Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(643,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.643");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.e (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: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 40 x^{14} - 116 x^{13} + 800 x^{12} - 2584 x^{11} + 9564 x^{10} - 27124 x^{9} + 33538 x^{8} + 44880 x^{7} - 233952 x^{6} + 263772 x^{5} + 797544 x^{4} + \cdots + 2313441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.3 | ||
Root | \(-2.02927 + 4.89908i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1057 |
Dual form | 1150.2.e.d.643.3 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.93185 | − | 1.93185i | 1.11536 | − | 1.11536i | 0.122941 | − | 0.992414i | \(-0.460767\pi\) |
0.992414 | − | 0.122941i | \(-0.0392326\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.73205 | −1.11536 | ||||||||
\(7\) | −3.35143 | + | 3.35143i | −1.26672 | + | 1.26672i | −0.318947 | + | 0.947772i | \(0.603329\pi\) |
−0.947772 | + | 0.318947i | \(0.896671\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 4.46410i | − | 1.48803i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73963i | 1.42905i | 0.699609 | + | 0.714526i | \(0.253358\pi\) | ||||
−0.699609 | + | 0.714526i | \(0.746642\pi\) | |||||||
\(12\) | 1.93185 | + | 1.93185i | 0.557678 | + | 0.557678i | ||||
\(13\) | −1.74238 | + | 1.74238i | −0.483250 | + | 0.483250i | −0.906168 | − | 0.422918i | \(-0.861006\pi\) |
0.422918 | + | 0.906168i | \(0.361006\pi\) | |||||||
\(14\) | 4.73963 | 1.26672 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | −3.15660 | + | 3.15660i | −0.744017 | + | 0.744017i | ||||
\(19\) | 4.73963 | 1.08735 | 0.543673 | − | 0.839297i | \(-0.317033\pi\) | ||||
0.543673 | + | 0.839297i | \(0.317033\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.9489i | 2.82568i | ||||||||
\(22\) | 3.35143 | − | 3.35143i | 0.714526 | − | 0.714526i | ||||
\(23\) | −2.83379 | − | 3.86906i | −0.590885 | − | 0.806755i | ||||
\(24\) | − | 2.73205i | − | 0.557678i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.46410 | 0.483250 | ||||||||
\(27\) | −2.82843 | − | 2.82843i | −0.544331 | − | 0.544331i | ||||
\(28\) | −3.35143 | − | 3.35143i | −0.633360 | − | 0.633360i | ||||
\(29\) | 9.19615i | 1.70768i | 0.520533 | + | 0.853841i | \(0.325733\pi\) | ||||
−0.520533 | + | 0.853841i | \(0.674267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 9.15626 | + | 9.15626i | 1.59390 | + | 1.59390i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | 2.45341 | − | 2.45341i | 0.403339 | − | 0.403339i | −0.476069 | − | 0.879408i | \(-0.657939\pi\) |
0.879408 | + | 0.476069i | \(0.157939\pi\) | |||||||
\(38\) | −3.35143 | − | 3.35143i | −0.543673 | − | 0.543673i | ||||
\(39\) | 6.73205i | 1.07799i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.464102 | −0.0724805 | −0.0362402 | − | 0.999343i | \(-0.511538\pi\) | ||||
−0.0362402 | + | 0.999343i | \(0.511538\pi\) | |||||||
\(42\) | 9.15626 | − | 9.15626i | 1.41284 | − | 1.41284i | ||||
\(43\) | 5.80484 | + | 5.80484i | 0.885230 | + | 0.885230i | 0.994060 | − | 0.108831i | \(-0.0347106\pi\) |
−0.108831 | + | 0.994060i | \(0.534711\pi\) | |||||||
\(44\) | −4.73963 | −0.714526 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.732051 | + | 4.73963i | −0.107935 | + | 0.698820i | ||||
\(47\) | 5.41662 | + | 5.41662i | 0.790095 | + | 0.790095i | 0.981509 | − | 0.191414i | \(-0.0613074\pi\) |
−0.191414 | + | 0.981509i | \(0.561307\pi\) | |||||||
\(48\) | −1.93185 | + | 1.93185i | −0.278839 | + | 0.278839i | ||||
\(49\) | − | 15.4641i | − | 2.20916i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.74238 | − | 1.74238i | −0.241625 | − | 0.241625i | ||||
\(53\) | −2.45341 | − | 2.45341i | −0.337002 | − | 0.337002i | 0.518236 | − | 0.855238i | \(-0.326589\pi\) |
−0.855238 | + | 0.518236i | \(0.826589\pi\) | |||||||
\(54\) | 4.00000i | 0.544331i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.73963i | 0.633360i | ||||||||
\(57\) | 9.15626 | − | 9.15626i | 1.21278 | − | 1.21278i | ||||
\(58\) | 6.50266 | − | 6.50266i | 0.853841 | − | 0.853841i | ||||
\(59\) | 4.73205i | 0.616061i | 0.951377 | + | 0.308030i | \(0.0996698\pi\) | ||||
−0.951377 | + | 0.308030i | \(0.900330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9489i | 1.65794i | 0.559294 | + | 0.828969i | \(0.311072\pi\) | ||||
−0.559294 | + | 0.828969i | \(0.688928\pi\) | |||||||
\(62\) | −4.89898 | − | 4.89898i | −0.622171 | − | 0.622171i | ||||
\(63\) | 14.9611 | + | 14.9611i | 1.88492 | + | 1.88492i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 12.9489i | − | 1.59390i | ||||||
\(67\) | −6.70285 | + | 6.70285i | −0.818884 | + | 0.818884i | −0.985946 | − | 0.167063i | \(-0.946572\pi\) |
0.167063 | + | 0.985946i | \(0.446572\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9489 | − | 2.00000i | −1.55887 | − | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | −3.15660 | − | 3.15660i | −0.372008 | − | 0.372008i | ||||
\(73\) | −4.70951 | + | 4.70951i | −0.551207 | + | 0.551207i | −0.926789 | − | 0.375582i | \(-0.877443\pi\) |
0.375582 | + | 0.926789i | \(0.377443\pi\) | |||||||
\(74\) | −3.46965 | −0.403339 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.73963i | 0.543673i | ||||||||
\(77\) | −15.8845 | − | 15.8845i | −1.81021 | − | 1.81021i | ||||
\(78\) | 4.76028 | − | 4.76028i | 0.538995 | − | 0.538995i | ||||
\(79\) | −1.26998 | −0.142884 | −0.0714420 | − | 0.997445i | \(-0.522760\pi\) | ||||
−0.0714420 | + | 0.997445i | \(0.522760\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.46410 | 0.273789 | ||||||||
\(82\) | 0.328169 | + | 0.328169i | 0.0362402 | + | 0.0362402i | ||||
\(83\) | −5.80484 | − | 5.80484i | −0.637164 | − | 0.637164i | 0.312691 | − | 0.949855i | \(-0.398770\pi\) |
−0.949855 | + | 0.312691i | \(0.898770\pi\) | |||||||
\(84\) | −12.9489 | −1.41284 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.20928i | − | 0.885230i | ||||||
\(87\) | 17.7656 | + | 17.7656i | 1.90467 | + | 1.90467i | ||||
\(88\) | 3.35143 | + | 3.35143i | 0.357263 | + | 0.357263i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 11.6789i | − | 1.22428i | ||||||
\(92\) | 3.86906 | − | 2.83379i | 0.403378 | − | 0.295443i | ||||
\(93\) | 13.3843 | − | 13.3843i | 1.38788 | − | 1.38788i | ||||
\(94\) | − | 7.66025i | − | 0.790095i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.73205 | 0.278839 | ||||||||
\(97\) | 9.15626 | − | 9.15626i | 0.929678 | − | 0.929678i | −0.0680071 | − | 0.997685i | \(-0.521664\pi\) |
0.997685 | + | 0.0680071i | \(0.0216641\pi\) | |||||||
\(98\) | −10.9348 | + | 10.9348i | −1.10458 | + | 1.10458i | ||||
\(99\) | 21.1582 | 2.12648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9282 | −1.68442 | −0.842210 | − | 0.539150i | \(-0.818745\pi\) | ||||
−0.842210 | + | 0.539150i | \(0.818745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.25825 | − | 8.25825i | −0.813710 | − | 0.813710i | 0.171478 | − | 0.985188i | \(-0.445146\pi\) |
−0.985188 | + | 0.171478i | \(0.945146\pi\) | |||||||
\(104\) | 2.46410i | 0.241625i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.46965i | 0.337002i | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 2.82843 | − | 2.82843i | 0.272166 | − | 0.272166i | ||||
\(109\) | −6.00961 | −0.575616 | −0.287808 | − | 0.957688i | \(-0.592927\pi\) | ||||
−0.287808 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.47926i | − | 0.899732i | ||||||
\(112\) | 3.35143 | − | 3.35143i | 0.316680 | − | 0.316680i | ||||
\(113\) | −4.24944 | − | 4.24944i | −0.399753 | − | 0.399753i | 0.478393 | − | 0.878146i | \(-0.341220\pi\) |
−0.878146 | + | 0.478393i | \(0.841220\pi\) | |||||||
\(114\) | −12.9489 | −1.21278 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.19615 | −0.853841 | ||||||||
\(117\) | 7.77817 | + | 7.77817i | 0.719092 | + | 0.719092i | ||||
\(118\) | 3.34607 | − | 3.34607i | 0.308030 | − | 0.308030i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.4641 | −1.04219 | ||||||||
\(122\) | 9.15626 | − | 9.15626i | 0.828969 | − | 0.828969i | ||||
\(123\) | −0.896575 | + | 0.896575i | −0.0808415 | + | 0.0808415i | ||||
\(124\) | 6.92820i | 0.622171i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 21.1582i | − | 1.88492i | ||||||
\(127\) | 1.55291 | + | 1.55291i | 0.137799 | + | 0.137799i | 0.772641 | − | 0.634843i | \(-0.218935\pi\) |
−0.634843 | + | 0.772641i | \(0.718935\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 22.4282 | 1.97469 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | −9.15626 | + | 9.15626i | −0.796950 | + | 0.796950i | ||||
\(133\) | −15.8845 | + | 15.8845i | −1.37736 | + | 1.37736i | ||||
\(134\) | 9.47926 | 0.818884 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 7.74205 | + | 10.5705i | 0.659047 | + | 0.899819i | ||||
\(139\) | − | 6.53590i | − | 0.554368i | −0.960817 | − | 0.277184i | \(-0.910599\pi\) | ||
0.960817 | − | 0.277184i | \(-0.0894011\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.9282 | 1.76247 | ||||||||
\(142\) | 6.69213 | + | 6.69213i | 0.561591 | + | 0.561591i | ||||
\(143\) | −8.25825 | − | 8.25825i | −0.690590 | − | 0.690590i | ||||
\(144\) | 4.46410i | 0.372008i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.66025 | 0.551207 | ||||||||
\(147\) | −29.8744 | − | 29.8744i | −2.46399 | − | 2.46399i | ||||
\(148\) | 2.45341 | + | 2.45341i | 0.201669 | + | 0.201669i | ||||
\(149\) | 18.9585 | 1.55314 | 0.776571 | − | 0.630029i | \(-0.216957\pi\) | ||||
0.776571 | + | 0.630029i | \(0.216957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3205 | 1.24677 | 0.623383 | − | 0.781917i | \(-0.285758\pi\) | ||||
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(152\) | 3.35143 | − | 3.35143i | 0.271836 | − | 0.271836i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.4641i | 1.81021i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.73205 | −0.538995 | ||||||||
\(157\) | −15.8591 | + | 15.8591i | −1.26570 | + | 1.26570i | −0.317405 | + | 0.948290i | \(0.602811\pi\) |
−0.948290 | + | 0.317405i | \(0.897189\pi\) | |||||||
\(158\) | 0.898012 | + | 0.898012i | 0.0714420 | + | 0.0714420i | ||||
\(159\) | −9.47926 | −0.751754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.4641 | + | 3.46965i | 1.77042 | + | 0.273447i | ||||
\(162\) | −1.74238 | − | 1.74238i | −0.136895 | − | 0.136895i | ||||
\(163\) | 7.86611 | − | 7.86611i | 0.616121 | − | 0.616121i | −0.328413 | − | 0.944534i | \(-0.606514\pi\) |
0.944534 | + | 0.328413i | \(0.106514\pi\) | |||||||
\(164\) | − | 0.464102i | − | 0.0362402i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.20928i | 0.637164i | ||||||||
\(167\) | 3.58630 | + | 3.58630i | 0.277516 | + | 0.277516i | 0.832117 | − | 0.554600i | \(-0.187129\pi\) |
−0.554600 | + | 0.832117i | \(0.687129\pi\) | |||||||
\(168\) | 9.15626 | + | 9.15626i | 0.706421 | + | 0.706421i | ||||
\(169\) | 6.92820i | 0.532939i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 21.1582i | − | 1.61801i | ||||||
\(172\) | −5.80484 | + | 5.80484i | −0.442615 | + | 0.442615i | ||||
\(173\) | −0.429705 | + | 0.429705i | −0.0326699 | + | 0.0326699i | −0.723253 | − | 0.690583i | \(-0.757354\pi\) |
0.690583 | + | 0.723253i | \(0.257354\pi\) | |||||||
\(174\) | − | 25.1244i | − | 1.90467i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.73963i | − | 0.357263i | ||||||
\(177\) | 9.14162 | + | 9.14162i | 0.687126 | + | 0.687126i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 22.1962i | − | 1.65902i | −0.558493 | − | 0.829509i | \(-0.688620\pi\) | ||
0.558493 | − | 0.829509i | \(-0.311380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.8978i | 1.92497i | 0.271335 | + | 0.962485i | \(0.412535\pi\) | ||||
−0.271335 | + | 0.962485i | \(0.587465\pi\) | |||||||
\(182\) | −8.25825 | + | 8.25825i | −0.612142 | + | 0.612142i | ||||
\(183\) | 25.0154 | + | 25.0154i | 1.84919 | + | 1.84919i | ||||
\(184\) | −4.73963 | − | 0.732051i | −0.349410 | − | 0.0539675i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.9282 | −1.38788 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.41662 | + | 5.41662i | −0.395047 | + | 0.395047i | ||||
\(189\) | 18.9585 | 1.37903 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.6885i | − | 1.27990i | −0.768417 | − | 0.639949i | \(-0.778955\pi\) | ||
0.768417 | − | 0.639949i | \(-0.221045\pi\) | |||||||
\(192\) | −1.93185 | − | 1.93185i | −0.139419 | − | 0.139419i | ||||
\(193\) | 7.07107 | − | 7.07107i | 0.508987 | − | 0.508987i | −0.405229 | − | 0.914215i | \(-0.632808\pi\) |
0.914215 | + | 0.405229i | \(0.132808\pi\) | |||||||
\(194\) | −12.9489 | −0.929678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.4641 | 1.10458 | ||||||||
\(197\) | 4.94975 | + | 4.94975i | 0.352655 | + | 0.352655i | 0.861096 | − | 0.508442i | \(-0.169778\pi\) |
−0.508442 | + | 0.861096i | \(0.669778\pi\) | |||||||
\(198\) | −14.9611 | − | 14.9611i | −1.06324 | − | 1.06324i | ||||
\(199\) | 17.6885 | 1.25391 | 0.626954 | − | 0.779056i | \(-0.284301\pi\) | ||||
0.626954 | + | 0.779056i | \(0.284301\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 25.8978i | 1.82669i | ||||||||
\(202\) | 11.9700 | + | 11.9700i | 0.842210 | + | 0.842210i | ||||
\(203\) | −30.8202 | − | 30.8202i | −2.16316 | − | 2.16316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.6789i | 0.813710i | ||||||||
\(207\) | −17.2719 | + | 12.6503i | −1.20048 | + | 0.879258i | ||||
\(208\) | 1.74238 | − | 1.74238i | 0.120813 | − | 0.120813i | ||||
\(209\) | 22.4641i | 1.55387i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2487 | −1.53166 | −0.765832 | − | 0.643040i | \(-0.777673\pi\) | ||||
−0.765832 | + | 0.643040i | \(0.777673\pi\) | |||||||
\(212\) | 2.45341 | − | 2.45341i | 0.168501 | − | 0.168501i | ||||
\(213\) | −18.2832 | + | 18.2832i | −1.25275 | + | 1.25275i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −23.2194 | + | 23.2194i | −1.57623 | + | 1.57623i | ||||
\(218\) | 4.24944 | + | 4.24944i | 0.287808 | + | 0.287808i | ||||
\(219\) | 18.1962i | 1.22958i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.70285 | + | 6.70285i | −0.449866 | + | 0.449866i | ||||
\(223\) | −3.34607 | + | 3.34607i | −0.224069 | + | 0.224069i | −0.810209 | − | 0.586140i | \(-0.800647\pi\) |
0.586140 | + | 0.810209i | \(0.300647\pi\) | |||||||
\(224\) | −4.73963 | −0.316680 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00961i | 0.399753i | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 9.15626 | + | 9.15626i | 0.606388 | + | 0.606388i | ||||
\(229\) | 6.93930 | 0.458562 | 0.229281 | − | 0.973360i | \(-0.426363\pi\) | ||||
0.229281 | + | 0.973360i | \(0.426363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −61.3731 | −4.03805 | ||||||||
\(232\) | 6.50266 | + | 6.50266i | 0.426921 | + | 0.426921i | ||||
\(233\) | 4.43211 | − | 4.43211i | 0.290357 | − | 0.290357i | −0.546864 | − | 0.837221i | \(-0.684179\pi\) |
0.837221 | + | 0.546864i | \(0.184179\pi\) | |||||||
\(234\) | − | 11.0000i | − | 0.719092i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.73205 | −0.308030 | ||||||||
\(237\) | −2.45341 | + | 2.45341i | −0.159366 | + | 0.159366i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.5167i | − | 1.52117i | −0.649241 | − | 0.760583i | \(-0.724913\pi\) | ||
0.649241 | − | 0.760583i | \(-0.275087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.4889i | − | 0.997726i | −0.866681 | − | 0.498863i | \(-0.833751\pi\) | ||
0.866681 | − | 0.498863i | \(-0.166249\pi\) | |||||||
\(242\) | 8.10634 | + | 8.10634i | 0.521096 | + | 0.521096i | ||||
\(243\) | 13.2456 | − | 13.2456i | 0.849703 | − | 0.849703i | ||||
\(244\) | −12.9489 | −0.828969 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.26795 | 0.0808415 | ||||||||
\(247\) | −8.25825 | + | 8.25825i | −0.525460 | + | 0.525460i | ||||
\(248\) | 4.89898 | − | 4.89898i | 0.311086 | − | 0.311086i | ||||
\(249\) | −22.4282 | −1.42133 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.47926i | − | 0.598326i | −0.954202 | − | 0.299163i | \(-0.903293\pi\) | ||
0.954202 | − | 0.299163i | \(-0.0967074\pi\) | |||||||
\(252\) | −14.9611 | + | 14.9611i | −0.942461 | + | 0.942461i | ||||
\(253\) | 18.3379 | − | 13.4311i | 1.15290 | − | 0.844406i | ||||
\(254\) | − | 2.19615i | − | 0.137799i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.656339 | − | 0.656339i | −0.0409413 | − | 0.0409413i | 0.686340 | − | 0.727281i | \(-0.259216\pi\) |
−0.727281 | + | 0.686340i | \(0.759216\pi\) | |||||||
\(258\) | −15.8591 | − | 15.8591i | −0.987345 | − | 0.987345i | ||||
\(259\) | 16.4449i | 1.02183i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.0526 | 2.54109 | ||||||||
\(262\) | −5.65685 | − | 5.65685i | −0.349482 | − | 0.349482i | ||||
\(263\) | 6.70285 | + | 6.70285i | 0.413315 | + | 0.413315i | 0.882892 | − | 0.469576i | \(-0.155593\pi\) |
−0.469576 | + | 0.882892i | \(0.655593\pi\) | |||||||
\(264\) | 12.9489 | 0.796950 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 22.4641 | 1.37736 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.70285 | − | 6.70285i | −0.409442 | − | 0.409442i | ||||
\(269\) | − | 15.5885i | − | 0.950445i | −0.879866 | − | 0.475223i | \(-0.842368\pi\) | ||
0.879866 | − | 0.475223i | \(-0.157632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.19615 | 0.254898 | 0.127449 | − | 0.991845i | \(-0.459321\pi\) | ||||
0.127449 | + | 0.991845i | \(0.459321\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.5620 | − | 22.5620i | −1.36551 | − | 1.36551i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.00000 | − | 12.9489i | 0.120386 | − | 0.779433i | ||||
\(277\) | 2.77766 | + | 2.77766i | 0.166893 | + | 0.166893i | 0.785612 | − | 0.618719i | \(-0.212348\pi\) |
−0.618719 | + | 0.785612i | \(0.712348\pi\) | |||||||
\(278\) | −4.62158 | + | 4.62158i | −0.277184 | + | 0.277184i | ||||
\(279\) | − | 30.9282i | − | 1.85162i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.4282i | − | 1.33795i | −0.743284 | − | 0.668976i | \(-0.766733\pi\) | ||
0.743284 | − | 0.668976i | \(-0.233267\pi\) | |||||||
\(282\) | −14.7985 | − | 14.7985i | −0.881236 | − | 0.881236i | ||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | − | 9.46410i | − | 0.561591i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.6789i | 0.690590i | ||||||||
\(287\) | 1.55540 | − | 1.55540i | 0.0918125 | − | 0.0918125i | ||||
\(288\) | 3.15660 | − | 3.15660i | 0.186004 | − | 0.186004i | ||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 35.3771i | − | 2.07384i | ||||||
\(292\) | −4.70951 | − | 4.70951i | −0.275603 | − | 0.275603i | ||||
\(293\) | −18.3125 | − | 18.3125i | −1.06983 | − | 1.06983i | −0.997371 | − | 0.0724578i | \(-0.976916\pi\) |
−0.0724578 | − | 0.997371i | \(-0.523084\pi\) | |||||||
\(294\) | 42.2487i | 2.46399i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 3.46965i | − | 0.201669i | ||||||
\(297\) | 13.4057 | − | 13.4057i | 0.777878 | − | 0.777878i | ||||
\(298\) | −13.4057 | − | 13.4057i | −0.776571 | − | 0.776571i | ||||
\(299\) | 11.6789 | + | 1.80385i | 0.675410 | + | 0.104319i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.9090 | −2.24268 | ||||||||
\(302\) | −10.8332 | − | 10.8332i | −0.623383 | − | 0.623383i | ||||
\(303\) | −32.7028 | + | 32.7028i | −1.87873 | + | 1.87873i | ||||
\(304\) | −4.73963 | −0.271836 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.10583 | − | 3.10583i | −0.177259 | − | 0.177259i | 0.612901 | − | 0.790160i | \(-0.290003\pi\) |
−0.790160 | + | 0.612901i | \(0.790003\pi\) | |||||||
\(308\) | 15.8845 | − | 15.8845i | 0.905104 | − | 0.905104i | ||||
\(309\) | −31.9074 | −1.81515 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.80385 | −0.215696 | −0.107848 | − | 0.994167i | \(-0.534396\pi\) | ||||
−0.107848 | + | 0.994167i | \(0.534396\pi\) | |||||||
\(312\) | 4.76028 | + | 4.76028i | 0.269498 | + | 0.269498i | ||||
\(313\) | −9.15626 | − | 9.15626i | −0.517543 | − | 0.517543i | 0.399284 | − | 0.916827i | \(-0.369259\pi\) |
−0.916827 | + | 0.399284i | \(0.869259\pi\) | |||||||
\(314\) | 22.4282 | 1.26570 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1.26998i | − | 0.0714420i | ||||||
\(317\) | 17.9551 | + | 17.9551i | 1.00846 | + | 1.00846i | 0.999964 | + | 0.00849332i | \(0.00270354\pi\) |
0.00849332 | + | 0.999964i | \(0.497296\pi\) | |||||||
\(318\) | 6.70285 | + | 6.70285i | 0.375877 | + | 0.375877i | ||||
\(319\) | −43.5864 | −2.44037 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.4311 | − | 18.3379i | −0.748486 | − | 1.02193i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.46410i | 0.136895i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.1244 | −0.616121 | ||||||||
\(327\) | −11.6097 | + | 11.6097i | −0.642017 | + | 0.642017i | ||||
\(328\) | −0.328169 | + | 0.328169i | −0.0181201 | + | 0.0181201i | ||||
\(329\) | −36.3068 | −2.00166 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.8564 | 1.86092 | 0.930458 | − | 0.366398i | \(-0.119409\pi\) | ||||
0.930458 | + | 0.366398i | \(0.119409\pi\) | |||||||
\(332\) | 5.80484 | − | 5.80484i | 0.318582 | − | 0.318582i | ||||
\(333\) | −10.9523 | − | 10.9523i | −0.600182 | − | 0.600182i | ||||
\(334\) | − | 5.07180i | − | 0.277516i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 12.9489i | − | 0.706421i | ||||||
\(337\) | 9.15626 | − | 9.15626i | 0.498773 | − | 0.498773i | −0.412283 | − | 0.911056i | \(-0.635268\pi\) |
0.911056 | + | 0.412283i | \(0.135268\pi\) | |||||||
\(338\) | 4.89898 | − | 4.89898i | 0.266469 | − | 0.266469i | ||||
\(339\) | −16.4186 | −0.891734 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.8371i | 1.77823i | ||||||||
\(342\) | −14.9611 | + | 14.9611i | −0.809004 | + | 0.809004i | ||||
\(343\) | 28.3668 | + | 28.3668i | 1.53166 | + | 1.53166i | ||||
\(344\) | 8.20928 | 0.442615 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.607695 | 0.0326699 | ||||||||
\(347\) | 21.8695 | + | 21.8695i | 1.17402 | + | 1.17402i | 0.981243 | + | 0.192776i | \(0.0617490\pi\) |
0.192776 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(348\) | −17.7656 | + | 17.7656i | −0.952336 | + | 0.952336i | ||||
\(349\) | 12.6603i | 0.677688i | 0.940843 | + | 0.338844i | \(0.110036\pi\) | ||||
−0.940843 | + | 0.338844i | \(0.889964\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.85641 | 0.526096 | ||||||||
\(352\) | −3.35143 | + | 3.35143i | −0.178632 | + | 0.178632i | ||||
\(353\) | 4.98691 | − | 4.98691i | 0.265427 | − | 0.265427i | −0.561828 | − | 0.827254i | \(-0.689902\pi\) |
0.827254 | + | 0.561828i | \(0.189902\pi\) | |||||||
\(354\) | − | 12.9282i | − | 0.687126i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.6950 | + | 15.6950i | −0.829509 | + | 0.829509i | ||||
\(359\) | −24.6278 | −1.29981 | −0.649904 | − | 0.760016i | \(-0.725191\pi\) | ||||
−0.649904 | + | 0.760016i | \(0.725191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.46410 | 0.182321 | ||||||||
\(362\) | 18.3125 | − | 18.3125i | 0.962485 | − | 0.962485i | ||||
\(363\) | −22.1469 | + | 22.1469i | −1.16241 | + | 1.16241i | ||||
\(364\) | 11.6789 | 0.612142 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 35.3771i | − | 1.84919i | ||||||
\(367\) | −3.35143 | + | 3.35143i | −0.174943 | + | 0.174943i | −0.789147 | − | 0.614204i | \(-0.789477\pi\) |
0.614204 | + | 0.789147i | \(0.289477\pi\) | |||||||
\(368\) | 2.83379 | + | 3.86906i | 0.147721 | + | 0.201689i | ||||
\(369\) | 2.07180i | 0.107853i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4449 | 0.853775 | ||||||||
\(372\) | 13.3843 | + | 13.3843i | 0.693942 | + | 0.693942i | ||||
\(373\) | 13.4057 | + | 13.4057i | 0.694121 | + | 0.694121i | 0.963136 | − | 0.269015i | \(-0.0866982\pi\) |
−0.269015 | + | 0.963136i | \(0.586698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.66025 | 0.395047 | ||||||||
\(377\) | −16.0232 | − | 16.0232i | −0.825238 | − | 0.825238i | ||||
\(378\) | −13.4057 | − | 13.4057i | −0.689515 | − | 0.689515i | ||||
\(379\) | 9.47926 | 0.486917 | 0.243458 | − | 0.969911i | \(-0.421718\pi\) | ||||
0.243458 | + | 0.969911i | \(0.421718\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | −12.5077 | + | 12.5077i | −0.639949 | + | 0.639949i | ||||
\(383\) | 5.14745 | + | 5.14745i | 0.263022 | + | 0.263022i | 0.826281 | − | 0.563258i | \(-0.190452\pi\) |
−0.563258 | + | 0.826281i | \(0.690452\pi\) | |||||||
\(384\) | 2.73205i | 0.139419i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | 25.9134 | − | 25.9134i | 1.31725 | − | 1.31725i | ||||
\(388\) | 9.15626 | + | 9.15626i | 0.464839 | + | 0.464839i | ||||
\(389\) | −19.8882 | −1.00837 | −0.504186 | − | 0.863595i | \(-0.668207\pi\) | ||||
−0.504186 | + | 0.863595i | \(0.668207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −10.9348 | − | 10.9348i | −0.552289 | − | 0.552289i | ||||
\(393\) | 15.4548 | − | 15.4548i | 0.779592 | − | 0.779592i | ||||
\(394\) | − | 7.00000i | − | 0.352655i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 21.1582i | 1.06324i | ||||||||
\(397\) | 16.4901 | + | 16.4901i | 0.827614 | + | 0.827614i | 0.987186 | − | 0.159572i | \(-0.0510115\pi\) |
−0.159572 | + | 0.987186i | \(0.551012\pi\) | |||||||
\(398\) | −12.5077 | − | 12.5077i | −0.626954 | − | 0.626954i | ||||
\(399\) | 61.3731i | 3.07250i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.4282i | 1.12001i | 0.828489 | + | 0.560005i | \(0.189201\pi\) | ||||
−0.828489 | + | 0.560005i | \(0.810799\pi\) | |||||||
\(402\) | 18.3125 | − | 18.3125i | 0.913346 | − | 0.913346i | ||||
\(403\) | −12.0716 | + | 12.0716i | −0.601328 | + | 0.601328i | ||||
\(404\) | − | 16.9282i | − | 0.842210i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 43.5864i | 2.16316i | ||||||||
\(407\) | 11.6283 | + | 11.6283i | 0.576392 | + | 0.576392i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.53590i | 0.174839i | 0.996172 | + | 0.0874195i | \(0.0278620\pi\) | ||||
−0.996172 | + | 0.0874195i | \(0.972138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.25825 | − | 8.25825i | 0.406855 | − | 0.406855i | ||||
\(413\) | −15.8591 | − | 15.8591i | −0.780376 | − | 0.780376i | ||||
\(414\) | 21.1582 | + | 3.26795i | 1.03987 | + | 0.160611i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.46410 | −0.120813 | ||||||||
\(417\) | −12.6264 | − | 12.6264i | −0.618317 | − | 0.618317i | ||||
\(418\) | 15.8845 | − | 15.8845i | 0.776937 | − | 0.776937i | ||||
\(419\) | 18.6182 | 0.909560 | 0.454780 | − | 0.890604i | \(-0.349718\pi\) | ||||
0.454780 | + | 0.890604i | \(0.349718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.9585i | − | 0.923982i | −0.886885 | − | 0.461991i | \(-0.847135\pi\) | ||
0.886885 | − | 0.461991i | \(-0.152865\pi\) | |||||||
\(422\) | 15.7322 | + | 15.7322i | 0.765832 | + | 0.765832i | ||||
\(423\) | 24.1803 | − | 24.1803i | 1.17569 | − | 1.17569i | ||||
\(424\) | −3.46965 | −0.168501 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25.8564 | 1.25275 | ||||||||
\(427\) | −43.3973 | − | 43.3973i | −2.10014 | − | 2.10014i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.9074 | −1.54051 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.8371i | − | 1.58171i | −0.612004 | − | 0.790854i | \(-0.709637\pi\) | ||
0.612004 | − | 0.790854i | \(-0.290363\pi\) | |||||||
\(432\) | 2.82843 | + | 2.82843i | 0.136083 | + | 0.136083i | ||||
\(433\) | 27.4688 | + | 27.4688i | 1.32007 | + | 1.32007i | 0.913719 | + | 0.406347i | \(0.133198\pi\) |
0.406347 | + | 0.913719i | \(0.366802\pi\) | |||||||
\(434\) | 32.8371 | 1.57623 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 6.00961i | − | 0.287808i | ||||||
\(437\) | −13.4311 | − | 18.3379i | −0.642497 | − | 0.877222i | ||||
\(438\) | 12.8666 | − | 12.8666i | 0.614791 | − | 0.614791i | ||||
\(439\) | − | 13.8564i | − | 0.661330i | −0.943748 | − | 0.330665i | \(-0.892727\pi\) | ||
0.943748 | − | 0.330665i | \(-0.107273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −69.0333 | −3.28730 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.5264 | + | 27.5264i | −1.30782 | + | 1.30782i | −0.384832 | + | 0.922987i | \(0.625741\pi\) |
−0.922987 | + | 0.384832i | \(0.874259\pi\) | |||||||
\(444\) | 9.47926 | 0.449866 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.73205 | 0.224069 | ||||||||
\(447\) | 36.6251 | − | 36.6251i | 1.73231 | − | 1.73231i | ||||
\(448\) | 3.35143 | + | 3.35143i | 0.158340 | + | 0.158340i | ||||
\(449\) | 18.5359i | 0.874763i | 0.899276 | + | 0.437382i | \(0.144094\pi\) | ||||
−0.899276 | + | 0.437382i | \(0.855906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.19967i | − | 0.103578i | ||||||
\(452\) | 4.24944 | − | 4.24944i | 0.199877 | − | 0.199877i | ||||
\(453\) | 29.5969 | − | 29.5969i | 1.39059 | − | 1.39059i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 12.9489i | − | 0.606388i | ||||||
\(457\) | −4.24944 | + | 4.24944i | −0.198780 | + | 0.198780i | −0.799477 | − | 0.600697i | \(-0.794890\pi\) |
0.600697 | + | 0.799477i | \(0.294890\pi\) | |||||||
\(458\) | −4.90683 | − | 4.90683i | −0.229281 | − | 0.229281i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.51666 | −0.396660 | −0.198330 | − | 0.980135i | \(-0.563552\pi\) | ||||
−0.198330 | + | 0.980135i | \(0.563552\pi\) | |||||||
\(462\) | 43.3973 | + | 43.3973i | 2.01903 | + | 2.01903i | ||||
\(463\) | 9.52056 | − | 9.52056i | 0.442458 | − | 0.442458i | −0.450379 | − | 0.892837i | \(-0.648711\pi\) |
0.892837 | + | 0.450379i | \(0.148711\pi\) | |||||||
\(464\) | − | 9.19615i | − | 0.426921i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.26795 | −0.290357 | ||||||||
\(467\) | 19.2105 | − | 19.2105i | 0.888958 | − | 0.888958i | −0.105465 | − | 0.994423i | \(-0.533633\pi\) |
0.994423 | + | 0.105465i | \(0.0336332\pi\) | |||||||
\(468\) | −7.77817 | + | 7.77817i | −0.359546 | + | 0.359546i | ||||
\(469\) | − | 44.9282i | − | 2.07459i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 61.2749i | 2.82340i | ||||||||
\(472\) | 3.34607 | + | 3.34607i | 0.154015 | + | 0.154015i | ||||
\(473\) | −27.5128 | + | 27.5128i | −1.26504 | + | 1.26504i | ||||
\(474\) | 3.46965 | 0.159366 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.9523 | + | 10.9523i | −0.501471 | + | 0.501471i | ||||
\(478\) | −16.6288 | + | 16.6288i | −0.760583 | + | 0.760583i | ||||
\(479\) | 20.2285 | 0.924264 | 0.462132 | − | 0.886811i | \(-0.347085\pi\) | ||||
0.462132 | + | 0.886811i | \(0.347085\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.54957i | 0.389827i | ||||||||
\(482\) | −10.9523 | + | 10.9523i | −0.498863 | + | 0.498863i | ||||
\(483\) | 50.1002 | − | 36.6945i | 2.27964 | − | 1.66966i | ||||
\(484\) | − | 11.4641i | − | 0.521096i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.7321 | −0.849703 | ||||||||
\(487\) | −0.0371647 | − | 0.0371647i | −0.00168410 | − | 0.00168410i | 0.706264 | − | 0.707948i | \(-0.250379\pi\) |
−0.707948 | + | 0.706264i | \(0.750379\pi\) | |||||||
\(488\) | 9.15626 | + | 9.15626i | 0.414485 | + | 0.414485i | ||||
\(489\) | − | 30.3923i | − | 1.37439i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1244 | 0.772811 | 0.386406 | − | 0.922329i | \(-0.373716\pi\) | ||||
0.386406 | + | 0.922329i | \(0.373716\pi\) | |||||||
\(492\) | −0.896575 | − | 0.896575i | −0.0404207 | − | 0.0404207i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 11.6789 | 0.525460 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.92820 | −0.311086 | ||||||||
\(497\) | 31.7182 | − | 31.7182i | 1.42276 | − | 1.42276i | ||||
\(498\) | 15.8591 | + | 15.8591i | 0.710664 | + | 0.710664i | ||||
\(499\) | − | 32.4449i | − | 1.45243i | −0.687467 | − | 0.726216i | \(-0.741277\pi\) | ||
0.687467 | − | 0.726216i | \(-0.258723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8564 | 0.619059 | ||||||||
\(502\) | −6.70285 | + | 6.70285i | −0.299163 | + | 0.299163i | ||||
\(503\) | 3.35143 | + | 3.35143i | 0.149433 | + | 0.149433i | 0.777865 | − | 0.628432i | \(-0.216303\pi\) |
−0.628432 | + | 0.777865i | \(0.716303\pi\) | |||||||
\(504\) | 21.1582 | 0.942461 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.4641 | − | 3.46965i | −0.998651 | − | 0.154245i | ||||
\(507\) | 13.3843 | + | 13.3843i | 0.594416 | + | 0.594416i | ||||
\(508\) | −1.55291 | + | 1.55291i | −0.0688994 | + | 0.0688994i | ||||
\(509\) | 6.92820i | 0.307087i | 0.988142 | + | 0.153544i | \(0.0490686\pi\) | ||||
−0.988142 | + | 0.153544i | \(0.950931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 31.5671i | − | 1.39645i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −13.4057 | − | 13.4057i | −0.591876 | − | 0.591876i | ||||
\(514\) | 0.928203i | 0.0409413i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 22.4282i | 0.987345i | ||||||||
\(517\) | −25.6728 | + | 25.6728i | −1.12909 | + | 1.12909i | ||||
\(518\) | 11.6283 | − | 11.6283i | 0.510917 | − | 0.510917i | ||||
\(519\) | 1.66025i | 0.0728771i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 36.3068i | − | 1.59063i | −0.606197 | − | 0.795314i | \(-0.707306\pi\) | ||
0.606197 | − | 0.795314i | \(-0.292694\pi\) | |||||||
\(522\) | −29.0285 | − | 29.0285i | −1.27054 | − | 1.27054i | ||||
\(523\) | −0.898012 | − | 0.898012i | −0.0392673 | − | 0.0392673i | 0.687200 | − | 0.726468i | \(-0.258839\pi\) |
−0.726468 | + | 0.687200i | \(0.758839\pi\) | |||||||
\(524\) | 8.00000i | 0.349482i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 9.47926i | − | 0.413315i | ||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −9.15626 | − | 9.15626i | −0.398475 | − | 0.398475i | ||||
\(529\) | −6.93930 | + | 21.9282i | −0.301709 | + | 0.953400i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.1244 | 0.916719 | ||||||||
\(532\) | −15.8845 | − | 15.8845i | −0.688681 | − | 0.688681i | ||||
\(533\) | 0.808643 | − | 0.808643i | 0.0350262 | − | 0.0350262i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.47926i | 0.409442i | ||||||||
\(537\) | −42.8797 | − | 42.8797i | −1.85039 | − | 1.85039i | ||||
\(538\) | −11.0227 | + | 11.0227i | −0.475223 | + | 0.475223i | ||||
\(539\) | 73.2941 | 3.15700 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.87564 | −0.424587 | −0.212294 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212294 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(542\) | −2.96713 | − | 2.96713i | −0.127449 | − | 0.127449i | ||||
\(543\) | 50.0308 | + | 50.0308i | 2.14703 | + | 2.14703i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 31.9074i | 1.36551i | ||||||||
\(547\) | −12.7651 | − | 12.7651i | −0.545796 | − | 0.545796i | 0.379426 | − | 0.925222i | \(-0.376121\pi\) |
−0.925222 | + | 0.379426i | \(0.876121\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 57.8053 | 2.46707 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.5864i | 1.85684i | ||||||||
\(552\) | −10.5705 | + | 7.74205i | −0.449909 | + | 0.329524i | ||||
\(553\) | 4.25624 | − | 4.25624i | 0.180994 | − | 0.180994i | ||||
\(554\) | − | 3.92820i | − | 0.166893i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.53590 | 0.277184 | ||||||||
\(557\) | −10.9523 | + | 10.9523i | −0.464063 | + | 0.464063i | −0.899985 | − | 0.435921i | \(-0.856423\pi\) |
0.435921 | + | 0.899985i | \(0.356423\pi\) | |||||||
\(558\) | −21.8695 | + | 21.8695i | −0.925812 | + | 0.925812i | ||||
\(559\) | −20.2285 | −0.855575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.8591 | + | 15.8591i | −0.668976 | + | 0.668976i | ||||
\(563\) | 4.00882 | + | 4.00882i | 0.168951 | + | 0.168951i | 0.786518 | − | 0.617567i | \(-0.211882\pi\) |
−0.617567 | + | 0.786518i | \(0.711882\pi\) | |||||||
\(564\) | 20.9282i | 0.881236i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.25825 | + | 8.25825i | −0.346814 | + | 0.346814i | ||||
\(568\) | −6.69213 | + | 6.69213i | −0.280796 | + | 0.280796i | ||||
\(569\) | 12.0192 | 0.503872 | 0.251936 | − | 0.967744i | \(-0.418933\pi\) | ||||
0.251936 | + | 0.967744i | \(0.418933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 23.3579i | − | 0.977496i | −0.872425 | − | 0.488748i | \(-0.837454\pi\) | ||
0.872425 | − | 0.488748i | \(-0.162546\pi\) | |||||||
\(572\) | 8.25825 | − | 8.25825i | 0.345295 | − | 0.345295i | ||||
\(573\) | −34.1716 | − | 34.1716i | −1.42754 | − | 1.42754i | ||||
\(574\) | −2.19967 | −0.0918125 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.46410 | −0.186004 | ||||||||
\(577\) | 29.0285 | + | 29.0285i | 1.20847 | + | 1.20847i | 0.971521 | + | 0.236953i | \(0.0761487\pi\) |
0.236953 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(578\) | 12.0208 | − | 12.0208i | 0.500000 | − | 0.500000i | ||||
\(579\) | − | 27.3205i | − | 1.13540i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.9090 | 1.61422 | ||||||||
\(582\) | −25.0154 | + | 25.0154i | −1.03692 | + | 1.03692i | ||||
\(583\) | 11.6283 | − | 11.6283i | 0.481594 | − | 0.481594i | ||||
\(584\) | 6.66025i | 0.275603i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8978i | 1.06983i | ||||||||
\(587\) | 5.03768 | + | 5.03768i | 0.207927 | + | 0.207927i | 0.803386 | − | 0.595459i | \(-0.203030\pi\) |
−0.595459 | + | 0.803386i | \(0.703030\pi\) | |||||||
\(588\) | 29.8744 | − | 29.8744i | 1.23200 | − | 1.23200i | ||||
\(589\) | 32.8371 | 1.35303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.1244 | 0.786671 | ||||||||
\(592\) | −2.45341 | + | 2.45341i | −0.100835 | + | 0.100835i | ||||
\(593\) | −8.39735 | + | 8.39735i | −0.344838 | + | 0.344838i | −0.858182 | − | 0.513345i | \(-0.828406\pi\) |
0.513345 | + | 0.858182i | \(0.328406\pi\) | |||||||
\(594\) | −18.9585 | −0.777878 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.9585i | 0.776571i | ||||||||
\(597\) | 34.1716 | − | 34.1716i | 1.39855 | − | 1.39855i | ||||
\(598\) | −6.98274 | − | 9.53377i | −0.285545 | − | 0.389865i | ||||
\(599\) | 3.21539i | 0.131377i | 0.997840 | + | 0.0656886i | \(0.0209244\pi\) | ||||
−0.997840 | + | 0.0656886i | \(0.979076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1769 | 1.02699 | 0.513494 | − | 0.858093i | \(-0.328351\pi\) | ||||
0.513494 | + | 0.858093i | \(0.328351\pi\) | |||||||
\(602\) | 27.5128 | + | 27.5128i | 1.12134 | + | 1.12134i | ||||
\(603\) | 29.9222 | + | 29.9222i | 1.21853 | + | 1.21853i | ||||
\(604\) | 15.3205i | 0.623383i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 46.2487 | 1.87873 | ||||||||
\(607\) | 8.52245 | + | 8.52245i | 0.345915 | + | 0.345915i | 0.858586 | − | 0.512670i | \(-0.171344\pi\) |
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(608\) | 3.35143 | + | 3.35143i | 0.135918 | + | 0.135918i | ||||
\(609\) | −119.080 | −4.82537 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.8756 | −0.763627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6728 | + | 25.6728i | 1.03691 | + | 1.03691i | 0.999292 | + | 0.0376213i | \(0.0119781\pi\) |
0.0376213 | + | 0.999292i | \(0.488022\pi\) | |||||||
\(614\) | 4.39230i | 0.177259i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.4641 | −0.905104 | ||||||||
\(617\) | −13.4057 | + | 13.4057i | −0.539693 | + | 0.539693i | −0.923439 | − | 0.383746i | \(-0.874634\pi\) |
0.383746 | + | 0.923439i | \(0.374634\pi\) | |||||||
\(618\) | 22.5620 | + | 22.5620i | 0.907575 | + | 0.907575i | ||||
\(619\) | 42.3164 | 1.70084 | 0.850420 | − | 0.526105i | \(-0.176348\pi\) | ||||
0.850420 | + | 0.526105i | \(0.176348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.92820 | + | 18.9585i | −0.117505 | + | 0.760779i | ||||
\(622\) | 2.68973 | + | 2.68973i | 0.107848 | + | 0.107848i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 6.73205i | − | 0.269498i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.9489i | 0.517543i | ||||||||
\(627\) | 43.3973 | + | 43.3973i | 1.73312 | + | 1.73312i | ||||
\(628\) | −15.8591 | − | 15.8591i | −0.632848 | − | 0.632848i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.1678i | − | 1.08153i | −0.841173 | − | 0.540767i | \(-0.818134\pi\) | ||
0.841173 | − | 0.540767i | \(-0.181866\pi\) | |||||||
\(632\) | −0.898012 | + | 0.898012i | −0.0357210 | + | 0.0357210i | ||||
\(633\) | −42.9812 | + | 42.9812i | −1.70835 | + | 1.70835i | ||||
\(634\) | − | 25.3923i | − | 1.00846i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 9.47926i | − | 0.375877i | ||||||
\(637\) | 26.9444 | + | 26.9444i | 1.06758 | + | 1.06758i | ||||
\(638\) | 30.8202 | + | 30.8202i | 1.22018 | + | 1.22018i | ||||
\(639\) | 42.2487i | 1.67133i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.0192i | − | 0.474731i | −0.971420 | − | 0.237365i | \(-0.923716\pi\) | ||
0.971420 | − | 0.237365i | \(-0.0762839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.3037 | + | 14.3037i | 0.564083 | + | 0.564083i | 0.930465 | − | 0.366381i | \(-0.119403\pi\) |
−0.366381 | + | 0.930465i | \(0.619403\pi\) | |||||||
\(644\) | −3.46965 | + | 22.4641i | −0.136723 | + | 0.885210i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.2557 | − | 34.2557i | −1.34673 | − | 1.34673i | −0.889188 | − | 0.457542i | \(-0.848730\pi\) |
−0.457542 | − | 0.889188i | \(-0.651270\pi\) | |||||||
\(648\) | 1.74238 | − | 1.74238i | 0.0684473 | − | 0.0684473i | ||||
\(649\) | −22.4282 | −0.880383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 89.7127i | 3.51612i | ||||||||
\(652\) | 7.86611 | + | 7.86611i | 0.308061 | + | 0.308061i | ||||
\(653\) | 20.7835 | − | 20.7835i | 0.813321 | − | 0.813321i | −0.171809 | − | 0.985130i | \(-0.554961\pi\) |
0.985130 | + | 0.171809i | \(0.0549612\pi\) | |||||||
\(654\) | 16.4186 | 0.642017 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.464102 | 0.0181201 | ||||||||
\(657\) | 21.0237 | + | 21.0237i | 0.820214 | + | 0.820214i | ||||
\(658\) | 25.6728 | + | 25.6728i | 1.00083 | + | 1.00083i | ||||
\(659\) | 21.1582 | 0.824206 | 0.412103 | − | 0.911137i | \(-0.364794\pi\) | ||||
0.412103 | + | 0.911137i | \(0.364794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.9681i | − | 0.971148i | −0.874196 | − | 0.485574i | \(-0.838611\pi\) | ||
0.874196 | − | 0.485574i | \(-0.161389\pi\) | |||||||
\(662\) | −23.9401 | − | 23.9401i | −0.930458 | − | 0.930458i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.20928 | −0.318582 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.4889i | 0.600182i | ||||||||
\(667\) | 35.5805 | − | 26.0599i | 1.37768 | − | 1.00904i | ||||
\(668\) | −3.58630 | + | 3.58630i | −0.138758 | + | 0.138758i | ||||
\(669\) | 12.9282i | 0.499833i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −61.3731 | −2.36928 | ||||||||
\(672\) | −9.15626 | + | 9.15626i | −0.353211 | + | 0.353211i | ||||
\(673\) | −11.4016 | + | 11.4016i | −0.439501 | + | 0.439501i | −0.891844 | − | 0.452343i | \(-0.850588\pi\) |
0.452343 | + | 0.891844i | \(0.350588\pi\) | |||||||
\(674\) | −12.9489 | −0.498773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.92820 | −0.266469 | ||||||||
\(677\) | −6.04546 | + | 6.04546i | −0.232346 | + | 0.232346i | −0.813671 | − | 0.581325i | \(-0.802534\pi\) |
0.581325 | + | 0.813671i | \(0.302534\pi\) | |||||||
\(678\) | 11.6097 | + | 11.6097i | 0.445867 | + | 0.445867i | ||||
\(679\) | 61.3731i | 2.35528i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.2194 | − | 23.2194i | 0.889115 | − | 0.889115i | ||||
\(683\) | 14.1421 | − | 14.1421i | 0.541134 | − | 0.541134i | −0.382727 | − | 0.923861i | \(-0.625015\pi\) |
0.923861 | + | 0.382727i | \(0.125015\pi\) | |||||||
\(684\) | 21.1582 | 0.809004 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 40.1167i | − | 1.53166i | ||||||
\(687\) | 13.4057 | − | 13.4057i | 0.511459 | − | 0.511459i | ||||
\(688\) | −5.80484 | − | 5.80484i | −0.221307 | − | 0.221307i | ||||
\(689\) | 8.54957 | 0.325713 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.2487 | −1.60722 | −0.803608 | − | 0.595158i | \(-0.797089\pi\) | ||||
−0.803608 | + | 0.595158i | \(0.797089\pi\) | |||||||
\(692\) | −0.429705 | − | 0.429705i | −0.0163349 | − | 0.0163349i | ||||
\(693\) | −70.9101 | + | 70.9101i | −2.69365 | + | 2.69365i | ||||
\(694\) | − | 30.9282i | − | 1.17402i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 25.1244 | 0.952336 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.95215 | − | 8.95215i | 0.338844 | − | 0.338844i | ||||
\(699\) | − | 17.1244i | − | 0.647703i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0192i | 0.453960i | 0.973899 | + | 0.226980i | \(0.0728852\pi\) | ||||
−0.973899 | + | 0.226980i | \(0.927115\pi\) | |||||||
\(702\) | −6.96953 | − | 6.96953i | −0.263048 | − | 0.263048i | ||||
\(703\) | 11.6283 | − | 11.6283i | 0.438569 | − | 0.438569i | ||||
\(704\) | 4.73963 | 0.178632 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.05256 | −0.265427 | ||||||||
\(707\) | 56.7336 | − | 56.7336i | 2.13369 | − | 2.13369i | ||||
\(708\) | −9.14162 | + | 9.14162i | −0.343563 | + | 0.343563i | ||||
\(709\) | 6.93930 | 0.260611 | 0.130305 | − | 0.991474i | \(-0.458404\pi\) | ||||
0.130305 | + | 0.991474i | \(0.458404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.66932i | 0.212616i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.6331 | − | 26.8057i | −0.735264 | − | 1.00388i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.1962 | 0.829509 | ||||||||
\(717\) | −45.4307 | − | 45.4307i | −1.69664 | − | 1.69664i | ||||
\(718\) | 17.4145 | + | 17.4145i | 0.649904 | + | 0.649904i | ||||
\(719\) | − | 4.48334i | − | 0.167200i | −0.996499 | − | 0.0836002i | \(-0.973358\pi\) | ||
0.996499 | − | 0.0836002i | \(-0.0266419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.3538 | 2.06148 | ||||||||
\(722\) | −2.44949 | − | 2.44949i | −0.0911606 | − | 0.0911606i | ||||
\(723\) | −29.9222 | − | 29.9222i | −1.11282 | − | 1.11282i | ||||
\(724\) | −25.8978 | −0.962485 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.3205 | 1.16241 | ||||||||
\(727\) | −4.90683 | + | 4.90683i | −0.181984 | + | 0.181984i | −0.792220 | − | 0.610236i | \(-0.791075\pi\) |
0.610236 | + | 0.792220i | \(0.291075\pi\) | |||||||
\(728\) | −8.25825 | − | 8.25825i | −0.306071 | − | 0.306071i | ||||
\(729\) | − | 43.7846i | − | 1.62165i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −25.0154 | + | 25.0154i | −0.924595 | + | 0.924595i | ||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 4.73963 | 0.174943 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.732051 | − | 4.73963i | 0.0269838 | − | 0.174705i | ||||
\(737\) | −31.7690 | − | 31.7690i | −1.17023 | − | 1.17023i | ||||
\(738\) | 1.46498 | − | 1.46498i | 0.0539267 | − | 0.0539267i | ||||
\(739\) | 12.0000i | 0.441427i | 0.975339 | + | 0.220714i | \(0.0708386\pi\) | ||||
−0.975339 | + | 0.220714i | \(0.929161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.9074i | 1.17215i | ||||||||
\(742\) | −11.6283 | − | 11.6283i | −0.426887 | − | 0.426887i | ||||
\(743\) | 13.1651 | + | 13.1651i | 0.482980 | + | 0.482980i | 0.906082 | − | 0.423102i | \(-0.139059\pi\) |
−0.423102 | + | 0.906082i | \(0.639059\pi\) | |||||||
\(744\) | − | 18.9282i | − | 0.693942i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 18.9585i | − | 0.694121i | ||||||
\(747\) | −25.9134 | + | 25.9134i | −0.948121 | + | 0.948121i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.1263i | 1.68317i | 0.540122 | + | 0.841587i | \(0.318378\pi\) | ||||
−0.540122 | + | 0.841587i | \(0.681622\pi\) | |||||||
\(752\) | −5.41662 | − | 5.41662i | −0.197524 | − | 0.197524i | ||||
\(753\) | −18.3125 | − | 18.3125i | −0.667346 | − | 0.667346i | ||||
\(754\) | 22.6603i | 0.825238i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.9585i | 0.689515i | ||||||||
\(757\) | 20.7659 | − | 20.7659i | 0.754751 | − | 0.754751i | −0.220611 | − | 0.975362i | \(-0.570805\pi\) |
0.975362 | + | 0.220611i | \(0.0708051\pi\) | |||||||
\(758\) | −6.70285 | − | 6.70285i | −0.243458 | − | 0.243458i | ||||
\(759\) | 9.47926 | − | 61.3731i | 0.344075 | − | 2.22770i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.71281 | −0.243339 | −0.121670 | − | 0.992571i | \(-0.538825\pi\) | ||||
−0.121670 | + | 0.992571i | \(0.538825\pi\) | |||||||
\(762\) | −4.24264 | − | 4.24264i | −0.153695 | − | 0.153695i | ||||
\(763\) | 20.1408 | − | 20.1408i | 0.729145 | − | 0.729145i | ||||
\(764\) | 17.6885 | 0.639949 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 7.27959i | − | 0.263022i | ||||||
\(767\) | −8.24504 | − | 8.24504i | −0.297711 | − | 0.297711i | ||||
\(768\) | 1.93185 | − | 1.93185i | 0.0697097 | − | 0.0697097i | ||||
\(769\) | −3.46965 | −0.125119 | −0.0625594 | − | 0.998041i | \(-0.519926\pi\) | ||||
−0.0625594 | + | 0.998041i | \(0.519926\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.53590 | −0.0913281 | ||||||||
\(772\) | 7.07107 | + | 7.07107i | 0.254493 | + | 0.254493i | ||||
\(773\) | −10.9523 | − | 10.9523i | −0.393926 | − | 0.393926i | 0.482158 | − | 0.876084i | \(-0.339853\pi\) |
−0.876084 | + | 0.482158i | \(0.839853\pi\) | |||||||
\(774\) | −36.6471 | −1.31725 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 12.9489i | − | 0.464839i | ||||||
\(777\) | 31.7690 | + | 31.7690i | 1.13971 | + | 1.13971i | ||||
\(778\) | 14.0631 | + | 14.0631i | 0.504186 | + | 0.504186i | ||||
\(779\) | −2.19967 | −0.0788114 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 44.8563i | − | 1.60509i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.0106 | − | 26.0106i | 0.929545 | − | 0.929545i | ||||
\(784\) | 15.4641i | 0.552289i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.8564 | −0.779592 | ||||||||
\(787\) | 32.6162 | − | 32.6162i | 1.16264 | − | 1.16264i | 0.178749 | − | 0.983895i | \(-0.442795\pi\) |
0.983895 | − | 0.178749i | \(-0.0572049\pi\) | |||||||
\(788\) | −4.94975 | + | 4.94975i | −0.176327 | + | 0.176327i | ||||
\(789\) | 25.8978 | 0.921987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.4833 | 1.01275 | ||||||||
\(792\) | 14.9611 | − | 14.9611i | 0.531620 | − | 0.531620i | ||||
\(793\) | −22.5620 | − | 22.5620i | −0.801199 | − | 0.801199i | ||||
\(794\) | − | 23.3205i | − | 0.827614i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.6885i | 0.626954i | ||||||||
\(797\) | −20.7659 | + | 20.7659i | −0.735567 | + | 0.735567i | −0.971717 | − | 0.236149i | \(-0.924115\pi\) |
0.236149 | + | 0.971717i | \(0.424115\pi\) | |||||||
\(798\) | 43.3973 | − | 43.3973i | 1.53625 | − | 1.53625i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.8591 | − | 15.8591i | 0.560005 | − | 0.560005i | ||||
\(803\) | −22.3213 | − | 22.3213i | −0.787703 | − | 0.787703i | ||||
\(804\) | −25.8978 | −0.913346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.0718 | 0.601328 | ||||||||
\(807\) | −30.1146 | − | 30.1146i | −1.06008 | − | 1.06008i | ||||
\(808\) | −11.9700 | + | 11.9700i | −0.421105 | + | 0.421105i | ||||
\(809\) | − | 18.8564i | − | 0.662956i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) | ||
0.943463 | − | 0.331478i | \(-0.107547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.78461 | 0.308469 | 0.154235 | − | 0.988034i | \(-0.450709\pi\) | ||||
0.154235 | + | 0.988034i | \(0.450709\pi\) | |||||||
\(812\) | 30.8202 | − | 30.8202i | 1.08158 | − | 1.08158i | ||||
\(813\) | 8.10634 | − | 8.10634i | 0.284302 | − | 0.284302i | ||||
\(814\) | − | 16.4449i | − | 0.576392i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.5128 | + | 27.5128i | 0.962551 | + | 0.962551i | ||||
\(818\) | 2.50026 | − | 2.50026i | 0.0874195 | − | 0.0874195i | ||||
\(819\) | −52.1359 | −1.82178 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.9090 | −1.42773 | −0.713866 | − | 0.700282i | \(-0.753058\pi\) | ||||
−0.713866 | + | 0.700282i | \(0.753058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.0507 | − | 35.0507i | 1.22179 | − | 1.22179i | 0.254797 | − | 0.966995i | \(-0.417991\pi\) |
0.966995 | − | 0.254797i | \(-0.0820087\pi\) | |||||||
\(824\) | −11.6789 | −0.406855 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.4282i | 0.780376i | ||||||||
\(827\) | 5.80484 | − | 5.80484i | 0.201854 | − | 0.201854i | −0.598940 | − | 0.800794i | \(-0.704411\pi\) |
0.800794 | + | 0.598940i | \(0.204411\pi\) | |||||||
\(828\) | −12.6503 | − | 17.2719i | −0.439629 | − | 0.600240i | ||||
\(829\) | 21.8756i | 0.759773i | 0.925033 | + | 0.379886i | \(0.124037\pi\) | ||||
−0.925033 | + | 0.379886i | \(0.875963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7321 | 0.372291 | ||||||||
\(832\) | 1.74238 | + | 1.74238i | 0.0604063 | + | 0.0604063i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.8564i | 0.618317i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.4641 | −0.776937 | ||||||||
\(837\) | −19.5959 | − | 19.5959i | −0.677334 | − | 0.677334i | ||||
\(838\) | −13.1651 | − | 13.1651i | −0.454780 | − | 0.454780i | ||||
\(839\) | 22.0879 | 0.762558 | 0.381279 | − | 0.924460i | \(-0.375484\pi\) | ||||
0.381279 | + | 0.924460i | \(0.375484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −55.5692 | −1.91618 | ||||||||
\(842\) | −13.4057 | + | 13.4057i | −0.461991 | + | 0.461991i | ||||
\(843\) | −43.3279 | − | 43.3279i | −1.49229 | − | 1.49229i | ||||
\(844\) | − | 22.2487i | − | 0.765832i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −34.1962 | −1.17569 | ||||||||
\(847\) | 38.4211 | − | 38.4211i | 1.32016 | − | 1.32016i | ||||
\(848\) | 2.45341 | + | 2.45341i | 0.0842506 | + | 0.0842506i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.4449 | − | 2.53996i | −0.563723 | − | 0.0870687i | ||||
\(852\) | −18.2832 | − | 18.2832i | −0.626373 | − | 0.626373i | ||||
\(853\) | −9.67286 | + | 9.67286i | −0.331192 | + | 0.331192i | −0.853039 | − | 0.521847i | \(-0.825243\pi\) |
0.521847 | + | 0.853039i | \(0.325243\pi\) | |||||||
\(854\) | 61.3731i | 2.10014i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.41421 | − | 1.41421i | −0.0483086 | − | 0.0483086i | 0.682540 | − | 0.730848i | \(-0.260875\pi\) |
−0.730848 | + | 0.682540i | \(0.760875\pi\) | |||||||
\(858\) | 22.5620 | + | 22.5620i | 0.770253 | + | 0.770253i | ||||
\(859\) | − | 0.732051i | − | 0.0249773i | −0.999922 | − | 0.0124886i | \(-0.996025\pi\) | ||
0.999922 | − | 0.0124886i | \(-0.00397536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 6.00961i | − | 0.204807i | ||||||
\(862\) | −23.2194 | + | 23.2194i | −0.790854 | + | 0.790854i | ||||
\(863\) | 4.10394 | − | 4.10394i | 0.139700 | − | 0.139700i | −0.633798 | − | 0.773498i | \(-0.718505\pi\) |
0.773498 | + | 0.633798i | \(0.218505\pi\) | |||||||
\(864\) | − | 4.00000i | − | 0.136083i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 38.8467i | − | 1.32007i | ||||||
\(867\) | 32.8415 | + | 32.8415i | 1.11536 | + | 1.11536i | ||||
\(868\) | −23.2194 | − | 23.2194i | −0.788116 | − | 0.788116i | ||||
\(869\) | − | 6.01924i | − | 0.204189i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 23.3579i | − | 0.791451i | ||||||
\(872\) | −4.24944 | + | 4.24944i | −0.143904 | + | 0.143904i | ||||
\(873\) | −40.8745 | − | 40.8745i | −1.38339 | − | 1.38339i | ||||
\(874\) | −3.46965 | + | 22.4641i | −0.117363 | + | 0.759860i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.1962 | −0.614791 | ||||||||
\(877\) | 15.9353 | + | 15.9353i | 0.538096 | + | 0.538096i | 0.922969 | − | 0.384873i | \(-0.125755\pi\) |
−0.384873 | + | 0.922969i | \(0.625755\pi\) | |||||||
\(878\) | −9.79796 | + | 9.79796i | −0.330665 | + | 0.330665i | ||||
\(879\) | −70.7542 | −2.38648 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4282i | 0.755624i | 0.925882 | + | 0.377812i | \(0.123324\pi\) | ||||
−0.925882 | + | 0.377812i | \(0.876676\pi\) | |||||||
\(882\) | 48.8139 | + | 48.8139i | 1.64365 | + | 1.64365i | ||||
\(883\) | −33.2576 | + | 33.2576i | −1.11921 | + | 1.11921i | −0.127349 | + | 0.991858i | \(0.540647\pi\) |
−0.991858 | + | 0.127349i | \(0.959353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.9282 | 1.30782 | ||||||||
\(887\) | −15.6579 | − | 15.6579i | −0.525740 | − | 0.525740i | 0.393559 | − | 0.919299i | \(-0.371244\pi\) |
−0.919299 | + | 0.393559i | \(0.871244\pi\) | |||||||
\(888\) | −6.70285 | − | 6.70285i | −0.224933 | − | 0.224933i | ||||
\(889\) | −10.4090 | −0.349105 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6789i | 0.391259i | ||||||||
\(892\) | −3.34607 | − | 3.34607i | −0.112035 | − | 0.112035i | ||||
\(893\) | 25.6728 | + | 25.6728i | 0.859106 | + | 0.859106i | ||||
\(894\) | −51.7957 | −1.73231 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 4.73963i | − | 0.158340i | ||||||
\(897\) | 26.0467 | − | 19.0772i | 0.869675 | − | 0.636969i | ||||
\(898\) | 13.1069 | − | 13.1069i | 0.437382 | − | 0.437382i | ||||
\(899\) | 63.7128i | 2.12494i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1.55540 | + | 1.55540i | −0.0517892 | + | 0.0517892i | ||||
\(903\) | −75.1663 | + | 75.1663i | −2.50138 | + | 2.50138i | ||||
\(904\) | −6.00961 | −0.199877 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −41.8564 | −1.39059 | ||||||||
\(907\) | 0.898012 | − | 0.898012i | 0.0298180 | − | 0.0298180i | −0.692041 | − | 0.721859i | \(-0.743288\pi\) |
0.721859 | + | 0.692041i | \(0.243288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 75.5692i | 2.50647i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.6471i | − | 1.21417i | −0.794636 | − | 0.607086i | \(-0.792338\pi\) | ||
0.794636 | − | 0.607086i | \(-0.207662\pi\) | |||||||
\(912\) | −9.15626 | + | 9.15626i | −0.303194 | + | 0.303194i | ||||
\(913\) | 27.5128 | − | 27.5128i | 0.910541 | − | 0.910541i | ||||
\(914\) | 6.00961 | 0.198780 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.93930i | 0.229281i | ||||||||
\(917\) | −26.8114 | + | 26.8114i | −0.885390 | + | 0.885390i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | 6.02219 | + | 6.02219i | 0.198330 | + | 0.198330i | ||||
\(923\) | 16.4901 | − | 16.4901i | 0.542778 | − | 0.542778i | ||||
\(924\) | − | 61.3731i | − | 2.01903i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.4641 | −0.442458 | ||||||||
\(927\) | −36.8657 | + | 36.8657i | −1.21083 | + | 1.21083i | ||||
\(928\) | −6.50266 | + | 6.50266i | −0.213460 | + | 0.213460i | ||||
\(929\) | − | 34.3205i | − | 1.12602i | −0.826450 | − | 0.563010i | \(-0.809643\pi\) | ||
0.826450 | − | 0.563010i | \(-0.190357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 73.2941i | − | 2.40212i | ||||||
\(932\) | 4.43211 | + | 4.43211i | 0.145179 | + | 0.145179i | ||||
\(933\) | −7.34847 | + | 7.34847i | −0.240578 | + | 0.240578i | ||||
\(934\) | −27.1678 | −0.888958 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.0000 | 0.359546 | ||||||||
\(937\) | −17.6551 | + | 17.6551i | −0.576768 | + | 0.576768i | −0.934011 | − | 0.357243i | \(-0.883717\pi\) |
0.357243 | + | 0.934011i | \(0.383717\pi\) | |||||||
\(938\) | −31.7690 | + | 31.7690i | −1.03730 | + | 1.03730i | ||||
\(939\) | −35.3771 | −1.15449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 43.9267i | − | 1.43197i | −0.698117 | − | 0.715984i | \(-0.745978\pi\) | ||
0.698117 | − | 0.715984i | \(-0.254022\pi\) | |||||||
\(942\) | 43.3279 | − | 43.3279i | 1.41170 | − | 1.41170i | ||||
\(943\) | 1.31517 | + | 1.79564i | 0.0428277 | + | 0.0584740i | ||||
\(944\) | − | 4.73205i | − | 0.154015i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.9090 | 1.26504 | ||||||||
\(947\) | −2.82843 | − | 2.82843i | −0.0919115 | − | 0.0919115i | 0.659656 | − | 0.751568i | \(-0.270702\pi\) |
−0.751568 | + | 0.659656i | \(0.770702\pi\) | |||||||
\(948\) | −2.45341 | − | 2.45341i | −0.0796832 | − | 0.0796832i | ||||
\(949\) | − | 16.4115i | − | 0.532741i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 69.3731 | 2.24958 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.15626 | − | 9.15626i | −0.296600 | − | 0.296600i | 0.543080 | − | 0.839681i | \(-0.317258\pi\) |
−0.839681 | + | 0.543080i | \(0.817258\pi\) | |||||||
\(954\) | 15.4889 | 0.501471 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.5167 | 0.760583 | ||||||||
\(957\) | −84.2024 | + | 84.2024i | −2.72188 | + | 2.72188i | ||||
\(958\) | −14.3037 | − | 14.3037i | −0.462132 | − | 0.462132i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 6.04546 | − | 6.04546i | 0.194913 | − | 0.194913i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.4889 | 0.498863 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −61.3731 | − | 9.47926i | −1.97465 | − | 0.304990i | ||||
\(967\) | −18.5606 | − | 18.5606i | −0.596870 | − | 0.596870i | 0.342608 | − | 0.939478i | \(-0.388690\pi\) |
−0.939478 | + | 0.342608i | \(0.888690\pi\) | |||||||
\(968\) | −8.10634 | + | 8.10634i | −0.260548 | + | 0.260548i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.13897i | 0.293284i | 0.989190 | + | 0.146642i | \(0.0468465\pi\) | ||||
−0.989190 | + | 0.146642i | \(0.953154\pi\) | |||||||
\(972\) | 13.2456 | + | 13.2456i | 0.424852 | + | 0.424852i | ||||
\(973\) | 21.9046 | + | 21.9046i | 0.702228 | + | 0.702228i | ||||
\(974\) | 0.0525589i | 0.00168410i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.9489i | − | 0.414485i | ||||||
\(977\) | 31.0608 | − | 31.0608i | 0.993724 | − | 0.993724i | −0.00625617 | − | 0.999980i | \(-0.501991\pi\) |
0.999980 | + | 0.00625617i | \(0.00199141\pi\) | |||||||
\(978\) | −21.4906 | + | 21.4906i | −0.687194 | + | 0.687194i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.8275i | 0.856537i | ||||||||
\(982\) | −12.1087 | − | 12.1087i | −0.386406 | − | 0.386406i | ||||
\(983\) | −24.7748 | − | 24.7748i | −0.790192 | − | 0.790192i | 0.191333 | − | 0.981525i | \(-0.438719\pi\) |
−0.981525 | + | 0.191333i | \(0.938719\pi\) | |||||||
\(984\) | 1.26795i | 0.0404207i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70.1393 | + | 70.1393i | −2.23256 | + | 2.23256i | ||||
\(988\) | −8.25825 | − | 8.25825i | −0.262730 | − | 0.262730i | ||||
\(989\) | 6.00961 | − | 38.9090i | 0.191095 | − | 1.23723i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1962 | 0.768616 | 0.384308 | − | 0.923205i | \(-0.374440\pi\) | ||||
0.384308 | + | 0.923205i | \(0.374440\pi\) | |||||||
\(992\) | 4.89898 | + | 4.89898i | 0.155543 | + | 0.155543i | ||||
\(993\) | 65.4056 | − | 65.4056i | 2.07558 | − | 2.07558i | ||||
\(994\) | −44.8563 | −1.42276 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 22.4282i | − | 0.710664i | ||||||
\(997\) | −24.4441 | − | 24.4441i | −0.774153 | − | 0.774153i | 0.204676 | − | 0.978830i | \(-0.434386\pi\) |
−0.978830 | + | 0.204676i | \(0.934386\pi\) | |||||||
\(998\) | −22.9420 | + | 22.9420i | −0.726216 | + | 0.726216i | ||||
\(999\) | −13.8786 | −0.439100 |
(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 | 1150.2.e.d.1057.3 | yes | 16 | |
5.2 | odd | 4 | inner | 1150.2.e.d.643.5 | yes | 16 | |
5.3 | odd | 4 | inner | 1150.2.e.d.643.4 | yes | 16 | |
5.4 | even | 2 | inner | 1150.2.e.d.1057.6 | yes | 16 | |
23.22 | odd | 2 | inner | 1150.2.e.d.1057.4 | yes | 16 | |
115.22 | even | 4 | inner | 1150.2.e.d.643.6 | yes | 16 | |
115.68 | even | 4 | inner | 1150.2.e.d.643.3 | ✓ | 16 | |
115.114 | odd | 2 | inner | 1150.2.e.d.1057.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.2.e.d.643.3 | ✓ | 16 | 115.68 | even | 4 | inner | |
1150.2.e.d.643.4 | yes | 16 | 5.3 | odd | 4 | inner | |
1150.2.e.d.643.5 | yes | 16 | 5.2 | odd | 4 | inner | |
1150.2.e.d.643.6 | yes | 16 | 115.22 | even | 4 | inner | |
1150.2.e.d.1057.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1150.2.e.d.1057.4 | yes | 16 | 23.22 | odd | 2 | inner | |
1150.2.e.d.1057.5 | yes | 16 | 115.114 | odd | 2 | inner | |
1150.2.e.d.1057.6 | yes | 16 | 5.4 | even | 2 | inner |