Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(4,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.c (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: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 4.5 | ||
Character | \(\chi\) | \(=\) | 17.4 |
Dual form | 17.10.c.a.13.8 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 12.8587i | − | 0.568279i | −0.958783 | − | 0.284139i | \(-0.908292\pi\) | ||
0.958783 | − | 0.284139i | \(-0.0917079\pi\) | |||||||
\(3\) | −144.765 | + | 144.765i | −1.03185 | + | 1.03185i | −0.0323791 | + | 0.999476i | \(0.510308\pi\) |
−0.999476 | + | 0.0323791i | \(0.989692\pi\) | |||||||
\(4\) | 346.654 | 0.677059 | ||||||||
\(5\) | −85.3199 | + | 85.3199i | −0.0610500 | + | 0.0610500i | −0.736973 | − | 0.675923i | \(-0.763745\pi\) |
0.675923 | + | 0.736973i | \(0.263745\pi\) | |||||||
\(6\) | 1861.49 | + | 1861.49i | 0.586381 | + | 0.586381i | ||||
\(7\) | −3200.21 | − | 3200.21i | −0.503775 | − | 0.503775i | 0.408834 | − | 0.912609i | \(-0.365936\pi\) |
−0.912609 | + | 0.408834i | \(0.865936\pi\) | |||||||
\(8\) | − | 11041.2i | − | 0.953037i | ||||||
\(9\) | − | 22230.9i | − | 1.12945i | ||||||
\(10\) | 1097.10 | + | 1097.10i | 0.0346934 | + | 0.0346934i | ||||
\(11\) | −40916.6 | − | 40916.6i | −0.842620 | − | 0.842620i | 0.146579 | − | 0.989199i | \(-0.453174\pi\) |
−0.989199 | + | 0.146579i | \(0.953174\pi\) | |||||||
\(12\) | −50183.5 | + | 50183.5i | −0.698627 | + | 0.698627i | ||||
\(13\) | −50786.7 | −0.493179 | −0.246590 | − | 0.969120i | \(-0.579310\pi\) | ||||
−0.246590 | + | 0.969120i | \(0.579310\pi\) | |||||||
\(14\) | −41150.5 | + | 41150.5i | −0.286285 | + | 0.286285i | ||||
\(15\) | − | 24702.7i | − | 0.125989i | ||||||
\(16\) | 35512.1 | 0.135468 | ||||||||
\(17\) | −51551.8 | − | 340485.i | −0.149701 | − | 0.988731i | ||||
\(18\) | −285861. | −0.641842 | ||||||||
\(19\) | − | 815845.i | − | 1.43621i | −0.695937 | − | 0.718103i | \(-0.745011\pi\) | ||
0.695937 | − | 0.718103i | \(-0.254989\pi\) | |||||||
\(20\) | −29576.5 | + | 29576.5i | −0.0413344 | + | 0.0413344i | ||||
\(21\) | 926557. | 1.03965 | ||||||||
\(22\) | −526133. | + | 526133.i | −0.478843 | + | 0.478843i | ||||
\(23\) | 526927. | + | 526927.i | 0.392622 | + | 0.392622i | 0.875621 | − | 0.482999i | \(-0.160452\pi\) |
−0.482999 | + | 0.875621i | \(0.660452\pi\) | |||||||
\(24\) | 1.59838e6 | + | 1.59838e6i | 0.983396 | + | 0.983396i | ||||
\(25\) | 1.93857e6i | 0.992546i | ||||||||
\(26\) | 653050.i | 0.280263i | ||||||||
\(27\) | 368852. | + | 368852.i | 0.133572 | + | 0.133572i | ||||
\(28\) | −1.10937e6 | − | 1.10937e6i | −0.341086 | − | 0.341086i | ||||
\(29\) | −714818. | + | 714818.i | −0.187674 | + | 0.187674i | −0.794690 | − | 0.607016i | \(-0.792367\pi\) |
0.607016 | + | 0.794690i | \(0.292367\pi\) | |||||||
\(30\) | −317644. | −0.0715971 | ||||||||
\(31\) | −924541. | + | 924541.i | −0.179804 | + | 0.179804i | −0.791270 | − | 0.611467i | \(-0.790580\pi\) |
0.611467 | + | 0.791270i | \(0.290580\pi\) | |||||||
\(32\) | − | 6.10972e6i | − | 1.03002i | ||||||
\(33\) | 1.18466e7 | 1.73892 | ||||||||
\(34\) | −4.37819e6 | + | 662888.i | −0.561875 | + | 0.0850717i | ||||
\(35\) | 546083. | 0.0615109 | ||||||||
\(36\) | − | 7.70645e6i | − | 0.764703i | ||||||
\(37\) | −1.11504e7 | + | 1.11504e7i | −0.978098 | + | 0.978098i | −0.999765 | − | 0.0216670i | \(-0.993103\pi\) |
0.0216670 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(38\) | −1.04907e7 | −0.816165 | ||||||||
\(39\) | 7.35215e6 | − | 7.35215e6i | 0.508889 | − | 0.508889i | ||||
\(40\) | 942031. | + | 942031.i | 0.0581829 | + | 0.0581829i | ||||
\(41\) | −3.49520e6 | − | 3.49520e6i | −0.193172 | − | 0.193172i | 0.603893 | − | 0.797065i | \(-0.293615\pi\) |
−0.797065 | + | 0.603893i | \(0.793615\pi\) | |||||||
\(42\) | − | 1.19143e7i | − | 0.590809i | ||||||
\(43\) | 4.64999e6i | 0.207417i | 0.994608 | + | 0.103708i | \(0.0330709\pi\) | ||||
−0.994608 | + | 0.103708i | \(0.966929\pi\) | |||||||
\(44\) | −1.41839e7 | − | 1.41839e7i | −0.570504 | − | 0.570504i | ||||
\(45\) | 1.89674e6 | + | 1.89674e6i | 0.0689528 | + | 0.0689528i | ||||
\(46\) | 6.77559e6 | − | 6.77559e6i | 0.223119 | − | 0.223119i | ||||
\(47\) | −3.34810e7 | −1.00082 | −0.500412 | − | 0.865787i | \(-0.666818\pi\) | ||||
−0.500412 | + | 0.865787i | \(0.666818\pi\) | |||||||
\(48\) | −5.14092e6 | + | 5.14092e6i | −0.139783 | + | 0.139783i | ||||
\(49\) | − | 1.98710e7i | − | 0.492421i | ||||||
\(50\) | 2.49274e7 | 0.564043 | ||||||||
\(51\) | 5.67533e7 | + | 4.18275e7i | 1.17470 | + | 0.865758i | ||||
\(52\) | −1.76054e7 | −0.333912 | ||||||||
\(53\) | 5.09370e7i | 0.886731i | 0.896341 | + | 0.443366i | \(0.146216\pi\) | ||||
−0.896341 | + | 0.443366i | \(0.853784\pi\) | |||||||
\(54\) | 4.74295e6 | − | 4.74295e6i | 0.0759061 | − | 0.0759061i | ||||
\(55\) | 6.98199e6 | 0.102884 | ||||||||
\(56\) | −3.53340e7 | + | 3.53340e7i | −0.480117 | + | 0.480117i | ||||
\(57\) | 1.18106e8 | + | 1.18106e8i | 1.48196 | + | 1.48196i | ||||
\(58\) | 9.19162e6 | + | 9.19162e6i | 0.106651 | + | 0.106651i | ||||
\(59\) | − | 1.72235e8i | − | 1.85049i | −0.379371 | − | 0.925245i | \(-0.623860\pi\) | ||
0.379371 | − | 0.925245i | \(-0.376140\pi\) | |||||||
\(60\) | − | 8.56330e6i | − | 0.0853023i | ||||||
\(61\) | 3.40091e7 | + | 3.40091e7i | 0.314492 | + | 0.314492i | 0.846647 | − | 0.532155i | \(-0.178618\pi\) |
−0.532155 | + | 0.846647i | \(0.678618\pi\) | |||||||
\(62\) | 1.18884e7 | + | 1.18884e7i | 0.102179 | + | 0.102179i | ||||
\(63\) | −7.11436e7 | + | 7.11436e7i | −0.568988 | + | 0.568988i | ||||
\(64\) | −6.03807e7 | −0.449871 | ||||||||
\(65\) | 4.33312e6 | − | 4.33312e6i | 0.0301086 | − | 0.0301086i | ||||
\(66\) | − | 1.52332e8i | − | 0.988194i | ||||||
\(67\) | 2.00253e8 | 1.21407 | 0.607033 | − | 0.794677i | \(-0.292360\pi\) | ||||
0.607033 | + | 0.794677i | \(0.292360\pi\) | |||||||
\(68\) | −1.78706e7 | − | 1.18031e8i | −0.101356 | − | 0.669429i | ||||
\(69\) | −1.52561e8 | −0.810259 | ||||||||
\(70\) | − | 7.02191e6i | − | 0.0349554i | ||||||
\(71\) | 7.24254e7 | − | 7.24254e7i | 0.338242 | − | 0.338242i | −0.517463 | − | 0.855706i | \(-0.673124\pi\) |
0.855706 | + | 0.517463i | \(0.173124\pi\) | |||||||
\(72\) | −2.45455e8 | −1.07641 | ||||||||
\(73\) | −3.09947e8 | + | 3.09947e8i | −1.27742 | + | 1.27742i | −0.335319 | + | 0.942105i | \(0.608844\pi\) |
−0.942105 | + | 0.335319i | \(0.891156\pi\) | |||||||
\(74\) | 1.43379e8 | + | 1.43379e8i | 0.555833 | + | 0.555833i | ||||
\(75\) | −2.80637e8 | − | 2.80637e8i | −1.02416 | − | 1.02416i | ||||
\(76\) | − | 2.82816e8i | − | 0.972396i | ||||||
\(77\) | 2.61883e8i | 0.848983i | ||||||||
\(78\) | −9.45390e7 | − | 9.45390e7i | −0.289191 | − | 0.289191i | ||||
\(79\) | 2.19857e8 | + | 2.19857e8i | 0.635064 | + | 0.635064i | 0.949334 | − | 0.314270i | \(-0.101760\pi\) |
−0.314270 | + | 0.949334i | \(0.601760\pi\) | |||||||
\(80\) | −3.02989e6 | + | 3.02989e6i | −0.00827031 | + | 0.00827031i | ||||
\(81\) | 3.30778e8 | 0.853795 | ||||||||
\(82\) | −4.49437e7 | + | 4.49437e7i | −0.109776 | + | 0.109776i | ||||
\(83\) | − | 8.30705e8i | − | 1.92130i | −0.277761 | − | 0.960650i | \(-0.589592\pi\) | ||
0.277761 | − | 0.960650i | \(-0.410408\pi\) | |||||||
\(84\) | 3.21195e8 | 0.703902 | ||||||||
\(85\) | 3.34486e7 | + | 2.46518e7i | 0.0695012 | + | 0.0512228i | ||||
\(86\) | 5.97928e7 | 0.117871 | ||||||||
\(87\) | − | 2.06962e8i | − | 0.387305i | ||||||
\(88\) | −4.51766e8 | + | 4.51766e8i | −0.803049 | + | 0.803049i | ||||
\(89\) | 6.52199e7 | 0.110186 | 0.0550928 | − | 0.998481i | \(-0.482455\pi\) | ||||
0.0550928 | + | 0.998481i | \(0.482455\pi\) | |||||||
\(90\) | 2.43896e7 | − | 2.43896e7i | 0.0391844 | − | 0.0391844i | ||||
\(91\) | 1.62528e8 | + | 1.62528e8i | 0.248452 | + | 0.248452i | ||||
\(92\) | 1.82661e8 | + | 1.82661e8i | 0.265829 | + | 0.265829i | ||||
\(93\) | − | 2.67683e8i | − | 0.371063i | ||||||
\(94\) | 4.30522e8i | 0.568748i | ||||||||
\(95\) | 6.96078e7 | + | 6.96078e7i | 0.0876803 | + | 0.0876803i | ||||
\(96\) | 8.84474e8 | + | 8.84474e8i | 1.06283 | + | 1.06283i | ||||
\(97\) | −1.59423e8 | + | 1.59423e8i | −0.182843 | + | 0.182843i | −0.792594 | − | 0.609750i | \(-0.791270\pi\) |
0.609750 | + | 0.792594i | \(0.291270\pi\) | |||||||
\(98\) | −2.55514e8 | −0.279832 | ||||||||
\(99\) | −9.09613e8 | + | 9.09613e8i | −0.951696 | + | 0.951696i | ||||
\(100\) | 6.72012e8i | 0.672012i | ||||||||
\(101\) | 1.79147e9 | 1.71303 | 0.856514 | − | 0.516124i | \(-0.172626\pi\) | ||||
0.856514 | + | 0.516124i | \(0.172626\pi\) | |||||||
\(102\) | 5.37847e8 | − | 7.29773e8i | 0.491992 | − | 0.667555i | ||||
\(103\) | −2.00302e9 | −1.75355 | −0.876773 | − | 0.480904i | \(-0.840308\pi\) | ||||
−0.876773 | + | 0.480904i | \(0.840308\pi\) | |||||||
\(104\) | 5.60744e8i | 0.470018i | ||||||||
\(105\) | −7.90538e7 | + | 7.90538e7i | −0.0634704 | + | 0.0634704i | ||||
\(106\) | 6.54983e8 | 0.503911 | ||||||||
\(107\) | 5.51678e8 | − | 5.51678e8i | 0.406873 | − | 0.406873i | −0.473774 | − | 0.880647i | \(-0.657109\pi\) |
0.880647 | + | 0.473774i | \(0.157109\pi\) | |||||||
\(108\) | 1.27864e8 | + | 1.27864e8i | 0.0904361 | + | 0.0904361i | ||||
\(109\) | −1.52440e9 | − | 1.52440e9i | −1.03438 | − | 1.03438i | −0.999388 | − | 0.0349930i | \(-0.988859\pi\) |
−0.0349930 | − | 0.999388i | \(-0.511141\pi\) | |||||||
\(110\) | − | 8.97793e7i | − | 0.0584668i | ||||||
\(111\) | − | 3.22838e9i | − | 2.01851i | ||||||
\(112\) | −1.13646e8 | − | 1.13646e8i | −0.0682454 | − | 0.0682454i | ||||
\(113\) | −8.00180e8 | − | 8.00180e8i | −0.461673 | − | 0.461673i | 0.437530 | − | 0.899204i | \(-0.355853\pi\) |
−0.899204 | + | 0.437530i | \(0.855853\pi\) | |||||||
\(114\) | 1.51869e9 | − | 1.51869e9i | 0.842164 | − | 0.842164i | ||||
\(115\) | −8.99147e7 | −0.0479392 | ||||||||
\(116\) | −2.47795e8 | + | 2.47795e8i | −0.127067 | + | 0.127067i | ||||
\(117\) | 1.12904e9i | 0.557021i | ||||||||
\(118\) | −2.21471e9 | −1.05159 | ||||||||
\(119\) | −9.24647e8 | + | 1.25460e9i | −0.422683 | + | 0.573514i | ||||
\(120\) | −2.72747e8 | −0.120073 | ||||||||
\(121\) | 9.90381e8i | 0.420018i | ||||||||
\(122\) | 4.37312e8 | − | 4.37312e8i | 0.178719 | − | 0.178719i | ||||
\(123\) | 1.01197e9 | 0.398651 | ||||||||
\(124\) | −3.20496e8 | + | 3.20496e8i | −0.121738 | + | 0.121738i | ||||
\(125\) | −3.32039e8 | − | 3.32039e8i | −0.121645 | − | 0.121645i | ||||
\(126\) | 9.14813e8 | + | 9.14813e8i | 0.323344 | + | 0.323344i | ||||
\(127\) | 3.66984e9i | 1.25179i | 0.779908 | + | 0.625894i | \(0.215266\pi\) | ||||
−0.779908 | + | 0.625894i | \(0.784734\pi\) | |||||||
\(128\) | − | 2.35176e9i | − | 0.774369i | ||||||
\(129\) | −6.73157e8 | − | 6.73157e8i | −0.214024 | − | 0.214024i | ||||
\(130\) | −5.57182e7 | − | 5.57182e7i | −0.0171101 | − | 0.0171101i | ||||
\(131\) | −1.34806e9 | + | 1.34806e9i | −0.399933 | + | 0.399933i | −0.878210 | − | 0.478276i | \(-0.841262\pi\) |
0.478276 | + | 0.878210i | \(0.341262\pi\) | |||||||
\(132\) | 4.10667e9 | 1.17735 | ||||||||
\(133\) | −2.61087e9 | + | 2.61087e9i | −0.723525 | + | 0.723525i | ||||
\(134\) | − | 2.57499e9i | − | 0.689928i | ||||||
\(135\) | −6.29408e7 | −0.0163091 | ||||||||
\(136\) | −3.75935e9 | + | 5.69192e8i | −0.942298 | + | 0.142670i | ||||
\(137\) | 2.68382e9 | 0.650895 | 0.325448 | − | 0.945560i | \(-0.394485\pi\) | ||||
0.325448 | + | 0.945560i | \(0.394485\pi\) | |||||||
\(138\) | 1.96174e9i | 0.460453i | ||||||||
\(139\) | 3.06981e9 | − | 3.06981e9i | 0.697501 | − | 0.697501i | −0.266370 | − | 0.963871i | \(-0.585824\pi\) |
0.963871 | + | 0.266370i | \(0.0858243\pi\) | |||||||
\(140\) | 1.89302e8 | 0.0416465 | ||||||||
\(141\) | 4.84688e9 | − | 4.84688e9i | 1.03271 | − | 1.03271i | ||||
\(142\) | −9.31295e8 | − | 9.31295e8i | −0.192216 | − | 0.192216i | ||||
\(143\) | 2.07802e9 | + | 2.07802e9i | 0.415563 | + | 0.415563i | ||||
\(144\) | − | 7.89467e8i | − | 0.153004i | ||||||
\(145\) | − | 1.21976e8i | − | 0.0229150i | ||||||
\(146\) | 3.98551e9 | + | 3.98551e9i | 0.725933 | + | 0.725933i | ||||
\(147\) | 2.87662e9 | + | 2.87662e9i | 0.508107 | + | 0.508107i | ||||
\(148\) | −3.86533e9 | + | 3.86533e9i | −0.662230 | + | 0.662230i | ||||
\(149\) | 7.27303e9 | 1.20886 | 0.604432 | − | 0.796657i | \(-0.293400\pi\) | ||||
0.604432 | + | 0.796657i | \(0.293400\pi\) | |||||||
\(150\) | −3.60862e9 | + | 3.60862e9i | −0.582010 | + | 0.582010i | ||||
\(151\) | 4.35149e9i | 0.681149i | 0.940218 | + | 0.340574i | \(0.110621\pi\) | ||||
−0.940218 | + | 0.340574i | \(0.889379\pi\) | |||||||
\(152\) | −9.00788e9 | −1.36876 | ||||||||
\(153\) | −7.56931e9 | + | 1.14604e9i | −1.11672 | + | 0.169079i | ||||
\(154\) | 3.36747e9 | 0.482459 | ||||||||
\(155\) | − | 1.57764e8i | − | 0.0219540i | ||||||
\(156\) | 2.54865e9 | − | 2.54865e9i | 0.344548 | − | 0.344548i | ||||
\(157\) | 8.25994e9 | 1.08500 | 0.542498 | − | 0.840057i | \(-0.317478\pi\) | ||||
0.542498 | + | 0.840057i | \(0.317478\pi\) | |||||||
\(158\) | 2.82707e9 | − | 2.82707e9i | 0.360894 | − | 0.360894i | ||||
\(159\) | −7.37391e9 | − | 7.37391e9i | −0.914978 | − | 0.914978i | ||||
\(160\) | 5.21280e8 | + | 5.21280e8i | 0.0628827 | + | 0.0628827i | ||||
\(161\) | − | 3.37255e9i | − | 0.395587i | ||||||
\(162\) | − | 4.25336e9i | − | 0.485194i | ||||||
\(163\) | −3.57804e9 | − | 3.57804e9i | −0.397009 | − | 0.397009i | 0.480168 | − | 0.877177i | \(-0.340576\pi\) |
−0.877177 | + | 0.480168i | \(0.840576\pi\) | |||||||
\(164\) | −1.21163e9 | − | 1.21163e9i | −0.130789 | − | 0.130789i | ||||
\(165\) | −1.01075e9 | + | 1.01075e9i | −0.106161 | + | 0.106161i | ||||
\(166\) | −1.06818e10 | −1.09183 | ||||||||
\(167\) | −1.03033e9 | + | 1.03033e9i | −0.102506 | + | 0.102506i | −0.756500 | − | 0.653994i | \(-0.773092\pi\) |
0.653994 | + | 0.756500i | \(0.273092\pi\) | |||||||
\(168\) | − | 1.02303e10i | − | 0.990822i | ||||||
\(169\) | −8.02521e9 | −0.756774 | ||||||||
\(170\) | 3.16990e8 | − | 4.30105e8i | 0.0291088 | − | 0.0394961i | ||||
\(171\) | −1.81370e10 | −1.62212 | ||||||||
\(172\) | 1.61194e9i | 0.140433i | ||||||||
\(173\) | 6.57271e9 | − | 6.57271e9i | 0.557875 | − | 0.557875i | −0.370827 | − | 0.928702i | \(-0.620926\pi\) |
0.928702 | + | 0.370827i | \(0.120926\pi\) | |||||||
\(174\) | −2.66125e9 | −0.220097 | ||||||||
\(175\) | 6.20381e9 | − | 6.20381e9i | 0.500020 | − | 0.500020i | ||||
\(176\) | −1.45303e9 | − | 1.45303e9i | −0.114148 | − | 0.114148i | ||||
\(177\) | 2.49336e10 | + | 2.49336e10i | 1.90944 | + | 1.90944i | ||||
\(178\) | − | 8.38642e8i | − | 0.0626162i | ||||||
\(179\) | − | 5.29738e9i | − | 0.385676i | −0.981231 | − | 0.192838i | \(-0.938231\pi\) | ||
0.981231 | − | 0.192838i | \(-0.0617692\pi\) | |||||||
\(180\) | 6.57513e8 | + | 6.57513e8i | 0.0466851 | + | 0.0466851i | ||||
\(181\) | 1.44218e10 | + | 1.44218e10i | 0.998771 | + | 0.998771i | 0.999999 | − | 0.00122856i | \(-0.000391062\pi\) |
−0.00122856 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(182\) | 2.08990e9 | − | 2.08990e9i | 0.141190 | − | 0.141190i | ||||
\(183\) | −9.84666e9 | −0.649021 | ||||||||
\(184\) | 5.81789e9 | − | 5.81789e9i | 0.374184 | − | 0.374184i | ||||
\(185\) | − | 1.90270e9i | − | 0.119426i | ||||||
\(186\) | −3.44205e9 | −0.210867 | ||||||||
\(187\) | −1.18222e10 | + | 1.60408e10i | −0.706984 | + | 0.959266i | ||||
\(188\) | −1.16063e10 | −0.677617 | ||||||||
\(189\) | − | 2.36081e9i | − | 0.134580i | ||||||
\(190\) | 8.95065e8 | − | 8.95065e8i | 0.0498269 | − | 0.0498269i | ||||
\(191\) | 1.13020e9 | 0.0614478 | 0.0307239 | − | 0.999528i | \(-0.490219\pi\) | ||||
0.0307239 | + | 0.999528i | \(0.490219\pi\) | |||||||
\(192\) | 8.74103e9 | − | 8.74103e9i | 0.464202 | − | 0.464202i | ||||
\(193\) | 2.52689e10 | + | 2.52689e10i | 1.31093 | + | 1.31093i | 0.920732 | + | 0.390195i | \(0.127592\pi\) |
0.390195 | + | 0.920732i | \(0.372408\pi\) | |||||||
\(194\) | 2.04998e9 | + | 2.04998e9i | 0.103906 | + | 0.103906i | ||||
\(195\) | 1.25457e9i | 0.0621354i | ||||||||
\(196\) | − | 6.88835e9i | − | 0.333398i | ||||||
\(197\) | −2.51679e10 | − | 2.51679e10i | −1.19055 | − | 1.19055i | −0.976912 | − | 0.213640i | \(-0.931468\pi\) |
−0.213640 | − | 0.976912i | \(-0.568532\pi\) | |||||||
\(198\) | 1.16964e10 | + | 1.16964e10i | 0.540829 | + | 0.540829i | ||||
\(199\) | 2.20881e10 | − | 2.20881e10i | 0.998436 | − | 0.998436i | −0.00156230 | − | 0.999999i | \(-0.500497\pi\) |
0.999999 | + | 0.00156230i | \(0.000497295\pi\) | |||||||
\(200\) | 2.14040e10 | 0.945933 | ||||||||
\(201\) | −2.89896e10 | + | 2.89896e10i | −1.25274 | + | 1.25274i | ||||
\(202\) | − | 2.30360e10i | − | 0.973477i | ||||||
\(203\) | 4.57513e9 | 0.189091 | ||||||||
\(204\) | 1.96738e10 | + | 1.44997e10i | 0.795339 | + | 0.586169i | ||||
\(205\) | 5.96420e8 | 0.0235863 | ||||||||
\(206\) | 2.57562e10i | 0.996503i | ||||||||
\(207\) | 1.17141e10 | − | 1.17141e10i | 0.443447 | − | 0.443447i | ||||
\(208\) | −1.80354e9 | −0.0668100 | ||||||||
\(209\) | −3.33816e10 | + | 3.33816e10i | −1.21018 | + | 1.21018i | ||||
\(210\) | 1.01653e9 | + | 1.01653e9i | 0.0360689 | + | 0.0360689i | ||||
\(211\) | −2.04603e10 | − | 2.04603e10i | −0.710627 | − | 0.710627i | 0.256039 | − | 0.966666i | \(-0.417582\pi\) |
−0.966666 | + | 0.256039i | \(0.917582\pi\) | |||||||
\(212\) | 1.76575e10i | 0.600370i | ||||||||
\(213\) | 2.09693e10i | 0.698034i | ||||||||
\(214\) | −7.09385e9 | − | 7.09385e9i | −0.231217 | − | 0.231217i | ||||
\(215\) | −3.96737e8 | − | 3.96737e8i | −0.0126628 | − | 0.0126628i | ||||
\(216\) | 4.07256e9 | − | 4.07256e9i | 0.127299 | − | 0.127299i | ||||
\(217\) | 5.91745e9 | 0.181161 | ||||||||
\(218\) | −1.96018e10 | + | 1.96018e10i | −0.587817 | + | 0.587817i | ||||
\(219\) | − | 8.97391e10i | − | 2.63623i | ||||||
\(220\) | 2.42034e9 | 0.0696585 | ||||||||
\(221\) | 2.61815e9 | + | 1.72921e10i | 0.0738293 | + | 0.487622i | ||||
\(222\) | −4.15127e10 | −1.14708 | ||||||||
\(223\) | − | 5.45398e10i | − | 1.47687i | −0.674326 | − | 0.738434i | \(-0.735566\pi\) | ||
0.674326 | − | 0.738434i | \(-0.264434\pi\) | |||||||
\(224\) | −1.95524e10 | + | 1.95524e10i | −0.518899 | + | 0.518899i | ||||
\(225\) | 4.30961e10 | 1.12103 | ||||||||
\(226\) | −1.02893e10 | + | 1.02893e10i | −0.262359 | + | 0.262359i | ||||
\(227\) | −6.48779e9 | − | 6.48779e9i | −0.162174 | − | 0.162174i | 0.621355 | − | 0.783529i | \(-0.286582\pi\) |
−0.783529 | + | 0.621355i | \(0.786582\pi\) | |||||||
\(228\) | 4.09419e10 | + | 4.09419e10i | 1.00337 | + | 1.00337i | ||||
\(229\) | − | 2.94750e10i | − | 0.708263i | −0.935196 | − | 0.354131i | \(-0.884777\pi\) | ||
0.935196 | − | 0.354131i | \(-0.115223\pi\) | |||||||
\(230\) | 1.15619e9i | 0.0272428i | ||||||||
\(231\) | −3.79115e10 | − | 3.79115e10i | −0.876027 | − | 0.876027i | ||||
\(232\) | 7.89243e9 | + | 7.89243e9i | 0.178861 | + | 0.178861i | ||||
\(233\) | 3.92131e10 | − | 3.92131e10i | 0.871625 | − | 0.871625i | −0.121025 | − | 0.992649i | \(-0.538618\pi\) |
0.992649 | + | 0.121025i | \(0.0386181\pi\) | |||||||
\(234\) | 1.45179e10 | 0.316543 | ||||||||
\(235\) | 2.85660e9 | − | 2.85660e9i | 0.0611003 | − | 0.0611003i | ||||
\(236\) | − | 5.97059e10i | − | 1.25289i | ||||||
\(237\) | −6.36552e10 | −1.31059 | ||||||||
\(238\) | 1.61325e10 | + | 1.18897e10i | 0.325916 | + | 0.240202i | ||||
\(239\) | −6.16221e10 | −1.22165 | −0.610823 | − | 0.791767i | \(-0.709161\pi\) | ||||
−0.610823 | + | 0.791767i | \(0.709161\pi\) | |||||||
\(240\) | − | 8.77245e8i | − | 0.0170675i | ||||||
\(241\) | 3.17781e10 | − | 3.17781e10i | 0.606808 | − | 0.606808i | −0.335302 | − | 0.942111i | \(-0.608838\pi\) |
0.942111 | + | 0.335302i | \(0.108838\pi\) | |||||||
\(242\) | 1.27350e10 | 0.238687 | ||||||||
\(243\) | −5.51452e10 | + | 5.51452e10i | −1.01456 | + | 1.01456i | ||||
\(244\) | 1.17894e10 | + | 1.17894e10i | 0.212930 | + | 0.212930i | ||||
\(245\) | 1.69539e9 | + | 1.69539e9i | 0.0300623 | + | 0.0300623i | ||||
\(246\) | − | 1.30126e10i | − | 0.226545i | ||||||
\(247\) | 4.14341e10i | 0.708307i | ||||||||
\(248\) | 1.02080e10 | + | 1.02080e10i | 0.171360 | + | 0.171360i | ||||
\(249\) | 1.20257e11 | + | 1.20257e11i | 1.98250 | + | 1.98250i | ||||
\(250\) | −4.26958e9 | + | 4.26958e9i | −0.0691282 | + | 0.0691282i | ||||
\(251\) | −3.67666e10 | −0.584685 | −0.292343 | − | 0.956314i | \(-0.594435\pi\) | ||||
−0.292343 | + | 0.956314i | \(0.594435\pi\) | |||||||
\(252\) | −2.46622e10 | + | 2.46622e10i | −0.385239 | + | 0.385239i | ||||
\(253\) | − | 4.31201e10i | − | 0.661663i | ||||||
\(254\) | 4.71893e10 | 0.711365 | ||||||||
\(255\) | −8.41091e9 | + | 1.27347e9i | −0.124570 | + | 0.0188607i | ||||
\(256\) | −6.11554e10 | −0.889929 | ||||||||
\(257\) | 1.06275e11i | 1.51962i | 0.650148 | + | 0.759808i | \(0.274707\pi\) | ||||
−0.650148 | + | 0.759808i | \(0.725293\pi\) | |||||||
\(258\) | −8.65591e9 | + | 8.65591e9i | −0.121625 | + | 0.121625i | ||||
\(259\) | 7.13671e10 | 0.985484 | ||||||||
\(260\) | 1.50209e9 | − | 1.50209e9i | 0.0203853 | − | 0.0203853i | ||||
\(261\) | 1.58911e10 | + | 1.58911e10i | 0.211968 | + | 0.211968i | ||||
\(262\) | 1.73342e10 | + | 1.73342e10i | 0.227274 | + | 0.227274i | ||||
\(263\) | 4.15683e10i | 0.535749i | 0.963454 | + | 0.267875i | \(0.0863213\pi\) | ||||
−0.963454 | + | 0.267875i | \(0.913679\pi\) | |||||||
\(264\) | − | 1.30800e11i | − | 1.65726i | ||||||
\(265\) | −4.34594e9 | − | 4.34594e9i | −0.0541349 | − | 0.0541349i | ||||
\(266\) | 3.35724e10 | + | 3.35724e10i | 0.411164 | + | 0.411164i | ||||
\(267\) | −9.44157e9 | + | 9.44157e9i | −0.113696 | + | 0.113696i | ||||
\(268\) | 6.94185e10 | 0.821994 | ||||||||
\(269\) | 1.36436e10 | − | 1.36436e10i | 0.158871 | − | 0.158871i | −0.623195 | − | 0.782066i | \(-0.714166\pi\) |
0.782066 | + | 0.623195i | \(0.214166\pi\) | |||||||
\(270\) | 8.09336e8i | 0.00926813i | ||||||||
\(271\) | −5.51694e10 | −0.621350 | −0.310675 | − | 0.950516i | \(-0.600555\pi\) | ||||
−0.310675 | + | 0.950516i | \(0.600555\pi\) | |||||||
\(272\) | −1.83071e9 | − | 1.20914e10i | −0.0202796 | − | 0.133941i | ||||
\(273\) | −4.70568e10 | −0.512732 | ||||||||
\(274\) | − | 3.45104e10i | − | 0.369890i | ||||||
\(275\) | 7.93194e10 | − | 7.93194e10i | 0.836339 | − | 0.836339i | ||||
\(276\) | −5.28860e10 | −0.548593 | ||||||||
\(277\) | 1.05739e11 | − | 1.05739e11i | 1.07914 | − | 1.07914i | 0.0825522 | − | 0.996587i | \(-0.473693\pi\) |
0.996587 | − | 0.0825522i | \(-0.0263071\pi\) | |||||||
\(278\) | −3.94737e10 | − | 3.94737e10i | −0.396375 | − | 0.396375i | ||||
\(279\) | 2.05534e10 | + | 2.05534e10i | 0.203079 | + | 0.203079i | ||||
\(280\) | − | 6.02939e9i | − | 0.0586222i | ||||||
\(281\) | 8.27561e10i | 0.791811i | 0.918291 | + | 0.395906i | \(0.129569\pi\) | ||||
−0.918291 | + | 0.395906i | \(0.870431\pi\) | |||||||
\(282\) | −6.23245e10 | − | 6.23245e10i | −0.586865 | − | 0.586865i | ||||
\(283\) | 3.63906e10 | + | 3.63906e10i | 0.337249 | + | 0.337249i | 0.855331 | − | 0.518082i | \(-0.173354\pi\) |
−0.518082 | + | 0.855331i | \(0.673354\pi\) | |||||||
\(284\) | 2.51066e10 | − | 2.51066e10i | 0.229010 | − | 0.229010i | ||||
\(285\) | −2.01536e10 | −0.180947 | ||||||||
\(286\) | 2.67206e10 | − | 2.67206e10i | 0.236156 | − | 0.236156i | ||||
\(287\) | 2.23707e10i | 0.194631i | ||||||||
\(288\) | −1.35825e11 | −1.16336 | ||||||||
\(289\) | −1.13273e11 | + | 3.51053e10i | −0.955179 | + | 0.296027i | ||||
\(290\) | −1.56846e9 | −0.0130221 | ||||||||
\(291\) | − | 4.61579e10i | − | 0.377336i | ||||||
\(292\) | −1.07445e11 | + | 1.07445e11i | −0.864891 | + | 0.864891i | ||||
\(293\) | −1.21927e11 | −0.966484 | −0.483242 | − | 0.875487i | \(-0.660541\pi\) | ||||
−0.483242 | + | 0.875487i | \(0.660541\pi\) | |||||||
\(294\) | 3.69896e10 | − | 3.69896e10i | 0.288746 | − | 0.288746i | ||||
\(295\) | 1.46951e10 | + | 1.46951e10i | 0.112972 | + | 0.112972i | ||||
\(296\) | 1.23113e11 | + | 1.23113e11i | 0.932164 | + | 0.932164i | ||||
\(297\) | − | 3.01843e10i | − | 0.225101i | ||||||
\(298\) | − | 9.35216e10i | − | 0.686972i | ||||||
\(299\) | −2.67609e10 | − | 2.67609e10i | −0.193633 | − | 0.193633i | ||||
\(300\) | −9.72840e10 | − | 9.72840e10i | −0.693419 | − | 0.693419i | ||||
\(301\) | 1.48809e10 | − | 1.48809e10i | 0.104491 | − | 0.104491i | ||||
\(302\) | 5.59545e10 | 0.387082 | ||||||||
\(303\) | −2.59343e11 | + | 2.59343e11i | −1.76760 | + | 1.76760i | ||||
\(304\) | − | 2.89724e10i | − | 0.194560i | ||||||
\(305\) | −5.80330e9 | −0.0383995 | ||||||||
\(306\) | 1.47366e10 | + | 9.73313e10i | 0.0960841 | + | 0.634609i | ||||
\(307\) | 9.71611e10 | 0.624266 | 0.312133 | − | 0.950038i | \(-0.398957\pi\) | ||||
0.312133 | + | 0.950038i | \(0.398957\pi\) | |||||||
\(308\) | 9.07828e10i | 0.574811i | ||||||||
\(309\) | 2.89967e11 | − | 2.89967e11i | 1.80940 | − | 1.80940i | ||||
\(310\) | −2.02863e9 | −0.0124760 | ||||||||
\(311\) | 1.57770e11 | − | 1.57770e11i | 0.956317 | − | 0.956317i | −0.0427677 | − | 0.999085i | \(-0.513618\pi\) |
0.999085 | + | 0.0427677i | \(0.0136175\pi\) | |||||||
\(312\) | −8.11763e10 | − | 8.11763e10i | −0.484991 | − | 0.484991i | ||||
\(313\) | −1.12949e10 | − | 1.12949e10i | −0.0665171 | − | 0.0665171i | 0.673066 | − | 0.739583i | \(-0.264977\pi\) |
−0.739583 | + | 0.673066i | \(0.764977\pi\) | |||||||
\(314\) | − | 1.06212e11i | − | 0.616581i | ||||||
\(315\) | − | 1.21399e10i | − | 0.0694734i | ||||||
\(316\) | 7.62142e10 | + | 7.62142e10i | 0.429976 | + | 0.429976i | ||||
\(317\) | −1.42973e11 | − | 1.42973e11i | −0.795220 | − | 0.795220i | 0.187118 | − | 0.982337i | \(-0.440085\pi\) |
−0.982337 | + | 0.187118i | \(0.940085\pi\) | |||||||
\(318\) | −9.48188e10 | + | 9.48188e10i | −0.519963 | + | 0.519963i | ||||
\(319\) | 5.84958e10 | 0.316276 | ||||||||
\(320\) | 5.15168e9 | − | 5.15168e9i | 0.0274646 | − | 0.0274646i | ||||
\(321\) | 1.59728e11i | 0.839667i | ||||||||
\(322\) | −4.33666e10 | −0.224804 | ||||||||
\(323\) | −2.77783e11 | + | 4.20583e10i | −1.42002 | + | 0.215001i | ||||
\(324\) | 1.14665e11 | 0.578069 | ||||||||
\(325\) | − | 9.84534e10i | − | 0.489503i | ||||||
\(326\) | −4.60089e10 | + | 4.60089e10i | −0.225612 | + | 0.225612i | ||||
\(327\) | 4.41361e11 | 2.13466 | ||||||||
\(328\) | −3.85911e10 | + | 3.85911e10i | −0.184100 | + | 0.184100i | ||||
\(329\) | 1.07146e11 | + | 1.07146e11i | 0.504191 | + | 0.504191i | ||||
\(330\) | 1.29969e10 | + | 1.29969e10i | 0.0603292 | + | 0.0603292i | ||||
\(331\) | 3.68035e11i | 1.68524i | 0.538505 | + | 0.842622i | \(0.318989\pi\) | ||||
−0.538505 | + | 0.842622i | \(0.681011\pi\) | |||||||
\(332\) | − | 2.87967e11i | − | 1.30083i | ||||||
\(333\) | 2.47884e11 | + | 2.47884e11i | 1.10471 | + | 1.10471i | ||||
\(334\) | 1.32486e10 | + | 1.32486e10i | 0.0582522 | + | 0.0582522i | ||||
\(335\) | −1.70856e10 | + | 1.70856e10i | −0.0741187 | + | 0.0741187i | ||||
\(336\) | 3.29040e10 | 0.140839 | ||||||||
\(337\) | −9.59112e10 | + | 9.59112e10i | −0.405074 | + | 0.405074i | −0.880017 | − | 0.474942i | \(-0.842469\pi\) |
0.474942 | + | 0.880017i | \(0.342469\pi\) | |||||||
\(338\) | 1.03194e11i | 0.430059i | ||||||||
\(339\) | 2.31676e11 | 0.952759 | ||||||||
\(340\) | 1.15951e10 | + | 8.54565e9i | 0.0470564 | + | 0.0346809i | ||||
\(341\) | 7.56581e10 | 0.303013 | ||||||||
\(342\) | 2.33218e11i | 0.921817i | ||||||||
\(343\) | −1.92731e11 | + | 1.92731e11i | −0.751845 | + | 0.751845i | ||||
\(344\) | 5.13413e10 | 0.197676 | ||||||||
\(345\) | 1.30165e10 | − | 1.30165e10i | 0.0494663 | − | 0.0494663i | ||||
\(346\) | −8.45164e10 | − | 8.45164e10i | −0.317029 | − | 0.317029i | ||||
\(347\) | −1.07632e11 | − | 1.07632e11i | −0.398528 | − | 0.398528i | 0.479186 | − | 0.877713i | \(-0.340932\pi\) |
−0.877713 | + | 0.479186i | \(0.840932\pi\) | |||||||
\(348\) | − | 7.17441e10i | − | 0.262228i | ||||||
\(349\) | − | 1.78457e11i | − | 0.643903i | −0.946756 | − | 0.321951i | \(-0.895661\pi\) | ||
0.946756 | − | 0.321951i | \(-0.104339\pi\) | |||||||
\(350\) | −7.97729e10 | − | 7.97729e10i | −0.284151 | − | 0.284151i | ||||
\(351\) | −1.87328e10 | − | 1.87328e10i | −0.0658749 | − | 0.0658749i | ||||
\(352\) | −2.49988e11 | + | 2.49988e11i | −0.867917 | + | 0.867917i | ||||
\(353\) | −2.96867e11 | −1.01760 | −0.508798 | − | 0.860886i | \(-0.669910\pi\) | ||||
−0.508798 | + | 0.860886i | \(0.669910\pi\) | |||||||
\(354\) | 3.20613e11 | − | 3.20613e11i | 1.08509 | − | 1.08509i | ||||
\(355\) | 1.23587e10i | 0.0412994i | ||||||||
\(356\) | 2.26088e10 | 0.0746022 | ||||||||
\(357\) | −4.77657e10 | − | 3.15479e11i | −0.155636 | − | 1.02793i | ||||
\(358\) | −6.81173e10 | −0.219171 | ||||||||
\(359\) | − | 1.67133e11i | − | 0.531052i | −0.964104 | − | 0.265526i | \(-0.914454\pi\) | ||
0.964104 | − | 0.265526i | \(-0.0855457\pi\) | |||||||
\(360\) | 2.09422e10 | − | 2.09422e10i | 0.0657146 | − | 0.0657146i | ||||
\(361\) | −3.42916e11 | −1.06269 | ||||||||
\(362\) | 1.85445e11 | − | 1.85445e11i | 0.567580 | − | 0.567580i | ||||
\(363\) | −1.43373e11 | − | 1.43373e11i | −0.433398 | − | 0.433398i | ||||
\(364\) | 5.63410e10 | + | 5.63410e10i | 0.168216 | + | 0.168216i | ||||
\(365\) | − | 5.28893e10i | − | 0.155973i | ||||||
\(366\) | 1.26615e11i | 0.368825i | ||||||||
\(367\) | −2.27989e11 | − | 2.27989e11i | −0.656020 | − | 0.656020i | 0.298416 | − | 0.954436i | \(-0.403542\pi\) |
−0.954436 | + | 0.298416i | \(0.903542\pi\) | |||||||
\(368\) | 1.87123e10 | + | 1.87123e10i | 0.0531877 | + | 0.0531877i | ||||
\(369\) | −7.77015e10 | + | 7.77015e10i | −0.218178 | + | 0.218178i | ||||
\(370\) | −2.44662e10 | −0.0678671 | ||||||||
\(371\) | 1.63009e11 | − | 1.63009e11i | 0.446713 | − | 0.446713i | ||||
\(372\) | − | 9.27934e10i | − | 0.251231i | ||||||
\(373\) | −3.84623e10 | −0.102883 | −0.0514417 | − | 0.998676i | \(-0.516382\pi\) | ||||
−0.0514417 | + | 0.998676i | \(0.516382\pi\) | |||||||
\(374\) | 2.06264e11 | + | 1.52018e11i | 0.545131 | + | 0.401764i | ||||
\(375\) | 9.61353e10 | 0.251040 | ||||||||
\(376\) | 3.69669e11i | 0.953823i | ||||||||
\(377\) | 3.63033e10 | − | 3.63033e10i | 0.0925571 | − | 0.0925571i | ||||
\(378\) | −3.03569e10 | −0.0764793 | ||||||||
\(379\) | −6.94178e10 | + | 6.94178e10i | −0.172820 | + | 0.172820i | −0.788217 | − | 0.615397i | \(-0.788996\pi\) |
0.615397 | + | 0.788217i | \(0.288996\pi\) | |||||||
\(380\) | 2.41299e10 | + | 2.41299e10i | 0.0593647 | + | 0.0593647i | ||||
\(381\) | −5.31266e11 | − | 5.31266e11i | −1.29166 | − | 1.29166i | ||||
\(382\) | − | 1.45329e10i | − | 0.0349195i | ||||||
\(383\) | 3.91752e11i | 0.930286i | 0.885236 | + | 0.465143i | \(0.153997\pi\) | ||||
−0.885236 | + | 0.465143i | \(0.846003\pi\) | |||||||
\(384\) | 3.40453e11 | + | 3.40453e11i | 0.799036 | + | 0.799036i | ||||
\(385\) | −2.23438e10 | − | 2.23438e10i | −0.0518304 | − | 0.0518304i | ||||
\(386\) | 3.24925e11 | − | 3.24925e11i | 0.744972 | − | 0.744972i | ||||
\(387\) | 1.03374e11 | 0.234267 | ||||||||
\(388\) | −5.52648e10 | + | 5.52648e10i | −0.123796 | + | 0.123796i | ||||
\(389\) | 4.40744e11i | 0.975917i | 0.872867 | + | 0.487959i | \(0.162258\pi\) | ||||
−0.872867 | + | 0.487959i | \(0.837742\pi\) | |||||||
\(390\) | 1.61321e10 | 0.0353102 | ||||||||
\(391\) | 1.52247e11 | − | 2.06575e11i | 0.329422 | − | 0.446974i | ||||
\(392\) | −2.19398e11 | −0.469295 | ||||||||
\(393\) | − | 3.90304e11i | − | 0.825346i | ||||||
\(394\) | −3.23626e11 | + | 3.23626e11i | −0.676566 | + | 0.676566i | ||||
\(395\) | −3.75163e10 | −0.0775413 | ||||||||
\(396\) | −3.15321e11 | + | 3.15321e11i | −0.644354 | + | 0.644354i | ||||
\(397\) | 2.39361e11 | + | 2.39361e11i | 0.483612 | + | 0.483612i | 0.906283 | − | 0.422671i | \(-0.138908\pi\) |
−0.422671 | + | 0.906283i | \(0.638908\pi\) | |||||||
\(398\) | −2.84025e11 | − | 2.84025e11i | −0.567390 | − | 0.567390i | ||||
\(399\) | − | 7.55927e11i | − | 1.49315i | ||||||
\(400\) | 6.88426e10i | 0.134458i | ||||||||
\(401\) | −1.21560e11 | − | 1.21560e11i | −0.234769 | − | 0.234769i | 0.579911 | − | 0.814680i | \(-0.303087\pi\) |
−0.814680 | + | 0.579911i | \(0.803087\pi\) | |||||||
\(402\) | 3.72769e11 | + | 3.72769e11i | 0.711905 | + | 0.711905i | ||||
\(403\) | 4.69544e10 | − | 4.69544e10i | 0.0886755 | − | 0.0886755i | ||||
\(404\) | 6.21022e11 | 1.15982 | ||||||||
\(405\) | −2.82219e10 | + | 2.82219e10i | −0.0521241 | + | 0.0521241i | ||||
\(406\) | − | 5.88302e10i | − | 0.107457i | ||||||
\(407\) | 9.12471e11 | 1.64833 | ||||||||
\(408\) | 4.61825e11 | − | 6.26623e11i | 0.825100 | − | 1.11953i | ||||
\(409\) | 1.81166e11 | 0.320126 | 0.160063 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160063 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(410\) | − | 7.66918e9i | − | 0.0134036i | ||||||
\(411\) | −3.88524e11 | + | 3.88524e11i | −0.671629 | + | 0.671629i | ||||
\(412\) | −6.94354e11 | −1.18725 | ||||||||
\(413\) | −5.51187e11 | + | 5.51187e11i | −0.932231 | + | 0.932231i | ||||
\(414\) | −1.50628e11 | − | 1.50628e11i | −0.252001 | − | 0.252001i | ||||
\(415\) | 7.08757e10 | + | 7.08757e10i | 0.117295 | + | 0.117295i | ||||
\(416\) | 3.10292e11i | 0.507985i | ||||||||
\(417\) | 8.88803e11i | 1.43944i | ||||||||
\(418\) | 4.29243e11 | + | 4.29243e11i | 0.687717 | + | 0.687717i | ||||
\(419\) | −3.78081e11 | − | 3.78081e11i | −0.599268 | − | 0.599268i | 0.340850 | − | 0.940118i | \(-0.389285\pi\) |
−0.940118 | + | 0.340850i | \(0.889285\pi\) | |||||||
\(420\) | −2.74043e10 | + | 2.74043e10i | −0.0429732 | + | 0.0429732i | ||||
\(421\) | 4.75293e10 | 0.0737381 | 0.0368691 | − | 0.999320i | \(-0.488262\pi\) | ||||
0.0368691 | + | 0.999320i | \(0.488262\pi\) | |||||||
\(422\) | −2.63093e11 | + | 2.63093e11i | −0.403835 | + | 0.403835i | ||||
\(423\) | 7.44314e11i | 1.13038i | ||||||||
\(424\) | 5.62404e11 | 0.845088 | ||||||||
\(425\) | 6.60053e11 | − | 9.99366e10i | 0.981361 | − | 0.148585i | ||||
\(426\) | 2.69638e11 | 0.396678 | ||||||||
\(427\) | − | 2.17672e11i | − | 0.316867i | ||||||
\(428\) | 1.91242e11 | − | 1.91242e11i | 0.275477 | − | 0.275477i | ||||
\(429\) | −6.01649e11 | −0.857601 | ||||||||
\(430\) | −5.10151e9 | + | 5.10151e9i | −0.00719600 | + | 0.00719600i | ||||
\(431\) | 5.96831e11 | + | 5.96831e11i | 0.833112 | + | 0.833112i | 0.987941 | − | 0.154829i | \(-0.0494827\pi\) |
−0.154829 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(432\) | 1.30987e10 | + | 1.30987e10i | 0.0180947 | + | 0.0180947i | ||||
\(433\) | 2.09001e10i | 0.0285728i | 0.999898 | + | 0.0142864i | \(0.00454766\pi\) | ||||
−0.999898 | + | 0.0142864i | \(0.995452\pi\) | |||||||
\(434\) | − | 7.60906e10i | − | 0.102950i | ||||||
\(435\) | 1.76580e10 | + | 1.76580e10i | 0.0236450 | + | 0.0236450i | ||||
\(436\) | −5.28440e11 | − | 5.28440e11i | −0.700337 | − | 0.700337i | ||||
\(437\) | 4.29891e11 | − | 4.29891e11i | 0.563886 | − | 0.563886i | ||||
\(438\) | −1.15393e12 | −1.49811 | ||||||||
\(439\) | 8.39039e11 | − | 8.39039e11i | 1.07818 | − | 1.07818i | 0.0815085 | − | 0.996673i | \(-0.474026\pi\) |
0.996673 | − | 0.0815085i | \(-0.0259738\pi\) | |||||||
\(440\) | − | 7.70893e10i | − | 0.0980522i | ||||||
\(441\) | −4.41750e11 | −0.556164 | ||||||||
\(442\) | 2.22354e11 | − | 3.36659e10i | 0.277105 | − | 0.0419556i | ||||
\(443\) | 4.19386e11 | 0.517366 | 0.258683 | − | 0.965962i | \(-0.416712\pi\) | ||||
0.258683 | + | 0.965962i | \(0.416712\pi\) | |||||||
\(444\) | − | 1.11913e12i | − | 1.36665i | ||||||
\(445\) | −5.56456e9 | + | 5.56456e9i | −0.00672683 | + | 0.00672683i | ||||
\(446\) | −7.01310e11 | −0.839273 | ||||||||
\(447\) | −1.05288e12 | + | 1.05288e12i | −1.24737 | + | 1.24737i | ||||
\(448\) | 1.93231e11 | + | 1.93231e11i | 0.226634 | + | 0.226634i | ||||
\(449\) | −4.83298e11 | − | 4.83298e11i | −0.561185 | − | 0.561185i | 0.368459 | − | 0.929644i | \(-0.379886\pi\) |
−0.929644 | + | 0.368459i | \(0.879886\pi\) | |||||||
\(450\) | − | 5.54160e11i | − | 0.637057i | ||||||
\(451\) | 2.86023e11i | 0.325542i | ||||||||
\(452\) | −2.77386e11 | − | 2.77386e11i | −0.312580 | − | 0.312580i | ||||
\(453\) | −6.29944e11 | − | 6.29944e11i | −0.702846 | − | 0.702846i | ||||
\(454\) | −8.34244e10 | + | 8.34244e10i | −0.0921599 | + | 0.0921599i | ||||
\(455\) | −2.77337e10 | −0.0303359 | ||||||||
\(456\) | 1.30403e12 | − | 1.30403e12i | 1.41236 | − | 1.41236i | ||||
\(457\) | − | 1.13726e12i | − | 1.21966i | −0.792533 | − | 0.609829i | \(-0.791238\pi\) | ||
0.792533 | − | 0.609829i | \(-0.208762\pi\) | |||||||
\(458\) | −3.79010e11 | −0.402491 | ||||||||
\(459\) | 1.06574e11 | − | 1.44604e11i | 0.112071 | − | 0.152063i | ||||
\(460\) | −3.11693e10 | −0.0324577 | ||||||||
\(461\) | 4.01702e11i | 0.414238i | 0.978316 | + | 0.207119i | \(0.0664087\pi\) | ||||
−0.978316 | + | 0.207119i | \(0.933591\pi\) | |||||||
\(462\) | −4.87492e11 | + | 4.87492e11i | −0.497828 | + | 0.497828i | ||||
\(463\) | 1.71828e12 | 1.73772 | 0.868859 | − | 0.495059i | \(-0.164854\pi\) | ||||
0.868859 | + | 0.495059i | \(0.164854\pi\) | |||||||
\(464\) | −2.53847e10 | + | 2.53847e10i | −0.0254238 | + | 0.0254238i | ||||
\(465\) | 2.28387e10 | + | 2.28387e10i | 0.0226534 | + | 0.0226534i | ||||
\(466\) | −5.04229e11 | − | 5.04229e11i | −0.495326 | − | 0.495326i | ||||
\(467\) | 1.25508e12i | 1.22108i | 0.791984 | + | 0.610542i | \(0.209048\pi\) | ||||
−0.791984 | + | 0.610542i | \(0.790952\pi\) | |||||||
\(468\) | 3.91385e11i | 0.377136i | ||||||||
\(469\) | −6.40851e11 | − | 6.40851e11i | −0.611616 | − | 0.611616i | ||||
\(470\) | −3.67321e10 | − | 3.67321e10i | −0.0347220 | − | 0.0347220i | ||||
\(471\) | −1.19575e12 | + | 1.19575e12i | −1.11956 | + | 1.11956i | ||||
\(472\) | −1.90167e12 | −1.76359 | ||||||||
\(473\) | 1.90262e11 | − | 1.90262e11i | 0.174774 | − | 0.174774i | ||||
\(474\) | 8.18522e11i | 0.744780i | ||||||||
\(475\) | 1.58157e12 | 1.42550 | ||||||||
\(476\) | −3.20533e11 | + | 4.34912e11i | −0.286181 | + | 0.388303i | ||||
\(477\) | 1.13238e12 | 1.00152 | ||||||||
\(478\) | 7.92379e11i | 0.694236i | ||||||||
\(479\) | −7.80669e11 | + | 7.80669e11i | −0.677575 | + | 0.677575i | −0.959451 | − | 0.281876i | \(-0.909043\pi\) |
0.281876 | + | 0.959451i | \(0.409043\pi\) | |||||||
\(480\) | −1.50927e11 | −0.129772 | ||||||||
\(481\) | 5.66292e11 | − | 5.66292e11i | 0.482378 | − | 0.482378i | ||||
\(482\) | −4.08625e11 | − | 4.08625e11i | −0.344836 | − | 0.344836i | ||||
\(483\) | 4.88228e11 | + | 4.88228e11i | 0.408188 | + | 0.408188i | ||||
\(484\) | 3.43320e11i | 0.284377i | ||||||||
\(485\) | − | 2.72040e10i | − | 0.0223252i | ||||||
\(486\) | 7.09095e11 | + | 7.09095e11i | 0.576555 | + | 0.576555i | ||||
\(487\) | −8.55242e11 | − | 8.55242e11i | −0.688983 | − | 0.688983i | 0.273024 | − | 0.962007i | \(-0.411976\pi\) |
−0.962007 | + | 0.273024i | \(0.911976\pi\) | |||||||
\(488\) | 3.75500e11 | − | 3.75500e11i | 0.299723 | − | 0.299723i | ||||
\(489\) | 1.03595e12 | 0.819312 | ||||||||
\(490\) | 2.18005e10 | − | 2.18005e10i | 0.0170838 | − | 0.0170838i | ||||
\(491\) | 8.42274e11i | 0.654014i | 0.945022 | + | 0.327007i | \(0.106040\pi\) | ||||
−0.945022 | + | 0.327007i | \(0.893960\pi\) | |||||||
\(492\) | 3.50803e11 | 0.269910 | ||||||||
\(493\) | 2.80235e11 | + | 2.06535e11i | 0.213654 | + | 0.157464i | ||||
\(494\) | 5.32788e11 | 0.402516 | ||||||||
\(495\) | − | 1.55216e11i | − | 0.116202i | ||||||
\(496\) | −3.28324e10 | + | 3.28324e10i | −0.0243576 | + | 0.0243576i | ||||
\(497\) | −4.63552e11 | −0.340796 | ||||||||
\(498\) | 1.54635e12 | − | 1.54635e12i | 1.12661 | − | 1.12661i | ||||
\(499\) | −1.20714e12 | − | 1.20714e12i | −0.871575 | − | 0.871575i | 0.121069 | − | 0.992644i | \(-0.461368\pi\) |
−0.992644 | + | 0.121069i | \(0.961368\pi\) | |||||||
\(500\) | −1.15103e11 | − | 1.15103e11i | −0.0823607 | − | 0.0823607i | ||||
\(501\) | − | 2.98311e11i | − | 0.211543i | ||||||
\(502\) | 4.72771e11i | 0.332264i | ||||||||
\(503\) | 9.27469e11 | + | 9.27469e11i | 0.646016 | + | 0.646016i | 0.952028 | − | 0.306011i | \(-0.0989946\pi\) |
−0.306011 | + | 0.952028i | \(0.598995\pi\) | |||||||
\(504\) | 7.85508e11 | + | 7.85508e11i | 0.542267 | + | 0.542267i | ||||
\(505\) | −1.52848e11 | + | 1.52848e11i | −0.104580 | + | 0.104580i | ||||
\(506\) | −5.54467e11 | −0.376009 | ||||||||
\(507\) | 1.16177e12 | − | 1.16177e12i | 0.780881 | − | 0.780881i | ||||
\(508\) | 1.27217e12i | 0.847534i | ||||||||
\(509\) | −2.27732e12 | −1.50382 | −0.751908 | − | 0.659268i | \(-0.770866\pi\) | ||||
−0.751908 | + | 0.659268i | \(0.770866\pi\) | |||||||
\(510\) | 1.63751e10 | + | 1.08153e11i | 0.0107181 | + | 0.0707903i | ||||
\(511\) | 1.98379e12 | 1.28707 | ||||||||
\(512\) | − | 4.17721e11i | − | 0.268641i | ||||||
\(513\) | 3.00926e11 | − | 3.00926e11i | 0.191837 | − | 0.191837i | ||||
\(514\) | 1.36656e12 | 0.863566 | ||||||||
\(515\) | 1.70897e11 | − | 1.70897e11i | 0.107054 | − | 0.107054i | ||||
\(516\) | −2.33353e11 | − | 2.33353e11i | −0.144907 | − | 0.144907i | ||||
\(517\) | 1.36993e12 | + | 1.36993e12i | 0.843315 | + | 0.843315i | ||||
\(518\) | − | 9.17688e11i | − | 0.560030i | ||||||
\(519\) | 1.90300e12i | 1.15129i | ||||||||
\(520\) | −4.78427e10 | − | 4.78427e10i | −0.0286946 | − | 0.0286946i | ||||
\(521\) | −2.26404e12 | − | 2.26404e12i | −1.34622 | − | 1.34622i | −0.889731 | − | 0.456485i | \(-0.849108\pi\) |
−0.456485 | − | 0.889731i | \(-0.650892\pi\) | |||||||
\(522\) | 2.04338e11 | − | 2.04338e11i | 0.120457 | − | 0.120457i | ||||
\(523\) | −2.74758e11 | −0.160580 | −0.0802902 | − | 0.996772i | \(-0.525585\pi\) | ||||
−0.0802902 | + | 0.996772i | \(0.525585\pi\) | |||||||
\(524\) | −4.67310e11 | + | 4.67310e11i | −0.270778 | + | 0.270778i | ||||
\(525\) | 1.79619e12i | 1.03190i | ||||||||
\(526\) | 5.34514e11 | 0.304455 | ||||||||
\(527\) | 3.62455e11 | + | 2.67131e11i | 0.204694 | + | 0.150861i | ||||
\(528\) | 4.20697e11 | 0.235568 | ||||||||
\(529\) | − | 1.24585e12i | − | 0.691695i | ||||||
\(530\) | −5.58831e10 | + | 5.58831e10i | −0.0307637 | + | 0.0307637i | ||||
\(531\) | −3.82894e12 | −2.09003 | ||||||||
\(532\) | −9.05070e11 | + | 9.05070e11i | −0.489869 | + | 0.489869i | ||||
\(533\) | 1.77510e11 | + | 1.77510e11i | 0.0952686 | + | 0.0952686i | ||||
\(534\) | 1.21406e11 | + | 1.21406e11i | 0.0646108 | + | 0.0646108i | ||||
\(535\) | 9.41383e10i | 0.0496791i | ||||||||
\(536\) | − | 2.21102e12i | − | 1.15705i | ||||||
\(537\) | 7.66876e11 | + | 7.66876e11i | 0.397961 | + | 0.397961i | ||||
\(538\) | −1.75439e11 | − | 1.75439e11i | −0.0902831 | − | 0.0902831i | ||||
\(539\) | −8.13051e11 | + | 8.13051e11i | −0.414924 | + | 0.414924i | ||||
\(540\) | −2.18187e10 | −0.0110422 | ||||||||
\(541\) | −5.43534e11 | + | 5.43534e11i | −0.272797 | + | 0.272797i | −0.830225 | − | 0.557428i | \(-0.811788\pi\) |
0.557428 | + | 0.830225i | \(0.311788\pi\) | |||||||
\(542\) | 7.09406e11i | 0.353100i | ||||||||
\(543\) | −4.17555e12 | −2.06117 | ||||||||
\(544\) | −2.08027e12 | + | 3.14967e11i | −1.01841 | + | 0.154195i | ||||
\(545\) | 2.60124e11 | 0.126298 | ||||||||
\(546\) | 6.05089e11i | 0.291375i | ||||||||
\(547\) | 2.30894e12 | − | 2.30894e12i | 1.10273 | − | 1.10273i | 0.108653 | − | 0.994080i | \(-0.465346\pi\) |
0.994080 | − | 0.108653i | \(-0.0346537\pi\) | |||||||
\(548\) | 9.30358e11 | 0.440694 | ||||||||
\(549\) | 7.56053e11 | − | 7.56053e11i | 0.355203 | − | 0.355203i | ||||
\(550\) | −1.01994e12 | − | 1.01994e12i | −0.475274 | − | 0.475274i | ||||
\(551\) | 5.83181e11 | + | 5.83181e11i | 0.269539 | + | 0.269539i | ||||
\(552\) | 1.68446e12i | 0.772207i | ||||||||
\(553\) | − | 1.40717e12i | − | 0.639859i | ||||||
\(554\) | −1.35967e12 | − | 1.35967e12i | −0.613252 | − | 0.613252i | ||||
\(555\) | 2.75445e11 | + | 2.75445e11i | 0.123230 | + | 0.123230i | ||||
\(556\) | 1.06416e12 | − | 1.06416e12i | 0.472249 | − | 0.472249i | ||||
\(557\) | 1.66914e12 | 0.734760 | 0.367380 | − | 0.930071i | \(-0.380255\pi\) | ||||
0.367380 | + | 0.930071i | \(0.380255\pi\) | |||||||
\(558\) | 2.64290e11 | − | 2.64290e11i | 0.115406 | − | 0.115406i | ||||
\(559\) | − | 2.36158e11i | − | 0.102294i | ||||||
\(560\) | 1.93926e10 | 0.00833276 | ||||||||
\(561\) | −6.10713e11 | − | 4.03359e12i | −0.260318 | − | 1.71933i | ||||
\(562\) | 1.06413e12 | 0.449970 | ||||||||
\(563\) | − | 1.13172e12i | − | 0.474734i | −0.971420 | − | 0.237367i | \(-0.923716\pi\) | ||
0.971420 | − | 0.237367i | \(-0.0762844\pi\) | |||||||
\(564\) | 1.68019e12 | − | 1.68019e12i | 0.699203 | − | 0.699203i | ||||
\(565\) | 1.36543e11 | 0.0563703 | ||||||||
\(566\) | 4.67936e11 | − | 4.67936e11i | 0.191652 | − | 0.191652i | ||||
\(567\) | −1.05856e12 | − | 1.05856e12i | −0.430121 | − | 0.430121i | ||||
\(568\) | −7.99660e11 | − | 7.99660e11i | −0.322358 | − | 0.322358i | ||||
\(569\) | 2.09042e12i | 0.836042i | 0.908437 | + | 0.418021i | \(0.137276\pi\) | ||||
−0.908437 | + | 0.418021i | \(0.862724\pi\) | |||||||
\(570\) | 2.59149e11i | 0.102828i | ||||||||
\(571\) | 4.43448e11 | + | 4.43448e11i | 0.174574 | + | 0.174574i | 0.788986 | − | 0.614412i | \(-0.210607\pi\) |
−0.614412 | + | 0.788986i | \(0.710607\pi\) | |||||||
\(572\) | 7.20353e11 | + | 7.20353e11i | 0.281361 | + | 0.281361i | ||||
\(573\) | −1.63614e11 | + | 1.63614e11i | −0.0634052 | + | 0.0634052i | ||||
\(574\) | 2.87658e11 | 0.110605 | ||||||||
\(575\) | −1.02148e12 | + | 1.02148e12i | −0.389696 | + | 0.389696i | ||||
\(576\) | 1.34232e12i | 0.508106i | ||||||||
\(577\) | 1.42436e12 | 0.534968 | 0.267484 | − | 0.963562i | \(-0.413808\pi\) | ||||
0.267484 | + | 0.963562i | \(0.413808\pi\) | |||||||
\(578\) | 4.51408e11 | + | 1.45654e12i | 0.168226 | + | 0.542808i | ||||
\(579\) | −7.31612e12 | −2.70537 | ||||||||
\(580\) | − | 4.22837e10i | − | 0.0155148i | ||||||
\(581\) | −2.65843e12 | + | 2.65843e12i | −0.967904 | + | 0.967904i | ||||
\(582\) | −5.93530e11 | −0.214432 | ||||||||
\(583\) | 2.08417e12 | − | 2.08417e12i | 0.747178 | − | 0.747178i | ||||
\(584\) | 3.42218e12 | + | 3.42218e12i | 1.21743 | + | 1.21743i | ||||
\(585\) | −9.63292e10 | − | 9.63292e10i | −0.0340061 | − | 0.0340061i | ||||
\(586\) | 1.56782e12i | 0.549233i | ||||||||
\(587\) | − | 3.09625e12i | − | 1.07638i | −0.842824 | − | 0.538189i | \(-0.819109\pi\) | ||
0.842824 | − | 0.538189i | \(-0.180891\pi\) | |||||||
\(588\) | 9.97193e11 | + | 9.97193e11i | 0.344018 | + | 0.344018i | ||||
\(589\) | 7.54283e11 | + | 7.54283e11i | 0.258235 | + | 0.258235i | ||||
\(590\) | 1.88959e11 | − | 1.88959e11i | 0.0641998 | − | 0.0641998i | ||||
\(591\) | 7.28687e12 | 2.45695 | ||||||||
\(592\) | −3.95974e11 | + | 3.95974e11i | −0.132501 | + | 0.132501i | ||||
\(593\) | − | 1.01140e12i | − | 0.335874i | −0.985798 | − | 0.167937i | \(-0.946289\pi\) | ||
0.985798 | − | 0.167937i | \(-0.0537106\pi\) | |||||||
\(594\) | −3.88130e11 | −0.127920 | ||||||||
\(595\) | −2.81516e10 | − | 1.85933e11i | −0.00920823 | − | 0.0608178i | ||||
\(596\) | 2.52123e12 | 0.818472 | ||||||||
\(597\) | 6.39519e12i | 2.06048i | ||||||||
\(598\) | −3.44110e11 | + | 3.44110e11i | −0.110038 | + | 0.110038i | ||||
\(599\) | 1.80697e12 | 0.573495 | 0.286747 | − | 0.958006i | \(-0.407426\pi\) | ||||
0.286747 | + | 0.958006i | \(0.407426\pi\) | |||||||
\(600\) | −3.09856e12 | + | 3.09856e12i | −0.976066 | + | 0.976066i | ||||
\(601\) | 9.99867e11 | + | 9.99867e11i | 0.312613 | + | 0.312613i | 0.845921 | − | 0.533308i | \(-0.179051\pi\) |
−0.533308 | + | 0.845921i | \(0.679051\pi\) | |||||||
\(602\) | −1.91349e11 | − | 1.91349e11i | −0.0593803 | − | 0.0593803i | ||||
\(603\) | − | 4.45181e12i | − | 1.37122i | ||||||
\(604\) | 1.50846e12i | 0.461178i | ||||||||
\(605\) | −8.44992e10 | − | 8.44992e10i | −0.0256421 | − | 0.0256421i | ||||
\(606\) | 3.33481e12 | + | 3.33481e12i | 1.00449 | + | 1.00449i | ||||
\(607\) | −8.41981e11 | + | 8.41981e11i | −0.251741 | + | 0.251741i | −0.821684 | − | 0.569943i | \(-0.806965\pi\) |
0.569943 | + | 0.821684i | \(0.306965\pi\) | |||||||
\(608\) | −4.98458e12 | −1.47932 | ||||||||
\(609\) | −6.62320e11 | + | 6.62320e11i | −0.195115 | + | 0.195115i | ||||
\(610\) | 7.46228e10i | 0.0218216i | ||||||||
\(611\) | 1.70039e12 | 0.493586 | ||||||||
\(612\) | −2.62393e12 | + | 3.97281e11i | −0.756086 | + | 0.114477i | ||||
\(613\) | −3.81378e11 | −0.109090 | −0.0545448 | − | 0.998511i | \(-0.517371\pi\) | ||||
−0.0545448 | + | 0.998511i | \(0.517371\pi\) | |||||||
\(614\) | − | 1.24936e12i | − | 0.354757i | ||||||
\(615\) | −8.63409e10 | + | 8.63409e10i | −0.0243376 | + | 0.0243376i | ||||
\(616\) | 2.89149e12 | 0.809112 | ||||||||
\(617\) | 1.41713e12 | − | 1.41713e12i | 0.393666 | − | 0.393666i | −0.482326 | − | 0.875992i | \(-0.660208\pi\) |
0.875992 | + | 0.482326i | \(0.160208\pi\) | |||||||
\(618\) | −3.72860e12 | − | 3.72860e12i | −1.02825 | − | 1.02825i | ||||
\(619\) | −8.49752e11 | − | 8.49752e11i | −0.232640 | − | 0.232640i | 0.581154 | − | 0.813794i | \(-0.302601\pi\) |
−0.813794 | + | 0.581154i | \(0.802601\pi\) | |||||||
\(620\) | − | 5.46894e10i | − | 0.0148642i | ||||||
\(621\) | 3.88716e11i | 0.104887i | ||||||||
\(622\) | −2.02871e12 | − | 2.02871e12i | −0.543455 | − | 0.543455i | ||||
\(623\) | −2.08717e11 | − | 2.08717e11i | −0.0555088 | − | 0.0555088i | ||||
\(624\) | 2.61090e11 | − | 2.61090e11i | 0.0689382 | − | 0.0689382i | ||||
\(625\) | −3.72960e12 | −0.977693 | ||||||||
\(626\) | −1.45238e11 | + | 1.45238e11i | −0.0378003 | + | 0.0378003i | ||||
\(627\) | − | 9.66498e12i | − | 2.49745i | ||||||
\(628\) | 2.86334e12 | 0.734607 | ||||||||
\(629\) | 4.37137e12 | + | 3.22172e12i | 1.11350 | + | 0.820654i | ||||
\(630\) | −1.56104e11 | −0.0394803 | ||||||||
\(631\) | 9.59070e11i | 0.240834i | 0.992723 | + | 0.120417i | \(0.0384232\pi\) | ||||
−0.992723 | + | 0.120417i | \(0.961577\pi\) | |||||||
\(632\) | 2.42747e12 | − | 2.42747e12i | 0.605240 | − | 0.605240i | ||||
\(633\) | 5.92389e12 | 1.46653 | ||||||||
\(634\) | −1.83844e12 | + | 1.83844e12i | −0.451907 | + | 0.451907i | ||||
\(635\) | −3.13111e11 | − | 3.13111e11i | −0.0764216 | − | 0.0764216i | ||||
\(636\) | −2.55620e12 | − | 2.55620e12i | −0.619494 | − | 0.619494i | ||||
\(637\) | 1.00918e12i | 0.242852i | ||||||||
\(638\) | − | 7.52179e11i | − | 0.179733i | ||||||
\(639\) | −1.61008e12 | − | 1.61008e12i | −0.382027 | − | 0.382027i | ||||
\(640\) | 2.00652e11 | + | 2.00652e11i | 0.0472752 | + | 0.0472752i | ||||
\(641\) | 1.25149e12 | − | 1.25149e12i | 0.292796 | − | 0.292796i | −0.545388 | − | 0.838184i | \(-0.683617\pi\) |
0.838184 | + | 0.545388i | \(0.183617\pi\) | |||||||
\(642\) | 2.05389e12 | 0.477165 | ||||||||
\(643\) | −5.32993e12 | + | 5.32993e12i | −1.22962 | + | 1.22962i | −0.265517 | + | 0.964106i | \(0.585543\pi\) |
−0.964106 | + | 0.265517i | \(0.914457\pi\) | |||||||
\(644\) | − | 1.16911e12i | − | 0.267836i | ||||||
\(645\) | 1.14867e11 | 0.0261323 | ||||||||
\(646\) | 5.40814e11 | + | 3.57193e12i | 0.122180 | + | 0.806968i | ||||
\(647\) | −5.30405e12 | −1.18998 | −0.594989 | − | 0.803734i | \(-0.702843\pi\) | ||||
−0.594989 | + | 0.803734i | \(0.702843\pi\) | |||||||
\(648\) | − | 3.65217e12i | − | 0.813698i | ||||||
\(649\) | −7.04725e12 | + | 7.04725e12i | −1.55926 | + | 1.55926i | ||||
\(650\) | −1.26598e12 | −0.278174 | ||||||||
\(651\) | −8.56641e11 | + | 8.56641e11i | −0.186932 | + | 0.186932i | ||||
\(652\) | −1.24034e12 | − | 1.24034e12i | −0.268799 | − | 0.268799i | ||||
\(653\) | −2.41467e11 | − | 2.41467e11i | −0.0519695 | − | 0.0519695i | 0.680644 | − | 0.732614i | \(-0.261700\pi\) |
−0.732614 | + | 0.680644i | \(0.761700\pi\) | |||||||
\(654\) | − | 5.67532e12i | − | 1.21308i | ||||||
\(655\) | − | 2.30032e11i | − | 0.0488318i | ||||||
\(656\) | −1.24122e11 | − | 1.24122e11i | −0.0261686 | − | 0.0261686i | ||||
\(657\) | 6.89042e12 | + | 6.89042e12i | 1.44278 | + | 1.44278i | ||||
\(658\) | 1.37776e12 | − | 1.37776e12i | 0.286521 | − | 0.286521i | ||||
\(659\) | 1.73640e12 | 0.358646 | 0.179323 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179323 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(660\) | −3.50381e11 | + | 3.50381e11i | −0.0718774 | + | 0.0718774i | ||||
\(661\) | − | 7.10034e12i | − | 1.44668i | −0.690492 | − | 0.723340i | \(-0.742606\pi\) | ||
0.690492 | − | 0.723340i | \(-0.257394\pi\) | |||||||
\(662\) | 4.73244e12 | 0.957689 | ||||||||
\(663\) | −2.88232e12 | − | 2.12428e12i | −0.579336 | − | 0.426974i | ||||
\(664\) | −9.17195e12 | −1.83107 | ||||||||
\(665\) | − | 4.45519e11i | − | 0.0883423i | ||||||
\(666\) | 3.18746e12 | − | 3.18746e12i | 0.627784 | − | 0.627784i | ||||
\(667\) | −7.53314e11 | −0.147370 | ||||||||
\(668\) | −3.57167e11 | + | 3.57167e11i | −0.0694029 | + | 0.0694029i | ||||
\(669\) | 7.89546e12 | + | 7.89546e12i | 1.52391 | + | 1.52391i | ||||
\(670\) | 2.19698e11 | + | 2.19698e11i | 0.0421201 | + | 0.0421201i | ||||
\(671\) | − | 2.78307e12i | − | 0.529996i | ||||||
\(672\) | − | 5.66100e12i | − | 1.07086i | ||||||
\(673\) | −6.04832e11 | − | 6.04832e11i | −0.113649 | − | 0.113649i | 0.647995 | − | 0.761645i | \(-0.275608\pi\) |
−0.761645 | + | 0.647995i | \(0.775608\pi\) | |||||||
\(674\) | 1.23329e12 | + | 1.23329e12i | 0.230195 | + | 0.230195i | ||||
\(675\) | −7.15044e11 | + | 7.15044e11i | −0.132576 | + | 0.132576i | ||||
\(676\) | −2.78197e12 | −0.512381 | ||||||||
\(677\) | −7.12737e12 | + | 7.12737e12i | −1.30401 | + | 1.30401i | −0.378342 | + | 0.925666i | \(0.623506\pi\) |
−0.925666 | + | 0.378342i | \(0.876494\pi\) | |||||||
\(678\) | − | 2.97905e12i | − | 0.541433i | ||||||
\(679\) | 1.02038e12 | 0.184224 | ||||||||
\(680\) | 2.72184e11 | − | 3.69311e11i | 0.0488172 | − | 0.0662373i | ||||
\(681\) | 1.87841e12 | 0.334679 | ||||||||
\(682\) | − | 9.72864e11i | − | 0.172196i | ||||||
\(683\) | 3.03863e12 | − | 3.03863e12i | 0.534300 | − | 0.534300i | −0.387549 | − | 0.921849i | \(-0.626678\pi\) |
0.921849 | + | 0.387549i | \(0.126678\pi\) | |||||||
\(684\) | −6.28727e12 | −1.09827 | ||||||||
\(685\) | −2.28983e11 | + | 2.28983e11i | −0.0397371 | + | 0.0397371i | ||||
\(686\) | 2.47827e12 | + | 2.47827e12i | 0.427258 | + | 0.427258i | ||||
\(687\) | 4.26696e12 | + | 4.26696e12i | 0.730824 | + | 0.730824i | ||||
\(688\) | 1.65131e11i | 0.0280983i | ||||||||
\(689\) | − | 2.58692e12i | − | 0.437318i | ||||||
\(690\) | −1.67375e11 | − | 1.67375e11i | −0.0281106 | − | 0.0281106i | ||||
\(691\) | −5.51319e12 | − | 5.51319e12i | −0.919923 | − | 0.919923i | 0.0771005 | − | 0.997023i | \(-0.475434\pi\) |
−0.997023 | + | 0.0771005i | \(0.975434\pi\) | |||||||
\(692\) | 2.27846e12 | − | 2.27846e12i | 0.377714 | − | 0.377714i | ||||
\(693\) | 5.82190e12 | 0.958882 | ||||||||
\(694\) | −1.38400e12 | + | 1.38400e12i | −0.226475 | + | 0.226475i | ||||
\(695\) | 5.23832e11i | 0.0851648i | ||||||||
\(696\) | −2.28510e12 | −0.369116 | ||||||||
\(697\) | −1.00988e12 | + | 1.37025e12i | −0.162077 | + | 0.219913i | ||||
\(698\) | −2.29473e12 | −0.365916 | ||||||||
\(699\) | 1.13534e13i | 1.79878i | ||||||||
\(700\) | 2.15058e12 | − | 2.15058e12i | 0.338543 | − | 0.338543i | ||||
\(701\) | 2.38474e12 | 0.373000 | 0.186500 | − | 0.982455i | \(-0.440286\pi\) | ||||
0.186500 | + | 0.982455i | \(0.440286\pi\) | |||||||
\(702\) | −2.40879e11 | + | 2.40879e11i | −0.0374353 | + | 0.0374353i | ||||
\(703\) | 9.09699e12 | + | 9.09699e12i | 1.40475 | + | 1.40475i | ||||
\(704\) | 2.47057e12 | + | 2.47057e12i | 0.379071 | + | 0.379071i | ||||
\(705\) | 8.27071e11i | 0.126093i | ||||||||
\(706\) | 3.81732e12i | 0.578279i | ||||||||
\(707\) | −5.73309e12 | − | 5.73309e12i | −0.862981 | − | 0.862981i | ||||
\(708\) | 8.64334e12 | + | 8.64334e12i | 1.29280 | + | 1.29280i | ||||
\(709\) | −3.97625e12 | + | 3.97625e12i | −0.590971 | + | 0.590971i | −0.937894 | − | 0.346923i | \(-0.887227\pi\) |
0.346923 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(710\) | 1.58916e11 | 0.0234696 | ||||||||
\(711\) | 4.88762e12 | − | 4.88762e12i | 0.717272 | − | 0.717272i | ||||
\(712\) | − | 7.20104e11i | − | 0.105011i | ||||||
\(713\) | −9.74332e11 | −0.141190 | ||||||||
\(714\) | −4.05665e12 | + | 6.14204e11i | −0.584151 | + | 0.0884445i | ||||
\(715\) | −3.54592e11 | −0.0507402 | ||||||||
\(716\) | − | 1.83636e12i | − | 0.261125i | ||||||
\(717\) | 8.92073e12 | − | 8.92073e12i | 1.26056 | − | 1.26056i | ||||
\(718\) | −2.14911e12 | −0.301786 | ||||||||
\(719\) | −1.08444e12 | + | 1.08444e12i | −0.151330 | + | 0.151330i | −0.778712 | − | 0.627382i | \(-0.784126\pi\) |
0.627382 | + | 0.778712i | \(0.284126\pi\) | |||||||
\(720\) | 6.73573e10 | + | 6.73573e10i | 0.00934089 | + | 0.00934089i | ||||
\(721\) | 6.41007e12 | + | 6.41007e12i | 0.883393 | + | 0.883393i | ||||
\(722\) | 4.40944e12i | 0.603902i | ||||||||
\(723\) | 9.20073e12i | 1.25228i | ||||||||
\(724\) | 4.99938e12 | + | 4.99938e12i | 0.676227 | + | 0.676227i | ||||
\(725\) | −1.38572e12 | − | 1.38572e12i | −0.186275 | − | 0.186275i | ||||
\(726\) | −1.84358e12 | + | 1.84358e12i | −0.246291 | + | 0.246291i | ||||
\(727\) | 1.19798e12 | 0.159054 | 0.0795268 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795268 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(728\) | 1.79450e12 | − | 1.79450e12i | 0.236784 | − | 0.236784i | ||||
\(729\) | − | 9.45552e12i | − | 1.23997i | ||||||
\(730\) | −6.80087e11 | −0.0886364 | ||||||||
\(731\) | 1.58325e12 | − | 2.39715e11i | 0.205080 | − | 0.0310504i | ||||
\(732\) | −3.41338e12 | −0.439426 | ||||||||
\(733\) | − | 8.71100e12i | − | 1.11455i | −0.830328 | − | 0.557276i | \(-0.811847\pi\) | ||
0.830328 | − | 0.557276i | \(-0.188153\pi\) | |||||||
\(734\) | −2.93164e12 | + | 2.93164e12i | −0.372802 | + | 0.372802i | ||||
\(735\) | −4.90866e11 | −0.0620398 | ||||||||
\(736\) | 3.21937e12 | − | 3.21937e12i | 0.404409 | − | 0.404409i | ||||
\(737\) | −8.19366e12 | − | 8.19366e12i | −1.02300 | − | 1.02300i | ||||
\(738\) | 9.99140e11 | + | 9.99140e11i | 0.123986 | + | 0.123986i | ||||
\(739\) | − | 1.05005e13i | − | 1.29512i | −0.762015 | − | 0.647560i | \(-0.775790\pi\) | ||
0.762015 | − | 0.647560i | \(-0.224210\pi\) | |||||||
\(740\) | − | 6.59580e11i | − | 0.0808583i | ||||||
\(741\) | −5.99821e12 | − | 5.99821e12i | −0.730870 | − | 0.730870i | ||||
\(742\) | −2.09608e12 | − | 2.09608e12i | −0.253858 | − | 0.253858i | ||||
\(743\) | 9.41077e12 | − | 9.41077e12i | 1.13286 | − | 1.13286i | 0.143158 | − | 0.989700i | \(-0.454274\pi\) |
0.989700 | − | 0.143158i | \(-0.0457256\pi\) | |||||||
\(744\) | −2.95553e12 | −0.353637 | ||||||||
\(745\) | −6.20535e11 | + | 6.20535e11i | −0.0738011 | + | 0.0738011i | ||||
\(746\) | 4.94575e11i | 0.0584665i | ||||||||
\(747\) | −1.84673e13 | −2.17001 | ||||||||
\(748\) | −4.09820e12 | + | 5.56061e12i | −0.478670 | + | 0.649480i | ||||
\(749\) | −3.53097e12 | −0.409945 | ||||||||
\(750\) | − | 1.23617e12i | − | 0.142661i | ||||||
\(751\) | −6.49504e12 | + | 6.49504e12i | −0.745079 | + | 0.745079i | −0.973551 | − | 0.228472i | \(-0.926627\pi\) |
0.228472 | + | 0.973551i | \(0.426627\pi\) | |||||||
\(752\) | −1.18898e12 | −0.135580 | ||||||||
\(753\) | 5.32253e12 | − | 5.32253e12i | 0.603310 | − | 0.603310i | ||||
\(754\) | −4.66812e11 | − | 4.66812e11i | −0.0525982 | − | 0.0525982i | ||||
\(755\) | −3.71269e11 | − | 3.71269e11i | −0.0415841 | − | 0.0415841i | ||||
\(756\) | − | 8.18383e11i | − | 0.0911189i | ||||||
\(757\) | − | 1.11837e13i | − | 1.23781i | −0.785467 | − | 0.618903i | \(-0.787577\pi\) | ||
0.785467 | − | 0.618903i | \(-0.212423\pi\) | |||||||
\(758\) | 8.92622e11 | + | 8.92622e11i | 0.0982101 | + | 0.0982101i | ||||
\(759\) | 6.24229e12 | + | 6.24229e12i | 0.682740 | + | 0.682740i | ||||
\(760\) | 7.68552e11 | − | 7.68552e11i | 0.0835626 | − | 0.0835626i | ||||
\(761\) | −4.29799e12 | −0.464553 | −0.232276 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232276 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(762\) | −6.83138e12 | + | 6.83138e12i | −0.734025 | + | 0.734025i | ||||
\(763\) | 9.75681e12i | 1.04219i | ||||||||
\(764\) | 3.91790e11 | 0.0416038 | ||||||||
\(765\) | 5.48032e11 | − | 7.43593e11i | 0.0578535 | − | 0.0784981i | ||||
\(766\) | 5.03741e12 | 0.528662 | ||||||||
\(767\) | 8.74723e12i | 0.912623i | ||||||||
\(768\) | 8.85318e12 | − | 8.85318e12i | 0.918277 | − | 0.918277i | ||||
\(769\) | 9.88894e12 | 1.01972 | 0.509860 | − | 0.860257i | \(-0.329697\pi\) | ||||
0.509860 | + | 0.860257i | \(0.329697\pi\) | |||||||
\(770\) | −2.87312e11 | + | 2.87312e11i | −0.0294541 | + | 0.0294541i | ||||
\(771\) | −1.53850e13 | − | 1.53850e13i | −1.56802 | − | 1.56802i | ||||
\(772\) | 8.75957e12 | + | 8.75957e12i | 0.887575 | + | 0.887575i | ||||
\(773\) | 1.06695e13i | 1.07482i | 0.843322 | + | 0.537409i | \(0.180597\pi\) | ||||
−0.843322 | + | 0.537409i | \(0.819403\pi\) | |||||||
\(774\) | − | 1.32925e12i | − | 0.133129i | ||||||
\(775\) | −1.79228e12 | − | 1.79228e12i | −0.178463 | − | 0.178463i | ||||
\(776\) | 1.76022e12 | + | 1.76022e12i | 0.174257 | + | 0.174257i | ||||
\(777\) | −1.03315e13 | + | 1.03315e13i | −1.01688 | + | 1.01688i | ||||
\(778\) | 5.66738e12 | 0.554593 | ||||||||
\(779\) | −2.85154e12 | + | 2.85154e12i | −0.277435 | + | 0.277435i | ||||
\(780\) | 4.34902e11i | 0.0420693i | ||||||||
\(781\) | −5.92679e12 | −0.570020 | ||||||||
\(782\) | −2.65628e12 | − | 1.95769e12i | −0.254006 | − | 0.187204i | ||||
\(783\) | −5.27324e11 | −0.0501360 | ||||||||
\(784\) | − | 7.05659e11i | − | 0.0667072i | ||||||
\(785\) | −7.04738e11 | + | 7.04738e11i | −0.0662390 | + | 0.0662390i | ||||
\(786\) | −5.01879e12 | −0.469027 | ||||||||
\(787\) | 9.85561e12 | − | 9.85561e12i | 0.915793 | − | 0.915793i | −0.0809272 | − | 0.996720i | \(-0.525788\pi\) |
0.996720 | + | 0.0809272i | \(0.0257881\pi\) | |||||||
\(788\) | −8.72455e12 | − | 8.72455e12i | −0.806074 | − | 0.806074i | ||||
\(789\) | −6.01764e12 | − | 6.01764e12i | −0.552815 | − | 0.552815i | ||||
\(790\) | 4.82410e11i | 0.0440651i | ||||||||
\(791\) | 5.12148e12i | 0.465159i | ||||||||
\(792\) | 1.00432e13 | + | 1.00432e13i | 0.907002 | + | 0.907002i | ||||
\(793\) | −1.72721e12 | − | 1.72721e12i | −0.155101 | − | 0.155101i | ||||
\(794\) | 3.07787e12 | − | 3.07787e12i | 0.274826 | − | 0.274826i | ||||
\(795\) | 1.25828e12 | 0.111719 | ||||||||
\(796\) | 7.65695e12 | − | 7.65695e12i | 0.676000 | − | 0.676000i | ||||
\(797\) | 5.24283e11i | 0.0460260i | 0.999735 | + | 0.0230130i | \(0.00732592\pi\) | ||||
−0.999735 | + | 0.0230130i | \(0.992674\pi\) | |||||||
\(798\) | −9.72023e12 | −0.848523 | ||||||||
\(799\) | 1.72601e12 | + | 1.13998e13i | 0.149824 | + | 0.989547i | ||||
\(800\) | 1.18441e13 | 1.02234 | ||||||||
\(801\) | − | 1.44990e12i | − | 0.124449i | ||||||
\(802\) | −1.56310e12 | + | 1.56310e12i | −0.133415 | + | 0.133415i | ||||
\(803\) | 2.53639e13 | 2.15277 | ||||||||
\(804\) | −1.00494e13 | + | 1.00494e13i | −0.848178 | + | 0.848178i | ||||
\(805\) | 2.87746e11 | + | 2.87746e11i | 0.0241506 | + | 0.0241506i | ||||
\(806\) | −6.03772e11 | − | 6.03772e11i | −0.0503924 | − | 0.0503924i | ||||
\(807\) | 3.95025e12i | 0.327864i | ||||||||
\(808\) | − | 1.97800e13i | − | 1.63258i | ||||||
\(809\) | −4.08467e12 | − | 4.08467e12i | −0.335266 | − | 0.335266i | 0.519316 | − | 0.854582i | \(-0.326187\pi\) |
−0.854582 | + | 0.519316i | \(0.826187\pi\) | |||||||
\(810\) | 3.62897e11 | + | 3.62897e11i | 0.0296211 | + | 0.0296211i | ||||
\(811\) | −2.94545e11 | + | 2.94545e11i | −0.0239088 | + | 0.0239088i | −0.718960 | − | 0.695051i | \(-0.755382\pi\) |
0.695051 | + | 0.718960i | \(0.255382\pi\) | |||||||
\(812\) | 1.58599e12 | 0.128026 | ||||||||
\(813\) | 7.98661e12 | − | 7.98661e12i | 0.641143 | − | 0.641143i | ||||
\(814\) | − | 1.17332e13i | − | 0.936712i | ||||||
\(815\) | 6.10556e11 | 0.0484748 | ||||||||
\(816\) | 2.01543e12 | + | 1.48538e12i | 0.159134 | + | 0.117282i | ||||
\(817\) | 3.79367e12 | 0.297893 | ||||||||
\(818\) | − | 2.32956e12i | − | 0.181921i | ||||||
\(819\) | 3.61315e12 | − | 3.61315e12i | 0.280613 | − | 0.280613i | ||||
\(820\) | 2.06752e11 | 0.0159693 | ||||||||
\(821\) | 7.14153e12 | − | 7.14153e12i | 0.548589 | − | 0.548589i | −0.377444 | − | 0.926032i | \(-0.623197\pi\) |
0.926032 | + | 0.377444i | \(0.123197\pi\) | |||||||
\(822\) | 4.99591e12 | + | 4.99591e12i | 0.381673 | + | 0.381673i | ||||
\(823\) | 3.38757e12 | + | 3.38757e12i | 0.257389 | + | 0.257389i | 0.823991 | − | 0.566602i | \(-0.191742\pi\) |
−0.566602 | + | 0.823991i | \(0.691742\pi\) | |||||||
\(824\) | 2.21156e13i | 1.67120i | ||||||||
\(825\) | 2.29654e13i | 1.72596i | ||||||||
\(826\) | 7.08754e12 | + | 7.08754e12i | 0.529767 | + | 0.529767i | ||||
\(827\) | −1.42921e13 | − | 1.42921e13i | −1.06248 | − | 1.06248i | −0.997913 | − | 0.0645681i | \(-0.979433\pi\) |
−0.0645681 | − | 0.997913i | \(-0.520567\pi\) | |||||||
\(828\) | 4.06073e12 | − | 4.06073e12i | 0.300240 | − | 0.300240i | ||||
\(829\) | −9.90972e12 | −0.728729 | −0.364364 | − | 0.931256i | \(-0.618714\pi\) | ||||
−0.364364 | + | 0.931256i | \(0.618714\pi\) | |||||||
\(830\) | 9.11368e11 | − | 9.11368e11i | 0.0666565 | − | 0.0666565i | ||||
\(831\) | 3.06147e13i | 2.22703i | ||||||||
\(832\) | 3.06654e12 | 0.221867 | ||||||||
\(833\) | −6.76577e12 | + | 1.02438e12i | −0.486872 | + | 0.0737157i | ||||
\(834\) | 1.14288e13 | 0.818003 | ||||||||
\(835\) | − | 1.75815e11i | − | 0.0125160i | ||||||
\(836\) | −1.15719e13 | + | 1.15719e13i | −0.819360 | + | 0.819360i | ||||
\(837\) | −6.82038e11 | −0.0480335 | ||||||||
\(838\) | −4.86162e12 | + | 4.86162e12i | −0.340551 | + | 0.340551i | ||||
\(839\) | 5.97618e12 | + | 5.97618e12i | 0.416385 | + | 0.416385i | 0.883956 | − | 0.467571i | \(-0.154871\pi\) |
−0.467571 | + | 0.883956i | \(0.654871\pi\) | |||||||
\(840\) | 8.72846e11 | + | 8.72846e11i | 0.0604896 | + | 0.0604896i | ||||
\(841\) | 1.34852e13i | 0.929557i | ||||||||
\(842\) | − | 6.11165e11i | − | 0.0419038i | ||||||
\(843\) | −1.19802e13 | − | 1.19802e13i | −0.817034 | − | 0.817034i | ||||
\(844\) | −7.09266e12 | − | 7.09266e12i | −0.481137 | − | 0.481137i | ||||
\(845\) | 6.84710e11 | − | 6.84710e11i | 0.0462010 | − | 0.0462010i | ||||
\(846\) | 9.57090e12 | 0.642371 | ||||||||
\(847\) | 3.16942e12 | − | 3.16942e12i | 0.211595 | − | 0.211595i | ||||
\(848\) | 1.80888e12i | 0.120124i | ||||||||
\(849\) | −1.05362e13 | −0.695984 | ||||||||
\(850\) | −1.28505e12 | − | 8.48742e12i | −0.0844376 | − | 0.557687i | ||||
\(851\) | −1.17509e13 | −0.768047 | ||||||||
\(852\) | 7.26911e12i | 0.472610i | ||||||||
\(853\) | 6.35933e12 | − | 6.35933e12i | 0.411283 | − | 0.411283i | −0.470902 | − | 0.882185i | \(-0.656072\pi\) |
0.882185 | + | 0.470902i | \(0.156072\pi\) | |||||||
\(854\) | −2.79898e12 | −0.180069 | ||||||||
\(855\) | 1.54745e12 | − | 1.54745e12i | 0.0990304 | − | 0.0990304i | ||||
\(856\) | −6.09117e12 | − | 6.09117e12i | −0.387765 | − | 0.387765i | ||||
\(857\) | 1.22041e12 | + | 1.22041e12i | 0.0772848 | + | 0.0772848i | 0.744692 | − | 0.667408i | \(-0.232596\pi\) |
−0.667408 | + | 0.744692i | \(0.732596\pi\) | |||||||
\(858\) | 7.73642e12i | 0.487357i | ||||||||
\(859\) | 4.15450e12i | 0.260345i | 0.991491 | + | 0.130173i | \(0.0415531\pi\) | ||||
−0.991491 | + | 0.130173i | \(0.958447\pi\) | |||||||
\(860\) | −1.37530e11 | − | 1.37530e11i | −0.00857346 | − | 0.00857346i | ||||
\(861\) | −3.23850e12 | − | 3.23850e12i | −0.200831 | − | 0.200831i | ||||
\(862\) | 7.67446e12 | − | 7.67446e12i | 0.473440 | − | 0.473440i | ||||
\(863\) | 3.76231e11 | 0.0230890 | 0.0115445 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115445 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(864\) | 2.25358e12 | − | 2.25358e12i | 0.137582 | − | 0.137582i | ||||
\(865\) | 1.12157e12i | 0.0681165i | ||||||||
\(866\) | 2.68748e11 | 0.0162373 | ||||||||
\(867\) | 1.13159e13 | − | 2.14800e13i | 0.680149 | − | 1.29106i | ||||
\(868\) | 2.05131e12 | 0.122657 | ||||||||
\(869\) | − | 1.79916e13i | − | 1.07024i | ||||||
\(870\) | 2.27058e11 | − | 2.27058e11i | 0.0134369 | − | 0.0134369i | ||||
\(871\) | −1.01702e13 | −0.598752 | ||||||||
\(872\) | −1.68312e13 | + | 1.68312e13i | −0.985803 | + | 0.985803i | ||||
\(873\) | 3.54413e12 | + | 3.54413e12i | 0.206512 | + | 0.206512i | ||||
\(874\) | −5.52783e12 | − | 5.52783e12i | −0.320445 | − | 0.320445i | ||||
\(875\) | 2.12519e12i | 0.122563i | ||||||||
\(876\) | − | 3.11085e13i | − | 1.78488i | ||||||
\(877\) | −1.35734e13 | − | 1.35734e13i | −0.774804 | − | 0.774804i | 0.204138 | − | 0.978942i | \(-0.434561\pi\) |
−0.978942 | + | 0.204138i | \(0.934561\pi\) | |||||||
\(878\) | −1.07889e13 | − | 1.07889e13i | −0.612708 | − | 0.612708i | ||||
\(879\) | 1.76507e13 | − | 1.76507e13i | 0.997271 | − | 0.997271i | ||||
\(880\) | 2.47945e11 | 0.0139375 | ||||||||
\(881\) | −8.65229e11 | + | 8.65229e11i | −0.0483882 | + | 0.0483882i | −0.730887 | − | 0.682499i | \(-0.760893\pi\) |
0.682499 | + | 0.730887i | \(0.260893\pi\) | |||||||
\(882\) | 5.68032e12i | 0.316056i | ||||||||
\(883\) | 1.57603e13 | 0.872451 | 0.436225 | − | 0.899837i | \(-0.356315\pi\) | ||||
0.436225 | + | 0.899837i | \(0.356315\pi\) | |||||||
\(884\) | 9.07591e11 | + | 5.99439e12i | 0.0499868 | + | 0.330149i | ||||
\(885\) | −4.25466e12 | −0.233142 | ||||||||
\(886\) | − | 5.39276e12i | − | 0.294008i | ||||||
\(887\) | 2.71858e12 | − | 2.71858e12i | 0.147464 | − | 0.147464i | −0.629520 | − | 0.776984i | \(-0.716748\pi\) |
0.776984 | + | 0.629520i | \(0.216748\pi\) | |||||||
\(888\) | −3.56451e13 | −1.92372 | ||||||||
\(889\) | 1.17443e13 | − | 1.17443e13i | 0.630620 | − | 0.630620i | ||||
\(890\) | 7.15529e10 | + | 7.15529e10i | 0.00382272 | + | 0.00382272i | ||||
\(891\) | −1.35343e13 | − | 1.35343e13i | −0.719425 | − | 0.719425i | ||||
\(892\) | − | 1.89064e13i | − | 0.999926i | ||||||
\(893\) | 2.73153e13i | 1.43739i | ||||||||
\(894\) | 1.35387e13 | + | 1.35387e13i | 0.708855 | + | 0.708855i | ||||
\(895\) | 4.51972e11 | + | 4.51972e11i | 0.0235455 | + | 0.0235455i | ||||
\(896\) | −7.52611e12 | + | 7.52611e12i | −0.390108 | + | 0.390108i | ||||
\(897\) | 7.74809e12 | 0.399603 | ||||||||
\(898\) | −6.21458e12 | + | 6.21458e12i | −0.318910 | + | 0.318910i | ||||
\(899\) | − | 1.32176e12i | − | 0.0674891i | ||||||
\(900\) | 1.49395e13 | 0.759003 | ||||||||
\(901\) | 1.73433e13 | − | 2.62590e12i | 0.876739 | − | 0.132744i | ||||
\(902\) | 3.67788e12 | 0.184998 | ||||||||
\(903\) | 4.30848e12i | 0.215640i | ||||||||
\(904\) | −8.83492e12 | + | 8.83492e12i | −0.439992 | + | 0.439992i | ||||
\(905\) | −2.46093e12 | −0.121950 | ||||||||
\(906\) | −8.10026e12 | + | 8.10026e12i | −0.399413 | + | 0.399413i | ||||
\(907\) | 2.12739e13 | + | 2.12739e13i | 1.04379 | + | 1.04379i | 0.998996 | + | 0.0447958i | \(0.0142637\pi\) |
0.0447958 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(908\) | −2.24902e12 | − | 2.24902e12i | −0.109801 | − | 0.109801i | ||||
\(909\) | − | 3.98261e13i | − | 1.93478i | ||||||
\(910\) | 3.56620e11i | 0.0172393i | ||||||||
\(911\) | 2.30275e13 | + | 2.30275e13i | 1.10768 | + | 1.10768i | 0.993455 | + | 0.114226i | \(0.0364388\pi\) |
0.114226 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(912\) | 4.19419e12 | + | 4.19419e12i | 0.200757 | + | 0.200757i | ||||
\(913\) | −3.39896e13 | + | 3.39896e13i | −1.61893 | + | 1.61893i | ||||
\(914\) | −1.46237e13 | −0.693105 | ||||||||
\(915\) | 8.40116e11 | − | 8.40116e11i | 0.0396227 | − | 0.0396227i | ||||
\(916\) | − | 1.02176e13i | − | 0.479536i | ||||||
\(917\) | 8.62813e12 | 0.402953 | ||||||||
\(918\) | −1.85941e12 | − | 1.37040e12i | −0.0864139 | − | 0.0636876i | ||||
\(919\) | 1.18128e13 | 0.546304 | 0.273152 | − | 0.961971i | \(-0.411934\pi\) | ||||
0.273152 | + | 0.961971i | \(0.411934\pi\) | |||||||
\(920\) | 9.92763e11i | 0.0456878i | ||||||||
\(921\) | −1.40655e13 | + | 1.40655e13i | −0.644152 | + | 0.644152i | ||||
\(922\) | 5.16535e12 | 0.235402 | ||||||||
\(923\) | −3.67825e12 | + | 3.67825e12i | −0.166814 | + | 0.166814i | ||||
\(924\) | −1.31422e13 | − | 1.31422e13i | −0.593122 | − | 0.593122i | ||||
\(925\) | −2.16158e13 | − | 2.16158e13i | −0.970807 | − | 0.970807i | ||||
\(926\) | − | 2.20948e13i | − | 0.987509i | ||||||
\(927\) | 4.45289e13i | 1.98054i | ||||||||
\(928\) | 4.36734e12 | + | 4.36734e12i | 0.193308 | + | 0.193308i | ||||
\(929\) | 2.34720e13 | + | 2.34720e13i | 1.03390 | + | 1.03390i | 0.999405 | + | 0.0344963i | \(0.0109827\pi\) |
0.0344963 | + | 0.999405i | \(0.489017\pi\) | |||||||
\(930\) | 2.93675e11 | − | 2.93675e11i | 0.0128734 | − | 0.0128734i | ||||
\(931\) | −1.62116e13 | −0.707217 | ||||||||
\(932\) | 1.35934e13 | − | 1.35934e13i | 0.590141 | − | 0.590141i | ||||
\(933\) | 4.56791e13i | 1.97356i | ||||||||
\(934\) | 1.61387e13 | 0.693916 | ||||||||
\(935\) | −3.59934e11 | − | 2.37727e12i | −0.0154018 | − | 0.101725i | ||||
\(936\) | 1.24659e13 | 0.530862 | ||||||||
\(937\) | − | 7.61249e12i | − | 0.322625i | −0.986903 | − | 0.161313i | \(-0.948427\pi\) | ||
0.986903 | − | 0.161313i | \(-0.0515728\pi\) | |||||||
\(938\) | −8.24050e12 | + | 8.24050e12i | −0.347569 | + | 0.347569i | ||||
\(939\) | 3.27022e12 | 0.137272 | ||||||||
\(940\) | 9.90251e11 | − | 9.90251e11i | 0.0413685 | − | 0.0413685i | ||||
\(941\) | −6.36153e12 | − | 6.36153e12i | −0.264490 | − | 0.264490i | 0.562386 | − | 0.826875i | \(-0.309884\pi\) |
−0.826875 | + | 0.562386i | \(0.809884\pi\) | |||||||
\(942\) | 1.53758e13 | + | 1.53758e13i | 0.636222 | + | 0.636222i | ||||
\(943\) | − | 3.68343e12i | − | 0.151687i | ||||||
\(944\) | − | 6.11642e12i | − | 0.250682i | ||||||
\(945\) | 2.01424e11 | + | 2.01424e11i | 0.00821613 | + | 0.00821613i | ||||
\(946\) | −2.44651e12 | − | 2.44651e12i | −0.0993202 | − | 0.0993202i | ||||
\(947\) | 2.91860e12 | − | 2.91860e12i | 0.117923 | − | 0.117923i | −0.645683 | − | 0.763606i | \(-0.723427\pi\) |
0.763606 | + | 0.645683i | \(0.223427\pi\) | |||||||
\(948\) | −2.20663e13 | −0.887345 | ||||||||
\(949\) | 1.57412e13 | − | 1.57412e13i | 0.629999 | − | 0.629999i | ||||
\(950\) | − | 2.03369e13i | − | 0.810081i | ||||||
\(951\) | 4.13950e13 | 1.64110 | ||||||||
\(952\) | 1.38522e13 | + | 1.02092e13i | 0.546580 | + | 0.402833i | ||||
\(953\) | 1.80381e13 | 0.708389 | 0.354195 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354195 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(954\) | − | 1.45609e13i | − | 0.569141i | ||||||
\(955\) | −9.64288e10 | + | 9.64288e10i | −0.00375139 | + | 0.00375139i | ||||
\(956\) | −2.13615e13 | −0.827127 | ||||||||
\(957\) | −8.46816e12 | + | 8.46816e12i | −0.326351 | + | 0.326351i | ||||
\(958\) | 1.00384e13 | + | 1.00384e13i | 0.385051 | + | 0.385051i | ||||
\(959\) | −8.58878e12 | − | 8.58878e12i | −0.327905 | − | 0.327905i | ||||
\(960\) | 1.49157e12i | 0.0566790i | ||||||||
\(961\) | 2.47301e13i | 0.935341i | ||||||||
\(962\) | −7.28177e12 | − | 7.28177e12i | −0.274125 | − | 0.274125i | ||||
\(963\) | −1.22643e13 | − | 1.22643e13i | −0.459542 | − | 0.459542i | ||||
\(964\) | 1.10160e13 | − | 1.10160e13i | 0.410845 | − | 0.410845i | ||||
\(965\) | −4.31188e12 | −0.160064 | ||||||||
\(966\) | 6.27797e12 | − | 6.27797e12i | 0.231965 | − | 0.231965i | ||||
\(967\) | − | 3.92827e12i | − | 0.144472i | −0.997388 | − | 0.0722358i | \(-0.976987\pi\) | ||
0.997388 | − | 0.0722358i | \(-0.0230134\pi\) | |||||||
\(968\) | 1.09350e13 | 0.400293 | ||||||||
\(969\) | 3.41248e13 | − | 4.63019e13i | 1.24341 | − | 1.68711i | ||||
\(970\) | −3.49808e11 | −0.0126869 | ||||||||
\(971\) | 3.04563e13i | 1.09949i | 0.835333 | + | 0.549744i | \(0.185275\pi\) | ||||
−0.835333 | + | 0.549744i | \(0.814725\pi\) | |||||||
\(972\) | −1.91163e13 | + | 1.91163e13i | −0.686920 | + | 0.686920i | ||||
\(973\) | −1.96481e13 | −0.702768 | ||||||||
\(974\) | −1.09973e13 | + | 1.09973e13i | −0.391535 | + | 0.391535i | ||||
\(975\) | 1.42526e13 | + | 1.42526e13i | 0.505096 | + | 0.505096i | ||||
\(976\) | 1.20773e12 | + | 1.20773e12i | 0.0426036 | + | 0.0426036i | ||||
\(977\) | − | 1.55251e13i | − | 0.545140i | −0.962136 | − | 0.272570i | \(-0.912126\pi\) | ||
0.962136 | − | 0.272570i | \(-0.0878736\pi\) | |||||||
\(978\) | − | 1.33210e13i | − | 0.465598i | ||||||
\(979\) | −2.66857e12 | − | 2.66857e12i | −0.0928447 | − | 0.0928447i | ||||
\(980\) | 5.87713e11 | + | 5.87713e11i | 0.0203539 | + | 0.0203539i | ||||
\(981\) | −3.38889e13 | + | 3.38889e13i | −1.16828 | + | 1.16828i | ||||
\(982\) | 1.08305e13 | 0.371662 | ||||||||
\(983\) | 2.83320e13 | − | 2.83320e13i | 0.967801 | − | 0.967801i | −0.0316963 | − | 0.999498i | \(-0.510091\pi\) |
0.999498 | + | 0.0316963i | \(0.0100909\pi\) | |||||||
\(984\) | − | 1.11733e13i | − | 0.379930i | ||||||
\(985\) | 4.29464e12 | 0.145366 | ||||||||
\(986\) | 2.65577e12 | − | 3.60346e12i | 0.0894837 | − | 0.121415i | ||||
\(987\) | −3.10221e13 | −1.04050 | ||||||||
\(988\) | 1.43633e13i | 0.479566i | ||||||||
\(989\) | −2.45021e12 | + | 2.45021e12i | −0.0814365 | + | 0.0814365i | ||||
\(990\) | −1.99588e12 | −0.0660352 | ||||||||
\(991\) | −1.75792e12 | + | 1.75792e12i | −0.0578985 | + | 0.0578985i | −0.735463 | − | 0.677565i | \(-0.763035\pi\) |
0.677565 | + | 0.735463i | \(0.263035\pi\) | |||||||
\(992\) | 5.64868e12 | + | 5.64868e12i | 0.185202 | + | 0.185202i | ||||
\(993\) | −5.32786e13 | − | 5.32786e13i | −1.73893 | − | 1.73893i | ||||
\(994\) | 5.96067e12i | 0.193667i | ||||||||
\(995\) | 3.76912e12i | 0.121909i | ||||||||
\(996\) | 4.16876e13 | + | 4.16876e13i | 1.34227 | + | 1.34227i | ||||
\(997\) | −1.73945e13 | − | 1.73945e13i | −0.557549 | − | 0.557549i | 0.371060 | − | 0.928609i | \(-0.378994\pi\) |
−0.928609 | + | 0.371060i | \(0.878994\pi\) | |||||||
\(998\) | −1.55222e13 | + | 1.55222e13i | −0.495298 | + | 0.495298i | ||||
\(999\) | −8.22569e12 | −0.261293 |
(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 | 17.10.c.a.4.5 | ✓ | 24 | |
17.8 | even | 8 | 289.10.a.f.1.10 | 24 | |||
17.9 | even | 8 | 289.10.a.f.1.9 | 24 | |||
17.13 | even | 4 | inner | 17.10.c.a.13.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
17.10.c.a.13.8 | yes | 24 | 17.13 | even | 4 | inner | |
289.10.a.f.1.9 | 24 | 17.9 | even | 8 | |||
289.10.a.f.1.10 | 24 | 17.8 | even | 8 |