Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 68.16 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.18 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.27619i | − | 0.225601i | −0.993618 | − | 0.112800i | \(-0.964018\pi\) | ||
0.993618 | − | 0.112800i | \(-0.0359821\pi\) | |||||||
\(3\) | 11.5059 | + | 10.5173i | 0.738106 | + | 0.674685i | ||||
\(4\) | 30.3713 | 0.949104 | ||||||||
\(5\) | 80.0597 | 1.43215 | 0.716075 | − | 0.698023i | \(-0.245937\pi\) | ||||
0.716075 | + | 0.698023i | \(0.245937\pi\) | |||||||
\(6\) | 13.4221 | − | 14.6838i | 0.152210 | − | 0.166517i | ||||
\(7\) | − | 196.848i | − | 1.51840i | −0.650856 | − | 0.759201i | \(-0.725590\pi\) | ||
0.650856 | − | 0.759201i | \(-0.274410\pi\) | |||||||
\(8\) | − | 79.5978i | − | 0.439720i | ||||||
\(9\) | 21.7727 | + | 242.023i | 0.0895995 | + | 0.995978i | ||||
\(10\) | − | 102.171i | − | 0.323095i | ||||||
\(11\) | −20.8886 | −0.0520508 | −0.0260254 | − | 0.999661i | \(-0.508285\pi\) | ||||
−0.0260254 | + | 0.999661i | \(0.508285\pi\) | |||||||
\(12\) | 349.450 | + | 319.425i | 0.700539 | + | 0.640347i | ||||
\(13\) | −791.678 | −1.29924 | −0.649621 | − | 0.760258i | \(-0.725073\pi\) | ||||
−0.649621 | + | 0.760258i | \(0.725073\pi\) | |||||||
\(14\) | −251.216 | −0.342553 | ||||||||
\(15\) | 921.160 | + | 842.012i | 1.05708 | + | 0.966251i | ||||
\(16\) | 870.301 | 0.849903 | ||||||||
\(17\) | −174.605 | −0.146533 | −0.0732663 | − | 0.997312i | \(-0.523342\pi\) | ||||
−0.0732663 | + | 0.997312i | \(0.523342\pi\) | |||||||
\(18\) | 308.867 | − | 27.7861i | 0.224694 | − | 0.0202137i | ||||
\(19\) | − | 892.972i | − | 0.567484i | −0.958901 | − | 0.283742i | \(-0.908424\pi\) | ||
0.958901 | − | 0.283742i | \(-0.0915759\pi\) | |||||||
\(20\) | 2431.52 | 1.35926 | ||||||||
\(21\) | 2070.32 | − | 2264.92i | 1.02444 | − | 1.12074i | ||||
\(22\) | 26.6578i | 0.0117427i | ||||||||
\(23\) | −2039.46 | + | 1508.96i | −0.803887 | + | 0.594781i | ||||
\(24\) | 837.154 | − | 915.846i | 0.296672 | − | 0.324560i | ||||
\(25\) | 3284.55 | 1.05106 | ||||||||
\(26\) | 1010.33i | 0.293110i | ||||||||
\(27\) | −2294.91 | + | 3013.68i | −0.605838 | + | 0.795588i | ||||
\(28\) | − | 5978.55i | − | 1.44112i | ||||||
\(29\) | 5427.01i | 1.19830i | 0.800637 | + | 0.599150i | \(0.204495\pi\) | ||||
−0.800637 | + | 0.599150i | \(0.795505\pi\) | |||||||
\(30\) | 1074.57 | − | 1175.58i | 0.217987 | − | 0.238478i | ||||
\(31\) | 3748.89 | 0.700647 | 0.350323 | − | 0.936629i | \(-0.386072\pi\) | ||||
0.350323 | + | 0.936629i | \(0.386072\pi\) | |||||||
\(32\) | − | 3657.80i | − | 0.631459i | ||||||
\(33\) | −240.343 | − | 219.692i | −0.0384190 | − | 0.0351179i | ||||
\(34\) | 222.829i | 0.0330579i | ||||||||
\(35\) | − | 15759.6i | − | 2.17458i | ||||||
\(36\) | 661.265 | + | 7350.55i | 0.0850393 | + | 0.945287i | ||||
\(37\) | 10793.1i | 1.29611i | 0.761596 | + | 0.648053i | \(0.224416\pi\) | ||||
−0.761596 | + | 0.648053i | \(0.775584\pi\) | |||||||
\(38\) | −1139.60 | −0.128025 | ||||||||
\(39\) | −9108.99 | − | 8326.32i | −0.958978 | − | 0.876580i | ||||
\(40\) | − | 6372.57i | − | 0.629745i | ||||||
\(41\) | 5102.57i | 0.474056i | 0.971503 | + | 0.237028i | \(0.0761733\pi\) | ||||
−0.971503 | + | 0.237028i | \(0.923827\pi\) | |||||||
\(42\) | −2890.48 | − | 2642.12i | −0.252840 | − | 0.231116i | ||||
\(43\) | 10175.5i | 0.839240i | 0.907700 | + | 0.419620i | \(0.137837\pi\) | ||||
−0.907700 | + | 0.419620i | \(0.862163\pi\) | |||||||
\(44\) | −634.414 | −0.0494016 | ||||||||
\(45\) | 1743.11 | + | 19376.2i | 0.128320 | + | 1.42639i | ||||
\(46\) | 1925.72 | + | 2602.74i | 0.134183 | + | 0.181358i | ||||
\(47\) | 2207.39i | 0.145759i | 0.997341 | + | 0.0728794i | \(0.0232188\pi\) | ||||
−0.997341 | + | 0.0728794i | \(0.976781\pi\) | |||||||
\(48\) | 10013.6 | + | 9153.22i | 0.627318 | + | 0.573417i | ||||
\(49\) | −21942.3 | −1.30555 | ||||||||
\(50\) | − | 4191.71i | − | 0.237119i | ||||||
\(51\) | −2008.99 | − | 1836.37i | −0.108157 | − | 0.0988634i | ||||
\(52\) | −24044.3 | −1.23312 | ||||||||
\(53\) | −38439.7 | −1.87971 | −0.939854 | − | 0.341576i | \(-0.889039\pi\) | ||||
−0.939854 | + | 0.341576i | \(0.889039\pi\) | |||||||
\(54\) | 3846.04 | + | 2928.75i | 0.179485 | + | 0.136678i | ||||
\(55\) | −1672.33 | −0.0745446 | ||||||||
\(56\) | −15668.7 | −0.667672 | ||||||||
\(57\) | 9391.65 | − | 10274.5i | 0.382873 | − | 0.418863i | ||||
\(58\) | 6925.91 | 0.270338 | ||||||||
\(59\) | − | 49618.2i | − | 1.85571i | −0.372937 | − | 0.927856i | \(-0.621649\pi\) | ||
0.372937 | − | 0.927856i | \(-0.378351\pi\) | |||||||
\(60\) | 27976.9 | + | 25573.0i | 1.00328 | + | 0.917073i | ||||
\(61\) | − | 28860.1i | − | 0.993053i | −0.868021 | − | 0.496527i | \(-0.834608\pi\) | ||
0.868021 | − | 0.496527i | \(-0.165392\pi\) | |||||||
\(62\) | − | 4784.31i | − | 0.158067i | ||||||
\(63\) | 47641.8 | − | 4285.92i | 1.51230 | − | 0.136048i | ||||
\(64\) | 23181.6 | 0.707445 | ||||||||
\(65\) | −63381.5 | −1.86071 | ||||||||
\(66\) | −280.369 | + | 306.723i | −0.00792263 | + | 0.00866736i | ||||
\(67\) | 61124.2i | 1.66351i | 0.555140 | + | 0.831757i | \(0.312665\pi\) | ||||
−0.555140 | + | 0.831757i | \(0.687335\pi\) | |||||||
\(68\) | −5302.99 | −0.139075 | ||||||||
\(69\) | −39336.0 | − | 4087.65i | −0.994644 | − | 0.103360i | ||||
\(70\) | −20112.3 | −0.490588 | ||||||||
\(71\) | − | 11772.5i | − | 0.277154i | −0.990352 | − | 0.138577i | \(-0.955747\pi\) | ||
0.990352 | − | 0.138577i | \(-0.0442529\pi\) | |||||||
\(72\) | 19264.5 | − | 1733.06i | 0.437951 | − | 0.0393987i | ||||
\(73\) | 48746.9 | 1.07063 | 0.535316 | − | 0.844652i | \(-0.320193\pi\) | ||||
0.535316 | + | 0.844652i | \(0.320193\pi\) | |||||||
\(74\) | 13774.0 | 0.292403 | ||||||||
\(75\) | 37791.8 | + | 34544.6i | 0.775790 | + | 0.709132i | ||||
\(76\) | − | 27120.7i | − | 0.538602i | ||||||
\(77\) | 4111.89i | 0.0790341i | ||||||||
\(78\) | −10626.0 | + | 11624.8i | −0.197757 | + | 0.216346i | ||||
\(79\) | − | 65855.0i | − | 1.18719i | −0.804763 | − | 0.593596i | \(-0.797708\pi\) | ||
0.804763 | − | 0.593596i | \(-0.202292\pi\) | |||||||
\(80\) | 69676.0 | 1.21719 | ||||||||
\(81\) | −58100.9 | + | 10539.0i | −0.983944 | + | 0.178478i | ||||
\(82\) | 6511.86 | 0.106947 | ||||||||
\(83\) | −53578.7 | −0.853683 | −0.426842 | − | 0.904326i | \(-0.640374\pi\) | ||||
−0.426842 | + | 0.904326i | \(0.640374\pi\) | |||||||
\(84\) | 62878.2 | − | 68788.8i | 0.972304 | − | 1.06370i | ||||
\(85\) | −13978.8 | −0.209857 | ||||||||
\(86\) | 12985.9 | 0.189333 | ||||||||
\(87\) | −57077.5 | + | 62442.8i | −0.808476 | + | 0.884472i | ||||
\(88\) | 1662.69i | 0.0228878i | ||||||||
\(89\) | 106893. | 1.43045 | 0.715227 | − | 0.698892i | \(-0.246323\pi\) | ||||
0.715227 | + | 0.698892i | \(0.246323\pi\) | |||||||
\(90\) | 24727.8 | − | 2224.55i | 0.321795 | − | 0.0289491i | ||||
\(91\) | 155841.i | 1.97277i | ||||||||
\(92\) | −61941.1 | + | 45829.1i | −0.762973 | + | 0.564510i | ||||
\(93\) | 43134.5 | + | 39428.3i | 0.517151 | + | 0.472716i | ||||
\(94\) | 2817.05 | 0.0328833 | ||||||||
\(95\) | − | 71491.0i | − | 0.812723i | ||||||
\(96\) | 38470.2 | − | 42086.4i | 0.426036 | − | 0.466083i | ||||
\(97\) | − | 59613.7i | − | 0.643304i | −0.946858 | − | 0.321652i | \(-0.895762\pi\) | ||
0.946858 | − | 0.321652i | \(-0.104238\pi\) | |||||||
\(98\) | 28002.6i | 0.294533i | ||||||||
\(99\) | −454.800 | − | 5055.51i | −0.00466372 | − | 0.0518414i | ||||
\(100\) | 99756.1 | 0.997561 | ||||||||
\(101\) | 8155.58i | 0.0795521i | 0.999209 | + | 0.0397760i | \(0.0126644\pi\) | ||||
−0.999209 | + | 0.0397760i | \(0.987336\pi\) | |||||||
\(102\) | −2343.57 | + | 2563.86i | −0.0223037 | + | 0.0244002i | ||||
\(103\) | − | 54139.3i | − | 0.502828i | −0.967880 | − | 0.251414i | \(-0.919104\pi\) | ||
0.967880 | − | 0.251414i | \(-0.0808956\pi\) | |||||||
\(104\) | 63015.8i | 0.571303i | ||||||||
\(105\) | 165749. | − | 181329.i | 1.46716 | − | 1.60507i | ||||
\(106\) | 49056.4i | 0.424064i | ||||||||
\(107\) | 60053.1 | 0.507079 | 0.253540 | − | 0.967325i | \(-0.418405\pi\) | ||||
0.253540 | + | 0.967325i | \(0.418405\pi\) | |||||||
\(108\) | −69699.5 | + | 91529.6i | −0.575003 | + | 0.755096i | ||||
\(109\) | − | 152525.i | − | 1.22963i | −0.788670 | − | 0.614816i | \(-0.789230\pi\) | ||
0.788670 | − | 0.614816i | \(-0.210770\pi\) | |||||||
\(110\) | 2134.22i | 0.0168173i | ||||||||
\(111\) | −113514. | + | 124184.i | −0.874463 | + | 0.956662i | ||||
\(112\) | − | 171317.i | − | 1.29049i | ||||||
\(113\) | 25828.9 | 0.190287 | 0.0951436 | − | 0.995464i | \(-0.469669\pi\) | ||||
0.0951436 | + | 0.995464i | \(0.469669\pi\) | |||||||
\(114\) | −13112.2 | − | 11985.6i | −0.0944959 | − | 0.0863766i | ||||
\(115\) | −163278. | + | 120807.i | −1.15129 | + | 0.851817i | ||||
\(116\) | 164826.i | 1.13731i | ||||||||
\(117\) | −17237.0 | − | 191604.i | −0.116412 | − | 1.29402i | ||||
\(118\) | −63322.3 | −0.418651 | ||||||||
\(119\) | 34370.7i | 0.222496i | ||||||||
\(120\) | 67022.3 | − | 73322.3i | 0.424880 | − | 0.464818i | ||||
\(121\) | −160615. | −0.997291 | ||||||||
\(122\) | −36831.0 | −0.224034 | ||||||||
\(123\) | −53665.3 | + | 58709.8i | −0.319838 | + | 0.349903i | ||||
\(124\) | 113859. | 0.664987 | ||||||||
\(125\) | 12773.4 | 0.0731192 | ||||||||
\(126\) | −5469.65 | − | 60800.1i | −0.0306926 | − | 0.341175i | ||||
\(127\) | 234394. | 1.28955 | 0.644775 | − | 0.764373i | \(-0.276951\pi\) | ||||
0.644775 | + | 0.764373i | \(0.276951\pi\) | |||||||
\(128\) | − | 146634.i | − | 0.791059i | ||||||
\(129\) | −107019. | + | 117079.i | −0.566223 | + | 0.619447i | ||||
\(130\) | 80886.9i | 0.419778i | ||||||||
\(131\) | 50125.1i | 0.255198i | 0.991826 | + | 0.127599i | \(0.0407270\pi\) | ||||
−0.991826 | + | 0.127599i | \(0.959273\pi\) | |||||||
\(132\) | −7299.52 | − | 6672.33i | −0.0364636 | − | 0.0333305i | ||||
\(133\) | −175780. | −0.861669 | ||||||||
\(134\) | 78006.3 | 0.375290 | ||||||||
\(135\) | −183730. | + | 241275.i | −0.867651 | + | 1.13940i | ||||
\(136\) | 13898.2i | 0.0644333i | ||||||||
\(137\) | −346120. | −1.57553 | −0.787763 | − | 0.615979i | \(-0.788761\pi\) | ||||
−0.787763 | + | 0.615979i | \(0.788761\pi\) | |||||||
\(138\) | −5216.62 | + | 50200.3i | −0.0233180 | + | 0.224393i | ||||
\(139\) | 5881.35 | 0.0258191 | 0.0129095 | − | 0.999917i | \(-0.495891\pi\) | ||||
0.0129095 | + | 0.999917i | \(0.495891\pi\) | |||||||
\(140\) | − | 478641.i | − | 2.06390i | ||||||
\(141\) | −23215.8 | + | 25398.1i | −0.0983413 | + | 0.107585i | ||||
\(142\) | −15023.9 | −0.0625262 | ||||||||
\(143\) | 16537.0 | 0.0676266 | ||||||||
\(144\) | 18948.8 | + | 210632.i | 0.0761509 | + | 0.846485i | ||||
\(145\) | 434485.i | 1.71615i | ||||||||
\(146\) | − | 62210.5i | − | 0.241536i | ||||||
\(147\) | −252467. | − | 230774.i | −0.963631 | − | 0.880833i | ||||
\(148\) | 327800.i | 1.23014i | ||||||||
\(149\) | 153793. | 0.567505 | 0.283753 | − | 0.958898i | \(-0.408421\pi\) | ||||
0.283753 | + | 0.958898i | \(0.408421\pi\) | |||||||
\(150\) | 44085.5 | − | 48229.6i | 0.159981 | − | 0.175019i | ||||
\(151\) | −90252.7 | −0.322120 | −0.161060 | − | 0.986945i | \(-0.551491\pi\) | ||||
−0.161060 | + | 0.986945i | \(0.551491\pi\) | |||||||
\(152\) | −71078.6 | −0.249534 | ||||||||
\(153\) | −3801.62 | − | 42258.4i | −0.0131293 | − | 0.145943i | ||||
\(154\) | 5247.56 | 0.0178302 | ||||||||
\(155\) | 300135. | 1.00343 | ||||||||
\(156\) | −276652. | − | 252881.i | −0.910170 | − | 0.831966i | ||||
\(157\) | − | 259521.i | − | 0.840280i | −0.907459 | − | 0.420140i | \(-0.861981\pi\) | ||
0.907459 | − | 0.420140i | \(-0.138019\pi\) | |||||||
\(158\) | −84043.6 | −0.267832 | ||||||||
\(159\) | −442285. | − | 404282.i | −1.38742 | − | 1.26821i | ||||
\(160\) | − | 292842.i | − | 0.904344i | ||||||
\(161\) | 297036. | + | 401464.i | 0.903118 | + | 1.22062i | ||||
\(162\) | 13449.7 | + | 74147.9i | 0.0402649 | + | 0.221979i | ||||
\(163\) | 223631. | 0.659271 | 0.329635 | − | 0.944108i | \(-0.393074\pi\) | ||||
0.329635 | + | 0.944108i | \(0.393074\pi\) | |||||||
\(164\) | 154972.i | 0.449928i | ||||||||
\(165\) | −19241.7 | − | 17588.4i | −0.0550218 | − | 0.0502941i | ||||
\(166\) | 68376.7i | 0.192592i | ||||||||
\(167\) | 635080.i | 1.76213i | 0.472998 | + | 0.881064i | \(0.343172\pi\) | ||||
−0.472998 | + | 0.881064i | \(0.656828\pi\) | |||||||
\(168\) | −180283. | − | 164793.i | −0.492812 | − | 0.450468i | ||||
\(169\) | 255461. | 0.688032 | ||||||||
\(170\) | 17839.7i | 0.0473439i | ||||||||
\(171\) | 216119. | − | 19442.4i | 0.565202 | − | 0.0508463i | ||||
\(172\) | 309044.i | 0.796526i | ||||||||
\(173\) | − | 273947.i | − | 0.695907i | −0.937512 | − | 0.347953i | \(-0.886877\pi\) | ||
0.937512 | − | 0.347953i | \(-0.113123\pi\) | |||||||
\(174\) | 79689.0 | + | 72841.9i | 0.199538 | + | 0.182393i | ||||
\(175\) | − | 646558.i | − | 1.59593i | ||||||
\(176\) | −18179.3 | −0.0442381 | ||||||||
\(177\) | 521849. | − | 570903.i | 1.25202 | − | 1.36971i | ||||
\(178\) | − | 136416.i | − | 0.322712i | ||||||
\(179\) | 100929.i | 0.235442i | 0.993047 | + | 0.117721i | \(0.0375589\pi\) | ||||
−0.993047 | + | 0.117721i | \(0.962441\pi\) | |||||||
\(180\) | 52940.7 | + | 588483.i | 0.121789 | + | 1.35379i | ||||
\(181\) | − | 347500.i | − | 0.788421i | −0.919020 | − | 0.394211i | \(-0.871018\pi\) | ||
0.919020 | − | 0.394211i | \(-0.128982\pi\) | |||||||
\(182\) | 198883. | 0.445060 | ||||||||
\(183\) | 303530. | − | 332062.i | 0.669999 | − | 0.732978i | ||||
\(184\) | 120110. | + | 162336.i | 0.261537 | + | 0.353485i | ||||
\(185\) | 864089.i | 1.85622i | ||||||||
\(186\) | 50318.0 | − | 55047.9i | 0.106645 | − | 0.116670i | ||||
\(187\) | 3647.25 | 0.00762714 | ||||||||
\(188\) | 67041.4i | 0.138340i | ||||||||
\(189\) | 593239. | + | 451750.i | 1.20802 | + | 0.919906i | ||||
\(190\) | −91236.2 | −0.183351 | ||||||||
\(191\) | 869385. | 1.72436 | 0.862182 | − | 0.506599i | \(-0.169097\pi\) | ||||
0.862182 | + | 0.506599i | \(0.169097\pi\) | |||||||
\(192\) | 266725. | + | 243808.i | 0.522169 | + | 0.477303i | ||||
\(193\) | 202279. | 0.390893 | 0.195447 | − | 0.980714i | \(-0.437384\pi\) | ||||
0.195447 | + | 0.980714i | \(0.437384\pi\) | |||||||
\(194\) | −76078.5 | −0.145130 | ||||||||
\(195\) | −729263. | − | 666602.i | −1.37340 | − | 1.25539i | ||||
\(196\) | −666418. | −1.23910 | ||||||||
\(197\) | − | 812892.i | − | 1.49234i | −0.665757 | − | 0.746169i | \(-0.731891\pi\) | ||
0.665757 | − | 0.746169i | \(-0.268109\pi\) | |||||||
\(198\) | −6451.80 | + | 580.413i | −0.0116955 | + | 0.00105214i | ||||
\(199\) | 40521.5i | 0.0725358i | 0.999342 | + | 0.0362679i | \(0.0115470\pi\) | ||||
−0.999342 | + | 0.0362679i | \(0.988453\pi\) | |||||||
\(200\) | − | 261443.i | − | 0.462170i | ||||||
\(201\) | −642862. | + | 703291.i | −1.12235 | + | 1.22785i | ||||
\(202\) | 10408.1 | 0.0179470 | ||||||||
\(203\) | 1.06830e6 | 1.81950 | ||||||||
\(204\) | −61015.8 | − | 55773.1i | −0.102652 | − | 0.0938317i | ||||
\(205\) | 408510.i | 0.678919i | ||||||||
\(206\) | −69092.1 | −0.113438 | ||||||||
\(207\) | −409606. | − | 460741.i | −0.664417 | − | 0.747362i | ||||
\(208\) | −688998. | −1.10423 | ||||||||
\(209\) | 18652.9i | 0.0295380i | ||||||||
\(210\) | −231411. | − | 211527.i | −0.362105 | − | 0.330992i | ||||
\(211\) | 716481. | 1.10789 | 0.553947 | − | 0.832552i | \(-0.313121\pi\) | ||||
0.553947 | + | 0.832552i | \(0.313121\pi\) | |||||||
\(212\) | −1.16747e6 | −1.78404 | ||||||||
\(213\) | 123815. | − | 135453.i | 0.186992 | − | 0.204569i | ||||
\(214\) | − | 76639.2i | − | 0.114398i | ||||||
\(215\) | 814650.i | 1.20192i | ||||||||
\(216\) | 239883. | + | 182670.i | 0.349836 | + | 0.266399i | ||||
\(217\) | − | 737964.i | − | 1.06386i | ||||||
\(218\) | −194651. | −0.277406 | ||||||||
\(219\) | 560879. | + | 512686.i | 0.790239 | + | 0.722340i | ||||
\(220\) | −50791.0 | −0.0707506 | ||||||||
\(221\) | 138231. | 0.190381 | ||||||||
\(222\) | 158483. | + | 144865.i | 0.215824 | + | 0.197280i | ||||
\(223\) | −145527. | −0.195966 | −0.0979831 | − | 0.995188i | \(-0.531239\pi\) | ||||
−0.0979831 | + | 0.995188i | \(0.531239\pi\) | |||||||
\(224\) | −720032. | −0.958809 | ||||||||
\(225\) | 71513.4 | + | 794935.i | 0.0941740 | + | 1.04683i | ||||
\(226\) | − | 32962.6i | − | 0.0429290i | ||||||
\(227\) | 544805. | 0.701740 | 0.350870 | − | 0.936424i | \(-0.385886\pi\) | ||||
0.350870 | + | 0.936424i | \(0.385886\pi\) | |||||||
\(228\) | 285237. | − | 312049.i | 0.363387 | − | 0.397545i | ||||
\(229\) | 1734.50i | 0.00218567i | 0.999999 | + | 0.00109284i | \(0.000347861\pi\) | ||||
−0.999999 | + | 0.00109284i | \(0.999652\pi\) | |||||||
\(230\) | 154172. | + | 208374.i | 0.192171 | + | 0.259732i | ||||
\(231\) | −43246.0 | + | 47311.1i | −0.0533231 | + | 0.0583355i | ||||
\(232\) | 431978. | 0.526917 | ||||||||
\(233\) | − | 309502.i | − | 0.373485i | −0.982409 | − | 0.186742i | \(-0.940207\pi\) | ||
0.982409 | − | 0.186742i | \(-0.0597930\pi\) | |||||||
\(234\) | −244524. | + | 21997.7i | −0.291932 | + | 0.0262625i | ||||
\(235\) | 176723.i | 0.208749i | ||||||||
\(236\) | − | 1.50697e6i | − | 1.76126i | ||||||
\(237\) | 692617. | − | 757723.i | 0.800981 | − | 0.876273i | ||||
\(238\) | 43863.6 | 0.0501952 | ||||||||
\(239\) | − | 1.15098e6i | − | 1.30339i | −0.758483 | − | 0.651693i | \(-0.774059\pi\) | ||
0.758483 | − | 0.651693i | \(-0.225941\pi\) | |||||||
\(240\) | 801687. | + | 732803.i | 0.898414 | + | 0.821220i | ||||
\(241\) | 1.55779e6i | 1.72769i | 0.503756 | + | 0.863846i | \(0.331951\pi\) | ||||
−0.503756 | + | 0.863846i | \(0.668049\pi\) | |||||||
\(242\) | 204975.i | 0.224990i | ||||||||
\(243\) | −779346. | − | 489804.i | −0.846671 | − | 0.532117i | ||||
\(244\) | − | 876518.i | − | 0.942511i | ||||||
\(245\) | −1.75670e6 | −1.86974 | ||||||||
\(246\) | 74925.0 | + | 68487.2i | 0.0789385 | + | 0.0721559i | ||||
\(247\) | 706946.i | 0.737300i | ||||||||
\(248\) | − | 298404.i | − | 0.308088i | ||||||
\(249\) | −616472. | − | 563503.i | −0.630108 | − | 0.575968i | ||||
\(250\) | − | 16301.3i | − | 0.0164958i | ||||||
\(251\) | −22290.6 | −0.0223325 | −0.0111663 | − | 0.999938i | \(-0.503554\pi\) | ||||
−0.0111663 | + | 0.999938i | \(0.503554\pi\) | |||||||
\(252\) | 1.44694e6 | − | 130169.i | 1.43533 | − | 0.129124i | ||||
\(253\) | 42601.4 | − | 31520.0i | 0.0418430 | − | 0.0309588i | ||||
\(254\) | − | 299132.i | − | 0.290924i | ||||||
\(255\) | −160839. | − | 147019.i | −0.154896 | − | 0.141587i | ||||
\(256\) | 554677. | 0.528982 | ||||||||
\(257\) | 1.38634e6i | 1.30929i | 0.755935 | + | 0.654647i | \(0.227183\pi\) | ||||
−0.755935 | + | 0.654647i | \(0.772817\pi\) | |||||||
\(258\) | 149415. | + | 136577.i | 0.139748 | + | 0.127740i | ||||
\(259\) | 2.12460e6 | 1.96801 | ||||||||
\(260\) | −1.92498e6 | −1.76601 | ||||||||
\(261\) | −1.31346e6 | + | 118161.i | −1.19348 | + | 0.107367i | ||||
\(262\) | 63969.2 | 0.0575729 | ||||||||
\(263\) | −1.66301e6 | −1.48254 | −0.741269 | − | 0.671208i | \(-0.765776\pi\) | ||||
−0.741269 | + | 0.671208i | \(0.765776\pi\) | |||||||
\(264\) | −17487.0 | + | 19130.7i | −0.0154420 | + | 0.0168936i | ||||
\(265\) | −3.07747e6 | −2.69203 | ||||||||
\(266\) | 224329.i | 0.194393i | ||||||||
\(267\) | 1.22990e6 | + | 1.12422e6i | 1.05583 | + | 0.965106i | ||||
\(268\) | 1.85642e6i | 1.57885i | ||||||||
\(269\) | − | 1.60222e6i | − | 1.35002i | −0.737809 | − | 0.675010i | \(-0.764139\pi\) | ||
0.737809 | − | 0.675010i | \(-0.235861\pi\) | |||||||
\(270\) | 307913. | + | 234474.i | 0.257050 | + | 0.195743i | ||||
\(271\) | −255594. | −0.211411 | −0.105705 | − | 0.994397i | \(-0.533710\pi\) | ||||
−0.105705 | + | 0.994397i | \(0.533710\pi\) | |||||||
\(272\) | −151959. | −0.124539 | ||||||||
\(273\) | −1.63902e6 | + | 1.79309e6i | −1.33100 | + | 1.45612i | ||||
\(274\) | 441716.i | 0.355440i | ||||||||
\(275\) | −68609.6 | −0.0547083 | ||||||||
\(276\) | −1.19469e6 | − | 124147.i | −0.944021 | − | 0.0980990i | ||||
\(277\) | −922483. | −0.722369 | −0.361184 | − | 0.932494i | \(-0.617627\pi\) | ||||
−0.361184 | + | 0.932494i | \(0.617627\pi\) | |||||||
\(278\) | − | 7505.74i | − | 0.00582480i | ||||||
\(279\) | 81623.5 | + | 907317.i | 0.0627776 | + | 0.697828i | ||||
\(280\) | −1.25443e6 | −0.956207 | ||||||||
\(281\) | −992232. | −0.749631 | −0.374815 | − | 0.927100i | \(-0.622294\pi\) | ||||
−0.374815 | + | 0.927100i | \(0.622294\pi\) | |||||||
\(282\) | 32412.8 | + | 29627.8i | 0.0242714 | + | 0.0221859i | ||||
\(283\) | − | 292415.i | − | 0.217037i | −0.994094 | − | 0.108518i | \(-0.965389\pi\) | ||
0.994094 | − | 0.108518i | \(-0.0346106\pi\) | |||||||
\(284\) | − | 357545.i | − | 0.263048i | ||||||
\(285\) | 751893. | − | 822570.i | 0.548332 | − | 0.599875i | ||||
\(286\) | − | 21104.4i | − | 0.0152566i | ||||||
\(287\) | 1.00443e6 | 0.719807 | ||||||||
\(288\) | 885270. | − | 79640.1i | 0.628919 | − | 0.0565784i | ||||
\(289\) | −1.38937e6 | −0.978528 | ||||||||
\(290\) | 554486. | 0.387164 | ||||||||
\(291\) | 626975. | − | 685910.i | 0.434028 | − | 0.474827i | ||||
\(292\) | 1.48051e6 | 1.01614 | ||||||||
\(293\) | 150873. | 0.102670 | 0.0513349 | − | 0.998681i | \(-0.483652\pi\) | ||||
0.0513349 | + | 0.998681i | \(0.483652\pi\) | |||||||
\(294\) | −294512. | + | 322196.i | −0.198717 | + | 0.217396i | ||||
\(295\) | − | 3.97241e6i | − | 2.65766i | ||||||
\(296\) | 859104. | 0.569923 | ||||||||
\(297\) | 47937.4 | − | 62951.6i | 0.0315343 | − | 0.0414110i | ||||
\(298\) | − | 196269.i | − | 0.128030i | ||||||
\(299\) | 1.61459e6 | − | 1.19461e6i | 1.04444 | − | 0.772766i | ||||
\(300\) | 1.14779e6 | + | 1.04917e6i | 0.736305 | + | 0.673040i | ||||
\(301\) | 2.00304e6 | 1.27430 | ||||||||
\(302\) | 115180.i | 0.0726706i | ||||||||
\(303\) | −85774.7 | + | 93837.5i | −0.0536726 | + | 0.0587178i | ||||
\(304\) | − | 777154.i | − | 0.482306i | ||||||
\(305\) | − | 2.31053e6i | − | 1.42220i | ||||||
\(306\) | −53929.8 | + | 4851.59i | −0.0329249 | + | 0.00296197i | ||||
\(307\) | 1.91204e6 | 1.15785 | 0.578924 | − | 0.815382i | \(-0.303473\pi\) | ||||
0.578924 | + | 0.815382i | \(0.303473\pi\) | |||||||
\(308\) | 124883.i | 0.0750116i | ||||||||
\(309\) | 569399. | − | 622923.i | 0.339251 | − | 0.371140i | ||||
\(310\) | − | 383030.i | − | 0.226375i | ||||||
\(311\) | 1.82521e6i | 1.07007i | 0.844829 | + | 0.535036i | \(0.179702\pi\) | ||||
−0.844829 | + | 0.535036i | \(0.820298\pi\) | |||||||
\(312\) | −662757. | + | 725056.i | −0.385450 | + | 0.421682i | ||||
\(313\) | 2.85121e6i | 1.64501i | 0.568759 | + | 0.822504i | \(0.307424\pi\) | ||||
−0.568759 | + | 0.822504i | \(0.692576\pi\) | |||||||
\(314\) | −331199. | −0.189568 | ||||||||
\(315\) | 3.81419e6 | − | 343129.i | 2.16584 | − | 0.194841i | ||||
\(316\) | − | 2.00010e6i | − | 1.12677i | ||||||
\(317\) | 2.10359e6i | 1.17575i | 0.808953 | + | 0.587873i | \(0.200035\pi\) | ||||
−0.808953 | + | 0.587873i | \(0.799965\pi\) | |||||||
\(318\) | −515942. | + | 564440.i | −0.286110 | + | 0.313004i | ||||
\(319\) | − | 113363.i | − | 0.0623725i | ||||||
\(320\) | 1.85591e6 | 1.01317 | ||||||||
\(321\) | 690966. | + | 631596.i | 0.374278 | + | 0.342119i | ||||
\(322\) | 512345. | − | 379075.i | 0.275374 | − | 0.203744i | ||||
\(323\) | 155917.i | 0.0831550i | ||||||||
\(324\) | −1.76460e6 | + | 320082.i | −0.933865 | + | 0.169394i | ||||
\(325\) | −2.60031e6 | −1.36558 | ||||||||
\(326\) | − | 285397.i | − | 0.148732i | ||||||
\(327\) | 1.60415e6 | − | 1.75494e6i | 0.829615 | − | 0.907598i | ||||
\(328\) | 406153. | 0.208452 | ||||||||
\(329\) | 434522. | 0.221320 | ||||||||
\(330\) | −22446.2 | + | 24556.2i | −0.0113464 | + | 0.0124130i | ||||
\(331\) | 1.56186e6 | 0.783559 | 0.391779 | − | 0.920059i | \(-0.371860\pi\) | ||||
0.391779 | + | 0.920059i | \(0.371860\pi\) | |||||||
\(332\) | −1.62726e6 | −0.810234 | ||||||||
\(333\) | −2.61216e6 | + | 234994.i | −1.29089 | + | 0.116130i | ||||
\(334\) | 810484. | 0.397538 | ||||||||
\(335\) | 4.89359e6i | 2.38240i | ||||||||
\(336\) | 1.80180e6 | − | 1.97116e6i | 0.870678 | − | 0.952521i | ||||
\(337\) | − | 1.97846e6i | − | 0.948970i | −0.880264 | − | 0.474485i | \(-0.842634\pi\) | ||
0.880264 | − | 0.474485i | \(-0.157366\pi\) | |||||||
\(338\) | − | 326018.i | − | 0.155221i | ||||||
\(339\) | 297185. | + | 271650.i | 0.140452 | + | 0.128384i | ||||
\(340\) | −424555. | −0.199176 | ||||||||
\(341\) | −78309.1 | −0.0364692 | ||||||||
\(342\) | −24812.2 | − | 275810.i | −0.0114710 | − | 0.127510i | ||||
\(343\) | 1.01088e6i | 0.463943i | ||||||||
\(344\) | 809950. | 0.369030 | ||||||||
\(345\) | −3.14923e6 | − | 327256.i | −1.42448 | − | 0.148026i | ||||
\(346\) | −349609. | −0.156997 | ||||||||
\(347\) | − | 1.37659e6i | − | 0.613734i | −0.951752 | − | 0.306867i | \(-0.900719\pi\) | ||
0.951752 | − | 0.306867i | \(-0.0992806\pi\) | |||||||
\(348\) | −1.73352e6 | + | 1.89647e6i | −0.767328 | + | 0.839456i | ||||
\(349\) | −1.69269e6 | −0.743897 | −0.371948 | − | 0.928253i | \(-0.621310\pi\) | ||||
−0.371948 | + | 0.928253i | \(0.621310\pi\) | |||||||
\(350\) | −825133. | −0.360042 | ||||||||
\(351\) | 1.81683e6 | − | 2.38587e6i | 0.787130 | − | 1.03366i | ||||
\(352\) | 76406.3i | 0.0328679i | ||||||||
\(353\) | − | 2.61540e6i | − | 1.11712i | −0.829463 | − | 0.558561i | \(-0.811353\pi\) | ||
0.829463 | − | 0.558561i | \(-0.188647\pi\) | |||||||
\(354\) | −728582. | − | 665980.i | −0.309008 | − | 0.282457i | ||||
\(355\) | − | 942499.i | − | 0.396927i | ||||||
\(356\) | 3.24648e6 | 1.35765 | ||||||||
\(357\) | −361487. | + | 395467.i | −0.150114 | + | 0.164225i | ||||
\(358\) | 128805. | 0.0531159 | ||||||||
\(359\) | −3.58025e6 | −1.46615 | −0.733073 | − | 0.680150i | \(-0.761915\pi\) | ||||
−0.733073 | + | 0.680150i | \(0.761915\pi\) | |||||||
\(360\) | 1.54231e6 | − | 138748.i | 0.627212 | − | 0.0564248i | ||||
\(361\) | 1.67870e6 | 0.677962 | ||||||||
\(362\) | −443476. | −0.177869 | ||||||||
\(363\) | −1.84802e6 | − | 1.68923e6i | −0.736106 | − | 0.672857i | ||||
\(364\) | 4.73309e6i | 1.87237i | ||||||||
\(365\) | 3.90266e6 | 1.53331 | ||||||||
\(366\) | −423774. | − | 387362.i | −0.165361 | − | 0.151152i | ||||
\(367\) | 3.14970e6i | 1.22068i | 0.792138 | + | 0.610342i | \(0.208968\pi\) | ||||
−0.792138 | + | 0.610342i | \(0.791032\pi\) | |||||||
\(368\) | −1.77494e6 | + | 1.31325e6i | −0.683226 | + | 0.505507i | ||||
\(369\) | −1.23494e6 | + | 111097.i | −0.472149 | + | 0.0424752i | ||||
\(370\) | 1.10274e6 | 0.418765 | ||||||||
\(371\) | 7.56680e6i | 2.85415i | ||||||||
\(372\) | 1.31005e6 | + | 1.19749e6i | 0.490830 | + | 0.448657i | ||||
\(373\) | 2.01867e6i | 0.751266i | 0.926769 | + | 0.375633i | \(0.122575\pi\) | ||||
−0.926769 | + | 0.375633i | \(0.877425\pi\) | |||||||
\(374\) | − | 4654.59i | − | 0.00172069i | ||||||
\(375\) | 146970. | + | 134342.i | 0.0539697 | + | 0.0493325i | ||||
\(376\) | 175703. | 0.0640930 | ||||||||
\(377\) | − | 4.29645e6i | − | 1.55688i | ||||||
\(378\) | 576519. | − | 757087.i | 0.207532 | − | 0.272531i | ||||
\(379\) | − | 1.69715e6i | − | 0.606908i | −0.952846 | − | 0.303454i | \(-0.901860\pi\) | ||
0.952846 | − | 0.303454i | \(-0.0981399\pi\) | |||||||
\(380\) | − | 2.17128e6i | − | 0.771359i | ||||||
\(381\) | 2.69693e6 | + | 2.46520e6i | 0.951824 | + | 0.870040i | ||||
\(382\) | − | 1.10950e6i | − | 0.389018i | ||||||
\(383\) | 1.88013e6 | 0.654924 | 0.327462 | − | 0.944864i | \(-0.393807\pi\) | ||||
0.327462 | + | 0.944864i | \(0.393807\pi\) | |||||||
\(384\) | 1.54219e6 | − | 1.68716e6i | 0.533716 | − | 0.583885i | ||||
\(385\) | 329196.i | 0.113189i | ||||||||
\(386\) | − | 258147.i | − | 0.0881859i | ||||||
\(387\) | −2.46271e6 | + | 221549.i | −0.835864 | + | 0.0751954i | ||||
\(388\) | − | 1.81055e6i | − | 0.610563i | ||||||
\(389\) | −1.23969e6 | −0.415373 | −0.207687 | − | 0.978195i | \(-0.566593\pi\) | ||||
−0.207687 | + | 0.978195i | \(0.566593\pi\) | |||||||
\(390\) | −850712. | + | 930679.i | −0.283218 | + | 0.309841i | ||||
\(391\) | 356100. | − | 263472.i | 0.117796 | − | 0.0871549i | ||||
\(392\) | 1.74656e6i | 0.574075i | ||||||||
\(393\) | −527181. | + | 576736.i | −0.172178 | + | 0.188363i | ||||
\(394\) | −1.03741e6 | −0.336673 | ||||||||
\(395\) | − | 5.27233e6i | − | 1.70024i | ||||||
\(396\) | −13812.9 | − | 153543.i | −0.00442636 | − | 0.0492029i | ||||
\(397\) | 556498. | 0.177210 | 0.0886049 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886049 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(398\) | 51713.2 | 0.0163641 | ||||||||
\(399\) | −2.02251e6 | − | 1.84873e6i | −0.636003 | − | 0.581356i | ||||
\(400\) | 2.85854e6 | 0.893295 | ||||||||
\(401\) | 2.64380e6 | 0.821047 | 0.410523 | − | 0.911850i | \(-0.365346\pi\) | ||||
0.410523 | + | 0.911850i | \(0.365346\pi\) | |||||||
\(402\) | 897534. | + | 820415.i | 0.277004 | + | 0.253203i | ||||
\(403\) | −2.96792e6 | −0.910310 | ||||||||
\(404\) | 247696.i | 0.0755032i | ||||||||
\(405\) | −4.65154e6 | + | 843746.i | −1.40916 | + | 0.255608i | ||||
\(406\) | − | 1.36335e6i | − | 0.410482i | ||||||
\(407\) | − | 225452.i | − | 0.0674633i | ||||||
\(408\) | −146171. | + | 159911.i | −0.0434722 | + | 0.0475586i | ||||
\(409\) | −3.94099e6 | −1.16492 | −0.582461 | − | 0.812859i | \(-0.697910\pi\) | ||||
−0.582461 | + | 0.812859i | \(0.697910\pi\) | |||||||
\(410\) | 521337. | 0.153165 | ||||||||
\(411\) | −3.98243e6 | − | 3.64025e6i | −1.16290 | − | 1.06298i | ||||
\(412\) | − | 1.64428e6i | − | 0.477236i | ||||||
\(413\) | −9.76726e6 | −2.81772 | ||||||||
\(414\) | −587994. | + | 522736.i | −0.168606 | + | 0.149893i | ||||
\(415\) | −4.28949e6 | −1.22260 | ||||||||
\(416\) | 2.89580e6i | 0.820418i | ||||||||
\(417\) | 67670.4 | + | 61856.0i | 0.0190572 | + | 0.0174197i | ||||
\(418\) | 23804.7 | 0.00666380 | ||||||||
\(419\) | 2.63743e6 | 0.733917 | 0.366958 | − | 0.930237i | \(-0.380399\pi\) | ||||
0.366958 | + | 0.930237i | \(0.380399\pi\) | |||||||
\(420\) | 5.03401e6 | − | 5.50721e6i | 1.39249 | − | 1.52338i | ||||
\(421\) | 599700.i | 0.164903i | 0.996595 | + | 0.0824515i | \(0.0262750\pi\) | ||||
−0.996595 | + | 0.0824515i | \(0.973725\pi\) | |||||||
\(422\) | − | 914367.i | − | 0.249942i | ||||||
\(423\) | −534239. | + | 48060.8i | −0.145172 | + | 0.0130599i | ||||
\(424\) | 3.05972e6i | 0.826545i | ||||||||
\(425\) | −573499. | −0.154014 | ||||||||
\(426\) | −172864. | − | 158011.i | −0.0461510 | − | 0.0421855i | ||||
\(427\) | −5.68106e6 | −1.50786 | ||||||||
\(428\) | 1.82389e6 | 0.481271 | ||||||||
\(429\) | 190274. | + | 173925.i | 0.0499156 | + | 0.0456267i | ||||
\(430\) | 1.03965e6 | 0.271154 | ||||||||
\(431\) | 6.87699e6 | 1.78322 | 0.891610 | − | 0.452804i | \(-0.149576\pi\) | ||||
0.891610 | + | 0.452804i | \(0.149576\pi\) | |||||||
\(432\) | −1.99726e6 | + | 2.62281e6i | −0.514903 | + | 0.676173i | ||||
\(433\) | 6.73591e6i | 1.72654i | 0.504743 | + | 0.863270i | \(0.331587\pi\) | ||||
−0.504743 | + | 0.863270i | \(0.668413\pi\) | |||||||
\(434\) | −941784. | −0.240009 | ||||||||
\(435\) | −4.56961e6 | + | 4.99915e6i | −1.15786 | + | 1.26670i | ||||
\(436\) | − | 4.63239e6i | − | 1.16705i | ||||||
\(437\) | 1.34746e6 | + | 1.82118e6i | 0.337529 | + | 0.456193i | ||||
\(438\) | 654286. | − | 715789.i | 0.162961 | − | 0.178279i | ||||
\(439\) | 1.75564e6 | 0.434784 | 0.217392 | − | 0.976084i | \(-0.430245\pi\) | ||||
0.217392 | + | 0.976084i | \(0.430245\pi\) | |||||||
\(440\) | 133114.i | 0.0327787i | ||||||||
\(441\) | −477743. | − | 5.31054e6i | −0.116976 | − | 1.30030i | ||||
\(442\) | − | 176409.i | − | 0.0429503i | ||||||
\(443\) | − | 7.53505e6i | − | 1.82422i | −0.409946 | − | 0.912110i | \(-0.634453\pi\) | ||
0.409946 | − | 0.912110i | \(-0.365547\pi\) | |||||||
\(444\) | −3.44757e6 | + | 3.77164e6i | −0.829957 | + | 0.907972i | ||||
\(445\) | 8.55781e6 | 2.04863 | ||||||||
\(446\) | 185720.i | 0.0442102i | ||||||||
\(447\) | 1.76953e6 | + | 1.61748e6i | 0.418879 | + | 0.382887i | ||||
\(448\) | − | 4.56326e6i | − | 1.07419i | ||||||
\(449\) | 5.86864e6i | 1.37379i | 0.726755 | + | 0.686897i | \(0.241028\pi\) | ||||
−0.726755 | + | 0.686897i | \(0.758972\pi\) | |||||||
\(450\) | 1.01449e6 | − | 91264.8i | 0.236165 | − | 0.0212458i | ||||
\(451\) | − | 106585.i | − | 0.0246750i | ||||||
\(452\) | 784458. | 0.180602 | ||||||||
\(453\) | −1.03844e6 | − | 949215.i | −0.237759 | − | 0.217330i | ||||
\(454\) | − | 695275.i | − | 0.158313i | ||||||
\(455\) | 1.24765e7i | 2.82531i | ||||||||
\(456\) | −817825. | − | 747555.i | −0.184182 | − | 0.168357i | ||||
\(457\) | 5.34684e6i | 1.19759i | 0.800904 | + | 0.598793i | \(0.204353\pi\) | ||||
−0.800904 | + | 0.598793i | \(0.795647\pi\) | |||||||
\(458\) | 2213.55 | 0.000493090 | ||||||||
\(459\) | 400703. | − | 526204.i | 0.0887750 | − | 0.116580i | ||||
\(460\) | −4.95898e6 | + | 3.66906e6i | −1.09269 | + | 0.808463i | ||||
\(461\) | − | 5.80691e6i | − | 1.27260i | −0.771441 | − | 0.636301i | \(-0.780464\pi\) | ||
0.771441 | − | 0.636301i | \(-0.219536\pi\) | |||||||
\(462\) | 60378.0 | + | 55190.1i | 0.0131605 | + | 0.0120297i | ||||
\(463\) | −4.53602e6 | −0.983383 | −0.491691 | − | 0.870769i | \(-0.663621\pi\) | ||||
−0.491691 | + | 0.870769i | \(0.663621\pi\) | |||||||
\(464\) | 4.72313e6i | 1.01844i | ||||||||
\(465\) | 3.45333e6 | + | 3.15661e6i | 0.740638 | + | 0.677000i | ||||
\(466\) | −394983. | −0.0842586 | ||||||||
\(467\) | 2.16503e6 | 0.459379 | 0.229689 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229689 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(468\) | −523509. | − | 5.81927e6i | −0.110487 | − | 1.22816i | ||||
\(469\) | 1.20322e7 | 2.52588 | ||||||||
\(470\) | 225532. | 0.0470939 | ||||||||
\(471\) | 2.72947e6 | − | 2.98603e6i | 0.566925 | − | 0.620215i | ||||
\(472\) | −3.94950e6 | −0.815994 | ||||||||
\(473\) | − | 212552.i | − | 0.0436831i | ||||||
\(474\) | −967000. | − | 883912.i | −0.197688 | − | 0.180702i | ||||
\(475\) | − | 2.93301e6i | − | 0.596457i | ||||||
\(476\) | 1.04389e6i | 0.211171i | ||||||||
\(477\) | −836935. | − | 9.30328e6i | −0.168421 | − | 1.87215i | ||||
\(478\) | −1.46887e6 | −0.294045 | ||||||||
\(479\) | 4.63191e6 | 0.922403 | 0.461202 | − | 0.887295i | \(-0.347418\pi\) | ||||
0.461202 | + | 0.887295i | \(0.347418\pi\) | |||||||
\(480\) | 3.07991e6 | − | 3.36942e6i | 0.610148 | − | 0.667501i | ||||
\(481\) | − | 8.54463e6i | − | 1.68396i | ||||||
\(482\) | 1.98804e6 | 0.389769 | ||||||||
\(483\) | −804647. | + | 7.74324e6i | −0.156941 | + | 1.51027i | ||||
\(484\) | −4.87808e6 | −0.946533 | ||||||||
\(485\) | − | 4.77265e6i | − | 0.921309i | ||||||
\(486\) | −625084. | + | 994595.i | −0.120046 | + | 0.191010i | ||||
\(487\) | 9.50630e6 | 1.81631 | 0.908153 | − | 0.418638i | \(-0.137492\pi\) | ||||
0.908153 | + | 0.418638i | \(0.137492\pi\) | |||||||
\(488\) | −2.29720e6 | −0.436665 | ||||||||
\(489\) | 2.57309e6 | + | 2.35200e6i | 0.486611 | + | 0.444800i | ||||
\(490\) | 2.24188e6i | 0.421815i | ||||||||
\(491\) | 4.09756e6i | 0.767047i | 0.923531 | + | 0.383523i | \(0.125289\pi\) | ||||
−0.923531 | + | 0.383523i | \(0.874711\pi\) | |||||||
\(492\) | −1.62989e6 | + | 1.78309e6i | −0.303560 | + | 0.332095i | ||||
\(493\) | − | 947583.i | − | 0.175590i | ||||||
\(494\) | 902199. | 0.166336 | ||||||||
\(495\) | −36411.2 | − | 404742.i | −0.00667916 | − | 0.0742447i | ||||
\(496\) | 3.26267e6 | 0.595482 | ||||||||
\(497\) | −2.31739e6 | −0.420832 | ||||||||
\(498\) | −719138. | + | 786737.i | −0.129939 | + | 0.142153i | ||||
\(499\) | −1443.25 | −0.000259472 | −0.000129736 | − | 1.00000i | \(-0.500041\pi\) | ||||
−0.000129736 | 1.00000i | \(0.500041\pi\) | ||||||||
\(500\) | 387945. | 0.0693978 | ||||||||
\(501\) | −6.67933e6 | + | 7.30718e6i | −1.18888 | + | 1.30064i | ||||
\(502\) | 28447.1i | 0.00503824i | ||||||||
\(503\) | −5.18638e6 | −0.913996 | −0.456998 | − | 0.889468i | \(-0.651075\pi\) | ||||
−0.456998 | + | 0.889468i | \(0.651075\pi\) | |||||||
\(504\) | −341150. | − | 3.79218e6i | −0.0598231 | − | 0.664986i | ||||
\(505\) | 652933.i | 0.113931i | ||||||||
\(506\) | −40225.5 | − | 54367.6i | −0.00698435 | − | 0.00943982i | ||||
\(507\) | 2.93932e6 | + | 2.68677e6i | 0.507840 | + | 0.464205i | ||||
\(508\) | 7.11887e6 | 1.22392 | ||||||||
\(509\) | 4.48149e6i | 0.766705i | 0.923602 | + | 0.383353i | \(0.125231\pi\) | ||||
−0.923602 | + | 0.383353i | \(0.874769\pi\) | |||||||
\(510\) | −187625. | + | 205262.i | −0.0319422 | + | 0.0349448i | ||||
\(511\) | − | 9.59576e6i | − | 1.62565i | ||||||
\(512\) | − | 5.40015e6i | − | 0.910398i | ||||||
\(513\) | 2.69113e6 | + | 2.04929e6i | 0.451484 | + | 0.343803i | ||||
\(514\) | 1.76924e6 | 0.295378 | ||||||||
\(515\) | − | 4.33437e6i | − | 0.720125i | ||||||
\(516\) | −3.25031e6 | + | 3.55584e6i | −0.537404 | + | 0.587920i | ||||
\(517\) | − | 46109.3i | − | 0.00758686i | ||||||
\(518\) | − | 2.71139e6i | − | 0.443985i | ||||||
\(519\) | 2.88118e6 | − | 3.15201e6i | 0.469518 | − | 0.513653i | ||||
\(520\) | 5.04503e6i | 0.818192i | ||||||||
\(521\) | 1.55720e6 | 0.251333 | 0.125667 | − | 0.992073i | \(-0.459893\pi\) | ||||
0.125667 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(522\) | 150796. | + | 1.67623e6i | 0.0242221 | + | 0.269250i | ||||
\(523\) | 5.42090e6i | 0.866597i | 0.901251 | + | 0.433298i | \(0.142650\pi\) | ||||
−0.901251 | + | 0.433298i | \(0.857350\pi\) | |||||||
\(524\) | 1.52237e6i | 0.242209i | ||||||||
\(525\) | 6.80005e6 | − | 7.43925e6i | 1.07675 | − | 1.17796i | ||||
\(526\) | 2.12232e6i | 0.334462i | ||||||||
\(527\) | −654576. | −0.102668 | ||||||||
\(528\) | −209170. | − | 191198.i | −0.0326524 | − | 0.0298468i | ||||
\(529\) | 1.88244e6 | − | 6.15491e6i | 0.292470 | − | 0.956275i | ||||
\(530\) | 3.92744e6i | 0.607324i | ||||||||
\(531\) | 1.20087e7 | − | 1.08032e6i | 1.84825 | − | 0.166271i | ||||
\(532\) | −5.33868e6 | −0.817814 | ||||||||
\(533\) | − | 4.03959e6i | − | 0.615913i | ||||||
\(534\) | 1.43473e6 | − | 1.56959e6i | 0.217729 | − | 0.238195i | ||||
\(535\) | 4.80783e6 | 0.726214 | ||||||||
\(536\) | 4.86535e6 | 0.731480 | ||||||||
\(537\) | −1.06150e6 | + | 1.16128e6i | −0.158849 | + | 0.173781i | ||||
\(538\) | −2.04473e6 | −0.304566 | ||||||||
\(539\) | 458344. | 0.0679547 | ||||||||
\(540\) | −5.58012e6 | + | 7.32783e6i | −0.823491 | + | 1.08141i | ||||
\(541\) | 5.88262e6 | 0.864127 | 0.432064 | − | 0.901843i | \(-0.357786\pi\) | ||||
0.432064 | + | 0.901843i | \(0.357786\pi\) | |||||||
\(542\) | 326187.i | 0.0476945i | ||||||||
\(543\) | 3.65476e6 | − | 3.99831e6i | 0.531936 | − | 0.581938i | ||||
\(544\) | 638670.i | 0.0925293i | ||||||||
\(545\) | − | 1.22111e7i | − | 1.76102i | ||||||
\(546\) | 2.28833e6 | + | 2.09171e6i | 0.328501 | + | 0.300275i | ||||
\(547\) | −8.94337e6 | −1.27801 | −0.639003 | − | 0.769204i | \(-0.720653\pi\) | ||||
−0.639003 | + | 0.769204i | \(0.720653\pi\) | |||||||
\(548\) | −1.05121e7 | −1.49534 | ||||||||
\(549\) | 6.98479e6 | − | 628361.i | 0.989059 | − | 0.0889771i | ||||
\(550\) | 87559.0i | 0.0123422i | ||||||||
\(551\) | 4.84617e6 | 0.680017 | ||||||||
\(552\) | −325368. | + | 3.13106e6i | −0.0454493 | + | 0.437365i | ||||
\(553\) | −1.29635e7 | −1.80264 | ||||||||
\(554\) | 1.17726e6i | 0.162967i | ||||||||
\(555\) | −9.08788e6 | + | 9.94214e6i | −1.25236 | + | 1.37008i | ||||
\(556\) | 178625. | 0.0245050 | ||||||||
\(557\) | 76523.7 | 0.0104510 | 0.00522550 | − | 0.999986i | \(-0.498337\pi\) | ||||
0.00522550 | + | 0.999986i | \(0.498337\pi\) | |||||||
\(558\) | 1.15791e6 | − | 104167.i | 0.157431 | − | 0.0141627i | ||||
\(559\) | − | 8.05575e6i | − | 1.09038i | ||||||
\(560\) | − | 1.37156e7i | − | 1.84818i | ||||||
\(561\) | 41965.0 | + | 38359.3i | 0.00562963 | + | 0.00514592i | ||||
\(562\) | 1.26628e6i | 0.169117i | ||||||||
\(563\) | −7.73965e6 | −1.02908 | −0.514542 | − | 0.857465i | \(-0.672038\pi\) | ||||
−0.514542 | + | 0.857465i | \(0.672038\pi\) | |||||||
\(564\) | −705095. | + | 771374.i | −0.0933361 | + | 0.102110i | ||||
\(565\) | 2.06785e6 | 0.272520 | ||||||||
\(566\) | −373177. | −0.0489637 | ||||||||
\(567\) | 2.07458e6 | + | 1.14371e7i | 0.271002 | + | 1.49402i | ||||
\(568\) | −937062. | −0.121870 | ||||||||
\(569\) | −1.52774e7 | −1.97819 | −0.989096 | − | 0.147271i | \(-0.952951\pi\) | ||||
−0.989096 | + | 0.147271i | \(0.952951\pi\) | |||||||
\(570\) | −1.04976e6 | − | 959559.i | −0.135332 | − | 0.123704i | ||||
\(571\) | − | 1.36736e6i | − | 0.175506i | −0.996142 | − | 0.0877532i | \(-0.972031\pi\) | ||
0.996142 | − | 0.0877532i | \(-0.0279687\pi\) | |||||||
\(572\) | 502252. | 0.0641847 | ||||||||
\(573\) | 1.00031e7 | + | 9.14359e6i | 1.27276 | + | 1.16340i | ||||
\(574\) | − | 1.28185e6i | − | 0.162389i | ||||||
\(575\) | −6.69870e6 | + | 4.95624e6i | −0.844930 | + | 0.625148i | ||||
\(576\) | 504725. | + | 5.61046e6i | 0.0633867 | + | 0.704600i | ||||
\(577\) | −7.52623e6 | −0.941105 | −0.470552 | − | 0.882372i | \(-0.655945\pi\) | ||||
−0.470552 | + | 0.882372i | \(0.655945\pi\) | |||||||
\(578\) | 1.77310e6i | 0.220757i | ||||||||
\(579\) | 2.32741e6 | + | 2.12743e6i | 0.288520 | + | 0.263730i | ||||
\(580\) | 1.31959e7i | 1.62880i | ||||||||
\(581\) | 1.05469e7i | 1.29624i | ||||||||
\(582\) | −875353. | − | 800140.i | −0.107121 | − | 0.0979171i | ||||
\(583\) | 802951. | 0.0978403 | ||||||||
\(584\) | − | 3.88015e6i | − | 0.470778i | ||||||
\(585\) | −1.37998e6 | − | 1.53398e7i | −0.166719 | − | 1.85323i | ||||
\(586\) | − | 192543.i | − | 0.0231624i | ||||||
\(587\) | − | 620332.i | − | 0.0743069i | −0.999310 | − | 0.0371534i | \(-0.988171\pi\) | ||
0.999310 | − | 0.0371534i | \(-0.0118290\pi\) | |||||||
\(588\) | −7.66775e6 | − | 7.00892e6i | −0.914587 | − | 0.836003i | ||||
\(589\) | − | 3.34766e6i | − | 0.397606i | ||||||
\(590\) | −5.06956e6 | −0.599571 | ||||||||
\(591\) | 8.54943e6 | − | 9.35307e6i | 1.00686 | − | 1.10150i | ||||
\(592\) | 9.39321e6i | 1.10156i | ||||||||
\(593\) | 4.96024e6i | 0.579250i | 0.957140 | + | 0.289625i | \(0.0935307\pi\) | ||||
−0.957140 | + | 0.289625i | \(0.906469\pi\) | |||||||
\(594\) | −80338.3 | − | 61177.4i | −0.00934236 | − | 0.00711418i | ||||
\(595\) | 2.75171e6i | 0.318647i | ||||||||
\(596\) | 4.67089e6 | 0.538622 | ||||||||
\(597\) | −426177. | + | 466237.i | −0.0489388 | + | 0.0535391i | ||||
\(598\) | −1.52455e6 | − | 2.06053e6i | −0.174337 | − | 0.235628i | ||||
\(599\) | 2.30566e6i | 0.262560i | 0.991345 | + | 0.131280i | \(0.0419087\pi\) | ||||
−0.991345 | + | 0.131280i | \(0.958091\pi\) | |||||||
\(600\) | 2.74967e6 | − | 3.00814e6i | 0.311819 | − | 0.341130i | ||||
\(601\) | −3.65731e6 | −0.413025 | −0.206512 | − | 0.978444i | \(-0.566211\pi\) | ||||
−0.206512 | + | 0.978444i | \(0.566211\pi\) | |||||||
\(602\) | − | 2.55626e6i | − | 0.287484i | ||||||
\(603\) | −1.47934e7 | + | 1.33084e6i | −1.65682 | + | 0.149050i | ||||
\(604\) | −2.74110e6 | −0.305726 | ||||||||
\(605\) | −1.28588e7 | −1.42827 | ||||||||
\(606\) | 119755. | + | 109465.i | 0.0132468 | + | 0.0121086i | ||||
\(607\) | 5.25634e6 | 0.579044 | 0.289522 | − | 0.957171i | \(-0.406504\pi\) | ||||
0.289522 | + | 0.957171i | \(0.406504\pi\) | |||||||
\(608\) | −3.26631e6 | −0.358343 | ||||||||
\(609\) | 1.22918e7 | + | 1.12356e7i | 1.34299 | + | 1.22759i | ||||
\(610\) | −2.94867e6 | −0.320850 | ||||||||
\(611\) | − | 1.74754e6i | − | 0.189376i | ||||||
\(612\) | −115460. | − | 1.28344e6i | −0.0124610 | − | 0.138515i | ||||
\(613\) | 3.67092e6i | 0.394570i | 0.980346 | + | 0.197285i | \(0.0632124\pi\) | ||||
−0.980346 | + | 0.197285i | \(0.936788\pi\) | |||||||
\(614\) | − | 2.44013e6i | − | 0.261212i | ||||||
\(615\) | −4.29642e6 | + | 4.70029e6i | −0.458057 | + | 0.501114i | ||||
\(616\) | 327297. | 0.0347528 | ||||||||
\(617\) | 1.73511e6 | 0.183490 | 0.0917451 | − | 0.995783i | \(-0.470755\pi\) | ||||
0.0917451 | + | 0.995783i | \(0.470755\pi\) | |||||||
\(618\) | −794969. | − | 726663.i | −0.0837296 | − | 0.0765353i | ||||
\(619\) | 7.42838e6i | 0.779233i | 0.920977 | + | 0.389617i | \(0.127393\pi\) | ||||
−0.920977 | + | 0.389617i | \(0.872607\pi\) | |||||||
\(620\) | 9.11551e6 | 0.952361 | ||||||||
\(621\) | 132853. | − | 9.60921e6i | 0.0138242 | − | 0.999904i | ||||
\(622\) | 2.32932e6 | 0.241409 | ||||||||
\(623\) | − | 2.10417e7i | − | 2.17200i | ||||||
\(624\) | −7.92756e6 | − | 7.24640e6i | −0.815038 | − | 0.745008i | ||||
\(625\) | −9.24158e6 | −0.946338 | ||||||||
\(626\) | 3.63869e6 | 0.371115 | ||||||||
\(627\) | −196178. | + | 214619.i | −0.0199289 | + | 0.0218022i | ||||
\(628\) | − | 7.88201e6i | − | 0.797513i | ||||||
\(629\) | − | 1.88452e6i | − | 0.189922i | ||||||
\(630\) | −437899. | − | 4.86763e6i | −0.0439564 | − | 0.488615i | ||||
\(631\) | 9.24226e6i | 0.924070i | 0.886862 | + | 0.462035i | \(0.152880\pi\) | ||||
−0.886862 | + | 0.462035i | \(0.847120\pi\) | |||||||
\(632\) | −5.24191e6 | −0.522032 | ||||||||
\(633\) | 8.24378e6 | + | 7.53545e6i | 0.817743 | + | 0.747480i | ||||
\(634\) | 2.68459e6 | 0.265249 | ||||||||
\(635\) | 1.87655e7 | 1.84683 | ||||||||
\(636\) | −1.34328e7 | − | 1.22786e7i | −1.31681 | − | 1.20366i | ||||
\(637\) | 1.73713e7 | 1.69622 | ||||||||
\(638\) | −144672. | −0.0140713 | ||||||||
\(639\) | 2.84920e6 | − | 256318.i | 0.276039 | − | 0.0248329i | ||||
\(640\) | − | 1.17394e7i | − | 1.13292i | ||||||
\(641\) | −8.97691e6 | −0.862942 | −0.431471 | − | 0.902127i | \(-0.642005\pi\) | ||||
−0.431471 | + | 0.902127i | \(0.642005\pi\) | |||||||
\(642\) | 806038. | − | 881805.i | 0.0771823 | − | 0.0844374i | ||||
\(643\) | 5.63467e6i | 0.537453i | 0.963216 | + | 0.268727i | \(0.0866029\pi\) | ||||
−0.963216 | + | 0.268727i | \(0.913397\pi\) | |||||||
\(644\) | 9.02138e6 | + | 1.21930e7i | 0.857153 | + | 1.15850i | ||||
\(645\) | −8.56792e6 | + | 9.37330e6i | −0.810916 | + | 0.887142i | ||||
\(646\) | 198980. | 0.0187598 | ||||||||
\(647\) | − | 1.01191e7i | − | 0.950349i | −0.879892 | − | 0.475174i | \(-0.842385\pi\) | ||
0.879892 | − | 0.475174i | \(-0.157615\pi\) | |||||||
\(648\) | 838878. | + | 4.62470e6i | 0.0784804 | + | 0.432660i | ||||
\(649\) | 1.03645e6i | 0.0965913i | ||||||||
\(650\) | 3.31849e6i | 0.308075i | ||||||||
\(651\) | 7.76139e6 | − | 8.49096e6i | 0.717773 | − | 0.785244i | ||||
\(652\) | 6.79198e6 | 0.625717 | ||||||||
\(653\) | − | 4.41505e6i | − | 0.405184i | −0.979263 | − | 0.202592i | \(-0.935063\pi\) | ||
0.979263 | − | 0.202592i | \(-0.0649365\pi\) | |||||||
\(654\) | −2.23964e6 | − | 2.04721e6i | −0.204755 | − | 0.187162i | ||||
\(655\) | 4.01300e6i | 0.365482i | ||||||||
\(656\) | 4.44077e6i | 0.402901i | ||||||||
\(657\) | 1.06135e6 | + | 1.17979e7i | 0.0959281 | + | 1.06633i | ||||
\(658\) | − | 554533.i | − | 0.0499301i | ||||||
\(659\) | −7.07020e6 | −0.634188 | −0.317094 | − | 0.948394i | \(-0.602707\pi\) | ||||
−0.317094 | + | 0.948394i | \(0.602707\pi\) | |||||||
\(660\) | −584397. | − | 534184.i | −0.0522214 | − | 0.0477344i | ||||
\(661\) | − | 1.36132e6i | − | 0.121187i | −0.998163 | − | 0.0605937i | \(-0.980701\pi\) | ||
0.998163 | − | 0.0605937i | \(-0.0192994\pi\) | |||||||
\(662\) | − | 1.99323e6i | − | 0.176772i | ||||||
\(663\) | 1.59048e6 | + | 1.45382e6i | 0.140522 | + | 0.128448i | ||||
\(664\) | 4.26474e6i | 0.375381i | ||||||||
\(665\) | −1.40729e7 | −1.23404 | ||||||||
\(666\) | 299897. | + | 3.33362e6i | 0.0261991 | + | 0.291226i | ||||
\(667\) | −8.18913e6 | − | 1.10682e7i | −0.712727 | − | 0.963299i | ||||
\(668\) | 1.92882e7i | 1.67244i | ||||||||
\(669\) | −1.67442e6 | − | 1.53055e6i | −0.144644 | − | 0.132216i | ||||
\(670\) | 6.24515e6 | 0.537472 | ||||||||
\(671\) | 602846.i | 0.0516892i | ||||||||
\(672\) | −8.28464e6 | − | 7.57280e6i | −0.707702 | − | 0.646894i | ||||
\(673\) | 1.60775e7 | 1.36830 | 0.684148 | − | 0.729344i | \(-0.260174\pi\) | ||||
0.684148 | + | 0.729344i | \(0.260174\pi\) | |||||||
\(674\) | −2.52489e6 | −0.214089 | ||||||||
\(675\) | −7.53774e6 | + | 9.89859e6i | −0.636769 | + | 0.836207i | ||||
\(676\) | 7.75870e6 | 0.653014 | ||||||||
\(677\) | 9.18709e6 | 0.770382 | 0.385191 | − | 0.922837i | \(-0.374135\pi\) | ||||
0.385191 | + | 0.922837i | \(0.374135\pi\) | |||||||
\(678\) | 346678. | − | 379265.i | 0.0289636 | − | 0.0316861i | ||||
\(679\) | −1.17349e7 | −0.976795 | ||||||||
\(680\) | 1.11268e6i | 0.0922782i | ||||||||
\(681\) | 6.26848e6 | + | 5.72988e6i | 0.517958 | + | 0.473454i | ||||
\(682\) | 99937.4i | 0.00822749i | ||||||||
\(683\) | − | 3.89239e6i | − | 0.319275i | −0.987176 | − | 0.159637i | \(-0.948967\pi\) | ||
0.987176 | − | 0.159637i | \(-0.0510325\pi\) | |||||||
\(684\) | 6.56383e6 | − | 590491.i | 0.536435 | − | 0.0482584i | ||||
\(685\) | −2.77103e7 | −2.25639 | ||||||||
\(686\) | 1.29008e6 | 0.104666 | ||||||||
\(687\) | −18242.3 | + | 19957.0i | −0.00147464 | + | 0.00161326i | ||||
\(688\) | 8.85577e6i | 0.713272i | ||||||||
\(689\) | 3.04319e7 | 2.44220 | ||||||||
\(690\) | −417641. | + | 4.01902e6i | −0.0333949 | + | 0.321364i | ||||
\(691\) | 1.11648e7 | 0.889518 | 0.444759 | − | 0.895650i | \(-0.353289\pi\) | ||||
0.444759 | + | 0.895650i | \(0.353289\pi\) | |||||||
\(692\) | − | 8.32013e6i | − | 0.660488i | ||||||
\(693\) | −995169. | + | 89526.8i | −0.0787162 | + | 0.00708141i | ||||
\(694\) | −1.75679e6 | −0.138459 | ||||||||
\(695\) | 470859. | 0.0369768 | ||||||||
\(696\) | 4.97031e6 | + | 4.54324e6i | 0.388920 | + | 0.355503i | ||||
\(697\) | − | 890934.i | − | 0.0694646i | ||||||
\(698\) | 2.16019e6i | 0.167824i | ||||||||
\(699\) | 3.25512e6 | − | 3.56110e6i | 0.251985 | − | 0.275671i | ||||
\(700\) | − | 1.96368e7i | − | 1.51470i | ||||||
\(701\) | −4.27810e6 | −0.328818 | −0.164409 | − | 0.986392i | \(-0.552572\pi\) | ||||
−0.164409 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(702\) | −3.04483e6 | − | 2.31862e6i | −0.233195 | − | 0.177577i | ||||
\(703\) | 9.63790e6 | 0.735519 | ||||||||
\(704\) | −484230. | −0.0368231 | ||||||||
\(705\) | −1.85865e6 | + | 2.03336e6i | −0.140840 | + | 0.154078i | ||||
\(706\) | −3.33775e6 | −0.252024 | ||||||||
\(707\) | 1.60541e6 | 0.120792 | ||||||||
\(708\) | 1.58493e7 | − | 1.73391e7i | 1.18830 | − | 1.30000i | ||||
\(709\) | − | 4.55553e6i | − | 0.340348i | −0.985414 | − | 0.170174i | \(-0.945567\pi\) | ||
0.985414 | − | 0.170174i | \(-0.0544330\pi\) | |||||||
\(710\) | −1.20281e6 | −0.0895470 | ||||||||
\(711\) | 1.59384e7 | − | 1.43384e6i | 1.18242 | − | 0.106372i | ||||
\(712\) | − | 8.50844e6i | − | 0.628999i | ||||||
\(713\) | −7.64571e6 | + | 5.65692e6i | −0.563241 | + | 0.416732i | ||||
\(714\) | 504692. | + | 461327.i | 0.0370494 | + | 0.0338660i | ||||
\(715\) | 1.32395e6 | 0.0968515 | ||||||||
\(716\) | 3.06535e6i | 0.223459i | ||||||||
\(717\) | 1.21052e7 | − | 1.32431e7i | 0.879375 | − | 0.962036i | ||||
\(718\) | 4.56909e6i | 0.330764i | ||||||||
\(719\) | − | 1.76274e6i | − | 0.127164i | −0.997977 | − | 0.0635821i | \(-0.979748\pi\) | ||
0.997977 | − | 0.0635821i | \(-0.0202525\pi\) | |||||||
\(720\) | 1.51703e6 | + | 1.68632e7i | 0.109060 | + | 1.21229i | ||||
\(721\) | −1.06572e7 | −0.763495 | ||||||||
\(722\) | − | 2.14234e6i | − | 0.152949i | ||||||
\(723\) | −1.63838e7 | + | 1.79238e7i | −1.16565 | + | 1.27522i | ||||
\(724\) | − | 1.05540e7i | − | 0.748294i | ||||||
\(725\) | 1.78253e7i | 1.25948i | ||||||||
\(726\) | −2.15579e6 | + | 2.35843e6i | −0.151797 | + | 0.166066i | ||||
\(727\) | 222075.i | 0.0155834i | 0.999970 | + | 0.00779172i | \(0.00248021\pi\) | ||||
−0.999970 | + | 0.00779172i | \(0.997520\pi\) | |||||||
\(728\) | 1.24046e7 | 0.867468 | ||||||||
\(729\) | −3.81568e6 | − | 1.38323e7i | −0.265921 | − | 0.963995i | ||||
\(730\) | − | 4.98055e6i | − | 0.345915i | ||||||
\(731\) | − | 1.77670e6i | − | 0.122976i | ||||||
\(732\) | 9.21861e6 | − | 1.00852e7i | 0.635898 | − | 0.695673i | ||||
\(733\) | − | 3.03919e6i | − | 0.208929i | −0.994529 | − | 0.104464i | \(-0.966687\pi\) | ||
0.994529 | − | 0.104464i | \(-0.0333128\pi\) | |||||||
\(734\) | 4.01962e6 | 0.275388 | ||||||||
\(735\) | −2.02124e7 | − | 1.84757e7i | −1.38007 | − | 1.26149i | ||||
\(736\) | 5.51946e6 | + | 7.45993e6i | 0.375580 | + | 0.507622i | ||||
\(737\) | − | 1.27680e6i | − | 0.0865872i | ||||||
\(738\) | 141781. | + | 1.57602e6i | 0.00958244 | + | 0.106517i | ||||
\(739\) | 1.00967e7 | 0.680096 | 0.340048 | − | 0.940408i | \(-0.389557\pi\) | ||||
0.340048 | + | 0.940408i | \(0.389557\pi\) | |||||||
\(740\) | 2.62435e7i | 1.76174i | ||||||||
\(741\) | −7.43517e6 | + | 8.13407e6i | −0.497445 | + | 0.544205i | ||||
\(742\) | 9.65669e6 | 0.643900 | ||||||||
\(743\) | 5.27625e6 | 0.350633 | 0.175317 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175317 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(744\) | 3.13840e6 | − | 3.43341e6i | 0.207863 | − | 0.227402i | ||||
\(745\) | 1.23126e7 | 0.812753 | ||||||||
\(746\) | 2.57621e6 | 0.169486 | ||||||||
\(747\) | −1.16655e6 | − | 1.29673e7i | −0.0764896 | − | 0.850250i | ||||
\(748\) | 110772. | 0.00723895 | ||||||||
\(749\) | − | 1.18214e7i | − | 0.769950i | ||||||
\(750\) | 171446. | − | 187562.i | 0.0111295 | − | 0.0121756i | ||||
\(751\) | 8.55220e6i | 0.553322i | 0.960968 | + | 0.276661i | \(0.0892279\pi\) | ||||
−0.960968 | + | 0.276661i | \(0.910772\pi\) | |||||||
\(752\) | 1.92109e6i | 0.123881i | ||||||||
\(753\) | −256474. | − | 234437.i | −0.0164838 | − | 0.0150674i | ||||
\(754\) | −5.48309e6 | −0.351234 | ||||||||
\(755\) | −7.22560e6 | −0.461325 | ||||||||
\(756\) | 1.80175e7 | + | 1.37202e7i | 1.14654 | + | 0.873086i | ||||
\(757\) | − | 2.04752e7i | − | 1.29864i | −0.760516 | − | 0.649320i | \(-0.775054\pi\) | ||
0.760516 | − | 0.649320i | \(-0.224946\pi\) | |||||||
\(758\) | −2.16589e6 | −0.136919 | ||||||||
\(759\) | 821674. | + | 85385.2i | 0.0517720 | + | 0.00537995i | ||||
\(760\) | −5.69053e6 | −0.357370 | ||||||||
\(761\) | 1.69707e6i | 0.106228i | 0.998588 | + | 0.0531140i | \(0.0169147\pi\) | ||||
−0.998588 | + | 0.0531140i | \(0.983085\pi\) | |||||||
\(762\) | 3.14607e6 | − | 3.44179e6i | 0.196282 | − | 0.214732i | ||||
\(763\) | −3.00243e7 | −1.86708 | ||||||||
\(764\) | 2.64044e7 | 1.63660 | ||||||||
\(765\) | −304356. | − | 3.38319e6i | −0.0188031 | − | 0.209013i | ||||
\(766\) | − | 2.39941e6i | − | 0.147751i | ||||||
\(767\) | 3.92816e7i | 2.41102i | ||||||||
\(768\) | 6.38208e6 | + | 5.83371e6i | 0.390444 | + | 0.356896i | ||||
\(769\) | 8.50809e6i | 0.518819i | 0.965767 | + | 0.259410i | \(0.0835280\pi\) | ||||
−0.965767 | + | 0.259410i | \(0.916472\pi\) | |||||||
\(770\) | 420117. | 0.0255355 | ||||||||
\(771\) | −1.45806e7 | + | 1.59511e7i | −0.883361 | + | 0.966397i | ||||
\(772\) | 6.14349e6 | 0.370998 | ||||||||
\(773\) | −1.74244e7 | −1.04884 | −0.524420 | − | 0.851460i | \(-0.675718\pi\) | ||||
−0.524420 | + | 0.851460i | \(0.675718\pi\) | |||||||
\(774\) | 282738. | + | 3.14289e6i | 0.0169642 | + | 0.188572i | ||||
\(775\) | 1.23134e7 | 0.736418 | ||||||||
\(776\) | −4.74512e6 | −0.282874 | ||||||||
\(777\) | 2.44455e7 | + | 2.23450e7i | 1.45260 | + | 1.32779i | ||||
\(778\) | 1.58208e6i | 0.0937087i | ||||||||
\(779\) | 4.55645e6 | 0.269019 | ||||||||
\(780\) | −2.21487e7 | − | 2.02456e7i | −1.30350 | − | 1.19150i | ||||
\(781\) | 245910.i | 0.0144261i | ||||||||
\(782\) | −336240. | − | 454451.i | −0.0196622 | − | 0.0265748i | ||||
\(783\) | −1.63553e7 | − | 1.24545e7i | −0.953354 | − | 0.725976i | ||||
\(784\) | −1.90964e7 | −1.10959 | ||||||||
\(785\) | − | 2.07772e7i | − | 1.20341i | ||||||
\(786\) | 736025. | + | 672784.i | 0.0424949 | + | 0.0388436i | ||||
\(787\) | − | 2.50321e7i | − | 1.44066i | −0.693634 | − | 0.720328i | \(-0.743991\pi\) | ||
0.693634 | − | 0.720328i | \(-0.256009\pi\) | |||||||
\(788\) | − | 2.46886e7i | − | 1.41638i | ||||||
\(789\) | −1.91345e7 | − | 1.74904e7i | −1.09427 | − | 1.00025i | ||||
\(790\) | −6.72850e6 | −0.383575 | ||||||||
\(791\) | − | 5.08438e6i | − | 0.288933i | ||||||
\(792\) | −402407. | + | 36201.1i | −0.0227957 | + | 0.00205073i | ||||
\(793\) | 2.28479e7i | 1.29022i | ||||||||
\(794\) | − | 710199.i | − | 0.0399787i | ||||||
\(795\) | −3.54091e7 | − | 3.23667e7i | −1.98700 | − | 1.81627i | ||||
\(796\) | 1.23069e6i | 0.0688440i | ||||||||
\(797\) | 2.04001e7 | 1.13759 | 0.568797 | − | 0.822478i | \(-0.307409\pi\) | ||||
0.568797 | + | 0.822478i | \(0.307409\pi\) | |||||||
\(798\) | −2.35934e6 | + | 2.58111e6i | −0.131154 | + | 0.143483i | ||||
\(799\) | − | 385422.i | − | 0.0213584i | ||||||
\(800\) | − | 1.20142e7i | − | 0.663698i | ||||||
\(801\) | 2.32734e6 | + | 2.58705e7i | 0.128168 | + | 1.42470i | ||||
\(802\) | − | 3.37400e6i | − | 0.185229i | ||||||
\(803\) | −1.01825e6 | −0.0557272 | ||||||||
\(804\) | −1.95246e7 | + | 2.13599e7i | −1.06523 | + | 1.16536i | ||||
\(805\) | 2.37806e7 | + | 3.21411e7i | 1.29340 | + | 1.74812i | ||||
\(806\) | 3.78763e6i | 0.205367i | ||||||||
\(807\) | 1.68510e7 | − | 1.84350e7i | 0.910839 | − | 0.996457i | ||||
\(808\) | 649166. | 0.0349806 | ||||||||
\(809\) | 1.70605e7i | 0.916475i | 0.888830 | + | 0.458238i | \(0.151519\pi\) | ||||
−0.888830 | + | 0.458238i | \(0.848481\pi\) | |||||||
\(810\) | 1.07678e6 | + | 5.93626e6i | 0.0576654 | + | 0.317907i | ||||
\(811\) | −2.15503e7 | −1.15054 | −0.575269 | − | 0.817964i | \(-0.695103\pi\) | ||||
−0.575269 | + | 0.817964i | \(0.695103\pi\) | |||||||
\(812\) | 3.24457e7 | 1.72690 | ||||||||
\(813\) | −2.94084e6 | − | 2.68816e6i | −0.156043 | − | 0.142636i | ||||
\(814\) | −287720. | −0.0152198 | ||||||||
\(815\) | 1.79039e7 | 0.944175 | ||||||||
\(816\) | −1.74843e6 | − | 1.59820e6i | −0.0919226 | − | 0.0840243i | ||||
\(817\) | 9.08646e6 | 0.476255 | ||||||||
\(818\) | 5.02946e6i | 0.262808i | ||||||||
\(819\) | −3.77170e7 | + | 3.39307e6i | −1.96484 | + | 0.176760i | ||||
\(820\) | 1.24070e7i | 0.644365i | ||||||||
\(821\) | − | 1.63166e7i | − | 0.844834i | −0.906402 | − | 0.422417i | \(-0.861182\pi\) | ||
0.906402 | − | 0.422417i | \(-0.138818\pi\) | |||||||
\(822\) | −4.64566e6 | + | 5.08235e6i | −0.239810 | + | 0.262352i | ||||
\(823\) | 1.20206e7 | 0.618624 | 0.309312 | − | 0.950961i | \(-0.399901\pi\) | ||||
0.309312 | + | 0.950961i | \(0.399901\pi\) | |||||||
\(824\) | −4.30937e6 | −0.221103 | ||||||||
\(825\) | −789417. | − | 721588.i | −0.0403805 | − | 0.0369109i | ||||
\(826\) | 1.24649e7i | 0.635680i | ||||||||
\(827\) | −2.90002e7 | −1.47447 | −0.737236 | − | 0.675635i | \(-0.763869\pi\) | ||||
−0.737236 | + | 0.675635i | \(0.763869\pi\) | |||||||
\(828\) | −1.24403e7 | − | 1.39933e7i | −0.630601 | − | 0.709324i | ||||
\(829\) | 4.57153e6 | 0.231034 | 0.115517 | − | 0.993306i | \(-0.463148\pi\) | ||||
0.115517 | + | 0.993306i | \(0.463148\pi\) | |||||||
\(830\) | 5.47421e6i | 0.275820i | ||||||||
\(831\) | −1.06140e7 | − | 9.70203e6i | −0.533184 | − | 0.487371i | ||||
\(832\) | −1.83523e7 | −0.919143 | ||||||||
\(833\) | 3.83124e6 | 0.191305 | ||||||||
\(834\) | 78940.1 | − | 86360.5i | 0.00392991 | − | 0.00429932i | ||||
\(835\) | 5.08443e7i | 2.52363i | ||||||||
\(836\) | 566514.i | 0.0280346i | ||||||||
\(837\) | −8.60338e6 | + | 1.12980e7i | −0.424478 | + | 0.557426i | ||||
\(838\) | − | 3.36587e6i | − | 0.165572i | ||||||
\(839\) | −1.67247e7 | −0.820263 | −0.410132 | − | 0.912026i | \(-0.634517\pi\) | ||||
−0.410132 | + | 0.912026i | \(0.634517\pi\) | |||||||
\(840\) | −1.44334e7 | − | 1.31932e7i | −0.705781 | − | 0.645139i | ||||
\(841\) | −8.94131e6 | −0.435924 | ||||||||
\(842\) | 765332. | 0.0372023 | ||||||||
\(843\) | −1.14165e7 | − | 1.04356e7i | −0.553306 | − | 0.505765i | ||||
\(844\) | 2.17605e7 | 1.05151 | ||||||||
\(845\) | 2.04522e7 | 0.985365 | ||||||||
\(846\) | 61334.8 | + | 681791.i | 0.00294633 | + | 0.0327511i | ||||
\(847\) | 3.16168e7i | 1.51429i | ||||||||
\(848\) | −3.34541e7 | −1.59757 | ||||||||
\(849\) | 3.07541e6 | − | 3.36450e6i | 0.146431 | − | 0.160196i | ||||
\(850\) | 731894.i | 0.0347457i | ||||||||
\(851\) | −1.62863e7 | − | 2.20120e7i | −0.770899 | − | 1.04192i | ||||
\(852\) | 3.76041e6 | − | 4.11389e6i | 0.177475 | − | 0.194157i | ||||
\(853\) | −1.92985e7 | −0.908137 | −0.454068 | − | 0.890967i | \(-0.650028\pi\) | ||||
−0.454068 | + | 0.890967i | \(0.650028\pi\) | |||||||
\(854\) | 7.25012e6i | 0.340174i | ||||||||
\(855\) | 1.73024e7 | − | 1.55655e6i | 0.809454 | − | 0.0728196i | ||||
\(856\) | − | 4.78009e6i | − | 0.222973i | ||||||
\(857\) | 1.36216e7i | 0.633545i | 0.948502 | + | 0.316772i | \(0.102599\pi\) | ||||
−0.948502 | + | 0.316772i | \(0.897401\pi\) | |||||||
\(858\) | 221962. | − | 242826.i | 0.0102934 | − | 0.0112610i | ||||
\(859\) | 2.08230e7 | 0.962854 | 0.481427 | − | 0.876486i | \(-0.340119\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340119\pi\) | |||||||
\(860\) | 2.47420e7i | 1.14075i | ||||||||
\(861\) | 1.15569e7 | + | 1.05639e7i | 0.531294 | + | 0.485643i | ||||
\(862\) | − | 8.77635e6i | − | 0.402296i | ||||||
\(863\) | − | 3.02999e7i | − | 1.38489i | −0.721473 | − | 0.692443i | \(-0.756535\pi\) | ||
0.721473 | − | 0.692443i | \(-0.243465\pi\) | |||||||
\(864\) | 1.10235e7 | + | 8.39432e6i | 0.502381 | + | 0.382562i | ||||
\(865\) | − | 2.19321e7i | − | 0.996643i | ||||||
\(866\) | 8.59631e6 | 0.389509 | ||||||||
\(867\) | −1.59860e7 | − | 1.46124e7i | −0.722257 | − | 0.660199i | ||||
\(868\) | − | 2.24130e7i | − | 1.00972i | ||||||
\(869\) | 1.37562e6i | 0.0617943i | ||||||||
\(870\) | 6.37987e6 | + | 5.83170e6i | 0.285768 | + | 0.261214i | ||||
\(871\) | − | 4.83907e7i | − | 2.16131i | ||||||
\(872\) | −1.21407e7 | −0.540694 | ||||||||
\(873\) | 1.44279e7 | − | 1.29795e6i | 0.640717 | − | 0.0576398i | ||||
\(874\) | 2.32417e6 | − | 1.71961e6i | 0.102918 | − | 0.0761469i | ||||
\(875\) | − | 2.51442e6i | − | 0.111024i | ||||||
\(876\) | 1.70346e7 | + | 1.55710e7i | 0.750020 | + | 0.685576i | ||||
\(877\) | 6.18389e6 | 0.271496 | 0.135748 | − | 0.990743i | \(-0.456656\pi\) | ||||
0.135748 | + | 0.990743i | \(0.456656\pi\) | |||||||
\(878\) | − | 2.24053e6i | − | 0.0980876i | ||||||
\(879\) | 1.73593e6 | + | 1.58678e6i | 0.0757811 | + | 0.0692698i | ||||
\(880\) | −1.45543e6 | −0.0633557 | ||||||||
\(881\) | −2.91955e7 | −1.26729 | −0.633645 | − | 0.773624i | \(-0.718442\pi\) | ||||
−0.633645 | + | 0.773624i | \(0.718442\pi\) | |||||||
\(882\) | −6.77727e6 | + | 609692.i | −0.293348 | + | 0.0263900i | ||||
\(883\) | −3.67569e7 | −1.58649 | −0.793244 | − | 0.608905i | \(-0.791609\pi\) | ||||
−0.793244 | + | 0.608905i | \(0.791609\pi\) | |||||||
\(884\) | 4.19826e6 | 0.180692 | ||||||||
\(885\) | 4.17791e7 | − | 4.57063e7i | 1.79308 | − | 1.96163i | ||||
\(886\) | −9.61617e6 | −0.411546 | ||||||||
\(887\) | 3.76607e7i | 1.60724i | 0.595145 | + | 0.803618i | \(0.297094\pi\) | ||||
−0.595145 | + | 0.803618i | \(0.702906\pi\) | |||||||
\(888\) | 9.88478e6 | + | 9.03545e6i | 0.420663 | + | 0.384519i | ||||
\(889\) | − | 4.61402e7i | − | 1.95806i | ||||||
\(890\) | − | 1.09214e7i | − | 0.462172i | ||||||
\(891\) | 1.21365e6 | − | 220144.i | 0.0512151 | − | 0.00928993i | ||||
\(892\) | −4.41985e6 | −0.185992 | ||||||||
\(893\) | 1.97114e6 | 0.0827158 | ||||||||
\(894\) | 2.06422e6 | − | 2.25826e6i | 0.0863798 | − | 0.0944995i | ||||
\(895\) | 8.08035e6i | 0.337188i | ||||||||
\(896\) | −2.88646e7 | −1.20115 | ||||||||
\(897\) | 3.11415e7 | + | 3.23610e6i | 1.29228 | + | 0.134289i | ||||
\(898\) | 7.48951e6 | 0.309929 | ||||||||
\(899\) | 2.03453e7i | 0.839585i | ||||||||
\(900\) | 2.17196e6 | + | 2.41432e7i | 0.0893810 | + | 0.993549i | ||||
\(901\) | 6.71177e6 | 0.275439 | ||||||||
\(902\) | −136024. | −0.00556670 | ||||||||
\(903\) | 2.30468e7 | + | 2.10666e7i | 0.940571 | + | 0.859754i | ||||
\(904\) | − | 2.05592e6i | − | 0.0836731i | ||||||
\(905\) | − | 2.78207e7i | − | 1.12914i | ||||||
\(906\) | −1.21138e6 | + | 1.32525e6i | −0.0490298 | + | 0.0536386i | ||||
\(907\) | 1.30537e7i | 0.526885i | 0.964675 | + | 0.263443i | \(0.0848579\pi\) | ||||
−0.964675 | + | 0.263443i | \(0.915142\pi\) | |||||||
\(908\) | 1.65464e7 | 0.666024 | ||||||||
\(909\) | −1.97384e6 | + | 177569.i | −0.0792321 | + | 0.00712783i | ||||
\(910\) | 1.59225e7 | 0.637393 | ||||||||
\(911\) | 2.20067e7 | 0.878534 | 0.439267 | − | 0.898357i | \(-0.355238\pi\) | ||||
0.439267 | + | 0.898357i | \(0.355238\pi\) | |||||||
\(912\) | 8.17356e6 | − | 8.94188e6i | 0.325405 | − | 0.355993i | ||||
\(913\) | 1.11918e6 | 0.0444349 | ||||||||
\(914\) | 6.82359e6 | 0.270176 | ||||||||
\(915\) | 2.43005e7 | − | 2.65847e7i | 0.959539 | − | 1.04974i | ||||
\(916\) | 52679.1i | 0.00207443i | ||||||||
\(917\) | 9.86705e6 | 0.387493 | ||||||||
\(918\) | −671538. | − | 511374.i | −0.0263005 | − | 0.0200277i | ||||
\(919\) | 6.53274e6i | 0.255156i | 0.991829 | + | 0.127578i | \(0.0407204\pi\) | ||||
−0.991829 | + | 0.127578i | \(0.959280\pi\) | |||||||
\(920\) | 9.61594e6 | + | 1.29966e7i | 0.374561 | + | 0.506244i | ||||
\(921\) | 2.19998e7 | + | 2.01095e7i | 0.854614 | + | 0.781183i | ||||
\(922\) | −7.41073e6 | −0.287100 | ||||||||
\(923\) | 9.32000e6i | 0.360091i | ||||||||
\(924\) | −1.31344e6 | + | 1.43690e6i | −0.0506092 | + | 0.0553664i | ||||
\(925\) | 3.54503e7i | 1.36228i | ||||||||
\(926\) | 5.78883e6i | 0.221852i | ||||||||
\(927\) | 1.31029e7 | − | 1.17876e6i | 0.500806 | − | 0.0450531i | ||||
\(928\) | 1.98509e7 | 0.756677 | ||||||||
\(929\) | − | 1.39556e7i | − | 0.530529i | −0.964176 | − | 0.265265i | \(-0.914541\pi\) | ||
0.964176 | − | 0.265265i | \(-0.0854593\pi\) | |||||||
\(930\) | 4.02844e6 | − | 4.40712e6i | 0.152732 | − | 0.167089i | ||||
\(931\) | 1.95939e7i | 0.740877i | ||||||||
\(932\) | − | 9.39998e6i | − | 0.354476i | ||||||
\(933\) | −1.91963e7 | + | 2.10008e7i | −0.721962 | + | 0.789826i | ||||
\(934\) | − | 2.76299e6i | − | 0.103636i | ||||||
\(935\) | 291998. | 0.0109232 | ||||||||
\(936\) | −1.52513e7 | + | 1.37202e6i | −0.569005 | + | 0.0511884i | ||||
\(937\) | − | 4.24419e7i | − | 1.57923i | −0.613602 | − | 0.789615i | \(-0.710280\pi\) | ||
0.613602 | − | 0.789615i | \(-0.289720\pi\) | |||||||
\(938\) | − | 1.53554e7i | − | 0.569842i | ||||||
\(939\) | −2.99870e7 | + | 3.28058e7i | −1.10986 | + | 1.21419i | ||||
\(940\) | 5.36731e6i | 0.198124i | ||||||||
\(941\) | −3.11592e6 | −0.114713 | −0.0573565 | − | 0.998354i | \(-0.518267\pi\) | ||||
−0.0573565 | + | 0.998354i | \(0.518267\pi\) | |||||||
\(942\) | −3.81075e6 | − | 3.48332e6i | −0.139921 | − | 0.127899i | ||||
\(943\) | −7.69956e6 | − | 1.04065e7i | −0.281960 | − | 0.381087i | ||||
\(944\) | − | 4.31827e7i | − | 1.57718i | ||||||
\(945\) | 4.74945e7 | + | 3.61669e7i | 1.73007 | + | 1.31744i | ||||
\(946\) | −271258. | −0.00985495 | ||||||||
\(947\) | − | 1.39901e7i | − | 0.506929i | −0.967345 | − | 0.253464i | \(-0.918430\pi\) | ||
0.967345 | − | 0.253464i | \(-0.0815701\pi\) | |||||||
\(948\) | 2.10357e7 | − | 2.30131e7i | 0.760215 | − | 0.831675i | ||||
\(949\) | −3.85919e7 | −1.39101 | ||||||||
\(950\) | −3.74308e6 | −0.134561 | ||||||||
\(951\) | −2.21241e7 | + | 2.42038e7i | −0.793259 | + | 0.867825i | ||||
\(952\) | 2.73583e6 | 0.0978357 | ||||||||
\(953\) | −7.04777e6 | −0.251373 | −0.125687 | − | 0.992070i | \(-0.540113\pi\) | ||||
−0.125687 | + | 0.992070i | \(0.540113\pi\) | |||||||
\(954\) | −1.18728e7 | + | 1.06809e6i | −0.422358 | + | 0.0379959i | ||||
\(955\) | 6.96027e7 | 2.46955 | ||||||||
\(956\) | − | 3.49568e7i | − | 1.23705i | ||||||
\(957\) | 1.19227e6 | − | 1.30434e6i | 0.0420818 | − | 0.0460375i | ||||
\(958\) | − | 5.91120e6i | − | 0.208095i | ||||||
\(959\) | 6.81332e7i | 2.39228i | ||||||||
\(960\) | 2.13539e7 | + | 1.95191e7i | 0.747825 | + | 0.683570i | ||||
\(961\) | −1.45749e7 | −0.509094 | ||||||||
\(962\) | −1.09046e7 | −0.379902 | ||||||||
\(963\) | 1.30752e6 | + | 1.45342e7i | 0.0454340 | + | 0.505040i | ||||
\(964\) | 4.73122e7i | 1.63976i | ||||||||
\(965\) | 1.61944e7 | 0.559818 | ||||||||
\(966\) | 9.88185e6 | + | 1.02688e6i | 0.340718 | + | 0.0354061i | ||||
\(967\) | −2.59611e7 | −0.892804 | −0.446402 | − | 0.894832i | \(-0.647295\pi\) | ||||
−0.446402 | + | 0.894832i | \(0.647295\pi\) | |||||||
\(968\) | 1.27846e7i | 0.438528i | ||||||||
\(969\) | −1.63983e6 | + | 1.79397e6i | −0.0561034 | + | 0.0613771i | ||||
\(970\) | −6.09082e6 | −0.207848 | ||||||||
\(971\) | 5.77704e6 | 0.196633 | 0.0983167 | − | 0.995155i | \(-0.468654\pi\) | ||||
0.0983167 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(972\) | −2.36698e7 | − | 1.48760e7i | −0.803579 | − | 0.505034i | ||||
\(973\) | − | 1.15774e6i | − | 0.0392037i | ||||||
\(974\) | − | 1.21319e7i | − | 0.409760i | ||||||
\(975\) | −2.99189e7 | − | 2.73482e7i | −1.00794 | − | 0.921334i | ||||
\(976\) | − | 2.51169e7i | − | 0.843999i | ||||||
\(977\) | 7.49681e6 | 0.251270 | 0.125635 | − | 0.992077i | \(-0.459903\pi\) | ||||
0.125635 | + | 0.992077i | \(0.459903\pi\) | |||||||
\(978\) | 3.00160e6 | − | 3.28375e6i | 0.100347 | − | 0.109780i | ||||
\(979\) | −2.23284e6 | −0.0744562 | ||||||||
\(980\) | −5.33532e7 | −1.77458 | ||||||||
\(981\) | 3.69145e7 | − | 3.32088e6i | 1.22469 | − | 0.110174i | ||||
\(982\) | 5.22928e6 | 0.173046 | ||||||||
\(983\) | 2.54694e7 | 0.840688 | 0.420344 | − | 0.907365i | \(-0.361909\pi\) | ||||
0.420344 | + | 0.907365i | \(0.361909\pi\) | |||||||
\(984\) | 4.67317e6 | + | 4.27164e6i | 0.153859 | + | 0.140639i | ||||
\(985\) | − | 6.50798e7i | − | 2.13725i | ||||||
\(986\) | −1.20930e6 | −0.0396133 | ||||||||
\(987\) | 4.99957e6 | + | 4.57000e6i | 0.163358 | + | 0.149322i | ||||
\(988\) | 2.14709e7i | 0.699774i | ||||||||
\(989\) | −1.53544e7 | − | 2.07526e7i | −0.499164 | − | 0.674654i | ||||
\(990\) | −516529. | + | 46467.6i | −0.0167497 | + | 0.00150682i | ||||
\(991\) | −4.73562e7 | −1.53177 | −0.765884 | − | 0.642979i | \(-0.777698\pi\) | ||||
−0.765884 | + | 0.642979i | \(0.777698\pi\) | |||||||
\(992\) | − | 1.37127e7i | − | 0.442429i | ||||||
\(993\) | 1.79706e7 | + | 1.64265e7i | 0.578349 | + | 0.528656i | ||||
\(994\) | 2.95744e6i | 0.0949400i | ||||||||
\(995\) | 3.24413e6i | 0.103882i | ||||||||
\(996\) | −1.87231e7 | − | 1.71143e7i | −0.598038 | − | 0.546653i | ||||
\(997\) | −2.11118e7 | −0.672648 | −0.336324 | − | 0.941746i | \(-0.609184\pi\) | ||||
−0.336324 | + | 0.941746i | \(0.609184\pi\) | |||||||
\(998\) | 1841.87i | 5.85372e-5i | ||||||||
\(999\) | −3.25269e7 | − | 2.47691e7i | −1.03117 | − | 0.785229i |
(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 | 69.6.c.b.68.16 | yes | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.17 | yes | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.15 | ✓ | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.18 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.15 | ✓ | 32 | 23.22 | odd | 2 | inner | |
69.6.c.b.68.16 | yes | 32 | 1.1 | even | 1 | trivial | |
69.6.c.b.68.17 | yes | 32 | 3.2 | odd | 2 | inner | |
69.6.c.b.68.18 | yes | 32 | 69.68 | even | 2 | inner |