Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,9,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.65");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), degree \(2\), not 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: | \(58.6625198488\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{25} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.6 | ||
Root | \(-2.97990 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.113 |
Dual form | 144.9.q.b.65.6 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 24.1444 | + | 77.3178i | 0.298079 | + | 0.954541i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −69.6596 | − | 40.2180i | −0.111455 | − | 0.0643487i | 0.443236 | − | 0.896405i | \(-0.353830\pi\) |
−0.554691 | + | 0.832056i | \(0.687164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −370.849 | − | 642.329i | −0.154456 | − | 0.267526i | 0.778405 | − | 0.627763i | \(-0.216029\pi\) |
−0.932861 | + | 0.360237i | \(0.882696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5395.10 | + | 3733.58i | −0.822298 | + | 0.569057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19777.4 | − | 11418.5i | 1.35083 | − | 0.779900i | 0.362461 | − | 0.931999i | \(-0.381937\pi\) |
0.988365 | + | 0.152099i | \(0.0486034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6499.12 | + | 11256.8i | −0.227552 | + | 0.394132i | −0.957082 | − | 0.289817i | \(-0.906406\pi\) |
0.729530 | + | 0.683949i | \(0.239739\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1427.68 | − | 6356.96i | 0.0282011 | − | 0.125570i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 105666.i | 1.26514i | 0.774502 | + | 0.632571i | \(0.218000\pi\) | ||||
−0.774502 | + | 0.632571i | \(0.782000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −118278. | −0.907594 | −0.453797 | − | 0.891105i | \(-0.649931\pi\) | ||||
−0.453797 | + | 0.891105i | \(0.649931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 40709.6 | − | 44181.8i | 0.209324 | − | 0.227178i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 77410.8 | + | 44693.1i | 0.276624 | + | 0.159709i | 0.631894 | − | 0.775055i | \(-0.282278\pi\) |
−0.355270 | + | 0.934764i | \(0.615611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −192078. | − | 332688.i | −0.491718 | − | 0.851681i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −418934. | − | 326993.i | −0.788298 | − | 0.615294i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −952037. | + | 549659.i | −1.34605 | + | 0.777143i | −0.987688 | − | 0.156439i | \(-0.949999\pi\) |
−0.358364 | + | 0.933582i | \(0.616665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −226348. | + | 392047.i | −0.245093 | + | 0.424513i | −0.962158 | − | 0.272493i | \(-0.912152\pi\) |
0.717065 | + | 0.697007i | \(0.245485\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.36037e6 | + | 1.25346e6i | 1.14710 | + | 1.05695i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59659.1i | 0.0397562i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.12547e6 | −1.13409 | −0.567046 | − | 0.823686i | \(-0.691914\pi\) | ||||
−0.567046 | + | 0.823686i | \(0.691914\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.02727e6 | − | 230709.i | −0.444044 | − | 0.0997257i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45174e6 | − | 838161.i | −0.513751 | − | 0.296614i | 0.220623 | − | 0.975359i | \(-0.429191\pi\) |
−0.734374 | + | 0.678745i | \(0.762524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 569118. | + | 985742.i | 0.166467 | + | 0.288330i | 0.937175 | − | 0.348859i | \(-0.113431\pi\) |
−0.770708 | + | 0.637188i | \(0.780097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 525977. | − | 43099.7i | 0.128268 | − | 0.0105105i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.10681e6 | − | 1.79372e6i | 0.636683 | − | 0.367589i | −0.146653 | − | 0.989188i | \(-0.546850\pi\) |
0.783336 | + | 0.621599i | \(0.213517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.60734e6 | − | 4.51605e6i | 0.452287 | − | 0.783384i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.16987e6 | + | 2.55124e6i | −1.20763 | + | 0.377112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.16039e7i | − | 1.47062i | −0.677730 | − | 0.735311i | \(-0.737036\pi\) | ||
0.677730 | − | 0.735311i | \(-0.262964\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.83692e6 | −0.200742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.85576e6 | − | 9.14504e6i | −0.270534 | − | 0.866336i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.34715e6 | − | 3.08718e6i | −0.441280 | − | 0.254773i | 0.262860 | − | 0.964834i | \(-0.415334\pi\) |
−0.704141 | + | 0.710061i | \(0.748668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.10379e7 | + | 1.91182e7i | 0.797198 | + | 1.38079i | 0.921434 | + | 0.388534i | \(0.127018\pi\) |
−0.124237 | + | 0.992253i | \(0.539648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.39895e6 | + | 2.08083e6i | 0.279246 | + | 0.132092i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 905451. | − | 522763.i | 0.0507238 | − | 0.0292854i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.84669e7 | − | 3.19855e7i | 0.916418 | − | 1.58728i | 0.111607 | − | 0.993752i | \(-0.464400\pi\) |
0.804811 | − | 0.593531i | \(-0.202267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.58654e6 | + | 7.06432e6i | −0.0699931 | + | 0.311655i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.51775e7i | 0.597267i | 0.954368 | + | 0.298633i | \(0.0965307\pi\) | ||||
−0.954368 | + | 0.298633i | \(0.903469\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.91641e7 | −1.73124 | −0.865618 | − | 0.500704i | \(-0.833074\pi\) | ||||
−0.865618 | + | 0.500704i | \(0.833074\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.10851e7 | − | 2.28836e7i | 0.666394 | − | 0.723234i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.46689e7 | − | 8.46908e6i | −0.417286 | − | 0.240920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.15777e7 | − | 5.46942e7i | −0.810722 | − | 1.40421i | −0.912359 | − | 0.409391i | \(-0.865741\pi\) |
0.101637 | − | 0.994822i | \(-0.467592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.51675e7 | − | 4.02861e7i | 0.352349 | − | 0.935869i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.45835e7 | + | 2.57403e7i | −0.939425 | + | 0.542377i | −0.889780 | − | 0.456390i | \(-0.849142\pi\) |
−0.0496450 | + | 0.998767i | \(0.515809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24967e6 | − | 7.36064e6i | 0.0814103 | − | 0.141007i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.54847e7 | − | 6.03383e7i | −1.14304 | − | 1.05321i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.17343e7i | − | 0.824553i | −0.911059 | − | 0.412277i | \(-0.864734\pi\) | ||
0.911059 | − | 0.412277i | \(-0.135266\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.64076e6 | 0.140587 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.57773e7 | − | 8.03505e6i | −0.478273 | − | 0.107413i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.23923e6 | + | 4.75692e6i | 0.101156 | + | 0.0584025i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.54739e6 | − | 7.87630e6i | −0.0513659 | − | 0.0889684i | 0.839199 | − | 0.543824i | \(-0.183024\pi\) |
−0.890565 | + | 0.454856i | \(0.849691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.40693e7 | + | 1.35445e8i | −0.666975 | + | 1.41001i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.46459e7 | + | 5.46438e7i | −0.909528 | + | 0.525117i | −0.880279 | − | 0.474456i | \(-0.842645\pi\) |
−0.0292491 | + | 0.999572i | \(0.509312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.55744e7 | + | 1.65540e8i | −0.849166 | + | 1.47080i | 0.0327875 | + | 0.999462i | \(0.489562\pi\) |
−0.881954 | + | 0.471336i | \(0.843772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.61272e6 | + | 1.44043e6i | −0.0379489 | + | 0.0118505i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.73989e8i | − | 1.32736i | −0.748019 | − | 0.663678i | \(-0.768995\pi\) | ||
0.748019 | − | 0.663678i | \(-0.231005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00364e8 | −0.711002 | −0.355501 | − | 0.934676i | \(-0.615690\pi\) | ||||
−0.355501 | + | 0.934676i | \(0.615690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.13181e7 | − | 1.64337e8i | −0.338048 | − | 1.08254i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.26056e8 | − | 7.27784e7i | −0.773124 | − | 0.446364i | 0.0608637 | − | 0.998146i | \(-0.480614\pi\) |
−0.833988 | + | 0.551783i | \(0.813948\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59493e6 | − | 6.22661e6i | −0.0205542 | − | 0.0356008i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.96479e6 | − | 8.49966e7i | −0.0371676 | − | 0.453584i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.78723e7 | − | 3.91861e7i | 0.338458 | − | 0.195409i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.53585e8 | − | 2.66018e8i | 0.716487 | − | 1.24099i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.97535e7 | − | 1.32482e8i | 0.129992 | − | 0.578811i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.23202e7i | 0.255263i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57730e8 | 0.606315 | 0.303157 | − | 0.952941i | \(-0.401959\pi\) | ||||
0.303157 | + | 0.952941i | \(0.401959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.24744e7 | + | 6.78031e7i | −0.225602 | + | 0.244845i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.71215e8 | − | 1.56586e8i | −0.920934 | − | 0.531701i | −0.0370008 | − | 0.999315i | \(-0.511780\pi\) |
−0.883933 | + | 0.467614i | \(0.845114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.38634e7 | + | 7.59737e7i | 0.140183 | + | 0.242804i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.60318e7 | + | 3.96268e7i | 0.0482665 | + | 0.119304i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.44998e7 | − | 4.87860e7i | 0.239869 | − | 0.138488i | −0.375248 | − | 0.926925i | \(-0.622442\pi\) |
0.615116 | + | 0.788436i | \(0.289109\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.51078e7 | + | 7.81290e7i | −0.120835 | + | 0.209292i | −0.920097 | − | 0.391690i | \(-0.871890\pi\) |
0.799262 | + | 0.600982i | \(0.205224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.13698e8 | + | 1.96904e8i | 0.540660 | + | 0.498170i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.96841e8i | 0.709872i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.84246e7 | 0.200033 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.12124e8 | + | 9.25570e7i | 0.882589 | + | 0.198217i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.31181e8 | + | 3.06678e8i | 1.07770 | + | 0.622210i | 0.930275 | − | 0.366863i | \(-0.119568\pi\) |
0.147425 | + | 0.989073i | \(0.452902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.34431e7 | − | 1.27207e8i | −0.141268 | − | 0.244683i | 0.786706 | − | 0.617327i | \(-0.211785\pi\) |
−0.927974 | + | 0.372644i | \(0.878451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.94512e8 | − | 5.70078e8i | −0.719938 | − | 1.04032i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.15347e7 | − | 1.82065e7i | 0.0546338 | − | 0.0315428i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.79253e8 | + | 4.83681e8i | −0.459621 | + | 0.796086i | −0.998941 | − | 0.0460145i | \(-0.985348\pi\) |
0.539320 | + | 0.842101i | \(0.318681\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.97189e8 | − | 2.80169e8i | 1.40377 | − | 0.438361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.62976e7i | − | 0.0986720i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.70277e6 | 0.00382876 | 0.00191438 | − | 0.999998i | \(-0.499391\pi\) | ||||
0.00191438 | + | 0.999998i | \(0.499391\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.43512e7 | − | 1.42026e8i | −0.0598370 | − | 0.191617i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.54080e8 | − | 3.77633e8i | −0.840940 | − | 0.485517i | 0.0166436 | − | 0.999861i | \(-0.494702\pi\) |
−0.857584 | + | 0.514344i | \(0.828035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.23388e8 | + | 5.60125e8i | 0.396440 | + | 0.686654i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.38124e8 | − | 4.41602e8i | 0.746313 | − | 0.516472i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.12759e8 | + | 4.69247e8i | −0.907355 | + | 0.523862i | −0.879579 | − | 0.475752i | \(-0.842176\pi\) |
−0.0277761 | + | 0.999614i | \(0.508843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42463e8 | + | 2.46754e8i | −0.151898 | + | 0.263095i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.09591e8 | − | 4.87968e8i | 0.111655 | − | 0.497163i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.19557e8i | 0.895708i | 0.894107 | + | 0.447854i | \(0.147812\pi\) | ||||
−0.894107 | + | 0.447854i | \(0.852188\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.65808e9 | 1.54487 | 0.772435 | − | 0.635094i | \(-0.219039\pi\) | ||||
0.772435 | + | 0.635094i | \(0.219039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.21167e9 | + | 1.31502e9i | −1.08039 | + | 1.17254i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.48059e8 | + | 8.54821e7i | 0.126401 | + | 0.0729774i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20655e9 | + | 2.08980e9i | 0.986684 | + | 1.70899i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.46757e7 | + | 3.90358e8i | −0.0428497 | + | 0.305926i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.35643e8 | + | 4.82459e8i | −0.627895 | + | 0.362516i | −0.779937 | − | 0.625859i | \(-0.784749\pi\) |
0.152041 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.96992e8 | + | 6.87610e8i | −0.286123 | + | 0.495579i | −0.972881 | − | 0.231307i | \(-0.925700\pi\) |
0.686758 | + | 0.726886i | \(0.259033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.22804e7 | + | 5.73858e7i | 0.0430738 | + | 0.0396886i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.07092e9i | − | 0.711038i | −0.934669 | − | 0.355519i | \(-0.884304\pi\) | ||
0.934669 | − | 0.355519i | \(-0.115696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01385e9 | 0.646486 | 0.323243 | − | 0.946316i | \(-0.395227\pi\) | ||||
0.323243 | + | 0.946316i | \(0.395227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.91892e9 | + | 6.55547e8i | 1.78829 | + | 0.401624i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.06123e8 | + | 4.07680e8i | 0.415811 | + | 0.240069i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.74183e7 | + | 1.16772e8i | 0.0381735 | + | 0.0661185i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.84504e8 | + | 4.78955e7i | −0.318351 | + | 0.0260863i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.33925e9 | + | 1.35056e9i | −1.22600 | + | 0.707832i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.50549e8 | − | 6.07168e8i | 0.176856 | − | 0.306323i | −0.763946 | − | 0.645280i | \(-0.776741\pi\) |
0.940802 | + | 0.338957i | \(0.110074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.17350e9 | + | 3.66452e8i | −0.570116 | + | 0.178032i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.15551e7i | − | 0.0428478i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.35764e8 | 0.151424 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.18704e9 | − | 3.80126e9i | −0.516045 | − | 1.65254i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.18946e9 | − | 6.86736e8i | −0.498633 | − | 0.287886i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.37390e9 | + | 2.37966e9i | 0.555566 | + | 0.962268i | 0.997859 | + | 0.0653978i | \(0.0208316\pi\) |
−0.442293 | + | 0.896870i | \(0.645835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.27839e9 | + | 1.07775e9i | 0.888994 | + | 0.420521i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.22472e9 | − | 1.28445e9i | 0.837862 | − | 0.483740i | −0.0186746 | − | 0.999826i | \(-0.505945\pi\) |
0.856537 | + | 0.516085i | \(0.172611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.26517e9 | + | 2.19134e9i | −0.460053 | + | 0.796835i | −0.998963 | − | 0.0455283i | \(-0.985503\pi\) |
0.538910 | + | 0.842363i | \(0.318836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00640e8 | − | 1.33865e9i | 0.105584 | − | 0.470130i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.19788e9i | 0.406434i | 0.979134 | + | 0.203217i | \(0.0651397\pi\) | ||||
−0.979134 | + | 0.203217i | \(0.934860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.88559e8 | −0.0946156 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.46641e9 | − | 3.76208e9i | 1.09872 | − | 1.19243i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.41385e9 | − | 8.16289e8i | −0.433324 | − | 0.250180i | 0.267438 | − | 0.963575i | \(-0.413823\pi\) |
−0.700762 | + | 0.713395i | \(0.747156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.78726e9 | + | 3.09563e9i | 0.529810 | + | 0.917659i | 0.999395 | + | 0.0347712i | \(0.0110702\pi\) |
−0.469585 | + | 0.882887i | \(0.655596\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48104e9 | + | 2.00035e8i | 0.998353 | + | 0.0573694i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.63253e8 | + | 2.09724e8i | −0.100819 | + | 0.0582082i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.68706e8 | − | 1.33144e9i | 0.206525 | − | 0.357712i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.06663e9 | − | 2.82562e9i | −0.797744 | − | 0.735049i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.65229e9i | 0.668230i | 0.942532 | + | 0.334115i | \(0.108437\pi\) | ||||
−0.942532 | + | 0.334115i | \(0.891563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.04132e9 | 0.498228 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.71715e8 | + | 1.50857e8i | 0.158864 | + | 0.0356784i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.52067e9 | − | 1.45531e9i | −0.577807 | − | 0.333597i | 0.182454 | − | 0.983214i | \(-0.441596\pi\) |
−0.760261 | + | 0.649617i | \(0.774929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.88228e8 | + | 1.36525e9i | 0.175167 | + | 0.303399i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.08414e9 | − | 6.51997e9i | 0.664617 | − | 1.40502i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.19663e9 | + | 4.15498e9i | −1.50420 | + | 0.868452i | −0.504215 | + | 0.863578i | \(0.668218\pi\) |
−0.999988 | + | 0.00487337i | \(0.998449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.66686e8 | + | 8.08323e8i | −0.0946326 | + | 0.163909i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.99999e9 | − | 1.24909e9i | 0.787070 | − | 0.245782i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.91667e9i | − | 0.748010i | −0.927427 | − | 0.374005i | \(-0.877984\pi\) | ||
0.927427 | − | 0.374005i | \(-0.122016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.26666e9 | −0.791063 | −0.395532 | − | 0.918452i | \(-0.629440\pi\) | ||||
−0.395532 | + | 0.918452i | \(0.629440\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.32770e8 | + | 7.45403e8i | 0.0419060 | + | 0.134196i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.59760e9 | − | 4.38648e9i | −1.32845 | − | 0.766982i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.34405e8 | + | 1.09882e9i | 0.107758 | + | 0.186642i | 0.914861 | − | 0.403768i | \(-0.132300\pi\) |
−0.807104 | + | 0.590409i | \(0.798966\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.42567e8 | − | 2.96022e9i | −0.0400327 | − | 0.488548i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.43672e8 | + | 3.13889e8i | −0.0871990 | + | 0.0503444i | −0.542965 | − | 0.839755i | \(-0.682699\pi\) |
0.455766 | + | 0.890099i | \(0.349365\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.75733e8 | − | 1.34361e9i | 0.120939 | − | 0.209473i | −0.799199 | − | 0.601066i | \(-0.794743\pi\) |
0.920138 | + | 0.391594i | \(0.128076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.68864e8 | + | 7.51892e8i | −0.0255951 | + | 0.113966i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.24332e9i | 0.183255i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.18954e9 | −0.600586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.99185e8 | − | 5.41763e8i | 0.0696129 | − | 0.0755504i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21204e9 | − | 2.43182e9i | −0.571507 | − | 0.329960i | 0.186244 | − | 0.982504i | \(-0.440369\pi\) |
−0.757751 | + | 0.652544i | \(0.773702\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.48320e8 | + | 4.30103e8i | 0.0327887 | + | 0.0567917i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.20192e10 | − | 1.68348e9i | −1.54472 | − | 0.216362i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00620e9 | + | 5.80932e8i | −0.125893 | + | 0.0726843i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.22114e8 | − | 7.31122e8i | 0.0514237 | − | 0.0890685i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.51011e9 | − | 5.99848e9i | −0.772356 | − | 0.711657i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.77568e9i | − | 0.205195i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.51737e10 | 1.70820 | 0.854101 | − | 0.520108i | \(-0.174108\pi\) | ||||
0.854101 | + | 0.520108i | \(0.174108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.51068e10 | − | 3.39276e9i | −1.65706 | − | 0.372151i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.31231e10 | − | 7.57662e9i | −1.40280 | − | 0.809905i | −0.408118 | − | 0.912929i | \(-0.633815\pi\) |
−0.994679 | + | 0.103024i | \(0.967148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.67865e9 | + | 9.83571e9i | 0.591654 | + | 1.02477i | 0.994010 | + | 0.109291i | \(0.0348581\pi\) |
−0.402356 | + | 0.915483i | \(0.631809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.22742e8 | − | 3.21867e8i | −0.0226235 | − | 0.0326914i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.44463e10 | + | 8.34059e9i | −1.43061 | + | 0.825961i | −0.997167 | − | 0.0752213i | \(-0.976034\pi\) |
−0.433440 | + | 0.901183i | \(0.642700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.25526e10 | + | 2.17417e10i | −1.21219 | + | 2.09957i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.34525e10 | − | 4.20086e9i | 1.26702 | − | 0.395656i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.24980e10i | − | 1.14824i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.99334e9 | 0.447566 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.42322e9 | − | 7.75991e9i | −0.211934 | − | 0.678681i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.30431e9 | − | 1.33040e9i | −0.196679 | − | 0.113553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.60334e9 | + | 2.77707e9i | 0.133571 | + | 0.231353i | 0.925051 | − | 0.379843i | \(-0.124022\pi\) |
−0.791479 | + | 0.611196i | \(0.790689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.14671e10 | − | 7.93562e9i | 0.932562 | − | 0.645363i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.57279e9 | + | 1.48540e9i | −0.204279 | + | 0.117941i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.82134e9 | − | 1.52790e10i | 0.683935 | − | 1.18461i | −0.289835 | − | 0.957077i | \(-0.593600\pi\) |
0.973770 | − | 0.227534i | \(-0.0730662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.58353e9 | − | 1.15036e10i | 0.195621 | − | 0.871031i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.03383e10i | 0.764592i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.14346e9 | −0.588345 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.94631e8 | − | 4.28290e8i | 0.0278557 | − | 0.0302316i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.55287e9 | + | 4.36065e9i | 0.520948 | + | 0.300769i | 0.737322 | − | 0.675541i | \(-0.236090\pi\) |
−0.216375 | + | 0.976310i | \(0.569423\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.08867e9 | − | 8.81384e9i | −0.343007 | − | 0.594105i | 0.641983 | − | 0.766719i | \(-0.278112\pi\) |
−0.984990 | + | 0.172614i | \(0.944779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.40359e9 | − | 2.59069e9i | 0.421886 | − | 0.170682i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.37900e10 | + | 7.96168e9i | −0.888109 | + | 0.512750i | −0.873324 | − | 0.487141i | \(-0.838040\pi\) |
−0.0147858 | + | 0.999891i | \(0.504707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.10410e8 | − | 1.05726e9i | 0.0384333 | − | 0.0665685i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.66852e9 | + | 4.30162e9i | 0.287413 | + | 0.264825i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.57548e9i | − | 0.335664i | −0.985816 | − | 0.167832i | \(-0.946323\pi\) | ||
0.985816 | − | 0.167832i | \(-0.0536766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.99376e9 | −0.176274 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.42761e10 | + | 5.45206e9i | 1.39815 | + | 0.314003i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.42475e9 | + | 1.97728e9i | 0.192955 | + | 0.111403i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.34540e9 | − | 4.06235e9i | −0.129286 | − | 0.223930i | 0.794114 | − | 0.607769i | \(-0.207935\pi\) |
−0.923400 | + | 0.383839i | \(0.874602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.09616e10 | − | 8.98217e8i | 0.591247 | − | 0.0484480i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.45353e9 | + | 4.30330e9i | −0.393429 | + | 0.227146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.98911e9 | + | 1.73016e10i | −0.516049 | + | 0.893824i | 0.483777 | + | 0.875191i | \(0.339265\pi\) |
−0.999826 | + | 0.0186325i | \(0.994069\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.81846e9 | + | 1.50468e9i | −0.243659 | + | 0.0760885i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.42892e10i | − | 0.707363i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.40327e10 | 1.64945 | 0.824726 | − | 0.565532i | \(-0.191329\pi\) | ||||
0.824726 | + | 0.565532i | \(0.191329\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.80828e9 | + | 1.21953e10i | 0.180729 | + | 0.578752i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.39611e10 | + | 8.06046e9i | 0.648822 | + | 0.374597i | 0.788005 | − | 0.615669i | \(-0.211114\pi\) |
−0.139183 | + | 0.990267i | \(0.544448\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.81218e8 | + | 1.17990e9i | 0.0310058 | + | 0.0537037i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.75079e9 | − | 3.19333e9i | −0.300962 | − | 0.142364i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.29807e10 | − | 1.32679e10i | 1.00361 | − | 0.579435i | 0.0942959 | − | 0.995544i | \(-0.469940\pi\) |
0.909315 | + | 0.416109i | \(0.136607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.72254e9 | + | 8.17969e9i | −0.202055 | + | 0.349969i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.55858e9 | − | 2.47504e10i | 0.233020 | − | 1.03756i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.07996e9i | 0.208676i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.50944e10 | 1.01022 | 0.505108 | − | 0.863056i | \(-0.331452\pi\) | ||||
0.505108 | + | 0.863056i | \(0.331452\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.81507e9 | + | 5.22576e9i | −0.189981 | + | 0.206185i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.71173e9 | − | 3.87502e9i | −0.259572 | − | 0.149864i | 0.364567 | − | 0.931177i | \(-0.381217\pi\) |
−0.624139 | + | 0.781313i | \(0.714550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.94213e9 | − | 5.09592e9i | −0.111543 | − | 0.193198i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.67678e9 | + | 2.19631e9i | −0.0994931 | + | 0.0816343i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.20364e10 | + | 2.42697e10i | −1.53196 | + | 0.884478i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.37487e10 | + | 2.38135e10i | −0.491326 | + | 0.851001i | −0.999950 | − | 0.00998745i | \(-0.996821\pi\) |
0.508624 | + | 0.860988i | \(0.330154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.81222e9 | + | 5.35543e9i | 0.203692 | + | 0.187684i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.57951e9i | 0.157405i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.14089e9 | 0.139605 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.12986e9 | − | 1.60126e9i | −0.235796 | − | 0.0529564i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.00646e10 | + | 1.73578e10i | 0.975439 | + | 0.563170i | 0.900890 | − | 0.434048i | \(-0.142915\pi\) |
0.0745486 | + | 0.997217i | \(0.476248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.79802e10 | + | 4.84631e10i | 0.890681 | + | 1.54271i | 0.839060 | + | 0.544039i | \(0.183106\pi\) |
0.0516215 | + | 0.998667i | \(0.483561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.00646e10 | + | 2.12768e10i | −0.314364 | + | 0.664577i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.51538e10 | − | 2.02961e10i | 1.07750 | − | 0.622094i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.18676e9 | − | 1.41799e10i | 0.246264 | − | 0.426541i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.29511e10 | + | 7.16704e9i | −0.677602 | + | 0.211598i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.05381e9i | − | 0.0305390i | −0.999883 | − | 0.0152695i | \(-0.995139\pi\) | ||
0.999883 | − | 0.0152695i | \(-0.00486062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.08239e10 | −0.307916 | −0.153958 | − | 0.988077i | \(-0.549202\pi\) | ||||
−0.153958 | + | 0.988077i | \(0.549202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.13496e9 | + | 6.83680e9i | 0.0596255 | + | 0.190940i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.15603e9 | − | 5.28624e9i | −0.251062 | − | 0.144951i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.63567e9 | + | 1.66895e10i | 0.259432 | + | 0.449350i | 0.966090 | − | 0.258206i | \(-0.0831312\pi\) |
−0.706658 | + | 0.707556i | \(0.749798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.79416e9 | + | 3.40993e10i | 0.0738750 | + | 0.901552i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.47005e10 | − | 2.00344e10i | 0.900993 | − | 0.520189i | 0.0234707 | − | 0.999725i | \(-0.492528\pi\) |
0.877522 | + | 0.479536i | \(0.159195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.08065e9 | + | 3.60379e9i | −0.0530590 | + | 0.0919008i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.08866e10 | + | 4.84743e10i | −0.272686 | + | 1.21418i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.89578e10i | 0.712493i | 0.934392 | + | 0.356247i | \(0.115944\pi\) | ||||
−0.934392 | + | 0.356247i | \(0.884056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.82822e10 | −0.925318 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.06215e9 | − | 8.74980e9i | 0.191451 | − | 0.207781i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.71571e8 | − | 3.87732e8i | −0.0156692 | − | 0.00904661i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.76429e9 | − | 4.78789e9i | −0.0633752 | − | 0.109769i | 0.832597 | − | 0.553879i | \(-0.186853\pi\) |
−0.895972 | + | 0.444110i | \(0.853520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.45520e10 | − | 4.42670e10i | 0.778435 | − | 0.997309i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.96113e10 | + | 2.86431e10i | −1.09844 | + | 0.634186i | −0.935811 | − | 0.352501i | \(-0.885331\pi\) |
−0.162631 | + | 0.986687i | \(0.551998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.30725e10 | − | 7.46037e10i | 0.937294 | − | 1.62344i | 0.166802 | − | 0.985990i | \(-0.446656\pi\) |
0.770492 | − | 0.637450i | \(-0.220011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.16908e9 | + | 1.99861e9i | 0.0463941 | + | 0.0427480i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.73366e10i | − | 0.364498i | −0.983252 | − | 0.182249i | \(-0.941662\pi\) | ||
0.983252 | − | 0.182249i | \(-0.0583377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.73936e10 | −0.566185 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.41395e10 | − | 9.91309e9i | −0.896900 | − | 0.201431i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.25114e10 | + | 1.29970e10i | 0.449736 | + | 0.259655i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.27186e10 | + | 3.93498e10i | 0.446281 | + | 0.772981i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.33241e10 | + | 6.26042e10i | 0.836867 | + | 1.20929i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.41007e10 | + | 8.14105e9i | −0.267855 | + | 0.154646i | −0.627912 | − | 0.778284i | \(-0.716090\pi\) |
0.360058 | + | 0.932930i | \(0.382757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38137e10 | − | 2.39260e10i | 0.258065 | − | 0.446982i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.12599e9 | − | 1.60071e9i | 0.0941865 | − | 0.0294120i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.31547e8i | 0.0132213i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.59101e10 | −1.52731 | −0.763657 | − | 0.645622i | \(-0.776598\pi\) | ||||
−0.763657 | + | 0.645622i | \(0.776598\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.52566e7 | + | 2.08972e8i | 0.00114127 | + | 0.00365471i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.42747e10 | + | 5.44295e10i | 1.62207 | + | 0.936502i | 0.986366 | + | 0.164569i | \(0.0526233\pi\) |
0.635704 | + | 0.771933i | \(0.280710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.80802e10 | − | 1.00598e11i | −0.983197 | − | 1.70295i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.91035e9 | − | 6.85828e9i | 0.165070 | − | 0.114234i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.74898e9 | − | 5.62857e9i | 0.159784 | − | 0.0922514i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.01210e10 | + | 1.75301e10i | −0.163238 | + | 0.282737i | −0.936028 | − | 0.351925i | \(-0.885527\pi\) |
0.772790 | + | 0.634662i | \(0.218861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.34054e10 | − | 5.96898e10i | 0.212780 | − | 0.947434i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.95990e9i | 0.139969i | 0.997548 | + | 0.0699844i | \(0.0222949\pi\) | ||||
−0.997548 | + | 0.0699844i | \(0.977705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.79066e9 | 0.135162 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.54997e10 | + | 3.85275e10i | −0.537270 | + | 0.583095i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.49283e10 | + | 4.32599e10i | 1.11628 | + | 0.644487i | 0.940450 | − | 0.339933i | \(-0.110404\pi\) |
0.175835 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.82324e10 | + | 3.15795e10i | 0.267400 | + | 0.463150i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.95508e10 | + | 3.86762e10i | 0.715454 | + | 0.558437i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.33153e10 | − | 7.68761e9i | 0.189288 | − | 0.109286i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.09632e10 | − | 7.09503e10i | 0.573365 | − | 0.993098i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.59047e10 | − | 5.15111e10i | −0.770511 | − | 0.709956i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.83590e10i | − | 1.06350i | −0.846901 | − | 0.531750i | \(-0.821534\pi\) | ||
0.846901 | − | 0.531750i | \(-0.178466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.36222e9 | 0.125133 | 0.0625665 | − | 0.998041i | \(-0.480071\pi\) | ||||
0.0625665 | + | 0.998041i | \(0.480071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.25182e10 | − | 5.05725e9i | −0.296412 | − | 0.0665698i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.14260e10 | − | 2.39173e10i | −0.537070 | − | 0.310078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.51605e10 | − | 6.08998e10i | −0.448986 | − | 0.777667i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.03747e10 | − | 3.30838e9i | 0.507845 | − | 0.0416138i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.88700e10 | − | 1.08946e10i | 0.233810 | − | 0.134990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.99749e9 | + | 1.21200e10i | −0.0854136 | + | 0.147941i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.10981e10 | + | 2.22021e10i | −0.854990 | + | 0.266991i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.19088e11i | − | 1.41095i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.87519e10 | 0.335642 | 0.167821 | − | 0.985817i | \(-0.446327\pi\) | ||||
0.167821 | + | 0.985817i | \(0.446327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00334e10 | + | 1.28199e11i | 0.460493 | + | 1.47464i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.99129e9 | + | 4.03642e9i | 0.0792449 | + | 0.0457521i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.14292e10 | − | 1.23719e11i | −0.797860 | − | 1.38193i | −0.921007 | − | 0.389545i | \(-0.872632\pi\) |
0.123147 | − | 0.992388i | \(-0.460701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.30930e11 | − | 6.19336e10i | −1.44128 | − | 0.681768i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.12605e11 | − | 6.50128e10i | 1.22167 | − | 0.705330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34211e10 | + | 4.05665e10i | −0.250442 | + | 0.433778i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.03449e9 | + | 1.35115e10i | −0.0319826 | + | 0.142408i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.20526e10i | − | 0.125216i | −0.998038 | − | 0.0626080i | \(-0.980058\pi\) | ||
0.998038 | − | 0.0626080i | \(-0.0199418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.47951e10 | −0.151520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.32448e11 | + | 1.43745e11i | −1.33719 | + | 1.45124i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.41550e10 | − | 4.28134e10i | −0.738086 | − | 0.426134i | 0.0832869 | − | 0.996526i | \(-0.473458\pi\) |
−0.821373 | + | 0.570391i | \(0.806792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.85400e9 | + | 1.01394e10i | 0.0574459 | + | 0.0994992i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.15017e10 | + | 5.19753e9i | −0.304791 | + | 0.0502881i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.77244e10 | − | 3.91007e10i | 0.646095 | − | 0.373023i | −0.140864 | − | 0.990029i | \(-0.544988\pi\) |
0.786958 | + | 0.617006i | \(0.211655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.68244e10 | − | 2.91408e10i | 0.158269 | − | 0.274130i | −0.775975 | − | 0.630763i | \(-0.782742\pi\) |
0.934245 | + | 0.356633i | \(0.116075\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.74787e10 | − | 5.29615e10i | −0.533198 | − | 0.491294i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.43382e10i | − | 0.314128i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.68149e10 | −0.512577 | −0.256288 | − | 0.966600i | \(-0.582500\pi\) | ||||
−0.256288 | + | 0.966600i | \(0.582500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.27497e10 | − | 1.40927e10i | −0.558338 | − | 0.125394i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.30675e10 | + | 1.90915e10i | 0.290200 | + | 0.167547i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.32499e11 | − | 2.29496e11i | −1.14694 | − | 1.98655i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.93322e9 | + | 6.20093e9i | −0.0250450 | + | 0.0529460i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52093e11 | + | 8.78111e10i | −1.28103 | + | 0.739600i | −0.977036 | − | 0.213075i | \(-0.931652\pi\) |
−0.303990 | + | 0.952675i | \(0.598319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.67722e10 | − | 4.63707e10i | 0.222445 | − | 0.385286i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.28013e10 | − | 2.58567e10i | 0.678715 | − | 0.211945i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.42615e10i | 0.115331i | 0.998336 | + | 0.0576655i | \(0.0183657\pi\) | ||||
−0.998336 | + | 0.0576655i | \(0.981634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.30394e9 | −0.0502972 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.44787e10 | + | 7.83883e10i | 0.192704 | + | 0.617098i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21666e11 | + | 7.02441e10i | 0.945068 | + | 0.545635i | 0.891545 | − | 0.452931i | \(-0.149622\pi\) |
0.0535228 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.75136e10 | − | 1.34257e11i | −0.594128 | − | 1.02906i | −0.993669 | − | 0.112344i | \(-0.964164\pi\) |
0.399542 | − | 0.916715i | \(-0.369169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.97900e10 | + | 2.41513e11i | 0.149685 | + | 1.82671i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.13974e10 | + | 1.23538e10i | −0.159713 | + | 0.0922101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.96405e10 | + | 1.03300e11i | −0.439325 | + | 0.760934i | −0.997638 | − | 0.0686970i | \(-0.978116\pi\) |
0.558312 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.44721e10 | + | 6.44391e10i | −0.105211 | + | 0.468468i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.66303e10i | 0.334583i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.07532e11 | −0.761546 | −0.380773 | − | 0.924669i | \(-0.624342\pi\) | ||||
−0.380773 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.40078e9 | + | 8.03202e9i | −0.0517341 | + | 0.0561467i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.08306e11 | + | 6.25304e10i | 0.747328 | + | 0.431470i | 0.824728 | − | 0.565530i | \(-0.191328\pi\) |
−0.0773997 | + | 0.997000i | \(0.524662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.18581e10 | − | 5.51798e10i | −0.216998 | − | 0.375852i | 0.736890 | − | 0.676012i | \(-0.236293\pi\) |
−0.953889 | + | 0.300160i | \(0.902960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.78157e10 | − | 4.40362e10i | −0.119794 | − | 0.296103i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.32304e10 | + | 1.91856e10i | −0.220589 | + | 0.127357i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.25239e10 | + | 1.25615e11i | −0.475293 | + | 0.823231i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.60902e11 | − | 1.48257e11i | −1.04110 | − | 0.959279i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.24590e11i | − | 1.43479i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.53724e10 | 0.538518 | 0.269259 | − | 0.963068i | \(-0.413221\pi\) | ||||
0.269259 | + | 0.963068i | \(0.413221\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.54087e10 | + | 1.24440e10i | 0.345115 | + | 0.0775077i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.09874e10 | − | 6.34356e9i | −0.0675770 | − | 0.0390156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.38909e10 | + | 5.87007e10i | 0.205838 | + | 0.356521i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.66666e10 | − | 8.18844e10i | −0.339878 | − | 0.491131i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.48018e10 | + | 2.00929e10i | −0.206144 | + | 0.119017i | −0.599518 | − | 0.800361i | \(-0.704641\pi\) |
0.393374 | + | 0.919378i | \(0.371308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.65057e10 | − | 4.59092e10i | 0.155058 | − | 0.268569i | −0.778022 | − | 0.628237i | \(-0.783777\pi\) |
0.933080 | + | 0.359668i | \(0.117110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.07884e9 | − | 2.21054e9i | 0.0409000 | − | 0.0127720i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8.40520e10i | − | 0.479657i | −0.970815 | − | 0.239829i | \(-0.922909\pi\) | ||
0.970815 | − | 0.239829i | \(-0.0770912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.41004e11 | −0.794791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.10681e9 | + | 2.59606e10i | 0.0451363 | + | 0.144541i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.79412e10 | + | 3.34523e10i | 0.318665 | + | 0.183981i | 0.650797 | − | 0.759251i | \(-0.274435\pi\) |
−0.332132 | + | 0.943233i | \(0.607768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.25951e10 | + | 2.18154e10i | 0.0684286 | + | 0.118522i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.65245e11 | − | 1.83558e11i | 1.42359 | − | 0.985172i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.98528e11 | − | 1.14620e11i | 1.05264 | − | 0.607741i | 0.129251 | − | 0.991612i | \(-0.458743\pi\) |
0.923387 | + | 0.383871i | \(0.125409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62836e11 | − | 2.82040e11i | 0.852989 | − | 1.47742i | −0.0255089 | − | 0.999675i | \(-0.508121\pi\) |
0.878498 | − | 0.477746i | \(-0.158546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.43781e10 | − | 1.08547e11i | 0.126167 | − | 0.561779i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.05639e9i | − | 0.0360825i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.82639e10 | −0.496467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.50819e11 | + | 1.63682e11i | −0.752922 | + | 0.817142i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.36602e11 | + | 2.52072e11i | 2.15375 | + | 1.24347i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.20089e10 | − | 2.08001e10i | −0.0585389 | − | 0.101392i | 0.835271 | − | 0.549839i | \(-0.185311\pi\) |
−0.893810 | + | 0.448446i | \(0.851977\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.83188e10 | + | 2.02182e11i | −0.136414 | + | 0.973930i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.50617e11 | + | 1.44694e11i | −1.19304 | + | 0.688804i | −0.958995 | − | 0.283421i | \(-0.908530\pi\) |
−0.234048 | + | 0.972225i | \(0.575197\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.37279e9 | + | 5.84184e9i | −0.0158675 | + | 0.0274834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.53025e11 | + | 1.40999e11i | 0.711499 | + | 0.655582i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.04015e11i | 0.477982i | 0.971022 | + | 0.238991i | \(0.0768166\pi\) | ||||
−0.971022 | + | 0.238991i | \(0.923183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.84829e9 | −0.0356462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.99977e11 | − | 4.49118e10i | −0.897744 | − | 0.201620i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30623e11 | + | 7.54152e10i | 0.579619 | + | 0.334643i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.51122e10 | + | 9.54571e10i | 0.241733 | + | 0.418694i | 0.961208 | − | 0.275825i | \(-0.0889509\pi\) |
−0.719475 | + | 0.694518i | \(0.755618\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.10760e11 | − | 9.07591e9i | 0.480231 | − | 0.0393511i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.28438e9 | − | 3.62829e9i | 0.0269354 | − | 0.0155511i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.85651e10 | − | 1.53399e11i | 0.375259 | − | 0.649968i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.26177e10 | + | 2.89221e10i | −0.387958 | + | 0.121149i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.57816e10i | 0.313828i | 0.987612 | + | 0.156914i | \(0.0501546\pi\) | ||||
−0.987612 | + | 0.156914i | \(0.949845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.51397e11 | 1.02929 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.96706e9 | − | 2.23107e10i | −0.0282029 | − | 0.0903145i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.01986e10 | + | 4.05292e10i | 0.280964 | + | 0.162215i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.71004e11 | + | 2.96187e11i | 0.676737 | + | 1.17214i | 0.975958 | + | 0.217959i | \(0.0699400\pi\) |
−0.299221 | + | 0.954184i | \(0.596727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.74570e11 | + | 1.77183e11i | 1.46573 | + | 0.693334i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.50436e10 | + | 2.02324e10i | −0.135597 | + | 0.0782871i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.19383e10 | − | 2.06778e10i | 0.0456793 | − | 0.0791189i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.89771e10 | − | 1.29025e11i | 0.109642 | − | 0.488199i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 8.86727e10i | − | 0.331799i | −0.986143 | − | 0.165899i | \(-0.946947\pi\) | ||
0.986143 | − | 0.165899i | \(-0.0530527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.41775e11 | 0.524635 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.96195e11 | + | 2.12929e11i | −0.718018 | + | 0.779260i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.65730e11 | + | 2.11154e11i | 1.32376 | + | 0.764271i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.21757e10 | + | 1.07691e11i | 0.222578 | + | 0.385517i | 0.955590 | − | 0.294699i | \(-0.0952193\pi\) |
−0.733012 | + | 0.680216i | \(0.761886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.85813e10 | + | 2.73976e11i | 0.242826 | + | 0.970070i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.04159e11 | + | 6.01364e10i | −0.364778 | + | 0.210605i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.20019e11 | + | 2.07878e11i | −0.415750 | + | 0.720101i | −0.995507 | − | 0.0946891i | \(-0.969814\pi\) |
0.579757 | + | 0.814790i | \(0.303148\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.49859e10 | − | 2.30223e10i | −0.0856142 | − | 0.0788858i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.43456e11i | − | 2.85886i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.80470e10 | −0.328743 | −0.164372 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164372 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.21504e11 | + | 2.72880e10i | 0.403011 | + | 0.0905104i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.60334e11 | − | 2.08039e11i | −1.18236 | − | 0.682636i | −0.225801 | − | 0.974173i | \(-0.572500\pi\) |
−0.956560 | + | 0.291537i | \(0.905833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.46679e10 | − | 4.27261e10i | −0.0800769 | − | 0.138697i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.44429e11 | − | 3.05328e11i | 0.463844 | − | 0.980582i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.11758e11 | + | 6.45237e10i | −0.355101 | + | 0.205018i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.91821e11 | − | 3.32243e11i | 0.603025 | − | 1.04447i | −0.389335 | − | 0.921096i | \(-0.627295\pi\) |
0.992360 | − | 0.123374i | \(-0.0393715\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.05069e11 | + | 6.40379e10i | −0.637854 | + | 0.199185i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.18149e10i | 0.0363616i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00507e11 | 0.610584 | 0.305292 | − | 0.952259i | \(-0.401246\pi\) | ||||
0.305292 | + | 0.952259i | \(0.401246\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.92863e10 | + | 1.57830e11i | 0.148511 | + | 0.475579i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.41971e11 | − | 8.19667e10i | −0.423311 | − | 0.244399i | 0.273182 | − | 0.961962i | \(-0.411924\pi\) |
−0.696493 | + | 0.717564i | \(0.745257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.72198e10 | + | 6.44665e10i | 0.109818 | + | 0.190211i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.55417e9 | + | 5.55779e10i | 0.0132973 | + | 0.162277i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.95036e10 | − | 4.01279e10i | 0.200829 | − | 0.115948i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.02003e11 | + | 5.23085e11i | −0.863588 | + | 1.49578i | 0.00485515 | + | 0.999988i | \(0.498455\pi\) |
−0.868443 | + | 0.495789i | \(0.834879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.16613e10 | − | 2.30030e11i | 0.146200 | − | 0.650979i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.78731e11i | 1.62091i | 0.585801 | + | 0.810455i | \(0.300780\pi\) | ||||
−0.585801 | + | 0.810455i | \(0.699220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.73906e11 | 0.482067 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.65270e10 | + | 9.39072e10i | −0.237393 | + | 0.257641i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.71709e11 | + | 9.91364e10i | 0.466277 | + | 0.269205i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73305e11 | + | 3.00173e11i | 0.465808 | + | 0.806803i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.78574e11 | + | 8.10384e10i | 1.53926 | + | 0.215598i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.89053e10 | − | 2.24620e10i | 0.102454 | − | 0.0591520i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.88724e11 | + | 3.26880e11i | −0.491958 | + | 0.852096i | −0.999957 | − | 0.00926121i | \(-0.997052\pi\) |
0.507999 | + | 0.861358i | \(0.330385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.95012e11 | − | 4.56109e11i | −1.27734 | − | 1.17696i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.07959e11i | 0.275774i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.86946e11 | −0.725616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.37656e10 | − | 1.65667e10i | −0.184665 | − | 0.0414731i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.07081e11 | + | 1.19558e11i | 0.513224 | + | 0.296310i | 0.734158 | − | 0.678979i | \(-0.237577\pi\) |
−0.220934 | + | 0.975289i | \(0.570910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.89535e11 | + | 3.28284e11i | 0.465053 | + | 0.805495i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.93154e11 | + | 2.79112e11i | 0.469217 | + | 0.678029i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.72340e11 | + | 5.61381e11i | −2.33860 | + | 1.35019i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.66635e9 | + | 4.61826e9i | −0.00634942 | + | 0.0109975i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.02828e11 | − | 9.45655e10i | 0.714007 | − | 0.222966i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.09694e11i | − | 0.489544i | −0.969581 | − | 0.244772i | \(-0.921287\pi\) | ||
0.969581 | − | 0.244772i | \(-0.0787131\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.14392e11 | −1.65140 | −0.825702 | − | 0.564107i | \(-0.809221\pi\) | ||||
−0.825702 | + | 0.564107i | \(0.809221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.03016e11 | − | 3.29889e11i | −0.235799 | − | 0.755102i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.88273e8 | − | 1.08700e8i | −0.000426735 | − | 0.000246376i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.73144e10 | − | 1.16592e11i | −0.151085 | − | 0.261686i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.20129e10 | + | 3.59946e10i | −0.115605 | + | 0.0800021i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.95004e11 | + | 3.43526e11i | −1.30963 | + | 0.756113i | −0.982033 | − | 0.188707i | \(-0.939570\pi\) |
−0.327592 | + | 0.944819i | \(0.606237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.54624e10 | − | 7.87432e10i | 0.0990953 | − | 0.171638i | −0.812215 | − | 0.583358i | \(-0.801738\pi\) |
0.911310 | + | 0.411720i | \(0.135072\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.55714e11 | − | 6.93339e11i | 0.336133 | − | 1.49668i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.03065e11i | − | 0.647908i | −0.946073 | − | 0.323954i | \(-0.894988\pi\) | ||
0.946073 | − | 0.323954i | \(-0.105012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.06427e11 | 1.49572 | 0.747858 | − | 0.663859i | \(-0.231082\pi\) | ||||
0.747858 | + | 0.663859i | \(0.231082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.96412e10 | + | 7.55812e10i | −0.146037 | + | 0.158493i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.77193e11 | + | 2.75507e11i | 0.991092 | + | 0.572207i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.03753e10 | + | 5.26115e10i | 0.0624848 | + | 0.108227i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.23021e11 | − | 9.02274e10i | 0.454407 | − | 0.183839i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.75197e10 | + | 4.47560e10i | −0.156446 | + | 0.0903241i | −0.576179 | − | 0.817323i | \(-0.695457\pi\) |
0.419733 | + | 0.907648i | \(0.362124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.54126e11 | − | 6.13364e11i | 0.707903 | − | 1.22612i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.73958e10 | − | 3.44569e10i | −0.0740479 | − | 0.0682285i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.20241e10i | − | 0.102042i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.27828e11 | −0.442663 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.22615e11 | + | 2.75374e10i | 0.236000 | + | 0.0530021i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.64534e11 | − | 9.49940e10i | −0.313717 | − | 0.181125i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.25979e11 | − | 7.37818e11i | −0.804623 | − | 1.39365i | −0.916545 | − | 0.399931i | \(-0.869034\pi\) |
0.111922 | − | 0.993717i | \(-0.464299\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.22118e10 | + | 5.09776e9i | −0.116415 | + | 0.00953927i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.19638e10 | + | 5.30953e10i | −0.170488 | + | 0.0984313i | −0.582816 | − | 0.812604i | \(-0.698049\pi\) |
0.412328 | + | 0.911035i | \(0.364716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.80076e11 | + | 3.11901e11i | −0.330737 | + | 0.572854i | −0.982657 | − | 0.185435i | \(-0.940631\pi\) |
0.651919 | + | 0.758288i | \(0.273964\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.61311e10 | + | 3.00193e10i | −0.174925 | + | 0.0546245i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.03087e12i | − | 1.85849i | −0.369462 | − | 0.929246i | \(-0.620458\pi\) | ||
0.369462 | − | 0.929246i | \(-0.379542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.54886e10 | 0.134839 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.01154e11 | − | 3.23926e11i | −0.179022 | − | 0.573284i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.24905e12 | − | 7.21141e11i | −2.19029 | − | 1.26456i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.40037e11 | + | 4.15756e11i | 0.417066 | + | 0.722380i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.39404e10 | + | 2.55154e10i | 0.0928661 | + | 0.0439284i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.00300e10 | − | 2.31113e10i | 0.0682895 | − | 0.0394269i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.55982e11 | + | 2.70169e11i | −0.263679 | + | 0.456706i | −0.967217 | − | 0.253952i | \(-0.918269\pi\) |
0.703537 | + | 0.710658i | \(0.251603\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.63262e10 | − | 3.84381e11i | 0.144606 | − | 0.643881i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.28854e10i | 0.120987i | 0.998169 | + | 0.0604933i | \(0.0192674\pi\) | ||||
−0.998169 | + | 0.0604933i | \(0.980733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.07132e12 | 1.76228 | 0.881142 | − | 0.472852i | \(-0.156776\pi\) | ||||
0.881142 | + | 0.472852i | \(0.156776\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.72591e10 | + | 2.95842e10i | −0.0444364 | + | 0.0482265i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.56195e11 | + | 2.05649e11i | 0.575432 | + | 0.332226i | 0.759316 | − | 0.650722i | \(-0.225534\pi\) |
−0.183884 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.84938e10 | − | 1.01314e11i | −0.0936489 | − | 0.162205i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.60033e11 | − | 9.69946e11i | −0.253921 | − | 1.53899i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.67469e11 | + | 2.12158e11i | −0.577849 | + | 0.333621i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.69827e10 | − | 6.40559e10i | 0.0576377 | − | 0.0998314i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.92106e10 | − | 6.37713e10i | −0.106906 | − | 0.0985043i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.97658e11i | − | 0.761889i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.22614e12 | 1.86055 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.67204e10 | + | 1.49844e10i | 0.100348 | + | 0.0225366i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.15501e11 | − | 6.66847e10i | −0.172184 | − | 0.0994104i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.64334e10 | + | 1.32387e11i | 0.112942 | + | 0.195621i | 0.916955 | − | 0.398991i | \(-0.130639\pi\) |
−0.804013 | + | 0.594611i | \(0.797306\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.06607e11 | − | 6.48177e11i | 0.449083 | − | 0.949376i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.19623e11 | + | 4.15475e11i | −1.04480 | + | 0.603213i | −0.921188 | − | 0.389118i | \(-0.872780\pi\) |
−0.123608 | + | 0.992331i | \(0.539447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.87832e11 | + | 1.01816e12i | −0.846000 | + | 1.46531i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.37292e11 | − | 4.28727e10i | 0.195867 | − | 0.0611641i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.32279e11i | 0.328498i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.99778e11 | 0.700673 | 0.350336 | − | 0.936624i | \(-0.386067\pi\) | ||||
0.350336 | + | 0.936624i | \(0.386067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.66360e11 | + | 1.17320e12i | 0.509178 | + | 1.63055i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.70851e11 | − | 9.86407e10i | −0.235402 | − | 0.135909i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.08255e11 | + | 7.07119e11i | 0.557654 | + | 0.965885i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.02422e11 | − | 1.24994e12i | −0.138700 | − | 1.69266i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.65549e11 | + | 2.11050e11i | −0.490775 | + | 0.283349i | −0.724896 | − | 0.688858i | \(-0.758112\pi\) |
0.234121 | + | 0.972207i | \(0.424779\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.08393e11 | + | 5.34152e11i | −0.410493 | + | 0.710994i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.68959e11 | − | 1.19758e12i | 0.354944 | − | 1.58044i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.94100e11i | − | 0.253968i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46649e12 | −1.90248 | −0.951240 | − | 0.308452i | \(-0.900189\pi\) | ||||
−0.951240 | + | 0.308452i | \(0.900189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.23368e11 | + | 6.76538e11i | −0.801830 | + | 0.870221i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.80375e11 | + | 1.04140e11i | 0.230048 | + | 0.132818i | 0.610594 | − | 0.791944i | \(-0.290931\pi\) |
−0.380546 | + | 0.924762i | \(0.624264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.49201e10 | − | 1.29765e11i | −0.0947440 | − | 0.164101i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.95081e10 | − | 2.49932e10i | 0.0244617 | − | 0.0313397i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.88417e11 | + | 2.24252e11i | −0.482945 | + | 0.278828i | −0.721643 | − | 0.692265i | \(-0.756613\pi\) |
0.238698 | + | 0.971094i | \(0.423279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.19523e11 | − | 5.53430e11i | 0.393947 | − | 0.682336i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.93674e11 | − | 9.15580e11i | −1.21485 | − | 1.11937i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.57158e12i | − | 1.90531i | −0.304053 | − | 0.952655i | \(-0.598340\pi\) | ||
0.304053 | − | 0.952655i | \(-0.401660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.76140e10 | 0.0933097 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.98409e12 | − | 4.45598e11i | −2.36545 | − | 0.531246i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.26733e10 | − | 3.61844e10i | −0.0740982 | − | 0.0427806i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.23978e11 | + | 5.61147e11i | 0.379859 | + | 0.657935i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.49603e11 | + | 9.38689e11i | 0.755340 | + | 1.09148i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.53086e10 | − | 3.19324e10i | 0.0637798 | − | 0.0368233i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.92009e10 | − | 8.52185e10i | 0.0562688 | − | 0.0974604i | −0.836519 | − | 0.547938i | \(-0.815413\pi\) |
0.892788 | + | 0.450478i | \(0.148746\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.66319e11 | − | 3.01757e11i | 1.09604 | − | 0.342264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.12176e11i | − | 0.238682i | −0.992853 | − | 0.119341i | \(-0.961922\pi\) | ||
0.992853 | − | 0.119341i | \(-0.0380781\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.69127e10 | 0.0746547 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.20561e11 | + | 3.86074e11i | 0.133410 | + | 0.427221i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.53074e11 | − | 5.50257e11i | −1.04604 | − | 0.603931i | −0.124502 | − | 0.992219i | \(-0.539733\pi\) |
−0.921538 | + | 0.388288i | \(0.873067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.90729e11 | − | 1.02317e12i | −0.643069 | − | 1.11383i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.41472e11 | − | 3.74716e11i | 0.584656 | − | 0.404600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.07234e11 | + | 3.50586e11i | −0.650342 | + | 0.375475i | −0.788587 | − | 0.614923i | \(-0.789187\pi\) |
0.138245 | + | 0.990398i | \(0.455854\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.30703e10 | + | 7.45999e10i | −0.0457544 | + | 0.0792489i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.72272e10 | − | 2.10286e11i | 0.0497649 | − | 0.221586i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.01743e11i | 0.106345i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.38686e12 | −1.43793 | −0.718963 | − | 0.695048i | \(-0.755383\pi\) | ||||
−0.718963 | + | 0.695048i | \(0.755383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.76005e11 | + | 1.91017e11i | −0.181021 | + | 0.196461i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.06240e10 | − | 4.07748e10i | −0.0720543 | − | 0.0416006i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.17360e11 | + | 5.49684e11i | 0.321197 | + | 0.556330i | 0.980735 | − | 0.195341i | \(-0.0625814\pi\) |
−0.659538 | + | 0.751671i | \(0.729248\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.90431e11 | + | 6.95013e11i | 0.894002 | + | 0.697800i |
(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 | 144.9.q.b.113.6 | 16 | ||
3.2 | odd | 2 | 432.9.q.c.17.4 | 16 | |||
4.3 | odd | 2 | 18.9.d.a.5.2 | ✓ | 16 | ||
9.2 | odd | 6 | inner | 144.9.q.b.65.6 | 16 | ||
9.7 | even | 3 | 432.9.q.c.305.4 | 16 | |||
12.11 | even | 2 | 54.9.d.a.17.6 | 16 | |||
36.7 | odd | 6 | 54.9.d.a.35.6 | 16 | |||
36.11 | even | 6 | 18.9.d.a.11.2 | yes | 16 | ||
36.23 | even | 6 | 162.9.b.c.161.13 | 16 | |||
36.31 | odd | 6 | 162.9.b.c.161.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.9.d.a.5.2 | ✓ | 16 | 4.3 | odd | 2 | ||
18.9.d.a.11.2 | yes | 16 | 36.11 | even | 6 | ||
54.9.d.a.17.6 | 16 | 12.11 | even | 2 | |||
54.9.d.a.35.6 | 16 | 36.7 | odd | 6 | |||
144.9.q.b.65.6 | 16 | 9.2 | odd | 6 | inner | ||
144.9.q.b.113.6 | 16 | 1.1 | even | 1 | trivial | ||
162.9.b.c.161.4 | 16 | 36.31 | odd | 6 | |||
162.9.b.c.161.13 | 16 | 36.23 | even | 6 | |||
432.9.q.c.17.4 | 16 | 3.2 | odd | 2 | |||
432.9.q.c.305.4 | 16 | 9.7 | even | 3 |