Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,7,Mod(8,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.8");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.b (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: | \(4.83113575602\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.4 | ||
Root | \(-7.64160i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.8 |
Dual form | 21.7.b.a.8.9 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.64160i | − | 0.955200i | −0.878577 | − | 0.477600i | \(-0.841507\pi\) | ||
0.878577 | − | 0.477600i | \(-0.158493\pi\) | |||||||
\(3\) | −4.69404 | + | 26.5888i | −0.173853 | + | 0.984772i | ||||
\(4\) | 5.60598 | 0.0875934 | ||||||||
\(5\) | − | 237.150i | − | 1.89720i | −0.316477 | − | 0.948600i | \(-0.602500\pi\) | ||
0.316477 | − | 0.948600i | \(-0.397500\pi\) | |||||||
\(6\) | 203.181 | + | 35.8700i | 0.940654 | + | 0.166065i | ||||
\(7\) | 129.642 | 0.377964 | ||||||||
\(8\) | − | 531.901i | − | 1.03887i | ||||||
\(9\) | −684.932 | − | 249.618i | −0.939550 | − | 0.342412i | ||||
\(10\) | −1812.21 | −1.81221 | ||||||||
\(11\) | − | 371.126i | − | 0.278833i | −0.990234 | − | 0.139416i | \(-0.955477\pi\) | ||
0.990234 | − | 0.139416i | \(-0.0445226\pi\) | |||||||
\(12\) | −26.3147 | + | 149.056i | −0.0152284 | + | 0.0862595i | ||||
\(13\) | 1997.63 | 0.909253 | 0.454627 | − | 0.890682i | \(-0.349773\pi\) | ||||
0.454627 | + | 0.890682i | \(0.349773\pi\) | |||||||
\(14\) | − | 990.671i | − | 0.361032i | ||||||
\(15\) | 6305.54 | + | 1113.19i | 1.86831 | + | 0.329835i | ||||
\(16\) | −3705.79 | −0.904734 | ||||||||
\(17\) | 1254.26i | 0.255294i | 0.991820 | + | 0.127647i | \(0.0407424\pi\) | ||||
−0.991820 | + | 0.127647i | \(0.959258\pi\) | |||||||
\(18\) | −1907.48 | + | 5233.97i | −0.327072 | + | 0.897458i | ||||
\(19\) | 3949.99 | 0.575884 | 0.287942 | − | 0.957648i | \(-0.407029\pi\) | ||||
0.287942 | + | 0.957648i | \(0.407029\pi\) | |||||||
\(20\) | − | 1329.46i | − | 0.166182i | ||||||
\(21\) | −608.544 | + | 3447.02i | −0.0657104 | + | 0.372209i | ||||
\(22\) | −2836.00 | −0.266341 | ||||||||
\(23\) | 17116.2i | 1.40677i | 0.710808 | + | 0.703386i | \(0.248330\pi\) | ||||
−0.710808 | + | 0.703386i | \(0.751670\pi\) | |||||||
\(24\) | 14142.6 | + | 2496.77i | 1.02305 | + | 0.180611i | ||||
\(25\) | −40615.1 | −2.59937 | ||||||||
\(26\) | − | 15265.1i | − | 0.868519i | ||||||
\(27\) | 9852.16 | − | 17039.8i | 0.500541 | − | 0.865713i | ||||
\(28\) | 726.769 | 0.0331072 | ||||||||
\(29\) | 25218.4i | 1.03401i | 0.855983 | + | 0.517003i | \(0.172953\pi\) | ||||
−0.855983 | + | 0.517003i | \(0.827047\pi\) | |||||||
\(30\) | 8506.57 | − | 48184.4i | 0.315058 | − | 1.78461i | ||||
\(31\) | 28673.2 | 0.962480 | 0.481240 | − | 0.876589i | \(-0.340187\pi\) | ||||
0.481240 | + | 0.876589i | \(0.340187\pi\) | |||||||
\(32\) | − | 5723.49i | − | 0.174667i | ||||||
\(33\) | 9867.81 | + | 1742.08i | 0.274586 | + | 0.0484760i | ||||
\(34\) | 9584.53 | 0.243856 | ||||||||
\(35\) | − | 30744.6i | − | 0.717074i | ||||||
\(36\) | −3839.71 | − | 1399.35i | −0.0822983 | − | 0.0299930i | ||||
\(37\) | −29150.0 | −0.575484 | −0.287742 | − | 0.957708i | \(-0.592905\pi\) | ||||
−0.287742 | + | 0.957708i | \(0.592905\pi\) | |||||||
\(38\) | − | 30184.2i | − | 0.550085i | ||||||
\(39\) | −9376.96 | + | 53114.6i | −0.158077 | + | 0.895407i | ||||
\(40\) | −126140. | −1.97094 | ||||||||
\(41\) | 3976.24i | 0.0576927i | 0.999584 | + | 0.0288463i | \(0.00918335\pi\) | ||||
−0.999584 | + | 0.0288463i | \(0.990817\pi\) | |||||||
\(42\) | 26340.8 | + | 4650.25i | 0.355534 | + | 0.0627666i | ||||
\(43\) | 84540.1 | 1.06330 | 0.531652 | − | 0.846963i | \(-0.321572\pi\) | ||||
0.531652 | + | 0.846963i | \(0.321572\pi\) | |||||||
\(44\) | − | 2080.52i | − | 0.0244239i | ||||||
\(45\) | −59197.0 | + | 162432.i | −0.649624 | + | 1.78251i | ||||
\(46\) | 130795. | 1.34375 | ||||||||
\(47\) | − | 73138.8i | − | 0.704457i | −0.935914 | − | 0.352228i | \(-0.885424\pi\) | ||
0.935914 | − | 0.352228i | \(-0.114576\pi\) | |||||||
\(48\) | 17395.1 | − | 98532.6i | 0.157291 | − | 0.890956i | ||||
\(49\) | 16807.0 | 0.142857 | ||||||||
\(50\) | 310365.i | 2.48292i | ||||||||
\(51\) | −33349.2 | − | 5887.54i | −0.251406 | − | 0.0443837i | ||||
\(52\) | 11198.7 | 0.0796446 | ||||||||
\(53\) | − | 40559.3i | − | 0.272435i | −0.990679 | − | 0.136218i | \(-0.956505\pi\) | ||
0.990679 | − | 0.136218i | \(-0.0434946\pi\) | |||||||
\(54\) | −130211. | − | 75286.2i | −0.826928 | − | 0.478117i | ||||
\(55\) | −88012.6 | −0.529001 | ||||||||
\(56\) | − | 68956.6i | − | 0.392656i | ||||||
\(57\) | −18541.4 | + | 105026.i | −0.100120 | + | 0.567115i | ||||
\(58\) | 192709. | 0.987683 | ||||||||
\(59\) | 37762.5i | 0.183867i | 0.995765 | + | 0.0919336i | \(0.0293047\pi\) | ||||
−0.995765 | + | 0.0919336i | \(0.970695\pi\) | |||||||
\(60\) | 35348.7 | + | 6240.53i | 0.163651 | + | 0.0288913i | ||||
\(61\) | 403748. | 1.77877 | 0.889387 | − | 0.457154i | \(-0.151131\pi\) | ||||
0.889387 | + | 0.457154i | \(0.151131\pi\) | |||||||
\(62\) | − | 219109.i | − | 0.919360i | ||||||
\(63\) | −88795.8 | − | 32361.0i | −0.355117 | − | 0.129420i | ||||
\(64\) | −280907. | −1.07158 | ||||||||
\(65\) | − | 473738.i | − | 1.72504i | ||||||
\(66\) | 13312.3 | − | 75405.8i | 0.0463043 | − | 0.262285i | ||||
\(67\) | −1923.98 | −0.00639701 | −0.00319850 | − | 0.999995i | \(-0.501018\pi\) | ||||
−0.00319850 | + | 0.999995i | \(0.501018\pi\) | |||||||
\(68\) | 7031.33i | 0.0223620i | ||||||||
\(69\) | −455100. | − | 80344.2i | −1.38535 | − | 0.244572i | ||||
\(70\) | −234938. | −0.684949 | ||||||||
\(71\) | 337786.i | 0.943772i | 0.881660 | + | 0.471886i | \(0.156427\pi\) | ||||
−0.881660 | + | 0.471886i | \(0.843573\pi\) | |||||||
\(72\) | −132772. | + | 364316.i | −0.355721 | + | 0.976069i | ||||
\(73\) | 169672. | 0.436155 | 0.218077 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218077 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(74\) | 222753.i | 0.549702i | ||||||||
\(75\) | 190649. | − | 1.07991e6i | 0.451909 | − | 2.55978i | ||||
\(76\) | 22143.6 | 0.0504437 | ||||||||
\(77\) | − | 48113.5i | − | 0.105389i | ||||||
\(78\) | 405881. | + | 71655.0i | 0.855292 | + | 0.150995i | ||||
\(79\) | −158380. | −0.321233 | −0.160617 | − | 0.987017i | \(-0.551348\pi\) | ||||
−0.160617 | + | 0.987017i | \(0.551348\pi\) | |||||||
\(80\) | 878828.i | 1.71646i | ||||||||
\(81\) | 406822. | + | 341943.i | 0.765508 | + | 0.643426i | ||||
\(82\) | 30384.8 | 0.0551081 | ||||||||
\(83\) | − | 32502.2i | − | 0.0568432i | −0.999596 | − | 0.0284216i | \(-0.990952\pi\) | ||
0.999596 | − | 0.0284216i | \(-0.00904810\pi\) | |||||||
\(84\) | −3411.48 | + | 19323.9i | −0.00575580 | + | 0.0326030i | ||||
\(85\) | 297447. | 0.484343 | ||||||||
\(86\) | − | 646021.i | − | 1.01567i | ||||||
\(87\) | −670528. | − | 118376.i | −1.01826 | − | 0.179766i | ||||
\(88\) | −197402. | −0.289670 | ||||||||
\(89\) | 1.05963e6i | 1.50308i | 0.659685 | + | 0.751542i | \(0.270690\pi\) | ||||
−0.659685 | + | 0.751542i | \(0.729310\pi\) | |||||||
\(90\) | 1.24124e6 | + | 452360.i | 1.70266 | + | 0.620521i | ||||
\(91\) | 258976. | 0.343665 | ||||||||
\(92\) | 95953.0i | 0.123224i | ||||||||
\(93\) | −134593. | + | 762388.i | −0.167330 | + | 0.947822i | ||||
\(94\) | −558897. | −0.672897 | ||||||||
\(95\) | − | 936741.i | − | 1.09257i | ||||||
\(96\) | 152181. | + | 26866.3i | 0.172007 | + | 0.0303665i | ||||
\(97\) | −748094. | −0.819673 | −0.409837 | − | 0.912159i | \(-0.634414\pi\) | ||||
−0.409837 | + | 0.912159i | \(0.634414\pi\) | |||||||
\(98\) | − | 128432.i | − | 0.136457i | ||||||
\(99\) | −92639.8 | + | 254196.i | −0.0954756 | + | 0.261977i | ||||
\(100\) | −227687. | −0.227687 | ||||||||
\(101\) | − | 896754.i | − | 0.870381i | −0.900338 | − | 0.435190i | \(-0.856681\pi\) | ||
0.900338 | − | 0.435190i | \(-0.143319\pi\) | |||||||
\(102\) | −44990.2 | + | 254841.i | −0.0423953 | + | 0.240143i | ||||
\(103\) | −1.29201e6 | −1.18237 | −0.591185 | − | 0.806536i | \(-0.701340\pi\) | ||||
−0.591185 | + | 0.806536i | \(0.701340\pi\) | |||||||
\(104\) | − | 1.06254e6i | − | 0.944595i | ||||||
\(105\) | 817462. | + | 144316.i | 0.706154 | + | 0.124666i | ||||
\(106\) | −309938. | −0.260230 | ||||||||
\(107\) | − | 78533.2i | − | 0.0641065i | −0.999486 | − | 0.0320532i | \(-0.989795\pi\) | ||
0.999486 | − | 0.0320532i | \(-0.0102046\pi\) | |||||||
\(108\) | 55231.0 | − | 95524.8i | 0.0438441 | − | 0.0758307i | ||||
\(109\) | −828451. | −0.639716 | −0.319858 | − | 0.947465i | \(-0.603635\pi\) | ||||
−0.319858 | + | 0.947465i | \(0.603635\pi\) | |||||||
\(110\) | 672557.i | 0.505302i | ||||||||
\(111\) | 136831. | − | 775064.i | 0.100050 | − | 0.566720i | ||||
\(112\) | −480425. | −0.341957 | ||||||||
\(113\) | − | 1.02476e6i | − | 0.710211i | −0.934826 | − | 0.355106i | \(-0.884445\pi\) | ||
0.934826 | − | 0.355106i | \(-0.115555\pi\) | |||||||
\(114\) | 802564. | + | 141686.i | 0.541708 | + | 0.0956341i | ||||
\(115\) | 4.05911e6 | 2.66893 | ||||||||
\(116\) | 141374.i | 0.0905721i | ||||||||
\(117\) | −1.36824e6 | − | 498645.i | −0.854289 | − | 0.311339i | ||||
\(118\) | 288565. | 0.175630 | ||||||||
\(119\) | 162604.i | 0.0964919i | ||||||||
\(120\) | 592108. | − | 3.35392e6i | 0.342655 | − | 1.94093i | ||||
\(121\) | 1.63383e6 | 0.922252 | ||||||||
\(122\) | − | 3.08528e6i | − | 1.69909i | ||||||
\(123\) | −105724. | − | 18664.6i | −0.0568141 | − | 0.0100301i | ||||
\(124\) | 160741. | 0.0843068 | ||||||||
\(125\) | 5.92641e6i | 3.03432i | ||||||||
\(126\) | −247289. | + | 678542.i | −0.123622 | + | 0.339207i | ||||
\(127\) | −2.83860e6 | −1.38577 | −0.692887 | − | 0.721046i | \(-0.743661\pi\) | ||||
−0.692887 | + | 0.721046i | \(0.743661\pi\) | |||||||
\(128\) | 1.78028e6i | 0.848902i | ||||||||
\(129\) | −396835. | + | 2.24782e6i | −0.184859 | + | 1.04711i | ||||
\(130\) | −3.62011e6 | −1.64775 | ||||||||
\(131\) | 1.90031e6i | 0.845298i | 0.906293 | + | 0.422649i | \(0.138900\pi\) | ||||
−0.906293 | + | 0.422649i | \(0.861100\pi\) | |||||||
\(132\) | 55318.7 | + | 9766.07i | 0.0240519 | + | 0.00424618i | ||||
\(133\) | 512084. | 0.217664 | ||||||||
\(134\) | 14702.3i | 0.00611042i | ||||||||
\(135\) | −4.04099e6 | − | 2.33644e6i | −1.64243 | − | 0.949627i | ||||
\(136\) | 667140. | 0.265217 | ||||||||
\(137\) | − | 1.83112e6i | − | 0.712122i | −0.934463 | − | 0.356061i | \(-0.884120\pi\) | ||
0.934463 | − | 0.356061i | \(-0.115880\pi\) | |||||||
\(138\) | −613958. | + | 3.47769e6i | −0.233615 | + | 1.32329i | ||||
\(139\) | 1.55745e6 | 0.579922 | 0.289961 | − | 0.957038i | \(-0.406358\pi\) | ||||
0.289961 | + | 0.957038i | \(0.406358\pi\) | |||||||
\(140\) | − | 172353.i | − | 0.0628110i | ||||||
\(141\) | 1.94468e6 | + | 343317.i | 0.693729 | + | 0.122472i | ||||
\(142\) | 2.58123e6 | 0.901491 | ||||||||
\(143\) | − | 741372.i | − | 0.253529i | ||||||
\(144\) | 2.53821e6 | + | 925033.i | 0.850043 | + | 0.309792i | ||||
\(145\) | 5.98054e6 | 1.96172 | ||||||||
\(146\) | − | 1.29656e6i | − | 0.416615i | ||||||
\(147\) | −78892.8 | + | 446878.i | −0.0248362 | + | 0.140682i | ||||
\(148\) | −163414. | −0.0504086 | ||||||||
\(149\) | 5.41574e6i | 1.63719i | 0.574371 | + | 0.818595i | \(0.305247\pi\) | ||||
−0.574371 | + | 0.818595i | \(0.694753\pi\) | |||||||
\(150\) | −8.25223e6 | − | 1.45686e6i | −2.44511 | − | 0.431664i | ||||
\(151\) | 3.62504e6 | 1.05289 | 0.526444 | − | 0.850210i | \(-0.323525\pi\) | ||||
0.526444 | + | 0.850210i | \(0.323525\pi\) | |||||||
\(152\) | − | 2.10100e6i | − | 0.598268i | ||||||
\(153\) | 313085. | − | 859081.i | 0.0874155 | − | 0.239861i | ||||
\(154\) | −367664. | −0.100667 | ||||||||
\(155\) | − | 6.79986e6i | − | 1.82602i | ||||||
\(156\) | −52567.0 | + | 297759.i | −0.0138465 | + | 0.0784317i | ||||
\(157\) | −2.59178e6 | −0.669728 | −0.334864 | − | 0.942266i | \(-0.608690\pi\) | ||||
−0.334864 | + | 0.942266i | \(0.608690\pi\) | |||||||
\(158\) | 1.21028e6i | 0.306842i | ||||||||
\(159\) | 1.07843e6 | + | 190387.i | 0.268286 | + | 0.0473638i | ||||
\(160\) | −1.35733e6 | −0.331379 | ||||||||
\(161\) | 2.21898e6i | 0.531710i | ||||||||
\(162\) | 2.61299e6 | − | 3.10877e6i | 0.614600 | − | 0.731213i | ||||
\(163\) | −3.68028e6 | −0.849802 | −0.424901 | − | 0.905240i | \(-0.639691\pi\) | ||||
−0.424901 | + | 0.905240i | \(0.639691\pi\) | |||||||
\(164\) | 22290.7i | 0.00505350i | ||||||||
\(165\) | 413135. | − | 2.34015e6i | 0.0919687 | − | 0.520945i | ||||
\(166\) | −248369. | −0.0542966 | ||||||||
\(167\) | − | 2.43800e6i | − | 0.523460i | −0.965141 | − | 0.261730i | \(-0.915707\pi\) | ||
0.965141 | − | 0.261730i | \(-0.0842930\pi\) | |||||||
\(168\) | 1.83348e6 | + | 323685.i | 0.386676 | + | 0.0682645i | ||||
\(169\) | −836286. | −0.173259 | ||||||||
\(170\) | − | 2.27297e6i | − | 0.462644i | ||||||
\(171\) | −2.70548e6 | − | 985990.i | −0.541072 | − | 0.197190i | ||||
\(172\) | 473930. | 0.0931383 | ||||||||
\(173\) | − | 3.19047e6i | − | 0.616192i | −0.951355 | − | 0.308096i | \(-0.900308\pi\) | ||
0.951355 | − | 0.308096i | \(-0.0996917\pi\) | |||||||
\(174\) | −904584. | + | 5.12390e6i | −0.171712 | + | 0.972642i | ||||
\(175\) | −5.26542e6 | −0.982469 | ||||||||
\(176\) | 1.37532e6i | 0.252269i | ||||||||
\(177\) | −1.00406e6 | − | 177259.i | −0.181067 | − | 0.0319659i | ||||
\(178\) | 8.09725e6 | 1.43575 | ||||||||
\(179\) | − | 6.29592e6i | − | 1.09774i | −0.835907 | − | 0.548871i | \(-0.815058\pi\) | ||
0.835907 | − | 0.548871i | \(-0.184942\pi\) | |||||||
\(180\) | −331857. | + | 910588.i | −0.0569027 | + | 0.156136i | ||||
\(181\) | −9.15543e6 | −1.54398 | −0.771992 | − | 0.635632i | \(-0.780740\pi\) | ||||
−0.771992 | + | 0.635632i | \(0.780740\pi\) | |||||||
\(182\) | − | 1.97899e6i | − | 0.328269i | ||||||
\(183\) | −1.89521e6 | + | 1.07352e7i | −0.309246 | + | 1.75169i | ||||
\(184\) | 9.10412e6 | 1.46145 | ||||||||
\(185\) | 6.91292e6i | 1.09181i | ||||||||
\(186\) | 5.82586e6 | + | 1.02851e6i | 0.905360 | + | 0.159834i | ||||
\(187\) | 465488. | 0.0711841 | ||||||||
\(188\) | − | 410014.i | − | 0.0617057i | ||||||
\(189\) | 1.27725e6 | − | 2.20907e6i | 0.189187 | − | 0.327209i | ||||
\(190\) | −7.15820e6 | −1.04362 | ||||||||
\(191\) | − | 5.98114e6i | − | 0.858388i | −0.903212 | − | 0.429194i | \(-0.858798\pi\) | ||
0.903212 | − | 0.429194i | \(-0.141202\pi\) | |||||||
\(192\) | 1.31859e6 | − | 7.46900e6i | 0.186297 | − | 1.05526i | ||||
\(193\) | −6.89082e6 | −0.958515 | −0.479257 | − | 0.877674i | \(-0.659094\pi\) | ||||
−0.479257 | + | 0.877674i | \(0.659094\pi\) | |||||||
\(194\) | 5.71663e6i | 0.782952i | ||||||||
\(195\) | 1.25961e7 | + | 2.22375e6i | 1.69877 | + | 0.299903i | ||||
\(196\) | 94219.6 | 0.0125133 | ||||||||
\(197\) | 2.96448e6i | 0.387748i | 0.981026 | + | 0.193874i | \(0.0621052\pi\) | ||||
−0.981026 | + | 0.193874i | \(0.937895\pi\) | |||||||
\(198\) | 1.94246e6 | + | 707916.i | 0.250240 | + | 0.0911982i | ||||
\(199\) | 1.22422e7 | 1.55346 | 0.776732 | − | 0.629831i | \(-0.216876\pi\) | ||||
0.776732 | + | 0.629831i | \(0.216876\pi\) | |||||||
\(200\) | 2.16032e7i | 2.70040i | ||||||||
\(201\) | 9031.26 | − | 51156.5i | 0.00111214 | − | 0.00629959i | ||||
\(202\) | −6.85263e6 | −0.831387 | ||||||||
\(203\) | 3.26936e6i | 0.390818i | ||||||||
\(204\) | −186955. | − | 33005.4i | −0.0220215 | − | 0.00388771i | ||||
\(205\) | 942965. | 0.109455 | ||||||||
\(206\) | 9.87300e6i | 1.12940i | ||||||||
\(207\) | 4.27252e6 | − | 1.17234e7i | 0.481696 | − | 1.32173i | ||||
\(208\) | −7.40280e6 | −0.822632 | ||||||||
\(209\) | − | 1.46594e6i | − | 0.160575i | ||||||
\(210\) | 1.10281e6 | − | 6.24672e6i | 0.119081 | − | 0.674518i | ||||
\(211\) | −9.10854e6 | −0.969620 | −0.484810 | − | 0.874619i | \(-0.661111\pi\) | ||||
−0.484810 | + | 0.874619i | \(0.661111\pi\) | |||||||
\(212\) | − | 227375.i | − | 0.0238635i | ||||||
\(213\) | −8.98135e6 | − | 1.58558e6i | −0.929400 | − | 0.164078i | ||||
\(214\) | −600119. | −0.0612345 | ||||||||
\(215\) | − | 2.00487e7i | − | 2.01730i | ||||||
\(216\) | −9.06350e6 | − | 5.24037e6i | −0.899362 | − | 0.519997i | ||||
\(217\) | 3.71725e6 | 0.363783 | ||||||||
\(218\) | 6.33069e6i | 0.611057i | ||||||||
\(219\) | −796446. | + | 4.51137e6i | −0.0758270 | + | 0.429513i | ||||
\(220\) | −493396. | −0.0463370 | ||||||||
\(221\) | 2.50554e6i | 0.232126i | ||||||||
\(222\) | −5.92273e6 | − | 1.04561e6i | −0.541331 | − | 0.0955676i | ||||
\(223\) | 1.63703e7 | 1.47619 | 0.738093 | − | 0.674699i | \(-0.235727\pi\) | ||||
0.738093 | + | 0.674699i | \(0.235727\pi\) | |||||||
\(224\) | − | 742004.i | − | 0.0660180i | ||||||
\(225\) | 2.78186e7 | + | 1.01383e7i | 2.44224 | + | 0.890055i | ||||
\(226\) | −7.83082e6 | −0.678393 | ||||||||
\(227\) | 1.15150e6i | 0.0984431i | 0.998788 | + | 0.0492216i | \(0.0156740\pi\) | ||||
−0.998788 | + | 0.0492216i | \(0.984326\pi\) | |||||||
\(228\) | −103943. | + | 588771.i | −0.00876980 | + | 0.0496755i | ||||
\(229\) | −1.53167e7 | −1.27544 | −0.637719 | − | 0.770269i | \(-0.720122\pi\) | ||||
−0.637719 | + | 0.770269i | \(0.720122\pi\) | |||||||
\(230\) | − | 3.10181e7i | − | 2.54936i | ||||||
\(231\) | 1.27928e6 | + | 225847.i | 0.103784 | + | 0.0183222i | ||||
\(232\) | 1.34137e7 | 1.07420 | ||||||||
\(233\) | − | 1.61419e7i | − | 1.27611i | −0.769992 | − | 0.638053i | \(-0.779740\pi\) | ||
0.769992 | − | 0.638053i | \(-0.220260\pi\) | |||||||
\(234\) | −3.81044e6 | + | 1.04555e7i | −0.297391 | + | 0.816017i | ||||
\(235\) | −1.73449e7 | −1.33650 | ||||||||
\(236\) | 211695.i | 0.0161055i | ||||||||
\(237\) | 743445. | − | 4.21115e6i | 0.0558475 | − | 0.316341i | ||||
\(238\) | 1.24256e6 | 0.0921690 | ||||||||
\(239\) | 1.41807e7i | 1.03874i | 0.854551 | + | 0.519368i | \(0.173832\pi\) | ||||
−0.854551 | + | 0.519368i | \(0.826168\pi\) | |||||||
\(240\) | −2.33670e7 | − | 4.12526e6i | −1.69032 | − | 0.298413i | ||||
\(241\) | 685364. | 0.0489633 | 0.0244816 | − | 0.999700i | \(-0.492206\pi\) | ||||
0.0244816 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(242\) | − | 1.24850e7i | − | 0.880935i | ||||||
\(243\) | −1.10015e7 | + | 9.21184e6i | −0.766714 | + | 0.641989i | ||||
\(244\) | 2.26340e6 | 0.155809 | ||||||||
\(245\) | − | 3.98578e6i | − | 0.271029i | ||||||
\(246\) | −142628. | + | 807897.i | −0.00958073 | + | 0.0542688i | ||||
\(247\) | 7.89062e6 | 0.523625 | ||||||||
\(248\) | − | 1.52513e7i | − | 0.999890i | ||||||
\(249\) | 864196. | + | 152567.i | 0.0559776 | + | 0.00988239i | ||||
\(250\) | 4.52873e7 | 2.89838 | ||||||||
\(251\) | 2.46524e7i | 1.55897i | 0.626422 | + | 0.779484i | \(0.284519\pi\) | ||||
−0.626422 | + | 0.779484i | \(0.715481\pi\) | |||||||
\(252\) | −497787. | − | 181415.i | −0.0311058 | − | 0.0113363i | ||||
\(253\) | 6.35227e6 | 0.392254 | ||||||||
\(254\) | 2.16914e7i | 1.32369i | ||||||||
\(255\) | −1.39623e6 | + | 7.90877e6i | −0.0842047 | + | 0.476967i | ||||
\(256\) | −4.37390e6 | −0.260705 | ||||||||
\(257\) | − | 1.72290e7i | − | 1.01499i | −0.861656 | − | 0.507493i | \(-0.830572\pi\) | ||
0.861656 | − | 0.507493i | \(-0.169428\pi\) | |||||||
\(258\) | 1.71769e7 | + | 3.03245e6i | 1.00020 | + | 0.176577i | ||||
\(259\) | −3.77906e6 | −0.217512 | ||||||||
\(260\) | − | 2.65576e6i | − | 0.151102i | ||||||
\(261\) | 6.29497e6 | − | 1.72729e7i | 0.354056 | − | 0.971501i | ||||
\(262\) | 1.45214e7 | 0.807428 | ||||||||
\(263\) | 2.08769e7i | 1.14762i | 0.818988 | + | 0.573810i | \(0.194535\pi\) | ||||
−0.818988 | + | 0.573810i | \(0.805465\pi\) | |||||||
\(264\) | 926615. | − | 5.24870e6i | 0.0503602 | − | 0.285259i | ||||
\(265\) | −9.61865e6 | −0.516864 | ||||||||
\(266\) | − | 3.91314e6i | − | 0.207912i | ||||||
\(267\) | −2.81743e7 | − | 4.97394e6i | −1.48019 | − | 0.261316i | ||||
\(268\) | −10785.8 | −0.000560336 | ||||||||
\(269\) | 3.16115e7i | 1.62401i | 0.583653 | + | 0.812003i | \(0.301623\pi\) | ||||
−0.583653 | + | 0.812003i | \(0.698377\pi\) | |||||||
\(270\) | −1.78541e7 | + | 3.08797e7i | −0.907084 | + | 1.56885i | ||||
\(271\) | −1.14722e7 | −0.576419 | −0.288209 | − | 0.957567i | \(-0.593060\pi\) | ||||
−0.288209 | + | 0.957567i | \(0.593060\pi\) | |||||||
\(272\) | − | 4.64801e6i | − | 0.230973i | ||||||
\(273\) | −1.21565e6 | + | 6.88588e6i | −0.0597474 | + | 0.338432i | ||||
\(274\) | −1.39927e7 | −0.680218 | ||||||||
\(275\) | 1.50733e7i | 0.724789i | ||||||||
\(276\) | −2.55128e6 | − | 450408.i | −0.121347 | − | 0.0214229i | ||||
\(277\) | 6.88096e6 | 0.323750 | 0.161875 | − | 0.986811i | \(-0.448246\pi\) | ||||
0.161875 | + | 0.986811i | \(0.448246\pi\) | |||||||
\(278\) | − | 1.19014e7i | − | 0.553941i | ||||||
\(279\) | −1.96392e7 | − | 7.15736e6i | −0.904298 | − | 0.329564i | ||||
\(280\) | −1.63531e7 | −0.744946 | ||||||||
\(281\) | 7.25799e6i | 0.327112i | 0.986534 | + | 0.163556i | \(0.0522965\pi\) | ||||
−0.986534 | + | 0.163556i | \(0.947703\pi\) | |||||||
\(282\) | 2.62349e6 | − | 1.48604e7i | 0.116985 | − | 0.662650i | ||||
\(283\) | 1.25835e7 | 0.555192 | 0.277596 | − | 0.960698i | \(-0.410462\pi\) | ||||
0.277596 | + | 0.960698i | \(0.410462\pi\) | |||||||
\(284\) | 1.89362e6i | 0.0826682i | ||||||||
\(285\) | 2.49068e7 | + | 4.39710e6i | 1.07593 | + | 0.189947i | ||||
\(286\) | −5.66527e6 | −0.242171 | ||||||||
\(287\) | 515487.i | 0.0218058i | ||||||||
\(288\) | −1.42869e6 | + | 3.92020e6i | −0.0598081 | + | 0.164109i | ||||
\(289\) | 2.25644e7 | 0.934825 | ||||||||
\(290\) | − | 4.57009e7i | − | 1.87383i | ||||||
\(291\) | 3.51158e6 | − | 1.98909e7i | 0.142503 | − | 0.807191i | ||||
\(292\) | 951175. | 0.0382043 | ||||||||
\(293\) | 1.89052e7i | 0.751584i | 0.926704 | + | 0.375792i | \(0.122629\pi\) | ||||
−0.926704 | + | 0.375792i | \(0.877371\pi\) | |||||||
\(294\) | 3.41487e6 | + | 602867.i | 0.134379 | + | 0.0237235i | ||||
\(295\) | 8.95537e6 | 0.348833 | ||||||||
\(296\) | 1.55049e7i | 0.597852i | ||||||||
\(297\) | −6.32392e6 | − | 3.65639e6i | −0.241389 | − | 0.139567i | ||||
\(298\) | 4.13849e7 | 1.56384 | ||||||||
\(299\) | 3.41918e7i | 1.27911i | ||||||||
\(300\) | 1.06877e6 | − | 6.05394e6i | 0.0395843 | − | 0.224220i | ||||
\(301\) | 1.09599e7 | 0.401891 | ||||||||
\(302\) | − | 2.77011e7i | − | 1.00572i | ||||||
\(303\) | 2.38436e7 | + | 4.20940e6i | 0.857126 | + | 0.151319i | ||||
\(304\) | −1.46378e7 | −0.521022 | ||||||||
\(305\) | − | 9.57489e7i | − | 3.37469i | ||||||
\(306\) | −6.56475e6 | − | 2.39247e6i | −0.229115 | − | 0.0834993i | ||||
\(307\) | −1.81640e7 | −0.627766 | −0.313883 | − | 0.949462i | \(-0.601630\pi\) | ||||
−0.313883 | + | 0.949462i | \(0.601630\pi\) | |||||||
\(308\) | − | 269723.i | − | 0.00923136i | ||||||
\(309\) | 6.06473e6 | − | 3.43529e7i | 0.205559 | − | 1.16436i | ||||
\(310\) | −5.19618e7 | −1.74421 | ||||||||
\(311\) | 467133.i | 0.0155296i | 0.999970 | + | 0.00776479i | \(0.00247163\pi\) | ||||
−0.999970 | + | 0.00776479i | \(0.997528\pi\) | |||||||
\(312\) | 2.82517e7 | + | 4.98761e6i | 0.930210 | + | 0.164221i | ||||
\(313\) | −3.52717e7 | −1.15025 | −0.575127 | − | 0.818064i | \(-0.695047\pi\) | ||||
−0.575127 | + | 0.818064i | \(0.695047\pi\) | |||||||
\(314\) | 1.98053e7i | 0.639724i | ||||||||
\(315\) | −7.67440e6 | + | 2.10579e7i | −0.245535 | + | 0.673727i | ||||
\(316\) | −887877. | −0.0281379 | ||||||||
\(317\) | − | 2.19049e7i | − | 0.687644i | −0.939035 | − | 0.343822i | \(-0.888278\pi\) | ||
0.939035 | − | 0.343822i | \(-0.111722\pi\) | |||||||
\(318\) | 1.45486e6 | − | 8.24089e6i | 0.0452419 | − | 0.256267i | ||||
\(319\) | 9.35920e6 | 0.288315 | ||||||||
\(320\) | 6.66172e7i | 2.03299i | ||||||||
\(321\) | 2.08811e6 | + | 368638.i | 0.0631302 | + | 0.0111451i | ||||
\(322\) | 1.69565e7 | 0.507889 | ||||||||
\(323\) | 4.95430e6i | 0.147020i | ||||||||
\(324\) | 2.28064e6 | + | 1.91692e6i | 0.0670534 | + | 0.0563599i | ||||
\(325\) | −8.11340e7 | −2.36348 | ||||||||
\(326\) | 2.81232e7i | 0.811730i | ||||||||
\(327\) | 3.88878e6 | − | 2.20275e7i | 0.111217 | − | 0.629974i | ||||
\(328\) | 2.11496e6 | 0.0599351 | ||||||||
\(329\) | − | 9.48185e6i | − | 0.266260i | ||||||
\(330\) | −1.78825e7 | − | 3.15701e6i | −0.497607 | − | 0.0878485i | ||||
\(331\) | 4.37918e7 | 1.20756 | 0.603780 | − | 0.797151i | \(-0.293661\pi\) | ||||
0.603780 | + | 0.797151i | \(0.293661\pi\) | |||||||
\(332\) | − | 182207.i | − | 0.00497909i | ||||||
\(333\) | 1.99658e7 | + | 7.27637e6i | 0.540696 | + | 0.197053i | ||||
\(334\) | −1.86302e7 | −0.500009 | ||||||||
\(335\) | 456273.i | 0.0121364i | ||||||||
\(336\) | 2.25514e6 | − | 1.27740e7i | 0.0594505 | − | 0.336750i | ||||
\(337\) | −1.47909e7 | −0.386461 | −0.193231 | − | 0.981153i | \(-0.561897\pi\) | ||||
−0.193231 | + | 0.981153i | \(0.561897\pi\) | |||||||
\(338\) | 6.39056e6i | 0.165497i | ||||||||
\(339\) | 2.72472e7 | + | 4.81027e6i | 0.699396 | + | 0.123473i | ||||
\(340\) | 1.66748e6 | 0.0424252 | ||||||||
\(341\) | − | 1.06414e7i | − | 0.268371i | ||||||
\(342\) | −7.53454e6 | + | 2.06742e7i | −0.188356 | + | 0.516832i | ||||
\(343\) | 2.17889e6 | 0.0539949 | ||||||||
\(344\) | − | 4.49669e7i | − | 1.10463i | ||||||
\(345\) | −1.90536e7 | + | 1.07927e8i | −0.464003 | + | 2.62829i | ||||
\(346\) | −2.43803e7 | −0.588586 | ||||||||
\(347\) | 5.20260e7i | 1.24518i | 0.782548 | + | 0.622590i | \(0.213920\pi\) | ||||
−0.782548 | + | 0.622590i | \(0.786080\pi\) | |||||||
\(348\) | −3.75896e6 | − | 663614.i | −0.0891929 | − | 0.0157463i | ||||
\(349\) | 4.15549e7 | 0.977565 | 0.488782 | − | 0.872406i | \(-0.337441\pi\) | ||||
0.488782 | + | 0.872406i | \(0.337441\pi\) | |||||||
\(350\) | 4.02362e7i | 0.938454i | ||||||||
\(351\) | 1.96810e7 | − | 3.40392e7i | 0.455119 | − | 0.787152i | ||||
\(352\) | −2.12414e6 | −0.0487029 | ||||||||
\(353\) | − | 3.86041e7i | − | 0.877626i | −0.898578 | − | 0.438813i | \(-0.855399\pi\) | ||
0.898578 | − | 0.438813i | \(-0.144601\pi\) | |||||||
\(354\) | −1.35454e6 | + | 7.67262e6i | −0.0305339 | + | 0.172955i | ||||
\(355\) | 8.01061e7 | 1.79052 | ||||||||
\(356\) | 5.94025e6i | 0.131660i | ||||||||
\(357\) | −4.32345e6 | − | 763271.i | −0.0950225 | − | 0.0167754i | ||||
\(358\) | −4.81109e7 | −1.04856 | ||||||||
\(359\) | − | 8.70557e7i | − | 1.88154i | −0.339044 | − | 0.940771i | \(-0.610103\pi\) | ||
0.339044 | − | 0.940771i | \(-0.389897\pi\) | |||||||
\(360\) | 8.63975e7 | + | 3.14869e7i | 1.85180 | + | 0.674874i | ||||
\(361\) | −3.14434e7 | −0.668357 | ||||||||
\(362\) | 6.99621e7i | 1.47481i | ||||||||
\(363\) | −7.66925e6 | + | 4.34415e7i | −0.160337 | + | 0.908208i | ||||
\(364\) | 1.45181e6 | 0.0301028 | ||||||||
\(365\) | − | 4.02376e7i | − | 0.827473i | ||||||
\(366\) | 8.20340e7 | + | 1.44824e7i | 1.67321 | + | 0.295392i | ||||
\(367\) | 4.56054e7 | 0.922609 | 0.461305 | − | 0.887242i | \(-0.347382\pi\) | ||||
0.461305 | + | 0.887242i | \(0.347382\pi\) | |||||||
\(368\) | − | 6.34291e7i | − | 1.27275i | ||||||
\(369\) | 992542. | − | 2.72345e6i | 0.0197547 | − | 0.0542052i | ||||
\(370\) | 5.28258e7 | 1.04290 | ||||||||
\(371\) | − | 5.25819e6i | − | 0.102971i | ||||||
\(372\) | −754527. | + | 4.27393e6i | −0.0146570 | + | 0.0830230i | ||||
\(373\) | −9.15611e7 | −1.76435 | −0.882174 | − | 0.470923i | \(-0.843921\pi\) | ||||
−0.882174 | + | 0.470923i | \(0.843921\pi\) | |||||||
\(374\) | − | 3.55707e6i | − | 0.0679951i | ||||||
\(375\) | −1.57576e8 | − | 2.78188e7i | −2.98812 | − | 0.527528i | ||||
\(376\) | −3.89026e7 | −0.731838 | ||||||||
\(377\) | 5.03770e7i | 0.940174i | ||||||||
\(378\) | −1.68809e7 | − | 9.76024e6i | −0.312550 | − | 0.180711i | ||||
\(379\) | 5.53674e7 | 1.01704 | 0.508518 | − | 0.861051i | \(-0.330193\pi\) | ||||
0.508518 | + | 0.861051i | \(0.330193\pi\) | |||||||
\(380\) | − | 5.25134e6i | − | 0.0957017i | ||||||
\(381\) | 1.33245e7 | − | 7.54749e7i | 0.240922 | − | 1.36467i | ||||
\(382\) | −4.57055e7 | −0.819932 | ||||||||
\(383\) | 1.49962e7i | 0.266923i | 0.991054 | + | 0.133461i | \(0.0426092\pi\) | ||||
−0.991054 | + | 0.133461i | \(0.957391\pi\) | |||||||
\(384\) | −4.73355e7 | − | 8.35670e6i | −0.835975 | − | 0.147585i | ||||
\(385\) | −1.14101e7 | −0.199944 | ||||||||
\(386\) | 5.26569e7i | 0.915573i | ||||||||
\(387\) | −5.79042e7 | − | 2.11027e7i | −0.999027 | − | 0.364088i | ||||
\(388\) | −4.19379e6 | −0.0717979 | ||||||||
\(389\) | 3.89798e7i | 0.662202i | 0.943595 | + | 0.331101i | \(0.107420\pi\) | ||||
−0.943595 | + | 0.331101i | \(0.892580\pi\) | |||||||
\(390\) | 1.69930e7 | − | 9.62546e7i | 0.286468 | − | 1.62266i | ||||
\(391\) | −2.14681e7 | −0.359140 | ||||||||
\(392\) | − | 8.93966e6i | − | 0.148410i | ||||||
\(393\) | −5.05269e7 | − | 8.92012e6i | −0.832425 | − | 0.146958i | ||||
\(394\) | 2.26533e7 | 0.370377 | ||||||||
\(395\) | 3.75599e7i | 0.609444i | ||||||||
\(396\) | −519337. | + | 1.42502e6i | −0.00836303 | + | 0.0229475i | ||||
\(397\) | −1.53003e7 | −0.244528 | −0.122264 | − | 0.992498i | \(-0.539015\pi\) | ||||
−0.122264 | + | 0.992498i | \(0.539015\pi\) | |||||||
\(398\) | − | 9.35502e7i | − | 1.48387i | ||||||
\(399\) | −2.40374e6 | + | 1.36157e7i | −0.0378416 | + | 0.214349i | ||||
\(400\) | 1.50511e8 | 2.35174 | ||||||||
\(401\) | 1.70287e7i | 0.264088i | 0.991244 | + | 0.132044i | \(0.0421540\pi\) | ||||
−0.991244 | + | 0.132044i | \(0.957846\pi\) | |||||||
\(402\) | −390917. | − | 69013.3i | −0.00601737 | − | 0.00106232i | ||||
\(403\) | 5.72785e7 | 0.875138 | ||||||||
\(404\) | − | 5.02718e6i | − | 0.0762396i | ||||||
\(405\) | 8.10918e7 | − | 9.64780e7i | 1.22071 | − | 1.45232i | ||||
\(406\) | 2.49831e7 | 0.373309 | ||||||||
\(407\) | 1.08183e7i | 0.160464i | ||||||||
\(408\) | −3.13159e6 | + | 1.77385e7i | −0.0461088 | + | 0.261178i | ||||
\(409\) | −1.18550e7 | −0.173274 | −0.0866368 | − | 0.996240i | \(-0.527612\pi\) | ||||
−0.0866368 | + | 0.996240i | \(0.527612\pi\) | |||||||
\(410\) | − | 7.20576e6i | − | 0.104551i | ||||||
\(411\) | 4.86872e7 | + | 8.59534e6i | 0.701277 | + | 0.123805i | ||||
\(412\) | −7.24296e6 | −0.103568 | ||||||||
\(413\) | 4.89559e6i | 0.0694953i | ||||||||
\(414\) | −8.95858e7 | − | 3.26488e7i | −1.26252 | − | 0.460115i | ||||
\(415\) | −7.70790e6 | −0.107843 | ||||||||
\(416\) | − | 1.14334e7i | − | 0.158817i | ||||||
\(417\) | −7.31074e6 | + | 4.14108e7i | −0.100821 | + | 0.571091i | ||||
\(418\) | −1.12022e7 | −0.153382 | ||||||||
\(419\) | − | 4.26289e7i | − | 0.579511i | −0.957101 | − | 0.289755i | \(-0.906426\pi\) | ||
0.957101 | − | 0.289755i | \(-0.0935740\pi\) | |||||||
\(420\) | 4.58267e6 | + | 809034.i | 0.0618544 | + | 0.0109199i | ||||
\(421\) | 5.55519e7 | 0.744479 | 0.372239 | − | 0.928137i | \(-0.378590\pi\) | ||||
0.372239 | + | 0.928137i | \(0.378590\pi\) | |||||||
\(422\) | 6.96038e7i | 0.926181i | ||||||||
\(423\) | −1.82568e7 | + | 5.00951e7i | −0.241214 | + | 0.661872i | ||||
\(424\) | −2.15735e7 | −0.283025 | ||||||||
\(425\) | − | 5.09418e7i | − | 0.663602i | ||||||
\(426\) | −1.21164e7 | + | 6.86318e7i | −0.156727 | + | 0.887763i | ||||
\(427\) | 5.23426e7 | 0.672314 | ||||||||
\(428\) | − | 440255.i | − | 0.00561530i | ||||||
\(429\) | 1.97122e7 | + | 3.48003e6i | 0.249669 | + | 0.0440770i | ||||
\(430\) | −1.53204e8 | −1.92692 | ||||||||
\(431\) | 2.33322e7i | 0.291423i | 0.989327 | + | 0.145711i | \(0.0465471\pi\) | ||||
−0.989327 | + | 0.145711i | \(0.953453\pi\) | |||||||
\(432\) | −3.65100e7 | + | 6.31460e7i | −0.452857 | + | 0.783240i | ||||
\(433\) | 9.98905e7 | 1.23044 | 0.615220 | − | 0.788356i | \(-0.289067\pi\) | ||||
0.615220 | + | 0.788356i | \(0.289067\pi\) | |||||||
\(434\) | − | 2.84057e7i | − | 0.347486i | ||||||
\(435\) | −2.80729e7 | + | 1.59016e8i | −0.341052 | + | 1.93184i | ||||
\(436\) | −4.64427e6 | −0.0560349 | ||||||||
\(437\) | 6.76088e7i | 0.810138i | ||||||||
\(438\) | 3.44741e7 | + | 6.08612e6i | 0.410271 | + | 0.0724300i | ||||
\(439\) | −7.98773e7 | −0.944126 | −0.472063 | − | 0.881565i | \(-0.656490\pi\) | ||||
−0.472063 | + | 0.881565i | \(0.656490\pi\) | |||||||
\(440\) | 4.68140e7i | 0.549563i | ||||||||
\(441\) | −1.15117e7 | − | 4.19533e6i | −0.134221 | − | 0.0489160i | ||||
\(442\) | 1.91463e7 | 0.221727 | ||||||||
\(443\) | 1.57447e7i | 0.181102i | 0.995892 | + | 0.0905512i | \(0.0288629\pi\) | ||||
−0.995892 | + | 0.0905512i | \(0.971137\pi\) | |||||||
\(444\) | 767073. | − | 4.34499e6i | 0.00876371 | − | 0.0496409i | ||||
\(445\) | 2.51291e8 | 2.85165 | ||||||||
\(446\) | − | 1.25095e8i | − | 1.41005i | ||||||
\(447\) | −1.43998e8 | − | 2.54217e7i | −1.61226 | − | 0.284631i | ||||
\(448\) | −3.64173e7 | −0.405018 | ||||||||
\(449\) | 9.89524e7i | 1.09317i | 0.837404 | + | 0.546584i | \(0.184072\pi\) | ||||
−0.837404 | + | 0.546584i | \(0.815928\pi\) | |||||||
\(450\) | 7.74727e7 | − | 2.12579e8i | 0.850180 | − | 2.33282i | ||||
\(451\) | 1.47569e6 | 0.0160866 | ||||||||
\(452\) | − | 5.74479e6i | − | 0.0622098i | ||||||
\(453\) | −1.70161e7 | + | 9.63856e7i | −0.183048 | + | 1.03685i | ||||
\(454\) | 8.79928e6 | 0.0940328 | ||||||||
\(455\) | − | 6.14162e7i | − | 0.652002i | ||||||
\(456\) | 5.58632e7 | + | 9.86220e6i | 0.589158 | + | 0.104011i | ||||
\(457\) | −1.16996e8 | −1.22581 | −0.612904 | − | 0.790157i | \(-0.709999\pi\) | ||||
−0.612904 | + | 0.790157i | \(0.709999\pi\) | |||||||
\(458\) | 1.17044e8i | 1.21830i | ||||||||
\(459\) | 2.13723e7 | + | 1.23571e7i | 0.221011 | + | 0.127785i | ||||
\(460\) | 2.27553e7 | 0.233780 | ||||||||
\(461\) | 2.65404e7i | 0.270897i | 0.990784 | + | 0.135449i | \(0.0432476\pi\) | ||||
−0.990784 | + | 0.135449i | \(0.956752\pi\) | |||||||
\(462\) | 1.72583e6 | − | 9.77575e6i | 0.0175014 | − | 0.0991343i | ||||
\(463\) | −1.32352e8 | −1.33349 | −0.666743 | − | 0.745288i | \(-0.732312\pi\) | ||||
−0.666743 | + | 0.745288i | \(0.732312\pi\) | |||||||
\(464\) | − | 9.34541e7i | − | 0.935501i | ||||||
\(465\) | 1.80800e8 | + | 3.19188e7i | 1.79821 | + | 0.317459i | ||||
\(466\) | −1.23350e8 | −1.21894 | ||||||||
\(467\) | − | 3.83535e7i | − | 0.376578i | −0.982114 | − | 0.188289i | \(-0.939706\pi\) | ||
0.982114 | − | 0.188289i | \(-0.0602941\pi\) | |||||||
\(468\) | −7.67032e6 | − | 2.79539e6i | −0.0748300 | − | 0.0272712i | ||||
\(469\) | −249429. | −0.00241784 | ||||||||
\(470\) | 1.32543e8i | 1.27662i | ||||||||
\(471\) | 1.21659e7 | − | 6.89123e7i | 0.116435 | − | 0.659529i | ||||
\(472\) | 2.00859e7 | 0.191014 | ||||||||
\(473\) | − | 3.13750e7i | − | 0.296484i | ||||||
\(474\) | −3.21799e7 | − | 5.68111e6i | −0.302169 | − | 0.0533455i | ||||
\(475\) | −1.60429e8 | −1.49694 | ||||||||
\(476\) | 911555.i | 0.00845205i | ||||||||
\(477\) | −1.01244e7 | + | 2.77804e7i | −0.0932851 | + | 0.255967i | ||||
\(478\) | 1.08363e8 | 0.992200 | ||||||||
\(479\) | − | 2.06135e8i | − | 1.87562i | −0.347149 | − | 0.937810i | \(-0.612850\pi\) | ||
0.347149 | − | 0.937810i | \(-0.387150\pi\) | |||||||
\(480\) | 6.37135e6 | − | 3.60897e7i | 0.0576113 | − | 0.326332i | ||||
\(481\) | −5.82309e7 | −0.523261 | ||||||||
\(482\) | − | 5.23728e6i | − | 0.0467697i | ||||||
\(483\) | −5.90000e7 | − | 1.04160e7i | −0.523613 | − | 0.0924396i | ||||
\(484\) | 9.15919e6 | 0.0807832 | ||||||||
\(485\) | 1.77410e8i | 1.55508i | ||||||||
\(486\) | 7.03932e7 | + | 8.40691e7i | 0.613228 | + | 0.732365i | ||||
\(487\) | 1.13519e8 | 0.982835 | 0.491418 | − | 0.870924i | \(-0.336479\pi\) | ||||
0.491418 | + | 0.870924i | \(0.336479\pi\) | |||||||
\(488\) | − | 2.14754e8i | − | 1.84791i | ||||||
\(489\) | 1.72754e7 | − | 9.78543e7i | 0.147741 | − | 0.836861i | ||||
\(490\) | −3.04577e7 | −0.258886 | ||||||||
\(491\) | − | 1.17371e8i | − | 0.991555i | −0.868450 | − | 0.495777i | \(-0.834883\pi\) | ||
0.868450 | − | 0.495777i | \(-0.165117\pi\) | |||||||
\(492\) | −592683. | − | 104633.i | −0.00497654 | − | 0.000878568i | ||||
\(493\) | −3.16304e7 | −0.263975 | ||||||||
\(494\) | − | 6.02969e7i | − | 0.500166i | ||||||
\(495\) | 6.02826e7 | + | 2.19695e7i | 0.497023 | + | 0.181136i | ||||
\(496\) | −1.06257e8 | −0.870788 | ||||||||
\(497\) | 4.37912e7i | 0.356712i | ||||||||
\(498\) | 1.16585e6 | − | 6.60384e6i | 0.00943965 | − | 0.0534698i | ||||
\(499\) | 1.90289e8 | 1.53148 | 0.765741 | − | 0.643149i | \(-0.222372\pi\) | ||||
0.765741 | + | 0.643149i | \(0.222372\pi\) | |||||||
\(500\) | 3.32233e7i | 0.265787i | ||||||||
\(501\) | 6.48235e7 | + | 1.14441e7i | 0.515489 | + | 0.0910053i | ||||
\(502\) | 1.88383e8 | 1.48913 | ||||||||
\(503\) | − | 1.97076e8i | − | 1.54857i | −0.632839 | − | 0.774284i | \(-0.718110\pi\) | ||
0.632839 | − | 0.774284i | \(-0.281890\pi\) | |||||||
\(504\) | −1.72128e7 | + | 4.72306e7i | −0.134450 | + | 0.368920i | ||||
\(505\) | −2.12665e8 | −1.65129 | ||||||||
\(506\) | − | 4.85415e7i | − | 0.374681i | ||||||
\(507\) | 3.92556e6 | − | 2.22359e7i | 0.0301216 | − | 0.170620i | ||||
\(508\) | −1.59131e7 | −0.121385 | ||||||||
\(509\) | − | 4.63513e7i | − | 0.351486i | −0.984436 | − | 0.175743i | \(-0.943767\pi\) | ||
0.984436 | − | 0.175743i | \(-0.0562328\pi\) | |||||||
\(510\) | 6.04357e7 | + | 1.06694e7i | 0.455599 | + | 0.0804323i | ||||
\(511\) | 2.19965e7 | 0.164851 | ||||||||
\(512\) | 1.47361e8i | 1.09793i | ||||||||
\(513\) | 3.89159e7 | − | 6.73071e7i | 0.288254 | − | 0.498550i | ||||
\(514\) | −1.31657e8 | −0.969514 | ||||||||
\(515\) | 3.06399e8i | 2.24319i | ||||||||
\(516\) | −2.22465e6 | + | 1.26012e7i | −0.0161924 | + | 0.0917200i | ||||
\(517\) | −2.71437e7 | −0.196425 | ||||||||
\(518\) | 2.88780e7i | 0.207768i | ||||||||
\(519\) | 8.48308e7 | + | 1.49762e7i | 0.606808 | + | 0.107127i | ||||
\(520\) | −2.51982e8 | −1.79209 | ||||||||
\(521\) | 6.26964e7i | 0.443332i | 0.975123 | + | 0.221666i | \(0.0711495\pi\) | ||||
−0.975123 | + | 0.221666i | \(0.928850\pi\) | |||||||
\(522\) | −1.31992e8 | − | 4.81036e7i | −0.927978 | − | 0.338194i | ||||
\(523\) | −3.94364e7 | −0.275672 | −0.137836 | − | 0.990455i | \(-0.544015\pi\) | ||||
−0.137836 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(524\) | 1.06531e7i | 0.0740425i | ||||||||
\(525\) | 2.47161e7 | − | 1.40001e8i | 0.170806 | − | 0.967508i | ||||
\(526\) | 1.59533e8 | 1.09621 | ||||||||
\(527\) | 3.59636e7i | 0.245715i | ||||||||
\(528\) | −3.65680e7 | − | 6.45579e6i | −0.248428 | − | 0.0438579i | ||||
\(529\) | −1.44928e8 | −0.979008 | ||||||||
\(530\) | 7.35019e7i | 0.493709i | ||||||||
\(531\) | 9.42620e6 | − | 2.58647e7i | 0.0629583 | − | 0.172752i | ||||
\(532\) | 2.87073e6 | 0.0190659 | ||||||||
\(533\) | 7.94305e6i | 0.0524573i | ||||||||
\(534\) | −3.80088e7 | + | 2.15296e8i | −0.249609 | + | 1.41388i | ||||
\(535\) | −1.86242e7 | −0.121623 | ||||||||
\(536\) | 1.02337e6i | 0.00664565i | ||||||||
\(537\) | 1.67401e8 | + | 2.95533e7i | 1.08103 | + | 0.190846i | ||||
\(538\) | 2.41562e8 | 1.55125 | ||||||||
\(539\) | − | 6.23752e6i | − | 0.0398332i | ||||||
\(540\) | −2.26537e7 | − | 1.30980e7i | −0.143866 | − | 0.0831811i | ||||
\(541\) | −1.29534e8 | −0.818070 | −0.409035 | − | 0.912519i | \(-0.634135\pi\) | ||||
−0.409035 | + | 0.912519i | \(0.634135\pi\) | |||||||
\(542\) | 8.76658e7i | 0.550595i | ||||||||
\(543\) | 4.29760e7 | − | 2.43432e8i | 0.268427 | − | 1.52047i | ||||
\(544\) | 7.17873e6 | 0.0445914 | ||||||||
\(545\) | 1.96467e8i | 1.21367i | ||||||||
\(546\) | 5.26191e7 | + | 9.28948e6i | 0.323270 | + | 0.0570707i | ||||
\(547\) | 2.17338e8 | 1.32792 | 0.663962 | − | 0.747766i | \(-0.268874\pi\) | ||||
0.663962 | + | 0.747766i | \(0.268874\pi\) | |||||||
\(548\) | − | 1.02652e7i | − | 0.0623771i | ||||||
\(549\) | −2.76540e8 | − | 1.00783e8i | −1.67125 | − | 0.609074i | ||||
\(550\) | 1.15184e8 | 0.692318 | ||||||||
\(551\) | 9.96125e7i | 0.595469i | ||||||||
\(552\) | −4.27351e7 | + | 2.42068e8i | −0.254079 | + | 1.43920i | ||||
\(553\) | −2.05327e7 | −0.121415 | ||||||||
\(554\) | − | 5.25816e7i | − | 0.309246i | ||||||
\(555\) | −1.83806e8 | − | 3.24495e7i | −1.07518 | − | 0.189815i | ||||
\(556\) | 8.73102e6 | 0.0507973 | ||||||||
\(557\) | 3.69027e7i | 0.213546i | 0.994283 | + | 0.106773i | \(0.0340519\pi\) | ||||
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(558\) | −5.46937e7 | + | 1.50075e8i | −0.314800 | + | 0.863785i | ||||
\(559\) | 1.68880e8 | 0.966812 | ||||||||
\(560\) | 1.13933e8i | 0.648762i | ||||||||
\(561\) | −2.18502e6 | + | 1.23768e7i | −0.0123756 | + | 0.0701001i | ||||
\(562\) | 5.54626e7 | 0.312458 | ||||||||
\(563\) | 1.54676e8i | 0.866758i | 0.901212 | + | 0.433379i | \(0.142679\pi\) | ||||
−0.901212 | + | 0.433379i | \(0.857321\pi\) | |||||||
\(564\) | 1.09018e7 | + | 1.92463e6i | 0.0607661 | + | 0.0107278i | ||||
\(565\) | −2.43022e8 | −1.34741 | ||||||||
\(566\) | − | 9.61583e7i | − | 0.530319i | ||||||
\(567\) | 5.27412e7 | + | 4.43301e7i | 0.289335 | + | 0.243192i | ||||
\(568\) | 1.79669e8 | 0.980456 | ||||||||
\(569\) | − | 9.86395e7i | − | 0.535444i | −0.963496 | − | 0.267722i | \(-0.913729\pi\) | ||
0.963496 | − | 0.267722i | \(-0.0862709\pi\) | |||||||
\(570\) | 3.36009e7 | − | 1.90328e8i | 0.181437 | − | 1.02773i | ||||
\(571\) | −3.30878e8 | −1.77729 | −0.888647 | − | 0.458591i | \(-0.848354\pi\) | ||||
−0.888647 | + | 0.458591i | \(0.848354\pi\) | |||||||
\(572\) | − | 4.15612e6i | − | 0.0222075i | ||||||
\(573\) | 1.59032e8 | + | 2.80757e7i | 0.845316 | + | 0.149234i | ||||
\(574\) | 3.93914e6 | 0.0208289 | ||||||||
\(575\) | − | 6.95177e8i | − | 3.65672i | ||||||
\(576\) | 1.92402e8 | + | 7.01196e7i | 1.00680 | + | 0.366920i | ||||
\(577\) | 3.52498e8 | 1.83497 | 0.917485 | − | 0.397769i | \(-0.130216\pi\) | ||||
0.917485 | + | 0.397769i | \(0.130216\pi\) | |||||||
\(578\) | − | 1.72428e8i | − | 0.892945i | ||||||
\(579\) | 3.23458e7 | − | 1.83219e8i | 0.166641 | − | 0.943918i | ||||
\(580\) | 3.35268e7 | 0.171834 | ||||||||
\(581\) | − | 4.21364e6i | − | 0.0214847i | ||||||
\(582\) | −1.51999e8 | − | 2.68341e7i | −0.771029 | − | 0.136119i | ||||
\(583\) | −1.50526e7 | −0.0759638 | ||||||||
\(584\) | − | 9.02485e7i | − | 0.453108i | ||||||
\(585\) | −1.18254e8 | + | 3.24478e8i | −0.590673 | + | 1.62076i | ||||
\(586\) | 1.44466e8 | 0.717913 | ||||||||
\(587\) | − | 2.05064e7i | − | 0.101386i | −0.998714 | − | 0.0506928i | \(-0.983857\pi\) | ||
0.998714 | − | 0.0506928i | \(-0.0161429\pi\) | |||||||
\(588\) | −442271. | + | 2.50519e6i | −0.00217549 | + | 0.0123228i | ||||
\(589\) | 1.13259e8 | 0.554277 | ||||||||
\(590\) | − | 6.84333e7i | − | 0.333205i | ||||||
\(591\) | −7.88219e7 | − | 1.39154e7i | −0.381843 | − | 0.0674113i | ||||
\(592\) | 1.08024e8 | 0.520660 | ||||||||
\(593\) | 1.11156e8i | 0.533049i | 0.963828 | + | 0.266525i | \(0.0858753\pi\) | ||||
−0.963828 | + | 0.266525i | \(0.914125\pi\) | |||||||
\(594\) | −2.79407e7 | + | 4.83249e7i | −0.133315 | + | 0.230575i | ||||
\(595\) | 3.85616e7 | 0.183064 | ||||||||
\(596\) | 3.03605e7i | 0.143407i | ||||||||
\(597\) | −5.74656e7 | + | 3.25507e8i | −0.270075 | + | 1.52981i | ||||
\(598\) | 2.61280e8 | 1.22181 | ||||||||
\(599\) | 8.38505e7i | 0.390144i | 0.980789 | + | 0.195072i | \(0.0624941\pi\) | ||||
−0.980789 | + | 0.195072i | \(0.937506\pi\) | |||||||
\(600\) | −5.74405e8 | − | 1.01406e8i | −2.65928 | − | 0.469475i | ||||
\(601\) | −3.34851e8 | −1.54251 | −0.771254 | − | 0.636527i | \(-0.780370\pi\) | ||||
−0.771254 | + | 0.636527i | \(0.780370\pi\) | |||||||
\(602\) | − | 8.37514e7i | − | 0.383886i | ||||||
\(603\) | 1.31780e6 | + | 480262.i | 0.00601031 | + | 0.00219041i | ||||
\(604\) | 2.03219e7 | 0.0922260 | ||||||||
\(605\) | − | 3.87462e8i | − | 1.74970i | ||||||
\(606\) | 3.21666e7 | − | 1.82204e8i | 0.144540 | − | 0.818727i | ||||
\(607\) | 1.44195e8 | 0.644737 | 0.322369 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322369 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(608\) | − | 2.26078e7i | − | 0.100588i | ||||||
\(609\) | −8.69284e7 | − | 1.53465e7i | −0.384866 | − | 0.0679450i | ||||
\(610\) | −7.31674e8 | −3.22351 | ||||||||
\(611\) | − | 1.46104e8i | − | 0.640530i | ||||||
\(612\) | 1.75515e6 | − | 4.81599e6i | 0.00765702 | − | 0.0210102i | ||||
\(613\) | −1.68868e8 | −0.733103 | −0.366552 | − | 0.930398i | \(-0.619462\pi\) | ||||
−0.366552 | + | 0.930398i | \(0.619462\pi\) | |||||||
\(614\) | 1.38802e8i | 0.599641i | ||||||||
\(615\) | −4.42632e6 | + | 2.50723e7i | −0.0190291 | + | 0.107788i | ||||
\(616\) | −2.55916e7 | −0.109485 | ||||||||
\(617\) | − | 5.46510e6i | − | 0.0232671i | −0.999932 | − | 0.0116336i | \(-0.996297\pi\) | ||
0.999932 | − | 0.0116336i | \(-0.00370316\pi\) | |||||||
\(618\) | −2.62511e8 | − | 4.63443e7i | −1.11220 | − | 0.196350i | ||||
\(619\) | −5.43333e6 | −0.0229084 | −0.0114542 | − | 0.999934i | \(-0.503646\pi\) | ||||
−0.0114542 | + | 0.999934i | \(0.503646\pi\) | |||||||
\(620\) | − | 3.81198e7i | − | 0.159947i | ||||||
\(621\) | 2.91657e8 | + | 1.68631e8i | 1.21786 | + | 0.704148i | ||||
\(622\) | 3.56964e6 | 0.0148338 | ||||||||
\(623\) | 1.37372e8i | 0.568112i | ||||||||
\(624\) | 3.47490e7 | − | 1.96832e8i | 0.143017 | − | 0.810105i | ||||
\(625\) | 7.70837e8 | 3.15735 | ||||||||
\(626\) | 2.69532e8i | 1.09872i | ||||||||
\(627\) | 3.89778e7 | + | 6.88121e6i | 0.158130 | + | 0.0279166i | ||||
\(628\) | −1.45294e7 | −0.0586637 | ||||||||
\(629\) | − | 3.65616e7i | − | 0.146917i | ||||||
\(630\) | 1.60916e8 | + | 5.86447e7i | 0.643544 | + | 0.234535i | ||||
\(631\) | −3.34903e8 | −1.33300 | −0.666502 | − | 0.745504i | \(-0.732209\pi\) | ||||
−0.666502 | + | 0.745504i | \(0.732209\pi\) | |||||||
\(632\) | 8.42427e7i | 0.333719i | ||||||||
\(633\) | 4.27559e7 | − | 2.42186e8i | 0.168572 | − | 0.954854i | ||||
\(634\) | −1.67389e8 | −0.656837 | ||||||||
\(635\) | 6.73173e8i | 2.62909i | ||||||||
\(636\) | 6.04563e6 | + | 1.06731e6i | 0.0235001 | + | 0.00414876i | ||||
\(637\) | 3.35742e7 | 0.129893 | ||||||||
\(638\) | − | 7.15193e7i | − | 0.275398i | ||||||
\(639\) | 8.43177e7 | − | 2.31361e8i | 0.323159 | − | 0.886721i | ||||
\(640\) | 4.22193e8 | 1.61054 | ||||||||
\(641\) | − | 2.97951e8i | − | 1.13128i | −0.824652 | − | 0.565640i | \(-0.808629\pi\) | ||
0.824652 | − | 0.565640i | \(-0.191371\pi\) | |||||||
\(642\) | 2.81699e6 | − | 1.59565e7i | 0.0106458 | − | 0.0603020i | ||||
\(643\) | 1.78960e8 | 0.673168 | 0.336584 | − | 0.941653i | \(-0.390728\pi\) | ||||
0.336584 | + | 0.941653i | \(0.390728\pi\) | |||||||
\(644\) | 1.24395e7i | 0.0465743i | ||||||||
\(645\) | 5.33071e8 | + | 9.41094e7i | 1.98658 | + | 0.350714i | ||||
\(646\) | 3.78588e7 | 0.140433 | ||||||||
\(647\) | − | 1.91354e8i | − | 0.706519i | −0.935525 | − | 0.353260i | \(-0.885073\pi\) | ||
0.935525 | − | 0.353260i | \(-0.114927\pi\) | |||||||
\(648\) | 1.81880e8 | − | 2.16389e8i | 0.668435 | − | 0.795263i | ||||
\(649\) | 1.40146e7 | 0.0512681 | ||||||||
\(650\) | 6.19993e8i | 2.25760i | ||||||||
\(651\) | −1.74489e7 | + | 9.88373e7i | −0.0632449 | + | 0.358243i | ||||
\(652\) | −2.06315e7 | −0.0744370 | ||||||||
\(653\) | 5.09898e8i | 1.83123i | 0.402053 | + | 0.915616i | \(0.368297\pi\) | ||||
−0.402053 | + | 0.915616i | \(0.631703\pi\) | |||||||
\(654\) | −1.68326e8 | − | 2.97165e7i | −0.601751 | − | 0.106234i | ||||
\(655\) | 4.50658e8 | 1.60370 | ||||||||
\(656\) | − | 1.47351e7i | − | 0.0521965i | ||||||
\(657\) | −1.16214e8 | − | 4.23531e7i | −0.409789 | − | 0.149345i | ||||
\(658\) | −7.24565e7 | −0.254331 | ||||||||
\(659\) | 3.97006e8i | 1.38720i | 0.720358 | + | 0.693602i | \(0.243978\pi\) | ||||
−0.720358 | + | 0.693602i | \(0.756022\pi\) | |||||||
\(660\) | 2.31602e6 | − | 1.31188e7i | 0.00805585 | − | 0.0456313i | ||||
\(661\) | −5.00309e8 | −1.73234 | −0.866172 | − | 0.499746i | \(-0.833427\pi\) | ||||
−0.866172 | + | 0.499746i | \(0.833427\pi\) | |||||||
\(662\) | − | 3.34639e8i | − | 1.15346i | ||||||
\(663\) | −6.66194e7 | − | 1.17611e7i | −0.228592 | − | 0.0403560i | ||||
\(664\) | −1.72880e7 | −0.0590526 | ||||||||
\(665\) | − | 1.21441e8i | − | 0.412952i | ||||||
\(666\) | 5.56031e7 | − | 1.52570e8i | 0.188225 | − | 0.516473i | ||||
\(667\) | −4.31643e8 | −1.45461 | ||||||||
\(668\) | − | 1.36673e7i | − | 0.0458516i | ||||||
\(669\) | −7.68427e7 | + | 4.35266e8i | −0.256640 | + | 1.45371i | ||||
\(670\) | 3.48665e6 | 0.0115927 | ||||||||
\(671\) | − | 1.49841e8i | − | 0.495980i | ||||||
\(672\) | 1.97290e7 | + | 3.48300e6i | 0.0650126 | + | 0.0114775i | ||||
\(673\) | −7.53490e7 | −0.247191 | −0.123595 | − | 0.992333i | \(-0.539442\pi\) | ||||
−0.123595 | + | 0.992333i | \(0.539442\pi\) | |||||||
\(674\) | 1.13026e8i | 0.369148i | ||||||||
\(675\) | −4.00147e8 | + | 6.92075e8i | −1.30109 | + | 2.25031i | ||||
\(676\) | −4.68820e6 | −0.0151763 | ||||||||
\(677\) | − | 5.23910e8i | − | 1.68846i | −0.535982 | − | 0.844229i | \(-0.680059\pi\) | ||
0.535982 | − | 0.844229i | \(-0.319941\pi\) | |||||||
\(678\) | 3.67582e7 | − | 2.08212e8i | 0.117941 | − | 0.668063i | ||||
\(679\) | −9.69842e7 | −0.309807 | ||||||||
\(680\) | − | 1.58212e8i | − | 0.503169i | ||||||
\(681\) | −3.06170e7 | − | 5.40518e6i | −0.0969440 | − | 0.0171147i | ||||
\(682\) | −8.13172e7 | −0.256348 | ||||||||
\(683\) | 4.41828e8i | 1.38673i | 0.720588 | + | 0.693363i | \(0.243872\pi\) | ||||
−0.720588 | + | 0.693363i | \(0.756128\pi\) | |||||||
\(684\) | −1.51668e7 | − | 5.52744e6i | −0.0473943 | − | 0.0172725i | ||||
\(685\) | −4.34249e8 | −1.35104 | ||||||||
\(686\) | − | 1.66502e7i | − | 0.0515759i | ||||||
\(687\) | 7.18974e7 | − | 4.07254e8i | 0.221739 | − | 1.25602i | ||||
\(688\) | −3.13288e8 | −0.962007 | ||||||||
\(689\) | − | 8.10225e7i | − | 0.247713i | ||||||
\(690\) | 8.24734e8 | + | 1.45600e8i | 2.51054 | + | 0.443215i | ||||
\(691\) | −8.95199e7 | −0.271322 | −0.135661 | − | 0.990755i | \(-0.543316\pi\) | ||||
−0.135661 | + | 0.990755i | \(0.543316\pi\) | |||||||
\(692\) | − | 1.78857e7i | − | 0.0539743i | ||||||
\(693\) | −1.20100e7 | + | 3.29544e7i | −0.0360864 | + | 0.0990180i | ||||
\(694\) | 3.97562e8 | 1.18940 | ||||||||
\(695\) | − | 3.69349e8i | − | 1.10023i | ||||||
\(696\) | −6.29644e7 | + | 3.56654e8i | −0.186753 | + | 1.05784i | ||||
\(697\) | −4.98722e6 | −0.0147286 | ||||||||
\(698\) | − | 3.17546e8i | − | 0.933770i | ||||||
\(699\) | 4.29194e8 | + | 7.57708e7i | 1.25667 | + | 0.221856i | ||||
\(700\) | −2.95178e7 | −0.0860578 | ||||||||
\(701\) | 1.38394e8i | 0.401758i | 0.979616 | + | 0.200879i | \(0.0643798\pi\) | ||||
−0.979616 | + | 0.200879i | \(0.935620\pi\) | |||||||
\(702\) | −2.60114e8 | − | 1.50394e8i | −0.751887 | − | 0.434730i | ||||
\(703\) | −1.15142e8 | −0.331412 | ||||||||
\(704\) | 1.04252e8i | 0.298790i | ||||||||
\(705\) | 8.14176e7 | − | 4.61180e8i | 0.232354 | − | 1.31614i | ||||
\(706\) | −2.94997e8 | −0.838308 | ||||||||
\(707\) | − | 1.16257e8i | − | 0.328973i | ||||||
\(708\) | −5.62873e6 | − | 993707.i | −0.0158603 | − | 0.00280000i | ||||
\(709\) | 5.08724e8 | 1.42739 | 0.713697 | − | 0.700455i | \(-0.247019\pi\) | ||||
0.713697 | + | 0.700455i | \(0.247019\pi\) | |||||||
\(710\) | − | 6.12138e8i | − | 1.71031i | ||||||
\(711\) | 1.08480e8 | + | 3.95347e7i | 0.301815 | + | 0.109994i | ||||
\(712\) | 5.63617e8 | 1.56151 | ||||||||
\(713\) | 4.90777e8i | 1.35399i | ||||||||
\(714\) | −5.83261e6 | + | 3.30381e7i | −0.0160239 | + | 0.0907654i | ||||
\(715\) | −1.75816e8 | −0.480996 | ||||||||
\(716\) | − | 3.52948e7i | − | 0.0961549i | ||||||
\(717\) | −3.77049e8 | − | 6.65650e7i | −1.02292 | − | 0.180588i | ||||
\(718\) | −6.65244e8 | −1.79725 | ||||||||
\(719\) | 3.91102e8i | 1.05221i | 0.850419 | + | 0.526106i | \(0.176349\pi\) | ||||
−0.850419 | + | 0.526106i | \(0.823651\pi\) | |||||||
\(720\) | 2.19372e8 | − | 6.01938e8i | 0.587737 | − | 1.61270i | ||||
\(721\) | −1.67498e8 | −0.446893 | ||||||||
\(722\) | 2.40278e8i | 0.638415i | ||||||||
\(723\) | −3.21713e6 | + | 1.82230e7i | −0.00851243 | + | 0.0482176i | ||||
\(724\) | −5.13251e7 | −0.135243 | ||||||||
\(725\) | − | 1.02425e9i | − | 2.68777i | ||||||
\(726\) | 3.31963e8 | + | 5.86053e7i | 0.867520 | + | 0.153154i | ||||
\(727\) | 8.62324e7 | 0.224423 | 0.112211 | − | 0.993684i | \(-0.464207\pi\) | ||||
0.112211 | + | 0.993684i | \(0.464207\pi\) | |||||||
\(728\) | − | 1.37750e8i | − | 0.357023i | ||||||
\(729\) | −1.93290e8 | − | 3.35758e8i | −0.498916 | − | 0.866650i | ||||
\(730\) | −3.07480e8 | −0.790402 | ||||||||
\(731\) | 1.06035e8i | 0.271454i | ||||||||
\(732\) | −1.06245e7 | + | 6.01812e7i | −0.0270879 | + | 0.153436i | ||||
\(733\) | −4.58012e7 | −0.116296 | −0.0581481 | − | 0.998308i | \(-0.518520\pi\) | ||||
−0.0581481 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(734\) | − | 3.48498e8i | − | 0.881276i | ||||||
\(735\) | 1.05977e8 | + | 1.87094e7i | 0.266901 | + | 0.0471193i | ||||
\(736\) | 9.79645e7 | 0.245717 | ||||||||
\(737\) | 714041.i | 0.00178369i | ||||||||
\(738\) | −2.08115e7 | − | 7.58460e6i | −0.0517768 | − | 0.0188697i | ||||
\(739\) | 2.96288e8 | 0.734143 | 0.367071 | − | 0.930193i | \(-0.380360\pi\) | ||||
0.367071 | + | 0.930193i | \(0.380360\pi\) | |||||||
\(740\) | 3.87537e7i | 0.0956352i | ||||||||
\(741\) | −3.70389e7 | + | 2.09802e8i | −0.0910340 | + | 0.515651i | ||||
\(742\) | −4.01809e7 | −0.0983577 | ||||||||
\(743\) | 6.59062e8i | 1.60679i | 0.595444 | + | 0.803397i | \(0.296976\pi\) | ||||
−0.595444 | + | 0.803397i | \(0.703024\pi\) | |||||||
\(744\) | 4.05515e8 | + | 7.15903e7i | 0.984663 | + | 0.173834i | ||||
\(745\) | 1.28434e9 | 3.10608 | ||||||||
\(746\) | 6.99673e8i | 1.68531i | ||||||||
\(747\) | −8.11314e6 | + | 2.22618e7i | −0.0194638 | + | 0.0534070i | ||||
\(748\) | 2.60951e6 | 0.00623526 | ||||||||
\(749\) | − | 1.01812e7i | − | 0.0242300i | ||||||
\(750\) | −2.12580e8 | + | 1.20414e9i | −0.503894 | + | 2.85425i | ||||
\(751\) | 1.44730e8 | 0.341694 | 0.170847 | − | 0.985298i | \(-0.445350\pi\) | ||||
0.170847 | + | 0.985298i | \(0.445350\pi\) | |||||||
\(752\) | 2.71037e8i | 0.637346i | ||||||||
\(753\) | −6.55478e8 | − | 1.15719e8i | −1.53523 | − | 0.271032i | ||||
\(754\) | 3.84961e8 | 0.898054 | ||||||||
\(755\) | − | 8.59679e8i | − | 1.99754i | ||||||
\(756\) | 7.16024e6 | − | 1.23840e7i | 0.0165715 | − | 0.0286613i | ||||
\(757\) | −4.17266e8 | −0.961890 | −0.480945 | − | 0.876751i | \(-0.659706\pi\) | ||||
−0.480945 | + | 0.876751i | \(0.659706\pi\) | |||||||
\(758\) | − | 4.23096e8i | − | 0.971473i | ||||||
\(759\) | −2.98178e7 | + | 1.68899e8i | −0.0681947 | + | 0.386280i | ||||
\(760\) | −4.98253e8 | −1.13504 | ||||||||
\(761\) | − | 5.60980e8i | − | 1.27290i | −0.771319 | − | 0.636448i | \(-0.780403\pi\) | ||
0.771319 | − | 0.636448i | \(-0.219597\pi\) | |||||||
\(762\) | −5.76749e8 | − | 1.01820e8i | −1.30353 | − | 0.230128i | ||||
\(763\) | −1.07402e8 | −0.241790 | ||||||||
\(764\) | − | 3.35301e7i | − | 0.0751891i | ||||||
\(765\) | −2.03731e8 | − | 7.42482e7i | −0.455064 | − | 0.165845i | ||||
\(766\) | 1.14595e8 | 0.254965 | ||||||||
\(767\) | 7.54354e7i | 0.167182i | ||||||||
\(768\) | 2.05313e7 | − | 1.16297e8i | 0.0453245 | − | 0.256735i | ||||
\(769\) | −3.01884e8 | −0.663836 | −0.331918 | − | 0.943308i | \(-0.607696\pi\) | ||||
−0.331918 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(770\) | 8.71915e7i | 0.190986i | ||||||||
\(771\) | 4.58098e8 | + | 8.08735e7i | 0.999529 | + | 0.176459i | ||||
\(772\) | −3.86298e7 | −0.0839595 | ||||||||
\(773\) | 5.60059e8i | 1.21254i | 0.795260 | + | 0.606268i | \(0.207334\pi\) | ||||
−0.795260 | + | 0.606268i | \(0.792666\pi\) | |||||||
\(774\) | −1.61259e8 | + | 4.42481e8i | −0.347776 | + | 0.954270i | ||||
\(775\) | −1.16457e9 | −2.50184 | ||||||||
\(776\) | 3.97912e8i | 0.851533i | ||||||||
\(777\) | 1.77391e7 | − | 1.00481e8i | 0.0378153 | − | 0.214200i | ||||
\(778\) | 2.97868e8 | 0.632535 | ||||||||
\(779\) | 1.57061e7i | 0.0332243i | ||||||||
\(780\) | 7.06136e7 | + | 1.24663e7i | 0.148801 | + | 0.0262695i | ||||
\(781\) | 1.25361e8 | 0.263154 | ||||||||
\(782\) | 1.64051e8i | 0.343050i | ||||||||
\(783\) | 4.29717e8 | + | 2.48456e8i | 0.895153 | + | 0.517563i | ||||
\(784\) | −6.22832e7 | −0.129248 | ||||||||
\(785\) | 6.14640e8i | 1.27061i | ||||||||
\(786\) | −6.81640e7 | + | 3.86107e8i | −0.140374 | + | 0.795133i | ||||
\(787\) | 6.20839e8 | 1.27366 | 0.636832 | − | 0.771003i | \(-0.280245\pi\) | ||||
0.636832 | + | 0.771003i | \(0.280245\pi\) | |||||||
\(788\) | 1.66188e7i | 0.0339641i | ||||||||
\(789\) | −5.55092e8 | − | 9.79969e7i | −1.13014 | − | 0.199518i | ||||
\(790\) | 2.87018e8 | 0.582140 | ||||||||
\(791\) | − | 1.32852e8i | − | 0.268435i | ||||||
\(792\) | 1.35207e8 | + | 4.92752e7i | 0.272160 | + | 0.0991866i | ||||
\(793\) | 8.06539e8 | 1.61736 | ||||||||
\(794\) | 1.16919e8i | 0.233573i | ||||||||
\(795\) | 4.51504e7 | − | 2.55749e8i | 0.0898586 | − | 0.508993i | ||||
\(796\) | 6.86297e7 | 0.136073 | ||||||||
\(797\) | − | 4.34439e8i | − | 0.858131i | −0.903273 | − | 0.429066i | \(-0.858843\pi\) | ||
0.903273 | − | 0.429066i | \(-0.141157\pi\) | |||||||
\(798\) | 1.04046e8 | + | 1.83685e7i | 0.204746 | + | 0.0361463i | ||||
\(799\) | 9.17349e7 | 0.179843 | ||||||||
\(800\) | 2.32461e8i | 0.454024i | ||||||||
\(801\) | 2.64502e8 | − | 7.25773e8i | 0.514674 | − | 1.41222i | ||||
\(802\) | 1.30127e8 | 0.252257 | ||||||||
\(803\) | − | 6.29696e7i | − | 0.121614i | ||||||
\(804\) | 50629.0 | − | 286782.i | 9.74163e−5 | − | 0.000551803i | ||||
\(805\) | 5.26230e8 | 1.00876 | ||||||||
\(806\) | − | 4.37699e8i | − | 0.835931i | ||||||
\(807\) | −8.40512e8 | − | 1.48386e8i | −1.59928 | − | 0.282339i | ||||
\(808\) | −4.76984e8 | −0.904211 | ||||||||
\(809\) | 5.94722e8i | 1.12323i | 0.827399 | + | 0.561615i | \(0.189820\pi\) | ||||
−0.827399 | + | 0.561615i | \(0.810180\pi\) | |||||||
\(810\) | −7.37246e8 | − | 6.19671e8i | −1.38726 | − | 1.16602i | ||||
\(811\) | 6.85167e8 | 1.28450 | 0.642250 | − | 0.766495i | \(-0.278001\pi\) | ||||
0.642250 | + | 0.766495i | \(0.278001\pi\) | |||||||
\(812\) | 1.83279e7i | 0.0342331i | ||||||||
\(813\) | 5.38509e7 | − | 3.05032e8i | 0.100212 | − | 0.567641i | ||||
\(814\) | 8.26693e7 | 0.153275 | ||||||||
\(815\) | 8.72778e8i | 1.61224i | ||||||||
\(816\) | 1.23585e8 | + | 2.18180e7i | 0.227455 | + | 0.0401554i | ||||
\(817\) | 3.33933e8 | 0.612340 | ||||||||
\(818\) | 9.05914e7i | 0.165511i | ||||||||
\(819\) | −1.77381e8 | − | 6.46452e7i | −0.322891 | − | 0.117675i | ||||
\(820\) | 5.28624e6 | 0.00958750 | ||||||||
\(821\) | − | 7.16117e8i | − | 1.29406i | −0.762465 | − | 0.647030i | \(-0.776011\pi\) | ||
0.762465 | − | 0.647030i | \(-0.223989\pi\) | |||||||
\(822\) | 6.56821e7 | − | 3.72048e8i | 0.118258 | − | 0.669860i | ||||
\(823\) | 3.75859e8 | 0.674257 | 0.337129 | − | 0.941459i | \(-0.390544\pi\) | ||||
0.337129 | + | 0.941459i | \(0.390544\pi\) | |||||||
\(824\) | 6.87219e8i | 1.22833i | ||||||||
\(825\) | −4.00782e8 | − | 7.07549e7i | −0.713751 | − | 0.126007i | ||||
\(826\) | 3.74102e7 | 0.0663818 | ||||||||
\(827\) | − | 1.04498e8i | − | 0.184752i | −0.995724 | − | 0.0923761i | \(-0.970554\pi\) | ||
0.995724 | − | 0.0923761i | \(-0.0294462\pi\) | |||||||
\(828\) | 2.39516e7 | − | 6.57213e7i | 0.0421933 | − | 0.115775i | ||||
\(829\) | −4.87724e8 | −0.856073 | −0.428036 | − | 0.903761i | \(-0.640795\pi\) | ||||
−0.428036 | + | 0.903761i | \(0.640795\pi\) | |||||||
\(830\) | 5.89007e7i | 0.103012i | ||||||||
\(831\) | −3.22995e7 | + | 1.82957e8i | −0.0562851 | + | 0.318820i | ||||
\(832\) | −5.61149e8 | −0.974334 | ||||||||
\(833\) | 2.10803e7i | 0.0364705i | ||||||||
\(834\) | 3.16444e8 | + | 5.58657e7i | 0.545506 | + | 0.0963046i | ||||
\(835\) | −5.78171e8 | −0.993109 | ||||||||
\(836\) | − | 8.21805e6i | − | 0.0140653i | ||||||
\(837\) | 2.82493e8 | − | 4.88587e8i | 0.481761 | − | 0.833231i | ||||
\(838\) | −3.25753e8 | −0.553549 | ||||||||
\(839\) | − | 6.05421e8i | − | 1.02511i | −0.858654 | − | 0.512556i | \(-0.828699\pi\) | ||
0.858654 | − | 0.512556i | \(-0.171301\pi\) | |||||||
\(840\) | 7.67620e7 | − | 4.34809e8i | 0.129511 | − | 0.733602i | ||||
\(841\) | −4.11442e7 | −0.0691704 | ||||||||
\(842\) | − | 4.24505e8i | − | 0.711126i | ||||||
\(843\) | −1.92981e8 | − | 3.40693e7i | −0.322131 | − | 0.0568696i | ||||
\(844\) | −5.10623e7 | −0.0849323 | ||||||||
\(845\) | 1.98325e8i | 0.328706i | ||||||||
\(846\) | 3.82807e8 | + | 1.39511e8i | 0.632220 | + | 0.230408i | ||||
\(847\) | 2.11812e8 | 0.348579 | ||||||||
\(848\) | 1.50304e8i | 0.246481i | ||||||||
\(849\) | −5.90677e7 | + | 3.34581e8i | −0.0965221 | + | 0.546737i | ||||
\(850\) | −3.89277e8 | −0.633873 | ||||||||
\(851\) | − | 4.98937e8i | − | 0.809575i | ||||||
\(852\) | −5.03492e7 | − | 8.88875e6i | −0.0814093 | − | 0.0143721i | ||||
\(853\) | 1.02486e9 | 1.65126 | 0.825630 | − | 0.564212i | \(-0.190820\pi\) | ||||
0.825630 | + | 0.564212i | \(0.190820\pi\) | |||||||
\(854\) | − | 3.99981e8i | − | 0.642194i | ||||||
\(855\) | −2.33828e8 | + | 6.41604e8i | −0.374108 | + | 1.02652i | ||||
\(856\) | −4.17719e7 | −0.0665982 | ||||||||
\(857\) | − | 8.50926e8i | − | 1.35191i | −0.736941 | − | 0.675957i | \(-0.763730\pi\) | ||
0.736941 | − | 0.675957i | \(-0.236270\pi\) | |||||||
\(858\) | 2.65930e7 | − | 1.50633e8i | 0.0421023 | − | 0.238483i | ||||
\(859\) | −4.93728e7 | −0.0778947 | −0.0389474 | − | 0.999241i | \(-0.512400\pi\) | ||||
−0.0389474 | + | 0.999241i | \(0.512400\pi\) | |||||||
\(860\) | − | 1.12392e8i | − | 0.176702i | ||||||
\(861\) | −1.37062e7 | − | 2.41972e6i | −0.0214737 | − | 0.00379101i | ||||
\(862\) | 1.78295e8 | 0.278367 | ||||||||
\(863\) | − | 2.86202e8i | − | 0.445288i | −0.974900 | − | 0.222644i | \(-0.928531\pi\) | ||
0.974900 | − | 0.222644i | \(-0.0714687\pi\) | |||||||
\(864\) | −9.75273e7 | − | 5.63888e7i | −0.151212 | − | 0.0874282i | ||||
\(865\) | −7.56619e8 | −1.16904 | ||||||||
\(866\) | − | 7.63323e8i | − | 1.17532i | ||||||
\(867\) | −1.05918e8 | + | 5.99961e8i | −0.162523 | + | 0.920589i | ||||
\(868\) | 2.08388e7 | 0.0318650 | ||||||||
\(869\) | 5.87791e7i | 0.0895702i | ||||||||
\(870\) | 1.21513e9 | + | 2.14522e8i | 1.84530 | + | 0.325772i | ||||
\(871\) | −3.84341e6 | −0.00581650 | ||||||||
\(872\) | 4.40654e8i | 0.664581i | ||||||||
\(873\) | 5.12393e8 | + | 1.86738e8i | 0.770124 | + | 0.280666i | ||||
\(874\) | 5.16640e8 | 0.773844 | ||||||||
\(875\) | 7.68311e8i | 1.14687i | ||||||||
\(876\) | −4.46486e6 | + | 2.52906e7i | −0.00664194 | + | 0.0376225i | ||||
\(877\) | −1.10070e9 | −1.63181 | −0.815907 | − | 0.578183i | \(-0.803762\pi\) | ||||
−0.815907 | + | 0.578183i | \(0.803762\pi\) | |||||||
\(878\) | 6.10390e8i | 0.901829i | ||||||||
\(879\) | −5.02666e8 | − | 8.87416e7i | −0.740138 | − | 0.130665i | ||||
\(880\) | 3.26156e8 | 0.478605 | ||||||||
\(881\) | 4.55028e8i | 0.665442i | 0.943025 | + | 0.332721i | \(0.107967\pi\) | ||||
−0.943025 | + | 0.332721i | \(0.892033\pi\) | |||||||
\(882\) | −3.20591e7 | + | 8.79674e7i | −0.0467245 | + | 0.128208i | ||||
\(883\) | −1.13638e7 | −0.0165059 | −0.00825297 | − | 0.999966i | \(-0.502627\pi\) | ||||
−0.00825297 | + | 0.999966i | \(0.502627\pi\) | |||||||
\(884\) | 1.40460e7i | 0.0203327i | ||||||||
\(885\) | −4.20369e7 | + | 2.38113e8i | −0.0606458 | + | 0.343521i | ||||
\(886\) | 1.20315e8 | 0.172989 | ||||||||
\(887\) | − | 7.74742e8i | − | 1.11016i | −0.831796 | − | 0.555081i | \(-0.812687\pi\) | ||
0.831796 | − | 0.555081i | \(-0.187313\pi\) | |||||||
\(888\) | −4.12257e8 | − | 7.27807e7i | −0.588748 | − | 0.103939i | ||||
\(889\) | −3.68001e8 | −0.523773 | ||||||||
\(890\) | − | 1.92026e9i | − | 2.72390i | ||||||
\(891\) | 1.26904e8 | − | 1.50982e8i | 0.179408 | − | 0.213449i | ||||
\(892\) | 9.17713e7 | 0.129304 | ||||||||
\(893\) | − | 2.88898e8i | − | 0.405686i | ||||||
\(894\) | −1.94263e8 | + | 1.10038e9i | −0.271880 | + | 1.54003i | ||||
\(895\) | −1.49308e9 | −2.08264 | ||||||||
\(896\) | 2.30798e8i | 0.320855i | ||||||||
\(897\) | −9.09121e8 | − | 1.60498e8i | −1.25963 | − | 0.222378i | ||||
\(898\) | 7.56154e8 | 1.04419 | ||||||||
\(899\) | 7.23093e8i | 0.995211i | ||||||||
\(900\) | 1.55950e8 | + | 5.68349e7i | 0.213924 | + | 0.0779629i | ||||
\(901\) | 5.08718e7 | 0.0695509 | ||||||||
\(902\) | − | 1.12766e7i | − | 0.0153659i | ||||||
\(903\) | −5.14464e7 | + | 2.91412e8i | −0.0698701 | + | 0.395771i | ||||
\(904\) | −5.45072e8 | −0.737816 | ||||||||
\(905\) | 2.17121e9i | 2.92925i | ||||||||
\(906\) | 7.36540e8 | + | 1.30030e8i | 0.990403 | + | 0.174848i | ||||
\(907\) | 5.02274e8 | 0.673161 | 0.336581 | − | 0.941655i | \(-0.390730\pi\) | ||||
0.336581 | + | 0.941655i | \(0.390730\pi\) | |||||||
\(908\) | 6.45527e6i | 0.00862296i | ||||||||
\(909\) | −2.23846e8 | + | 6.14215e8i | −0.298029 | + | 0.817766i | ||||
\(910\) | −4.69318e8 | −0.622792 | ||||||||
\(911\) | 4.84534e8i | 0.640869i | 0.947271 | + | 0.320434i | \(0.103829\pi\) | ||||
−0.947271 | + | 0.320434i | \(0.896171\pi\) | |||||||
\(912\) | 6.87107e7 | − | 3.89203e8i | 0.0905815 | − | 0.513088i | ||||
\(913\) | −1.20624e7 | −0.0158497 | ||||||||
\(914\) | 8.94036e8i | 1.17089i | ||||||||
\(915\) | 2.54585e9 | + | 4.49449e8i | 3.32330 | + | 0.586702i | ||||
\(916\) | −8.58652e7 | −0.111720 | ||||||||
\(917\) | 2.46359e8i | 0.319493i | ||||||||
\(918\) | 9.44283e7 | − | 1.63319e8i | 0.122060 | − | 0.211109i | ||||
\(919\) | −6.90401e7 | −0.0889518 | −0.0444759 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444759 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(920\) | − | 2.15904e9i | − | 2.77267i | ||||||
\(921\) | 8.52628e7 | − | 4.82961e8i | 0.109139 | − | 0.618206i | ||||
\(922\) | 2.02811e8 | 0.258761 | ||||||||
\(923\) | 6.74772e8i | 0.858128i | ||||||||
\(924\) | 7.17162e6 | + | 1.26609e6i | 0.00909078 | + | 0.00160490i | ||||
\(925\) | 1.18393e9 | 1.49590 | ||||||||
\(926\) | 1.01138e9i | 1.27374i | ||||||||
\(927\) | 8.84937e8 | + | 3.22508e8i | 1.11089 | + | 0.404857i | ||||
\(928\) | 1.44337e8 | 0.180607 | ||||||||
\(929\) | − | 6.54937e8i | − | 0.816868i | −0.912788 | − | 0.408434i | \(-0.866075\pi\) | ||
0.912788 | − | 0.408434i | \(-0.133925\pi\) | |||||||
\(930\) | 2.43911e8 | − | 1.38160e9i | 0.303237 | − | 1.71765i | ||||
\(931\) | 6.63875e7 | 0.0822692 | ||||||||
\(932\) | − | 9.04911e7i | − | 0.111778i | ||||||
\(933\) | −1.24205e7 | − | 2.19274e6i | −0.0152931 | − | 0.00269987i | ||||
\(934\) | −2.93082e8 | −0.359707 | ||||||||
\(935\) | − | 1.10390e8i | − | 0.135051i | ||||||
\(936\) | −2.65230e8 | + | 7.27768e8i | −0.323441 | + | 0.887494i | ||||
\(937\) | −9.35425e6 | −0.0113708 | −0.00568539 | − | 0.999984i | \(-0.501810\pi\) | ||||
−0.00568539 | + | 0.999984i | \(0.501810\pi\) | |||||||
\(938\) | 1.90603e6i | 0.00230952i | ||||||||
\(939\) | 1.65567e8 | − | 9.37834e8i | 0.199976 | − | 1.13274i | ||||
\(940\) | −9.72349e7 | −0.117068 | ||||||||
\(941\) | − | 6.78408e8i | − | 0.814184i | −0.913387 | − | 0.407092i | \(-0.866543\pi\) | ||
0.913387 | − | 0.407092i | \(-0.133457\pi\) | |||||||
\(942\) | −5.26600e8 | − | 9.29670e7i | −0.629982 | − | 0.111218i | ||||
\(943\) | −6.80581e7 | −0.0811605 | ||||||||
\(944\) | − | 1.39940e8i | − | 0.166351i | ||||||
\(945\) | −5.23882e8 | − | 3.02900e8i | −0.620780 | − | 0.358925i | ||||
\(946\) | −2.39755e8 | −0.283201 | ||||||||
\(947\) | − | 5.91553e8i | − | 0.696536i | −0.937395 | − | 0.348268i | \(-0.886770\pi\) | ||
0.937395 | − | 0.348268i | \(-0.113230\pi\) | |||||||
\(948\) | 4.16773e6 | − | 2.36076e7i | 0.00489187 | − | 0.0277094i | ||||
\(949\) | 3.38941e8 | 0.396575 | ||||||||
\(950\) | 1.22594e9i | 1.42987i | ||||||||
\(951\) | 5.82426e8 | + | 1.02823e8i | 0.677172 | + | 0.119549i | ||||
\(952\) | 8.64893e7 | 0.100242 | ||||||||
\(953\) | 2.85033e8i | 0.329319i | 0.986350 | + | 0.164659i | \(0.0526525\pi\) | ||||
−0.986350 | + | 0.164659i | \(0.947348\pi\) | |||||||
\(954\) | 2.12287e8 | + | 7.73662e7i | 0.244499 | + | 0.0891059i | ||||
\(955\) | −1.41843e9 | −1.62853 | ||||||||
\(956\) | 7.94968e7i | 0.0909863i | ||||||||
\(957\) | −4.39325e7 | + | 2.48850e8i | −0.0501245 | + | 0.283924i | ||||
\(958\) | −1.57520e9 | −1.79159 | ||||||||
\(959\) | − | 2.37389e8i | − | 0.269157i | ||||||
\(960\) | −1.77127e9 | − | 3.12704e8i | −2.00204 | − | 0.353443i | ||||
\(961\) | −6.53497e7 | −0.0736331 | ||||||||
\(962\) | 4.44977e8i | 0.499818i | ||||||||
\(963\) | −1.96033e7 | + | 5.37899e7i | −0.0219508 | + | 0.0602313i | ||||
\(964\) | 3.84213e6 | 0.00428886 | ||||||||
\(965\) | 1.63416e9i | 1.81849i | ||||||||
\(966\) | −7.95946e7 | + | 4.50854e8i | −0.0882983 | + | 0.500155i | ||||
\(967\) | −4.63129e7 | −0.0512180 | −0.0256090 | − | 0.999672i | \(-0.508152\pi\) | ||||
−0.0256090 | + | 0.999672i | \(0.508152\pi\) | |||||||
\(968\) | − | 8.69034e8i | − | 0.958099i | ||||||
\(969\) | −1.31729e8 | − | 2.32557e7i | −0.144781 | − | 0.0255599i | ||||
\(970\) | 1.35570e9 | 1.48542 | ||||||||
\(971\) | − | 2.13841e8i | − | 0.233578i | −0.993157 | − | 0.116789i | \(-0.962740\pi\) | ||
0.993157 | − | 0.116789i | \(-0.0372602\pi\) | |||||||
\(972\) | −6.16742e7 | + | 5.16413e7i | −0.0671591 | + | 0.0562340i | ||||
\(973\) | 2.01911e8 | 0.219190 | ||||||||
\(974\) | − | 8.67465e8i | − | 0.938804i | ||||||
\(975\) | 3.80846e8 | − | 2.15726e9i | 0.410900 | − | 2.32749i | ||||
\(976\) | −1.49621e9 | −1.60932 | ||||||||
\(977\) | − | 1.17477e9i | − | 1.25971i | −0.776715 | − | 0.629853i | \(-0.783115\pi\) | ||
0.776715 | − | 0.629853i | \(-0.216885\pi\) | |||||||
\(978\) | −7.47763e8 | − | 1.32011e8i | −0.799369 | − | 0.141122i | ||||
\(979\) | 3.93255e8 | 0.419109 | ||||||||
\(980\) | − | 2.23442e7i | − | 0.0237403i | ||||||
\(981\) | 5.67432e8 | + | 2.06796e8i | 0.601045 | + | 0.219046i | ||||
\(982\) | −8.96903e8 | −0.947133 | ||||||||
\(983\) | 1.03034e8i | 0.108473i | 0.998528 | + | 0.0542364i | \(0.0172725\pi\) | ||||
−0.998528 | + | 0.0542364i | \(0.982728\pi\) | |||||||
\(984\) | −9.92774e6 | + | 5.62344e7i | −0.0104199 | + | 0.0590224i | ||||
\(985\) | 7.03026e8 | 0.735635 | ||||||||
\(986\) | 2.41706e8i | 0.252149i | ||||||||
\(987\) | 2.52111e8 | + | 4.45082e7i | 0.262205 | + | 0.0462902i | ||||
\(988\) | 4.42346e7 | 0.0458661 | ||||||||
\(989\) | 1.44700e9i | 1.49583i | ||||||||
\(990\) | 1.67882e8 | − | 4.60656e8i | 0.173021 | − | 0.474756i | ||||
\(991\) | 7.91671e7 | 0.0813437 | 0.0406718 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406718 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(992\) | − | 1.64111e8i | − | 0.168114i | ||||||
\(993\) | −2.05561e8 | + | 1.16437e9i | −0.209939 | + | 1.18917i | ||||
\(994\) | 3.34635e8 | 0.340732 | ||||||||
\(995\) | − | 2.90325e9i | − | 2.94723i | ||||||
\(996\) | 4.84466e6 | + | 855286.i | 0.00490326 | + | 0.000865632i | ||||
\(997\) | −3.55491e8 | −0.358709 | −0.179355 | − | 0.983784i | \(-0.557401\pi\) | ||||
−0.179355 | + | 0.983784i | \(0.557401\pi\) | |||||||
\(998\) | − | 1.45411e9i | − | 1.46287i | ||||||
\(999\) | −2.87190e8 | + | 4.96711e8i | −0.288054 | + | 0.498204i |
(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 | 21.7.b.a.8.4 | ✓ | 12 | |
3.2 | odd | 2 | inner | 21.7.b.a.8.9 | yes | 12 | |
4.3 | odd | 2 | 336.7.d.a.113.7 | 12 | |||
7.6 | odd | 2 | 147.7.b.b.50.4 | 12 | |||
12.11 | even | 2 | 336.7.d.a.113.8 | 12 | |||
21.20 | even | 2 | 147.7.b.b.50.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.7.b.a.8.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
21.7.b.a.8.9 | yes | 12 | 3.2 | odd | 2 | inner | |
147.7.b.b.50.4 | 12 | 7.6 | odd | 2 | |||
147.7.b.b.50.9 | 12 | 21.20 | even | 2 | |||
336.7.d.a.113.7 | 12 | 4.3 | odd | 2 | |||
336.7.d.a.113.8 | 12 | 12.11 | even | 2 |