Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,15,Mod(12,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.12");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.0554007641\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 12.14 | ||
Character | \(\chi\) | \(=\) | 29.12 |
Dual form | 29.15.c.a.17.14 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −50.6787 | − | 50.6787i | −0.395927 | − | 0.395927i | 0.480867 | − | 0.876794i | \(-0.340322\pi\) |
−0.876794 | + | 0.480867i | \(0.840322\pi\) | |||||||
\(3\) | 910.227 | + | 910.227i | 0.416199 | + | 0.416199i | 0.883891 | − | 0.467692i | \(-0.154914\pi\) |
−0.467692 | + | 0.883891i | \(0.654914\pi\) | |||||||
\(4\) | − | 11247.3i | − | 0.686483i | ||||||
\(5\) | 127648.i | 1.63390i | 0.576712 | + | 0.816948i | \(0.304336\pi\) | ||||
−0.576712 | + | 0.816948i | \(0.695664\pi\) | |||||||
\(6\) | − | 92258.2i | − | 0.329569i | ||||||
\(7\) | −1.54934e6 | −1.88131 | −0.940657 | − | 0.339358i | \(-0.889790\pi\) | ||||
−0.940657 | + | 0.339358i | \(0.889790\pi\) | |||||||
\(8\) | −1.40032e6 | + | 1.40032e6i | −0.667724 | + | 0.667724i | ||||
\(9\) | − | 3.12594e6i | − | 0.653557i | ||||||
\(10\) | 6.46904e6 | − | 6.46904e6i | 0.646904 | − | 0.646904i | ||||
\(11\) | 1.89478e6 | + | 1.89478e6i | 0.0972321 | + | 0.0972321i | 0.754050 | − | 0.656818i | \(-0.228098\pi\) |
−0.656818 | + | 0.754050i | \(0.728098\pi\) | |||||||
\(12\) | 1.02376e7 | − | 1.02376e7i | 0.285714 | − | 0.285714i | ||||
\(13\) | − | 7.31778e7i | − | 1.16621i | −0.812398 | − | 0.583104i | \(-0.801838\pi\) | ||
0.812398 | − | 0.583104i | \(-0.198162\pi\) | |||||||
\(14\) | 7.85187e7 | + | 7.85187e7i | 0.744863 | + | 0.744863i | ||||
\(15\) | −1.16189e8 | + | 1.16189e8i | −0.680026 | + | 0.680026i | ||||
\(16\) | −4.23438e7 | −0.157743 | ||||||||
\(17\) | 1.23124e8 | + | 1.23124e8i | 0.300055 | + | 0.300055i | 0.841035 | − | 0.540980i | \(-0.181947\pi\) |
−0.540980 | + | 0.841035i | \(0.681947\pi\) | |||||||
\(18\) | −1.58419e8 | + | 1.58419e8i | −0.258761 | + | 0.258761i | ||||
\(19\) | 1.31336e7 | + | 1.31336e7i | 0.0146930 | + | 0.0146930i | 0.714415 | − | 0.699722i | \(-0.246693\pi\) |
−0.699722 | + | 0.714415i | \(0.746693\pi\) | |||||||
\(20\) | 1.43570e9 | 1.12164 | ||||||||
\(21\) | −1.41025e9 | − | 1.41025e9i | −0.783001 | − | 0.783001i | ||||
\(22\) | − | 1.92050e8i | − | 0.0769936i | ||||||
\(23\) | 3.45143e9 | 1.01369 | 0.506843 | − | 0.862038i | \(-0.330812\pi\) | ||||
0.506843 | + | 0.862038i | \(0.330812\pi\) | |||||||
\(24\) | −2.54922e9 | −0.555813 | ||||||||
\(25\) | −1.01905e10 | −1.66962 | ||||||||
\(26\) | −3.70855e9 | + | 3.70855e9i | −0.461733 | + | 0.461733i | ||||
\(27\) | 7.19891e9 | − | 7.19891e9i | 0.688209 | − | 0.688209i | ||||
\(28\) | 1.74260e10i | 1.29149i | ||||||||
\(29\) | 1.05990e10 | + | 1.36096e10i | 0.614437 | + | 0.788966i | ||||
\(30\) | 1.17766e10 | 0.538481 | ||||||||
\(31\) | 2.10814e10 | + | 2.10814e10i | 0.766245 | + | 0.766245i | 0.977443 | − | 0.211198i | \(-0.0677364\pi\) |
−0.211198 | + | 0.977443i | \(0.567736\pi\) | |||||||
\(32\) | 2.50888e10 | + | 2.50888e10i | 0.730179 | + | 0.730179i | ||||
\(33\) | 3.44936e9i | 0.0809358i | ||||||||
\(34\) | − | 1.24795e10i | − | 0.237600i | ||||||
\(35\) | − | 1.97771e11i | − | 3.07387i | ||||||
\(36\) | −3.51585e10 | −0.448656 | ||||||||
\(37\) | −3.02037e9 | + | 3.02037e9i | −0.0318162 | + | 0.0318162i | −0.722836 | − | 0.691020i | \(-0.757162\pi\) |
0.691020 | + | 0.722836i | \(0.257162\pi\) | |||||||
\(38\) | − | 1.33119e9i | − | 0.0116347i | ||||||
\(39\) | 6.66084e10 | − | 6.66084e10i | 0.485374 | − | 0.485374i | ||||
\(40\) | −1.78748e11 | − | 1.78748e11i | −1.09099 | − | 1.09099i | ||||
\(41\) | 2.27317e11 | − | 2.27317e11i | 1.16720 | − | 1.16720i | 0.184338 | − | 0.982863i | \(-0.440986\pi\) |
0.982863 | − | 0.184338i | \(-0.0590141\pi\) | |||||||
\(42\) | 1.42940e11i | 0.620023i | ||||||||
\(43\) | −2.66277e10 | − | 2.66277e10i | −0.0979613 | − | 0.0979613i | 0.656428 | − | 0.754389i | \(-0.272067\pi\) |
−0.754389 | + | 0.656428i | \(0.772067\pi\) | |||||||
\(44\) | 2.13112e10 | − | 2.13112e10i | 0.0667482 | − | 0.0667482i | ||||
\(45\) | 3.99020e11 | 1.06784 | ||||||||
\(46\) | −1.74914e11 | − | 1.74914e11i | −0.401346 | − | 0.401346i | ||||
\(47\) | 3.95665e11 | − | 3.95665e11i | 0.780986 | − | 0.780986i | −0.199011 | − | 0.979997i | \(-0.563773\pi\) |
0.979997 | + | 0.199011i | \(0.0637731\pi\) | |||||||
\(48\) | −3.85425e10 | − | 3.85425e10i | −0.0656525 | − | 0.0656525i | ||||
\(49\) | 1.72224e12 | 2.53934 | ||||||||
\(50\) | 5.16442e11 | + | 5.16442e11i | 0.661046 | + | 0.661046i | ||||
\(51\) | 2.24142e11i | 0.249765i | ||||||||
\(52\) | −8.23056e11 | −0.800582 | ||||||||
\(53\) | −4.44734e11 | −0.378590 | −0.189295 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189295 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(54\) | −7.29662e11 | −0.544961 | ||||||||
\(55\) | −2.41865e11 | + | 2.41865e11i | −0.158867 | + | 0.158867i | ||||
\(56\) | 2.16958e12 | − | 2.16958e12i | 1.25620 | − | 1.25620i | ||||
\(57\) | 2.39092e10i | 0.0122304i | ||||||||
\(58\) | 1.52574e11 | − | 1.22686e12i | 0.0691009 | − | 0.555645i | ||||
\(59\) | −2.41238e12 | −0.969354 | −0.484677 | − | 0.874693i | \(-0.661063\pi\) | ||||
−0.484677 | + | 0.874693i | \(0.661063\pi\) | |||||||
\(60\) | 1.30682e12 | + | 1.30682e12i | 0.466827 | + | 0.466827i | ||||
\(61\) | −1.51318e12 | − | 1.51318e12i | −0.481483 | − | 0.481483i | 0.424122 | − | 0.905605i | \(-0.360583\pi\) |
−0.905605 | + | 0.424122i | \(0.860583\pi\) | |||||||
\(62\) | − | 2.13676e12i | − | 0.606755i | ||||||
\(63\) | 4.84316e12i | 1.22955i | ||||||||
\(64\) | − | 1.84917e12i | − | 0.420452i | ||||||
\(65\) | 9.34100e12 | 1.90546 | ||||||||
\(66\) | 1.74809e11 | − | 1.74809e11i | 0.0320447 | − | 0.0320447i | ||||
\(67\) | − | 8.36251e12i | − | 1.37979i | −0.723909 | − | 0.689895i | \(-0.757657\pi\) | ||
0.723909 | − | 0.689895i | \(-0.242343\pi\) | |||||||
\(68\) | 1.38482e12 | − | 1.38482e12i | 0.205983 | − | 0.205983i | ||||
\(69\) | 3.14158e12 | + | 3.14158e12i | 0.421896 | + | 0.421896i | ||||
\(70\) | −1.00228e13 | + | 1.00228e13i | −1.21703 | + | 1.21703i | ||||
\(71\) | 7.18905e12i | 0.790429i | 0.918589 | + | 0.395215i | \(0.129330\pi\) | ||||
−0.918589 | + | 0.395215i | \(0.870670\pi\) | |||||||
\(72\) | 4.37732e12 | + | 4.37732e12i | 0.436396 | + | 0.436396i | ||||
\(73\) | −6.97575e12 | + | 6.97575e12i | −0.631438 | + | 0.631438i | −0.948429 | − | 0.316991i | \(-0.897328\pi\) |
0.316991 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(74\) | 3.06137e11 | 0.0251938 | ||||||||
\(75\) | −9.27569e12 | − | 9.27569e12i | −0.694892 | − | 0.694892i | ||||
\(76\) | 1.47719e11 | − | 1.47719e11i | 0.0100865 | − | 0.0100865i | ||||
\(77\) | −2.93566e12 | − | 2.93566e12i | −0.182924 | − | 0.182924i | ||||
\(78\) | −6.75125e12 | −0.384346 | ||||||||
\(79\) | −1.62138e13 | − | 1.62138e13i | −0.844299 | − | 0.844299i | 0.145115 | − | 0.989415i | \(-0.453645\pi\) |
−0.989415 | + | 0.145115i | \(0.953645\pi\) | |||||||
\(80\) | − | 5.40511e12i | − | 0.257736i | ||||||
\(81\) | −1.84599e12 | −0.0806928 | ||||||||
\(82\) | −2.30403e13 | −0.924253 | ||||||||
\(83\) | 4.05979e13 | 1.49609 | 0.748044 | − | 0.663650i | \(-0.230993\pi\) | ||||
0.748044 | + | 0.663650i | \(0.230993\pi\) | |||||||
\(84\) | −1.58616e13 | + | 1.58616e13i | −0.537518 | + | 0.537518i | ||||
\(85\) | −1.57166e13 | + | 1.57166e13i | −0.490259 | + | 0.490259i | ||||
\(86\) | 2.69891e12i | 0.0775710i | ||||||||
\(87\) | −2.74034e12 | + | 2.20353e13i | −0.0726390 | + | 0.584095i | ||||
\(88\) | −5.30659e12 | −0.129848 | ||||||||
\(89\) | 1.71467e13 | + | 1.71467e13i | 0.387660 | + | 0.387660i | 0.873852 | − | 0.486192i | \(-0.161615\pi\) |
−0.486192 | + | 0.873852i | \(0.661615\pi\) | |||||||
\(90\) | −2.02218e13 | − | 2.02218e13i | −0.422788 | − | 0.422788i | ||||
\(91\) | 1.13377e14i | 2.19400i | ||||||||
\(92\) | − | 3.88194e13i | − | 0.695879i | ||||||
\(93\) | 3.83778e13i | 0.637821i | ||||||||
\(94\) | −4.01036e13 | −0.618427 | ||||||||
\(95\) | −1.67649e12 | + | 1.67649e12i | −0.0240068 | + | 0.0240068i | ||||
\(96\) | 4.56730e13i | 0.607800i | ||||||||
\(97\) | 9.87187e13 | − | 9.87187e13i | 1.22179 | − | 1.22179i | 0.254797 | − | 0.966994i | \(-0.417991\pi\) |
0.966994 | − | 0.254797i | \(-0.0820088\pi\) | |||||||
\(98\) | −8.72809e13 | − | 8.72809e13i | −1.00540 | − | 1.00540i | ||||
\(99\) | 5.92296e12 | − | 5.92296e12i | 0.0635467 | − | 0.0635467i | ||||
\(100\) | 1.14616e14i | 1.14616i | ||||||||
\(101\) | −6.86082e13 | − | 6.86082e13i | −0.639921 | − | 0.639921i | 0.310615 | − | 0.950536i | \(-0.399465\pi\) |
−0.950536 | + | 0.310615i | \(0.899465\pi\) | |||||||
\(102\) | 1.13592e13 | − | 1.13592e13i | 0.0988888 | − | 0.0988888i | ||||
\(103\) | −9.82041e13 | −0.798489 | −0.399245 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399245 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(104\) | 1.02472e14 | + | 1.02472e14i | 0.778705 | + | 0.778705i | ||||
\(105\) | 1.80016e14 | − | 1.80016e14i | 1.27934 | − | 1.27934i | ||||
\(106\) | 2.25385e13 | + | 2.25385e13i | 0.149894 | + | 0.149894i | ||||
\(107\) | 7.70763e12 | 0.0479993 | 0.0239996 | − | 0.999712i | \(-0.492360\pi\) | ||||
0.0239996 | + | 0.999712i | \(0.492360\pi\) | |||||||
\(108\) | −8.09686e13 | − | 8.09686e13i | −0.472444 | − | 0.472444i | ||||
\(109\) | 9.06346e13i | 0.495802i | 0.968785 | + | 0.247901i | \(0.0797409\pi\) | ||||
−0.968785 | + | 0.247901i | \(0.920259\pi\) | |||||||
\(110\) | 2.45148e13 | 0.125800 | ||||||||
\(111\) | −5.49845e12 | −0.0264837 | ||||||||
\(112\) | 6.56051e13 | 0.296764 | ||||||||
\(113\) | 2.19996e14 | − | 2.19996e14i | 0.935119 | − | 0.935119i | −0.0629012 | − | 0.998020i | \(-0.520035\pi\) |
0.998020 | + | 0.0629012i | \(0.0200353\pi\) | |||||||
\(114\) | 1.21169e12 | − | 1.21169e12i | 0.00484235 | − | 0.00484235i | ||||
\(115\) | 4.40568e14i | 1.65626i | ||||||||
\(116\) | 1.53072e14 | − | 1.19210e14i | 0.541612 | − | 0.421801i | ||||
\(117\) | −2.28749e14 | −0.762182 | ||||||||
\(118\) | 1.22256e14 | + | 1.22256e14i | 0.383793 | + | 0.383793i | ||||
\(119\) | −1.90762e14 | − | 1.90762e14i | −0.564498 | − | 0.564498i | ||||
\(120\) | − | 3.25403e14i | − | 0.908140i | ||||||
\(121\) | − | 3.72569e14i | − | 0.981092i | ||||||
\(122\) | 1.53372e14i | 0.381264i | ||||||||
\(123\) | 4.13821e14 | 0.971576 | ||||||||
\(124\) | 2.37110e14 | − | 2.37110e14i | 0.526015 | − | 0.526015i | ||||
\(125\) | − | 5.21699e14i | − | 1.09408i | ||||||
\(126\) | 2.45445e14 | − | 2.45445e14i | 0.486810 | − | 0.486810i | ||||
\(127\) | 2.60386e14 | + | 2.60386e14i | 0.488642 | + | 0.488642i | 0.907878 | − | 0.419235i | \(-0.137702\pi\) |
−0.419235 | + | 0.907878i | \(0.637702\pi\) | |||||||
\(128\) | 3.17341e14 | − | 3.17341e14i | 0.563711 | − | 0.563711i | ||||
\(129\) | − | 4.84745e13i | − | 0.0815428i | ||||||
\(130\) | −4.73390e14 | − | 4.73390e14i | −0.754424 | − | 0.754424i | ||||
\(131\) | −3.47808e14 | + | 3.47808e14i | −0.525341 | + | 0.525341i | −0.919179 | − | 0.393839i | \(-0.871147\pi\) |
0.393839 | + | 0.919179i | \(0.371147\pi\) | |||||||
\(132\) | 3.87961e13 | 0.0555611 | ||||||||
\(133\) | −2.03485e13 | − | 2.03485e13i | −0.0276421 | − | 0.0276421i | ||||
\(134\) | −4.23801e14 | + | 4.23801e14i | −0.546296 | + | 0.546296i | ||||
\(135\) | 9.18927e14 | + | 9.18927e14i | 1.12446 | + | 1.12446i | ||||
\(136\) | −3.44826e14 | −0.400708 | ||||||||
\(137\) | 5.99309e14 | + | 5.99309e14i | 0.661617 | + | 0.661617i | 0.955761 | − | 0.294144i | \(-0.0950345\pi\) |
−0.294144 | + | 0.955761i | \(0.595034\pi\) | |||||||
\(138\) | − | 3.18423e14i | − | 0.334080i | ||||||
\(139\) | −1.03801e15 | −1.03538 | −0.517688 | − | 0.855569i | \(-0.673207\pi\) | ||||
−0.517688 | + | 0.855569i | \(0.673207\pi\) | |||||||
\(140\) | −2.22440e15 | −2.11016 | ||||||||
\(141\) | 7.20291e14 | 0.650091 | ||||||||
\(142\) | 3.64331e14 | − | 3.64331e14i | 0.312952 | − | 0.312952i | ||||
\(143\) | 1.38656e14 | − | 1.38656e14i | 0.113393 | − | 0.113393i | ||||
\(144\) | 1.32364e14i | 0.103094i | ||||||||
\(145\) | −1.73724e15 | + | 1.35294e15i | −1.28909 | + | 1.00393i | ||||
\(146\) | 7.07043e14 | 0.500007 | ||||||||
\(147\) | 1.56763e15 | + | 1.56763e15i | 1.05687 | + | 1.05687i | ||||
\(148\) | 3.39712e13 | + | 3.39712e13i | 0.0218413 | + | 0.0218413i | ||||
\(149\) | 1.13462e15i | 0.695902i | 0.937513 | + | 0.347951i | \(0.113122\pi\) | ||||
−0.937513 | + | 0.347951i | \(0.886878\pi\) | |||||||
\(150\) | 9.40159e14i | 0.550253i | ||||||||
\(151\) | − | 2.06213e15i | − | 1.15206i | −0.817427 | − | 0.576032i | \(-0.804600\pi\) | ||
0.817427 | − | 0.576032i | \(-0.195400\pi\) | |||||||
\(152\) | −3.67826e13 | −0.0196217 | ||||||||
\(153\) | 3.84879e14 | − | 3.84879e14i | 0.196103 | − | 0.196103i | ||||
\(154\) | 2.97551e14i | 0.144849i | ||||||||
\(155\) | −2.69100e15 | + | 2.69100e15i | −1.25197 | + | 1.25197i | ||||
\(156\) | −7.49168e14 | − | 7.49168e14i | −0.333202 | − | 0.333202i | ||||
\(157\) | 2.48226e15 | − | 2.48226e15i | 1.05572 | − | 1.05572i | 0.0573697 | − | 0.998353i | \(-0.481729\pi\) |
0.998353 | − | 0.0573697i | \(-0.0182714\pi\) | |||||||
\(158\) | 1.64339e15i | 0.668562i | ||||||||
\(159\) | −4.04809e14 | − | 4.04809e14i | −0.157569 | − | 0.157569i | ||||
\(160\) | −3.20253e15 | + | 3.20253e15i | −1.19304 | + | 1.19304i | ||||
\(161\) | −5.34744e15 | −1.90706 | ||||||||
\(162\) | 9.35524e13 | + | 9.35524e13i | 0.0319484 | + | 0.0319484i | ||||
\(163\) | 3.10038e15 | − | 3.10038e15i | 1.01415 | − | 1.01415i | 0.0142515 | − | 0.999898i | \(-0.495463\pi\) |
0.999898 | − | 0.0142515i | \(-0.00453654\pi\) | |||||||
\(164\) | −2.55672e15 | − | 2.55672e15i | −0.801264 | − | 0.801264i | ||||
\(165\) | −4.40304e14 | −0.132241 | ||||||||
\(166\) | −2.05745e15 | − | 2.05745e15i | −0.592341 | − | 0.592341i | ||||
\(167\) | 6.63789e15i | 1.83238i | 0.400749 | + | 0.916188i | \(0.368750\pi\) | ||||
−0.400749 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(168\) | 3.94962e15 | 1.04566 | ||||||||
\(169\) | −1.41761e15 | −0.360039 | ||||||||
\(170\) | 1.59299e15 | 0.388213 | ||||||||
\(171\) | 4.10550e13 | − | 4.10550e13i | 0.00960270 | − | 0.00960270i | ||||
\(172\) | −2.99491e14 | + | 2.99491e14i | −0.0672488 | + | 0.0672488i | ||||
\(173\) | − | 3.53787e15i | − | 0.762814i | −0.924407 | − | 0.381407i | \(-0.875440\pi\) | ||
0.924407 | − | 0.381407i | \(-0.124560\pi\) | |||||||
\(174\) | 1.25559e15 | − | 9.77841e14i | 0.260019 | − | 0.202499i | ||||
\(175\) | 1.57886e16 | 3.14107 | ||||||||
\(176\) | −8.02322e13 | − | 8.02322e13i | −0.0153377 | − | 0.0153377i | ||||
\(177\) | −2.19582e15 | − | 2.19582e15i | −0.403444 | − | 0.403444i | ||||
\(178\) | − | 1.73794e15i | − | 0.306970i | ||||||
\(179\) | 2.95252e15i | 0.501443i | 0.968059 | + | 0.250721i | \(0.0806678\pi\) | ||||
−0.968059 | + | 0.250721i | \(0.919332\pi\) | |||||||
\(180\) | − | 4.48792e15i | − | 0.733057i | ||||||
\(181\) | −9.05569e15 | −1.42289 | −0.711445 | − | 0.702742i | \(-0.751959\pi\) | ||||
−0.711445 | + | 0.702742i | \(0.751959\pi\) | |||||||
\(182\) | 5.74582e15 | − | 5.74582e15i | 0.868665 | − | 0.868665i | ||||
\(183\) | − | 2.75467e15i | − | 0.400786i | ||||||
\(184\) | −4.83310e15 | + | 4.83310e15i | −0.676863 | + | 0.676863i | ||||
\(185\) | −3.85545e14 | − | 3.85545e14i | −0.0519843 | − | 0.0519843i | ||||
\(186\) | 1.94493e15 | − | 1.94493e15i | 0.252531 | − | 0.252531i | ||||
\(187\) | 4.66586e14i | 0.0583499i | ||||||||
\(188\) | −4.45019e15 | − | 4.45019e15i | −0.536134 | − | 0.536134i | ||||
\(189\) | −1.11536e16 | + | 1.11536e16i | −1.29474 | + | 1.29474i | ||||
\(190\) | 1.69924e14 | 0.0190099 | ||||||||
\(191\) | 5.81319e15 | + | 5.81319e15i | 0.626875 | + | 0.626875i | 0.947281 | − | 0.320405i | \(-0.103819\pi\) |
−0.320405 | + | 0.947281i | \(0.603819\pi\) | |||||||
\(192\) | 1.68316e15 | − | 1.68316e15i | 0.174992 | − | 0.174992i | ||||
\(193\) | 1.23009e16 | + | 1.23009e16i | 1.23321 | + | 1.23321i | 0.962724 | + | 0.270484i | \(0.0871837\pi\) |
0.270484 | + | 0.962724i | \(0.412816\pi\) | |||||||
\(194\) | −1.00059e16 | −0.967481 | ||||||||
\(195\) | 8.50244e15 | + | 8.50244e15i | 0.793051 | + | 0.793051i | ||||
\(196\) | − | 1.93706e16i | − | 1.74322i | ||||||
\(197\) | 1.05160e15 | 0.0913241 | 0.0456621 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456621 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(198\) | −6.00336e14 | −0.0503197 | ||||||||
\(199\) | 6.92169e15 | 0.560068 | 0.280034 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280034 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(200\) | 1.42700e16 | − | 1.42700e16i | 1.11484 | − | 1.11484i | ||||
\(201\) | 7.61179e15 | − | 7.61179e15i | 0.574267 | − | 0.574267i | ||||
\(202\) | 6.95395e15i | 0.506724i | ||||||||
\(203\) | −1.64214e16 | − | 2.10859e16i | −1.15595 | − | 1.48429i | ||||
\(204\) | 2.52100e15 | 0.171460 | ||||||||
\(205\) | 2.90166e16 | + | 2.90166e16i | 1.90708 | + | 1.90708i | ||||
\(206\) | 4.97685e15 | + | 4.97685e15i | 0.316144 | + | 0.316144i | ||||
\(207\) | − | 1.07890e16i | − | 0.662502i | ||||||
\(208\) | 3.09863e15i | 0.183961i | ||||||||
\(209\) | 4.97707e13i | 0.00285726i | ||||||||
\(210\) | −1.82460e16 | −1.01305 | ||||||||
\(211\) | 9.41752e15 | − | 9.41752e15i | 0.505777 | − | 0.505777i | −0.407450 | − | 0.913227i | \(-0.633582\pi\) |
0.913227 | + | 0.407450i | \(0.133582\pi\) | |||||||
\(212\) | 5.00207e15i | 0.259896i | ||||||||
\(213\) | −6.54367e15 | + | 6.54367e15i | −0.328976 | + | 0.328976i | ||||
\(214\) | −3.90612e14 | − | 3.90612e14i | −0.0190042 | − | 0.0190042i | ||||
\(215\) | 3.39897e15 | − | 3.39897e15i | 0.160058 | − | 0.160058i | ||||
\(216\) | 2.01615e16i | 0.919068i | ||||||||
\(217\) | −3.26624e16 | − | 3.26624e16i | −1.44155 | − | 1.44155i | ||||
\(218\) | 4.59324e15 | − | 4.59324e15i | 0.196302 | − | 0.196302i | ||||
\(219\) | −1.26990e16 | −0.525608 | ||||||||
\(220\) | 2.72034e15 | + | 2.72034e15i | 0.109060 | + | 0.109060i | ||||
\(221\) | 9.00995e15 | − | 9.00995e15i | 0.349926 | − | 0.349926i | ||||
\(222\) | 2.78654e14 | + | 2.78654e14i | 0.0104856 | + | 0.0104856i | ||||
\(223\) | 2.07196e16 | 0.755522 | 0.377761 | − | 0.925903i | \(-0.376694\pi\) | ||||
0.377761 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(224\) | −3.88711e16 | − | 3.88711e16i | −1.37370 | − | 1.37370i | ||||
\(225\) | 3.18550e16i | 1.09119i | ||||||||
\(226\) | −2.22983e16 | −0.740477 | ||||||||
\(227\) | −3.48359e16 | −1.12162 | −0.560810 | − | 0.827945i | \(-0.689510\pi\) | ||||
−0.560810 | + | 0.827945i | \(0.689510\pi\) | |||||||
\(228\) | 2.68915e14 | 0.00839598 | ||||||||
\(229\) | −1.09156e16 | + | 1.09156e16i | −0.330520 | + | 0.330520i | −0.852784 | − | 0.522264i | \(-0.825088\pi\) |
0.522264 | + | 0.852784i | \(0.325088\pi\) | |||||||
\(230\) | 2.23274e16 | − | 2.23274e16i | 0.655758 | − | 0.655758i | ||||
\(231\) | − | 5.34424e15i | − | 0.152266i | ||||||
\(232\) | −3.38997e16 | − | 4.21582e15i | −0.937086 | − | 0.116538i | ||||
\(233\) | 5.04344e16 | 1.35281 | 0.676403 | − | 0.736532i | \(-0.263538\pi\) | ||||
0.676403 | + | 0.736532i | \(0.263538\pi\) | |||||||
\(234\) | 1.15927e16 | + | 1.15927e16i | 0.301769 | + | 0.301769i | ||||
\(235\) | 5.05059e16 | + | 5.05059e16i | 1.27605 | + | 1.27605i | ||||
\(236\) | 2.71329e16i | 0.665445i | ||||||||
\(237\) | − | 2.95166e16i | − | 0.702793i | ||||||
\(238\) | 1.93351e16i | 0.447000i | ||||||||
\(239\) | −2.68038e16 | −0.601744 | −0.300872 | − | 0.953665i | \(-0.597278\pi\) | ||||
−0.300872 | + | 0.953665i | \(0.597278\pi\) | |||||||
\(240\) | 4.91988e15 | − | 4.91988e15i | 0.107269 | − | 0.107269i | ||||
\(241\) | − | 2.93237e16i | − | 0.621011i | −0.950572 | − | 0.310505i | \(-0.899502\pi\) | ||
0.950572 | − | 0.310505i | \(-0.100498\pi\) | |||||||
\(242\) | −1.88813e16 | + | 1.88813e16i | −0.388441 | + | 0.388441i | ||||
\(243\) | −3.61124e16 | − | 3.61124e16i | −0.721793 | − | 0.721793i | ||||
\(244\) | −1.70192e16 | + | 1.70192e16i | −0.330530 | + | 0.330530i | ||||
\(245\) | 2.19841e17i | 4.14902i | ||||||||
\(246\) | −2.09719e16 | − | 2.09719e16i | −0.384673 | − | 0.384673i | ||||
\(247\) | 9.61091e14 | − | 9.61091e14i | 0.0171351 | − | 0.0171351i | ||||
\(248\) | −5.90414e16 | −1.02328 | ||||||||
\(249\) | 3.69533e16 | + | 3.69533e16i | 0.622670 | + | 0.622670i | ||||
\(250\) | −2.64390e16 | + | 2.64390e16i | −0.433176 | + | 0.433176i | ||||
\(251\) | 6.51793e15 | + | 6.51793e15i | 0.103847 | + | 0.103847i | 0.757121 | − | 0.653274i | \(-0.226605\pi\) |
−0.653274 | + | 0.757121i | \(0.726605\pi\) | |||||||
\(252\) | 5.44726e16 | 0.844063 | ||||||||
\(253\) | 6.53969e15 | + | 6.53969e15i | 0.0985629 | + | 0.0985629i | ||||
\(254\) | − | 2.63920e16i | − | 0.386933i | ||||||
\(255\) | −2.86113e16 | −0.408090 | ||||||||
\(256\) | −6.24616e16 | −0.866829 | ||||||||
\(257\) | 3.72639e16 | 0.503218 | 0.251609 | − | 0.967829i | \(-0.419040\pi\) | ||||
0.251609 | + | 0.967829i | \(0.419040\pi\) | |||||||
\(258\) | −2.45662e15 | + | 2.45662e15i | −0.0322850 | + | 0.0322850i | ||||
\(259\) | 4.67959e15 | − | 4.67959e15i | 0.0598563 | − | 0.0598563i | ||||
\(260\) | − | 1.05061e17i | − | 1.30807i | ||||||
\(261\) | 4.25427e16 | − | 3.31317e16i | 0.515634 | − | 0.401569i | ||||
\(262\) | 3.52529e16 | 0.415993 | ||||||||
\(263\) | −6.09866e16 | − | 6.09866e16i | −0.700719 | − | 0.700719i | 0.263846 | − | 0.964565i | \(-0.415009\pi\) |
−0.964565 | + | 0.263846i | \(0.915009\pi\) | |||||||
\(264\) | −4.83020e15 | − | 4.83020e15i | −0.0540428 | − | 0.0540428i | ||||
\(265\) | − | 5.67694e16i | − | 0.618576i | ||||||
\(266\) | 2.06247e15i | 0.0218885i | ||||||||
\(267\) | 3.12148e16i | 0.322687i | ||||||||
\(268\) | −9.40560e16 | −0.947203 | ||||||||
\(269\) | 1.03576e17 | − | 1.03576e17i | 1.01624 | − | 1.01624i | 0.0163698 | − | 0.999866i | \(-0.494789\pi\) |
0.999866 | − | 0.0163698i | \(-0.00521091\pi\) | |||||||
\(270\) | − | 9.31400e16i | − | 0.890409i | ||||||
\(271\) | 2.94413e16 | − | 2.94413e16i | 0.274266 | − | 0.274266i | −0.556549 | − | 0.830815i | \(-0.687875\pi\) |
0.830815 | + | 0.556549i | \(0.187875\pi\) | |||||||
\(272\) | −5.21355e15 | − | 5.21355e15i | −0.0473316 | − | 0.0473316i | ||||
\(273\) | −1.03199e17 | + | 1.03199e17i | −0.913142 | + | 0.913142i | ||||
\(274\) | − | 6.07444e16i | − | 0.523904i | ||||||
\(275\) | −1.93088e16 | − | 1.93088e16i | −0.162340 | − | 0.162340i | ||||
\(276\) | 3.53345e16 | − | 3.53345e16i | 0.289624 | − | 0.289624i | ||||
\(277\) | 1.48833e17 | 1.18944 | 0.594718 | − | 0.803934i | \(-0.297264\pi\) | ||||
0.594718 | + | 0.803934i | \(0.297264\pi\) | |||||||
\(278\) | 5.26050e16 | + | 5.26050e16i | 0.409934 | + | 0.409934i | ||||
\(279\) | 6.58993e16 | − | 6.58993e16i | 0.500785 | − | 0.500785i | ||||
\(280\) | 2.76942e17 | + | 2.76942e17i | 2.05250 | + | 2.05250i | ||||
\(281\) | −9.02326e16 | −0.652258 | −0.326129 | − | 0.945325i | \(-0.605744\pi\) | ||||
−0.326129 | + | 0.945325i | \(0.605744\pi\) | |||||||
\(282\) | −3.65034e16 | − | 3.65034e16i | −0.257389 | − | 0.257389i | ||||
\(283\) | − | 3.25620e16i | − | 0.223978i | −0.993709 | − | 0.111989i | \(-0.964278\pi\) | ||
0.993709 | − | 0.111989i | \(-0.0357222\pi\) | |||||||
\(284\) | 8.08577e16 | 0.542617 | ||||||||
\(285\) | −3.05197e15 | −0.0199832 | ||||||||
\(286\) | −1.40538e16 | −0.0897905 | ||||||||
\(287\) | −3.52193e17 | + | 3.52193e17i | −2.19587 | + | 2.19587i | ||||
\(288\) | 7.84260e16 | − | 7.84260e16i | 0.477213 | − | 0.477213i | ||||
\(289\) | − | 1.38059e17i | − | 0.819934i | ||||||
\(290\) | 1.56606e17 | + | 1.94757e16i | 0.907866 | + | 0.112904i | ||||
\(291\) | 1.79713e17 | 1.01702 | ||||||||
\(292\) | 7.84586e16 | + | 7.84586e16i | 0.433472 | + | 0.433472i | ||||
\(293\) | −5.05255e16 | − | 5.05255e16i | −0.272544 | − | 0.272544i | 0.557579 | − | 0.830124i | \(-0.311730\pi\) |
−0.830124 | + | 0.557579i | \(0.811730\pi\) | |||||||
\(294\) | − | 1.58891e17i | − | 0.836889i | ||||||
\(295\) | − | 3.07936e17i | − | 1.58382i | ||||||
\(296\) | − | 8.45897e15i | − | 0.0424889i | ||||||
\(297\) | 2.72807e16 | 0.133832 | ||||||||
\(298\) | 5.75012e16 | − | 5.75012e16i | 0.275526 | − | 0.275526i | ||||
\(299\) | − | 2.52568e17i | − | 1.18217i | ||||||
\(300\) | −1.04327e17 | + | 1.04327e17i | −0.477032 | + | 0.477032i | ||||
\(301\) | 4.12554e16 | + | 4.12554e16i | 0.184296 | + | 0.184296i | ||||
\(302\) | −1.04506e17 | + | 1.04506e17i | −0.456134 | + | 0.456134i | ||||
\(303\) | − | 1.24898e17i | − | 0.532669i | ||||||
\(304\) | −5.56129e14 | − | 5.56129e14i | −0.00231772 | − | 0.00231772i | ||||
\(305\) | 1.93154e17 | − | 1.93154e17i | 0.786693 | − | 0.786693i | ||||
\(306\) | −3.90103e16 | −0.155285 | ||||||||
\(307\) | 1.92600e17 | + | 1.92600e17i | 0.749356 | + | 0.749356i | 0.974358 | − | 0.225002i | \(-0.0722389\pi\) |
−0.225002 | + | 0.974358i | \(0.572239\pi\) | |||||||
\(308\) | −3.30184e16 | + | 3.30184e16i | −0.125574 | + | 0.125574i | ||||
\(309\) | −8.93881e16 | − | 8.93881e16i | −0.332331 | − | 0.332331i | ||||
\(310\) | 2.72753e17 | 0.991374 | ||||||||
\(311\) | −2.54972e17 | − | 2.54972e17i | −0.906086 | − | 0.906086i | 0.0898681 | − | 0.995954i | \(-0.471355\pi\) |
−0.995954 | + | 0.0898681i | \(0.971355\pi\) | |||||||
\(312\) | 1.86546e17i | 0.648193i | ||||||||
\(313\) | −2.30770e17 | −0.784097 | −0.392048 | − | 0.919945i | \(-0.628233\pi\) | ||||
−0.392048 | + | 0.919945i | \(0.628233\pi\) | |||||||
\(314\) | −2.51595e17 | −0.835978 | ||||||||
\(315\) | −6.18220e17 | −2.00895 | ||||||||
\(316\) | −1.82363e17 | + | 1.82363e17i | −0.579597 | + | 0.579597i | ||||
\(317\) | 1.99259e17 | − | 1.99259e17i | 0.619444 | − | 0.619444i | −0.325945 | − | 0.945389i | \(-0.605682\pi\) |
0.945389 | + | 0.325945i | \(0.105682\pi\) | |||||||
\(318\) | 4.10303e16i | 0.124771i | ||||||||
\(319\) | −5.70444e15 | + | 4.58698e16i | −0.0169699 | + | 0.136456i | ||||
\(320\) | 2.36043e17 | 0.686975 | ||||||||
\(321\) | 7.01570e15 | + | 7.01570e15i | 0.0199772 | + | 0.0199772i | ||||
\(322\) | 2.71001e17 | + | 2.71001e17i | 0.755058 | + | 0.755058i | ||||
\(323\) | 3.23414e15i | 0.00881741i | ||||||||
\(324\) | 2.07625e16i | 0.0553942i | ||||||||
\(325\) | 7.45720e17i | 1.94712i | ||||||||
\(326\) | −3.14247e17 | −0.803059 | ||||||||
\(327\) | −8.24981e16 | + | 8.24981e16i | −0.206353 | + | 0.206353i | ||||
\(328\) | 6.36634e17i | 1.55874i | ||||||||
\(329\) | −6.13022e17 | + | 6.13022e17i | −1.46928 | + | 1.46928i | ||||
\(330\) | 2.23140e16 | + | 2.23140e16i | 0.0523577 | + | 0.0523577i | ||||
\(331\) | 3.81816e17 | − | 3.81816e17i | 0.877119 | − | 0.877119i | −0.116117 | − | 0.993236i | \(-0.537045\pi\) |
0.993236 | + | 0.116117i | \(0.0370447\pi\) | |||||||
\(332\) | − | 4.56619e17i | − | 1.02704i | ||||||
\(333\) | 9.44150e15 | + | 9.44150e15i | 0.0207937 | + | 0.0207937i | ||||
\(334\) | 3.36399e17 | − | 3.36399e17i | 0.725487 | − | 0.725487i | ||||
\(335\) | 1.06746e18 | 2.25443 | ||||||||
\(336\) | 5.97156e16 | + | 5.97156e16i | 0.123513 | + | 0.123513i | ||||
\(337\) | −8.53481e16 | + | 8.53481e16i | −0.172896 | + | 0.172896i | −0.788250 | − | 0.615355i | \(-0.789013\pi\) |
0.615355 | + | 0.788250i | \(0.289013\pi\) | |||||||
\(338\) | 7.18426e16 | + | 7.18426e16i | 0.142549 | + | 0.142549i | ||||
\(339\) | 4.00494e17 | 0.778391 | ||||||||
\(340\) | 1.76770e17 | + | 1.76770e17i | 0.336554 | + | 0.336554i | ||||
\(341\) | 7.98892e16i | 0.149007i | ||||||||
\(342\) | −4.16123e15 | −0.00760394 | ||||||||
\(343\) | −1.61754e18 | −2.89599 | ||||||||
\(344\) | 7.45746e16 | 0.130822 | ||||||||
\(345\) | −4.01017e17 | + | 4.01017e17i | −0.689333 | + | 0.689333i | ||||
\(346\) | −1.79294e17 | + | 1.79294e17i | −0.302019 | + | 0.302019i | ||||
\(347\) | − | 2.47326e16i | − | 0.0408284i | −0.999792 | − | 0.0204142i | \(-0.993502\pi\) | ||
0.999792 | − | 0.0204142i | \(-0.00649850\pi\) | |||||||
\(348\) | 2.47838e17 | + | 3.08215e16i | 0.400972 | + | 0.0498655i | ||||
\(349\) | −9.03583e17 | −1.43282 | −0.716408 | − | 0.697682i | \(-0.754215\pi\) | ||||
−0.716408 | + | 0.697682i | \(0.754215\pi\) | |||||||
\(350\) | −8.00146e17 | − | 8.00146e17i | −1.24364 | − | 1.24364i | ||||
\(351\) | −5.26800e17 | − | 5.26800e17i | −0.802594 | − | 0.802594i | ||||
\(352\) | 9.50753e16i | 0.141994i | ||||||||
\(353\) | − | 4.27954e17i | − | 0.626577i | −0.949658 | − | 0.313288i | \(-0.898569\pi\) | ||
0.949658 | − | 0.313288i | \(-0.101431\pi\) | |||||||
\(354\) | 2.22562e17i | 0.319469i | ||||||||
\(355\) | −9.17668e17 | −1.29148 | ||||||||
\(356\) | 1.92855e17 | − | 1.92855e17i | 0.266122 | − | 0.266122i | ||||
\(357\) | − | 3.47273e17i | − | 0.469887i | ||||||
\(358\) | 1.49630e17 | − | 1.49630e17i | 0.198535 | − | 0.198535i | ||||
\(359\) | 1.06381e18 | + | 1.06381e18i | 1.38421 | + | 1.38421i | 0.836989 | + | 0.547219i | \(0.184314\pi\) |
0.547219 | + | 0.836989i | \(0.315686\pi\) | |||||||
\(360\) | −5.58756e17 | + | 5.58756e17i | −0.713025 | + | 0.713025i | ||||
\(361\) | − | 7.98662e17i | − | 0.999568i | ||||||
\(362\) | 4.58930e17 | + | 4.58930e17i | 0.563361 | + | 0.563361i | ||||
\(363\) | 3.39123e17 | − | 3.39123e17i | 0.408330 | − | 0.408330i | ||||
\(364\) | 1.27520e18 | 1.50615 | ||||||||
\(365\) | −8.90441e17 | − | 8.90441e17i | −1.03170 | − | 1.03170i | ||||
\(366\) | −1.39603e17 | + | 1.39603e17i | −0.158682 | + | 0.158682i | ||||
\(367\) | 9.47267e17 | + | 9.47267e17i | 1.05636 | + | 1.05636i | 0.998314 | + | 0.0580412i | \(0.0184855\pi\) |
0.0580412 | + | 0.998314i | \(0.481515\pi\) | |||||||
\(368\) | −1.46147e17 | −0.159902 | ||||||||
\(369\) | −7.10581e17 | − | 7.10581e17i | −0.762832 | − | 0.762832i | ||||
\(370\) | 3.90778e16i | 0.0411640i | ||||||||
\(371\) | 6.89045e17 | 0.712246 | ||||||||
\(372\) | 4.31648e17 | 0.437854 | ||||||||
\(373\) | 1.23394e18 | 1.22837 | 0.614187 | − | 0.789160i | \(-0.289484\pi\) | ||||
0.614187 | + | 0.789160i | \(0.289484\pi\) | |||||||
\(374\) | 2.36460e16 | − | 2.36460e16i | 0.0231023 | − | 0.0231023i | ||||
\(375\) | 4.74864e17 | − | 4.74864e17i | 0.455356 | − | 0.455356i | ||||
\(376\) | 1.10812e18i | 1.04297i | ||||||||
\(377\) | 9.95918e17 | − | 7.75608e17i | 0.920098 | − | 0.716561i | ||||
\(378\) | 1.13050e18 | 1.02524 | ||||||||
\(379\) | −7.58083e17 | − | 7.58083e17i | −0.674904 | − | 0.674904i | 0.283938 | − | 0.958843i | \(-0.408359\pi\) |
−0.958843 | + | 0.283938i | \(0.908359\pi\) | |||||||
\(380\) | 1.88560e16 | + | 1.88560e16i | 0.0164803 | + | 0.0164803i | ||||
\(381\) | 4.74020e17i | 0.406745i | ||||||||
\(382\) | − | 5.89210e17i | − | 0.496394i | ||||||
\(383\) | 6.42828e17i | 0.531745i | 0.964008 | + | 0.265872i | \(0.0856600\pi\) | ||||
−0.964008 | + | 0.265872i | \(0.914340\pi\) | |||||||
\(384\) | 5.77705e17 | 0.469232 | ||||||||
\(385\) | 3.74732e17 | − | 3.74732e17i | 0.298879 | − | 0.298879i | ||||
\(386\) | − | 1.24679e18i | − | 0.976521i | ||||||
\(387\) | −8.32366e16 | + | 8.32366e16i | −0.0640232 | + | 0.0640232i | ||||
\(388\) | −1.11032e18 | − | 1.11032e18i | −0.838740 | − | 0.838740i | ||||
\(389\) | −1.41465e18 | + | 1.41465e18i | −1.04954 | + | 1.04954i | −0.0508364 | + | 0.998707i | \(0.516189\pi\) |
−0.998707 | + | 0.0508364i | \(0.983811\pi\) | |||||||
\(390\) | − | 8.61784e17i | − | 0.627981i | ||||||
\(391\) | 4.24954e17 | + | 4.24954e17i | 0.304162 | + | 0.304162i | ||||
\(392\) | −2.41169e18 | + | 2.41169e18i | −1.69558 | + | 1.69558i | ||||
\(393\) | −6.33169e17 | −0.437293 | ||||||||
\(394\) | −5.32935e16 | − | 5.32935e16i | −0.0361577 | − | 0.0361577i | ||||
\(395\) | 2.06967e18 | − | 2.06967e18i | 1.37950 | − | 1.37950i | ||||
\(396\) | −6.66176e16 | − | 6.66176e16i | −0.0436237 | − | 0.0436237i | ||||
\(397\) | 1.75929e18 | 1.13189 | 0.565946 | − | 0.824443i | \(-0.308511\pi\) | ||||
0.565946 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(398\) | −3.50782e17 | − | 3.50782e17i | −0.221746 | − | 0.221746i | ||||
\(399\) | − | 3.70436e16i | − | 0.0230093i | ||||||
\(400\) | 4.31506e17 | 0.263370 | ||||||||
\(401\) | −3.34717e17 | −0.200755 | −0.100378 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100378 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(402\) | −7.71510e17 | −0.454736 | ||||||||
\(403\) | 1.54269e18 | − | 1.54269e18i | 0.893601 | − | 0.893601i | ||||
\(404\) | −7.71660e17 | + | 7.71660e17i | −0.439295 | + | 0.439295i | ||||
\(405\) | − | 2.35637e17i | − | 0.131844i | ||||||
\(406\) | −2.36389e17 | + | 1.90082e18i | −0.130001 | + | 1.04534i | ||||
\(407\) | −1.14459e16 | −0.00618711 | ||||||||
\(408\) | −3.13871e17 | − | 3.13871e17i | −0.166774 | − | 0.166774i | ||||
\(409\) | −3.29146e17 | − | 3.29146e17i | −0.171920 | − | 0.171920i | 0.615903 | − | 0.787822i | \(-0.288791\pi\) |
−0.787822 | + | 0.615903i | \(0.788791\pi\) | |||||||
\(410\) | − | 2.94105e18i | − | 1.51013i | ||||||
\(411\) | 1.09102e18i | 0.550729i | ||||||||
\(412\) | 1.10454e18i | 0.548150i | ||||||||
\(413\) | 3.73761e18 | 1.82366 | ||||||||
\(414\) | −5.46770e17 | + | 5.46770e17i | −0.262302 | + | 0.262302i | ||||
\(415\) | 5.18224e18i | 2.44445i | ||||||||
\(416\) | 1.83594e18 | − | 1.83594e18i | 0.851540 | − | 0.851540i | ||||
\(417\) | −9.44826e17 | − | 9.44826e17i | −0.430923 | − | 0.430923i | ||||
\(418\) | 2.52231e15 | − | 2.52231e15i | 0.00113127 | − | 0.00113127i | ||||
\(419\) | 2.97088e18i | 1.31035i | 0.755477 | + | 0.655175i | \(0.227405\pi\) | ||||
−0.755477 | + | 0.655175i | \(0.772595\pi\) | |||||||
\(420\) | −2.02471e18 | − | 2.02471e18i | −0.878248 | − | 0.878248i | ||||
\(421\) | 2.00354e18 | − | 2.00354e18i | 0.854718 | − | 0.854718i | −0.135992 | − | 0.990710i | \(-0.543422\pi\) |
0.990710 | + | 0.135992i | \(0.0434222\pi\) | |||||||
\(422\) | −9.54535e17 | −0.400502 | ||||||||
\(423\) | −1.23683e18 | − | 1.23683e18i | −0.510418 | − | 0.510418i | ||||
\(424\) | 6.22769e17 | − | 6.22769e17i | 0.252794 | − | 0.252794i | ||||
\(425\) | −1.25470e18 | − | 1.25470e18i | −0.500976 | − | 0.500976i | ||||
\(426\) | 6.63249e17 | 0.260501 | ||||||||
\(427\) | 2.34443e18 | + | 2.34443e18i | 0.905821 | + | 0.905821i | ||||
\(428\) | − | 8.66904e16i | − | 0.0329507i | ||||||
\(429\) | 2.52416e17 | 0.0943879 | ||||||||
\(430\) | −3.44511e17 | −0.126743 | ||||||||
\(431\) | −3.84467e18 | −1.39161 | −0.695806 | − | 0.718230i | \(-0.744953\pi\) | ||||
−0.695806 | + | 0.718230i | \(0.744953\pi\) | |||||||
\(432\) | −3.04829e17 | + | 3.04829e17i | −0.108560 | + | 0.108560i | ||||
\(433\) | −7.50207e16 | + | 7.50207e16i | −0.0262885 | + | 0.0262885i | −0.720129 | − | 0.693840i | \(-0.755917\pi\) |
0.693840 | + | 0.720129i | \(0.255917\pi\) | |||||||
\(434\) | 3.31057e18i | 1.14150i | ||||||||
\(435\) | −2.81276e18 | − | 3.49799e17i | −0.954350 | − | 0.118684i | ||||
\(436\) | 1.01940e18 | 0.340360 | ||||||||
\(437\) | 4.53298e16 | + | 4.53298e16i | 0.0148941 | + | 0.0148941i | ||||
\(438\) | 6.43570e17 | + | 6.43570e17i | 0.208102 | + | 0.208102i | ||||
\(439\) | 3.07042e18i | 0.977116i | 0.872532 | + | 0.488558i | \(0.162477\pi\) | ||||
−0.872532 | + | 0.488558i | \(0.837523\pi\) | |||||||
\(440\) | − | 6.77376e17i | − | 0.212159i | ||||||
\(441\) | − | 5.38363e18i | − | 1.65961i | ||||||
\(442\) | −9.13225e17 | −0.277091 | ||||||||
\(443\) | 1.24585e18 | − | 1.24585e18i | 0.372082 | − | 0.372082i | −0.496153 | − | 0.868235i | \(-0.665254\pi\) |
0.868235 | + | 0.496153i | \(0.165254\pi\) | |||||||
\(444\) | 6.18430e16i | 0.0181807i | ||||||||
\(445\) | −2.18874e18 | + | 2.18874e18i | −0.633396 | + | 0.633396i | ||||
\(446\) | −1.05004e18 | − | 1.05004e18i | −0.299132 | − | 0.299132i | ||||
\(447\) | −1.03277e18 | + | 1.03277e18i | −0.289634 | + | 0.289634i | ||||
\(448\) | 2.86500e18i | 0.791003i | ||||||||
\(449\) | −1.94044e18 | − | 1.94044e18i | −0.527444 | − | 0.527444i | 0.392366 | − | 0.919809i | \(-0.371657\pi\) |
−0.919809 | + | 0.392366i | \(0.871657\pi\) | |||||||
\(450\) | 1.61437e18 | − | 1.61437e18i | 0.432031 | − | 0.432031i | ||||
\(451\) | 8.61432e17 | 0.226979 | ||||||||
\(452\) | −2.47438e18 | − | 2.47438e18i | −0.641943 | − | 0.641943i | ||||
\(453\) | 1.87701e18 | − | 1.87701e18i | 0.479488 | − | 0.479488i | ||||
\(454\) | 1.76544e18 | + | 1.76544e18i | 0.444080 | + | 0.444080i | ||||
\(455\) | −1.44724e19 | −3.58477 | ||||||||
\(456\) | −3.34805e16 | − | 3.34805e16i | −0.00816655 | − | 0.00816655i | ||||
\(457\) | 3.62949e18i | 0.871831i | 0.899987 | + | 0.435916i | \(0.143575\pi\) | ||||
−0.899987 | + | 0.435916i | \(0.856425\pi\) | |||||||
\(458\) | 1.10637e18 | 0.261723 | ||||||||
\(459\) | 1.77272e18 | 0.413001 | ||||||||
\(460\) | 4.95522e18 | 1.13699 | ||||||||
\(461\) | 4.94910e18 | − | 4.94910e18i | 1.11846 | − | 1.11846i | 0.126490 | − | 0.991968i | \(-0.459629\pi\) |
0.991968 | − | 0.126490i | \(-0.0403712\pi\) | |||||||
\(462\) | −2.70839e17 | + | 2.70839e17i | −0.0602861 | + | 0.0602861i | ||||
\(463\) | 4.68821e18i | 1.02787i | 0.857828 | + | 0.513937i | \(0.171814\pi\) | ||||
−0.857828 | + | 0.513937i | \(0.828186\pi\) | |||||||
\(464\) | −4.48801e17 | − | 5.76281e17i | −0.0969231 | − | 0.124454i | ||||
\(465\) | −4.89885e18 | −1.04213 | ||||||||
\(466\) | −2.55595e18 | − | 2.55595e18i | −0.535613 | − | 0.535613i | ||||
\(467\) | 3.10142e18 | + | 3.10142e18i | 0.640239 | + | 0.640239i | 0.950614 | − | 0.310375i | \(-0.100455\pi\) |
−0.310375 | + | 0.950614i | \(0.600455\pi\) | |||||||
\(468\) | 2.57282e18i | 0.523226i | ||||||||
\(469\) | 1.29564e19i | 2.59582i | ||||||||
\(470\) | − | 5.11915e18i | − | 1.01045i | ||||||
\(471\) | 4.51884e18 | 0.878782 | ||||||||
\(472\) | 3.37811e18 | − | 3.37811e18i | 0.647261 | − | 0.647261i | ||||
\(473\) | − | 1.00907e17i | − | 0.0190500i | ||||||
\(474\) | −1.49586e18 | + | 1.49586e18i | −0.278255 | + | 0.278255i | ||||
\(475\) | −1.33839e17 | − | 1.33839e17i | −0.0245316 | − | 0.0245316i | ||||
\(476\) | −2.14556e18 | + | 2.14556e18i | −0.387518 | + | 0.387518i | ||||
\(477\) | 1.39021e18i | 0.247430i | ||||||||
\(478\) | 1.35838e18 | + | 1.35838e18i | 0.238247 | + | 0.238247i | ||||
\(479\) | −2.23154e18 | + | 2.23154e18i | −0.385706 | + | 0.385706i | −0.873153 | − | 0.487447i | \(-0.837928\pi\) |
0.487447 | + | 0.873153i | \(0.337928\pi\) | |||||||
\(480\) | −5.83007e18 | −0.993082 | ||||||||
\(481\) | 2.21024e17 | + | 2.21024e17i | 0.0371043 | + | 0.0371043i | ||||
\(482\) | −1.48609e18 | + | 1.48609e18i | −0.245875 | + | 0.245875i | ||||
\(483\) | −4.86739e18 | − | 4.86739e18i | −0.793718 | − | 0.793718i | ||||
\(484\) | −4.19042e18 | −0.673503 | ||||||||
\(485\) | 1.26013e19 | + | 1.26013e19i | 1.99628 | + | 1.99628i | ||||
\(486\) | 3.66026e18i | 0.571555i | ||||||||
\(487\) | −4.96126e18 | −0.763640 | −0.381820 | − | 0.924237i | \(-0.624703\pi\) | ||||
−0.381820 | + | 0.924237i | \(0.624703\pi\) | |||||||
\(488\) | 4.23786e18 | 0.642996 | ||||||||
\(489\) | 5.64411e18 | 0.844177 | ||||||||
\(490\) | 1.11412e19 | − | 1.11412e19i | 1.64271 | − | 1.64271i | ||||
\(491\) | −2.54320e17 | + | 2.54320e17i | −0.0369666 | + | 0.0369666i | −0.725348 | − | 0.688382i | \(-0.758321\pi\) |
0.688382 | + | 0.725348i | \(0.258321\pi\) | |||||||
\(492\) | − | 4.65439e18i | − | 0.666971i | ||||||
\(493\) | −3.70679e17 | + | 2.98065e18i | −0.0523684 | + | 0.421098i | ||||
\(494\) | −9.74136e16 | −0.0135685 | ||||||||
\(495\) | 7.56055e17 | + | 7.56055e17i | 0.103829 | + | 0.103829i | ||||
\(496\) | −8.92668e17 | − | 8.92668e17i | −0.120870 | − | 0.120870i | ||||
\(497\) | − | 1.11383e19i | − | 1.48705i | ||||||
\(498\) | − | 3.74549e18i | − | 0.493064i | ||||||
\(499\) | − | 4.29483e18i | − | 0.557497i | −0.960364 | − | 0.278749i | \(-0.910080\pi\) | ||
0.960364 | − | 0.278749i | \(-0.0899196\pi\) | |||||||
\(500\) | −5.86772e18 | −0.751069 | ||||||||
\(501\) | −6.04199e18 | + | 6.04199e18i | −0.762633 | + | 0.762633i | ||||
\(502\) | − | 6.60640e17i | − | 0.0822316i | ||||||
\(503\) | −1.18264e18 | + | 1.18264e18i | −0.145170 | + | 0.145170i | −0.775956 | − | 0.630787i | \(-0.782732\pi\) |
0.630787 | + | 0.775956i | \(0.282732\pi\) | |||||||
\(504\) | −6.78197e18 | − | 6.78197e18i | −0.820998 | − | 0.820998i | ||||
\(505\) | 8.75771e18 | − | 8.75771e18i | 1.04556 | − | 1.04556i | ||||
\(506\) | − | 6.62845e17i | − | 0.0780474i | ||||||
\(507\) | −1.29035e18 | − | 1.29035e18i | −0.149848 | − | 0.149848i | ||||
\(508\) | 2.92865e18 | − | 2.92865e18i | 0.335445 | − | 0.335445i | ||||
\(509\) | 1.46422e19 | 1.65417 | 0.827086 | − | 0.562076i | \(-0.189997\pi\) | ||||
0.827086 | + | 0.562076i | \(0.189997\pi\) | |||||||
\(510\) | 1.44998e18 | + | 1.44998e18i | 0.161574 | + | 0.161574i | ||||
\(511\) | 1.08078e19 | − | 1.08078e19i | 1.18793 | − | 1.18793i | ||||
\(512\) | −2.03384e18 | − | 2.03384e18i | −0.220510 | − | 0.220510i | ||||
\(513\) | 1.89096e17 | 0.0202237 | ||||||||
\(514\) | −1.88848e18 | − | 1.88848e18i | −0.199238 | − | 0.199238i | ||||
\(515\) | − | 1.25356e19i | − | 1.30465i | ||||||
\(516\) | −5.45210e17 | −0.0559778 | ||||||||
\(517\) | 1.49940e18 | 0.151874 | ||||||||
\(518\) | −4.74311e17 | −0.0473974 | ||||||||
\(519\) | 3.22026e18 | − | 3.22026e18i | 0.317482 | − | 0.317482i | ||||
\(520\) | −1.30804e19 | + | 1.30804e19i | −1.27232 | + | 1.27232i | ||||
\(521\) | − | 8.79802e18i | − | 0.844347i | −0.906515 | − | 0.422174i | \(-0.861267\pi\) | ||
0.906515 | − | 0.422174i | \(-0.138733\pi\) | |||||||
\(522\) | −3.83508e18 | − | 4.76936e17i | −0.363146 | − | 0.0451613i | ||||
\(523\) | 1.34686e19 | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283388\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283388\pi\) | |||||||
\(524\) | 3.91192e18 | + | 3.91192e18i | 0.360638 | + | 0.360638i | ||||
\(525\) | 1.43712e19 | + | 1.43712e19i | 1.30731 | + | 1.30731i | ||||
\(526\) | 6.18144e18i | 0.554867i | ||||||||
\(527\) | 5.19126e18i | 0.459832i | ||||||||
\(528\) | − | 1.46059e17i | − | 0.0127671i | ||||||
\(529\) | 3.19509e17 | 0.0275609 | ||||||||
\(530\) | −2.87700e18 | + | 2.87700e18i | −0.244911 | + | 0.244911i | ||||
\(531\) | 7.54097e18i | 0.633528i | ||||||||
\(532\) | −2.28867e17 | + | 2.28867e17i | −0.0189759 | + | 0.0189759i | ||||
\(533\) | −1.66346e19 | − | 1.66346e19i | −1.36120 | − | 1.36120i | ||||
\(534\) | 1.58192e18 | − | 1.58192e18i | 0.127761 | − | 0.127761i | ||||
\(535\) | 9.83865e17i | 0.0784258i | ||||||||
\(536\) | 1.17102e19 | + | 1.17102e19i | 0.921319 | + | 0.921319i | ||||
\(537\) | −2.68746e18 | + | 2.68746e18i | −0.208700 | + | 0.208700i | ||||
\(538\) | −1.04982e19 | −0.804711 | ||||||||
\(539\) | 3.26327e18 | + | 3.26327e18i | 0.246906 | + | 0.246906i | ||||
\(540\) | 1.03355e19 | − | 1.03355e19i | 0.771924 | − | 0.771924i | ||||
\(541\) | −1.47156e19 | − | 1.47156e19i | −1.08492 | − | 1.08492i | −0.996043 | − | 0.0888737i | \(-0.971673\pi\) |
−0.0888737 | − | 0.996043i | \(-0.528327\pi\) | |||||||
\(542\) | −2.98409e18 | −0.217179 | ||||||||
\(543\) | −8.24273e18 | − | 8.24273e18i | −0.592206 | − | 0.592206i | ||||
\(544\) | 6.17807e18i | 0.438188i | ||||||||
\(545\) | −1.15693e19 | −0.810090 | ||||||||
\(546\) | 1.04600e19 | 0.723075 | ||||||||
\(547\) | −6.68236e18 | −0.456056 | −0.228028 | − | 0.973655i | \(-0.573228\pi\) | ||||
−0.228028 | + | 0.973655i | \(0.573228\pi\) | |||||||
\(548\) | 6.74064e18 | − | 6.74064e18i | 0.454189 | − | 0.454189i | ||||
\(549\) | −4.73010e18 | + | 4.73010e18i | −0.314676 | + | 0.314676i | ||||
\(550\) | 1.95709e18i | 0.128550i | ||||||||
\(551\) | −3.95403e16 | + | 3.17946e17i | −0.00256436 | + | 0.0206202i | ||||
\(552\) | −8.79844e18 | −0.563420 | ||||||||
\(553\) | 2.51208e19 | + | 2.51208e19i | 1.58839 | + | 1.58839i | ||||
\(554\) | −7.54267e18 | − | 7.54267e18i | −0.470930 | − | 0.470930i | ||||
\(555\) | − | 7.01867e17i | − | 0.0432717i | ||||||
\(556\) | 1.16749e19i | 0.710769i | ||||||||
\(557\) | − | 2.32795e19i | − | 1.39955i | −0.714364 | − | 0.699774i | \(-0.753284\pi\) | ||
0.714364 | − | 0.699774i | \(-0.246716\pi\) | |||||||
\(558\) | −6.67937e18 | −0.396548 | ||||||||
\(559\) | −1.94856e18 | + | 1.94856e18i | −0.114243 | + | 0.114243i | ||||
\(560\) | 8.37437e18i | 0.484882i | ||||||||
\(561\) | −4.24699e17 | + | 4.24699e17i | −0.0242852 | + | 0.0242852i | ||||
\(562\) | 4.57287e18 | + | 4.57287e18i | 0.258246 | + | 0.258246i | ||||
\(563\) | −1.83350e19 | + | 1.83350e19i | −1.02264 | + | 1.02264i | −0.0229000 | + | 0.999738i | \(0.507290\pi\) |
−0.999738 | + | 0.0229000i | \(0.992710\pi\) | |||||||
\(564\) | − | 8.10136e18i | − | 0.446277i | ||||||
\(565\) | 2.80821e19 | + | 2.80821e19i | 1.52789 | + | 1.52789i | ||||
\(566\) | −1.65020e18 | + | 1.65020e18i | −0.0886790 | + | 0.0886790i | ||||
\(567\) | 2.86007e18 | 0.151808 | ||||||||
\(568\) | −1.00670e19 | − | 1.00670e19i | −0.527789 | − | 0.527789i | ||||
\(569\) | −7.77395e18 | + | 7.77395e18i | −0.402583 | + | 0.402583i | −0.879142 | − | 0.476559i | \(-0.841884\pi\) |
0.476559 | + | 0.879142i | \(0.341884\pi\) | |||||||
\(570\) | 1.54670e17 | + | 1.54670e17i | 0.00791190 | + | 0.00791190i | ||||
\(571\) | 8.59674e17 | 0.0434391 | 0.0217195 | − | 0.999764i | \(-0.493086\pi\) | ||||
0.0217195 | + | 0.999764i | \(0.493086\pi\) | |||||||
\(572\) | −1.55951e18 | − | 1.55951e18i | −0.0778423 | − | 0.0778423i | ||||
\(573\) | 1.05827e19i | 0.521810i | ||||||||
\(574\) | 3.56973e19 | 1.73881 | ||||||||
\(575\) | −3.51718e19 | −1.69247 | ||||||||
\(576\) | −5.78039e18 | −0.274789 | ||||||||
\(577\) | −1.95893e19 | + | 1.95893e19i | −0.920002 | + | 0.920002i | −0.997029 | − | 0.0770267i | \(-0.975457\pi\) |
0.0770267 | + | 0.997029i | \(0.475457\pi\) | |||||||
\(578\) | −6.99663e18 | + | 6.99663e18i | −0.324634 | + | 0.324634i | ||||
\(579\) | 2.23933e19i | 1.02652i | ||||||||
\(580\) | 1.52169e19 | + | 1.95393e19i | 0.689178 | + | 0.884938i | ||||
\(581\) | −6.29001e19 | −2.81461 | ||||||||
\(582\) | −9.10761e18 | − | 9.10761e18i | −0.402665 | − | 0.402665i | ||||
\(583\) | −8.42672e17 | − | 8.42672e17i | −0.0368111 | − | 0.0368111i | ||||
\(584\) | − | 1.95366e19i | − | 0.843253i | ||||||
\(585\) | − | 2.91994e19i | − | 1.24533i | ||||||
\(586\) | 5.12113e18i | 0.215815i | ||||||||
\(587\) | 2.91015e19 | 1.21185 | 0.605924 | − | 0.795522i | \(-0.292803\pi\) | ||||
0.605924 | + | 0.795522i | \(0.292803\pi\) | |||||||
\(588\) | 1.76317e19 | − | 1.76317e19i | 0.725526 | − | 0.725526i | ||||
\(589\) | 5.53752e17i | 0.0225169i | ||||||||
\(590\) | −1.56058e19 | + | 1.56058e19i | −0.627078 | + | 0.627078i | ||||
\(591\) | 9.57192e17 | + | 9.57192e17i | 0.0380090 | + | 0.0380090i | ||||
\(592\) | 1.27894e17 | − | 1.27894e17i | 0.00501879 | − | 0.00501879i | ||||
\(593\) | − | 5.04546e18i | − | 0.195667i | −0.995203 | − | 0.0978335i | \(-0.968809\pi\) | ||
0.995203 | − | 0.0978335i | \(-0.0311913\pi\) | |||||||
\(594\) | −1.38255e18 | − | 1.38255e18i | −0.0529877 | − | 0.0529877i | ||||
\(595\) | 2.43504e19 | − | 2.43504e19i | 0.922331 | − | 0.922331i | ||||
\(596\) | 1.27615e19 | 0.477725 | ||||||||
\(597\) | 6.30031e18 | + | 6.30031e18i | 0.233100 | + | 0.233100i | ||||
\(598\) | −1.27998e19 | + | 1.27998e19i | −0.468053 | + | 0.468053i | ||||
\(599\) | 2.08967e19 | + | 2.08967e19i | 0.755250 | + | 0.755250i | 0.975454 | − | 0.220204i | \(-0.0706723\pi\) |
−0.220204 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(600\) | 2.59779e19 | 0.927993 | ||||||||
\(601\) | −3.49596e19 | − | 3.49596e19i | −1.23437 | − | 1.23437i | −0.962269 | − | 0.272102i | \(-0.912281\pi\) |
−0.272102 | − | 0.962269i | \(-0.587719\pi\) | |||||||
\(602\) | − | 4.18154e18i | − | 0.145936i | ||||||
\(603\) | −2.61407e19 | −0.901771 | ||||||||
\(604\) | −2.31935e19 | −0.790874 | ||||||||
\(605\) | 4.75578e19 | 1.60300 | ||||||||
\(606\) | −6.32967e18 | + | 6.32967e18i | −0.210898 | + | 0.210898i | ||||
\(607\) | 9.04753e17 | − | 9.04753e17i | 0.0297995 | − | 0.0297995i | −0.692050 | − | 0.721850i | \(-0.743292\pi\) |
0.721850 | + | 0.692050i | \(0.243292\pi\) | |||||||
\(608\) | 6.59014e17i | 0.0214570i | ||||||||
\(609\) | 4.24573e18 | − | 3.41402e19i | 0.136657 | − | 1.09887i | ||||
\(610\) | −1.95776e19 | −0.622946 | ||||||||
\(611\) | −2.89539e19 | − | 2.89539e19i | −0.910791 | − | 0.910791i | ||||
\(612\) | −4.32887e18 | − | 4.32887e18i | −0.134621 | − | 0.134621i | ||||
\(613\) | − | 2.72706e19i | − | 0.838438i | −0.907885 | − | 0.419219i | \(-0.862304\pi\) | ||
0.907885 | − | 0.419219i | \(-0.137696\pi\) | |||||||
\(614\) | − | 1.95214e19i | − | 0.593381i | ||||||
\(615\) | 5.28235e19i | 1.58745i | ||||||||
\(616\) | 8.22173e18 | 0.244286 | ||||||||
\(617\) | −1.27945e19 | + | 1.27945e19i | −0.375861 | + | 0.375861i | −0.869606 | − | 0.493746i | \(-0.835627\pi\) |
0.493746 | + | 0.869606i | \(0.335627\pi\) | |||||||
\(618\) | 9.06014e18i | 0.263157i | ||||||||
\(619\) | 2.37106e19 | − | 2.37106e19i | 0.680939 | − | 0.680939i | −0.279273 | − | 0.960212i | \(-0.590093\pi\) |
0.960212 | + | 0.279273i | \(0.0900933\pi\) | |||||||
\(620\) | 3.02666e19 | + | 3.02666e19i | 0.859453 | + | 0.859453i | ||||
\(621\) | 2.48465e19 | − | 2.48465e19i | 0.697628 | − | 0.697628i | ||||
\(622\) | 2.58432e19i | 0.717488i | ||||||||
\(623\) | −2.65661e19 | − | 2.65661e19i | −0.729310 | − | 0.729310i | ||||
\(624\) | −2.82046e18 | + | 2.82046e18i | −0.0765645 | + | 0.0765645i | ||||
\(625\) | 4.39582e18 | 0.117999 | ||||||||
\(626\) | 1.16951e19 | + | 1.16951e19i | 0.310445 | + | 0.310445i | ||||
\(627\) | −4.53027e16 | + | 4.53027e16i | −0.00118919 | + | 0.00118919i | ||||
\(628\) | −2.79188e19 | − | 2.79188e19i | −0.724736 | − | 0.724736i | ||||
\(629\) | −7.43761e17 | −0.0190932 | ||||||||
\(630\) | 3.13305e19 | + | 3.13305e19i | 0.795397 | + | 0.795397i | ||||
\(631\) | 6.68559e19i | 1.67855i | 0.543707 | + | 0.839275i | \(0.317020\pi\) | ||||
−0.543707 | + | 0.839275i | \(0.682980\pi\) | |||||||
\(632\) | 4.54091e19 | 1.12752 | ||||||||
\(633\) | 1.71442e19 | 0.421008 | ||||||||
\(634\) | −2.01963e19 | −0.490509 | ||||||||
\(635\) | −3.32377e19 | + | 3.32377e19i | −0.798390 | + | 0.798390i | ||||
\(636\) | −4.55302e18 | + | 4.55302e18i | −0.108168 | + | 0.108168i | ||||
\(637\) | − | 1.26030e20i | − | 2.96140i | ||||||
\(638\) | 2.61371e18 | − | 2.03553e18i | 0.0607454 | − | 0.0473077i | ||||
\(639\) | 2.24725e19 | 0.516590 | ||||||||
\(640\) | 4.05080e19 | + | 4.05080e19i | 0.921045 | + | 0.921045i | ||||
\(641\) | 1.97345e19 | + | 1.97345e19i | 0.443834 | + | 0.443834i | 0.893298 | − | 0.449464i | \(-0.148385\pi\) |
−0.449464 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(642\) | − | 7.11092e17i | − | 0.0158191i | ||||||
\(643\) | − | 8.08294e19i | − | 1.77866i | −0.457267 | − | 0.889330i | \(-0.651171\pi\) | ||
0.457267 | − | 0.889330i | \(-0.348829\pi\) | |||||||
\(644\) | 6.01446e19i | 1.30917i | ||||||||
\(645\) | 6.18768e18 | 0.133232 | ||||||||
\(646\) | 1.63902e17 | − | 1.63902e17i | 0.00349105 | − | 0.00349105i | ||||
\(647\) | 4.58508e19i | 0.966089i | 0.875596 | + | 0.483044i | \(0.160469\pi\) | ||||
−0.875596 | + | 0.483044i | \(0.839531\pi\) | |||||||
\(648\) | 2.58498e18 | − | 2.58498e18i | 0.0538805 | − | 0.0538805i | ||||
\(649\) | −4.57093e18 | − | 4.57093e18i | −0.0942523 | − | 0.0942523i | ||||
\(650\) | 3.77921e19 | − | 3.77921e19i | 0.770916 | − | 0.770916i | ||||
\(651\) | − | 5.94603e19i | − | 1.19994i | ||||||
\(652\) | −3.48711e19 | − | 3.48711e19i | −0.696197 | − | 0.696197i | ||||
\(653\) | 3.31802e19 | − | 3.31802e19i | 0.655371 | − | 0.655371i | −0.298910 | − | 0.954281i | \(-0.596623\pi\) |
0.954281 | + | 0.298910i | \(0.0966231\pi\) | |||||||
\(654\) | 8.36179e18 | 0.163401 | ||||||||
\(655\) | −4.43971e19 | − | 4.43971e19i | −0.858352 | − | 0.858352i | ||||
\(656\) | −9.62549e18 | + | 9.62549e18i | −0.184118 | + | 0.184118i | ||||
\(657\) | 2.18058e19 | + | 2.18058e19i | 0.412680 | + | 0.412680i | ||||
\(658\) | 6.21342e19 | 1.16346 | ||||||||
\(659\) | −1.60928e19 | − | 1.60928e19i | −0.298149 | − | 0.298149i | 0.542139 | − | 0.840289i | \(-0.317614\pi\) |
−0.840289 | + | 0.542139i | \(0.817614\pi\) | |||||||
\(660\) | 4.95225e18i | 0.0907810i | ||||||||
\(661\) | 3.97483e19 | 0.720955 | 0.360477 | − | 0.932768i | \(-0.382614\pi\) | ||||
0.360477 | + | 0.932768i | \(0.382614\pi\) | |||||||
\(662\) | −3.86999e19 | −0.694550 | ||||||||
\(663\) | 1.64022e19 | 0.291278 | ||||||||
\(664\) | −5.68500e19 | + | 5.68500e19i | −0.998974 | + | 0.998974i | ||||
\(665\) | 2.59745e18 | − | 2.59745e18i | 0.0451644 | − | 0.0451644i | ||||
\(666\) | − | 9.56965e17i | − | 0.0164656i | ||||||
\(667\) | 3.65815e19 | + | 4.69724e19i | 0.622846 | + | 0.799765i | ||||
\(668\) | 7.46586e19 | 1.25790 | ||||||||
\(669\) | 1.88595e19 | + | 1.88595e19i | 0.314448 | + | 0.314448i | ||||
\(670\) | −5.40974e19 | − | 5.40974e19i | −0.892591 | − | 0.892591i | ||||
\(671\) | − | 5.73427e18i | − | 0.0936312i | ||||||
\(672\) | − | 7.07631e19i | − | 1.14346i | ||||||
\(673\) | − | 7.37017e19i | − | 1.17862i | −0.807909 | − | 0.589308i | \(-0.799401\pi\) | ||
0.807909 | − | 0.589308i | \(-0.200599\pi\) | |||||||
\(674\) | 8.65066e18 | 0.136908 | ||||||||
\(675\) | −7.33606e19 | + | 7.33606e19i | −1.14904 | + | 1.14904i | ||||
\(676\) | 1.59444e19i | 0.247161i | ||||||||
\(677\) | 3.24437e19 | − | 3.24437e19i | 0.497748 | − | 0.497748i | −0.412988 | − | 0.910736i | \(-0.635515\pi\) |
0.910736 | + | 0.412988i | \(0.135515\pi\) | |||||||
\(678\) | −2.02965e19 | − | 2.02965e19i | −0.308186 | − | 0.308186i | ||||
\(679\) | −1.52949e20 | + | 1.52949e20i | −2.29857 | + | 2.29857i | ||||
\(680\) | − | 4.40164e19i | − | 0.654715i | ||||||
\(681\) | −3.17086e19 | − | 3.17086e19i | −0.466817 | − | 0.466817i | ||||
\(682\) | 4.04868e18 | − | 4.04868e18i | 0.0589960 | − | 0.0589960i | ||||
\(683\) | 6.15172e19 | 0.887261 | 0.443630 | − | 0.896210i | \(-0.353690\pi\) | ||||
0.443630 | + | 0.896210i | \(0.353690\pi\) | |||||||
\(684\) | −4.61760e17 | − | 4.61760e17i | −0.00659209 | − | 0.00659209i | ||||
\(685\) | −7.65007e19 | + | 7.65007e19i | −1.08101 | + | 1.08101i | ||||
\(686\) | 8.19749e19 | + | 8.19749e19i | 1.14660 | + | 1.14660i | ||||
\(687\) | −1.98713e19 | −0.275124 | ||||||||
\(688\) | 1.12752e18 | + | 1.12752e18i | 0.0154527 | + | 0.0154527i | ||||
\(689\) | 3.25446e19i | 0.441514i | ||||||||
\(690\) | 4.06460e19 | 0.545851 | ||||||||
\(691\) | −1.06913e20 | −1.42130 | −0.710651 | − | 0.703545i | \(-0.751599\pi\) | ||||
−0.710651 | + | 0.703545i | \(0.751599\pi\) | |||||||
\(692\) | −3.97916e19 | −0.523659 | ||||||||
\(693\) | −9.17671e18 | + | 9.17671e18i | −0.119551 | + | 0.119551i | ||||
\(694\) | −1.25341e18 | + | 1.25341e18i | −0.0161651 | + | 0.0161651i | ||||
\(695\) | − | 1.32500e20i | − | 1.69170i | ||||||
\(696\) | −2.70191e19 | − | 3.46938e19i | −0.341512 | − | 0.438517i | ||||
\(697\) | 5.59765e19 | 0.700449 | ||||||||
\(698\) | 4.57924e19 | + | 4.57924e19i | 0.567290 | + | 0.567290i | ||||
\(699\) | 4.59068e19 | + | 4.59068e19i | 0.563037 | + | 0.563037i | ||||
\(700\) | − | 1.77580e20i | − | 2.15629i | ||||||
\(701\) | − | 4.54817e18i | − | 0.0546777i | −0.999626 | − | 0.0273389i | \(-0.991297\pi\) | ||
0.999626 | − | 0.0273389i | \(-0.00870332\pi\) | |||||||
\(702\) | 5.33950e19i | 0.635537i | ||||||||
\(703\) | −7.93370e16 | −0.000934950 | ||||||||
\(704\) | 3.50377e18 | − | 3.50377e18i | 0.0408815 | − | 0.0408815i | ||||
\(705\) | 9.19438e19i | 1.06218i | ||||||||
\(706\) | −2.16881e19 | + | 2.16881e19i | −0.248079 | + | 0.248079i | ||||
\(707\) | 1.06298e20 | + | 1.06298e20i | 1.20389 | + | 1.20389i | ||||
\(708\) | −2.46971e19 | + | 2.46971e19i | −0.276958 | + | 0.276958i | ||||
\(709\) | 3.87889e19i | 0.430709i | 0.976536 | + | 0.215355i | \(0.0690908\pi\) | ||||
−0.976536 | + | 0.215355i | \(0.930909\pi\) | |||||||
\(710\) | 4.65062e19 | + | 4.65062e19i | 0.511331 | + | 0.511331i | ||||
\(711\) | −5.06835e19 | + | 5.06835e19i | −0.551797 | + | 0.551797i | ||||
\(712\) | −4.80217e19 | −0.517700 | ||||||||
\(713\) | 7.27610e19 | + | 7.27610e19i | 0.776733 | + | 0.776733i | ||||
\(714\) | −1.75993e19 | + | 1.75993e19i | −0.186041 | + | 0.186041i | ||||
\(715\) | 1.76991e19 | + | 1.76991e19i | 0.185272 | + | 0.185272i | ||||
\(716\) | 3.32080e19 | 0.344232 | ||||||||
\(717\) | −2.43976e19 | − | 2.43976e19i | −0.250445 | − | 0.250445i | ||||
\(718\) | − | 1.07825e20i | − | 1.09609i | ||||||
\(719\) | −7.63956e19 | −0.769071 | −0.384535 | − | 0.923110i | \(-0.625638\pi\) | ||||
−0.384535 | + | 0.923110i | \(0.625638\pi\) | |||||||
\(720\) | −1.68961e19 | −0.168445 | ||||||||
\(721\) | 1.52152e20 | 1.50221 | ||||||||
\(722\) | −4.04751e19 | + | 4.04751e19i | −0.395756 | + | 0.395756i | ||||
\(723\) | 2.66912e19 | − | 2.66912e19i | 0.258464 | − | 0.258464i | ||||
\(724\) | 1.01852e20i | 0.976790i | ||||||||
\(725\) | −1.08009e20 | − | 1.38689e20i | −1.02587 | − | 1.31727i | ||||
\(726\) | −3.43726e19 | −0.323337 | ||||||||
\(727\) | −9.48122e19 | − | 9.48122e19i | −0.883330 | − | 0.883330i | 0.110541 | − | 0.993872i | \(-0.464742\pi\) |
−0.993872 | + | 0.110541i | \(0.964742\pi\) | |||||||
\(728\) | −1.58765e20 | − | 1.58765e20i | −1.46499 | − | 1.46499i | ||||
\(729\) | − | 5.69117e19i | − | 0.520127i | ||||||
\(730\) | 9.02527e19i | 0.816959i | ||||||||
\(731\) | − | 6.55703e18i | − | 0.0587875i | ||||||
\(732\) | −3.09827e19 | −0.275133 | ||||||||
\(733\) | 2.83631e19 | − | 2.83631e19i | 0.249474 | − | 0.249474i | −0.571281 | − | 0.820755i | \(-0.693553\pi\) |
0.820755 | + | 0.571281i | \(0.193553\pi\) | |||||||
\(734\) | − | 9.60125e19i | − | 0.836479i | ||||||
\(735\) | −2.00105e20 | + | 2.00105e20i | −1.72682 | + | 1.72682i | ||||
\(736\) | 8.65920e19 | + | 8.65920e19i | 0.740173 | + | 0.740173i | ||||
\(737\) | 1.58451e19 | − | 1.58451e19i | 0.134160 | − | 0.134160i | ||||
\(738\) | 7.20226e19i | 0.604051i | ||||||||
\(739\) | −1.60798e19 | − | 1.60798e19i | −0.133589 | − | 0.133589i | 0.637151 | − | 0.770739i | \(-0.280113\pi\) |
−0.770739 | + | 0.637151i | \(0.780113\pi\) | |||||||
\(740\) | −4.33635e18 | + | 4.33635e18i | −0.0356864 | + | 0.0356864i | ||||
\(741\) | 1.74962e18 | 0.0142632 | ||||||||
\(742\) | −3.49199e19 | − | 3.49199e19i | −0.281998 | − | 0.281998i | ||||
\(743\) | 1.97729e19 | − | 1.97729e19i | 0.158179 | − | 0.158179i | −0.623580 | − | 0.781759i | \(-0.714322\pi\) |
0.781759 | + | 0.623580i | \(0.214322\pi\) | |||||||
\(744\) | −5.37411e19 | − | 5.37411e19i | −0.425889 | − | 0.425889i | ||||
\(745\) | −1.44833e20 | −1.13703 | ||||||||
\(746\) | −6.25342e19 | − | 6.25342e19i | −0.486347 | − | 0.486347i | ||||
\(747\) | − | 1.26907e20i | − | 0.977778i | ||||||
\(748\) | 5.24785e18 | 0.0400563 | ||||||||
\(749\) | −1.19418e19 | −0.0903017 | ||||||||
\(750\) | −4.81310e19 | −0.360575 | ||||||||
\(751\) | 5.76514e19 | − | 5.76514e19i | 0.427888 | − | 0.427888i | −0.460020 | − | 0.887908i | \(-0.652158\pi\) |
0.887908 | + | 0.460020i | \(0.152158\pi\) | |||||||
\(752\) | −1.67540e19 | + | 1.67540e19i | −0.123195 | + | 0.123195i | ||||
\(753\) | 1.18656e19i | 0.0864420i | ||||||||
\(754\) | −8.97786e19 | − | 1.11650e19i | −0.647997 | − | 0.0805860i | ||||
\(755\) | 2.63227e20 | 1.88235 | ||||||||
\(756\) | 1.25448e20 | + | 1.25448e20i | 0.888816 | + | 0.888816i | ||||
\(757\) | 1.90179e20 | + | 1.90179e20i | 1.33503 | + | 1.33503i | 0.900804 | + | 0.434227i | \(0.142978\pi\) |
0.434227 | + | 0.900804i | \(0.357022\pi\) | |||||||
\(758\) | 7.68372e19i | 0.534426i | ||||||||
\(759\) | 1.19052e19i | 0.0820436i | ||||||||
\(760\) | − | 4.69523e18i | − | 0.0320599i | ||||||
\(761\) | 1.64408e20 | 1.11232 | 0.556162 | − | 0.831074i | \(-0.312273\pi\) | ||||
0.556162 | + | 0.831074i | \(0.312273\pi\) | |||||||
\(762\) | 2.40227e19 | − | 2.40227e19i | 0.161041 | − | 0.161041i | ||||
\(763\) | − | 1.40424e20i | − | 0.932760i | ||||||
\(764\) | 6.53830e19 | − | 6.53830e19i | 0.430339 | − | 0.430339i | ||||
\(765\) | 4.91291e19 | + | 4.91291e19i | 0.320412 | + | 0.320412i | ||||
\(766\) | 3.25776e19 | − | 3.25776e19i | 0.210532 | − | 0.210532i | ||||
\(767\) | 1.76533e20i | 1.13047i | ||||||||
\(768\) | −5.68543e19 | − | 5.68543e19i | −0.360774 | − | 0.360774i | ||||
\(769\) | 3.21513e19 | − | 3.21513e19i | 0.202169 | − | 0.202169i | −0.598760 | − | 0.800929i | \(-0.704340\pi\) |
0.800929 | + | 0.598760i | \(0.204340\pi\) | |||||||
\(770\) | −3.79818e19 | −0.236669 | ||||||||
\(771\) | 3.39186e19 | + | 3.39186e19i | 0.209439 | + | 0.209439i | ||||
\(772\) | 1.38353e20 | − | 1.38353e20i | 0.846577 | − | 0.846577i | ||||
\(773\) | 4.26417e19 | + | 4.26417e19i | 0.258570 | + | 0.258570i | 0.824472 | − | 0.565902i | \(-0.191472\pi\) |
−0.565902 | + | 0.824472i | \(0.691472\pi\) | |||||||
\(774\) | 8.43664e18 | 0.0506971 | ||||||||
\(775\) | −2.14831e20 | − | 2.14831e20i | −1.27933 | − | 1.27933i | ||||
\(776\) | 2.76475e20i | 1.63164i | ||||||||
\(777\) | 8.51899e18 | 0.0498243 | ||||||||
\(778\) | 1.43385e20 | 0.831085 | ||||||||
\(779\) | 5.97101e18 | 0.0342993 | ||||||||
\(780\) | 9.56299e19 | − | 9.56299e19i | 0.544417 | − | 0.544417i | ||||
\(781\) | −1.36217e19 | + | 1.36217e19i | −0.0768551 | + | 0.0768551i | ||||
\(782\) | − | 4.30722e19i | − | 0.240852i | ||||||
\(783\) | 1.74275e20 | + | 2.16731e19i | 0.965834 | + | 0.120113i | ||||
\(784\) | −7.29263e19 | −0.400564 | ||||||||
\(785\) | 3.16856e20 | + | 3.16856e20i | 1.72494 | + | 1.72494i | ||||
\(786\) | 3.20882e19 | + | 3.20882e19i | 0.173136 | + | 0.173136i | ||||
\(787\) | 4.01025e19i | 0.214461i | 0.994234 | + | 0.107231i | \(0.0341983\pi\) | ||||
−0.994234 | + | 0.107231i | \(0.965802\pi\) | |||||||
\(788\) | − | 1.18277e19i | − | 0.0626925i | ||||||
\(789\) | − | 1.11023e20i | − | 0.583278i | ||||||
\(790\) | −2.09776e20 | −1.09236 | ||||||||
\(791\) | −3.40850e20 | + | 3.40850e20i | −1.75925 | + | 1.75925i | ||||
\(792\) | 1.65881e19i | 0.0848633i | ||||||||
\(793\) | −1.10731e20 | + | 1.10731e20i | −0.561509 | + | 0.561509i | ||||
\(794\) | −8.91586e19 | − | 8.91586e19i | −0.448146 | − | 0.448146i | ||||
\(795\) | 5.16731e19 | − | 5.16731e19i | 0.257451 | − | 0.257451i | ||||
\(796\) | − | 7.78506e19i | − | 0.384477i | ||||||
\(797\) | −1.10064e20 | − | 1.10064e20i | −0.538813 | − | 0.538813i | 0.384367 | − | 0.923180i | \(-0.374420\pi\) |
−0.923180 | + | 0.384367i | \(0.874420\pi\) | |||||||
\(798\) | −1.87732e18 | + | 1.87732e18i | −0.00910999 | + | 0.00910999i | ||||
\(799\) | 9.74320e19 | 0.468677 | ||||||||
\(800\) | −2.55668e20 | − | 2.55668e20i | −1.21912 | − | 1.21912i | ||||
\(801\) | 5.35996e19 | − | 5.35996e19i | 0.253358 | − | 0.253358i | ||||
\(802\) | 1.69630e19 | + | 1.69630e19i | 0.0794845 | + | 0.0794845i | ||||
\(803\) | −2.64350e19 | −0.122792 | ||||||||
\(804\) | −8.56124e19 | − | 8.56124e19i | −0.394225 | − | 0.394225i | ||||
\(805\) | − | 6.82591e20i | − | 3.11594i | ||||||
\(806\) | −1.56363e20 | −0.707602 | ||||||||
\(807\) | 1.88556e20 | 0.845913 | ||||||||
\(808\) | 1.92147e20 | 0.854582 | ||||||||
\(809\) | 1.04064e20 | − | 1.04064e20i | 0.458840 | − | 0.458840i | −0.439435 | − | 0.898274i | \(-0.644821\pi\) |
0.898274 | + | 0.439435i | \(0.144821\pi\) | |||||||
\(810\) | −1.19418e19 | + | 1.19418e19i | −0.0522004 | + | 0.0522004i | ||||
\(811\) | − | 3.24340e20i | − | 1.40558i | −0.711398 | − | 0.702789i | \(-0.751938\pi\) | ||
0.711398 | − | 0.702789i | \(-0.248062\pi\) | |||||||
\(812\) | −2.37160e20 | + | 1.84697e20i | −1.01894 | + | 0.793540i | ||||
\(813\) | 5.35966e19 | 0.228299 | ||||||||
\(814\) | 5.80061e17 | + | 5.80061e17i | 0.00244964 | + | 0.00244964i | ||||
\(815\) | 3.95758e20 | + | 3.95758e20i | 1.65702 | + | 1.65702i | ||||
\(816\) | − | 9.49103e18i | − | 0.0393987i | ||||||
\(817\) | − | 6.99438e17i | − | 0.00287869i | ||||||
\(818\) | 3.33614e19i | 0.136135i | ||||||||
\(819\) | 3.54411e20 | 1.43390 | ||||||||
\(820\) | 3.26360e20 | − | 3.26360e20i | 1.30918 | − | 1.30918i | ||||
\(821\) | − | 2.82495e20i | − | 1.12359i | −0.827276 | − | 0.561796i | \(-0.810111\pi\) | ||
0.827276 | − | 0.561796i | \(-0.189889\pi\) | |||||||
\(822\) | 5.52912e19 | − | 5.52912e19i | 0.218049 | − | 0.218049i | ||||
\(823\) | −2.41904e20 | − | 2.41904e20i | −0.945896 | − | 0.945896i | 0.0527135 | − | 0.998610i | \(-0.483213\pi\) |
−0.998610 | + | 0.0527135i | \(0.983213\pi\) | |||||||
\(824\) | 1.37517e20 | − | 1.37517e20i | 0.533171 | − | 0.533171i | ||||
\(825\) | − | 3.51508e19i | − | 0.135132i | ||||||
\(826\) | −1.89417e20 | − | 1.89417e20i | −0.722036 | − | 0.722036i | ||||
\(827\) | −2.47711e20 | + | 2.47711e20i | −0.936284 | + | 0.936284i | −0.998088 | − | 0.0618044i | \(-0.980314\pi\) |
0.0618044 | + | 0.998088i | \(0.480314\pi\) | |||||||
\(828\) | −1.21347e20 | −0.454796 | ||||||||
\(829\) | 2.93644e20 | + | 2.93644e20i | 1.09129 | + | 1.09129i | 0.995391 | + | 0.0958980i | \(0.0305722\pi\) |
0.0958980 | + | 0.995391i | \(0.469428\pi\) | |||||||
\(830\) | 2.62629e20 | − | 2.62629e20i | 0.967824 | − | 0.967824i | ||||
\(831\) | 1.35472e20 | + | 1.35472e20i | 0.495043 | + | 0.495043i | ||||
\(832\) | −1.35318e20 | −0.490335 | ||||||||
\(833\) | 2.12050e20 | + | 2.12050e20i | 0.761943 | + | 0.761943i | ||||
\(834\) | 9.57650e19i | 0.341228i | ||||||||
\(835\) | −8.47314e20 | −2.99391 | ||||||||
\(836\) | 5.59788e17 | 0.00196146 | ||||||||
\(837\) | 3.03526e20 | 1.05467 | ||||||||
\(838\) | 1.50560e20 | − | 1.50560e20i | 0.518803 | − | 0.518803i | ||||
\(839\) | −2.74646e20 | + | 2.74646e20i | −0.938511 | + | 0.938511i | −0.998216 | − | 0.0597050i | \(-0.980984\pi\) |
0.0597050 | + | 0.998216i | \(0.480984\pi\) | |||||||
\(840\) | 5.04161e20i | 1.70850i | ||||||||
\(841\) | −7.28824e19 | + | 2.88494e20i | −0.244935 | + | 0.969540i | ||||
\(842\) | −2.03073e20 | −0.676812 | ||||||||
\(843\) | −8.21322e19 | − | 8.21322e19i | −0.271469 | − | 0.271469i | ||||
\(844\) | −1.05922e20 | − | 1.05922e20i | −0.347208 | − | 0.347208i | ||||
\(845\) | − | 1.80955e20i | − | 0.588267i | ||||||
\(846\) | 1.25361e20i | 0.404177i | ||||||||
\(847\) | 5.77238e20i | 1.84574i | ||||||||
\(848\) | 1.88317e19 | 0.0597199 | ||||||||
\(849\) | 2.96388e19 | − | 2.96388e19i | 0.0932195 | − | 0.0932195i | ||||
\(850\) | 1.27173e20i | 0.396700i | ||||||||
\(851\) | −1.04246e19 | + | 1.04246e19i | −0.0322517 | + | 0.0322517i | ||||
\(852\) | 7.35989e19 | + | 7.35989e19i | 0.225837 | + | 0.225837i | ||||
\(853\) | −5.42825e19 | + | 5.42825e19i | −0.165203 | + | 0.165203i | −0.784867 | − | 0.619664i | \(-0.787269\pi\) |
0.619664 | + | 0.784867i | \(0.287269\pi\) | |||||||
\(854\) | − | 2.37625e20i | − | 0.717278i | ||||||
\(855\) | 5.24059e18 | + | 5.24059e18i | 0.0156898 | + | 0.0156898i | ||||
\(856\) | −1.07931e19 | + | 1.07931e19i | −0.0320503 | + | 0.0320503i | ||||
\(857\) | −8.74425e19 | −0.257547 | −0.128774 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128774 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(858\) | −1.27921e19 | − | 1.27921e19i | −0.0373707 | − | 0.0373707i | ||||
\(859\) | 1.61190e19 | − | 1.61190e19i | 0.0467075 | − | 0.0467075i | −0.683367 | − | 0.730075i | \(-0.739485\pi\) |
0.730075 | + | 0.683367i | \(0.239485\pi\) | |||||||
\(860\) | −3.82294e19 | − | 3.82294e19i | −0.109878 | − | 0.109878i | ||||
\(861\) | −6.41151e20 | −1.82784 | ||||||||
\(862\) | 1.94843e20 | + | 1.94843e20i | 0.550977 | + | 0.550977i | ||||
\(863\) | 1.39081e20i | 0.390114i | 0.980792 | + | 0.195057i | \(0.0624892\pi\) | ||||
−0.980792 | + | 0.195057i | \(0.937511\pi\) | |||||||
\(864\) | 3.61223e20 | 1.00503 | ||||||||
\(865\) | 4.51602e20 | 1.24636 | ||||||||
\(866\) | 7.60390e18 | 0.0208167 | ||||||||
\(867\) | 1.25665e20 | − | 1.25665e20i | 0.341256 | − | 0.341256i | ||||
\(868\) | −3.67365e20 | + | 3.67365e20i | −0.989599 | + | 0.989599i | ||||
\(869\) | − | 6.14433e19i | − | 0.164186i | ||||||
\(870\) | 1.24820e20 | + | 1.60274e20i | 0.330863 | + | 0.424844i | ||||
\(871\) | −6.11950e20 | −1.60912 | ||||||||
\(872\) | −1.26917e20 | − | 1.26917e20i | −0.331059 | − | 0.331059i | ||||
\(873\) | −3.08589e20 | − | 3.08589e20i | −0.798510 | − | 0.798510i | ||||
\(874\) | − | 4.59451e18i | − | 0.0117939i | ||||||
\(875\) | 8.08290e20i | 2.05831i | ||||||||
\(876\) | 1.42830e20i | 0.360821i | ||||||||
\(877\) | 4.08889e20 | 1.02473 | 0.512364 | − | 0.858768i | \(-0.328770\pi\) | ||||
0.512364 | + | 0.858768i | \(0.328770\pi\) | |||||||
\(878\) | 1.55605e20 | − | 1.55605e20i | 0.386866 | − | 0.386866i | ||||
\(879\) | − | 9.19794e19i | − | 0.226865i | ||||||
\(880\) | 1.02415e19 | − | 1.02415e19i | 0.0250602 | − | 0.0250602i | ||||
\(881\) | −2.33349e20 | − | 2.33349e20i | −0.566467 | − | 0.566467i | 0.364670 | − | 0.931137i | \(-0.381182\pi\) |
−0.931137 | + | 0.364670i | \(0.881182\pi\) | |||||||
\(882\) | −2.72835e20 | + | 2.72835e20i | −0.657083 | + | 0.657083i | ||||
\(883\) | 2.07902e19i | 0.0496745i | 0.999692 | + | 0.0248372i | \(0.00790675\pi\) | ||||
−0.999692 | + | 0.0248372i | \(0.992093\pi\) | |||||||
\(884\) | −1.01338e20 | − | 1.01338e20i | −0.240219 | − | 0.240219i | ||||
\(885\) | 2.80292e20 | − | 2.80292e20i | 0.659186 | − | 0.659186i | ||||
\(886\) | −1.26276e20 | −0.294635 | ||||||||
\(887\) | −2.71401e20 | − | 2.71401e20i | −0.628269 | − | 0.628269i | 0.319364 | − | 0.947632i | \(-0.396531\pi\) |
−0.947632 | + | 0.319364i | \(0.896531\pi\) | |||||||
\(888\) | 7.69959e18 | − | 7.69959e18i | 0.0176838 | − | 0.0176838i | ||||
\(889\) | −4.03427e20 | − | 4.03427e20i | −0.919290 | − | 0.919290i | ||||
\(890\) | 2.21845e20 | 0.501557 | ||||||||
\(891\) | −3.49774e18 | − | 3.49774e18i | −0.00784592 | − | 0.00784592i | ||||
\(892\) | − | 2.33040e20i | − | 0.518654i | ||||||
\(893\) | 1.03931e19 | 0.0229500 | ||||||||
\(894\) | 1.04678e20 | 0.229348 | ||||||||
\(895\) | −3.76883e20 | −0.819305 | ||||||||
\(896\) | −4.91670e20 | + | 4.91670e20i | −1.06052 | + | 1.06052i | ||||
\(897\) | 2.29894e20 | − | 2.29894e20i | 0.492018 | − | 0.492018i | ||||
\(898\) | 1.96678e20i | 0.417658i | ||||||||
\(899\) | −6.34679e19 | + | 5.10350e20i | −0.133732 | + | 1.07535i | ||||
\(900\) | 3.58284e20 | 0.749082 | ||||||||
\(901\) | −5.47575e19 | − | 5.47575e19i | −0.113598 | − | 0.113598i | ||||
\(902\) | −4.36562e19 | − | 4.36562e19i | −0.0898670 | − | 0.0898670i | ||||
\(903\) | 7.51037e19i | 0.153408i | ||||||||
\(904\) | 6.16131e20i | 1.24880i | ||||||||
\(905\) | − | 1.15594e21i | − | 2.32485i | ||||||
\(906\) | −1.90248e20 | −0.379685 | ||||||||
\(907\) | −6.72713e20 | + | 6.72713e20i | −1.33223 | + | 1.33223i | −0.428857 | + | 0.903372i | \(0.641084\pi\) |
−0.903372 | + | 0.428857i | \(0.858916\pi\) | |||||||
\(908\) | 3.91811e20i | 0.769974i | ||||||||
\(909\) | −2.14465e20 | + | 2.14465e20i | −0.418225 | + | 0.418225i | ||||
\(910\) | 7.33443e20 | + | 7.33443e20i | 1.41931 | + | 1.41931i | ||||
\(911\) | 7.57407e19 | − | 7.57407e19i | 0.145446 | − | 0.145446i | −0.630634 | − | 0.776080i | \(-0.717205\pi\) |
0.776080 | + | 0.630634i | \(0.217205\pi\) | |||||||
\(912\) | − | 1.01241e18i | − | 0.00192926i | ||||||
\(913\) | 7.69240e19 | + | 7.69240e19i | 0.145468 | + | 0.145468i | ||||
\(914\) | 1.83938e20 | − | 1.83938e20i | 0.345182 | − | 0.345182i | ||||
\(915\) | 3.51629e20 | 0.654842 | ||||||||
\(916\) | 1.22771e20 | + | 1.22771e20i | 0.226896 | + | 0.226896i | ||||
\(917\) | 5.38875e20 | − | 5.38875e20i | 0.988331 | − | 0.988331i | ||||
\(918\) | −8.98390e19 | − | 8.98390e19i | −0.163518 | − | 0.163518i | ||||
\(919\) | 9.57161e20 | 1.72893 | 0.864463 | − | 0.502696i | \(-0.167659\pi\) | ||||
0.864463 | + | 0.502696i | \(0.167659\pi\) | |||||||
\(920\) | −6.16936e20 | − | 6.16936e20i | −1.10592 | − | 1.10592i | ||||
\(921\) | 3.50620e20i | 0.623763i | ||||||||
\(922\) | −5.01628e20 | −0.885656 | ||||||||
\(923\) | 5.26078e20 | 0.921804 | ||||||||
\(924\) | −6.01085e19 | −0.104528 | ||||||||
\(925\) | 3.07792e19 | − | 3.07792e19i | 0.0531208 | − | 0.0531208i | ||||
\(926\) | 2.37592e20 | − | 2.37592e20i | 0.406964 | − | 0.406964i | ||||
\(927\) | 3.06980e20i | 0.521858i | ||||||||
\(928\) | −7.55325e19 | + | 6.07362e20i | −0.127438 | + | 1.02474i | ||||
\(929\) | 4.36676e20 | 0.731222 | 0.365611 | − | 0.930768i | \(-0.380860\pi\) | ||||
0.365611 | + | 0.930768i | \(0.380860\pi\) | |||||||
\(930\) | 2.48267e20 | + | 2.48267e20i | 0.412609 | + | 0.412609i | ||||
\(931\) | 2.26193e19 | + | 2.26193e19i | 0.0373106 | + | 0.0373106i | ||||
\(932\) | − | 5.67253e20i | − | 0.928679i | ||||||
\(933\) | − | 4.64164e20i | − | 0.754224i | ||||||
\(934\) | − | 3.14352e20i | − | 0.506976i | ||||||
\(935\) | −5.95588e19 | −0.0953377 | ||||||||
\(936\) | 3.20322e20 | − | 3.20322e20i | 0.508928 | − | 0.508928i | ||||
\(937\) | − | 4.94475e20i | − | 0.779771i | −0.920863 | − | 0.389885i | \(-0.872515\pi\) | ||
0.920863 | − | 0.389885i | \(-0.127485\pi\) | |||||||
\(938\) | 6.56613e20 | − | 6.56613e20i | 1.02775 | − | 1.02775i | ||||
\(939\) | −2.10054e20 | − | 2.10054e20i | −0.326340 | − | 0.326340i | ||||
\(940\) | 5.68058e20 | − | 5.68058e20i | 0.875987 | − | 0.875987i | ||||
\(941\) | 1.43520e20i | 0.219677i | 0.993949 | + | 0.109838i | \(0.0350334\pi\) | ||||
−0.993949 | + | 0.109838i | \(0.964967\pi\) | |||||||
\(942\) | −2.29009e20 | − | 2.29009e20i | −0.347933 | − | 0.347933i | ||||
\(943\) | 7.84569e20 | − | 7.84569e20i | 1.18318 | − | 1.18318i | ||||
\(944\) | 1.02150e20 | 0.152909 | ||||||||
\(945\) | −1.42373e21 | − | 1.42373e21i | −2.11547 | − | 2.11547i | ||||
\(946\) | −5.11384e18 | + | 5.11384e18i | −0.00754239 | + | 0.00754239i | ||||
\(947\) | −4.49306e20 | − | 4.49306e20i | −0.657798 | − | 0.657798i | 0.297061 | − | 0.954859i | \(-0.403994\pi\) |
−0.954859 | + | 0.297061i | \(0.903994\pi\) | |||||||
\(948\) | −3.31983e20 | −0.482456 | ||||||||
\(949\) | 5.10470e20 | + | 5.10470e20i | 0.736388 | + | 0.736388i | ||||
\(950\) | 1.35655e19i | 0.0194255i | ||||||||
\(951\) | 3.62741e20 | 0.515624 | ||||||||
\(952\) | 5.34255e20 | 0.753858 | ||||||||
\(953\) | 1.67187e19 | 0.0234181 | 0.0117091 | − | 0.999931i | \(-0.496273\pi\) | ||||
0.0117091 | + | 0.999931i | \(0.496273\pi\) | |||||||
\(954\) | 7.04540e19 | − | 7.04540e19i | 0.0979642 | − | 0.0979642i | ||||
\(955\) | −7.42043e20 | + | 7.42043e20i | −1.02425 | + | 1.02425i | ||||
\(956\) | 3.01472e20i | 0.413087i | ||||||||
\(957\) | −4.69443e19 | + | 3.65596e19i | −0.0638556 | + | 0.0497299i | ||||
\(958\) | 2.26183e20 | 0.305423 | ||||||||
\(959\) | −9.28536e20 | − | 9.28536e20i | −1.24471 | − | 1.24471i | ||||
\(960\) | 2.14853e20 | + | 2.14853e20i | 0.285919 | + | 0.285919i | ||||
\(961\) | 1.31908e20i | 0.174264i | ||||||||
\(962\) | − | 2.24024e19i | − | 0.0293812i | ||||||
\(963\) | − | 2.40936e19i | − | 0.0313702i | ||||||
\(964\) | −3.29814e20 | −0.426314 | ||||||||
\(965\) | −1.57019e21 | + | 1.57019e21i | −2.01493 | + | 2.01493i | ||||
\(966\) | 4.93346e20i | 0.628509i | ||||||||
\(967\) | 2.04905e20 | − | 2.04905e20i | 0.259160 | − | 0.259160i | −0.565552 | − | 0.824712i | \(-0.691337\pi\) |
0.824712 | + | 0.565552i | \(0.191337\pi\) | |||||||
\(968\) | 5.21716e20 | + | 5.21716e20i | 0.655099 | + | 0.655099i | ||||
\(969\) | −2.94380e18 | + | 2.94380e18i | −0.00366980 | + | 0.00366980i | ||||
\(970\) | − | 1.27723e21i | − | 1.58076i | ||||||
\(971\) | −1.56543e20 | − | 1.56543e20i | −0.192353 | − | 0.192353i | 0.604359 | − | 0.796712i | \(-0.293429\pi\) |
−0.796712 | + | 0.604359i | \(0.793429\pi\) | |||||||
\(972\) | −4.06169e20 | + | 4.06169e20i | −0.495499 | + | 0.495499i | ||||
\(973\) | 1.60823e21 | 1.94787 | ||||||||
\(974\) | 2.51430e20 | + | 2.51430e20i | 0.302346 | + | 0.302346i | ||||
\(975\) | −6.78775e20 | + | 6.78775e20i | −0.810388 | + | 0.810388i | ||||
\(976\) | 6.40737e19 | + | 6.40737e19i | 0.0759506 | + | 0.0759506i | ||||
\(977\) | 4.87350e20 | 0.573560 | 0.286780 | − | 0.957996i | \(-0.407415\pi\) | ||||
0.286780 | + | 0.957996i | \(0.407415\pi\) | |||||||
\(978\) | −2.86036e20 | − | 2.86036e20i | −0.334232 | − | 0.334232i | ||||
\(979\) | 6.49784e19i | 0.0753859i | ||||||||
\(980\) | 2.47263e21 | 2.84824 | ||||||||
\(981\) | 2.83318e20 | 0.324035 | ||||||||
\(982\) | 2.57772e19 | 0.0292722 | ||||||||
\(983\) | 8.01735e19 | − | 8.01735e19i | 0.0903974 | − | 0.0903974i | −0.660462 | − | 0.750859i | \(-0.729640\pi\) |
0.750859 | + | 0.660462i | \(0.229640\pi\) | |||||||
\(984\) | −5.79482e20 | + | 5.79482e20i | −0.648745 | + | 0.648745i | ||||
\(985\) | 1.34234e20i | 0.149214i | ||||||||
\(986\) | 1.69841e20 | − | 1.32270e20i | 0.187458 | − | 0.145990i | ||||
\(987\) | −1.11598e21 | −1.22303 | ||||||||
\(988\) | −1.08097e19 | − | 1.08097e19i | −0.0117629 | − | 0.0117629i | ||||
\(989\) | −9.19035e19 | − | 9.19035e19i | −0.0993020 | − | 0.0993020i | ||||
\(990\) | − | 7.66317e19i | − | 0.0822171i | ||||||
\(991\) | − | 9.53010e20i | − | 1.01527i | −0.861572 | − | 0.507635i | \(-0.830520\pi\) | ||
0.861572 | − | 0.507635i | \(-0.169480\pi\) | |||||||
\(992\) | 1.05781e21i | 1.11899i | ||||||||
\(993\) | 6.95079e20 | 0.730112 | ||||||||
\(994\) | −5.64474e20 | + | 5.64474e20i | −0.588762 | + | 0.588762i | ||||
\(995\) | 8.83541e20i | 0.915092i | ||||||||
\(996\) | 4.15627e20 | − | 4.15627e20i | 0.427453 | − | 0.427453i | ||||
\(997\) | −2.28483e20 | − | 2.28483e20i | −0.233340 | − | 0.233340i | 0.580745 | − | 0.814085i | \(-0.302761\pi\) |
−0.814085 | + | 0.580745i | \(0.802761\pi\) | |||||||
\(998\) | −2.17656e20 | + | 2.17656e20i | −0.220728 | + | 0.220728i | ||||
\(999\) | 4.34867e19i | 0.0437924i |
(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 | 29.15.c.a.12.14 | ✓ | 68 | |
29.17 | odd | 4 | inner | 29.15.c.a.17.14 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.15.c.a.12.14 | ✓ | 68 | 1.1 | even | 1 | trivial | |
29.15.c.a.17.14 | yes | 68 | 29.17 | odd | 4 | inner |