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 | 68.28 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.75944i | 1.54847i | 0.632901 | + | 0.774233i | \(0.281864\pi\) | ||||
−0.632901 | + | 0.774233i | \(0.718136\pi\) | |||||||
\(3\) | 10.6432 | − | 11.3896i | 0.682761 | − | 0.730642i | ||||
\(4\) | −44.7279 | −1.39775 | ||||||||
\(5\) | 43.1688 | 0.772227 | 0.386113 | − | 0.922451i | \(-0.373817\pi\) | ||||
0.386113 | + | 0.922451i | \(0.373817\pi\) | |||||||
\(6\) | 99.7663 | + | 93.2285i | 1.13137 | + | 1.05723i | ||||
\(7\) | − | 151.444i | − | 1.16818i | −0.811690 | − | 0.584088i | \(-0.801452\pi\) | ||
0.811690 | − | 0.584088i | \(-0.198548\pi\) | |||||||
\(8\) | − | 111.489i | − | 0.615895i | ||||||
\(9\) | −16.4449 | − | 242.443i | −0.0676743 | − | 0.997707i | ||||
\(10\) | 378.135i | 1.19577i | ||||||||
\(11\) | 610.914 | 1.52229 | 0.761146 | − | 0.648580i | \(-0.224637\pi\) | ||||
0.761146 | + | 0.648580i | \(0.224637\pi\) | |||||||
\(12\) | −476.047 | + | 509.431i | −0.954326 | + | 1.02125i | ||||
\(13\) | 132.232 | 0.217009 | 0.108505 | − | 0.994096i | \(-0.465394\pi\) | ||||
0.108505 | + | 0.994096i | \(0.465394\pi\) | |||||||
\(14\) | 1326.57 | 1.80888 | ||||||||
\(15\) | 459.454 | − | 491.674i | 0.527246 | − | 0.564221i | ||||
\(16\) | −454.710 | −0.444053 | ||||||||
\(17\) | 1720.33 | 1.44374 | 0.721872 | − | 0.692026i | \(-0.243282\pi\) | ||||
0.721872 | + | 0.692026i | \(0.243282\pi\) | |||||||
\(18\) | 2123.67 | − | 144.048i | 1.54492 | − | 0.104791i | ||||
\(19\) | 554.256i | 0.352230i | 0.984370 | + | 0.176115i | \(0.0563530\pi\) | ||||
−0.984370 | + | 0.176115i | \(0.943647\pi\) | |||||||
\(20\) | −1930.85 | −1.07938 | ||||||||
\(21\) | −1724.89 | − | 1611.85i | −0.853518 | − | 0.797585i | ||||
\(22\) | 5351.26i | 2.35722i | ||||||||
\(23\) | −2536.22 | + | 62.8693i | −0.999693 | + | 0.0247810i | ||||
\(24\) | −1269.81 | − | 1186.60i | −0.449999 | − | 0.420509i | ||||
\(25\) | −1261.46 | −0.403666 | ||||||||
\(26\) | 1158.28i | 0.336031i | ||||||||
\(27\) | −2936.35 | − | 2393.07i | −0.775172 | − | 0.631750i | ||||
\(28\) | 6773.79i | 1.63281i | ||||||||
\(29\) | 7005.84i | 1.54691i | 0.633851 | + | 0.773455i | \(0.281473\pi\) | ||||
−0.633851 | + | 0.773455i | \(0.718527\pi\) | |||||||
\(30\) | 4306.79 | + | 4024.56i | 0.873677 | + | 0.816423i | ||||
\(31\) | 4819.56 | 0.900748 | 0.450374 | − | 0.892840i | \(-0.351291\pi\) | ||||
0.450374 | + | 0.892840i | \(0.351291\pi\) | |||||||
\(32\) | − | 7550.66i | − | 1.30350i | ||||||
\(33\) | 6502.07 | − | 6958.05i | 1.03936 | − | 1.11225i | ||||
\(34\) | 15069.2i | 2.23559i | ||||||||
\(35\) | − | 6537.67i | − | 0.902097i | ||||||
\(36\) | 735.543 | + | 10844.0i | 0.0945915 | + | 1.39454i | ||||
\(37\) | − | 1324.61i | − | 0.159069i | −0.996832 | − | 0.0795343i | \(-0.974657\pi\) | ||
0.996832 | − | 0.0795343i | \(-0.0253433\pi\) | |||||||
\(38\) | −4854.97 | −0.545416 | ||||||||
\(39\) | 1407.37 | − | 1506.07i | 0.148166 | − | 0.158556i | ||||
\(40\) | − | 4812.84i | − | 0.475611i | ||||||
\(41\) | − | 231.107i | − | 0.0214710i | −0.999942 | − | 0.0107355i | \(-0.996583\pi\) | ||
0.999942 | − | 0.0107355i | \(-0.00341729\pi\) | |||||||
\(42\) | 14118.9 | − | 15109.1i | 1.23503 | − | 1.32164i | ||||
\(43\) | − | 18413.9i | − | 1.51871i | −0.650675 | − | 0.759357i | \(-0.725514\pi\) | ||
0.650675 | − | 0.759357i | \(-0.274486\pi\) | |||||||
\(44\) | −27324.9 | −2.12778 | ||||||||
\(45\) | −709.905 | − | 10466.0i | −0.0522599 | − | 0.770456i | ||||
\(46\) | −550.700 | − | 22215.8i | −0.0383726 | − | 1.54799i | ||||
\(47\) | 11782.0i | 0.777990i | 0.921240 | + | 0.388995i | \(0.127178\pi\) | ||||
−0.921240 | + | 0.388995i | \(0.872822\pi\) | |||||||
\(48\) | −4839.57 | + | 5178.96i | −0.303182 | + | 0.324444i | ||||
\(49\) | −6128.42 | −0.364635 | ||||||||
\(50\) | − | 11049.7i | − | 0.625063i | ||||||
\(51\) | 18309.8 | − | 19593.9i | 0.985733 | − | 1.05486i | ||||
\(52\) | −5914.46 | −0.303324 | ||||||||
\(53\) | −1891.55 | −0.0924973 | −0.0462487 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462487 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(54\) | 20961.9 | − | 25720.8i | 0.978244 | − | 1.20033i | ||||
\(55\) | 26372.4 | 1.17556 | ||||||||
\(56\) | −16884.4 | −0.719474 | ||||||||
\(57\) | 6312.74 | + | 5899.05i | 0.257354 | + | 0.240489i | ||||
\(58\) | −61367.2 | −2.39534 | ||||||||
\(59\) | − | 7712.06i | − | 0.288430i | −0.989546 | − | 0.144215i | \(-0.953934\pi\) | ||
0.989546 | − | 0.144215i | \(-0.0460657\pi\) | |||||||
\(60\) | −20550.4 | + | 21991.5i | −0.736956 | + | 0.788637i | ||||
\(61\) | − | 1208.84i | − | 0.0415953i | −0.999784 | − | 0.0207977i | \(-0.993379\pi\) | ||
0.999784 | − | 0.0207977i | \(-0.00662058\pi\) | |||||||
\(62\) | 42216.7i | 1.39478i | ||||||||
\(63\) | −36716.6 | + | 2490.48i | −1.16550 | + | 0.0790555i | ||||
\(64\) | 51588.8 | 1.57437 | ||||||||
\(65\) | 5708.30 | 0.167580 | ||||||||
\(66\) | 60948.6 | + | 56954.5i | 1.72228 | + | 1.60942i | ||||
\(67\) | 41089.5i | 1.11826i | 0.829080 | + | 0.559131i | \(0.188865\pi\) | ||||
−0.829080 | + | 0.559131i | \(0.811135\pi\) | |||||||
\(68\) | −76946.8 | −2.01799 | ||||||||
\(69\) | −26277.4 | + | 29555.6i | −0.664445 | + | 0.747337i | ||||
\(70\) | 57266.4 | 1.39687 | ||||||||
\(71\) | 8193.96i | 0.192907i | 0.995337 | + | 0.0964535i | \(0.0307499\pi\) | ||||
−0.995337 | + | 0.0964535i | \(0.969250\pi\) | |||||||
\(72\) | −27029.7 | + | 1833.42i | −0.614483 | + | 0.0416803i | ||||
\(73\) | −78243.7 | −1.71847 | −0.859235 | − | 0.511581i | \(-0.829060\pi\) | ||||
−0.859235 | + | 0.511581i | \(0.829060\pi\) | |||||||
\(74\) | 11602.9 | 0.246312 | ||||||||
\(75\) | −13425.9 | + | 14367.5i | −0.275607 | + | 0.294935i | ||||
\(76\) | − | 24790.7i | − | 0.492328i | ||||||
\(77\) | − | 92519.5i | − | 1.77831i | ||||||
\(78\) | 13192.3 | + | 12327.8i | 0.245519 | + | 0.229429i | ||||
\(79\) | − | 77477.3i | − | 1.39671i | −0.715751 | − | 0.698356i | \(-0.753915\pi\) | ||
0.715751 | − | 0.698356i | \(-0.246085\pi\) | |||||||
\(80\) | −19629.3 | −0.342910 | ||||||||
\(81\) | −58508.1 | + | 7973.88i | −0.990840 | + | 0.135038i | ||||
\(82\) | 2024.37 | 0.0332472 | ||||||||
\(83\) | −17093.4 | −0.272354 | −0.136177 | − | 0.990685i | \(-0.543482\pi\) | ||||
−0.136177 | + | 0.990685i | \(0.543482\pi\) | |||||||
\(84\) | 77150.5 | + | 72094.7i | 1.19300 | + | 1.11482i | ||||
\(85\) | 74264.7 | 1.11490 | ||||||||
\(86\) | 161296. | 2.35168 | ||||||||
\(87\) | 79793.5 | + | 74564.5i | 1.13024 | + | 1.05617i | ||||
\(88\) | − | 68110.1i | − | 0.937573i | ||||||
\(89\) | −135956. | −1.81938 | −0.909691 | − | 0.415286i | \(-0.863681\pi\) | ||||
−0.909691 | + | 0.415286i | \(0.863681\pi\) | |||||||
\(90\) | 91676.0 | − | 6218.37i | 1.19303 | − | 0.0809227i | ||||
\(91\) | − | 20025.8i | − | 0.253505i | ||||||
\(92\) | 113439. | − | 2812.01i | 1.39732 | − | 0.0346376i | ||||
\(93\) | 51295.5 | − | 54892.7i | 0.614996 | − | 0.658124i | ||||
\(94\) | −103204. | −1.20469 | ||||||||
\(95\) | 23926.5i | 0.272001i | ||||||||
\(96\) | −85998.8 | − | 80363.1i | −0.952388 | − | 0.889976i | ||||
\(97\) | 75181.6i | 0.811302i | 0.914028 | + | 0.405651i | \(0.132955\pi\) | ||||
−0.914028 | + | 0.405651i | \(0.867045\pi\) | |||||||
\(98\) | − | 53681.6i | − | 0.564625i | ||||||
\(99\) | −10046.4 | − | 148112.i | −0.103020 | − | 1.51880i | ||||
\(100\) | 56422.2 | 0.564222 | ||||||||
\(101\) | 182646.i | 1.78159i | 0.454410 | + | 0.890793i | \(0.349850\pi\) | ||||
−0.454410 | + | 0.890793i | \(0.650150\pi\) | |||||||
\(102\) | 171631. | + | 160384.i | 1.63341 | + | 1.52637i | ||||
\(103\) | 60433.1i | 0.561283i | 0.959813 | + | 0.280642i | \(0.0905472\pi\) | ||||
−0.959813 | + | 0.280642i | \(0.909453\pi\) | |||||||
\(104\) | − | 14742.4i | − | 0.133655i | ||||||
\(105\) | −74461.3 | − | 69581.7i | −0.659109 | − | 0.615917i | ||||
\(106\) | − | 16569.0i | − | 0.143229i | ||||||
\(107\) | 19007.4 | 0.160495 | 0.0802477 | − | 0.996775i | \(-0.474429\pi\) | ||||
0.0802477 | + | 0.996775i | \(0.474429\pi\) | |||||||
\(108\) | 131337. | + | 107037.i | 1.08349 | + | 0.883026i | ||||
\(109\) | 95078.3i | 0.766505i | 0.923644 | + | 0.383253i | \(0.125196\pi\) | ||||
−0.923644 | + | 0.383253i | \(0.874804\pi\) | |||||||
\(110\) | 231008.i | 1.82031i | ||||||||
\(111\) | −15086.8 | − | 14098.1i | −0.116222 | − | 0.108606i | ||||
\(112\) | 68863.3i | 0.518732i | ||||||||
\(113\) | −68259.2 | −0.502881 | −0.251440 | − | 0.967873i | \(-0.580904\pi\) | ||||
−0.251440 | + | 0.967873i | \(0.580904\pi\) | |||||||
\(114\) | −51672.4 | + | 55296.1i | −0.372389 | + | 0.398503i | ||||
\(115\) | −109485. | + | 2713.99i | −0.771989 | + | 0.0191366i | ||||
\(116\) | − | 313356.i | − | 2.16219i | ||||||
\(117\) | −2174.54 | − | 32058.7i | −0.0146860 | − | 0.216512i | ||||
\(118\) | 67553.3 | 0.446624 | ||||||||
\(119\) | − | 260535.i | − | 1.68655i | ||||||
\(120\) | −54816.2 | − | 51224.0i | −0.347501 | − | 0.324729i | ||||
\(121\) | 212165. | 1.31738 | ||||||||
\(122\) | 10588.8 | 0.0644089 | ||||||||
\(123\) | −2632.21 | − | 2459.71i | −0.0156876 | − | 0.0146596i | ||||
\(124\) | −215569. | −1.25902 | ||||||||
\(125\) | −189358. | −1.08395 | ||||||||
\(126\) | −21815.2 | − | 321617.i | −0.122415 | − | 1.80473i | ||||
\(127\) | −162337. | −0.893116 | −0.446558 | − | 0.894755i | \(-0.647350\pi\) | ||||
−0.446558 | + | 0.894755i | \(0.647350\pi\) | |||||||
\(128\) | 210268.i | 1.13435i | ||||||||
\(129\) | −209727. | − | 195983.i | −1.10964 | − | 1.03692i | ||||
\(130\) | 50001.5i | 0.259492i | ||||||||
\(131\) | 120535.i | 0.613669i | 0.951763 | + | 0.306835i | \(0.0992699\pi\) | ||||
−0.951763 | + | 0.306835i | \(0.900730\pi\) | |||||||
\(132\) | −290824. | + | 311219.i | −1.45276 | + | 1.55464i | ||||
\(133\) | 83939.0 | 0.411466 | ||||||||
\(134\) | −359921. | −1.73159 | ||||||||
\(135\) | −126759. | − | 103306.i | −0.598608 | − | 0.487854i | ||||
\(136\) | − | 191798.i | − | 0.889195i | ||||||
\(137\) | 324305. | 1.47623 | 0.738113 | − | 0.674677i | \(-0.235717\pi\) | ||||
0.738113 | + | 0.674677i | \(0.235717\pi\) | |||||||
\(138\) | −258890. | − | 230175.i | −1.15723 | − | 1.02887i | ||||
\(139\) | 168785. | 0.740964 | 0.370482 | − | 0.928840i | \(-0.379193\pi\) | ||||
0.370482 | + | 0.928840i | \(0.379193\pi\) | |||||||
\(140\) | 292416.i | 1.26090i | ||||||||
\(141\) | 134192. | + | 125398.i | 0.568432 | + | 0.531182i | ||||
\(142\) | −71774.5 | −0.298710 | ||||||||
\(143\) | 80782.4 | 0.330352 | ||||||||
\(144\) | 7477.65 | + | 110241.i | 0.0300510 | + | 0.443035i | ||||
\(145\) | 302433.i | 1.19456i | ||||||||
\(146\) | − | 685371.i | − | 2.66099i | ||||||
\(147\) | −65226.0 | + | 69800.1i | −0.248959 | + | 0.266417i | ||||
\(148\) | 59247.1i | 0.222338i | ||||||||
\(149\) | 346489. | 1.27857 | 0.639283 | − | 0.768971i | \(-0.279231\pi\) | ||||
0.639283 | + | 0.768971i | \(0.279231\pi\) | |||||||
\(150\) | −125851. | − | 117604.i | −0.456697 | − | 0.426769i | ||||
\(151\) | −484291. | −1.72848 | −0.864239 | − | 0.503082i | \(-0.832199\pi\) | ||||
−0.864239 | + | 0.503082i | \(0.832199\pi\) | |||||||
\(152\) | 61793.4 | 0.216937 | ||||||||
\(153\) | −28290.6 | − | 417083.i | −0.0977044 | − | 1.44043i | ||||
\(154\) | 810419. | 2.75365 | ||||||||
\(155\) | 208055. | 0.695581 | ||||||||
\(156\) | −62948.7 | + | 67363.1i | −0.207098 | + | 0.221621i | ||||
\(157\) | 129167.i | 0.418218i | 0.977892 | + | 0.209109i | \(0.0670564\pi\) | ||||
−0.977892 | + | 0.209109i | \(0.932944\pi\) | |||||||
\(158\) | 678658. | 2.16276 | ||||||||
\(159\) | −20132.2 | + | 21544.0i | −0.0631536 | + | 0.0675824i | ||||
\(160\) | − | 325953.i | − | 1.00659i | ||||||
\(161\) | 9521.21 | + | 384096.i | 0.0289486 | + | 1.16782i | ||||
\(162\) | −69846.7 | − | 512499.i | −0.209102 | − | 1.53428i | ||||
\(163\) | −54105.7 | −0.159505 | −0.0797525 | − | 0.996815i | \(-0.525413\pi\) | ||||
−0.0797525 | + | 0.996815i | \(0.525413\pi\) | |||||||
\(164\) | 10336.9i | 0.0300110i | ||||||||
\(165\) | 280687. | − | 300370.i | 0.802623 | − | 0.858909i | ||||
\(166\) | − | 149729.i | − | 0.421730i | ||||||
\(167\) | 46358.5i | 0.128629i | 0.997930 | + | 0.0643144i | \(0.0204861\pi\) | ||||
−0.997930 | + | 0.0643144i | \(0.979514\pi\) | |||||||
\(168\) | −179704. | + | 192306.i | −0.491229 | + | 0.525678i | ||||
\(169\) | −353808. | −0.952907 | ||||||||
\(170\) | 650517.i | 1.72638i | ||||||||
\(171\) | 134375. | − | 9114.66i | 0.351422 | − | 0.0238369i | ||||
\(172\) | 823617.i | 2.12277i | ||||||||
\(173\) | − | 371854.i | − | 0.944620i | −0.881433 | − | 0.472310i | \(-0.843420\pi\) | ||
0.881433 | − | 0.472310i | \(-0.156580\pi\) | |||||||
\(174\) | −653143. | + | 698947.i | −1.63544 | + | 1.75013i | ||||
\(175\) | 191041.i | 0.471553i | ||||||||
\(176\) | −277789. | −0.675979 | ||||||||
\(177\) | −87837.0 | − | 82080.9i | −0.210739 | − | 0.196929i | ||||
\(178\) | − | 1.19090e6i | − | 2.81725i | ||||||
\(179\) | − | 320039.i | − | 0.746570i | −0.927717 | − | 0.373285i | \(-0.878231\pi\) | ||
0.927717 | − | 0.373285i | \(-0.121769\pi\) | |||||||
\(180\) | 31752.5 | + | 468120.i | 0.0730461 | + | 1.07690i | ||||
\(181\) | − | 512556.i | − | 1.16291i | −0.813580 | − | 0.581453i | \(-0.802484\pi\) | ||
0.813580 | − | 0.581453i | \(-0.197516\pi\) | |||||||
\(182\) | 175415. | 0.392544 | ||||||||
\(183\) | −13768.2 | − | 12865.9i | −0.0303913 | − | 0.0283997i | ||||
\(184\) | 7009.23 | + | 282760.i | 0.0152625 | + | 0.615706i | ||||
\(185\) | − | 57181.9i | − | 0.122837i | ||||||
\(186\) | 480830. | + | 449320.i | 1.01908 | + | 0.952299i | ||||
\(187\) | 1.05098e6 | 2.19780 | ||||||||
\(188\) | − | 526983.i | − | 1.08743i | ||||||
\(189\) | −362417. | + | 444694.i | −0.737995 | + | 0.905537i | ||||
\(190\) | −209583. | −0.421185 | ||||||||
\(191\) | 269982. | 0.535489 | 0.267745 | − | 0.963490i | \(-0.413722\pi\) | ||||
0.267745 | + | 0.963490i | \(0.413722\pi\) | |||||||
\(192\) | 549070. | − | 587575.i | 1.07492 | − | 1.15030i | ||||
\(193\) | −624538. | −1.20688 | −0.603442 | − | 0.797407i | \(-0.706205\pi\) | ||||
−0.603442 | + | 0.797407i | \(0.706205\pi\) | |||||||
\(194\) | −658549. | −1.25627 | ||||||||
\(195\) | 60754.5 | − | 65015.1i | 0.114417 | − | 0.122441i | ||||
\(196\) | 274111. | 0.509667 | ||||||||
\(197\) | 733978.i | 1.34747i | 0.738975 | + | 0.673733i | \(0.235310\pi\) | ||||
−0.738975 | + | 0.673733i | \(0.764690\pi\) | |||||||
\(198\) | 1.29738e6 | − | 88000.8i | 2.35181 | − | 0.159523i | ||||
\(199\) | 896250.i | 1.60434i | 0.597095 | + | 0.802170i | \(0.296321\pi\) | ||||
−0.597095 | + | 0.802170i | \(0.703679\pi\) | |||||||
\(200\) | 140638.i | 0.248616i | ||||||||
\(201\) | 467991. | + | 437323.i | 0.817048 | + | 0.763505i | ||||
\(202\) | −1.59988e6 | −2.75872 | ||||||||
\(203\) | 1.06099e6 | 1.80706 | ||||||||
\(204\) | −818960. | + | 876392.i | −1.37780 | + | 1.47443i | ||||
\(205\) | − | 9976.60i | − | 0.0165805i | ||||||
\(206\) | −529360. | −0.869127 | ||||||||
\(207\) | 56949.9 | + | 613854.i | 0.0923777 | + | 0.995724i | ||||
\(208\) | −60127.3 | −0.0963636 | ||||||||
\(209\) | 338602.i | 0.536197i | ||||||||
\(210\) | 609497. | − | 652240.i | 0.953726 | − | 1.02061i | ||||
\(211\) | 1.08224e6 | 1.67347 | 0.836737 | − | 0.547605i | \(-0.184460\pi\) | ||||
0.836737 | + | 0.547605i | \(0.184460\pi\) | |||||||
\(212\) | 84605.2 | 0.129288 | ||||||||
\(213\) | 93325.7 | + | 87209.9i | 0.140946 | + | 0.131709i | ||||
\(214\) | 166494.i | 0.248522i | ||||||||
\(215\) | − | 794908.i | − | 1.17279i | ||||||
\(216\) | −266801. | + | 327370.i | −0.389092 | + | 0.477425i | ||||
\(217\) | − | 729896.i | − | 1.05223i | ||||||
\(218\) | −832833. | −1.18691 | ||||||||
\(219\) | −832763. | + | 891162.i | −1.17330 | + | 1.25559i | ||||
\(220\) | −1.17958e6 | −1.64313 | ||||||||
\(221\) | 227483. | 0.313306 | ||||||||
\(222\) | 123492. | − | 132152.i | 0.168173 | − | 0.179966i | ||||
\(223\) | 472939. | 0.636859 | 0.318430 | − | 0.947947i | \(-0.396845\pi\) | ||||
0.318430 | + | 0.947947i | \(0.396845\pi\) | |||||||
\(224\) | −1.14350e6 | −1.52271 | ||||||||
\(225\) | 20744.5 | + | 305831.i | 0.0273178 | + | 0.402741i | ||||
\(226\) | − | 597913.i | − | 0.778694i | ||||||
\(227\) | 410057. | 0.528177 | 0.264089 | − | 0.964498i | \(-0.414929\pi\) | ||||
0.264089 | + | 0.964498i | \(0.414929\pi\) | |||||||
\(228\) | −282355. | − | 263852.i | −0.359715 | − | 0.336142i | ||||
\(229\) | 395268.i | 0.498085i | 0.968493 | + | 0.249042i | \(0.0801158\pi\) | ||||
−0.968493 | + | 0.249042i | \(0.919884\pi\) | |||||||
\(230\) | −23773.1 | − | 959031.i | −0.0296323 | − | 1.19540i | ||||
\(231\) | −1.05376e6 | − | 984703.i | −1.29930 | − | 1.21416i | ||||
\(232\) | 781073. | 0.952734 | ||||||||
\(233\) | − | 1.00983e6i | − | 1.21859i | −0.792944 | − | 0.609294i | \(-0.791453\pi\) | ||
0.792944 | − | 0.609294i | \(-0.208547\pi\) | |||||||
\(234\) | 280817. | − | 19047.7i | 0.335261 | − | 0.0227407i | ||||
\(235\) | 508614.i | 0.600785i | ||||||||
\(236\) | 344944.i | 0.403151i | ||||||||
\(237\) | −882434. | − | 824606.i | −1.02050 | − | 0.953621i | ||||
\(238\) | 2.28214e6 | 2.61156 | ||||||||
\(239\) | 1.07223e6i | 1.21421i | 0.794623 | + | 0.607103i | \(0.207668\pi\) | ||||
−0.794623 | + | 0.607103i | \(0.792332\pi\) | |||||||
\(240\) | −208918. | + | 223569.i | −0.234125 | + | 0.250544i | ||||
\(241\) | − | 1.41714e6i | − | 1.57170i | −0.618415 | − | 0.785851i | \(-0.712225\pi\) | ||
0.618415 | − | 0.785851i | \(-0.287775\pi\) | |||||||
\(242\) | 1.85844e6i | 2.03991i | ||||||||
\(243\) | −531894. | + | 751250.i | −0.577843 | + | 0.816148i | ||||
\(244\) | 54068.8i | 0.0581397i | ||||||||
\(245\) | −264556. | −0.281581 | ||||||||
\(246\) | 21545.7 | − | 23056.7i | 0.0226999 | − | 0.0242918i | ||||
\(247\) | 73290.4i | 0.0764372i | ||||||||
\(248\) | − | 537328.i | − | 0.554766i | ||||||
\(249\) | −181928. | + | 194687.i | −0.185952 | + | 0.198993i | ||||
\(250\) | − | 1.65867e6i | − | 1.67846i | ||||||
\(251\) | 387993. | 0.388722 | 0.194361 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194361 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(252\) | 1.64226e6 | − | 111394.i | 1.62907 | − | 0.110499i | ||||
\(253\) | −1.54941e6 | + | 38407.7i | −1.52183 | + | 0.0377240i | ||||
\(254\) | − | 1.42198e6i | − | 1.38296i | ||||||
\(255\) | 790414. | − | 845843.i | 0.761209 | − | 0.814591i | ||||
\(256\) | −190992. | −0.182144 | ||||||||
\(257\) | 972339.i | 0.918301i | 0.888359 | + | 0.459150i | \(0.151846\pi\) | ||||
−0.888359 | + | 0.459150i | \(0.848154\pi\) | |||||||
\(258\) | 1.71670e6 | − | 1.83709e6i | 1.60563 | − | 1.71823i | ||||
\(259\) | −200605. | −0.185820 | ||||||||
\(260\) | −255320. | −0.234235 | ||||||||
\(261\) | 1.69852e6 | − | 115210.i | 1.54336 | − | 0.104686i | ||||
\(262\) | −1.05582e6 | −0.950246 | ||||||||
\(263\) | 1.47839e6 | 1.31795 | 0.658977 | − | 0.752163i | \(-0.270989\pi\) | ||||
0.658977 | + | 0.752163i | \(0.270989\pi\) | |||||||
\(264\) | −775746. | − | 724909.i | −0.685030 | − | 0.640138i | ||||
\(265\) | −81656.1 | −0.0714289 | ||||||||
\(266\) | 735259.i | 0.637142i | ||||||||
\(267\) | −1.44701e6 | + | 1.54848e6i | −1.24220 | + | 1.32932i | ||||
\(268\) | − | 1.83784e6i | − | 1.56304i | ||||||
\(269\) | − | 1.39260e6i | − | 1.17340i | −0.809805 | − | 0.586699i | \(-0.800427\pi\) | ||
0.809805 | − | 0.586699i | \(-0.199573\pi\) | |||||||
\(270\) | 904901. | − | 1.11033e6i | 0.755426 | − | 0.926925i | ||||
\(271\) | −1.26005e6 | −1.04223 | −0.521115 | − | 0.853486i | \(-0.674484\pi\) | ||||
−0.521115 | + | 0.853486i | \(0.674484\pi\) | |||||||
\(272\) | −782253. | −0.641099 | ||||||||
\(273\) | −228085. | − | 213139.i | −0.185221 | − | 0.173083i | ||||
\(274\) | 2.84073e6i | 2.28588i | ||||||||
\(275\) | −770641. | −0.614498 | ||||||||
\(276\) | 1.17533e6 | − | 1.32196e6i | 0.928726 | − | 1.04459i | ||||
\(277\) | 1.23028e6 | 0.963397 | 0.481699 | − | 0.876337i | \(-0.340020\pi\) | ||||
0.481699 | + | 0.876337i | \(0.340020\pi\) | |||||||
\(278\) | 1.47846e6i | 1.14736i | ||||||||
\(279\) | −79257.0 | − | 1.16847e6i | −0.0609575 | − | 0.898683i | ||||
\(280\) | −728878. | −0.555597 | ||||||||
\(281\) | −2.37975e6 | −1.79790 | −0.898951 | − | 0.438050i | \(-0.855669\pi\) | ||||
−0.898951 | + | 0.438050i | \(0.855669\pi\) | |||||||
\(282\) | −1.09842e6 | + | 1.17545e6i | −0.822516 | + | 0.880198i | ||||
\(283\) | 1.01299e6i | 0.751863i | 0.926647 | + | 0.375932i | \(0.122677\pi\) | ||||
−0.926647 | + | 0.375932i | \(0.877323\pi\) | |||||||
\(284\) | − | 366498.i | − | 0.269635i | ||||||
\(285\) | 272513. | + | 254655.i | 0.198735 | + | 0.185712i | ||||
\(286\) | 707609.i | 0.511538i | ||||||||
\(287\) | −34999.8 | −0.0250819 | ||||||||
\(288\) | −1.83060e6 | + | 124169.i | −1.30051 | + | 0.0882132i | ||||
\(289\) | 1.53969e6 | 1.08440 | ||||||||
\(290\) | −2.64915e6 | −1.84974 | ||||||||
\(291\) | 856287. | + | 800173.i | 0.592771 | + | 0.553925i | ||||
\(292\) | 3.49967e6 | 2.40198 | ||||||||
\(293\) | −1.28525e6 | −0.874618 | −0.437309 | − | 0.899311i | \(-0.644068\pi\) | ||||
−0.437309 | + | 0.899311i | \(0.644068\pi\) | |||||||
\(294\) | −611410. | − | 571343.i | −0.412538 | − | 0.385504i | ||||
\(295\) | − | 332920.i | − | 0.222733i | ||||||
\(296\) | −147680. | −0.0979696 | ||||||||
\(297\) | −1.79386e6 | − | 1.46196e6i | −1.18004 | − | 0.961709i | ||||
\(298\) | 3.03505e6i | 1.97982i | ||||||||
\(299\) | −335369. | + | 8313.34i | −0.216943 | + | 0.00537771i | ||||
\(300\) | 600513. | − | 642625.i | 0.385229 | − | 0.412244i | ||||
\(301\) | −2.78869e6 | −1.77412 | ||||||||
\(302\) | − | 4.24212e6i | − | 2.67649i | ||||||
\(303\) | 2.08026e6 | + | 1.94394e6i | 1.30170 | + | 1.21640i | ||||
\(304\) | − | 252026.i | − | 0.156409i | ||||||
\(305\) | − | 52184.2i | − | 0.0321210i | ||||||
\(306\) | 3.65341e6 | − | 247810.i | 2.23046 | − | 0.151292i | ||||
\(307\) | 440102. | 0.266507 | 0.133253 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133253 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(308\) | 4.13820e6i | 2.48562i | ||||||||
\(309\) | 688308. | + | 643201.i | 0.410097 | + | 0.383222i | ||||
\(310\) | 1.82244e6i | 1.07708i | ||||||||
\(311\) | 459889.i | 0.269620i | 0.990871 | + | 0.134810i | \(0.0430424\pi\) | ||||
−0.990871 | + | 0.134810i | \(0.956958\pi\) | |||||||
\(312\) | −167910. | − | 156906.i | −0.0976539 | − | 0.0912544i | ||||
\(313\) | − | 2.79451e6i | − | 1.61230i | −0.591712 | − | 0.806149i | \(-0.701548\pi\) | ||
0.591712 | − | 0.806149i | \(-0.298452\pi\) | |||||||
\(314\) | −1.13143e6 | −0.647597 | ||||||||
\(315\) | −1.58501e6 | + | 107511.i | −0.900028 | + | 0.0610488i | ||||
\(316\) | 3.46539e6i | 1.95225i | ||||||||
\(317\) | − | 2.26703e6i | − | 1.26709i | −0.773704 | − | 0.633547i | \(-0.781598\pi\) | ||
0.773704 | − | 0.633547i | \(-0.218402\pi\) | |||||||
\(318\) | −188713. | − | 176347.i | −0.104649 | − | 0.0977911i | ||||
\(319\) | 4.27996e6i | 2.35485i | ||||||||
\(320\) | 2.22703e6 | 1.21577 | ||||||||
\(321\) | 202299. | − | 216486.i | 0.109580 | − | 0.117265i | ||||
\(322\) | −3.36447e6 | + | 83400.5i | −1.80832 | + | 0.0448259i | ||||
\(323\) | 953505.i | 0.508530i | ||||||||
\(324\) | 2.61694e6 | − | 356655.i | 1.38494 | − | 0.188749i | ||||
\(325\) | −166805. | −0.0875993 | ||||||||
\(326\) | − | 473936.i | − | 0.246988i | ||||||
\(327\) | 1.08290e6 | + | 1.01194e6i | 0.560041 | + | 0.523340i | ||||
\(328\) | −25765.8 | −0.0132239 | ||||||||
\(329\) | 1.78432e6 | 0.908830 | ||||||||
\(330\) | 2.63108e6 | + | 2.45866e6i | 1.32999 | + | 1.24283i | ||||
\(331\) | 85093.5 | 0.0426900 | 0.0213450 | − | 0.999772i | \(-0.493205\pi\) | ||||
0.0213450 | + | 0.999772i | \(0.493205\pi\) | |||||||
\(332\) | 764551. | 0.380681 | ||||||||
\(333\) | −321143. | + | 21783.1i | −0.158704 | + | 0.0107649i | ||||
\(334\) | −406075. | −0.199177 | ||||||||
\(335\) | 1.77378e6i | 0.863551i | ||||||||
\(336\) | 784324. | + | 732926.i | 0.379007 | + | 0.354170i | ||||
\(337\) | − | 2.25704e6i | − | 1.08259i | −0.840832 | − | 0.541297i | \(-0.817934\pi\) | ||
0.840832 | − | 0.541297i | \(-0.182066\pi\) | |||||||
\(338\) | − | 3.09916e6i | − | 1.47554i | ||||||
\(339\) | −726496. | + | 777443.i | −0.343347 | + | 0.367426i | ||||
\(340\) | −3.32170e6 | −1.55834 | ||||||||
\(341\) | 2.94434e6 | 1.37120 | ||||||||
\(342\) | 79839.3 | + | 1.17705e6i | 0.0369106 | + | 0.544165i | ||||
\(343\) | − | 1.61721e6i | − | 0.742218i | ||||||
\(344\) | −2.05295e6 | −0.935368 | ||||||||
\(345\) | −1.13436e6 | + | 1.27588e6i | −0.513102 | + | 0.577113i | ||||
\(346\) | 3.25723e6 | 1.46271 | ||||||||
\(347\) | 895437.i | 0.399219i | 0.979876 | + | 0.199610i | \(0.0639674\pi\) | ||||
−0.979876 | + | 0.199610i | \(0.936033\pi\) | |||||||
\(348\) | −3.56899e6 | − | 3.33511e6i | −1.57978 | − | 1.47626i | ||||
\(349\) | 1.69659e6 | 0.745614 | 0.372807 | − | 0.927909i | \(-0.378395\pi\) | ||||
0.372807 | + | 0.927909i | \(0.378395\pi\) | |||||||
\(350\) | −1.67341e6 | −0.730183 | ||||||||
\(351\) | −388279. | − | 316440.i | −0.168220 | − | 0.137096i | ||||
\(352\) | − | 4.61280e6i | − | 1.98430i | ||||||
\(353\) | 603075.i | 0.257593i | 0.991671 | + | 0.128797i | \(0.0411114\pi\) | ||||
−0.991671 | + | 0.128797i | \(0.958889\pi\) | |||||||
\(354\) | 718983. | − | 769404.i | 0.304937 | − | 0.326322i | ||||
\(355\) | 353723.i | 0.148968i | ||||||||
\(356\) | 6.08103e6 | 2.54303 | ||||||||
\(357\) | −2.96738e6 | − | 2.77292e6i | −1.23226 | − | 1.15151i | ||||
\(358\) | 2.80337e6 | 1.15604 | ||||||||
\(359\) | 3.74407e6 | 1.53323 | 0.766617 | − | 0.642105i | \(-0.221939\pi\) | ||||
0.766617 | + | 0.642105i | \(0.221939\pi\) | |||||||
\(360\) | −1.16684e6 | + | 79146.5i | −0.474520 | + | 0.0321866i | ||||
\(361\) | 2.16890e6 | 0.875934 | ||||||||
\(362\) | 4.48970e6 | 1.80072 | ||||||||
\(363\) | 2.25811e6 | − | 2.41647e6i | 0.899453 | − | 0.962529i | ||||
\(364\) | 895712.i | 0.354336i | ||||||||
\(365\) | −3.37768e6 | −1.32705 | ||||||||
\(366\) | 112698. | − | 120602.i | 0.0439759 | − | 0.0470598i | ||||
\(367\) | − | 4.16068e6i | − | 1.61250i | −0.591577 | − | 0.806249i | \(-0.701494\pi\) | ||
0.591577 | − | 0.806249i | \(-0.298506\pi\) | |||||||
\(368\) | 1.15324e6 | − | 28587.3i | 0.443917 | − | 0.0110041i | ||||
\(369\) | −56030.2 | + | 3800.52i | −0.0214218 | + | 0.00145304i | ||||
\(370\) | 500882. | 0.190209 | ||||||||
\(371\) | 286465.i | 0.108053i | ||||||||
\(372\) | −2.29434e6 | + | 2.45523e6i | −0.859607 | + | 0.919890i | ||||
\(373\) | − | 3.99193e6i | − | 1.48563i | −0.669496 | − | 0.742816i | \(-0.733490\pi\) | ||
0.669496 | − | 0.742816i | \(-0.266510\pi\) | |||||||
\(374\) | 9.20596e6i | 3.40322i | ||||||||
\(375\) | −2.01537e6 | + | 2.15671e6i | −0.740078 | + | 0.791978i | ||||
\(376\) | 1.31356e6 | 0.479161 | ||||||||
\(377\) | 926396.i | 0.335694i | ||||||||
\(378\) | −3.89527e6 | − | 3.17457e6i | −1.40219 | − | 1.14276i | ||||
\(379\) | − | 98283.1i | − | 0.0351464i | −0.999846 | − | 0.0175732i | \(-0.994406\pi\) | ||
0.999846 | − | 0.0175732i | \(-0.00559401\pi\) | |||||||
\(380\) | − | 1.07018e6i | − | 0.380189i | ||||||
\(381\) | −1.72778e6 | + | 1.84895e6i | −0.609785 | + | 0.652547i | ||||
\(382\) | 2.36489e6i | 0.829186i | ||||||||
\(383\) | 2.81372e6 | 0.980130 | 0.490065 | − | 0.871686i | \(-0.336973\pi\) | ||||
0.490065 | + | 0.871686i | \(0.336973\pi\) | |||||||
\(384\) | 2.39487e6 | + | 2.23793e6i | 0.828807 | + | 0.774494i | ||||
\(385\) | − | 3.99395e6i | − | 1.37326i | ||||||
\(386\) | − | 5.47061e6i | − | 1.86882i | ||||||
\(387\) | −4.46433e6 | + | 302815.i | −1.51523 | + | 0.102778i | ||||
\(388\) | − | 3.36271e6i | − | 1.13399i | ||||||
\(389\) | −2.68573e6 | −0.899889 | −0.449944 | − | 0.893057i | \(-0.648556\pi\) | ||||
−0.449944 | + | 0.893057i | \(0.648556\pi\) | |||||||
\(390\) | 569496. | + | 532176.i | 0.189596 | + | 0.177171i | ||||
\(391\) | −4.36314e6 | + | 108156.i | −1.44330 | + | 0.0357775i | ||||
\(392\) | 683251.i | 0.224577i | ||||||||
\(393\) | 1.37284e6 | + | 1.28288e6i | 0.448372 | + | 0.418990i | ||||
\(394\) | −6.42924e6 | −2.08650 | ||||||||
\(395\) | − | 3.34460e6i | − | 1.07858i | ||||||
\(396\) | 449354. | + | 6.62472e6i | 0.143996 | + | 2.12290i | ||||
\(397\) | 3.49044e6 | 1.11149 | 0.555743 | − | 0.831354i | \(-0.312434\pi\) | ||||
0.555743 | + | 0.831354i | \(0.312434\pi\) | |||||||
\(398\) | −7.85065e6 | −2.48427 | ||||||||
\(399\) | 893379. | − | 956029.i | 0.280933 | − | 0.300635i | ||||
\(400\) | 573597. | 0.179249 | ||||||||
\(401\) | −1.45743e6 | −0.452613 | −0.226307 | − | 0.974056i | \(-0.572665\pi\) | ||||
−0.226307 | + | 0.974056i | \(0.572665\pi\) | |||||||
\(402\) | −3.83071e6 | + | 4.09934e6i | −1.18226 | + | 1.26517i | ||||
\(403\) | 637300. | 0.195471 | ||||||||
\(404\) | − | 8.16936e6i | − | 2.49020i | ||||||
\(405\) | −2.52572e6 | + | 344223.i | −0.765153 | + | 0.104280i | ||||
\(406\) | 9.29372e6i | 2.79817i | ||||||||
\(407\) | − | 809224.i | − | 0.242149i | ||||||
\(408\) | −2.18450e6 | − | 2.04134e6i | −0.649683 | − | 0.607108i | ||||
\(409\) | −397052. | −0.117365 | −0.0586825 | − | 0.998277i | \(-0.518690\pi\) | ||||
−0.0586825 | + | 0.998277i | \(0.518690\pi\) | |||||||
\(410\) | 87389.4 | 0.0256743 | ||||||||
\(411\) | 3.45164e6 | − | 3.69370e6i | 1.00791 | − | 1.07859i | ||||
\(412\) | − | 2.70304e6i | − | 0.784531i | ||||||
\(413\) | −1.16795e6 | −0.336937 | ||||||||
\(414\) | −5.37702e6 | + | 498850.i | −1.54184 | + | 0.143044i | ||||
\(415\) | −737901. | −0.210319 | ||||||||
\(416\) | − | 998439.i | − | 0.282871i | ||||||
\(417\) | 1.79641e6 | − | 1.92239e6i | 0.505901 | − | 0.541379i | ||||
\(418\) | −2.96597e6 | −0.830283 | ||||||||
\(419\) | 4.90111e6 | 1.36383 | 0.681913 | − | 0.731433i | \(-0.261148\pi\) | ||||
0.681913 | + | 0.731433i | \(0.261148\pi\) | |||||||
\(420\) | 3.33049e6 | + | 3.11224e6i | 0.921267 | + | 0.860895i | ||||
\(421\) | 4.82268e6i | 1.32612i | 0.748566 | + | 0.663061i | \(0.230743\pi\) | ||||
−0.748566 | + | 0.663061i | \(0.769257\pi\) | |||||||
\(422\) | 9.47985e6i | 2.59132i | ||||||||
\(423\) | 2.85646e6 | − | 193753.i | 0.776207 | − | 0.0526500i | ||||
\(424\) | 210887.i | 0.0569687i | ||||||||
\(425\) | −2.17013e6 | −0.582791 | ||||||||
\(426\) | −763910. | + | 817481.i | −0.203947 | + | 0.218250i | ||||
\(427\) | −183072. | −0.0485906 | ||||||||
\(428\) | −850159. | −0.224332 | ||||||||
\(429\) | 859783. | − | 920077.i | 0.225551 | − | 0.241369i | ||||
\(430\) | 6.96295e6 | 1.81603 | ||||||||
\(431\) | −3.02169e6 | −0.783533 | −0.391767 | − | 0.920065i | \(-0.628136\pi\) | ||||
−0.391767 | + | 0.920065i | \(0.628136\pi\) | |||||||
\(432\) | 1.33519e6 | + | 1.08815e6i | 0.344217 | + | 0.280531i | ||||
\(433\) | − | 3.30312e6i | − | 0.846650i | −0.905978 | − | 0.423325i | \(-0.860863\pi\) | ||
0.905978 | − | 0.423325i | \(-0.139137\pi\) | |||||||
\(434\) | 6.39348e6 | 1.62934 | ||||||||
\(435\) | 3.44459e6 | + | 3.21886e6i | 0.872799 | + | 0.815602i | ||||
\(436\) | − | 4.25265e6i | − | 1.07138i | ||||||
\(437\) | −34845.7 | − | 1.40571e6i | −0.00872862 | − | 0.352122i | ||||
\(438\) | −7.80609e6 | − | 7.29454e6i | −1.94423 | − | 1.81682i | ||||
\(439\) | −3.90756e6 | −0.967708 | −0.483854 | − | 0.875149i | \(-0.660763\pi\) | ||||
−0.483854 | + | 0.875149i | \(0.660763\pi\) | |||||||
\(440\) | − | 2.94023e6i | − | 0.724019i | ||||||
\(441\) | 100781. | + | 1.48579e6i | 0.0246764 | + | 0.363799i | ||||
\(442\) | 1.99263e6i | 0.485143i | ||||||||
\(443\) | 2.12284e6i | 0.513934i | 0.966420 | + | 0.256967i | \(0.0827231\pi\) | ||||
−0.966420 | + | 0.256967i | \(0.917277\pi\) | |||||||
\(444\) | 674799. | + | 630578.i | 0.162449 | + | 0.151803i | ||||
\(445\) | −5.86906e6 | −1.40497 | ||||||||
\(446\) | 4.14269e6i | 0.986154i | ||||||||
\(447\) | 3.68775e6 | − | 3.94636e6i | 0.872956 | − | 0.934174i | ||||
\(448\) | − | 7.81284e6i | − | 1.83914i | ||||||
\(449\) | 551494.i | 0.129100i | 0.997914 | + | 0.0645499i | \(0.0205612\pi\) | ||||
−0.997914 | + | 0.0645499i | \(0.979439\pi\) | |||||||
\(450\) | −2.67891e6 | + | 181710.i | −0.623630 | + | 0.0423007i | ||||
\(451\) | − | 141186.i | − | 0.0326852i | ||||||
\(452\) | 3.05309e6 | 0.702899 | ||||||||
\(453\) | −5.15440e6 | + | 5.51586e6i | −1.18014 | + | 1.26290i | ||||
\(454\) | 3.59187e6i | 0.817864i | ||||||||
\(455\) | − | 864490.i | − | 0.195763i | ||||||
\(456\) | 657679. | − | 703800.i | 0.148116 | − | 0.158503i | ||||
\(457\) | 146258.i | 0.0327590i | 0.999866 | + | 0.0163795i | \(0.00521398\pi\) | ||||
−0.999866 | + | 0.0163795i | \(0.994786\pi\) | |||||||
\(458\) | −3.46233e6 | −0.771267 | ||||||||
\(459\) | −5.05150e6 | − | 4.11687e6i | −1.11915 | − | 0.912086i | ||||
\(460\) | 4.89704e6 | − | 121391.i | 1.07904 | − | 0.0267480i | ||||
\(461\) | 5.82484e6i | 1.27653i | 0.769816 | + | 0.638266i | \(0.220348\pi\) | ||||
−0.769816 | + | 0.638266i | \(0.779652\pi\) | |||||||
\(462\) | 8.62545e6 | − | 9.23033e6i | 1.88008 | − | 2.01193i | ||||
\(463\) | 4.42318e6 | 0.958920 | 0.479460 | − | 0.877564i | \(-0.340833\pi\) | ||||
0.479460 | + | 0.877564i | \(0.340833\pi\) | |||||||
\(464\) | − | 3.18563e6i | − | 0.686910i | ||||||
\(465\) | 2.21436e6 | − | 2.36965e6i | 0.474916 | − | 0.508221i | ||||
\(466\) | 8.84552e6 | 1.88694 | ||||||||
\(467\) | 1.31195e6 | 0.278371 | 0.139185 | − | 0.990266i | \(-0.455552\pi\) | ||||
0.139185 | + | 0.990266i | \(0.455552\pi\) | |||||||
\(468\) | 97262.4 | + | 1.43392e6i | 0.0205272 | + | 0.302628i | ||||
\(469\) | 6.22277e6 | 1.30633 | ||||||||
\(470\) | −4.45518e6 | −0.930295 | ||||||||
\(471\) | 1.47116e6 | + | 1.37475e6i | 0.305568 | + | 0.285543i | ||||
\(472\) | −859809. | −0.177643 | ||||||||
\(473\) | − | 1.12493e7i | − | 2.31193i | ||||||
\(474\) | 7.22309e6 | − | 7.72963e6i | 1.47665 | − | 1.58020i | ||||
\(475\) | − | 699169.i | − | 0.142183i | ||||||
\(476\) | 1.16532e7i | 2.35736i | ||||||||
\(477\) | 31106.3 | + | 458594.i | 0.00625969 | + | 0.0922853i | ||||
\(478\) | −9.39212e6 | −1.88016 | ||||||||
\(479\) | 491382. | 0.0978545 | 0.0489273 | − | 0.998802i | \(-0.484420\pi\) | ||||
0.0489273 | + | 0.998802i | \(0.484420\pi\) | |||||||
\(480\) | −3.71246e6 | − | 3.46918e6i | −0.735460 | − | 0.687264i | ||||
\(481\) | − | 175156.i | − | 0.0345194i | ||||||
\(482\) | 1.24134e7 | 2.43373 | ||||||||
\(483\) | 4.47602e6 | + | 3.97956e6i | 0.873021 | + | 0.776189i | ||||
\(484\) | −9.48967e6 | −1.84136 | ||||||||
\(485\) | 3.24550e6i | 0.626509i | ||||||||
\(486\) | −6.58054e6 | − | 4.65910e6i | −1.26378 | − | 0.894770i | ||||
\(487\) | −2.13183e6 | −0.407315 | −0.203657 | − | 0.979042i | \(-0.565283\pi\) | ||||
−0.203657 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(488\) | −134772. | −0.0256184 | ||||||||
\(489\) | −575858. | + | 616241.i | −0.108904 | + | 0.116541i | ||||
\(490\) | − | 2.31737e6i | − | 0.436018i | ||||||
\(491\) | − | 4.98864e6i | − | 0.933854i | −0.884296 | − | 0.466927i | \(-0.845361\pi\) | ||
0.884296 | − | 0.466927i | \(-0.154639\pi\) | |||||||
\(492\) | 117733. | + | 110018.i | 0.0219273 | + | 0.0204904i | ||||
\(493\) | 1.20524e7i | 2.23334i | ||||||||
\(494\) | −641983. | −0.118360 | ||||||||
\(495\) | −433690. | − | 6.39380e6i | −0.0795549 | − | 1.17286i | ||||
\(496\) | −2.19150e6 | −0.399980 | ||||||||
\(497\) | 1.24093e6 | 0.225349 | ||||||||
\(498\) | −1.70535e6 | − | 1.59359e6i | −0.308134 | − | 0.287941i | ||||
\(499\) | 3.54759e6 | 0.637797 | 0.318898 | − | 0.947789i | \(-0.396687\pi\) | ||||
0.318898 | + | 0.947789i | \(0.396687\pi\) | |||||||
\(500\) | 8.46958e6 | 1.51508 | ||||||||
\(501\) | 528004. | + | 493403.i | 0.0939816 | + | 0.0878228i | ||||
\(502\) | 3.39860e6i | 0.601923i | ||||||||
\(503\) | 442972. | 0.0780651 | 0.0390325 | − | 0.999238i | \(-0.487572\pi\) | ||||
0.0390325 | + | 0.999238i | \(0.487572\pi\) | |||||||
\(504\) | 277661. | + | 4.09350e6i | 0.0486899 | + | 0.717825i | ||||
\(505\) | 7.88460e6i | 1.37579i | ||||||||
\(506\) | −336430. | − | 1.35720e7i | −0.0584143 | − | 2.35649i | ||||
\(507\) | −3.76564e6 | + | 4.02972e6i | −0.650608 | + | 0.696233i | ||||
\(508\) | 7.26098e6 | 1.24835 | ||||||||
\(509\) | 5.88309e6i | 1.00649i | 0.864143 | + | 0.503247i | \(0.167861\pi\) | ||||
−0.864143 | + | 0.503247i | \(0.832139\pi\) | |||||||
\(510\) | 7.40912e6 | + | 6.92358e6i | 1.26137 | + | 1.17871i | ||||
\(511\) | 1.18496e7i | 2.00748i | ||||||||
\(512\) | 5.05561e6i | 0.852311i | ||||||||
\(513\) | 1.32637e6 | − | 1.62749e6i | 0.222521 | − | 0.273039i | ||||
\(514\) | −8.51715e6 | −1.42196 | ||||||||
\(515\) | 2.60882e6i | 0.433438i | ||||||||
\(516\) | 9.38064e6 | + | 8.76591e6i | 1.55099 | + | 1.44935i | ||||
\(517\) | 7.19778e6i | 1.18433i | ||||||||
\(518\) | − | 1.75719e6i | − | 0.287736i | ||||||
\(519\) | −4.23526e6 | − | 3.95771e6i | −0.690179 | − | 0.644950i | ||||
\(520\) | − | 636412.i | − | 0.103212i | ||||||
\(521\) | −8.70774e6 | −1.40544 | −0.702718 | − | 0.711468i | \(-0.748031\pi\) | ||||
−0.702718 | + | 0.711468i | \(0.748031\pi\) | |||||||
\(522\) | 1.00918e6 | + | 1.48780e7i | 0.162103 | + | 2.38984i | ||||
\(523\) | 4.34219e6i | 0.694153i | 0.937837 | + | 0.347076i | \(0.112826\pi\) | ||||
−0.937837 | + | 0.347076i | \(0.887174\pi\) | |||||||
\(524\) | − | 5.39127e6i | − | 0.857754i | ||||||
\(525\) | 2.17587e6 | + | 2.03328e6i | 0.344536 | + | 0.321958i | ||||
\(526\) | 1.29499e7i | 2.04081i | ||||||||
\(527\) | 8.29125e6 | 1.30045 | ||||||||
\(528\) | −2.95656e6 | + | 3.16390e6i | −0.461532 | + | 0.493898i | ||||
\(529\) | 6.42844e6 | − | 318900.i | 0.998772 | − | 0.0495468i | ||||
\(530\) | − | 715262.i | − | 0.110605i | ||||||
\(531\) | −1.86973e6 | + | 126824.i | −0.287769 | + | 0.0195193i | ||||
\(532\) | −3.75441e6 | −0.575125 | ||||||||
\(533\) | − | 30559.7i | − | 0.00465941i | ||||||
\(534\) | −1.35638e7 | − | 1.26750e7i | −2.05840 | − | 1.92351i | ||||
\(535\) | 820525. | 0.123939 | ||||||||
\(536\) | 4.58102e6 | 0.688732 | ||||||||
\(537\) | −3.64511e6 | − | 3.40624e6i | −0.545475 | − | 0.509729i | ||||
\(538\) | 1.21984e7 | 1.81697 | ||||||||
\(539\) | −3.74394e6 | −0.555081 | ||||||||
\(540\) | 5.66964e6 | + | 4.62065e6i | 0.836702 | + | 0.681896i | ||||
\(541\) | 9.64282e6 | 1.41648 | 0.708241 | − | 0.705971i | \(-0.249489\pi\) | ||||
0.708241 | + | 0.705971i | \(0.249489\pi\) | |||||||
\(542\) | − | 1.10373e7i | − | 1.61386i | ||||||
\(543\) | −5.83779e6 | − | 5.45523e6i | −0.849668 | − | 0.793987i | ||||
\(544\) | − | 1.29896e7i | − | 1.88192i | ||||||
\(545\) | 4.10441e6i | 0.591916i | ||||||||
\(546\) | 1.86698e6 | − | 1.99790e6i | 0.268014 | − | 0.286809i | ||||
\(547\) | −4.65385e6 | −0.665034 | −0.332517 | − | 0.943097i | \(-0.607898\pi\) | ||||
−0.332517 | + | 0.943097i | \(0.607898\pi\) | |||||||
\(548\) | −1.45055e7 | −2.06339 | ||||||||
\(549\) | −293075. | + | 19879.2i | −0.0415000 | + | 0.00281493i | ||||
\(550\) | − | 6.75039e6i | − | 0.951529i | ||||||
\(551\) | −3.88302e6 | −0.544868 | ||||||||
\(552\) | 3.29512e6 | + | 2.92964e6i | 0.460281 | + | 0.409229i | ||||
\(553\) | −1.17335e7 | −1.63161 | ||||||||
\(554\) | 1.07766e7i | 1.49179i | ||||||||
\(555\) | −651278. | − | 608598.i | −0.0897499 | − | 0.0838684i | ||||
\(556\) | −7.54940e6 | −1.03568 | ||||||||
\(557\) | −1.19450e7 | −1.63136 | −0.815680 | − | 0.578504i | \(-0.803637\pi\) | ||||
−0.815680 | + | 0.578504i | \(0.803637\pi\) | |||||||
\(558\) | 1.02351e7 | − | 694247.i | 1.39158 | − | 0.0943906i | ||||
\(559\) | − | 2.43491e6i | − | 0.329575i | ||||||
\(560\) | 2.97275e6i | 0.400579i | ||||||||
\(561\) | 1.11857e7 | − | 1.19702e7i | 1.50057 | − | 1.60581i | ||||
\(562\) | − | 2.08453e7i | − | 2.78399i | ||||||
\(563\) | −5.15603e6 | −0.685558 | −0.342779 | − | 0.939416i | \(-0.611368\pi\) | ||||
−0.342779 | + | 0.939416i | \(0.611368\pi\) | |||||||
\(564\) | −6.00212e6 | − | 5.60879e6i | −0.794523 | − | 0.742457i | ||||
\(565\) | −2.94667e6 | −0.388338 | ||||||||
\(566\) | −8.87322e6 | −1.16423 | ||||||||
\(567\) | 1.20760e6 | + | 8.86073e6i | 0.157749 | + | 1.15748i | ||||
\(568\) | 913536. | 0.118810 | ||||||||
\(569\) | 1.87013e6 | 0.242154 | 0.121077 | − | 0.992643i | \(-0.461365\pi\) | ||||
0.121077 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(570\) | −2.23063e6 | + | 2.38706e6i | −0.287569 | + | 0.307735i | ||||
\(571\) | 7.63524e6i | 0.980015i | 0.871718 | + | 0.490007i | \(0.163006\pi\) | ||||
−0.871718 | + | 0.490007i | \(0.836994\pi\) | |||||||
\(572\) | −3.61322e6 | −0.461748 | ||||||||
\(573\) | 2.87347e6 | − | 3.07497e6i | 0.365611 | − | 0.391251i | ||||
\(574\) | − | 306579.i | − | 0.0388385i | ||||||
\(575\) | 3.19933e6 | − | 79306.9i | 0.403542 | − | 0.0100033i | ||||
\(576\) | −848371. | − | 1.25073e7i | −0.106544 | − | 1.57076i | ||||
\(577\) | −3.94420e6 | −0.493196 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(578\) | 1.34868e7i | 1.67915i | ||||||||
\(579\) | −6.64708e6 | + | 7.11322e6i | −0.824014 | + | 0.881800i | ||||
\(580\) | − | 1.35272e7i | − | 1.66970i | ||||||
\(581\) | 2.58870e6i | 0.318157i | ||||||||
\(582\) | −7.00907e6 | + | 7.50060e6i | −0.857735 | + | 0.917885i | ||||
\(583\) | −1.15558e6 | −0.140808 | ||||||||
\(584\) | 8.72330e6i | 1.05840i | ||||||||
\(585\) | −93872.1 | − | 1.38394e6i | −0.0113409 | − | 0.167196i | ||||
\(586\) | − | 1.12581e7i | − | 1.35432i | ||||||
\(587\) | − | 1.46795e7i | − | 1.75839i | −0.476464 | − | 0.879194i | \(-0.658082\pi\) | ||
0.476464 | − | 0.879194i | \(-0.341918\pi\) | |||||||
\(588\) | 2.91742e6 | − | 3.12201e6i | 0.347981 | − | 0.372384i | ||||
\(589\) | 2.67127e6i | 0.317270i | ||||||||
\(590\) | 2.91619e6 | 0.344895 | ||||||||
\(591\) | 8.35970e6 | + | 7.81187e6i | 0.984514 | + | 0.919997i | ||||
\(592\) | 602315.i | 0.0706349i | ||||||||
\(593\) | − | 9.13831e6i | − | 1.06716i | −0.845750 | − | 0.533580i | \(-0.820846\pi\) | ||
0.845750 | − | 0.533580i | \(-0.179154\pi\) | |||||||
\(594\) | 1.28059e7 | − | 1.57132e7i | 1.48917 | − | 1.82725i | ||||
\(595\) | − | 1.12470e7i | − | 1.30240i | ||||||
\(596\) | −1.54977e7 | −1.78711 | ||||||||
\(597\) | 1.02079e7 | + | 9.53896e6i | 1.17220 | + | 1.09538i | ||||
\(598\) | −72820.2 | − | 2.93765e6i | −0.00832720 | − | 0.335928i | ||||
\(599\) | 7.63288e6i | 0.869203i | 0.900623 | + | 0.434602i | \(0.143111\pi\) | ||||
−0.900623 | + | 0.434602i | \(0.856889\pi\) | |||||||
\(600\) | 1.60181e6 | + | 1.49684e6i | 0.181649 | + | 0.169745i | ||||
\(601\) | −7.47363e6 | −0.844006 | −0.422003 | − | 0.906594i | \(-0.638673\pi\) | ||||
−0.422003 | + | 0.906594i | \(0.638673\pi\) | |||||||
\(602\) | − | 2.44274e7i | − | 2.74717i | ||||||
\(603\) | 9.96185e6 | − | 675710.i | 1.11570 | − | 0.0756776i | ||||
\(604\) | 2.16613e7 | 2.41597 | ||||||||
\(605\) | 9.15889e6 | 1.01731 | ||||||||
\(606\) | −1.70278e7 | + | 1.82219e7i | −1.88355 | + | 2.01564i | ||||
\(607\) | 7.40886e6 | 0.816168 | 0.408084 | − | 0.912944i | \(-0.366197\pi\) | ||||
0.408084 | + | 0.912944i | \(0.366197\pi\) | |||||||
\(608\) | 4.18499e6 | 0.459130 | ||||||||
\(609\) | 1.12924e7 | − | 1.20843e7i | 1.23379 | − | 1.32032i | ||||
\(610\) | 457104. | 0.0497383 | ||||||||
\(611\) | 1.55796e6i | 0.168831i | ||||||||
\(612\) | 1.26538e6 | + | 1.86552e7i | 0.136566 | + | 2.01336i | ||||
\(613\) | − | 1.25160e7i | − | 1.34528i | −0.739969 | − | 0.672641i | \(-0.765160\pi\) | ||
0.739969 | − | 0.672641i | \(-0.234840\pi\) | |||||||
\(614\) | 3.85505e6i | 0.412676i | ||||||||
\(615\) | −113629. | − | 106183.i | −0.0121144 | − | 0.0113205i | ||||
\(616\) | −1.03149e7 | −1.09525 | ||||||||
\(617\) | 4.97604e6 | 0.526225 | 0.263112 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263112 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(618\) | −5.63409e6 | + | 6.02919e6i | −0.593406 | + | 0.635021i | ||||
\(619\) | 5.54618e6i | 0.581792i | 0.956755 | + | 0.290896i | \(0.0939534\pi\) | ||||
−0.956755 | + | 0.290896i | \(0.906047\pi\) | |||||||
\(620\) | −9.30583e6 | −0.972246 | ||||||||
\(621\) | 7.59766e6 | + | 5.88473e6i | 0.790589 | + | 0.612347i | ||||
\(622\) | −4.02838e6 | −0.417498 | ||||||||
\(623\) | 2.05898e7i | 2.12536i | ||||||||
\(624\) | −639946. | + | 684824.i | −0.0657933 | + | 0.0704073i | ||||
\(625\) | −4.23230e6 | −0.433388 | ||||||||
\(626\) | 2.44784e7 | 2.49659 | ||||||||
\(627\) | 3.85654e6 | + | 3.60381e6i | 0.391768 | + | 0.366095i | ||||
\(628\) | − | 5.77737e6i | − | 0.584563i | ||||||
\(629\) | − | 2.27878e6i | − | 0.229654i | ||||||
\(630\) | −941737. | − | 1.38838e7i | −0.0945319 | − | 1.39366i | ||||
\(631\) | 3.82572e6i | 0.382507i | 0.981541 | + | 0.191254i | \(0.0612553\pi\) | ||||
−0.981541 | + | 0.191254i | \(0.938745\pi\) | |||||||
\(632\) | −8.63786e6 | −0.860228 | ||||||||
\(633\) | 1.15185e7 | − | 1.23263e7i | 1.14258 | − | 1.22271i | ||||
\(634\) | 1.98579e7 | 1.96205 | ||||||||
\(635\) | −7.00788e6 | −0.689688 | ||||||||
\(636\) | 900469. | − | 963617.i | 0.0882726 | − | 0.0944630i | ||||
\(637\) | −810374. | −0.0791292 | ||||||||
\(638\) | −3.74901e7 | −3.64640 | ||||||||
\(639\) | 1.98657e6 | − | 134748.i | 0.192465 | − | 0.0130548i | ||||
\(640\) | 9.07703e6i | 0.875979i | ||||||||
\(641\) | −4.33390e6 | −0.416614 | −0.208307 | − | 0.978063i | \(-0.566795\pi\) | ||||
−0.208307 | + | 0.978063i | \(0.566795\pi\) | |||||||
\(642\) | 1.89630e6 | + | 1.77203e6i | 0.181580 | + | 0.169681i | ||||
\(643\) | − | 1.11605e7i | − | 1.06453i | −0.846578 | − | 0.532265i | \(-0.821341\pi\) | ||
0.846578 | − | 0.532265i | \(-0.178659\pi\) | |||||||
\(644\) | −425863. | − | 1.71798e7i | −0.0404628 | − | 1.63231i | ||||
\(645\) | −9.05366e6 | − | 8.46036e6i | −0.856890 | − | 0.800736i | ||||
\(646\) | −8.35217e6 | −0.787441 | ||||||||
\(647\) | 3.89565e6i | 0.365863i | 0.983126 | + | 0.182932i | \(0.0585587\pi\) | ||||
−0.983126 | + | 0.182932i | \(0.941441\pi\) | |||||||
\(648\) | 888999. | + | 6.52301e6i | 0.0831695 | + | 0.610254i | ||||
\(649\) | − | 4.71140e6i | − | 0.439075i | ||||||
\(650\) | − | 1.46112e6i | − | 0.135644i | ||||||
\(651\) | −8.31320e6 | − | 7.76842e6i | −0.768804 | − | 0.718423i | ||||
\(652\) | 2.42003e6 | 0.222947 | ||||||||
\(653\) | − | 1.74450e6i | − | 0.160099i | −0.996791 | − | 0.0800495i | \(-0.974492\pi\) | ||
0.996791 | − | 0.0800495i | \(-0.0255078\pi\) | |||||||
\(654\) | −8.86400e6 | + | 9.48561e6i | −0.810374 | + | 0.867204i | ||||
\(655\) | 5.20334e6i | 0.473892i | ||||||||
\(656\) | 105087.i | 0.00953428i | ||||||||
\(657\) | 1.28671e6 | + | 1.89696e7i | 0.116296 | + | 1.71453i | ||||
\(658\) | 1.56296e7i | 1.40729i | ||||||||
\(659\) | 732273. | 0.0656839 | 0.0328420 | − | 0.999461i | \(-0.489544\pi\) | ||||
0.0328420 | + | 0.999461i | \(0.489544\pi\) | |||||||
\(660\) | −1.25545e7 | + | 1.34349e7i | −1.12186 | + | 1.20054i | ||||
\(661\) | − | 6.40243e6i | − | 0.569956i | −0.958534 | − | 0.284978i | \(-0.908014\pi\) | ||
0.958534 | − | 0.284978i | \(-0.0919863\pi\) | |||||||
\(662\) | 745372.i | 0.0661041i | ||||||||
\(663\) | 2.42115e6 | − | 2.59094e6i | 0.213913 | − | 0.228914i | ||||
\(664\) | 1.90572e6i | 0.167741i | ||||||||
\(665\) | 3.62354e6 | 0.317745 | ||||||||
\(666\) | −190808. | − | 2.81303e6i | −0.0166690 | − | 0.245748i | ||||
\(667\) | −440452. | − | 1.77683e7i | −0.0383340 | − | 1.54643i | ||||
\(668\) | − | 2.07352e6i | − | 0.179790i | ||||||
\(669\) | 5.03359e6 | − | 5.38658e6i | 0.434823 | − | 0.465316i | ||||
\(670\) | −1.55373e7 | −1.33718 | ||||||||
\(671\) | − | 738497.i | − | 0.0633203i | ||||||
\(672\) | −1.21705e7 | + | 1.30240e7i | −1.03965 | + | 1.11256i | ||||
\(673\) | −1.55698e7 | −1.32509 | −0.662546 | − | 0.749021i | \(-0.730524\pi\) | ||||
−0.662546 | + | 0.749021i | \(0.730524\pi\) | |||||||
\(674\) | 1.97704e7 | 1.67636 | ||||||||
\(675\) | 3.70407e6 | + | 3.01875e6i | 0.312911 | + | 0.255016i | ||||
\(676\) | 1.58251e7 | 1.33192 | ||||||||
\(677\) | −445662. | −0.0373710 | −0.0186855 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186855 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(678\) | −6.80997e6 | − | 6.36370e6i | −0.568946 | − | 0.531662i | ||||
\(679\) | 1.13858e7 | 0.947743 | ||||||||
\(680\) | − | 8.27969e6i | − | 0.686660i | ||||||
\(681\) | 4.36432e6 | − | 4.67038e6i | 0.360619 | − | 0.385908i | ||||
\(682\) | 2.57907e7i | 2.12326i | ||||||||
\(683\) | − | 5.85494e6i | − | 0.480254i | −0.970741 | − | 0.240127i | \(-0.922811\pi\) | ||
0.970741 | − | 0.240127i | \(-0.0771891\pi\) | |||||||
\(684\) | −6.01032e6 | + | 407679.i | −0.491199 | + | 0.0333179i | ||||
\(685\) | 1.39999e7 | 1.13998 | ||||||||
\(686\) | 1.41659e7 | 1.14930 | ||||||||
\(687\) | 4.50194e6 | + | 4.20692e6i | 0.363921 | + | 0.340073i | ||||
\(688\) | 8.37301e6i | 0.674389i | ||||||||
\(689\) | −250124. | −0.0200728 | ||||||||
\(690\) | −1.11760e7 | − | 9.93638e6i | −0.893640 | − | 0.794522i | ||||
\(691\) | 801751. | 0.0638770 | 0.0319385 | − | 0.999490i | \(-0.489832\pi\) | ||||
0.0319385 | + | 0.999490i | \(0.489832\pi\) | |||||||
\(692\) | 1.66322e7i | 1.32034i | ||||||||
\(693\) | −2.24307e7 | + | 1.52147e6i | −1.77423 | + | 0.120346i | ||||
\(694\) | −7.84353e6 | −0.618177 | ||||||||
\(695\) | 7.28625e6 | 0.572192 | ||||||||
\(696\) | 8.31311e6 | − | 8.89609e6i | 0.650490 | − | 0.696107i | ||||
\(697\) | − | 397581.i | − | 0.0309987i | ||||||
\(698\) | 1.48612e7i | 1.15456i | ||||||||
\(699\) | −1.15015e7 | − | 1.07478e7i | −0.890351 | − | 0.832004i | ||||
\(700\) | − | 8.54483e6i | − | 0.659111i | ||||||
\(701\) | −2.12413e7 | −1.63263 | −0.816313 | − | 0.577610i | \(-0.803985\pi\) | ||||
−0.816313 | + | 0.577610i | \(0.803985\pi\) | |||||||
\(702\) | 2.77184e6 | − | 3.40111e6i | 0.212288 | − | 0.260482i | ||||
\(703\) | 734174. | 0.0560287 | ||||||||
\(704\) | 3.15163e7 | 2.39665 | ||||||||
\(705\) | 5.79290e6 | + | 5.41328e6i | 0.438958 | + | 0.410193i | ||||
\(706\) | −5.28260e6 | −0.398874 | ||||||||
\(707\) | 2.76607e7 | 2.08121 | ||||||||
\(708\) | 3.92876e6 | + | 3.67130e6i | 0.294559 | + | 0.275256i | ||||
\(709\) | 3.90485e6i | 0.291735i | 0.989304 | + | 0.145868i | \(0.0465974\pi\) | ||||
−0.989304 | + | 0.145868i | \(0.953403\pi\) | |||||||
\(710\) | −3.09842e6 | −0.230672 | ||||||||
\(711\) | −1.87838e7 | + | 1.27410e6i | −1.39351 | + | 0.0945215i | ||||
\(712\) | 1.51576e7i | 1.12055i | ||||||||
\(713\) | −1.22234e7 | + | 303002.i | −0.900471 | + | 0.0223214i | ||||
\(714\) | 2.42893e7 | − | 2.59926e7i | 1.78307 | − | 1.90811i | ||||
\(715\) | 3.48728e6 | 0.255106 | ||||||||
\(716\) | 1.43147e7i | 1.04352i | ||||||||
\(717\) | 1.22122e7 | + | 1.14119e7i | 0.887149 | + | 0.829013i | ||||
\(718\) | 3.27960e7i | 2.37416i | ||||||||
\(719\) | − | 1.90699e7i | − | 1.37571i | −0.725848 | − | 0.687855i | \(-0.758552\pi\) | ||
0.725848 | − | 0.687855i | \(-0.241448\pi\) | |||||||
\(720\) | 322801. | + | 4.75898e6i | 0.0232062 | + | 0.342123i | ||||
\(721\) | 9.15226e6 | 0.655677 | ||||||||
\(722\) | 1.89984e7i | 1.35635i | ||||||||
\(723\) | −1.61406e7 | − | 1.50829e7i | −1.14835 | − | 1.07310i | ||||
\(724\) | 2.29255e7i | 1.62545i | ||||||||
\(725\) | − | 8.83756e6i | − | 0.624435i | ||||||
\(726\) | 2.11669e7 | + | 1.97798e7i | 1.49044 | + | 1.39277i | ||||
\(727\) | 1.09662e7i | 0.769522i | 0.923016 | + | 0.384761i | \(0.125716\pi\) | ||||
−0.923016 | + | 0.384761i | \(0.874284\pi\) | |||||||
\(728\) | −2.23266e6 | −0.156133 | ||||||||
\(729\) | 2.89537e6 | + | 1.40538e7i | 0.201783 | + | 0.979430i | ||||
\(730\) | − | 2.95866e7i | − | 2.05489i | ||||||
\(731\) | − | 3.16781e7i | − | 2.19263i | ||||||
\(732\) | 615821. | + | 575465.i | 0.0424793 | + | 0.0396955i | ||||
\(733\) | 945012.i | 0.0649647i | 0.999472 | + | 0.0324824i | \(0.0103413\pi\) | ||||
−0.999472 | + | 0.0324824i | \(0.989659\pi\) | |||||||
\(734\) | 3.64452e7 | 2.49690 | ||||||||
\(735\) | −2.81573e6 | + | 3.01319e6i | −0.192252 | + | 0.205735i | ||||
\(736\) | 474705. | + | 1.91501e7i | 0.0323020 | + | 1.30310i | ||||
\(737\) | 2.51021e7i | 1.70232i | ||||||||
\(738\) | −33290.4 | − | 490793.i | −0.00224998 | − | 0.0331709i | ||||
\(739\) | −2.68786e7 | −1.81049 | −0.905243 | − | 0.424894i | \(-0.860311\pi\) | ||||
−0.905243 | + | 0.424894i | \(0.860311\pi\) | |||||||
\(740\) | 2.55762e6i | 0.171695i | ||||||||
\(741\) | 834746. | + | 780044.i | 0.0558482 | + | 0.0521883i | ||||
\(742\) | −2.50928e6 | −0.167317 | ||||||||
\(743\) | −1.24569e7 | −0.827825 | −0.413912 | − | 0.910317i | \(-0.635838\pi\) | ||||
−0.413912 | + | 0.910317i | \(0.635838\pi\) | |||||||
\(744\) | −6.11993e6 | − | 5.71888e6i | −0.405335 | − | 0.378773i | ||||
\(745\) | 1.49575e7 | 0.987343 | ||||||||
\(746\) | 3.49671e7 | 2.30045 | ||||||||
\(747\) | 281098. | + | 4.14417e6i | 0.0184313 | + | 0.271729i | ||||
\(748\) | −4.70079e7 | −3.07197 | ||||||||
\(749\) | − | 2.87856e6i | − | 0.187487i | ||||||
\(750\) | −1.88916e7 | − | 1.76536e7i | −1.22635 | − | 1.14599i | ||||
\(751\) | − | 5.77627e6i | − | 0.373721i | −0.982386 | − | 0.186861i | \(-0.940169\pi\) | ||
0.982386 | − | 0.186861i | \(-0.0598313\pi\) | |||||||
\(752\) | − | 5.35739e6i | − | 0.345469i | ||||||
\(753\) | 4.12948e6 | − | 4.41907e6i | 0.265404 | − | 0.284017i | ||||
\(754\) | −8.11471e6 | −0.519810 | ||||||||
\(755\) | −2.09062e7 | −1.33478 | ||||||||
\(756\) | 1.62101e7 | − | 1.98902e7i | 1.03153 | − | 1.26571i | ||||
\(757\) | − | 8.56985e6i | − | 0.543542i | −0.962362 | − | 0.271771i | \(-0.912391\pi\) | ||
0.962362 | − | 0.271771i | \(-0.0876094\pi\) | |||||||
\(758\) | 860906. | 0.0544230 | ||||||||
\(759\) | −1.60532e7 | + | 1.80559e7i | −1.01148 | + | 1.13767i | ||||
\(760\) | 2.66755e6 | 0.167524 | ||||||||
\(761\) | 1.26939e7i | 0.794570i | 0.917695 | + | 0.397285i | \(0.130048\pi\) | ||||
−0.917695 | + | 0.397285i | \(0.869952\pi\) | |||||||
\(762\) | −1.61957e7 | − | 1.51344e7i | −1.01045 | − | 0.944230i | ||||
\(763\) | 1.43991e7 | 0.895413 | ||||||||
\(764\) | −1.20757e7 | −0.748477 | ||||||||
\(765\) | −1.22127e6 | − | 1.80049e7i | −0.0754500 | − | 1.11234i | ||||
\(766\) | 2.46466e7i | 1.51770i | ||||||||
\(767\) | − | 1.01978e6i | − | 0.0625919i | ||||||
\(768\) | −2.03276e6 | + | 2.17531e6i | −0.124361 | + | 0.133082i | ||||
\(769\) | − | 216230.i | − | 0.0131856i | −0.999978 | − | 0.00659281i | \(-0.997901\pi\) | ||
0.999978 | − | 0.00659281i | \(-0.00209857\pi\) | |||||||
\(770\) | 3.49848e7 | 2.12644 | ||||||||
\(771\) | 1.10745e7 | + | 1.03488e7i | 0.670949 | + | 0.626980i | ||||
\(772\) | 2.79343e7 | 1.68692 | ||||||||
\(773\) | 2.26652e7 | 1.36430 | 0.682150 | − | 0.731212i | \(-0.261045\pi\) | ||||
0.682150 | + | 0.731212i | \(0.261045\pi\) | |||||||
\(774\) | −2.65249e6 | − | 3.91051e7i | −0.159148 | − | 2.34628i | ||||
\(775\) | −6.07966e6 | −0.363601 | ||||||||
\(776\) | 8.38192e6 | 0.499677 | ||||||||
\(777\) | −2.13508e6 | + | 2.28481e6i | −0.126871 | + | 0.135768i | ||||
\(778\) | − | 2.35255e7i | − | 1.39345i | ||||||
\(779\) | 128092. | 0.00756274 | ||||||||
\(780\) | −2.71742e6 | + | 2.90798e6i | −0.159926 | + | 0.171142i | ||||
\(781\) | 5.00580e6i | 0.293661i | ||||||||
\(782\) | −947388. | − | 3.82187e7i | −0.0554002 | − | 2.23490i | ||||
\(783\) | 1.67654e7 | − | 2.05716e7i | 0.977261 | − | 1.19912i | ||||
\(784\) | 2.78666e6 | 0.161917 | ||||||||
\(785\) | 5.57599e6i | 0.322959i | ||||||||
\(786\) | −1.12373e7 | + | 1.20253e7i | −0.648791 | + | 0.694289i | ||||
\(787\) | − | 3.17556e7i | − | 1.82761i | −0.406154 | − | 0.913805i | \(-0.633130\pi\) | ||
0.406154 | − | 0.913805i | \(-0.366870\pi\) | |||||||
\(788\) | − | 3.28293e7i | − | 1.88341i | ||||||
\(789\) | 1.57348e7 | − | 1.68383e7i | 0.899848 | − | 0.962953i | ||||
\(790\) | 2.92968e7 | 1.67014 | ||||||||
\(791\) | 1.03375e7i | 0.587453i | ||||||||
\(792\) | −1.65128e7 | + | 1.12006e6i | −0.935423 | + | 0.0634496i | ||||
\(793\) | − | 159847.i | − | 0.00902657i | ||||||
\(794\) | 3.05743e7i | 1.72110i | ||||||||
\(795\) | −869082. | + | 930028.i | −0.0487689 | + | 0.0521889i | ||||
\(796\) | − | 4.00874e7i | − | 2.24246i | ||||||
\(797\) | −1.43657e7 | −0.801091 | −0.400546 | − | 0.916277i | \(-0.631179\pi\) | ||||
−0.400546 | + | 0.916277i | \(0.631179\pi\) | |||||||
\(798\) | 8.37428e6 | + | 7.82550e6i | 0.465522 | + | 0.435016i | ||||
\(799\) | 2.02690e7i | 1.12322i | ||||||||
\(800\) | 9.52482e6i | 0.526177i | ||||||||
\(801\) | 2.23578e6 | + | 3.29616e7i | 0.123125 | + | 1.81521i | ||||
\(802\) | − | 1.27663e7i | − | 0.700856i | ||||||
\(803\) | −4.78001e7 | −2.61602 | ||||||||
\(804\) | −2.09323e7 | − | 1.95605e7i | −1.14203 | − | 1.06719i | ||||
\(805\) | 411019. | + | 1.65809e7i | 0.0223549 | + | 0.901820i | ||||
\(806\) | 5.58240e6i | 0.302680i | ||||||||
\(807\) | −1.58611e7 | − | 1.48217e7i | −0.857333 | − | 0.801150i | ||||
\(808\) | 2.03630e7 | 1.09727 | ||||||||
\(809\) | 1.33708e7i | 0.718266i | 0.933286 | + | 0.359133i | \(0.116928\pi\) | ||||
−0.933286 | + | 0.359133i | \(0.883072\pi\) | |||||||
\(810\) | −3.01520e6 | − | 2.21239e7i | −0.161474 | − | 1.18481i | ||||
\(811\) | −2.90401e7 | −1.55041 | −0.775203 | − | 0.631712i | \(-0.782352\pi\) | ||||
−0.775203 | + | 0.631712i | \(0.782352\pi\) | |||||||
\(812\) | −4.74560e7 | −2.52581 | ||||||||
\(813\) | −1.34109e7 | + | 1.43514e7i | −0.711595 | + | 0.761497i | ||||
\(814\) | 7.08835e6 | 0.374960 | ||||||||
\(815\) | −2.33568e6 | −0.123174 | ||||||||
\(816\) | −8.32567e6 | + | 8.90953e6i | −0.437718 | + | 0.468414i | ||||
\(817\) | 1.02060e7 | 0.534936 | ||||||||
\(818\) | − | 3.47795e6i | − | 0.181736i | ||||||
\(819\) | −4.85512e6 | + | 329322.i | −0.252924 | + | 0.0171558i | ||||
\(820\) | 446232.i | 0.0231753i | ||||||||
\(821\) | − | 6.75457e6i | − | 0.349736i | −0.984592 | − | 0.174868i | \(-0.944050\pi\) | ||
0.984592 | − | 0.174868i | \(-0.0559498\pi\) | |||||||
\(822\) | 3.23548e7 | + | 3.02345e7i | 1.67016 | + | 1.56071i | ||||
\(823\) | 8.26650e6 | 0.425424 | 0.212712 | − | 0.977115i | \(-0.431770\pi\) | ||||
0.212712 | + | 0.977115i | \(0.431770\pi\) | |||||||
\(824\) | 6.73762e6 | 0.345692 | ||||||||
\(825\) | −8.20208e6 | + | 8.77727e6i | −0.419555 | + | 0.448978i | ||||
\(826\) | − | 1.02306e7i | − | 0.521735i | ||||||
\(827\) | 2.07606e7 | 1.05554 | 0.527771 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527771 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(828\) | −2.54725e6 | − | 2.74564e7i | −0.129121 | − | 1.39177i | ||||
\(829\) | −1.74380e7 | −0.881274 | −0.440637 | − | 0.897685i | \(-0.645247\pi\) | ||||
−0.440637 | + | 0.897685i | \(0.645247\pi\) | |||||||
\(830\) | − | 6.46360e6i | − | 0.325671i | ||||||
\(831\) | 1.30941e7 | − | 1.40124e7i | 0.657770 | − | 0.703898i | ||||
\(832\) | 6.82169e6 | 0.341652 | ||||||||
\(833\) | −1.05429e7 | −0.526440 | ||||||||
\(834\) | 1.68391e7 | + | 1.57356e7i | 0.838307 | + | 0.783371i | ||||
\(835\) | 2.00124e6i | 0.0993307i | ||||||||
\(836\) | − | 1.51450e7i | − | 0.749467i | ||||||
\(837\) | −1.41519e7 | − | 1.15335e7i | −0.698234 | − | 0.569048i | ||||
\(838\) | 4.29310e7i | 2.11184i | ||||||||
\(839\) | 1.80301e7 | 0.884288 | 0.442144 | − | 0.896944i | \(-0.354218\pi\) | ||||
0.442144 | + | 0.896944i | \(0.354218\pi\) | |||||||
\(840\) | −7.75759e6 | + | 8.30161e6i | −0.379340 | + | 0.405942i | ||||
\(841\) | −2.85706e7 | −1.39293 | ||||||||
\(842\) | −4.22440e7 | −2.05345 | ||||||||
\(843\) | −2.53282e7 | + | 2.71044e7i | −1.22754 | + | 1.31362i | ||||
\(844\) | −4.84064e7 | −2.33909 | ||||||||
\(845\) | −1.52734e7 | −0.735860 | ||||||||
\(846\) | 1.69717e6 | + | 2.50210e7i | 0.0815267 | + | 1.20193i | ||||
\(847\) | − | 3.21312e7i | − | 1.53893i | ||||||
\(848\) | 860109. | 0.0410737 | ||||||||
\(849\) | 1.15375e7 | + | 1.07814e7i | 0.549343 | + | 0.513343i | ||||
\(850\) | − | 1.90091e7i | − | 0.902431i | ||||||
\(851\) | 83277.5 | + | 3.35950e6i | 0.00394188 | + | 0.159020i | ||||
\(852\) | −4.17426e6 | − | 3.90071e6i | −0.197006 | − | 0.184096i | ||||
\(853\) | 2.85948e7 | 1.34560 | 0.672799 | − | 0.739826i | \(-0.265092\pi\) | ||||
0.672799 | + | 0.739826i | \(0.265092\pi\) | |||||||
\(854\) | − | 1.60361e6i | − | 0.0752409i | ||||||
\(855\) | 5.80082e6 | − | 393469.i | 0.271378 | − | 0.0184075i | ||||
\(856\) | − | 2.11911e6i | − | 0.0988484i | ||||||
\(857\) | 5.96691e6i | 0.277522i | 0.990326 | + | 0.138761i | \(0.0443120\pi\) | ||||
−0.990326 | + | 0.138761i | \(0.955688\pi\) | |||||||
\(858\) | 8.05936e6 | + | 7.53122e6i | 0.373751 | + | 0.349258i | ||||
\(859\) | 3.92119e7 | 1.81315 | 0.906577 | − | 0.422041i | \(-0.138686\pi\) | ||||
0.906577 | + | 0.422041i | \(0.138686\pi\) | |||||||
\(860\) | 3.55545e7i | 1.63926i | ||||||||
\(861\) | −372510. | + | 398633.i | −0.0171250 | + | 0.0183259i | ||||
\(862\) | − | 2.64684e7i | − | 1.21327i | ||||||
\(863\) | 1.60530e6i | 0.0733716i | 0.999327 | + | 0.0366858i | \(0.0116801\pi\) | ||||
−0.999327 | + | 0.0366858i | \(0.988320\pi\) | |||||||
\(864\) | −1.80692e7 | + | 2.21713e7i | −0.823484 | + | 1.01043i | ||||
\(865\) | − | 1.60525e7i | − | 0.729461i | ||||||
\(866\) | 2.89335e7 | 1.31101 | ||||||||
\(867\) | 1.63872e7 | − | 1.75364e7i | 0.740385 | − | 0.792306i | ||||
\(868\) | 3.26467e7i | 1.47075i | ||||||||
\(869\) | − | 4.73320e7i | − | 2.12620i | ||||||
\(870\) | −2.81954e7 | + | 3.01727e7i | −1.26293 | + | 1.35150i | ||||
\(871\) | 5.43334e6i | 0.242673i | ||||||||
\(872\) | 1.06002e7 | 0.472087 | ||||||||
\(873\) | 1.82273e7 | − | 1.23635e6i | 0.809442 | − | 0.0549043i | ||||
\(874\) | 1.23133e7 | − | 305229.i | 0.545248 | − | 0.0135160i | ||||
\(875\) | 2.86772e7i | 1.26624i | ||||||||
\(876\) | 3.72477e7 | − | 3.98598e7i | 1.63998 | − | 1.75499i | ||||
\(877\) | 1.49689e7 | 0.657192 | 0.328596 | − | 0.944471i | \(-0.393425\pi\) | ||||
0.328596 | + | 0.944471i | \(0.393425\pi\) | |||||||
\(878\) | − | 3.42280e7i | − | 1.49846i | ||||||
\(879\) | −1.36792e7 | + | 1.46384e7i | −0.597155 | + | 0.639032i | ||||
\(880\) | −1.19918e7 | −0.522009 | ||||||||
\(881\) | −1.06909e6 | −0.0464062 | −0.0232031 | − | 0.999731i | \(-0.507386\pi\) | ||||
−0.0232031 | + | 0.999731i | \(0.507386\pi\) | |||||||
\(882\) | −1.30147e7 | + | 882786.i | −0.563330 | + | 0.0382106i | ||||
\(883\) | 303833. | 0.0131139 | 0.00655696 | − | 0.999979i | \(-0.497913\pi\) | ||||
0.00655696 | + | 0.999979i | \(0.497913\pi\) | |||||||
\(884\) | −1.01748e7 | −0.437922 | ||||||||
\(885\) | −3.79182e6 | − | 3.54333e6i | −0.162738 | − | 0.152074i | ||||
\(886\) | −1.85949e7 | −0.795808 | ||||||||
\(887\) | 4.42729e7i | 1.88942i | 0.327906 | + | 0.944710i | \(0.393657\pi\) | ||||
−0.327906 | + | 0.944710i | \(0.606343\pi\) | |||||||
\(888\) | −1.57178e6 | + | 1.68201e6i | −0.0668899 | + | 0.0715807i | ||||
\(889\) | 2.45850e7i | 1.04332i | ||||||||
\(890\) | − | 5.14097e7i | − | 2.17556i | ||||||
\(891\) | −3.57434e7 | + | 4.87135e6i | −1.50835 | + | 0.205568i | ||||
\(892\) | −2.11536e7 | −0.890167 | ||||||||
\(893\) | −6.53024e6 | −0.274031 | ||||||||
\(894\) | 3.45679e7 | + | 3.23026e7i | 1.44654 | + | 1.35174i | ||||
\(895\) | − | 1.38157e7i | − | 0.576521i | ||||||
\(896\) | 3.18440e7 | 1.32513 | ||||||||
\(897\) | −3.47471e6 | + | 3.90819e6i | −0.144191 | + | 0.162179i | ||||
\(898\) | −4.83078e6 | −0.199906 | ||||||||
\(899\) | 3.37650e7i | 1.39338i | ||||||||
\(900\) | −927856. | − | 1.36792e7i | −0.0381834 | − | 0.562929i | ||||
\(901\) | −3.25410e6 | −0.133542 | ||||||||
\(902\) | 1.23671e6 | 0.0506119 | ||||||||
\(903\) | −2.96806e7 | + | 3.17620e7i | −1.21130 | + | 1.29625i | ||||
\(904\) | 7.61015e6i | 0.309722i | ||||||||
\(905\) | − | 2.21264e7i | − | 0.898027i | ||||||
\(906\) | −4.83159e7 | − | 4.51497e7i | −1.95555 | − | 1.82740i | ||||
\(907\) | − | 2.24802e7i | − | 0.907365i | −0.891163 | − | 0.453682i | \(-0.850110\pi\) | ||
0.891163 | − | 0.453682i | \(-0.149890\pi\) | |||||||
\(908\) | −1.83410e7 | −0.738257 | ||||||||
\(909\) | 4.42812e7 | − | 3.00359e6i | 1.77750 | − | 0.120568i | ||||
\(910\) | 7.57245e6 | 0.303133 | ||||||||
\(911\) | −1.79023e7 | −0.714681 | −0.357341 | − | 0.933974i | \(-0.616316\pi\) | ||||
−0.357341 | + | 0.933974i | \(0.616316\pi\) | |||||||
\(912\) | −2.87047e6 | − | 2.68236e6i | −0.114279 | − | 0.106790i | ||||
\(913\) | −1.04426e7 | −0.414602 | ||||||||
\(914\) | −1.28114e6 | −0.0507261 | ||||||||
\(915\) | −594356. | − | 555406.i | −0.0234689 | − | 0.0219310i | ||||
\(916\) | − | 1.76795e7i | − | 0.696196i | ||||||
\(917\) | 1.82543e7 | 0.716874 | ||||||||
\(918\) | 3.60615e7 | − | 4.42483e7i | 1.41233 | − | 1.73297i | ||||
\(919\) | − | 1.24506e7i | − | 0.486297i | −0.969989 | − | 0.243149i | \(-0.921820\pi\) | ||
0.969989 | − | 0.243149i | \(-0.0781803\pi\) | |||||||
\(920\) | 302580. | + | 1.22064e7i | 0.0117861 | + | 0.475465i | ||||
\(921\) | 4.68410e6 | − | 5.01258e6i | 0.181960 | − | 0.194721i | ||||
\(922\) | −5.10223e7 | −1.97667 | ||||||||
\(923\) | 1.08350e6i | 0.0418626i | ||||||||
\(924\) | 4.71323e7 | + | 4.40437e7i | 1.81610 | + | 1.69708i | ||||
\(925\) | 1.67094e6i | 0.0642106i | ||||||||
\(926\) | 3.87446e7i | 1.48485i | ||||||||
\(927\) | 1.46516e7 | − | 993814.i | 0.559996 | − | 0.0379844i | ||||
\(928\) | 5.28986e7 | 2.01639 | ||||||||
\(929\) | − | 2.16576e7i | − | 0.823325i | −0.911336 | − | 0.411662i | \(-0.864948\pi\) | ||
0.911336 | − | 0.411662i | \(-0.135052\pi\) | |||||||
\(930\) | 2.07568e7 | + | 1.93966e7i | 0.786962 | + | 0.735391i | ||||
\(931\) | − | 3.39671e6i | − | 0.128435i | ||||||
\(932\) | 4.51674e7i | 1.70328i | ||||||||
\(933\) | 5.23795e6 | + | 4.89469e6i | 0.196996 | + | 0.184086i | ||||
\(934\) | 1.14919e7i | 0.431048i | ||||||||
\(935\) | 4.53693e7 | 1.69720 | ||||||||
\(936\) | −3.57419e6 | + | 242437.i | −0.133349 | + | 0.00904501i | ||||
\(937\) | − | 3.14740e7i | − | 1.17112i | −0.810628 | − | 0.585562i | \(-0.800874\pi\) | ||
0.810628 | − | 0.585562i | \(-0.199126\pi\) | |||||||
\(938\) | 5.45080e7i | 2.02280i | ||||||||
\(939\) | −3.18283e7 | − | 2.97425e7i | −1.17801 | − | 1.10081i | ||||
\(940\) | − | 2.27492e7i | − | 0.839744i | ||||||
\(941\) | 3.65269e7 | 1.34474 | 0.672370 | − | 0.740215i | \(-0.265276\pi\) | ||||
0.672370 | + | 0.740215i | \(0.265276\pi\) | |||||||
\(942\) | −1.20421e7 | + | 1.28865e7i | −0.442154 | + | 0.473161i | ||||
\(943\) | 14529.5 | + | 586137.i | 0.000532074 | + | 0.0214644i | ||||
\(944\) | 3.50675e6i | 0.128078i | ||||||||
\(945\) | −1.56451e7 | + | 1.91969e7i | −0.569900 | + | 0.699280i | ||||
\(946\) | 9.85379e7 | 3.57994 | ||||||||
\(947\) | − | 4.50703e7i | − | 1.63311i | −0.577266 | − | 0.816556i | \(-0.695881\pi\) | ||
0.577266 | − | 0.816556i | \(-0.304119\pi\) | |||||||
\(948\) | 3.94694e7 | + | 3.68829e7i | 1.42639 | + | 1.33292i | ||||
\(949\) | −1.03463e7 | −0.372924 | ||||||||
\(950\) | 6.12433e6 | 0.220166 | ||||||||
\(951\) | −2.58205e7 | − | 2.41284e7i | −0.925791 | − | 0.865122i | ||||
\(952\) | −2.90468e7 | −1.03874 | ||||||||
\(953\) | 2.82396e7 | 1.00723 | 0.503613 | − | 0.863930i | \(-0.332004\pi\) | ||||
0.503613 | + | 0.863930i | \(0.332004\pi\) | |||||||
\(954\) | −4.01703e6 | + | 272474.i | −0.142901 | + | 0.00969292i | ||||
\(955\) | 1.16548e7 | 0.413519 | ||||||||
\(956\) | − | 4.79585e7i | − | 1.69715i | ||||||
\(957\) | 4.87469e7 | + | 4.55525e7i | 1.72055 | + | 1.60780i | ||||
\(958\) | 4.30424e6i | 0.151524i | ||||||||
\(959\) | − | 4.91142e7i | − | 1.72449i | ||||||
\(960\) | 2.37027e7 | − | 2.53649e7i | 0.830079 | − | 0.888290i | ||||
\(961\) | −5.40099e6 | −0.188654 | ||||||||
\(962\) | 1.53427e6 | 0.0534521 | ||||||||
\(963\) | −312574. | − | 4.60820e6i | −0.0108614 | − | 0.160128i | ||||
\(964\) | 6.33857e7i | 2.19684i | ||||||||
\(965\) | −2.69606e7 | −0.931988 | ||||||||
\(966\) | −3.48588e7 | + | 3.92075e7i | −1.20190 | + | 1.35184i | ||||
\(967\) | −2.39847e7 | −0.824838 | −0.412419 | − | 0.910994i | \(-0.635316\pi\) | ||||
−0.412419 | + | 0.910994i | \(0.635316\pi\) | |||||||
\(968\) | − | 2.36540e7i | − | 0.811365i | ||||||
\(969\) | 1.08600e7 | + | 1.01483e7i | 0.371553 | + | 0.347204i | ||||
\(970\) | −2.84288e7 | −0.970128 | ||||||||
\(971\) | 1.37433e7 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(972\) | 2.37905e7 | − | 3.36018e7i | 0.807677 | − | 1.14077i | ||||
\(973\) | − | 2.55616e7i | − | 0.865576i | ||||||
\(974\) | − | 1.86737e7i | − | 0.630713i | ||||||
\(975\) | −1.77534e6 | + | 1.89984e6i | −0.0598094 | + | 0.0640037i | ||||
\(976\) | 549672.i | 0.0184705i | ||||||||
\(977\) | 1.51346e7 | 0.507266 | 0.253633 | − | 0.967301i | \(-0.418374\pi\) | ||||
0.253633 | + | 0.967301i | \(0.418374\pi\) | |||||||
\(978\) | −5.39793e6 | − | 5.04419e6i | −0.180460 | − | 0.168634i | ||||
\(979\) | −8.30575e7 | −2.76963 | ||||||||
\(980\) | 1.18330e7 | 0.393578 | ||||||||
\(981\) | 2.30511e7 | − | 1.56355e6i | 0.764748 | − | 0.0518727i | ||||
\(982\) | 4.36978e7 | 1.44604 | ||||||||
\(983\) | 3.85715e7 | 1.27316 | 0.636580 | − | 0.771210i | \(-0.280348\pi\) | ||||
0.636580 | + | 0.771210i | \(0.280348\pi\) | |||||||
\(984\) | −274231. | + | 293462.i | −0.00902877 | + | 0.00966194i | ||||
\(985\) | 3.16849e7i | 1.04055i | ||||||||
\(986\) | −1.05572e8 | −3.45825 | ||||||||
\(987\) | 1.89908e7 | − | 2.03226e7i | 0.620514 | − | 0.664029i | ||||
\(988\) | − | 3.27812e6i | − | 0.106840i | ||||||
\(989\) | 1.15767e6 | + | 4.67017e7i | 0.0376353 | + | 1.51825i | ||||
\(990\) | 5.60062e7 | − | 3.79889e6i | 1.81613 | − | 0.123188i | ||||
\(991\) | 1.69044e7 | 0.546784 | 0.273392 | − | 0.961903i | \(-0.411854\pi\) | ||||
0.273392 | + | 0.961903i | \(0.411854\pi\) | |||||||
\(992\) | − | 3.63908e7i | − | 1.17412i | ||||||
\(993\) | 905667. | − | 969179.i | 0.0291471 | − | 0.0311911i | ||||
\(994\) | 1.08699e7i | 0.348946i | ||||||||
\(995\) | 3.86900e7i | 1.23891i | ||||||||
\(996\) | 8.13726e6 | − | 8.70791e6i | 0.259914 | − | 0.278141i | ||||
\(997\) | −1.14588e7 | −0.365090 | −0.182545 | − | 0.983197i | \(-0.558434\pi\) | ||||
−0.182545 | + | 0.983197i | \(0.558434\pi\) | |||||||
\(998\) | 3.10749e7i | 0.987606i | ||||||||
\(999\) | −3.16989e6 | + | 3.88952e6i | −0.100492 | + | 0.123306i |
(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.68.28 | yes | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.5 | ✓ | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.27 | yes | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.5 | ✓ | 32 | 3.2 | odd | 2 | inner | |
69.6.c.b.68.6 | yes | 32 | 69.68 | even | 2 | inner | |
69.6.c.b.68.27 | yes | 32 | 23.22 | odd | 2 | inner | |
69.6.c.b.68.28 | yes | 32 | 1.1 | even | 1 | trivial |