Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −78.8162 | −1.74161 | −0.870804 | − | 0.491630i | \(-0.836401\pi\) | ||||
−0.870804 | + | 0.491630i | \(0.836401\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 4163.99 | 2.03320 | ||||||||
\(5\) | 6894.11 | 0.986604 | 0.493302 | − | 0.869858i | \(-0.335790\pi\) | ||||
0.493302 | + | 0.869858i | \(0.335790\pi\) | |||||||
\(6\) | −19152.3 | −1.00552 | ||||||||
\(7\) | 41129.0 | 0.924930 | 0.462465 | − | 0.886638i | \(-0.346965\pi\) | ||||
0.462465 | + | 0.886638i | \(0.346965\pi\) | |||||||
\(8\) | −166774. | −1.79943 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −543367. | −1.71828 | ||||||||
\(11\) | −469594. | −0.879149 | −0.439575 | − | 0.898206i | \(-0.644871\pi\) | ||||
−0.439575 | + | 0.898206i | \(0.644871\pi\) | |||||||
\(12\) | 1.01185e6 | 1.17387 | ||||||||
\(13\) | 1.92887e6 | 1.44083 | 0.720417 | − | 0.693541i | \(-0.243951\pi\) | ||||
0.720417 | + | 0.693541i | \(0.243951\pi\) | |||||||
\(14\) | −3.24163e6 | −1.61087 | ||||||||
\(15\) | 1.67527e6 | 0.569616 | ||||||||
\(16\) | 4.61666e6 | 1.10070 | ||||||||
\(17\) | −6.53047e6 | −1.11551 | −0.557757 | − | 0.830004i | \(-0.688338\pi\) | ||||
−0.557757 | + | 0.830004i | \(0.688338\pi\) | |||||||
\(18\) | −4.65402e6 | −0.580536 | ||||||||
\(19\) | 1.40980e7 | 1.30621 | 0.653103 | − | 0.757269i | \(-0.273467\pi\) | ||||
0.653103 | + | 0.757269i | \(0.273467\pi\) | |||||||
\(20\) | 2.87070e7 | 2.00596 | ||||||||
\(21\) | 9.99434e6 | 0.534008 | ||||||||
\(22\) | 3.70116e7 | 1.53113 | ||||||||
\(23\) | 4.11538e6 | 0.133324 | 0.0666618 | − | 0.997776i | \(-0.478765\pi\) | ||||
0.0666618 | + | 0.997776i | \(0.478765\pi\) | |||||||
\(24\) | −4.05262e7 | −1.03890 | ||||||||
\(25\) | −1.29943e6 | −0.0266124 | ||||||||
\(26\) | −1.52026e8 | −2.50937 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.71261e8 | 1.88057 | ||||||||
\(29\) | −1.20032e8 | −1.08670 | −0.543350 | − | 0.839506i | \(-0.682844\pi\) | ||||
−0.543350 | + | 0.839506i | \(0.682844\pi\) | |||||||
\(30\) | −1.32038e8 | −0.992048 | ||||||||
\(31\) | −6.86675e7 | −0.430786 | −0.215393 | − | 0.976527i | \(-0.569103\pi\) | ||||
−0.215393 | + | 0.976527i | \(0.569103\pi\) | |||||||
\(32\) | −2.23139e7 | −0.117558 | ||||||||
\(33\) | −1.14111e8 | −0.507577 | ||||||||
\(34\) | 5.14707e8 | 1.94279 | ||||||||
\(35\) | 2.83548e8 | 0.912539 | ||||||||
\(36\) | 2.45880e8 | 0.677733 | ||||||||
\(37\) | −4.59827e8 | −1.09015 | −0.545073 | − | 0.838388i | \(-0.683498\pi\) | ||||
−0.545073 | + | 0.838388i | \(0.683498\pi\) | |||||||
\(38\) | −1.11115e9 | −2.27490 | ||||||||
\(39\) | 4.68715e8 | 0.831866 | ||||||||
\(40\) | −1.14976e9 | −1.77532 | ||||||||
\(41\) | −9.53500e8 | −1.28531 | −0.642657 | − | 0.766154i | \(-0.722168\pi\) | ||||
−0.642657 | + | 0.766154i | \(0.722168\pi\) | |||||||
\(42\) | −7.87716e8 | −0.930033 | ||||||||
\(43\) | −1.75893e9 | −1.82461 | −0.912307 | − | 0.409506i | \(-0.865701\pi\) | ||||
−0.912307 | + | 0.409506i | \(0.865701\pi\) | |||||||
\(44\) | −1.95538e9 | −1.78749 | ||||||||
\(45\) | 4.07090e8 | 0.328868 | ||||||||
\(46\) | −3.24359e8 | −0.232198 | ||||||||
\(47\) | −7.20564e8 | −0.458284 | −0.229142 | − | 0.973393i | \(-0.573592\pi\) | ||||
−0.229142 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(48\) | 1.12185e9 | 0.635488 | ||||||||
\(49\) | −2.85733e8 | −0.144505 | ||||||||
\(50\) | 1.02416e8 | 0.0463484 | ||||||||
\(51\) | −1.58690e9 | −0.644043 | ||||||||
\(52\) | 8.03178e9 | 2.92950 | ||||||||
\(53\) | −4.93630e9 | −1.62138 | −0.810690 | − | 0.585476i | \(-0.800908\pi\) | ||||
−0.810690 | + | 0.585476i | \(0.800908\pi\) | |||||||
\(54\) | −1.13093e9 | −0.335173 | ||||||||
\(55\) | −3.23743e9 | −0.867372 | ||||||||
\(56\) | −6.85926e9 | −1.66434 | ||||||||
\(57\) | 3.42580e9 | 0.754138 | ||||||||
\(58\) | 9.46049e9 | 1.89260 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | 6.97580e9 | 1.15814 | ||||||||
\(61\) | −6.74509e9 | −1.02252 | −0.511262 | − | 0.859425i | \(-0.670822\pi\) | ||||
−0.511262 | + | 0.859425i | \(0.670822\pi\) | |||||||
\(62\) | 5.41211e9 | 0.750261 | ||||||||
\(63\) | 2.42863e9 | 0.308310 | ||||||||
\(64\) | −7.69623e9 | −0.895959 | ||||||||
\(65\) | 1.32978e10 | 1.42153 | ||||||||
\(66\) | 8.99382e9 | 0.884000 | ||||||||
\(67\) | −8.57249e9 | −0.775703 | −0.387851 | − | 0.921722i | \(-0.626783\pi\) | ||||
−0.387851 | + | 0.921722i | \(0.626783\pi\) | |||||||
\(68\) | −2.71928e10 | −2.26806 | ||||||||
\(69\) | 1.00004e9 | 0.0769744 | ||||||||
\(70\) | −2.23481e10 | −1.58929 | ||||||||
\(71\) | 3.87295e8 | 0.0254754 | 0.0127377 | − | 0.999919i | \(-0.495945\pi\) | ||||
0.0127377 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(72\) | −9.84786e9 | −0.599809 | ||||||||
\(73\) | −6.36342e9 | −0.359265 | −0.179633 | − | 0.983734i | \(-0.557491\pi\) | ||||
−0.179633 | + | 0.983734i | \(0.557491\pi\) | |||||||
\(74\) | 3.62418e10 | 1.89861 | ||||||||
\(75\) | −3.15762e8 | −0.0153647 | ||||||||
\(76\) | 5.87038e10 | 2.65577 | ||||||||
\(77\) | −1.93139e10 | −0.813151 | ||||||||
\(78\) | −3.69423e10 | −1.44878 | ||||||||
\(79\) | 9.47459e9 | 0.346427 | 0.173213 | − | 0.984884i | \(-0.444585\pi\) | ||||
0.173213 | + | 0.984884i | \(0.444585\pi\) | |||||||
\(80\) | 3.18278e10 | 1.08595 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 7.51512e10 | 2.23851 | ||||||||
\(83\) | 2.58868e10 | 0.721355 | 0.360677 | − | 0.932691i | \(-0.382546\pi\) | ||||
0.360677 | + | 0.932691i | \(0.382546\pi\) | |||||||
\(84\) | 4.16164e10 | 1.08575 | ||||||||
\(85\) | −4.50217e10 | −1.10057 | ||||||||
\(86\) | 1.38632e11 | 3.17776 | ||||||||
\(87\) | −2.91679e10 | −0.627406 | ||||||||
\(88\) | 7.83162e10 | 1.58197 | ||||||||
\(89\) | −5.07898e10 | −0.964120 | −0.482060 | − | 0.876138i | \(-0.660111\pi\) | ||||
−0.482060 | + | 0.876138i | \(0.660111\pi\) | |||||||
\(90\) | −3.20853e10 | −0.572759 | ||||||||
\(91\) | 7.93323e10 | 1.33267 | ||||||||
\(92\) | 1.71364e10 | 0.271073 | ||||||||
\(93\) | −1.66862e10 | −0.248715 | ||||||||
\(94\) | 5.67921e10 | 0.798151 | ||||||||
\(95\) | 9.71928e10 | 1.28871 | ||||||||
\(96\) | −5.42229e9 | −0.0678720 | ||||||||
\(97\) | 2.09497e10 | 0.247704 | 0.123852 | − | 0.992301i | \(-0.460475\pi\) | ||||
0.123852 | + | 0.992301i | \(0.460475\pi\) | |||||||
\(98\) | 2.25204e10 | 0.251671 | ||||||||
\(99\) | −2.77291e10 | −0.293050 | ||||||||
\(100\) | −5.41083e9 | −0.0541083 | ||||||||
\(101\) | −1.72710e11 | −1.63513 | −0.817563 | − | 0.575839i | \(-0.804675\pi\) | ||||
−0.817563 | + | 0.575839i | \(0.804675\pi\) | |||||||
\(102\) | 1.25074e11 | 1.12167 | ||||||||
\(103\) | 1.85002e11 | 1.57243 | 0.786216 | − | 0.617952i | \(-0.212037\pi\) | ||||
0.786216 | + | 0.617952i | \(0.212037\pi\) | |||||||
\(104\) | −3.21685e11 | −2.59268 | ||||||||
\(105\) | 6.89021e10 | 0.526855 | ||||||||
\(106\) | 3.89061e11 | 2.82381 | ||||||||
\(107\) | 1.71381e11 | 1.18128 | 0.590638 | − | 0.806937i | \(-0.298876\pi\) | ||||
0.590638 | + | 0.806937i | \(0.298876\pi\) | |||||||
\(108\) | 5.97487e10 | 0.391289 | ||||||||
\(109\) | 4.45873e10 | 0.277566 | 0.138783 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138783 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(110\) | 2.55162e11 | 1.51062 | ||||||||
\(111\) | −1.11738e11 | −0.629397 | ||||||||
\(112\) | 1.89879e11 | 1.01807 | ||||||||
\(113\) | 4.97055e9 | 0.0253789 | 0.0126895 | − | 0.999919i | \(-0.495961\pi\) | ||||
0.0126895 | + | 0.999919i | \(0.495961\pi\) | |||||||
\(114\) | −2.70009e11 | −1.31341 | ||||||||
\(115\) | 2.83719e10 | 0.131538 | ||||||||
\(116\) | −4.99814e11 | −2.20948 | ||||||||
\(117\) | 1.13898e11 | 0.480278 | ||||||||
\(118\) | 5.63476e10 | 0.226738 | ||||||||
\(119\) | −2.68592e11 | −1.03177 | ||||||||
\(120\) | −2.79392e11 | −1.02498 | ||||||||
\(121\) | −6.47932e10 | −0.227096 | ||||||||
\(122\) | 5.31622e11 | 1.78084 | ||||||||
\(123\) | −2.31700e11 | −0.742077 | ||||||||
\(124\) | −2.85931e11 | −0.875874 | ||||||||
\(125\) | −3.45585e11 | −1.01286 | ||||||||
\(126\) | −1.91415e11 | −0.536955 | ||||||||
\(127\) | −1.07878e11 | −0.289742 | −0.144871 | − | 0.989451i | \(-0.546277\pi\) | ||||
−0.144871 | + | 0.989451i | \(0.546277\pi\) | |||||||
\(128\) | 6.52286e11 | 1.67797 | ||||||||
\(129\) | −4.27419e11 | −1.05344 | ||||||||
\(130\) | −1.04808e12 | −2.47575 | ||||||||
\(131\) | −5.39694e10 | −0.122224 | −0.0611118 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611118 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(132\) | −4.75159e11 | −1.03201 | ||||||||
\(133\) | 5.79835e11 | 1.20815 | ||||||||
\(134\) | 6.75651e11 | 1.35097 | ||||||||
\(135\) | 9.89229e10 | 0.189872 | ||||||||
\(136\) | 1.08911e12 | 2.00729 | ||||||||
\(137\) | −6.06664e11 | −1.07395 | −0.536976 | − | 0.843598i | \(-0.680433\pi\) | ||||
−0.536976 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(138\) | −7.88192e10 | −0.134059 | ||||||||
\(139\) | 5.61474e11 | 0.917801 | 0.458900 | − | 0.888488i | \(-0.348243\pi\) | ||||
0.458900 | + | 0.888488i | \(0.348243\pi\) | |||||||
\(140\) | 1.18069e12 | 1.85537 | ||||||||
\(141\) | −1.75097e11 | −0.264590 | ||||||||
\(142\) | −3.05251e10 | −0.0443682 | ||||||||
\(143\) | −9.05784e11 | −1.26671 | ||||||||
\(144\) | 2.72609e11 | 0.366899 | ||||||||
\(145\) | −8.27516e11 | −1.07214 | ||||||||
\(146\) | 5.01541e11 | 0.625699 | ||||||||
\(147\) | −6.94332e10 | −0.0834300 | ||||||||
\(148\) | −1.91472e12 | −2.21649 | ||||||||
\(149\) | 2.28609e11 | 0.255016 | 0.127508 | − | 0.991838i | \(-0.459302\pi\) | ||||
0.127508 | + | 0.991838i | \(0.459302\pi\) | |||||||
\(150\) | 2.48872e10 | 0.0267592 | ||||||||
\(151\) | −1.57142e12 | −1.62899 | −0.814496 | − | 0.580169i | \(-0.802986\pi\) | ||||
−0.814496 | + | 0.580169i | \(0.802986\pi\) | |||||||
\(152\) | −2.35118e12 | −2.35042 | ||||||||
\(153\) | −3.85618e11 | −0.371838 | ||||||||
\(154\) | 1.52225e12 | 1.41619 | ||||||||
\(155\) | −4.73401e11 | −0.425016 | ||||||||
\(156\) | 1.95172e12 | 1.69135 | ||||||||
\(157\) | 5.60897e10 | 0.0469283 | 0.0234641 | − | 0.999725i | \(-0.492530\pi\) | ||||
0.0234641 | + | 0.999725i | \(0.492530\pi\) | |||||||
\(158\) | −7.46751e11 | −0.603340 | ||||||||
\(159\) | −1.19952e12 | −0.936104 | ||||||||
\(160\) | −1.53835e11 | −0.115983 | ||||||||
\(161\) | 1.69262e11 | 0.123315 | ||||||||
\(162\) | −2.74815e11 | −0.193512 | ||||||||
\(163\) | 1.44082e12 | 0.980795 | 0.490398 | − | 0.871499i | \(-0.336852\pi\) | ||||
0.490398 | + | 0.871499i | \(0.336852\pi\) | |||||||
\(164\) | −3.97036e12 | −2.61330 | ||||||||
\(165\) | −7.86695e11 | −0.500778 | ||||||||
\(166\) | −2.04030e12 | −1.25632 | ||||||||
\(167\) | 1.12221e12 | 0.668550 | 0.334275 | − | 0.942476i | \(-0.391509\pi\) | ||||
0.334275 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(168\) | −1.66680e12 | −0.960909 | ||||||||
\(169\) | 1.92837e12 | 1.07600 | ||||||||
\(170\) | 3.54844e12 | 1.91676 | ||||||||
\(171\) | 8.32470e11 | 0.435402 | ||||||||
\(172\) | −7.32415e12 | −3.70980 | ||||||||
\(173\) | −3.67297e12 | −1.80204 | −0.901018 | − | 0.433781i | \(-0.857179\pi\) | ||||
−0.901018 | + | 0.433781i | \(0.857179\pi\) | |||||||
\(174\) | 2.29890e12 | 1.09270 | ||||||||
\(175\) | −5.34444e10 | −0.0246146 | ||||||||
\(176\) | −2.16796e12 | −0.967678 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 4.00305e12 | 1.67912 | ||||||||
\(179\) | 2.46501e10 | 0.0100260 | 0.00501300 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501300 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(180\) | 1.69512e12 | 0.668654 | ||||||||
\(181\) | 3.13928e12 | 1.20115 | 0.600577 | − | 0.799567i | \(-0.294938\pi\) | ||||
0.600577 | + | 0.799567i | \(0.294938\pi\) | |||||||
\(182\) | −6.25267e12 | −2.32099 | ||||||||
\(183\) | −1.63906e12 | −0.590354 | ||||||||
\(184\) | −6.86340e11 | −0.239906 | ||||||||
\(185\) | −3.17010e12 | −1.07554 | ||||||||
\(186\) | 1.31514e12 | 0.433164 | ||||||||
\(187\) | 3.06667e12 | 0.980704 | ||||||||
\(188\) | −3.00042e12 | −0.931782 | ||||||||
\(189\) | 5.90156e11 | 0.178003 | ||||||||
\(190\) | −7.66037e12 | −2.24442 | ||||||||
\(191\) | −1.65434e12 | −0.470913 | −0.235457 | − | 0.971885i | \(-0.575659\pi\) | ||||
−0.235457 | + | 0.971885i | \(0.575659\pi\) | |||||||
\(192\) | −1.87018e12 | −0.517282 | ||||||||
\(193\) | 6.12757e12 | 1.64711 | 0.823556 | − | 0.567234i | \(-0.191987\pi\) | ||||
0.823556 | + | 0.567234i | \(0.191987\pi\) | |||||||
\(194\) | −1.65117e12 | −0.431403 | ||||||||
\(195\) | 3.23137e12 | 0.820722 | ||||||||
\(196\) | −1.18979e12 | −0.293807 | ||||||||
\(197\) | 7.65084e12 | 1.83715 | 0.918576 | − | 0.395245i | \(-0.129340\pi\) | ||||
0.918576 | + | 0.395245i | \(0.129340\pi\) | |||||||
\(198\) | 2.18550e12 | 0.510378 | ||||||||
\(199\) | −5.25431e12 | −1.19350 | −0.596752 | − | 0.802426i | \(-0.703542\pi\) | ||||
−0.596752 | + | 0.802426i | \(0.703542\pi\) | |||||||
\(200\) | 2.16712e11 | 0.0478871 | ||||||||
\(201\) | −2.08311e12 | −0.447852 | ||||||||
\(202\) | 1.36124e13 | 2.84775 | ||||||||
\(203\) | −4.93681e12 | −1.00512 | ||||||||
\(204\) | −6.60785e12 | −1.30947 | ||||||||
\(205\) | −6.57353e12 | −1.26810 | ||||||||
\(206\) | −1.45812e13 | −2.73856 | ||||||||
\(207\) | 2.43009e11 | 0.0444412 | ||||||||
\(208\) | 8.90493e12 | 1.58592 | ||||||||
\(209\) | −6.62031e12 | −1.14835 | ||||||||
\(210\) | −5.43060e12 | −0.917575 | ||||||||
\(211\) | −3.17714e12 | −0.522977 | −0.261488 | − | 0.965207i | \(-0.584213\pi\) | ||||
−0.261488 | + | 0.965207i | \(0.584213\pi\) | |||||||
\(212\) | −2.05547e13 | −3.29659 | ||||||||
\(213\) | 9.41127e10 | 0.0147082 | ||||||||
\(214\) | −1.35076e13 | −2.05732 | ||||||||
\(215\) | −1.21262e13 | −1.80017 | ||||||||
\(216\) | −2.39303e12 | −0.346300 | ||||||||
\(217\) | −2.82423e12 | −0.398447 | ||||||||
\(218\) | −3.51420e12 | −0.483410 | ||||||||
\(219\) | −1.54631e12 | −0.207422 | ||||||||
\(220\) | −1.34806e13 | −1.76354 | ||||||||
\(221\) | −1.25964e13 | −1.60727 | ||||||||
\(222\) | 8.80676e12 | 1.09616 | ||||||||
\(223\) | 4.88782e12 | 0.593524 | 0.296762 | − | 0.954951i | \(-0.404093\pi\) | ||||
0.296762 | + | 0.954951i | \(0.404093\pi\) | |||||||
\(224\) | −9.17750e11 | −0.108733 | ||||||||
\(225\) | −7.67303e10 | −0.00887080 | ||||||||
\(226\) | −3.91760e11 | −0.0442001 | ||||||||
\(227\) | 1.40691e13 | 1.54926 | 0.774628 | − | 0.632417i | \(-0.217937\pi\) | ||||
0.774628 | + | 0.632417i | \(0.217937\pi\) | |||||||
\(228\) | 1.42650e13 | 1.53331 | ||||||||
\(229\) | 1.66346e13 | 1.74549 | 0.872747 | − | 0.488173i | \(-0.162336\pi\) | ||||
0.872747 | + | 0.488173i | \(0.162336\pi\) | |||||||
\(230\) | −2.23616e12 | −0.229087 | ||||||||
\(231\) | −4.69328e12 | −0.469473 | ||||||||
\(232\) | 2.00183e13 | 1.95544 | ||||||||
\(233\) | −1.03722e13 | −0.989494 | −0.494747 | − | 0.869037i | \(-0.664739\pi\) | ||||
−0.494747 | + | 0.869037i | \(0.664739\pi\) | |||||||
\(234\) | −8.97698e12 | −0.836456 | ||||||||
\(235\) | −4.96765e12 | −0.452145 | ||||||||
\(236\) | −2.97694e12 | −0.264700 | ||||||||
\(237\) | 2.30233e12 | 0.200010 | ||||||||
\(238\) | 2.11694e13 | 1.79694 | ||||||||
\(239\) | 8.65379e12 | 0.717824 | 0.358912 | − | 0.933371i | \(-0.383148\pi\) | ||||
0.358912 | + | 0.933371i | \(0.383148\pi\) | |||||||
\(240\) | 7.73415e12 | 0.626976 | ||||||||
\(241\) | 1.61354e13 | 1.27846 | 0.639229 | − | 0.769017i | \(-0.279254\pi\) | ||||
0.639229 | + | 0.769017i | \(0.279254\pi\) | |||||||
\(242\) | 5.10675e12 | 0.395513 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −2.80865e13 | −2.07899 | ||||||||
\(245\) | −1.96988e12 | −0.142569 | ||||||||
\(246\) | 1.82617e13 | 1.29241 | ||||||||
\(247\) | 2.71931e13 | 1.88202 | ||||||||
\(248\) | 1.14520e13 | 0.775169 | ||||||||
\(249\) | 6.29049e12 | 0.416474 | ||||||||
\(250\) | 2.72377e13 | 1.76401 | ||||||||
\(251\) | 1.02192e13 | 0.647460 | 0.323730 | − | 0.946150i | \(-0.395063\pi\) | ||||
0.323730 | + | 0.946150i | \(0.395063\pi\) | |||||||
\(252\) | 1.01128e13 | 0.626855 | ||||||||
\(253\) | −1.93256e12 | −0.117211 | ||||||||
\(254\) | 8.50253e12 | 0.504618 | ||||||||
\(255\) | −1.09403e13 | −0.635415 | ||||||||
\(256\) | −3.56488e13 | −2.02640 | ||||||||
\(257\) | −2.69070e12 | −0.149704 | −0.0748520 | − | 0.997195i | \(-0.523848\pi\) | ||||
−0.0748520 | + | 0.997195i | \(0.523848\pi\) | |||||||
\(258\) | 3.36875e13 | 1.83468 | ||||||||
\(259\) | −1.89122e13 | −1.00831 | ||||||||
\(260\) | 5.53720e13 | 2.89026 | ||||||||
\(261\) | −7.08779e12 | −0.362233 | ||||||||
\(262\) | 4.25366e12 | 0.212866 | ||||||||
\(263\) | 2.08710e13 | 1.02279 | 0.511395 | − | 0.859346i | \(-0.329129\pi\) | ||||
0.511395 | + | 0.859346i | \(0.329129\pi\) | |||||||
\(264\) | 1.90308e13 | 0.913348 | ||||||||
\(265\) | −3.40314e13 | −1.59966 | ||||||||
\(266\) | −4.57004e13 | −2.10412 | ||||||||
\(267\) | −1.23419e13 | −0.556635 | ||||||||
\(268\) | −3.56958e13 | −1.57716 | ||||||||
\(269\) | −9.86757e12 | −0.427142 | −0.213571 | − | 0.976928i | \(-0.568510\pi\) | ||||
−0.213571 | + | 0.976928i | \(0.568510\pi\) | |||||||
\(270\) | −7.79672e12 | −0.330683 | ||||||||
\(271\) | −3.66647e13 | −1.52376 | −0.761881 | − | 0.647717i | \(-0.775724\pi\) | ||||
−0.761881 | + | 0.647717i | \(0.775724\pi\) | |||||||
\(272\) | −3.01490e13 | −1.22785 | ||||||||
\(273\) | 1.92778e13 | 0.769417 | ||||||||
\(274\) | 4.78149e13 | 1.87040 | ||||||||
\(275\) | 6.10206e11 | 0.0233963 | ||||||||
\(276\) | 4.16415e12 | 0.156504 | ||||||||
\(277\) | 4.73040e13 | 1.74285 | 0.871423 | − | 0.490532i | \(-0.163198\pi\) | ||||
0.871423 | + | 0.490532i | \(0.163198\pi\) | |||||||
\(278\) | −4.42533e13 | −1.59845 | ||||||||
\(279\) | −4.05475e12 | −0.143595 | ||||||||
\(280\) | −4.72885e13 | −1.64205 | ||||||||
\(281\) | 1.44433e13 | 0.491792 | 0.245896 | − | 0.969296i | \(-0.420918\pi\) | ||||
0.245896 | + | 0.969296i | \(0.420918\pi\) | |||||||
\(282\) | 1.38005e13 | 0.460813 | ||||||||
\(283\) | −4.09853e13 | −1.34215 | −0.671077 | − | 0.741387i | \(-0.734168\pi\) | ||||
−0.671077 | + | 0.741387i | \(0.734168\pi\) | |||||||
\(284\) | 1.61269e12 | 0.0517966 | ||||||||
\(285\) | 2.36179e13 | 0.744035 | ||||||||
\(286\) | 7.13904e13 | 2.20611 | ||||||||
\(287\) | −3.92165e13 | −1.18883 | ||||||||
\(288\) | −1.31762e12 | −0.0391859 | ||||||||
\(289\) | 8.37514e12 | 0.244373 | ||||||||
\(290\) | 6.52216e13 | 1.86725 | ||||||||
\(291\) | 5.09077e12 | 0.143012 | ||||||||
\(292\) | −2.64972e13 | −0.730457 | ||||||||
\(293\) | −2.69413e12 | −0.0728863 | −0.0364432 | − | 0.999336i | \(-0.511603\pi\) | ||||
−0.0364432 | + | 0.999336i | \(0.511603\pi\) | |||||||
\(294\) | 5.47246e12 | 0.145302 | ||||||||
\(295\) | −4.92876e12 | −0.128445 | ||||||||
\(296\) | 7.66874e13 | 1.96164 | ||||||||
\(297\) | −6.73816e12 | −0.169192 | ||||||||
\(298\) | −1.80181e13 | −0.444139 | ||||||||
\(299\) | 7.93803e12 | 0.192097 | ||||||||
\(300\) | −1.31483e12 | −0.0312394 | ||||||||
\(301\) | −7.23429e13 | −1.68764 | ||||||||
\(302\) | 1.23853e14 | 2.83707 | ||||||||
\(303\) | −4.19686e13 | −0.944040 | ||||||||
\(304\) | 6.50855e13 | 1.43774 | ||||||||
\(305\) | −4.65013e13 | −1.00883 | ||||||||
\(306\) | 3.03929e13 | 0.647597 | ||||||||
\(307\) | −3.92324e13 | −0.821077 | −0.410538 | − | 0.911843i | \(-0.634659\pi\) | ||||
−0.410538 | + | 0.911843i | \(0.634659\pi\) | |||||||
\(308\) | −8.04230e13 | −1.65330 | ||||||||
\(309\) | 4.49555e13 | 0.907844 | ||||||||
\(310\) | 3.73117e13 | 0.740211 | ||||||||
\(311\) | 8.66964e12 | 0.168974 | 0.0844868 | − | 0.996425i | \(-0.473075\pi\) | ||||
0.0844868 | + | 0.996425i | \(0.473075\pi\) | |||||||
\(312\) | −7.81696e13 | −1.49688 | ||||||||
\(313\) | 1.16560e13 | 0.219308 | 0.109654 | − | 0.993970i | \(-0.465026\pi\) | ||||
0.109654 | + | 0.993970i | \(0.465026\pi\) | |||||||
\(314\) | −4.42077e12 | −0.0817307 | ||||||||
\(315\) | 1.67432e13 | 0.304180 | ||||||||
\(316\) | 3.94521e13 | 0.704355 | ||||||||
\(317\) | 6.66638e13 | 1.16967 | 0.584836 | − | 0.811152i | \(-0.301159\pi\) | ||||
0.584836 | + | 0.811152i | \(0.301159\pi\) | |||||||
\(318\) | 9.45417e13 | 1.63033 | ||||||||
\(319\) | 5.63665e13 | 0.955371 | ||||||||
\(320\) | −5.30586e13 | −0.883956 | ||||||||
\(321\) | 4.16455e13 | 0.682010 | ||||||||
\(322\) | −1.33405e13 | −0.214766 | ||||||||
\(323\) | −9.20663e13 | −1.45709 | ||||||||
\(324\) | 1.45189e13 | 0.225911 | ||||||||
\(325\) | −2.50643e12 | −0.0383440 | ||||||||
\(326\) | −1.13560e14 | −1.70816 | ||||||||
\(327\) | 1.08347e13 | 0.160253 | ||||||||
\(328\) | 1.59019e14 | 2.31283 | ||||||||
\(329\) | −2.96361e13 | −0.423880 | ||||||||
\(330\) | 6.20043e13 | 0.872158 | ||||||||
\(331\) | 4.14677e13 | 0.573662 | 0.286831 | − | 0.957981i | \(-0.407398\pi\) | ||||
0.286831 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(332\) | 1.07792e14 | 1.46666 | ||||||||
\(333\) | −2.71523e13 | −0.363382 | ||||||||
\(334\) | −8.84484e13 | −1.16435 | ||||||||
\(335\) | −5.90996e13 | −0.765312 | ||||||||
\(336\) | 4.61405e13 | 0.587782 | ||||||||
\(337\) | 1.12179e14 | 1.40588 | 0.702939 | − | 0.711250i | \(-0.251871\pi\) | ||||
0.702939 | + | 0.711250i | \(0.251871\pi\) | |||||||
\(338\) | −1.51987e14 | −1.87397 | ||||||||
\(339\) | 1.20784e12 | 0.0146525 | ||||||||
\(340\) | −1.87470e14 | −2.23768 | ||||||||
\(341\) | 3.22459e13 | 0.378726 | ||||||||
\(342\) | −6.56121e13 | −0.758299 | ||||||||
\(343\) | −9.30774e13 | −1.05859 | ||||||||
\(344\) | 2.93344e14 | 3.28326 | ||||||||
\(345\) | 6.89437e12 | 0.0759433 | ||||||||
\(346\) | 2.89489e14 | 3.13844 | ||||||||
\(347\) | −1.50039e14 | −1.60101 | −0.800504 | − | 0.599328i | \(-0.795435\pi\) | ||||
−0.800504 | + | 0.599328i | \(0.795435\pi\) | |||||||
\(348\) | −1.21455e14 | −1.27564 | ||||||||
\(349\) | 1.07318e14 | 1.10951 | 0.554757 | − | 0.832012i | \(-0.312811\pi\) | ||||
0.554757 | + | 0.832012i | \(0.312811\pi\) | |||||||
\(350\) | 4.21228e12 | 0.0428690 | ||||||||
\(351\) | 2.76771e13 | 0.277289 | ||||||||
\(352\) | 1.04785e13 | 0.103351 | ||||||||
\(353\) | −2.15659e13 | −0.209414 | −0.104707 | − | 0.994503i | \(-0.533391\pi\) | ||||
−0.104707 | + | 0.994503i | \(0.533391\pi\) | |||||||
\(354\) | 1.36925e13 | 0.130907 | ||||||||
\(355\) | 2.67005e12 | 0.0251341 | ||||||||
\(356\) | −2.11488e14 | −1.96025 | ||||||||
\(357\) | −6.52678e13 | −0.595694 | ||||||||
\(358\) | −1.94283e12 | −0.0174614 | ||||||||
\(359\) | −1.95610e14 | −1.73130 | −0.865650 | − | 0.500650i | \(-0.833095\pi\) | ||||
−0.865650 | + | 0.500650i | \(0.833095\pi\) | |||||||
\(360\) | −6.78922e13 | −0.591774 | ||||||||
\(361\) | 8.22621e13 | 0.706172 | ||||||||
\(362\) | −2.47426e14 | −2.09194 | ||||||||
\(363\) | −1.57448e13 | −0.131114 | ||||||||
\(364\) | 3.30339e14 | 2.70958 | ||||||||
\(365\) | −4.38701e13 | −0.354452 | ||||||||
\(366\) | 1.29184e14 | 1.02817 | ||||||||
\(367\) | −1.86834e14 | −1.46485 | −0.732423 | − | 0.680849i | \(-0.761611\pi\) | ||||
−0.732423 | + | 0.680849i | \(0.761611\pi\) | |||||||
\(368\) | 1.89993e13 | 0.146749 | ||||||||
\(369\) | −5.63032e13 | −0.428438 | ||||||||
\(370\) | 2.49855e14 | 1.87318 | ||||||||
\(371\) | −2.03025e14 | −1.49966 | ||||||||
\(372\) | −6.94812e13 | −0.505686 | ||||||||
\(373\) | −1.90329e14 | −1.36492 | −0.682458 | − | 0.730925i | \(-0.739089\pi\) | ||||
−0.682458 | + | 0.730925i | \(0.739089\pi\) | |||||||
\(374\) | −2.41703e14 | −1.70800 | ||||||||
\(375\) | −8.39771e13 | −0.584775 | ||||||||
\(376\) | 1.20172e14 | 0.824649 | ||||||||
\(377\) | −2.31526e14 | −1.56575 | ||||||||
\(378\) | −4.65138e13 | −0.310011 | ||||||||
\(379\) | 2.18200e14 | 1.43331 | 0.716653 | − | 0.697430i | \(-0.245673\pi\) | ||||
0.716653 | + | 0.697430i | \(0.245673\pi\) | |||||||
\(380\) | 4.04710e14 | 2.62020 | ||||||||
\(381\) | −2.62143e13 | −0.167283 | ||||||||
\(382\) | 1.30389e14 | 0.820146 | ||||||||
\(383\) | 1.50934e14 | 0.935825 | 0.467913 | − | 0.883775i | \(-0.345006\pi\) | ||||
0.467913 | + | 0.883775i | \(0.345006\pi\) | |||||||
\(384\) | 1.58506e14 | 0.968774 | ||||||||
\(385\) | −1.33152e14 | −0.802259 | ||||||||
\(386\) | −4.82952e14 | −2.86862 | ||||||||
\(387\) | −1.03863e14 | −0.608205 | ||||||||
\(388\) | 8.72342e13 | 0.503631 | ||||||||
\(389\) | −1.25855e14 | −0.716389 | −0.358195 | − | 0.933647i | \(-0.616608\pi\) | ||||
−0.358195 | + | 0.933647i | \(0.616608\pi\) | |||||||
\(390\) | −2.54684e14 | −1.42938 | ||||||||
\(391\) | −2.68754e13 | −0.148724 | ||||||||
\(392\) | 4.76530e13 | 0.260026 | ||||||||
\(393\) | −1.31146e13 | −0.0705659 | ||||||||
\(394\) | −6.03010e14 | −3.19960 | ||||||||
\(395\) | 6.53188e13 | 0.341786 | ||||||||
\(396\) | −1.15464e14 | −0.595828 | ||||||||
\(397\) | −1.64721e14 | −0.838306 | −0.419153 | − | 0.907916i | \(-0.637673\pi\) | ||||
−0.419153 | + | 0.907916i | \(0.637673\pi\) | |||||||
\(398\) | 4.14125e14 | 2.07862 | ||||||||
\(399\) | 1.40900e14 | 0.697525 | ||||||||
\(400\) | −5.99905e12 | −0.0292922 | ||||||||
\(401\) | −1.25477e14 | −0.604323 | −0.302162 | − | 0.953257i | \(-0.597708\pi\) | ||||
−0.302162 | + | 0.953257i | \(0.597708\pi\) | |||||||
\(402\) | 1.64183e14 | 0.779983 | ||||||||
\(403\) | −1.32451e14 | −0.620692 | ||||||||
\(404\) | −7.19165e14 | −3.32454 | ||||||||
\(405\) | 2.40383e13 | 0.109623 | ||||||||
\(406\) | 3.89100e14 | 1.75053 | ||||||||
\(407\) | 2.15932e14 | 0.958402 | ||||||||
\(408\) | 2.64655e14 | 1.15891 | ||||||||
\(409\) | −1.51053e14 | −0.652607 | −0.326304 | − | 0.945265i | \(-0.605803\pi\) | ||||
−0.326304 | + | 0.945265i | \(0.605803\pi\) | |||||||
\(410\) | 5.18100e14 | 2.20853 | ||||||||
\(411\) | −1.47419e14 | −0.620046 | ||||||||
\(412\) | 7.70347e14 | 3.19707 | ||||||||
\(413\) | −2.94041e13 | −0.120416 | ||||||||
\(414\) | −1.91531e13 | −0.0773992 | ||||||||
\(415\) | 1.78466e14 | 0.711691 | ||||||||
\(416\) | −4.30406e13 | −0.169381 | ||||||||
\(417\) | 1.36438e14 | 0.529893 | ||||||||
\(418\) | 5.21788e14 | 1.99997 | ||||||||
\(419\) | 1.26362e13 | 0.0478013 | 0.0239007 | − | 0.999714i | \(-0.492391\pi\) | ||||
0.0239007 | + | 0.999714i | \(0.492391\pi\) | |||||||
\(420\) | 2.86908e14 | 1.07120 | ||||||||
\(421\) | −2.87292e14 | −1.05870 | −0.529350 | − | 0.848404i | \(-0.677564\pi\) | ||||
−0.529350 | + | 0.848404i | \(0.677564\pi\) | |||||||
\(422\) | 2.50410e14 | 0.910820 | ||||||||
\(423\) | −4.25486e13 | −0.152761 | ||||||||
\(424\) | 8.23249e14 | 2.91755 | ||||||||
\(425\) | 8.48591e12 | 0.0296865 | ||||||||
\(426\) | −7.41760e12 | −0.0256160 | ||||||||
\(427\) | −2.77419e14 | −0.945763 | ||||||||
\(428\) | 7.13628e14 | 2.40177 | ||||||||
\(429\) | −2.20106e14 | −0.731334 | ||||||||
\(430\) | 9.55743e14 | 3.13519 | ||||||||
\(431\) | 3.33625e14 | 1.08052 | 0.540260 | − | 0.841498i | \(-0.318326\pi\) | ||||
0.540260 | + | 0.841498i | \(0.318326\pi\) | |||||||
\(432\) | 6.62441e13 | 0.211829 | ||||||||
\(433\) | −2.21538e14 | −0.699463 | −0.349732 | − | 0.936850i | \(-0.613727\pi\) | ||||
−0.349732 | + | 0.936850i | \(0.613727\pi\) | |||||||
\(434\) | 2.22595e14 | 0.693939 | ||||||||
\(435\) | −2.01086e14 | −0.619001 | ||||||||
\(436\) | 1.85661e14 | 0.564346 | ||||||||
\(437\) | 5.80185e13 | 0.174148 | ||||||||
\(438\) | 1.21874e14 | 0.361247 | ||||||||
\(439\) | −1.01863e14 | −0.298168 | −0.149084 | − | 0.988825i | \(-0.547632\pi\) | ||||
−0.149084 | + | 0.988825i | \(0.547632\pi\) | |||||||
\(440\) | 5.39920e14 | 1.56077 | ||||||||
\(441\) | −1.68723e13 | −0.0481683 | ||||||||
\(442\) | 9.92801e14 | 2.79924 | ||||||||
\(443\) | −1.00942e14 | −0.281093 | −0.140546 | − | 0.990074i | \(-0.544886\pi\) | ||||
−0.140546 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(444\) | −4.65276e14 | −1.27969 | ||||||||
\(445\) | −3.50150e14 | −0.951205 | ||||||||
\(446\) | −3.85239e14 | −1.03369 | ||||||||
\(447\) | 5.55519e13 | 0.147234 | ||||||||
\(448\) | −3.16538e14 | −0.828699 | ||||||||
\(449\) | 2.46092e14 | 0.636417 | 0.318209 | − | 0.948021i | \(-0.396919\pi\) | ||||
0.318209 | + | 0.948021i | \(0.396919\pi\) | |||||||
\(450\) | 6.04759e12 | 0.0154495 | ||||||||
\(451\) | 4.47758e14 | 1.12998 | ||||||||
\(452\) | 2.06973e13 | 0.0516004 | ||||||||
\(453\) | −3.81855e14 | −0.940499 | ||||||||
\(454\) | −1.10887e15 | −2.69820 | ||||||||
\(455\) | 5.46925e14 | 1.31482 | ||||||||
\(456\) | −5.71336e14 | −1.35702 | ||||||||
\(457\) | 6.75579e14 | 1.58539 | 0.792696 | − | 0.609617i | \(-0.208677\pi\) | ||||
0.792696 | + | 0.609617i | \(0.208677\pi\) | |||||||
\(458\) | −1.31108e15 | −3.03997 | ||||||||
\(459\) | −9.37051e13 | −0.214681 | ||||||||
\(460\) | 1.18140e14 | 0.267442 | ||||||||
\(461\) | 2.11996e14 | 0.474213 | 0.237107 | − | 0.971484i | \(-0.423801\pi\) | ||||
0.237107 | + | 0.971484i | \(0.423801\pi\) | |||||||
\(462\) | 3.69907e14 | 0.817638 | ||||||||
\(463\) | 3.43294e14 | 0.749844 | 0.374922 | − | 0.927056i | \(-0.377669\pi\) | ||||
0.374922 | + | 0.927056i | \(0.377669\pi\) | |||||||
\(464\) | −5.54149e14 | −1.19613 | ||||||||
\(465\) | −1.15036e14 | −0.245383 | ||||||||
\(466\) | 8.17497e14 | 1.72331 | ||||||||
\(467\) | −9.00452e13 | −0.187594 | −0.0937968 | − | 0.995591i | \(-0.529900\pi\) | ||||
−0.0937968 | + | 0.995591i | \(0.529900\pi\) | |||||||
\(468\) | 4.74269e14 | 0.976500 | ||||||||
\(469\) | −3.52578e14 | −0.717471 | ||||||||
\(470\) | 3.91531e14 | 0.787459 | ||||||||
\(471\) | 1.36298e13 | 0.0270941 | ||||||||
\(472\) | 1.19231e14 | 0.234265 | ||||||||
\(473\) | 8.25981e14 | 1.60411 | ||||||||
\(474\) | −1.81461e14 | −0.348338 | ||||||||
\(475\) | −1.83194e13 | −0.0347613 | ||||||||
\(476\) | −1.11841e15 | −2.09780 | ||||||||
\(477\) | −2.91484e14 | −0.540460 | ||||||||
\(478\) | −6.82059e14 | −1.25017 | ||||||||
\(479\) | 5.26598e14 | 0.954188 | 0.477094 | − | 0.878852i | \(-0.341690\pi\) | ||||
0.477094 | + | 0.878852i | \(0.341690\pi\) | |||||||
\(480\) | −3.73818e13 | −0.0669628 | ||||||||
\(481\) | −8.86945e14 | −1.57072 | ||||||||
\(482\) | −1.27173e15 | −2.22657 | ||||||||
\(483\) | 4.11305e13 | 0.0711959 | ||||||||
\(484\) | −2.69798e14 | −0.461732 | ||||||||
\(485\) | 1.44429e14 | 0.244386 | ||||||||
\(486\) | −6.67801e13 | −0.111724 | ||||||||
\(487\) | −7.04142e14 | −1.16480 | −0.582400 | − | 0.812903i | \(-0.697886\pi\) | ||||
−0.582400 | + | 0.812903i | \(0.697886\pi\) | |||||||
\(488\) | 1.12491e15 | 1.83996 | ||||||||
\(489\) | 3.50120e14 | 0.566263 | ||||||||
\(490\) | 1.55258e14 | 0.248300 | ||||||||
\(491\) | 4.33955e14 | 0.686272 | 0.343136 | − | 0.939286i | \(-0.388511\pi\) | ||||
0.343136 | + | 0.939286i | \(0.388511\pi\) | |||||||
\(492\) | −9.64799e14 | −1.50879 | ||||||||
\(493\) | 7.83868e14 | 1.21223 | ||||||||
\(494\) | −2.14325e15 | −3.27775 | ||||||||
\(495\) | −1.91167e14 | −0.289124 | ||||||||
\(496\) | −3.17015e14 | −0.474166 | ||||||||
\(497\) | 1.59291e13 | 0.0235630 | ||||||||
\(498\) | −4.95792e14 | −0.725335 | ||||||||
\(499\) | 3.20518e13 | 0.0463767 | 0.0231884 | − | 0.999731i | \(-0.492618\pi\) | ||||
0.0231884 | + | 0.999731i | \(0.492618\pi\) | |||||||
\(500\) | −1.43901e15 | −2.05935 | ||||||||
\(501\) | 2.72697e14 | 0.385988 | ||||||||
\(502\) | −8.05441e14 | −1.12762 | ||||||||
\(503\) | −1.28261e13 | −0.0177611 | −0.00888054 | − | 0.999961i | \(-0.502827\pi\) | ||||
−0.00888054 | + | 0.999961i | \(0.502827\pi\) | |||||||
\(504\) | −4.05032e14 | −0.554781 | ||||||||
\(505\) | −1.19068e15 | −1.61322 | ||||||||
\(506\) | 1.52317e14 | 0.204136 | ||||||||
\(507\) | 4.68593e14 | 0.621230 | ||||||||
\(508\) | −4.49203e14 | −0.589104 | ||||||||
\(509\) | −2.01034e13 | −0.0260808 | −0.0130404 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130404 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(510\) | 8.62272e14 | 1.10664 | ||||||||
\(511\) | −2.61721e14 | −0.332295 | ||||||||
\(512\) | 1.47382e15 | 1.85123 | ||||||||
\(513\) | 2.02290e14 | 0.251379 | ||||||||
\(514\) | 2.12071e14 | 0.260726 | ||||||||
\(515\) | 1.27542e15 | 1.55137 | ||||||||
\(516\) | −1.77977e15 | −2.14186 | ||||||||
\(517\) | 3.38373e14 | 0.402900 | ||||||||
\(518\) | 1.49059e15 | 1.75608 | ||||||||
\(519\) | −8.92531e14 | −1.04041 | ||||||||
\(520\) | −2.21773e15 | −2.55794 | ||||||||
\(521\) | −2.88358e14 | −0.329097 | −0.164549 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164549 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(522\) | 5.58633e14 | 0.630868 | ||||||||
\(523\) | −5.55798e14 | −0.621094 | −0.310547 | − | 0.950558i | \(-0.600512\pi\) | ||||
−0.310547 | + | 0.950558i | \(0.600512\pi\) | |||||||
\(524\) | −2.24728e14 | −0.248505 | ||||||||
\(525\) | −1.29870e13 | −0.0142112 | ||||||||
\(526\) | −1.64497e15 | −1.78130 | ||||||||
\(527\) | 4.48431e14 | 0.480549 | ||||||||
\(528\) | −5.26814e14 | −0.558689 | ||||||||
\(529\) | −9.35873e14 | −0.982225 | ||||||||
\(530\) | 2.68223e15 | 2.78598 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 2.41443e15 | 2.45640 | ||||||||
\(533\) | −1.83917e15 | −1.85192 | ||||||||
\(534\) | 9.72742e14 | 0.969440 | ||||||||
\(535\) | 1.18152e15 | 1.16545 | ||||||||
\(536\) | 1.42967e15 | 1.39582 | ||||||||
\(537\) | 5.98998e12 | 0.00578851 | ||||||||
\(538\) | 7.77724e14 | 0.743915 | ||||||||
\(539\) | 1.34179e14 | 0.127041 | ||||||||
\(540\) | 4.11914e14 | 0.386048 | ||||||||
\(541\) | −5.01411e14 | −0.465167 | −0.232584 | − | 0.972576i | \(-0.574718\pi\) | ||||
−0.232584 | + | 0.972576i | \(0.574718\pi\) | |||||||
\(542\) | 2.88977e15 | 2.65380 | ||||||||
\(543\) | 7.62846e14 | 0.693486 | ||||||||
\(544\) | 1.45721e14 | 0.131138 | ||||||||
\(545\) | 3.07390e14 | 0.273847 | ||||||||
\(546\) | −1.51940e15 | −1.34002 | ||||||||
\(547\) | −2.59756e14 | −0.226796 | −0.113398 | − | 0.993550i | \(-0.536174\pi\) | ||||
−0.113398 | + | 0.993550i | \(0.536174\pi\) | |||||||
\(548\) | −2.52614e15 | −2.18356 | ||||||||
\(549\) | −3.98291e14 | −0.340841 | ||||||||
\(550\) | −4.80941e13 | −0.0407471 | ||||||||
\(551\) | −1.69221e15 | −1.41945 | ||||||||
\(552\) | −1.66781e14 | −0.138510 | ||||||||
\(553\) | 3.89680e14 | 0.320421 | ||||||||
\(554\) | −3.72832e15 | −3.03535 | ||||||||
\(555\) | −7.70333e14 | −0.620965 | ||||||||
\(556\) | 2.33797e15 | 1.86607 | ||||||||
\(557\) | −1.04084e15 | −0.822587 | −0.411293 | − | 0.911503i | \(-0.634923\pi\) | ||||
−0.411293 | + | 0.911503i | \(0.634923\pi\) | |||||||
\(558\) | 3.19580e14 | 0.250087 | ||||||||
\(559\) | −3.39274e15 | −2.62897 | ||||||||
\(560\) | 1.30904e15 | 1.00443 | ||||||||
\(561\) | 7.45201e14 | 0.566210 | ||||||||
\(562\) | −1.13836e15 | −0.856509 | ||||||||
\(563\) | −8.78087e14 | −0.654246 | −0.327123 | − | 0.944982i | \(-0.606079\pi\) | ||||
−0.327123 | + | 0.944982i | \(0.606079\pi\) | |||||||
\(564\) | −7.29103e14 | −0.537965 | ||||||||
\(565\) | 3.42675e13 | 0.0250389 | ||||||||
\(566\) | 3.23030e15 | 2.33751 | ||||||||
\(567\) | 1.43408e14 | 0.102770 | ||||||||
\(568\) | −6.45909e13 | −0.0458411 | ||||||||
\(569\) | −2.14884e15 | −1.51038 | −0.755191 | − | 0.655505i | \(-0.772456\pi\) | ||||
−0.755191 | + | 0.655505i | \(0.772456\pi\) | |||||||
\(570\) | −1.86147e15 | −1.29582 | ||||||||
\(571\) | 5.35406e14 | 0.369134 | 0.184567 | − | 0.982820i | \(-0.440912\pi\) | ||||
0.184567 | + | 0.982820i | \(0.440912\pi\) | |||||||
\(572\) | −3.77168e15 | −2.57547 | ||||||||
\(573\) | −4.02004e14 | −0.271882 | ||||||||
\(574\) | 3.09089e15 | 2.07047 | ||||||||
\(575\) | −5.34767e12 | −0.00354806 | ||||||||
\(576\) | −4.54454e14 | −0.298653 | ||||||||
\(577\) | 5.44577e14 | 0.354480 | 0.177240 | − | 0.984168i | \(-0.443283\pi\) | ||||
0.177240 | + | 0.984168i | \(0.443283\pi\) | |||||||
\(578\) | −6.60097e14 | −0.425603 | ||||||||
\(579\) | 1.48900e15 | 0.950961 | ||||||||
\(580\) | −3.44577e15 | −2.17988 | ||||||||
\(581\) | 1.06470e15 | 0.667202 | ||||||||
\(582\) | −4.01235e14 | −0.249071 | ||||||||
\(583\) | 2.31806e15 | 1.42543 | ||||||||
\(584\) | 1.06126e15 | 0.646471 | ||||||||
\(585\) | 7.85222e14 | 0.473844 | ||||||||
\(586\) | 2.12341e14 | 0.126939 | ||||||||
\(587\) | 2.93282e15 | 1.73691 | 0.868453 | − | 0.495771i | \(-0.165114\pi\) | ||||
0.868453 | + | 0.495771i | \(0.165114\pi\) | |||||||
\(588\) | −2.89119e14 | −0.169630 | ||||||||
\(589\) | −9.68072e14 | −0.562695 | ||||||||
\(590\) | 3.88466e14 | 0.223701 | ||||||||
\(591\) | 1.85915e15 | 1.06068 | ||||||||
\(592\) | −2.12287e15 | −1.19992 | ||||||||
\(593\) | −1.20511e15 | −0.674877 | −0.337438 | − | 0.941348i | \(-0.609560\pi\) | ||||
−0.337438 | + | 0.941348i | \(0.609560\pi\) | |||||||
\(594\) | 5.31076e14 | 0.294667 | ||||||||
\(595\) | −1.85170e15 | −1.01795 | ||||||||
\(596\) | 9.51924e14 | 0.518499 | ||||||||
\(597\) | −1.27680e15 | −0.689070 | ||||||||
\(598\) | −6.25645e14 | −0.334558 | ||||||||
\(599\) | −1.80492e15 | −0.956335 | −0.478168 | − | 0.878269i | \(-0.658699\pi\) | ||||
−0.478168 | + | 0.878269i | \(0.658699\pi\) | |||||||
\(600\) | 5.26611e13 | 0.0276476 | ||||||||
\(601\) | 2.52227e15 | 1.31215 | 0.656074 | − | 0.754697i | \(-0.272216\pi\) | ||||
0.656074 | + | 0.754697i | \(0.272216\pi\) | |||||||
\(602\) | 5.70179e15 | 2.93921 | ||||||||
\(603\) | −5.06197e14 | −0.258568 | ||||||||
\(604\) | −6.54338e15 | −3.31206 | ||||||||
\(605\) | −4.46691e14 | −0.224054 | ||||||||
\(606\) | 3.30781e15 | 1.64415 | ||||||||
\(607\) | −1.47629e15 | −0.727167 | −0.363583 | − | 0.931562i | \(-0.618447\pi\) | ||||
−0.363583 | + | 0.931562i | \(0.618447\pi\) | |||||||
\(608\) | −3.14581e14 | −0.153555 | ||||||||
\(609\) | −1.19964e15 | −0.580307 | ||||||||
\(610\) | 3.66506e15 | 1.75698 | ||||||||
\(611\) | −1.38987e15 | −0.660311 | ||||||||
\(612\) | −1.60571e15 | −0.756021 | ||||||||
\(613\) | −6.61911e14 | −0.308864 | −0.154432 | − | 0.988003i | \(-0.549355\pi\) | ||||
−0.154432 | + | 0.988003i | \(0.549355\pi\) | |||||||
\(614\) | 3.09215e15 | 1.42999 | ||||||||
\(615\) | −1.59737e15 | −0.732136 | ||||||||
\(616\) | 3.22107e15 | 1.46321 | ||||||||
\(617\) | 3.35290e15 | 1.50957 | 0.754783 | − | 0.655974i | \(-0.227742\pi\) | ||||
0.754783 | + | 0.655974i | \(0.227742\pi\) | |||||||
\(618\) | −3.54322e15 | −1.58111 | ||||||||
\(619\) | 1.77549e15 | 0.785270 | 0.392635 | − | 0.919694i | \(-0.371564\pi\) | ||||
0.392635 | + | 0.919694i | \(0.371564\pi\) | |||||||
\(620\) | −1.97124e15 | −0.864141 | ||||||||
\(621\) | 5.90512e13 | 0.0256581 | ||||||||
\(622\) | −6.83308e14 | −0.294286 | ||||||||
\(623\) | −2.08893e15 | −0.891743 | ||||||||
\(624\) | 2.16390e15 | 0.915633 | ||||||||
\(625\) | −2.31905e15 | −0.972679 | ||||||||
\(626\) | −9.18679e14 | −0.381949 | ||||||||
\(627\) | −1.60874e15 | −0.663000 | ||||||||
\(628\) | 2.33557e14 | 0.0954145 | ||||||||
\(629\) | 3.00289e15 | 1.21608 | ||||||||
\(630\) | −1.31964e15 | −0.529762 | ||||||||
\(631\) | 3.54099e15 | 1.40917 | 0.704585 | − | 0.709620i | \(-0.251133\pi\) | ||||
0.704585 | + | 0.709620i | \(0.251133\pi\) | |||||||
\(632\) | −1.58012e15 | −0.623370 | ||||||||
\(633\) | −7.72044e14 | −0.301941 | ||||||||
\(634\) | −5.25419e15 | −2.03711 | ||||||||
\(635\) | −7.43722e14 | −0.285861 | ||||||||
\(636\) | −4.99480e15 | −1.90329 | ||||||||
\(637\) | −5.51142e14 | −0.208208 | ||||||||
\(638\) | −4.44259e15 | −1.66388 | ||||||||
\(639\) | 2.28694e13 | 0.00849180 | ||||||||
\(640\) | 4.49693e15 | 1.65549 | ||||||||
\(641\) | 3.15496e15 | 1.15153 | 0.575765 | − | 0.817615i | \(-0.304704\pi\) | ||||
0.575765 | + | 0.817615i | \(0.304704\pi\) | |||||||
\(642\) | −3.28234e15 | −1.18779 | ||||||||
\(643\) | −4.92157e15 | −1.76581 | −0.882904 | − | 0.469554i | \(-0.844415\pi\) | ||||
−0.882904 | + | 0.469554i | \(0.844415\pi\) | |||||||
\(644\) | 7.04803e14 | 0.250724 | ||||||||
\(645\) | −2.94667e15 | −1.03933 | ||||||||
\(646\) | 7.25631e15 | 2.53768 | ||||||||
\(647\) | 4.06035e15 | 1.40796 | 0.703979 | − | 0.710221i | \(-0.251405\pi\) | ||||
0.703979 | + | 0.710221i | \(0.251405\pi\) | |||||||
\(648\) | −5.81506e14 | −0.199936 | ||||||||
\(649\) | 3.35724e14 | 0.114456 | ||||||||
\(650\) | 1.97548e14 | 0.0667803 | ||||||||
\(651\) | −6.86287e14 | −0.230044 | ||||||||
\(652\) | 5.99957e15 | 1.99415 | ||||||||
\(653\) | 1.19641e15 | 0.394328 | 0.197164 | − | 0.980371i | \(-0.436827\pi\) | ||||
0.197164 | + | 0.980371i | \(0.436827\pi\) | |||||||
\(654\) | −8.53951e14 | −0.279097 | ||||||||
\(655\) | −3.72071e14 | −0.120586 | ||||||||
\(656\) | −4.40199e15 | −1.41474 | ||||||||
\(657\) | −3.75754e14 | −0.119755 | ||||||||
\(658\) | 2.33580e15 | 0.738234 | ||||||||
\(659\) | −3.89731e15 | −1.22150 | −0.610752 | − | 0.791822i | \(-0.709133\pi\) | ||||
−0.610752 | + | 0.791822i | \(0.709133\pi\) | |||||||
\(660\) | −3.27579e15 | −1.01818 | ||||||||
\(661\) | 6.16282e15 | 1.89964 | 0.949820 | − | 0.312797i | \(-0.101266\pi\) | ||||
0.949820 | + | 0.312797i | \(0.101266\pi\) | |||||||
\(662\) | −3.26832e15 | −0.999094 | ||||||||
\(663\) | −3.06093e15 | −0.927959 | ||||||||
\(664\) | −4.31725e15 | −1.29802 | ||||||||
\(665\) | 3.99744e15 | 1.19196 | ||||||||
\(666\) | 2.14004e15 | 0.632870 | ||||||||
\(667\) | −4.93979e14 | −0.144883 | ||||||||
\(668\) | 4.67288e15 | 1.35930 | ||||||||
\(669\) | 1.18774e15 | 0.342671 | ||||||||
\(670\) | 4.65801e15 | 1.33287 | ||||||||
\(671\) | 3.16745e15 | 0.898951 | ||||||||
\(672\) | −2.23013e14 | −0.0627769 | ||||||||
\(673\) | −2.03701e14 | −0.0568736 | −0.0284368 | − | 0.999596i | \(-0.509053\pi\) | ||||
−0.0284368 | + | 0.999596i | \(0.509053\pi\) | |||||||
\(674\) | −8.84153e15 | −2.44849 | ||||||||
\(675\) | −1.86455e13 | −0.00512156 | ||||||||
\(676\) | 8.02970e15 | 2.18772 | ||||||||
\(677\) | 1.64809e15 | 0.445393 | 0.222697 | − | 0.974888i | \(-0.428514\pi\) | ||||
0.222697 | + | 0.974888i | \(0.428514\pi\) | |||||||
\(678\) | −9.51977e13 | −0.0255190 | ||||||||
\(679\) | 8.61638e14 | 0.229109 | ||||||||
\(680\) | 7.50847e15 | 1.98040 | ||||||||
\(681\) | 3.41878e15 | 0.894464 | ||||||||
\(682\) | −2.54149e15 | −0.659592 | ||||||||
\(683\) | −5.85577e15 | −1.50755 | −0.753773 | − | 0.657135i | \(-0.771768\pi\) | ||||
−0.753773 | + | 0.657135i | \(0.771768\pi\) | |||||||
\(684\) | 3.46640e15 | 0.885258 | ||||||||
\(685\) | −4.18240e15 | −1.05957 | ||||||||
\(686\) | 7.33600e15 | 1.84364 | ||||||||
\(687\) | 4.04222e15 | 1.00776 | ||||||||
\(688\) | −8.12037e15 | −2.00835 | ||||||||
\(689\) | −9.52147e15 | −2.33614 | ||||||||
\(690\) | −5.43388e14 | −0.132263 | ||||||||
\(691\) | 1.41036e15 | 0.340567 | 0.170283 | − | 0.985395i | \(-0.445532\pi\) | ||||
0.170283 | + | 0.985395i | \(0.445532\pi\) | |||||||
\(692\) | −1.52942e16 | −3.66390 | ||||||||
\(693\) | −1.14047e15 | −0.271050 | ||||||||
\(694\) | 1.18255e16 | 2.78833 | ||||||||
\(695\) | 3.87086e15 | 0.905506 | ||||||||
\(696\) | 4.86445e15 | 1.12897 | ||||||||
\(697\) | 6.22680e15 | 1.43379 | ||||||||
\(698\) | −8.45840e15 | −1.93234 | ||||||||
\(699\) | −2.52044e15 | −0.571284 | ||||||||
\(700\) | −2.22542e14 | −0.0500464 | ||||||||
\(701\) | 4.55950e15 | 1.01734 | 0.508672 | − | 0.860960i | \(-0.330136\pi\) | ||||
0.508672 | + | 0.860960i | \(0.330136\pi\) | |||||||
\(702\) | −2.18141e15 | −0.482928 | ||||||||
\(703\) | −6.48262e15 | −1.42396 | ||||||||
\(704\) | 3.61410e15 | 0.787682 | ||||||||
\(705\) | −1.20714e15 | −0.261046 | ||||||||
\(706\) | 1.69974e15 | 0.364718 | ||||||||
\(707\) | −7.10341e15 | −1.51238 | ||||||||
\(708\) | −7.23396e14 | −0.152825 | ||||||||
\(709\) | 8.37079e15 | 1.75474 | 0.877369 | − | 0.479816i | \(-0.159297\pi\) | ||||
0.877369 | + | 0.479816i | \(0.159297\pi\) | |||||||
\(710\) | −2.10443e14 | −0.0437738 | ||||||||
\(711\) | 5.59465e14 | 0.115476 | ||||||||
\(712\) | 8.47043e15 | 1.73486 | ||||||||
\(713\) | −2.82593e14 | −0.0574340 | ||||||||
\(714\) | 5.14416e15 | 1.03747 | ||||||||
\(715\) | −6.24457e15 | −1.24974 | ||||||||
\(716\) | 1.02643e14 | 0.0203848 | ||||||||
\(717\) | 2.10287e15 | 0.414436 | ||||||||
\(718\) | 1.54173e16 | 3.01525 | ||||||||
\(719\) | −7.11696e15 | −1.38129 | −0.690646 | − | 0.723193i | \(-0.742674\pi\) | ||||
−0.690646 | + | 0.723193i | \(0.742674\pi\) | |||||||
\(720\) | 1.87940e15 | 0.361984 | ||||||||
\(721\) | 7.60894e15 | 1.45439 | ||||||||
\(722\) | −6.48359e15 | −1.22987 | ||||||||
\(723\) | 3.92091e15 | 0.738118 | ||||||||
\(724\) | 1.30719e16 | 2.44218 | ||||||||
\(725\) | 1.55974e14 | 0.0289197 | ||||||||
\(726\) | 1.24094e15 | 0.228349 | ||||||||
\(727\) | 1.56846e15 | 0.286441 | 0.143221 | − | 0.989691i | \(-0.454254\pi\) | ||||
0.143221 | + | 0.989691i | \(0.454254\pi\) | |||||||
\(728\) | −1.32306e16 | −2.39804 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 3.45767e15 | 0.617317 | ||||||||
\(731\) | 1.14866e16 | 2.03538 | ||||||||
\(732\) | −6.82501e15 | −1.20031 | ||||||||
\(733\) | −5.61723e14 | −0.0980507 | −0.0490253 | − | 0.998798i | \(-0.515612\pi\) | ||||
−0.0490253 | + | 0.998798i | \(0.515612\pi\) | |||||||
\(734\) | 1.47255e16 | 2.55119 | ||||||||
\(735\) | −4.78680e14 | −0.0823123 | ||||||||
\(736\) | −9.18304e13 | −0.0156732 | ||||||||
\(737\) | 4.02559e15 | 0.681959 | ||||||||
\(738\) | 4.43760e15 | 0.746171 | ||||||||
\(739\) | −9.25820e15 | −1.54519 | −0.772595 | − | 0.634899i | \(-0.781042\pi\) | ||||
−0.772595 | + | 0.634899i | \(0.781042\pi\) | |||||||
\(740\) | −1.32003e16 | −2.18679 | ||||||||
\(741\) | 6.60792e15 | 1.08659 | ||||||||
\(742\) | 1.60017e16 | 2.61182 | ||||||||
\(743\) | 1.04514e16 | 1.69331 | 0.846653 | − | 0.532146i | \(-0.178614\pi\) | ||||
0.846653 | + | 0.532146i | \(0.178614\pi\) | |||||||
\(744\) | 2.78283e15 | 0.447544 | ||||||||
\(745\) | 1.57605e15 | 0.251600 | ||||||||
\(746\) | 1.50010e16 | 2.37715 | ||||||||
\(747\) | 1.52859e15 | 0.240452 | ||||||||
\(748\) | 1.27696e16 | 1.99397 | ||||||||
\(749\) | 7.04871e15 | 1.09260 | ||||||||
\(750\) | 6.61875e15 | 1.01845 | ||||||||
\(751\) | 7.19109e15 | 1.09844 | 0.549218 | − | 0.835679i | \(-0.314926\pi\) | ||||
0.549218 | + | 0.835679i | \(0.314926\pi\) | |||||||
\(752\) | −3.32660e15 | −0.504432 | ||||||||
\(753\) | 2.48327e15 | 0.373811 | ||||||||
\(754\) | 1.82480e16 | 2.72693 | ||||||||
\(755\) | −1.08335e16 | −1.60717 | ||||||||
\(756\) | 2.45740e15 | 0.361915 | ||||||||
\(757\) | −1.28041e16 | −1.87207 | −0.936035 | − | 0.351907i | \(-0.885533\pi\) | ||||
−0.936035 | + | 0.351907i | \(0.885533\pi\) | |||||||
\(758\) | −1.71977e16 | −2.49626 | ||||||||
\(759\) | −4.69612e14 | −0.0676720 | ||||||||
\(760\) | −1.62093e16 | −2.31893 | ||||||||
\(761\) | −7.01690e15 | −0.996621 | −0.498310 | − | 0.866999i | \(-0.666046\pi\) | ||||
−0.498310 | + | 0.866999i | \(0.666046\pi\) | |||||||
\(762\) | 2.06611e15 | 0.291341 | ||||||||
\(763\) | 1.83383e15 | 0.256729 | ||||||||
\(764\) | −6.88865e15 | −0.957460 | ||||||||
\(765\) | −2.65849e15 | −0.366857 | ||||||||
\(766\) | −1.18961e16 | −1.62984 | ||||||||
\(767\) | −1.37899e15 | −0.187581 | ||||||||
\(768\) | −8.66267e15 | −1.16994 | ||||||||
\(769\) | 9.89121e15 | 1.32634 | 0.663169 | − | 0.748469i | \(-0.269211\pi\) | ||||
0.663169 | + | 0.748469i | \(0.269211\pi\) | |||||||
\(770\) | 1.04945e16 | 1.39722 | ||||||||
\(771\) | −6.53840e14 | −0.0864316 | ||||||||
\(772\) | 2.55152e16 | 3.34891 | ||||||||
\(773\) | 1.66297e15 | 0.216719 | 0.108359 | − | 0.994112i | \(-0.465440\pi\) | ||||
0.108359 | + | 0.994112i | \(0.465440\pi\) | |||||||
\(774\) | 8.18607e15 | 1.05925 | ||||||||
\(775\) | 8.92289e13 | 0.0114643 | ||||||||
\(776\) | −3.49387e15 | −0.445725 | ||||||||
\(777\) | −4.59567e15 | −0.582148 | ||||||||
\(778\) | 9.91944e15 | 1.24767 | ||||||||
\(779\) | −1.34424e16 | −1.67888 | ||||||||
\(780\) | 1.34554e16 | 1.66869 | ||||||||
\(781\) | −1.81871e14 | −0.0223967 | ||||||||
\(782\) | 2.11822e15 | 0.259020 | ||||||||
\(783\) | −1.72233e15 | −0.209135 | ||||||||
\(784\) | −1.31914e15 | −0.159056 | ||||||||
\(785\) | 3.86688e14 | 0.0462996 | ||||||||
\(786\) | 1.03364e15 | 0.122898 | ||||||||
\(787\) | −6.06654e14 | −0.0716275 | −0.0358138 | − | 0.999358i | \(-0.511402\pi\) | ||||
−0.0358138 | + | 0.999358i | \(0.511402\pi\) | |||||||
\(788\) | 3.18580e16 | 3.73529 | ||||||||
\(789\) | 5.07165e15 | 0.590508 | ||||||||
\(790\) | −5.14818e15 | −0.595258 | ||||||||
\(791\) | 2.04434e14 | 0.0234737 | ||||||||
\(792\) | 4.62449e15 | 0.527322 | ||||||||
\(793\) | −1.30104e16 | −1.47329 | ||||||||
\(794\) | 1.29827e16 | 1.46000 | ||||||||
\(795\) | −8.26963e15 | −0.923564 | ||||||||
\(796\) | −2.18789e16 | −2.42663 | ||||||||
\(797\) | −1.30937e15 | −0.144225 | −0.0721126 | − | 0.997396i | \(-0.522974\pi\) | ||||
−0.0721126 | + | 0.997396i | \(0.522974\pi\) | |||||||
\(798\) | −1.11052e16 | −1.21481 | ||||||||
\(799\) | 4.70562e15 | 0.511223 | ||||||||
\(800\) | 2.89955e13 | 0.00312850 | ||||||||
\(801\) | −2.99908e15 | −0.321373 | ||||||||
\(802\) | 9.88960e15 | 1.05249 | ||||||||
\(803\) | 2.98822e15 | 0.315848 | ||||||||
\(804\) | −8.67407e15 | −0.910573 | ||||||||
\(805\) | 1.16691e15 | 0.121663 | ||||||||
\(806\) | 1.04392e16 | 1.08100 | ||||||||
\(807\) | −2.39782e15 | −0.246611 | ||||||||
\(808\) | 2.88037e16 | 2.94229 | ||||||||
\(809\) | −2.48188e15 | −0.251805 | −0.125902 | − | 0.992043i | \(-0.540183\pi\) | ||||
−0.125902 | + | 0.992043i | \(0.540183\pi\) | |||||||
\(810\) | −1.89460e15 | −0.190920 | ||||||||
\(811\) | −8.82367e15 | −0.883150 | −0.441575 | − | 0.897224i | \(-0.645580\pi\) | ||||
−0.441575 | + | 0.897224i | \(0.645580\pi\) | |||||||
\(812\) | −2.05568e16 | −2.04361 | ||||||||
\(813\) | −8.90953e15 | −0.879745 | ||||||||
\(814\) | −1.70189e16 | −1.66916 | ||||||||
\(815\) | 9.93318e15 | 0.967657 | ||||||||
\(816\) | −7.32620e15 | −0.708897 | ||||||||
\(817\) | −2.47973e16 | −2.38332 | ||||||||
\(818\) | 1.19054e16 | 1.13659 | ||||||||
\(819\) | 4.68449e15 | 0.444223 | ||||||||
\(820\) | −2.73721e16 | −2.57829 | ||||||||
\(821\) | −9.53702e15 | −0.892329 | −0.446165 | − | 0.894951i | \(-0.647210\pi\) | ||||
−0.446165 | + | 0.894951i | \(0.647210\pi\) | |||||||
\(822\) | 1.16190e16 | 1.07988 | ||||||||
\(823\) | −5.52313e15 | −0.509902 | −0.254951 | − | 0.966954i | \(-0.582059\pi\) | ||||
−0.254951 | + | 0.966954i | \(0.582059\pi\) | |||||||
\(824\) | −3.08536e16 | −2.82948 | ||||||||
\(825\) | 1.48280e14 | 0.0135078 | ||||||||
\(826\) | 2.31752e15 | 0.209717 | ||||||||
\(827\) | −1.99655e16 | −1.79473 | −0.897365 | − | 0.441290i | \(-0.854521\pi\) | ||||
−0.897365 | + | 0.441290i | \(0.854521\pi\) | |||||||
\(828\) | 1.01189e15 | 0.0903578 | ||||||||
\(829\) | 1.15384e16 | 1.02352 | 0.511761 | − | 0.859128i | \(-0.328993\pi\) | ||||
0.511761 | + | 0.859128i | \(0.328993\pi\) | |||||||
\(830\) | −1.40660e16 | −1.23949 | ||||||||
\(831\) | 1.14949e16 | 1.00623 | ||||||||
\(832\) | −1.48450e16 | −1.29093 | ||||||||
\(833\) | 1.86597e15 | 0.161197 | ||||||||
\(834\) | −1.07535e16 | −0.922865 | ||||||||
\(835\) | 7.73665e15 | 0.659595 | ||||||||
\(836\) | −2.75669e16 | −2.33482 | ||||||||
\(837\) | −9.85304e14 | −0.0829049 | ||||||||
\(838\) | −9.95938e14 | −0.0832512 | ||||||||
\(839\) | 1.15818e16 | 0.961805 | 0.480903 | − | 0.876774i | \(-0.340309\pi\) | ||||
0.480903 | + | 0.876774i | \(0.340309\pi\) | |||||||
\(840\) | −1.14911e16 | −0.948037 | ||||||||
\(841\) | 2.20726e15 | 0.180915 | ||||||||
\(842\) | 2.26433e16 | 1.84384 | ||||||||
\(843\) | 3.50972e15 | 0.283936 | ||||||||
\(844\) | −1.32296e16 | −1.06332 | ||||||||
\(845\) | 1.32944e16 | 1.06159 | ||||||||
\(846\) | 3.35352e15 | 0.266050 | ||||||||
\(847\) | −2.66488e15 | −0.210048 | ||||||||
\(848\) | −2.27893e16 | −1.78465 | ||||||||
\(849\) | −9.95943e15 | −0.774893 | ||||||||
\(850\) | −6.68827e14 | −0.0517023 | ||||||||
\(851\) | −1.89236e15 | −0.145342 | ||||||||
\(852\) | 3.91884e14 | 0.0299048 | ||||||||
\(853\) | 1.66923e15 | 0.126560 | 0.0632800 | − | 0.997996i | \(-0.479844\pi\) | ||||
0.0632800 | + | 0.997996i | \(0.479844\pi\) | |||||||
\(854\) | 2.18651e16 | 1.64715 | ||||||||
\(855\) | 5.73914e15 | 0.429569 | ||||||||
\(856\) | −2.85819e16 | −2.12562 | ||||||||
\(857\) | −1.29440e16 | −0.956478 | −0.478239 | − | 0.878230i | \(-0.658725\pi\) | ||||
−0.478239 | + | 0.878230i | \(0.658725\pi\) | |||||||
\(858\) | 1.73479e16 | 1.27370 | ||||||||
\(859\) | 2.32871e15 | 0.169884 | 0.0849422 | − | 0.996386i | \(-0.472929\pi\) | ||||
0.0849422 | + | 0.996386i | \(0.472929\pi\) | |||||||
\(860\) | −5.04935e16 | −3.66011 | ||||||||
\(861\) | −9.52960e15 | −0.686369 | ||||||||
\(862\) | −2.62950e16 | −1.88184 | ||||||||
\(863\) | 5.04983e15 | 0.359101 | 0.179551 | − | 0.983749i | \(-0.442536\pi\) | ||||
0.179551 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(864\) | −3.20181e14 | −0.0226240 | ||||||||
\(865\) | −2.53218e16 | −1.77790 | ||||||||
\(866\) | 1.74608e16 | 1.21819 | ||||||||
\(867\) | 2.03516e15 | 0.141089 | ||||||||
\(868\) | −1.17600e16 | −0.810122 | ||||||||
\(869\) | −4.44921e15 | −0.304561 | ||||||||
\(870\) | 1.58489e16 | 1.07806 | ||||||||
\(871\) | −1.65352e16 | −1.11766 | ||||||||
\(872\) | −7.43602e15 | −0.499459 | ||||||||
\(873\) | 1.23706e15 | 0.0825679 | ||||||||
\(874\) | −4.57280e15 | −0.303298 | ||||||||
\(875\) | −1.42135e16 | −0.936824 | ||||||||
\(876\) | −6.43883e15 | −0.421730 | ||||||||
\(877\) | 4.02349e15 | 0.261882 | 0.130941 | − | 0.991390i | \(-0.458200\pi\) | ||||
0.130941 | + | 0.991390i | \(0.458200\pi\) | |||||||
\(878\) | 8.02844e15 | 0.519292 | ||||||||
\(879\) | −6.54673e14 | −0.0420809 | ||||||||
\(880\) | −1.49461e16 | −0.954715 | ||||||||
\(881\) | −4.97677e15 | −0.315922 | −0.157961 | − | 0.987445i | \(-0.550492\pi\) | ||||
−0.157961 | + | 0.987445i | \(0.550492\pi\) | |||||||
\(882\) | 1.32981e15 | 0.0838903 | ||||||||
\(883\) | −7.93370e15 | −0.497384 | −0.248692 | − | 0.968583i | \(-0.580001\pi\) | ||||
−0.248692 | + | 0.968583i | \(0.580001\pi\) | |||||||
\(884\) | −5.24513e16 | −3.26790 | ||||||||
\(885\) | −1.19769e15 | −0.0741577 | ||||||||
\(886\) | 7.95583e15 | 0.489553 | ||||||||
\(887\) | 2.57465e16 | 1.57449 | 0.787243 | − | 0.616643i | \(-0.211508\pi\) | ||||
0.787243 | + | 0.616643i | \(0.211508\pi\) | |||||||
\(888\) | 1.86350e16 | 1.13255 | ||||||||
\(889\) | −4.43691e15 | −0.267991 | ||||||||
\(890\) | 2.75975e16 | 1.65663 | ||||||||
\(891\) | −1.63737e15 | −0.0976833 | ||||||||
\(892\) | 2.03528e16 | 1.20675 | ||||||||
\(893\) | −1.01585e16 | −0.598613 | ||||||||
\(894\) | −4.37839e15 | −0.256424 | ||||||||
\(895\) | 1.69941e14 | 0.00989169 | ||||||||
\(896\) | 2.68279e16 | 1.55200 | ||||||||
\(897\) | 1.92894e15 | 0.110907 | ||||||||
\(898\) | −1.93960e16 | −1.10839 | ||||||||
\(899\) | 8.24233e15 | 0.468135 | ||||||||
\(900\) | −3.19504e14 | −0.0180361 | ||||||||
\(901\) | 3.22364e16 | 1.80867 | ||||||||
\(902\) | −3.52906e16 | −1.96799 | ||||||||
\(903\) | −1.75793e16 | −0.974360 | ||||||||
\(904\) | −8.28960e14 | −0.0456675 | ||||||||
\(905\) | 2.16425e16 | 1.18506 | ||||||||
\(906\) | 3.00963e16 | 1.63798 | ||||||||
\(907\) | −2.73038e15 | −0.147701 | −0.0738503 | − | 0.997269i | \(-0.523529\pi\) | ||||
−0.0738503 | + | 0.997269i | \(0.523529\pi\) | |||||||
\(908\) | 5.85835e16 | 3.14995 | ||||||||
\(909\) | −1.01984e16 | −0.545042 | ||||||||
\(910\) | −4.31066e16 | −2.28990 | ||||||||
\(911\) | 3.03460e16 | 1.60232 | 0.801161 | − | 0.598449i | \(-0.204216\pi\) | ||||
0.801161 | + | 0.598449i | \(0.204216\pi\) | |||||||
\(912\) | 1.58158e16 | 0.830078 | ||||||||
\(913\) | −1.21563e16 | −0.634178 | ||||||||
\(914\) | −5.32465e16 | −2.76113 | ||||||||
\(915\) | −1.12998e16 | −0.582446 | ||||||||
\(916\) | 6.92665e16 | 3.54894 | ||||||||
\(917\) | −2.21971e15 | −0.113048 | ||||||||
\(918\) | 7.38548e15 | 0.373890 | ||||||||
\(919\) | 8.32053e15 | 0.418712 | 0.209356 | − | 0.977839i | \(-0.432863\pi\) | ||||
0.209356 | + | 0.977839i | \(0.432863\pi\) | |||||||
\(920\) | −4.73170e15 | −0.236692 | ||||||||
\(921\) | −9.53347e15 | −0.474049 | ||||||||
\(922\) | −1.67088e16 | −0.825893 | ||||||||
\(923\) | 7.47041e14 | 0.0367058 | ||||||||
\(924\) | −1.95428e16 | −0.954532 | ||||||||
\(925\) | 5.97515e14 | 0.0290114 | ||||||||
\(926\) | −2.70571e16 | −1.30593 | ||||||||
\(927\) | 1.09242e16 | 0.524144 | ||||||||
\(928\) | 2.67840e15 | 0.127750 | ||||||||
\(929\) | 9.21014e15 | 0.436697 | 0.218348 | − | 0.975871i | \(-0.429933\pi\) | ||||
0.218348 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(930\) | 9.06674e15 | 0.427361 | ||||||||
\(931\) | −4.02826e15 | −0.188753 | ||||||||
\(932\) | −4.31897e16 | −2.01184 | ||||||||
\(933\) | 2.10672e15 | 0.0975570 | ||||||||
\(934\) | 7.09702e15 | 0.326714 | ||||||||
\(935\) | 2.11419e16 | 0.967567 | ||||||||
\(936\) | −1.89952e16 | −0.864225 | ||||||||
\(937\) | 3.22835e15 | 0.146020 | 0.0730102 | − | 0.997331i | \(-0.476739\pi\) | ||||
0.0730102 | + | 0.997331i | \(0.476739\pi\) | |||||||
\(938\) | 2.77888e16 | 1.24955 | ||||||||
\(939\) | 2.83240e15 | 0.126618 | ||||||||
\(940\) | −2.06852e16 | −0.919300 | ||||||||
\(941\) | −1.25668e16 | −0.555240 | −0.277620 | − | 0.960691i | \(-0.589546\pi\) | ||||
−0.277620 | + | 0.960691i | \(0.589546\pi\) | |||||||
\(942\) | −1.07425e15 | −0.0471872 | ||||||||
\(943\) | −3.92402e15 | −0.171363 | ||||||||
\(944\) | −3.30056e15 | −0.143299 | ||||||||
\(945\) | 4.06860e15 | 0.175618 | ||||||||
\(946\) | −6.51007e16 | −2.79373 | ||||||||
\(947\) | 2.63934e16 | 1.12609 | 0.563043 | − | 0.826428i | \(-0.309631\pi\) | ||||
0.563043 | + | 0.826428i | \(0.309631\pi\) | |||||||
\(948\) | 9.58687e15 | 0.406659 | ||||||||
\(949\) | −1.22742e16 | −0.517641 | ||||||||
\(950\) | 1.44386e15 | 0.0605405 | ||||||||
\(951\) | 1.61993e16 | 0.675310 | ||||||||
\(952\) | 4.47942e16 | 1.85660 | ||||||||
\(953\) | −1.33878e16 | −0.551696 | −0.275848 | − | 0.961201i | \(-0.588959\pi\) | ||||
−0.275848 | + | 0.961201i | \(0.588959\pi\) | |||||||
\(954\) | 2.29736e16 | 0.941269 | ||||||||
\(955\) | −1.14052e16 | −0.464605 | ||||||||
\(956\) | 3.60343e16 | 1.45948 | ||||||||
\(957\) | 1.36971e16 | 0.551584 | ||||||||
\(958\) | −4.15045e16 | −1.66182 | ||||||||
\(959\) | −2.49515e16 | −0.993330 | ||||||||
\(960\) | −1.28932e16 | −0.510352 | ||||||||
\(961\) | −2.06932e16 | −0.814423 | ||||||||
\(962\) | 6.99056e16 | 2.73558 | ||||||||
\(963\) | 1.01199e16 | 0.393758 | ||||||||
\(964\) | 6.71877e16 | 2.59936 | ||||||||
\(965\) | 4.22441e16 | 1.62505 | ||||||||
\(966\) | −3.24175e15 | −0.123995 | ||||||||
\(967\) | 3.19970e15 | 0.121693 | 0.0608463 | − | 0.998147i | \(-0.480620\pi\) | ||||
0.0608463 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(968\) | 1.08058e16 | 0.408643 | ||||||||
\(969\) | −2.23721e16 | −0.841252 | ||||||||
\(970\) | −1.13834e16 | −0.425624 | ||||||||
\(971\) | −2.83042e16 | −1.05231 | −0.526157 | − | 0.850387i | \(-0.676368\pi\) | ||||
−0.526157 | + | 0.850387i | \(0.676368\pi\) | |||||||
\(972\) | 3.52810e15 | 0.130430 | ||||||||
\(973\) | 2.30929e16 | 0.848901 | ||||||||
\(974\) | 5.54978e16 | 2.02862 | ||||||||
\(975\) | −6.09064e14 | −0.0221379 | ||||||||
\(976\) | −3.11398e16 | −1.12549 | ||||||||
\(977\) | −1.41657e16 | −0.509118 | −0.254559 | − | 0.967057i | \(-0.581930\pi\) | ||||
−0.254559 | + | 0.967057i | \(0.581930\pi\) | |||||||
\(978\) | −2.75951e16 | −0.986207 | ||||||||
\(979\) | 2.38506e16 | 0.847605 | ||||||||
\(980\) | −8.20255e15 | −0.289871 | ||||||||
\(981\) | 2.63284e15 | 0.0925219 | ||||||||
\(982\) | −3.42027e16 | −1.19522 | ||||||||
\(983\) | −5.37875e16 | −1.86912 | −0.934559 | − | 0.355808i | \(-0.884206\pi\) | ||||
−0.934559 | + | 0.355808i | \(0.884206\pi\) | |||||||
\(984\) | 3.86417e16 | 1.33531 | ||||||||
\(985\) | 5.27457e16 | 1.81254 | ||||||||
\(986\) | −6.17815e16 | −2.11123 | ||||||||
\(987\) | −7.20157e15 | −0.244727 | ||||||||
\(988\) | 1.13232e17 | 3.82653 | ||||||||
\(989\) | −7.23866e15 | −0.243264 | ||||||||
\(990\) | 1.50671e16 | 0.503541 | ||||||||
\(991\) | 5.04112e16 | 1.67541 | 0.837707 | − | 0.546120i | \(-0.183896\pi\) | ||||
0.837707 | + | 0.546120i | \(0.183896\pi\) | |||||||
\(992\) | 1.53224e15 | 0.0506423 | ||||||||
\(993\) | 1.00766e16 | 0.331204 | ||||||||
\(994\) | −1.25547e15 | −0.0410374 | ||||||||
\(995\) | −3.62238e16 | −1.17752 | ||||||||
\(996\) | 2.61935e16 | 0.846775 | ||||||||
\(997\) | −3.33872e16 | −1.07339 | −0.536694 | − | 0.843777i | \(-0.680327\pi\) | ||||
−0.536694 | + | 0.843777i | \(0.680327\pi\) | |||||||
\(998\) | −2.52620e15 | −0.0807701 | ||||||||
\(999\) | −6.59802e15 | −0.209799 |
(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 | 177.12.a.b.1.3 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.3 | ✓ | 27 | 1.1 | even | 1 | trivial |