Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,2,Mod(17,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.u (of order \(9\), degree \(6\), 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: | \(2.42745222145\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 225.1 | ||
Root | \(-0.976256 + 1.69092i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.225 |
Dual form | 304.2.u.f.177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.83476 | + | 0.667798i | −1.05930 | + | 0.385554i | −0.812165 | − | 0.583428i | \(-0.801711\pi\) |
−0.247135 | + | 0.968981i | \(0.579489\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.302047 | − | 1.71299i | 0.135079 | − | 0.766073i | −0.839725 | − | 0.543012i | \(-0.817284\pi\) |
0.974804 | − | 0.223061i | \(-0.0716050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.962609 | + | 1.66729i | 0.363832 | + | 0.630176i | 0.988588 | − | 0.150644i | \(-0.0481348\pi\) |
−0.624756 | + | 0.780820i | \(0.714802\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.622259 | − | 0.522138i | 0.207420 | − | 0.174046i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27748 | − | 3.94470i | 0.686685 | − | 1.18937i | −0.286220 | − | 0.958164i | \(-0.592399\pi\) |
0.972904 | − | 0.231209i | \(-0.0742680\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.57934 | + | 0.938803i | 0.715381 | + | 0.260377i | 0.673963 | − | 0.738765i | \(-0.264591\pi\) |
0.0414171 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.589750 | + | 3.34464i | 0.152273 | + | 0.863581i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.84088 | + | 3.22288i | 0.931550 | + | 0.781663i | 0.976095 | − | 0.217344i | \(-0.0697393\pi\) |
−0.0445449 | + | 0.999007i | \(0.514184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.18751 | + | 1.21026i | 0.960682 | + | 0.277652i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.87957 | − | 2.41625i | −0.628374 | − | 0.527268i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.198055 | − | 1.12322i | −0.0412972 | − | 0.234208i | 0.957172 | − | 0.289520i | \(-0.0934958\pi\) |
−0.998469 | + | 0.0553120i | \(0.982385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.85536 | + | 0.675294i | 0.371071 | + | 0.135059i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13575 | − | 3.69923i | 0.411026 | − | 0.711918i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.83721 | − | 3.21980i | 0.712552 | − | 0.597902i | −0.212762 | − | 0.977104i | \(-0.568246\pi\) |
0.925314 | + | 0.379202i | \(0.123801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.999936 | + | 1.73194i | 0.179594 | + | 0.311066i | 0.941741 | − | 0.336338i | \(-0.109188\pi\) |
−0.762148 | + | 0.647403i | \(0.775855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.54436 | + | 8.75848i | −0.268838 | + | 1.52466i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.14680 | − | 1.14534i | 0.531907 | − | 0.193598i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.06608 | −1.16166 | −0.580828 | − | 0.814026i | \(-0.697271\pi\) | ||||
−0.580828 | + | 0.814026i | \(0.697271\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.35941 | −0.858192 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.3600 | + | 3.77075i | −1.61797 | + | 0.588892i | −0.982993 | − | 0.183642i | \(-0.941211\pi\) |
−0.634974 | + | 0.772534i | \(0.718989\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.05998 | + | 6.01147i | −0.161646 | + | 0.916741i | 0.790809 | + | 0.612063i | \(0.209660\pi\) |
−0.952455 | + | 0.304678i | \(0.901451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.706466 | − | 1.22363i | −0.105314 | − | 0.182409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.72021 | − | 5.63892i | 0.980243 | − | 0.822522i | −0.00388290 | − | 0.999992i | \(-0.501236\pi\) |
0.984126 | + | 0.177471i | \(0.0567915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.64677 | − | 2.85228i | 0.235252 | − | 0.407469i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.19933 | − | 3.34828i | −1.28816 | − | 0.468853i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.00933315 | + | 0.0529309i | 0.00128201 | + | 0.00727062i | 0.985442 | − | 0.170012i | \(-0.0543805\pi\) |
−0.984160 | + | 0.177282i | \(0.943269\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.06934 | − | 5.09278i | −0.818389 | − | 0.686710i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.49130 | + | 0.575879i | −1.12470 | + | 0.0762770i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.83451 | − | 2.37844i | −0.369022 | − | 0.309646i | 0.439353 | − | 0.898315i | \(-0.355208\pi\) |
−0.808375 | + | 0.588669i | \(0.799652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.60306 | − | 14.7627i | −0.333288 | − | 1.89017i | −0.443518 | − | 0.896266i | \(-0.646270\pi\) |
0.110229 | − | 0.993906i | \(-0.464842\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.46955 | + | 0.534871i | 0.185145 | + | 0.0673874i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.38724 | − | 4.13483i | 0.296101 | − | 0.512862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.72449 | + | 8.15982i | −1.18804 | + | 0.996880i | −0.188144 | + | 0.982141i | \(0.560247\pi\) |
−0.999891 | + | 0.0147389i | \(0.995308\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.11347 | + | 1.92859i | 0.134046 | + | 0.232174i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.359347 | − | 2.03796i | 0.0426466 | − | 0.241861i | −0.956031 | − | 0.293265i | \(-0.905258\pi\) |
0.998678 | + | 0.0514034i | \(0.0163694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.670002 | − | 0.243861i | 0.0784178 | − | 0.0285418i | −0.302513 | − | 0.953145i | \(-0.597826\pi\) |
0.380931 | + | 0.924603i | \(0.375603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.85509 | −0.445148 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.76928 | 0.999352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5802 | + | 3.85086i | −1.19036 | + | 0.433256i | −0.859850 | − | 0.510546i | \(-0.829443\pi\) |
−0.330511 | + | 0.943802i | \(0.607221\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.87142 | + | 10.6133i | −0.207935 | + | 1.17926i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.99262 | + | 8.64748i | 0.548012 | + | 0.949184i | 0.998411 | + | 0.0563567i | \(0.0179484\pi\) |
−0.450399 | + | 0.892827i | \(0.648718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.68089 | − | 5.60593i | 0.724645 | − | 0.608049i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.89018 | + | 8.47005i | −0.524283 | + | 0.908084i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2229 | + | 5.54068i | 1.61362 | + | 0.587311i | 0.982152 | − | 0.188088i | \(-0.0602289\pi\) |
0.631472 | + | 0.775399i | \(0.282451\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.917642 | + | 5.20421i | 0.0961950 | + | 0.545549i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.99123 | − | 2.50994i | −0.310176 | − | 0.260269i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.33799 | − | 6.80762i | 0.342470 | − | 0.698447i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.285278 | + | 0.239377i | 0.0289656 | + | 0.0243050i | 0.657156 | − | 0.753755i | \(-0.271759\pi\) |
−0.628190 | + | 0.778060i | \(0.716204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.642497 | − | 3.64378i | −0.0645734 | − | 0.366214i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.4750 | − | 6.36040i | −1.73883 | − | 0.632883i | −0.739637 | − | 0.673006i | \(-0.765003\pi\) |
−0.999195 | + | 0.0401224i | \(0.987225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.48973 | − | 7.77645i | 0.442387 | − | 0.766236i | −0.555479 | − | 0.831530i | \(-0.687465\pi\) |
0.997866 | + | 0.0652941i | \(0.0207986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00877 | + | 4.20286i | −0.488806 | + | 0.410157i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.74332 | + | 6.48362i | 0.361881 | + | 0.626796i | 0.988270 | − | 0.152714i | \(-0.0488015\pi\) |
−0.626390 | + | 0.779510i | \(0.715468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.91266 | + | 16.5185i | −0.278982 | + | 1.58219i | 0.447039 | + | 0.894515i | \(0.352479\pi\) |
−0.726021 | + | 0.687672i | \(0.758633\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9646 | − | 4.71871i | 1.23054 | − | 0.447881i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6659 | 1.00336 | 0.501682 | − | 0.865052i | \(-0.332715\pi\) | ||||
0.501682 | + | 0.865052i | \(0.332715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.98389 | −0.184999 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.09520 | − | 0.762592i | 0.193702 | − | 0.0705016i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.67620 | + | 9.50623i | −0.153657 | + | 0.871435i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.87379 | − | 8.44164i | −0.443071 | − | 0.767422i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.4901 | − | 13.8368i | 1.48686 | − | 1.24763i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.06572 | − | 10.5061i | 0.542534 | − | 0.939697i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3628 | + | 3.77175i | 0.919550 | + | 0.334689i | 0.758059 | − | 0.652185i | \(-0.226148\pi\) |
0.161491 | + | 0.986874i | \(0.448370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.06963 | − | 11.7375i | −0.182221 | − | 1.03343i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7437 | − | 9.01505i | −0.938683 | − | 0.787648i | 0.0386728 | − | 0.999252i | \(-0.487687\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.01309 | + | 8.14680i | 0.174557 | + | 0.706417i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.69166 | − | 4.77587i | −0.489860 | − | 0.411041i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.53142 | + | 8.68510i | 0.130838 | + | 0.742019i | 0.977668 | + | 0.210155i | \(0.0673969\pi\) |
−0.846830 | + | 0.531863i | \(0.821492\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.75603 | + | 2.09502i | 0.488220 | + | 0.177698i | 0.574388 | − | 0.818583i | \(-0.305240\pi\) |
−0.0861681 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.56431 | + | 14.8338i | −0.721245 | + | 1.24923i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.57769 | − | 8.03663i | 0.800926 | − | 0.672057i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.35647 | − | 7.54564i | −0.361786 | − | 0.626631i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.11667 | + | 6.33297i | −0.0921016 | + | 0.522334i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.28488 | − | 0.831630i | 0.187185 | − | 0.0681298i | −0.246727 | − | 0.969085i | \(-0.579355\pi\) |
0.433912 | + | 0.900955i | \(0.357133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4850 | −0.934636 | −0.467318 | − | 0.884089i | \(-0.654780\pi\) | ||||
−0.467318 | + | 0.884089i | \(0.654780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.07281 | 0.329267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.26882 | − | 1.18975i | 0.262558 | − | 0.0955634i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.462101 | + | 2.62071i | −0.0368797 | + | 0.209155i | −0.997679 | − | 0.0680888i | \(-0.978310\pi\) |
0.960800 | + | 0.277244i | \(0.0894210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0524713 | − | 0.0908830i | −0.00416124 | − | 0.00720749i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.68209 | − | 1.41144i | 0.132567 | − | 0.111237i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.05611 | + | 3.56129i | −0.161047 | + | 0.278942i | −0.935245 | − | 0.354002i | \(-0.884820\pi\) |
0.774197 | + | 0.632944i | \(0.218154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.5367 | + | 5.29094i | 1.13168 | + | 0.411899i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.59827 | − | 14.7355i | −0.201060 | − | 1.14027i | −0.903521 | − | 0.428545i | \(-0.859027\pi\) |
0.702461 | − | 0.711722i | \(-0.252085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.18693 | − | 3.51325i | −0.322071 | − | 0.270250i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.23764 | − | 1.43336i | 0.247589 | − | 0.109612i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.88231 | − | 4.09674i | −0.371195 | − | 0.311470i | 0.438039 | − | 0.898956i | \(-0.355673\pi\) |
−0.809234 | + | 0.587486i | \(0.800118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.660072 | + | 3.74346i | 0.0498968 | + | 0.282979i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.78897 | + | 2.47098i | 0.510290 | + | 0.185730i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.59062 | − | 2.75504i | 0.118889 | − | 0.205922i | −0.800439 | − | 0.599415i | \(-0.795400\pi\) |
0.919328 | + | 0.393493i | \(0.128733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.48401 | + | 2.92343i | −0.258964 | + | 0.217297i | −0.763021 | − | 0.646374i | \(-0.776285\pi\) |
0.504057 | + | 0.863671i | \(0.331840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.6345 | + | 25.3477i | 1.08181 | + | 1.87376i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.13428 | + | 12.1041i | −0.156916 | + | 0.889913i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.4608 | − | 7.81110i | 1.56937 | − | 0.571204i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.22358 | 0.598178 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.968712 | 0.0700935 | 0.0350468 | − | 0.999386i | \(-0.488842\pi\) | ||||
0.0350468 | + | 0.999386i | \(0.488842\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.2895 | + | 5.20094i | −1.02858 | + | 0.374372i | −0.800540 | − | 0.599280i | \(-0.795454\pi\) |
−0.228039 | + | 0.973652i | \(0.573231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.61879 | + | 9.18062i | −0.115924 | + | 0.657438i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.22940 | − | 14.2537i | −0.586320 | − | 1.01554i | −0.994709 | − | 0.102729i | \(-0.967243\pi\) |
0.408389 | − | 0.912808i | \(-0.366091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8080 | + | 14.1036i | −1.19149 | + | 0.999775i | −0.191653 | + | 0.981463i | \(0.561385\pi\) |
−0.999832 | + | 0.0183119i | \(0.994171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.3930 | − | 21.4653i | 0.874135 | − | 1.51405i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.06207 | + | 3.29832i | 0.636033 | + | 0.231497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.33004 | + | 18.8856i | 0.232580 | + | 1.31903i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.709718 | − | 0.595524i | −0.0493288 | − | 0.0413918i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.3111 | − | 13.7622i | 0.989917 | − | 0.951949i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0895 | − | 11.8225i | −0.969962 | − | 0.813895i | 0.0125831 | − | 0.999921i | \(-0.495995\pi\) |
−0.982545 | + | 0.186026i | \(0.940439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.701629 | + | 3.97914i | 0.0480748 | + | 0.272646i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.97744 | + | 3.63149i | 0.680456 | + | 0.247666i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.92509 | + | 3.33436i | −0.130684 | + | 0.226351i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.06644 | + | 0.894853i | −0.0720636 | + | 0.0604685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.88129 | + | 11.9187i | 0.462886 | + | 0.801741i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.38895 | − | 19.2197i | 0.226941 | − | 1.28705i | −0.631998 | − | 0.774970i | \(-0.717765\pi\) |
0.858939 | − | 0.512077i | \(-0.171124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.50711 | − | 0.548543i | 0.100474 | − | 0.0365695i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.30867 | −0.485094 | −0.242547 | − | 0.970140i | \(-0.577983\pi\) | ||||
−0.242547 | + | 0.970140i | \(0.577983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1319 | 1.39644 | 0.698218 | − | 0.715885i | \(-0.253977\pi\) | ||||
0.698218 | + | 0.715885i | \(0.253977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0895 | + | 5.85611i | −1.05861 | + | 0.385304i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.826691 | − | 4.68840i | 0.0541583 | − | 0.307147i | −0.945681 | − | 0.325097i | \(-0.894603\pi\) |
0.999839 | + | 0.0179503i | \(0.00571406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.62961 | − | 13.2149i | −0.497701 | − | 0.862044i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.8405 | − | 14.1308i | 1.09391 | − | 0.917896i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4370 | + | 18.0774i | −0.675114 | + | 1.16933i | 0.301322 | + | 0.953522i | \(0.402572\pi\) |
−0.976436 | + | 0.215809i | \(0.930761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.64094 | − | 2.41710i | −0.427781 | − | 0.155699i | 0.119152 | − | 0.992876i | \(-0.461982\pi\) |
−0.546933 | + | 0.837177i | \(0.684205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.42875 | − | 8.10284i | −0.0916543 | − | 0.519797i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.38854 | − | 3.68242i | −0.280373 | − | 0.235261i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.66483 | + | 7.05292i | 0.614959 | + | 0.448767i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.9350 | − | 12.5320i | −0.946470 | − | 0.794182i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.11124 | + | 11.9734i | 0.133260 | + | 0.755756i | 0.976055 | + | 0.217522i | \(0.0697973\pi\) |
−0.842795 | + | 0.538234i | \(0.819092\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.88185 | − | 1.77685i | −0.306919 | − | 0.111709i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.51421 | + | 14.7470i | −0.533180 | + | 0.923495i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.252279 | + | 0.211687i | −0.0157367 | + | 0.0132047i | −0.650622 | − | 0.759402i | \(-0.725492\pi\) |
0.634885 | + | 0.772606i | \(0.281047\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.80187 | − | 11.7812i | −0.422648 | − | 0.732047i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.706560 | − | 4.00710i | 0.0437350 | − | 0.248033i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.33131 | + | 3.03235i | −0.513731 | + | 0.186983i | −0.585859 | − | 0.810413i | \(-0.699243\pi\) |
0.0721288 | + | 0.997395i | \(0.477021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0934893 | 0.00574300 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.6304 | −1.93575 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8291 | + | 3.94146i | −0.660261 | + | 0.240315i | −0.650349 | − | 0.759636i | \(-0.725377\pi\) |
−0.00991170 | + | 0.999951i | \(0.503155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.516800 | − | 2.93092i | 0.0313934 | − | 0.178041i | −0.965079 | − | 0.261958i | \(-0.915632\pi\) |
0.996473 | + | 0.0839170i | \(0.0267431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.15901 | − | 8.93567i | −0.312238 | − | 0.540812i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.88936 | − | 5.78086i | 0.415444 | − | 0.348599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8352 | + | 27.4274i | −0.951445 | + | 1.64795i | −0.209144 | + | 0.977885i | \(0.567068\pi\) |
−0.742301 | + | 0.670066i | \(0.766266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.52653 | + | 0.555612i | 0.0913910 | + | 0.0332636i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.59294 | − | 14.7053i | −0.154682 | − | 0.877245i | −0.959076 | − | 0.283149i | \(-0.908621\pi\) |
0.804394 | − | 0.594096i | \(-0.202490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2583 | + | 11.9642i | 0.847571 | + | 0.711196i | 0.959253 | − | 0.282548i | \(-0.0911796\pi\) |
−0.111683 | + | 0.993744i | \(0.535624\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.57829 | + | 14.7195i | −0.0934899 | + | 0.871906i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2596 | − | 13.6434i | −0.959774 | − | 0.805346i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41338 | + | 8.01566i | 0.0831399 | + | 0.471510i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.683273 | − | 0.248691i | −0.0400542 | − | 0.0145785i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.68375 | + | 9.84455i | −0.332048 | + | 0.575125i | −0.982913 | − | 0.184069i | \(-0.941073\pi\) |
0.650865 | + | 0.759193i | \(0.274406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.93040 | + | 4.13709i | −0.287059 | + | 0.240871i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.72825 | − | 16.8498i | −0.564490 | − | 0.977726i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.543636 | − | 3.08311i | 0.0314393 | − | 0.178301i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0432 | + | 4.01940i | −0.636520 | + | 0.231674i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.3100 | 2.08595 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.0747 | −1.49303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0165 | + | 3.64570i | −0.571670 | + | 0.208071i | −0.611649 | − | 0.791130i | \(-0.709493\pi\) |
0.0399784 | + | 0.999201i | \(0.487271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.04449 | + | 17.2662i | −0.173195 | + | 0.982238i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7091 | − | 22.0128i | −0.720668 | − | 1.24823i | −0.960733 | − | 0.277476i | \(-0.910502\pi\) |
0.240065 | − | 0.970757i | \(-0.422831\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.29381 | + | 1.08564i | −0.0731305 | + | 0.0613638i | −0.678620 | − | 0.734489i | \(-0.737422\pi\) |
0.605490 | + | 0.795853i | \(0.292977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.36010 | − | 2.35576i | 0.0766330 | − | 0.132732i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4942 | − | 6.73135i | −1.03874 | − | 0.378070i | −0.234337 | − | 0.972155i | \(-0.575292\pi\) |
−0.804402 | + | 0.594085i | \(0.797514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.96201 | − | 22.4697i | −0.221830 | − | 1.25806i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.1979 | − | 9.39611i | −0.625003 | − | 0.524440i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1832 | + | 18.1443i | 0.677892 | + | 1.00958i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.15163 | + | 3.48363i | 0.230291 | + | 0.193237i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.68700 | − | 32.2526i | −0.314492 | − | 1.78357i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.8706 | + | 5.77644i | 0.874977 | + | 0.318466i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50354 | − | 7.80036i | 0.247537 | − | 0.428747i | −0.715305 | − | 0.698813i | \(-0.753712\pi\) |
0.962842 | + | 0.270066i | \(0.0870455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.39693 | + | 3.68946i | −0.240950 | + | 0.202181i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0404 | + | 19.1226i | 0.603204 | + | 1.04478i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.90637 | + | 10.8115i | −0.103846 | + | 0.588942i | 0.887828 | + | 0.460174i | \(0.152213\pi\) |
−0.991675 | + | 0.128767i | \(0.958898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.5694 | + | 7.12267i | −1.06286 | + | 0.386850i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.10931 | 0.493297 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8173 | 1.07003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.63997 | − | 1.32484i | 0.195969 | − | 0.0713270i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.486415 | + | 2.75859i | −0.0261121 | + | 0.148089i | −0.995076 | − | 0.0991121i | \(-0.968400\pi\) |
0.968964 | + | 0.247201i | \(0.0795109\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8890 | − | 29.2526i | −0.904048 | − | 1.56586i | −0.822190 | − | 0.569213i | \(-0.807248\pi\) |
−0.0818576 | − | 0.996644i | \(-0.526085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.98169 | − | 7.53653i | 0.479407 | − | 0.402270i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.25317 | + | 2.17056i | −0.0666996 | + | 0.115527i | −0.897447 | − | 0.441123i | \(-0.854580\pi\) |
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.38246 | − | 1.23112i | −0.179523 | − | 0.0653409i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.27281 | − | 18.5610i | −0.173215 | − | 0.982354i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.3680 | − | 13.7343i | −0.863868 | − | 0.724871i | 0.0989298 | − | 0.995094i | \(-0.468458\pi\) |
−0.962798 | + | 0.270223i | \(0.912903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0705 | + | 10.1360i | 0.845818 | + | 0.533471i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.5795 | + | 12.2337i | 0.765228 | + | 0.642102i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.215360 | − | 1.22137i | −0.0112724 | − | 0.0639292i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.36473 | + | 1.22466i | 0.175638 | + | 0.0639268i | 0.428342 | − | 0.903617i | \(-0.359098\pi\) |
−0.252705 | + | 0.967543i | \(0.581320\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.47779 | + | 7.75575i | −0.233104 | + | 0.403748i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0792670 | + | 0.0665129i | −0.00411534 | + | 0.00345318i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.7609 | + | 30.7627i | 0.919622 | + | 1.59283i | 0.799989 | + | 0.600014i | \(0.204838\pi\) |
0.119633 | + | 0.992818i | \(0.461828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.11317 | + | 23.3269i | −0.212403 | + | 1.20460i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.9202 | − | 4.70258i | 0.665426 | − | 0.242195i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.31674 | 0.375836 | 0.187918 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187918 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.5320 | −1.10312 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.92985 | − | 2.52226i | 0.354099 | − | 0.128881i | −0.158845 | − | 0.987304i | \(-0.550777\pi\) |
0.512944 | + | 0.858422i | \(0.328555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.64873 | − | 15.0217i | 0.134992 | − | 0.765576i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.47923 | + | 4.29415i | 0.126026 | + | 0.218284i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00096 | − | 5.03540i | 0.304261 | − | 0.255305i | −0.477854 | − | 0.878439i | \(-0.658585\pi\) |
0.782115 | + | 0.623134i | \(0.214141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.85931 | − | 4.95247i | 0.144602 | − | 0.250457i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.7324 | + | 9.36582i | 1.29803 | + | 0.472443i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.40080 | + | 19.2869i | 0.171113 | + | 0.970428i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.3729 | + | 12.8994i | 0.771546 | + | 0.647404i | 0.941104 | − | 0.338116i | \(-0.109790\pi\) |
−0.169558 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.13396 | − | 13.6031i | −0.457270 | − | 0.681006i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.85171 | + | 4.07107i | 0.242283 | + | 0.203300i | 0.755841 | − | 0.654755i | \(-0.227228\pi\) |
−0.513558 | + | 0.858055i | \(0.671673\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.953225 | + | 5.40601i | 0.0474835 | + | 0.269292i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.6153 | + | 6.41145i | 0.875312 | + | 0.318587i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.0928 | + | 27.8736i | −0.797691 | + | 1.38164i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9939 | − | 12.5813i | 0.741398 | − | 0.622107i | −0.191814 | − | 0.981431i | \(-0.561437\pi\) |
0.933213 | + | 0.359324i | \(0.116993\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.60968 | − | 14.9124i | −0.424684 | − | 0.735575i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.23701 | − | 7.01545i | 0.0608695 | − | 0.345208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.3211 | − | 5.94038i | 0.801169 | − | 0.291602i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9600 | −0.585683 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.06493 | 0.442851 | 0.221426 | − | 0.975177i | \(-0.428929\pi\) | ||||
0.221426 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5586 | − | 8.57464i | 1.14818 | − | 0.417902i | 0.303317 | − | 0.952890i | \(-0.401906\pi\) |
0.844860 | + | 0.534987i | \(0.179684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.23742 | − | 7.01775i | 0.0601653 | − | 0.341215i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.94980 | + | 8.57331i | 0.240101 | + | 0.415867i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.1080 | − | 18.5508i | 1.06988 | − | 0.897735i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.2059 | + | 21.1413i | −0.589307 | + | 1.02071i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.18508 | + | 2.25119i | 0.297925 | + | 0.108436i | 0.486658 | − | 0.873593i | \(-0.338216\pi\) |
−0.188733 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.41428 | − | 19.3634i | −0.164080 | − | 0.930544i | −0.950008 | − | 0.312226i | \(-0.898925\pi\) |
0.785928 | − | 0.618318i | \(-0.212186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.0321 | + | 10.9352i | 0.624839 | + | 0.524302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.530035 | − | 4.94321i | 0.0253550 | − | 0.236466i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9204 | + | 10.8415i | 0.616657 | + | 0.517437i | 0.896751 | − | 0.442536i | \(-0.145921\pi\) |
−0.280094 | + | 0.959973i | \(0.590366\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.464568 | − | 2.63470i | −0.0221223 | − | 0.125462i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.5201 | − | 12.9283i | −1.68761 | − | 0.614240i | −0.693290 | − | 0.720659i | \(-0.743839\pi\) |
−0.994321 | + | 0.106419i | \(0.966062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0892 | − | 24.4032i | 0.667891 | − | 1.15682i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.63686 | + | 3.05168i | −0.172017 | + | 0.144340i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.02262 | + | 12.1635i | 0.331418 | + | 0.574033i | 0.982790 | − | 0.184726i | \(-0.0591397\pi\) |
−0.651372 | + | 0.758758i | \(0.725806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.72026 | + | 49.4551i | −0.410621 | + | 2.32875i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.0722 | − | 7.66966i | 0.990059 | − | 0.360352i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.19193 | 0.430924 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.9491 | −0.512177 | −0.256089 | − | 0.966653i | \(-0.582434\pi\) | ||||
−0.256089 | + | 0.966653i | \(0.582434\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.1254 | − | 7.32503i | 0.939371 | − | 0.341903i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.36371 | − | 7.73396i | 0.0635141 | − | 0.360206i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.999956 | − | 0.00938355i | \(-0.00298692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.88710 | − | 17.1250i | −0.459492 | − | 0.795864i | 0.539442 | − | 0.842023i | \(-0.318635\pi\) |
−0.998934 | + | 0.0461588i | \(0.985302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.20300 | + | 4.36583i | −0.241283 | + | 0.202461i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.56124 | − | 7.90030i | 0.211069 | − | 0.365582i | −0.740980 | − | 0.671527i | \(-0.765639\pi\) |
0.952049 | + | 0.305944i | \(0.0989722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.9657 | − | 8.35881i | −1.06046 | − | 0.385974i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.902258 | − | 5.11696i | −0.0415739 | − | 0.235777i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.2994 | + | 17.8723i | 0.979347 | + | 0.821769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.95205 | + | 5.07326i | 0.318982 | + | 0.232777i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0334449 | + | 0.0280636i | 0.00153134 | + | 0.00128494i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.06849 | + | 34.4161i | 0.277276 | + | 1.57251i | 0.731637 | + | 0.681694i | \(0.238757\pi\) |
−0.454361 | + | 0.890818i | \(0.650132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2258 | − | 6.63366i | −0.831026 | − | 0.302469i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.14367 | + | 3.71295i | −0.0975405 | + | 0.168945i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.496218 | − | 0.416376i | 0.0225321 | − | 0.0189067i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9182 | − | 25.8391i | −0.676009 | − | 1.17088i | −0.976173 | − | 0.216994i | \(-0.930375\pi\) |
0.300164 | − | 0.953888i | \(-0.402959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.39425 | − | 7.90719i | 0.0630502 | − | 0.357575i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.74192 | + | 2.45386i | −0.304259 | + | 0.110741i | −0.489638 | − | 0.871926i | \(-0.662871\pi\) |
0.185379 | + | 0.982667i | \(0.440649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.1153 | 1.13114 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.43583 | −0.289269 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.74377 | − | 1.36262i | 0.167931 | − | 0.0611220i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.81846 | − | 15.9843i | 0.126172 | − | 0.715556i | −0.854433 | − | 0.519561i | \(-0.826095\pi\) |
0.980605 | − | 0.195994i | \(-0.0627935\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6075 | + | 25.3010i | 0.652617 | + | 1.13037i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2611 | + | 11.9665i | −0.635869 | + | 0.533558i | −0.902747 | − | 0.430173i | \(-0.858453\pi\) |
0.266877 | + | 0.963731i | \(0.414008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1736 | + | 28.0135i | −0.719715 | + | 1.24658i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0282 | + | 3.64995i | 0.445366 | + | 0.162100i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.734939 | − | 4.16805i | −0.0325756 | − | 0.184745i | 0.964178 | − | 0.265255i | \(-0.0854562\pi\) |
−0.996754 | + | 0.0805099i | \(0.974345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05154 | + | 0.882344i | 0.0465172 | + | 0.0390326i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.4205 | − | 12.9058i | 0.592531 | − | 0.569804i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9649 | − | 10.0397i | −0.527236 | − | 0.442403i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.93877 | − | 39.3517i | −0.305167 | − | 1.73069i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.6937 | + | 4.25615i | 0.513295 | + | 0.186824i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.40530 | + | 11.0943i | −0.280621 | + | 0.486050i | −0.971538 | − | 0.236884i | \(-0.923874\pi\) |
0.690917 | + | 0.722934i | \(0.257207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7911 | + | 20.8022i | −1.08404 | + | 0.909618i | −0.996250 | − | 0.0865209i | \(-0.972425\pi\) |
−0.0877905 | + | 0.996139i | \(0.527981\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.71095 | − | 6.42755i | −0.161959 | − | 0.280521i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.74120 | + | 9.87485i | −0.0758479 | + | 0.430155i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.3905 | − | 7.42154i | 0.886545 | − | 0.322676i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00567 | −0.130435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.2621 | −1.31080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.2370 | − | 4.45392i | 0.529054 | − | 0.192560i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.07860 | + | 6.11706i | −0.0465451 | + | 0.263971i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.50094 | − | 12.9920i | −0.323088 | − | 0.559605i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1268 | − | 11.8538i | 0.607359 | − | 0.509634i | −0.286443 | − | 0.958097i | \(-0.592473\pi\) |
0.893801 | + | 0.448463i | \(0.148028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.44006 | − | 7.69040i | 0.190541 | − | 0.330027i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.4163 | + | 9.97872i | 1.17439 | + | 0.427442i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.66428 | − | 32.1238i | −0.242187 | − | 1.37351i | −0.826935 | − | 0.562297i | \(-0.809918\pi\) |
0.584748 | − | 0.811215i | \(-0.301193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.32795 | − | 7.82708i | −0.398107 | − | 0.334052i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.9652 | − | 8.83894i | 0.850544 | − | 0.376552i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.6051 | − | 13.9333i | −0.706119 | − | 0.592504i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.16722 | − | 23.6335i | −0.176888 | − | 1.00318i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2636 | − | 4.46359i | −0.519625 | − | 0.189128i | 0.0688747 | − | 0.997625i | \(-0.478059\pi\) |
−0.588500 | + | 0.808497i | \(0.700281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.37765 | + | 14.5105i | −0.354337 | + | 0.613730i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.1592 | + | 28.6630i | −1.44220 | + | 1.21015i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.12500 | − | 15.8050i | −0.384573 | − | 0.666100i | 0.607137 | − | 0.794597i | \(-0.292318\pi\) |
−0.991710 | + | 0.128498i | \(0.958985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.22160 | − | 18.2706i | 0.135534 | − | 0.768649i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.4969 | + | 7.09631i | −0.818795 | + | 0.298017i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.4274 | −1.44327 | −0.721636 | − | 0.692273i | \(-0.756610\pi\) | ||||
−0.721636 | + | 0.692273i | \(0.756610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6525 | −0.696884 | −0.348442 | − | 0.937330i | \(-0.613289\pi\) | ||||
−0.348442 | + | 0.937330i | \(0.613289\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.77735 | + | 0.646904i | −0.0742500 | + | 0.0270248i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.391044 | − | 2.21772i | 0.0163077 | − | 0.0924855i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7394 | + | 32.4576i | 0.780130 | + | 1.35123i | 0.931865 | + | 0.362804i | \(0.118181\pi\) |
−0.151735 | + | 0.988421i | \(0.548486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.7446 | − | 19.0850i | 0.945233 | − | 0.793144i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.61189 | + | 16.6483i | −0.398769 | + | 0.690687i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.230053 | + | 0.0837324i | 0.00952781 | + | 0.00346784i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.673464 | − | 3.81940i | −0.0278443 | − | 0.157913i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.0297 | + | 21.8415i | 1.07436 | + | 0.901494i | 0.995440 | − | 0.0953871i | \(-0.0304089\pi\) |
0.0789185 | + | 0.996881i | \(0.474853\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09115 | + | 8.46270i | 0.0861643 | + | 0.348700i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.6176 | + | 20.6566i | 1.01263 | + | 0.849700i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.29313 | + | 18.6762i | 0.135232 | + | 0.766941i | 0.974698 | + | 0.223528i | \(0.0717574\pi\) |
−0.839465 | + | 0.543414i | \(0.817132\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.7778 | + | 5.74265i | 0.646827 | + | 0.235426i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.4203 | − | 37.1010i | 0.876673 | − | 1.51844i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.6598 | − | 21.5311i | 1.04843 | − | 0.879738i | 0.0555029 | − | 0.998459i | \(-0.482324\pi\) |
0.992928 | + | 0.118721i | \(0.0378794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.50056 | + | 12.9914i | 0.305954 | + | 0.529928i | 0.977473 | − | 0.211059i | \(-0.0676912\pi\) |
−0.671519 | + | 0.740987i | \(0.734358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.79061 | + | 10.1550i | −0.0729192 | + | 0.413545i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9326 | + | 5.79898i | −0.647751 | + | 0.235762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.06547 | 0.286779 | 0.143389 | − | 0.989666i | \(-0.454200\pi\) | ||||
0.143389 | + | 0.989666i | \(0.454200\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.8293 | −0.763003 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.6276 | − | 8.23576i | 0.915413 | − | 0.333183i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.54668 | + | 25.7855i | −0.183639 | + | 1.04147i | 0.744053 | + | 0.668120i | \(0.232901\pi\) |
−0.927692 | + | 0.373346i | \(0.878210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.7216 | − | 32.4268i | −0.754928 | − | 1.30757i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.3641 | + | 27.9958i | −1.34319 | + | 1.12707i | −0.362395 | + | 0.932025i | \(0.618041\pi\) |
−0.980794 | + | 0.195045i | \(0.937515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4919 | − | 21.6365i | 0.502090 | − | 0.869646i | −0.497907 | − | 0.867231i | \(-0.665898\pi\) |
0.999997 | − | 0.00241526i | \(-0.000768802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.57806 | − | 1.66628i | −0.183711 | − | 0.0668654i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.41579 | + | 30.7145i | 0.216979 | + | 1.23055i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.60229 | − | 7.21818i | −0.344092 | − | 0.288727i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.0670 | + | 34.8072i | −0.681592 | + | 1.39007i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.1399 | − | 22.7731i | −1.08214 | − | 0.908024i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.07717 | + | 45.8079i | 0.321547 | + | 1.82358i | 0.532905 | + | 0.846175i | \(0.321100\pi\) |
−0.211358 | + | 0.977409i | \(0.567789\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.7459 | + | 12.2825i | 1.34128 | + | 0.488186i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.59103 | − | 16.6121i | 0.380608 | − | 0.659233i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.92531 | − | 5.81102i | 0.274391 | − | 0.230241i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.840488 | − | 1.45577i | −0.0332492 | − | 0.0575893i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23030 | − | 6.97736i | 0.0485938 | − | 0.275589i | −0.950823 | − | 0.309734i | \(-0.899760\pi\) |
0.999417 | + | 0.0341454i | \(0.0108709\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.150167 | − | 0.0546563i | 0.00592200 | − | 0.00215543i | −0.339057 | − | 0.940766i | \(-0.610108\pi\) |
0.344979 | + | 0.938610i | \(0.387886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.7313 | −0.816295 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.8979 | 0.742955 | 0.371478 | − | 0.928442i | \(-0.378851\pi\) | ||||
0.371478 | + | 0.928442i | \(0.378851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.8378 | + | 5.76447i | −0.621686 | + | 0.226275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.30541 | − | 7.40333i | 0.0511629 | − | 0.290159i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.62463 | + | 9.74215i | 0.220109 | + | 0.381240i | 0.954841 | − | 0.297118i | \(-0.0960254\pi\) |
−0.734732 | + | 0.678358i | \(0.762692\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.6878 | + | 15.6809i | −0.730193 | + | 0.612705i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.289586 | − | 0.501578i | 0.0112978 | − | 0.0195684i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8940 | − | 4.32904i | −0.463323 | − | 0.168636i | 0.0998025 | − | 0.995007i | \(-0.468179\pi\) |
−0.563125 | + | 0.826372i | \(0.690401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.642263 | − | 3.64245i | −0.0249811 | − | 0.141675i | 0.969766 | − | 0.244036i | \(-0.0784715\pi\) |
−0.994747 | + | 0.102361i | \(0.967360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.5848 | − | 17.2727i | −0.799449 | − | 0.670817i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.5634 | − | 0.987692i | 0.564746 | − | 0.0383010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.37653 | − | 3.67235i | −0.169460 | − | 0.142194i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.61697 | + | 37.5267i | 0.255827 | + | 1.45087i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.1629 | − | 23.3534i | −2.47698 | − | 0.901548i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1273 | − | 19.2730i | 0.428926 | − | 0.742921i | −0.567852 | − | 0.823130i | \(-0.692226\pi\) |
0.996778 | + | 0.0802094i | \(0.0255589\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.46065 | − | 5.42113i | 0.248671 | − | 0.208659i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.9484 | − | 20.6952i | −0.459213 | − | 0.795380i | 0.539707 | − | 0.841853i | \(-0.318535\pi\) |
−0.998920 | + | 0.0464733i | \(0.985202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.124499 | + | 0.706068i | −0.00477783 | + | 0.0270964i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4097 | − | 4.88072i | 0.513860 | − | 0.187030i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.9375 | −1.03073 | −0.515367 | − | 0.856970i | \(-0.672344\pi\) | ||||
−0.515367 | + | 0.856970i | \(0.672344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3401 | 0.586114 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.7720 | + | 14.1119i | −1.47924 | + | 0.538401i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0256184 | + | 0.145289i | −0.000975982 | + | 0.00553507i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.6869 | + | 23.7063i | 0.520673 | + | 0.901831i | 0.999711 | + | 0.0240374i | \(0.00765207\pi\) |
−0.479039 | + | 0.877794i | \(0.659015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.45676 | − | 4.57877i | 0.207285 | − | 0.173933i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.32735 | − | 9.22724i | 0.202078 | − | 0.350009i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.9444 | − | 18.9062i | −1.96753 | − | 0.716123i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.61412 | + | 9.15415i | 0.0610517 | + | 0.346242i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7609 | − | 14.9032i | −0.670821 | − | 0.562886i | 0.242487 | − | 0.970155i | \(-0.422037\pi\) |
−0.913308 | + | 0.407269i | \(0.866481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.5893 | − | 8.55178i | −1.11598 | − | 0.322537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.8234 | + | 19.1511i | 0.859579 | + | 0.721272i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.21703 | − | 35.2585i | −0.233815 | − | 1.32603i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.177739 | + | 0.0646919i | 0.00667515 | + | 0.00242955i | 0.345356 | − | 0.938472i | \(-0.387758\pi\) |
−0.338680 | + | 0.940901i | \(0.609981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.57292 | + | 7.92054i | −0.171498 | + | 0.297043i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74731 | − | 1.46617i | 0.0654374 | − | 0.0549085i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8738 | − | 18.8339i | −0.406656 | − | 0.704349i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.07734 | − | 40.1376i | 0.264308 | − | 1.49896i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7370 | + | 3.90793i | −0.400421 | + | 0.145741i | −0.534377 | − | 0.845246i | \(-0.679454\pi\) |
0.133957 | + | 0.990987i | \(0.457232\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2874 | 0.643818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.7987 | 0.513178 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.29370 | − | 3.38263i | 0.345159 | − | 0.125628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.22332 | + | 29.6229i | −0.193722 | + | 1.09865i | 0.720504 | + | 0.693451i | \(0.243910\pi\) |
−0.914226 | + | 0.405204i | \(0.867201\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.13313 | − | 14.0870i | −0.301227 | − | 0.521741i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.4455 | + | 19.6731i | −0.867164 | + | 0.727637i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3368 | − | 28.2962i | 0.603414 | − | 1.04514i | −0.388885 | − | 0.921286i | \(-0.627140\pi\) |
0.992300 | − | 0.123858i | \(-0.0395269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.5110 | + | 3.82570i | 0.387705 | + | 0.141113i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0408 | + | 56.9440i | 0.369856 | + | 2.09756i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5685 | + | 16.4199i | 0.719838 | + | 0.604016i | 0.927341 | − | 0.374218i | \(-0.122089\pi\) |
−0.207502 | + | 0.978235i | \(0.566533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.4426 | − | 6.48627i | −0.824449 | − | 0.238279i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.6914 | − | 14.8449i | −0.649035 | − | 0.544605i | 0.257743 | − | 0.966214i | \(-0.417021\pi\) |
−0.906778 | + | 0.421608i | \(0.861466\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.734433 | − | 4.16518i | −0.0269076 | − | 0.152600i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.62188 | + | 2.77414i | 0.278870 | + | 0.101500i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.20671 | + | 12.4824i | −0.263328 | + | 0.456097i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.91762 | − | 8.32187i | 0.361899 | − | 0.303670i | −0.443648 | − | 0.896201i | \(-0.646316\pi\) |
0.805547 | + | 0.592532i | \(0.201871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.8694 | − | 20.5585i | −0.432547 | − | 0.749193i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.46900 | + | 19.6737i | −0.126250 | + | 0.715999i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4280 | + | 5.97928i | −0.597084 | + | 0.217321i | −0.622842 | − | 0.782347i | \(-0.714022\pi\) |
0.0257583 | + | 0.999668i | \(0.491800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.1436 | 0.368189 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.43066 | −0.160611 | −0.0803057 | − | 0.996770i | \(-0.525590\pi\) | ||||
−0.0803057 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.3449 | + | 11.0446i | −1.09856 | + | 0.399843i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.23018 | − | 6.97669i | 0.0444772 | − | 0.252243i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.07829 | − | 8.79585i | −0.183366 | − | 0.317600i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3561 | − | 26.3109i | 1.13073 | − | 0.948794i | 0.131633 | − | 0.991299i | \(-0.457978\pi\) |
0.999096 | + | 0.0425043i | \(0.0135336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.321507 | − | 0.556867i | 0.0115788 | − | 0.0200551i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.12589 | − | 2.59361i | −0.256300 | − | 0.0932857i | 0.210675 | − | 0.977556i | \(-0.432434\pi\) |
−0.466975 | + | 0.884271i | \(0.654656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.685668 | + | 3.88861i | 0.0246299 | + | 0.139683i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.3473 | + | 17.0734i | 0.729954 | + | 0.612504i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.9464 | + | 3.25172i | −1.71786 | + | 0.116505i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.22073 | − | 6.05892i | −0.258378 | − | 0.216805i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.71546 | − | 21.0714i | −0.132780 | − | 0.753031i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.34967 | + | 1.58315i | 0.155246 | + | 0.0565051i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.4525 | − | 26.7645i | 0.550821 | − | 0.954050i | −0.447394 | − | 0.894337i | \(-0.647648\pi\) |
0.998216 | − | 0.0597134i | \(-0.0190187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.2610 | − | 11.1273i | 0.472103 | − | 0.396141i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2671 | + | 17.7831i | 0.365056 | + | 0.632295i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.14509 | − | 40.5218i | 0.253730 | − | 1.43897i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.171530 | + | 0.0624320i | −0.00608356 | + | 0.00221423i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9708 | −0.636559 | −0.318279 | − | 0.947997i | \(-0.603105\pi\) | ||||
−0.318279 | + | 0.947997i | \(0.603105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.9851 | 1.55608 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.3656 | − | 4.50071i | 0.436917 | − | 0.159025i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.563955 | − | 3.19835i | 0.0199015 | − | 0.112867i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.90971 | − | 3.30772i | −0.0673086 | − | 0.116582i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.2367 | − | 14.4633i | 0.606759 | − | 0.509132i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.52462 | + | 4.37277i | −0.0887608 | + | 0.153738i | −0.906988 | − | 0.421157i | \(-0.861624\pi\) |
0.818227 | + | 0.574896i | \(0.194957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.5490 | + | 6.75127i | 0.651342 | + | 0.237069i | 0.646494 | − | 0.762919i | \(-0.276235\pi\) |
0.00484814 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.00906 | + | 5.72265i | 0.0353892 | + | 0.200702i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.47942 | + | 4.59778i | 0.191936 | + | 0.161053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.7141 | + | 23.8903i | −0.409826 | + | 0.835815i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.28832 | + | 2.75923i | 0.114903 | + | 0.0964153i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.349550 | + | 1.98240i | 0.0121994 | + | 0.0691862i | 0.990300 | − | 0.138948i | \(-0.0443721\pi\) |
−0.978100 | + | 0.208134i | \(0.933261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.4124 | + | 14.7089i | 1.40869 | + | 0.512721i | 0.930745 | − | 0.365670i | \(-0.119160\pi\) |
0.477944 | + | 0.878390i | \(0.341382\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.77988 | + | 15.2072i | −0.305676 | + | 0.529447i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.7538 | + | 21.6100i | −0.895547 | + | 0.751453i | −0.969315 | − | 0.245823i | \(-0.920942\pi\) |
0.0737683 | + | 0.997275i | \(0.476497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3799 | + | 30.1028i | 0.603627 | + | 1.04551i | 0.992267 | + | 0.124123i | \(0.0396118\pi\) |
−0.388639 | + | 0.921390i | \(0.627055\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7379 | − | 60.8974i | 0.372492 | − | 2.11251i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5176 | − | 5.64794i | 0.537653 | − | 0.195690i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.0266 | −0.900687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.54246 | 0.295271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.4556 | − | 6.35333i | 0.602636 | − | 0.219341i | −0.0226423 | − | 0.999744i | \(-0.507208\pi\) |
0.625278 | + | 0.780402i | \(0.284986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.678741 | + | 3.84933i | −0.0234049 | + | 0.132736i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.5776 | + | 25.2492i | 0.502080 | + | 0.869628i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.28281 | + | 6.11101i | −0.250536 | + | 0.210225i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.38310 | − | 16.2520i | 0.322407 | − | 0.558426i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.1503 | − | 12.4297i | −1.17204 | − | 0.426586i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.39947 | + | 7.93678i | 0.0479732 | + | 0.272069i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.57133 | − | 1.31850i | −0.0538012 | − | 0.0451446i | 0.615491 | − | 0.788144i | \(-0.288958\pi\) |
−0.669292 | + | 0.743000i | \(0.733402\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.47742 | − | 5.97900i | −0.0505267 | − | 0.204477i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.4175 | + | 12.9368i | 0.526651 | + | 0.441913i | 0.866943 | − | 0.498407i | \(-0.166081\pi\) |
−0.340292 | + | 0.940320i | \(0.610526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65890 | + | 9.40808i | 0.0566009 | + | 0.320999i | 0.999941 | − | 0.0108268i | \(-0.00344635\pi\) |
−0.943341 | + | 0.331826i | \(0.892335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.9435 | + | 14.1743i | 1.32719 | + | 0.483058i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.3643 | + | 30.0759i | −0.591089 | + | 1.02380i | 0.402997 | + | 0.915201i | \(0.367969\pi\) |
−0.994086 | + | 0.108595i | \(0.965365\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.49237 | + | 7.12594i | −0.288749 | + | 0.242289i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.94606 | − | 13.7630i | −0.269862 | − | 0.467415i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.90554 | + | 50.5058i | −0.302100 | + | 1.71329i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.7432 | + | 11.9176i | −1.10946 | + | 0.403811i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.302505 | 0.0102382 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.3557 | 0.789566 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.1774 | − | 9.16382i | 0.850180 | − | 0.309440i | 0.120066 | − | 0.992766i | \(-0.461689\pi\) |
0.730114 | + | 0.683326i | \(0.239467\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.85415 | − | 21.8580i | 0.129997 | − | 0.737252i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.87940 | + | 13.6475i | 0.265464 | + | 0.459797i | 0.967685 | − | 0.252162i | \(-0.0811416\pi\) |
−0.702221 | + | 0.711959i | \(0.747808\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7063 | + | 26.6047i | −1.06700 | + | 0.895320i | −0.994777 | − | 0.102069i | \(-0.967454\pi\) |
−0.0722232 | + | 0.997388i | \(0.523009\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.28336 | − | 10.8831i | 0.211213 | − | 0.365831i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.7848 | + | 15.9363i | 1.47015 | + | 0.535090i | 0.948141 | − | 0.317851i | \(-0.102961\pi\) |
0.522007 | + | 0.852941i | \(0.325183\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.68673 | + | 20.9085i | 0.123649 | + | 0.701249i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.6044 | + | 31.5538i | 1.25979 | + | 1.05709i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.9655 | − | 15.4799i | 1.17008 | − | 0.518015i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.23892 | − | 3.55688i | −0.141692 | − | 0.118893i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06145 | + | 6.01981i | 0.0354409 | + | 0.200996i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.41346 | + | 3.42622i | 0.313957 | + | 0.114271i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.134743 | + | 0.233381i | −0.00448893 | + | 0.00777505i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.5775 | − | 14.7493i | 0.584943 | − | 0.490825i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.95548 | + | 6.85108i | 0.131484 | + | 0.227738i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.423530 | + | 2.40196i | −0.0140631 | + | 0.0797557i | −0.991032 | − | 0.133628i | \(-0.957337\pi\) |
0.976968 | + | 0.213384i | \(0.0684484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.1950 | + | 5.16656i | −0.470819 | + | 0.171364i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.8844 | 0.990115 | 0.495057 | − | 0.868860i | \(-0.335147\pi\) | ||||
0.495057 | + | 0.868860i | \(0.335147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.4823 | 1.50524 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 47.8407 | − | 17.4126i | 1.58157 | − | 0.575643i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.68868 | − | 26.5908i | 0.154834 | − | 0.878107i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1737 | + | 34.9419i | 0.665469 | + | 1.15263i | 0.979158 | + | 0.203100i | \(0.0651016\pi\) |
−0.313689 | + | 0.949526i | \(0.601565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.9432 | − | 13.3780i | 0.525348 | − | 0.440819i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.84012 | − | 4.91923i | 0.0934837 | − | 0.161919i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1101 | − | 4.77168i | −0.431057 | − | 0.156892i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.26660 | − | 7.18323i | −0.0416005 | − | 0.235928i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.3558 | − | 33.8625i | −1.32403 | − | 1.11099i | −0.985433 | − | 0.170062i | \(-0.945603\pi\) |
−0.338597 | − | 0.940932i | \(-0.609952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3479 | − | 9.95096i | 0.339137 | − | 0.326130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.0183 | + | 31.9012i | 1.24466 | + | 1.04440i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.89818 | − | 39.1215i | −0.225595 | − | 1.27941i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0102 | − | 10.9228i | −0.980391 | − | 0.356833i | −0.198399 | − | 0.980121i | \(-0.563574\pi\) |
−0.781992 | + | 0.623288i | \(0.785796\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.64885 | − | 2.85589i | 0.0538081 | − | 0.0931984i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.29042 | + | 1.08279i | −0.0420666 | + | 0.0352981i | −0.663579 | − | 0.748107i | \(-0.730963\pi\) |
0.621512 | + | 0.783405i | \(0.286519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.28725 | + | 10.8898i | 0.204741 | + | 0.354622i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.48391 | − | 14.0869i | 0.0808015 | − | 0.458248i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2449 | − | 10.6443i | 0.950332 | − | 0.345892i | 0.180094 | − | 0.983649i | \(-0.442360\pi\) |
0.770238 | + | 0.637757i | \(0.220138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.95710 | 0.0635302 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.4277 | 1.24610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9284 | + | 7.98128i | −0.710330 | + | 0.258539i | −0.671815 | − | 0.740719i | \(-0.734485\pi\) |
−0.0385151 | + | 0.999258i | \(0.512263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.292596 | − | 1.65940i | 0.00946819 | − | 0.0536968i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.2745 | + | 38.5806i | 0.720034 | + | 1.24713i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.0064 | + | 10.9137i | −0.419999 | + | 0.352421i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5003 | − | 23.3831i | 0.435492 | − | 0.754295i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.71466 | + | 2.07997i | 0.184152 | + | 0.0670260i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.59308 | + | 26.0487i | 0.147857 | + | 0.838536i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.7482 | − | 35.0309i | −1.34253 | − | 1.12652i | −0.980968 | − | 0.194171i | \(-0.937798\pi\) |
−0.361565 | − | 0.932347i | \(-0.617757\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.4700 | − | 25.1546i | −1.10734 | − | 0.808081i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.3904 | − | 18.7878i | −0.718543 | − | 0.602929i | 0.208439 | − | 0.978035i | \(-0.433162\pi\) |
−0.926982 | + | 0.375107i | \(0.877606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.04780 | + | 11.6137i | 0.0656495 | + | 0.372317i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.94360 | − | 3.61918i | −0.318450 | − | 0.115906i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0031 | − | 29.4502i | 0.543977 | − | 0.942196i | −0.454693 | − | 0.890648i | \(-0.650251\pi\) |
0.998671 | − | 0.0515482i | \(-0.0164156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.5261 | − | 47.4310i | 1.80658 | − | 1.51590i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.81251 | + | 11.7996i | 0.217507 | + | 0.376733i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.94855 | − | 33.7359i | 0.189729 | − | 1.07601i | −0.729998 | − | 0.683450i | \(-0.760479\pi\) |
0.919727 | − | 0.392559i | \(-0.128410\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.9022 | + | 9.79159i | −0.857175 | + | 0.311986i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.9763 | −1.04965 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.96216 | 0.221384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.2569 | + | 15.0163i | −1.31057 | + | 0.477008i | −0.900424 | − | 0.435013i | \(-0.856744\pi\) |
−0.410144 | + | 0.912021i | \(0.634522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.05385 | + | 17.3193i | −0.0969111 | + | 0.549610i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.0825 | + | 33.0518i | 0.604955 | + | 1.04781i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.1321 | + | 37.0312i | −1.39768 | + | 1.17279i | −0.435559 | + | 0.900160i | \(0.643449\pi\) |
−0.962119 | + | 0.272631i | \(0.912106\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.0914 | + | 26.1391i | −0.477471 | + | 0.827003i |
(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 | 304.2.u.f.225.1 | 18 | ||
4.3 | odd | 2 | 152.2.q.c.73.3 | yes | 18 | ||
19.5 | even | 9 | 5776.2.a.cd.1.8 | 9 | |||
19.6 | even | 9 | inner | 304.2.u.f.177.1 | 18 | ||
19.14 | odd | 18 | 5776.2.a.ce.1.2 | 9 | |||
76.43 | odd | 18 | 2888.2.a.y.1.2 | 9 | |||
76.63 | odd | 18 | 152.2.q.c.25.3 | ✓ | 18 | ||
76.71 | even | 18 | 2888.2.a.x.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.q.c.25.3 | ✓ | 18 | 76.63 | odd | 18 | ||
152.2.q.c.73.3 | yes | 18 | 4.3 | odd | 2 | ||
304.2.u.f.177.1 | 18 | 19.6 | even | 9 | inner | ||
304.2.u.f.225.1 | 18 | 1.1 | even | 1 | trivial | ||
2888.2.a.x.1.8 | 9 | 76.71 | even | 18 | |||
2888.2.a.y.1.2 | 9 | 76.43 | odd | 18 | |||
5776.2.a.cd.1.8 | 9 | 19.5 | even | 9 | |||
5776.2.a.ce.1.2 | 9 | 19.14 | odd | 18 |