Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(13,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.13");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 75402 x^{8} + 1918432665 x^{6} + 20025190470928 x^{4} + \cdots + 13\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{2}\cdot 5^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.4 | ||
Root | \(75.9602i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.13 |
Dual form | 20.11.f.a.17.4 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 186.378 | + | 186.378i | 0.766989 | + | 0.766989i | 0.977575 | − | 0.210586i | \(-0.0675372\pi\) |
−0.210586 | + | 0.977575i | \(0.567537\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −473.688 | + | 3088.89i | −0.151580 | + | 0.988445i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7250.16 | + | 7250.16i | −0.431378 | + | 0.431378i | −0.889097 | − | 0.457719i | \(-0.848667\pi\) |
0.457719 | + | 0.889097i | \(0.348667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10424.8i | 0.176545i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32274.9 | −0.200402 | −0.100201 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100201 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −123469. | − | 123469.i | −0.332537 | − | 0.332537i | 0.521012 | − | 0.853549i | \(-0.325555\pi\) |
−0.853549 | + | 0.521012i | \(0.825555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −663988. | + | 487417.i | −0.874387 | + | 0.641866i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.34533e6 | + | 1.34533e6i | −0.947510 | + | 0.947510i | −0.998689 | − | 0.0511797i | \(-0.983702\pi\) |
0.0511797 | + | 0.998689i | \(0.483702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80845e6i | 1.53808i | 0.639198 | + | 0.769042i | \(0.279266\pi\) | ||||
−0.639198 | + | 0.769042i | \(0.720734\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70255e6 | −0.661724 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.48258e6 | − | 1.48258e6i | −0.230345 | − | 0.230345i | 0.582492 | − | 0.812837i | \(-0.302078\pi\) |
−0.812837 | + | 0.582492i | \(0.802078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.31686e6 | − | 2.92634e6i | −0.954047 | − | 0.299657i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.06250e6 | − | 9.06250e6i | 0.631581 | − | 0.631581i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.97669e7i | 0.963717i | 0.876249 | + | 0.481859i | \(0.160038\pi\) | ||||
−0.876249 | + | 0.481859i | \(0.839962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84620e7 | 1.34346 | 0.671729 | − | 0.740797i | \(-0.265552\pi\) | ||||
0.671729 | + | 0.740797i | \(0.265552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.01534e6 | − | 6.01534e6i | −0.153706 | − | 0.153706i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.89606e7 | − | 2.58293e7i | −0.361005 | − | 0.491781i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.70494e7 | − | 6.70494e7i | 0.966910 | − | 0.966910i | −0.0325595 | − | 0.999470i | \(-0.510366\pi\) |
0.999470 | + | 0.0325595i | \(0.0103658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.60238e7i | − | 0.510104i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28370e8 | 1.10801 | 0.554005 | − | 0.832513i | \(-0.313099\pi\) | ||||
0.554005 | + | 0.832513i | \(0.313099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.08862e7 | − | 3.08862e7i | −0.210098 | − | 0.210098i | 0.594211 | − | 0.804309i | \(-0.297464\pi\) |
−0.804309 | + | 0.594211i | \(0.797464\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.22011e7 | − | 4.93811e6i | −0.174505 | − | 0.0267608i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.99277e8 | + | 1.99277e8i | −0.868897 | + | 0.868897i | −0.992350 | − | 0.123453i | \(-0.960603\pi\) |
0.123453 | + | 0.992350i | \(0.460603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.77345e8i | 0.627827i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.01480e8 | −1.45346 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65599e8 | + | 3.65599e8i | 0.874231 | + | 0.874231i | 0.992930 | − | 0.118699i | \(-0.0378724\pi\) |
−0.118699 | + | 0.992930i | \(0.537872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.52882e7 | − | 9.96936e7i | 0.0303769 | − | 0.198086i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.09813e8 | + | 7.09813e8i | −1.17969 | + | 1.17969i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.07362e9i | − | 1.50172i | −0.660460 | − | 0.750861i | \(-0.729639\pi\) | ||
0.660460 | − | 0.750861i | \(-0.270361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.62425e8 | 0.310710 | 0.155355 | − | 0.987859i | \(-0.450348\pi\) | ||||
0.155355 | + | 0.987859i | \(0.450348\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.55816e7 | − | 7.55816e7i | −0.0761577 | − | 0.0761577i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.39867e8 | − | 3.22895e8i | 0.379100 | − | 0.278288i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.30058e8 | + | 5.30058e8i | −0.392599 | + | 0.392599i | −0.875613 | − | 0.483014i | \(-0.839542\pi\) |
0.483014 | + | 0.875613i | \(0.339542\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5.52641e8i | − | 0.353344i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34904e9 | 1.30196 | 0.650980 | − | 0.759095i | \(-0.274358\pi\) | ||||
0.650980 | + | 0.759095i | \(0.274358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.92115e9 | + | 1.92115e9i | 0.926717 | + | 0.926717i | 0.997492 | − | 0.0707753i | \(-0.0225473\pi\) |
−0.0707753 | + | 0.997492i | \(0.522547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.19106e9 | − | 2.28187e9i | −0.501910 | − | 0.961578i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.33998e8 | − | 2.33998e8i | 0.0864488 | − | 0.0864488i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.63376e9i | − | 1.18092i | −0.807067 | − | 0.590460i | \(-0.798946\pi\) | ||
0.807067 | − | 0.590460i | \(-0.201054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.99368e9 | 1.14538 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.23817e9 | − | 1.23817e9i | −0.314334 | − | 0.314334i | 0.532252 | − | 0.846586i | \(-0.321346\pi\) |
−0.846586 | + | 0.532252i | \(0.821346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.51831e9 | − | 4.79284e9i | −0.792938 | − | 1.08019i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.68413e9 | + | 3.68413e9i | −0.739161 | + | 0.739161i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.01544e9i | 1.61450i | 0.590213 | + | 0.807248i | \(0.299044\pi\) | ||||
−0.590213 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.79034e9 | 0.286898 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.16849e9 | + | 7.16849e9i | 1.03042 | + | 1.03042i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.17639e10 | − | 1.80402e9i | −1.52031 | − | 0.233143i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.05456e9 | + | 9.05456e9i | −1.05441 | + | 1.05441i | −0.0559755 | + | 0.998432i | \(0.517827\pi\) |
−0.998432 | + | 0.0559755i | \(0.982173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.36460e8i | − | 0.0353799i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.39687e9 | 0.323200 | 0.161600 | − | 0.986856i | \(-0.448334\pi\) | ||||
0.161600 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.76080e9 | − | 5.76080e9i | −0.496931 | − | 0.496931i | 0.413550 | − | 0.910481i | \(-0.364289\pi\) |
−0.910481 | + | 0.413550i | \(0.864289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.28016e9 | − | 8.34787e9i | 0.100304 | − | 0.654078i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.05439e10 | + | 1.05439e10i | −0.751766 | + | 0.751766i | −0.974809 | − | 0.223043i | \(-0.928401\pi\) |
0.223043 | + | 0.974809i | \(0.428401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.24234e10i | − | 1.45737i | −0.684850 | − | 0.728684i | \(-0.740132\pi\) | ||
0.684850 | − | 0.728684i | \(-0.259868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.49931e10 | 1.48322 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.43697e10 | + | 1.43697e10i | 0.779930 | + | 0.779930i | 0.979819 | − | 0.199889i | \(-0.0640580\pi\) |
−0.199889 | + | 0.979819i | \(0.564058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.28180e9 | − | 3.87724e9i | 0.262599 | − | 0.192767i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28714e9 | − | 1.28714e9i | 0.0587078 | − | 0.0587078i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.95077e10i | − | 0.817469i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.48958e10 | −0.959839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.39254e10 | + | 2.39254e10i | 0.849832 | + | 0.849832i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.34524e10 | − | 2.73926e10i | 0.440809 | − | 0.897601i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.20236e9 | + | 6.20236e9i | −0.187732 | + | 0.187732i | −0.794715 | − | 0.606983i | \(-0.792380\pi\) |
0.606983 | + | 0.794715i | \(0.292380\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.15131e10i | − | 0.322286i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.92527e10 | 1.01745 | 0.508724 | − | 0.860929i | \(-0.330117\pi\) | ||||
0.508724 | + | 0.860929i | \(0.330117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.76119e10 | − | 2.76119e10i | −0.663495 | − | 0.663495i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.37003e10 | + | 3.22859e10i | 0.528548 | + | 0.720018i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.80246e9 | − | 1.80246e9i | 0.0373477 | − | 0.0373477i | −0.688186 | − | 0.725534i | \(-0.741593\pi\) |
0.725534 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.12218e10i | − | 0.216266i | −0.994136 | − | 0.108133i | \(-0.965513\pi\) | ||
0.994136 | − | 0.108133i | \(-0.0344873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.42819e10 | −1.33287 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.98494e9 | + | 3.98494e9i | 0.0666409 | + | 0.0666409i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.10579e10 | − | 9.36337e9i | −0.952581 | − | 0.146080i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.30534e10 | + | 3.30534e10i | −0.481536 | + | 0.481536i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.11142e11i | 1.51338i | 0.653776 | + | 0.756688i | \(0.273184\pi\) | ||||
−0.653776 | + | 0.756688i | \(0.726816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.52396e9 | −0.108582 | −0.0542908 | − | 0.998525i | \(-0.517290\pi\) | ||||
−0.0542908 | + | 0.998525i | \(0.517290\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.40248e10 | − | 1.40248e10i | −0.167278 | − | 0.167278i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.82190e10 | + | 1.18805e11i | −0.203641 | + | 1.32793i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.61882e10 | − | 7.61882e10i | 0.798711 | − | 0.798711i | −0.184181 | − | 0.982892i | \(-0.558963\pi\) |
0.982892 | + | 0.184181i | \(0.0589634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.36280e11i | 1.34105i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.14979e10 | 0.198731 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.36707e11 | − | 1.36707e11i | −1.18810 | − | 1.18810i | −0.977592 | − | 0.210511i | \(-0.932487\pi\) |
−0.210511 | − | 0.977592i | \(-0.567513\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.14301e10 | − | 1.57313e10i | 0.175229 | − | 0.128631i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.44257e11 | − | 1.44257e11i | 1.11059 | − | 1.11059i | 0.117520 | − | 0.993071i | \(-0.462506\pi\) |
0.993071 | − | 0.117520i | \(-0.0374943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.07369e11i | − | 0.778838i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.97024e10 | −0.271541 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.24683e10 | + | 2.24683e10i | 0.144990 | + | 0.144990i | 0.775876 | − | 0.630885i | \(-0.217308\pi\) |
−0.630885 | + | 0.775876i | \(0.717308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.87653e10 | − | 4.63323e10i | 0.540820 | − | 0.282289i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00099e11 | − | 2.00099e11i | 1.15180 | − | 1.15180i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.80959e10i | 0.316141i | 0.987428 | + | 0.158070i | \(0.0505273\pi\) | ||||
−0.987428 | + | 0.158070i | \(0.949473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27285e11 | −0.655214 | −0.327607 | − | 0.944814i | \(-0.606242\pi\) | ||||
−0.327607 | + | 0.944814i | \(0.606242\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.89103e10 | + | 4.89103e10i | 0.238311 | + | 0.238311i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.75348e11 | + | 2.38869e11i | 0.809173 | + | 1.10230i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.34203e10 | − | 4.34203e10i | 0.189882 | − | 0.189882i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.31409e11i | 0.544900i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.09552e10 | −0.0824375 | −0.0412187 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412187 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.68304e11 | − | 1.68304e11i | −0.628502 | − | 0.628502i | 0.319189 | − | 0.947691i | \(-0.396589\pi\) |
−0.947691 | + | 0.319189i | \(0.896589\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.42162e11 | + | 2.18009e10i | 0.504210 | + | 0.0773217i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.52718e11 | + | 1.52718e11i | −0.514705 | + | 0.514705i | −0.915965 | − | 0.401259i | \(-0.868573\pi\) |
0.401259 | + | 0.915965i | \(0.368573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.50951e11i | − | 1.12456i | −0.826948 | − | 0.562278i | \(-0.809925\pi\) | ||
0.826948 | − | 0.562278i | \(-0.190075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.97583e11 | −0.602239 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.43314e11 | − | 1.43314e11i | −0.415726 | − | 0.415726i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.08073e10 | + | 3.96520e11i | −0.167952 | + | 1.09521i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.54556e10 | − | 1.54556e10i | 0.0406662 | − | 0.0406662i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.22917e11i | − | 0.308235i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.84043e11 | −1.63558 | −0.817788 | − | 0.575519i | \(-0.804800\pi\) | ||||
−0.817788 | + | 0.575519i | \(0.804800\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.37809e11 | + | 4.37809e11i | 0.998590 | + | 0.998590i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.10035e11 | − | 8.07737e10i | 0.239517 | − | 0.175824i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.78856e11 | + | 2.78856e11i | −0.579537 | + | 0.579537i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.16122e11i | 1.42156i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.32212e11 | 0.630164 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.61330e11 | − | 3.61330e11i | −0.655209 | − | 0.655209i | 0.299033 | − | 0.954243i | \(-0.403336\pi\) |
−0.954243 | + | 0.299033i | \(0.903336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.05066e10 | − | 9.71266e10i | 0.0529031 | − | 0.168432i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.54034e11 | + | 2.54034e11i | −0.421466 | + | 0.421466i | −0.885708 | − | 0.464242i | \(-0.846327\pi\) |
0.464242 | + | 0.885708i | \(0.346327\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.11963e11i | − | 0.177785i | −0.996041 | − | 0.0888926i | \(-0.971667\pi\) | ||
0.996041 | − | 0.0888926i | \(-0.0283328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.72244e10 | 0.132611 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00272e11 | + | 2.00272e11i | 0.291636 | + | 0.291636i | 0.837726 | − | 0.546090i | \(-0.183884\pi\) |
−0.546090 | + | 0.837726i | \(0.683884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.21150e11 | − | 7.09941e11i | −0.727149 | − | 0.990565i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.77254e11 | − | 6.77254e11i | 0.905754 | − | 0.905754i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.47488e11i | − | 0.573842i | −0.957954 | − | 0.286921i | \(-0.907368\pi\) | ||
0.957954 | − | 0.286921i | \(-0.0926316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.59973e12 | 1.96771 | 0.983854 | − | 0.178975i | \(-0.0572780\pi\) | ||||
0.983854 | + | 0.178975i | \(0.0572780\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.09205e11 | + | 2.09205e11i | 0.246911 | + | 0.246911i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.47801e11 | − | 8.40065e10i | −0.620572 | − | 0.0951661i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.70224e11 | − | 4.70224e11i | 0.511470 | − | 0.511470i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.61538e11i | − | 0.482181i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.49953e11 | 0.652399 | 0.326199 | − | 0.945301i | \(-0.394232\pi\) | ||||
0.326199 | + | 0.945301i | \(0.394232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.78500e10 | + | 4.78500e10i | 0.0461614 | + | 0.0461614i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.37545e11 | − | 1.54902e12i | 0.220316 | − | 1.43666i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.14568e11 | + | 6.14568e11i | −0.548156 | + | 0.548156i | −0.925907 | − | 0.377751i | \(-0.876697\pi\) |
0.377751 | + | 0.925907i | \(0.376697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.72238e11i | 0.834207i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.06067e11 | −0.170140 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.57274e11 | + | 1.57274e11i | 0.124991 | + | 0.124991i | 0.766835 | − | 0.641844i | \(-0.221830\pi\) |
−0.641844 | + | 0.766835i | \(0.721830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.30248e12 | + | 9.56117e11i | −0.996645 | + | 0.731613i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.68028e12 | + | 1.68028e12i | −1.23830 | + | 1.23830i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.16275e12i | − | 0.825517i | −0.910840 | − | 0.412759i | \(-0.864565\pi\) | ||
0.910840 | − | 0.412759i | \(-0.135435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.12479e12 | 1.45368 | 0.726841 | − | 0.686806i | \(-0.240988\pi\) | ||||
0.726841 | + | 0.686806i | \(0.240988\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.33680e11 | + | 3.33680e11i | 0.220048 | + | 0.220048i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00701e11 | + | 9.44473e10i | 0.191193 | + | 0.0600518i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.10855e12 | + | 1.10855e12i | −0.679764 | + | 0.679764i | −0.959947 | − | 0.280183i | \(-0.909605\pi\) |
0.280183 | + | 0.959947i | \(0.409605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00960e11i | 0.237181i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.29651e12 | −0.740020 | −0.370010 | − | 0.929028i | \(-0.620646\pi\) | ||||
−0.370010 | + | 0.929028i | \(0.620646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.32307e12 | + | 1.32307e12i | 0.728870 | + | 0.728870i | 0.970395 | − | 0.241525i | \(-0.0776475\pi\) |
−0.241525 | + | 0.970395i | \(0.577648\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.85630e12 | − | 2.52876e12i | −0.987245 | − | 1.34488i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.30702e11 | + | 9.30702e11i | −0.477971 | + | 0.477971i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.60382e12i | − | 0.795550i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.37515e12 | −1.61744 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.23005e11 | − | 5.23005e11i | −0.242196 | − | 0.242196i | 0.575562 | − | 0.817758i | \(-0.304783\pi\) |
−0.817758 | + | 0.575562i | \(0.804783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.31629e12 | + | 5.08560e11i | 1.48437 | + | 0.227631i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.92491e11 | + | 2.92491e11i | −0.126570 | + | 0.126570i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.66103e11i | 0.153196i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.47861e11 | 0.181263 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.33103e11 | + | 6.33103e11i | 0.247891 | + | 0.247891i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.24307e11 | + | 8.10601e11i | −0.0470975 | + | 0.307120i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.47818e12 | + | 2.47818e12i | −0.908742 | + | 0.908742i | −0.996171 | − | 0.0874289i | \(-0.972135\pi\) |
0.0874289 | + | 0.996171i | \(0.472135\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.14738e12i | − | 0.762282i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.13390e12 | 1.76460 | 0.882298 | − | 0.470691i | \(-0.155995\pi\) | ||||
0.882298 | + | 0.470691i | \(0.155995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.01009e12 | + | 3.01009e12i | 1.00198 | + | 1.00198i | 0.999998 | + | 0.00198008i | \(0.000630280\pi\) |
0.00198008 | + | 0.999998i | \(0.499370\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.69266e11 | − | 1.97661e11i | 0.0868216 | − | 0.0637337i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.19749e12 | − | 3.19749e12i | 0.998878 | − | 0.998878i | −0.00112099 | − | 0.999999i | \(-0.500357\pi\) |
0.999999 | + | 0.00112099i | \(0.000356822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.37976e11i | − | 0.193130i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.93031e12 | −1.15319 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.12362e12 | − | 5.12362e12i | −1.45735 | − | 1.45735i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.89029e11 | + | 1.51165e12i | 0.217609 | + | 0.416903i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.17924e12 | − | 4.17924e12i | 1.11779 | − | 1.11779i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.88958e12i | − | 0.749646i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.37117e12 | 1.10016 | 0.550082 | − | 0.835110i | \(-0.314596\pi\) | ||||
0.550082 | + | 0.835110i | \(0.314596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.98978e11 | + | 6.98978e11i | 0.170703 | + | 0.170703i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.38621e12 | − | 1.88837e12i | −0.328553 | − | 0.447573i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.87588e12 | − | 2.87588e12i | 0.661640 | − | 0.661640i | −0.294127 | − | 0.955766i | \(-0.595029\pi\) |
0.955766 | + | 0.294127i | \(0.0950287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.35641e12i | 1.19640i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.24136e12 | −0.269231 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.33378e12 | − | 3.33378e12i | −0.702208 | − | 0.702208i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.70705e12 | + | 2.61779e11i | 0.349261 | + | 0.0535599i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.91536e12 | + | 2.91536e12i | −0.579488 | + | 0.579488i | −0.934762 | − | 0.355275i | \(-0.884387\pi\) |
0.355275 | + | 0.934762i | \(0.384387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.62234e12i | 1.66532i | 0.553784 | + | 0.832660i | \(0.313183\pi\) | ||||
−0.553784 | + | 0.832660i | \(0.686817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.23787e12 | −0.420048 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.32642e12 | + | 1.32642e12i | 0.241996 | + | 0.241996i | 0.817676 | − | 0.575679i | \(-0.195262\pi\) |
−0.575679 | + | 0.817676i | \(0.695262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.11271e12 | + | 7.25591e12i | −0.197351 | + | 1.28692i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.63581e12 | − | 3.63581e12i | 0.626990 | − | 0.626990i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.42823e12i | 0.742605i | 0.928512 | + | 0.371303i | \(0.121089\pi\) | ||||
−0.928512 | + | 0.371303i | \(0.878911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.37322e12 | −1.36570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.64003e12 | − | 4.64003e12i | −0.736186 | − | 0.736186i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.84425e12 | + | 5.02420e12i | −1.05648 | + | 0.775537i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.04313e12 | − | 2.04313e12i | 0.306878 | − | 0.306878i | −0.536819 | − | 0.843697i | \(-0.680374\pi\) |
0.843697 | + | 0.536819i | \(0.180374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.33823e12i | 0.195614i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.30131e12 | −0.754247 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.01411e12 | + | 3.01411e12i | 0.417461 | + | 0.417461i | 0.884328 | − | 0.466867i | \(-0.154617\pi\) |
−0.466867 | + | 0.884328i | \(0.654617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.61263e12 | − | 2.59815e12i | 1.02655 | − | 0.350354i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.44060e12 | − | 2.44060e12i | 0.320472 | − | 0.320472i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.63889e11i | 0.0976864i | 0.998806 | + | 0.0488432i | \(0.0155535\pi\) | ||||
−0.998806 | + | 0.0488432i | \(0.984447\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.31197e12 | −0.287977 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.82634e12 | − | 9.82634e12i | −1.19233 | − | 1.19233i | −0.976410 | − | 0.215924i | \(-0.930724\pi\) |
−0.215924 | − | 0.976410i | \(-0.569276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.11953e11 | + | 8.33637e11i | 0.0723459 | + | 0.0985538i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.21983e11 | − | 3.21983e11i | 0.0370919 | − | 0.0370919i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.58595e12i | 0.178050i | 0.996029 | + | 0.0890250i | \(0.0283751\pi\) | ||||
−0.996029 | + | 0.0890250i | \(0.971625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.98911e12 | 0.436508 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31585e12 | + | 7.31585e12i | 0.780372 | + | 0.780372i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.12243e13 | + | 1.72127e12i | 1.16728 | + | 0.179004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.83039e12 | − | 3.83039e12i | 0.388410 | − | 0.388410i | −0.485710 | − | 0.874120i | \(-0.661439\pi\) |
0.874120 | + | 0.485710i | \(0.161439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.02925e13i | − | 1.01779i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.10170e11 | −0.0588477 | −0.0294238 | − | 0.999567i | \(-0.509367\pi\) | ||||
−0.0294238 | + | 0.999567i | \(0.509367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.74885e12 | − | 4.74885e12i | −0.446749 | − | 0.446749i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.89176e12 | + | 1.23360e13i | −0.173616 | + | 1.13214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.16401e12 | + | 2.16401e12i | −0.193770 | + | 0.193770i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.67942e13i | − | 1.46738i | −0.679486 | − | 0.733689i | \(-0.737797\pi\) | ||
0.679486 | − | 0.733689i | \(-0.262203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.71880e11 | 0.0572905 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.78390e12 | + | 7.78390e12i | 0.647809 | + | 0.647809i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.41109e12 | − | 3.23807e12i | 0.358348 | − | 0.263055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.09150e12 | − | 2.09150e12i | 0.165874 | − | 0.165874i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.70046e12i | 0.131673i | 0.997830 | + | 0.0658363i | \(0.0209715\pi\) | ||||
−0.997830 | + | 0.0658363i | \(0.979028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.12084e12 | 0.0847487 | 0.0423743 | − | 0.999102i | \(-0.486508\pi\) | ||||
0.0423743 | + | 0.999102i | \(0.486508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.07743e12 | − | 2.07743e12i | −0.153400 | − | 0.153400i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.64711e13 | − | 8.59735e12i | 1.18790 | − | 0.620040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.90262e12 | + | 1.90262e12i | −0.134033 | + | 0.134033i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.48541e12i | 0.102226i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.32023e12 | −0.0887695 | −0.0443847 | − | 0.999015i | \(-0.514133\pi\) | ||||
−0.0443847 | + | 0.999015i | \(0.514133\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.74616e12 | + | 1.74616e12i | 0.114721 | + | 0.114721i | 0.762137 | − | 0.647416i | \(-0.224150\pi\) |
−0.647416 | + | 0.762137i | \(0.724150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.63475e12 | − | 1.31250e13i | −0.618578 | − | 0.842662i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.64632e12 | − | 5.64632e12i | 0.354289 | − | 0.354289i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.77138e12i | 0.231301i | 0.993290 | + | 0.115651i | \(0.0368953\pi\) | ||||
−0.993290 | + | 0.115651i | \(0.963105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.84879e12 | −0.110840 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.11940e12 | + | 5.11940e12i | 0.300055 | + | 0.300055i | 0.841035 | − | 0.540980i | \(-0.181947\pi\) |
−0.540980 | + | 0.841035i | \(0.681947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.78477e13 | − | 4.27051e12i | −1.59584 | − | 0.244726i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.07145e13 | + | 2.07145e13i | −1.16074 | + | 1.16074i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.94777e11i | − | 0.0490324i | −0.999699 | − | 0.0245162i | \(-0.992195\pi\) | ||
0.999699 | − | 0.0245162i | \(-0.00780453\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.14312e12 | −0.222047 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.58868e12 | − | 1.58868e12i | −0.0832810 | − | 0.0832810i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.48061e11 | + | 5.53015e12i | −0.0434881 | + | 0.283583i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.40263e13 | + | 1.40263e13i | −0.703660 | + | 0.703660i | −0.965194 | − | 0.261534i | \(-0.915772\pi\) |
0.261534 | + | 0.965194i | \(0.415772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.43841e13i | 1.19686i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.77271e13 | 0.851397 | 0.425699 | − | 0.904865i | \(-0.360028\pi\) | ||||
0.425699 | + | 0.904865i | \(0.360028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.62363e12 | + | 7.62363e12i | 0.358308 | + | 0.358308i | 0.863189 | − | 0.504881i | \(-0.168464\pi\) |
−0.504881 | + | 0.863189i | \(0.668464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.55383e13 | + | 1.87471e13i | −1.17470 | + | 0.862320i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.07668e13 | + | 1.07668e13i | −0.484733 | + | 0.484733i | −0.906639 | − | 0.421906i | \(-0.861361\pi\) |
0.421906 | + | 0.906639i | \(0.361361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.68602e12i | − | 0.338717i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.83997e13 | 1.22521 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.96849e11 | + | 9.96849e11i | 0.0421040 | + | 0.0421040i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.11448e13 | − | 3.54828e13i | 0.460898 | − | 1.46740i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.81131e12 | + | 3.81131e12i | −0.154341 | + | 0.154341i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.92794e13i | 1.16114i | 0.814211 | + | 0.580569i | \(0.197170\pi\) | ||||
−0.814211 | + | 0.580569i | \(0.802830\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.65570e13 | −0.643067 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00674e12 | + | 4.00674e12i | 0.152425 | + | 0.152425i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.36795e13 | − | 3.22576e13i | −0.882397 | − | 1.20205i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.67002e13 | − | 1.67002e13i | 0.609644 | − | 0.609644i | −0.333209 | − | 0.942853i | \(-0.608131\pi\) |
0.942853 | + | 0.333209i | \(0.108131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.09586e13i | − | 1.82252i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.55034e13 | 1.24412 | 0.622059 | − | 0.782970i | \(-0.286296\pi\) | ||||
0.622059 | + | 0.782970i | \(0.286296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.65930e13 | − | 2.65930e13i | −0.913131 | − | 0.913131i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.03929e12 | + | 1.59377e11i | 0.0349711 | + | 0.00536290i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.70309e13 | + | 1.70309e13i | −0.561637 | + | 0.561637i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.76933e13i | − | 0.571883i | −0.958247 | − | 0.285941i | \(-0.907694\pi\) | ||
0.958247 | − | 0.285941i | \(-0.0923062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.37727e13 | 1.70362 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.72856e13 | + | 2.72856e13i | 0.847411 | + | 0.847411i | 0.989809 | − | 0.142399i | \(-0.0454815\pi\) |
−0.142399 | + | 0.989809i | \(0.545481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.60906e12 | + | 1.04926e13i | −0.0489908 | + | 0.319466i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00114e13 | − | 2.00114e13i | 0.597361 | − | 0.597361i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.27994e12i | − | 0.183809i | −0.995768 | − | 0.0919045i | \(-0.970705\pi\) | ||
0.995768 | − | 0.0919045i | \(-0.0292954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.78573e13 | −0.799530 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.45141e13 | + | 3.45141e13i | 0.971425 | + | 0.971425i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.05233e13 | − | 1.50657e13i | 0.566514 | − | 0.415864i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.43165e12 | − | 6.43165e12i | 0.174128 | − | 0.174128i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.37521e12i | 0.222412i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.02225e13 | −0.526800 | −0.263400 | − | 0.964687i | \(-0.584844\pi\) | ||||
−0.263400 | + | 0.964687i | \(0.584844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.99902e12 | + | 9.99902e12i | 0.255534 | + | 0.255534i | 0.823235 | − | 0.567701i | \(-0.192167\pi\) |
−0.567701 | + | 0.823235i | \(0.692167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.51793e13 | + | 7.90858e12i | 0.631316 | + | 0.198290i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.17441e13 | + | 5.17441e13i | −1.27294 | + | 1.27294i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.70304e13i | − | 0.893883i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.11923e13 | 0.265122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.58496e13 | − | 1.58496e13i | −0.368454 | − | 0.368454i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.75744e13 | − | 3.75635e13i | −0.629126 | − | 0.857032i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.08278e13 | + | 1.08278e13i | −0.242476 | + | 0.242476i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.72380e12i | − | 0.125817i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.80088e13 | −0.820159 | −0.410079 | − | 0.912050i | \(-0.634499\pi\) | ||||
−0.410079 | + | 0.912050i | \(0.634499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.37231e13 | − | 2.37231e13i | −0.502542 | − | 0.502542i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92635e13 | + | 1.06217e13i | 1.44053 | + | 0.220908i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.19171e13 | − | 1.19171e13i | 0.243352 | − | 0.243352i | −0.574883 | − | 0.818236i | \(-0.694952\pi\) |
0.818236 | + | 0.574883i | \(0.194952\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.73573e12i | 0.0548544i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.52814e13 | −1.48228 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.63454e13 | + | 2.63454e13i | 0.509423 | + | 0.509423i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.18389e13 | + | 7.72010e13i | −0.224827 | + | 1.46608i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.13146e13 | − | 2.13146e13i | 0.397559 | − | 0.397559i | −0.479812 | − | 0.877371i | \(-0.659295\pi\) |
0.877371 | + | 0.479812i | \(0.159295\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.62696e12i | 0.139731i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.61852e13 | 0.291276 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.72944e13 | − | 3.72944e13i | −0.659328 | − | 0.659328i | 0.295893 | − | 0.955221i | \(-0.404383\pi\) |
−0.955221 | + | 0.295893i | \(0.904383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.11932e13 | + | 3.75797e13i | −0.889140 | + | 0.652696i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.89549e13 | + | 2.89549e13i | −0.494090 | + | 0.494090i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.65415e13i | 1.28332i | 0.766988 | + | 0.641661i | \(0.221754\pi\) | ||||
−0.766988 | + | 0.641661i | \(0.778246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.05290e12 | −0.0997202 | −0.0498601 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498601 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.90559e12 | − | 3.90559e12i | −0.0632287 | − | 0.0632287i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.47444e12 | + | 1.81515e13i | 0.150735 | + | 0.288784i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.45547e13 | + | 3.45547e13i | −0.540292 | + | 0.540292i | −0.923615 | − | 0.383323i | \(-0.874780\pi\) |
0.383323 | + | 0.923615i | \(0.374780\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 6.27363e13i | − | 0.964109i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.79539e13 | 0.271193 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17997e13 | − | 1.17997e13i | −0.175197 | − | 0.175197i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.36613e12 | + | 4.58553e12i | 0.0491305 | + | 0.0669284i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.97080e13 | − | 8.97080e13i | 1.28718 | − | 1.28718i | 0.350694 | − | 0.936490i | \(-0.385946\pi\) |
0.936490 | − | 0.350694i | \(-0.114054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.46481e14i | 2.06635i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.69266e13 | −0.789547 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.66464e13 | − | 5.66464e13i | −0.772501 | − | 0.772501i | 0.206042 | − | 0.978543i | \(-0.433942\pi\) |
−0.978543 | + | 0.206042i | \(0.933942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.02572e13 | + | 9.24057e12i | 0.808023 | + | 0.123912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.54097e13 | − | 6.54097e13i | 0.862523 | − | 0.862523i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.21070e13i | 0.286679i | 0.989674 | + | 0.143339i | \(0.0457840\pi\) | ||||
−0.989674 | + | 0.143339i | \(0.954216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.42854e12 | −0.0182188 | −0.00910942 | − | 0.999959i | \(-0.502900\pi\) | ||||
−0.00910942 | + | 0.999959i | \(0.502900\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.52576e12 | − | 5.52576e12i | −0.0693115 | − | 0.0693115i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.17928e13 | − | 7.69003e13i | 0.145493 | − | 0.948748i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.10881e14 | − | 1.10881e14i | 1.34560 | − | 1.34560i | 0.455220 | − | 0.890379i | \(-0.349561\pi\) |
0.890379 | − | 0.455220i | \(-0.150439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 5.34211e13i | − | 0.637715i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.92090e13 | 0.577881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.08895e13 | + | 6.08895e13i | 0.703460 | + | 0.703460i | 0.965152 | − | 0.261691i | \(-0.0842802\pi\) |
−0.261691 | + | 0.965152i | \(0.584280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.52360e13 | + | 6.25697e13i | −0.968829 | + | 0.711194i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.12126e13 | − | 8.12126e13i | 0.908234 | − | 0.908234i | −0.0878960 | − | 0.996130i | \(-0.528014\pi\) |
0.996130 | + | 0.0878960i | \(0.0280143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.32089e13i | − | 1.02566i | −0.858490 | − | 0.512831i | \(-0.828597\pi\) | ||
0.858490 | − | 0.512831i | \(-0.171403\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.68717e13 | −0.290963 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.53634e13 | − | 6.53634e13i | −0.696457 | − | 0.696457i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.82405e13 | + | 5.45287e13i | 0.820411 | + | 0.571774i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.29091e13 | − | 2.29091e13i | 0.236413 | − | 0.236413i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.80407e14i | 1.83231i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.46630e13 | 0.546445 | 0.273222 | − | 0.961951i | \(-0.411910\pi\) | ||||
0.273222 | + | 0.961951i | \(0.411910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.27491e14 | − | 1.27491e14i | −1.25447 | − | 1.25447i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.62204e13 | − | 2.20964e13i | −0.157106 | − | 0.214019i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.18966e13 | − | 2.18966e13i | 0.208776 | − | 0.208776i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.44883e13i | 0.229855i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.03783e12 | −0.0373128 | −0.0186564 | − | 0.999826i | \(-0.505939\pi\) | ||||
−0.0186564 | + | 0.999826i | \(0.505939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.71348e13 | + | 8.71348e13i | 0.792751 | + | 0.792751i | 0.981941 | − | 0.189190i | \(-0.0605861\pi\) |
−0.189190 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55626e13 | + | 5.45360e12i | 0.318562 | + | 0.0488522i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.50155e14 | + | 1.50155e14i | −1.32440 | + | 1.32440i | −0.414225 | + | 0.910174i | \(0.635947\pi\) |
−0.910174 | + | 0.414225i | \(0.864053\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.46509e13i | 0.300947i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.03945e14 | −0.888998 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.04798e13 | − | 1.04798e13i | −0.0882644 | − | 0.0882644i | 0.661596 | − | 0.749860i | \(-0.269879\pi\) |
−0.749860 | + | 0.661596i | \(0.769879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.85935e13 | + | 1.21247e14i | −0.154225 | + | 1.00569i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00276e13 | + | 2.00276e13i | −0.163607 | + | 0.163607i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.12979e13i | − | 0.0909013i | −0.998967 | − | 0.0454507i | \(-0.985528\pi\) | ||
0.998967 | − | 0.0454507i | \(-0.0144724\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.56609e13 | −0.758101 | −0.379050 | − | 0.925376i | \(-0.623749\pi\) | ||||
−0.379050 | + | 0.925376i | \(0.623749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.19171e13 | + | 6.19171e13i | 0.483329 | + | 0.483329i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.83695e13 | − | 7.22107e13i | 0.756401 | − | 0.555256i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.93060e13 | − | 2.93060e13i | 0.221987 | − | 0.221987i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.34688e14i | − | 1.00508i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.46972e12 | −0.0622668 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.19067e13 | + | 7.19067e13i | 0.520827 | + | 0.520827i | 0.917821 | − | 0.396994i | \(-0.129947\pi\) |
−0.396994 | + | 0.917821i | \(0.629947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.10954e14 | + | 5.79141e13i | −0.791816 | + | 0.413300i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.71244e14 | + | 1.71244e14i | −1.20413 | + | 1.20413i | −0.231227 | + | 0.972900i | \(0.574274\pi\) |
−0.972900 | + | 0.231227i | \(0.925726\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.31294e14i | − | 0.909696i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.46929e13 | −0.646520 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.53293e14 | − | 1.53293e14i | −1.03138 | − | 1.03138i | −0.999491 | − | 0.0318872i | \(-0.989848\pi\) |
−0.0318872 | − | 0.999491i | \(-0.510152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.71381e12 | + | 6.42142e12i | 0.0312550 | + | 0.0425773i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.08674e13 | − | 2.08674e13i | 0.136359 | − | 0.136359i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.02801e13i | − | 0.581428i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.85081e13 | 0.371386 | 0.185693 | − | 0.982608i | \(-0.440547\pi\) | ||||
0.185693 | + | 0.982608i | \(0.440547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.43939e12 | + | 2.43939e12i | 0.0152621 | + | 0.0152621i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.46629e13 | + | 5.31563e12i | 0.213767 | + | 0.0327817i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.72700e14 | + | 1.72700e14i | −1.04985 | + | 1.04985i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.46529e13i | 0.447364i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.06770e14 | 0.630754 | 0.315377 | − | 0.948966i | \(-0.397869\pi\) | ||||
0.315377 | + | 0.948966i | \(0.397869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.55354e14 | + | 2.55354e14i | 1.48719 | + | 1.48719i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.51865e13 | − | 2.29449e14i | 0.202037 | − | 1.31747i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.46279e13 | + | 2.46279e13i | −0.139421 | + | 0.139421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39815e14i | 0.780409i | 0.920728 | + | 0.390204i | \(0.127596\pi\) | ||||
−0.920728 | + | 0.390204i | \(0.872404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.78813e13 | 0.208486 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.70229e13 | − | 5.70229e13i | −0.309458 | − | 0.309458i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.41966e13 | + | 1.04214e13i | −0.0759723 | + | 0.0557694i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.34021e13 | − | 8.34021e13i | 0.440130 | − | 0.440130i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 6.98686e13i | − | 0.363612i | −0.983334 | − | 0.181806i | \(-0.941806\pi\) | ||
0.983334 | − | 0.181806i | \(-0.0581942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.35335e13 | 0.428730 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.98154e14 | + | 2.98154e14i | 1.50921 | + | 1.50921i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.78448e13 | − | 1.84166e14i | 0.288785 | − | 0.919431i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.53649e13 | − | 5.53649e13i | 0.272623 | − | 0.272623i | −0.557532 | − | 0.830155i | \(-0.688252\pi\) |
0.830155 | + | 0.557532i | \(0.188252\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.57840e14i | − | 0.766621i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.31043e13 | 0.398140 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.77070e14 | − | 2.77070e14i | −1.30939 | − | 1.30939i | −0.921852 | − | 0.387541i | \(-0.873324\pi\) |
−0.387541 | − | 0.921852i | \(-0.626676\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.64412e13 | − | 1.17755e14i | −0.402981 | − | 0.548964i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.71076e13 | − | 1.71076e13i | 0.0786775 | − | 0.0786775i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.82183e14i | − | 0.826581i | −0.910599 | − | 0.413291i | \(-0.864379\pi\) | ||
0.910599 | − | 0.413291i | \(-0.135621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.75279e14 | 0.784584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.92009e13 | − | 4.92009e13i | −0.217285 | − | 0.217285i | 0.590069 | − | 0.807353i | \(-0.299101\pi\) |
−0.807353 | + | 0.590069i | \(0.799101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.43305e14 | − | 5.26466e13i | −1.49589 | − | 0.229398i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.29077e13 | − | 1.29077e13i | 0.0554941 | − | 0.0554941i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.52890e14i | − | 0.648590i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.76620e14 | 1.57654 | 0.788269 | − | 0.615331i | \(-0.210978\pi\) | ||||
0.788269 | + | 0.615331i | \(0.210978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.21137e14 | + | 1.21137e14i | 0.500383 | + | 0.500383i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.03770e12 | − | 2.63296e13i | 0.0164588 | − | 0.107327i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.39645e13 | + | 9.39645e13i | −0.377993 | + | 0.377993i | −0.870378 | − | 0.492384i | \(-0.836125\pi\) |
0.492384 | + | 0.870378i | \(0.336125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.78364e13i | 0.0708106i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.12361e14 | 1.22386 | 0.611932 | − | 0.790910i | \(-0.290393\pi\) | ||||
0.611932 | + | 0.790910i | \(0.290393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.62573e14 | + | 1.62573e14i | 0.628676 | + | 0.628676i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.99645e13 | − | 3.66777e13i | 0.190701 | − | 0.139989i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.32558e14 | + | 1.32558e14i | −0.499378 | + | 0.499378i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.65626e14i | 1.35958i | 0.733406 | + | 0.679790i | \(0.237929\pi\) | ||||
−0.733406 | + | 0.679790i | \(0.762071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.29084e14 | −0.840860 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.98060e14 | − | 2.98060e14i | −1.07996 | − | 1.07996i | −0.996512 | − | 0.0834454i | \(-0.973408\pi\) |
−0.0834454 | − | 0.996512i | \(-0.526592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.58346e14 | − | 1.12553e14i | −1.28172 | − | 0.402577i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.81204e14 | + | 1.81204e14i | −0.639828 | + | 0.639828i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.88890e14i | 1.70421i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.58148e13 | −0.260915 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.79138e14 | + | 1.79138e14i | 0.608666 | + | 0.608666i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.99248e14 | + | 2.71427e14i | 0.668413 | + | 0.910550i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.35390e14 | − | 1.35390e14i | 0.448450 | − | 0.448450i | −0.446389 | − | 0.894839i | \(-0.647290\pi\) |
0.894839 | + | 0.446389i | \(0.147290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.86251e13i | 0.191734i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.08365e14 | −0.672889 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.24012e13 | − | 3.24012e13i | −0.103323 | − | 0.103323i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.20953e14 | − | 6.45541e13i | −1.32556 | − | 0.203277i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.63733e14 | + | 3.63733e14i | −1.13108 | + | 1.13108i | −0.141077 | + | 0.989999i | \(0.545056\pi\) |
−0.989999 | + | 0.141077i | \(0.954944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.36187e14i | − | 1.64658i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.39843e13 | −0.285031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.20049e13 | − | 6.20049e13i | −0.185716 | − | 0.185716i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.01833e13 | + | 6.64045e13i | −0.0301237 | + | 0.196435i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.16712e14 | − | 2.16712e14i | 0.633163 | − | 0.633163i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.70403e14i | 0.780314i | 0.920748 | + | 0.390157i | \(0.127579\pi\) | ||||
−0.920748 | + | 0.390157i | \(0.872421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.25247e14 | −1.49713 | −0.748565 | − | 0.663061i | \(-0.769257\pi\) | ||||
−0.748565 | + | 0.663061i | \(0.769257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.96015e14 | + | 3.96015e14i | 1.11496 | + | 1.11496i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.87031e14 | − | 3.57517e14i | 1.35447 | − | 0.994281i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.17629e14 | − | 1.17629e14i | 0.323149 | − | 0.323149i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.86639e13i | 0.0506505i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.84037e14 | 1.83385 | 0.916925 | − | 0.399061i | \(-0.130664\pi\) | ||||
0.916925 | + | 0.399061i | \(0.130664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.05629e14 | − | 2.05629e14i | −0.544610 | − | 0.544610i | 0.380267 | − | 0.924877i | \(-0.375832\pi\) |
−0.924877 | + | 0.380267i | \(0.875832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.84412e13 | + | 7.36471e13i | 0.100584 | + | 0.192702i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.20671e14 | + | 4.20671e14i | −1.08746 | + | 1.08746i | −0.0916761 | + | 0.995789i | \(0.529222\pi\) |
−0.995789 | + | 0.0916761i | \(0.970778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.52280e14i | − | 1.66595i | −0.553311 | − | 0.832975i | \(-0.686636\pi\) | ||
0.553311 | − | 0.832975i | \(-0.313364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.13221e14 | −1.04274 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.38588e14 | − | 2.38588e14i | −0.594872 | − | 0.594872i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.77261e14 | + | 5.13926e14i | 0.929414 | + | 1.26610i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.48562e14 | − | 3.48562e14i | 0.848502 | − | 0.848502i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.02853e13i | − | 0.0728488i | −0.999336 | − | 0.0364244i | \(-0.988403\pi\) | ||
0.999336 | − | 0.0364244i | \(-0.0115968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.99750e13 | 0.0712491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41641e14 | − | 2.41641e14i | −0.567587 | − | 0.567587i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.31653e14 | + | 5.08597e13i | 0.769839 | + | 0.118056i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.80498e14 | − | 1.80498e14i | 0.414053 | − | 0.414053i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.93183e14i | 1.11807i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.98812e14 | −0.445445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.91456e14 | + | 2.91456e14i | 0.645399 | + | 0.645399i | 0.951878 | − | 0.306479i | \(-0.0991508\pi\) |
−0.306479 | + | 0.951878i | \(0.599151\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.88066e13 | − | 1.22636e14i | 0.0411603 | − | 0.268404i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.05558e14 | − | 3.05558e14i | 0.660982 | − | 0.660982i | −0.294629 | − | 0.955612i | \(-0.595196\pi\) |
0.955612 | + | 0.294629i | \(0.0951961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.89475e14i | − | 1.26037i | −0.776443 | − | 0.630187i | \(-0.782978\pi\) | ||
0.776443 | − | 0.630187i | \(-0.217022\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.46926e14 | −0.733197 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.31410e14 | + | 4.31410e14i | 0.901231 | + | 0.901231i | 0.995543 | − | 0.0943117i | \(-0.0300650\pi\) |
−0.0943117 | + | 0.995543i | \(0.530065\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00450e13 | + | 5.87591e13i | −0.165293 | + | 0.121337i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.98918e14 | − | 2.98918e14i | 0.610178 | − | 0.610178i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.17279e14i | 0.236658i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.30891e14 | 0.261108 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.43921e13 | − | 9.43921e13i | −0.186151 | − | 0.186151i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.01068e14 | + | 2.96133e14i | 0.197050 | + | 0.577360i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.06135e13 | + | 5.06135e13i | −0.0975593 | + | 0.0975593i | −0.754202 | − | 0.656643i | \(-0.771976\pi\) |
0.656643 | + | 0.754202i | \(0.271976\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1.94954e14i | − | 0.371524i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.33506e14 | 0.816800 | 0.408400 | − | 0.912803i | \(-0.366087\pi\) | ||||
0.408400 | + | 0.912803i | \(0.366087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.45003e14 | − | 5.45003e14i | −1.01530 | − | 1.01530i | −0.999881 | − | 0.0154219i | \(-0.995091\pi\) |
−0.0154219 | − | 0.999881i | \(-0.504909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.23300e14 | + | 7.12869e14i | 0.963905 | + | 1.31309i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.99448e14 | − | 4.99448e14i | 0.909645 | − | 0.909645i | −0.0865986 | − | 0.996243i | \(-0.527600\pi\) |
0.996243 | + | 0.0865986i | \(0.0275998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.99362e13i | − | 0.161967i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.28896e14 | −0.229535 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.58937e14 | − | 7.58937e14i | −1.33644 | − | 1.33644i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.79452e14 | − | 2.75193e13i | −0.312488 | − | 0.0479207i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.82338e13 | + | 6.82338e13i | −0.117500 | + | 0.117500i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.60277e14i | 1.29471i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.83703e14 | −1.65668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.34715e13 | + | 8.34715e13i | 0.139027 | + | 0.139027i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.02932e13 | − | 3.93168e14i | 0.0993174 | − | 0.647643i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.77914e13 | − | 9.77914e13i | 0.159318 | − | 0.159318i | −0.622947 | − | 0.782264i | \(-0.714065\pi\) |
0.782264 | + | 0.622947i | \(0.214065\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.54117e13i | 0.0570595i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.85912e14 | 1.09314 | 0.546571 | − | 0.837413i | \(-0.315933\pi\) | ||||
0.546571 | + | 0.837413i | \(0.315933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.99619e13 | + | 3.99619e13i | 0.0629930 | + | 0.0629930i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.74247e14 | + | 1.27910e14i | −0.271681 | + | 0.199434i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.84588e14 | + | 2.84588e14i | −0.438905 | + | 0.438905i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.85058e14i | 1.04508i | 0.852615 | + | 0.522540i | \(0.175015\pi\) | ||||
−0.852615 | + | 0.522540i | \(0.824985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.23757e14 | −1.39399 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.90032e14 | − | 2.90032e14i | −0.432950 | − | 0.432950i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.20899e14 | + | 4.28481e14i | −1.21222 | + | 0.632736i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00553e13 | − | 6.00553e13i | 0.0877309 | − | 0.0877309i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.11675e15i | 1.61391i | 0.590614 | + | 0.806954i | \(0.298886\pi\) | ||||
−0.590614 | + | 0.806954i | \(0.701114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.75411e14 | −0.965651 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.56848e14 | + | 9.56848e14i | 1.35343 | + | 1.35343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.13553e14 | + | 1.54688e14i | 0.158906 | + | 0.216471i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.19683e14 | − | 8.19683e14i | 1.13488 | − | 1.13488i | 0.145520 | − | 0.989355i | \(-0.453514\pi\) |
0.989355 | − | 0.145520i | \(-0.0464856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12203e15i | 1.53701i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.97374e14 | −0.538582 | −0.269291 | − | 0.963059i | \(-0.586789\pi\) | ||||
−0.269291 | + | 0.963059i | \(0.586789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90318e14 | − | 1.90318e14i | −0.255224 | − | 0.255224i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.05909e14 | − | 6.22470e13i | −0.538604 | − | 0.0825960i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.07249e14 | + | 5.07249e14i | −0.665995 | + | 0.665995i | −0.956786 | − | 0.290792i | \(-0.906081\pi\) |
0.290792 | + | 0.956786i | \(0.406081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.74404e14i | − | 0.616335i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.19189e15 | 1.53226 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.83456e14 | − | 6.83456e14i | −0.869453 | − | 0.869453i | 0.122958 | − | 0.992412i | \(-0.460762\pi\) |
−0.992412 | + | 0.122958i | \(0.960762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.92622e12 | − | 6.47283e13i | 0.0124959 | − | 0.0814849i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.18905e14 | − | 1.18905e14i | 0.148129 | − | 0.148129i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.61363e13i | 0.0322219i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.59700e14 | 0.804877 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.09918e14 | − | 1.09918e14i | −0.132721 | − | 0.132721i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.99594e14 | − | 4.40148e14i | 0.716508 | − | 0.525971i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.78260e14 | + | 2.78260e14i | −0.329093 | + | 0.329093i | −0.852241 | − | 0.523149i | \(-0.824757\pi\) |
0.523149 | + | 0.852241i | \(0.324757\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.90986e15i | − | 2.23554i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.23796e14 | −0.143420 | −0.0717101 | − | 0.997426i | \(-0.522846\pi\) | ||||
−0.0717101 | + | 0.997426i | \(0.522846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.13599e13 | + | 8.13599e13i | 0.0932924 | + | 0.0932924i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.34681e14 | + | 4.28797e14i | −0.152857 | + | 0.486664i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.70589e14 | − | 4.70589e14i | 0.528651 | − | 0.528651i | −0.391519 | − | 0.920170i | \(-0.628050\pi\) |
0.920170 | + | 0.391519i | \(0.128050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.90972e14i | − | 0.323548i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33760e14 | 0.257291 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.15213e14 | − | 8.15213e14i | −0.888185 | − | 0.888185i | 0.106164 | − | 0.994349i | \(-0.466143\pi\) |
−0.994349 | + | 0.106164i | \(0.966143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.99388e14 | − | 5.44069e14i | −0.430739 | − | 0.586777i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.38556e14 | − | 5.38556e14i | 0.574970 | − | 0.574970i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.15824e13i | 0.0967900i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.87602e14 | 0.510150 | 0.255075 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255075 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.14692e14 | + | 8.14692e14i | 0.843815 | + | 0.843815i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.08405e15 | + | 1.66241e14i | 1.11156 | + | 0.170461i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05598e14 | + | 2.05598e14i | −0.208710 | + | 0.208710i | −0.803719 | − | 0.595009i | \(-0.797149\pi\) |
0.595009 | + | 0.803719i | \(0.297149\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.21527e15i | − | 1.22136i |
(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 | 20.11.f.a.13.4 | ✓ | 10 | |
3.2 | odd | 2 | 180.11.l.a.73.3 | 10 | |||
4.3 | odd | 2 | 80.11.p.e.33.2 | 10 | |||
5.2 | odd | 4 | inner | 20.11.f.a.17.4 | yes | 10 | |
5.3 | odd | 4 | 100.11.f.b.57.2 | 10 | |||
5.4 | even | 2 | 100.11.f.b.93.2 | 10 | |||
15.2 | even | 4 | 180.11.l.a.37.3 | 10 | |||
20.7 | even | 4 | 80.11.p.e.17.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.f.a.13.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
20.11.f.a.17.4 | yes | 10 | 5.2 | odd | 4 | inner | |
80.11.p.e.17.2 | 10 | 20.7 | even | 4 | |||
80.11.p.e.33.2 | 10 | 4.3 | odd | 2 | |||
100.11.f.b.57.2 | 10 | 5.3 | odd | 4 | |||
100.11.f.b.93.2 | 10 | 5.4 | even | 2 | |||
180.11.l.a.37.3 | 10 | 15.2 | even | 4 | |||
180.11.l.a.73.3 | 10 | 3.2 | odd | 2 |