Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.17 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.10 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62206i | 0.640296i | 0.947368 | + | 0.320148i | \(0.103733\pi\) | ||||
−0.947368 | + | 0.320148i | \(0.896267\pi\) | |||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 18.8807 | 0.590021 | ||||||||
\(5\) | 5.26063 | + | 55.6536i | 0.0941051 | + | 0.995562i | ||||
\(6\) | −32.5985 | −0.369675 | ||||||||
\(7\) | 168.040i | 1.29619i | 0.761560 | + | 0.648095i | \(0.224434\pi\) | ||||
−0.761560 | + | 0.648095i | \(0.775566\pi\) | |||||||
\(8\) | 184.293i | 1.01808i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | −201.581 | + | 19.0543i | −0.637454 | + | 0.0602551i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 169.926i | 0.340649i | ||||||||
\(13\) | 155.005i | 0.254383i | 0.991878 | + | 0.127191i | \(0.0405962\pi\) | ||||
−0.991878 | + | 0.127191i | \(0.959404\pi\) | |||||||
\(14\) | −608.652 | −0.829944 | ||||||||
\(15\) | −500.883 | + | 47.3457i | −0.574788 | + | 0.0543316i | ||||
\(16\) | −63.3377 | −0.0618532 | ||||||||
\(17\) | − | 426.797i | − | 0.358178i | −0.983833 | − | 0.179089i | \(-0.942685\pi\) | ||
0.983833 | − | 0.179089i | \(-0.0573150\pi\) | |||||||
\(18\) | − | 293.387i | − | 0.213432i | ||||||
\(19\) | 1674.14 | 1.06392 | 0.531959 | − | 0.846770i | \(-0.321456\pi\) | ||||
0.531959 | + | 0.846770i | \(0.321456\pi\) | |||||||
\(20\) | 99.3244 | + | 1050.78i | 0.0555240 | + | 0.587403i | ||||
\(21\) | −1512.36 | −0.748355 | ||||||||
\(22\) | 438.269i | 0.193056i | ||||||||
\(23\) | 11.2327i | 0.00442757i | 0.999998 | + | 0.00221379i | \(0.000704670\pi\) | ||||
−0.999998 | + | 0.00221379i | \(0.999295\pi\) | |||||||
\(24\) | −1658.64 | −0.587791 | ||||||||
\(25\) | −3069.65 | + | 585.547i | −0.982288 | + | 0.187375i | ||||
\(26\) | −561.437 | −0.162880 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 3172.72i | 0.764780i | ||||||||
\(29\) | 1107.81 | 0.244609 | 0.122304 | − | 0.992493i | \(-0.460972\pi\) | ||||
0.122304 | + | 0.992493i | \(0.460972\pi\) | |||||||
\(30\) | −171.489 | − | 1814.23i | −0.0347883 | − | 0.368034i | ||||
\(31\) | 7186.50 | 1.34312 | 0.671558 | − | 0.740952i | \(-0.265625\pi\) | ||||
0.671558 | + | 0.740952i | \(0.265625\pi\) | |||||||
\(32\) | 5667.96i | 0.978480i | ||||||||
\(33\) | 1089.00i | 0.174078i | ||||||||
\(34\) | 1545.88 | 0.229340 | ||||||||
\(35\) | −9352.05 | + | 883.999i | −1.29044 | + | 0.121978i | ||||
\(36\) | −1529.34 | −0.196674 | ||||||||
\(37\) | − | 4576.30i | − | 0.549554i | −0.961508 | − | 0.274777i | \(-0.911396\pi\) | ||
0.961508 | − | 0.274777i | \(-0.0886040\pi\) | |||||||
\(38\) | 6063.84i | 0.681222i | ||||||||
\(39\) | −1395.05 | −0.146868 | ||||||||
\(40\) | −10256.6 | + | 969.497i | −1.01357 | + | 0.0958069i | ||||
\(41\) | −14041.6 | −1.30454 | −0.652268 | − | 0.757988i | \(-0.726182\pi\) | ||||
−0.652268 | + | 0.757988i | \(0.726182\pi\) | |||||||
\(42\) | − | 5477.87i | − | 0.479169i | ||||||
\(43\) | − | 20306.0i | − | 1.67476i | −0.546621 | − | 0.837380i | \(-0.684086\pi\) | ||
0.546621 | − | 0.837380i | \(-0.315914\pi\) | |||||||
\(44\) | 2284.56 | 0.177898 | ||||||||
\(45\) | −426.111 | − | 4507.94i | −0.0313684 | − | 0.331854i | ||||
\(46\) | −40.6856 | −0.00283495 | ||||||||
\(47\) | 10551.8i | 0.696756i | 0.937354 | + | 0.348378i | \(0.113267\pi\) | ||||
−0.937354 | + | 0.348378i | \(0.886733\pi\) | |||||||
\(48\) | − | 570.039i | − | 0.0357110i | ||||||
\(49\) | −11430.6 | −0.680107 | ||||||||
\(50\) | −2120.88 | − | 11118.5i | −0.119975 | − | 0.628955i | ||||
\(51\) | 3841.17 | 0.206794 | ||||||||
\(52\) | 2926.60i | 0.150091i | ||||||||
\(53\) | − | 27069.4i | − | 1.32370i | −0.749637 | − | 0.661849i | \(-0.769772\pi\) | ||
0.749637 | − | 0.661849i | \(-0.230228\pi\) | |||||||
\(54\) | 2640.48 | 0.123225 | ||||||||
\(55\) | 636.537 | + | 6734.09i | 0.0283737 | + | 0.300173i | ||||
\(56\) | −30968.6 | −1.31963 | ||||||||
\(57\) | 15067.3i | 0.614253i | ||||||||
\(58\) | 4012.57i | 0.156622i | ||||||||
\(59\) | −22773.1 | −0.851709 | −0.425854 | − | 0.904792i | \(-0.640026\pi\) | ||||
−0.425854 | + | 0.904792i | \(0.640026\pi\) | |||||||
\(60\) | −9457.01 | + | 893.919i | −0.339137 | + | 0.0320568i | ||||
\(61\) | −916.341 | −0.0315306 | −0.0157653 | − | 0.999876i | \(-0.505018\pi\) | ||||
−0.0157653 | + | 0.999876i | \(0.505018\pi\) | |||||||
\(62\) | 26029.9i | 0.859991i | ||||||||
\(63\) | − | 13611.3i | − | 0.432063i | ||||||
\(64\) | −22556.5 | −0.688369 | ||||||||
\(65\) | −8626.59 | + | 815.425i | −0.253254 | + | 0.0239387i | ||||
\(66\) | −3944.42 | −0.111461 | ||||||||
\(67\) | − | 25328.4i | − | 0.689321i | −0.938727 | − | 0.344660i | \(-0.887994\pi\) | ||
0.938727 | − | 0.344660i | \(-0.112006\pi\) | |||||||
\(68\) | − | 8058.22i | − | 0.211333i | ||||||
\(69\) | −101.095 | −0.00255626 | ||||||||
\(70\) | −3201.90 | − | 33873.7i | −0.0781020 | − | 0.826261i | ||||
\(71\) | −16788.6 | −0.395248 | −0.197624 | − | 0.980278i | \(-0.563323\pi\) | ||||
−0.197624 | + | 0.980278i | \(0.563323\pi\) | |||||||
\(72\) | − | 14927.7i | − | 0.339361i | ||||||
\(73\) | 55976.9i | 1.22942i | 0.788752 | + | 0.614712i | \(0.210728\pi\) | ||||
−0.788752 | + | 0.614712i | \(0.789272\pi\) | |||||||
\(74\) | 16575.6 | 0.351877 | ||||||||
\(75\) | −5269.92 | − | 27626.9i | −0.108181 | − | 0.567125i | ||||
\(76\) | 31608.9 | 0.627735 | ||||||||
\(77\) | 20332.9i | 0.390816i | ||||||||
\(78\) | − | 5052.94i | − | 0.0940389i | ||||||
\(79\) | 47517.8 | 0.856621 | 0.428310 | − | 0.903632i | \(-0.359109\pi\) | ||||
0.428310 | + | 0.903632i | \(0.359109\pi\) | |||||||
\(80\) | −333.196 | − | 3524.97i | −0.00582070 | − | 0.0615787i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 50859.4i | − | 0.835289i | ||||||
\(83\) | 24415.3i | 0.389016i | 0.980901 | + | 0.194508i | \(0.0623110\pi\) | ||||
−0.980901 | + | 0.194508i | \(0.937689\pi\) | |||||||
\(84\) | −28554.5 | −0.441546 | ||||||||
\(85\) | 23752.8 | − | 2245.22i | 0.356589 | − | 0.0337064i | ||||
\(86\) | 73549.4 | 1.07234 | ||||||||
\(87\) | 9970.33i | 0.141225i | ||||||||
\(88\) | 22299.4i | 0.306964i | ||||||||
\(89\) | 22081.6 | 0.295499 | 0.147749 | − | 0.989025i | \(-0.452797\pi\) | ||||
0.147749 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(90\) | 16328.0 | − | 1543.40i | 0.212485 | − | 0.0200850i | ||||
\(91\) | −26047.1 | −0.329728 | ||||||||
\(92\) | 212.082i | 0.00261236i | ||||||||
\(93\) | 64678.5i | 0.775448i | ||||||||
\(94\) | −38219.1 | −0.446130 | ||||||||
\(95\) | 8807.05 | + | 93172.1i | 0.100120 | + | 1.05920i | ||||
\(96\) | −51011.6 | −0.564925 | ||||||||
\(97\) | − | 15706.3i | − | 0.169490i | −0.996403 | − | 0.0847449i | \(-0.972992\pi\) | ||
0.996403 | − | 0.0847449i | \(-0.0270075\pi\) | |||||||
\(98\) | − | 41402.1i | − | 0.435469i | ||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −57957.1 | + | 11055.5i | −0.579571 | + | 0.110555i | ||||
\(101\) | 10765.2 | 0.105007 | 0.0525033 | − | 0.998621i | \(-0.483280\pi\) | ||||
0.0525033 | + | 0.998621i | \(0.483280\pi\) | |||||||
\(102\) | 13913.0i | 0.132409i | ||||||||
\(103\) | 28684.5i | 0.266412i | 0.991088 | + | 0.133206i | \(0.0425272\pi\) | ||||
−0.991088 | + | 0.133206i | \(0.957473\pi\) | |||||||
\(104\) | −28566.3 | −0.258983 | ||||||||
\(105\) | −7955.99 | − | 84168.5i | −0.0704240 | − | 0.745034i | ||||
\(106\) | 98046.9 | 0.847558 | ||||||||
\(107\) | 121918.i | 1.02946i | 0.857354 | + | 0.514728i | \(0.172107\pi\) | ||||
−0.857354 | + | 0.514728i | \(0.827893\pi\) | |||||||
\(108\) | − | 13764.0i | − | 0.113550i | ||||||
\(109\) | 169782. | 1.36876 | 0.684378 | − | 0.729128i | \(-0.260074\pi\) | ||||
0.684378 | + | 0.729128i | \(0.260074\pi\) | |||||||
\(110\) | −24391.3 | + | 2305.57i | −0.192200 | + | 0.0181676i | ||||
\(111\) | 41186.7 | 0.317285 | ||||||||
\(112\) | − | 10643.3i | − | 0.0801735i | ||||||
\(113\) | 220268.i | 1.62276i | 0.584519 | + | 0.811380i | \(0.301283\pi\) | ||||
−0.584519 | + | 0.811380i | \(0.698717\pi\) | |||||||
\(114\) | −54574.6 | −0.393304 | ||||||||
\(115\) | −625.142 | + | 59.0912i | −0.00440792 | + | 0.000416657i | ||||
\(116\) | 20916.3 | 0.144324 | ||||||||
\(117\) | − | 12555.4i | − | 0.0847942i | ||||||
\(118\) | − | 82485.3i | − | 0.545346i | ||||||
\(119\) | 71719.1 | 0.464267 | ||||||||
\(120\) | −8725.47 | − | 92309.1i | −0.0553141 | − | 0.585183i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − | 3319.04i | − | 0.0201889i | ||||||
\(123\) | − | 126374.i | − | 0.753174i | ||||||
\(124\) | 135686. | 0.792467 | ||||||||
\(125\) | −48736.1 | − | 167757.i | −0.278982 | − | 0.960296i | ||||
\(126\) | 49300.8 | 0.276648 | ||||||||
\(127\) | − | 230988.i | − | 1.27081i | −0.772180 | − | 0.635404i | \(-0.780834\pi\) | ||
0.772180 | − | 0.635404i | \(-0.219166\pi\) | |||||||
\(128\) | 99673.7i | 0.537720i | ||||||||
\(129\) | 182754. | 0.966923 | ||||||||
\(130\) | −2953.52 | − | 31246.0i | −0.0153278 | − | 0.162157i | ||||
\(131\) | 175894. | 0.895513 | 0.447757 | − | 0.894155i | \(-0.352223\pi\) | ||||
0.447757 | + | 0.894155i | \(0.352223\pi\) | |||||||
\(132\) | 20561.1i | 0.102710i | ||||||||
\(133\) | 281323.i | 1.37904i | ||||||||
\(134\) | 91741.1 | 0.441369 | ||||||||
\(135\) | 40571.5 | − | 3835.00i | 0.191596 | − | 0.0181105i | ||||
\(136\) | 78655.7 | 0.364655 | ||||||||
\(137\) | − | 8437.54i | − | 0.0384073i | −0.999816 | − | 0.0192037i | \(-0.993887\pi\) | ||
0.999816 | − | 0.0192037i | \(-0.00611309\pi\) | |||||||
\(138\) | − | 366.170i | − | 0.00163676i | ||||||
\(139\) | 75054.6 | 0.329489 | 0.164744 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164744 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(140\) | −176573. | + | 16690.5i | −0.761386 | + | 0.0719696i | ||||
\(141\) | −94965.9 | −0.402272 | ||||||||
\(142\) | − | 60809.5i | − | 0.253076i | ||||||
\(143\) | 18755.6i | 0.0766992i | ||||||||
\(144\) | 5130.35 | 0.0206177 | ||||||||
\(145\) | 5827.80 | + | 61653.9i | 0.0230189 | + | 0.243523i | ||||
\(146\) | −202752. | −0.787194 | ||||||||
\(147\) | − | 102875.i | − | 0.392660i | ||||||
\(148\) | − | 86403.7i | − | 0.324248i | ||||||
\(149\) | 119523. | 0.441049 | 0.220524 | − | 0.975381i | \(-0.429223\pi\) | ||||
0.220524 | + | 0.975381i | \(0.429223\pi\) | |||||||
\(150\) | 100066. | − | 19088.0i | 0.363127 | − | 0.0692678i | ||||
\(151\) | 372713. | 1.33025 | 0.665124 | − | 0.746733i | \(-0.268379\pi\) | ||||
0.665124 | + | 0.746733i | \(0.268379\pi\) | |||||||
\(152\) | 308532.i | 1.08316i | ||||||||
\(153\) | 34570.6i | 0.119393i | ||||||||
\(154\) | −73646.9 | −0.250238 | ||||||||
\(155\) | 37805.6 | + | 399955.i | 0.126394 | + | 1.33716i | ||||
\(156\) | −26339.4 | −0.0866552 | ||||||||
\(157\) | − | 407799.i | − | 1.32038i | −0.751101 | − | 0.660188i | \(-0.770477\pi\) | ||
0.751101 | − | 0.660188i | \(-0.229523\pi\) | |||||||
\(158\) | 172112.i | 0.548491i | ||||||||
\(159\) | 243624. | 0.764237 | ||||||||
\(160\) | −315442. | + | 29817.1i | −0.974137 | + | 0.0920799i | ||||
\(161\) | −1887.55 | −0.00573897 | ||||||||
\(162\) | 23764.3i | 0.0711440i | ||||||||
\(163\) | 360328.i | 1.06225i | 0.847292 | + | 0.531127i | \(0.178231\pi\) | ||||
−0.847292 | + | 0.531127i | \(0.821769\pi\) | |||||||
\(164\) | −265115. | −0.769704 | ||||||||
\(165\) | −60606.8 | + | 5728.83i | −0.173305 | + | 0.0163816i | ||||
\(166\) | −88433.8 | −0.249085 | ||||||||
\(167\) | − | 69666.3i | − | 0.193300i | −0.995318 | − | 0.0966500i | \(-0.969187\pi\) | ||
0.995318 | − | 0.0966500i | \(-0.0308127\pi\) | |||||||
\(168\) | − | 278718.i | − | 0.761888i | ||||||
\(169\) | 347266. | 0.935289 | ||||||||
\(170\) | 8132.33 | + | 86034.1i | 0.0215821 | + | 0.228322i | ||||
\(171\) | −135605. | −0.354639 | ||||||||
\(172\) | − | 383391.i | − | 0.988144i | ||||||
\(173\) | 627131.i | 1.59310i | 0.604572 | + | 0.796550i | \(0.293344\pi\) | ||||
−0.604572 | + | 0.796550i | \(0.706656\pi\) | |||||||
\(174\) | −36113.1 | −0.0904257 | ||||||||
\(175\) | −98395.5 | − | 515825.i | −0.242873 | − | 1.27323i | ||||
\(176\) | −7663.86 | −0.0186494 | ||||||||
\(177\) | − | 204957.i | − | 0.491734i | ||||||
\(178\) | 79980.8i | 0.189206i | ||||||||
\(179\) | 662582. | 1.54564 | 0.772818 | − | 0.634628i | \(-0.218846\pi\) | ||||
0.772818 | + | 0.634628i | \(0.218846\pi\) | |||||||
\(180\) | −8045.27 | − | 85113.1i | −0.0185080 | − | 0.195801i | ||||
\(181\) | −525680. | −1.19268 | −0.596341 | − | 0.802731i | \(-0.703379\pi\) | ||||
−0.596341 | + | 0.802731i | \(0.703379\pi\) | |||||||
\(182\) | − | 94344.1i | − | 0.211123i | ||||||
\(183\) | − | 8247.07i | − | 0.0182042i | ||||||
\(184\) | −2070.11 | −0.00450764 | ||||||||
\(185\) | 254688. | − | 24074.2i | 0.547115 | − | 0.0517158i | ||||
\(186\) | −234269. | −0.496516 | ||||||||
\(187\) | − | 51642.5i | − | 0.107995i | ||||||
\(188\) | 199225.i | 0.411101i | ||||||||
\(189\) | 122501. | 0.249452 | ||||||||
\(190\) | −337475. | + | 31899.6i | −0.678199 | + | 0.0641065i | ||||
\(191\) | −824338. | −1.63502 | −0.817508 | − | 0.575918i | \(-0.804645\pi\) | ||||
−0.817508 | + | 0.575918i | \(0.804645\pi\) | |||||||
\(192\) | − | 203008.i | − | 0.397430i | ||||||
\(193\) | − | 783372.i | − | 1.51382i | −0.653518 | − | 0.756911i | \(-0.726707\pi\) | ||
0.653518 | − | 0.756911i | \(-0.273293\pi\) | |||||||
\(194\) | 56889.0 | 0.108524 | ||||||||
\(195\) | −7338.82 | − | 77639.3i | −0.0138210 | − | 0.146216i | ||||
\(196\) | −215817. | −0.401278 | ||||||||
\(197\) | 272361.i | 0.500010i | 0.968245 | + | 0.250005i | \(0.0804323\pi\) | ||||
−0.968245 | + | 0.250005i | \(0.919568\pi\) | |||||||
\(198\) | − | 35499.8i | − | 0.0643521i | ||||||
\(199\) | −982522. | −1.75877 | −0.879386 | − | 0.476109i | \(-0.842047\pi\) | ||||
−0.879386 | + | 0.476109i | \(0.842047\pi\) | |||||||
\(200\) | −107912. | − | 565715.i | −0.190763 | − | 1.00005i | ||||
\(201\) | 227956. | 0.397979 | ||||||||
\(202\) | 38992.0i | 0.0672353i | ||||||||
\(203\) | 186157.i | 0.317059i | ||||||||
\(204\) | 72524.0 | 0.122013 | ||||||||
\(205\) | −73867.6 | − | 781465.i | −0.122763 | − | 1.29875i | ||||
\(206\) | −103897. | −0.170583 | ||||||||
\(207\) | − | 909.851i | − | 0.00147586i | ||||||
\(208\) | − | 9817.66i | − | 0.0157344i | ||||||
\(209\) | 202571. | 0.320783 | ||||||||
\(210\) | 304863. | − | 28817.1i | 0.477042 | − | 0.0450922i | ||||
\(211\) | −430400. | −0.665527 | −0.332764 | − | 0.943010i | \(-0.607981\pi\) | ||||
−0.332764 | + | 0.943010i | \(0.607981\pi\) | |||||||
\(212\) | − | 511089.i | − | 0.781010i | ||||||
\(213\) | − | 151098.i | − | 0.228197i | ||||||
\(214\) | −441593. | −0.659156 | ||||||||
\(215\) | 1.13010e6 | − | 106822.i | 1.66733 | − | 0.157603i | ||||
\(216\) | 134349. | 0.195930 | ||||||||
\(217\) | 1.20762e6i | 1.74093i | ||||||||
\(218\) | 614961.i | 0.876408i | ||||||||
\(219\) | −503792. | −0.709808 | ||||||||
\(220\) | 12018.2 | + | 127144.i | 0.0167411 | + | 0.177109i | ||||
\(221\) | 66155.7 | 0.0911143 | ||||||||
\(222\) | 149181.i | 0.203156i | ||||||||
\(223\) | 532033.i | 0.716434i | 0.933638 | + | 0.358217i | \(0.116615\pi\) | ||||
−0.933638 | + | 0.358217i | \(0.883385\pi\) | |||||||
\(224\) | −952446. | −1.26829 | ||||||||
\(225\) | 248642. | − | 47429.3i | 0.327429 | − | 0.0624583i | ||||
\(226\) | −797822. | −1.03905 | ||||||||
\(227\) | − | 792684.i | − | 1.02102i | −0.859871 | − | 0.510512i | \(-0.829456\pi\) | ||
0.859871 | − | 0.510512i | \(-0.170544\pi\) | |||||||
\(228\) | 284481.i | 0.362423i | ||||||||
\(229\) | −286558. | −0.361097 | −0.180549 | − | 0.983566i | \(-0.557787\pi\) | ||||
−0.180549 | + | 0.983566i | \(0.557787\pi\) | |||||||
\(230\) | −214.032 | − | 2264.30i | −0.000266784 | − | 0.00282237i | ||||
\(231\) | −182996. | −0.225638 | ||||||||
\(232\) | 204162.i | 0.249032i | ||||||||
\(233\) | 1.41434e6i | 1.70673i | 0.521312 | + | 0.853366i | \(0.325443\pi\) | ||||
−0.521312 | + | 0.853366i | \(0.674557\pi\) | |||||||
\(234\) | 45476.4 | 0.0542934 | ||||||||
\(235\) | −587244. | + | 55509.0i | −0.693664 | + | 0.0655682i | ||||
\(236\) | −429971. | −0.502527 | ||||||||
\(237\) | 427660.i | 0.494570i | ||||||||
\(238\) | 259771.i | 0.297268i | ||||||||
\(239\) | −1.00694e6 | −1.14028 | −0.570138 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570138 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(240\) | 31724.7 | − | 2998.77i | 0.0355525 | − | 0.00336058i | ||||
\(241\) | 1.08716e6 | 1.20573 | 0.602866 | − | 0.797843i | \(-0.294025\pi\) | ||||
0.602866 | + | 0.797843i | \(0.294025\pi\) | |||||||
\(242\) | 53030.6i | 0.0582087i | ||||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | −17301.1 | −0.0186037 | ||||||||
\(245\) | −60132.0 | − | 636152.i | −0.0640015 | − | 0.677089i | ||||
\(246\) | 457735. | 0.482254 | ||||||||
\(247\) | 259500.i | 0.270642i | ||||||||
\(248\) | 1.32442e6i | 1.36740i | ||||||||
\(249\) | −219738. | −0.224598 | ||||||||
\(250\) | 607625. | − | 176525.i | 0.614874 | − | 0.178631i | ||||
\(251\) | 312788. | 0.313376 | 0.156688 | − | 0.987648i | \(-0.449918\pi\) | ||||
0.156688 | + | 0.987648i | \(0.449918\pi\) | |||||||
\(252\) | − | 256990.i | − | 0.254927i | ||||||
\(253\) | 1359.16i | 0.00133496i | ||||||||
\(254\) | 836652. | 0.813693 | ||||||||
\(255\) | 20207.0 | + | 213775.i | 0.0194604 | + | 0.205877i | ||||
\(256\) | −1.08283e6 | −1.03267 | ||||||||
\(257\) | − | 1.50645e6i | − | 1.42273i | −0.702822 | − | 0.711366i | \(-0.748077\pi\) | ||
0.702822 | − | 0.711366i | \(-0.251923\pi\) | |||||||
\(258\) | 661945.i | 0.619117i | ||||||||
\(259\) | 769003. | 0.712326 | ||||||||
\(260\) | −162876. | + | 15395.8i | −0.149425 | + | 0.0141243i | ||||
\(261\) | −89732.9 | −0.0815362 | ||||||||
\(262\) | 637097.i | 0.573393i | ||||||||
\(263\) | 189662.i | 0.169079i | 0.996420 | + | 0.0845397i | \(0.0269420\pi\) | ||||
−0.996420 | + | 0.0845397i | \(0.973058\pi\) | |||||||
\(264\) | −200695. | −0.177226 | ||||||||
\(265\) | 1.50651e6 | − | 142402.i | 1.31782 | − | 0.124567i | ||||
\(266\) | −1.01897e6 | −0.882993 | ||||||||
\(267\) | 198734.i | 0.170606i | ||||||||
\(268\) | − | 478218.i | − | 0.406714i | ||||||
\(269\) | −1.60463e6 | −1.35206 | −0.676029 | − | 0.736875i | \(-0.736301\pi\) | ||||
−0.676029 | + | 0.736875i | \(0.736301\pi\) | |||||||
\(270\) | 13890.6 | + | 146952.i | 0.0115961 | + | 0.122678i | ||||
\(271\) | 1.71899e6 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(272\) | 27032.3i | 0.0221545i | ||||||||
\(273\) | − | 234424.i | − | 0.190369i | ||||||
\(274\) | 30561.3 | 0.0245921 | ||||||||
\(275\) | −371428. | + | 70851.1i | −0.296171 | + | 0.0564957i | ||||
\(276\) | −1908.73 | −0.00150825 | ||||||||
\(277\) | − | 756133.i | − | 0.592105i | −0.955172 | − | 0.296053i | \(-0.904330\pi\) | ||
0.955172 | − | 0.296053i | \(-0.0956704\pi\) | |||||||
\(278\) | 271852.i | 0.210970i | ||||||||
\(279\) | −582107. | −0.447705 | ||||||||
\(280\) | −162915. | − | 1.72352e6i | −0.124184 | − | 1.31377i | ||||
\(281\) | 772332. | 0.583497 | 0.291748 | − | 0.956495i | \(-0.405763\pi\) | ||||
0.291748 | + | 0.956495i | \(0.405763\pi\) | |||||||
\(282\) | − | 343972.i | − | 0.257573i | ||||||
\(283\) | 1.93103e6i | 1.43325i | 0.697458 | + | 0.716625i | \(0.254314\pi\) | ||||
−0.697458 | + | 0.716625i | \(0.745686\pi\) | |||||||
\(284\) | −316981. | −0.233205 | ||||||||
\(285\) | −838548. | + | 79263.4i | −0.611528 | + | 0.0578044i | ||||
\(286\) | −67933.9 | −0.0491102 | ||||||||
\(287\) | − | 2.35955e6i | − | 1.69093i | ||||||
\(288\) | − | 459105.i | − | 0.326160i | ||||||
\(289\) | 1.23770e6 | 0.871708 | ||||||||
\(290\) | −223314. | + | 21108.6i | −0.155927 | + | 0.0147389i | ||||
\(291\) | 141356. | 0.0978550 | ||||||||
\(292\) | 1.05688e6i | 0.725386i | ||||||||
\(293\) | − | 1.70779e6i | − | 1.16216i | −0.813847 | − | 0.581080i | \(-0.802630\pi\) | ||
0.813847 | − | 0.581080i | \(-0.197370\pi\) | |||||||
\(294\) | 372619. | 0.251418 | ||||||||
\(295\) | −119801. | − | 1.26740e6i | −0.0801501 | − | 0.847929i | ||||
\(296\) | 843379. | 0.559492 | ||||||||
\(297\) | − | 88209.0i | − | 0.0580259i | ||||||
\(298\) | 432920.i | 0.282402i | ||||||||
\(299\) | −1741.13 | −0.00112630 | ||||||||
\(300\) | −99499.7 | − | 521614.i | −0.0638291 | − | 0.334616i | ||||
\(301\) | 3.41222e6 | 2.17081 | ||||||||
\(302\) | 1.34999e6i | 0.851752i | ||||||||
\(303\) | 96886.4i | 0.0606256i | ||||||||
\(304\) | −106036. | −0.0658068 | ||||||||
\(305\) | −4820.53 | − | 50997.7i | −0.00296719 | − | 0.0313907i | ||||
\(306\) | −125217. | −0.0764467 | ||||||||
\(307\) | 256601.i | 0.155386i | 0.996977 | + | 0.0776931i | \(0.0247554\pi\) | ||||
−0.996977 | + | 0.0776931i | \(0.975245\pi\) | |||||||
\(308\) | 383899.i | 0.230590i | ||||||||
\(309\) | −258160. | −0.153813 | ||||||||
\(310\) | −1.44866e6 | + | 136934.i | −0.856175 | + | 0.0809295i | ||||
\(311\) | 2.08034e6 | 1.21964 | 0.609822 | − | 0.792539i | \(-0.291241\pi\) | ||||
0.609822 | + | 0.792539i | \(0.291241\pi\) | |||||||
\(312\) | − | 257097.i | − | 0.149524i | ||||||
\(313\) | 1.05439e6i | 0.608331i | 0.952619 | + | 0.304166i | \(0.0983776\pi\) | ||||
−0.952619 | + | 0.304166i | \(0.901622\pi\) | |||||||
\(314\) | 1.47707e6 | 0.845431 | ||||||||
\(315\) | 757516. | − | 71603.9i | 0.430146 | − | 0.0406593i | ||||
\(316\) | 897169. | 0.505425 | ||||||||
\(317\) | − | 2.35341e6i | − | 1.31538i | −0.753291 | − | 0.657688i | \(-0.771535\pi\) | ||
0.753291 | − | 0.657688i | \(-0.228465\pi\) | |||||||
\(318\) | 882422.i | 0.489338i | ||||||||
\(319\) | 134045. | 0.0737523 | ||||||||
\(320\) | −118661. | − | 1.25535e6i | −0.0647791 | − | 0.685315i | ||||
\(321\) | −1.09726e6 | −0.594356 | ||||||||
\(322\) | − | 6836.82i | − | 0.00367464i | ||||||
\(323\) | − | 714519.i | − | 0.381072i | ||||||
\(324\) | 123876. | 0.0655579 | ||||||||
\(325\) | −90762.7 | − | 475811.i | −0.0476649 | − | 0.249877i | ||||
\(326\) | −1.30513e6 | −0.680157 | ||||||||
\(327\) | 1.52804e6i | 0.790251i | ||||||||
\(328\) | − | 2.58776e6i | − | 1.32813i | ||||||
\(329\) | −1.77312e6 | −0.903127 | ||||||||
\(330\) | −20750.2 | − | 219521.i | −0.0104891 | − | 0.110967i | ||||
\(331\) | −376896. | −0.189083 | −0.0945414 | − | 0.995521i | \(-0.530138\pi\) | ||||
−0.0945414 | + | 0.995521i | \(0.530138\pi\) | |||||||
\(332\) | 460978.i | 0.229528i | ||||||||
\(333\) | 370680.i | 0.183185i | ||||||||
\(334\) | 252336. | 0.123769 | ||||||||
\(335\) | 1.40962e6 | − | 133244.i | 0.686262 | − | 0.0648686i | ||||
\(336\) | 95789.6 | 0.0462882 | ||||||||
\(337\) | 3.13928e6i | 1.50576i | 0.658159 | + | 0.752879i | \(0.271335\pi\) | ||||
−0.658159 | + | 0.752879i | \(0.728665\pi\) | |||||||
\(338\) | 1.25782e6i | 0.598862i | ||||||||
\(339\) | −1.98241e6 | −0.936901 | ||||||||
\(340\) | 448469. | − | 42391.4i | 0.210395 | − | 0.0198875i | ||||
\(341\) | 869567. | 0.404965 | ||||||||
\(342\) | − | 491171.i | − | 0.227074i | ||||||
\(343\) | 903460.i | 0.414642i | ||||||||
\(344\) | 3.74225e6 | 1.70505 | ||||||||
\(345\) | −531.821 | − | 5626.28i | −0.000240557 | − | 0.00254491i | ||||
\(346\) | −2.27151e6 | −1.02006 | ||||||||
\(347\) | − | 1.74141e6i | − | 0.776384i | −0.921579 | − | 0.388192i | \(-0.873100\pi\) | ||
0.921579 | − | 0.388192i | \(-0.126900\pi\) | |||||||
\(348\) | 188247.i | 0.0833257i | ||||||||
\(349\) | 4.40916e6 | 1.93772 | 0.968862 | − | 0.247602i | \(-0.0796425\pi\) | ||||
0.968862 | + | 0.247602i | \(0.0796425\pi\) | |||||||
\(350\) | 1.86835e6 | − | 356394.i | 0.815245 | − | 0.155511i | ||||
\(351\) | 112999. | 0.0489560 | ||||||||
\(352\) | 685823.i | 0.295023i | ||||||||
\(353\) | 1.97624e6i | 0.844116i | 0.906569 | + | 0.422058i | \(0.138692\pi\) | ||||
−0.906569 | + | 0.422058i | \(0.861308\pi\) | |||||||
\(354\) | 742368. | 0.314855 | ||||||||
\(355\) | −88318.9 | − | 934349.i | −0.0371948 | − | 0.393494i | ||||
\(356\) | 416916. | 0.174350 | ||||||||
\(357\) | 645472.i | 0.268045i | ||||||||
\(358\) | 2.39991e6i | 0.989664i | ||||||||
\(359\) | −340087. | −0.139269 | −0.0696343 | − | 0.997573i | \(-0.522183\pi\) | ||||
−0.0696343 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(360\) | 830782. | − | 78529.3i | 0.337855 | − | 0.0319356i | ||||
\(361\) | 326652. | 0.131922 | ||||||||
\(362\) | − | 1.90404e6i | − | 0.763669i | ||||||
\(363\) | 131769.i | 0.0524864i | ||||||||
\(364\) | −491787. | −0.194547 | ||||||||
\(365\) | −3.11532e6 | + | 294474.i | −1.22397 | + | 0.115695i | ||||
\(366\) | 29871.4 | 0.0116561 | ||||||||
\(367\) | − | 3.60337e6i | − | 1.39651i | −0.715850 | − | 0.698254i | \(-0.753961\pi\) | ||
0.715850 | − | 0.698254i | \(-0.246039\pi\) | |||||||
\(368\) | − | 711.455i | − | 0.000273859i | ||||||
\(369\) | 1.13737e6 | 0.434845 | ||||||||
\(370\) | 87198.3 | + | 922494.i | 0.0331134 | + | 0.350315i | ||||
\(371\) | 4.54875e6 | 1.71576 | ||||||||
\(372\) | 1.22118e6i | 0.457531i | ||||||||
\(373\) | 1.94994e6i | 0.725687i | 0.931850 | + | 0.362844i | \(0.118194\pi\) | ||||
−0.931850 | + | 0.362844i | \(0.881806\pi\) | |||||||
\(374\) | 187052. | 0.0691486 | ||||||||
\(375\) | 1.50981e6 | − | 438625.i | 0.554427 | − | 0.161070i | ||||
\(376\) | −1.94462e6 | −0.709356 | ||||||||
\(377\) | 171717.i | 0.0622242i | ||||||||
\(378\) | 443707.i | 0.159723i | ||||||||
\(379\) | −2.15699e6 | −0.771349 | −0.385674 | − | 0.922635i | \(-0.626031\pi\) | ||||
−0.385674 | + | 0.922635i | \(0.626031\pi\) | |||||||
\(380\) | 166283. | + | 1.75915e6i | 0.0590730 | + | 0.624949i | ||||
\(381\) | 2.07889e6 | 0.733701 | ||||||||
\(382\) | − | 2.98580e6i | − | 1.04689i | ||||||
\(383\) | − | 1.66805e6i | − | 0.581049i | −0.956868 | − | 0.290525i | \(-0.906170\pi\) | ||
0.956868 | − | 0.290525i | \(-0.0938298\pi\) | |||||||
\(384\) | −897064. | −0.310453 | ||||||||
\(385\) | −1.13160e6 | + | 106964.i | −0.389081 | + | 0.0367777i | ||||
\(386\) | 2.83742e6 | 0.969294 | ||||||||
\(387\) | 1.64478e6i | 0.558253i | ||||||||
\(388\) | − | 296545.i | − | 0.100003i | ||||||
\(389\) | −1.58917e6 | −0.532473 | −0.266236 | − | 0.963908i | \(-0.585780\pi\) | ||||
−0.266236 | + | 0.963908i | \(0.585780\pi\) | |||||||
\(390\) | 281214. | − | 26581.6i | 0.0936215 | − | 0.00884953i | ||||
\(391\) | 4794.09 | 0.00158586 | ||||||||
\(392\) | − | 2.10657e6i | − | 0.692406i | ||||||
\(393\) | 1.58304e6i | 0.517025i | ||||||||
\(394\) | −986506. | −0.320154 | ||||||||
\(395\) | 249974. | + | 2.64454e6i | 0.0806124 | + | 0.852819i | ||||
\(396\) | −185050. | −0.0592994 | ||||||||
\(397\) | 4.07780e6i | 1.29852i | 0.760566 | + | 0.649261i | \(0.224922\pi\) | ||||
−0.760566 | + | 0.649261i | \(0.775078\pi\) | |||||||
\(398\) | − | 3.55875e6i | − | 1.12613i | ||||||
\(399\) | −2.53191e6 | −0.796189 | ||||||||
\(400\) | 194425. | − | 37087.2i | 0.0607577 | − | 0.0115897i | ||||
\(401\) | −4.89367e6 | −1.51976 | −0.759878 | − | 0.650066i | \(-0.774741\pi\) | ||||
−0.759878 | + | 0.650066i | \(0.774741\pi\) | |||||||
\(402\) | 825670.i | 0.254824i | ||||||||
\(403\) | 1.11394e6i | 0.341665i | ||||||||
\(404\) | 203254. | 0.0619562 | ||||||||
\(405\) | 34515.0 | + | 365143.i | 0.0104561 | + | 0.110618i | ||||
\(406\) | −674273. | −0.203012 | ||||||||
\(407\) | − | 553732.i | − | 0.165697i | ||||||
\(408\) | 707901.i | 0.210534i | ||||||||
\(409\) | −508943. | −0.150439 | −0.0752196 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752196 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(410\) | 2.83051e6 | − | 267553.i | 0.831582 | − | 0.0786049i | ||||
\(411\) | 75937.8 | 0.0221745 | ||||||||
\(412\) | 541583.i | 0.157189i | ||||||||
\(413\) | − | 3.82679e6i | − | 1.10398i | ||||||
\(414\) | 3295.53 | 0.000944985 | ||||||||
\(415\) | −1.35880e6 | + | 128440.i | −0.387290 | + | 0.0366084i | ||||
\(416\) | −878562. | −0.248908 | ||||||||
\(417\) | 675492.i | 0.190230i | ||||||||
\(418\) | 733725.i | 0.205396i | ||||||||
\(419\) | −6.78930e6 | −1.88925 | −0.944626 | − | 0.328148i | \(-0.893575\pi\) | ||||
−0.944626 | + | 0.328148i | \(0.893575\pi\) | |||||||
\(420\) | −150215. | − | 1.58916e6i | −0.0415517 | − | 0.439586i | ||||
\(421\) | −3.93204e6 | −1.08122 | −0.540608 | − | 0.841275i | \(-0.681806\pi\) | ||||
−0.540608 | + | 0.841275i | \(0.681806\pi\) | |||||||
\(422\) | − | 1.55893e6i | − | 0.426134i | ||||||
\(423\) | − | 854693.i | − | 0.232252i | ||||||
\(424\) | 4.98869e6 | 1.34764 | ||||||||
\(425\) | 249910. | + | 1.31012e6i | 0.0671136 | + | 0.351834i | ||||
\(426\) | 547285. | 0.146113 | ||||||||
\(427\) | − | 153982.i | − | 0.0408697i | ||||||
\(428\) | 2.30189e6i | 0.607401i | ||||||||
\(429\) | −168800. | −0.0442823 | ||||||||
\(430\) | 386917. | + | 4.09329e6i | 0.100913 | + | 1.06758i | ||||
\(431\) | −3.24173e6 | −0.840589 | −0.420295 | − | 0.907388i | \(-0.638073\pi\) | ||||
−0.420295 | + | 0.907388i | \(0.638073\pi\) | |||||||
\(432\) | 46173.2i | 0.0119037i | ||||||||
\(433\) | 5.96730e6i | 1.52953i | 0.644309 | + | 0.764765i | \(0.277145\pi\) | ||||
−0.644309 | + | 0.764765i | \(0.722855\pi\) | |||||||
\(434\) | −4.37408e6 | −1.11471 | ||||||||
\(435\) | −554885. | + | 52450.2i | −0.140598 | + | 0.0132900i | ||||
\(436\) | 3.20560e6 | 0.807595 | ||||||||
\(437\) | 18805.2i | 0.00471057i | ||||||||
\(438\) | − | 1.82476e6i | − | 0.454487i | ||||||
\(439\) | −2.85969e6 | −0.708203 | −0.354101 | − | 0.935207i | \(-0.615213\pi\) | ||||
−0.354101 | + | 0.935207i | \(0.615213\pi\) | |||||||
\(440\) | −1.24104e6 | + | 117309.i | −0.305602 | + | 0.0288869i | ||||
\(441\) | 925875. | 0.226702 | ||||||||
\(442\) | 239620.i | 0.0583401i | ||||||||
\(443\) | − | 2.52822e6i | − | 0.612077i | −0.952019 | − | 0.306038i | \(-0.900996\pi\) | ||
0.952019 | − | 0.306038i | \(-0.0990036\pi\) | |||||||
\(444\) | 777633. | 0.187205 | ||||||||
\(445\) | 116163. | + | 1.22892e6i | 0.0278079 | + | 0.294187i | ||||
\(446\) | −1.92705e6 | −0.458730 | ||||||||
\(447\) | 1.07571e6i | 0.254640i | ||||||||
\(448\) | − | 3.79040e6i | − | 0.892257i | ||||||
\(449\) | −5.72753e6 | −1.34076 | −0.670380 | − | 0.742018i | \(-0.733869\pi\) | ||||
−0.670380 | + | 0.742018i | \(0.733869\pi\) | |||||||
\(450\) | 171792. | + | 900595.i | 0.0399918 | + | 0.209652i | ||||
\(451\) | −1.69903e6 | −0.393333 | ||||||||
\(452\) | 4.15880e6i | 0.957464i | ||||||||
\(453\) | 3.35442e6i | 0.768019i | ||||||||
\(454\) | 2.87115e6 | 0.653757 | ||||||||
\(455\) | −137024. | − | 1.44962e6i | −0.0310291 | − | 0.328265i | ||||
\(456\) | −2.77679e6 | −0.625362 | ||||||||
\(457\) | − | 4.94045e6i | − | 1.10656i | −0.832994 | − | 0.553281i | \(-0.813375\pi\) | ||
0.832994 | − | 0.553281i | \(-0.186625\pi\) | |||||||
\(458\) | − | 1.03793e6i | − | 0.231209i | ||||||
\(459\) | −311135. | −0.0689314 | ||||||||
\(460\) | −11803.1 | + | 1115.68i | −0.00260077 | + | 0.000245836i | ||||
\(461\) | 6.18580e6 | 1.35564 | 0.677818 | − | 0.735229i | \(-0.262926\pi\) | ||||
0.677818 | + | 0.735229i | \(0.262926\pi\) | |||||||
\(462\) | − | 662822.i | − | 0.144475i | ||||||
\(463\) | 1.23230e6i | 0.267155i | 0.991038 | + | 0.133577i | \(0.0426465\pi\) | ||||
−0.991038 | + | 0.133577i | \(0.957354\pi\) | |||||||
\(464\) | −70166.4 | −0.0151298 | ||||||||
\(465\) | −3.59959e6 | + | 340250.i | −0.772007 | + | 0.0729736i | ||||
\(466\) | −5.12284e6 | −1.09281 | ||||||||
\(467\) | − | 7.74380e6i | − | 1.64309i | −0.570142 | − | 0.821546i | \(-0.693112\pi\) | ||
0.570142 | − | 0.821546i | \(-0.306888\pi\) | |||||||
\(468\) | − | 237055.i | − | 0.0500304i | ||||||
\(469\) | 4.25620e6 | 0.893490 | ||||||||
\(470\) | −201057. | − | 2.12703e6i | −0.0419831 | − | 0.444150i | ||||
\(471\) | 3.67019e6 | 0.762319 | ||||||||
\(472\) | − | 4.19691e6i | − | 0.867111i | ||||||
\(473\) | − | 2.45702e6i | − | 0.504959i | ||||||
\(474\) | −1.54901e6 | −0.316671 | ||||||||
\(475\) | −5.13903e6 | + | 980288.i | −1.04507 | + | 0.199352i | ||||
\(476\) | 1.35411e6 | 0.273927 | ||||||||
\(477\) | 2.19262e6i | 0.441233i | ||||||||
\(478\) | − | 3.64721e6i | − | 0.730114i | ||||||
\(479\) | 3.36135e6 | 0.669384 | 0.334692 | − | 0.942328i | \(-0.391368\pi\) | ||||
0.334692 | + | 0.942328i | \(0.391368\pi\) | |||||||
\(480\) | −268353. | − | 2.83898e6i | −0.0531623 | − | 0.562418i | ||||
\(481\) | 709349. | 0.139797 | ||||||||
\(482\) | 3.93776e6i | 0.772025i | ||||||||
\(483\) | − | 16988.0i | − | 0.00331340i | ||||||
\(484\) | 276432. | 0.0536383 | ||||||||
\(485\) | 874111. | − | 82624.9i | 0.168738 | − | 0.0159499i | ||||
\(486\) | −213879. | −0.0410750 | ||||||||
\(487\) | 397760.i | 0.0759973i | 0.999278 | + | 0.0379987i | \(0.0120983\pi\) | ||||
−0.999278 | + | 0.0379987i | \(0.987902\pi\) | |||||||
\(488\) | − | 168875.i | − | 0.0321008i | ||||||
\(489\) | −3.24295e6 | −0.613293 | ||||||||
\(490\) | 2.30418e6 | − | 217802.i | 0.433537 | − | 0.0409799i | ||||
\(491\) | −585823. | −0.109664 | −0.0548318 | − | 0.998496i | \(-0.517462\pi\) | ||||
−0.0548318 | + | 0.998496i | \(0.517462\pi\) | |||||||
\(492\) | − | 2.38603e6i | − | 0.444389i | ||||||
\(493\) | − | 472812.i | − | 0.0876135i | ||||||
\(494\) | −939926. | −0.173291 | ||||||||
\(495\) | −51559.5 | − | 545461.i | −0.00945792 | − | 0.100058i | ||||
\(496\) | −455177. | −0.0830760 | ||||||||
\(497\) | − | 2.82117e6i | − | 0.512316i | ||||||
\(498\) | − | 795904.i | − | 0.143809i | ||||||
\(499\) | −7.82230e6 | −1.40632 | −0.703158 | − | 0.711034i | \(-0.748227\pi\) | ||||
−0.703158 | + | 0.711034i | \(0.748227\pi\) | |||||||
\(500\) | −920171. | − | 3.16737e6i | −0.164605 | − | 0.566595i | ||||
\(501\) | 626997. | 0.111602 | ||||||||
\(502\) | 1.13294e6i | 0.200653i | ||||||||
\(503\) | − | 4.04320e6i | − | 0.712534i | −0.934384 | − | 0.356267i | \(-0.884049\pi\) | ||
0.934384 | − | 0.356267i | \(-0.115951\pi\) | |||||||
\(504\) | 2.50846e6 | 0.439876 | ||||||||
\(505\) | 56631.5 | + | 599120.i | 0.00988166 | + | 0.104541i | ||||
\(506\) | −4922.96 | −0.000854771 | ||||||||
\(507\) | 3.12540e6i | 0.539990i | ||||||||
\(508\) | − | 4.36121e6i | − | 0.749804i | ||||||
\(509\) | 1.07585e7 | 1.84060 | 0.920299 | − | 0.391216i | \(-0.127946\pi\) | ||||
0.920299 | + | 0.391216i | \(0.127946\pi\) | |||||||
\(510\) | −774307. | + | 73191.0i | −0.131822 | + | 0.0124604i | ||||
\(511\) | −9.40637e6 | −1.59357 | ||||||||
\(512\) | − | 732521.i | − | 0.123494i | ||||||
\(513\) | − | 1.22045e6i | − | 0.204751i | ||||||
\(514\) | 5.45646e6 | 0.910969 | ||||||||
\(515\) | −1.59640e6 | + | 150899.i | −0.265230 | + | 0.0250707i | ||||
\(516\) | 3.45052e6 | 0.570505 | ||||||||
\(517\) | 1.27676e6i | 0.210080i | ||||||||
\(518\) | 2.78537e6i | 0.456099i | ||||||||
\(519\) | −5.64418e6 | −0.919777 | ||||||||
\(520\) | −150277. | − | 1.58982e6i | −0.0243716 | − | 0.257834i | ||||
\(521\) | −3.48830e6 | −0.563014 | −0.281507 | − | 0.959559i | \(-0.590834\pi\) | ||||
−0.281507 | + | 0.959559i | \(0.590834\pi\) | |||||||
\(522\) | − | 325018.i | − | 0.0522073i | ||||||
\(523\) | − | 5.47692e6i | − | 0.875552i | −0.899084 | − | 0.437776i | \(-0.855766\pi\) | ||
0.899084 | − | 0.437776i | \(-0.144234\pi\) | |||||||
\(524\) | 3.32099e6 | 0.528372 | ||||||||
\(525\) | 4.64243e6 | − | 885559.i | 0.735101 | − | 0.140223i | ||||
\(526\) | −686967. | −0.108261 | ||||||||
\(527\) | − | 3.06718e6i | − | 0.481075i | ||||||
\(528\) | − | 68974.7i | − | 0.0107673i | ||||||
\(529\) | 6.43622e6 | 0.999980 | ||||||||
\(530\) | 515789. | + | 5.45667e6i | 0.0797595 | + | 0.843797i | ||||
\(531\) | 1.84462e6 | 0.283903 | ||||||||
\(532\) | 5.31158e6i | 0.813663i | ||||||||
\(533\) | − | 2.17651e6i | − | 0.331851i | ||||||
\(534\) | −719828. | −0.109238 | ||||||||
\(535\) | −6.78517e6 | + | 641365.i | −1.02489 | + | 0.0968770i | ||||
\(536\) | 4.66785e6 | 0.701786 | ||||||||
\(537\) | 5.96324e6i | 0.892374i | ||||||||
\(538\) | − | 5.81208e6i | − | 0.865717i | ||||||
\(539\) | −1.38310e6 | −0.205060 | ||||||||
\(540\) | 766018. | − | 72407.5i | 0.113046 | − | 0.0106856i | ||||
\(541\) | −7.78523e6 | −1.14361 | −0.571806 | − | 0.820389i | \(-0.693757\pi\) | ||||
−0.571806 | + | 0.820389i | \(0.693757\pi\) | |||||||
\(542\) | 6.22630e6i | 0.910399i | ||||||||
\(543\) | − | 4.73112e6i | − | 0.688596i | ||||||
\(544\) | 2.41907e6 | 0.350470 | ||||||||
\(545\) | 893162. | + | 9.44899e6i | 0.128807 | + | 1.36268i | ||||
\(546\) | 849097. | 0.121892 | ||||||||
\(547\) | 3.92034e6i | 0.560215i | 0.959969 | + | 0.280108i | \(0.0903702\pi\) | ||||
−0.959969 | + | 0.280108i | \(0.909630\pi\) | |||||||
\(548\) | − | 159307.i | − | 0.0226612i | ||||||
\(549\) | 74223.6 | 0.0105102 | ||||||||
\(550\) | −256627. | − | 1.34533e6i | −0.0361739 | − | 0.189637i | ||||
\(551\) | 1.85464e6 | 0.260244 | ||||||||
\(552\) | − | 18631.0i | − | 0.00260249i | ||||||
\(553\) | 7.98491e6i | 1.11034i | ||||||||
\(554\) | 2.73876e6 | 0.379122 | ||||||||
\(555\) | 216668. | + | 2.29219e6i | 0.0298581 | + | 0.315877i | ||||
\(556\) | 1.41708e6 | 0.194405 | ||||||||
\(557\) | 5.56520e6i | 0.760051i | 0.924976 | + | 0.380026i | \(0.124085\pi\) | ||||
−0.924976 | + | 0.380026i | \(0.875915\pi\) | |||||||
\(558\) | − | 2.10843e6i | − | 0.286664i | ||||||
\(559\) | 3.14753e6 | 0.426030 | ||||||||
\(560\) | 592337. | − | 55990.4i | 0.0798177 | − | 0.00754473i | ||||
\(561\) | 464782. | 0.0623508 | ||||||||
\(562\) | 2.79743e6i | 0.373610i | ||||||||
\(563\) | 6.49216e6i | 0.863213i | 0.902062 | + | 0.431607i | \(0.142053\pi\) | ||||
−0.902062 | + | 0.431607i | \(0.857947\pi\) | |||||||
\(564\) | −1.79302e6 | −0.237349 | ||||||||
\(565\) | −1.22587e7 | + | 1.15875e6i | −1.61556 | + | 0.152710i | ||||
\(566\) | −6.99429e6 | −0.917704 | ||||||||
\(567\) | 1.10251e6i | 0.144021i | ||||||||
\(568\) | − | 3.09403e6i | − | 0.402396i | ||||||
\(569\) | 1.02437e7 | 1.32641 | 0.663204 | − | 0.748439i | \(-0.269196\pi\) | ||||
0.663204 | + | 0.748439i | \(0.269196\pi\) | |||||||
\(570\) | −287097. | − | 3.03727e6i | −0.0370119 | − | 0.391558i | ||||
\(571\) | −1.42962e7 | −1.83498 | −0.917488 | − | 0.397764i | \(-0.869786\pi\) | ||||
−0.917488 | + | 0.397764i | \(0.869786\pi\) | |||||||
\(572\) | 354119.i | 0.0452542i | ||||||||
\(573\) | − | 7.41904e6i | − | 0.943976i | ||||||
\(574\) | 8.54643e6 | 1.08269 | ||||||||
\(575\) | −6577.28 | − | 34480.5i | −0.000829616 | − | 0.00434915i | ||||
\(576\) | 1.82708e6 | 0.229456 | ||||||||
\(577\) | − | 5.37436e6i | − | 0.672027i | −0.941857 | − | 0.336014i | \(-0.890921\pi\) | ||
0.941857 | − | 0.336014i | \(-0.109079\pi\) | |||||||
\(578\) | 4.48303e6i | 0.558151i | ||||||||
\(579\) | 7.05035e6 | 0.874006 | ||||||||
\(580\) | 110033. | + | 1.16407e6i | 0.0135817 | + | 0.143684i | ||||
\(581\) | −4.10276e6 | −0.504238 | ||||||||
\(582\) | 512001.i | 0.0626561i | ||||||||
\(583\) | − | 3.27540e6i | − | 0.399110i | ||||||
\(584\) | −1.03161e7 | −1.25166 | ||||||||
\(585\) | 698754. | − | 66049.4i | 0.0844179 | − | 0.00797956i | ||||
\(586\) | 6.18572e6 | 0.744126 | ||||||||
\(587\) | 1.17715e7i | 1.41006i | 0.709178 | + | 0.705030i | \(0.249066\pi\) | ||||
−0.709178 | + | 0.705030i | \(0.750934\pi\) | |||||||
\(588\) | − | 1.94235e6i | − | 0.231678i | ||||||
\(589\) | 1.20312e7 | 1.42897 | ||||||||
\(590\) | 4.59061e6 | − | 433925.i | 0.542925 | − | 0.0513198i | ||||
\(591\) | −2.45125e6 | −0.288681 | ||||||||
\(592\) | 289852.i | 0.0339917i | ||||||||
\(593\) | 3.16466e6i | 0.369564i | 0.982780 | + | 0.184782i | \(0.0591579\pi\) | ||||
−0.982780 | + | 0.184782i | \(0.940842\pi\) | |||||||
\(594\) | 319498. | 0.0371537 | ||||||||
\(595\) | 377288. | + | 3.99143e6i | 0.0436899 | + | 0.462207i | ||||
\(596\) | 2.25668e6 | 0.260228 | ||||||||
\(597\) | − | 8.84270e6i | − | 1.01543i | ||||||
\(598\) | − | 6306.47i | − | 0.000721163i | ||||||
\(599\) | −4.34303e6 | −0.494567 | −0.247284 | − | 0.968943i | \(-0.579538\pi\) | ||||
−0.247284 | + | 0.968943i | \(0.579538\pi\) | |||||||
\(600\) | 5.09143e6 | − | 971209.i | 0.577380 | − | 0.110137i | ||||
\(601\) | 8.05946e6 | 0.910165 | 0.455082 | − | 0.890449i | \(-0.349610\pi\) | ||||
0.455082 | + | 0.890449i | \(0.349610\pi\) | |||||||
\(602\) | 1.23593e7i | 1.38996i | ||||||||
\(603\) | 2.05160e6i | 0.229774i | ||||||||
\(604\) | 7.03708e6 | 0.784874 | ||||||||
\(605\) | 77020.9 | + | 814825.i | 0.00855501 | + | 0.0905057i | ||||
\(606\) | −350928. | −0.0388183 | ||||||||
\(607\) | − | 284560.i | − | 0.0313475i | −0.999877 | − | 0.0156737i | \(-0.995011\pi\) | ||
0.999877 | − | 0.0156737i | \(-0.00498931\pi\) | |||||||
\(608\) | 9.48897e6i | 1.04102i | ||||||||
\(609\) | −1.67542e6 | −0.183054 | ||||||||
\(610\) | 184717. | − | 17460.3i | 0.0200993 | − | 0.00189988i | ||||
\(611\) | −1.63558e6 | −0.177243 | ||||||||
\(612\) | 652716.i | 0.0704443i | ||||||||
\(613\) | − | 1.43183e7i | − | 1.53901i | −0.638644 | − | 0.769503i | \(-0.720504\pi\) | ||
0.638644 | − | 0.769503i | \(-0.279496\pi\) | |||||||
\(614\) | −929424. | −0.0994931 | ||||||||
\(615\) | 7.03318e6 | − | 664808.i | 0.749832 | − | 0.0708775i | ||||
\(616\) | −3.74720e6 | −0.397883 | ||||||||
\(617\) | − | 1.35489e7i | − | 1.43282i | −0.697679 | − | 0.716411i | \(-0.745784\pi\) | ||
0.697679 | − | 0.716411i | \(-0.254216\pi\) | |||||||
\(618\) | − | 935072.i | − | 0.0984859i | ||||||
\(619\) | 1.25027e7 | 1.31152 | 0.655762 | − | 0.754968i | \(-0.272348\pi\) | ||||
0.655762 | + | 0.754968i | \(0.272348\pi\) | |||||||
\(620\) | 713795. | + | 7.55142e6i | 0.0745752 | + | 0.788950i | ||||
\(621\) | 8188.65 | 0.000852086 | ||||||||
\(622\) | 7.53511e6i | 0.780932i | ||||||||
\(623\) | 3.71060e6i | 0.383022i | ||||||||
\(624\) | 88358.9 | 0.00908425 | ||||||||
\(625\) | 9.07990e6 | − | 3.59485e6i | 0.929781 | − | 0.368112i | ||||
\(626\) | −3.81906e6 | −0.389512 | ||||||||
\(627\) | 1.82314e6i | 0.185204i | ||||||||
\(628\) | − | 7.69953e6i | − | 0.779050i | ||||||
\(629\) | −1.95315e6 | −0.196838 | ||||||||
\(630\) | 259354. | + | 2.74377e6i | 0.0260340 | + | 0.275420i | ||||
\(631\) | 272233. | 0.0272187 | 0.0136093 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136093 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(632\) | 8.75719e6i | 0.872112i | ||||||||
\(633\) | − | 3.87360e6i | − | 0.384242i | ||||||
\(634\) | 8.52419e6 | 0.842229 | ||||||||
\(635\) | 1.28553e7 | − | 1.21514e6i | 1.26517 | − | 0.119590i | ||||
\(636\) | 4.59980e6 | 0.450916 | ||||||||
\(637\) | − | 1.77179e6i | − | 0.173007i | ||||||
\(638\) | 485521.i | 0.0472233i | ||||||||
\(639\) | 1.35988e6 | 0.131749 | ||||||||
\(640\) | −5.54720e6 | + | 524347.i | −0.535333 | + | 0.0506021i | ||||
\(641\) | 1.57242e7 | 1.51156 | 0.755779 | − | 0.654827i | \(-0.227258\pi\) | ||||
0.755779 | + | 0.654827i | \(0.227258\pi\) | |||||||
\(642\) | − | 3.97434e6i | − | 0.380564i | ||||||
\(643\) | − | 5.47692e6i | − | 0.522407i | −0.965284 | − | 0.261203i | \(-0.915881\pi\) | ||
0.965284 | − | 0.261203i | \(-0.0841193\pi\) | |||||||
\(644\) | −35638.2 | −0.00338611 | ||||||||
\(645\) | 961400. | + | 1.01709e7i | 0.0909924 | + | 0.962632i | ||||
\(646\) | 2.58803e6 | 0.243999 | ||||||||
\(647\) | 3.91671e6i | 0.367841i | 0.982941 | + | 0.183921i | \(0.0588789\pi\) | ||||
−0.982941 | + | 0.183921i | \(0.941121\pi\) | |||||||
\(648\) | 1.20915e6i | 0.113120i | ||||||||
\(649\) | −2.75554e6 | −0.256800 | ||||||||
\(650\) | 1.72342e6 | − | 328748.i | 0.159995 | − | 0.0305196i | ||||
\(651\) | −1.08686e7 | −1.00513 | ||||||||
\(652\) | 6.80323e6i | 0.626753i | ||||||||
\(653\) | − | 1.51457e7i | − | 1.38997i | −0.719024 | − | 0.694985i | \(-0.755411\pi\) | ||
0.719024 | − | 0.694985i | \(-0.244589\pi\) | |||||||
\(654\) | −5.53465e6 | −0.505995 | ||||||||
\(655\) | 925312. | + | 9.78912e6i | 0.0842723 | + | 0.891539i | ||||
\(656\) | 889361. | 0.0806898 | ||||||||
\(657\) | − | 4.53413e6i | − | 0.409808i | ||||||
\(658\) | − | 6.42235e6i | − | 0.578269i | ||||||
\(659\) | −1.56274e6 | −0.140176 | −0.0700880 | − | 0.997541i | \(-0.522328\pi\) | ||||
−0.0700880 | + | 0.997541i | \(0.522328\pi\) | |||||||
\(660\) | −1.14430e6 | + | 108164.i | −0.102254 | + | 0.00966549i | ||||
\(661\) | 1.33712e7 | 1.19033 | 0.595163 | − | 0.803605i | \(-0.297088\pi\) | ||||
0.595163 | + | 0.803605i | \(0.297088\pi\) | |||||||
\(662\) | − | 1.36514e6i | − | 0.121069i | ||||||
\(663\) | 595401.i | 0.0526049i | ||||||||
\(664\) | −4.49957e6 | −0.396051 | ||||||||
\(665\) | −1.56567e7 | + | 1.47994e6i | −1.37292 | + | 0.129775i | ||||
\(666\) | −1.34263e6 | −0.117292 | ||||||||
\(667\) | 12443.8i | 0.00108302i | ||||||||
\(668\) | − | 1.31535e6i | − | 0.114051i | ||||||
\(669\) | −4.78829e6 | −0.413633 | ||||||||
\(670\) | 482616. | + | 5.10572e6i | 0.0415351 | + | 0.439410i | ||||
\(671\) | −110877. | −0.00950684 | ||||||||
\(672\) | − | 8.57201e6i | − | 0.732250i | ||||||
\(673\) | − | 1.30303e7i | − | 1.10896i | −0.832196 | − | 0.554481i | \(-0.812917\pi\) | ||
0.832196 | − | 0.554481i | \(-0.187083\pi\) | |||||||
\(674\) | −1.13707e7 | −0.964130 | ||||||||
\(675\) | 426863. | + | 2.23778e6i | 0.0360603 | + | 0.189042i | ||||
\(676\) | 6.55663e6 | 0.551841 | ||||||||
\(677\) | − | 1.20799e7i | − | 1.01296i | −0.862253 | − | 0.506478i | \(-0.830947\pi\) | ||
0.862253 | − | 0.506478i | \(-0.169053\pi\) | |||||||
\(678\) | − | 7.18040e6i | − | 0.599894i | ||||||
\(679\) | 2.63929e6 | 0.219691 | ||||||||
\(680\) | 413779. | + | 4.37747e6i | 0.0343159 | + | 0.363037i | ||||
\(681\) | 7.13416e6 | 0.589488 | ||||||||
\(682\) | 3.14962e6i | 0.259297i | ||||||||
\(683\) | − | 1.84029e7i | − | 1.50950i | −0.656011 | − | 0.754752i | \(-0.727757\pi\) | ||
0.656011 | − | 0.754752i | \(-0.272243\pi\) | |||||||
\(684\) | −2.56032e6 | −0.209245 | ||||||||
\(685\) | 469580. | − | 44386.8i | 0.0382369 | − | 0.00361433i | ||||
\(686\) | −3.27238e6 | −0.265494 | ||||||||
\(687\) | − | 2.57903e6i | − | 0.208480i | ||||||
\(688\) | 1.28613e6i | 0.103589i | ||||||||
\(689\) | 4.19589e6 | 0.336726 | ||||||||
\(690\) | 20378.7 | − | 1926.29i | 0.00162950 | − | 0.000154028i | ||||
\(691\) | 5.23001e6 | 0.416684 | 0.208342 | − | 0.978056i | \(-0.433193\pi\) | ||||
0.208342 | + | 0.978056i | \(0.433193\pi\) | |||||||
\(692\) | 1.18407e7i | 0.939963i | ||||||||
\(693\) | − | 1.64696e6i | − | 0.130272i | ||||||
\(694\) | 6.30748e6 | 0.497115 | ||||||||
\(695\) | 394835. | + | 4.17706e6i | 0.0310065 | + | 0.328026i | ||||
\(696\) | −1.83746e6 | −0.143779 | ||||||||
\(697\) | 5.99290e6i | 0.467257i | ||||||||
\(698\) | 1.59702e7i | 1.24072i | ||||||||
\(699\) | −1.27291e7 | −0.985382 | ||||||||
\(700\) | −1.85777e6 | − | 9.73914e6i | −0.143301 | − | 0.751234i | ||||
\(701\) | 4.83055e6 | 0.371280 | 0.185640 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185640 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(702\) | 409288.i | 0.0313463i | ||||||||
\(703\) | − | 7.66137e6i | − | 0.584680i | ||||||
\(704\) | −2.72934e6 | −0.207551 | ||||||||
\(705\) | −499581. | − | 5.28520e6i | −0.0378558 | − | 0.400487i | ||||
\(706\) | −7.15804e6 | −0.540484 | ||||||||
\(707\) | 1.80898e6i | 0.136109i | ||||||||
\(708\) | − | 3.86974e6i | − | 0.290134i | ||||||
\(709\) | 6.13980e6 | 0.458711 | 0.229355 | − | 0.973343i | \(-0.426338\pi\) | ||||
0.229355 | + | 0.973343i | \(0.426338\pi\) | |||||||
\(710\) | 3.38427e6 | − | 319896.i | 0.251953 | − | 0.0238157i | ||||
\(711\) | −3.84894e6 | −0.285540 | ||||||||
\(712\) | 4.06948e6i | 0.300842i | ||||||||
\(713\) | 80724.0i | 0.00594674i | ||||||||
\(714\) | −2.33794e6 | −0.171628 | ||||||||
\(715\) | −1.04382e6 | + | 98666.4i | −0.0763589 | + | 0.00721779i | ||||
\(716\) | 1.25100e7 | 0.911959 | ||||||||
\(717\) | − | 9.06249e6i | − | 0.658339i | ||||||
\(718\) | − | 1.23181e6i | − | 0.0891731i | ||||||
\(719\) | −1.31130e7 | −0.945974 | −0.472987 | − | 0.881069i | \(-0.656824\pi\) | ||||
−0.472987 | + | 0.881069i | \(0.656824\pi\) | |||||||
\(720\) | 26988.9 | + | 285523.i | 0.00194023 | + | 0.0205262i | ||||
\(721\) | −4.82015e6 | −0.345321 | ||||||||
\(722\) | 1.18315e6i | 0.0844690i | ||||||||
\(723\) | 9.78444e6i | 0.696130i | ||||||||
\(724\) | −9.92520e6 | −0.703708 | ||||||||
\(725\) | −3.40060e6 | + | 648677.i | −0.240276 | + | 0.0458335i | ||||
\(726\) | −477275. | −0.0336068 | ||||||||
\(727\) | − | 2.62296e7i | − | 1.84059i | −0.391229 | − | 0.920293i | \(-0.627950\pi\) | ||
0.391229 | − | 0.920293i | \(-0.372050\pi\) | |||||||
\(728\) | − | 4.80029e6i | − | 0.335691i | ||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −1.06660e6 | − | 1.12839e7i | −0.0740790 | − | 0.783701i | ||||
\(731\) | −8.66653e6 | −0.599863 | ||||||||
\(732\) | − | 155710.i | − | 0.0107409i | ||||||
\(733\) | − | 261993.i | − | 0.0180106i | −0.999959 | − | 0.00900532i | \(-0.997133\pi\) | ||
0.999959 | − | 0.00900532i | \(-0.00286652\pi\) | |||||||
\(734\) | 1.30516e7 | 0.894178 | ||||||||
\(735\) | 5.72537e6 | − | 541188.i | 0.390917 | − | 0.0369513i | ||||
\(736\) | −63666.6 | −0.00433229 | ||||||||
\(737\) | − | 3.06474e6i | − | 0.207838i | ||||||
\(738\) | 4.11961e6i | 0.278430i | ||||||||
\(739\) | −2.14527e7 | −1.44501 | −0.722506 | − | 0.691365i | \(-0.757010\pi\) | ||||
−0.722506 | + | 0.691365i | \(0.757010\pi\) | |||||||
\(740\) | 4.80868e6 | − | 454538.i | 0.322809 | − | 0.0305134i | ||||
\(741\) | −2.33550e6 | −0.156255 | ||||||||
\(742\) | 1.64758e7i | 1.09860i | ||||||||
\(743\) | 1.11848e7i | 0.743283i | 0.928376 | + | 0.371642i | \(0.121205\pi\) | ||||
−0.928376 | + | 0.371642i | \(0.878795\pi\) | |||||||
\(744\) | −1.19198e7 | −0.789471 | ||||||||
\(745\) | 628768. | + | 6.65190e6i | 0.0415049 | + | 0.439092i | ||||
\(746\) | −7.06280e6 | −0.464654 | ||||||||
\(747\) | − | 1.97764e6i | − | 0.129672i | ||||||
\(748\) | − | 975045.i | − | 0.0637192i | ||||||
\(749\) | −2.04871e7 | −1.33437 | ||||||||
\(750\) | 1.58873e6 | + | 5.46863e6i | 0.103133 | + | 0.354997i | ||||
\(751\) | 5.63342e6 | 0.364479 | 0.182239 | − | 0.983254i | \(-0.441665\pi\) | ||||
0.182239 | + | 0.983254i | \(0.441665\pi\) | |||||||
\(752\) | − | 668325.i | − | 0.0430966i | ||||||
\(753\) | 2.81509e6i | 0.180928i | ||||||||
\(754\) | −621968. | −0.0398419 | ||||||||
\(755\) | 1.96071e6 | + | 2.07428e7i | 0.125183 | + | 1.32434i | ||||
\(756\) | 2.31291e6 | 0.147182 | ||||||||
\(757\) | 7.69867e6i | 0.488288i | 0.969739 | + | 0.244144i | \(0.0785069\pi\) | ||||
−0.969739 | + | 0.244144i | \(0.921493\pi\) | |||||||
\(758\) | − | 7.81276e6i | − | 0.493891i | ||||||
\(759\) | −12232.4 | −0.000770741 | ||||||||
\(760\) | −1.71709e7 | + | 1.62308e6i | −1.07835 | + | 0.101931i | ||||
\(761\) | 2.39899e7 | 1.50164 | 0.750822 | − | 0.660505i | \(-0.229658\pi\) | ||||
0.750822 | + | 0.660505i | \(0.229658\pi\) | |||||||
\(762\) | 7.52987e6i | 0.469786i | ||||||||
\(763\) | 2.85303e7i | 1.77417i | ||||||||
\(764\) | −1.55641e7 | −0.964694 | ||||||||
\(765\) | −1.92398e6 | + | 181863.i | −0.118863 | + | 0.0112355i | ||||
\(766\) | 6.04179e6 | 0.372043 | ||||||||
\(767\) | − | 3.52994e6i | − | 0.216660i | ||||||
\(768\) | − | 9.74549e6i | − | 0.596212i | ||||||
\(769\) | 2.03436e7 | 1.24054 | 0.620272 | − | 0.784387i | \(-0.287022\pi\) | ||||
0.620272 | + | 0.784387i | \(0.287022\pi\) | |||||||
\(770\) | −387429. | − | 4.09872e6i | −0.0235486 | − | 0.249127i | ||||
\(771\) | 1.35581e7 | 0.821415 | ||||||||
\(772\) | − | 1.47906e7i | − | 0.893188i | ||||||
\(773\) | − | 1.86605e7i | − | 1.12324i | −0.827394 | − | 0.561622i | \(-0.810178\pi\) | ||
0.827394 | − | 0.561622i | \(-0.189822\pi\) | |||||||
\(774\) | −5.95750e6 | −0.357447 | ||||||||
\(775\) | −2.20601e7 | + | 4.20803e6i | −1.31933 | + | 0.251666i | ||||
\(776\) | 2.89455e6 | 0.172555 | ||||||||
\(777\) | 6.92102e6i | 0.411261i | ||||||||
\(778\) | − | 5.75608e6i | − | 0.340940i | ||||||
\(779\) | −2.35076e7 | −1.38792 | ||||||||
\(780\) | −138562. | − | 1.46588e6i | −0.00815469 | − | 0.0862706i | ||||
\(781\) | −2.03143e6 | −0.119172 | ||||||||
\(782\) | 17364.5i | 0.00101542i | ||||||||
\(783\) | − | 807596.i | − | 0.0470750i | ||||||
\(784\) | 723985. | 0.0420668 | ||||||||
\(785\) | 2.26955e7 | − | 2.14528e6i | 1.31452 | − | 0.124254i | ||||
\(786\) | −5.73388e6 | −0.331049 | ||||||||
\(787\) | 2.98644e7i | 1.71877i | 0.511333 | + | 0.859383i | \(0.329152\pi\) | ||||
−0.511333 | + | 0.859383i | \(0.670848\pi\) | |||||||
\(788\) | 5.14235e6i | 0.295017i | ||||||||
\(789\) | −1.70696e6 | −0.0976180 | ||||||||
\(790\) | −9.57867e6 | + | 905420.i | −0.546057 | + | 0.0516157i | ||||
\(791\) | −3.70138e7 | −2.10341 | ||||||||
\(792\) | − | 1.80625e6i | − | 0.102321i | ||||||
\(793\) | − | 142037.i | − | 0.00802084i | ||||||
\(794\) | −1.47700e7 | −0.831438 | ||||||||
\(795\) | 1.28162e6 | + | 1.35586e7i | 0.0719186 | + | 0.760846i | ||||
\(796\) | −1.85507e7 | −1.03771 | ||||||||
\(797\) | 2.60350e7i | 1.45182i | 0.687791 | + | 0.725909i | \(0.258581\pi\) | ||||
−0.687791 | + | 0.725909i | \(0.741419\pi\) | |||||||
\(798\) | − | 9.17073e6i | − | 0.509796i | ||||||
\(799\) | 4.50346e6 | 0.249563 | ||||||||
\(800\) | −3.31885e6 | − | 1.73987e7i | −0.183343 | − | 0.961149i | ||||
\(801\) | −1.78861e6 | −0.0984995 | ||||||||
\(802\) | − | 1.77252e7i | − | 0.973093i | ||||||
\(803\) | 6.77320e6i | 0.370685i | ||||||||
\(804\) | 4.30396e6 | 0.234816 | ||||||||
\(805\) | −9929.71 | − | 105049.i | −0.000540066 | − | 0.00571350i | ||||
\(806\) | −4.03477e6 | −0.218767 | ||||||||
\(807\) | − | 1.44417e7i | − | 0.780611i | ||||||
\(808\) | 1.98394e6i | 0.106906i | ||||||||
\(809\) | 1.97670e7 | 1.06186 | 0.530932 | − | 0.847414i | \(-0.321842\pi\) | ||||
0.530932 | + | 0.847414i | \(0.321842\pi\) | |||||||
\(810\) | −1.32257e6 | + | 125015.i | −0.0708282 | + | 0.00669501i | ||||
\(811\) | 7.26108e6 | 0.387658 | 0.193829 | − | 0.981035i | \(-0.437909\pi\) | ||||
0.193829 | + | 0.981035i | \(0.437909\pi\) | |||||||
\(812\) | 3.51478e6i | 0.187072i | ||||||||
\(813\) | 1.54710e7i | 0.820901i | ||||||||
\(814\) | 2.00565e6 | 0.106095 | ||||||||
\(815\) | −2.00535e7 | + | 1.89555e6i | −1.05754 | + | 0.0999635i | ||||
\(816\) | −243291. | −0.0127909 | ||||||||
\(817\) | − | 3.39951e7i | − | 1.78181i | ||||||
\(818\) | − | 1.84342e6i | − | 0.0963256i | ||||||
\(819\) | 2.10981e6 | 0.109909 | ||||||||
\(820\) | −1.39467e6 | − | 1.47546e7i | −0.0724331 | − | 0.766289i | ||||
\(821\) | 3.10030e7 | 1.60526 | 0.802631 | − | 0.596476i | \(-0.203433\pi\) | ||||
0.802631 | + | 0.596476i | \(0.203433\pi\) | |||||||
\(822\) | 275051.i | 0.0141982i | ||||||||
\(823\) | 2.56767e7i | 1.32142i | 0.750643 | + | 0.660709i | \(0.229744\pi\) | ||||
−0.750643 | + | 0.660709i | \(0.770256\pi\) | |||||||
\(824\) | −5.28635e6 | −0.271230 | ||||||||
\(825\) | −637660. | − | 3.34285e6i | −0.0326178 | − | 0.170994i | ||||
\(826\) | 1.38609e7 | 0.706871 | ||||||||
\(827\) | − | 1.60345e7i | − | 0.815254i | −0.913149 | − | 0.407627i | \(-0.866356\pi\) | ||
0.913149 | − | 0.407627i | \(-0.133644\pi\) | |||||||
\(828\) | − | 17178.6i | − | 0.000870787i | ||||||
\(829\) | 1.90352e7 | 0.961992 | 0.480996 | − | 0.876723i | \(-0.340275\pi\) | ||||
0.480996 | + | 0.876723i | \(0.340275\pi\) | |||||||
\(830\) | −465218. | − | 4.92166e6i | −0.0234402 | − | 0.247980i | ||||
\(831\) | 6.80520e6 | 0.341852 | ||||||||
\(832\) | − | 3.49637e6i | − | 0.175109i | ||||||
\(833\) | 4.87853e6i | 0.243599i | ||||||||
\(834\) | −2.44667e6 | −0.121804 | ||||||||
\(835\) | 3.87718e6 | − | 366489.i | 0.192442 | − | 0.0181905i | ||||
\(836\) | 3.82468e6 | 0.189269 | ||||||||
\(837\) | − | 5.23896e6i | − | 0.258483i | ||||||
\(838\) | − | 2.45912e7i | − | 1.20968i | ||||||
\(839\) | −2.86604e7 | −1.40565 | −0.702826 | − | 0.711362i | \(-0.748079\pi\) | ||||
−0.702826 | + | 0.711362i | \(0.748079\pi\) | |||||||
\(840\) | 1.55117e7 | − | 1.46623e6i | 0.758507 | − | 0.0716976i | ||||
\(841\) | −1.92839e7 | −0.940167 | ||||||||
\(842\) | − | 1.42421e7i | − | 0.692297i | ||||||
\(843\) | 6.95099e6i | 0.336882i | ||||||||
\(844\) | −8.12625e6 | −0.392676 | ||||||||
\(845\) | 1.82684e6 | + | 1.93266e7i | 0.0880155 | + | 0.931139i | ||||
\(846\) | 3.09575e6 | 0.148710 | ||||||||
\(847\) | 2.46028e6i | 0.117835i | ||||||||
\(848\) | 1.71451e6i | 0.0818749i | ||||||||
\(849\) | −1.73792e7 | −0.827488 | ||||||||
\(850\) | −4.74533e6 | + | 905187.i | −0.225278 | + | 0.0429726i | ||||
\(851\) | 51404.3 | 0.00243319 | ||||||||
\(852\) | − | 2.85283e6i | − | 0.134641i | ||||||
\(853\) | 5.22750e6i | 0.245992i | 0.992407 | + | 0.122996i | \(0.0392503\pi\) | ||||
−0.992407 | + | 0.122996i | \(0.960750\pi\) | |||||||
\(854\) | 557733. | 0.0261687 | ||||||||
\(855\) | −713371. | − | 7.54694e6i | −0.0333734 | − | 0.353066i | ||||
\(856\) | −2.24686e7 | −1.04807 | ||||||||
\(857\) | − | 9.88397e6i | − | 0.459705i | −0.973225 | − | 0.229853i | \(-0.926176\pi\) | ||
0.973225 | − | 0.229853i | \(-0.0738244\pi\) | |||||||
\(858\) | − | 611405.i | − | 0.0283538i | ||||||
\(859\) | 1.37127e7 | 0.634076 | 0.317038 | − | 0.948413i | \(-0.397312\pi\) | ||||
0.317038 | + | 0.948413i | \(0.397312\pi\) | |||||||
\(860\) | 2.13371e7 | − | 2.01688e6i | 0.983759 | − | 0.0929894i | ||||
\(861\) | 2.12360e7 | 0.976257 | ||||||||
\(862\) | − | 1.17417e7i | − | 0.538226i | ||||||
\(863\) | − | 3.39850e7i | − | 1.55332i | −0.629921 | − | 0.776659i | \(-0.716913\pi\) | ||
0.629921 | − | 0.776659i | \(-0.283087\pi\) | |||||||
\(864\) | 4.13194e6 | 0.188308 | ||||||||
\(865\) | −3.49021e7 | + | 3.29911e6i | −1.58603 | + | 0.149919i | ||||
\(866\) | −2.16139e7 | −0.979352 | ||||||||
\(867\) | 1.11393e7i | 0.503281i | ||||||||
\(868\) | 2.28007e7i | 1.02719i | ||||||||
\(869\) | 5.74965e6 | 0.258281 | ||||||||
\(870\) | −189978. | − | 2.00983e6i | −0.00850952 | − | 0.0900244i | ||||
\(871\) | 3.92603e6 | 0.175351 | ||||||||
\(872\) | 3.12896e7i | 1.39351i | ||||||||
\(873\) | 1.27221e6i | 0.0564966i | ||||||||
\(874\) | −68113.4 | −0.00301616 | ||||||||
\(875\) | 2.81899e7 | − | 8.18963e6i | 1.24473 | − | 0.361613i | ||||
\(876\) | −9.51193e6 | −0.418802 | ||||||||
\(877\) | 1.66649e7i | 0.731653i | 0.930683 | + | 0.365826i | \(0.119214\pi\) | ||||
−0.930683 | + | 0.365826i | \(0.880786\pi\) | |||||||
\(878\) | − | 1.03580e7i | − | 0.453459i | ||||||
\(879\) | 1.53701e7 | 0.670973 | ||||||||
\(880\) | −40316.8 | − | 426522.i | −0.00175501 | − | 0.0185667i | ||||
\(881\) | −1.85938e7 | −0.807103 | −0.403551 | − | 0.914957i | \(-0.632224\pi\) | ||||
−0.403551 | + | 0.914957i | \(0.632224\pi\) | |||||||
\(882\) | 3.35357e6i | 0.145156i | ||||||||
\(883\) | 1.41760e7i | 0.611859i | 0.952054 | + | 0.305929i | \(0.0989672\pi\) | ||||
−0.952054 | + | 0.305929i | \(0.901033\pi\) | |||||||
\(884\) | 1.24907e6 | 0.0537594 | ||||||||
\(885\) | 1.14066e7 | − | 1.07821e6i | 0.489552 | − | 0.0462747i | ||||
\(886\) | 9.15737e6 | 0.391910 | ||||||||
\(887\) | − | 1.10264e7i | − | 0.470570i | −0.971926 | − | 0.235285i | \(-0.924398\pi\) | ||
0.971926 | − | 0.235285i | \(-0.0756023\pi\) | |||||||
\(888\) | 7.59041e6i | 0.323023i | ||||||||
\(889\) | 3.88153e7 | 1.64721 | ||||||||
\(890\) | −4.45122e6 | + | 420750.i | −0.188367 | + | 0.0178053i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.00451e7i | 0.422711i | ||||||||
\(893\) | 1.76652e7i | 0.741291i | ||||||||
\(894\) | −3.89628e6 | −0.163045 | ||||||||
\(895\) | 3.48560e6 | + | 3.68751e7i | 0.145452 | + | 1.53878i | ||||
\(896\) | −1.67492e7 | −0.696986 | ||||||||
\(897\) | − | 15670.2i | − | 0.000650268i | ||||||
\(898\) | − | 2.07454e7i | − | 0.858483i | ||||||
\(899\) | 7.96131e6 | 0.328538 | ||||||||
\(900\) | 4.69453e6 | − | 895497.i | 0.193190 | − | 0.0368517i | ||||
\(901\) | −1.15531e7 | −0.474120 | ||||||||
\(902\) | − | 6.15399e6i | − | 0.251849i | ||||||
\(903\) | 3.07100e7i | 1.25332i | ||||||||
\(904\) | −4.05937e7 | −1.65211 | ||||||||
\(905\) | −2.76541e6 | − | 2.92560e7i | −0.112237 | − | 1.18739i | ||||
\(906\) | −1.21499e7 | −0.491759 | ||||||||
\(907\) | − | 1.14062e7i | − | 0.460388i | −0.973145 | − | 0.230194i | \(-0.926064\pi\) | ||
0.973145 | − | 0.230194i | \(-0.0739360\pi\) | |||||||
\(908\) | − | 1.49664e7i | − | 0.602426i | ||||||
\(909\) | −871978. | −0.0350022 | ||||||||
\(910\) | 5.25059e6 | − | 496310.i | 0.210187 | − | 0.0198678i | ||||
\(911\) | 2.17910e7 | 0.869922 | 0.434961 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434961 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(912\) | − | 954326.i | − | 0.0379935i | ||||||
\(913\) | 2.95425e6i | 0.117293i | ||||||||
\(914\) | 1.78946e7 | 0.708527 | ||||||||
\(915\) | 458979. | − | 43384.8i | 0.0181234 | − | 0.00171311i | ||||
\(916\) | −5.41042e6 | −0.213055 | ||||||||
\(917\) | 2.95572e7i | 1.16075i | ||||||||
\(918\) | − | 1.12695e6i | − | 0.0441365i | ||||||
\(919\) | −3.12982e7 | −1.22245 | −0.611225 | − | 0.791457i | \(-0.709323\pi\) | ||||
−0.611225 | + | 0.791457i | \(0.709323\pi\) | |||||||
\(920\) | −10890.1 | − | 115209.i | −0.000424192 | − | 0.00448763i | ||||
\(921\) | −2.30941e6 | −0.0897123 | ||||||||
\(922\) | 2.24053e7i | 0.868008i | ||||||||
\(923\) | − | 2.60232e6i | − | 0.100544i | ||||||
\(924\) | −3.45509e6 | −0.133131 | ||||||||
\(925\) | 2.67964e6 | + | 1.40476e7i | 0.102973 | + | 0.539820i | ||||
\(926\) | −4.46345e6 | −0.171058 | ||||||||
\(927\) | − | 2.32344e6i | − | 0.0888040i | ||||||
\(928\) | 6.27904e6i | 0.239345i | ||||||||
\(929\) | 3.00058e7 | 1.14069 | 0.570343 | − | 0.821407i | \(-0.306810\pi\) | ||||
0.570343 | + | 0.821407i | \(0.306810\pi\) | |||||||
\(930\) | −1.23241e6 | − | 1.30379e7i | −0.0467247 | − | 0.494313i | ||||
\(931\) | −1.91364e7 | −0.723578 | ||||||||
\(932\) | 2.67038e7i | 1.00701i | ||||||||
\(933\) | 1.87230e7i | 0.704161i | ||||||||
\(934\) | 2.80485e7 | 1.05206 | ||||||||
\(935\) | 2.87409e6 | − | 271672.i | 0.107516 | − | 0.0101629i | ||||
\(936\) | 2.31387e6 | 0.0863276 | ||||||||
\(937\) | − | 2.12772e7i | − | 0.791711i | −0.918313 | − | 0.395855i | \(-0.870448\pi\) | ||
0.918313 | − | 0.395855i | \(-0.129552\pi\) | |||||||
\(938\) | 1.54162e7i | 0.572098i | ||||||||
\(939\) | −9.48950e6 | −0.351220 | ||||||||
\(940\) | −1.10876e7 | + | 1.04805e6i | −0.409276 | + | 0.0386867i | ||||
\(941\) | 4.12864e7 | 1.51996 | 0.759982 | − | 0.649944i | \(-0.225208\pi\) | ||||
0.759982 | + | 0.649944i | \(0.225208\pi\) | |||||||
\(942\) | 1.32937e7i | 0.488110i | ||||||||
\(943\) | − | 157725.i | − | 0.00577593i | ||||||
\(944\) | 1.44239e6 | 0.0526809 | ||||||||
\(945\) | 644435. | + | 6.81765e6i | 0.0234747 | + | 0.248345i | ||||
\(946\) | 8.89948e6 | 0.323323 | ||||||||
\(947\) | − | 1.15296e7i | − | 0.417771i | −0.977940 | − | 0.208886i | \(-0.933016\pi\) | ||
0.977940 | − | 0.208886i | \(-0.0669836\pi\) | |||||||
\(948\) | 8.07452e6i | 0.291807i | ||||||||
\(949\) | −8.67670e6 | −0.312744 | ||||||||
\(950\) | −3.55066e6 | − | 1.86139e7i | −0.127644 | − | 0.669157i | ||||
\(951\) | 2.11807e7 | 0.759432 | ||||||||
\(952\) | 1.32173e7i | 0.472663i | ||||||||
\(953\) | − | 9.67798e6i | − | 0.345185i | −0.984993 | − | 0.172593i | \(-0.944786\pi\) | ||
0.984993 | − | 0.172593i | \(-0.0552144\pi\) | |||||||
\(954\) | −7.94180e6 | −0.282519 | ||||||||
\(955\) | −4.33654e6 | − | 4.58774e7i | −0.153863 | − | 1.62776i | ||||
\(956\) | −1.90118e7 | −0.672788 | ||||||||
\(957\) | 1.20641e6i | 0.0425809i | ||||||||
\(958\) | 1.21750e7i | 0.428604i | ||||||||
\(959\) | 1.41785e6 | 0.0497832 | ||||||||
\(960\) | 1.12982e7 | − | 1.06795e6i | 0.395667 | − | 0.0374002i | ||||
\(961\) | 2.30167e7 | 0.803959 | ||||||||
\(962\) | 2.56931e6i | 0.0895113i | ||||||||
\(963\) | − | 9.87534e6i | − | 0.343152i | ||||||
\(964\) | 2.05263e7 | 0.711408 | ||||||||
\(965\) | 4.35975e7 | − | 4.12104e6i | 1.50710 | − | 0.142458i | ||||
\(966\) | 61531.4 | 0.00212155 | ||||||||
\(967\) | − | 3.88946e7i | − | 1.33759i | −0.743447 | − | 0.668795i | \(-0.766811\pi\) | ||
0.743447 | − | 0.668795i | \(-0.233189\pi\) | |||||||
\(968\) | 2.69823e6i | 0.0925531i | ||||||||
\(969\) | 6.43067e6 | 0.220012 | ||||||||
\(970\) | 299272. | + | 3.16608e6i | 0.0102126 | + | 0.108042i | ||||
\(971\) | 2.79477e7 | 0.951259 | 0.475629 | − | 0.879646i | \(-0.342220\pi\) | ||||
0.475629 | + | 0.879646i | \(0.342220\pi\) | |||||||
\(972\) | 1.11489e6i | 0.0378499i | ||||||||
\(973\) | 1.26122e7i | 0.427080i | ||||||||
\(974\) | −1.44071e6 | −0.0486608 | ||||||||
\(975\) | 4.28230e6 | − | 816864.i | 0.144267 | − | 0.0275194i | ||||
\(976\) | 58038.9 | 0.00195027 | ||||||||
\(977\) | − | 7.01873e6i | − | 0.235246i | −0.993058 | − | 0.117623i | \(-0.962473\pi\) | ||
0.993058 | − | 0.117623i | \(-0.0375274\pi\) | |||||||
\(978\) | − | 1.17462e7i | − | 0.392689i | ||||||
\(979\) | 2.67187e6 | 0.0890962 | ||||||||
\(980\) | −1.13533e6 | − | 1.20110e7i | −0.0377623 | − | 0.399497i | ||||
\(981\) | −1.37524e7 | −0.456252 | ||||||||
\(982\) | − | 2.12188e6i | − | 0.0702171i | ||||||
\(983\) | − | 4.12903e7i | − | 1.36290i | −0.731864 | − | 0.681450i | \(-0.761350\pi\) | ||
0.731864 | − | 0.681450i | \(-0.238650\pi\) | |||||||
\(984\) | 2.32899e7 | 0.766795 | ||||||||
\(985\) | −1.51579e7 | + | 1.43279e6i | −0.497791 | + | 0.0470535i | ||||
\(986\) | 1.71255e6 | 0.0560985 | ||||||||
\(987\) | − | 1.59581e7i | − | 0.521421i | ||||||
\(988\) | 4.89955e6i | 0.159685i | ||||||||
\(989\) | 228091. | 0.00741512 | ||||||||
\(990\) | 1.97569e6 | − | 186751.i | 0.0640666 | − | 0.00605586i | ||||
\(991\) | 2.63627e6 | 0.0852717 | 0.0426359 | − | 0.999091i | \(-0.486424\pi\) | ||||
0.0426359 | + | 0.999091i | \(0.486424\pi\) | |||||||
\(992\) | 4.07328e7i | 1.31421i | ||||||||
\(993\) | − | 3.39207e6i | − | 0.109167i | ||||||
\(994\) | 1.02184e7 | 0.328034 | ||||||||
\(995\) | −5.16869e6 | − | 5.46809e7i | −0.165509 | − | 1.75097i | ||||
\(996\) | −4.14880e6 | −0.132518 | ||||||||
\(997\) | − | 4.09967e7i | − | 1.30620i | −0.757270 | − | 0.653102i | \(-0.773467\pi\) | ||
0.757270 | − | 0.653102i | \(-0.226533\pi\) | |||||||
\(998\) | − | 2.83328e7i | − | 0.900458i | ||||||
\(999\) | −3.33612e6 | −0.105762 |
(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 | 165.6.c.b.34.17 | yes | 26 | |
5.2 | odd | 4 | 825.6.a.y.1.4 | 13 | |||
5.3 | odd | 4 | 825.6.a.v.1.10 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.10 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.10 | ✓ | 26 | 5.4 | even | 2 | inner | |
165.6.c.b.34.17 | yes | 26 | 1.1 | even | 1 | trivial | |
825.6.a.v.1.10 | 13 | 5.3 | odd | 4 | |||
825.6.a.y.1.4 | 13 | 5.2 | odd | 4 |