Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.8 | ||
Root | \(59.5904i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.10.b.a.16.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.8575 | 0.524034 | 0.262017 | − | 0.965063i | \(-0.415612\pi\) | ||||
0.262017 | + | 0.965063i | \(0.415612\pi\) | |||||||
\(3\) | 59.5904i | 0.424747i | 0.977189 | + | 0.212374i | \(0.0681194\pi\) | ||||
−0.977189 | + | 0.212374i | \(0.931881\pi\) | |||||||
\(4\) | −371.399 | −0.725388 | ||||||||
\(5\) | − | 633.821i | − | 0.453525i | −0.973950 | − | 0.226763i | \(-0.927186\pi\) | ||
0.973950 | − | 0.226763i | \(-0.0728142\pi\) | |||||||
\(6\) | 706.595i | 0.222582i | ||||||||
\(7\) | − | 10932.1i | − | 1.72093i | −0.509512 | − | 0.860463i | \(-0.670174\pi\) | ||
0.509512 | − | 0.860463i | \(-0.329826\pi\) | |||||||
\(8\) | −10474.9 | −0.904162 | ||||||||
\(9\) | 16132.0 | 0.819590 | ||||||||
\(10\) | − | 7515.55i | − | 0.237663i | ||||||
\(11\) | − | 26182.2i | − | 0.539186i | −0.962974 | − | 0.269593i | \(-0.913111\pi\) | ||
0.962974 | − | 0.269593i | \(-0.0868891\pi\) | |||||||
\(12\) | − | 22131.8i | − | 0.308107i | ||||||
\(13\) | −132465. | −1.28634 | −0.643172 | − | 0.765722i | \(-0.722382\pi\) | ||||
−0.643172 | + | 0.765722i | \(0.722382\pi\) | |||||||
\(14\) | − | 129628.i | − | 0.901824i | ||||||
\(15\) | 37769.6 | 0.192634 | ||||||||
\(16\) | 65949.4 | 0.251577 | ||||||||
\(17\) | 97124.1 | − | 330386.i | 0.282038 | − | 0.959403i | ||||
\(18\) | 191286. | 0.429493 | ||||||||
\(19\) | −834785. | −1.46955 | −0.734774 | − | 0.678312i | \(-0.762712\pi\) | ||||
−0.734774 | + | 0.678312i | \(0.762712\pi\) | |||||||
\(20\) | 235400.i | 0.328982i | ||||||||
\(21\) | 651448. | 0.730959 | ||||||||
\(22\) | − | 310456.i | − | 0.282552i | ||||||
\(23\) | 1.27202e6i | 0.947805i | 0.880577 | + | 0.473902i | \(0.157155\pi\) | ||||
−0.880577 | + | 0.473902i | \(0.842845\pi\) | |||||||
\(24\) | − | 624205.i | − | 0.384040i | ||||||
\(25\) | 1.55140e6 | 0.794315 | ||||||||
\(26\) | −1.57071e6 | −0.674088 | ||||||||
\(27\) | 2.13423e6i | 0.772866i | ||||||||
\(28\) | 4.06017e6i | 1.24834i | ||||||||
\(29\) | 6.34953e6i | 1.66706i | 0.552476 | + | 0.833529i | \(0.313683\pi\) | ||||
−0.552476 | + | 0.833529i | \(0.686317\pi\) | |||||||
\(30\) | 447855. | 0.100947 | ||||||||
\(31\) | − | 8.52001e6i | − | 1.65696i | −0.560018 | − | 0.828480i | \(-0.689206\pi\) | ||
0.560018 | − | 0.828480i | \(-0.310794\pi\) | |||||||
\(32\) | 6.14516e6 | 1.03600 | ||||||||
\(33\) | 1.56021e6 | 0.229018 | ||||||||
\(34\) | 1.15165e6 | − | 3.91756e6i | 0.147797 | − | 0.502760i | ||||
\(35\) | −6.92899e6 | −0.780484 | ||||||||
\(36\) | −5.99140e6 | −0.594521 | ||||||||
\(37\) | − | 8.05093e6i | − | 0.706217i | −0.935582 | − | 0.353109i | \(-0.885125\pi\) | ||
0.935582 | − | 0.353109i | \(-0.114875\pi\) | |||||||
\(38\) | −9.89850e6 | −0.770093 | ||||||||
\(39\) | − | 7.89366e6i | − | 0.546371i | ||||||
\(40\) | 6.63923e6i | 0.410060i | ||||||||
\(41\) | − | 2.36819e7i | − | 1.30885i | −0.756127 | − | 0.654425i | \(-0.772911\pi\) | ||
0.756127 | − | 0.654425i | \(-0.227089\pi\) | |||||||
\(42\) | 7.72457e6 | 0.383047 | ||||||||
\(43\) | 2.89782e6 | 0.129260 | 0.0646298 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646298 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(44\) | 9.72403e6i | 0.391119i | ||||||||
\(45\) | − | 1.02248e7i | − | 0.371705i | ||||||
\(46\) | 1.50830e7i | 0.496682i | ||||||||
\(47\) | 2.63358e7 | 0.787238 | 0.393619 | − | 0.919274i | \(-0.371223\pi\) | ||||
0.393619 | + | 0.919274i | \(0.371223\pi\) | |||||||
\(48\) | 3.92995e6i | 0.106857i | ||||||||
\(49\) | −7.91572e7 | −1.96159 | ||||||||
\(50\) | 1.83957e7 | 0.416248 | ||||||||
\(51\) | 1.96878e7 | + | 5.78766e6i | 0.407504 | + | 0.119795i | ||||
\(52\) | 4.91975e7 | 0.933099 | ||||||||
\(53\) | 2.45299e6 | 0.0427027 | 0.0213513 | − | 0.999772i | \(-0.493203\pi\) | ||||
0.0213513 | + | 0.999772i | \(0.493203\pi\) | |||||||
\(54\) | 2.53067e7i | 0.405008i | ||||||||
\(55\) | −1.65948e7 | −0.244534 | ||||||||
\(56\) | 1.14513e8i | 1.55600i | ||||||||
\(57\) | − | 4.97452e7i | − | 0.624186i | ||||||
\(58\) | 7.52898e7i | 0.873595i | ||||||||
\(59\) | −8.84531e6 | −0.0950340 | −0.0475170 | − | 0.998870i | \(-0.515131\pi\) | ||||
−0.0475170 | + | 0.998870i | \(0.515131\pi\) | |||||||
\(60\) | −1.40276e7 | −0.139734 | ||||||||
\(61\) | 6.18808e7i | 0.572231i | 0.958195 | + | 0.286116i | \(0.0923642\pi\) | ||||
−0.958195 | + | 0.286116i | \(0.907636\pi\) | |||||||
\(62\) | − | 1.01026e8i | − | 0.868304i | ||||||
\(63\) | − | 1.76356e8i | − | 1.41045i | ||||||
\(64\) | 3.91004e7 | 0.291320 | ||||||||
\(65\) | 8.39593e7i | 0.583389i | ||||||||
\(66\) | 1.85002e7 | 0.120013 | ||||||||
\(67\) | 1.46096e8 | 0.885730 | 0.442865 | − | 0.896588i | \(-0.353962\pi\) | ||||
0.442865 | + | 0.896588i | \(0.353962\pi\) | |||||||
\(68\) | −3.60718e7 | + | 1.22705e8i | −0.204587 | + | 0.695940i | ||||
\(69\) | −7.58002e7 | −0.402577 | ||||||||
\(70\) | −8.21608e7 | −0.409000 | ||||||||
\(71\) | − | 2.08285e8i | − | 0.972737i | −0.873754 | − | 0.486369i | \(-0.838321\pi\) | ||
0.873754 | − | 0.486369i | \(-0.161679\pi\) | |||||||
\(72\) | −1.68981e8 | −0.741042 | ||||||||
\(73\) | − | 7.44027e7i | − | 0.306645i | −0.988176 | − | 0.153323i | \(-0.951003\pi\) | ||
0.988176 | − | 0.153323i | \(-0.0489974\pi\) | |||||||
\(74\) | − | 9.54641e7i | − | 0.370082i | ||||||
\(75\) | 9.24483e7i | 0.337383i | ||||||||
\(76\) | 3.10038e8 | 1.06599 | ||||||||
\(77\) | −2.86226e8 | −0.927899 | ||||||||
\(78\) | − | 9.35993e7i | − | 0.286317i | ||||||
\(79\) | − | 1.47713e8i | − | 0.426676i | −0.976978 | − | 0.213338i | \(-0.931566\pi\) | ||
0.976978 | − | 0.213338i | \(-0.0684335\pi\) | |||||||
\(80\) | − | 4.18001e7i | − | 0.114097i | ||||||
\(81\) | 1.90346e8 | 0.491317 | ||||||||
\(82\) | − | 2.80809e8i | − | 0.685882i | ||||||
\(83\) | −5.69010e7 | −0.131604 | −0.0658019 | − | 0.997833i | \(-0.520961\pi\) | ||||
−0.0658019 | + | 0.997833i | \(0.520961\pi\) | |||||||
\(84\) | −2.41947e8 | −0.530229 | ||||||||
\(85\) | −2.09405e8 | − | 6.15593e7i | −0.435114 | − | 0.127911i | ||||
\(86\) | 3.43609e7 | 0.0677364 | ||||||||
\(87\) | −3.78371e8 | −0.708078 | ||||||||
\(88\) | 2.74256e8i | 0.487511i | ||||||||
\(89\) | 1.03356e9 | 1.74614 | 0.873071 | − | 0.487592i | \(-0.162125\pi\) | ||||
0.873071 | + | 0.487592i | \(0.162125\pi\) | |||||||
\(90\) | − | 1.21241e8i | − | 0.194786i | ||||||
\(91\) | 1.44812e9i | 2.21370i | ||||||||
\(92\) | − | 4.72427e8i | − | 0.687527i | ||||||
\(93\) | 5.07710e8 | 0.703789 | ||||||||
\(94\) | 3.12277e8 | 0.412539 | ||||||||
\(95\) | 5.29104e8i | 0.666477i | ||||||||
\(96\) | 3.66193e8i | 0.440037i | ||||||||
\(97\) | 1.03075e9i | 1.18217i | 0.806609 | + | 0.591086i | \(0.201301\pi\) | ||||
−0.806609 | + | 0.591086i | \(0.798699\pi\) | |||||||
\(98\) | −9.38609e8 | −1.02794 | ||||||||
\(99\) | − | 4.22370e8i | − | 0.441911i | ||||||
\(100\) | −5.76187e8 | −0.576187 | ||||||||
\(101\) | −4.52386e8 | −0.432576 | −0.216288 | − | 0.976330i | \(-0.569395\pi\) | ||||
−0.216288 | + | 0.976330i | \(0.569395\pi\) | |||||||
\(102\) | 2.33449e8 | + | 6.86274e7i | 0.213546 | + | 0.0627765i | ||||
\(103\) | −2.13433e8 | −0.186850 | −0.0934250 | − | 0.995626i | \(-0.529782\pi\) | ||||
−0.0934250 | + | 0.995626i | \(0.529782\pi\) | |||||||
\(104\) | 1.38756e9 | 1.16306 | ||||||||
\(105\) | − | 4.12901e8i | − | 0.331508i | ||||||
\(106\) | 2.90865e7 | 0.0223776 | ||||||||
\(107\) | − | 1.25133e9i | − | 0.922881i | −0.887171 | − | 0.461440i | \(-0.847333\pi\) | ||
0.887171 | − | 0.461440i | \(-0.152667\pi\) | |||||||
\(108\) | − | 7.92650e8i | − | 0.560628i | ||||||
\(109\) | 9.41035e8i | 0.638538i | 0.947664 | + | 0.319269i | \(0.103437\pi\) | ||||
−0.947664 | + | 0.319269i | \(0.896563\pi\) | |||||||
\(110\) | −1.96773e8 | −0.128144 | ||||||||
\(111\) | 4.79758e8 | 0.299964 | ||||||||
\(112\) | − | 7.20965e8i | − | 0.432946i | ||||||
\(113\) | − | 7.72792e7i | − | 0.0445871i | −0.999751 | − | 0.0222936i | \(-0.992903\pi\) | ||
0.999751 | − | 0.0222936i | \(-0.00709685\pi\) | |||||||
\(114\) | − | 5.89855e8i | − | 0.327095i | ||||||
\(115\) | 8.06233e8 | 0.429854 | ||||||||
\(116\) | − | 2.35821e9i | − | 1.20926i | ||||||
\(117\) | −2.13693e9 | −1.05427 | ||||||||
\(118\) | −1.04884e8 | −0.0498010 | ||||||||
\(119\) | −3.61181e9 | − | 1.06177e9i | −1.65106 | − | 0.485366i | ||||
\(120\) | −3.95634e8 | −0.174172 | ||||||||
\(121\) | 1.67244e9 | 0.709279 | ||||||||
\(122\) | 7.33754e8i | 0.299869i | ||||||||
\(123\) | 1.41122e9 | 0.555930 | ||||||||
\(124\) | 3.16432e9i | 1.20194i | ||||||||
\(125\) | − | 2.22124e9i | − | 0.813767i | ||||||
\(126\) | − | 2.09115e9i | − | 0.739126i | ||||||
\(127\) | 3.54892e9 | 1.21054 | 0.605271 | − | 0.796020i | \(-0.293065\pi\) | ||||
0.605271 | + | 0.796020i | \(0.293065\pi\) | |||||||
\(128\) | −2.68269e9 | −0.883335 | ||||||||
\(129\) | 1.72682e8i | 0.0549026i | ||||||||
\(130\) | 9.95550e8i | 0.305716i | ||||||||
\(131\) | − | 2.85977e9i | − | 0.848419i | −0.905564 | − | 0.424209i | \(-0.860552\pi\) | ||
0.905564 | − | 0.424209i | \(-0.139448\pi\) | |||||||
\(132\) | −5.79459e8 | −0.166127 | ||||||||
\(133\) | 9.12596e9i | 2.52898i | ||||||||
\(134\) | 1.73234e9 | 0.464153 | ||||||||
\(135\) | 1.35272e9 | 0.350514 | ||||||||
\(136\) | −1.01737e9 | + | 3.46077e9i | −0.255008 | + | 0.867456i | ||||
\(137\) | −1.35821e8 | −0.0329400 | −0.0164700 | − | 0.999864i | \(-0.505243\pi\) | ||||
−0.0164700 | + | 0.999864i | \(0.505243\pi\) | |||||||
\(138\) | −8.98803e8 | −0.210964 | ||||||||
\(139\) | − | 4.19737e8i | − | 0.0953698i | −0.998862 | − | 0.0476849i | \(-0.984816\pi\) | ||
0.998862 | − | 0.0476849i | \(-0.0151843\pi\) | |||||||
\(140\) | 2.57342e9 | 0.566154 | ||||||||
\(141\) | 1.56936e9i | 0.334377i | ||||||||
\(142\) | − | 2.46975e9i | − | 0.509747i | ||||||
\(143\) | 3.46823e9i | 0.693578i | ||||||||
\(144\) | 1.06389e9 | 0.206190 | ||||||||
\(145\) | 4.02447e9 | 0.756053 | ||||||||
\(146\) | − | 8.82233e8i | − | 0.160692i | ||||||
\(147\) | − | 4.71701e9i | − | 0.833179i | ||||||
\(148\) | 2.99011e9i | 0.512282i | ||||||||
\(149\) | −8.05680e9 | −1.33913 | −0.669567 | − | 0.742751i | \(-0.733520\pi\) | ||||
−0.669567 | + | 0.742751i | \(0.733520\pi\) | |||||||
\(150\) | 1.09621e9i | 0.176800i | ||||||||
\(151\) | −5.71660e9 | −0.894832 | −0.447416 | − | 0.894326i | \(-0.647656\pi\) | ||||
−0.447416 | + | 0.894326i | \(0.647656\pi\) | |||||||
\(152\) | 8.74432e9 | 1.32871 | ||||||||
\(153\) | 1.56681e9 | − | 5.32978e9i | 0.231155 | − | 0.786317i | ||||
\(154\) | −3.39394e9 | −0.486251 | ||||||||
\(155\) | −5.40016e9 | −0.751474 | ||||||||
\(156\) | 2.93170e9i | 0.396331i | ||||||||
\(157\) | −3.73112e9 | −0.490107 | −0.245053 | − | 0.969510i | \(-0.578806\pi\) | ||||
−0.245053 | + | 0.969510i | \(0.578806\pi\) | |||||||
\(158\) | − | 1.75152e9i | − | 0.223593i | ||||||
\(159\) | 1.46175e8i | 0.0181378i | ||||||||
\(160\) | − | 3.89493e9i | − | 0.469851i | ||||||
\(161\) | 1.39059e10 | 1.63110 | ||||||||
\(162\) | 2.25704e9 | 0.257467 | ||||||||
\(163\) | − | 3.76537e9i | − | 0.417795i | −0.977938 | − | 0.208898i | \(-0.933012\pi\) | ||
0.977938 | − | 0.208898i | \(-0.0669876\pi\) | |||||||
\(164\) | 8.79544e9i | 0.949425i | ||||||||
\(165\) | − | 9.88891e8i | − | 0.103865i | ||||||
\(166\) | −6.74705e8 | −0.0689648 | ||||||||
\(167\) | − | 7.70007e9i | − | 0.766074i | −0.923733 | − | 0.383037i | \(-0.874878\pi\) | ||
0.923733 | − | 0.383037i | \(-0.125122\pi\) | |||||||
\(168\) | −6.82387e9 | −0.660905 | ||||||||
\(169\) | 6.94255e9 | 0.654680 | ||||||||
\(170\) | −2.48303e9 | − | 7.29942e8i | −0.228014 | − | 0.0670298i | ||||
\(171\) | −1.34667e10 | −1.20443 | ||||||||
\(172\) | −1.07625e9 | −0.0937634 | ||||||||
\(173\) | − | 5.96147e9i | − | 0.505995i | −0.967467 | − | 0.252997i | \(-0.918584\pi\) | ||
0.967467 | − | 0.252997i | \(-0.0814164\pi\) | |||||||
\(174\) | −4.48655e9 | −0.371057 | ||||||||
\(175\) | − | 1.69600e10i | − | 1.36696i | ||||||
\(176\) | − | 1.72670e9i | − | 0.135647i | ||||||
\(177\) | − | 5.27095e8i | − | 0.0403654i | ||||||
\(178\) | 1.22554e10 | 0.915038 | ||||||||
\(179\) | 4.90200e9 | 0.356890 | 0.178445 | − | 0.983950i | \(-0.442893\pi\) | ||||
0.178445 | + | 0.983950i | \(0.442893\pi\) | |||||||
\(180\) | 3.79748e9i | 0.269630i | ||||||||
\(181\) | 6.71648e9i | 0.465144i | 0.972579 | + | 0.232572i | \(0.0747142\pi\) | ||||
−0.972579 | + | 0.232572i | \(0.925286\pi\) | |||||||
\(182\) | 1.71712e10i | 1.16006i | ||||||||
\(183\) | −3.68750e9 | −0.243054 | ||||||||
\(184\) | − | 1.33243e10i | − | 0.856969i | ||||||
\(185\) | −5.10285e9 | −0.320287 | ||||||||
\(186\) | 6.02019e9 | 0.368810 | ||||||||
\(187\) | −8.65022e9 | − | 2.54292e9i | −0.517297 | − | 0.152071i | ||||
\(188\) | −9.78108e9 | −0.571053 | ||||||||
\(189\) | 2.33316e10 | 1.33005 | ||||||||
\(190\) | 6.27387e9i | 0.349257i | ||||||||
\(191\) | −1.84682e10 | −1.00409 | −0.502046 | − | 0.864841i | \(-0.667419\pi\) | ||||
−0.502046 | + | 0.864841i | \(0.667419\pi\) | |||||||
\(192\) | 2.33001e9i | 0.123738i | ||||||||
\(193\) | 3.37714e10i | 1.75203i | 0.482287 | + | 0.876013i | \(0.339806\pi\) | ||||
−0.482287 | + | 0.876013i | \(0.660194\pi\) | |||||||
\(194\) | 1.22222e10i | 0.619498i | ||||||||
\(195\) | −5.00316e9 | −0.247793 | ||||||||
\(196\) | 2.93989e10 | 1.42291 | ||||||||
\(197\) | 6.25236e9i | 0.295765i | 0.989005 | + | 0.147882i | \(0.0472457\pi\) | ||||
−0.989005 | + | 0.147882i | \(0.952754\pi\) | |||||||
\(198\) | − | 5.00827e9i | − | 0.231576i | ||||||
\(199\) | − | 1.46173e10i | − | 0.660735i | −0.943852 | − | 0.330368i | \(-0.892827\pi\) | ||
0.943852 | − | 0.330368i | \(-0.107173\pi\) | |||||||
\(200\) | −1.62508e10 | −0.718189 | ||||||||
\(201\) | 8.70591e9i | 0.376211i | ||||||||
\(202\) | −5.36418e9 | −0.226685 | ||||||||
\(203\) | 6.94137e10 | 2.86889 | ||||||||
\(204\) | −7.31203e9 | − | 2.14953e9i | −0.295599 | − | 0.0868977i | ||||
\(205\) | −1.50101e10 | −0.593597 | ||||||||
\(206\) | −2.53078e9 | −0.0979157 | ||||||||
\(207\) | 2.05202e10i | 0.776811i | ||||||||
\(208\) | −8.73600e9 | −0.323614 | ||||||||
\(209\) | 2.18565e10i | 0.792359i | ||||||||
\(210\) | − | 4.89599e9i | − | 0.173722i | ||||||
\(211\) | − | 2.69240e10i | − | 0.935122i | −0.883961 | − | 0.467561i | \(-0.845133\pi\) | ||
0.883961 | − | 0.467561i | \(-0.154867\pi\) | |||||||
\(212\) | −9.11039e8 | −0.0309760 | ||||||||
\(213\) | 1.24118e10 | 0.413167 | ||||||||
\(214\) | − | 1.48377e10i | − | 0.483621i | ||||||
\(215\) | − | 1.83670e9i | − | 0.0586225i | ||||||
\(216\) | − | 2.23559e10i | − | 0.698796i | ||||||
\(217\) | −9.31416e10 | −2.85151 | ||||||||
\(218\) | 1.11584e10i | 0.334616i | ||||||||
\(219\) | 4.43369e9 | 0.130247 | ||||||||
\(220\) | 6.16329e9 | 0.177382 | ||||||||
\(221\) | −1.28656e10 | + | 4.37646e10i | −0.362797 | + | 1.23412i | ||||
\(222\) | 5.68874e9 | 0.157191 | ||||||||
\(223\) | 1.09042e10 | 0.295273 | 0.147636 | − | 0.989042i | \(-0.452834\pi\) | ||||
0.147636 | + | 0.989042i | \(0.452834\pi\) | |||||||
\(224\) | − | 6.71795e10i | − | 1.78287i | ||||||
\(225\) | 2.50271e10 | 0.651012 | ||||||||
\(226\) | − | 9.16341e8i | − | 0.0233652i | ||||||
\(227\) | − | 5.73714e10i | − | 1.43410i | −0.697022 | − | 0.717050i | \(-0.745492\pi\) | ||
0.697022 | − | 0.717050i | \(-0.254508\pi\) | |||||||
\(228\) | 1.84753e10i | 0.452777i | ||||||||
\(229\) | 4.85190e10 | 1.16587 | 0.582937 | − | 0.812517i | \(-0.301903\pi\) | ||||
0.582937 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(230\) | 9.55994e9 | 0.225258 | ||||||||
\(231\) | − | 1.70563e10i | − | 0.394123i | ||||||
\(232\) | − | 6.65109e10i | − | 1.50729i | ||||||
\(233\) | 1.92873e9i | 0.0428717i | 0.999770 | + | 0.0214358i | \(0.00682376\pi\) | ||||
−0.999770 | + | 0.0214358i | \(0.993176\pi\) | |||||||
\(234\) | −2.53387e10 | −0.552475 | ||||||||
\(235\) | − | 1.66922e10i | − | 0.357032i | ||||||
\(236\) | 3.28514e9 | 0.0689366 | ||||||||
\(237\) | 8.80230e9 | 0.181229 | ||||||||
\(238\) | −4.28272e10 | − | 1.25900e10i | −0.865213 | − | 0.254348i | ||||
\(239\) | −9.39248e10 | −1.86204 | −0.931021 | − | 0.364965i | \(-0.881081\pi\) | ||||
−0.931021 | + | 0.364965i | \(0.881081\pi\) | |||||||
\(240\) | 2.49088e9 | 0.0484622 | ||||||||
\(241\) | 4.52039e10i | 0.863175i | 0.902071 | + | 0.431588i | \(0.142046\pi\) | ||||
−0.902071 | + | 0.431588i | \(0.857954\pi\) | |||||||
\(242\) | 1.98310e10 | 0.371686 | ||||||||
\(243\) | 5.33508e10i | 0.981551i | ||||||||
\(244\) | − | 2.29825e10i | − | 0.415090i | ||||||
\(245\) | 5.01715e10i | 0.889630i | ||||||||
\(246\) | 1.67335e10 | 0.291326 | ||||||||
\(247\) | 1.10580e11 | 1.89034 | ||||||||
\(248\) | 8.92465e10i | 1.49816i | ||||||||
\(249\) | − | 3.39075e9i | − | 0.0558983i | ||||||
\(250\) | − | 2.63384e10i | − | 0.426442i | ||||||
\(251\) | −4.87193e10 | −0.774763 | −0.387382 | − | 0.921919i | \(-0.626620\pi\) | ||||
−0.387382 | + | 0.921919i | \(0.626620\pi\) | |||||||
\(252\) | 6.54986e10i | 1.02313i | ||||||||
\(253\) | 3.33043e10 | 0.511043 | ||||||||
\(254\) | 4.20814e10 | 0.634365 | ||||||||
\(255\) | 3.66834e9 | − | 1.24785e10i | 0.0543299 | − | 0.184813i | ||||
\(256\) | −5.18295e10 | −0.754218 | ||||||||
\(257\) | 8.25999e10 | 1.18108 | 0.590542 | − | 0.807007i | \(-0.298914\pi\) | ||||
0.590542 | + | 0.807007i | \(0.298914\pi\) | |||||||
\(258\) | 2.04758e9i | 0.0287708i | ||||||||
\(259\) | −8.80135e10 | −1.21535 | ||||||||
\(260\) | − | 3.11824e10i | − | 0.423184i | ||||||
\(261\) | 1.02431e11i | 1.36630i | ||||||||
\(262\) | − | 3.39098e10i | − | 0.444600i | ||||||
\(263\) | 3.46665e10 | 0.446795 | 0.223398 | − | 0.974727i | \(-0.428285\pi\) | ||||
0.223398 | + | 0.974727i | \(0.428285\pi\) | |||||||
\(264\) | −1.63430e10 | −0.207069 | ||||||||
\(265\) | − | 1.55476e9i | − | 0.0193667i | ||||||
\(266\) | 1.08211e11i | 1.32527i | ||||||||
\(267\) | 6.15901e10i | 0.741669i | ||||||||
\(268\) | −5.42599e10 | −0.642499 | ||||||||
\(269\) | − | 1.26130e11i | − | 1.46871i | −0.678768 | − | 0.734353i | \(-0.737486\pi\) | ||
0.678768 | − | 0.734353i | \(-0.262514\pi\) | |||||||
\(270\) | 1.60399e10 | 0.183681 | ||||||||
\(271\) | 5.63928e10 | 0.635129 | 0.317564 | − | 0.948237i | \(-0.397135\pi\) | ||||
0.317564 | + | 0.948237i | \(0.397135\pi\) | |||||||
\(272\) | 6.40528e9 | − | 2.17887e10i | 0.0709542 | − | 0.241364i | ||||
\(273\) | −8.62942e10 | −0.940264 | ||||||||
\(274\) | −1.61050e9 | −0.0172617 | ||||||||
\(275\) | − | 4.06189e10i | − | 0.428283i | ||||||
\(276\) | 2.81521e10 | 0.292025 | ||||||||
\(277\) | − | 4.76405e10i | − | 0.486203i | −0.970001 | − | 0.243102i | \(-0.921835\pi\) | ||
0.970001 | − | 0.243102i | \(-0.0781648\pi\) | |||||||
\(278\) | − | 4.97705e9i | − | 0.0499770i | ||||||
\(279\) | − | 1.37445e11i | − | 1.35803i | ||||||
\(280\) | 7.25807e10 | 0.705684 | ||||||||
\(281\) | 1.14333e11 | 1.09394 | 0.546969 | − | 0.837153i | \(-0.315782\pi\) | ||||
0.546969 | + | 0.837153i | \(0.315782\pi\) | |||||||
\(282\) | 1.86087e10i | 0.175225i | ||||||||
\(283\) | − | 2.54590e10i | − | 0.235941i | −0.993017 | − | 0.117970i | \(-0.962361\pi\) | ||
0.993017 | − | 0.117970i | \(-0.0376388\pi\) | |||||||
\(284\) | 7.73568e10i | 0.705612i | ||||||||
\(285\) | −3.15295e10 | −0.283084 | ||||||||
\(286\) | 4.11246e10i | 0.363459i | ||||||||
\(287\) | −2.58893e11 | −2.25243 | ||||||||
\(288\) | 9.91337e10 | 0.849093 | ||||||||
\(289\) | −9.97217e10 | − | 6.41769e10i | −0.840910 | − | 0.541176i | ||||
\(290\) | 4.77202e10 | 0.396197 | ||||||||
\(291\) | −6.14228e10 | −0.502124 | ||||||||
\(292\) | 2.76331e10i | 0.222437i | ||||||||
\(293\) | 4.43928e10 | 0.351891 | 0.175946 | − | 0.984400i | \(-0.443702\pi\) | ||||
0.175946 | + | 0.984400i | \(0.443702\pi\) | |||||||
\(294\) | − | 5.59321e10i | − | 0.436614i | ||||||
\(295\) | 5.60634e9i | 0.0431003i | ||||||||
\(296\) | 8.43329e10i | 0.638535i | ||||||||
\(297\) | 5.58787e10 | 0.416718 | ||||||||
\(298\) | −9.55337e10 | −0.701752 | ||||||||
\(299\) | − | 1.68499e11i | − | 1.21920i | ||||||
\(300\) | − | 3.43352e10i | − | 0.244734i | ||||||
\(301\) | − | 3.16792e10i | − | 0.222446i | ||||||
\(302\) | −6.77848e10 | −0.468922 | ||||||||
\(303\) | − | 2.69578e10i | − | 0.183735i | ||||||
\(304\) | −5.50536e10 | −0.369704 | ||||||||
\(305\) | 3.92213e10 | 0.259521 | ||||||||
\(306\) | 1.85784e10 | − | 6.31980e10i | 0.121133 | − | 0.412057i | ||||
\(307\) | 1.77005e11 | 1.13727 | 0.568635 | − | 0.822590i | \(-0.307472\pi\) | ||||
0.568635 | + | 0.822590i | \(0.307472\pi\) | |||||||
\(308\) | 1.06304e11 | 0.673088 | ||||||||
\(309\) | − | 1.27185e10i | − | 0.0793640i | ||||||
\(310\) | −6.40326e10 | −0.393798 | ||||||||
\(311\) | − | 1.16929e11i | − | 0.708764i | −0.935101 | − | 0.354382i | \(-0.884691\pi\) | ||
0.935101 | − | 0.354382i | \(-0.115309\pi\) | |||||||
\(312\) | 8.26855e10i | 0.494008i | ||||||||
\(313\) | 6.60894e10i | 0.389208i | 0.980882 | + | 0.194604i | \(0.0623422\pi\) | ||||
−0.980882 | + | 0.194604i | \(0.937658\pi\) | |||||||
\(314\) | −4.42419e10 | −0.256833 | ||||||||
\(315\) | −1.11778e11 | −0.639677 | ||||||||
\(316\) | 5.48606e10i | 0.309506i | ||||||||
\(317\) | 2.15865e11i | 1.20065i | 0.799757 | + | 0.600324i | \(0.204962\pi\) | ||||
−0.799757 | + | 0.600324i | \(0.795038\pi\) | |||||||
\(318\) | 1.73327e9i | 0.00950484i | ||||||||
\(319\) | 1.66245e11 | 0.898854 | ||||||||
\(320\) | − | 2.47826e10i | − | 0.132121i | ||||||
\(321\) | 7.45674e10 | 0.391991 | ||||||||
\(322\) | 1.64889e11 | 0.854753 | ||||||||
\(323\) | −8.10778e10 | + | 2.75801e11i | −0.414468 | + | 1.40989i | ||||
\(324\) | −7.06945e10 | −0.356396 | ||||||||
\(325\) | −2.05506e11 | −1.02176 | ||||||||
\(326\) | − | 4.46480e10i | − | 0.218939i | ||||||
\(327\) | −5.60767e10 | −0.271217 | ||||||||
\(328\) | 2.48067e11i | 1.18341i | ||||||||
\(329\) | − | 2.87905e11i | − | 1.35478i | ||||||
\(330\) | − | 1.17258e10i | − | 0.0544289i | ||||||
\(331\) | 2.19673e11 | 1.00589 | 0.502946 | − | 0.864318i | \(-0.332249\pi\) | ||||
0.502946 | + | 0.864318i | \(0.332249\pi\) | |||||||
\(332\) | 2.11330e10 | 0.0954639 | ||||||||
\(333\) | − | 1.29877e11i | − | 0.578808i | ||||||
\(334\) | − | 9.13039e10i | − | 0.401449i | ||||||
\(335\) | − | 9.25987e10i | − | 0.401701i | ||||||
\(336\) | 4.29626e10 | 0.183892 | ||||||||
\(337\) | 3.65398e11i | 1.54323i | 0.636088 | + | 0.771617i | \(0.280552\pi\) | ||||
−0.636088 | + | 0.771617i | \(0.719448\pi\) | |||||||
\(338\) | 8.23215e10 | 0.343074 | ||||||||
\(339\) | 4.60510e9 | 0.0189383 | ||||||||
\(340\) | 7.77730e10 | + | 2.28631e10i | 0.315626 | + | 0.0927853i | ||||
\(341\) | −2.23072e11 | −0.893410 | ||||||||
\(342\) | −1.59682e11 | −0.631160 | ||||||||
\(343\) | 4.24205e11i | 1.65482i | ||||||||
\(344\) | −3.03544e10 | −0.116872 | ||||||||
\(345\) | 4.80438e10i | 0.182579i | ||||||||
\(346\) | − | 7.06883e10i | − | 0.265158i | ||||||
\(347\) | 3.18226e11i | 1.17829i | 0.808026 | + | 0.589147i | \(0.200536\pi\) | ||||
−0.808026 | + | 0.589147i | \(0.799464\pi\) | |||||||
\(348\) | 1.40527e11 | 0.513632 | ||||||||
\(349\) | −1.05189e11 | −0.379537 | −0.189769 | − | 0.981829i | \(-0.560774\pi\) | ||||
−0.189769 | + | 0.981829i | \(0.560774\pi\) | |||||||
\(350\) | − | 2.01104e11i | − | 0.716332i | ||||||
\(351\) | − | 2.82711e11i | − | 0.994171i | ||||||
\(352\) | − | 1.60894e11i | − | 0.558595i | ||||||
\(353\) | 2.74596e11 | 0.941258 | 0.470629 | − | 0.882331i | \(-0.344027\pi\) | ||||
0.470629 | + | 0.882331i | \(0.344027\pi\) | |||||||
\(354\) | − | 6.25005e9i | − | 0.0211529i | ||||||
\(355\) | −1.32015e11 | −0.441161 | ||||||||
\(356\) | −3.83862e11 | −1.26663 | ||||||||
\(357\) | 6.32713e10 | − | 2.15229e11i | 0.206158 | − | 0.701284i | ||||
\(358\) | 5.81256e10 | 0.187022 | ||||||||
\(359\) | 3.36158e11 | 1.06812 | 0.534058 | − | 0.845448i | \(-0.320666\pi\) | ||||
0.534058 | + | 0.845448i | \(0.320666\pi\) | |||||||
\(360\) | 1.07104e11i | 0.336081i | ||||||||
\(361\) | 3.74179e11 | 1.15957 | ||||||||
\(362\) | 7.96408e10i | 0.243751i | ||||||||
\(363\) | 9.96614e10i | 0.301264i | ||||||||
\(364\) | − | 5.37832e11i | − | 1.60579i | ||||||
\(365\) | −4.71580e10 | −0.139071 | ||||||||
\(366\) | −4.37247e10 | −0.127368 | ||||||||
\(367\) | 4.27664e11i | 1.23057i | 0.788306 | + | 0.615283i | \(0.210958\pi\) | ||||
−0.788306 | + | 0.615283i | \(0.789042\pi\) | |||||||
\(368\) | 8.38890e10i | 0.238446i | ||||||||
\(369\) | − | 3.82037e11i | − | 1.07272i | ||||||
\(370\) | −6.05072e10 | −0.167841 | ||||||||
\(371\) | − | 2.68164e10i | − | 0.0734882i | ||||||
\(372\) | −1.88563e11 | −0.510521 | ||||||||
\(373\) | −6.59774e11 | −1.76484 | −0.882420 | − | 0.470463i | \(-0.844087\pi\) | ||||
−0.882420 | + | 0.470463i | \(0.844087\pi\) | |||||||
\(374\) | −1.02570e11 | − | 3.01528e10i | −0.271081 | − | 0.0796902i | ||||
\(375\) | 1.32364e11 | 0.345645 | ||||||||
\(376\) | −2.75866e11 | −0.711790 | ||||||||
\(377\) | − | 8.41093e11i | − | 2.14441i | ||||||
\(378\) | 2.76655e11 | 0.696989 | ||||||||
\(379\) | − | 3.76630e11i | − | 0.937645i | −0.883292 | − | 0.468823i | \(-0.844678\pi\) | ||
0.883292 | − | 0.468823i | \(-0.155322\pi\) | |||||||
\(380\) | − | 1.96509e11i | − | 0.483455i | ||||||
\(381\) | 2.11482e11i | 0.514174i | ||||||||
\(382\) | −2.18987e11 | −0.526178 | ||||||||
\(383\) | −2.37194e11 | −0.563261 | −0.281630 | − | 0.959523i | \(-0.590875\pi\) | ||||
−0.281630 | + | 0.959523i | \(0.590875\pi\) | |||||||
\(384\) | − | 1.59862e11i | − | 0.375194i | ||||||
\(385\) | 1.81416e11i | 0.420826i | ||||||||
\(386\) | 4.00445e11i | 0.918121i | ||||||||
\(387\) | 4.67475e10 | 0.105940 | ||||||||
\(388\) | − | 3.82820e11i | − | 0.857534i | ||||||
\(389\) | −3.64753e10 | −0.0807656 | −0.0403828 | − | 0.999184i | \(-0.512858\pi\) | ||||
−0.0403828 | + | 0.999184i | \(0.512858\pi\) | |||||||
\(390\) | −5.93252e10 | −0.129852 | ||||||||
\(391\) | 4.20258e11 | + | 1.23544e11i | 0.909327 | + | 0.267317i | ||||
\(392\) | 8.29166e11 | 1.77359 | ||||||||
\(393\) | 1.70415e11 | 0.360363 | ||||||||
\(394\) | 7.41376e10i | 0.154991i | ||||||||
\(395\) | −9.36238e10 | −0.193508 | ||||||||
\(396\) | 1.56868e11i | 0.320557i | ||||||||
\(397\) | 5.75210e11i | 1.16217i | 0.813844 | + | 0.581084i | \(0.197371\pi\) | ||||
−0.813844 | + | 0.581084i | \(0.802629\pi\) | |||||||
\(398\) | − | 1.73325e11i | − | 0.346248i | ||||||
\(399\) | −5.43819e11 | −1.07418 | ||||||||
\(400\) | 1.02314e11 | 0.199831 | ||||||||
\(401\) | 3.39949e11i | 0.656545i | 0.944583 | + | 0.328273i | \(0.106466\pi\) | ||||
−0.944583 | + | 0.328273i | \(0.893534\pi\) | |||||||
\(402\) | 1.03231e11i | 0.197148i | ||||||||
\(403\) | 1.12860e12i | 2.13142i | ||||||||
\(404\) | 1.68015e11 | 0.313786 | ||||||||
\(405\) | − | 1.20646e11i | − | 0.222825i | ||||||
\(406\) | 8.23076e11 | 1.50339 | ||||||||
\(407\) | −2.10791e11 | −0.380782 | ||||||||
\(408\) | −2.06229e11 | − | 6.06254e10i | −0.368449 | − | 0.108314i | ||||
\(409\) | −1.12478e11 | −0.198752 | −0.0993760 | − | 0.995050i | \(-0.531685\pi\) | ||||
−0.0993760 | + | 0.995050i | \(0.531685\pi\) | |||||||
\(410\) | −1.77983e11 | −0.311065 | ||||||||
\(411\) | − | 8.09362e9i | − | 0.0139912i | ||||||
\(412\) | 7.92686e10 | 0.135539 | ||||||||
\(413\) | 9.66978e10i | 0.163547i | ||||||||
\(414\) | 2.43319e11i | 0.407075i | ||||||||
\(415\) | 3.60650e10i | 0.0596857i | ||||||||
\(416\) | −8.14021e11 | −1.33265 | ||||||||
\(417\) | 2.50123e10 | 0.0405081 | ||||||||
\(418\) | 2.59164e11i | 0.415223i | ||||||||
\(419\) | − | 2.86731e10i | − | 0.0454477i | −0.999742 | − | 0.0227239i | \(-0.992766\pi\) | ||
0.999742 | − | 0.0227239i | \(-0.00723385\pi\) | |||||||
\(420\) | 1.53351e11i | 0.240472i | ||||||||
\(421\) | 7.41818e11 | 1.15087 | 0.575437 | − | 0.817846i | \(-0.304832\pi\) | ||||
0.575437 | + | 0.817846i | \(0.304832\pi\) | |||||||
\(422\) | − | 3.19252e11i | − | 0.490036i | ||||||
\(423\) | 4.24849e11 | 0.645212 | ||||||||
\(424\) | −2.56949e10 | −0.0386101 | ||||||||
\(425\) | 1.50678e11 | − | 5.12559e11i | 0.224027 | − | 0.762068i | ||||
\(426\) | 1.47173e11 | 0.216514 | ||||||||
\(427\) | 6.76487e11 | 0.984768 | ||||||||
\(428\) | 4.64743e11i | 0.669447i | ||||||||
\(429\) | −2.06673e11 | −0.294595 | ||||||||
\(430\) | − | 2.17787e10i | − | 0.0307202i | ||||||
\(431\) | 9.85196e10i | 0.137523i | 0.997633 | + | 0.0687614i | \(0.0219047\pi\) | ||||
−0.997633 | + | 0.0687614i | \(0.978095\pi\) | |||||||
\(432\) | 1.40751e11i | 0.194435i | ||||||||
\(433\) | −6.29756e11 | −0.860948 | −0.430474 | − | 0.902603i | \(-0.641654\pi\) | ||||
−0.430474 | + | 0.902603i | \(0.641654\pi\) | |||||||
\(434\) | −1.10443e12 | −1.49429 | ||||||||
\(435\) | 2.39819e11i | 0.321131i | ||||||||
\(436\) | − | 3.49500e11i | − | 0.463188i | ||||||
\(437\) | − | 1.06186e12i | − | 1.39284i | ||||||
\(438\) | 5.25726e10 | 0.0682537 | ||||||||
\(439\) | − | 3.19248e10i | − | 0.0410240i | −0.999790 | − | 0.0205120i | \(-0.993470\pi\) | ||
0.999790 | − | 0.0205120i | \(-0.00652962\pi\) | |||||||
\(440\) | 1.73829e11 | 0.221099 | ||||||||
\(441\) | −1.27696e12 | −1.60770 | ||||||||
\(442\) | −1.52554e11 | + | 5.18941e11i | −0.190118 | + | 0.646722i | ||||
\(443\) | 9.76504e11 | 1.20464 | 0.602320 | − | 0.798255i | \(-0.294243\pi\) | ||||
0.602320 | + | 0.798255i | \(0.294243\pi\) | |||||||
\(444\) | −1.78182e11 | −0.217590 | ||||||||
\(445\) | − | 6.55091e11i | − | 0.791920i | ||||||
\(446\) | 1.29297e11 | 0.154733 | ||||||||
\(447\) | − | 4.80108e11i | − | 0.568794i | ||||||
\(448\) | − | 4.27449e11i | − | 0.501341i | ||||||
\(449\) | − | 3.18417e11i | − | 0.369733i | −0.982764 | − | 0.184867i | \(-0.940815\pi\) | ||
0.982764 | − | 0.184867i | \(-0.0591853\pi\) | |||||||
\(450\) | 2.96760e11 | 0.341153 | ||||||||
\(451\) | −6.20044e11 | −0.705713 | ||||||||
\(452\) | 2.87014e10i | 0.0323430i | ||||||||
\(453\) | − | 3.40654e11i | − | 0.380077i | ||||||
\(454\) | − | 6.80284e11i | − | 0.751517i | ||||||
\(455\) | 9.17851e11 | 1.00397 | ||||||||
\(456\) | 5.21077e11i | 0.564365i | ||||||||
\(457\) | 5.17641e11 | 0.555144 | 0.277572 | − | 0.960705i | \(-0.410470\pi\) | ||||
0.277572 | + | 0.960705i | \(0.410470\pi\) | |||||||
\(458\) | 5.75315e11 | 0.610958 | ||||||||
\(459\) | 7.05119e11 | + | 2.07285e11i | 0.741490 | + | 0.217977i | ||||
\(460\) | −2.99434e11 | −0.311811 | ||||||||
\(461\) | −1.03511e12 | −1.06741 | −0.533704 | − | 0.845671i | \(-0.679200\pi\) | ||||
−0.533704 | + | 0.845671i | \(0.679200\pi\) | |||||||
\(462\) | − | 2.02246e11i | − | 0.206534i | ||||||
\(463\) | −4.59441e11 | −0.464638 | −0.232319 | − | 0.972640i | \(-0.574631\pi\) | ||||
−0.232319 | + | 0.972640i | \(0.574631\pi\) | |||||||
\(464\) | 4.18748e11i | 0.419393i | ||||||||
\(465\) | − | 3.21797e11i | − | 0.319186i | ||||||
\(466\) | 2.28700e10i | 0.0224662i | ||||||||
\(467\) | −1.31601e12 | −1.28036 | −0.640182 | − | 0.768223i | \(-0.721141\pi\) | ||||
−0.640182 | + | 0.768223i | \(0.721141\pi\) | |||||||
\(468\) | 7.93653e11 | 0.764758 | ||||||||
\(469\) | − | 1.59714e12i | − | 1.52428i | ||||||
\(470\) | − | 1.97928e11i | − | 0.187097i | ||||||
\(471\) | − | 2.22339e11i | − | 0.208171i | ||||||
\(472\) | 9.26540e10 | 0.0859261 | ||||||||
\(473\) | − | 7.58711e10i | − | 0.0696949i | ||||||
\(474\) | 1.04374e11 | 0.0949703 | ||||||||
\(475\) | −1.29508e12 | −1.16728 | ||||||||
\(476\) | 1.34142e12 | + | 3.94340e11i | 1.19766 | + | 0.352079i | ||||
\(477\) | 3.95717e10 | 0.0349987 | ||||||||
\(478\) | −1.11372e12 | −0.975773 | ||||||||
\(479\) | 2.08121e12i | 1.80637i | 0.429251 | + | 0.903185i | \(0.358777\pi\) | ||||
−0.429251 | + | 0.903185i | \(0.641223\pi\) | |||||||
\(480\) | 2.32100e11 | 0.199568 | ||||||||
\(481\) | 1.06647e12i | 0.908438i | ||||||||
\(482\) | 5.36006e11i | 0.452333i | ||||||||
\(483\) | 8.28655e11i | 0.692806i | ||||||||
\(484\) | −6.21143e11 | −0.514503 | ||||||||
\(485\) | 6.53311e11 | 0.536145 | ||||||||
\(486\) | 6.32609e11i | 0.514366i | ||||||||
\(487\) | − | 7.18370e11i | − | 0.578719i | −0.957220 | − | 0.289360i | \(-0.906558\pi\) | ||
0.957220 | − | 0.289360i | \(-0.0934424\pi\) | |||||||
\(488\) | − | 6.48197e11i | − | 0.517390i | ||||||
\(489\) | 2.24380e11 | 0.177457 | ||||||||
\(490\) | 5.94910e11i | 0.466196i | ||||||||
\(491\) | 9.78925e11 | 0.760121 | 0.380060 | − | 0.924962i | \(-0.375903\pi\) | ||||
0.380060 | + | 0.924962i | \(0.375903\pi\) | |||||||
\(492\) | −5.24124e11 | −0.403265 | ||||||||
\(493\) | 2.09780e12 | + | 6.16693e11i | 1.59938 | + | 0.470173i | ||||
\(494\) | 1.31121e12 | 0.990604 | ||||||||
\(495\) | −2.67707e11 | −0.200418 | ||||||||
\(496\) | − | 5.61889e11i | − | 0.416853i | ||||||
\(497\) | −2.27699e12 | −1.67401 | ||||||||
\(498\) | − | 4.02059e10i | − | 0.0292926i | ||||||
\(499\) | − | 1.70045e12i | − | 1.22775i | −0.789402 | − | 0.613876i | \(-0.789609\pi\) | ||
0.789402 | − | 0.613876i | \(-0.210391\pi\) | |||||||
\(500\) | 8.24966e11i | 0.590297i | ||||||||
\(501\) | 4.58850e11 | 0.325388 | ||||||||
\(502\) | −5.77690e11 | −0.406002 | ||||||||
\(503\) | − | 1.03194e11i | − | 0.0718787i | −0.999354 | − | 0.0359393i | \(-0.988558\pi\) | ||
0.999354 | − | 0.0359393i | \(-0.0114423\pi\) | |||||||
\(504\) | 1.84732e12i | 1.27528i | ||||||||
\(505\) | 2.86731e11i | 0.196184i | ||||||||
\(506\) | 3.94906e11 | 0.267804 | ||||||||
\(507\) | 4.13709e11i | 0.278073i | ||||||||
\(508\) | −1.31807e12 | −0.878113 | ||||||||
\(509\) | 7.49118e11 | 0.494675 | 0.247338 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247338 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(510\) | 4.34975e10 | − | 1.47965e11i | 0.0284707 | − | 0.0968484i | ||||
\(511\) | −8.13378e11 | −0.527714 | ||||||||
\(512\) | 7.58967e11 | 0.488099 | ||||||||
\(513\) | − | 1.78162e12i | − | 1.13576i | ||||||
\(514\) | 9.79431e11 | 0.618928 | ||||||||
\(515\) | 1.35278e11i | 0.0847412i | ||||||||
\(516\) | − | 6.41339e10i | − | 0.0398257i | ||||||
\(517\) | − | 6.89528e11i | − | 0.424467i | ||||||
\(518\) | −1.04362e12 | −0.636883 | ||||||||
\(519\) | 3.55246e11 | 0.214920 | ||||||||
\(520\) | − | 8.79468e11i | − | 0.527479i | ||||||
\(521\) | 1.51334e12i | 0.899843i | 0.893068 | + | 0.449921i | \(0.148548\pi\) | ||||
−0.893068 | + | 0.449921i | \(0.851452\pi\) | |||||||
\(522\) | 1.21457e12i | 0.715990i | ||||||||
\(523\) | 1.87630e12 | 1.09659 | 0.548295 | − | 0.836285i | \(-0.315277\pi\) | ||||
0.548295 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(524\) | 1.06212e12i | 0.615433i | ||||||||
\(525\) | 1.01065e12 | 0.580611 | ||||||||
\(526\) | 4.11059e11 | 0.234136 | ||||||||
\(527\) | −2.81489e12 | − | 8.27498e11i | −1.58969 | − | 0.467325i | ||||
\(528\) | 1.02895e11 | 0.0576156 | ||||||||
\(529\) | 1.83116e11 | 0.101666 | ||||||||
\(530\) | − | 1.84356e10i | − | 0.0101488i | ||||||
\(531\) | −1.42692e11 | −0.0778889 | ||||||||
\(532\) | − | 3.38937e12i | − | 1.83450i | ||||||
\(533\) | 3.13703e12i | 1.68363i | ||||||||
\(534\) | 7.30307e11i | 0.388660i | ||||||||
\(535\) | −7.93121e11 | −0.418550 | ||||||||
\(536\) | −1.53034e12 | −0.800844 | ||||||||
\(537\) | 2.92112e11i | 0.151588i | ||||||||
\(538\) | − | 1.49560e12i | − | 0.769652i | ||||||
\(539\) | 2.07251e12i | 1.05766i | ||||||||
\(540\) | −5.02398e11 | −0.254259 | ||||||||
\(541\) | − | 2.51866e12i | − | 1.26410i | −0.774927 | − | 0.632050i | \(-0.782214\pi\) | ||
0.774927 | − | 0.632050i | \(-0.217786\pi\) | |||||||
\(542\) | 6.68679e11 | 0.332829 | ||||||||
\(543\) | −4.00237e11 | −0.197569 | ||||||||
\(544\) | 5.96844e11 | − | 2.03027e12i | 0.292190 | − | 0.993939i | ||||
\(545\) | 5.96448e11 | 0.289593 | ||||||||
\(546\) | −1.02324e12 | −0.492730 | ||||||||
\(547\) | 2.33711e12i | 1.11618i | 0.829779 | + | 0.558091i | \(0.188466\pi\) | ||||
−0.829779 | + | 0.558091i | \(0.811534\pi\) | |||||||
\(548\) | 5.04437e10 | 0.0238943 | ||||||||
\(549\) | 9.98260e11i | 0.468995i | ||||||||
\(550\) | − | 4.81640e11i | − | 0.224435i | ||||||
\(551\) | − | 5.30050e12i | − | 2.44982i | ||||||
\(552\) | 7.94002e11 | 0.363995 | ||||||||
\(553\) | −1.61482e12 | −0.734278 | ||||||||
\(554\) | − | 5.64899e11i | − | 0.254787i | ||||||
\(555\) | − | 3.04081e11i | − | 0.136041i | ||||||
\(556\) | 1.55890e11i | 0.0691802i | ||||||||
\(557\) | 7.35788e11 | 0.323895 | 0.161948 | − | 0.986799i | \(-0.448222\pi\) | ||||
0.161948 | + | 0.986799i | \(0.448222\pi\) | |||||||
\(558\) | − | 1.62975e12i | − | 0.711653i | ||||||
\(559\) | −3.83860e11 | −0.166272 | ||||||||
\(560\) | −4.56963e11 | −0.196352 | ||||||||
\(561\) | 1.51534e11 | − | 5.15470e11i | 0.0645916 | − | 0.219720i | ||||
\(562\) | 1.35571e12 | 0.573261 | ||||||||
\(563\) | 2.80471e12 | 1.17652 | 0.588262 | − | 0.808670i | \(-0.299812\pi\) | ||||
0.588262 | + | 0.808670i | \(0.299812\pi\) | |||||||
\(564\) | − | 5.82858e11i | − | 0.242553i | ||||||
\(565\) | −4.89812e10 | −0.0202214 | ||||||||
\(566\) | − | 3.01881e11i | − | 0.123641i | ||||||
\(567\) | − | 2.08089e12i | − | 0.845521i | ||||||
\(568\) | 2.18177e12i | 0.879512i | ||||||||
\(569\) | −7.41576e11 | −0.296586 | −0.148293 | − | 0.988943i | \(-0.547378\pi\) | ||||
−0.148293 | + | 0.988943i | \(0.547378\pi\) | |||||||
\(570\) | −3.73862e11 | −0.148346 | ||||||||
\(571\) | 2.37109e12i | 0.933440i | 0.884405 | + | 0.466720i | \(0.154564\pi\) | ||||
−0.884405 | + | 0.466720i | \(0.845436\pi\) | |||||||
\(572\) | − | 1.28810e12i | − | 0.503114i | ||||||
\(573\) | − | 1.10052e12i | − | 0.426485i | ||||||
\(574\) | −3.06984e12 | −1.18035 | ||||||||
\(575\) | 1.97341e12i | 0.752855i | ||||||||
\(576\) | 6.30767e11 | 0.238763 | ||||||||
\(577\) | 1.64213e12 | 0.616759 | 0.308380 | − | 0.951263i | \(-0.400213\pi\) | ||||
0.308380 | + | 0.951263i | \(0.400213\pi\) | |||||||
\(578\) | −1.18245e12 | − | 7.60979e11i | −0.440665 | − | 0.283594i | ||||
\(579\) | −2.01245e12 | −0.744168 | ||||||||
\(580\) | −1.49468e12 | −0.548432 | ||||||||
\(581\) | 6.22047e11i | 0.226481i | ||||||||
\(582\) | −7.28323e11 | −0.263130 | ||||||||
\(583\) | − | 6.42247e10i | − | 0.0230247i | ||||||
\(584\) | 7.79364e11i | 0.277257i | ||||||||
\(585\) | 1.35443e12i | 0.478140i | ||||||||
\(586\) | 5.26389e11 | 0.184403 | ||||||||
\(587\) | 4.40209e12 | 1.53034 | 0.765168 | − | 0.643830i | \(-0.222656\pi\) | ||||
0.765168 | + | 0.643830i | \(0.222656\pi\) | |||||||
\(588\) | 1.75189e12i | 0.604379i | ||||||||
\(589\) | 7.11238e12i | 2.43498i | ||||||||
\(590\) | 6.64774e10i | 0.0225860i | ||||||||
\(591\) | −3.72581e11 | −0.125625 | ||||||||
\(592\) | − | 5.30954e11i | − | 0.177668i | ||||||
\(593\) | −3.23487e12 | −1.07426 | −0.537132 | − | 0.843498i | \(-0.680492\pi\) | ||||
−0.537132 | + | 0.843498i | \(0.680492\pi\) | |||||||
\(594\) | 6.62584e11 | 0.218374 | ||||||||
\(595\) | −6.72972e11 | + | 2.28924e12i | −0.220126 | + | 0.748799i | ||||
\(596\) | 2.99229e12 | 0.971393 | ||||||||
\(597\) | 8.71049e11 | 0.280645 | ||||||||
\(598\) | − | 1.99798e12i | − | 0.638904i | ||||||
\(599\) | 4.90816e12 | 1.55775 | 0.778875 | − | 0.627179i | \(-0.215791\pi\) | ||||
0.778875 | + | 0.627179i | \(0.215791\pi\) | |||||||
\(600\) | − | 9.68389e11i | − | 0.305049i | ||||||
\(601\) | − | 1.05961e12i | − | 0.331292i | −0.986185 | − | 0.165646i | \(-0.947029\pi\) | ||
0.986185 | − | 0.165646i | \(-0.0529710\pi\) | |||||||
\(602\) | − | 3.75637e11i | − | 0.116569i | ||||||
\(603\) | 2.35682e12 | 0.725936 | ||||||||
\(604\) | 2.12314e12 | 0.649101 | ||||||||
\(605\) | − | 1.06003e12i | − | 0.321676i | ||||||
\(606\) | − | 3.19653e11i | − | 0.0962836i | ||||||
\(607\) | 5.76988e11i | 0.172511i | 0.996273 | + | 0.0862556i | \(0.0274902\pi\) | ||||
−0.996273 | + | 0.0862556i | \(0.972510\pi\) | |||||||
\(608\) | −5.12989e12 | −1.52245 | ||||||||
\(609\) | 4.13639e12i | 1.21855i | ||||||||
\(610\) | 4.65068e11 | 0.135998 | ||||||||
\(611\) | −3.48858e12 | −1.01266 | ||||||||
\(612\) | −5.81910e11 | + | 1.97947e12i | −0.167677 | + | 0.570385i | ||||
\(613\) | −5.09644e12 | −1.45779 | −0.728895 | − | 0.684625i | \(-0.759966\pi\) | ||||
−0.728895 | + | 0.684625i | \(0.759966\pi\) | |||||||
\(614\) | 2.09884e12 | 0.595967 | ||||||||
\(615\) | − | 8.94458e11i | − | 0.252128i | ||||||
\(616\) | 2.99820e12 | 0.838971 | ||||||||
\(617\) | 5.92498e12i | 1.64590i | 0.568113 | + | 0.822951i | \(0.307674\pi\) | ||||
−0.568113 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(618\) | − | 1.50810e11i | − | 0.0415894i | ||||||
\(619\) | 3.09980e12i | 0.848644i | 0.905511 | + | 0.424322i | \(0.139487\pi\) | ||||
−0.905511 | + | 0.424322i | \(0.860513\pi\) | |||||||
\(620\) | 2.00561e12 | 0.545110 | ||||||||
\(621\) | −2.71478e12 | −0.732526 | ||||||||
\(622\) | − | 1.38649e12i | − | 0.371417i | ||||||
\(623\) | − | 1.12990e13i | − | 3.00498i | ||||||
\(624\) | − | 5.20582e11i | − | 0.137454i | ||||||
\(625\) | 1.62220e12 | 0.425251 | ||||||||
\(626\) | 7.83657e11i | 0.203958i | ||||||||
\(627\) | −1.30244e12 | −0.336552 | ||||||||
\(628\) | 1.38573e12 | 0.355518 | ||||||||
\(629\) | −2.65991e12 | − | 7.81939e11i | −0.677547 | − | 0.199180i | ||||
\(630\) | −1.32542e12 | −0.335212 | ||||||||
\(631\) | −3.86695e11 | −0.0971040 | −0.0485520 | − | 0.998821i | \(-0.515461\pi\) | ||||
−0.0485520 | + | 0.998821i | \(0.515461\pi\) | |||||||
\(632\) | 1.54729e12i | 0.385784i | ||||||||
\(633\) | 1.60441e12 | 0.397191 | ||||||||
\(634\) | 2.55963e12i | 0.629180i | ||||||||
\(635\) | − | 2.24938e12i | − | 0.549011i | ||||||
\(636\) | − | 5.42892e10i | − | 0.0131570i | ||||||
\(637\) | 1.04856e13 | 2.52328 | ||||||||
\(638\) | 1.97125e12 | 0.471030 | ||||||||
\(639\) | − | 3.36005e12i | − | 0.797245i | ||||||
\(640\) | 1.70034e12i | 0.400615i | ||||||||
\(641\) | − | 5.83791e12i | − | 1.36583i | −0.730499 | − | 0.682914i | \(-0.760712\pi\) | ||
0.730499 | − | 0.682914i | \(-0.239288\pi\) | |||||||
\(642\) | 8.84185e11 | 0.205417 | ||||||||
\(643\) | − | 4.53130e12i | − | 1.04538i | −0.852523 | − | 0.522689i | \(-0.824929\pi\) | ||
0.852523 | − | 0.522689i | \(-0.175071\pi\) | |||||||
\(644\) | −5.16462e12 | −1.18318 | ||||||||
\(645\) | 1.09449e11 | 0.0248997 | ||||||||
\(646\) | −9.61383e11 | + | 3.27032e12i | −0.217195 | + | 0.738830i | ||||
\(647\) | −8.18289e12 | −1.83585 | −0.917925 | − | 0.396754i | \(-0.870137\pi\) | ||||
−0.917925 | + | 0.396754i | \(0.870137\pi\) | |||||||
\(648\) | −1.99387e12 | −0.444231 | ||||||||
\(649\) | 2.31589e11i | 0.0512410i | ||||||||
\(650\) | −2.43680e12 | −0.535438 | ||||||||
\(651\) | − | 5.55034e12i | − | 1.21117i | ||||||
\(652\) | 1.39845e12i | 0.303064i | ||||||||
\(653\) | − | 2.43949e12i | − | 0.525036i | −0.964927 | − | 0.262518i | \(-0.915447\pi\) | ||
0.964927 | − | 0.262518i | \(-0.0845529\pi\) | |||||||
\(654\) | −6.64931e11 | −0.142127 | ||||||||
\(655\) | −1.81258e12 | −0.384779 | ||||||||
\(656\) | − | 1.56181e12i | − | 0.329276i | ||||||
\(657\) | − | 1.20026e12i | − | 0.251323i | ||||||
\(658\) | − | 3.41385e12i | − | 0.709950i | ||||||
\(659\) | −1.61269e12 | −0.333094 | −0.166547 | − | 0.986034i | \(-0.553262\pi\) | ||||
−0.166547 | + | 0.986034i | \(0.553262\pi\) | |||||||
\(660\) | 3.67273e11i | 0.0753427i | ||||||||
\(661\) | 7.30795e11 | 0.148898 | 0.0744491 | − | 0.997225i | \(-0.476280\pi\) | ||||
0.0744491 | + | 0.997225i | \(0.476280\pi\) | |||||||
\(662\) | 2.60478e12 | 0.527121 | ||||||||
\(663\) | −2.60795e12 | − | 7.66664e11i | −0.524190 | − | 0.154097i | ||||
\(664\) | 5.96034e11 | 0.118991 | ||||||||
\(665\) | 5.78422e12 | 1.14696 | ||||||||
\(666\) | − | 1.54003e12i | − | 0.303315i | ||||||
\(667\) | −8.07674e12 | −1.58005 | ||||||||
\(668\) | 2.85980e12i | 0.555701i | ||||||||
\(669\) | 6.49787e11i | 0.125416i | ||||||||
\(670\) | − | 1.09799e12i | − | 0.210505i | ||||||
\(671\) | 1.62017e12 | 0.308539 | ||||||||
\(672\) | 4.00325e12 | 0.757271 | ||||||||
\(673\) | 4.80522e12i | 0.902911i | 0.892294 | + | 0.451456i | \(0.149095\pi\) | ||||
−0.892294 | + | 0.451456i | \(0.850905\pi\) | |||||||
\(674\) | 4.33272e12i | 0.808707i | ||||||||
\(675\) | 3.31103e12i | 0.613899i | ||||||||
\(676\) | −2.57846e12 | −0.474897 | ||||||||
\(677\) | − | 2.48514e12i | − | 0.454675i | −0.973816 | − | 0.227337i | \(-0.926998\pi\) | ||
0.973816 | − | 0.227337i | \(-0.0730020\pi\) | |||||||
\(678\) | 5.46051e10 | 0.00992429 | ||||||||
\(679\) | 1.12683e13 | 2.03443 | ||||||||
\(680\) | 2.19351e12 | + | 6.44830e11i | 0.393413 | + | 0.115652i | ||||
\(681\) | 3.41878e12 | 0.609130 | ||||||||
\(682\) | −2.64509e12 | −0.468177 | ||||||||
\(683\) | − | 8.09671e11i | − | 0.142369i | −0.997463 | − | 0.0711845i | \(-0.977322\pi\) | ||
0.997463 | − | 0.0711845i | \(-0.0226779\pi\) | |||||||
\(684\) | 5.00154e12 | 0.873677 | ||||||||
\(685\) | 8.60861e10i | 0.0149391i | ||||||||
\(686\) | 5.03002e12i | 0.867184i | ||||||||
\(687\) | 2.89126e12i | 0.495202i | ||||||||
\(688\) | 1.91109e11 | 0.0325187 | ||||||||
\(689\) | −3.24937e11 | −0.0549303 | ||||||||
\(690\) | 5.69680e11i | 0.0956776i | ||||||||
\(691\) | − | 3.01668e12i | − | 0.503359i | −0.967811 | − | 0.251679i | \(-0.919017\pi\) | ||
0.967811 | − | 0.251679i | \(-0.0809829\pi\) | |||||||
\(692\) | 2.21408e12i | 0.367043i | ||||||||
\(693\) | −4.61740e12 | −0.760497 | ||||||||
\(694\) | 3.77338e12i | 0.617465i | ||||||||
\(695\) | −2.66038e11 | −0.0432526 | ||||||||
\(696\) | 3.96341e12 | 0.640217 | ||||||||
\(697\) | −7.82417e12 | − | 2.30009e12i | −1.25571 | − | 0.369145i | ||||
\(698\) | −1.24728e12 | −0.198890 | ||||||||
\(699\) | −1.14934e11 | −0.0182096 | ||||||||
\(700\) | 6.29893e12i | 0.991575i | ||||||||
\(701\) | −4.71932e12 | −0.738156 | −0.369078 | − | 0.929398i | \(-0.620326\pi\) | ||||
−0.369078 | + | 0.929398i | \(0.620326\pi\) | |||||||
\(702\) | − | 3.35226e12i | − | 0.520979i | ||||||
\(703\) | 6.72080e12i | 1.03782i | ||||||||
\(704\) | − | 1.02373e12i | − | 0.157076i | ||||||
\(705\) | 9.94693e11 | 0.151648 | ||||||||
\(706\) | 3.25604e12 | 0.493251 | ||||||||
\(707\) | 4.94552e12i | 0.744432i | ||||||||
\(708\) | 1.95763e11i | 0.0292806i | ||||||||
\(709\) | 8.19568e12i | 1.21808i | 0.793138 | + | 0.609041i | \(0.208446\pi\) | ||||
−0.793138 | + | 0.609041i | \(0.791554\pi\) | |||||||
\(710\) | −1.56538e12 | −0.231183 | ||||||||
\(711\) | − | 2.38291e12i | − | 0.349699i | ||||||
\(712\) | −1.08264e13 | −1.57880 | ||||||||
\(713\) | 1.08376e13 | 1.57048 | ||||||||
\(714\) | 7.50242e11 | − | 2.55209e12i | 0.108034 | − | 0.367497i | ||||
\(715\) | 2.19824e12 | 0.314555 | ||||||||
\(716\) | −1.82060e12 | −0.258884 | ||||||||
\(717\) | − | 5.59701e12i | − | 0.790897i | ||||||
\(718\) | 3.98601e12 | 0.559729 | ||||||||
\(719\) | − | 1.16808e13i | − | 1.63001i | −0.579452 | − | 0.815006i | \(-0.696733\pi\) | ||
0.579452 | − | 0.815006i | \(-0.303267\pi\) | |||||||
\(720\) | − | 6.74319e11i | − | 0.0935124i | ||||||
\(721\) | 2.33327e12i | 0.321555i | ||||||||
\(722\) | 4.43684e12 | 0.607654 | ||||||||
\(723\) | −2.69372e12 | −0.366631 | ||||||||
\(724\) | − | 2.49449e12i | − | 0.337410i | ||||||
\(725\) | 9.85064e12i | 1.32417i | ||||||||
\(726\) | 1.18174e12i | 0.157873i | ||||||||
\(727\) | −5.18587e12 | −0.688520 | −0.344260 | − | 0.938874i | \(-0.611870\pi\) | ||||
−0.344260 | + | 0.938874i | \(0.611870\pi\) | |||||||
\(728\) | − | 1.51690e13i | − | 2.00155i | ||||||
\(729\) | 5.67392e11 | 0.0744063 | ||||||||
\(730\) | −5.59178e11 | −0.0728781 | ||||||||
\(731\) | 2.81448e11 | − | 9.57397e11i | 0.0364561 | − | 0.124012i | ||||
\(732\) | 1.36953e12 | 0.176308 | ||||||||
\(733\) | 9.00169e10 | 0.0115175 | 0.00575873 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575873 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(734\) | 5.07104e12i | 0.644859i | ||||||||
\(735\) | −2.98974e12 | −0.377868 | ||||||||
\(736\) | 7.81677e12i | 0.981923i | ||||||||
\(737\) | − | 3.82511e12i | − | 0.477573i | ||||||
\(738\) | − | 4.53001e12i | − | 0.562142i | ||||||
\(739\) | 1.27401e13 | 1.57135 | 0.785677 | − | 0.618638i | \(-0.212315\pi\) | ||||
0.785677 | + | 0.618638i | \(0.212315\pi\) | |||||||
\(740\) | 1.89519e12 | 0.232333 | ||||||||
\(741\) | 6.58951e12i | 0.802918i | ||||||||
\(742\) | − | 3.17976e11i | − | 0.0385103i | ||||||
\(743\) | 7.98450e11i | 0.0961165i | 0.998845 | + | 0.0480583i | \(0.0153033\pi\) | ||||
−0.998845 | + | 0.0480583i | \(0.984697\pi\) | |||||||
\(744\) | −5.31823e12 | −0.636340 | ||||||||
\(745\) | 5.10657e12i | 0.607332i | ||||||||
\(746\) | −7.82329e12 | −0.924836 | ||||||||
\(747\) | −9.17926e11 | −0.107861 | ||||||||
\(748\) | 3.21268e12 | + | 9.44438e11i | 0.375241 | + | 0.110310i | ||||
\(749\) | −1.36797e13 | −1.58821 | ||||||||
\(750\) | 1.56952e12 | 0.181130 | ||||||||
\(751\) | − | 9.56992e12i | − | 1.09781i | −0.835883 | − | 0.548907i | \(-0.815044\pi\) | ||
0.835883 | − | 0.548907i | \(-0.184956\pi\) | |||||||
\(752\) | 1.73683e12 | 0.198051 | ||||||||
\(753\) | − | 2.90320e12i | − | 0.329078i | ||||||
\(754\) | − | 9.97328e12i | − | 1.12374i | ||||||
\(755\) | 3.62330e12i | 0.405829i | ||||||||
\(756\) | −8.66533e12 | −0.964799 | ||||||||
\(757\) | 1.18435e13 | 1.31084 | 0.655418 | − | 0.755267i | \(-0.272493\pi\) | ||||
0.655418 | + | 0.755267i | \(0.272493\pi\) | |||||||
\(758\) | − | 4.46590e12i | − | 0.491358i | ||||||
\(759\) | 1.98461e12i | 0.217064i | ||||||||
\(760\) | − | 5.54233e12i | − | 0.602603i | ||||||
\(761\) | 7.12456e12 | 0.770064 | 0.385032 | − | 0.922903i | \(-0.374190\pi\) | ||||
0.385032 | + | 0.922903i | \(0.374190\pi\) | |||||||
\(762\) | 2.50765e12i | 0.269445i | ||||||||
\(763\) | 1.02875e13 | 1.09888 | ||||||||
\(764\) | 6.85906e12 | 0.728357 | ||||||||
\(765\) | −3.37813e12 | − | 9.93074e11i | −0.356615 | − | 0.104835i | ||||
\(766\) | −2.81254e12 | −0.295168 | ||||||||
\(767\) | 1.17170e12 | 0.122246 | ||||||||
\(768\) | − | 3.08854e12i | − | 0.320352i | ||||||
\(769\) | −1.51364e13 | −1.56082 | −0.780411 | − | 0.625267i | \(-0.784990\pi\) | ||||
−0.780411 | + | 0.625267i | \(0.784990\pi\) | |||||||
\(770\) | 2.15115e12i | 0.220527i | ||||||||
\(771\) | 4.92216e12i | 0.501662i | ||||||||
\(772\) | − | 1.25426e13i | − | 1.27090i | ||||||
\(773\) | −6.55361e12 | −0.660196 | −0.330098 | − | 0.943947i | \(-0.607082\pi\) | ||||
−0.330098 | + | 0.943947i | \(0.607082\pi\) | |||||||
\(774\) | 5.54310e11 | 0.0555161 | ||||||||
\(775\) | − | 1.32179e13i | − | 1.31615i | ||||||
\(776\) | − | 1.07970e13i | − | 1.06888i | ||||||
\(777\) | − | 5.24476e12i | − | 0.516216i | ||||||
\(778\) | −4.32508e11 | −0.0423239 | ||||||||
\(779\) | 1.97693e13i | 1.92342i | ||||||||
\(780\) | 1.85817e12 | 0.179746 | ||||||||
\(781\) | −5.45335e12 | −0.524486 | ||||||||
\(782\) | 4.98322e12 | + | 1.46493e12i | 0.476518 | + | 0.140083i | ||||
\(783\) | −1.35514e13 | −1.28841 | ||||||||
\(784\) | −5.22037e12 | −0.493491 | ||||||||
\(785\) | 2.36486e12i | 0.222276i | ||||||||
\(786\) | 2.02070e12 | 0.188843 | ||||||||
\(787\) | 1.72441e13i | 1.60234i | 0.598439 | + | 0.801168i | \(0.295788\pi\) | ||||
−0.598439 | + | 0.801168i | \(0.704212\pi\) | |||||||
\(788\) | − | 2.32212e12i | − | 0.214544i | ||||||
\(789\) | 2.06579e12i | 0.189775i | ||||||||
\(790\) | −1.11015e12 | −0.101405 | ||||||||
\(791\) | −8.44824e11 | −0.0767312 | ||||||||
\(792\) | 4.42430e12i | 0.399559i | ||||||||
\(793\) | − | 8.19706e12i | − | 0.736086i | ||||||
\(794\) | 6.82057e12i | 0.609015i | ||||||||
\(795\) | 9.26487e10 | 0.00822597 | ||||||||
\(796\) | 5.42884e12i | 0.479290i | ||||||||
\(797\) | 1.92951e13 | 1.69389 | 0.846944 | − | 0.531682i | \(-0.178440\pi\) | ||||
0.846944 | + | 0.531682i | \(0.178440\pi\) | |||||||
\(798\) | −6.44835e12 | −0.562906 | ||||||||
\(799\) | 2.55784e12 | − | 8.70097e12i | 0.222031 | − | 0.755278i | ||||
\(800\) | 9.53358e12 | 0.822908 | ||||||||
\(801\) | 1.66733e13 | 1.43112 | ||||||||
\(802\) | 4.03096e12i | 0.344052i | ||||||||
\(803\) | −1.94803e12 | −0.165339 | ||||||||
\(804\) | − | 3.23337e12i | − | 0.272899i | ||||||
\(805\) | − | 8.81382e12i | − | 0.739746i | ||||||
\(806\) | 1.33825e13i | 1.11694i | ||||||||
\(807\) | 7.51616e12 | 0.623829 | ||||||||
\(808\) | 4.73871e12 | 0.391119 | ||||||||
\(809\) | − | 3.75180e12i | − | 0.307944i | −0.988075 | − | 0.153972i | \(-0.950794\pi\) | ||
0.988075 | − | 0.153972i | \(-0.0492065\pi\) | |||||||
\(810\) | − | 1.43056e12i | − | 0.116768i | ||||||
\(811\) | − | 4.21763e12i | − | 0.342353i | −0.985240 | − | 0.171177i | \(-0.945243\pi\) | ||
0.985240 | − | 0.171177i | \(-0.0547569\pi\) | |||||||
\(812\) | −2.57802e13 | −2.08106 | ||||||||
\(813\) | 3.36047e12i | 0.269769i | ||||||||
\(814\) | −2.49946e12 | −0.199543 | ||||||||
\(815\) | −2.38657e12 | −0.189481 | ||||||||
\(816\) | 1.29840e12 | + | 3.81693e11i | 0.102519 | + | 0.0301376i | ||||
\(817\) | −2.41905e12 | −0.189953 | ||||||||
\(818\) | −1.33371e12 | −0.104153 | ||||||||
\(819\) | 2.33611e13i | 1.81433i | ||||||||
\(820\) | 5.57474e12 | 0.430588 | ||||||||
\(821\) | − | 2.89064e12i | − | 0.222050i | −0.993818 | − | 0.111025i | \(-0.964587\pi\) | ||
0.993818 | − | 0.111025i | \(-0.0354133\pi\) | |||||||
\(822\) | − | 9.59704e10i | − | 0.00733186i | ||||||
\(823\) | − | 1.85820e11i | − | 0.0141186i | −0.999975 | − | 0.00705931i | \(-0.997753\pi\) | ||
0.999975 | − | 0.00705931i | \(-0.00224707\pi\) | |||||||
\(824\) | 2.23569e12 | 0.168943 | ||||||||
\(825\) | 2.42050e12 | 0.181912 | ||||||||
\(826\) | 1.14660e12i | 0.0857040i | ||||||||
\(827\) | 2.19451e13i | 1.63141i | 0.578470 | + | 0.815704i | \(0.303650\pi\) | ||||
−0.578470 | + | 0.815704i | \(0.696350\pi\) | |||||||
\(828\) | − | 7.62119e12i | − | 0.563490i | ||||||
\(829\) | 7.80531e12 | 0.573977 | 0.286989 | − | 0.957934i | \(-0.407346\pi\) | ||||
0.286989 | + | 0.957934i | \(0.407346\pi\) | |||||||
\(830\) | 4.27642e11i | 0.0312773i | ||||||||
\(831\) | 2.83892e12 | 0.206513 | ||||||||
\(832\) | −5.17944e12 | −0.374738 | ||||||||
\(833\) | −7.68807e12 | + | 2.61524e13i | −0.553242 | + | 1.88196i | ||||
\(834\) | 2.96584e11 | 0.0212276 | ||||||||
\(835\) | −4.88047e12 | −0.347434 | ||||||||
\(836\) | − | 8.11748e12i | − | 0.574768i | ||||||
\(837\) | 1.81836e13 | 1.28061 | ||||||||
\(838\) | − | 3.39993e11i | − | 0.0238161i | ||||||
\(839\) | − | 1.83657e13i | − | 1.27962i | −0.768535 | − | 0.639808i | \(-0.779014\pi\) | ||
0.768535 | − | 0.639808i | \(-0.220986\pi\) | |||||||
\(840\) | 4.32511e12i | 0.299737i | ||||||||
\(841\) | −2.58094e13 | −1.77908 | ||||||||
\(842\) | 8.79613e12 | 0.603097 | ||||||||
\(843\) | 6.81314e12i | 0.464647i | ||||||||
\(844\) | 9.99954e12i | 0.678327i | ||||||||
\(845\) | − | 4.40033e12i | − | 0.296914i | ||||||
\(846\) | 5.03766e12 | 0.338113 | ||||||||
\(847\) | − | 1.82833e13i | − | 1.22062i | ||||||
\(848\) | 1.61773e11 | 0.0107430 | ||||||||
\(849\) | 1.51711e12 | 0.100215 | ||||||||
\(850\) | 1.78667e12 | − | 6.07769e12i | 0.117398 | − | 0.399350i | ||||
\(851\) | 1.02409e13 | 0.669356 | ||||||||
\(852\) | −4.60972e12 | −0.299707 | ||||||||
\(853\) | − | 1.15587e13i | − | 0.747544i | −0.927521 | − | 0.373772i | \(-0.878064\pi\) | ||
0.927521 | − | 0.373772i | \(-0.121936\pi\) | |||||||
\(854\) | 8.02147e12 | 0.516052 | ||||||||
\(855\) | 8.53551e12i | 0.546238i | ||||||||
\(856\) | 1.31076e13i | 0.834434i | ||||||||
\(857\) | − | 3.67551e12i | − | 0.232757i | −0.993205 | − | 0.116379i | \(-0.962871\pi\) | ||
0.993205 | − | 0.116379i | \(-0.0371286\pi\) | |||||||
\(858\) | −2.45063e12 | −0.154378 | ||||||||
\(859\) | −2.36948e13 | −1.48485 | −0.742426 | − | 0.669928i | \(-0.766325\pi\) | ||||
−0.742426 | + | 0.669928i | \(0.766325\pi\) | |||||||
\(860\) | 6.82147e11i | 0.0425241i | ||||||||
\(861\) | − | 1.54275e13i | − | 0.956715i | ||||||
\(862\) | 1.16820e12i | 0.0720666i | ||||||||
\(863\) | 8.18769e12 | 0.502473 | 0.251237 | − | 0.967926i | \(-0.419163\pi\) | ||||
0.251237 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(864\) | 1.31152e13i | 0.800686i | ||||||||
\(865\) | −3.77850e12 | −0.229481 | ||||||||
\(866\) | −7.46736e12 | −0.451166 | ||||||||
\(867\) | 3.82432e12 | − | 5.94245e12i | 0.229863 | − | 0.357174i | ||||
\(868\) | 3.45927e13 | 2.06845 | ||||||||
\(869\) | −3.86746e12 | −0.230058 | ||||||||
\(870\) | 2.84367e12i | 0.168284i | ||||||||
\(871\) | −1.93526e13 | −1.13935 | ||||||||
\(872\) | − | 9.85728e12i | − | 0.577342i | ||||||
\(873\) | 1.66281e13i | 0.968896i | ||||||||
\(874\) | − | 1.25911e13i | − | 0.729898i | ||||||
\(875\) | −2.42828e13 | −1.40043 | ||||||||
\(876\) | −1.64667e12 | −0.0944794 | ||||||||
\(877\) | − | 1.34379e13i | − | 0.767064i | −0.923528 | − | 0.383532i | \(-0.874708\pi\) | ||
0.923528 | − | 0.383532i | \(-0.125292\pi\) | |||||||
\(878\) | − | 3.78549e11i | − | 0.0214979i | ||||||
\(879\) | 2.64538e12i | 0.149465i | ||||||||
\(880\) | −1.09442e12 | −0.0615192 | ||||||||
\(881\) | − | 3.19613e13i | − | 1.78745i | −0.448618 | − | 0.893724i | \(-0.648084\pi\) | ||
0.448618 | − | 0.893724i | \(-0.351916\pi\) | |||||||
\(882\) | −1.51416e13 | −0.842489 | ||||||||
\(883\) | 9.21484e12 | 0.510111 | 0.255056 | − | 0.966926i | \(-0.417906\pi\) | ||||
0.255056 | + | 0.966926i | \(0.417906\pi\) | |||||||
\(884\) | 4.77826e12 | − | 1.62541e13i | 0.263169 | − | 0.895218i | ||||
\(885\) | −3.34084e11 | −0.0183067 | ||||||||
\(886\) | 1.15789e13 | 0.631272 | ||||||||
\(887\) | − | 5.95887e12i | − | 0.323227i | −0.986854 | − | 0.161614i | \(-0.948330\pi\) | ||
0.986854 | − | 0.161614i | \(-0.0516698\pi\) | |||||||
\(888\) | −5.02543e12 | −0.271216 | ||||||||
\(889\) | − | 3.87972e13i | − | 2.08325i | ||||||
\(890\) | − | 7.76776e12i | − | 0.414993i | ||||||
\(891\) | − | 4.98368e12i | − | 0.264911i | ||||||
\(892\) | −4.04982e12 | −0.214187 | ||||||||
\(893\) | −2.19847e13 | −1.15688 | ||||||||
\(894\) | − | 5.69289e12i | − | 0.298067i | ||||||
\(895\) | − | 3.10699e12i | − | 0.161859i | ||||||
\(896\) | 2.93274e13i | 1.52016i | ||||||||
\(897\) | 1.00409e13 | 0.517853 | ||||||||
\(898\) | − | 3.77565e12i | − | 0.193753i | ||||||
\(899\) | 5.40981e13 | 2.76225 | ||||||||
\(900\) | −9.29504e12 | −0.472237 | ||||||||
\(901\) | 2.38245e11 | − | 8.10434e11i | 0.0120438 | − | 0.0409691i | ||||
\(902\) | −7.35220e12 | −0.369818 | ||||||||
\(903\) | 1.88778e12 | 0.0944834 | ||||||||
\(904\) | 8.09494e11i | 0.0403140i | ||||||||
\(905\) | 4.25704e12 | 0.210955 | ||||||||
\(906\) | − | 4.03932e12i | − | 0.199173i | ||||||
\(907\) | 3.49523e13i | 1.71491i | 0.514555 | + | 0.857457i | \(0.327957\pi\) | ||||
−0.514555 | + | 0.857457i | \(0.672043\pi\) | |||||||
\(908\) | 2.13077e13i | 1.04028i | ||||||||
\(909\) | −7.29788e12 | −0.354535 | ||||||||
\(910\) | 1.08834e13 | 0.526115 | ||||||||
\(911\) | 1.82282e12i | 0.0876819i | 0.999039 | + | 0.0438410i | \(0.0139595\pi\) | ||||
−0.999039 | + | 0.0438410i | \(0.986041\pi\) | |||||||
\(912\) | − | 3.28066e12i | − | 0.157031i | ||||||
\(913\) | 1.48979e12i | 0.0709589i | ||||||||
\(914\) | 6.13795e12 | 0.290914 | ||||||||
\(915\) | 2.33721e12i | 0.110231i | ||||||||
\(916\) | −1.80199e13 | −0.845712 | ||||||||
\(917\) | −3.12633e13 | −1.46007 | ||||||||
\(918\) | 8.36097e12 | + | 2.45789e12i | 0.388566 | + | 0.114227i | ||||
\(919\) | −1.16854e13 | −0.540411 | −0.270206 | − | 0.962803i | \(-0.587092\pi\) | ||||
−0.270206 | + | 0.962803i | \(0.587092\pi\) | |||||||
\(920\) | −8.44524e12 | −0.388657 | ||||||||
\(921\) | 1.05478e13i | 0.483052i | ||||||||
\(922\) | −1.22738e13 | −0.559358 | ||||||||
\(923\) | 2.75905e13i | 1.25127i | ||||||||
\(924\) | 6.33470e12i | 0.285892i | ||||||||
\(925\) | − | 1.24902e13i | − | 0.560959i | ||||||
\(926\) | −5.44783e12 | −0.243486 | ||||||||
\(927\) | −3.44309e12 | −0.153140 | ||||||||
\(928\) | 3.90189e13i | 1.72707i | ||||||||
\(929\) | 2.03224e13i | 0.895166i | 0.894242 | + | 0.447583i | \(0.147715\pi\) | ||||
−0.894242 | + | 0.447583i | \(0.852285\pi\) | |||||||
\(930\) | − | 3.81572e12i | − | 0.167264i | ||||||
\(931\) | 6.60793e13 | 2.88265 | ||||||||
\(932\) | − | 7.16329e11i | − | 0.0310986i | ||||||
\(933\) | 6.96787e12 | 0.301046 | ||||||||
\(934\) | −1.56046e13 | −0.670954 | ||||||||
\(935\) | −1.61176e12 | + | 5.48269e12i | −0.0689679 | + | 0.234607i | ||||
\(936\) | 2.23842e13 | 0.953235 | ||||||||
\(937\) | −1.03126e13 | −0.437061 | −0.218530 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218530 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(938\) | − | 1.89381e13i | − | 0.798773i | ||||||
\(939\) | −3.93829e12 | −0.165315 | ||||||||
\(940\) | 6.19945e12i | 0.258987i | ||||||||
\(941\) | − | 9.97481e12i | − | 0.414717i | −0.978265 | − | 0.207358i | \(-0.933513\pi\) | ||
0.978265 | − | 0.207358i | \(-0.0664866\pi\) | |||||||
\(942\) | − | 2.63639e12i | − | 0.109089i | ||||||
\(943\) | 3.01239e13 | 1.24053 | ||||||||
\(944\) | −5.83343e11 | −0.0239084 | ||||||||
\(945\) | − | 1.47881e13i | − | 0.603209i | ||||||
\(946\) | − | 8.99644e11i | − | 0.0365225i | ||||||
\(947\) | − | 7.55330e12i | − | 0.305184i | −0.988289 | − | 0.152592i | \(-0.951238\pi\) | ||
0.988289 | − | 0.152592i | \(-0.0487620\pi\) | |||||||
\(948\) | −3.26916e12 | −0.131462 | ||||||||
\(949\) | 9.85578e12i | 0.394451i | ||||||||
\(950\) | −1.53565e13 | −0.611696 | ||||||||
\(951\) | −1.28635e13 | −0.509972 | ||||||||
\(952\) | 3.78335e13 | + | 1.11220e13i | 1.49283 | + | 0.438850i | ||||
\(953\) | 5.11924e12 | 0.201042 | 0.100521 | − | 0.994935i | \(-0.467949\pi\) | ||||
0.100521 | + | 0.994935i | \(0.467949\pi\) | |||||||
\(954\) | 4.69222e11 | 0.0183405 | ||||||||
\(955\) | 1.17055e13i | 0.455381i | ||||||||
\(956\) | 3.48836e13 | 1.35070 | ||||||||
\(957\) | 9.90657e12i | 0.381786i | ||||||||
\(958\) | 2.46781e13i | 0.946599i | ||||||||
\(959\) | 1.48481e12i | 0.0566874i | ||||||||
\(960\) | 1.47681e12 | 0.0561181 | ||||||||
\(961\) | −4.61509e13 | −1.74552 | ||||||||
\(962\) | 1.26457e13i | 0.476052i | ||||||||
\(963\) | − | 2.01865e13i | − | 0.756384i | ||||||
\(964\) | − | 1.67887e13i | − | 0.626137i | ||||||
\(965\) | 2.14050e13 | 0.794588 | ||||||||
\(966\) | 9.82581e12i | 0.363054i | ||||||||
\(967\) | −2.96090e13 | −1.08894 | −0.544471 | − | 0.838780i | \(-0.683269\pi\) | ||||
−0.544471 | + | 0.838780i | \(0.683269\pi\) | |||||||
\(968\) | −1.75187e13 | −0.641303 | ||||||||
\(969\) | −1.64351e13 | − | 4.83146e12i | −0.598846 | − | 0.176044i | ||||
\(970\) | 7.74666e12 | 0.280958 | ||||||||
\(971\) | −2.36780e13 | −0.854790 | −0.427395 | − | 0.904065i | \(-0.640569\pi\) | ||||
−0.427395 | + | 0.904065i | \(0.640569\pi\) | |||||||
\(972\) | − | 1.98144e13i | − | 0.712006i | ||||||
\(973\) | −4.58861e12 | −0.164124 | ||||||||
\(974\) | − | 8.51810e12i | − | 0.303269i | ||||||
\(975\) | − | 1.22462e13i | − | 0.433990i | ||||||
\(976\) | 4.08100e12i | 0.143960i | ||||||||
\(977\) | 1.30708e13 | 0.458961 | 0.229480 | − | 0.973313i | \(-0.426297\pi\) | ||||
0.229480 | + | 0.973313i | \(0.426297\pi\) | |||||||
\(978\) | 2.66059e12 | 0.0929937 | ||||||||
\(979\) | − | 2.70608e13i | − | 0.941496i | ||||||
\(980\) | − | 1.86336e13i | − | 0.645328i | ||||||
\(981\) | 1.51808e13i | 0.523339i | ||||||||
\(982\) | 1.16076e13 | 0.398329 | ||||||||
\(983\) | − | 1.05637e13i | − | 0.360850i | −0.983589 | − | 0.180425i | \(-0.942253\pi\) | ||
0.983589 | − | 0.180425i | \(-0.0577473\pi\) | |||||||
\(984\) | −1.47824e13 | −0.502651 | ||||||||
\(985\) | 3.96288e12 | 0.134137 | ||||||||
\(986\) | 2.48747e13 | + | 7.31246e12i | 0.838130 | + | 0.246387i | ||||
\(987\) | 1.71564e13 | 0.575438 | ||||||||
\(988\) | −4.10693e13 | −1.37123 | ||||||||
\(989\) | 3.68608e12i | 0.122513i | ||||||||
\(990\) | −3.17435e12 | −0.105026 | ||||||||
\(991\) | 4.60965e13i | 1.51823i | 0.650958 | + | 0.759113i | \(0.274367\pi\) | ||||
−0.650958 | + | 0.759113i | \(0.725633\pi\) | |||||||
\(992\) | − | 5.23568e13i | − | 1.71661i | ||||||
\(993\) | 1.30904e13i | 0.427250i | ||||||||
\(994\) | −2.69995e13 | −0.877238 | ||||||||
\(995\) | −9.26473e12 | −0.299660 | ||||||||
\(996\) | 1.25932e12i | 0.0405480i | ||||||||
\(997\) | − | 2.60737e13i | − | 0.835748i | −0.908505 | − | 0.417874i | \(-0.862775\pi\) | ||
0.908505 | − | 0.417874i | \(-0.137225\pi\) | |||||||
\(998\) | − | 2.01631e13i | − | 0.643384i | ||||||
\(999\) | 1.71825e13 | 0.545811 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 17.10.b.a.16.8 | yes | 12 | |
3.2 | odd | 2 | 153.10.d.b.118.6 | 12 | |||
4.3 | odd | 2 | 272.10.b.c.33.5 | 12 | |||
17.4 | even | 4 | 289.10.a.c.1.6 | 12 | |||
17.13 | even | 4 | 289.10.a.c.1.5 | 12 | |||
17.16 | even | 2 | inner | 17.10.b.a.16.7 | ✓ | 12 | |
51.50 | odd | 2 | 153.10.d.b.118.5 | 12 | |||
68.67 | odd | 2 | 272.10.b.c.33.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.b.a.16.7 | ✓ | 12 | 17.16 | even | 2 | inner | |
17.10.b.a.16.8 | yes | 12 | 1.1 | even | 1 | trivial | |
153.10.d.b.118.5 | 12 | 51.50 | odd | 2 | |||
153.10.d.b.118.6 | 12 | 3.2 | odd | 2 | |||
272.10.b.c.33.5 | 12 | 4.3 | odd | 2 | |||
272.10.b.c.33.8 | 12 | 68.67 | odd | 2 | |||
289.10.a.c.1.5 | 12 | 17.13 | even | 4 | |||
289.10.a.c.1.6 | 12 | 17.4 | even | 4 |