Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,22,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), 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: | \(69.8693360718\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.22.b.a.24.1 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 288.000i | 0.198874i | 0.995044 | + | 0.0994369i | \(0.0317041\pi\) | ||||
−0.995044 | + | 0.0994369i | \(0.968296\pi\) | |||||||
\(3\) | − 128844.i | − 1.25977i | −0.776689 | − | 0.629885i | \(-0.783102\pi\) | ||||
0.776689 | − | 0.629885i | \(-0.216898\pi\) | |||||||
\(4\) | 2.01421e6 | 0.960449 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.71071e7 | 0.250535 | ||||||||
\(7\) | 7.68079e8i | 1.02772i | 0.857873 | + | 0.513862i | \(0.171786\pi\) | ||||
−0.857873 | + | 0.513862i | \(0.828214\pi\) | |||||||
\(8\) | 1.18407e9i | 0.389882i | ||||||||
\(9\) | −6.14042e9 | −0.587019 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.47249e10 | −1.10114 | −0.550568 | − | 0.834790i | \(-0.685589\pi\) | ||||
−0.550568 | + | 0.834790i | \(0.685589\pi\) | |||||||
\(12\) | − 2.59519e11i | − 1.20994i | ||||||||
\(13\) | − 8.06218e10i | − 0.162199i | −0.996706 | − | 0.0810993i | \(-0.974157\pi\) | ||||
0.996706 | − | 0.0810993i | \(-0.0258431\pi\) | |||||||
\(14\) | −2.21207e11 | −0.204387 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.88309e12 | 0.882912 | ||||||||
\(17\) | − 3.05228e12i | − 0.367207i | −0.983000 | − | 0.183604i | \(-0.941224\pi\) | ||||
0.983000 | − | 0.183604i | \(-0.0587763\pi\) | |||||||
\(18\) | − 1.76844e12i | − 0.116743i | ||||||||
\(19\) | 7.92079e12 | 0.296385 | 0.148192 | − | 0.988959i | \(-0.452655\pi\) | ||||
0.148192 | + | 0.988959i | \(0.452655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.89623e13 | 1.29469 | ||||||||
\(22\) | − 2.72808e13i | − 0.218987i | ||||||||
\(23\) | − 7.38454e13i | − 0.371690i | −0.982579 | − | 0.185845i | \(-0.940498\pi\) | ||||
0.982579 | − | 0.185845i | \(-0.0595023\pi\) | |||||||
\(24\) | 1.52561e14 | 0.491161 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.32191e13 | 0.0322571 | ||||||||
\(27\) | − 5.56597e14i | − 0.520261i | ||||||||
\(28\) | 1.54707e15i | 0.987076i | ||||||||
\(29\) | 4.25303e15 | 1.87724 | 0.938620 | − | 0.344954i | \(-0.112105\pi\) | ||||
0.938620 | + | 0.344954i | \(0.112105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.90054e15 | 0.416466 | 0.208233 | − | 0.978079i | \(-0.433229\pi\) | ||||
0.208233 | + | 0.978079i | \(0.433229\pi\) | |||||||
\(32\) | 3.60151e15i | 0.565470i | ||||||||
\(33\) | 1.22047e16i | 1.38718i | ||||||||
\(34\) | 8.79057e14 | 0.0730279 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.23681e16 | −0.563802 | ||||||||
\(37\) | − 2.21914e16i | − 0.758695i | −0.925254 | − | 0.379347i | \(-0.876149\pi\) | ||||
0.925254 | − | 0.379347i | \(-0.123851\pi\) | |||||||
\(38\) | 2.28119e15i | 0.0589431i | ||||||||
\(39\) | −1.03876e16 | −0.204333 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.06228e16 | −0.239948 | −0.119974 | − | 0.992777i | \(-0.538281\pi\) | ||||
−0.119974 | + | 0.992777i | \(0.538281\pi\) | |||||||
\(42\) | 2.85012e16i | 0.257481i | ||||||||
\(43\) | − 1.93606e17i | − 1.36615i | −0.730346 | − | 0.683077i | \(-0.760641\pi\) | ||||
0.730346 | − | 0.683077i | \(-0.239359\pi\) | |||||||
\(44\) | −1.90796e17 | −1.05759 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.12675e16 | 0.0739195 | ||||||||
\(47\) | − 1.46961e17i | − 0.407543i | −0.979019 | − | 0.203771i | \(-0.934680\pi\) | ||||
0.979019 | − | 0.203771i | \(-0.0653199\pi\) | |||||||
\(48\) | − 5.00313e17i | − 1.11227i | ||||||||
\(49\) | −3.13992e16 | −0.0562160 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.93268e17 | −0.462596 | ||||||||
\(52\) | − 1.62389e17i | − 0.155784i | ||||||||
\(53\) | 2.03827e18i | 1.60090i | 0.599399 | + | 0.800450i | \(0.295406\pi\) | ||||
−0.599399 | + | 0.800450i | \(0.704594\pi\) | |||||||
\(54\) | 1.60300e17 | 0.103466 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.09460e17 | −0.400691 | ||||||||
\(57\) | − 1.02055e18i | − 0.373376i | ||||||||
\(58\) | 1.22487e18i | 0.373334i | ||||||||
\(59\) | 5.97588e18 | 1.52214 | 0.761072 | − | 0.648667i | \(-0.224673\pi\) | ||||
0.761072 | + | 0.648667i | \(0.224673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.19062e18 | 1.11114 | 0.555572 | − | 0.831468i | \(-0.312499\pi\) | ||||
0.555572 | + | 0.831468i | \(0.312499\pi\) | |||||||
\(62\) | 5.47356e17i | 0.0828242i | ||||||||
\(63\) | − 4.71633e18i | − 0.603293i | ||||||||
\(64\) | 7.10619e18 | 0.770455 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.51496e18 | −0.275873 | ||||||||
\(67\) | − 1.69613e19i | − 1.13677i | −0.822761 | − | 0.568387i | \(-0.807568\pi\) | ||||
0.822761 | − | 0.568387i | \(-0.192432\pi\) | |||||||
\(68\) | − 6.14793e18i | − 0.352684i | ||||||||
\(69\) | −9.51454e18 | −0.468244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.63276e18 | −0.205357 | −0.102678 | − | 0.994715i | \(-0.532741\pi\) | ||||
−0.102678 | + | 0.994715i | \(0.532741\pi\) | |||||||
\(72\) | − 7.27070e18i | − 0.228868i | ||||||||
\(73\) | − 4.32848e19i | − 1.17881i | −0.807837 | − | 0.589407i | \(-0.799362\pi\) | ||||
0.807837 | − | 0.589407i | \(-0.200638\pi\) | |||||||
\(74\) | 6.39113e18 | 0.150885 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59541e19 | 0.284662 | ||||||||
\(77\) | − 7.27562e19i | − 1.13166i | ||||||||
\(78\) | − 2.99164e18i | − 0.0406365i | ||||||||
\(79\) | 5.12649e19 | 0.609166 | 0.304583 | − | 0.952486i | \(-0.401483\pi\) | ||||
0.304583 | + | 0.952486i | \(0.401483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.35945e20 | −1.24243 | ||||||||
\(82\) | − 5.93937e18i | − 0.0477194i | ||||||||
\(83\) | 4.89119e19i | 0.346014i | 0.984921 | + | 0.173007i | \(0.0553484\pi\) | ||||
−0.984921 | + | 0.173007i | \(0.944652\pi\) | |||||||
\(84\) | 1.99331e20 | 1.24349 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.57585e19 | 0.271692 | ||||||||
\(87\) | − 5.47978e20i | − 2.36489i | ||||||||
\(88\) | − 1.12161e20i | − 0.429313i | ||||||||
\(89\) | 5.04303e20 | 1.71434 | 0.857170 | − | 0.515034i | \(-0.172221\pi\) | ||||
0.857170 | + | 0.515034i | \(0.172221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.19239e19 | 0.166695 | ||||||||
\(92\) | − 1.48740e20i | − 0.356990i | ||||||||
\(93\) | − 2.44873e20i | − 0.524651i | ||||||||
\(94\) | 4.23246e19 | 0.0810496 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.64033e20 | 0.712362 | ||||||||
\(97\) | − 8.08275e20i | − 1.11290i | −0.830881 | − | 0.556450i | \(-0.812163\pi\) | ||||
0.830881 | − | 0.556450i | \(-0.187837\pi\) | |||||||
\(98\) | − 9.04297e18i | − 0.0111799i | ||||||||
\(99\) | 5.81651e20 | 0.646388 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00202e21 | −0.902612 | −0.451306 | − | 0.892369i | \(-0.649042\pi\) | ||||
−0.451306 | + | 0.892369i | \(0.649042\pi\) | |||||||
\(102\) | − 1.13261e20i | − 0.0919983i | ||||||||
\(103\) | − 5.89747e20i | − 0.432389i | −0.976350 | − | 0.216195i | \(-0.930635\pi\) | ||||
0.976350 | − | 0.216195i | \(-0.0693646\pi\) | |||||||
\(104\) | 9.54620e19 | 0.0632383 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.87021e20 | −0.318377 | ||||||||
\(107\) | − 1.12210e21i | − 0.551445i | −0.961237 | − | 0.275723i | \(-0.911083\pi\) | ||||
0.961237 | − | 0.275723i | \(-0.0889171\pi\) | |||||||
\(108\) | − 1.12110e21i | − 0.499684i | ||||||||
\(109\) | −1.72394e21 | −0.697499 | −0.348750 | − | 0.937216i | \(-0.613394\pi\) | ||||
−0.348750 | + | 0.937216i | \(0.613394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.85923e21 | −0.955781 | ||||||||
\(112\) | 2.98252e21i | 0.907389i | ||||||||
\(113\) | 4.95810e20i | 0.137402i | 0.997637 | + | 0.0687008i | \(0.0218854\pi\) | ||||
−0.997637 | + | 0.0687008i | \(0.978115\pi\) | |||||||
\(114\) | 2.93917e20 | 0.0742547 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.56649e21 | 1.80299 | ||||||||
\(117\) | 4.95052e20i | 0.0952136i | ||||||||
\(118\) | 1.72105e21i | 0.302715i | ||||||||
\(119\) | 2.34439e21 | 0.377387 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.57256e21 | 0.212501 | ||||||||
\(122\) | 1.78290e21i | 0.220978i | ||||||||
\(123\) | 2.65712e21i | 0.302279i | ||||||||
\(124\) | 3.82809e21 | 0.399994 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.35830e21 | 0.119979 | ||||||||
\(127\) | − 1.63609e21i | − 0.133005i | −0.997786 | − | 0.0665027i | \(-0.978816\pi\) | ||||
0.997786 | − | 0.0665027i | \(-0.0211841\pi\) | |||||||
\(128\) | 9.59949e21i | 0.718693i | ||||||||
\(129\) | −2.49450e22 | −1.72104 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.38650e22 | −0.813898 | −0.406949 | − | 0.913451i | \(-0.633407\pi\) | ||||
−0.406949 | + | 0.913451i | \(0.633407\pi\) | |||||||
\(132\) | 2.45829e22i | 1.33231i | ||||||||
\(133\) | 6.08379e21i | 0.304601i | ||||||||
\(134\) | 4.88486e21 | 0.226075 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.61412e21 | 0.143167 | ||||||||
\(137\) | 4.00789e22i | 1.47011i | 0.678007 | + | 0.735055i | \(0.262844\pi\) | ||||
−0.678007 | + | 0.735055i | \(0.737156\pi\) | |||||||
\(138\) | − 2.74019e21i | − 0.0931215i | ||||||||
\(139\) | −4.47585e22 | −1.41000 | −0.705001 | − | 0.709206i | \(-0.749054\pi\) | ||||
−0.705001 | + | 0.709206i | \(0.749054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.89350e22 | −0.513410 | ||||||||
\(142\) | − 1.62223e21i | − 0.0408400i | ||||||||
\(143\) | 7.63689e21i | 0.178603i | ||||||||
\(144\) | −2.38438e22 | −0.518286 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.24660e22 | 0.234435 | ||||||||
\(147\) | 4.04560e21i | 0.0708191i | ||||||||
\(148\) | − 4.46982e22i | − 0.728688i | ||||||||
\(149\) | −4.93289e22 | −0.749283 | −0.374641 | − | 0.927170i | \(-0.622234\pi\) | ||||
−0.374641 | + | 0.927170i | \(0.622234\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70415e22 | 0.753239 | 0.376620 | − | 0.926368i | \(-0.377086\pi\) | ||||
0.376620 | + | 0.926368i | \(0.377086\pi\) | |||||||
\(152\) | 9.37878e21i | 0.115555i | ||||||||
\(153\) | 1.87423e22i | 0.215557i | ||||||||
\(154\) | 2.09538e22 | 0.225058 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.09229e22 | −0.196251 | ||||||||
\(157\) | − 6.35623e22i | − 0.557511i | −0.960362 | − | 0.278756i | \(-0.910078\pi\) | ||||
0.960362 | − | 0.278756i | \(-0.0899219\pi\) | |||||||
\(158\) | 1.47643e22i | 0.121147i | ||||||||
\(159\) | 2.62618e23 | 2.01677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.67191e22 | 0.381995 | ||||||||
\(162\) | − 3.91522e22i | − 0.247086i | ||||||||
\(163\) | 8.68484e22i | 0.513797i | 0.966438 | + | 0.256899i | \(0.0827006\pi\) | ||||
−0.966438 | + | 0.256899i | \(0.917299\pi\) | |||||||
\(164\) | −4.15386e22 | −0.230458 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.40866e22 | −0.0688132 | ||||||||
\(167\) | 1.89411e23i | 0.868726i | 0.900738 | + | 0.434363i | \(0.143026\pi\) | ||||
−0.900738 | + | 0.434363i | \(0.856974\pi\) | |||||||
\(168\) | 1.17179e23i | 0.504778i | ||||||||
\(169\) | 2.40565e23 | 0.973692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.86370e22 | −0.173983 | ||||||||
\(172\) | − 3.89962e23i | − 1.31212i | ||||||||
\(173\) | − 4.18508e23i | − 1.32501i | −0.749057 | − | 0.662506i | \(-0.769493\pi\) | ||||
0.749057 | − | 0.662506i | \(-0.230507\pi\) | |||||||
\(174\) | 1.57818e23 | 0.470314 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.67825e23 | −0.972206 | ||||||||
\(177\) | − 7.69957e23i | − 1.91755i | ||||||||
\(178\) | 1.45239e23i | 0.340937i | ||||||||
\(179\) | −4.76752e23 | −1.05520 | −0.527601 | − | 0.849493i | \(-0.676908\pi\) | ||||
−0.527601 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.88627e22 | −0.0568476 | −0.0284238 | − | 0.999596i | \(-0.509049\pi\) | ||||
−0.0284238 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(182\) | 1.78341e22i | 0.0331513i | ||||||||
\(183\) | − 7.97624e23i | − 1.39979i | ||||||||
\(184\) | 8.74383e22 | 0.144915 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.05235e22 | 0.104339 | ||||||||
\(187\) | 2.89127e23i | 0.404345i | ||||||||
\(188\) | − 2.96009e23i | − 0.391424i | ||||||||
\(189\) | 4.27510e23 | 0.534685 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.86378e23 | 0.992587 | 0.496293 | − | 0.868155i | \(-0.334694\pi\) | ||||
0.496293 | + | 0.868155i | \(0.334694\pi\) | |||||||
\(192\) | − 9.15590e23i | − 0.970595i | ||||||||
\(193\) | 8.63509e22i | 0.0866792i | 0.999060 | + | 0.0433396i | \(0.0137997\pi\) | ||||
−0.999060 | + | 0.0433396i | \(0.986200\pi\) | |||||||
\(194\) | 2.32783e23 | 0.221327 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.32445e22 | −0.0539926 | ||||||||
\(197\) | 6.99008e23i | 0.565701i | 0.959164 | + | 0.282850i | \(0.0912800\pi\) | ||||
−0.959164 | + | 0.282850i | \(0.908720\pi\) | |||||||
\(198\) | 1.67516e23i | 0.128550i | ||||||||
\(199\) | 1.24542e24 | 0.906483 | 0.453242 | − | 0.891388i | \(-0.350268\pi\) | ||||
0.453242 | + | 0.891388i | \(0.350268\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.18536e24 | −1.43207 | ||||||||
\(202\) | − 2.88581e23i | − 0.179506i | ||||||||
\(203\) | 3.26666e24i | 1.92928i | ||||||||
\(204\) | −7.92124e23 | −0.444300 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.69847e23 | 0.0859909 | ||||||||
\(207\) | 4.53442e23i | 0.218189i | ||||||||
\(208\) | − 3.13061e23i | − 0.143207i | ||||||||
\(209\) | −7.50296e23 | −0.326360 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.50841e24 | 1.38085 | 0.690423 | − | 0.723406i | \(-0.257425\pi\) | ||||
0.690423 | + | 0.723406i | \(0.257425\pi\) | |||||||
\(212\) | 4.10549e24i | 1.53758i | ||||||||
\(213\) | 7.25747e23i | 0.258702i | ||||||||
\(214\) | 3.23165e23 | 0.109668 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.59051e23 | 0.202840 | ||||||||
\(217\) | 1.45977e24i | 0.428012i | ||||||||
\(218\) | − 4.96495e23i | − 0.138714i | ||||||||
\(219\) | −5.57698e24 | −1.48503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.46081e23 | −0.0595605 | ||||||||
\(222\) | − 8.23459e23i | − 0.190080i | ||||||||
\(223\) | − 4.72350e24i | − 1.04007i | −0.854145 | − | 0.520035i | \(-0.825919\pi\) | ||||
0.854145 | − | 0.520035i | \(-0.174081\pi\) | |||||||
\(224\) | −2.76624e24 | −0.581147 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.42793e23 | −0.0273256 | ||||||||
\(227\) | 5.44317e24i | 0.994444i | 0.867623 | + | 0.497222i | \(0.165647\pi\) | ||||
−0.867623 | + | 0.497222i | \(0.834353\pi\) | |||||||
\(228\) | − 2.05559e24i | − 0.358609i | ||||||||
\(229\) | −6.90677e24 | −1.15081 | −0.575403 | − | 0.817870i | \(-0.695155\pi\) | ||||
−0.575403 | + | 0.817870i | \(0.695155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.37420e24 | −1.42564 | ||||||||
\(232\) | 5.03589e24i | 0.731902i | ||||||||
\(233\) | 4.53650e24i | 0.630208i | 0.949057 | + | 0.315104i | \(0.102039\pi\) | ||||
−0.949057 | + | 0.315104i | \(0.897961\pi\) | |||||||
\(234\) | −1.42575e23 | −0.0189355 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.20367e25 | 1.46194 | ||||||||
\(237\) | − 6.60518e24i | − 0.767409i | ||||||||
\(238\) | 6.75185e23i | 0.0750525i | ||||||||
\(239\) | 2.73493e24 | 0.290916 | 0.145458 | − | 0.989364i | \(-0.453534\pi\) | ||||
0.145458 | + | 0.989364i | \(0.453534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.08907e24 | −0.788351 | −0.394175 | − | 0.919035i | \(-0.628970\pi\) | ||||
−0.394175 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(242\) | 4.52898e23i | 0.0422609i | ||||||||
\(243\) | 1.16935e25i | 1.04491i | ||||||||
\(244\) | 1.24692e25 | 1.06720 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.65252e23 | −0.0601154 | ||||||||
\(247\) | − 6.38588e23i | − 0.0480732i | ||||||||
\(248\) | 2.25038e24i | 0.162373i | ||||||||
\(249\) | 6.30200e24 | 0.435898 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.63927e24 | 0.422227 | 0.211113 | − | 0.977462i | \(-0.432291\pi\) | ||||
0.211113 | + | 0.977462i | \(0.432291\pi\) | |||||||
\(252\) | − 9.49967e24i | − 0.579432i | ||||||||
\(253\) | 6.99500e24i | 0.409282i | ||||||||
\(254\) | 4.71195e23 | 0.0264513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.21381e25 | 0.627526 | ||||||||
\(257\) | − 1.57278e24i | − 0.0780497i | −0.999238 | − | 0.0390249i | \(-0.987575\pi\) | ||||
0.999238 | − | 0.0390249i | \(-0.0124252\pi\) | |||||||
\(258\) | − 7.18415e24i | − 0.342270i | ||||||||
\(259\) | 1.70448e25 | 0.779729 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.61154e25 | −1.10197 | ||||||||
\(262\) | − 3.99311e24i | − 0.161863i | ||||||||
\(263\) | − 3.40077e25i | − 1.32447i | −0.749296 | − | 0.662235i | \(-0.769608\pi\) | ||||
0.749296 | − | 0.662235i | \(-0.230392\pi\) | |||||||
\(264\) | −1.44513e25 | −0.540836 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.75213e24 | −0.0605772 | ||||||||
\(267\) | − 6.49765e25i | − 2.15967i | ||||||||
\(268\) | − 3.41636e25i | − 1.09181i | ||||||||
\(269\) | 3.57975e25 | 1.10015 | 0.550077 | − | 0.835114i | \(-0.314598\pi\) | ||||
0.550077 | + | 0.835114i | \(0.314598\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.46104e25 | 0.699746 | 0.349873 | − | 0.936797i | \(-0.386225\pi\) | ||||
0.349873 | + | 0.936797i | \(0.386225\pi\) | |||||||
\(272\) | − 1.18523e25i | − 0.324212i | ||||||||
\(273\) | − 7.97852e24i | − 0.209998i | ||||||||
\(274\) | −1.15427e25 | −0.292366 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.91643e25 | −0.449725 | ||||||||
\(277\) | 6.11679e25i | 1.38193i | 0.722888 | + | 0.690965i | \(0.242814\pi\) | ||||
−0.722888 | + | 0.690965i | \(0.757186\pi\) | |||||||
\(278\) | − 1.28904e25i | − 0.280413i | ||||||||
\(279\) | −1.16701e25 | −0.244473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73710e25 | 0.337605 | 0.168802 | − | 0.985650i | \(-0.446010\pi\) | ||||
0.168802 | + | 0.985650i | \(0.446010\pi\) | |||||||
\(282\) | − 5.45327e24i | − 0.102104i | ||||||||
\(283\) | 7.57237e25i | 1.36607i | 0.730383 | + | 0.683037i | \(0.239341\pi\) | ||||
−0.730383 | + | 0.683037i | \(0.760659\pi\) | |||||||
\(284\) | −1.13455e25 | −0.197235 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.19943e24 | −0.0355194 | ||||||||
\(287\) | − 1.58399e25i | − 0.246600i | ||||||||
\(288\) | − 2.21148e25i | − 0.331941i | ||||||||
\(289\) | 5.97755e25 | 0.865159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.04141e26 | −1.40200 | ||||||||
\(292\) | − 8.71845e25i | − 1.13219i | ||||||||
\(293\) | 4.88684e25i | 0.612235i | 0.951994 | + | 0.306118i | \(0.0990301\pi\) | ||||
−0.951994 | + | 0.306118i | \(0.900970\pi\) | |||||||
\(294\) | −1.16513e24 | −0.0140841 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.62762e25 | 0.295801 | ||||||||
\(297\) | 5.27236e25i | 0.572878i | ||||||||
\(298\) | − 1.42067e25i | − 0.149013i | ||||||||
\(299\) | −5.95355e24 | −0.0602877 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.48705e26 | 1.40403 | ||||||||
\(302\) | 1.64279e25i | 0.149800i | ||||||||
\(303\) | 1.29104e26i | 1.13708i | ||||||||
\(304\) | 3.07571e25 | 0.261681 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.39778e24 | −0.0428687 | ||||||||
\(307\) | 2.17987e26i | 1.67293i | 0.548019 | + | 0.836466i | \(0.315382\pi\) | ||||
−0.548019 | + | 0.836466i | \(0.684618\pi\) | |||||||
\(308\) | − 1.46546e26i | − 1.08691i | ||||||||
\(309\) | −7.59854e25 | −0.544711 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.04644e25 | −0.271075 | −0.135538 | − | 0.990772i | \(-0.543276\pi\) | ||||
−0.135538 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(312\) | − 1.22997e25i | − 0.0796657i | ||||||||
\(313\) | − 8.74174e24i | − 0.0547498i | −0.999625 | − | 0.0273749i | \(-0.991285\pi\) | ||||
0.999625 | − | 0.0273749i | \(-0.00871478\pi\) | |||||||
\(314\) | 1.83060e25 | 0.110874 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.03258e26 | 0.585073 | ||||||||
\(317\) | 3.19758e25i | 0.175267i | 0.996153 | + | 0.0876334i | \(0.0279304\pi\) | ||||
−0.996153 | + | 0.0876334i | \(0.972070\pi\) | |||||||
\(318\) | 7.56341e25i | 0.401082i | ||||||||
\(319\) | −4.02868e26 | −2.06710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.44576e26 | −0.694694 | ||||||||
\(322\) | 1.63351e25i | 0.0759688i | ||||||||
\(323\) | − 2.41765e25i | − 0.108835i | ||||||||
\(324\) | −2.73822e26 | −1.19329 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.50123e25 | −0.102181 | ||||||||
\(327\) | 2.22119e26i | 0.878688i | ||||||||
\(328\) | − 2.44189e25i | − 0.0935514i | ||||||||
\(329\) | 1.12877e26 | 0.418841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.52215e26 | −0.878166 | −0.439083 | − | 0.898446i | \(-0.644697\pi\) | ||||
−0.439083 | + | 0.898446i | \(0.644697\pi\) | |||||||
\(332\) | 9.85186e25i | 0.332329i | ||||||||
\(333\) | 1.36265e26i | 0.445368i | ||||||||
\(334\) | −5.45504e25 | −0.172767 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.84279e26 | 1.14310 | ||||||||
\(337\) | 1.53127e26i | 0.441507i | 0.975330 | + | 0.220753i | \(0.0708516\pi\) | ||||
−0.975330 | + | 0.220753i | \(0.929148\pi\) | |||||||
\(338\) | 6.92826e25i | 0.193642i | ||||||||
\(339\) | 6.38821e25 | 0.173094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.80029e26 | −0.458586 | ||||||||
\(342\) | − 1.40075e25i | − 0.0346007i | ||||||||
\(343\) | 4.04890e26i | 0.969949i | ||||||||
\(344\) | 2.29243e26 | 0.532639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.20530e26 | 0.263510 | ||||||||
\(347\) | − 3.23436e26i | − 0.686008i | −0.939334 | − | 0.343004i | \(-0.888556\pi\) | ||||
0.939334 | − | 0.343004i | \(-0.111444\pi\) | |||||||
\(348\) | − 1.10374e27i | − 2.27136i | ||||||||
\(349\) | 6.77854e26 | 1.35353 | 0.676767 | − | 0.736197i | \(-0.263380\pi\) | ||||
0.676767 | + | 0.736197i | \(0.263380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.48739e25 | −0.0843857 | ||||||||
\(352\) | − 3.41153e26i | − 0.622660i | ||||||||
\(353\) | 6.84291e26i | 1.21229i | 0.795354 | + | 0.606145i | \(0.207285\pi\) | ||||
−0.795354 | + | 0.606145i | \(0.792715\pi\) | |||||||
\(354\) | 2.21748e26 | 0.381351 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.01577e27 | 1.64654 | ||||||||
\(357\) | − 3.02061e26i | − 0.475421i | ||||||||
\(358\) | − 1.37304e26i | − 0.209852i | ||||||||
\(359\) | 6.85500e25 | 0.101746 | 0.0508728 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508728 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.51471e26 | −0.912156 | ||||||||
\(362\) | − 8.31247e24i | − 0.0113055i | ||||||||
\(363\) | − 2.02615e26i | − 0.267703i | ||||||||
\(364\) | 1.24728e26 | 0.160102 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.29716e26 | 0.278381 | ||||||||
\(367\) | − 1.13575e27i | − 1.33749i | −0.743492 | − | 0.668745i | \(-0.766832\pi\) | ||||
0.743492 | − | 0.668745i | \(-0.233168\pi\) | |||||||
\(368\) | − 2.86748e26i | − 0.328170i | ||||||||
\(369\) | 1.26633e26 | 0.140854 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.56555e27 | −1.64528 | ||||||||
\(372\) | − 4.93226e26i | − 0.503901i | ||||||||
\(373\) | 3.82975e26i | 0.380389i | 0.981746 | + | 0.190195i | \(0.0609119\pi\) | ||||
−0.981746 | + | 0.190195i | \(0.939088\pi\) | |||||||
\(374\) | −8.32687e25 | −0.0804136 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.74012e26 | 0.158894 | ||||||||
\(377\) | − 3.42887e26i | − 0.304486i | ||||||||
\(378\) | 1.23123e26i | 0.106335i | ||||||||
\(379\) | −7.14767e25 | −0.0600417 | −0.0300208 | − | 0.999549i | \(-0.509557\pi\) | ||||
−0.0300208 | + | 0.999549i | \(0.509557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.10801e26 | −0.167556 | ||||||||
\(382\) | 2.55277e26i | 0.197400i | ||||||||
\(383\) | − 1.38425e27i | − 1.04142i | −0.853732 | − | 0.520712i | \(-0.825666\pi\) | ||||
0.853732 | − | 0.520712i | \(-0.174334\pi\) | |||||||
\(384\) | 1.23684e27 | 0.905388 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.48690e25 | −0.0172382 | ||||||||
\(387\) | 1.18882e27i | 0.801958i | ||||||||
\(388\) | − 1.62803e27i | − 1.06888i | ||||||||
\(389\) | −1.63213e27 | −1.04300 | −0.521500 | − | 0.853251i | \(-0.674627\pi\) | ||||
−0.521500 | + | 0.853251i | \(0.674627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.25397e26 | −0.136487 | ||||||||
\(392\) | − 3.71789e25i | − 0.0219176i | ||||||||
\(393\) | 1.78642e27i | 1.02532i | ||||||||
\(394\) | −2.01314e26 | −0.112503 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.17157e27 | 0.620823 | ||||||||
\(397\) | − 1.21029e27i | − 0.624581i | −0.949987 | − | 0.312291i | \(-0.898904\pi\) | ||||
0.949987 | − | 0.312291i | \(-0.101096\pi\) | |||||||
\(398\) | 3.58682e26i | 0.180276i | ||||||||
\(399\) | 7.83860e26 | 0.383728 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.51358e26 | −0.302555 | −0.151277 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151277 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(402\) | − 6.29385e26i | − 0.284802i | ||||||||
\(403\) | − 1.53225e26i | − 0.0675502i | ||||||||
\(404\) | −2.01827e27 | −0.866913 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.40799e26 | −0.383684 | ||||||||
\(407\) | 2.10208e27i | 0.835427i | ||||||||
\(408\) | − 4.65658e26i | − 0.180358i | ||||||||
\(409\) | 4.45251e27 | 1.68078 | 0.840389 | − | 0.541984i | \(-0.182327\pi\) | ||||
0.840389 | + | 0.541984i | \(0.182327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.16393e27 | 1.85200 | ||||||||
\(412\) | − 1.18787e27i | − 0.415288i | ||||||||
\(413\) | 4.58995e27i | 1.56434i | ||||||||
\(414\) | −1.30591e26 | −0.0433921 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.90360e26 | 0.0917185 | ||||||||
\(417\) | 5.76686e27i | 1.77628i | ||||||||
\(418\) | − 2.16085e26i | − 0.0649044i | ||||||||
\(419\) | −4.92912e27 | −1.44385 | −0.721925 | − | 0.691972i | \(-0.756742\pi\) | ||||
−0.721925 | + | 0.691972i | \(0.756742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.50145e27 | 0.418359 | 0.209180 | − | 0.977877i | \(-0.432921\pi\) | ||||
0.209180 | + | 0.977877i | \(0.432921\pi\) | |||||||
\(422\) | 1.01042e27i | 0.274614i | ||||||||
\(423\) | 9.02400e26i | 0.239235i | ||||||||
\(424\) | −2.41345e27 | −0.624162 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.09015e26 | −0.0514490 | ||||||||
\(427\) | 4.75488e27i | 1.14195i | ||||||||
\(428\) | − 2.26014e27i | − 0.529635i | ||||||||
\(429\) | 9.83968e26 | 0.224998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.19221e27 | −1.56621 | −0.783107 | − | 0.621887i | \(-0.786366\pi\) | ||||
−0.783107 | + | 0.621887i | \(0.786366\pi\) | |||||||
\(432\) | − 2.16132e27i | − 0.459345i | ||||||||
\(433\) | 4.23104e27i | 0.877656i | 0.898571 | + | 0.438828i | \(0.144606\pi\) | ||||
−0.898571 | + | 0.438828i | \(0.855394\pi\) | |||||||
\(434\) | −4.20412e26 | −0.0851203 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.47237e27 | −0.669913 | ||||||||
\(437\) | − 5.84914e26i | − 0.110163i | ||||||||
\(438\) | − 1.60617e27i | − 0.295334i | ||||||||
\(439\) | −4.53235e27 | −0.813665 | −0.406832 | − | 0.913503i | \(-0.633367\pi\) | ||||
−0.406832 | + | 0.913503i | \(0.633367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.92804e26 | 0.0329998 | ||||||||
\(442\) | − 7.08712e25i | − 0.0118450i | ||||||||
\(443\) | − 4.61186e27i | − 0.752726i | −0.926472 | − | 0.376363i | \(-0.877174\pi\) | ||||
0.926472 | − | 0.376363i | \(-0.122826\pi\) | |||||||
\(444\) | −5.75909e27 | −0.917979 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.36037e27 | 0.206843 | ||||||||
\(447\) | 6.35573e27i | 0.943923i | ||||||||
\(448\) | 5.45811e27i | 0.791815i | ||||||||
\(449\) | 1.25692e26 | 0.0178123 | 0.00890615 | − | 0.999960i | \(-0.497165\pi\) | ||||
0.00890615 | + | 0.999960i | \(0.497165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.95349e27 | 0.264216 | ||||||||
\(452\) | 9.98664e26i | 0.131967i | ||||||||
\(453\) | − 7.34945e27i | − 0.948907i | ||||||||
\(454\) | −1.56763e27 | −0.197769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20840e27 | 0.145573 | ||||||||
\(457\) | − 1.15924e28i | − 1.36475i | −0.731003 | − | 0.682374i | \(-0.760948\pi\) | ||||
0.731003 | − | 0.682374i | \(-0.239052\pi\) | |||||||
\(458\) | − 1.98915e27i | − 0.228865i | ||||||||
\(459\) | −1.69889e27 | −0.191044 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.02514e28 | 1.10134 | 0.550671 | − | 0.834723i | \(-0.314372\pi\) | ||||
0.550671 | + | 0.834723i | \(0.314372\pi\) | |||||||
\(462\) | − 2.69977e27i | − 0.283522i | ||||||||
\(463\) | − 5.72801e27i | − 0.588035i | −0.955800 | − | 0.294017i | \(-0.905008\pi\) | ||||
0.955800 | − | 0.294017i | \(-0.0949924\pi\) | |||||||
\(464\) | 1.65149e28 | 1.65744 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.30651e27 | −0.125332 | ||||||||
\(467\) | − 1.12658e28i | − 1.05666i | −0.849040 | − | 0.528329i | \(-0.822819\pi\) | ||||
0.849040 | − | 0.528329i | \(-0.177181\pi\) | |||||||
\(468\) | 9.97138e26i | 0.0914479i | ||||||||
\(469\) | 1.30276e28 | 1.16829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.18963e27 | −0.702335 | ||||||||
\(472\) | 7.07587e27i | 0.593457i | ||||||||
\(473\) | 1.83393e28i | 1.50432i | ||||||||
\(474\) | 1.90229e27 | 0.152618 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.72210e27 | 0.362462 | ||||||||
\(477\) | − 1.25158e28i | − 0.939759i | ||||||||
\(478\) | 7.87660e26i | 0.0578557i | ||||||||
\(479\) | 1.17373e28 | 0.843422 | 0.421711 | − | 0.906730i | \(-0.361430\pi\) | ||||
0.421711 | + | 0.906730i | \(0.361430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.78911e27 | −0.123059 | ||||||||
\(482\) | − 2.32965e27i | − 0.156782i | ||||||||
\(483\) | − 7.30792e27i | − 0.481226i | ||||||||
\(484\) | 3.16747e27 | 0.204097 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.36773e27 | −0.207805 | ||||||||
\(487\) | − 4.75272e27i | − 0.287004i | −0.989650 | − | 0.143502i | \(-0.954164\pi\) | ||||
0.989650 | − | 0.143502i | \(-0.0458363\pi\) | |||||||
\(488\) | 7.33013e27i | 0.433215i | ||||||||
\(489\) | 1.11899e28 | 0.647266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.59837e28 | −1.43994 | −0.719971 | − | 0.694004i | \(-0.755845\pi\) | ||||
−0.719971 | + | 0.694004i | \(0.755845\pi\) | |||||||
\(492\) | 5.35200e27i | 0.290324i | ||||||||
\(493\) | − 1.29815e28i | − 0.689336i | ||||||||
\(494\) | 1.83913e26 | 0.00956049 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.37997e27 | 0.367703 | ||||||||
\(497\) | − 4.32640e27i | − 0.211050i | ||||||||
\(498\) | 1.81498e27i | 0.0866887i | ||||||||
\(499\) | −3.84508e28 | −1.79825 | −0.899124 | − | 0.437695i | \(-0.855795\pi\) | ||||
−0.899124 | + | 0.437695i | \(0.855795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.44045e28 | 1.09439 | ||||||||
\(502\) | 1.91211e27i | 0.0839699i | ||||||||
\(503\) | − 3.27446e28i | − 1.40824i | −0.710083 | − | 0.704118i | \(-0.751343\pi\) | ||||
0.710083 | − | 0.704118i | \(-0.248657\pi\) | |||||||
\(504\) | 5.58447e27 | 0.235213 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.01456e27 | −0.0813954 | ||||||||
\(507\) | − 3.09953e28i | − 1.22663i | ||||||||
\(508\) | − 3.29543e27i | − 0.127745i | ||||||||
\(509\) | 2.02472e28 | 0.768826 | 0.384413 | − | 0.923161i | \(-0.374404\pi\) | ||||
0.384413 | + | 0.923161i | \(0.374404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.32461e28 | 1.21149 | ||||||||
\(512\) | 2.36274e28i | 0.843492i | ||||||||
\(513\) | − 4.40869e27i | − 0.154197i | ||||||||
\(514\) | 4.52962e26 | 0.0155220 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.02443e28 | −1.65297 | ||||||||
\(517\) | 1.39208e28i | 0.448760i | ||||||||
\(518\) | 4.90889e27i | 0.155068i | ||||||||
\(519\) | −5.39222e28 | −1.66921 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.75207e27 | 0.141282 | 0.0706411 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706411 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(522\) | − 7.52124e27i | − 0.219154i | ||||||||
\(523\) | − 1.28180e26i | − 0.00366061i | −0.999998 | − | 0.00183030i | \(-0.999417\pi\) | ||||
0.999998 | − | 0.00183030i | \(-0.000582604\pi\) | |||||||
\(524\) | −2.79269e28 | −0.781708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.79422e27 | 0.263402 | ||||||||
\(527\) | − 5.80099e27i | − 0.152929i | ||||||||
\(528\) | 4.73921e28i | 1.22476i | ||||||||
\(529\) | 3.40184e28 | 0.861846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.66944e28 | −0.893527 | ||||||||
\(532\) | 1.22540e28i | 0.292554i | ||||||||
\(533\) | 1.66265e27i | 0.0389192i | ||||||||
\(534\) | 1.87132e28 | 0.429502 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.00834e28 | 0.443208 | ||||||||
\(537\) | 6.14266e28i | 1.32931i | ||||||||
\(538\) | 1.03097e28i | 0.218792i | ||||||||
\(539\) | 2.97429e27 | 0.0619014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.42747e28 | 0.686123 | 0.343061 | − | 0.939313i | \(-0.388536\pi\) | ||||
0.343061 | + | 0.939313i | \(0.388536\pi\) | |||||||
\(542\) | 7.08778e27i | 0.139161i | ||||||||
\(543\) | 3.71879e27i | 0.0716149i | ||||||||
\(544\) | 1.09928e28 | 0.207645 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.29781e27 | 0.0417630 | ||||||||
\(547\) | 7.30329e28i | 1.30212i | 0.759026 | + | 0.651061i | \(0.225676\pi\) | ||||
−0.759026 | + | 0.651061i | \(0.774324\pi\) | |||||||
\(548\) | 8.07273e28i | 1.41197i | ||||||||
\(549\) | −3.80130e28 | −0.652263 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.36874e28 | 0.556385 | ||||||||
\(552\) | − 1.12659e28i | − 0.182560i | ||||||||
\(553\) | 3.93755e28i | 0.626055i | ||||||||
\(554\) | −1.76164e28 | −0.274830 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.01529e28 | −1.35424 | ||||||||
\(557\) | 3.32597e28i | 0.490274i | 0.969488 | + | 0.245137i | \(0.0788330\pi\) | ||||
−0.969488 | + | 0.245137i | \(0.921167\pi\) | |||||||
\(558\) | − 3.36100e27i | − 0.0486193i | ||||||||
\(559\) | −1.56089e28 | −0.221588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.72523e28 | 0.509382 | ||||||||
\(562\) | 5.00285e27i | 0.0671407i | ||||||||
\(563\) | − 8.28332e28i | − 1.09110i | −0.838077 | − | 0.545552i | \(-0.816320\pi\) | ||||
0.838077 | − | 0.545552i | \(-0.183680\pi\) | |||||||
\(564\) | −3.81390e28 | −0.493104 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.18084e28 | −0.271676 | ||||||||
\(567\) | − 1.04417e29i | − 1.27687i | ||||||||
\(568\) | − 6.66959e27i | − 0.0800648i | ||||||||
\(569\) | −7.35414e28 | −0.866669 | −0.433335 | − | 0.901233i | \(-0.642663\pi\) | ||||
−0.433335 | + | 0.901233i | \(0.642663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09131e29 | 1.23956 | 0.619780 | − | 0.784776i | \(-0.287222\pi\) | ||||
0.619780 | + | 0.784776i | \(0.287222\pi\) | |||||||
\(572\) | 1.53823e28i | 0.171539i | ||||||||
\(573\) | − 1.14204e29i | − 1.25043i | ||||||||
\(574\) | 4.56190e27 | 0.0490423 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.36350e28 | −0.452271 | ||||||||
\(577\) | − 1.30727e28i | − 0.133051i | −0.997785 | − | 0.0665257i | \(-0.978809\pi\) | ||||
0.997785 | − | 0.0665257i | \(-0.0211914\pi\) | |||||||
\(578\) | 1.72153e28i | 0.172057i | ||||||||
\(579\) | 1.11258e28 | 0.109196 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.75682e28 | −0.355607 | ||||||||
\(582\) | − 2.99927e28i | − 0.278820i | ||||||||
\(583\) | − 1.93075e29i | − 1.76281i | ||||||||
\(584\) | 5.12523e28 | 0.459598 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40741e28 | −0.121758 | ||||||||
\(587\) | 1.71459e29i | 1.45701i | 0.685043 | + | 0.728503i | \(0.259784\pi\) | ||||
−0.685043 | + | 0.728503i | \(0.740216\pi\) | |||||||
\(588\) | 8.14867e27i | 0.0680182i | ||||||||
\(589\) | 1.50538e28 | 0.123434 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00630e28 | 0.712652 | ||||||||
\(592\) | − 8.61713e28i | − 0.669861i | ||||||||
\(593\) | 2.35277e29i | 1.79682i | 0.439153 | + | 0.898412i | \(0.355279\pi\) | ||||
−0.439153 | + | 0.898412i | \(0.644721\pi\) | |||||||
\(594\) | −1.51844e28 | −0.113931 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.93587e28 | −0.719648 | ||||||||
\(597\) | − 1.60465e29i | − 1.14196i | ||||||||
\(598\) | − 1.71462e27i | − 0.0119896i | ||||||||
\(599\) | 1.33384e29 | 0.916481 | 0.458240 | − | 0.888828i | \(-0.348480\pi\) | ||||
0.458240 | + | 0.888828i | \(0.348480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.64474e28 | −0.241816 | −0.120908 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120908 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(602\) | 4.28269e28i | 0.279225i | ||||||||
\(603\) | 1.04150e29i | 0.667308i | ||||||||
\(604\) | 1.14893e29 | 0.723448 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.71820e28 | −0.226136 | ||||||||
\(607\) | − 2.71228e29i | − 1.62126i | −0.585559 | − | 0.810630i | \(-0.699125\pi\) | ||||
0.585559 | − | 0.810630i | \(-0.300875\pi\) | |||||||
\(608\) | 2.85268e28i | 0.167597i | ||||||||
\(609\) | 4.20890e29 | 2.43045 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18482e28 | −0.0661029 | ||||||||
\(612\) | 3.77509e28i | 0.207032i | ||||||||
\(613\) | − 2.02699e29i | − 1.09274i | −0.837544 | − | 0.546370i | \(-0.816009\pi\) | ||||
0.837544 | − | 0.546370i | \(-0.183991\pi\) | |||||||
\(614\) | −6.27803e28 | −0.332702 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.61486e28 | 0.441215 | ||||||||
\(617\) | − 3.04169e29i | − 1.53151i | −0.643130 | − | 0.765757i | \(-0.722364\pi\) | ||||
0.643130 | − | 0.765757i | \(-0.277636\pi\) | |||||||
\(618\) | − 2.18838e28i | − 0.108329i | ||||||||
\(619\) | −1.21487e29 | −0.591262 | −0.295631 | − | 0.955302i | \(-0.595530\pi\) | ||||
−0.295631 | + | 0.955302i | \(0.595530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.11022e28 | −0.193376 | ||||||||
\(622\) | − 1.16538e28i | − 0.0539097i | ||||||||
\(623\) | 3.87345e29i | 1.76187i | ||||||||
\(624\) | −4.03361e28 | −0.180408 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.51762e27 | 0.0108883 | ||||||||
\(627\) | 9.66712e28i | 0.411138i | ||||||||
\(628\) | − 1.28028e29i | − 0.535461i | ||||||||
\(629\) | −6.77345e28 | −0.278598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.79118e29 | −0.712577 | −0.356288 | − | 0.934376i | \(-0.615958\pi\) | ||||
−0.356288 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(632\) | 6.07014e28i | 0.237503i | ||||||||
\(633\) | − 4.52038e29i | − 1.73955i | ||||||||
\(634\) | −9.20904e27 | −0.0348560 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.28968e29 | 1.93700 | ||||||||
\(637\) | 2.53146e27i | 0.00911815i | ||||||||
\(638\) | − 1.16026e29i | − 0.411091i | ||||||||
\(639\) | 3.45875e28 | 0.120548 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.41742e29 | −1.15263 | −0.576315 | − | 0.817228i | \(-0.695510\pi\) | ||||
−0.576315 | + | 0.817228i | \(0.695510\pi\) | |||||||
\(642\) | − 4.16379e28i | − 0.138156i | ||||||||
\(643\) | 7.57582e28i | 0.247294i | 0.992326 | + | 0.123647i | \(0.0394591\pi\) | ||||
−0.992326 | + | 0.123647i | \(0.960541\pi\) | |||||||
\(644\) | 1.14244e29 | 0.366887 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.96283e27 | 0.0216443 | ||||||||
\(647\) | 2.99088e29i | 0.914755i | 0.889273 | + | 0.457377i | \(0.151211\pi\) | ||||
−0.889273 | + | 0.457377i | \(0.848789\pi\) | |||||||
\(648\) | − 1.60969e29i | − 0.484400i | ||||||||
\(649\) | −5.66065e29 | −1.67609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88082e29 | 0.539196 | ||||||||
\(652\) | 1.74931e29i | 0.493476i | ||||||||
\(653\) | 5.40507e28i | 0.150042i | 0.997182 | + | 0.0750210i | \(0.0239024\pi\) | ||||
−0.997182 | + | 0.0750210i | \(0.976098\pi\) | |||||||
\(654\) | −6.39703e28 | −0.174748 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.00802e28 | −0.211853 | ||||||||
\(657\) | 2.65787e29i | 0.691985i | ||||||||
\(658\) | 3.25086e28i | 0.0832966i | ||||||||
\(659\) | −2.26606e28 | −0.0571446 | −0.0285723 | − | 0.999592i | \(-0.509096\pi\) | ||||
−0.0285723 | + | 0.999592i | \(0.509096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.87483e29 | −0.457980 | −0.228990 | − | 0.973429i | \(-0.573542\pi\) | ||||
−0.228990 | + | 0.973429i | \(0.573542\pi\) | |||||||
\(662\) | − 7.26379e28i | − 0.174644i | ||||||||
\(663\) | 3.17060e28i | 0.0750325i | ||||||||
\(664\) | −5.79151e28 | −0.134905 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.92443e28 | −0.0885720 | ||||||||
\(667\) | − 3.14067e29i | − 0.697752i | ||||||||
\(668\) | 3.81513e29i | 0.834367i | ||||||||
\(669\) | −6.08595e29 | −1.31025 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.86406e29 | −1.22352 | ||||||||
\(672\) | 3.56414e29i | 0.732111i | ||||||||
\(673\) | 7.53001e29i | 1.52278i | 0.648294 | + | 0.761390i | \(0.275483\pi\) | ||||
−0.648294 | + | 0.761390i | \(0.724517\pi\) | |||||||
\(674\) | −4.41005e28 | −0.0878041 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.84547e29 | 0.935181 | ||||||||
\(677\) | 8.12052e29i | 1.54313i | 0.636150 | + | 0.771565i | \(0.280526\pi\) | ||||
−0.636150 | + | 0.771565i | \(0.719474\pi\) | |||||||
\(678\) | 1.83981e28i | 0.0344239i | ||||||||
\(679\) | 6.20819e29 | 1.14375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.01320e29 | 1.25277 | ||||||||
\(682\) | − 5.18482e28i | − 0.0912007i | ||||||||
\(683\) | 4.69973e29i | 0.814058i | 0.913415 | + | 0.407029i | \(0.133435\pi\) | ||||
−0.913415 | + | 0.407029i | \(0.866565\pi\) | |||||||
\(684\) | −9.79650e28 | −0.167102 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.16608e29 | −0.192897 | ||||||||
\(687\) | 8.89896e29i | 1.44975i | ||||||||
\(688\) | − 7.51789e29i | − 1.20619i | ||||||||
\(689\) | 1.64329e29 | 0.259664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.58806e29 | 0.549971 | 0.274985 | − | 0.961448i | \(-0.411327\pi\) | ||||
0.274985 | + | 0.961448i | \(0.411327\pi\) | |||||||
\(692\) | − 8.42962e29i | − 1.27261i | ||||||||
\(693\) | 4.46754e29i | 0.664308i | ||||||||
\(694\) | 9.31496e28 | 0.136429 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.48845e29 | 0.922027 | ||||||||
\(697\) | 6.29466e28i | 0.0881106i | ||||||||
\(698\) | 1.95222e29i | 0.269183i | ||||||||
\(699\) | 5.84501e29 | 0.793917 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.33110e29 | −0.966339 | −0.483170 | − | 0.875527i | \(-0.660515\pi\) | ||||
−0.483170 | + | 0.875527i | \(0.660515\pi\) | |||||||
\(702\) | − 1.29237e28i | − 0.0167821i | ||||||||
\(703\) | − 1.75774e29i | − 0.224865i | ||||||||
\(704\) | −6.73133e29 | −0.848376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.97076e29 | −0.241093 | ||||||||
\(707\) | − 7.69629e29i | − 0.927636i | ||||||||
\(708\) | − 1.55085e30i | − 1.84171i | ||||||||
\(709\) | −1.20909e30 | −1.41473 | −0.707365 | − | 0.706848i | \(-0.750116\pi\) | ||||
−0.707365 | + | 0.706848i | \(0.750116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.14788e29 | −0.357592 | ||||||||
\(712\) | 5.97131e29i | 0.668390i | ||||||||
\(713\) | − 1.40346e29i | − 0.154796i | ||||||||
\(714\) | 8.69936e28 | 0.0945488 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.60277e29 | −1.01347 | ||||||||
\(717\) | − 3.52379e29i | − 0.366488i | ||||||||
\(718\) | 1.97424e28i | 0.0202345i | ||||||||
\(719\) | 5.25189e29 | 0.530472 | 0.265236 | − | 0.964183i | \(-0.414550\pi\) | ||||
0.265236 | + | 0.964183i | \(0.414550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.52972e29 | 0.444377 | ||||||||
\(722\) | − 1.87624e29i | − 0.181404i | ||||||||
\(723\) | 1.04223e30i | 0.993140i | ||||||||
\(724\) | −5.81356e28 | −0.0545993 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.83532e28 | 0.0532390 | ||||||||
\(727\) | − 7.23318e29i | − 0.650456i | −0.945636 | − | 0.325228i | \(-0.894559\pi\) | ||||
0.945636 | − | 0.325228i | \(-0.105441\pi\) | |||||||
\(728\) | 7.33223e28i | 0.0649915i | ||||||||
\(729\) | 8.46052e28 | 0.0739193 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.90940e29 | −0.501662 | ||||||||
\(732\) | − 1.60658e30i | − 1.34442i | ||||||||
\(733\) | − 2.11409e30i | − 1.74394i | −0.489560 | − | 0.871969i | \(-0.662843\pi\) | ||||
0.489560 | − | 0.871969i | \(-0.337157\pi\) | |||||||
\(734\) | 3.27097e29 | 0.265992 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.65955e29 | 0.210180 | ||||||||
\(737\) | 1.60666e30i | 1.25174i | ||||||||
\(738\) | 3.64702e28i | 0.0280122i | ||||||||
\(739\) | 7.42069e29 | 0.561924 | 0.280962 | − | 0.959719i | \(-0.409347\pi\) | ||||
0.280962 | + | 0.959719i | \(0.409347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.22782e28 | −0.0605611 | ||||||||
\(742\) | − 4.50878e29i | − 0.327204i | ||||||||
\(743\) | 1.69968e30i | 1.21614i | 0.793882 | + | 0.608071i | \(0.208057\pi\) | ||||
−0.793882 | + | 0.608071i | \(0.791943\pi\) | |||||||
\(744\) | 2.89948e29 | 0.204552 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.10297e29 | −0.0756494 | ||||||||
\(747\) | − 3.00339e29i | − 0.203117i | ||||||||
\(748\) | 5.82362e29i | 0.388353i | ||||||||
\(749\) | 8.61862e29 | 0.566733 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.90225e29 | 0.377397 | 0.188698 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188698 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(752\) | − 5.70661e29i | − 0.359824i | ||||||||
\(753\) | − 8.55430e29i | − 0.531909i | ||||||||
\(754\) | 9.87515e28 | 0.0605542 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.61095e29 | 0.513537 | ||||||||
\(757\) | − 1.33308e30i | − 0.784058i | −0.919953 | − | 0.392029i | \(-0.871773\pi\) | ||||
0.919953 | − | 0.392029i | \(-0.128227\pi\) | |||||||
\(758\) | − 2.05853e28i | − 0.0119407i | ||||||||
\(759\) | 9.01264e29 | 0.515601 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.86217e29 | −0.437526 | −0.218763 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218763 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(762\) | − 6.07106e28i | − 0.0333225i | ||||||||
\(763\) | − 1.32412e30i | − 0.716837i | ||||||||
\(764\) | 1.78535e30 | 0.953329 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.98665e29 | 0.207112 | ||||||||
\(767\) | − 4.81786e29i | − 0.246890i | ||||||||
\(768\) | − 1.56392e30i | − 0.790537i | ||||||||
\(769\) | 1.65083e30 | 0.823142 | 0.411571 | − | 0.911378i | \(-0.364980\pi\) | ||||
0.411571 | + | 0.911378i | \(0.364980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.02644e29 | −0.0983247 | ||||||||
\(772\) | 1.73929e29i | 0.0832510i | ||||||||
\(773\) | 3.77930e30i | 1.78454i | 0.451499 | + | 0.892271i | \(0.350889\pi\) | ||||
−0.451499 | + | 0.892271i | \(0.649111\pi\) | |||||||
\(774\) | −3.42381e29 | −0.159488 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.57056e29 | 0.433899 | ||||||||
\(777\) | − 2.19612e30i | − 0.982278i | ||||||||
\(778\) | − 4.70054e29i | − 0.207425i | ||||||||
\(779\) | −1.63349e29 | −0.0711169 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.33563e29 | 0.226126 | ||||||||
\(782\) | − 6.49144e28i | − 0.0271438i | ||||||||
\(783\) | − 2.36723e30i | − 0.976655i | ||||||||
\(784\) | −1.21926e29 | −0.0496337 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.14488e29 | −0.203910 | ||||||||
\(787\) | 3.58219e30i | 1.40092i | 0.713691 | + | 0.700461i | \(0.247022\pi\) | ||||
−0.713691 | + | 0.700461i | \(0.752978\pi\) | |||||||
\(788\) | 1.40795e30i | 0.543327i | ||||||||
\(789\) | −4.38169e30 | −1.66853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.80821e29 | −0.141211 | ||||||||
\(792\) | 6.88717e29i | 0.252015i | ||||||||
\(793\) | − 4.99099e29i | − 0.180226i | ||||||||
\(794\) | 3.48564e29 | 0.124213 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.50854e30 | 0.870631 | ||||||||
\(797\) | 4.45901e30i | 1.52731i | 0.645626 | + | 0.763654i | \(0.276596\pi\) | ||||
−0.645626 | + | 0.763654i | \(0.723404\pi\) | |||||||
\(798\) | 2.25752e29i | 0.0763134i | ||||||||
\(799\) | −4.48565e29 | −0.149653 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.09664e30 | −1.00635 | ||||||||
\(802\) | − 1.87591e29i | − 0.0601702i | ||||||||
\(803\) | 4.10015e30i | 1.29803i | ||||||||
\(804\) | −4.40178e30 | −1.37543 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.41288e28 | 0.0134340 | ||||||||
\(807\) | − 4.61229e30i | − 1.38594i | ||||||||
\(808\) | − 1.18646e30i | − 0.351912i | ||||||||
\(809\) | −3.09156e30 | −0.905144 | −0.452572 | − | 0.891728i | \(-0.649493\pi\) | ||||
−0.452572 | + | 0.891728i | \(0.649493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.85711e29 | −0.281210 | −0.140605 | − | 0.990066i | \(-0.544905\pi\) | ||||
−0.140605 | + | 0.990066i | \(0.544905\pi\) | |||||||
\(812\) | 6.57974e30i | 1.85298i | ||||||||
\(813\) | − 3.17090e30i | − 0.881518i | ||||||||
\(814\) | −6.05400e29 | −0.166144 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.52710e30 | −0.408432 | ||||||||
\(817\) | − 1.53351e30i | − 0.404907i | ||||||||
\(818\) | 1.28232e30i | 0.334262i | ||||||||
\(819\) | −3.80239e29 | −0.0978533 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.81930e30 | −1.45971 | −0.729856 | − | 0.683601i | \(-0.760413\pi\) | ||||
−0.729856 | + | 0.683601i | \(0.760413\pi\) | |||||||
\(822\) | 1.48721e30i | 0.368314i | ||||||||
\(823\) | 1.82848e30i | 0.447086i | 0.974694 | + | 0.223543i | \(0.0717624\pi\) | ||||
−0.974694 | + | 0.223543i | \(0.928238\pi\) | |||||||
\(824\) | 6.98303e29 | 0.168581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.32191e30 | −0.311107 | ||||||||
\(827\) | 3.80997e30i | 0.885347i | 0.896683 | + | 0.442673i | \(0.145970\pi\) | ||||
−0.896683 | + | 0.442673i | \(0.854030\pi\) | |||||||
\(828\) | 9.13327e29i | 0.209560i | ||||||||
\(829\) | −9.24247e29 | −0.209395 | −0.104697 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104697 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.88112e30 | 1.74091 | ||||||||
\(832\) | − 5.72914e29i | − 0.124967i | ||||||||
\(833\) | 9.58392e28i | 0.0206429i | ||||||||
\(834\) | −1.66086e30 | −0.353255 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.51125e30 | −0.313452 | ||||||||
\(837\) | − 1.05784e30i | − 0.216671i | ||||||||
\(838\) | − 1.41959e30i | − 0.287144i | ||||||||
\(839\) | −2.18057e30 | −0.435582 | −0.217791 | − | 0.975995i | \(-0.569885\pi\) | ||||
−0.217791 | + | 0.975995i | \(0.569885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.29554e31 | 2.52403 | ||||||||
\(842\) | 4.32418e29i | 0.0832007i | ||||||||
\(843\) | − 2.23815e30i | − 0.425304i | ||||||||
\(844\) | 7.06668e30 | 1.32623 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.59891e29 | −0.0475776 | ||||||||
\(847\) | 1.20785e30i | 0.218393i | ||||||||
\(848\) | 7.91477e30i | 1.41345i | ||||||||
\(849\) | 9.75655e30 | 1.72094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.63874e30 | −0.282000 | ||||||||
\(852\) | 1.46181e30i | 0.248470i | ||||||||
\(853\) | − 4.27754e30i | − 0.718173i | −0.933304 | − | 0.359087i | \(-0.883088\pi\) | ||||
0.933304 | − | 0.359087i | \(-0.116912\pi\) | |||||||
\(854\) | −1.36941e30 | −0.227104 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.32865e30 | 0.214998 | ||||||||
\(857\) | 1.76322e29i | 0.0281843i | 0.999901 | + | 0.0140922i | \(0.00448582\pi\) | ||||
−0.999901 | + | 0.0140922i | \(0.995514\pi\) | |||||||
\(858\) | 2.83383e29i | 0.0447463i | ||||||||
\(859\) | −4.74009e30 | −0.739365 | −0.369682 | − | 0.929158i | \(-0.620533\pi\) | ||||
−0.369682 | + | 0.929158i | \(0.620533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.04088e30 | −0.310659 | ||||||||
\(862\) | − 2.07136e30i | − 0.311479i | ||||||||
\(863\) | 8.10824e29i | 0.120452i | 0.998185 | + | 0.0602259i | \(0.0191821\pi\) | ||||
−0.998185 | + | 0.0602259i | \(0.980818\pi\) | |||||||
\(864\) | 2.00459e30 | 0.294192 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.21854e30 | −0.174543 | ||||||||
\(867\) | − 7.70171e30i | − 1.08990i | ||||||||
\(868\) | 2.94027e30i | 0.411084i | ||||||||
\(869\) | −4.85607e30 | −0.670775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.36745e30 | −0.184383 | ||||||||
\(872\) | − 2.04127e30i | − 0.271942i | ||||||||
\(873\) | 4.96315e30i | 0.653293i | ||||||||
\(874\) | 1.68455e29 | 0.0219086 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.12332e31 | −1.42630 | ||||||||
\(877\) | − 1.55255e30i | − 0.194782i | −0.995246 | − | 0.0973912i | \(-0.968950\pi\) | ||||
0.995246 | − | 0.0973912i | \(-0.0310498\pi\) | |||||||
\(878\) | − 1.30532e30i | − 0.161817i | ||||||||
\(879\) | 6.29641e30 | 0.771275 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.75722e30 | −0.688598 | −0.344299 | − | 0.938860i | \(-0.611883\pi\) | ||||
−0.344299 | + | 0.938860i | \(0.611883\pi\) | |||||||
\(882\) | 5.55276e28i | 0.00656280i | ||||||||
\(883\) | − 1.29134e31i | − 1.50818i | −0.656774 | − | 0.754088i | \(-0.728079\pi\) | ||||
0.656774 | − | 0.754088i | \(-0.271921\pi\) | |||||||
\(884\) | −4.95657e29 | −0.0572048 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.32822e30 | 0.149698 | ||||||||
\(887\) | 4.22752e30i | 0.470856i | 0.971892 | + | 0.235428i | \(0.0756492\pi\) | ||||
−0.971892 | + | 0.235428i | \(0.924351\pi\) | |||||||
\(888\) | − 3.38554e30i | − 0.372642i | ||||||||
\(889\) | 1.25665e30 | 0.136693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.28774e31 | 1.36808 | ||||||||
\(892\) | − 9.51411e30i | − 0.998935i | ||||||||
\(893\) | − 1.16404e30i | − 0.120789i | ||||||||
\(894\) | −1.83045e30 | −0.187722 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.37317e30 | −0.738618 | ||||||||
\(897\) | 7.67079e29i | 0.0759486i | ||||||||
\(898\) | 3.61992e28i | 0.00354240i | ||||||||
\(899\) | 8.08306e30 | 0.781806 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.22137e30 | 0.587862 | ||||||||
\(902\) | 5.62606e29i | 0.0525455i | ||||||||
\(903\) | − 1.91597e31i | − 1.76875i | ||||||||
\(904\) | −5.87074e29 | −0.0535704 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.11664e30 | 0.188713 | ||||||||
\(907\) | − 1.34786e31i | − 1.18787i | −0.804513 | − | 0.593935i | \(-0.797574\pi\) | ||||
0.804513 | − | 0.593935i | \(-0.202426\pi\) | |||||||
\(908\) | 1.09637e31i | 0.955113i | ||||||||
\(909\) | 6.15281e30 | 0.529850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28886e31 | −1.08458 | −0.542292 | − | 0.840190i | \(-0.682443\pi\) | ||||
−0.542292 | + | 0.840190i | \(0.682443\pi\) | |||||||
\(912\) | − 3.96287e30i | − 0.329658i | ||||||||
\(913\) | − 4.63317e30i | − 0.381009i | ||||||||
\(914\) | 3.33860e30 | 0.271413 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.39117e31 | −1.10529 | ||||||||
\(917\) | − 1.06494e31i | − 0.836463i | ||||||||
\(918\) | − 4.89281e29i | − 0.0379936i | ||||||||
\(919\) | −1.25018e30 | −0.0959753 | −0.0479876 | − | 0.998848i | \(-0.515281\pi\) | ||||
−0.0479876 | + | 0.998848i | \(0.515281\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.80864e31 | 2.10751 | ||||||||
\(922\) | 2.95239e30i | 0.219028i | ||||||||
\(923\) | 4.54123e29i | 0.0333086i | ||||||||
\(924\) | −1.88816e31 | −1.36925 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.64967e30 | 0.116945 | ||||||||
\(927\) | 3.62130e30i | 0.253821i | ||||||||
\(928\) | 1.53173e31i | 1.06152i | ||||||||
\(929\) | 1.41245e31 | 0.967850 | 0.483925 | − | 0.875109i | \(-0.339211\pi\) | ||||
0.483925 | + | 0.875109i | \(0.339211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.48706e29 | −0.0166615 | ||||||||
\(932\) | 9.13746e30i | 0.605283i | ||||||||
\(933\) | 5.21360e30i | 0.341492i | ||||||||
\(934\) | 3.24455e30 | 0.210142 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.86177e29 | −0.0371221 | ||||||||
\(937\) | 7.12851e30i | 0.446409i | 0.974772 | + | 0.223204i | \(0.0716518\pi\) | ||||
−0.974772 | + | 0.223204i | \(0.928348\pi\) | |||||||
\(938\) | 3.75196e30i | 0.232342i | ||||||||
\(939\) | −1.12632e30 | −0.0689721 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.07254e29 | −0.00642275 | −0.00321138 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321138 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(942\) | − 2.35861e30i | − 0.139676i | ||||||||
\(943\) | 1.52290e30i | 0.0891864i | ||||||||
\(944\) | 2.32049e31 | 1.34392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.28172e30 | −0.299170 | ||||||||
\(947\) | − 2.92935e31i | − 1.64095i | −0.571680 | − | 0.820477i | \(-0.693708\pi\) | ||||
0.571680 | − | 0.820477i | \(-0.306292\pi\) | |||||||
\(948\) | − 1.33042e31i | − 0.737058i | ||||||||
\(949\) | −3.48969e30 | −0.191202 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.11989e30 | 0.220796 | ||||||||
\(952\) | 2.77593e30i | 0.147137i | ||||||||
\(953\) | 3.04320e31i | 1.59535i | 0.603088 | + | 0.797675i | \(0.293937\pi\) | ||||
−0.603088 | + | 0.797675i | \(0.706063\pi\) | |||||||
\(954\) | 3.60456e30 | 0.186893 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.50872e30 | 0.279410 | ||||||||
\(957\) | 5.19071e31i | 2.60406i | ||||||||
\(958\) | 3.38034e30i | 0.167735i | ||||||||
\(959\) | −3.07838e31 | −1.51087 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.72134e31 | −0.826556 | ||||||||
\(962\) | − 5.15264e29i | − 0.0244733i | ||||||||
\(963\) | 6.89017e30i | 0.323709i | ||||||||
\(964\) | −1.62931e31 | −0.757171 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.10468e30 | 0.0957032 | ||||||||
\(967\) | 3.78485e31i | 1.70244i | 0.524813 | + | 0.851218i | \(0.324135\pi\) | ||||
−0.524813 | + | 0.851218i | \(0.675865\pi\) | |||||||
\(968\) | 1.86203e30i | 0.0828504i | ||||||||
\(969\) | −3.11500e30 | −0.137106 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.62334e31 | −0.699212 | −0.349606 | − | 0.936897i | \(-0.613684\pi\) | ||||
−0.349606 | + | 0.936897i | \(0.613684\pi\) | |||||||
\(972\) | 2.35532e31i | 1.00358i | ||||||||
\(973\) | − 3.43780e31i | − 1.44909i | ||||||||
\(974\) | 1.36878e30 | 0.0570776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.40387e31 | 0.981043 | ||||||||
\(977\) | − 2.98858e30i | − 0.120662i | −0.998178 | − | 0.0603312i | \(-0.980784\pi\) | ||||
0.998178 | − | 0.0603312i | \(-0.0192157\pi\) | |||||||
\(978\) | 3.22269e30i | 0.128724i | ||||||||
\(979\) | −4.77701e31 | −1.88772 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05857e31 | 0.409445 | ||||||||
\(982\) | − 7.48330e30i | − 0.286367i | ||||||||
\(983\) | − 2.41371e31i | − 0.913846i | −0.889506 | − | 0.456923i | \(-0.848951\pi\) | ||||
0.889506 | − | 0.456923i | \(-0.151049\pi\) | |||||||
\(984\) | −3.14623e30 | −0.117853 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.73866e30 | 0.137091 | ||||||||
\(987\) | − 1.45436e31i | − 0.527643i | ||||||||
\(988\) | − 1.28625e30i | − 0.0461718i | ||||||||
\(989\) | −1.42969e31 | −0.507786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.29436e31 | −0.797790 | −0.398895 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398895 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(992\) | 6.84481e30i | 0.235499i | ||||||||
\(993\) | 3.24964e31i | 1.10629i | ||||||||
\(994\) | 1.24600e30 | 0.0419723 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.26935e31 | 0.418658 | ||||||||
\(997\) | − 3.55036e31i | − 1.15871i | −0.815076 | − | 0.579354i | \(-0.803305\pi\) | ||||
0.815076 | − | 0.579354i | \(-0.196695\pi\) | |||||||
\(998\) | − 1.10738e31i | − 0.357624i | ||||||||
\(999\) | −1.23517e31 | −0.394719 |
(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 | 25.22.b.a.24.2 | 2 | ||
5.2 | odd | 4 | 1.22.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 25.22.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 25.22.b.a.24.1 | 2 | ||
15.2 | even | 4 | 9.22.a.c.1.1 | 1 | |||
20.7 | even | 4 | 16.22.a.c.1.1 | 1 | |||
35.27 | even | 4 | 49.22.a.a.1.1 | 1 | |||
40.27 | even | 4 | 64.22.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 64.22.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.22.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
9.22.a.c.1.1 | 1 | 15.2 | even | 4 | |||
16.22.a.c.1.1 | 1 | 20.7 | even | 4 | |||
25.22.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
25.22.b.a.24.1 | 2 | 5.4 | even | 2 | inner | ||
25.22.b.a.24.2 | 2 | 1.1 | even | 1 | trivial | ||
49.22.a.a.1.1 | 1 | 35.27 | even | 4 | |||
64.22.a.a.1.1 | 1 | 40.27 | even | 4 | |||
64.22.a.g.1.1 | 1 | 40.37 | odd | 4 |