ||
36.7 | odd | 6 | 144.2.x.e.133.7 | yes | 72 | ||
36.11 | even | 6 | 432.2.y.e.181.12 | 72 | |||
48.29 | odd | 4 | 1728.2.bc.e.145.14 | 72 | |||
48.35 | even | 4 | 432.2.y.e.253.12 | 72 | |||
144.29 | odd | 12 | 1728.2.bc.e.721.5 | 72 | |||
144.61 | even | 12 | inner | 576.2.bb.e.529.18 | 72 | ||
144.83 | even | 12 | 432.2.y.e.397.2 | 72 | |||
144.115 | odd | 12 | 144.2.x.e.61.17 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.7 | ✓ | 72 | 16.3 | odd | 4 | ||
144.2.x.e.61.17 | yes | 72 | 144.115 | odd | 12 | ||
144.2.x.e.85.17 | yes | 72 | 4.3 | odd | 2 | ||
144.2.x.e.133.7 | yes | 72 | 36.7 | odd | 6 | ||
432.2.y.e.37.2 | 72 | 12.11 | even | 2 | |||
432.2.y.e.181.12 | 72 | 36.11 | even | 6 | |||
432.2.y.e.253.12 | 72 | 48.35 | even | 4 | |||
432.2.y.e.397.2 | 72 | 144.83 | even | 12 | |||
576.2.bb.e.49.18 | 72 | 1.1 | even | 1 | trivial | ||
576.2.bb.e.241.11 | 72 | 9.7 | even | 3 | inner | ||
576.2.bb.e.337.11 | 72 | 16.13 | even | 4 | inner | ||
576.2.bb.e.529.18 | 72 | 144.61 | even | 12 | inner | ||
1728.2.bc.e.145.14 | 72 | 48.29 | odd | 4 | |||
1728.2.bc.e.721.5 | 72 | 144.29 | odd | 12 | |||
1728.2.bc.e.1009.5 | 72 | 3.2 | odd | 2 | |||
1728.2.bc.e.1585.14 | 72 | 9.2 | odd | 6 |