Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(131,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.f (of order \(2\), degree \(1\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 131.20 | ||
Character | \(\chi\) | \(=\) | 429.131 |
Dual form | 429.2.f.a.131.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.791616 | −0.559757 | −0.279878 | − | 0.960035i | \(-0.590294\pi\) | ||||
−0.279878 | + | 0.960035i | \(0.590294\pi\) | |||||||
\(3\) | −0.917209 | + | 1.46926i | −0.529551 | + | 0.848278i | ||||
\(4\) | −1.37334 | −0.686672 | ||||||||
\(5\) | − | 1.17632i | − | 0.526068i | −0.964787 | − | 0.263034i | \(-0.915277\pi\) | ||
0.964787 | − | 0.263034i | \(-0.0847231\pi\) | |||||||
\(6\) | 0.726077 | − | 1.16309i | 0.296420 | − | 0.474829i | ||||
\(7\) | 0.422249i | 0.159595i | 0.996811 | + | 0.0797976i | \(0.0254274\pi\) | ||||
−0.996811 | + | 0.0797976i | \(0.974573\pi\) | |||||||
\(8\) | 2.67039 | 0.944126 | ||||||||
\(9\) | −1.31745 | − | 2.69524i | −0.439151 | − | 0.898413i | ||||
\(10\) | 0.931196i | 0.294470i | ||||||||
\(11\) | 1.23267 | − | 3.07905i | 0.371665 | − | 0.928367i | ||||
\(12\) | 1.25964 | − | 2.01780i | 0.363628 | − | 0.582489i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | − | 0.334259i | − | 0.0893345i | ||||||
\(15\) | 1.72833 | + | 1.07894i | 0.446252 | + | 0.278580i | ||||
\(16\) | 0.632764 | 0.158191 | ||||||||
\(17\) | 0.541327 | 0.131291 | 0.0656456 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656456 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(18\) | 1.04292 | + | 2.13359i | 0.245818 | + | 0.502893i | ||||
\(19\) | 6.79972i | 1.55996i | 0.625803 | + | 0.779981i | \(0.284771\pi\) | ||||
−0.625803 | + | 0.779981i | \(0.715229\pi\) | |||||||
\(20\) | 1.61550i | 0.361236i | ||||||||
\(21\) | −0.620394 | − | 0.387291i | −0.135381 | − | 0.0845138i | ||||
\(22\) | −0.975803 | + | 2.43742i | −0.208042 | + | 0.519660i | ||||
\(23\) | 1.90837i | 0.397923i | 0.980007 | + | 0.198962i | \(0.0637569\pi\) | ||||
−0.980007 | + | 0.198962i | \(0.936243\pi\) | |||||||
\(24\) | −2.44931 | + | 3.92350i | −0.499963 | + | 0.800882i | ||||
\(25\) | 3.61626 | 0.723252 | ||||||||
\(26\) | − | 0.791616i | − | 0.155249i | ||||||
\(27\) | 5.16839 | + | 0.536417i | 0.994657 | + | 0.103233i | ||||
\(28\) | − | 0.579894i | − | 0.109590i | ||||||
\(29\) | 10.1937 | 1.89292 | 0.946460 | − | 0.322822i | \(-0.104632\pi\) | ||||
0.946460 | + | 0.322822i | \(0.104632\pi\) | |||||||
\(30\) | −1.36817 | − | 0.854102i | −0.249793 | − | 0.155937i | ||||
\(31\) | −1.41929 | −0.254912 | −0.127456 | − | 0.991844i | \(-0.540681\pi\) | ||||
−0.127456 | + | 0.991844i | \(0.540681\pi\) | |||||||
\(32\) | −5.84169 | −1.03267 | ||||||||
\(33\) | 3.39330 | + | 4.63525i | 0.590698 | + | 0.806893i | ||||
\(34\) | −0.428523 | −0.0734911 | ||||||||
\(35\) | 0.496702 | 0.0839579 | ||||||||
\(36\) | 1.80932 | + | 3.70149i | 0.301553 | + | 0.616915i | ||||
\(37\) | −6.19734 | −1.01884 | −0.509418 | − | 0.860519i | \(-0.670139\pi\) | ||||
−0.509418 | + | 0.860519i | \(0.670139\pi\) | |||||||
\(38\) | − | 5.38276i | − | 0.873199i | ||||||
\(39\) | −1.46926 | − | 0.917209i | −0.235270 | − | 0.146871i | ||||
\(40\) | − | 3.14125i | − | 0.496675i | ||||||
\(41\) | 10.8583 | 1.69578 | 0.847890 | − | 0.530173i | \(-0.177873\pi\) | ||||
0.847890 | + | 0.530173i | \(0.177873\pi\) | |||||||
\(42\) | 0.491114 | + | 0.306586i | 0.0757805 | + | 0.0473072i | ||||
\(43\) | 9.30752i | 1.41938i | 0.704512 | + | 0.709692i | \(0.251166\pi\) | ||||
−0.704512 | + | 0.709692i | \(0.748834\pi\) | |||||||
\(44\) | −1.69288 | + | 4.22859i | −0.255212 | + | 0.637484i | ||||
\(45\) | −3.17047 | + | 1.54975i | −0.472626 | + | 0.231023i | ||||
\(46\) | − | 1.51070i | − | 0.222740i | ||||||
\(47\) | − | 1.34691i | − | 0.196467i | −0.995163 | − | 0.0982335i | \(-0.968681\pi\) | ||
0.995163 | − | 0.0982335i | \(-0.0313192\pi\) | |||||||
\(48\) | −0.580377 | + | 0.929696i | −0.0837703 | + | 0.134190i | ||||
\(49\) | 6.82171 | 0.974529 | ||||||||
\(50\) | −2.86269 | −0.404846 | ||||||||
\(51\) | −0.496511 | + | 0.795351i | −0.0695254 | + | 0.111371i | ||||
\(52\) | − | 1.37334i | − | 0.190449i | ||||||
\(53\) | 4.75439i | 0.653066i | 0.945186 | + | 0.326533i | \(0.105880\pi\) | ||||
−0.945186 | + | 0.326533i | \(0.894120\pi\) | |||||||
\(54\) | −4.09138 | − | 0.424636i | −0.556766 | − | 0.0577856i | ||||
\(55\) | −3.62195 | − | 1.45002i | −0.488384 | − | 0.195521i | ||||
\(56\) | 1.12757i | 0.150678i | ||||||||
\(57\) | −9.99056 | − | 6.23676i | −1.32328 | − | 0.826080i | ||||
\(58\) | −8.06948 | −1.05957 | ||||||||
\(59\) | − | 7.23149i | − | 0.941460i | −0.882277 | − | 0.470730i | \(-0.843991\pi\) | ||
0.882277 | − | 0.470730i | \(-0.156009\pi\) | |||||||
\(60\) | −2.37359 | − | 1.48175i | −0.306429 | − | 0.191293i | ||||
\(61\) | − | 12.4925i | − | 1.59951i | −0.600330 | − | 0.799753i | \(-0.704964\pi\) | ||
0.600330 | − | 0.799753i | \(-0.295036\pi\) | |||||||
\(62\) | 1.12353 | 0.142689 | ||||||||
\(63\) | 1.13806 | − | 0.556294i | 0.143382 | − | 0.0700864i | ||||
\(64\) | 3.35885 | 0.419856 | ||||||||
\(65\) | 1.17632 | 0.145905 | ||||||||
\(66\) | −2.68619 | − | 3.66933i | −0.330647 | − | 0.451664i | ||||
\(67\) | 9.42183 | 1.15106 | 0.575530 | − | 0.817781i | \(-0.304796\pi\) | ||||
0.575530 | + | 0.817781i | \(0.304796\pi\) | |||||||
\(68\) | −0.743429 | −0.0901540 | ||||||||
\(69\) | −2.80390 | − | 1.75038i | −0.337549 | − | 0.210721i | ||||
\(70\) | −0.393197 | −0.0469960 | ||||||||
\(71\) | 6.54436i | 0.776673i | 0.921518 | + | 0.388336i | \(0.126950\pi\) | ||||
−0.921518 | + | 0.388336i | \(0.873050\pi\) | |||||||
\(72\) | −3.51812 | − | 7.19735i | −0.414614 | − | 0.848216i | ||||
\(73\) | − | 4.36845i | − | 0.511288i | −0.966771 | − | 0.255644i | \(-0.917712\pi\) | ||
0.966771 | − | 0.255644i | \(-0.0822876\pi\) | |||||||
\(74\) | 4.90591 | 0.570300 | ||||||||
\(75\) | −3.31687 | + | 5.31323i | −0.382999 | + | 0.613519i | ||||
\(76\) | − | 9.33835i | − | 1.07118i | ||||||
\(77\) | 1.30012 | + | 0.520495i | 0.148163 | + | 0.0593159i | ||||
\(78\) | 1.16309 | + | 0.726077i | 0.131694 | + | 0.0822121i | ||||
\(79\) | − | 4.73363i | − | 0.532574i | −0.963894 | − | 0.266287i | \(-0.914203\pi\) | ||
0.963894 | − | 0.266287i | \(-0.0857970\pi\) | |||||||
\(80\) | − | 0.744336i | − | 0.0832192i | ||||||
\(81\) | −5.52863 | + | 7.10171i | −0.614293 | + | 0.789078i | ||||
\(82\) | −8.59559 | −0.949224 | ||||||||
\(83\) | 10.7329 | 1.17808 | 0.589042 | − | 0.808102i | \(-0.299505\pi\) | ||||
0.589042 | + | 0.808102i | \(0.299505\pi\) | |||||||
\(84\) | 0.852015 | + | 0.531884i | 0.0929624 | + | 0.0580333i | ||||
\(85\) | − | 0.636776i | − | 0.0690681i | ||||||
\(86\) | − | 7.36798i | − | 0.794510i | ||||||
\(87\) | −9.34974 | + | 14.9772i | −1.00240 | + | 1.60572i | ||||
\(88\) | 3.29172 | − | 8.22226i | 0.350898 | − | 0.876496i | ||||
\(89\) | − | 12.0717i | − | 1.27960i | −0.768543 | − | 0.639799i | \(-0.779018\pi\) | ||
0.768543 | − | 0.639799i | \(-0.220982\pi\) | |||||||
\(90\) | 2.50980 | − | 1.22681i | 0.264556 | − | 0.129317i | ||||
\(91\) | −0.422249 | −0.0442637 | ||||||||
\(92\) | − | 2.62085i | − | 0.273243i | ||||||
\(93\) | 1.30179 | − | 2.08531i | 0.134989 | − | 0.216237i | ||||
\(94\) | 1.06624i | 0.109974i | ||||||||
\(95\) | 7.99867 | 0.820646 | ||||||||
\(96\) | 5.35805 | − | 8.58297i | 0.546854 | − | 0.875995i | ||||
\(97\) | −15.2047 | −1.54381 | −0.771904 | − | 0.635740i | \(-0.780695\pi\) | ||||
−0.771904 | + | 0.635740i | \(0.780695\pi\) | |||||||
\(98\) | −5.40017 | −0.545500 | ||||||||
\(99\) | −9.92275 | + | 0.734152i | −0.997274 | + | 0.0737851i | ||||
\(100\) | −4.96637 | −0.496637 | ||||||||
\(101\) | −8.07804 | −0.803795 | −0.401898 | − | 0.915685i | \(-0.631649\pi\) | ||||
−0.401898 | + | 0.915685i | \(0.631649\pi\) | |||||||
\(102\) | 0.393046 | − | 0.629612i | 0.0389173 | − | 0.0623409i | ||||
\(103\) | 19.6417 | 1.93535 | 0.967677 | − | 0.252193i | \(-0.0811518\pi\) | ||||
0.967677 | + | 0.252193i | \(0.0811518\pi\) | |||||||
\(104\) | 2.67039i | 0.261854i | ||||||||
\(105\) | −0.455580 | + | 0.729784i | −0.0444600 | + | 0.0712197i | ||||
\(106\) | − | 3.76365i | − | 0.365558i | ||||||
\(107\) | −8.50876 | −0.822573 | −0.411287 | − | 0.911506i | \(-0.634920\pi\) | ||||
−0.411287 | + | 0.911506i | \(0.634920\pi\) | |||||||
\(108\) | −7.09798 | − | 0.736685i | −0.683003 | − | 0.0708875i | ||||
\(109\) | 12.8446i | 1.23029i | 0.788415 | + | 0.615144i | \(0.210902\pi\) | ||||
−0.788415 | + | 0.615144i | \(0.789098\pi\) | |||||||
\(110\) | 2.86720 | + | 1.14786i | 0.273376 | + | 0.109444i | ||||
\(111\) | 5.68426 | − | 9.10550i | 0.539526 | − | 0.864256i | ||||
\(112\) | 0.267184i | 0.0252465i | ||||||||
\(113\) | 8.30598i | 0.781361i | 0.920526 | + | 0.390680i | \(0.127760\pi\) | ||||
−0.920526 | + | 0.390680i | \(0.872240\pi\) | |||||||
\(114\) | 7.90868 | + | 4.93712i | 0.740716 | + | 0.462404i | ||||
\(115\) | 2.24486 | 0.209335 | ||||||||
\(116\) | −13.9994 | −1.29982 | ||||||||
\(117\) | 2.69524 | − | 1.31745i | 0.249175 | − | 0.121799i | ||||
\(118\) | 5.72456i | 0.526989i | ||||||||
\(119\) | 0.228575i | 0.0209534i | ||||||||
\(120\) | 4.61531 | + | 2.88118i | 0.421318 | + | 0.263015i | ||||
\(121\) | −7.96104 | − | 7.59091i | −0.723731 | − | 0.690082i | ||||
\(122\) | 9.88929i | 0.895334i | ||||||||
\(123\) | −9.95932 | + | 15.9536i | −0.898002 | + | 1.43849i | ||||
\(124\) | 1.94918 | 0.175041 | ||||||||
\(125\) | − | 10.1355i | − | 0.906548i | ||||||
\(126\) | −0.900908 | + | 0.440371i | −0.0802593 | + | 0.0392314i | ||||
\(127\) | 12.2654i | 1.08838i | 0.838962 | + | 0.544189i | \(0.183163\pi\) | ||||
−0.838962 | + | 0.544189i | \(0.816837\pi\) | |||||||
\(128\) | 9.02447 | 0.797658 | ||||||||
\(129\) | −13.6752 | − | 8.53695i | −1.20403 | − | 0.751636i | ||||
\(130\) | −0.931196 | −0.0816713 | ||||||||
\(131\) | −6.42870 | −0.561679 | −0.280839 | − | 0.959755i | \(-0.590613\pi\) | ||||
−0.280839 | + | 0.959755i | \(0.590613\pi\) | |||||||
\(132\) | −4.66017 | − | 6.36579i | −0.405616 | − | 0.554071i | ||||
\(133\) | −2.87117 | −0.248962 | ||||||||
\(134\) | −7.45847 | −0.644314 | ||||||||
\(135\) | 0.631000 | − | 6.07970i | 0.0543078 | − | 0.523257i | ||||
\(136\) | 1.44556 | 0.123955 | ||||||||
\(137\) | − | 10.8763i | − | 0.929224i | −0.885514 | − | 0.464612i | \(-0.846194\pi\) | ||
0.885514 | − | 0.464612i | \(-0.153806\pi\) | |||||||
\(138\) | 2.21961 | + | 1.38563i | 0.188946 | + | 0.117952i | ||||
\(139\) | 3.19422i | 0.270930i | 0.990782 | + | 0.135465i | \(0.0432529\pi\) | ||||
−0.990782 | + | 0.135465i | \(0.956747\pi\) | |||||||
\(140\) | −0.682143 | −0.0576516 | ||||||||
\(141\) | 1.97896 | + | 1.23540i | 0.166659 | + | 0.104039i | ||||
\(142\) | − | 5.18062i | − | 0.434748i | ||||||
\(143\) | 3.07905 | + | 1.23267i | 0.257483 | + | 0.103081i | ||||
\(144\) | −0.833637 | − | 1.70545i | −0.0694698 | − | 0.142121i | ||||
\(145\) | − | 11.9911i | − | 0.995804i | ||||||
\(146\) | 3.45813i | 0.286197i | ||||||||
\(147\) | −6.25693 | + | 10.0229i | −0.516063 | + | 0.826672i | ||||
\(148\) | 8.51108 | 0.699606 | ||||||||
\(149\) | −0.226481 | −0.0185540 | −0.00927702 | − | 0.999957i | \(-0.502953\pi\) | ||||
−0.00927702 | + | 0.999957i | \(0.502953\pi\) | |||||||
\(150\) | 2.62569 | − | 4.20604i | 0.214386 | − | 0.343422i | ||||
\(151\) | 15.0745i | 1.22674i | 0.789795 | + | 0.613371i | \(0.210187\pi\) | ||||
−0.789795 | + | 0.613371i | \(0.789813\pi\) | |||||||
\(152\) | 18.1579i | 1.47280i | ||||||||
\(153\) | −0.713174 | − | 1.45901i | −0.0576567 | − | 0.117954i | ||||
\(154\) | −1.02920 | − | 0.412032i | −0.0829352 | − | 0.0332025i | ||||
\(155\) | 1.66955i | 0.134101i | ||||||||
\(156\) | 2.01780 | + | 1.25964i | 0.161553 | + | 0.100852i | ||||
\(157\) | 9.13891 | 0.729365 | 0.364682 | − | 0.931132i | \(-0.381178\pi\) | ||||
0.364682 | + | 0.931132i | \(0.381178\pi\) | |||||||
\(158\) | 3.74721i | 0.298112i | ||||||||
\(159\) | −6.98544 | − | 4.36077i | −0.553981 | − | 0.345832i | ||||
\(160\) | 6.87172i | 0.543257i | ||||||||
\(161\) | −0.805808 | −0.0635066 | ||||||||
\(162\) | 4.37655 | − | 5.62182i | 0.343854 | − | 0.441692i | ||||
\(163\) | 13.8258 | 1.08292 | 0.541461 | − | 0.840726i | \(-0.317871\pi\) | ||||
0.541461 | + | 0.840726i | \(0.317871\pi\) | |||||||
\(164\) | −14.9122 | −1.16444 | ||||||||
\(165\) | 5.45255 | − | 3.99162i | 0.424480 | − | 0.310747i | ||||
\(166\) | −8.49630 | −0.659441 | ||||||||
\(167\) | 0.223671 | 0.0173082 | 0.00865410 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865410 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(168\) | −1.65670 | − | 1.03422i | −0.127817 | − | 0.0797917i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0.504082i | 0.0386613i | ||||||||
\(171\) | 18.3269 | − | 8.95831i | 1.40149 | − | 0.685059i | ||||
\(172\) | − | 12.7824i | − | 0.974651i | ||||||
\(173\) | 3.40843 | 0.259138 | 0.129569 | − | 0.991570i | \(-0.458641\pi\) | ||||
0.129569 | + | 0.991570i | \(0.458641\pi\) | |||||||
\(174\) | 7.40140 | − | 11.8562i | 0.561099 | − | 0.898814i | ||||
\(175\) | 1.52696i | 0.115428i | ||||||||
\(176\) | 0.779991 | − | 1.94831i | 0.0587940 | − | 0.146859i | ||||
\(177\) | 10.6249 | + | 6.63279i | 0.798620 | + | 0.498551i | ||||
\(178\) | 9.55615i | 0.716263i | ||||||||
\(179\) | − | 15.5363i | − | 1.16124i | −0.814176 | − | 0.580618i | \(-0.802811\pi\) | ||
0.814176 | − | 0.580618i | \(-0.197189\pi\) | |||||||
\(180\) | 4.35415 | − | 2.12834i | 0.324539 | − | 0.158637i | ||||
\(181\) | 8.58522 | 0.638134 | 0.319067 | − | 0.947732i | \(-0.396630\pi\) | ||||
0.319067 | + | 0.947732i | \(0.396630\pi\) | |||||||
\(182\) | 0.334259 | 0.0247769 | ||||||||
\(183\) | 18.3548 | + | 11.4583i | 1.35683 | + | 0.847020i | ||||
\(184\) | 5.09610i | 0.375690i | ||||||||
\(185\) | 7.29007i | 0.535977i | ||||||||
\(186\) | −1.03052 | + | 1.65076i | −0.0755611 | + | 0.121040i | ||||
\(187\) | 0.667279 | − | 1.66677i | 0.0487963 | − | 0.121886i | ||||
\(188\) | 1.84977i | 0.134908i | ||||||||
\(189\) | −0.226502 | + | 2.18235i | −0.0164756 | + | 0.158743i | ||||
\(190\) | −6.33187 | −0.459362 | ||||||||
\(191\) | − | 0.793049i | − | 0.0573830i | −0.999588 | − | 0.0286915i | \(-0.990866\pi\) | ||
0.999588 | − | 0.0286915i | \(-0.00913405\pi\) | |||||||
\(192\) | −3.08077 | + | 4.93502i | −0.222335 | + | 0.356154i | ||||
\(193\) | 1.61649i | 0.116357i | 0.998306 | + | 0.0581786i | \(0.0185293\pi\) | ||||
−0.998306 | + | 0.0581786i | \(0.981471\pi\) | |||||||
\(194\) | 12.0363 | 0.864157 | ||||||||
\(195\) | −1.07894 | + | 1.72833i | −0.0772642 | + | 0.123768i | ||||
\(196\) | −9.36855 | −0.669182 | ||||||||
\(197\) | −13.5082 | −0.962418 | −0.481209 | − | 0.876606i | \(-0.659802\pi\) | ||||
−0.481209 | + | 0.876606i | \(0.659802\pi\) | |||||||
\(198\) | 7.85501 | − | 0.581166i | 0.558231 | − | 0.0413017i | ||||
\(199\) | −9.07824 | −0.643539 | −0.321770 | − | 0.946818i | \(-0.604278\pi\) | ||||
−0.321770 | + | 0.946818i | \(0.604278\pi\) | |||||||
\(200\) | 9.65684 | 0.682842 | ||||||||
\(201\) | −8.64179 | + | 13.8431i | −0.609545 | + | 0.976419i | ||||
\(202\) | 6.39470 | 0.449930 | ||||||||
\(203\) | 4.30427i | 0.302101i | ||||||||
\(204\) | 0.681880 | − | 1.09229i | 0.0477412 | − | 0.0764757i | ||||
\(205\) | − | 12.7729i | − | 0.892095i | ||||||
\(206\) | −15.5487 | −1.08333 | ||||||||
\(207\) | 5.14352 | − | 2.51419i | 0.357499 | − | 0.174748i | ||||
\(208\) | 0.632764i | 0.0438743i | ||||||||
\(209\) | 20.9366 | + | 8.38182i | 1.44822 | + | 0.579783i | ||||
\(210\) | 0.360644 | − | 0.577709i | 0.0248868 | − | 0.0398657i | ||||
\(211\) | 12.7812i | 0.879895i | 0.898024 | + | 0.439947i | \(0.145003\pi\) | ||||
−0.898024 | + | 0.439947i | \(0.854997\pi\) | |||||||
\(212\) | − | 6.52942i | − | 0.448442i | ||||||
\(213\) | −9.61537 | − | 6.00255i | −0.658835 | − | 0.411288i | ||||
\(214\) | 6.73567 | 0.460441 | ||||||||
\(215\) | 10.9487 | 0.746692 | ||||||||
\(216\) | 13.8016 | + | 1.43244i | 0.939082 | + | 0.0974654i | ||||
\(217\) | − | 0.599295i | − | 0.0406828i | ||||||
\(218\) | − | 10.1680i | − | 0.688662i | ||||||
\(219\) | 6.41839 | + | 4.00678i | 0.433715 | + | 0.270753i | ||||
\(220\) | 4.97419 | + | 1.99138i | 0.335360 | + | 0.134259i | ||||
\(221\) | 0.541327i | 0.0364136i | ||||||||
\(222\) | −4.49975 | + | 7.20806i | −0.302003 | + | 0.483773i | ||||
\(223\) | 0.105455 | 0.00706177 | 0.00353089 | − | 0.999994i | \(-0.498876\pi\) | ||||
0.00353089 | + | 0.999994i | \(0.498876\pi\) | |||||||
\(224\) | − | 2.46665i | − | 0.164810i | ||||||
\(225\) | −4.76426 | − | 9.74669i | −0.317617 | − | 0.649780i | ||||
\(226\) | − | 6.57514i | − | 0.437372i | ||||||
\(227\) | 10.5968 | 0.703336 | 0.351668 | − | 0.936125i | \(-0.385615\pi\) | ||||
0.351668 | + | 0.936125i | \(0.385615\pi\) | |||||||
\(228\) | 13.7205 | + | 8.56523i | 0.908661 | + | 0.567246i | ||||
\(229\) | 2.63421 | 0.174074 | 0.0870368 | − | 0.996205i | \(-0.472260\pi\) | ||||
0.0870368 | + | 0.996205i | \(0.472260\pi\) | |||||||
\(230\) | −1.77707 | −0.117176 | ||||||||
\(231\) | −1.95723 | + | 1.43282i | −0.128776 | + | 0.0942725i | ||||
\(232\) | 27.2211 | 1.78715 | ||||||||
\(233\) | −13.5027 | −0.884594 | −0.442297 | − | 0.896869i | \(-0.645836\pi\) | ||||
−0.442297 | + | 0.896869i | \(0.645836\pi\) | |||||||
\(234\) | −2.13359 | + | 1.04292i | −0.139477 | + | 0.0681776i | ||||
\(235\) | −1.58440 | −0.103355 | ||||||||
\(236\) | 9.93133i | 0.646474i | ||||||||
\(237\) | 6.95493 | + | 4.34173i | 0.451771 | + | 0.282025i | ||||
\(238\) | − | 0.180944i | − | 0.0117288i | ||||||
\(239\) | −19.0742 | −1.23381 | −0.616903 | − | 0.787039i | \(-0.711613\pi\) | ||||
−0.616903 | + | 0.787039i | \(0.711613\pi\) | |||||||
\(240\) | 1.09362 | + | 0.682712i | 0.0705931 | + | 0.0440688i | ||||
\(241\) | − | 12.4200i | − | 0.800041i | −0.916506 | − | 0.400020i | \(-0.869003\pi\) | ||
0.916506 | − | 0.400020i | \(-0.130997\pi\) | |||||||
\(242\) | 6.30208 | + | 6.00908i | 0.405113 | + | 0.386278i | ||||
\(243\) | −5.36334 | − | 14.6368i | −0.344059 | − | 0.938948i | ||||
\(244\) | 17.1566i | 1.09834i | ||||||||
\(245\) | − | 8.02453i | − | 0.512669i | ||||||
\(246\) | 7.88396 | − | 12.6292i | 0.502663 | − | 0.805206i | ||||
\(247\) | −6.79972 | −0.432656 | ||||||||
\(248\) | −3.79007 | −0.240670 | ||||||||
\(249\) | −9.84428 | + | 15.7694i | −0.623856 | + | 0.999343i | ||||
\(250\) | 8.02343i | 0.507446i | ||||||||
\(251\) | 22.0224i | 1.39004i | 0.718990 | + | 0.695020i | \(0.244605\pi\) | ||||
−0.718990 | + | 0.695020i | \(0.755395\pi\) | |||||||
\(252\) | −1.56295 | + | 0.763983i | −0.0984567 | + | 0.0481264i | ||||
\(253\) | 5.87596 | + | 2.35240i | 0.369419 | + | 0.147894i | ||||
\(254\) | − | 9.70949i | − | 0.609227i | ||||||
\(255\) | 0.935590 | + | 0.584057i | 0.0585889 | + | 0.0365751i | ||||
\(256\) | −13.8616 | −0.866350 | ||||||||
\(257\) | − | 1.30241i | − | 0.0812423i | −0.999175 | − | 0.0406211i | \(-0.987066\pi\) | ||
0.999175 | − | 0.0406211i | \(-0.0129337\pi\) | |||||||
\(258\) | 10.8255 | + | 6.75798i | 0.673965 | + | 0.420734i | ||||
\(259\) | − | 2.61682i | − | 0.162601i | ||||||
\(260\) | −1.61550 | −0.100189 | ||||||||
\(261\) | −13.4297 | − | 27.4744i | −0.831278 | − | 1.70062i | ||||
\(262\) | 5.08906 | 0.314403 | ||||||||
\(263\) | 5.40110 | 0.333046 | 0.166523 | − | 0.986038i | \(-0.446746\pi\) | ||||
0.166523 | + | 0.986038i | \(0.446746\pi\) | |||||||
\(264\) | 9.06145 | + | 12.3779i | 0.557693 | + | 0.761809i | ||||
\(265\) | 5.59270 | 0.343557 | ||||||||
\(266\) | 2.27287 | 0.139358 | ||||||||
\(267\) | 17.7365 | + | 11.0723i | 1.08545 | + | 0.677612i | ||||
\(268\) | −12.9394 | −0.790401 | ||||||||
\(269\) | 22.0497i | 1.34439i | 0.740373 | + | 0.672197i | \(0.234649\pi\) | ||||
−0.740373 | + | 0.672197i | \(0.765351\pi\) | |||||||
\(270\) | −0.499509 | + | 4.81279i | −0.0303992 | + | 0.292897i | ||||
\(271\) | − | 22.6385i | − | 1.37519i | −0.726093 | − | 0.687596i | \(-0.758666\pi\) | ||
0.726093 | − | 0.687596i | \(-0.241334\pi\) | |||||||
\(272\) | 0.342533 | 0.0207691 | ||||||||
\(273\) | 0.387291 | − | 0.620394i | 0.0234399 | − | 0.0375480i | ||||
\(274\) | 8.60984i | 0.520140i | ||||||||
\(275\) | 4.45767 | − | 11.1346i | 0.268807 | − | 0.671444i | ||||
\(276\) | 3.85071 | + | 2.40387i | 0.231786 | + | 0.144696i | ||||
\(277\) | 19.5316i | 1.17354i | 0.809754 | + | 0.586770i | \(0.199601\pi\) | ||||
−0.809754 | + | 0.586770i | \(0.800399\pi\) | |||||||
\(278\) | − | 2.52860i | − | 0.151655i | ||||||
\(279\) | 1.86985 | + | 3.82533i | 0.111945 | + | 0.229017i | ||||
\(280\) | 1.32639 | 0.0792669 | ||||||||
\(281\) | 13.0649 | 0.779385 | 0.389693 | − | 0.920945i | \(-0.372581\pi\) | ||||
0.389693 | + | 0.920945i | \(0.372581\pi\) | |||||||
\(282\) | −1.56658 | − | 0.977961i | −0.0932883 | − | 0.0582367i | ||||
\(283\) | 25.9250i | 1.54108i | 0.637392 | + | 0.770540i | \(0.280013\pi\) | ||||
−0.637392 | + | 0.770540i | \(0.719987\pi\) | |||||||
\(284\) | − | 8.98766i | − | 0.533320i | ||||||
\(285\) | −7.33645 | + | 11.7521i | −0.434574 | + | 0.696136i | ||||
\(286\) | −2.43742 | − | 0.975803i | −0.144128 | − | 0.0577004i | ||||
\(287\) | 4.58490i | 0.270638i | ||||||||
\(288\) | 7.69616 | + | 15.7448i | 0.453500 | + | 0.927769i | ||||
\(289\) | −16.7070 | −0.982763 | ||||||||
\(290\) | 9.49232i | 0.557408i | ||||||||
\(291\) | 13.9459 | − | 22.3397i | 0.817525 | − | 1.30958i | ||||
\(292\) | 5.99939i | 0.351088i | ||||||||
\(293\) | −20.8778 | −1.21969 | −0.609847 | − | 0.792519i | \(-0.708769\pi\) | ||||
−0.609847 | + | 0.792519i | \(0.708769\pi\) | |||||||
\(294\) | 4.95309 | − | 7.93426i | 0.288870 | − | 0.462735i | ||||
\(295\) | −8.50657 | −0.495272 | ||||||||
\(296\) | −16.5493 | −0.961910 | ||||||||
\(297\) | 8.02258 | − | 15.2525i | 0.465517 | − | 0.885039i | ||||
\(298\) | 0.179286 | 0.0103857 | ||||||||
\(299\) | −1.90837 | −0.110364 | ||||||||
\(300\) | 4.55521 | − | 7.29690i | 0.262995 | − | 0.421287i | ||||
\(301\) | −3.93009 | −0.226527 | ||||||||
\(302\) | − | 11.9332i | − | 0.686677i | ||||||
\(303\) | 7.40925 | − | 11.8687i | 0.425651 | − | 0.681842i | ||||
\(304\) | 4.30262i | 0.246772i | ||||||||
\(305\) | −14.6953 | −0.841449 | ||||||||
\(306\) | 0.564559 | + | 1.15497i | 0.0322737 | + | 0.0660254i | ||||
\(307\) | − | 15.9078i | − | 0.907908i | −0.891025 | − | 0.453954i | \(-0.850013\pi\) | ||
0.891025 | − | 0.453954i | \(-0.149987\pi\) | |||||||
\(308\) | −1.78552 | − | 0.714819i | −0.101739 | − | 0.0407306i | ||||
\(309\) | −18.0156 | + | 28.8588i | −1.02487 | + | 1.64172i | ||||
\(310\) | − | 1.32164i | − | 0.0750641i | ||||||
\(311\) | − | 12.7429i | − | 0.722582i | −0.932453 | − | 0.361291i | \(-0.882336\pi\) | ||
0.932453 | − | 0.361291i | \(-0.117664\pi\) | |||||||
\(312\) | −3.92350 | − | 2.44931i | −0.222125 | − | 0.138665i | ||||
\(313\) | −10.5689 | −0.597391 | −0.298696 | − | 0.954348i | \(-0.596552\pi\) | ||||
−0.298696 | + | 0.954348i | \(0.596552\pi\) | |||||||
\(314\) | −7.23451 | −0.408267 | ||||||||
\(315\) | −0.654381 | − | 1.33873i | −0.0368702 | − | 0.0754289i | ||||
\(316\) | 6.50090i | 0.365704i | ||||||||
\(317\) | − | 20.9384i | − | 1.17602i | −0.808855 | − | 0.588008i | \(-0.799912\pi\) | ||
0.808855 | − | 0.588008i | \(-0.200088\pi\) | |||||||
\(318\) | 5.52978 | + | 3.45206i | 0.310095 | + | 0.193582i | ||||
\(319\) | 12.5655 | − | 31.3868i | 0.703531 | − | 1.75732i | ||||
\(320\) | − | 3.95109i | − | 0.220873i | ||||||
\(321\) | 7.80432 | − | 12.5016i | 0.435594 | − | 0.697771i | ||||
\(322\) | 0.637891 | 0.0355483 | ||||||||
\(323\) | 3.68087i | 0.204809i | ||||||||
\(324\) | 7.59272 | − | 9.75309i | 0.421818 | − | 0.541838i | ||||
\(325\) | 3.61626i | 0.200594i | ||||||||
\(326\) | −10.9447 | −0.606173 | ||||||||
\(327\) | −18.8720 | − | 11.7812i | −1.04363 | − | 0.651500i | ||||
\(328\) | 28.9959 | 1.60103 | ||||||||
\(329\) | 0.568732 | 0.0313552 | ||||||||
\(330\) | −4.31632 | + | 3.15983i | −0.237606 | + | 0.173943i | ||||
\(331\) | −20.5719 | −1.13073 | −0.565367 | − | 0.824840i | \(-0.691265\pi\) | ||||
−0.565367 | + | 0.824840i | \(0.691265\pi\) | |||||||
\(332\) | −14.7399 | −0.808958 | ||||||||
\(333\) | 8.16470 | + | 16.7033i | 0.447423 | + | 0.915336i | ||||
\(334\) | −0.177062 | −0.00968839 | ||||||||
\(335\) | − | 11.0831i | − | 0.605536i | ||||||
\(336\) | −0.392563 | − | 0.245064i | −0.0214161 | − | 0.0133693i | ||||
\(337\) | − | 15.3510i | − | 0.836223i | −0.908396 | − | 0.418112i | \(-0.862692\pi\) | ||
0.908396 | − | 0.418112i | \(-0.137308\pi\) | |||||||
\(338\) | 0.791616 | 0.0430582 | ||||||||
\(339\) | −12.2036 | − | 7.61832i | −0.662811 | − | 0.413770i | ||||
\(340\) | 0.874513i | 0.0474271i | ||||||||
\(341\) | −1.74952 | + | 4.37007i | −0.0947419 | + | 0.236652i | ||||
\(342\) | −14.5078 | + | 7.09154i | −0.784494 | + | 0.383467i | ||||
\(343\) | 5.83620i | 0.315125i | ||||||||
\(344\) | 24.8547i | 1.34008i | ||||||||
\(345\) | −2.05901 | + | 3.29829i | −0.110853 | + | 0.177574i | ||||
\(346\) | −2.69817 | −0.145055 | ||||||||
\(347\) | 21.9603 | 1.17889 | 0.589446 | − | 0.807808i | \(-0.299346\pi\) | ||||
0.589446 | + | 0.807808i | \(0.299346\pi\) | |||||||
\(348\) | 12.8404 | − | 20.5688i | 0.688319 | − | 1.10260i | ||||
\(349\) | 0.253359i | 0.0135620i | 0.999977 | + | 0.00678100i | \(0.00215848\pi\) | ||||
−0.999977 | + | 0.00678100i | \(0.997842\pi\) | |||||||
\(350\) | − | 1.20877i | − | 0.0646114i | ||||||
\(351\) | −0.536417 | + | 5.16839i | −0.0286318 | + | 0.275868i | ||||
\(352\) | −7.20089 | + | 17.9868i | −0.383809 | + | 0.958701i | ||||
\(353\) | − | 7.85980i | − | 0.418335i | −0.977880 | − | 0.209167i | \(-0.932925\pi\) | ||
0.977880 | − | 0.209167i | \(-0.0670754\pi\) | |||||||
\(354\) | −8.41087 | − | 5.25062i | −0.447033 | − | 0.279067i | ||||
\(355\) | 7.69829 | 0.408583 | ||||||||
\(356\) | 16.5786i | 0.878664i | ||||||||
\(357\) | −0.335836 | − | 0.209651i | −0.0177743 | − | 0.0110959i | ||||
\(358\) | 12.2988i | 0.650010i | ||||||||
\(359\) | −11.6282 | −0.613713 | −0.306856 | − | 0.951756i | \(-0.599277\pi\) | ||||
−0.306856 | + | 0.951756i | \(0.599277\pi\) | |||||||
\(360\) | −8.46641 | + | 4.13845i | −0.446219 | + | 0.218115i | ||||
\(361\) | −27.2361 | −1.43348 | ||||||||
\(362\) | −6.79619 | −0.357200 | ||||||||
\(363\) | 18.4550 | − | 4.73439i | 0.968634 | − | 0.248491i | ||||
\(364\) | 0.579894 | 0.0303947 | ||||||||
\(365\) | −5.13871 | −0.268972 | ||||||||
\(366\) | −14.5299 | − | 9.07055i | −0.759492 | − | 0.474125i | ||||
\(367\) | −37.8638 | −1.97647 | −0.988237 | − | 0.152930i | \(-0.951129\pi\) | ||||
−0.988237 | + | 0.152930i | \(0.951129\pi\) | |||||||
\(368\) | 1.20755i | 0.0629479i | ||||||||
\(369\) | −14.3053 | − | 29.2657i | −0.744703 | − | 1.52351i | ||||
\(370\) | − | 5.77094i | − | 0.300017i | ||||||
\(371\) | −2.00754 | −0.104226 | ||||||||
\(372\) | −1.78780 | + | 2.86385i | −0.0926933 | + | 0.148484i | ||||
\(373\) | 8.38711i | 0.434268i | 0.976142 | + | 0.217134i | \(0.0696709\pi\) | ||||
−0.976142 | + | 0.217134i | \(0.930329\pi\) | |||||||
\(374\) | −0.528229 | + | 1.31944i | −0.0273141 | + | 0.0682267i | ||||
\(375\) | 14.8917 | + | 9.29639i | 0.769005 | + | 0.480063i | ||||
\(376\) | − | 3.59678i | − | 0.185490i | ||||||
\(377\) | 10.1937i | 0.525001i | ||||||||
\(378\) | 0.179302 | − | 1.72758i | 0.00922231 | − | 0.0888572i | ||||
\(379\) | −5.28430 | −0.271436 | −0.135718 | − | 0.990747i | \(-0.543334\pi\) | ||||
−0.135718 | + | 0.990747i | \(0.543334\pi\) | |||||||
\(380\) | −10.9849 | −0.563515 | ||||||||
\(381\) | −18.0211 | − | 11.2499i | −0.923248 | − | 0.576352i | ||||
\(382\) | 0.627790i | 0.0321206i | ||||||||
\(383\) | − | 0.100678i | − | 0.00514442i | −0.999997 | − | 0.00257221i | \(-0.999181\pi\) | ||
0.999997 | − | 0.00257221i | \(-0.000818760\pi\) | |||||||
\(384\) | −8.27733 | + | 13.2593i | −0.422401 | + | 0.676636i | ||||
\(385\) | 0.612270 | − | 1.52937i | 0.0312042 | − | 0.0779438i | ||||
\(386\) | − | 1.27964i | − | 0.0651318i | ||||||
\(387\) | 25.0860 | − | 12.2622i | 1.27519 | − | 0.623324i | ||||
\(388\) | 20.8813 | 1.06009 | ||||||||
\(389\) | 2.95150i | 0.149647i | 0.997197 | + | 0.0748234i | \(0.0238393\pi\) | ||||
−0.997197 | + | 0.0748234i | \(0.976161\pi\) | |||||||
\(390\) | 0.854102 | − | 1.36817i | 0.0432491 | − | 0.0692800i | ||||
\(391\) | 1.03305i | 0.0522438i | ||||||||
\(392\) | 18.2166 | 0.920079 | ||||||||
\(393\) | 5.89647 | − | 9.44544i | 0.297438 | − | 0.476460i | ||||
\(394\) | 10.6933 | 0.538720 | ||||||||
\(395\) | −5.56828 | −0.280170 | ||||||||
\(396\) | 13.6274 | − | 1.00824i | 0.684801 | − | 0.0506662i | ||||
\(397\) | 3.61071 | 0.181217 | 0.0906083 | − | 0.995887i | \(-0.471119\pi\) | ||||
0.0906083 | + | 0.995887i | \(0.471119\pi\) | |||||||
\(398\) | 7.18647 | 0.360225 | ||||||||
\(399\) | 2.63347 | − | 4.21850i | 0.131838 | − | 0.211189i | ||||
\(400\) | 2.28824 | 0.114412 | ||||||||
\(401\) | 19.4088i | 0.969229i | 0.874728 | + | 0.484614i | \(0.161040\pi\) | ||||
−0.874728 | + | 0.484614i | \(0.838960\pi\) | |||||||
\(402\) | 6.84098 | − | 10.9584i | 0.341197 | − | 0.546557i | ||||
\(403\) | − | 1.41929i | − | 0.0707000i | ||||||
\(404\) | 11.0939 | 0.551944 | ||||||||
\(405\) | 8.35390 | + | 6.50346i | 0.415109 | + | 0.323160i | ||||
\(406\) | − | 3.40733i | − | 0.169103i | ||||||
\(407\) | −7.63928 | + | 19.0819i | −0.378665 | + | 0.945854i | ||||
\(408\) | −1.32588 | + | 2.12390i | −0.0656408 | + | 0.105149i | ||||
\(409\) | − | 36.3038i | − | 1.79511i | −0.440904 | − | 0.897554i | \(-0.645342\pi\) | ||
0.440904 | − | 0.897554i | \(-0.354658\pi\) | |||||||
\(410\) | 10.1112i | 0.499356i | ||||||||
\(411\) | 15.9801 | + | 9.97583i | 0.788240 | + | 0.492072i | ||||
\(412\) | −26.9748 | −1.32895 | ||||||||
\(413\) | 3.05349 | 0.150252 | ||||||||
\(414\) | −4.07169 | + | 1.99027i | −0.200113 | + | 0.0978166i | ||||
\(415\) | − | 12.6253i | − | 0.619753i | ||||||
\(416\) | − | 5.84169i | − | 0.286412i | ||||||
\(417\) | −4.69314 | − | 2.92977i | −0.229824 | − | 0.143471i | ||||
\(418\) | −16.5738 | − | 6.63518i | −0.810650 | − | 0.324537i | ||||
\(419\) | − | 16.9815i | − | 0.829601i | −0.909912 | − | 0.414800i | \(-0.863851\pi\) | ||
0.909912 | − | 0.414800i | \(-0.136149\pi\) | |||||||
\(420\) | 0.625668 | − | 1.00225i | 0.0305295 | − | 0.0489046i | ||||
\(421\) | 29.4877 | 1.43714 | 0.718571 | − | 0.695454i | \(-0.244797\pi\) | ||||
0.718571 | + | 0.695454i | \(0.244797\pi\) | |||||||
\(422\) | − | 10.1178i | − | 0.492527i | ||||||
\(423\) | −3.63024 | + | 1.77449i | −0.176509 | + | 0.0862787i | ||||
\(424\) | 12.6961i | 0.616577i | ||||||||
\(425\) | 1.95758 | 0.0949567 | ||||||||
\(426\) | 7.61168 | + | 4.75171i | 0.368787 | + | 0.230221i | ||||
\(427\) | 5.27496 | 0.255273 | ||||||||
\(428\) | 11.6855 | 0.564838 | ||||||||
\(429\) | −4.63525 | + | 3.39330i | −0.223792 | + | 0.163830i | ||||
\(430\) | −8.66713 | −0.417966 | ||||||||
\(431\) | −20.6901 | −0.996608 | −0.498304 | − | 0.867002i | \(-0.666044\pi\) | ||||
−0.498304 | + | 0.867002i | \(0.666044\pi\) | |||||||
\(432\) | 3.27037 | + | 0.339425i | 0.157346 | + | 0.0163306i | ||||
\(433\) | 11.5038 | 0.552839 | 0.276419 | − | 0.961037i | \(-0.410852\pi\) | ||||
0.276419 | + | 0.961037i | \(0.410852\pi\) | |||||||
\(434\) | 0.474411i | 0.0227725i | ||||||||
\(435\) | 17.6180 | + | 10.9983i | 0.844719 | + | 0.527329i | ||||
\(436\) | − | 17.6400i | − | 0.844804i | ||||||
\(437\) | −12.9764 | −0.620745 | ||||||||
\(438\) | −5.08090 | − | 3.17183i | −0.242775 | − | 0.151556i | ||||
\(439\) | − | 20.8711i | − | 0.996122i | −0.867142 | − | 0.498061i | \(-0.834046\pi\) | ||
0.867142 | − | 0.498061i | \(-0.165954\pi\) | |||||||
\(440\) | −9.67204 | − | 3.87213i | −0.461096 | − | 0.184596i | ||||
\(441\) | −8.98728 | − | 18.3861i | −0.427966 | − | 0.875530i | ||||
\(442\) | − | 0.428523i | − | 0.0203828i | ||||||
\(443\) | 1.76046i | 0.0836418i | 0.999125 | + | 0.0418209i | \(0.0133159\pi\) | ||||
−0.999125 | + | 0.0418209i | \(0.986684\pi\) | |||||||
\(444\) | −7.80644 | + | 12.5050i | −0.370477 | + | 0.593461i | ||||
\(445\) | −14.2002 | −0.673155 | ||||||||
\(446\) | −0.0834797 | −0.00395288 | ||||||||
\(447\) | 0.207730 | − | 0.332759i | 0.00982531 | − | 0.0157390i | ||||
\(448\) | 1.41827i | 0.0670070i | ||||||||
\(449\) | − | 13.7401i | − | 0.648435i | −0.945983 | − | 0.324217i | \(-0.894899\pi\) | ||
0.945983 | − | 0.324217i | \(-0.105101\pi\) | |||||||
\(450\) | 3.77146 | + | 7.71564i | 0.177788 | + | 0.363719i | ||||
\(451\) | 13.3847 | − | 33.4331i | 0.630261 | − | 1.57431i | ||||
\(452\) | − | 11.4070i | − | 0.536539i | ||||||
\(453\) | −22.1483 | − | 13.8264i | −1.04062 | − | 0.649622i | ||||
\(454\) | −8.38861 | −0.393697 | ||||||||
\(455\) | 0.496702i | 0.0232857i | ||||||||
\(456\) | −26.6787 | − | 16.6546i | −1.24934 | − | 0.779924i | ||||
\(457\) | 9.95393i | 0.465625i | 0.972522 | + | 0.232813i | \(0.0747929\pi\) | ||||
−0.972522 | + | 0.232813i | \(0.925207\pi\) | |||||||
\(458\) | −2.08528 | −0.0974389 | ||||||||
\(459\) | 2.79779 | + | 0.290377i | 0.130590 | + | 0.0135536i | ||||
\(460\) | −3.08297 | −0.143744 | ||||||||
\(461\) | −3.21744 | −0.149851 | −0.0749257 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749257 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(462\) | 1.54937 | − | 1.13424i | 0.0720834 | − | 0.0527697i | ||||
\(463\) | 11.4070 | 0.530130 | 0.265065 | − | 0.964231i | \(-0.414607\pi\) | ||||
0.265065 | + | 0.964231i | \(0.414607\pi\) | |||||||
\(464\) | 6.45020 | 0.299443 | ||||||||
\(465\) | −2.45300 | − | 1.53132i | −0.113755 | − | 0.0710135i | ||||
\(466\) | 10.6890 | 0.495157 | ||||||||
\(467\) | 35.6119i | 1.64792i | 0.566647 | + | 0.823961i | \(0.308240\pi\) | ||||
−0.566647 | + | 0.823961i | \(0.691760\pi\) | |||||||
\(468\) | −3.70149 | + | 1.80932i | −0.171102 | + | 0.0836357i | ||||
\(469\) | 3.97836i | 0.183704i | ||||||||
\(470\) | 1.25424 | 0.0578537 | ||||||||
\(471\) | −8.38230 | + | 13.4274i | −0.386236 | + | 0.618704i | ||||
\(472\) | − | 19.3109i | − | 0.888857i | ||||||
\(473\) | 28.6583 | + | 11.4731i | 1.31771 | + | 0.527535i | ||||
\(474\) | −5.50563 | − | 3.43698i | −0.252882 | − | 0.157866i | ||||
\(475\) | 24.5896i | 1.12825i | ||||||||
\(476\) | − | 0.313912i | − | 0.0143881i | ||||||
\(477\) | 12.8142 | − | 6.26369i | 0.586723 | − | 0.286795i | ||||
\(478\) | 15.0994 | 0.690631 | ||||||||
\(479\) | 10.5084 | 0.480140 | 0.240070 | − | 0.970756i | \(-0.422830\pi\) | ||||
0.240070 | + | 0.970756i | \(0.422830\pi\) | |||||||
\(480\) | −10.0963 | − | 6.30281i | −0.460833 | − | 0.287682i | ||||
\(481\) | − | 6.19734i | − | 0.282574i | ||||||
\(482\) | 9.83184i | 0.447828i | ||||||||
\(483\) | 0.739095 | − | 1.18394i | 0.0336300 | − | 0.0538713i | ||||
\(484\) | 10.9332 | + | 10.4249i | 0.496966 | + | 0.473860i | ||||
\(485\) | 17.8857i | 0.812147i | ||||||||
\(486\) | 4.24571 | + | 11.5867i | 0.192589 | + | 0.525583i | ||||
\(487\) | −17.2377 | −0.781113 | −0.390557 | − | 0.920579i | \(-0.627717\pi\) | ||||
−0.390557 | + | 0.920579i | \(0.627717\pi\) | |||||||
\(488\) | − | 33.3600i | − | 1.51014i | ||||||
\(489\) | −12.6812 | + | 20.3137i | −0.573463 | + | 0.918619i | ||||
\(490\) | 6.35235i | 0.286970i | ||||||||
\(491\) | −29.3071 | −1.32261 | −0.661306 | − | 0.750116i | \(-0.729998\pi\) | ||||
−0.661306 | + | 0.750116i | \(0.729998\pi\) | |||||||
\(492\) | 13.6776 | − | 21.9099i | 0.616633 | − | 0.987773i | ||||
\(493\) | 5.51812 | 0.248524 | ||||||||
\(494\) | 5.38276 | 0.242182 | ||||||||
\(495\) | 0.863601 | + | 11.6724i | 0.0388160 | + | 0.524634i | ||||
\(496\) | −0.898078 | −0.0403249 | ||||||||
\(497\) | −2.76335 | −0.123953 | ||||||||
\(498\) | 7.79289 | − | 12.4833i | 0.349208 | − | 0.559389i | ||||
\(499\) | −9.01669 | −0.403643 | −0.201821 | − | 0.979422i | \(-0.564686\pi\) | ||||
−0.201821 | + | 0.979422i | \(0.564686\pi\) | |||||||
\(500\) | 13.9196i | 0.622501i | ||||||||
\(501\) | −0.205153 | + | 0.328631i | −0.00916558 | + | 0.0146822i | ||||
\(502\) | − | 17.4333i | − | 0.778084i | ||||||
\(503\) | −28.0113 | −1.24896 | −0.624481 | − | 0.781040i | \(-0.714690\pi\) | ||||
−0.624481 | + | 0.781040i | \(0.714690\pi\) | |||||||
\(504\) | 3.03907 | − | 1.48552i | 0.135371 | − | 0.0661704i | ||||
\(505\) | 9.50239i | 0.422851i | ||||||||
\(506\) | −4.65150 | − | 1.86219i | −0.206785 | − | 0.0827846i | ||||
\(507\) | 0.917209 | − | 1.46926i | 0.0407347 | − | 0.0652522i | ||||
\(508\) | − | 16.8446i | − | 0.747359i | ||||||
\(509\) | − | 34.8187i | − | 1.54331i | −0.636039 | − | 0.771657i | \(-0.719428\pi\) | ||
0.636039 | − | 0.771657i | \(-0.280572\pi\) | |||||||
\(510\) | −0.740628 | − | 0.462349i | −0.0327956 | − | 0.0204732i | ||||
\(511\) | 1.84457 | 0.0815992 | ||||||||
\(512\) | −7.07587 | −0.312712 | ||||||||
\(513\) | −3.64748 | + | 35.1436i | −0.161040 | + | 1.55163i | ||||
\(514\) | 1.03101i | 0.0454759i | ||||||||
\(515\) | − | 23.1050i | − | 1.01813i | ||||||
\(516\) | 18.7807 | + | 11.7242i | 0.826775 | + | 0.516128i | ||||
\(517\) | −4.14720 | − | 1.66030i | −0.182393 | − | 0.0730198i | ||||
\(518\) | 2.07152i | 0.0910172i | ||||||||
\(519\) | −3.12625 | + | 5.00788i | −0.137227 | + | 0.219821i | ||||
\(520\) | 3.14125 | 0.137753 | ||||||||
\(521\) | − | 1.34449i | − | 0.0589031i | −0.999566 | − | 0.0294516i | \(-0.990624\pi\) | ||
0.999566 | − | 0.0294516i | \(-0.00937608\pi\) | |||||||
\(522\) | 10.6312 | + | 21.7492i | 0.465313 | + | 0.951936i | ||||
\(523\) | 19.6953i | 0.861215i | 0.902539 | + | 0.430608i | \(0.141701\pi\) | ||||
−0.902539 | + | 0.430608i | \(0.858299\pi\) | |||||||
\(524\) | 8.82883 | 0.385689 | ||||||||
\(525\) | −2.24351 | − | 1.40055i | −0.0979147 | − | 0.0611248i | ||||
\(526\) | −4.27559 | −0.186425 | ||||||||
\(527\) | −0.768302 | −0.0334678 | ||||||||
\(528\) | 2.14716 | + | 2.93302i | 0.0934431 | + | 0.127643i | ||||
\(529\) | 19.3581 | 0.841657 | ||||||||
\(530\) | −4.42727 | −0.192308 | ||||||||
\(531\) | −19.4906 | + | 9.52715i | −0.845820 | + | 0.413443i | ||||
\(532\) | 3.94311 | 0.170956 | ||||||||
\(533\) | 10.8583i | 0.470324i | ||||||||
\(534\) | −14.0405 | − | 8.76499i | −0.607590 | − | 0.379298i | ||||
\(535\) | 10.0091i | 0.432729i | ||||||||
\(536\) | 25.1600 | 1.08675 | ||||||||
\(537\) | 22.8268 | + | 14.2500i | 0.985051 | + | 0.614934i | ||||
\(538\) | − | 17.4549i | − | 0.752533i | ||||||
\(539\) | 8.40893 | − | 21.0043i | 0.362198 | − | 0.904721i | ||||
\(540\) | −0.866580 | + | 8.34952i | −0.0372917 | + | 0.359306i | ||||
\(541\) | − | 9.95304i | − | 0.427915i | −0.976843 | − | 0.213957i | \(-0.931365\pi\) | ||
0.976843 | − | 0.213957i | \(-0.0686354\pi\) | |||||||
\(542\) | 17.9210i | 0.769773i | ||||||||
\(543\) | −7.87444 | + | 12.6139i | −0.337925 | + | 0.541315i | ||||
\(544\) | −3.16227 | −0.135581 | ||||||||
\(545\) | 15.1094 | 0.647215 | ||||||||
\(546\) | −0.306586 | + | 0.491114i | −0.0131207 | + | 0.0210177i | ||||
\(547\) | 19.4132i | 0.830049i | 0.909810 | + | 0.415024i | \(0.136227\pi\) | ||||
−0.909810 | + | 0.415024i | \(0.863773\pi\) | |||||||
\(548\) | 14.9369i | 0.638072i | ||||||||
\(549\) | −33.6704 | + | 16.4583i | −1.43702 | + | 0.702425i | ||||
\(550\) | −3.52876 | + | 8.81435i | −0.150467 | + | 0.375845i | ||||
\(551\) | 69.3141i | 2.95288i | ||||||||
\(552\) | −7.48750 | − | 4.67419i | −0.318689 | − | 0.198947i | ||||
\(553\) | 1.99877 | 0.0849963 | ||||||||
\(554\) | − | 15.4615i | − | 0.656897i | ||||||
\(555\) | −10.7110 | − | 6.68653i | −0.454657 | − | 0.283827i | ||||
\(556\) | − | 4.38677i | − | 0.186040i | ||||||
\(557\) | 5.43523 | 0.230298 | 0.115149 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115149 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(558\) | −1.48020 | − | 3.02819i | −0.0626620 | − | 0.128194i | ||||
\(559\) | −9.30752 | −0.393666 | ||||||||
\(560\) | 0.314295 | 0.0132814 | ||||||||
\(561\) | 1.83689 | + | 2.50919i | 0.0775534 | + | 0.105938i | ||||
\(562\) | −10.3424 | −0.436266 | ||||||||
\(563\) | 28.2108 | 1.18894 | 0.594472 | − | 0.804116i | \(-0.297361\pi\) | ||||
0.594472 | + | 0.804116i | \(0.297361\pi\) | |||||||
\(564\) | −2.71780 | − | 1.69663i | −0.114440 | − | 0.0714409i | ||||
\(565\) | 9.77052 | 0.411049 | ||||||||
\(566\) | − | 20.5226i | − | 0.862630i | ||||||
\(567\) | −2.99869 | − | 2.33446i | −0.125933 | − | 0.0980381i | ||||
\(568\) | 17.4760i | 0.733277i | ||||||||
\(569\) | 30.8157 | 1.29186 | 0.645930 | − | 0.763397i | \(-0.276470\pi\) | ||||
0.645930 | + | 0.763397i | \(0.276470\pi\) | |||||||
\(570\) | 5.80765 | − | 9.30317i | 0.243256 | − | 0.389667i | ||||
\(571\) | 25.0705i | 1.04917i | 0.851359 | + | 0.524584i | \(0.175779\pi\) | ||||
−0.851359 | + | 0.524584i | \(0.824221\pi\) | |||||||
\(572\) | −4.22859 | − | 1.69288i | −0.176806 | − | 0.0707830i | ||||
\(573\) | 1.16520 | + | 0.727392i | 0.0486768 | + | 0.0303873i | ||||
\(574\) | − | 3.62948i | − | 0.151492i | ||||||
\(575\) | 6.90117i | 0.287799i | ||||||||
\(576\) | −4.42512 | − | 9.05290i | −0.184380 | − | 0.377204i | ||||
\(577\) | 11.7783 | 0.490338 | 0.245169 | − | 0.969480i | \(-0.421157\pi\) | ||||
0.245169 | + | 0.969480i | \(0.421157\pi\) | |||||||
\(578\) | 13.2255 | 0.550108 | ||||||||
\(579\) | −2.37504 | − | 1.48266i | −0.0987033 | − | 0.0616171i | ||||
\(580\) | 16.4679i | 0.683791i | ||||||||
\(581\) | 4.53194i | 0.188017i | ||||||||
\(582\) | −11.0398 | + | 17.6845i | −0.457615 | + | 0.733045i | ||||
\(583\) | 14.6390 | + | 5.86061i | 0.606285 | + | 0.242721i | ||||
\(584\) | − | 11.6655i | − | 0.482721i | ||||||
\(585\) | −1.54975 | − | 3.17047i | −0.0640744 | − | 0.131083i | ||||
\(586\) | 16.5272 | 0.682733 | ||||||||
\(587\) | − | 15.2718i | − | 0.630333i | −0.949036 | − | 0.315167i | \(-0.897940\pi\) | ||
0.949036 | − | 0.315167i | \(-0.102060\pi\) | |||||||
\(588\) | 8.59292 | − | 13.7648i | 0.354366 | − | 0.567653i | ||||
\(589\) | − | 9.65079i | − | 0.397654i | ||||||
\(590\) | 6.73394 | 0.277232 | ||||||||
\(591\) | 12.3898 | − | 19.8470i | 0.509650 | − | 0.816398i | ||||
\(592\) | −3.92145 | −0.161171 | ||||||||
\(593\) | −8.12540 | −0.333670 | −0.166835 | − | 0.985985i | \(-0.553355\pi\) | ||||
−0.166835 | + | 0.985985i | \(0.553355\pi\) | |||||||
\(594\) | −6.35080 | + | 12.0741i | −0.260577 | + | 0.495406i | ||||
\(595\) | 0.268878 | 0.0110229 | ||||||||
\(596\) | 0.311036 | 0.0127405 | ||||||||
\(597\) | 8.32664 | − | 13.3383i | 0.340787 | − | 0.545900i | ||||
\(598\) | 1.51070 | 0.0617770 | ||||||||
\(599\) | − | 19.6292i | − | 0.802025i | −0.916072 | − | 0.401013i | \(-0.868658\pi\) | ||
0.916072 | − | 0.401013i | \(-0.131342\pi\) | |||||||
\(600\) | −8.85735 | + | 14.1884i | −0.361600 | + | 0.579240i | ||||
\(601\) | 6.88725i | 0.280937i | 0.990085 | + | 0.140468i | \(0.0448608\pi\) | ||||
−0.990085 | + | 0.140468i | \(0.955139\pi\) | |||||||
\(602\) | 3.11112 | 0.126800 | ||||||||
\(603\) | −12.4128 | − | 25.3941i | −0.505489 | − | 1.03413i | ||||
\(604\) | − | 20.7024i | − | 0.842369i | ||||||
\(605\) | −8.92936 | + | 9.36476i | −0.363030 | + | 0.380732i | ||||
\(606\) | −5.86528 | + | 9.39549i | −0.238261 | + | 0.381666i | ||||
\(607\) | 5.66395i | 0.229893i | 0.993372 | + | 0.114946i | \(0.0366696\pi\) | ||||
−0.993372 | + | 0.114946i | \(0.963330\pi\) | |||||||
\(608\) | − | 39.7218i | − | 1.61093i | ||||||
\(609\) | −6.32410 | − | 3.94792i | −0.256265 | − | 0.159978i | ||||
\(610\) | 11.6330 | 0.471007 | ||||||||
\(611\) | 1.34691 | 0.0544901 | ||||||||
\(612\) | 0.979433 | + | 2.00372i | 0.0395912 | + | 0.0809955i | ||||
\(613\) | 42.1982i | 1.70437i | 0.523240 | + | 0.852185i | \(0.324723\pi\) | ||||
−0.523240 | + | 0.852185i | \(0.675277\pi\) | |||||||
\(614\) | 12.5929i | 0.508208i | ||||||||
\(615\) | 18.7667 | + | 11.7154i | 0.756745 | + | 0.472410i | ||||
\(616\) | 3.47184 | + | 1.38993i | 0.139885 | + | 0.0560017i | ||||
\(617\) | − | 31.3719i | − | 1.26298i | −0.775383 | − | 0.631492i | \(-0.782443\pi\) | ||
0.775383 | − | 0.631492i | \(-0.217557\pi\) | |||||||
\(618\) | 14.2614 | − | 22.8451i | 0.573677 | − | 0.918963i | ||||
\(619\) | 32.2357 | 1.29566 | 0.647832 | − | 0.761783i | \(-0.275676\pi\) | ||||
0.647832 | + | 0.761783i | \(0.275676\pi\) | |||||||
\(620\) | − | 2.29286i | − | 0.0920836i | ||||||
\(621\) | −1.02368 | + | 9.86321i | −0.0410790 | + | 0.395797i | ||||
\(622\) | 10.0875i | 0.404470i | ||||||||
\(623\) | 5.09726 | 0.204218 | ||||||||
\(624\) | −0.929696 | − | 0.580377i | −0.0372176 | − | 0.0232337i | ||||
\(625\) | 6.15867 | 0.246347 | ||||||||
\(626\) | 8.36653 | 0.334394 | ||||||||
\(627\) | −31.5184 | + | 23.0735i | −1.25872 | + | 0.921466i | ||||
\(628\) | −12.5509 | −0.500834 | ||||||||
\(629\) | −3.35479 | −0.133764 | ||||||||
\(630\) | 0.518019 | + | 1.05976i | 0.0206384 | + | 0.0422218i | ||||
\(631\) | 8.14185 | 0.324122 | 0.162061 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162061 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(632\) | − | 12.6406i | − | 0.502818i | ||||||
\(633\) | −18.7789 | − | 11.7230i | −0.746395 | − | 0.465949i | ||||
\(634\) | 16.5751i | 0.658283i | ||||||||
\(635\) | 14.4281 | 0.572561 | ||||||||
\(636\) | 9.59341 | + | 5.98884i | 0.380404 | + | 0.237473i | ||||
\(637\) | 6.82171i | 0.270286i | ||||||||
\(638\) | −9.94702 | + | 24.8463i | −0.393806 | + | 0.983674i | ||||
\(639\) | 17.6386 | − | 8.62189i | 0.697773 | − | 0.341077i | ||||
\(640\) | − | 10.6157i | − | 0.419622i | ||||||
\(641\) | − | 47.5292i | − | 1.87729i | −0.344886 | − | 0.938644i | \(-0.612083\pi\) | ||
0.344886 | − | 0.938644i | \(-0.387917\pi\) | |||||||
\(642\) | −6.17802 | + | 9.89645i | −0.243827 | + | 0.390582i | ||||
\(643\) | −10.9378 | −0.431343 | −0.215671 | − | 0.976466i | \(-0.569194\pi\) | ||||
−0.215671 | + | 0.976466i | \(0.569194\pi\) | |||||||
\(644\) | 1.10665 | 0.0436082 | ||||||||
\(645\) | −10.0422 | + | 16.0864i | −0.395412 | + | 0.633403i | ||||
\(646\) | − | 2.91384i | − | 0.114643i | ||||||
\(647\) | − | 29.9198i | − | 1.17627i | −0.808763 | − | 0.588134i | \(-0.799863\pi\) | ||
0.808763 | − | 0.588134i | \(-0.200137\pi\) | |||||||
\(648\) | −14.7636 | + | 18.9643i | −0.579970 | + | 0.744990i | ||||
\(649\) | −22.2661 | − | 8.91406i | −0.874020 | − | 0.349907i | ||||
\(650\) | − | 2.86269i | − | 0.112284i | ||||||
\(651\) | 0.880521 | + | 0.549679i | 0.0345103 | + | 0.0215436i | ||||
\(652\) | −18.9876 | −0.743613 | ||||||||
\(653\) | 39.1984i | 1.53395i | 0.641675 | + | 0.766976i | \(0.278240\pi\) | ||||
−0.641675 | + | 0.766976i | \(0.721760\pi\) | |||||||
\(654\) | 14.9394 | + | 9.32616i | 0.584177 | + | 0.364682i | ||||
\(655\) | 7.56224i | 0.295481i | ||||||||
\(656\) | 6.87073 | 0.268257 | ||||||||
\(657\) | −11.7740 | + | 5.75523i | −0.459348 | + | 0.224533i | ||||
\(658\) | −0.450217 | −0.0175513 | ||||||||
\(659\) | 43.4608 | 1.69299 | 0.846496 | − | 0.532396i | \(-0.178708\pi\) | ||||
0.846496 | + | 0.532396i | \(0.178708\pi\) | |||||||
\(660\) | −7.48823 | + | 5.48187i | −0.291479 | + | 0.213382i | ||||
\(661\) | −23.7769 | −0.924813 | −0.462407 | − | 0.886668i | \(-0.653014\pi\) | ||||
−0.462407 | + | 0.886668i | \(0.653014\pi\) | |||||||
\(662\) | 16.2850 | 0.632936 | ||||||||
\(663\) | −0.795351 | − | 0.496511i | −0.0308889 | − | 0.0192829i | ||||
\(664\) | 28.6610 | 1.11226 | ||||||||
\(665\) | 3.37743i | 0.130971i | ||||||||
\(666\) | −6.46331 | − | 13.2226i | −0.250448 | − | 0.512365i | ||||
\(667\) | 19.4533i | 0.753236i | ||||||||
\(668\) | −0.307178 | −0.0118851 | ||||||||
\(669\) | −0.0967241 | + | 0.154941i | −0.00373957 | + | 0.00599035i | ||||
\(670\) | 8.77358i | 0.338953i | ||||||||
\(671\) | −38.4651 | − | 15.3992i | −1.48493 | − | 0.594480i | ||||
\(672\) | 3.62415 | + | 2.26243i | 0.139805 | + | 0.0872753i | ||||
\(673\) | 24.4544i | 0.942648i | 0.881960 | + | 0.471324i | \(0.156224\pi\) | ||||
−0.881960 | + | 0.471324i | \(0.843776\pi\) | |||||||
\(674\) | 12.1521i | 0.468082i | ||||||||
\(675\) | 18.6903 | + | 1.93982i | 0.719388 | + | 0.0746639i | ||||
\(676\) | 1.37334 | 0.0528209 | ||||||||
\(677\) | 31.1795 | 1.19832 | 0.599162 | − | 0.800628i | \(-0.295501\pi\) | ||||
0.599162 | + | 0.800628i | \(0.295501\pi\) | |||||||
\(678\) | 9.66060 | + | 6.03078i | 0.371013 | + | 0.231611i | ||||
\(679\) | − | 6.42019i | − | 0.246384i | ||||||
\(680\) | − | 1.70044i | − | 0.0652090i | ||||||
\(681\) | −9.71950 | + | 15.5695i | −0.372452 | + | 0.596624i | ||||
\(682\) | 1.38495 | − | 3.45941i | 0.0530325 | − | 0.132468i | ||||
\(683\) | − | 35.0644i | − | 1.34170i | −0.741592 | − | 0.670851i | \(-0.765929\pi\) | ||
0.741592 | − | 0.670851i | \(-0.234071\pi\) | |||||||
\(684\) | −25.1691 | + | 12.3028i | −0.962365 | + | 0.470411i | ||||
\(685\) | −12.7940 | −0.488835 | ||||||||
\(686\) | − | 4.62003i | − | 0.176394i | ||||||
\(687\) | −2.41612 | + | 3.87034i | −0.0921809 | + | 0.147663i | ||||
\(688\) | 5.88947i | 0.224534i | ||||||||
\(689\) | −4.75439 | −0.181128 | ||||||||
\(690\) | 1.62994 | − | 2.61098i | 0.0620509 | − | 0.0993982i | ||||
\(691\) | 35.7462 | 1.35985 | 0.679924 | − | 0.733282i | \(-0.262013\pi\) | ||||
0.679924 | + | 0.733282i | \(0.262013\pi\) | |||||||
\(692\) | −4.68095 | −0.177943 | ||||||||
\(693\) | −0.309995 | − | 4.18987i | −0.0117757 | − | 0.159160i | ||||
\(694\) | −17.3841 | −0.659892 | ||||||||
\(695\) | 3.75744 | 0.142528 | ||||||||
\(696\) | −24.9675 | + | 39.9949i | −0.946390 | + | 1.51600i | ||||
\(697\) | 5.87789 | 0.222641 | ||||||||
\(698\) | − | 0.200563i | − | 0.00759142i | ||||||
\(699\) | 12.3848 | − | 19.8390i | 0.468438 | − | 0.750381i | ||||
\(700\) | − | 2.09705i | − | 0.0792609i | ||||||
\(701\) | 29.8148 | 1.12609 | 0.563044 | − | 0.826427i | \(-0.309630\pi\) | ||||
0.563044 | + | 0.826427i | \(0.309630\pi\) | |||||||
\(702\) | 0.424636 | − | 4.09138i | 0.0160269 | − | 0.154419i | ||||
\(703\) | − | 42.1401i | − | 1.58935i | ||||||
\(704\) | 4.14036 | − | 10.3420i | 0.156046 | − | 0.389780i | ||||
\(705\) | 1.45323 | − | 2.32790i | 0.0547318 | − | 0.0876738i | ||||
\(706\) | 6.22194i | 0.234166i | ||||||||
\(707\) | − | 3.41095i | − | 0.128282i | ||||||
\(708\) | −14.5917 | − | 9.10911i | −0.548390 | − | 0.342341i | ||||
\(709\) | −43.4189 | −1.63063 | −0.815315 | − | 0.579018i | \(-0.803436\pi\) | ||||
−0.815315 | + | 0.579018i | \(0.803436\pi\) | |||||||
\(710\) | −6.09409 | −0.228707 | ||||||||
\(711\) | −12.7583 | + | 6.23633i | −0.478472 | + | 0.233881i | ||||
\(712\) | − | 32.2362i | − | 1.20810i | ||||||
\(713\) | − | 2.70854i | − | 0.101436i | ||||||
\(714\) | 0.265853 | + | 0.165963i | 0.00994931 | + | 0.00621102i | ||||
\(715\) | 1.45002 | − | 3.62195i | 0.0542277 | − | 0.135453i | ||||
\(716\) | 21.3367i | 0.797389i | ||||||||
\(717\) | 17.4950 | − | 28.0249i | 0.653363 | − | 1.04661i | ||||
\(718\) | 9.20506 | 0.343530 | ||||||||
\(719\) | 21.0525i | 0.785124i | 0.919725 | + | 0.392562i | \(0.128411\pi\) | ||||
−0.919725 | + | 0.392562i | \(0.871589\pi\) | |||||||
\(720\) | −2.00616 | + | 0.980627i | −0.0747653 | + | 0.0365458i | ||||
\(721\) | 8.29369i | 0.308873i | ||||||||
\(722\) | 21.5606 | 0.802401 | ||||||||
\(723\) | 18.2482 | + | 11.3917i | 0.678657 | + | 0.423662i | ||||
\(724\) | −11.7905 | −0.438189 | ||||||||
\(725\) | 36.8630 | 1.36906 | ||||||||
\(726\) | −14.6092 | + | 3.74782i | −0.542200 | + | 0.139095i | ||||
\(727\) | −12.2570 | −0.454586 | −0.227293 | − | 0.973826i | \(-0.572988\pi\) | ||||
−0.227293 | + | 0.973826i | \(0.572988\pi\) | |||||||
\(728\) | −1.12757 | −0.0417906 | ||||||||
\(729\) | 26.4245 | + | 5.54482i | 0.978686 | + | 0.205364i | ||||
\(730\) | 4.06789 | 0.150559 | ||||||||
\(731\) | 5.03842i | 0.186353i | ||||||||
\(732\) | −25.2075 | − | 15.7362i | −0.931694 | − | 0.581625i | ||||
\(733\) | 16.8459i | 0.622216i | 0.950375 | + | 0.311108i | \(0.100700\pi\) | ||||
−0.950375 | + | 0.311108i | \(0.899300\pi\) | |||||||
\(734\) | 29.9736 | 1.10634 | ||||||||
\(735\) | 11.7901 | + | 7.36018i | 0.434886 | + | 0.271484i | ||||
\(736\) | − | 11.1481i | − | 0.410925i | ||||||
\(737\) | 11.6140 | − | 29.0102i | 0.427808 | − | 1.06861i | ||||
\(738\) | 11.3243 | + | 23.1672i | 0.416853 | + | 0.852795i | ||||
\(739\) | 22.0444i | 0.810915i | 0.914114 | + | 0.405458i | \(0.132888\pi\) | ||||
−0.914114 | + | 0.405458i | \(0.867112\pi\) | |||||||
\(740\) | − | 10.0118i | − | 0.368040i | ||||||
\(741\) | 6.23676 | − | 9.99056i | 0.229113 | − | 0.367012i | ||||
\(742\) | 1.58920 | 0.0583413 | ||||||||
\(743\) | −10.9486 | −0.401664 | −0.200832 | − | 0.979626i | \(-0.564364\pi\) | ||||
−0.200832 | + | 0.979626i | \(0.564364\pi\) | |||||||
\(744\) | 3.47629 | − | 5.56860i | 0.127447 | − | 0.204155i | ||||
\(745\) | 0.266415i | 0.00976068i | ||||||||
\(746\) | − | 6.63937i | − | 0.243085i | ||||||
\(747\) | −14.1400 | − | 28.9276i | −0.517357 | − | 1.05841i | ||||
\(748\) | −0.916404 | + | 2.28905i | −0.0335071 | + | 0.0836960i | ||||
\(749\) | − | 3.59282i | − | 0.131279i | ||||||
\(750\) | −11.7885 | − | 7.35917i | −0.430456 | − | 0.268719i | ||||
\(751\) | 10.8100 | 0.394461 | 0.197230 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197230 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(752\) | − | 0.852276i | − | 0.0310793i | ||||||
\(753\) | −32.3566 | − | 20.1991i | −1.17914 | − | 0.736097i | ||||
\(754\) | − | 8.06948i | − | 0.293873i | ||||||
\(755\) | 17.7324 | 0.645349 | ||||||||
\(756\) | 0.311065 | − | 2.99712i | 0.0113133 | − | 0.109004i | ||||
\(757\) | 24.5936 | 0.893869 | 0.446934 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446934 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(758\) | 4.18313 | 0.151938 | ||||||||
\(759\) | −8.84577 | + | 6.47568i | −0.321081 | + | 0.235052i | ||||
\(760\) | 21.3596 | 0.774794 | ||||||||
\(761\) | 28.5614 | 1.03535 | 0.517675 | − | 0.855577i | \(-0.326798\pi\) | ||||
0.517675 | + | 0.855577i | \(0.326798\pi\) | |||||||
\(762\) | 14.2658 | + | 8.90563i | 0.516794 | + | 0.322617i | ||||
\(763\) | −5.42361 | −0.196348 | ||||||||
\(764\) | 1.08913i | 0.0394033i | ||||||||
\(765\) | −1.71626 | + | 0.838923i | −0.0620517 | + | 0.0303313i | ||||
\(766\) | 0.0796985i | 0.00287962i | ||||||||
\(767\) | 7.23149 | 0.261114 | ||||||||
\(768\) | 12.7140 | − | 20.3663i | 0.458777 | − | 0.734906i | ||||
\(769\) | − | 50.7381i | − | 1.82966i | −0.403837 | − | 0.914831i | \(-0.632324\pi\) | ||
0.403837 | − | 0.914831i | \(-0.367676\pi\) | |||||||
\(770\) | −0.484683 | + | 1.21067i | −0.0174668 | + | 0.0436296i | ||||
\(771\) | 1.91358 | + | 1.19459i | 0.0689160 | + | 0.0430219i | ||||
\(772\) | − | 2.21999i | − | 0.0798993i | ||||||
\(773\) | 25.9915i | 0.934850i | 0.884033 | + | 0.467425i | \(0.154818\pi\) | ||||
−0.884033 | + | 0.467425i | \(0.845182\pi\) | |||||||
\(774\) | −19.8585 | + | 9.70697i | −0.713798 | + | 0.348910i | ||||
\(775\) | −5.13253 | −0.184366 | ||||||||
\(776\) | −40.6026 | −1.45755 | ||||||||
\(777\) | 3.84479 | + | 2.40017i | 0.137931 | + | 0.0861057i | ||||
\(778\) | − | 2.33645i | − | 0.0837658i | ||||||
\(779\) | 73.8333i | 2.64535i | ||||||||
\(780\) | 1.48175 | − | 2.37359i | 0.0530552 | − | 0.0849881i | ||||
\(781\) | 20.1504 | + | 8.06705i | 0.721038 | + | 0.288662i | ||||
\(782\) | − | 0.817782i | − | 0.0292438i | ||||||
\(783\) | 52.6849 | + | 5.46806i | 1.88281 | + | 0.195413i | ||||
\(784\) | 4.31653 | 0.154162 | ||||||||
\(785\) | − | 10.7503i | − | 0.383695i | ||||||
\(786\) | −4.66774 | + | 7.47716i | −0.166493 | + | 0.266702i | ||||
\(787\) | − | 28.5816i | − | 1.01882i | −0.860523 | − | 0.509411i | \(-0.829863\pi\) | ||
0.860523 | − | 0.509411i | \(-0.170137\pi\) | |||||||
\(788\) | 18.5514 | 0.660866 | ||||||||
\(789\) | −4.95394 | + | 7.93562i | −0.176365 | + | 0.282516i | ||||
\(790\) | 4.40793 | 0.156827 | ||||||||
\(791\) | −3.50719 | −0.124701 | ||||||||
\(792\) | −26.4976 | + | 1.96047i | −0.941553 | + | 0.0696624i | ||||
\(793\) | 12.4925 | 0.443623 | ||||||||
\(794\) | −2.85830 | −0.101437 | ||||||||
\(795\) | −5.12968 | + | 8.21714i | −0.181931 | + | 0.291432i | ||||
\(796\) | 12.4675 | 0.441900 | ||||||||
\(797\) | − | 24.1772i | − | 0.856402i | −0.903684 | − | 0.428201i | \(-0.859148\pi\) | ||
0.903684 | − | 0.428201i | \(-0.140852\pi\) | |||||||
\(798\) | −2.08470 | + | 3.33943i | −0.0737974 | + | 0.118215i | ||||
\(799\) | − | 0.729119i | − | 0.0257944i | ||||||
\(800\) | −21.1251 | −0.746885 | ||||||||
\(801\) | −32.5361 | + | 15.9039i | −1.14961 | + | 0.561937i | ||||
\(802\) | − | 15.3643i | − | 0.542532i | ||||||
\(803\) | −13.4507 | − | 5.38487i | −0.474663 | − | 0.190028i | ||||
\(804\) | 11.8682 | − | 19.0114i | 0.418558 | − | 0.670480i | ||||
\(805\) | 0.947892i | 0.0334088i | ||||||||
\(806\) | 1.12353i | 0.0395748i | ||||||||
\(807\) | −32.3967 | − | 20.2242i | −1.14042 | − | 0.711925i | ||||
\(808\) | −21.5715 | −0.758884 | ||||||||
\(809\) | −4.86200 | −0.170939 | −0.0854694 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854694 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(810\) | −6.61308 | − | 5.14824i | −0.232360 | − | 0.180891i | ||||
\(811\) | 21.7622i | 0.764175i | 0.924126 | + | 0.382088i | \(0.124795\pi\) | ||||
−0.924126 | + | 0.382088i | \(0.875205\pi\) | |||||||
\(812\) | − | 5.91125i | − | 0.207444i | ||||||
\(813\) | 33.2619 | + | 20.7643i | 1.16655 | + | 0.728235i | ||||
\(814\) | 6.04738 | − | 15.1055i | 0.211960 | − | 0.529448i | ||||
\(815\) | − | 16.2637i | − | 0.569691i | ||||||
\(816\) | −0.314174 | + | 0.503270i | −0.0109983 | + | 0.0176180i | ||||
\(817\) | −63.2885 | −2.21418 | ||||||||
\(818\) | 28.7387i | 1.00482i | ||||||||
\(819\) | 0.556294 | + | 1.13806i | 0.0194385 | + | 0.0397671i | ||||
\(820\) | 17.5415i | 0.612577i | ||||||||
\(821\) | −49.4231 | −1.72488 | −0.862439 | − | 0.506161i | \(-0.831064\pi\) | ||||
−0.862439 | + | 0.506161i | \(0.831064\pi\) | |||||||
\(822\) | −12.6501 | − | 7.89703i | −0.441223 | − | 0.275440i | ||||
\(823\) | −2.99642 | −0.104449 | −0.0522244 | − | 0.998635i | \(-0.516631\pi\) | ||||
−0.0522244 | + | 0.998635i | \(0.516631\pi\) | |||||||
\(824\) | 52.4510 | 1.82722 | ||||||||
\(825\) | 12.2711 | + | 16.7623i | 0.427224 | + | 0.583587i | ||||
\(826\) | −2.41719 | −0.0841049 | ||||||||
\(827\) | −2.61482 | −0.0909263 | −0.0454632 | − | 0.998966i | \(-0.514476\pi\) | ||||
−0.0454632 | + | 0.998966i | \(0.514476\pi\) | |||||||
\(828\) | −7.06382 | + | 3.45285i | −0.245485 | + | 0.119995i | ||||
\(829\) | −5.87331 | −0.203989 | −0.101994 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101994 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(830\) | 9.99440i | 0.346911i | ||||||||
\(831\) | −28.6970 | − | 17.9146i | −0.995488 | − | 0.621449i | ||||
\(832\) | 3.35885i | 0.116447i | ||||||||
\(833\) | 3.69278 | 0.127947 | ||||||||
\(834\) | 3.71517 | + | 2.31925i | 0.128646 | + | 0.0803091i | ||||
\(835\) | − | 0.263110i | − | 0.00910529i | ||||||
\(836\) | −28.7532 | − | 11.5111i | −0.994451 | − | 0.398121i | ||||
\(837\) | −7.33546 | − | 0.761332i | −0.253551 | − | 0.0263155i | ||||
\(838\) | 13.4428i | 0.464375i | ||||||||
\(839\) | 26.6273i | 0.919275i | 0.888107 | + | 0.459638i | \(0.152021\pi\) | ||||
−0.888107 | + | 0.459638i | \(0.847979\pi\) | |||||||
\(840\) | −1.21658 | + | 1.94881i | −0.0419759 | + | 0.0672404i | ||||
\(841\) | 74.9111 | 2.58314 | ||||||||
\(842\) | −23.3429 | −0.804450 | ||||||||
\(843\) | −11.9832 | + | 19.1957i | −0.412724 | + | 0.661135i | ||||
\(844\) | − | 17.5530i | − | 0.604199i | ||||||
\(845\) | 1.17632i | 0.0404668i | ||||||||
\(846\) | 2.87376 | − | 1.40472i | 0.0988019 | − | 0.0482951i | ||||
\(847\) | 3.20525 | − | 3.36154i | 0.110134 | − | 0.115504i | ||||
\(848\) | 3.00841i | 0.103309i | ||||||||
\(849\) | −38.0905 | − | 23.7786i | −1.30726 | − | 0.816081i | ||||
\(850\) | −1.54965 | −0.0531526 | ||||||||
\(851\) | − | 11.8268i | − | 0.405418i | ||||||
\(852\) | 13.2052 | + | 8.24357i | 0.452403 | + | 0.282420i | ||||
\(853\) | 10.3225i | 0.353435i | 0.984262 | + | 0.176717i | \(0.0565479\pi\) | ||||
−0.984262 | + | 0.176717i | \(0.943452\pi\) | |||||||
\(854\) | −4.17574 | −0.142891 | ||||||||
\(855\) | −10.5379 | − | 21.5583i | −0.360388 | − | 0.737279i | ||||
\(856\) | −22.7217 | −0.776613 | ||||||||
\(857\) | −11.2266 | −0.383492 | −0.191746 | − | 0.981445i | \(-0.561415\pi\) | ||||
−0.191746 | + | 0.981445i | \(0.561415\pi\) | |||||||
\(858\) | 3.66933 | − | 2.68619i | 0.125269 | − | 0.0917050i | ||||
\(859\) | 3.85761 | 0.131620 | 0.0658099 | − | 0.997832i | \(-0.479037\pi\) | ||||
0.0658099 | + | 0.997832i | \(0.479037\pi\) | |||||||
\(860\) | −15.0363 | −0.512733 | ||||||||
\(861\) | −6.73642 | − | 4.20532i | −0.229576 | − | 0.143317i | ||||
\(862\) | 16.3786 | 0.557858 | ||||||||
\(863\) | − | 24.3417i | − | 0.828600i | −0.910140 | − | 0.414300i | \(-0.864026\pi\) | ||
0.910140 | − | 0.414300i | \(-0.135974\pi\) | |||||||
\(864\) | −30.1921 | − | 3.13358i | −1.02716 | − | 0.106607i | ||||
\(865\) | − | 4.00942i | − | 0.136324i | ||||||
\(866\) | −9.10661 | −0.309455 | ||||||||
\(867\) | 15.3238 | − | 24.5469i | 0.520423 | − | 0.833656i | ||||
\(868\) | 0.823039i | 0.0279358i | ||||||||
\(869\) | −14.5750 | − | 5.83501i | −0.494425 | − | 0.197939i | ||||
\(870\) | −13.9467 | − | 8.70645i | −0.472837 | − | 0.295176i | ||||
\(871\) | 9.42183i | 0.319247i | ||||||||
\(872\) | 34.3001i | 1.16155i | ||||||||
\(873\) | 20.0315 | + | 40.9804i | 0.677965 | + | 1.38698i | ||||
\(874\) | 10.2723 | 0.347466 | ||||||||
\(875\) | 4.27971 | 0.144681 | ||||||||
\(876\) | −8.81466 | − | 5.50269i | −0.297820 | − | 0.185919i | ||||
\(877\) | 27.8512i | 0.940469i | 0.882542 | + | 0.470234i | \(0.155831\pi\) | ||||
−0.882542 | + | 0.470234i | \(0.844169\pi\) | |||||||
\(878\) | 16.5219i | 0.557586i | ||||||||
\(879\) | 19.1493 | − | 30.6749i | 0.645891 | − | 1.03464i | ||||
\(880\) | −2.29184 | − | 0.917522i | −0.0772580 | − | 0.0309297i | ||||
\(881\) | 38.5115i | 1.29749i | 0.761008 | + | 0.648743i | \(0.224705\pi\) | ||||
−0.761008 | + | 0.648743i | \(0.775295\pi\) | |||||||
\(882\) | 7.11447 | + | 14.5548i | 0.239557 | + | 0.490084i | ||||
\(883\) | −19.2648 | −0.648312 | −0.324156 | − | 0.946004i | \(-0.605080\pi\) | ||||
−0.324156 | + | 0.946004i | \(0.605080\pi\) | |||||||
\(884\) | − | 0.743429i | − | 0.0250042i | ||||||
\(885\) | 7.80231 | − | 12.4984i | 0.262272 | − | 0.420128i | ||||
\(886\) | − | 1.39360i | − | 0.0468191i | ||||||
\(887\) | −31.9919 | −1.07418 | −0.537091 | − | 0.843524i | \(-0.680477\pi\) | ||||
−0.537091 | + | 0.843524i | \(0.680477\pi\) | |||||||
\(888\) | 15.1792 | − | 24.3153i | 0.509380 | − | 0.815967i | ||||
\(889\) | −5.17906 | −0.173700 | ||||||||
\(890\) | 11.2411 | 0.376803 | ||||||||
\(891\) | 15.0515 | + | 25.7770i | 0.504244 | + | 0.863561i | ||||
\(892\) | −0.144826 | −0.00484912 | ||||||||
\(893\) | 9.15861 | 0.306481 | ||||||||
\(894\) | −0.164443 | + | 0.263418i | −0.00549978 | + | 0.00881000i | ||||
\(895\) | −18.2757 | −0.610889 | ||||||||
\(896\) | 3.81057i | 0.127302i | ||||||||
\(897\) | 1.75038 | − | 2.80390i | 0.0584434 | − | 0.0936193i | ||||
\(898\) | 10.8769i | 0.362966i | ||||||||
\(899\) | −14.4678 | −0.482529 | ||||||||
\(900\) | 6.54297 | + | 13.3856i | 0.218099 | + | 0.446186i | ||||
\(901\) | 2.57368i | 0.0857418i | ||||||||
\(902\) | −10.5955 | + | 26.4662i | −0.352793 | + | 0.881228i | ||||
\(903\) | 3.60472 | − | 5.77433i | 0.119958 | − | 0.192158i | ||||
\(904\) | 22.1802i | 0.737703i | ||||||||
\(905\) | − | 10.0990i | − | 0.335702i | ||||||
\(906\) | 17.5329 | + | 10.9452i | 0.582493 | + | 0.363631i | ||||
\(907\) | 34.1655 | 1.13445 | 0.567223 | − | 0.823564i | \(-0.308018\pi\) | ||||
0.567223 | + | 0.823564i | \(0.308018\pi\) | |||||||
\(908\) | −14.5531 | −0.482961 | ||||||||
\(909\) | 10.6424 | + | 21.7723i | 0.352988 | + | 0.722140i | ||||
\(910\) | − | 0.393197i | − | 0.0130344i | ||||||
\(911\) | − | 40.1272i | − | 1.32947i | −0.747077 | − | 0.664737i | \(-0.768544\pi\) | ||
0.747077 | − | 0.664737i | \(-0.231456\pi\) | |||||||
\(912\) | −6.32167 | − | 3.94640i | −0.209331 | − | 0.130678i | ||||
\(913\) | 13.2301 | − | 33.0470i | 0.437852 | − | 1.09370i | ||||
\(914\) | − | 7.87969i | − | 0.260637i | ||||||
\(915\) | 13.4786 | − | 21.5912i | 0.445590 | − | 0.713782i | ||||
\(916\) | −3.61768 | −0.119531 | ||||||||
\(917\) | − | 2.71452i | − | 0.0896412i | ||||||
\(918\) | −2.21478 | − | 0.229867i | −0.0730985 | − | 0.00758674i | ||||
\(919\) | − | 25.1316i | − | 0.829016i | −0.910046 | − | 0.414508i | \(-0.863954\pi\) | ||
0.910046 | − | 0.414508i | \(-0.136046\pi\) | |||||||
\(920\) | 5.99467 | 0.197638 | ||||||||
\(921\) | 23.3727 | + | 14.5908i | 0.770158 | + | 0.480784i | ||||
\(922\) | 2.54698 | 0.0838803 | ||||||||
\(923\) | −6.54436 | −0.215410 | ||||||||
\(924\) | 2.68795 | − | 1.96775i | 0.0884271 | − | 0.0647343i | ||||
\(925\) | −22.4112 | −0.736876 | ||||||||
\(926\) | −9.02999 | −0.296744 | ||||||||
\(927\) | −25.8770 | − | 52.9391i | −0.849913 | − | 1.73875i | ||||
\(928\) | −59.5483 | −1.95477 | ||||||||
\(929\) | − | 6.58674i | − | 0.216104i | −0.994145 | − | 0.108052i | \(-0.965539\pi\) | ||
0.994145 | − | 0.108052i | \(-0.0344613\pi\) | |||||||
\(930\) | 1.94183 | + | 1.21222i | 0.0636752 | + | 0.0397503i | ||||
\(931\) | 46.3857i | 1.52023i | ||||||||
\(932\) | 18.5439 | 0.607426 | ||||||||
\(933\) | 18.7226 | + | 11.6879i | 0.612950 | + | 0.382644i | ||||
\(934\) | − | 28.1909i | − | 0.922435i | ||||||
\(935\) | −1.96066 | − | 0.784936i | −0.0641205 | − | 0.0256702i | ||||
\(936\) | 7.19735 | − | 3.51812i | 0.235253 | − | 0.114993i | ||||
\(937\) | − | 24.1549i | − | 0.789107i | −0.918873 | − | 0.394554i | \(-0.870899\pi\) | ||
0.918873 | − | 0.394554i | \(-0.129101\pi\) | |||||||
\(938\) | − | 3.14933i | − | 0.102829i | ||||||
\(939\) | 9.69392 | − | 15.5285i | 0.316349 | − | 0.506754i | ||||
\(940\) | 2.17593 | 0.0709710 | ||||||||
\(941\) | −26.9975 | −0.880094 | −0.440047 | − | 0.897975i | \(-0.645038\pi\) | ||||
−0.440047 | + | 0.897975i | \(0.645038\pi\) | |||||||
\(942\) | 6.63556 | − | 10.6294i | 0.216198 | − | 0.346324i | ||||
\(943\) | 20.7216i | 0.674790i | ||||||||
\(944\) | − | 4.57583i | − | 0.148931i | ||||||
\(945\) | 2.56715 | + | 0.266439i | 0.0835093 | + | 0.00866727i | ||||
\(946\) | −22.6863 | − | 9.08230i | −0.737597 | − | 0.295291i | ||||
\(947\) | 21.8752i | 0.710849i | 0.934705 | + | 0.355424i | \(0.115664\pi\) | ||||
−0.934705 | + | 0.355424i | \(0.884336\pi\) | |||||||
\(948\) | −9.55151 | − | 5.96269i | −0.310219 | − | 0.193659i | ||||
\(949\) | 4.36845 | 0.141806 | ||||||||
\(950\) | − | 19.4655i | − | 0.631544i | ||||||
\(951\) | 30.7639 | + | 19.2049i | 0.997589 | + | 0.622761i | ||||
\(952\) | 0.610385i | 0.0197827i | ||||||||
\(953\) | −6.95238 | −0.225210 | −0.112605 | − | 0.993640i | \(-0.535919\pi\) | ||||
−0.112605 | + | 0.993640i | \(0.535919\pi\) | |||||||
\(954\) | −10.1439 | + | 4.95843i | −0.328422 | + | 0.160535i | ||||
\(955\) | −0.932883 | −0.0301874 | ||||||||
\(956\) | 26.1954 | 0.847220 | ||||||||
\(957\) | 34.5902 | + | 47.2502i | 1.11814 | + | 1.52738i | ||||
\(958\) | −8.31860 | −0.268762 | ||||||||
\(959\) | 4.59250 | 0.148300 | ||||||||
\(960\) | 5.80518 | + | 3.62398i | 0.187361 | + | 0.116963i | ||||
\(961\) | −28.9856 | −0.935020 | ||||||||
\(962\) | 4.90591i | 0.158173i | ||||||||
\(963\) | 11.2099 | + | 22.9332i | 0.361234 | + | 0.739010i | ||||
\(964\) | 17.0569i | 0.549366i | ||||||||
\(965\) | 1.90151 | 0.0612118 | ||||||||
\(966\) | −0.585079 | + | 0.937228i | −0.0188246 | + | 0.0301548i | ||||
\(967\) | − | 1.81373i | − | 0.0583255i | −0.999575 | − | 0.0291628i | \(-0.990716\pi\) | ||
0.999575 | − | 0.0291628i | \(-0.00928411\pi\) | |||||||
\(968\) | −21.2591 | − | 20.2707i | −0.683293 | − | 0.651525i | ||||
\(969\) | −5.40816 | − | 3.37613i | −0.173735 | − | 0.108457i | ||||
\(970\) | − | 14.1586i | − | 0.454605i | ||||||
\(971\) | 31.7380i | 1.01852i | 0.860612 | + | 0.509261i | \(0.170081\pi\) | ||||
−0.860612 | + | 0.509261i | \(0.829919\pi\) | |||||||
\(972\) | 7.36572 | + | 20.1013i | 0.236255 | + | 0.644750i | ||||
\(973\) | −1.34876 | −0.0432392 | ||||||||
\(974\) | 13.6456 | 0.437234 | ||||||||
\(975\) | −5.31323 | − | 3.31687i | −0.170160 | − | 0.106225i | ||||
\(976\) | − | 7.90483i | − | 0.253027i | ||||||
\(977\) | 35.4339i | 1.13363i | 0.823845 | + | 0.566815i | \(0.191825\pi\) | ||||
−0.823845 | + | 0.566815i | \(0.808175\pi\) | |||||||
\(978\) | 10.0386 | − | 16.0807i | 0.321000 | − | 0.514204i | ||||
\(979\) | −37.1693 | − | 14.8804i | −1.18794 | − | 0.475581i | ||||
\(980\) | 11.0205i | 0.352035i | ||||||||
\(981\) | 34.6192 | − | 16.9221i | 1.10531 | − | 0.540282i | ||||
\(982\) | 23.2000 | 0.740342 | ||||||||
\(983\) | − | 39.1279i | − | 1.24799i | −0.781430 | − | 0.623993i | \(-0.785509\pi\) | ||
0.781430 | − | 0.623993i | \(-0.214491\pi\) | |||||||
\(984\) | −26.5953 | + | 42.6025i | −0.847827 | + | 1.35812i | ||||
\(985\) | 15.8900i | 0.506297i | ||||||||
\(986\) | −4.36823 | −0.139113 | ||||||||
\(987\) | −0.521646 | + | 0.835615i | −0.0166042 | + | 0.0265979i | ||||
\(988\) | 9.33835 | 0.297093 | ||||||||
\(989\) | −17.7622 | −0.564806 | ||||||||
\(990\) | −0.683640 | − | 9.24003i | −0.0217275 | − | 0.293667i | ||||
\(991\) | −16.9838 | −0.539508 | −0.269754 | − | 0.962929i | \(-0.586942\pi\) | ||||
−0.269754 | + | 0.962929i | \(0.586942\pi\) | |||||||
\(992\) | 8.29107 | 0.263242 | ||||||||
\(993\) | 18.8687 | − | 30.2255i | 0.598781 | − | 0.959176i | ||||
\(994\) | 2.18751 | 0.0693837 | ||||||||
\(995\) | 10.6789i | 0.338545i | ||||||||
\(996\) | 13.5196 | − | 21.6568i | 0.428385 | − | 0.686221i | ||||
\(997\) | − | 53.9445i | − | 1.70844i | −0.519913 | − | 0.854219i | \(-0.674036\pi\) | ||
0.519913 | − | 0.854219i | \(-0.325964\pi\) | |||||||
\(998\) | 7.13776 | 0.225942 | ||||||||
\(999\) | −32.0303 | − | 3.32436i | −1.01339 | − | 0.105178i |
(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 | 429.2.f.a.131.20 | yes | 48 | |
3.2 | odd | 2 | inner | 429.2.f.a.131.29 | yes | 48 | |
11.10 | odd | 2 | inner | 429.2.f.a.131.30 | yes | 48 | |
33.32 | even | 2 | inner | 429.2.f.a.131.19 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.f.a.131.19 | ✓ | 48 | 33.32 | even | 2 | inner | |
429.2.f.a.131.20 | yes | 48 | 1.1 | even | 1 | trivial | |
429.2.f.a.131.29 | yes | 48 | 3.2 | odd | 2 | inner | |
429.2.f.a.131.30 | yes | 48 | 11.10 | odd | 2 | inner |