Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,12,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(49.1739635558\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.12.e.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −457.250 | − | 457.250i | −1.08639 | − | 1.08639i | −0.995897 | − | 0.0904954i | \(-0.971155\pi\) |
−0.0904954 | − | 0.995897i | \(-0.528845\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5575.43 | − | 5575.43i | 0.797890 | − | 0.797890i | −0.184872 | − | 0.982763i | \(-0.559187\pi\) |
0.982763 | + | 0.184872i | \(0.0591872\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 55452.7i | 1.24705i | 0.781804 | + | 0.623525i | \(0.214300\pi\) | ||||
−0.781804 | + | 0.623525i | \(0.785700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 241008.i | 1.36050i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 593916. | − | 593916.i | 1.11190 | − | 1.11190i | 0.119004 | − | 0.992894i | \(-0.462030\pi\) |
0.992894 | − | 0.119004i | \(-0.0379702\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −320484. | − | 320484.i | −0.239396 | − | 0.239396i | 0.577204 | − | 0.816600i | \(-0.304144\pi\) |
−0.816600 | + | 0.577204i | \(0.804144\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.09873e6 | −1.73364 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.66759e6 | −1.65139 | −0.825694 | − | 0.564118i | \(-0.809216\pi\) | ||||
−0.825694 | + | 0.564118i | \(0.809216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.35824e6 | − | 6.35824e6i | −0.589104 | − | 0.589104i | 0.348285 | − | 0.937389i | \(-0.386764\pi\) |
−0.937389 | + | 0.348285i | \(0.886764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53557e7 | − | 2.53557e7i | 1.35478 | − | 1.35478i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.96028e7i | − | 0.635060i | −0.948248 | − | 0.317530i | \(-0.897147\pi\) | ||
0.948248 | − | 0.317530i | \(-0.102853\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.33426e7i | − | 0.273257i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.92004e7 | − | 2.92004e7i | 0.391641 | − | 0.391641i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.64662e7 | − | 7.64662e7i | −0.692278 | − | 0.692278i | 0.270454 | − | 0.962733i | \(-0.412826\pi\) |
−0.962733 | + | 0.270454i | \(0.912826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.66832e8 | 1.04662 | 0.523311 | − | 0.852142i | \(-0.324696\pi\) | ||||
0.523311 | + | 0.852142i | \(0.324696\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.43136e8 | −2.41591 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.09173e8 | + | 3.09173e8i | 0.995008 | + | 0.995008i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.74973e7 | − | 2.74973e7i | 0.0651899 | − | 0.0651899i | −0.673760 | − | 0.738950i | \(-0.735322\pi\) |
0.738950 | + | 0.673760i | \(0.235322\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.93082e8i | 0.520157i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.15454e8i | 0.829630i | 0.909906 | + | 0.414815i | \(0.136154\pi\) | ||||
−0.909906 | + | 0.414815i | \(0.863846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.26623e8 | + | 8.26623e8i | −0.857493 | + | 0.857493i | −0.991042 | − | 0.133549i | \(-0.957363\pi\) |
0.133549 | + | 0.991042i | \(0.457363\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.34372e9 | + | 1.34372e9i | 1.08553 | + | 1.08553i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.20677e9 | −0.767514 | −0.383757 | − | 0.923434i | \(-0.625370\pi\) | ||||
−0.383757 | + | 0.923434i | \(0.625370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.09768e9 | −0.555132 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.42051e9 | + | 4.42051e9i | 1.79406 | + | 1.79406i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.02601e8 | − | 6.02601e8i | 0.197930 | − | 0.197930i | −0.601182 | − | 0.799112i | \(-0.705303\pi\) |
0.799112 | + | 0.601182i | \(0.205303\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.62267e9i | − | 1.77435i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.81461e9i | 1.28000i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.88524e9 | + | 3.88524e9i | −0.707508 | + | 0.707508i | −0.966011 | − | 0.258502i | \(-0.916771\pi\) |
0.258502 | + | 0.966011i | \(0.416771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.43319e9 | − | 2.43319e9i | −0.368861 | − | 0.368861i | 0.498201 | − | 0.867062i | \(-0.333994\pi\) |
−0.867062 | + | 0.498201i | \(0.833994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.33645e10 | −1.69661 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.57367e9 | −0.382024 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.86750e9 | − | 8.86750e9i | −0.802398 | − | 0.802398i | 0.181072 | − | 0.983470i | \(-0.442043\pi\) |
−0.983470 | + | 0.181072i | \(0.942043\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.96337e9 | + | 8.96337e9i | −0.689924 | + | 0.689924i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.93481e10i | 1.93045i | 0.261418 | + | 0.965226i | \(0.415810\pi\) | ||||
−0.261418 | + | 0.965226i | \(0.584190\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.45154e9i | − | 0.420698i | −0.977626 | − | 0.210349i | \(-0.932540\pi\) | ||
0.977626 | − | 0.210349i | \(-0.0674600\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.10092e9 | + | 6.10092e9i | −0.296865 | + | 0.296865i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.29342e10 | + | 3.29342e10i | 1.38659 | + | 1.38659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.31480e10 | 0.846378 | 0.423189 | − | 0.906042i | \(-0.360911\pi\) | ||||
0.423189 | + | 0.906042i | \(0.360911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.59901e10 | 0.509546 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.40857e9 | − | 4.40857e9i | −0.122848 | − | 0.122848i | 0.643010 | − | 0.765858i | \(-0.277685\pi\) |
−0.765858 | + | 0.643010i | \(0.777685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.39010e10 | + | 5.39010e10i | −1.31763 | + | 1.31763i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.99284e10i | 1.50417i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.82749e10i | 0.916382i | 0.888854 | + | 0.458191i | \(0.151502\pi\) | ||||
−0.888854 | + | 0.458191i | \(0.848498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.77717e10 | − | 1.77717e10i | 0.298539 | − | 0.298539i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.62839e10 | − | 7.62839e10i | −1.13704 | − | 1.13704i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.08998e10 | −0.940081 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.19031e10 | 1.08664 | 0.543320 | − | 0.839526i | \(-0.317167\pi\) | ||||
0.543320 | + | 0.839526i | \(0.317167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43138e11 | + | 1.43138e11i | 1.51273 | + | 1.51273i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.97475e10 | + | 8.97475e10i | −0.849679 | + | 0.849679i | −0.990093 | − | 0.140414i | \(-0.955157\pi\) |
0.140414 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.00244e11i | − | 0.852031i | −0.904716 | − | 0.426015i | \(-0.859917\pi\) | ||
0.904716 | − | 0.426015i | \(-0.140083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.82738e11i | − | 2.16194i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.34076e10 | − | 2.34076e10i | 0.161341 | − | 0.161341i | −0.621819 | − | 0.783161i | \(-0.713606\pi\) |
0.783161 | + | 0.621819i | \(0.213606\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45007e10 | + | 4.45007e10i | 0.277026 | + | 0.277026i | 0.831921 | − | 0.554894i | \(-0.187241\pi\) |
−0.554894 | + | 0.831921i | \(0.687241\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.51463e10 | −0.141644 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.35044e11 | −1.20010 | −0.600049 | − | 0.799963i | \(-0.704852\pi\) | ||||
−0.600049 | + | 0.799963i | \(0.704852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.09294e11 | − | 1.09294e11i | −0.506708 | − | 0.506708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.72391e10 | − | 7.72391e10i | 0.325698 | − | 0.325698i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.36094e11i | − | 2.05936i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.20160e11i | − | 1.47263i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.81416e11 | − | 2.81416e11i | 0.901304 | − | 0.901304i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.97847e11 | + | 1.97847e11i | 0.579861 | + | 0.579861i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.24519e11 | −1.67736 | −0.838678 | − | 0.544628i | \(-0.816671\pi\) | ||||
−0.838678 | + | 0.544628i | \(0.816671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.55946e11 | 1.86315 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.84655e11 | + | 4.84655e11i | 1.09759 | + | 1.09759i | 0.994692 | + | 0.102900i | \(0.0328121\pi\) |
0.102900 | + | 0.994692i | \(0.467188\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.52582e11 | − | 3.52582e11i | 0.734642 | − | 0.734642i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.25609e11i | − | 0.624972i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.03802e11i | 0.891860i | 0.895068 | + | 0.445930i | \(0.147127\pi\) | ||||
−0.895068 | + | 0.445930i | \(0.852873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.16836e11 | + | 2.16836e11i | −0.354446 | + | 0.354446i | −0.861761 | − | 0.507315i | \(-0.830638\pi\) |
0.507315 | + | 0.861761i | \(0.330638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.51796e11 | + | 5.51796e11i | 0.833822 | + | 0.833822i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.80681e11 | −0.532369 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.52664e11 | −1.10472 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.01913e11 | + | 5.01913e11i | 0.603091 | + | 0.603091i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.15167e11 | + | 4.15167e11i | −0.463126 | + | 0.463126i | −0.899679 | − | 0.436553i | \(-0.856199\pi\) |
0.436553 | + | 0.899679i | \(0.356199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.26377e11i | − | 0.338334i | −0.985587 | − | 0.169167i | \(-0.945892\pi\) | ||
0.985587 | − | 0.169167i | \(-0.0541078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.32997e12i | − | 2.24671i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.30160e11 | − | 9.30160e11i | 0.835090 | − | 0.835090i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.29021e11 | − | 7.29021e11i | −0.609947 | − | 0.609947i | 0.332985 | − | 0.942932i | \(-0.391944\pi\) |
−0.942932 | + | 0.332985i | \(0.891944\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.51078e11 | −0.430060 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.08703e12 | 0.791951 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.04342e11 | + | 8.04342e11i | 0.547531 | + | 0.547531i | 0.925726 | − | 0.378195i | \(-0.123455\pi\) |
−0.378195 | + | 0.925726i | \(0.623455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.02821e12 | + | 3.02821e12i | −1.92763 | + | 1.92763i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.08675e11i | 0.303040i | 0.988454 | + | 0.151520i | \(0.0484168\pi\) | ||||
−0.988454 | + | 0.151520i | \(0.951583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.58674e12i | − | 0.885379i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.53239e12 | − | 1.53239e12i | 0.801474 | − | 0.801474i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.77981e11 | − | 8.77981e11i | −0.430756 | − | 0.430756i | 0.458129 | − | 0.888886i | \(-0.348520\pi\) |
−0.888886 | + | 0.458129i | \(0.848520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.39886e11 | 0.340766 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.55305e12 | 1.53726 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.50802e12 | − | 1.50802e12i | −0.613360 | − | 0.613360i | 0.330460 | − | 0.943820i | \(-0.392796\pi\) |
−0.943820 | + | 0.330460i | \(0.892796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.49068e11 | + | 4.49068e11i | −0.171822 | + | 0.171822i | −0.787780 | − | 0.615957i | \(-0.788769\pi\) |
0.615957 | + | 0.787780i | \(0.288769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.22516e12i | 0.801456i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.06618e11i | − | 0.104029i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.74173e12 | + | 5.74173e12i | −1.83618 | + | 1.83618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.61924e12 | + | 1.61924e12i | 0.488395 | + | 0.488395i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.96899e12 | −1.41444 | −0.707220 | − | 0.706993i | \(-0.750051\pi\) | ||||
−0.707220 | + | 0.706993i | \(0.750051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.71012e12 | −0.728489 | −0.364244 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364244 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.63406e12 | + | 1.63406e12i | 0.415028 | + | 0.415028i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.19796e12 | + | 5.19796e12i | −1.24816 | + | 1.24816i | −0.291623 | + | 0.956533i | \(0.594195\pi\) |
−0.956533 | + | 0.291623i | \(0.905805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24035e12i | 0.281742i | 0.990028 | + | 0.140871i | \(0.0449903\pi\) | ||||
−0.990028 | + | 0.140871i | \(0.955010\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.10933e12i | 1.74344i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.24026e12 | − | 4.24026e12i | 0.863305 | − | 0.863305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.43142e12 | + | 3.43142e12i | 0.661954 | + | 0.661954i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.72443e12 | 0.863997 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.55252e12 | −1.31005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.59805e12 | + | 2.59805e12i | 0.427656 | + | 0.427656i | 0.887829 | − | 0.460173i | \(-0.152213\pi\) |
−0.460173 | + | 0.887829i | \(0.652213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.34194e13 | − | 1.34194e13i | 2.09723 | − | 2.09723i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.21755e12i | 1.36837i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.25129e12i | 1.30519i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.40722e12 | + | 3.40722e12i | −0.457043 | + | 0.457043i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.09831e12 | + | 3.09831e12i | 0.395336 | + | 0.395336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.31901e12 | −0.403025 | −0.201512 | − | 0.979486i | \(-0.564586\pi\) | ||||
−0.201512 | + | 0.979486i | \(0.564586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.21568e12 | 0.371766 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.66770e12 | − | 2.66770e12i | −0.293762 | − | 0.293762i | 0.544803 | − | 0.838564i | \(-0.316605\pi\) |
−0.838564 | + | 0.544803i | \(0.816605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.06633e12 | − | 5.06633e12i | 0.531616 | − | 0.531616i | −0.389437 | − | 0.921053i | \(-0.627330\pi\) |
0.921053 | + | 0.389437i | \(0.127330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.01184e13i | − | 3.01277i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.26560e13i | − | 1.20737i | −0.797224 | − | 0.603683i | \(-0.793699\pi\) | ||
0.797224 | − | 0.603683i | \(-0.206301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.72826e12 | + | 6.72826e12i | −0.612392 | + | 0.612392i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.05844e13 | − | 1.05844e13i | −0.919498 | − | 0.919498i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.75926e12 | −0.311828 | −0.155914 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155914 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.53115e12 | −0.438250 | −0.219125 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219125 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.24842e13 | − | 1.24842e13i | −0.945207 | − | 0.945207i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.12002e12 | + | 6.12002e12i | −0.442934 | + | 0.442934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07543e12i | 0.282059i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.03164e12i | 0.266922i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.06972e12 | − | 3.06972e12i | 0.194488 | − | 0.194488i | −0.603144 | − | 0.797632i | \(-0.706086\pi\) |
0.797632 | + | 0.603144i | \(0.206086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.16424e13 | − | 1.16424e13i | −0.706122 | − | 0.706122i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.92924e13 | 2.86292 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.71375e12 | 0.0953489 | 0.0476745 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476745 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.52480e12 | + | 1.52480e12i | 0.0812950 | + | 0.0812950i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.84290e13 | − | 1.84290e13i | 0.941842 | − | 0.941842i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.01496e13i | 0.497384i | 0.968583 | + | 0.248692i | \(0.0800007\pi\) | ||||
−0.968583 | + | 0.248692i | \(0.919999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.71951e12i | − | 0.315853i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.20737e13 | − | 2.20737e13i | 0.995550 | − | 0.995550i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.30252e13 | − | 1.30252e13i | −0.563828 | − | 0.563828i | 0.366564 | − | 0.930393i | \(-0.380534\pi\) |
−0.930393 | + | 0.366564i | \(0.880534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.84540e13 | 0.766934 | 0.383467 | − | 0.923554i | \(-0.374730\pi\) | ||||
0.383467 | + | 0.923554i | \(0.374730\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.62522e13 | −0.648661 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.92441e12 | − | 7.92441e12i | −0.303834 | − | 0.303834i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.56562e13 | − | 1.56562e13i | 0.576828 | − | 0.576828i | −0.357200 | − | 0.934028i | \(-0.616268\pi\) |
0.934028 | + | 0.357200i | \(0.116268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.02078e13i | 1.42393i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.12053e13i | 1.74353i | 0.489922 | + | 0.871766i | \(0.337025\pi\) | ||||
−0.489922 | + | 0.871766i | \(0.662975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.68160e10 | + | 3.68160e10i | −0.00120562 | + | 0.00120562i | −0.707709 | − | 0.706504i | \(-0.750271\pi\) |
0.706504 | + | 0.707709i | \(0.250271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.24189e13 | + | 3.24189e13i | 1.02130 | + | 1.02130i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.41286e13 | −1.03459 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.91905e13 | 1.72708 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.20227e13 | − | 4.20227e13i | −1.18052 | − | 1.18052i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.30934e12 | − | 7.30934e12i | 0.197745 | − | 0.197745i | −0.601287 | − | 0.799033i | \(-0.705345\pi\) |
0.799033 | + | 0.601287i | \(0.205345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.33237e13i | 1.12903i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.46851e13i | − | 0.870929i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.28237e12 | + | 6.28237e12i | −0.152031 | + | 0.152031i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.58385e13 | − | 4.58385e13i | −1.06934 | − | 1.06934i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.20741e13 | 1.84617 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.71322e13 | −0.588621 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00023e13 | − | 5.00023e13i | −1.04648 | − | 1.04648i | −0.998866 | − | 0.0476101i | \(-0.984840\pi\) |
−0.0476101 | − | 0.998866i | \(-0.515160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.58367e13 | + | 4.58367e13i | −0.925639 | + | 0.925639i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.72624e13i | − | 1.70077i | −0.526163 | − | 0.850384i | \(-0.676370\pi\) | ||
0.526163 | − | 0.850384i | \(-0.323630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00784e13i | 0.942229i | 0.882072 | + | 0.471114i | \(0.156148\pi\) | ||||
−0.882072 | + | 0.471114i | \(0.843852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.45130e13 | + | 7.45130e13i | −1.35371 | + | 1.35371i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.46587e13 | + | 5.46587e13i | 0.959033 | + | 0.959033i | 0.999193 | − | 0.0401607i | \(-0.0127870\pi\) |
−0.0401607 | + | 0.999193i | \(0.512787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.08290e13 | −1.53949 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.14062e13 | −0.350560 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.14689e13 | + | 6.14689e13i | 0.972840 | + | 0.972840i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.27610e12 | + | 4.27610e12i | −0.0654168 | + | 0.0654168i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.06959e13i | − | 0.601919i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.69187e13i | − | 0.957128i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.49745e13 | − | 1.49745e13i | 0.207156 | − | 0.207156i | −0.595901 | − | 0.803058i | \(-0.703205\pi\) |
0.803058 | + | 0.595901i | \(0.203205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.62706e12 | + | 6.62706e12i | 0.0886906 | + | 0.0886906i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.88802e13 | −1.28045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.74796e12 | −0.0845684 | −0.0422842 | − | 0.999106i | \(-0.513463\pi\) | ||||
−0.0422842 | + | 0.999106i | \(0.513463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.07474e14 | + | 1.07474e14i | 1.30378 | + | 1.30378i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.90842e13 | − | 9.90842e13i | 1.16374 | − | 1.16374i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.87789e13i | 0.554772i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.99492e13i | 1.10097i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.73980e13 | − | 9.73980e13i | 1.03929 | − | 1.03929i | 0.0400971 | − | 0.999196i | \(-0.487233\pi\) |
0.999196 | − | 0.0400971i | \(-0.0127667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.34720e12 | − | 8.34720e12i | −0.0862980 | − | 0.0862980i | 0.662640 | − | 0.748938i | \(-0.269436\pi\) |
−0.748938 | + | 0.662640i | \(0.769436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.87165e13 | −0.187515 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.06184e13 | −0.879945 | −0.439973 | − | 0.898011i | \(-0.645012\pi\) | ||||
−0.439973 | + | 0.898011i | \(0.645012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.63628e14 | + | 1.63628e14i | 1.54029 | + | 1.54029i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.45129e14 | + | 2.45129e14i | −2.23728 | + | 2.23728i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.14917e13i | 0.632756i | 0.948633 | + | 0.316378i | \(0.102467\pi\) | ||||
−0.948633 | + | 0.316378i | \(0.897533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 3.56358e13i | − | 0.305912i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.92118e14 | + | 1.92118e14i | −1.59986 | + | 1.59986i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.15455e13 | − | 4.15455e13i | −0.335671 | − | 0.335671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.19051e12 | −0.0328552 | −0.0164276 | − | 0.999865i | \(-0.505229\pi\) | ||||
−0.0164276 | + | 0.999865i | \(0.505229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.48329e14 | −1.12871 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.34159e13 | + | 3.34159e13i | 0.246829 | + | 0.246829i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.12134e14 | − | 1.12134e14i | 0.804153 | − | 0.804153i | −0.179589 | − | 0.983742i | \(-0.557477\pi\) |
0.983742 | + | 0.179589i | \(0.0574768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.80931e14i | − | 1.25991i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.90124e13i | 0.331458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.04153e14 | − | 1.04153e14i | 0.684154 | − | 0.684154i | −0.276779 | − | 0.960934i | \(-0.589267\pi\) |
0.960934 | + | 0.276779i | \(0.0892671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.85561e14 | + | 2.85561e14i | 1.82227 | + | 1.82227i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.29233e14 | 0.801274 | 0.400637 | − | 0.916237i | \(-0.368789\pi\) | ||||
0.400637 | + | 0.916237i | \(0.368789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.67245e14 | 2.21270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.99223e14 | − | 1.99223e14i | −1.16662 | − | 1.16662i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.24630e14 | + | 2.24630e14i | −1.27863 | + | 1.27863i | −0.337198 | + | 0.941434i | \(0.609479\pi\) |
−0.941434 | + | 0.337198i | \(0.890521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.89512e14i | 1.04873i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.43217e14i | − | 2.38483i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.29060e14 | − | 1.29060e14i | 0.675316 | − | 0.675316i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.06448e14 | − | 2.06448e14i | −1.05066 | − | 1.05066i | −0.998646 | − | 0.0520169i | \(-0.983435\pi\) |
−0.0520169 | − | 0.998646i | \(-0.516565\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.22436e14 | −1.59622 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.77354e14 | 0.854177 | 0.427089 | − | 0.904210i | \(-0.359539\pi\) | ||||
0.427089 | + | 0.904210i | \(0.359539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.34670e13 | − | 5.34670e13i | −0.250558 | − | 0.250558i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.91516e13 | − | 8.91516e13i | 0.406562 | − | 0.406562i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.26621e13i | − | 0.144969i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.56385e14i | − | 1.53972i | −0.638213 | − | 0.769860i | \(-0.720326\pi\) | ||
0.638213 | − | 0.769860i | \(-0.279674\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.30363e14 | − | 2.30363e14i | 0.968910 | − | 0.968910i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.15447e14 | − | 2.15447e14i | −0.882298 | − | 0.882298i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.91593e13 | −0.196039 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.98296e14 | 0.770135 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.71801e14 | − | 2.71801e14i | −1.02819 | − | 1.02819i | −0.999591 | − | 0.0286012i | \(-0.990895\pi\) |
−0.0286012 | − | 0.999591i | \(-0.509105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.71653e13 | − | 5.71653e13i | 0.210660 | − | 0.210660i | −0.593888 | − | 0.804548i | \(-0.702408\pi\) |
0.804548 | + | 0.593888i | \(0.202408\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.90841e14i | − | 1.04420i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.28991e14i | 0.451254i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.34927e14 | − | 1.34927e14i | 0.459988 | − | 0.459988i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.74066e14 | + | 1.74066e14i | 0.578361 | + | 0.578361i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.62177e13 | −0.149687 | −0.0748434 | − | 0.997195i | \(-0.523846\pi\) | ||||
−0.0748434 | + | 0.997195i | \(0.523846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.17070e14 | −0.685356 | −0.342678 | − | 0.939453i | \(-0.611334\pi\) | ||||
−0.342678 | + | 0.939453i | \(0.611334\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.89880e14 | + | 3.89880e14i | 1.20016 | + | 1.20016i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.24639e14 | + | 1.24639e14i | −0.374117 | + | 0.374117i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.67074e14i | − | 0.781766i | −0.920440 | − | 0.390883i | \(-0.872170\pi\) | ||
0.920440 | − | 0.390883i | \(-0.127830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.64549e14i | − | 0.755255i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.39831e14 | + | 2.39831e14i | −0.667858 | + | 0.667858i | −0.957220 | − | 0.289362i | \(-0.906557\pi\) |
0.289362 | + | 0.957220i | \(0.406557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.69153e14 | + | 2.69153e14i | 0.731172 | + | 0.731172i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.79670e14 | 1.00627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.87700e14 | 1.51985 | 0.759925 | − | 0.650011i | \(-0.225236\pi\) | ||||
0.759925 | + | 0.650011i | \(0.225236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.65528e14 | + | 3.65528e14i | 0.922464 | + | 0.922464i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.49236e14 | + | 1.49236e14i | −0.367564 | + | 0.367564i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.98170e14i | − | 0.476403i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.52197e14i | 1.06118i | 0.847629 | + | 0.530589i | \(0.178029\pi\) | ||||
−0.847629 | + | 0.530589i | \(0.821971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82297e14 | + | 2.82297e14i | −0.646751 | + | 0.646751i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.12674e14 | − | 5.12674e14i | −1.14680 | − | 1.14680i | −0.987179 | − | 0.159616i | \(-0.948974\pi\) |
−0.159616 | − | 0.987179i | \(-0.551026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.55229e14 | −0.557486 | −0.278743 | − | 0.960366i | \(-0.589918\pi\) | ||||
−0.278743 | + | 0.960366i | \(0.589918\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.50631e14 | −1.81447 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.22952e14 | − | 1.22952e14i | −0.256148 | − | 0.256148i | 0.567337 | − | 0.823485i | \(-0.307974\pi\) |
−0.823485 | + | 0.567337i | \(0.807974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.91727e14 | − | 4.91727e14i | 1.00063 | − | 1.00063i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.66690e14i | 1.32528i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.81888e14i | 1.90689i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.48358e13 | + | 8.48358e13i | −0.160977 | + | 0.160977i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.45232e14 | + | 1.45232e14i | 0.269284 | + | 0.269284i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.71050e14 | −0.491139 | −0.245569 | − | 0.969379i | \(-0.578975\pi\) | ||||
−0.245569 | + | 0.969379i | \(0.578975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.76249e13 | −0.0312124 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.97043e14 | − | 4.97043e14i | −0.860369 | − | 0.860369i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.12399e14 | − | 5.12399e14i | 0.867019 | − | 0.867019i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.77246e14i | 0.624045i | 0.950075 | + | 0.312022i | \(0.101006\pi\) | ||||
−0.950075 | + | 0.312022i | \(0.898994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.35571e14i | − | 1.18967i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.41994e14 | − | 4.41994e14i | 0.698985 | − | 0.698985i | −0.265207 | − | 0.964192i | \(-0.585440\pi\) |
0.964192 | + | 0.265207i | \(0.0854402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.39245e14 | + | 7.39245e14i | 1.14322 | + | 1.14322i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.59611e15 | 2.41399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.62743e15 | −2.40737 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.44840e14 | + | 5.44840e14i | 0.788344 | + | 0.788344i | 0.981223 | − | 0.192878i | \(-0.0617823\pi\) |
−0.192878 | + | 0.981223i | \(0.561782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.32592e14 | − | 2.32592e14i | 0.329220 | − | 0.329220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.71015e14i | − | 0.513768i | −0.966442 | − | 0.256884i | \(-0.917304\pi\) | ||
0.966442 | − | 0.256884i | \(-0.0826958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00076e15i | 1.35590i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.25537e14 | + | 7.25537e14i | −0.961869 | + | 0.961869i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.69790e14 | − | 7.69790e14i | −0.998676 | − | 0.998676i | 0.00132283 | − | 0.999999i | \(-0.499579\pi\) |
−0.999999 | + | 0.00132283i | \(0.999579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.13208e14 | 0.524631 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.71326e14 | −0.461434 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.58905e14 | − | 5.58905e14i | −0.679827 | − | 0.679827i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.16720e14 | + | 7.16720e14i | −0.853398 | + | 0.853398i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.02914e14i | 0.935941i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01193e14i | 0.115489i | 0.998331 | + | 0.0577447i | \(0.0183909\pi\) | ||||
−0.998331 | + | 0.0577447i | \(0.981609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.30526e14 | + | 2.30526e14i | −0.257608 | + | 0.257608i | −0.824081 | − | 0.566472i | \(-0.808308\pi\) |
0.566472 | + | 0.824081i | \(0.308308\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.38313e14 | − | 3.38313e14i | −0.370205 | − | 0.370205i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.61286e15 | −1.72838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.68541e14 | 0.596699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.36373e14 | − | 9.36373e14i | −0.962562 | − | 0.962562i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.97243e14 | − | 1.97243e14i | 0.198610 | − | 0.198610i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.61015e14i | − | 0.257465i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.37908e15i | 1.33270i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.51928e14 | + | 6.51928e14i | −0.617250 | + | 0.617250i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.94835e14 | − | 3.94835e14i | −0.366295 | − | 0.366295i | 0.499829 | − | 0.866124i | \(-0.333396\pi\) |
−0.866124 | + | 0.499829i | \(0.833396\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.10672e14 | 0.373333 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.96221e14 | 0.442073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.85865e14 | − | 2.85865e14i | −0.249592 | − | 0.249592i | 0.571211 | − | 0.820803i | \(-0.306474\pi\) |
−0.820803 | + | 0.571211i | \(0.806474\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.86419e14 | − | 5.86419e14i | 0.501834 | − | 0.501834i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.72382e14i | 0.815648i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.28362e15i | 1.05547i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.40201e14 | + | 1.40201e14i | −0.113016 | + | 0.113016i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.89000e13 | + | 6.89000e13i | 0.0544522 | + | 0.0544522i | 0.733809 | − | 0.679356i | \(-0.237741\pi\) |
−0.679356 | + | 0.733809i | \(0.737741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.29838e14 | 0.410562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.25081e15 | 3.98961 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.79657e14 | − | 2.79657e14i | −0.208367 | − | 0.208367i | 0.595206 | − | 0.803573i | \(-0.297070\pi\) |
−0.803573 | + | 0.595206i | \(0.797070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.31047e15 | + | 1.31047e15i | −0.957547 | + | 0.957547i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.86694e14i | 0.635429i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.64126e15i | − | 1.15361i | −0.816881 | − | 0.576807i | \(-0.804299\pi\) | ||
0.816881 | − | 0.576807i | \(-0.195701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.29829e15 | − | 1.29829e15i | 0.895100 | − | 0.895100i | −0.0998976 | − | 0.994998i | \(-0.531852\pi\) |
0.994998 | + | 0.0998976i | \(0.0318515\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.27207e15 | + | 2.27207e15i | 1.53664 | + | 1.53664i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.61553e14 | −0.173535 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.84725e15 | −1.20242 | −0.601212 | − | 0.799089i | \(-0.705315\pi\) | ||||
−0.601212 | + | 0.799089i | \(0.705315\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.23920e15 | + | 1.23920e15i | 0.791424 | + | 0.791424i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.44467e14 | − | 2.44467e14i | 0.153198 | − | 0.153198i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.15788e14i | − | 0.440157i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 8.61282e14i | − | 0.519742i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.54803e14 | + | 7.54803e14i | −0.447017 | + | 0.447017i | −0.894362 | − | 0.447345i | \(-0.852370\pi\) |
0.447345 | + | 0.894362i | \(0.352370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.06076e15 | − | 1.06076e15i | −0.616570 | − | 0.616570i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.75354e15 | 2.71198 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.83705e15 | −1.58879 | −0.794393 | − | 0.607404i | \(-0.792211\pi\) | ||||
−0.794393 | + | 0.607404i | \(0.792211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.98896e15 | − | 2.98896e15i | −1.64315 | − | 1.64315i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.67150e14 | − | 5.67150e14i | 0.306083 | − | 0.306083i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.42147e15i | 0.753167i | 0.926383 | + | 0.376584i | \(0.122901\pi\) | ||||
−0.926383 | + | 0.376584i | \(0.877099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.37212e15i | − | 0.713810i | −0.934141 | − | 0.356905i | \(-0.883832\pi\) | ||
0.934141 | − | 0.356905i | \(-0.116168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.13714e15 | − | 2.13714e15i | 1.09166 | − | 1.09166i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.34257e15 | − | 2.34257e15i | −1.17500 | − | 1.17500i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.58569e14 | −0.472156 | −0.236078 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236078 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.87772e15 | −1.87578 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.86750e14 | + | 3.86750e14i | 0.183740 | + | 0.183740i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16692e15 | − | 1.16692e15i | 0.544512 | − | 0.544512i | −0.380336 | − | 0.924848i | \(-0.624192\pi\) |
0.924848 | + | 0.380336i | \(0.124192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 3.13803e15i | − | 1.43828i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.66121e15i | − | 0.747920i | −0.927445 | − | 0.373960i | \(-0.878000\pi\) | ||
0.927445 | − | 0.373960i | \(-0.122000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.32258e15 | − | 1.32258e15i | 0.584958 | − | 0.584958i | −0.351304 | − | 0.936262i | \(-0.614262\pi\) |
0.936262 | + | 0.351304i | \(0.114262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.72409e14 | − | 5.72409e14i | −0.248715 | − | 0.248715i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.67698e15 | −1.14277 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.85766e15 | 1.19859 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.45339e15 | + | 3.45339e15i | 1.42323 | + | 1.42323i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.65832e14 | + | 2.65832e14i | −0.107654 | + | 0.107654i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 3.87984e15i | − | 1.54402i | −0.635612 | − | 0.772009i | \(-0.719252\pi\) | ||
0.635612 | − | 0.772009i | \(-0.280748\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.37592e15i | − | 0.929204i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.48196e15 | + | 3.48196e15i | −1.33835 | + | 1.33835i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.51788e14 | + | 3.51788e14i | 0.132897 | + | 0.132897i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.07312e15 | −2.62637 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.57445e14 | −0.203462 | −0.101731 | − | 0.994812i | \(-0.532438\pi\) | ||||
−0.101731 | + | 0.994812i | \(0.532438\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.17954e15 | + | 3.17954e15i | 1.14079 | + | 1.14079i | 0.988307 | + | 0.152480i | \(0.0487260\pi\) |
0.152480 | + | 0.988307i | \(0.451274\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.21472e15 | − | 4.21472e15i | 1.48659 | − | 1.48659i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.20708e15i | − | 0.765324i | −0.923888 | − | 0.382662i | \(-0.875007\pi\) | ||
0.923888 | − | 0.382662i | \(-0.124993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.61501e15i | 1.57335i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.23015e15 | − | 4.23015e15i | 1.41795 | − | 1.41795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.46010e15 | + | 2.46010e15i | 0.810832 | + | 0.810832i | 0.984759 | − | 0.173926i | \(-0.0556455\pi\) |
−0.173926 | + | 0.984759i | \(0.555645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.40432e15 | 1.75152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.79588e15 | 0.572358 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.41322e13 | − | 9.41322e13i | −0.0295032 | − | 0.0295032i | 0.692201 | − | 0.721704i | \(-0.256641\pi\) |
−0.721704 | + | 0.692201i | \(0.756641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.97944e15 | + | 1.97944e15i | −0.610148 | + | 0.610148i | −0.942984 | − | 0.332837i | \(-0.891994\pi\) |
0.332837 | + | 0.942984i | \(0.391994\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.83340e15i | − | 0.858981i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.93159e15i | − | 1.17233i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.49895e15 | + | 1.49895e15i | −0.439638 | + | 0.439638i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.51762e15 | + | 1.51762e15i | 0.437843 | + | 0.437843i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.89022e15 | −0.820272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41200e15 | 0.394231 | 0.197116 | − | 0.980380i | \(-0.436843\pi\) | ||||
0.197116 | + | 0.980380i | \(0.436843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.89610e14 | − | 3.89610e14i | −0.107019 | − | 0.107019i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.85721e15 | + | 4.85721e15i | −1.31265 | + | 1.31265i | −0.393194 | + | 0.919456i | \(0.628630\pi\) |
−0.919456 | + | 0.393194i | \(0.871370\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.09628e15i | 1.35509i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.43961e15i | 0.638281i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.68637e14 | − | 8.68637e14i | 0.223627 | − | 0.223627i | −0.586397 | − | 0.810024i | \(-0.699454\pi\) |
0.810024 | + | 0.586397i | \(0.199454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.80891e15 | + | 2.80891e15i | 0.711606 | + | 0.711606i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.63316e15 | −1.15509 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.86248e14 | −0.0947676 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.10027e15 | + | 4.10027e15i | 0.990110 | + | 0.990110i | 0.999952 | − | 0.00984162i | \(-0.00313273\pi\) |
−0.00984162 | + | 0.999952i | \(0.503133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.93741e15 | + | 7.93741e15i | −1.88645 | + | 1.88645i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.41791e15i | 0.565618i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.94996e15i | − | 1.37004i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.78696e15 | + | 5.78696e15i | −1.31167 | + | 1.31167i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.09473e14 | + | 4.09473e14i | 0.0913643 | + | 0.0913643i | 0.751312 | − | 0.659947i | \(-0.229421\pi\) |
−0.659947 | + | 0.751312i | \(0.729421\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.49669e14 | −0.0768073 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.15299e15 | 1.33060 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.97674e15 | − | 4.97674e15i | −1.05959 | − | 1.05959i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.23628e13 | + | 4.23628e13i | −0.00888035 | + | 0.00888035i | −0.711533 | − | 0.702653i | \(-0.751999\pi\) |
0.702653 | + | 0.711533i | \(0.251999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.57885e15i | 1.15149i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.27037e15i | − | 0.664668i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.12246e15 | + | 2.12246e15i | −0.424772 | + | 0.424772i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.71892e15 | + | 1.71892e15i | 0.338767 | + | 0.338767i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.44205e15 | −0.668049 | −0.334025 | − | 0.942564i | \(-0.608407\pi\) | ||||
−0.334025 | + | 0.942564i | \(0.608407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.55882e15 | 1.06252 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.52912e15 | + | 2.52912e15i | 0.476111 | + | 0.476111i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.02026e15 | + | 1.02026e15i | −0.189170 | + | 0.189170i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.86644e14i | − | 0.161924i | −0.996717 | − | 0.0809618i | \(-0.974201\pi\) | ||
0.996717 | − | 0.0809618i | \(-0.0257992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.58422e15i | 1.54419i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.99145e15 | − | 7.99145e15i | 1.41605 | − | 1.41605i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.89968e15 | − | 7.89968e15i | −1.37892 | − | 1.37892i | −0.846455 | − | 0.532461i | \(-0.821267\pi\) |
−0.532461 | − | 0.846455i | \(-0.678733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.59676e15 | 0.962401 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.05331e16 | −1.78437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.16961e15 | − | 3.16961e15i | −0.529007 | − | 0.529007i | 0.391269 | − | 0.920276i | \(-0.372036\pi\) |
−0.920276 | + | 0.391269i | \(0.872036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.86349e15 | − | 1.86349e15i | 0.306427 | − | 0.306427i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.94649e15i | − | 0.315364i | −0.987490 | − | 0.157682i | \(-0.949598\pi\) | ||
0.987490 | − | 0.157682i | \(-0.0504022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.62947e15i | 0.739047i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.06250e15 | − | 1.06250e15i | 0.167134 | − | 0.167134i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29801e15 | + | 1.29801e15i | 0.201201 | + | 0.201201i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.22162e14 | 0.125585 | 0.0627925 | − | 0.998027i | \(-0.479999\pi\) | ||||
0.0627925 | + | 0.998027i | \(0.479999\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.80726e15 | −0.422581 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.81969e15 | − | 1.81969e15i | −0.269954 | − | 0.269954i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22234e15 | − | 1.22234e15i | 0.178716 | − | 0.178716i | −0.612080 | − | 0.790796i | \(-0.709667\pi\) |
0.790796 | + | 0.612080i | \(0.209667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.06470e16i | 1.53425i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.64079e15i | − | 1.08523i | −0.839981 | − | 0.542616i | \(-0.817434\pi\) | ||
0.839981 | − | 0.542616i | \(-0.182566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.46768e15 | + | 2.46768e15i | −0.345466 | + | 0.345466i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.29906e16 | − | 1.29906e16i | −1.79263 | − | 1.79263i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.49031e15 | 0.338750 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.51581e15 | 0.605537 | 0.302768 | − | 0.953064i | \(-0.402089\pi\) | ||||
0.302768 | + | 0.953064i | \(0.402089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.83613e14 | − | 7.83613e14i | −0.103586 | − | 0.103586i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.07717e15 | + | 1.07717e15i | −0.140377 | + | 0.140377i | −0.773803 | − | 0.633426i | \(-0.781648\pi\) |
0.633426 | + | 0.773803i | \(0.281648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.22598e15i | − | 0.285997i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.39443e15i | − | 0.176637i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.91321e15 | − | 3.91321e15i | 0.488739 | − | 0.488739i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.74303e16 | + | 1.74303e16i | 2.14647 | + | 2.14647i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.46569e15 | −0.542249 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.12921e15 | −0.973342 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.70724e15 | + | 4.70724e15i | 0.555783 | + | 0.555783i | 0.928104 | − | 0.372321i | \(-0.121438\pi\) |
−0.372321 | + | 0.928104i | \(0.621438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.64090e15 | − | 4.64090e15i | 0.540354 | − | 0.540354i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.30338e16i | − | 1.49658i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.55960e15i | 0.176608i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.07250e15 | + | 3.07250e15i | −0.343141 | + | 0.343141i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.24872e15 | + | 7.24872e15i | 0.798436 | + | 0.798436i | 0.982849 | − | 0.184412i | \(-0.0590382\pi\) |
−0.184412 | + | 0.982849i | \(0.559038\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.16666e16 | 1.26746 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.16346e16 | −1.24673 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.42559e15 | − | 4.42559e15i | −0.467773 | − | 0.467773i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.06064e15 | − | 6.06064e15i | 0.631890 | − | 0.631890i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.19115e16i | 1.22508i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.03410e16i | 1.04917i | 0.851360 | + | 0.524583i | \(0.175779\pi\) | ||||
−0.851360 | + | 0.524583i | \(0.824221\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.11196e16 | + | 1.11196e16i | −1.11295 | + | 1.11295i | −0.120200 | + | 0.992750i | \(0.538354\pi\) |
−0.992750 | + | 0.120200i | \(0.961646\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.43807e15 | − | 8.43807e15i | −0.833192 | − | 0.833192i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.96910e15 | 0.873740 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05117e16 | 1.01031 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.28312e15 | + | 4.28312e15i | 0.406161 | + | 0.406161i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.05917e15 | − | 7.05917e15i | 0.660490 | − | 0.660490i | −0.295005 | − | 0.955496i | \(-0.595321\pi\) |
0.955496 | + | 0.295005i | \(0.0953215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.30797e16i | − | 1.20753i | −0.797163 | − | 0.603764i | \(-0.793667\pi\) | ||
0.797163 | − | 0.603764i | \(-0.206333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.24687e15i | 0.660167i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.30624e15 | + | 8.30624e15i | −0.746662 | + | 0.746662i | −0.973851 | − | 0.227189i | \(-0.927047\pi\) |
0.227189 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.07494e16 | − | 1.07494e16i | −0.953531 | − | 0.953531i | 0.0454367 | − | 0.998967i | \(-0.485532\pi\) |
−0.998967 | + | 0.0454367i | \(0.985532\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.43176e16 | −1.25332 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.06119e16 | 0.916739 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.83608e15 | + | 2.83608e15i | 0.241793 | + | 0.241793i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.87156e15 | − | 4.87156e15i | 0.409900 | − | 0.409900i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.21546e15i | − | 0.599202i | −0.954065 | − | 0.299601i | \(-0.903146\pi\) | ||
0.954065 | − | 0.299601i | \(-0.0968535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 5.06335e14i | − | 0.0415011i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.34136e16 | − | 2.34136e16i | 1.89416 | − | 1.89416i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.84676e15 | − | 8.84676e15i | −0.706435 | − | 0.706435i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.32990e16 | 1.83645 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.36682e13 | 0.00261956 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.39023e14 | − | 5.39023e14i | −0.0413995 | − | 0.0413995i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.11551e15 | − | 2.11551e15i | 0.160397 | − | 0.160397i | −0.622346 | − | 0.782742i | \(-0.713820\pi\) |
0.782742 | + | 0.622346i | \(0.213820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.70874e16i | − | 1.27898i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 5.60408e15i | − | 0.414104i | −0.978330 | − | 0.207052i | \(-0.933613\pi\) | ||
0.978330 | − | 0.207052i | \(-0.0663870\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.84823e14 | − | 2.84823e14i | 0.0207784 | − | 0.0207784i | −0.696641 | − | 0.717420i | \(-0.745323\pi\) |
0.717420 | + | 0.696641i | \(0.245323\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.56053e16 | + | 1.56053e16i | 1.12397 | + | 1.12397i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.14058e15 | −0.152220 | −0.0761102 | − | 0.997099i | \(-0.524250\pi\) | ||||
−0.0761102 | + | 0.997099i | \(0.524250\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.79024e15 | −0.687392 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.70648e16 | − | 2.70648e16i | −1.87629 | − | 1.87629i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.37479e16 | − | 1.37479e16i | 0.941086 | − | 0.941086i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.68378e15i | 0.384182i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.21494e16i | 1.47837i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.09711e16 | + | 1.09711e16i | −0.723115 | + | 0.723115i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.91657e14 | − | 6.91657e14i | −0.0450187 | − | 0.0450187i | 0.684239 | − | 0.729258i | \(-0.260134\pi\) |
−0.729258 | + | 0.684239i | \(0.760134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.68439e15 | −0.429658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.27110e16 | −0.806889 | −0.403444 | − | 0.915004i | \(-0.632187\pi\) | ||||
−0.403444 | + | 0.915004i | \(0.632187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.13706e16 | − | 1.13706e16i | −0.712850 | − | 0.712850i | 0.254280 | − | 0.967131i | \(-0.418161\pi\) |
−0.967131 | + | 0.254280i | \(0.918161\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.98098e16 | − | 1.98098e16i | 1.22657 | − | 1.22657i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.64514e15i | − | 0.284066i | −0.989862 | − | 0.142033i | \(-0.954636\pi\) | ||
0.989862 | − | 0.142033i | \(-0.0453639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.46313e16i | − | 2.09175i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.49676e15 | − | 9.49676e15i | 0.566563 | − | 0.566563i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.67294e15 | + | 7.67294e15i | 0.452146 | + | 0.452146i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.68157e16 | −0.978788 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.74523e15 | 0.330331 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.27570e16 | − | 1.27570e16i | −0.724554 | − | 0.724554i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.82570e15 | + | 5.82570e15i | −0.326860 | + | 0.326860i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.19193e16i | 2.32344i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.00749e15i | 0.274191i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.40963e16 | + | 1.40963e16i | −0.762543 | + | 0.762543i | −0.976781 | − | 0.214239i | \(-0.931273\pi\) |
0.214239 | + | 0.976781i | \(0.431273\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.16299e16 | − | 2.16299e16i | −1.15599 | − | 1.15599i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.45183e16 | 1.29461 | 0.647305 | − | 0.762231i | \(-0.275896\pi\) | ||||
0.647305 | + | 0.762231i | \(0.275896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.23664e15 | −0.273189 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.24062e16 | + | 1.24062e16i | 0.639474 | + | 0.639474i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.68755e16 | + | 2.68755e16i | −1.36875 | + | 1.36875i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.71814e16i | 0.864615i | 0.901726 | + | 0.432307i | \(0.142300\pi\) | ||||
−0.901726 | + | 0.432307i | \(0.857700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.57271e16i | 2.27377i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.40559e15 | − | 9.40559e15i | 0.462143 | − | 0.462143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.66887e14 | − | 3.66887e14i | −0.0178136 | − | 0.0178136i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.41597e16 | 1.15918 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.37942e16 | 0.654047 | 0.327024 | − | 0.945016i | \(-0.393954\pi\) | ||||
0.327024 | + | 0.945016i | \(0.393954\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.97930e15 | + | 6.97930e15i | 0.327031 | + | 0.327031i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.99007e16 | + | 3.99007e16i | −1.84770 | + | 1.84770i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.40252e16i | 2.93013i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.53690e16i | − | 1.59976i | −0.600160 | − | 0.799880i | \(-0.704896\pi\) | ||
0.600160 | − | 0.799880i | \(-0.295104\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.28983e16 | − | 2.28983e16i | 1.02363 | − | 1.02363i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.22717e16 | − | 2.22717e16i | −0.984034 | − | 0.984034i | 0.0158400 | − | 0.999875i | \(-0.494958\pi\) |
−0.999875 | + | 0.0158400i | \(0.994958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20646e16 | 0.526865 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.80559e16 | 0.779371 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.09342e16 | + | 2.09342e16i | 0.893163 | + | 0.893163i | 0.994820 | − | 0.101656i | \(-0.0324142\pi\) |
−0.101656 | + | 0.994820i | \(0.532414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.38810e15 | + | 2.38810e15i | −0.100714 | + | 0.100714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.99854e16i | − | 2.08377i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.34667e16i | 0.967035i | 0.875335 | + | 0.483517i | \(0.160641\pi\) | ||||
−0.875335 | + | 0.483517i | \(0.839359\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.77043e16 | + | 2.77043e16i | −1.12857 | + | 1.12857i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.15315e16 | + | 4.15315e16i | 1.67249 | + | 1.67249i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.79372e16 | −1.11219 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.42445e15 | 0.0954191 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.64141e15 | + | 5.64141e15i | 0.219504 | + | 0.219504i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.51101e16 | + | 1.51101e16i | −0.581254 | + | 0.581254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.94438e16i | − | 1.50014i | −0.661357 | − | 0.750071i | \(-0.730019\pi\) | ||
0.661357 | − | 0.750071i | \(-0.269981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.62133e16i | − | 2.11377i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.82080e16 | + | 1.82080e16i | −0.676948 | + | 0.676948i | −0.959308 | − | 0.282360i | \(-0.908883\pi\) |
0.282360 | + | 0.959308i | \(0.408883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.20241e16 | − | 1.20241e16i | −0.442012 | − | 0.442012i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.91049e15 | 0.142137 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.68239e16 | −0.604652 | −0.302326 | − | 0.953205i | \(-0.597763\pi\) | ||||
−0.302326 | + | 0.953205i | \(0.597763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.86712e16 | + | 2.86712e16i | 1.01892 | + | 1.01892i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.07250e16 | + | 1.07250e16i | −0.376893 | + | 0.376893i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.79195e16i | 0.622704i | 0.950295 | + | 0.311352i | \(0.100782\pi\) | ||||
−0.950295 | + | 0.311352i | \(0.899218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.79617e16i | 1.99178i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.05986e16 | + | 3.05986e16i | −1.03982 | + | 1.03982i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.62041e16 | + | 1.62041e16i | 0.544560 | + | 0.544560i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.56476e16 | −1.84945 | −0.924723 | − | 0.380641i | \(-0.875704\pi\) | ||||
−0.924723 | + | 0.380641i | \(0.875704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.36942e16 | −0.450106 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.91548e15 | + | 6.91548e15i | 0.224800 | + | 0.224800i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.04105e16 | − | 1.04105e16i | 0.334695 | − | 0.334695i | −0.519671 | − | 0.854366i | \(-0.673945\pi\) |
0.854366 | + | 0.519671i | \(0.173945\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.60586e15i | − | 0.0510620i |
(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 | 64.12.e.a.17.2 | 42 | ||
4.3 | odd | 2 | 16.12.e.a.13.21 | yes | 42 | ||
8.3 | odd | 2 | 128.12.e.b.33.2 | 42 | |||
8.5 | even | 2 | 128.12.e.a.33.20 | 42 | |||
16.3 | odd | 4 | 128.12.e.b.97.2 | 42 | |||
16.5 | even | 4 | inner | 64.12.e.a.49.2 | 42 | ||
16.11 | odd | 4 | 16.12.e.a.5.21 | ✓ | 42 | ||
16.13 | even | 4 | 128.12.e.a.97.20 | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.21 | ✓ | 42 | 16.11 | odd | 4 | ||
16.12.e.a.13.21 | yes | 42 | 4.3 | odd | 2 | ||
64.12.e.a.17.2 | 42 | 1.1 | even | 1 | trivial | ||
64.12.e.a.49.2 | 42 | 16.5 | even | 4 | inner | ||
128.12.e.a.33.20 | 42 | 8.5 | even | 2 | |||
128.12.e.a.97.20 | 42 | 16.13 | even | 4 | |||
128.12.e.b.33.2 | 42 | 8.3 | odd | 2 | |||
128.12.e.b.97.2 | 42 | 16.3 | odd | 4 |