Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), 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: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 10424 x^{18} + 44844916 x^{16} + 103219343022 x^{14} + 138101513095620 x^{12} + \cdots + 73\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 11^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(44.9177i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.43 |
Dual form | 74.7.d.b.31.9 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | + | 4.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | − | 47.9177i | − | 1.77473i | −0.461069 | − | 0.887364i | \(-0.652534\pi\) | ||
0.461069 | − | 0.887364i | \(-0.347466\pi\) | |||||||
\(4\) | − | 32.0000i | − | 0.500000i | ||||||
\(5\) | 99.4727 | + | 99.4727i | 0.795781 | + | 0.795781i | 0.982427 | − | 0.186646i | \(-0.0597617\pi\) |
−0.186646 | + | 0.982427i | \(0.559762\pi\) | |||||||
\(6\) | 191.671 | + | 191.671i | 0.887364 | + | 0.887364i | ||||
\(7\) | 584.317 | 1.70355 | 0.851775 | − | 0.523908i | \(-0.175527\pi\) | ||||
0.851775 | + | 0.523908i | \(0.175527\pi\) | |||||||
\(8\) | 128.000 | + | 128.000i | 0.250000 | + | 0.250000i | ||||
\(9\) | −1567.10 | −2.14966 | ||||||||
\(10\) | −795.781 | −0.795781 | ||||||||
\(11\) | 2321.43i | 1.74413i | 0.489393 | + | 0.872064i | \(0.337219\pi\) | ||||
−0.489393 | + | 0.872064i | \(0.662781\pi\) | |||||||
\(12\) | −1533.37 | −0.887364 | ||||||||
\(13\) | 510.323 | + | 510.323i | 0.232282 | + | 0.232282i | 0.813645 | − | 0.581363i | \(-0.197480\pi\) |
−0.581363 | + | 0.813645i | \(0.697480\pi\) | |||||||
\(14\) | −2337.27 | + | 2337.27i | −0.851775 | + | 0.851775i | ||||
\(15\) | 4766.50 | − | 4766.50i | 1.41230 | − | 1.41230i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | 2288.22 | + | 2288.22i | 0.465749 | + | 0.465749i | 0.900534 | − | 0.434785i | \(-0.143176\pi\) |
−0.434785 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(18\) | 6268.42 | − | 6268.42i | 1.07483 | − | 1.07483i | ||||
\(19\) | 4480.83 | + | 4480.83i | 0.653277 | + | 0.653277i | 0.953781 | − | 0.300504i | \(-0.0971547\pi\) |
−0.300504 | + | 0.953781i | \(0.597155\pi\) | |||||||
\(20\) | 3183.12 | − | 3183.12i | 0.397891 | − | 0.397891i | ||||
\(21\) | − | 27999.1i | − | 3.02334i | ||||||
\(22\) | −9285.73 | − | 9285.73i | −0.872064 | − | 0.872064i | ||||
\(23\) | 6697.16 | + | 6697.16i | 0.550437 | + | 0.550437i | 0.926567 | − | 0.376130i | \(-0.122745\pi\) |
−0.376130 | + | 0.926567i | \(0.622745\pi\) | |||||||
\(24\) | 6133.46 | − | 6133.46i | 0.443682 | − | 0.443682i | ||||
\(25\) | 4164.62i | 0.266535i | ||||||||
\(26\) | −4082.59 | −0.232282 | ||||||||
\(27\) | 40160.0i | 2.04034i | ||||||||
\(28\) | − | 18698.2i | − | 0.851775i | ||||||
\(29\) | −9387.24 | + | 9387.24i | −0.384897 | + | 0.384897i | −0.872863 | − | 0.487966i | \(-0.837739\pi\) |
0.487966 | + | 0.872863i | \(0.337739\pi\) | |||||||
\(30\) | 38132.0i | 1.41230i | ||||||||
\(31\) | 37480.5 | − | 37480.5i | 1.25811 | − | 1.25811i | 0.306121 | − | 0.951993i | \(-0.400969\pi\) |
0.951993 | − | 0.306121i | \(-0.0990312\pi\) | |||||||
\(32\) | 4096.00 | − | 4096.00i | 0.125000 | − | 0.125000i | ||||
\(33\) | 111238. | 3.09535 | ||||||||
\(34\) | −18305.8 | −0.465749 | ||||||||
\(35\) | 58123.6 | + | 58123.6i | 1.35565 | + | 1.35565i | ||||
\(36\) | 50147.3i | 1.07483i | ||||||||
\(37\) | −50508.9 | + | 3817.73i | −0.997156 | + | 0.0753703i | ||||
\(38\) | −35846.6 | −0.653277 | ||||||||
\(39\) | 24453.5 | − | 24453.5i | 0.412237 | − | 0.412237i | ||||
\(40\) | 25465.0i | 0.397891i | ||||||||
\(41\) | − | 20314.8i | − | 0.294754i | −0.989080 | − | 0.147377i | \(-0.952917\pi\) | ||
0.989080 | − | 0.147377i | \(-0.0470831\pi\) | |||||||
\(42\) | 111997. | + | 111997.i | 1.51167 | + | 1.51167i | ||||
\(43\) | −32203.7 | − | 32203.7i | −0.405042 | − | 0.405042i | 0.474963 | − | 0.880006i | \(-0.342461\pi\) |
−0.880006 | + | 0.474963i | \(0.842461\pi\) | |||||||
\(44\) | 74285.9 | 0.872064 | ||||||||
\(45\) | −155884. | − | 155884.i | −1.71066 | − | 1.71066i | ||||
\(46\) | −53577.3 | −0.550437 | ||||||||
\(47\) | −180149. | −1.73515 | −0.867577 | − | 0.497303i | \(-0.834324\pi\) | ||||
−0.867577 | + | 0.497303i | \(0.834324\pi\) | |||||||
\(48\) | 49067.7i | 0.443682i | ||||||||
\(49\) | 223778. | 1.90208 | ||||||||
\(50\) | −16658.5 | − | 16658.5i | −0.133268 | − | 0.133268i | ||||
\(51\) | 109646. | − | 109646.i | 0.826577 | − | 0.826577i | ||||
\(52\) | 16330.3 | − | 16330.3i | 0.116141 | − | 0.116141i | ||||
\(53\) | 84857.9 | 0.569987 | 0.284993 | − | 0.958530i | \(-0.408009\pi\) | ||||
0.284993 | + | 0.958530i | \(0.408009\pi\) | |||||||
\(54\) | −160640. | − | 160640.i | −1.02017 | − | 1.02017i | ||||
\(55\) | −230919. | + | 230919.i | −1.38794 | + | 1.38794i | ||||
\(56\) | 74792.6 | + | 74792.6i | 0.425887 | + | 0.425887i | ||||
\(57\) | 214711. | − | 214711.i | 1.15939 | − | 1.15939i | ||||
\(58\) | − | 75098.0i | − | 0.384897i | ||||||
\(59\) | −157289. | − | 157289.i | −0.765846 | − | 0.765846i | 0.211526 | − | 0.977372i | \(-0.432157\pi\) |
−0.977372 | + | 0.211526i | \(0.932157\pi\) | |||||||
\(60\) | −152528. | − | 152528.i | −0.706148 | − | 0.706148i | ||||
\(61\) | 227937. | − | 227937.i | 1.00421 | − | 1.00421i | 0.00422274 | − | 0.999991i | \(-0.498656\pi\) |
0.999991 | − | 0.00422274i | \(-0.00134414\pi\) | |||||||
\(62\) | 299844.i | 1.25811i | ||||||||
\(63\) | −915686. | −3.66206 | ||||||||
\(64\) | 32768.0i | 0.125000i | ||||||||
\(65\) | 101526.i | 0.369691i | ||||||||
\(66\) | −444951. | + | 444951.i | −1.54768 | + | 1.54768i | ||||
\(67\) | 125717.i | 0.417995i | 0.977916 | + | 0.208997i | \(0.0670200\pi\) | ||||
−0.977916 | + | 0.208997i | \(0.932980\pi\) | |||||||
\(68\) | 73223.1 | − | 73223.1i | 0.232874 | − | 0.232874i | ||||
\(69\) | 320912. | − | 320912.i | 0.976876 | − | 0.976876i | ||||
\(70\) | −464989. | −1.35565 | ||||||||
\(71\) | 376847. | 1.05291 | 0.526454 | − | 0.850204i | \(-0.323521\pi\) | ||||
0.526454 | + | 0.850204i | \(0.323521\pi\) | |||||||
\(72\) | −200589. | − | 200589.i | −0.537416 | − | 0.537416i | ||||
\(73\) | − | 163197.i | − | 0.419511i | −0.977754 | − | 0.209755i | \(-0.932733\pi\) | ||
0.977754 | − | 0.209755i | \(-0.0672667\pi\) | |||||||
\(74\) | 186765. | − | 217307.i | 0.460893 | − | 0.536263i | ||||
\(75\) | 199559. | 0.473028 | ||||||||
\(76\) | 143386. | − | 143386.i | 0.326639 | − | 0.326639i | ||||
\(77\) | 1.35645e6i | 2.97121i | ||||||||
\(78\) | 195628.i | 0.412237i | ||||||||
\(79\) | −109373. | − | 109373.i | −0.221834 | − | 0.221834i | 0.587436 | − | 0.809270i | \(-0.300137\pi\) |
−0.809270 | + | 0.587436i | \(0.800137\pi\) | |||||||
\(80\) | −101860. | − | 101860.i | −0.198945 | − | 0.198945i | ||||
\(81\) | 781955. | 1.47139 | ||||||||
\(82\) | 81259.0 | + | 81259.0i | 0.147377 | + | 0.147377i | ||||
\(83\) | −431565. | −0.754766 | −0.377383 | − | 0.926057i | \(-0.623176\pi\) | ||||
−0.377383 | + | 0.926057i | \(0.623176\pi\) | |||||||
\(84\) | −895972. | −1.51167 | ||||||||
\(85\) | 455231.i | 0.741268i | ||||||||
\(86\) | 257630. | 0.405042 | ||||||||
\(87\) | 449815. | + | 449815.i | 0.683087 | + | 0.683087i | ||||
\(88\) | −297143. | + | 297143.i | −0.436032 | + | 0.436032i | ||||
\(89\) | −579015. | + | 579015.i | −0.821333 | + | 0.821333i | −0.986299 | − | 0.164966i | \(-0.947249\pi\) |
0.164966 | + | 0.986299i | \(0.447249\pi\) | |||||||
\(90\) | 1.24707e6 | 1.71066 | ||||||||
\(91\) | 298191. | + | 298191.i | 0.395704 | + | 0.395704i | ||||
\(92\) | 214309. | − | 214309.i | 0.275218 | − | 0.275218i | ||||
\(93\) | −1.79598e6 | − | 1.79598e6i | −2.23281 | − | 2.23281i | ||||
\(94\) | 720596. | − | 720596.i | 0.867577 | − | 0.867577i | ||||
\(95\) | 891440.i | 1.03973i | ||||||||
\(96\) | −196271. | − | 196271.i | −0.221841 | − | 0.221841i | ||||
\(97\) | 865584. | + | 865584.i | 0.948405 | + | 0.948405i | 0.998733 | − | 0.0503277i | \(-0.0160266\pi\) |
−0.0503277 | + | 0.998733i | \(0.516027\pi\) | |||||||
\(98\) | −895112. | + | 895112.i | −0.951040 | + | 0.951040i | ||||
\(99\) | − | 3.63793e6i | − | 3.74928i | ||||||
\(100\) | 133268. | 0.133268 | ||||||||
\(101\) | 514075.i | 0.498956i | 0.968380 | + | 0.249478i | \(0.0802590\pi\) | ||||
−0.968380 | + | 0.249478i | \(0.919741\pi\) | |||||||
\(102\) | 877171.i | 0.826577i | ||||||||
\(103\) | −170638. | + | 170638.i | −0.156158 | + | 0.156158i | −0.780862 | − | 0.624704i | \(-0.785220\pi\) |
0.624704 | + | 0.780862i | \(0.285220\pi\) | |||||||
\(104\) | 130643.i | 0.116141i | ||||||||
\(105\) | 2.78515e6 | − | 2.78515e6i | 2.40592 | − | 2.40592i | ||||
\(106\) | −339432. | + | 339432.i | −0.284993 | + | 0.284993i | ||||
\(107\) | 75819.8 | 0.0618916 | 0.0309458 | − | 0.999521i | \(-0.490148\pi\) | ||||
0.0309458 | + | 0.999521i | \(0.490148\pi\) | |||||||
\(108\) | 1.28512e6 | 1.02017 | ||||||||
\(109\) | −1.12474e6 | − | 1.12474e6i | −0.868509 | − | 0.868509i | 0.123798 | − | 0.992307i | \(-0.460492\pi\) |
−0.992307 | + | 0.123798i | \(0.960492\pi\) | |||||||
\(110\) | − | 1.84735e6i | − | 1.38794i | ||||||
\(111\) | 182937. | + | 2.42027e6i | 0.133762 | + | 1.76968i | ||||
\(112\) | −598341. | −0.425887 | ||||||||
\(113\) | 1.23966e6 | − | 1.23966e6i | 0.859149 | − | 0.859149i | −0.132089 | − | 0.991238i | \(-0.542169\pi\) |
0.991238 | + | 0.132089i | \(0.0421685\pi\) | |||||||
\(114\) | 1.71769e6i | 1.15939i | ||||||||
\(115\) | 1.33237e6i | 0.876054i | ||||||||
\(116\) | 300392. | + | 300392.i | 0.192448 | + | 0.192448i | ||||
\(117\) | −799730. | − | 799730.i | −0.499328 | − | 0.499328i | ||||
\(118\) | 1.25831e6 | 0.765846 | ||||||||
\(119\) | 1.33705e6 | + | 1.33705e6i | 0.793426 | + | 0.793426i | ||||
\(120\) | 1.22022e6 | 0.706148 | ||||||||
\(121\) | −3.61749e6 | −2.04198 | ||||||||
\(122\) | 1.82350e6i | 1.00421i | ||||||||
\(123\) | −973436. | −0.523109 | ||||||||
\(124\) | −1.19937e6 | − | 1.19937e6i | −0.629057 | − | 0.629057i | ||||
\(125\) | 1.13999e6 | − | 1.13999e6i | 0.583677 | − | 0.583677i | ||||
\(126\) | 3.66275e6 | − | 3.66275e6i | 1.83103 | − | 1.83103i | ||||
\(127\) | 27525.2 | 0.0134375 | 0.00671876 | − | 0.999977i | \(-0.497861\pi\) | ||||
0.00671876 | + | 0.999977i | \(0.497861\pi\) | |||||||
\(128\) | −131072. | − | 131072.i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −1.54313e6 | + | 1.54313e6i | −0.718840 | + | 0.718840i | ||||
\(130\) | −406106. | − | 406106.i | −0.184846 | − | 0.184846i | ||||
\(131\) | 620017. | − | 620017.i | 0.275797 | − | 0.275797i | −0.555631 | − | 0.831429i | \(-0.687523\pi\) |
0.831429 | + | 0.555631i | \(0.187523\pi\) | |||||||
\(132\) | − | 3.55961e6i | − | 1.54768i | ||||||
\(133\) | 2.61823e6 | + | 2.61823e6i | 1.11289 | + | 1.11289i | ||||
\(134\) | −502869. | − | 502869.i | −0.208997 | − | 0.208997i | ||||
\(135\) | −3.99482e6 | + | 3.99482e6i | −1.62366 | + | 1.62366i | ||||
\(136\) | 585785.i | 0.232874i | ||||||||
\(137\) | 3.33029e6 | 1.29515 | 0.647575 | − | 0.762001i | \(-0.275783\pi\) | ||||
0.647575 | + | 0.762001i | \(0.275783\pi\) | |||||||
\(138\) | 2.56730e6i | 0.976876i | ||||||||
\(139\) | 3.44670e6i | 1.28339i | 0.766959 | + | 0.641696i | \(0.221769\pi\) | ||||
−0.766959 | + | 0.641696i | \(0.778231\pi\) | |||||||
\(140\) | 1.85996e6 | − | 1.85996e6i | 0.677826 | − | 0.677826i | ||||
\(141\) | 8.63232e6i | 3.07943i | ||||||||
\(142\) | −1.50739e6 | + | 1.50739e6i | −0.526454 | + | 0.526454i | ||||
\(143\) | −1.18468e6 | + | 1.18468e6i | −0.405129 | + | 0.405129i | ||||
\(144\) | 1.60471e6 | 0.537416 | ||||||||
\(145\) | −1.86755e6 | −0.612587 | ||||||||
\(146\) | 652787. | + | 652787.i | 0.209755 | + | 0.209755i | ||||
\(147\) | − | 1.07229e7i | − | 3.37568i | ||||||
\(148\) | 122167. | + | 1.61629e6i | 0.0376852 | + | 0.498578i | ||||
\(149\) | −865567. | −0.261663 | −0.130831 | − | 0.991405i | \(-0.541765\pi\) | ||||
−0.130831 | + | 0.991405i | \(0.541765\pi\) | |||||||
\(150\) | −798235. | + | 798235.i | −0.236514 | + | 0.236514i | ||||
\(151\) | − | 3.89833e6i | − | 1.13226i | −0.824315 | − | 0.566132i | \(-0.808439\pi\) | ||
0.824315 | − | 0.566132i | \(-0.191561\pi\) | |||||||
\(152\) | 1.14709e6i | 0.326639i | ||||||||
\(153\) | −3.58588e6 | − | 3.58588e6i | −1.00120 | − | 1.00120i | ||||
\(154\) | −5.42582e6 | − | 5.42582e6i | −1.48560 | − | 1.48560i | ||||
\(155\) | 7.45656e6 | 2.00237 | ||||||||
\(156\) | −782512. | − | 782512.i | −0.206119 | − | 0.206119i | ||||
\(157\) | −6.01870e6 | −1.55526 | −0.777631 | − | 0.628721i | \(-0.783579\pi\) | ||||
−0.777631 | + | 0.628721i | \(0.783579\pi\) | |||||||
\(158\) | 874984. | 0.221834 | ||||||||
\(159\) | − | 4.06619e6i | − | 1.01157i | ||||||
\(160\) | 814880. | 0.198945 | ||||||||
\(161\) | 3.91327e6 | + | 3.91327e6i | 0.937696 | + | 0.937696i | ||||
\(162\) | −3.12782e6 | + | 3.12782e6i | −0.735693 | + | 0.735693i | ||||
\(163\) | −1.57647e6 | + | 1.57647e6i | −0.364017 | + | 0.364017i | −0.865290 | − | 0.501272i | \(-0.832865\pi\) |
0.501272 | + | 0.865290i | \(0.332865\pi\) | |||||||
\(164\) | −650072. | −0.147377 | ||||||||
\(165\) | 1.10651e7 | + | 1.10651e7i | 2.46322 | + | 2.46322i | ||||
\(166\) | 1.72626e6 | − | 1.72626e6i | 0.377383 | − | 0.377383i | ||||
\(167\) | −1.97250e6 | − | 1.97250e6i | −0.423514 | − | 0.423514i | 0.462897 | − | 0.886412i | \(-0.346810\pi\) |
−0.886412 | + | 0.462897i | \(0.846810\pi\) | |||||||
\(168\) | 3.58389e6 | − | 3.58389e6i | 0.755835 | − | 0.755835i | ||||
\(169\) | − | 4.30595e6i | − | 0.892090i | ||||||
\(170\) | −1.82092e6 | − | 1.82092e6i | −0.370634 | − | 0.370634i | ||||
\(171\) | −7.02192e6 | − | 7.02192e6i | −1.40433 | − | 1.40433i | ||||
\(172\) | −1.03052e6 | + | 1.03052e6i | −0.202521 | + | 0.202521i | ||||
\(173\) | − | 2.54782e6i | − | 0.492074i | −0.969260 | − | 0.246037i | \(-0.920871\pi\) | ||
0.969260 | − | 0.246037i | \(-0.0791285\pi\) | |||||||
\(174\) | −3.59852e6 | −0.683087 | ||||||||
\(175\) | 2.43346e6i | 0.454056i | ||||||||
\(176\) | − | 2.37715e6i | − | 0.436032i | ||||||
\(177\) | −7.53691e6 | + | 7.53691e6i | −1.35917 | + | 1.35917i | ||||
\(178\) | − | 4.63212e6i | − | 0.821333i | ||||||
\(179\) | 3.78571e6 | − | 3.78571e6i | 0.660067 | − | 0.660067i | −0.295328 | − | 0.955396i | \(-0.595429\pi\) |
0.955396 | + | 0.295328i | \(0.0954291\pi\) | |||||||
\(180\) | −4.98829e6 | + | 4.98829e6i | −0.855331 | + | 0.855331i | ||||
\(181\) | −365638. | −0.0616616 | −0.0308308 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308308 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(182\) | −2.38553e6 | −0.395704 | ||||||||
\(183\) | −1.09222e7 | − | 1.09222e7i | −1.78221 | − | 1.78221i | ||||
\(184\) | 1.71447e6i | 0.275218i | ||||||||
\(185\) | −5.40402e6 | − | 4.64450e6i | −0.853496 | − | 0.733539i | ||||
\(186\) | 1.43678e7 | 2.23281 | ||||||||
\(187\) | −5.31196e6 | + | 5.31196e6i | −0.812325 | + | 0.812325i | ||||
\(188\) | 5.76476e6i | 0.867577i | ||||||||
\(189\) | 2.34662e7i | 3.47582i | ||||||||
\(190\) | −3.56576e6 | − | 3.56576e6i | −0.519866 | − | 0.519866i | ||||
\(191\) | 2.17096e6 | + | 2.17096e6i | 0.311567 | + | 0.311567i | 0.845517 | − | 0.533949i | \(-0.179293\pi\) |
−0.533949 | + | 0.845517i | \(0.679293\pi\) | |||||||
\(192\) | 1.57017e6 | 0.221841 | ||||||||
\(193\) | −5.00770e6 | − | 5.00770e6i | −0.696573 | − | 0.696573i | 0.267097 | − | 0.963670i | \(-0.413936\pi\) |
−0.963670 | + | 0.267097i | \(0.913936\pi\) | |||||||
\(194\) | −6.92467e6 | −0.948405 | ||||||||
\(195\) | 4.86491e6 | 0.656102 | ||||||||
\(196\) | − | 7.16089e6i | − | 0.951040i | ||||||
\(197\) | 1.16858e7 | 1.52847 | 0.764237 | − | 0.644936i | \(-0.223116\pi\) | ||||
0.764237 | + | 0.644936i | \(0.223116\pi\) | |||||||
\(198\) | 1.45517e7 | + | 1.45517e7i | 1.87464 | + | 1.87464i | ||||
\(199\) | −5.16119e6 | + | 5.16119e6i | −0.654924 | + | 0.654924i | −0.954174 | − | 0.299251i | \(-0.903263\pi\) |
0.299251 | + | 0.954174i | \(0.403263\pi\) | |||||||
\(200\) | −533071. | + | 533071.i | −0.0666339 | + | 0.0666339i | ||||
\(201\) | 6.02408e6 | 0.741827 | ||||||||
\(202\) | −2.05630e6 | − | 2.05630e6i | −0.249478 | − | 0.249478i | ||||
\(203\) | −5.48513e6 | + | 5.48513e6i | −0.655690 | + | 0.655690i | ||||
\(204\) | −3.50868e6 | − | 3.50868e6i | −0.413289 | − | 0.413289i | ||||
\(205\) | 2.02076e6 | − | 2.02076e6i | 0.234560 | − | 0.234560i | ||||
\(206\) | − | 1.36511e6i | − | 0.156158i | ||||||
\(207\) | −1.04951e7 | − | 1.04951e7i | −1.18325 | − | 1.18325i | ||||
\(208\) | −522571. | − | 522571.i | −0.0580705 | − | 0.0580705i | ||||
\(209\) | −1.04019e7 | + | 1.04019e7i | −1.13940 | + | 1.13940i | ||||
\(210\) | 2.22812e7i | 2.40592i | ||||||||
\(211\) | 1.32797e7 | 1.41365 | 0.706825 | − | 0.707388i | \(-0.250127\pi\) | ||||
0.706825 | + | 0.707388i | \(0.250127\pi\) | |||||||
\(212\) | − | 2.71545e6i | − | 0.284993i | ||||||
\(213\) | − | 1.80576e7i | − | 1.86863i | ||||||
\(214\) | −303279. | + | 303279.i | −0.0309458 | + | 0.0309458i | ||||
\(215\) | − | 6.40678e6i | − | 0.644650i | ||||||
\(216\) | −5.14048e6 | + | 5.14048e6i | −0.510085 | + | 0.510085i | ||||
\(217\) | 2.19005e7 | − | 2.19005e7i | 2.14326 | − | 2.14326i | ||||
\(218\) | 8.99796e6 | 0.868509 | ||||||||
\(219\) | −7.82001e6 | −0.744517 | ||||||||
\(220\) | 7.38941e6 | + | 7.38941e6i | 0.693972 | + | 0.693972i | ||||
\(221\) | 2.33547e6i | 0.216370i | ||||||||
\(222\) | −1.04128e7 | − | 8.94933e6i | −0.951721 | − | 0.817960i | ||||
\(223\) | 1.23019e7 | 1.10932 | 0.554659 | − | 0.832078i | \(-0.312849\pi\) | ||||
0.554659 | + | 0.832078i | \(0.312849\pi\) | |||||||
\(224\) | 2.39336e6 | − | 2.39336e6i | 0.212944 | − | 0.212944i | ||||
\(225\) | − | 6.52639e6i | − | 0.572961i | ||||||
\(226\) | 9.91731e6i | 0.859149i | ||||||||
\(227\) | −1.21261e7 | − | 1.21261e7i | −1.03668 | − | 1.03668i | −0.999301 | − | 0.0373797i | \(-0.988099\pi\) |
−0.0373797 | − | 0.999301i | \(-0.511901\pi\) | |||||||
\(228\) | −6.87075e6 | − | 6.87075e6i | −0.579695 | − | 0.579695i | ||||
\(229\) | 1.06403e7 | 0.886026 | 0.443013 | − | 0.896515i | \(-0.353910\pi\) | ||||
0.443013 | + | 0.896515i | \(0.353910\pi\) | |||||||
\(230\) | −5.32947e6 | − | 5.32947e6i | −0.438027 | − | 0.438027i | ||||
\(231\) | 6.49981e7 | 5.27309 | ||||||||
\(232\) | −2.40313e6 | −0.192448 | ||||||||
\(233\) | 2.08290e6i | 0.164665i | 0.996605 | + | 0.0823326i | \(0.0262370\pi\) | ||||
−0.996605 | + | 0.0823326i | \(0.973763\pi\) | |||||||
\(234\) | 6.39784e6 | 0.499328 | ||||||||
\(235\) | −1.79199e7 | − | 1.79199e7i | −1.38080 | − | 1.38080i | ||||
\(236\) | −5.03324e6 | + | 5.03324e6i | −0.382923 | + | 0.382923i | ||||
\(237\) | −5.24090e6 | + | 5.24090e6i | −0.393696 | + | 0.393696i | ||||
\(238\) | −1.06964e7 | −0.793426 | ||||||||
\(239\) | 1.20833e6 | + | 1.20833e6i | 0.0885103 | + | 0.0885103i | 0.749976 | − | 0.661465i | \(-0.230065\pi\) |
−0.661465 | + | 0.749976i | \(0.730065\pi\) | |||||||
\(240\) | −4.88089e6 | + | 4.88089e6i | −0.353074 | + | 0.353074i | ||||
\(241\) | −8.60535e6 | − | 8.60535e6i | −0.614777 | − | 0.614777i | 0.329410 | − | 0.944187i | \(-0.393150\pi\) |
−0.944187 | + | 0.329410i | \(0.893150\pi\) | |||||||
\(242\) | 1.44700e7 | − | 1.44700e7i | 1.02099 | − | 1.02099i | ||||
\(243\) | − | 8.19284e6i | − | 0.570973i | ||||||
\(244\) | −7.29400e6 | − | 7.29400e6i | −0.502107 | − | 0.502107i | ||||
\(245\) | 2.22598e7 | + | 2.22598e7i | 1.51364 | + | 1.51364i | ||||
\(246\) | 3.89374e6 | − | 3.89374e6i | 0.261554 | − | 0.261554i | ||||
\(247\) | 4.57334e6i | 0.303489i | ||||||||
\(248\) | 9.59500e6 | 0.629057 | ||||||||
\(249\) | 2.06796e7i | 1.33950i | ||||||||
\(250\) | 9.11996e6i | 0.583677i | ||||||||
\(251\) | −8.57273e6 | + | 8.57273e6i | −0.542123 | + | 0.542123i | −0.924151 | − | 0.382028i | \(-0.875226\pi\) |
0.382028 | + | 0.924151i | \(0.375226\pi\) | |||||||
\(252\) | 2.93020e7i | 1.83103i | ||||||||
\(253\) | −1.55470e7 | + | 1.55470e7i | −0.960031 | + | 0.960031i | ||||
\(254\) | −110101. | + | 110101.i | −0.00671876 | + | 0.00671876i | ||||
\(255\) | 2.18136e7 | 1.31555 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 7.88320e6 | + | 7.88320e6i | 0.464412 | + | 0.464412i | 0.900098 | − | 0.435687i | \(-0.143494\pi\) |
−0.435687 | + | 0.900098i | \(0.643494\pi\) | |||||||
\(258\) | − | 1.23450e7i | − | 0.718840i | ||||||
\(259\) | −2.95132e7 | + | 2.23077e6i | −1.69870 | + | 0.128397i | ||||
\(260\) | 3.24885e6 | 0.184846 | ||||||||
\(261\) | 1.47108e7 | − | 1.47108e7i | 0.827398 | − | 0.827398i | ||||
\(262\) | 4.96014e6i | 0.275797i | ||||||||
\(263\) | − | 2.38221e7i | − | 1.30952i | −0.755836 | − | 0.654761i | \(-0.772769\pi\) | ||
0.755836 | − | 0.654761i | \(-0.227231\pi\) | |||||||
\(264\) | 1.42384e7 | + | 1.42384e7i | 0.773838 | + | 0.773838i | ||||
\(265\) | 8.44104e6 | + | 8.44104e6i | 0.453585 | + | 0.453585i | ||||
\(266\) | −2.09458e7 | −1.11289 | ||||||||
\(267\) | 2.77450e7 | + | 2.77450e7i | 1.45764 | + | 1.45764i | ||||
\(268\) | 4.02296e6 | 0.208997 | ||||||||
\(269\) | 2.57738e7 | 1.32410 | 0.662050 | − | 0.749460i | \(-0.269687\pi\) | ||||
0.662050 | + | 0.749460i | \(0.269687\pi\) | |||||||
\(270\) | − | 3.19586e7i | − | 1.62366i | ||||||
\(271\) | −3.04399e7 | −1.52945 | −0.764724 | − | 0.644358i | \(-0.777125\pi\) | ||||
−0.764724 | + | 0.644358i | \(0.777125\pi\) | |||||||
\(272\) | −2.34314e6 | − | 2.34314e6i | −0.116437 | − | 0.116437i | ||||
\(273\) | 1.42886e7 | − | 1.42886e7i | 0.702267 | − | 0.702267i | ||||
\(274\) | −1.33212e7 | + | 1.33212e7i | −0.647575 | + | 0.647575i | ||||
\(275\) | −9.66788e6 | −0.464872 | ||||||||
\(276\) | −1.02692e7 | − | 1.02692e7i | −0.488438 | − | 0.488438i | ||||
\(277\) | −1.44072e7 | + | 1.44072e7i | −0.677859 | + | 0.677859i | −0.959515 | − | 0.281656i | \(-0.909116\pi\) |
0.281656 | + | 0.959515i | \(0.409116\pi\) | |||||||
\(278\) | −1.37868e7 | − | 1.37868e7i | −0.641696 | − | 0.641696i | ||||
\(279\) | −5.87358e7 | + | 5.87358e7i | −2.70452 | + | 2.70452i | ||||
\(280\) | 1.48796e7i | 0.677826i | ||||||||
\(281\) | 7.31677e6 | + | 7.31677e6i | 0.329762 | + | 0.329762i | 0.852496 | − | 0.522734i | \(-0.175088\pi\) |
−0.522734 | + | 0.852496i | \(0.675088\pi\) | |||||||
\(282\) | −3.45293e7 | − | 3.45293e7i | −1.53971 | − | 1.53971i | ||||
\(283\) | −9.61950e6 | + | 9.61950e6i | −0.424417 | + | 0.424417i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.462304 | + | 0.886721i | \(0.347023\pi\) | |||||||
\(284\) | − | 1.20591e7i | − | 0.526454i | ||||||
\(285\) | 4.27157e7 | 1.84524 | ||||||||
\(286\) | − | 9.47745e6i | − | 0.405129i | ||||||
\(287\) | − | 1.18703e7i | − | 0.502128i | ||||||
\(288\) | −6.41886e6 | + | 6.41886e6i | −0.268708 | + | 0.268708i | ||||
\(289\) | − | 1.36656e7i | − | 0.566157i | ||||||
\(290\) | 7.47019e6 | − | 7.47019e6i | 0.306294 | − | 0.306294i | ||||
\(291\) | 4.14768e7 | − | 4.14768e7i | 1.68316 | − | 1.68316i | ||||
\(292\) | −5.22230e6 | −0.209755 | ||||||||
\(293\) | −4.24413e7 | −1.68727 | −0.843637 | − | 0.536913i | \(-0.819590\pi\) | ||||
−0.843637 | + | 0.536913i | \(0.819590\pi\) | |||||||
\(294\) | 4.28917e7 | + | 4.28917e7i | 1.68784 | + | 1.68784i | ||||
\(295\) | − | 3.12919e7i | − | 1.21889i | ||||||
\(296\) | −6.95381e6 | − | 5.97647e6i | −0.268131 | − | 0.230446i | ||||
\(297\) | −9.32288e7 | −3.55861 | ||||||||
\(298\) | 3.46227e6 | − | 3.46227e6i | 0.130831 | − | 0.130831i | ||||
\(299\) | 6.83544e6i | 0.255713i | ||||||||
\(300\) | − | 6.38588e6i | − | 0.236514i | ||||||
\(301\) | −1.88172e7 | − | 1.88172e7i | −0.690010 | − | 0.690010i | ||||
\(302\) | 1.55933e7 | + | 1.55933e7i | 0.566132 | + | 0.566132i | ||||
\(303\) | 2.46333e7 | 0.885512 | ||||||||
\(304\) | −4.58837e6 | − | 4.58837e6i | −0.163319 | − | 0.163319i | ||||
\(305\) | 4.53471e7 | 1.59827 | ||||||||
\(306\) | 2.86871e7 | 1.00120 | ||||||||
\(307\) | 3.80818e7i | 1.31614i | 0.752956 | + | 0.658070i | \(0.228627\pi\) | ||||
−0.752956 | + | 0.658070i | \(0.771373\pi\) | |||||||
\(308\) | 4.34065e7 | 1.48560 | ||||||||
\(309\) | 8.17658e6 | + | 8.17658e6i | 0.277138 | + | 0.277138i | ||||
\(310\) | −2.98262e7 | + | 2.98262e7i | −1.00118 | + | 1.00118i | ||||
\(311\) | −1.60757e6 | + | 1.60757e6i | −0.0534427 | + | 0.0534427i | −0.733323 | − | 0.679880i | \(-0.762032\pi\) |
0.679880 | + | 0.733323i | \(0.262032\pi\) | |||||||
\(312\) | 6.26010e6 | 0.206119 | ||||||||
\(313\) | −3.70086e7 | − | 3.70086e7i | −1.20690 | − | 1.20690i | −0.972027 | − | 0.234868i | \(-0.924534\pi\) |
−0.234868 | − | 0.972027i | \(-0.575466\pi\) | |||||||
\(314\) | 2.40748e7 | − | 2.40748e7i | 0.777631 | − | 0.777631i | ||||
\(315\) | −9.10857e7 | − | 9.10857e7i | −2.91420 | − | 2.91420i | ||||
\(316\) | −3.49993e6 | + | 3.49993e6i | −0.110917 | + | 0.110917i | ||||
\(317\) | − | 2.84100e7i | − | 0.891853i | −0.895070 | − | 0.445926i | \(-0.852874\pi\) | ||
0.895070 | − | 0.445926i | \(-0.147126\pi\) | |||||||
\(318\) | 1.62648e7 | + | 1.62648e7i | 0.505786 | + | 0.505786i | ||||
\(319\) | −2.17919e7 | − | 2.17919e7i | −0.671309 | − | 0.671309i | ||||
\(320\) | −3.25952e6 | + | 3.25952e6i | −0.0994727 | + | 0.0994727i | ||||
\(321\) | − | 3.63311e6i | − | 0.109841i | ||||||
\(322\) | −3.13061e7 | −0.937696 | ||||||||
\(323\) | 2.05063e7i | 0.608526i | ||||||||
\(324\) | − | 2.50226e7i | − | 0.735693i | ||||||
\(325\) | −2.12530e6 | + | 2.12530e6i | −0.0619114 | + | 0.0619114i | ||||
\(326\) | − | 1.26117e7i | − | 0.364017i | ||||||
\(327\) | −5.38952e7 | + | 5.38952e7i | −1.54137 | + | 1.54137i | ||||
\(328\) | 2.60029e6 | − | 2.60029e6i | 0.0736885 | − | 0.0736885i | ||||
\(329\) | −1.05264e8 | −2.95592 | ||||||||
\(330\) | −8.85209e7 | −2.46322 | ||||||||
\(331\) | 2.49851e7 | + | 2.49851e7i | 0.688964 | + | 0.688964i | 0.962003 | − | 0.273039i | \(-0.0880288\pi\) |
−0.273039 | + | 0.962003i | \(0.588029\pi\) | |||||||
\(332\) | 1.38101e7i | 0.377383i | ||||||||
\(333\) | 7.91527e7 | − | 5.98278e6i | 2.14355 | − | 0.162021i | ||||
\(334\) | 1.57800e7 | 0.423514 | ||||||||
\(335\) | −1.25054e7 | + | 1.25054e7i | −0.332632 | + | 0.332632i | ||||
\(336\) | 2.86711e7i | 0.755835i | ||||||||
\(337\) | 2.50890e7i | 0.655530i | 0.944759 | + | 0.327765i | \(0.106296\pi\) | ||||
−0.944759 | + | 0.327765i | \(0.893704\pi\) | |||||||
\(338\) | 1.72238e7 | + | 1.72238e7i | 0.446045 | + | 0.446045i | ||||
\(339\) | −5.94018e7 | − | 5.94018e7i | −1.52476 | − | 1.52476i | ||||
\(340\) | 1.45674e7 | 0.370634 | ||||||||
\(341\) | 8.70084e7 | + | 8.70084e7i | 2.19431 | + | 2.19431i | ||||
\(342\) | 5.61754e7 | 1.40433 | ||||||||
\(343\) | 6.20130e7 | 1.53674 | ||||||||
\(344\) | − | 8.24415e6i | − | 0.202521i | ||||||
\(345\) | 6.38440e7 | 1.55476 | ||||||||
\(346\) | 1.01913e7 | + | 1.01913e7i | 0.246037 | + | 0.246037i | ||||
\(347\) | −2.63783e7 | + | 2.63783e7i | −0.631333 | + | 0.631333i | −0.948402 | − | 0.317069i | \(-0.897301\pi\) |
0.317069 | + | 0.948402i | \(0.397301\pi\) | |||||||
\(348\) | 1.43941e7 | − | 1.43941e7i | 0.341544 | − | 0.341544i | ||||
\(349\) | 8.57236e6 | 0.201662 | 0.100831 | − | 0.994904i | \(-0.467850\pi\) | ||||
0.100831 | + | 0.994904i | \(0.467850\pi\) | |||||||
\(350\) | −9.73383e6 | − | 9.73383e6i | −0.227028 | − | 0.227028i | ||||
\(351\) | −2.04946e7 | + | 2.04946e7i | −0.473934 | + | 0.473934i | ||||
\(352\) | 9.50859e6 | + | 9.50859e6i | 0.218016 | + | 0.218016i | ||||
\(353\) | 3.50606e7 | − | 3.50606e7i | 0.797069 | − | 0.797069i | −0.185564 | − | 0.982632i | \(-0.559411\pi\) |
0.982632 | + | 0.185564i | \(0.0594111\pi\) | |||||||
\(354\) | − | 6.02953e7i | − | 1.35917i | ||||||
\(355\) | 3.74860e7 | + | 3.74860e7i | 0.837884 | + | 0.837884i | ||||
\(356\) | 1.85285e7 | + | 1.85285e7i | 0.410667 | + | 0.410667i | ||||
\(357\) | 6.40683e7 | − | 6.40683e7i | 1.40812 | − | 1.40812i | ||||
\(358\) | 3.02857e7i | 0.660067i | ||||||||
\(359\) | −6.23917e7 | −1.34848 | −0.674239 | − | 0.738513i | \(-0.735528\pi\) | ||||
−0.674239 | + | 0.738513i | \(0.735528\pi\) | |||||||
\(360\) | − | 3.99063e7i | − | 0.855331i | ||||||
\(361\) | − | 6.89025e6i | − | 0.146458i | ||||||
\(362\) | 1.46255e6 | − | 1.46255e6i | 0.0308308 | − | 0.0308308i | ||||
\(363\) | 1.73342e8i | 3.62396i | ||||||||
\(364\) | 9.54211e6 | − | 9.54211e6i | 0.197852 | − | 0.197852i | ||||
\(365\) | 1.62336e7 | − | 1.62336e7i | 0.333839 | − | 0.333839i | ||||
\(366\) | 8.73779e7 | 1.78221 | ||||||||
\(367\) | −3.49273e6 | −0.0706588 | −0.0353294 | − | 0.999376i | \(-0.511248\pi\) | ||||
−0.0353294 | + | 0.999376i | \(0.511248\pi\) | |||||||
\(368\) | −6.85789e6 | − | 6.85789e6i | −0.137609 | − | 0.137609i | ||||
\(369\) | 3.18353e7i | 0.633622i | ||||||||
\(370\) | 4.01941e7 | − | 3.03808e6i | 0.793518 | − | 0.0599783i | ||||
\(371\) | 4.95840e7 | 0.971000 | ||||||||
\(372\) | −5.74713e7 | + | 5.74713e7i | −1.11641 | + | 1.11641i | ||||
\(373\) | 6.33314e7i | 1.22037i | 0.792258 | + | 0.610186i | \(0.208905\pi\) | ||||
−0.792258 | + | 0.610186i | \(0.791095\pi\) | |||||||
\(374\) | − | 4.24957e7i | − | 0.812325i | ||||||
\(375\) | −5.46259e7 | − | 5.46259e7i | −1.03587 | − | 1.03587i | ||||
\(376\) | −2.30591e7 | − | 2.30591e7i | −0.433788 | − | 0.433788i | ||||
\(377\) | −9.58106e6 | −0.178809 | ||||||||
\(378\) | −9.38648e7 | − | 9.38648e7i | −1.73791 | − | 1.73791i | ||||
\(379\) | 2.22223e7 | 0.408199 | 0.204100 | − | 0.978950i | \(-0.434573\pi\) | ||||
0.204100 | + | 0.978950i | \(0.434573\pi\) | |||||||
\(380\) | 2.85261e7 | 0.519866 | ||||||||
\(381\) | − | 1.31894e6i | − | 0.0238480i | ||||||
\(382\) | −1.73677e7 | −0.311567 | ||||||||
\(383\) | −4.35674e7 | − | 4.35674e7i | −0.775471 | − | 0.775471i | 0.203586 | − | 0.979057i | \(-0.434740\pi\) |
−0.979057 | + | 0.203586i | \(0.934740\pi\) | |||||||
\(384\) | −6.28067e6 | + | 6.28067e6i | −0.110921 | + | 0.110921i | ||||
\(385\) | −1.34930e8 | + | 1.34930e8i | −2.36443 | + | 2.36443i | ||||
\(386\) | 4.00616e7 | 0.696573 | ||||||||
\(387\) | 5.04666e7 | + | 5.04666e7i | 0.870704 | + | 0.870704i | ||||
\(388\) | 2.76987e7 | − | 2.76987e7i | 0.474203 | − | 0.474203i | ||||
\(389\) | 3.82239e7 | + | 3.82239e7i | 0.649361 | + | 0.649361i | 0.952839 | − | 0.303477i | \(-0.0981477\pi\) |
−0.303477 | + | 0.952839i | \(0.598148\pi\) | |||||||
\(390\) | −1.94596e7 | + | 1.94596e7i | −0.328051 | + | 0.328051i | ||||
\(391\) | 3.06492e7i | 0.512730i | ||||||||
\(392\) | 2.86436e7 | + | 2.86436e7i | 0.475520 | + | 0.475520i | ||||
\(393\) | −2.97098e7 | − | 2.97098e7i | −0.489465 | − | 0.489465i | ||||
\(394\) | −4.67430e7 | + | 4.67430e7i | −0.764237 | + | 0.764237i | ||||
\(395\) | − | 2.17592e7i | − | 0.353063i | ||||||
\(396\) | −1.16414e8 | −1.87464 | ||||||||
\(397\) | − | 7.53055e7i | − | 1.20352i | −0.798675 | − | 0.601762i | \(-0.794465\pi\) | ||
0.798675 | − | 0.601762i | \(-0.205535\pi\) | |||||||
\(398\) | − | 4.12895e7i | − | 0.654924i | ||||||
\(399\) | 1.25459e8 | − | 1.25459e8i | 1.97508 | − | 1.97508i | ||||
\(400\) | − | 4.26457e6i | − | 0.0666339i | ||||||
\(401\) | 1.97491e6 | − | 1.97491e6i | 0.0306277 | − | 0.0306277i | −0.691627 | − | 0.722255i | \(-0.743106\pi\) |
0.722255 | + | 0.691627i | \(0.243106\pi\) | |||||||
\(402\) | −2.40963e7 | + | 2.40963e7i | −0.370914 | + | 0.370914i | ||||
\(403\) | 3.82543e7 | 0.584474 | ||||||||
\(404\) | 1.64504e7 | 0.249478 | ||||||||
\(405\) | 7.77832e7 | + | 7.77832e7i | 1.17090 | + | 1.17090i | ||||
\(406\) | − | 4.38810e7i | − | 0.655690i | ||||||
\(407\) | −8.86261e6 | − | 1.17253e8i | −0.131455 | − | 1.73917i | ||||
\(408\) | 2.80695e7 | 0.413289 | ||||||||
\(409\) | 5.22993e7 | − | 5.22993e7i | 0.764409 | − | 0.764409i | −0.212707 | − | 0.977116i | \(-0.568228\pi\) |
0.977116 | + | 0.212707i | \(0.0682281\pi\) | |||||||
\(410\) | 1.61661e7i | 0.234560i | ||||||||
\(411\) | − | 1.59580e8i | − | 2.29854i | ||||||
\(412\) | 5.46042e6 | + | 5.46042e6i | 0.0780790 | + | 0.0780790i | ||||
\(413\) | −9.19065e7 | − | 9.19065e7i | −1.30466 | − | 1.30466i | ||||
\(414\) | 8.39612e7 | 1.18325 | ||||||||
\(415\) | −4.29289e7 | − | 4.29289e7i | −0.600628 | − | 0.600628i | ||||
\(416\) | 4.18057e6 | 0.0580705 | ||||||||
\(417\) | 1.65158e8 | 2.27767 | ||||||||
\(418\) | − | 8.32155e7i | − | 1.13940i | ||||||
\(419\) | −1.07204e8 | −1.45737 | −0.728685 | − | 0.684849i | \(-0.759868\pi\) | ||||
−0.728685 | + | 0.684849i | \(0.759868\pi\) | |||||||
\(420\) | −8.91247e7 | − | 8.91247e7i | −1.20296 | − | 1.20296i | ||||
\(421\) | −1.70302e7 | + | 1.70302e7i | −0.228230 | + | 0.228230i | −0.811953 | − | 0.583723i | \(-0.801595\pi\) |
0.583723 | + | 0.811953i | \(0.301595\pi\) | |||||||
\(422\) | −5.31189e7 | + | 5.31189e7i | −0.706825 | + | 0.706825i | ||||
\(423\) | 2.82312e8 | 3.73000 | ||||||||
\(424\) | 1.08618e7 | + | 1.08618e7i | 0.142497 | + | 0.142497i | ||||
\(425\) | −9.52957e6 | + | 9.52957e6i | −0.124139 | + | 0.124139i | ||||
\(426\) | 7.22306e7 | + | 7.22306e7i | 0.934313 | + | 0.934313i | ||||
\(427\) | 1.33188e8 | − | 1.33188e8i | 1.71073 | − | 1.71073i | ||||
\(428\) | − | 2.42624e6i | − | 0.0309458i | ||||||
\(429\) | 5.67672e7 | + | 5.67672e7i | 0.718995 | + | 0.718995i | ||||
\(430\) | 2.56271e7 | + | 2.56271e7i | 0.322325 | + | 0.322325i | ||||
\(431\) | −6.41397e7 | + | 6.41397e7i | −0.801116 | + | 0.801116i | −0.983270 | − | 0.182154i | \(-0.941693\pi\) |
0.182154 | + | 0.983270i | \(0.441693\pi\) | |||||||
\(432\) | − | 4.11238e7i | − | 0.510085i | ||||||
\(433\) | 3.07303e7 | 0.378533 | 0.189266 | − | 0.981926i | \(-0.439389\pi\) | ||||
0.189266 | + | 0.981926i | \(0.439389\pi\) | |||||||
\(434\) | 1.75204e8i | 2.14326i | ||||||||
\(435\) | 8.94886e7i | 1.08718i | ||||||||
\(436\) | −3.59918e7 | + | 3.59918e7i | −0.434255 | + | 0.434255i | ||||
\(437\) | 6.00176e7i | 0.719175i | ||||||||
\(438\) | 3.12800e7 | − | 3.12800e7i | 0.372259 | − | 0.372259i | ||||
\(439\) | −4.71802e7 | + | 4.71802e7i | −0.557655 | + | 0.557655i | −0.928639 | − | 0.370984i | \(-0.879021\pi\) |
0.370984 | + | 0.928639i | \(0.379021\pi\) | |||||||
\(440\) | −5.91153e7 | −0.693972 | ||||||||
\(441\) | −3.50683e8 | −4.08883 | ||||||||
\(442\) | −9.34187e6 | − | 9.34187e6i | −0.108185 | − | 0.108185i | ||||
\(443\) | 1.68600e7i | 0.193931i | 0.995288 | + | 0.0969654i | \(0.0309136\pi\) | ||||
−0.995288 | + | 0.0969654i | \(0.969086\pi\) | |||||||
\(444\) | 7.74487e7 | − | 5.85398e6i | 0.884840 | − | 0.0668809i | ||||
\(445\) | −1.15192e8 | −1.30720 | ||||||||
\(446\) | −4.92074e7 | + | 4.92074e7i | −0.554659 | + | 0.554659i | ||||
\(447\) | 4.14760e7i | 0.464381i | ||||||||
\(448\) | 1.91469e7i | 0.212944i | ||||||||
\(449\) | −1.20944e7 | − | 1.20944e7i | −0.133612 | − | 0.133612i | 0.637138 | − | 0.770750i | \(-0.280118\pi\) |
−0.770750 | + | 0.637138i | \(0.780118\pi\) | |||||||
\(450\) | 2.61056e7 | + | 2.61056e7i | 0.286481 | + | 0.286481i | ||||
\(451\) | 4.71593e7 | 0.514089 | ||||||||
\(452\) | −3.96692e7 | − | 3.96692e7i | −0.429574 | − | 0.429574i | ||||
\(453\) | −1.86799e8 | −2.00946 | ||||||||
\(454\) | 9.70091e7 | 1.03668 | ||||||||
\(455\) | 5.93237e7i | 0.629787i | ||||||||
\(456\) | 5.49660e7 | 0.579695 | ||||||||
\(457\) | −5.90150e7 | − | 5.90150e7i | −0.618321 | − | 0.618321i | 0.326780 | − | 0.945101i | \(-0.394036\pi\) |
−0.945101 | + | 0.326780i | \(0.894036\pi\) | |||||||
\(458\) | −4.25611e7 | + | 4.25611e7i | −0.443013 | + | 0.443013i | ||||
\(459\) | −9.18950e7 | + | 9.18950e7i | −0.950285 | + | 0.950285i | ||||
\(460\) | 4.26358e7 | 0.438027 | ||||||||
\(461\) | 1.01611e7 | + | 1.01611e7i | 0.103714 | + | 0.103714i | 0.757060 | − | 0.653346i | \(-0.226635\pi\) |
−0.653346 | + | 0.757060i | \(0.726635\pi\) | |||||||
\(462\) | −2.59993e8 | + | 2.59993e8i | −2.63654 | + | 2.63654i | ||||
\(463\) | −1.62689e7 | − | 1.62689e7i | −0.163914 | − | 0.163914i | 0.620384 | − | 0.784298i | \(-0.286977\pi\) |
−0.784298 | + | 0.620384i | \(0.786977\pi\) | |||||||
\(464\) | 9.61254e6 | − | 9.61254e6i | 0.0962242 | − | 0.0962242i | ||||
\(465\) | − | 3.57301e8i | − | 3.55366i | ||||||
\(466\) | −8.33162e6 | − | 8.33162e6i | −0.0823326 | − | 0.0823326i | ||||
\(467\) | 6.98986e7 | + | 6.98986e7i | 0.686306 | + | 0.686306i | 0.961413 | − | 0.275108i | \(-0.0887135\pi\) |
−0.275108 | + | 0.961413i | \(0.588713\pi\) | |||||||
\(468\) | −2.55914e7 | + | 2.55914e7i | −0.249664 | + | 0.249664i | ||||
\(469\) | 7.34588e7i | 0.712075i | ||||||||
\(470\) | 1.43359e8 | 1.38080 | ||||||||
\(471\) | 2.88402e8i | 2.76017i | ||||||||
\(472\) | − | 4.02659e7i | − | 0.382923i | ||||||
\(473\) | 7.47587e7 | − | 7.47587e7i | 0.706445 | − | 0.706445i | ||||
\(474\) | − | 4.19272e7i | − | 0.393696i | ||||||
\(475\) | −1.86609e7 | + | 1.86609e7i | −0.174122 | + | 0.174122i | ||||
\(476\) | 4.27856e7 | − | 4.27856e7i | 0.396713 | − | 0.396713i | ||||
\(477\) | −1.32981e8 | −1.22528 | ||||||||
\(478\) | −9.66668e6 | −0.0885103 | ||||||||
\(479\) | 6.31168e6 | + | 6.31168e6i | 0.0574300 | + | 0.0574300i | 0.735238 | − | 0.677809i | \(-0.237070\pi\) |
−0.677809 | + | 0.735238i | \(0.737070\pi\) | |||||||
\(480\) | − | 3.90472e7i | − | 0.353074i | ||||||
\(481\) | −2.77242e7 | − | 2.38276e7i | −0.249128 | − | 0.214114i | ||||
\(482\) | 6.88428e7 | 0.614777 | ||||||||
\(483\) | 1.87515e8 | − | 1.87515e8i | 1.66416 | − | 1.66416i | ||||
\(484\) | 1.15760e8i | 1.02099i | ||||||||
\(485\) | 1.72204e8i | 1.50945i | ||||||||
\(486\) | 3.27714e7 | + | 3.27714e7i | 0.285487 | + | 0.285487i | ||||
\(487\) | 5.25302e7 | + | 5.25302e7i | 0.454802 | + | 0.454802i | 0.896945 | − | 0.442143i | \(-0.145782\pi\) |
−0.442143 | + | 0.896945i | \(0.645782\pi\) | |||||||
\(488\) | 5.83520e7 | 0.502107 | ||||||||
\(489\) | 7.55406e7 | + | 7.55406e7i | 0.646032 | + | 0.646032i | ||||
\(490\) | −1.78078e8 | −1.51364 | ||||||||
\(491\) | −1.12092e8 | −0.946959 | −0.473480 | − | 0.880805i | \(-0.657002\pi\) | ||||
−0.473480 | + | 0.880805i | \(0.657002\pi\) | |||||||
\(492\) | 3.11499e7i | 0.261554i | ||||||||
\(493\) | −4.29602e7 | −0.358530 | ||||||||
\(494\) | −1.82934e7 | − | 1.82934e7i | −0.151744 | − | 0.151744i | ||||
\(495\) | 3.61874e8 | − | 3.61874e8i | 2.98361 | − | 2.98361i | ||||
\(496\) | −3.83800e7 | + | 3.83800e7i | −0.314528 | + | 0.314528i | ||||
\(497\) | 2.20198e8 | 1.79368 | ||||||||
\(498\) | −8.27184e7 | − | 8.27184e7i | −0.669752 | − | 0.669752i | ||||
\(499\) | 1.17680e8 | − | 1.17680e8i | 0.947111 | − | 0.947111i | −0.0515592 | − | 0.998670i | \(-0.516419\pi\) |
0.998670 | + | 0.0515592i | \(0.0164191\pi\) | |||||||
\(500\) | −3.64798e7 | − | 3.64798e7i | −0.291839 | − | 0.291839i | ||||
\(501\) | −9.45177e7 | + | 9.45177e7i | −0.751623 | + | 0.751623i | ||||
\(502\) | − | 6.85819e7i | − | 0.542123i | ||||||
\(503\) | −1.08461e8 | − | 1.08461e8i | −0.852259 | − | 0.852259i | 0.138152 | − | 0.990411i | \(-0.455884\pi\) |
−0.990411 | + | 0.138152i | \(0.955884\pi\) | |||||||
\(504\) | −1.17208e8 | − | 1.17208e8i | −0.915514 | − | 0.915514i | ||||
\(505\) | −5.11364e7 | + | 5.11364e7i | −0.397060 | + | 0.397060i | ||||
\(506\) | − | 1.24376e8i | − | 0.960031i | ||||||
\(507\) | −2.06331e8 | −1.58322 | ||||||||
\(508\) | − | 880806.i | − | 0.00671876i | ||||||
\(509\) | 1.02069e7i | 0.0773997i | 0.999251 | + | 0.0386998i | \(0.0123216\pi\) | ||||
−0.999251 | + | 0.0386998i | \(0.987678\pi\) | |||||||
\(510\) | −8.72545e7 | + | 8.72545e7i | −0.657775 | + | 0.657775i | ||||
\(511\) | − | 9.53587e7i | − | 0.714657i | ||||||
\(512\) | −4.19430e6 | + | 4.19430e6i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −1.79950e8 | + | 1.79950e8i | −1.33291 | + | 1.33291i | ||||
\(514\) | −6.30656e7 | −0.464412 | ||||||||
\(515\) | −3.39477e7 | −0.248535 | ||||||||
\(516\) | 4.93801e7 | + | 4.93801e7i | 0.359420 | + | 0.359420i | ||||
\(517\) | − | 4.18204e8i | − | 3.02633i | ||||||
\(518\) | 1.09130e8 | − | 1.26976e8i | 0.785153 | − | 0.913550i | ||||
\(519\) | −1.22086e8 | −0.873299 | ||||||||
\(520\) | −1.29954e7 | + | 1.29954e7i | −0.0924228 | + | 0.0924228i | ||||
\(521\) | − | 6.32068e7i | − | 0.446941i | −0.974711 | − | 0.223471i | \(-0.928261\pi\) | ||
0.974711 | − | 0.223471i | \(-0.0717387\pi\) | |||||||
\(522\) | 1.17686e8i | 0.827398i | ||||||||
\(523\) | −6.91679e7 | − | 6.91679e7i | −0.483504 | − | 0.483504i | 0.422745 | − | 0.906249i | \(-0.361067\pi\) |
−0.906249 | + | 0.422745i | \(0.861067\pi\) | |||||||
\(524\) | −1.98405e7 | − | 1.98405e7i | −0.137899 | − | 0.137899i | ||||
\(525\) | 1.16606e8 | 0.805827 | ||||||||
\(526\) | 9.52884e7 | + | 9.52884e7i | 0.654761 | + | 0.654761i | ||||
\(527\) | 1.71527e8 | 1.17193 | ||||||||
\(528\) | −1.13907e8 | −0.773838 | ||||||||
\(529\) | − | 5.83320e7i | − | 0.394039i | ||||||
\(530\) | −6.75283e7 | −0.453585 | ||||||||
\(531\) | 2.46488e8 | + | 2.46488e8i | 1.64631 | + | 1.64631i | ||||
\(532\) | 8.37832e7 | − | 8.37832e7i | 0.556445 | − | 0.556445i | ||||
\(533\) | 1.03671e7 | − | 1.03671e7i | 0.0684661 | − | 0.0684661i | ||||
\(534\) | −2.21960e8 | −1.45764 | ||||||||
\(535\) | 7.54200e6 | + | 7.54200e6i | 0.0492522 | + | 0.0492522i | ||||
\(536\) | −1.60918e7 | + | 1.60918e7i | −0.104499 | + | 0.104499i | ||||
\(537\) | −1.81402e8 | − | 1.81402e8i | −1.17144 | − | 1.17144i | ||||
\(538\) | −1.03095e8 | + | 1.03095e8i | −0.662050 | + | 0.662050i | ||||
\(539\) | 5.19485e8i | 3.31747i | ||||||||
\(540\) | 1.27834e8 | + | 1.27834e8i | 0.811832 | + | 0.811832i | ||||
\(541\) | 2.50822e7 | + | 2.50822e7i | 0.158407 | + | 0.158407i | 0.781860 | − | 0.623454i | \(-0.214271\pi\) |
−0.623454 | + | 0.781860i | \(0.714271\pi\) | |||||||
\(542\) | 1.21759e8 | − | 1.21759e8i | 0.764724 | − | 0.764724i | ||||
\(543\) | 1.75205e7i | 0.109433i | ||||||||
\(544\) | 1.87451e7 | 0.116437 | ||||||||
\(545\) | − | 2.23763e8i | − | 1.38229i | ||||||
\(546\) | 1.14309e8i | 0.702267i | ||||||||
\(547\) | 4.60044e7 | − | 4.60044e7i | 0.281085 | − | 0.281085i | −0.552457 | − | 0.833541i | \(-0.686310\pi\) |
0.833541 | + | 0.552457i | \(0.186310\pi\) | |||||||
\(548\) | − | 1.06569e8i | − | 0.647575i | ||||||
\(549\) | −3.57202e8 | + | 3.57202e8i | −2.15872 | + | 2.15872i | ||||
\(550\) | 3.86715e7 | − | 3.86715e7i | 0.232436 | − | 0.232436i | ||||
\(551\) | −8.41252e7 | −0.502888 | ||||||||
\(552\) | 8.21536e7 | 0.488438 | ||||||||
\(553\) | −6.39085e7 | − | 6.39085e7i | −0.377906 | − | 0.377906i | ||||
\(554\) | − | 1.15257e8i | − | 0.677859i | ||||||
\(555\) | −2.22554e8 | + | 2.58948e8i | −1.30183 | + | 1.51472i | ||||
\(556\) | 1.10294e8 | 0.641696 | ||||||||
\(557\) | 2.92932e7 | − | 2.92932e7i | 0.169512 | − | 0.169512i | −0.617253 | − | 0.786765i | \(-0.711754\pi\) |
0.786765 | + | 0.617253i | \(0.211754\pi\) | |||||||
\(558\) | − | 4.69886e8i | − | 2.70452i | ||||||
\(559\) | − | 3.28686e7i | − | 0.188168i | ||||||
\(560\) | −5.95186e7 | − | 5.95186e7i | −0.338913 | − | 0.338913i | ||||
\(561\) | 2.54537e8 | + | 2.54537e8i | 1.44166 | + | 1.44166i | ||||
\(562\) | −5.85341e7 | −0.329762 | ||||||||
\(563\) | −5.62286e7 | − | 5.62286e7i | −0.315088 | − | 0.315088i | 0.531789 | − | 0.846877i | \(-0.321520\pi\) |
−0.846877 | + | 0.531789i | \(0.821520\pi\) | |||||||
\(564\) | 2.76234e8 | 1.53971 | ||||||||
\(565\) | 2.46625e8 | 1.36739 | ||||||||
\(566\) | − | 7.69560e7i | − | 0.424417i | ||||||
\(567\) | 4.56910e8 | 2.50658 | ||||||||
\(568\) | 4.82364e7 | + | 4.82364e7i | 0.263227 | + | 0.263227i | ||||
\(569\) | 1.11760e8 | − | 1.11760e8i | 0.606664 | − | 0.606664i | −0.335409 | − | 0.942073i | \(-0.608874\pi\) |
0.942073 | + | 0.335409i | \(0.108874\pi\) | |||||||
\(570\) | −1.70863e8 | + | 1.70863e8i | −0.922621 | + | 0.922621i | ||||
\(571\) | 8.49006e7 | 0.456039 | 0.228020 | − | 0.973657i | \(-0.426775\pi\) | ||||
0.228020 | + | 0.973657i | \(0.426775\pi\) | |||||||
\(572\) | 3.79098e7 | + | 3.79098e7i | 0.202565 | + | 0.202565i | ||||
\(573\) | 1.04027e8 | − | 1.04027e8i | 0.552948 | − | 0.552948i | ||||
\(574\) | 4.74811e7 | + | 4.74811e7i | 0.251064 | + | 0.251064i | ||||
\(575\) | −2.78911e7 | + | 2.78911e7i | −0.146711 | + | 0.146711i | ||||
\(576\) | − | 5.13509e7i | − | 0.268708i | ||||||
\(577\) | 3.59998e7 | + | 3.59998e7i | 0.187401 | + | 0.187401i | 0.794572 | − | 0.607170i | \(-0.207695\pi\) |
−0.607170 | + | 0.794572i | \(0.707695\pi\) | |||||||
\(578\) | 5.46626e7 | + | 5.46626e7i | 0.283078 | + | 0.283078i | ||||
\(579\) | −2.39958e8 | + | 2.39958e8i | −1.23623 | + | 1.23623i | ||||
\(580\) | 5.97615e7i | 0.306294i | ||||||||
\(581\) | −2.52171e8 | −1.28578 | ||||||||
\(582\) | 3.31814e8i | 1.68316i | ||||||||
\(583\) | 1.96992e8i | 0.994129i | ||||||||
\(584\) | 2.08892e7 | − | 2.08892e7i | 0.104878 | − | 0.104878i | ||||
\(585\) | − | 1.59103e8i | − | 0.794711i | ||||||
\(586\) | 1.69765e8 | − | 1.69765e8i | 0.843637 | − | 0.843637i | ||||
\(587\) | −1.53658e8 | + | 1.53658e8i | −0.759700 | + | 0.759700i | −0.976268 | − | 0.216568i | \(-0.930514\pi\) |
0.216568 | + | 0.976268i | \(0.430514\pi\) | |||||||
\(588\) | −3.43133e8 | −1.68784 | ||||||||
\(589\) | 3.35887e8 | 1.64379 | ||||||||
\(590\) | 1.25167e8 | + | 1.25167e8i | 0.609446 | + | 0.609446i | ||||
\(591\) | − | 5.59954e8i | − | 2.71263i | ||||||
\(592\) | 5.17211e7 | − | 3.90936e6i | 0.249289 | − | 0.0188426i | ||||
\(593\) | 1.68437e8 | 0.807742 | 0.403871 | − | 0.914816i | \(-0.367664\pi\) | ||||
0.403871 | + | 0.914816i | \(0.367664\pi\) | |||||||
\(594\) | 3.72915e8 | − | 3.72915e8i | 1.77931 | − | 1.77931i | ||||
\(595\) | 2.66000e8i | 1.26279i | ||||||||
\(596\) | 2.76981e7i | 0.130831i | ||||||||
\(597\) | 2.47312e8 | + | 2.47312e8i | 1.16231 | + | 1.16231i | ||||
\(598\) | −2.73417e7 | − | 2.73417e7i | −0.127856 | − | 0.127856i | ||||
\(599\) | 1.27445e8 | 0.592985 | 0.296493 | − | 0.955035i | \(-0.404183\pi\) | ||||
0.296493 | + | 0.955035i | \(0.404183\pi\) | |||||||
\(600\) | 2.55435e7 | + | 2.55435e7i | 0.118257 | + | 0.118257i | ||||
\(601\) | 5.04366e7 | 0.232339 | 0.116170 | − | 0.993229i | \(-0.462938\pi\) | ||||
0.116170 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(602\) | 1.50537e8 | 0.690010 | ||||||||
\(603\) | − | 1.97012e8i | − | 0.898548i | ||||||
\(604\) | −1.24746e8 | −0.566132 | ||||||||
\(605\) | −3.59841e8 | − | 3.59841e8i | −1.62497 | − | 1.62497i | ||||
\(606\) | −9.85331e7 | + | 9.85331e7i | −0.442756 | + | 0.442756i | ||||
\(607\) | 2.27693e8 | − | 2.27693e8i | 1.01809 | − | 1.01809i | 0.0182524 | − | 0.999833i | \(-0.494190\pi\) |
0.999833 | − | 0.0182524i | \(-0.00581025\pi\) | |||||||
\(608\) | 3.67069e7 | 0.163319 | ||||||||
\(609\) | 2.62835e8 | + | 2.62835e8i | 1.16367 | + | 1.16367i | ||||
\(610\) | −1.81388e8 | + | 1.81388e8i | −0.799134 | + | 0.799134i | ||||
\(611\) | −9.19342e7 | − | 9.19342e7i | −0.403045 | − | 0.403045i | ||||
\(612\) | −1.14748e8 | + | 1.14748e8i | −0.500601 | + | 0.500601i | ||||
\(613\) | − | 3.32577e8i | − | 1.44381i | −0.691991 | − | 0.721906i | \(-0.743266\pi\) | ||
0.691991 | − | 0.721906i | \(-0.256734\pi\) | |||||||
\(614\) | −1.52327e8 | − | 1.52327e8i | −0.658070 | − | 0.658070i | ||||
\(615\) | −9.68302e7 | − | 9.68302e7i | −0.416280 | − | 0.416280i | ||||
\(616\) | −1.73626e8 | + | 1.73626e8i | −0.742802 | + | 0.742802i | ||||
\(617\) | 3.44563e8i | 1.46694i | 0.679720 | + | 0.733472i | \(0.262101\pi\) | ||||
−0.679720 | + | 0.733472i | \(0.737899\pi\) | |||||||
\(618\) | −6.54127e7 | −0.277138 | ||||||||
\(619\) | 2.47789e7i | 0.104474i | 0.998635 | + | 0.0522372i | \(0.0166352\pi\) | ||||
−0.998635 | + | 0.0522372i | \(0.983365\pi\) | |||||||
\(620\) | − | 2.38610e8i | − | 1.00118i | ||||||
\(621\) | −2.68958e8 | + | 2.68958e8i | −1.12308 | + | 1.12308i | ||||
\(622\) | − | 1.28605e7i | − | 0.0534427i | ||||||
\(623\) | −3.38328e8 | + | 3.38328e8i | −1.39918 | + | 1.39918i | ||||
\(624\) | −2.50404e7 | + | 2.50404e7i | −0.103059 | + | 0.103059i | ||||
\(625\) | 2.91869e8 | 1.19549 | ||||||||
\(626\) | 2.96069e8 | 1.20690 | ||||||||
\(627\) | 4.98437e8 | + | 4.98437e8i | 2.02212 | + | 2.02212i | ||||
\(628\) | 1.92598e8i | 0.777631i | ||||||||
\(629\) | −1.24311e8 | − | 1.06840e8i | −0.499527 | − | 0.429320i | ||||
\(630\) | 7.28686e8 | 2.91420 | ||||||||
\(631\) | −1.32122e8 | + | 1.32122e8i | −0.525881 | + | 0.525881i | −0.919341 | − | 0.393461i | \(-0.871278\pi\) |
0.393461 | + | 0.919341i | \(0.371278\pi\) | |||||||
\(632\) | − | 2.79995e7i | − | 0.110917i | ||||||
\(633\) | − | 6.36334e8i | − | 2.50885i | ||||||
\(634\) | 1.13640e8 | + | 1.13640e8i | 0.445926 | + | 0.445926i | ||||
\(635\) | 2.73800e6 | + | 2.73800e6i | 0.0106933 | + | 0.0106933i | ||||
\(636\) | −1.30118e8 | −0.505786 | ||||||||
\(637\) | 1.14199e8 | + | 1.14199e8i | 0.441819 | + | 0.441819i | ||||
\(638\) | 1.74335e8 | 0.671309 | ||||||||
\(639\) | −5.90559e8 | −2.26340 | ||||||||
\(640\) | − | 2.60762e7i | − | 0.0994727i | ||||||
\(641\) | −4.98476e8 | −1.89265 | −0.946325 | − | 0.323217i | \(-0.895236\pi\) | ||||
−0.946325 | + | 0.323217i | \(0.895236\pi\) | |||||||
\(642\) | 1.45324e7 | + | 1.45324e7i | 0.0549204 | + | 0.0549204i | ||||
\(643\) | −1.16095e8 | + | 1.16095e8i | −0.436696 | + | 0.436696i | −0.890898 | − | 0.454203i | \(-0.849924\pi\) |
0.454203 | + | 0.890898i | \(0.349924\pi\) | |||||||
\(644\) | 1.25225e8 | − | 1.25225e8i | 0.468848 | − | 0.468848i | ||||
\(645\) | −3.06998e8 | −1.14408 | ||||||||
\(646\) | −8.20251e7 | − | 8.20251e7i | −0.304263 | − | 0.304263i | ||||
\(647\) | −1.18646e8 | + | 1.18646e8i | −0.438066 | + | 0.438066i | −0.891361 | − | 0.453295i | \(-0.850249\pi\) |
0.453295 | + | 0.891361i | \(0.350249\pi\) | |||||||
\(648\) | 1.00090e8 | + | 1.00090e8i | 0.367847 | + | 0.367847i | ||||
\(649\) | 3.65135e8 | − | 3.65135e8i | 1.33573 | − | 1.33573i | ||||
\(650\) | − | 1.70024e7i | − | 0.0619114i | ||||||
\(651\) | −1.04942e9 | − | 1.04942e9i | −3.80370 | − | 3.80370i | ||||
\(652\) | 5.04469e7 | + | 5.04469e7i | 0.182009 | + | 0.182009i | ||||
\(653\) | −4.58717e7 | + | 4.58717e7i | −0.164742 | + | 0.164742i | −0.784664 | − | 0.619922i | \(-0.787164\pi\) |
0.619922 | + | 0.784664i | \(0.287164\pi\) | |||||||
\(654\) | − | 4.31161e8i | − | 1.54137i | ||||||
\(655\) | 1.23350e8 | 0.438948 | ||||||||
\(656\) | 2.08023e7i | 0.0736885i | ||||||||
\(657\) | 2.55746e8i | 0.901806i | ||||||||
\(658\) | 4.21057e8 | − | 4.21057e8i | 1.47796 | − | 1.47796i | ||||
\(659\) | − | 5.04763e7i | − | 0.176373i | −0.996104 | − | 0.0881863i | \(-0.971893\pi\) | ||
0.996104 | − | 0.0881863i | \(-0.0281071\pi\) | |||||||
\(660\) | 3.54083e8 | − | 3.54083e8i | 1.23161 | − | 1.23161i | ||||
\(661\) | −5.55721e7 | + | 5.55721e7i | −0.192421 | + | 0.192421i | −0.796741 | − | 0.604320i | \(-0.793445\pi\) |
0.604320 | + | 0.796741i | \(0.293445\pi\) | |||||||
\(662\) | −1.99880e8 | −0.688964 | ||||||||
\(663\) | 1.11910e8 | 0.383998 | ||||||||
\(664\) | −5.52403e7 | − | 5.52403e7i | −0.188691 | − | 0.188691i | ||||
\(665\) | 5.20884e8i | 1.77123i | ||||||||
\(666\) | −2.92680e8 | + | 3.40542e8i | −0.990764 | + | 1.15278i | ||||
\(667\) | −1.25736e8 | −0.423722 | ||||||||
\(668\) | −6.31201e7 | + | 6.31201e7i | −0.211757 | + | 0.211757i | ||||
\(669\) | − | 5.89476e8i | − | 1.96874i | ||||||
\(670\) | − | 1.00044e8i | − | 0.332632i | ||||||
\(671\) | 5.29142e8 | + | 5.29142e8i | 1.75148 | + | 1.75148i | ||||
\(672\) | −1.14684e8 | − | 1.14684e8i | −0.377917 | − | 0.377917i | ||||
\(673\) | 4.22585e8 | 1.38634 | 0.693168 | − | 0.720776i | \(-0.256214\pi\) | ||||
0.693168 | + | 0.720776i | \(0.256214\pi\) | |||||||
\(674\) | −1.00356e8 | − | 1.00356e8i | −0.327765 | − | 0.327765i | ||||
\(675\) | −1.67251e8 | −0.543823 | ||||||||
\(676\) | −1.37790e8 | −0.446045 | ||||||||
\(677\) | − | 1.97832e8i | − | 0.637573i | −0.947827 | − | 0.318786i | \(-0.896725\pi\) | ||
0.947827 | − | 0.318786i | \(-0.103275\pi\) | |||||||
\(678\) | 4.75214e8 | 1.52476 | ||||||||
\(679\) | 5.05776e8 | + | 5.05776e8i | 1.61566 | + | 1.61566i | ||||
\(680\) | −5.82696e7 | + | 5.82696e7i | −0.185317 | + | 0.185317i | ||||
\(681\) | −5.81057e8 | + | 5.81057e8i | −1.83983 | + | 1.83983i | ||||
\(682\) | −6.96067e8 | −2.19431 | ||||||||
\(683\) | 2.99117e8 | + | 2.99117e8i | 0.938813 | + | 0.938813i | 0.998233 | − | 0.0594199i | \(-0.0189251\pi\) |
−0.0594199 | + | 0.998233i | \(0.518925\pi\) | |||||||
\(684\) | −2.24702e8 | + | 2.24702e8i | −0.702163 | + | 0.702163i | ||||
\(685\) | 3.31273e8 | + | 3.31273e8i | 1.03066 | + | 1.03066i | ||||
\(686\) | −2.48052e8 | + | 2.48052e8i | −0.768370 | + | 0.768370i | ||||
\(687\) | − | 5.09858e8i | − | 1.57246i | ||||||
\(688\) | 3.29766e7 | + | 3.29766e7i | 0.101261 | + | 0.101261i | ||||
\(689\) | 4.33050e7 | + | 4.33050e7i | 0.132398 | + | 0.132398i | ||||
\(690\) | −2.55376e8 | + | 2.55376e8i | −0.777379 | + | 0.777379i | ||||
\(691\) | 4.48252e8i | 1.35859i | 0.733866 | + | 0.679295i | \(0.237714\pi\) | ||||
−0.733866 | + | 0.679295i | \(0.762286\pi\) | |||||||
\(692\) | −8.15303e7 | −0.246037 | ||||||||
\(693\) | − | 2.12570e9i | − | 6.38709i | ||||||
\(694\) | − | 2.11026e8i | − | 0.631333i | ||||||
\(695\) | −3.42852e8 | + | 3.42852e8i | −1.02130 | + | 1.02130i | ||||
\(696\) | 1.15153e8i | 0.341544i | ||||||||
\(697\) | 4.64847e7 | − | 4.64847e7i | 0.137281 | − | 0.137281i | ||||
\(698\) | −3.42894e7 | + | 3.42894e7i | −0.100831 | + | 0.100831i | ||||
\(699\) | 9.98080e7 | 0.292236 | ||||||||
\(700\) | 7.78707e7 | 0.227028 | ||||||||
\(701\) | −3.85035e8 | − | 3.85035e8i | −1.11775 | − | 1.11775i | −0.992071 | − | 0.125682i | \(-0.959888\pi\) |
−0.125682 | − | 0.992071i | \(-0.540112\pi\) | |||||||
\(702\) | − | 1.63957e8i | − | 0.473934i | ||||||
\(703\) | −2.43428e8 | − | 2.09215e8i | −0.700657 | − | 0.602181i | ||||
\(704\) | −7.60687e7 | −0.218016 | ||||||||
\(705\) | −8.58679e8 | + | 8.58679e8i | −2.45055 | + | 2.45055i | ||||
\(706\) | 2.80485e8i | 0.797069i | ||||||||
\(707\) | 3.00383e8i | 0.849996i | ||||||||
\(708\) | 2.41181e8 | + | 2.41181e8i | 0.679585 | + | 0.679585i | ||||
\(709\) | −1.62158e8 | − | 1.62158e8i | −0.454987 | − | 0.454987i | 0.442019 | − | 0.897006i | \(-0.354262\pi\) |
−0.897006 | + | 0.442019i | \(0.854262\pi\) | |||||||
\(710\) | −2.99888e8 | −0.837884 | ||||||||
\(711\) | 1.71399e8 | + | 1.71399e8i | 0.476869 | + | 0.476869i | ||||
\(712\) | −1.48228e8 | −0.410667 | ||||||||
\(713\) | 5.02025e8 | 1.38502 | ||||||||
\(714\) | 5.12546e8i | 1.40812i | ||||||||
\(715\) | −2.35687e8 | −0.644788 | ||||||||
\(716\) | −1.21143e8 | − | 1.21143e8i | −0.330034 | − | 0.330034i | ||||
\(717\) | 5.79006e7 | − | 5.79006e7i | 0.157082 | − | 0.157082i | ||||
\(718\) | 2.49567e8 | − | 2.49567e8i | 0.674239 | − | 0.674239i | ||||
\(719\) | −2.28189e8 | −0.613915 | −0.306958 | − | 0.951723i | \(-0.599311\pi\) | ||||
−0.306958 | + | 0.951723i | \(0.599311\pi\) | |||||||
\(720\) | 1.59625e8 | + | 1.59625e8i | 0.427665 | + | 0.427665i | ||||
\(721\) | −9.97068e7 | + | 9.97068e7i | −0.266023 | + | 0.266023i | ||||
\(722\) | 2.75610e7 | + | 2.75610e7i | 0.0732291 | + | 0.0732291i | ||||
\(723\) | −4.12348e8 | + | 4.12348e8i | −1.09106 | + | 1.09106i | ||||
\(724\) | 1.17004e7i | 0.0308308i | ||||||||
\(725\) | −3.90943e7 | − | 3.90943e7i | −0.102589 | − | 0.102589i | ||||
\(726\) | −6.93367e8 | − | 6.93367e8i | −1.81198 | − | 1.81198i | ||||
\(727\) | 2.39344e8 | − | 2.39344e8i | 0.622902 | − | 0.622902i | −0.323370 | − | 0.946273i | \(-0.604816\pi\) |
0.946273 | + | 0.323370i | \(0.104816\pi\) | |||||||
\(728\) | 7.63369e7i | 0.197852i | ||||||||
\(729\) | 1.77463e8 | 0.458064 | ||||||||
\(730\) | 1.29869e8i | 0.333839i | ||||||||
\(731\) | − | 1.47378e8i | − | 0.377296i | ||||||
\(732\) | −3.49511e8 | + | 3.49511e8i | −0.891104 | + | 0.891104i | ||||
\(733\) | 4.92138e8i | 1.24961i | 0.780780 | + | 0.624805i | \(0.214822\pi\) | ||||
−0.780780 | + | 0.624805i | \(0.785178\pi\) | |||||||
\(734\) | 1.39709e7 | − | 1.39709e7i | 0.0353294 | − | 0.0353294i | ||||
\(735\) | 1.06664e9 | − | 1.06664e9i | 2.68630 | − | 2.68630i | ||||
\(736\) | 5.48631e7 | 0.137609 | ||||||||
\(737\) | −2.91844e8 | −0.729036 | ||||||||
\(738\) | −1.27341e8 | − | 1.27341e8i | −0.316811 | − | 0.316811i | ||||
\(739\) | 1.39352e8i | 0.345286i | 0.984984 | + | 0.172643i | \(0.0552306\pi\) | ||||
−0.984984 | + | 0.172643i | \(0.944769\pi\) | |||||||
\(740\) | −1.48624e8 | + | 1.72929e8i | −0.366770 | + | 0.426748i | ||||
\(741\) | 2.19144e8 | 0.538611 | ||||||||
\(742\) | −1.98336e8 | + | 1.98336e8i | −0.485500 | + | 0.485500i | ||||
\(743\) | 3.18952e8i | 0.777604i | 0.921321 | + | 0.388802i | \(0.127111\pi\) | ||||
−0.921321 | + | 0.388802i | \(0.872889\pi\) | |||||||
\(744\) | − | 4.59770e8i | − | 1.11641i | ||||||
\(745\) | −8.61003e7 | − | 8.61003e7i | −0.208226 | − | 0.208226i | ||||
\(746\) | −2.53325e8 | − | 2.53325e8i | −0.610186 | − | 0.610186i | ||||
\(747\) | 6.76307e8 | 1.62249 | ||||||||
\(748\) | 1.69983e8 | + | 1.69983e8i | 0.406162 | + | 0.406162i | ||||
\(749\) | 4.43029e7 | 0.105435 | ||||||||
\(750\) | 4.37007e8 | 1.03587 | ||||||||
\(751\) | 3.93490e8i | 0.928996i | 0.885574 | + | 0.464498i | \(0.153765\pi\) | ||||
−0.885574 | + | 0.464498i | \(0.846235\pi\) | |||||||
\(752\) | 1.84472e8 | 0.433788 | ||||||||
\(753\) | 4.10786e8 | + | 4.10786e8i | 0.962122 | + | 0.962122i | ||||
\(754\) | 3.83242e7 | − | 3.83242e7i | 0.0894045 | − | 0.0894045i | ||||
\(755\) | 3.87777e8 | − | 3.87777e8i | 0.901034 | − | 0.901034i | ||||
\(756\) | 7.50918e8 | 1.73791 | ||||||||
\(757\) | 9.19159e7 | + | 9.19159e7i | 0.211886 | + | 0.211886i | 0.805068 | − | 0.593182i | \(-0.202129\pi\) |
−0.593182 | + | 0.805068i | \(0.702129\pi\) | |||||||
\(758\) | −8.88894e7 | + | 8.88894e7i | −0.204100 | + | 0.204100i | ||||
\(759\) | 7.44977e8 | + | 7.44977e8i | 1.70380 | + | 1.70380i | ||||
\(760\) | −1.14104e8 | + | 1.14104e8i | −0.259933 | + | 0.259933i | ||||
\(761\) | 3.19052e8i | 0.723949i | 0.932188 | + | 0.361974i | \(0.117897\pi\) | ||||
−0.932188 | + | 0.361974i | \(0.882103\pi\) | |||||||
\(762\) | 5.27578e6 | + | 5.27578e6i | 0.0119240 | + | 0.0119240i | ||||
\(763\) | −6.57208e8 | − | 6.57208e8i | −1.47955 | − | 1.47955i | ||||
\(764\) | 6.94708e7 | − | 6.94708e7i | 0.155784 | − | 0.155784i | ||||
\(765\) | − | 7.13395e8i | − | 1.59348i | ||||||
\(766\) | 3.48539e8 | 0.775471 | ||||||||
\(767\) | − | 1.60536e8i | − | 0.355784i | ||||||
\(768\) | − | 5.02453e7i | − | 0.110921i | ||||||
\(769\) | 4.83459e8 | − | 4.83459e8i | 1.06312 | − | 1.06312i | 0.0652467 | − | 0.997869i | \(-0.479217\pi\) |
0.997869 | − | 0.0652467i | \(-0.0207834\pi\) | |||||||
\(770\) | − | 1.07944e9i | − | 2.36443i | ||||||
\(771\) | 3.77745e8 | − | 3.77745e8i | 0.824205 | − | 0.824205i | ||||
\(772\) | −1.60247e8 | + | 1.60247e8i | −0.348287 | + | 0.348287i | ||||
\(773\) | −7.51538e8 | −1.62709 | −0.813547 | − | 0.581499i | \(-0.802466\pi\) | ||||
−0.813547 | + | 0.581499i | \(0.802466\pi\) | |||||||
\(774\) | −4.03732e8 | −0.870704 | ||||||||
\(775\) | 1.56092e8 | + | 1.56092e8i | 0.335332 | + | 0.335332i | ||||
\(776\) | 2.21589e8i | 0.474203i | ||||||||
\(777\) | 1.06893e8 | + | 1.41421e9i | 0.227870 | + | 3.01474i | ||||
\(778\) | −3.05791e8 | −0.649361 | ||||||||
\(779\) | 9.10269e7 | − | 9.10269e7i | 0.192556 | − | 0.192556i | ||||
\(780\) | − | 1.55677e8i | − | 0.328051i | ||||||
\(781\) | 8.74826e8i | 1.83640i | ||||||||
\(782\) | −1.22597e8 | − | 1.22597e8i | −0.256365 | − | 0.256365i | ||||
\(783\) | −3.76992e8 | − | 3.76992e8i | −0.785320 | − | 0.785320i | ||||
\(784\) | −2.29149e8 | −0.475520 | ||||||||
\(785\) | −5.98696e8 | − | 5.98696e8i | −1.23765 | − | 1.23765i | ||||
\(786\) | 2.37678e8 | 0.489465 | ||||||||
\(787\) | −6.40968e8 | −1.31496 | −0.657480 | − | 0.753472i | \(-0.728377\pi\) | ||||
−0.657480 | + | 0.753472i | \(0.728377\pi\) | |||||||
\(788\) | − | 3.73944e8i | − | 0.764237i | ||||||
\(789\) | −1.14150e9 | −2.32405 | ||||||||
\(790\) | 8.70369e7 | + | 8.70369e7i | 0.176532 | + | 0.176532i | ||||
\(791\) | 7.24357e8 | − | 7.24357e8i | 1.46360 | − | 1.46360i | ||||
\(792\) | 4.65655e8 | − | 4.65655e8i | 0.937321 | − | 0.937321i | ||||
\(793\) | 2.32644e8 | 0.466521 | ||||||||
\(794\) | 3.01222e8 | + | 3.01222e8i | 0.601762 | + | 0.601762i | ||||
\(795\) | 4.04475e8 | − | 4.04475e8i | 0.804990 | − | 0.804990i | ||||
\(796\) | 1.65158e8 | + | 1.65158e8i | 0.327462 | + | 0.327462i | ||||
\(797\) | 3.11851e8 | − | 3.11851e8i | 0.615988 | − | 0.615988i | −0.328511 | − | 0.944500i | \(-0.606547\pi\) |
0.944500 | + | 0.328511i | \(0.106547\pi\) | |||||||
\(798\) | 1.00367e9i | 1.97508i | ||||||||
\(799\) | −4.12221e8 | − | 4.12221e8i | −0.808145 | − | 0.808145i | ||||
\(800\) | 1.70583e7 | + | 1.70583e7i | 0.0333169 | + | 0.0333169i | ||||
\(801\) | 9.07376e8 | − | 9.07376e8i | 1.76559 | − | 1.76559i | ||||
\(802\) | 1.57993e7i | 0.0306277i | ||||||||
\(803\) | 3.78850e8 | 0.731680 | ||||||||
\(804\) | − | 1.92771e8i | − | 0.370914i | ||||||
\(805\) | 7.78526e8i | 1.49240i | ||||||||
\(806\) | −1.53017e8 | + | 1.53017e8i | −0.292237 | + | 0.292237i | ||||
\(807\) | − | 1.23502e9i | − | 2.34992i | ||||||
\(808\) | −6.58016e7 | + | 6.58016e7i | −0.124739 | + | 0.124739i | ||||
\(809\) | −2.08625e8 | + | 2.08625e8i | −0.394022 | + | 0.394022i | −0.876118 | − | 0.482096i | \(-0.839876\pi\) |
0.482096 | + | 0.876118i | \(0.339876\pi\) | |||||||
\(810\) | −6.22265e8 | −1.17090 | ||||||||
\(811\) | 4.09701e8 | 0.768077 | 0.384039 | − | 0.923317i | \(-0.374533\pi\) | ||||
0.384039 | + | 0.923317i | \(0.374533\pi\) | |||||||
\(812\) | 1.75524e8 | + | 1.75524e8i | 0.327845 | + | 0.327845i | ||||
\(813\) | 1.45861e9i | 2.71436i | ||||||||
\(814\) | 5.04463e8 | + | 4.33562e8i | 0.935311 | + | 0.803855i | ||||
\(815\) | −3.13631e8 | −0.579356 | ||||||||
\(816\) | −1.12278e8 | + | 1.12278e8i | −0.206644 | + | 0.206644i | ||||
\(817\) | − | 2.88598e8i | − | 0.529210i | ||||||
\(818\) | 4.18394e8i | 0.764409i | ||||||||
\(819\) | −4.67296e8 | − | 4.67296e8i | −0.850630 | − | 0.850630i | ||||
\(820\) | −6.46644e7 | − | 6.46644e7i | −0.117280 | − | 0.117280i | ||||
\(821\) | 1.57717e8 | 0.285003 | 0.142501 | − | 0.989795i | \(-0.454486\pi\) | ||||
0.142501 | + | 0.989795i | \(0.454486\pi\) | |||||||
\(822\) | 6.38319e8 | + | 6.38319e8i | 1.14927 | + | 1.14927i | ||||
\(823\) | 9.79212e7 | 0.175662 | 0.0878309 | − | 0.996135i | \(-0.472006\pi\) | ||||
0.0878309 | + | 0.996135i | \(0.472006\pi\) | |||||||
\(824\) | −4.36834e7 | −0.0780790 | ||||||||
\(825\) | 4.63262e8i | 0.825021i | ||||||||
\(826\) | 7.35252e8 | 1.30466 | ||||||||
\(827\) | −9.55503e7 | − | 9.55503e7i | −0.168933 | − | 0.168933i | 0.617577 | − | 0.786510i | \(-0.288114\pi\) |
−0.786510 | + | 0.617577i | \(0.788114\pi\) | |||||||
\(828\) | −3.35845e8 | + | 3.35845e8i | −0.591626 | + | 0.591626i | ||||
\(829\) | 6.51713e8 | − | 6.51713e8i | 1.14391 | − | 1.14391i | 0.156185 | − | 0.987728i | \(-0.450080\pi\) |
0.987728 | − | 0.156185i | \(-0.0499195\pi\) | |||||||
\(830\) | 3.43431e8 | 0.600628 | ||||||||
\(831\) | 6.90358e8 | + | 6.90358e8i | 1.20302 | + | 1.20302i | ||||
\(832\) | −1.67223e7 | + | 1.67223e7i | −0.0290352 | + | 0.0290352i | ||||
\(833\) | 5.12054e8 | + | 5.12054e8i | 0.885891 | + | 0.885891i | ||||
\(834\) | −6.60632e8 | + | 6.60632e8i | −1.13884 | + | 1.13884i | ||||
\(835\) | − | 3.92420e8i | − | 0.674050i | ||||||
\(836\) | 3.32862e8 | + | 3.32862e8i | 0.569699 | + | 0.569699i | ||||
\(837\) | 1.50522e9 | + | 1.50522e9i | 2.56698 | + | 2.56698i | ||||
\(838\) | 4.28817e8 | − | 4.28817e8i | 0.728685 | − | 0.728685i | ||||
\(839\) | − | 8.63943e8i | − | 1.46285i | −0.681923 | − | 0.731424i | \(-0.738856\pi\) | ||
0.681923 | − | 0.731424i | \(-0.261144\pi\) | |||||||
\(840\) | 7.12998e8 | 1.20296 | ||||||||
\(841\) | 4.18583e8i | 0.703709i | ||||||||
\(842\) | − | 1.36241e8i | − | 0.228230i | ||||||
\(843\) | 3.50602e8 | − | 3.50602e8i | 0.585238 | − | 0.585238i | ||||
\(844\) | − | 4.24952e8i | − | 0.706825i | ||||||
\(845\) | 4.28324e8 | − | 4.28324e8i | 0.709909 | − | 0.709909i | ||||
\(846\) | −1.12925e9 | + | 1.12925e9i | −1.86500 | + | 1.86500i | ||||
\(847\) | −2.11376e9 | −3.47861 | ||||||||
\(848\) | −8.68945e7 | −0.142497 | ||||||||
\(849\) | 4.60944e8 | + | 4.60944e8i | 0.753226 | + | 0.753226i | ||||
\(850\) | − | 7.62366e7i | − | 0.124139i | ||||||
\(851\) | −3.63834e8 | − | 3.12698e8i | −0.590357 | − | 0.507384i | ||||
\(852\) | −5.77845e8 | −0.934313 | ||||||||
\(853\) | −4.81440e7 | + | 4.81440e7i | −0.0775703 | + | 0.0775703i | −0.744827 | − | 0.667257i | \(-0.767468\pi\) |
0.667257 | + | 0.744827i | \(0.267468\pi\) | |||||||
\(854\) | 1.06550e9i | 1.71073i | ||||||||
\(855\) | − | 1.39698e9i | − | 2.23507i | ||||||
\(856\) | 9.70494e6 | + | 9.70494e6i | 0.0154729 | + | 0.0154729i | ||||
\(857\) | 1.12023e8 | + | 1.12023e8i | 0.177978 | + | 0.177978i | 0.790474 | − | 0.612496i | \(-0.209834\pi\) |
−0.612496 | + | 0.790474i | \(0.709834\pi\) | |||||||
\(858\) | −4.54138e8 | −0.718995 | ||||||||
\(859\) | −4.46687e7 | − | 4.46687e7i | −0.0704731 | − | 0.0704731i | 0.670992 | − | 0.741465i | \(-0.265869\pi\) |
−0.741465 | + | 0.670992i | \(0.765869\pi\) | |||||||
\(860\) | −2.05017e8 | −0.322325 | ||||||||
\(861\) | −5.68796e8 | −0.891142 | ||||||||
\(862\) | − | 5.13118e8i | − | 0.801116i | ||||||
\(863\) | −1.54894e8 | −0.240992 | −0.120496 | − | 0.992714i | \(-0.538449\pi\) | ||||
−0.120496 | + | 0.992714i | \(0.538449\pi\) | |||||||
\(864\) | 1.64495e8 | + | 1.64495e8i | 0.255042 | + | 0.255042i | ||||
\(865\) | 2.53439e8 | − | 2.53439e8i | 0.391584 | − | 0.391584i | ||||
\(866\) | −1.22921e8 | + | 1.22921e8i | −0.189266 | + | 0.189266i | ||||
\(867\) | −6.54826e8 | −1.00477 | ||||||||
\(868\) | −7.00816e8 | − | 7.00816e8i | −1.07163 | − | 1.07163i | ||||
\(869\) | 2.53902e8 | − | 2.53902e8i | 0.386907 | − | 0.386907i | ||||
\(870\) | −3.57954e8 | − | 3.57954e8i | −0.543588 | − | 0.543588i | ||||
\(871\) | −6.41565e7 | + | 6.41565e7i | −0.0970926 | + | 0.0970926i | ||||
\(872\) | − | 2.87935e8i | − | 0.434255i | ||||||
\(873\) | −1.35646e9 | − | 1.35646e9i | −2.03875 | − | 2.03875i | ||||
\(874\) | −2.40071e8 | − | 2.40071e8i | −0.359588 | − | 0.359588i | ||||
\(875\) | 6.66119e8 | − | 6.66119e8i | 0.994323 | − | 0.994323i | ||||
\(876\) | 2.50240e8i | 0.372259i | ||||||||
\(877\) | −1.64303e8 | −0.243583 | −0.121792 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121792 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(878\) | − | 3.77441e8i | − | 0.557655i | ||||||
\(879\) | 2.03369e9i | 2.99446i | ||||||||
\(880\) | 2.36461e8 | − | 2.36461e8i | 0.346986 | − | 0.346986i | ||||
\(881\) | 1.02031e9i | 1.49212i | 0.665880 | + | 0.746059i | \(0.268056\pi\) | ||||
−0.665880 | + | 0.746059i | \(0.731944\pi\) | |||||||
\(882\) | 1.40273e9 | − | 1.40273e9i | 2.04442 | − | 2.04442i | ||||
\(883\) | −3.83520e8 | + | 3.83520e8i | −0.557065 | + | 0.557065i | −0.928471 | − | 0.371406i | \(-0.878876\pi\) |
0.371406 | + | 0.928471i | \(0.378876\pi\) | |||||||
\(884\) | 7.47350e7 | 0.108185 | ||||||||
\(885\) | −1.49943e9 | −2.16320 | ||||||||
\(886\) | −6.74401e7 | − | 6.74401e7i | −0.0969654 | − | 0.0969654i | ||||
\(887\) | 6.20856e8i | 0.889651i | 0.895617 | + | 0.444826i | \(0.146734\pi\) | ||||
−0.895617 | + | 0.444826i | \(0.853266\pi\) | |||||||
\(888\) | −2.86379e8 | + | 3.33211e8i | −0.408980 | + | 0.475861i | ||||
\(889\) | 1.60835e7 | 0.0228915 | ||||||||
\(890\) | 4.60769e8 | − | 4.60769e8i | 0.653602 | − | 0.653602i | ||||
\(891\) | 1.81526e9i | 2.56629i | ||||||||
\(892\) | − | 3.93659e8i | − | 0.554659i | ||||||
\(893\) | −8.07216e8 | − | 8.07216e8i | −1.13354 | − | 1.13354i | ||||
\(894\) | −1.65904e8 | − | 1.65904e8i | −0.232190 | − | 0.232190i | ||||
\(895\) | 7.53149e8 | 1.05054 | ||||||||
\(896\) | −7.65877e7 | − | 7.65877e7i | −0.106472 | − | 0.106472i | ||||
\(897\) | 3.27538e8 | 0.453821 | ||||||||
\(898\) | 9.67551e7 | 0.133612 | ||||||||
\(899\) | 7.03677e8i | 0.968487i | ||||||||
\(900\) | −2.08844e8 | −0.286481 | ||||||||
\(901\) | 1.94174e8 | + | 1.94174e8i | 0.265470 | + | 0.265470i | ||||
\(902\) | −1.88637e8 | + | 1.88637e8i | −0.257044 | + | 0.257044i | ||||
\(903\) | −9.01676e8 | + | 9.01676e8i | −1.22458 | + | 1.22458i | ||||
\(904\) | 3.17354e8 | 0.429574 | ||||||||
\(905\) | −3.63709e7 | − | 3.63709e7i | −0.0490692 | − | 0.0490692i | ||||
\(906\) | 7.47195e8 | − | 7.47195e8i | 1.00473 | − | 1.00473i | ||||
\(907\) | 2.57761e8 | + | 2.57761e8i | 0.345458 | + | 0.345458i | 0.858414 | − | 0.512957i | \(-0.171450\pi\) |
−0.512957 | + | 0.858414i | \(0.671450\pi\) | |||||||
\(908\) | −3.88037e8 | + | 3.88037e8i | −0.518340 | + | 0.518340i | ||||
\(909\) | − | 8.05609e8i | − | 1.07259i | ||||||
\(910\) | −2.37295e8 | − | 2.37295e8i | −0.314894 | − | 0.314894i | ||||
\(911\) | −1.43651e8 | − | 1.43651e8i | −0.189999 | − | 0.189999i | 0.605696 | − | 0.795696i | \(-0.292895\pi\) |
−0.795696 | + | 0.605696i | \(0.792895\pi\) | |||||||
\(912\) | −2.19864e8 | + | 2.19864e8i | −0.289847 | + | 0.289847i | ||||
\(913\) | − | 1.00185e9i | − | 1.31641i | ||||||
\(914\) | 4.72120e8 | 0.618321 | ||||||||
\(915\) | − | 2.17293e9i | − | 2.83649i | ||||||
\(916\) | − | 3.40489e8i | − | 0.443013i | ||||||
\(917\) | 3.62287e8 | − | 3.62287e8i | 0.469834 | − | 0.469834i | ||||
\(918\) | − | 7.35160e8i | − | 0.950285i | ||||||
\(919\) | 9.40712e8 | − | 9.40712e8i | 1.21202 | − | 1.21202i | 0.241660 | − | 0.970361i | \(-0.422308\pi\) |
0.970361 | − | 0.241660i | \(-0.0776918\pi\) | |||||||
\(920\) | −1.70543e8 | + | 1.70543e8i | −0.219014 | + | 0.219014i | ||||
\(921\) | 1.82479e9 | 2.33579 | ||||||||
\(922\) | −8.12889e7 | −0.103714 | ||||||||
\(923\) | 1.92314e8 | + | 1.92314e8i | 0.244571 | + | 0.244571i | ||||
\(924\) | − | 2.07994e9i | − | 2.63654i | ||||||
\(925\) | −1.58994e7 | − | 2.10350e8i | −0.0200889 | − | 0.265777i | ||||
\(926\) | 1.30151e8 | 0.163914 | ||||||||
\(927\) | 2.67408e8 | − | 2.67408e8i | 0.335687 | − | 0.335687i | ||||
\(928\) | 7.69003e7i | 0.0962242i | ||||||||
\(929\) | 6.68787e8i | 0.834143i | 0.908874 | + | 0.417072i | \(0.136944\pi\) | ||||
−0.908874 | + | 0.417072i | \(0.863056\pi\) | |||||||
\(930\) | 1.42920e9 | + | 1.42920e9i | 1.77683 | + | 1.77683i | ||||
\(931\) | 1.00271e9 | + | 1.00271e9i | 1.24259 | + | 1.24259i | ||||
\(932\) | 6.66529e7 | 0.0823326 | ||||||||
\(933\) | 7.70309e7 | + | 7.70309e7i | 0.0948463 | + | 0.0948463i | ||||
\(934\) | −5.59189e8 | −0.686306 | ||||||||
\(935\) | −1.05679e9 | −1.29287 | ||||||||
\(936\) | − | 2.04731e8i | − | 0.249664i | ||||||
\(937\) | −1.11237e9 | −1.35216 | −0.676081 | − | 0.736827i | \(-0.736323\pi\) | ||||
−0.676081 | + | 0.736827i | \(0.736323\pi\) | |||||||
\(938\) | −2.93835e8 | − | 2.93835e8i | −0.356037 | − | 0.356037i | ||||
\(939\) | −1.77337e9 | + | 1.77337e9i | −2.14191 | + | 2.14191i | ||||
\(940\) | −5.73436e8 | + | 5.73436e8i | −0.690401 | + | 0.690401i | ||||
\(941\) | 1.48618e9 | 1.78362 | 0.891812 | − | 0.452406i | \(-0.149434\pi\) | ||||
0.891812 | + | 0.452406i | \(0.149434\pi\) | |||||||
\(942\) | −1.15361e9 | − | 1.15361e9i | −1.38008 | − | 1.38008i | ||||
\(943\) | 1.36051e8 | − | 1.36051e8i | 0.162243 | − | 0.162243i | ||||
\(944\) | 1.61064e8 | + | 1.61064e8i | 0.191462 | + | 0.191462i | ||||
\(945\) | −2.33424e9 | + | 2.33424e9i | −2.76599 | + | 2.76599i | ||||
\(946\) | 5.98070e8i | 0.706445i | ||||||||
\(947\) | −6.35766e8 | − | 6.35766e8i | −0.748596 | − | 0.748596i | 0.225620 | − | 0.974215i | \(-0.427559\pi\) |
−0.974215 | + | 0.225620i | \(0.927559\pi\) | |||||||
\(948\) | 1.67709e8 | + | 1.67709e8i | 0.196848 | + | 0.196848i | ||||
\(949\) | 8.32831e7 | − | 8.32831e7i | 0.0974447 | − | 0.0974447i | ||||
\(950\) | − | 1.49287e8i | − | 0.174122i | ||||||
\(951\) | −1.36134e9 | −1.58280 | ||||||||
\(952\) | 3.42284e8i | 0.396713i | ||||||||
\(953\) | − | 7.63640e8i | − | 0.882288i | −0.897436 | − | 0.441144i | \(-0.854573\pi\) | ||
0.897436 | − | 0.441144i | \(-0.145427\pi\) | |||||||
\(954\) | 5.31925e8 | − | 5.31925e8i | 0.612639 | − | 0.612639i | ||||
\(955\) | 4.31903e8i | 0.495879i | ||||||||
\(956\) | 3.86667e7 | − | 3.86667e7i | 0.0442551 | − | 0.0442551i | ||||
\(957\) | −1.04422e9 | + | 1.04422e9i | −1.19139 | + | 1.19139i | ||||
\(958\) | −5.04935e7 | −0.0574300 | ||||||||
\(959\) | 1.94595e9 | 2.20635 | ||||||||
\(960\) | 1.56189e8 | + | 1.56189e8i | 0.176537 | + | 0.176537i | ||||
\(961\) | − | 1.92207e9i | − | 2.16570i | ||||||
\(962\) | 2.06207e8 | − | 1.55862e7i | 0.231621 | − | 0.0175072i | ||||
\(963\) | −1.18818e8 | −0.133046 | ||||||||
\(964\) | −2.75371e8 | + | 2.75371e8i | −0.307388 | + | 0.307388i | ||||
\(965\) | − | 9.96259e8i | − | 1.10864i | ||||||
\(966\) | 1.50012e9i | 1.66416i | ||||||||
\(967\) | −7.33020e8 | − | 7.33020e8i | −0.810656 | − | 0.810656i | 0.174077 | − | 0.984732i | \(-0.444306\pi\) |
−0.984732 | + | 0.174077i | \(0.944306\pi\) | |||||||
\(968\) | −4.63039e8 | − | 4.63039e8i | −0.510495 | − | 0.510495i | ||||
\(969\) | 9.82613e8 | 1.07997 | ||||||||
\(970\) | −6.88815e8 | − | 6.88815e8i | −0.754723 | − | 0.754723i | ||||
\(971\) | −7.95210e8 | −0.868609 | −0.434304 | − | 0.900766i | \(-0.643006\pi\) | ||||
−0.434304 | + | 0.900766i | \(0.643006\pi\) | |||||||
\(972\) | −2.62171e8 | −0.285487 | ||||||||
\(973\) | 2.01397e9i | 2.18632i | ||||||||
\(974\) | −4.20241e8 | −0.454802 | ||||||||
\(975\) | 1.01840e8 | + | 1.01840e8i | 0.109876 | + | 0.109876i | ||||
\(976\) | −2.33408e8 | + | 2.33408e8i | −0.251053 | + | 0.251053i | ||||
\(977\) | 1.07884e8 | − | 1.07884e8i | 0.115684 | − | 0.115684i | −0.646895 | − | 0.762579i | \(-0.723933\pi\) |
0.762579 | + | 0.646895i | \(0.223933\pi\) | |||||||
\(978\) | −6.04325e8 | −0.646032 | ||||||||
\(979\) | −1.34414e9 | − | 1.34414e9i | −1.43251 | − | 1.43251i | ||||
\(980\) | 7.12313e8 | − | 7.12313e8i | 0.756820 | − | 0.756820i | ||||
\(981\) | 1.76259e9 | + | 1.76259e9i | 1.86700 | + | 1.86700i | ||||
\(982\) | 4.48369e8 | − | 4.48369e8i | 0.473480 | − | 0.473480i | ||||
\(983\) | 1.13574e8i | 0.119569i | 0.998211 | + | 0.0597843i | \(0.0190413\pi\) | ||||
−0.998211 | + | 0.0597843i | \(0.980959\pi\) | |||||||
\(984\) | −1.24600e8 | − | 1.24600e8i | −0.130777 | − | 0.130777i | ||||
\(985\) | 1.16241e9 | + | 1.16241e9i | 1.21633 | + | 1.21633i | ||||
\(986\) | 1.71841e8 | − | 1.71841e8i | 0.179265 | − | 0.179265i | ||||
\(987\) | 5.04401e9i | 5.24596i | ||||||||
\(988\) | 1.46347e8 | 0.151744 | ||||||||
\(989\) | − | 4.31347e8i | − | 0.445900i | ||||||
\(990\) | 2.89499e9i | 2.98361i | ||||||||
\(991\) | −6.93258e8 | + | 6.93258e8i | −0.712318 | + | 0.712318i | −0.967020 | − | 0.254702i | \(-0.918023\pi\) |
0.254702 | + | 0.967020i | \(0.418023\pi\) | |||||||
\(992\) | − | 3.07040e8i | − | 0.314528i | ||||||
\(993\) | 1.19723e9 | − | 1.19723e9i | 1.22272 | − | 1.22272i | ||||
\(994\) | −8.80794e8 | + | 8.80794e8i | −0.896840 | + | 0.896840i | ||||
\(995\) | −1.02679e9 | −1.04235 | ||||||||
\(996\) | 6.61747e8 | 0.669752 | ||||||||
\(997\) | −1.03574e9 | − | 1.03574e9i | −1.04511 | − | 1.04511i | −0.998933 | − | 0.0461798i | \(-0.985295\pi\) |
−0.0461798 | − | 0.998933i | \(-0.514705\pi\) | |||||||
\(998\) | 9.41439e8i | 0.947111i | ||||||||
\(999\) | −1.53320e8 | − | 2.02844e9i | −0.153781 | − | 2.03454i |
(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 | 74.7.d.b.43.2 | yes | 20 | |
37.31 | odd | 4 | inner | 74.7.d.b.31.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.b.31.9 | ✓ | 20 | 37.31 | odd | 4 | inner | |
74.7.d.b.43.2 | yes | 20 | 1.1 | even | 1 | trivial |