Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,22,Mod(35,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.35");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(201.223687887\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 35.41 | ||
Character | \(\chi\) | \(=\) | 72.35 |
Dual form | 72.22.f.a.35.42 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −145.330 | − | 1440.84i | −0.100355 | − | 0.994952i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.05491e6 | + | 418795.i | −0.979858 | + | 0.199697i | ||||
\(5\) | 1.63057e7 | 0.746715 | 0.373358 | − | 0.927688i | \(-0.378206\pi\) | ||||
0.373358 | + | 0.927688i | \(0.378206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.11046e9i | − | 1.48584i | −0.669379 | − | 0.742921i | \(-0.733440\pi\) | ||
0.669379 | − | 0.742921i | \(-0.266560\pi\) | |||||||
\(8\) | 9.02058e8 | + | 2.89994e9i | 0.297023 | + | 0.954870i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.36971e9 | − | 2.34940e10i | −0.0749367 | − | 0.742946i | ||||
\(11\) | − | 1.11865e11i | − | 1.30039i | −0.759769 | − | 0.650193i | \(-0.774688\pi\) | ||
0.759769 | − | 0.650193i | \(-0.225312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58848e11i | 0.319577i | 0.987151 | + | 0.159789i | \(0.0510812\pi\) | ||||
−0.987151 | + | 0.159789i | \(0.948919\pi\) | |||||||
\(14\) | −1.60000e12 | + | 1.61383e11i | −1.47834 | + | 0.149112i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.04727e12 | − | 1.72117e12i | 0.920242 | − | 0.391350i | ||||
\(17\) | 3.55129e12i | 0.427241i | 0.976917 | + | 0.213621i | \(0.0685256\pi\) | ||||
−0.976917 | + | 0.213621i | \(0.931474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.97170e12 | 0.148615 | 0.0743077 | − | 0.997235i | \(-0.476325\pi\) | ||||
0.0743077 | + | 0.997235i | \(0.476325\pi\) | |||||||
\(20\) | −3.35068e13 | + | 6.82876e12i | −0.731675 | + | 0.149117i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.61180e14 | + | 1.62574e13i | −1.29382 | + | 0.130500i | ||||
\(23\) | −9.68326e13 | −0.487393 | −0.243696 | − | 0.969852i | \(-0.578360\pi\) | ||||
−0.243696 | + | 0.969852i | \(0.578360\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.10961e14 | −0.442416 | ||||||||
\(26\) | 2.28875e14 | − | 2.30853e13i | 0.317964 | − | 0.0320712i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.65054e14 | + | 2.28189e15i | 0.296718 | + | 1.45591i | ||||
\(29\) | 4.54212e14 | 0.200484 | 0.100242 | − | 0.994963i | \(-0.468038\pi\) | ||||
0.100242 | + | 0.994963i | \(0.468038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.94527e15i | 1.74105i | 0.492125 | + | 0.870525i | \(0.336220\pi\) | ||||
−0.492125 | + | 0.870525i | \(0.663780\pi\) | |||||||
\(32\) | −3.06813e15 | − | 5.58134e15i | −0.481725 | − | 0.876322i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.11686e15 | − | 5.16109e14i | 0.425084 | − | 0.0428759i | ||||
\(35\) | − | 1.81068e16i | − | 1.10950i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.51812e15i | 0.0519026i | 0.999663 | + | 0.0259513i | \(0.00826149\pi\) | ||||
−0.999663 | + | 0.0259513i | \(0.991739\pi\) | |||||||
\(38\) | −5.77207e14 | − | 5.72261e15i | −0.0149143 | − | 0.147865i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.47087e16 | + | 4.72856e16i | 0.221791 | + | 0.713016i | ||||
\(41\) | − | 3.00638e16i | − | 0.349795i | −0.984587 | − | 0.174898i | \(-0.944041\pi\) | ||
0.984587 | − | 0.174898i | \(-0.0559594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85924e17 | −1.31195 | −0.655975 | − | 0.754783i | \(-0.727742\pi\) | ||||
−0.655975 | + | 0.754783i | \(0.727742\pi\) | |||||||
\(44\) | 4.68487e16 | + | 2.29873e17i | 0.259683 | + | 1.27419i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.40727e16 | + | 1.39521e17i | 0.0489124 | + | 0.484932i | ||||
\(47\) | 2.24282e17 | 0.621968 | 0.310984 | − | 0.950415i | \(-0.399341\pi\) | ||||
0.310984 | + | 0.950415i | \(0.399341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74570e17 | −1.20773 | ||||||||
\(50\) | 3.06589e16 | + | 3.03961e17i | 0.0443988 | + | 0.440183i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.65246e16 | − | 3.26418e17i | −0.0638186 | − | 0.313140i | ||||
\(53\) | −3.35928e17 | −0.263846 | −0.131923 | − | 0.991260i | \(-0.542115\pi\) | ||||
−0.131923 | + | 0.991260i | \(0.542115\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.82404e18i | − | 0.971018i | ||||||
\(56\) | 3.22026e18 | − | 1.00170e18i | 1.41879 | − | 0.441329i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.60105e16 | − | 6.54448e17i | −0.0201196 | − | 0.199472i | ||||
\(59\) | − | 4.52223e18i | − | 1.15188i | −0.817493 | − | 0.575939i | \(-0.804637\pi\) | ||
0.817493 | − | 0.575939i | \(-0.195363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.11219e18i | − | 0.738091i | −0.929411 | − | 0.369045i | \(-0.879685\pi\) | ||
0.929411 | − | 0.369045i | \(-0.120315\pi\) | |||||||
\(62\) | 1.14479e19 | − | 1.15469e18i | 1.73226 | − | 0.174723i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.59595e18 | + | 5.23183e18i | −0.823555 | + | 0.567237i | ||||
\(65\) | 2.59013e18i | 0.238633i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.73554e18 | 0.451427 | 0.225713 | − | 0.974194i | \(-0.427529\pi\) | ||||
0.225713 | + | 0.974194i | \(0.427529\pi\) | |||||||
\(68\) | −1.48727e18 | − | 7.29759e18i | −0.0853188 | − | 0.418635i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.60891e19 | + | 2.63146e18i | −1.10390 | + | 0.111344i | ||||
\(71\) | −3.53935e19 | −1.29036 | −0.645180 | − | 0.764030i | \(-0.723218\pi\) | ||||
−0.645180 | + | 0.764030i | \(0.723218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.43223e19 | −0.662392 | −0.331196 | − | 0.943562i | \(-0.607452\pi\) | ||||
−0.331196 | + | 0.943562i | \(0.607452\pi\) | |||||||
\(74\) | 2.18738e18 | − | 2.20629e17i | 0.0516406 | − | 0.00520870i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.16150e18 | + | 1.66333e18i | −0.145622 | + | 0.0296781i | ||||
\(77\) | −1.24222e20 | −1.93217 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.60458e19i | − | 0.784804i | −0.919794 | − | 0.392402i | \(-0.871644\pi\) | ||
0.919794 | − | 0.392402i | \(-0.128356\pi\) | |||||||
\(80\) | 6.59936e19 | − | 2.80650e19i | 0.687159 | − | 0.292227i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.33173e19 | + | 4.36917e18i | −0.348029 | + | 0.0351037i | ||||
\(83\) | − | 1.15265e20i | − | 0.815416i | −0.913112 | − | 0.407708i | \(-0.866328\pi\) | ||
0.913112 | − | 0.407708i | \(-0.133672\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.79064e19i | 0.319027i | ||||||||
\(86\) | 2.70203e19 | + | 2.67888e20i | 0.131661 | + | 1.30533i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.24403e20 | − | 1.00909e20i | 1.24170 | − | 0.386244i | ||||
\(89\) | 3.32918e20i | 1.13173i | 0.824498 | + | 0.565864i | \(0.191457\pi\) | ||||
−0.824498 | + | 0.565864i | \(0.808543\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.76394e20 | 0.474841 | ||||||||
\(92\) | 1.98982e20 | − | 4.05530e19i | 0.477576 | − | 0.0973310i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.25949e19 | − | 3.23156e20i | −0.0624177 | − | 0.618828i | ||||
\(95\) | 6.47615e19 | 0.110973 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.05599e20 | −0.971527 | −0.485764 | − | 0.874090i | \(-0.661458\pi\) | ||||
−0.485764 | + | 0.874090i | \(0.661458\pi\) | |||||||
\(98\) | 9.80351e19 | + | 9.71950e20i | 0.121202 | + | 1.20163i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.33505e20 | − | 8.83493e19i | 0.433505 | − | 0.0883493i | ||||
\(101\) | −4.33813e20 | −0.390777 | −0.195388 | − | 0.980726i | \(-0.562597\pi\) | ||||
−0.195388 | + | 0.980726i | \(0.562597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.27275e21i | 0.933154i | 0.884480 | + | 0.466577i | \(0.154513\pi\) | ||||
−0.884480 | + | 0.466577i | \(0.845487\pi\) | |||||||
\(104\) | −4.60649e20 | + | 1.43290e20i | −0.305155 | + | 0.0949217i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.88204e19 | + | 4.84020e20i | 0.0264783 | + | 0.262514i | ||||
\(107\) | 8.28270e20i | 0.407045i | 0.979070 | + | 0.203522i | \(0.0652390\pi\) | ||||
−0.979070 | + | 0.203522i | \(0.934761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.48776e21i | 1.81573i | 0.419264 | + | 0.907865i | \(0.362288\pi\) | ||||
−0.419264 | + | 0.907865i | \(0.637712\pi\) | |||||||
\(110\) | −2.62816e21 | + | 2.65088e20i | −0.966116 | + | 0.0974467i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.91129e21 | − | 4.49432e21i | −0.581483 | − | 1.36733i | ||||
\(113\) | 5.07033e21i | 1.40512i | 0.711625 | + | 0.702559i | \(0.247959\pi\) | ||||
−0.711625 | + | 0.702559i | \(0.752041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.57893e21 | −0.363944 | ||||||||
\(116\) | −9.33364e20 | + | 1.90222e20i | −0.196446 | + | 0.0400360i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.51582e21 | + | 6.57215e20i | −1.14606 | + | 0.115597i | ||||
\(119\) | 3.94356e21 | 0.634813 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.11360e21 | −0.691004 | ||||||||
\(122\) | −5.92502e21 | + | 5.97624e20i | −0.734364 | + | 0.0740712i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.32744e21 | − | 1.63268e22i | −0.347683 | − | 1.70598i | ||||
\(125\) | −1.12150e22 | −1.07707 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.94148e22i | − | 1.57832i | −0.614189 | − | 0.789159i | \(-0.710517\pi\) | ||
0.614189 | − | 0.789159i | \(-0.289483\pi\) | |||||||
\(128\) | 8.64217e21 | + | 1.01842e22i | 0.647021 | + | 0.762472i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.73197e21 | − | 3.76423e20i | 0.237428 | − | 0.0239481i | ||||
\(131\) | 1.87459e22i | 1.10042i | 0.835027 | + | 0.550210i | \(0.185452\pi\) | ||||
−0.835027 | + | 0.550210i | \(0.814548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.41041e21i | − | 0.220819i | ||||||
\(134\) | −9.78875e20 | − | 9.70487e21i | −0.0453030 | − | 0.449148i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.02985e22 | + | 3.20348e21i | −0.407960 | + | 0.126900i | ||||
\(137\) | − | 2.45808e22i | − | 0.901634i | −0.892616 | − | 0.450817i | \(-0.851133\pi\) | ||
0.892616 | − | 0.450817i | \(-0.148867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.63179e22 | −1.14410 | −0.572052 | − | 0.820217i | \(-0.693852\pi\) | ||||
−0.572052 | + | 0.820217i | \(0.693852\pi\) | |||||||
\(140\) | 7.58305e21 | + | 3.72079e22i | 0.221564 | + | 1.08715i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.14373e21 | + | 5.09965e22i | 0.129494 | + | 1.28385i | ||||
\(143\) | 1.77695e22 | 0.415573 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.40625e21 | 0.149704 | ||||||||
\(146\) | 3.53476e21 | + | 3.50447e22i | 0.0664744 | + | 0.659048i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.35783e20 | − | 3.11961e21i | −0.0103648 | − | 0.0508572i | ||||
\(149\) | −1.21824e23 | −1.85045 | −0.925226 | − | 0.379417i | \(-0.876124\pi\) | ||||
−0.925226 | + | 0.379417i | \(0.876124\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.36202e23i | − | 1.79856i | −0.437377 | − | 0.899278i | \(-0.644092\pi\) | ||
0.437377 | − | 0.899278i | \(-0.355908\pi\) | |||||||
\(152\) | 3.58271e21 | + | 1.15177e22i | 0.0441422 | + | 0.141909i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.80531e22 | + | 1.78984e23i | 0.193903 | + | 1.92241i | ||||
\(155\) | 1.29553e23i | 1.30007i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.33706e23i | 1.17275i | 0.810041 | + | 0.586374i | \(0.199445\pi\) | ||||
−0.810041 | + | 0.586374i | \(0.800555\pi\) | |||||||
\(158\) | −9.51617e22 | + | 9.59843e21i | −0.780842 | + | 0.0787591i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.00281e22 | − | 9.10078e22i | −0.359711 | − | 0.654363i | ||||
\(161\) | 1.07528e23i | 0.724189i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.99703e23 | 1.18145 | 0.590725 | − | 0.806873i | \(-0.298842\pi\) | ||||
0.590725 | + | 0.806873i | \(0.298842\pi\) | |||||||
\(164\) | 1.25906e22 | + | 6.17785e22i | 0.0698531 | + | 0.342749i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.66079e23 | + | 1.67515e22i | −0.811299 | + | 0.0818312i | ||||
\(167\) | 3.55809e23 | 1.63190 | 0.815950 | − | 0.578122i | \(-0.196214\pi\) | ||||
0.815950 | + | 0.578122i | \(0.196214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.21832e23 | 0.897871 | ||||||||
\(170\) | 8.34341e22 | − | 8.41553e21i | 0.317417 | − | 0.0320161i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.82058e23 | − | 7.78642e22i | 1.28552 | − | 0.261993i | ||||
\(173\) | −1.00471e22 | −0.0318095 | −0.0159048 | − | 0.999874i | \(-0.505063\pi\) | ||||
−0.0159048 | + | 0.999874i | \(0.505063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34263e23i | 0.657361i | ||||||||
\(176\) | −1.92540e23 | − | 4.52749e23i | −0.508905 | − | 1.19667i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.79683e23 | − | 4.83829e22i | 1.12602 | − | 0.113575i | ||||
\(179\) | − | 5.41545e23i | − | 1.19861i | −0.800521 | − | 0.599304i | \(-0.795444\pi\) | ||
0.800521 | − | 0.599304i | \(-0.204556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.99303e23i | − | 0.392544i | −0.980549 | − | 0.196272i | \(-0.937116\pi\) | ||
0.980549 | − | 0.196272i | \(-0.0628836\pi\) | |||||||
\(182\) | −2.56352e22 | − | 2.54156e23i | −0.0476527 | − | 0.472444i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.73486e22 | − | 2.80809e23i | −0.144767 | − | 0.465397i | ||||
\(185\) | 2.47541e22i | 0.0387565i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.97267e23 | 0.555578 | ||||||||
\(188\) | −4.60880e23 | + | 9.39284e22i | −0.609440 | + | 0.124205i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.41178e21 | − | 9.33112e22i | −0.0111368 | − | 0.110413i | ||||
\(191\) | 5.97999e23 | 0.669653 | 0.334827 | − | 0.942280i | \(-0.391322\pi\) | ||||
0.334827 | + | 0.942280i | \(0.391322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.77346e23 | −0.780301 | −0.390151 | − | 0.920751i | \(-0.627577\pi\) | ||||
−0.390151 | + | 0.920751i | \(0.627577\pi\) | |||||||
\(194\) | 1.02545e23 | + | 1.01666e24i | 0.0974978 | + | 0.966623i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.38618e24 | − | 2.82507e23i | 1.18340 | − | 0.241179i | ||||
\(197\) | −6.47549e23 | −0.524056 | −0.262028 | − | 0.965060i | \(-0.584391\pi\) | ||||
−0.262028 | + | 0.965060i | \(0.584391\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.53895e24i | 1.84798i | 0.382421 | + | 0.923988i | \(0.375090\pi\) | ||||
−0.382421 | + | 0.923988i | \(0.624910\pi\) | |||||||
\(200\) | −1.90299e23 | − | 6.11773e23i | −0.131408 | − | 0.422450i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.30460e22 | + | 6.25057e23i | 0.0392165 | + | 0.388804i | ||||
\(203\) | − | 5.04383e23i | − | 0.297887i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4.90212e23i | − | 0.261197i | ||||||
\(206\) | 1.83384e24 | − | 1.84969e23i | 0.928444 | − | 0.0936469i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.73404e23 | + | 6.42899e23i | 0.125066 | + | 0.294088i | ||||
\(209\) | − | 4.44296e23i | − | 0.193257i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.63403e24 | 0.643125 | 0.321563 | − | 0.946888i | \(-0.395792\pi\) | ||||
0.321563 | + | 0.946888i | \(0.395792\pi\) | |||||||
\(212\) | 6.90303e23 | − | 1.40685e23i | 0.258531 | − | 0.0526892i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.19341e24 | − | 1.20372e23i | 0.404990 | − | 0.0408490i | ||||
\(215\) | −3.03163e24 | −0.979653 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.82289e24 | 2.58692 | ||||||||
\(218\) | 6.46616e24 | − | 6.52205e23i | 1.80656 | − | 0.182218i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.63901e23 | + | 3.74825e24i | 0.193910 | + | 0.951459i | ||||
\(221\) | −5.64115e23 | −0.136536 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.60866e24i | 1.23497i | 0.786581 | + | 0.617487i | \(0.211849\pi\) | ||||
−0.786581 | + | 0.617487i | \(0.788151\pi\) | |||||||
\(224\) | −6.19784e24 | + | 3.40703e24i | −1.30208 | + | 0.715767i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.30556e24 | − | 7.36871e23i | 1.39802 | − | 0.141011i | ||||
\(227\) | 1.04509e25i | 1.90934i | 0.297668 | + | 0.954670i | \(0.403791\pi\) | ||||
−0.297668 | + | 0.954670i | \(0.596209\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.63833e24i | − | 1.60594i | −0.596019 | − | 0.802970i | \(-0.703252\pi\) | ||
0.596019 | − | 0.802970i | \(-0.296748\pi\) | |||||||
\(230\) | 2.29465e23 | + | 2.27498e24i | 0.0365236 | + | 0.362106i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.09725e23 | + | 1.31719e24i | 0.0595483 | + | 0.191436i | ||||
\(233\) | 5.20857e24i | 0.723572i | 0.932261 | + | 0.361786i | \(0.117833\pi\) | ||||
−0.932261 | + | 0.361786i | \(0.882167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.65709e24 | 0.464433 | ||||||||
\(236\) | 1.89389e24 | + | 9.29277e24i | 0.230027 | + | 1.12868i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.73117e23 | − | 5.68206e24i | −0.0637067 | − | 0.631608i | ||||
\(239\) | −3.45429e24 | −0.367436 | −0.183718 | − | 0.982979i | \(-0.558813\pi\) | ||||
−0.183718 | + | 0.982979i | \(0.558813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.19485e24 | 0.213908 | 0.106954 | − | 0.994264i | \(-0.465890\pi\) | ||||
0.106954 | + | 0.994264i | \(0.465890\pi\) | |||||||
\(242\) | 7.43159e23 | + | 7.36790e24i | 0.0693458 | + | 0.687515i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.72216e24 | + | 8.45018e24i | 0.147395 | + | 0.723224i | ||||
\(245\) | −1.09994e25 | −0.901827 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.30896e23i | 0.0474941i | ||||||||
\(248\) | −2.30408e25 | + | 7.16710e24i | −1.66248 | + | 0.517131i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.62988e24 | + | 1.61591e25i | 0.108090 | + | 1.07164i | ||||
\(251\) | 9.76703e24i | 0.621138i | 0.950551 | + | 0.310569i | \(0.100520\pi\) | ||||
−0.950551 | + | 0.310569i | \(0.899480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.08322e25i | 0.633799i | ||||||||
\(254\) | −2.79737e25 | + | 2.82155e24i | −1.57035 | + | 0.158392i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.34179e25 | − | 1.39321e25i | 0.693691 | − | 0.720273i | ||||
\(257\) | 1.72645e25i | 0.856755i | 0.903600 | + | 0.428378i | \(0.140915\pi\) | ||||
−0.903600 | + | 0.428378i | \(0.859085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68581e24 | 0.0771191 | ||||||||
\(260\) | −1.08473e24 | − | 5.32248e24i | −0.0476543 | − | 0.233826i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.70099e25 | − | 2.72434e24i | 1.09486 | − | 0.110433i | ||||
\(263\) | 2.33601e25 | 0.909785 | 0.454893 | − | 0.890546i | \(-0.349678\pi\) | ||||
0.454893 | + | 0.890546i | \(0.349678\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.47756e24 | −0.197018 | ||||||||
\(266\) | −6.35471e24 | + | 6.40964e23i | −0.219704 | + | 0.0221603i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.38409e25 | + | 2.82081e24i | −0.442334 | + | 0.0901486i | ||||
\(269\) | 4.42164e25 | 1.35889 | 0.679445 | − | 0.733726i | \(-0.262221\pi\) | ||||
0.679445 | + | 0.733726i | \(0.262221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.41966e25i | − | 0.403652i | −0.979421 | − | 0.201826i | \(-0.935313\pi\) | ||
0.979421 | − | 0.201826i | \(-0.0646875\pi\) | |||||||
\(272\) | 6.11239e24 | + | 1.43730e25i | 0.167201 | + | 0.393165i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.54171e25 | + | 3.57233e24i | −0.897082 | + | 0.0904837i | ||||
\(275\) | 2.35992e25i | 0.575312i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.72266e25i | 0.389191i | 0.980884 | + | 0.194596i | \(0.0623394\pi\) | ||||
−0.980884 | + | 0.194596i | \(0.937661\pi\) | |||||||
\(278\) | 5.27808e24 | + | 5.23284e25i | 0.114817 | + | 1.13833i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.25087e25 | − | 1.63334e25i | 1.05943 | − | 0.329547i | ||||
\(281\) | 8.21760e25i | 1.59709i | 0.601937 | + | 0.798544i | \(0.294396\pi\) | ||||
−0.601937 | + | 0.798544i | \(0.705604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.40601e25 | 1.33606 | 0.668031 | − | 0.744133i | \(-0.267137\pi\) | ||||
0.668031 | + | 0.744133i | \(0.267137\pi\) | |||||||
\(284\) | 7.27305e25 | − | 1.48226e25i | 1.26437 | − | 0.257681i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.58244e24 | − | 2.56031e25i | −0.0417050 | − | 0.413476i | ||||
\(287\) | −3.33846e25 | −0.519740 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.64802e25 | 0.817465 | ||||||||
\(290\) | −1.07635e24 | − | 1.06712e25i | −0.0150236 | − | 0.148949i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.99802e25 | − | 1.01861e25i | 0.649049 | − | 0.132278i | ||||
\(293\) | −1.43600e26 | −1.79905 | −0.899526 | − | 0.436868i | \(-0.856088\pi\) | ||||
−0.899526 | + | 0.436868i | \(0.856088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.37382e25i | − | 0.860124i | ||||||
\(296\) | −4.40247e24 | + | 1.36944e24i | −0.0495603 | + | 0.0154163i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.77047e25 | + | 1.75530e26i | 0.185702 | + | 1.84111i | ||||
\(299\) | − | 1.53816e25i | − | 0.155760i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.06461e26i | 1.94935i | ||||||||
\(302\) | −1.96245e26 | + | 1.97942e25i | −1.78948 | + | 0.180495i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.60745e25 | − | 6.83599e24i | 0.136762 | − | 0.0581606i | ||||
\(305\) | − | 6.70522e25i | − | 0.551143i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.33744e25 | 0.486363 | 0.243182 | − | 0.969981i | \(-0.421809\pi\) | ||||
0.243182 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(308\) | 2.55264e26 | − | 5.20235e25i | 1.89325 | − | 0.385848i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.86666e26 | − | 1.88280e25i | 1.29350 | − | 0.130469i | ||||
\(311\) | −1.41945e26 | −0.950904 | −0.475452 | − | 0.879742i | \(-0.657715\pi\) | ||||
−0.475452 | + | 0.879742i | \(0.657715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.07188e25 | 0.129763 | 0.0648814 | − | 0.997893i | \(-0.479333\pi\) | ||||
0.0648814 | + | 0.997893i | \(0.479333\pi\) | |||||||
\(314\) | 1.92649e26 | − | 1.94315e25i | 1.16683 | − | 0.117691i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.76597e25 | + | 1.35718e26i | 0.156723 | + | 0.768996i | ||||
\(317\) | −3.12103e23 | −0.00171071 | −0.000855355 | − | 1.00000i | \(-0.500272\pi\) | ||||
−0.000855355 | 1.00000i | \(0.500272\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.08105e25i | − | 0.260706i | ||||||
\(320\) | −1.23858e26 | + | 8.53088e25i | −0.614961 | + | 0.423564i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.54932e26 | − | 1.56271e25i | 0.720533 | − | 0.0726761i | ||||
\(323\) | 1.41047e25i | 0.0634946i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.35106e25i | − | 0.141386i | ||||||
\(326\) | −2.90228e25 | − | 2.87741e26i | −0.118565 | − | 1.17549i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.71833e25 | − | 2.71193e25i | 0.334009 | − | 0.103897i | ||||
\(329\) | − | 2.49056e26i | − | 0.924146i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.11279e26 | −0.735636 | −0.367818 | − | 0.929898i | \(-0.619895\pi\) | ||||
−0.367818 | + | 0.929898i | \(0.619895\pi\) | |||||||
\(332\) | 4.82726e25 | + | 2.36860e26i | 0.162836 | + | 0.798991i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.17096e25 | − | 5.12665e26i | −0.163770 | − | 1.62366i | ||||
\(335\) | 1.09828e26 | 0.337087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.56530e25 | −0.0451320 | −0.0225660 | − | 0.999745i | \(-0.507184\pi\) | ||||
−0.0225660 | + | 0.999745i | \(0.507184\pi\) | |||||||
\(338\) | −3.22388e25 | − | 3.19625e26i | −0.0901060 | − | 0.893338i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.42509e25 | − | 1.18993e26i | −0.0637089 | − | 0.312601i | ||||
\(341\) | 8.88801e26 | 2.26404 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.28840e26i | 0.308647i | ||||||||
\(344\) | −1.67715e26 | − | 5.39170e26i | −0.389679 | − | 1.25274i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.46014e24 | + | 1.44763e25i | 0.00319225 | + | 0.0316489i | ||||
\(347\) | 1.30011e26i | 0.275753i | 0.990449 | + | 0.137877i | \(0.0440277\pi\) | ||||
−0.990449 | + | 0.137877i | \(0.955972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.13554e26i | − | 0.426424i | −0.977006 | − | 0.213212i | \(-0.931608\pi\) | ||
0.977006 | − | 0.213212i | \(-0.0683924\pi\) | |||||||
\(350\) | 3.37536e26 | − | 3.40454e25i | 0.654042 | − | 0.0659696i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.24359e26 | + | 3.43217e26i | −1.13956 | + | 0.626428i | ||||
\(353\) | 5.09456e26i | 0.902553i | 0.892384 | + | 0.451276i | \(0.149031\pi\) | ||||
−0.892384 | + | 0.451276i | \(0.850969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.77117e26 | −0.963532 | ||||||||
\(356\) | −1.39425e26 | − | 6.84117e26i | −0.226003 | − | 1.10893i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.80281e26 | + | 7.87026e25i | −1.19256 | + | 0.120287i | ||||
\(359\) | 7.36779e25 | 0.109357 | 0.0546784 | − | 0.998504i | \(-0.482587\pi\) | ||||
0.0546784 | + | 0.998504i | \(0.482587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.98435e26 | −0.977913 | ||||||||
\(362\) | −2.87164e26 | + | 2.89647e25i | −0.390563 | + | 0.0393939i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.62473e26 | + | 7.38728e25i | −0.465276 | + | 0.0948244i | ||||
\(365\) | −3.96593e26 | −0.494618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.97792e26i | 0.586211i | 0.956080 | + | 0.293106i | \(0.0946888\pi\) | ||||
−0.956080 | + | 0.293106i | \(0.905311\pi\) | |||||||
\(368\) | −3.91907e26 | + | 1.66666e26i | −0.448520 | + | 0.190741i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.56668e25 | − | 3.59751e24i | 0.0385608 | − | 0.00388941i | ||||
\(371\) | 3.73034e26i | 0.392033i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.55131e27i | − | 1.54083i | −0.637541 | − | 0.770417i | \(-0.720048\pi\) | ||
0.637541 | − | 0.770417i | \(-0.279952\pi\) | |||||||
\(374\) | −5.77347e25 | − | 5.72399e26i | −0.0557552 | − | 0.552774i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.02316e26 | + | 6.50406e26i | 0.184739 | + | 0.593899i | ||||
\(377\) | 7.21504e25i | 0.0640700i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.10808e27 | −0.930807 | −0.465404 | − | 0.885099i | \(-0.654091\pi\) | ||||
−0.465404 | + | 0.885099i | \(0.654091\pi\) | |||||||
\(380\) | −1.33079e26 | + | 2.71218e25i | −0.108738 | + | 0.0221611i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.69071e25 | − | 8.61623e26i | −0.0672032 | − | 0.666273i | ||||
\(383\) | −1.00156e27 | −0.753512 | −0.376756 | − | 0.926313i | \(-0.622960\pi\) | ||||
−0.376756 | + | 0.926313i | \(0.622960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.02552e27 | −1.44278 | ||||||||
\(386\) | 1.12972e26 | + | 1.12003e27i | 0.0783073 | + | 0.776362i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.44994e27 | − | 2.95502e26i | 0.951958 | − | 0.194011i | ||||
\(389\) | −2.07322e26 | −0.132487 | −0.0662437 | − | 0.997803i | \(-0.521101\pi\) | ||||
−0.0662437 | + | 0.997803i | \(0.521101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.43881e26i | − | 0.208234i | ||||||
\(392\) | −6.08502e26 | − | 1.95621e27i | −0.358722 | − | 1.15322i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.41082e25 | + | 9.33017e26i | 0.0525917 | + | 0.521410i | ||||
\(395\) | − | 1.07693e27i | − | 0.586025i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.03012e27i | − | 1.56372i | −0.623452 | − | 0.781862i | \(-0.714270\pi\) | ||
0.623452 | − | 0.781862i | \(-0.285730\pi\) | |||||||
\(398\) | 3.65823e27 | − | 3.68985e26i | 1.83865 | − | 0.185454i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.53814e26 | + | 3.63100e26i | −0.407130 | + | 0.173139i | ||||
\(401\) | 2.85606e27i | 1.32663i | 0.748338 | + | 0.663317i | \(0.230852\pi\) | ||||
−0.748338 | + | 0.663317i | \(0.769148\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.26209e27 | −0.556399 | ||||||||
\(404\) | 8.91448e26 | − | 1.81679e26i | 0.382905 | − | 0.0780370i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.26737e26 | + | 7.33019e25i | −0.296383 | + | 0.0298945i | ||||
\(407\) | 1.69826e26 | 0.0674935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.73951e27 | −1.03414 | −0.517068 | − | 0.855944i | \(-0.672977\pi\) | ||||
−0.517068 | + | 0.855944i | \(0.672977\pi\) | |||||||
\(410\) | −7.06319e26 | + | 7.12425e25i | −0.259879 | + | 0.0262125i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.33023e26 | − | 2.61539e27i | −0.186348 | − | 0.914359i | ||||
\(413\) | −5.02174e27 | −1.71151 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.87949e27i | − | 0.608883i | ||||||
\(416\) | 8.86583e26 | − | 4.87365e26i | 0.280053 | − | 0.153948i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.40161e26 | + | 6.45695e25i | −0.192282 | + | 0.0193944i | ||||
\(419\) | 3.99947e27i | 1.17153i | 0.810479 | + | 0.585767i | \(0.199207\pi\) | ||||
−0.810479 | + | 0.585767i | \(0.800793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.93177e27i | 1.65281i | 0.563078 | + | 0.826404i | \(0.309617\pi\) | ||||
−0.563078 | + | 0.826404i | \(0.690383\pi\) | |||||||
\(422\) | −2.37474e26 | − | 2.35439e27i | −0.0645409 | − | 0.639878i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.03027e26 | − | 9.74173e26i | −0.0783682 | − | 0.251939i | ||||
\(425\) | − | 7.49183e26i | − | 0.189018i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.56641e27 | −1.09669 | ||||||||
\(428\) | −3.46875e26 | − | 1.70202e27i | −0.0812857 | − | 0.398846i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.40586e26 | + | 4.36811e27i | 0.0983133 | + | 0.974707i | ||||
\(431\) | 6.64122e27 | 1.44623 | 0.723114 | − | 0.690729i | \(-0.242710\pi\) | ||||
0.723114 | + | 0.690729i | \(0.242710\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.26150e27 | −0.261677 | −0.130838 | − | 0.991404i | \(-0.541767\pi\) | ||||
−0.130838 | + | 0.991404i | \(0.541767\pi\) | |||||||
\(434\) | −1.28223e27 | − | 1.27124e28i | −0.259611 | − | 2.57386i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.87945e27 | − | 9.22194e27i | −0.362596 | − | 1.77916i | ||||
\(437\) | −3.84590e26 | −0.0724341 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.22822e27i | 0.220495i | 0.993904 | + | 0.110247i | \(0.0351643\pi\) | ||||
−0.993904 | + | 0.110247i | \(0.964836\pi\) | |||||||
\(440\) | 5.28962e27 | − | 1.64539e27i | 0.927196 | − | 0.288414i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.19827e25 | + | 8.12801e26i | 0.0137021 | + | 0.135847i | ||||
\(443\) | 4.92335e27i | 0.803566i | 0.915735 | + | 0.401783i | \(0.131609\pi\) | ||||
−0.915735 | + | 0.401783i | \(0.868391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.42847e27i | 0.845079i | ||||||||
\(446\) | 8.08120e27 | − | 8.15106e26i | 1.22874 | − | 0.123936i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.80973e27 | + | 8.43498e27i | 0.842824 | + | 1.22367i | ||||
\(449\) | − | 5.33955e27i | − | 0.756690i | −0.925665 | − | 0.378345i | \(-0.876493\pi\) | ||
0.925665 | − | 0.378345i | \(-0.123507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.36310e27 | −0.454869 | ||||||||
\(452\) | −2.12343e27 | − | 1.04191e28i | −0.280598 | − | 1.37682i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.50581e28 | − | 1.51883e27i | 1.89970 | − | 0.191612i | ||||
\(455\) | 2.87622e27 | 0.354571 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.93225e26 | −0.0816120 | −0.0408060 | − | 0.999167i | \(-0.512993\pi\) | ||||
−0.0408060 | + | 0.999167i | \(0.512993\pi\) | |||||||
\(458\) | −1.38873e28 | + | 1.40074e27i | −1.59783 | + | 0.161164i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.24455e27 | − | 6.61246e26i | 0.356613 | − | 0.0726785i | ||||
\(461\) | 5.45652e27 | 0.586214 | 0.293107 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293107 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.88783e27i | − | 0.399123i | −0.979885 | − | 0.199561i | \(-0.936048\pi\) | ||
0.979885 | − | 0.199561i | \(-0.0639518\pi\) | |||||||
\(464\) | 1.83832e27 | − | 7.81777e26i | 0.184494 | − | 0.0784592i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.50474e27 | − | 7.56961e26i | 0.719919 | − | 0.0726142i | ||||
\(467\) | 7.16230e27i | 0.671777i | 0.941902 | + | 0.335888i | \(0.109037\pi\) | ||||
−0.941902 | + | 0.335888i | \(0.890963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.47953e27i | − | 0.670749i | ||||||
\(470\) | −5.31484e26 | − | 5.26929e27i | −0.0466082 | − | 0.462088i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.31142e28 | − | 4.07931e27i | 1.09989 | − | 0.342134i | ||||
\(473\) | 2.07985e28i | 1.70604i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.37873e26 | −0.0657499 | ||||||||
\(476\) | −8.10367e27 | + | 1.65154e27i | −0.622026 | + | 0.126770i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.02012e26 | + | 4.97710e27i | 0.0368741 | + | 0.365581i | ||||
\(479\) | −1.15399e28 | −0.829237 | −0.414618 | − | 0.909995i | \(-0.636085\pi\) | ||||
−0.414618 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.41151e26 | −0.0165869 | ||||||||
\(482\) | −3.18978e26 | − | 3.16244e27i | −0.0214668 | − | 0.212828i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.05080e28 | − | 2.14155e27i | 0.677085 | − | 0.137991i | ||||
\(485\) | −1.15053e28 | −0.725454 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.47074e28i | − | 0.888143i | −0.895991 | − | 0.444071i | \(-0.853534\pi\) | ||
0.895991 | − | 0.444071i | \(-0.146466\pi\) | |||||||
\(488\) | 1.19251e28 | − | 3.70943e27i | 0.704781 | − | 0.219230i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.59853e27 | + | 1.58483e28i | 0.0905030 | + | 0.897274i | ||||
\(491\) | 2.27891e28i | 1.26291i | 0.775413 | + | 0.631454i | \(0.217542\pi\) | ||||
−0.775413 | + | 0.631454i | \(0.782458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.61304e27i | 0.0856549i | ||||||||
\(494\) | 9.09022e26 | − | 9.16880e25i | 0.0472543 | − | 0.00476628i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.36752e28 | + | 3.21566e28i | 0.681359 | + | 1.60219i | ||||
\(497\) | 3.93030e28i | 1.91727i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.62317e28 | 1.22679 | 0.613395 | − | 0.789776i | \(-0.289803\pi\) | ||||
0.613395 | + | 0.789776i | \(0.289803\pi\) | |||||||
\(500\) | 2.30459e28 | − | 4.69680e27i | 1.05538 | − | 0.215089i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.40728e28 | − | 1.41944e27i | 0.618003 | − | 0.0623345i | ||||
\(503\) | −3.85150e28 | −1.65640 | −0.828202 | − | 0.560430i | \(-0.810636\pi\) | ||||
−0.828202 | + | 0.560430i | \(0.810636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.07364e27 | −0.291799 | ||||||||
\(506\) | 1.56075e28 | − | 1.57424e27i | 0.630599 | − | 0.0636050i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.13084e27 | + | 3.98957e28i | 0.315186 | + | 1.54653i | ||||
\(509\) | 1.78188e28 | 0.676614 | 0.338307 | − | 0.941036i | \(-0.390146\pi\) | ||||
0.338307 | + | 0.941036i | \(0.390146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.70089e28i | 0.984209i | ||||||||
\(512\) | −2.20240e28 | − | 1.73084e28i | −0.786252 | − | 0.617906i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.48755e28 | − | 2.50905e27i | 0.852430 | − | 0.0859798i | ||||
\(515\) | 2.07532e28i | 0.696801i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.50894e28i | − | 0.808798i | ||||||
\(518\) | −2.44999e26 | − | 2.42899e27i | −0.00773930 | − | 0.0767298i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.51121e27 | + | 2.33644e27i | −0.227864 | + | 0.0708794i | ||||
\(521\) | 5.09896e28i | 1.51595i | 0.652283 | + | 0.757976i | \(0.273812\pi\) | ||||
−0.652283 | + | 0.757976i | \(0.726188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.90651e28 | −0.830050 | −0.415025 | − | 0.909810i | \(-0.636227\pi\) | ||||
−0.415025 | + | 0.909810i | \(0.636227\pi\) | |||||||
\(524\) | −7.85070e27 | − | 3.85212e28i | −0.219751 | − | 1.07825i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.39492e27 | − | 3.36582e28i | −0.0913017 | − | 0.905193i | ||||
\(527\) | −2.82160e28 | −0.743848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.00950e28 | −0.762448 | ||||||||
\(530\) | 7.96052e26 | + | 7.89230e27i | 0.0197717 | + | 0.196023i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.84706e27 | + | 9.06299e27i | 0.0440969 | + | 0.216371i | ||||
\(533\) | 4.77557e27 | 0.111786 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.35055e28i | 0.303946i | ||||||||
\(536\) | 6.07585e27 | + | 1.95327e28i | 0.134084 | + | 0.431054i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.42596e27 | − | 6.37089e28i | −0.136372 | − | 1.35203i | ||||
\(539\) | 7.54610e28i | 1.57051i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.69364e28i | − | 0.339040i | −0.985527 | − | 0.169520i | \(-0.945778\pi\) | ||
0.985527 | − | 0.169520i | \(-0.0542217\pi\) | |||||||
\(542\) | −2.04551e28 | + | 2.06319e27i | −0.401614 | + | 0.0405085i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.98210e28 | − | 1.08958e28i | 0.374401 | − | 0.205813i | ||||
\(545\) | 7.31761e28i | 1.35583i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.12464e28 | −1.09198 | −0.545989 | − | 0.837793i | \(-0.683846\pi\) | ||||
−0.545989 | + | 0.837793i | \(0.683846\pi\) | |||||||
\(548\) | 1.02943e28 | + | 5.05114e28i | 0.180054 | + | 0.883473i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.40027e28 | − | 3.42966e27i | 0.572408 | − | 0.0577356i | ||||
\(551\) | 1.80399e27 | 0.0297950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.33411e28 | −1.16609 | ||||||||
\(554\) | 2.48209e28 | − | 2.50354e27i | 0.387226 | − | 0.0390573i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.46301e28 | − | 1.52098e28i | 1.12106 | − | 0.228474i | ||||
\(557\) | 2.20360e28 | 0.324828 | 0.162414 | − | 0.986723i | \(-0.448072\pi\) | ||||
0.162414 | + | 0.986723i | \(0.448072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.95336e28i | − | 0.419269i | ||||||
\(560\) | −3.11650e28 | − | 7.32831e28i | −0.434203 | − | 1.02101i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.18403e29 | − | 1.19426e28i | 1.58902 | − | 0.160276i | ||||
\(563\) | 1.16331e29i | 1.53235i | 0.642630 | + | 0.766177i | \(0.277843\pi\) | ||||
−0.642630 | + | 0.766177i | \(0.722157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.26754e28i | 1.04922i | ||||||||
\(566\) | −1.07631e28 | − | 1.06709e29i | −0.134081 | − | 1.32932i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.19270e28 | − | 1.02639e29i | −0.383266 | − | 1.23213i | ||||
\(569\) | − | 1.25615e29i | − | 1.48035i | −0.672415 | − | 0.740174i | \(-0.734743\pi\) | ||
0.672415 | − | 0.740174i | \(-0.265257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.01329e28 | −0.683019 | −0.341510 | − | 0.939878i | \(-0.610938\pi\) | ||||
−0.341510 | + | 0.939878i | \(0.610938\pi\) | |||||||
\(572\) | −3.65148e28 | + | 7.44180e27i | −0.407203 | + | 0.0829888i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.85178e27 | + | 4.81020e28i | 0.0521586 | + | 0.517116i | ||||
\(575\) | 2.04279e28 | 0.215631 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.21390e29 | 1.23548 | 0.617742 | − | 0.786381i | \(-0.288048\pi\) | ||||
0.617742 | + | 0.786381i | \(0.288048\pi\) | |||||||
\(578\) | −8.20826e27 | − | 8.13792e28i | −0.0820369 | − | 0.813338i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.52192e28 | + | 3.10170e27i | −0.146689 | + | 0.0298955i | ||||
\(581\) | −1.27997e29 | −1.21158 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.75787e28i | 0.343101i | ||||||||
\(584\) | −2.19401e28 | − | 7.05333e28i | −0.196745 | − | 0.632498i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.08693e28 | + | 2.06905e29i | 0.180544 | + | 1.78997i | ||||
\(587\) | − | 2.68343e28i | − | 0.228029i | −0.993479 | − | 0.114014i | \(-0.963629\pi\) | ||
0.993479 | − | 0.114014i | \(-0.0363710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.15563e28i | 0.258747i | ||||||||
\(590\) | −1.06245e29 | + | 1.07164e28i | −0.855782 | + | 0.0863179i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.61296e27 | + | 6.14426e27i | 0.0203121 | + | 0.0477630i | ||||
\(593\) | 1.49316e29i | 1.14033i | 0.821529 | + | 0.570167i | \(0.193122\pi\) | ||||
−0.821529 | + | 0.570167i | \(0.806878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.43026e28 | 0.474024 | ||||||||
\(596\) | 2.50338e29 | − | 5.10194e28i | 1.81318 | − | 0.369530i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.21625e28 | + | 2.23541e27i | −0.154973 | + | 0.0156313i | ||||
\(599\) | 7.15442e27 | 0.0491578 | 0.0245789 | − | 0.999698i | \(-0.492176\pi\) | ||||
0.0245789 | + | 0.999698i | \(0.492176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.36815e29 | −1.57118 | −0.785591 | − | 0.618746i | \(-0.787641\pi\) | ||||
−0.785591 | + | 0.618746i | \(0.787641\pi\) | |||||||
\(602\) | 2.97478e29 | − | 3.00049e28i | 1.93951 | − | 0.195627i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.70406e28 | + | 2.79882e29i | 0.359167 | + | 1.76233i | ||||
\(605\) | −8.33809e28 | −0.515983 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.40146e28i | − | 0.263097i | −0.991310 | − | 0.131548i | \(-0.958005\pi\) | ||
0.991310 | − | 0.131548i | \(-0.0419949\pi\) | |||||||
\(608\) | −1.21857e28 | − | 2.21674e28i | −0.0715918 | − | 0.130235i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.66117e28 | + | 9.74468e27i | −0.548361 | + | 0.0553101i | ||||
\(611\) | 3.56267e28i | 0.198767i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.86148e29i | − | 1.00351i | −0.865009 | − | 0.501757i | \(-0.832687\pi\) | ||
0.865009 | − | 0.501757i | \(-0.167313\pi\) | |||||||
\(614\) | −9.21019e27 | − | 9.13126e28i | −0.0488091 | − | 0.483908i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.12055e29 | − | 3.60236e29i | −0.573898 | − | 1.84497i | ||||
\(617\) | − | 1.09610e29i | − | 0.551896i | −0.961173 | − | 0.275948i | \(-0.911008\pi\) | ||
0.961173 | − | 0.275948i | \(-0.0889918\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.29036e29 | 0.627999 | 0.314000 | − | 0.949423i | \(-0.398331\pi\) | ||||
0.314000 | + | 0.949423i | \(0.398331\pi\) | |||||||
\(620\) | −5.42564e28 | − | 2.66221e29i | −0.259620 | − | 1.27388i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.06289e28 | + | 2.04521e29i | 0.0954282 | + | 0.946104i | ||||
\(623\) | 3.69691e29 | 1.68157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.22755e28 | −0.361851 | ||||||||
\(626\) | −3.01107e27 | − | 2.98526e28i | −0.0130224 | − | 0.129108i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.59954e28 | − | 2.74754e29i | −0.234194 | − | 1.14913i | ||||
\(629\) | −5.39131e27 | −0.0221749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.81005e29i | − | 1.91356i | −0.290820 | − | 0.956778i | \(-0.593928\pi\) | ||
0.290820 | − | 0.956778i | \(-0.406072\pi\) | |||||||
\(632\) | 1.91529e29 | − | 5.95772e28i | 0.749386 | − | 0.233105i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.53579e25 | + | 4.49692e26i | 0.000171679 | + | 0.00170207i | ||||
\(635\) | − | 3.16573e29i | − | 1.17855i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.07154e29i | − | 0.385961i | ||||||
\(638\) | −7.32100e28 | + | 7.38429e27i | −0.259390 | + | 0.0261632i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.40917e29 | + | 1.66061e29i | 0.483140 | + | 0.569350i | ||||
\(641\) | − | 2.63338e29i | − | 0.888185i | −0.895981 | − | 0.444093i | \(-0.853526\pi\) | ||
0.895981 | − | 0.444093i | \(-0.146474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.17468e29 | −1.36272 | −0.681362 | − | 0.731947i | \(-0.738612\pi\) | ||||
−0.681362 | + | 0.731947i | \(0.738612\pi\) | |||||||
\(644\) | −4.50324e28 | − | 2.20961e29i | −0.144618 | − | 0.709602i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.03227e28 | − | 2.04983e27i | 0.0631741 | − | 0.00637202i | ||||
\(647\) | 1.80457e29 | 0.551922 | 0.275961 | − | 0.961169i | \(-0.411004\pi\) | ||||
0.275961 | + | 0.961169i | \(0.411004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.05880e29 | −1.49789 | ||||||||
\(650\) | −4.82835e28 | + | 4.87009e27i | −0.140672 | + | 0.0141888i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.10372e29 | + | 8.36348e28i | −1.15765 | + | 0.235932i | ||||
\(653\) | −1.58788e29 | −0.440788 | −0.220394 | − | 0.975411i | \(-0.570734\pi\) | ||||
−0.220394 | + | 0.975411i | \(0.570734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.05666e29i | 0.821700i | ||||||||
\(656\) | −5.17450e28 | − | 1.21676e29i | −0.136892 | − | 0.321896i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.58851e29 | + | 3.61953e28i | −0.919480 | + | 0.0927428i | ||||
\(659\) | − | 3.19695e29i | − | 0.806193i | −0.915157 | − | 0.403097i | \(-0.867934\pi\) | ||
0.915157 | − | 0.403097i | \(-0.132066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.08534e29i | 0.509404i | 0.967020 | + | 0.254702i | \(0.0819774\pi\) | ||||
−0.967020 | + | 0.254702i | \(0.918023\pi\) | |||||||
\(662\) | 3.07052e28 | + | 3.04421e29i | 0.0738249 | + | 0.731923i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.34263e29 | − | 1.03976e29i | 0.778616 | − | 0.242197i | ||||
\(665\) | − | 7.19149e28i | − | 0.164889i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.39825e28 | −0.0977144 | ||||||||
\(668\) | −7.31155e29 | + | 1.49011e29i | −1.59903 | + | 0.325886i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.59613e28 | − | 1.58245e29i | −0.0338284 | − | 0.335385i | ||||
\(671\) | −4.60011e29 | −0.959803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.94384e28 | −0.0999784 | −0.0499892 | − | 0.998750i | \(-0.515919\pi\) | ||||
−0.0499892 | + | 0.998750i | \(0.515919\pi\) | |||||||
\(674\) | 2.27485e27 | + | 2.25536e28i | 0.00452923 | + | 0.0449041i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.55845e29 | + | 9.29022e28i | −0.879785 | + | 0.179302i | ||||
\(677\) | 7.99489e29 | 1.51926 | 0.759629 | − | 0.650356i | \(-0.225380\pi\) | ||||
0.759629 | + | 0.650356i | \(0.225380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.83538e29i | 1.44354i | ||||||||
\(680\) | −1.67925e29 | + | 5.22350e28i | −0.304630 | + | 0.0947584i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.29169e29 | − | 1.28062e30i | −0.227208 | − | 2.25261i | ||||
\(683\) | 8.76090e29i | 1.51751i | 0.651377 | + | 0.758755i | \(0.274192\pi\) | ||||
−0.651377 | + | 0.758755i | \(0.725808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4.00808e29i | − | 0.673264i | ||||||
\(686\) | 1.85638e29 | − | 1.87243e28i | 0.307089 | − | 0.0309743i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.52485e29 | + | 3.20008e29i | −1.20731 | + | 0.513431i | ||||
\(689\) | − | 5.33614e28i | − | 0.0843190i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.37190e29 | 1.12995 | 0.564976 | − | 0.825107i | \(-0.308885\pi\) | ||||
0.564976 | + | 0.825107i | \(0.308885\pi\) | |||||||
\(692\) | 2.06459e28 | − | 4.20768e27i | 0.0311688 | − | 0.00635227i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.87326e29 | − | 1.88945e28i | 0.274361 | − | 0.0276733i | ||||
\(695\) | −5.92190e29 | −0.854320 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.06765e29 | 0.149447 | ||||||||
\(698\) | −3.07698e29 | + | 3.10358e28i | −0.424271 | + | 0.0427938i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.81081e28 | − | 4.81389e29i | −0.131273 | − | 0.644120i | ||||
\(701\) | 1.52884e29 | 0.201523 | 0.100761 | − | 0.994911i | \(-0.467872\pi\) | ||||
0.100761 | + | 0.994911i | \(0.467872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.02954e27i | 0.00771353i | ||||||||
\(704\) | 5.85261e29 | + | 8.49724e29i | 0.737626 | + | 1.07094i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.34047e29 | − | 7.40392e28i | 0.897996 | − | 0.0905759i | ||||
\(707\) | 4.81731e29i | 0.580632i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.07083e29i | − | 0.125296i | −0.998036 | − | 0.0626478i | \(-0.980046\pi\) | ||
0.998036 | − | 0.0626478i | \(-0.0199545\pi\) | |||||||
\(710\) | 8.38723e28 | + | 8.31535e29i | 0.0966954 | + | 0.958668i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.65443e29 | + | 3.00312e29i | −1.08065 | + | 0.336149i | ||||
\(713\) | − | 7.69361e29i | − | 0.848575i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.89745e29 | 0.310315 | ||||||||
\(716\) | 2.26796e29 | + | 1.11283e30i | 0.239359 | + | 1.17447i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.07076e28 | − | 1.06158e29i | −0.0109745 | − | 0.108805i | ||||
\(719\) | −9.44904e28 | −0.0954409 | −0.0477204 | − | 0.998861i | \(-0.515196\pi\) | ||||
−0.0477204 | + | 0.998861i | \(0.515196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.41334e30 | 1.38652 | ||||||||
\(722\) | 1.01503e29 | + | 1.00634e30i | 0.0981387 | + | 0.972977i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.34671e28 | + | 4.09550e29i | 0.0783900 | + | 0.384638i | ||||
\(725\) | −9.58208e28 | −0.0886973 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.63722e29i | 0.237157i | 0.992945 | + | 0.118578i | \(0.0378337\pi\) | ||||
−0.992945 | + | 0.118578i | \(0.962166\pi\) | |||||||
\(728\) | 1.59117e29 | + | 5.11531e29i | 0.141039 | + | 0.453411i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.76368e28 | + | 5.71428e29i | 0.0496375 | + | 0.492121i | ||||
\(731\) | − | 6.60272e29i | − | 0.560519i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.11045e29i | 0.751533i | 0.926714 | + | 0.375767i | \(0.122621\pi\) | ||||
−0.926714 | + | 0.375767i | \(0.877379\pi\) | |||||||
\(734\) | 7.17241e29 | − | 7.23440e28i | 0.583252 | − | 0.0588294i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.97095e29 | + | 5.40456e29i | 0.234789 | + | 0.427113i | ||||
\(737\) | − | 7.53474e29i | − | 0.587029i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.20104e29 | 0.621016 | 0.310508 | − | 0.950571i | \(-0.399501\pi\) | ||||
0.310508 | + | 0.950571i | \(0.399501\pi\) | |||||||
\(740\) | −1.03669e28 | − | 5.08675e28i | −0.00773956 | − | 0.0379758i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.37484e29 | − | 5.42130e28i | 0.390054 | − | 0.0393426i | ||||
\(743\) | −1.76727e30 | −1.26451 | −0.632253 | − | 0.774762i | \(-0.717870\pi\) | ||||
−0.632253 | + | 0.774762i | \(0.717870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.98643e30 | −1.38176 | ||||||||
\(746\) | −2.23519e30 | + | 2.25451e29i | −1.53305 | + | 0.154631i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.16348e29 | + | 1.66373e29i | −0.544388 | + | 0.110947i | ||||
\(749\) | 9.19758e29 | 0.604804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.69678e29i | − | 0.428200i | −0.976812 | − | 0.214100i | \(-0.931318\pi\) | ||
0.976812 | − | 0.214100i | \(-0.0686818\pi\) | |||||||
\(752\) | 9.07731e29 | − | 3.86029e29i | 0.572361 | − | 0.243407i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.03958e29 | − | 1.04856e28i | 0.0637466 | − | 0.00642976i | ||||
\(755\) | − | 2.22087e30i | − | 1.34301i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.50830e30i | − | 0.887117i | −0.896245 | − | 0.443559i | \(-0.853716\pi\) | ||
0.896245 | − | 0.443559i | \(-0.146284\pi\) | |||||||
\(758\) | 1.61037e29 | + | 1.59657e30i | 0.0934113 | + | 0.926108i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.84186e28 | + | 1.87805e29i | 0.0329616 | + | 0.105965i | ||||
\(761\) | − | 3.23153e30i | − | 1.79833i | −0.437612 | − | 0.899164i | \(-0.644176\pi\) | ||
0.437612 | − | 0.899164i | \(-0.355824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.98346e30 | 2.69789 | ||||||||
\(764\) | −1.22883e30 | + | 2.50439e29i | −0.656165 | + | 0.133728i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.45557e29 | + | 1.44309e30i | 0.0756188 | + | 0.749708i | ||||
\(767\) | 7.18345e29 | 0.368114 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.74415e30 | 1.36830 | 0.684149 | − | 0.729342i | \(-0.260174\pi\) | ||||
0.684149 | + | 0.729342i | \(0.260174\pi\) | |||||||
\(770\) | 2.94369e29 | + | 2.91846e30i | 0.144790 | + | 1.43550i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.59738e30 | − | 3.25549e29i | 0.764584 | − | 0.155824i | ||||
\(773\) | −1.08380e30 | −0.511760 | −0.255880 | − | 0.966709i | \(-0.582365\pi\) | ||||
−0.255880 | + | 0.966709i | \(0.582365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.67614e30i | − | 0.770269i | ||||||
\(776\) | −6.36492e29 | − | 2.04620e30i | −0.288566 | − | 0.927682i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.01301e28 | + | 2.98719e29i | 0.0132958 | + | 0.131819i | ||||
\(779\) | − | 1.19405e29i | − | 0.0519850i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.95931e30i | 1.67797i | ||||||||
\(782\) | −4.95479e29 | + | 4.99762e28i | −0.207183 | + | 0.0208974i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.73017e30 | + | 1.16105e30i | −1.11140 | + | 0.472643i | ||||
\(785\) | 2.18017e30i | 0.875708i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.42912e30 | 1.34106 | 0.670530 | − | 0.741882i | \(-0.266067\pi\) | ||||
0.670530 | + | 0.741882i | \(0.266067\pi\) | |||||||
\(788\) | 1.33066e30 | − | 2.71191e29i | 0.513500 | − | 0.104652i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.55168e30 | + | 1.56509e29i | −0.583066 | + | 0.0588106i | ||||
\(791\) | 5.63039e30 | 2.08778 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.53211e29 | 0.235877 | ||||||||
\(794\) | −4.36593e30 | + | 4.40367e29i | −1.55583 | + | 0.156928i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.06330e30 | − | 5.21731e30i | −0.369036 | − | 1.81075i | ||||
\(797\) | 3.20924e30 | 1.09923 | 0.549617 | − | 0.835417i | \(-0.314774\pi\) | ||||
0.549617 | + | 0.835417i | \(0.314774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.96493e29i | 0.265730i | ||||||||
\(800\) | 6.47255e29 | + | 1.17744e30i | 0.213123 | + | 0.387699i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.11514e30 | − | 4.15071e29i | 1.31994 | − | 0.133135i | ||||
\(803\) | 2.72082e30i | 0.861365i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75333e30i | 0.540763i | ||||||||
\(806\) | 1.83419e29 | + | 1.81847e30i | 0.0558376 | + | 0.553591i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.91325e29 | − | 1.25803e30i | −0.116070 | − | 0.373141i | ||||
\(809\) | − | 5.95892e30i | − | 1.74465i | −0.488928 | − | 0.872324i | \(-0.662612\pi\) | ||
0.488928 | − | 0.872324i | \(-0.337388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.78707e30 | 1.65097 | 0.825486 | − | 0.564422i | \(-0.190901\pi\) | ||||
0.825486 | + | 0.564422i | \(0.190901\pi\) | |||||||
\(812\) | 2.11233e29 | + | 1.03646e30i | 0.0594872 | + | 0.291887i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.46807e28 | − | 2.44692e29i | −0.00677332 | − | 0.0671527i | ||||
\(815\) | 3.25631e30 | 0.882207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.38436e29 | −0.194976 | ||||||||
\(818\) | 3.98132e29 | + | 3.94720e30i | 0.103781 | + | 1.02892i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.05299e29 | + | 1.00734e30i | 0.0521603 | + | 0.255936i | ||||
\(821\) | −6.18104e30 | −1.55045 | −0.775226 | − | 0.631684i | \(-0.782364\pi\) | ||||
−0.775226 | + | 0.631684i | \(0.782364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.87831e30i | 0.459272i | 0.973277 | + | 0.229636i | \(0.0737535\pi\) | ||||
−0.973277 | + | 0.229636i | \(0.926246\pi\) | |||||||
\(824\) | −3.69091e30 | + | 1.14810e30i | −0.891042 | + | 0.277168i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.29809e29 | + | 7.23554e30i | 0.171759 | + | 1.70287i | ||||
\(827\) | − | 1.15089e30i | − | 0.267441i | −0.991019 | − | 0.133720i | \(-0.957308\pi\) | ||
0.991019 | − | 0.133720i | \(-0.0426924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.33044e30i | 0.527977i | 0.964526 | + | 0.263988i | \(0.0850381\pi\) | ||||
−0.964526 | + | 0.263988i | \(0.914962\pi\) | |||||||
\(830\) | −2.70805e30 | + | 2.73145e29i | −0.605809 | + | 0.0611046i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.31064e29 | − | 1.20660e30i | −0.181276 | − | 0.263189i | ||||
\(833\) | − | 2.39560e30i | − | 0.515990i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.80172e30 | 1.21856 | ||||||||
\(836\) | 1.86069e29 | + | 9.12988e29i | 0.0385930 | + | 0.189365i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.76261e30 | − | 5.81242e29i | 1.16562 | − | 0.117570i | ||||
\(839\) | −2.46941e30 | −0.493279 | −0.246639 | − | 0.969107i | \(-0.579326\pi\) | ||||
−0.246639 | + | 0.969107i | \(0.579326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.92653e30 | −0.959806 | ||||||||
\(842\) | 8.54676e30 | − | 8.62063e29i | 1.64446 | − | 0.165868i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.35779e30 | + | 6.84326e29i | −0.630171 | + | 0.128430i | ||||
\(845\) | 3.61713e30 | 0.670454 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.67844e30i | 1.02672i | ||||||||
\(848\) | −1.35959e30 | + | 5.78191e29i | −0.242802 | + | 0.103256i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.07946e30 | + | 1.08879e29i | −0.188064 | + | 0.0189690i | ||||
\(851\) | − | 1.47004e29i | − | 0.0252970i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.99217e30i | − | 1.17394i | −0.809607 | − | 0.586972i | \(-0.800320\pi\) | ||
0.809607 | − | 0.586972i | \(-0.199680\pi\) | |||||||
\(854\) | 6.63636e29 | + | 6.57948e30i | 0.110058 | + | 1.09115i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.40193e30 | + | 7.47148e29i | −0.388675 | + | 0.120902i | ||||
\(857\) | − | 7.25707e30i | − | 1.16001i | −0.814612 | − | 0.580006i | \(-0.803050\pi\) | ||
0.814612 | − | 0.580006i | \(-0.196950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.16920e31 | −1.82372 | −0.911861 | − | 0.410499i | \(-0.865355\pi\) | ||||
−0.911861 | + | 0.410499i | \(0.865355\pi\) | |||||||
\(860\) | 6.22973e30 | − | 1.26963e30i | 0.959921 | − | 0.195634i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.65168e29 | − | 9.56897e30i | −0.145136 | − | 1.43893i | ||||
\(863\) | −9.99164e30 | −1.48431 | −0.742153 | − | 0.670230i | \(-0.766195\pi\) | ||||
−0.742153 | + | 0.670230i | \(0.766195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63825e29 | −0.0237526 | ||||||||
\(866\) | 1.83334e29 | + | 1.81763e30i | 0.0262606 | + | 0.260356i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.81302e31 | + | 3.69498e30i | −2.53482 | + | 0.516601i | ||||
\(869\) | −7.38824e30 | −1.02055 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.06993e30i | 0.144266i | ||||||||
\(872\) | −1.30142e31 | + | 4.04822e30i | −1.73379 | + | 0.539313i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.58925e28 | + | 5.54135e29i | 0.00726914 | + | 0.0720685i | ||||
\(875\) | 1.24538e31i | 1.60036i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.48068e31i | − | 1.85766i | −0.370507 | − | 0.928830i | \(-0.620816\pi\) | ||
0.370507 | − | 0.928830i | \(-0.379184\pi\) | |||||||
\(878\) | 1.76967e30 | − | 1.78497e29i | 0.219382 | − | 0.0221278i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.13950e30 | − | 7.38240e30i | −0.380007 | − | 0.893572i | ||||
\(881\) | − | 9.26792e30i | − | 1.10850i | −0.832351 | − | 0.554249i | \(-0.813005\pi\) | ||
0.832351 | − | 0.554249i | \(-0.186995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.86015e30 | 0.450834 | 0.225417 | − | 0.974262i | \(-0.427626\pi\) | ||||
0.225417 | + | 0.974262i | \(0.427626\pi\) | |||||||
\(884\) | 1.15921e30 | − | 2.36249e29i | 0.133786 | − | 0.0272659i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.09377e30 | − | 7.15509e29i | 0.799509 | − | 0.0806420i | ||||
\(887\) | −5.26751e30 | −0.586688 | −0.293344 | − | 0.956007i | \(-0.594768\pi\) | ||||
−0.293344 | + | 0.956007i | \(0.594768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.15593e31 | −2.34513 | ||||||||
\(890\) | 7.82158e30 | − | 7.88919e29i | 0.840813 | − | 0.0848081i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.34888e30 | − | 1.15253e31i | −0.246621 | − | 1.21010i | ||||
\(893\) | 8.90784e29 | 0.0924340 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 8.83027e30i | − | 0.895019i | ||||||
\(896\) | 1.13092e31 | − | 9.59677e30i | 1.13291 | − | 0.961371i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.69345e30 | + | 7.75996e29i | −0.752870 | + | 0.0759377i | ||||
\(899\) | 3.60884e30i | 0.349052i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.19298e30i | − | 0.112726i | ||||||
\(902\) | 4.88759e29 | + | 4.84570e30i | 0.0456484 | + | 0.452572i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.47037e31 | + | 4.57374e30i | −1.34171 | + | 0.417352i | ||||
\(905\) | − | 3.24978e30i | − | 0.293119i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.72788e31 | 1.52278 | 0.761389 | − | 0.648295i | \(-0.224518\pi\) | ||||
0.761389 | + | 0.648295i | \(0.224518\pi\) | |||||||
\(908\) | −4.37680e30 | − | 2.14757e31i | −0.381290 | − | 1.87088i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.18001e29 | − | 4.14419e30i | −0.0355830 | − | 0.352781i | ||||
\(911\) | 1.44748e31 | 1.21806 | 0.609030 | − | 0.793147i | \(-0.291559\pi\) | ||||
0.609030 | + | 0.793147i | \(0.291559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.28942e31 | −1.06036 | ||||||||
\(914\) | 1.00746e29 | + | 9.98829e29i | 0.00819019 | + | 0.0812000i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.03649e30 | + | 1.98059e31i | 0.320702 | + | 1.57359i | ||||
\(917\) | 2.08165e31 | 1.63505 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.88347e31i | 1.44592i | 0.690889 | + | 0.722961i | \(0.257219\pi\) | ||||
−0.690889 | + | 0.722961i | \(0.742781\pi\) | |||||||
\(920\) | −1.42428e30 | − | 4.57879e30i | −0.108100 | − | 0.347519i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.92995e29 | − | 7.86199e30i | −0.0588296 | − | 0.583254i | ||||
\(923\) | − | 5.62218e30i | − | 0.412370i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3.20264e29i | − | 0.0229626i | ||||||
\(926\) | −5.60175e30 | + | 5.65017e29i | −0.397108 | + | 0.0400541i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.39358e30 | − | 2.53511e30i | −0.0965780 | − | 0.175688i | ||||
\(929\) | 8.49947e29i | 0.0582408i | 0.999576 | + | 0.0291204i | \(0.00927062\pi\) | ||||
−0.999576 | + | 0.0291204i | \(0.990729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.67919e30 | −0.179487 | ||||||||
\(932\) | −2.18133e30 | − | 1.07032e31i | −0.144495 | − | 0.708997i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.03198e31 | − | 1.04090e30i | 0.668385 | − | 0.0674163i | ||||
\(935\) | 6.47772e30 | 0.414859 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.87088e31 | −1.17160 | −0.585802 | − | 0.810455i | \(-0.699220\pi\) | ||||
−0.585802 | + | 0.810455i | \(0.699220\pi\) | |||||||
\(938\) | −1.07768e31 | + | 1.08700e30i | −0.667362 | + | 0.0673131i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.51499e30 | + | 1.53157e30i | −0.455078 | + | 0.0927459i | ||||
\(941\) | 1.07614e31 | 0.644435 | 0.322218 | − | 0.946666i | \(-0.395572\pi\) | ||||
0.322218 | + | 0.946666i | \(0.395572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.91116e30i | 0.170488i | ||||||||
\(944\) | −7.78354e30 | − | 1.83027e31i | −0.450787 | − | 1.06001i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.99674e31 | − | 3.02264e30i | 1.69743 | − | 0.171210i | ||||
\(947\) | 1.28020e31i | 0.717140i | 0.933503 | + | 0.358570i | \(0.116735\pi\) | ||||
−0.933503 | + | 0.358570i | \(0.883265\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.86354e30i | − | 0.211685i | ||||||
\(950\) | 1.21768e29 | + | 1.20724e30i | 0.00659835 | + | 0.0654180i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.55732e30 | + | 1.14361e31i | 0.188554 | + | 0.606164i | ||||
\(953\) | 6.97019e30i | 0.365400i | 0.983169 | + | 0.182700i | \(0.0584838\pi\) | ||||
−0.983169 | + | 0.182700i | \(0.941516\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.75081e30 | 0.500040 | ||||||||
\(956\) | 7.09826e30 | − | 1.44664e30i | 0.360035 | − | 0.0733758i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.67709e30 | + | 1.66272e31i | 0.0832182 | + | 0.825050i | ||||
\(959\) | −2.72960e31 | −1.33969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.23019e31 | −2.03125 | ||||||||
\(962\) | 3.50464e28 | + | 3.47460e29i | 0.00166458 | + | 0.0165032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.51023e30 | + | 9.19194e29i | −0.209599 | + | 0.0427168i | ||||
\(965\) | −1.26752e31 | −0.582663 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.09810e31i | − | 1.39353i | −0.717297 | − | 0.696767i | \(-0.754621\pi\) | ||
0.717297 | − | 0.696767i | \(-0.245379\pi\) | |||||||
\(968\) | −4.61277e30 | − | 1.48291e31i | −0.205244 | − | 0.659819i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.67206e30 | + | 1.65774e31i | 0.0728031 | + | 0.721792i | ||||
\(971\) | 1.90715e31i | 0.821452i | 0.911759 | + | 0.410726i | \(0.134725\pi\) | ||||
−0.911759 | + | 0.410726i | \(0.865275\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.03295e31i | 1.69996i | ||||||||
\(974\) | −2.11911e31 | + | 2.13743e30i | −0.883659 | + | 0.0891297i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.07779e30 | − | 1.66431e31i | −0.288851 | − | 0.679222i | ||||
\(977\) | − | 2.79068e31i | − | 1.12672i | −0.826211 | − | 0.563361i | \(-0.809508\pi\) | ||
0.826211 | − | 0.563361i | \(-0.190492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.72420e31 | 1.47168 | ||||||||
\(980\) | 2.26027e31 | − | 4.60648e30i | 0.883662 | − | 0.180092i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.28356e31 | − | 3.31194e30i | 1.25653 | − | 0.126739i | ||||
\(983\) | 1.95416e31 | 0.739856 | 0.369928 | − | 0.929060i | \(-0.379382\pi\) | ||||
0.369928 | + | 0.929060i | \(0.379382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.05588e31 | −0.391320 | ||||||||
\(986\) | 2.32414e30 | − | 2.34423e29i | 0.0852225 | − | 0.00859592i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.64216e29 | − | 1.29643e30i | −0.00948443 | − | 0.0465374i | ||||
\(989\) | 1.80035e31 | 0.639435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.14391e31i | − | 1.09319i | −0.837396 | − | 0.546596i | \(-0.815923\pi\) | ||
0.837396 | − | 0.546596i | \(-0.184077\pi\) | |||||||
\(992\) | 4.43453e31 | − | 2.43771e31i | 1.52572 | − | 0.838707i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.66295e31 | − | 5.71190e30i | 1.90759 | − | 0.192408i | ||||
\(995\) | 4.13994e31i | 1.37991i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.20318e31i | − | 0.719036i | −0.933138 | − | 0.359518i | \(-0.882941\pi\) | ||
0.933138 | − | 0.359518i | \(-0.117059\pi\) | |||||||
\(998\) | −3.81225e30 | − | 3.77958e31i | −0.123115 | − | 1.22060i | ||||
\(999\) | 0 | 0 |
(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 | 72.22.f.a.35.41 | ✓ | 84 | |
3.2 | odd | 2 | inner | 72.22.f.a.35.44 | yes | 84 | |
8.3 | odd | 2 | inner | 72.22.f.a.35.43 | yes | 84 | |
24.11 | even | 2 | inner | 72.22.f.a.35.42 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.22.f.a.35.41 | ✓ | 84 | 1.1 | even | 1 | trivial | |
72.22.f.a.35.42 | yes | 84 | 24.11 | even | 2 | inner | |
72.22.f.a.35.43 | yes | 84 | 8.3 | odd | 2 | inner | |
72.22.f.a.35.44 | yes | 84 | 3.2 | odd | 2 | inner |