Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,6,Mod(32,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82111008971\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.10 | ||
Character | \(\chi\) | \(=\) | 55.43 |
Dual form | 55.6.e.b.32.10 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.88475 | − | 2.88475i | −0.509957 | − | 0.509957i | 0.404556 | − | 0.914513i | \(-0.367426\pi\) |
−0.914513 | + | 0.404556i | \(0.867426\pi\) | |||||||
\(3\) | 5.55436 | + | 5.55436i | 0.356312 | + | 0.356312i | 0.862452 | − | 0.506139i | \(-0.168928\pi\) |
−0.506139 | + | 0.862452i | \(0.668928\pi\) | |||||||
\(4\) | − | 15.3564i | − | 0.479888i | ||||||
\(5\) | −11.0950 | − | 54.7896i | −0.198473 | − | 0.980106i | ||||
\(6\) | − | 32.0459i | − | 0.363408i | ||||||
\(7\) | 103.743 | + | 103.743i | 0.800227 | + | 0.800227i | 0.983131 | − | 0.182904i | \(-0.0585497\pi\) |
−0.182904 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(8\) | −136.612 | + | 136.612i | −0.754679 | + | 0.754679i | ||||
\(9\) | − | 181.298i | − | 0.746083i | ||||||
\(10\) | −126.048 | + | 190.061i | −0.398599 | + | 0.601025i | ||||
\(11\) | −271.739 | − | 295.311i | −0.677128 | − | 0.735865i | ||||
\(12\) | 85.2950 | − | 85.2950i | 0.170990 | − | 0.170990i | ||||
\(13\) | −40.9640 | + | 40.9640i | −0.0672271 | + | 0.0672271i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.672694 | + | 0.739921i | \(0.265137\pi\) | |||||||
\(14\) | − | 598.545i | − | 0.816163i | ||||||
\(15\) | 242.696 | − | 365.947i | 0.278506 | − | 0.419942i | ||||
\(16\) | 296.775 | 0.289820 | ||||||||
\(17\) | −752.091 | − | 752.091i | −0.631173 | − | 0.631173i | 0.317190 | − | 0.948362i | \(-0.397261\pi\) |
−0.948362 | + | 0.317190i | \(0.897261\pi\) | |||||||
\(18\) | −523.000 | + | 523.000i | −0.380470 | + | 0.380470i | ||||
\(19\) | −2333.79 | −1.48312 | −0.741562 | − | 0.670884i | \(-0.765915\pi\) | ||||
−0.741562 | + | 0.670884i | \(0.765915\pi\) | |||||||
\(20\) | −841.372 | + | 170.379i | −0.470341 | + | 0.0952447i | ||||
\(21\) | 1152.45i | 0.570262i | ||||||||
\(22\) | −67.9994 | + | 1635.80i | −0.0299536 | + | 0.720566i | ||||
\(23\) | −1568.23 | − | 1568.23i | −0.618146 | − | 0.618146i | 0.326910 | − | 0.945056i | \(-0.393993\pi\) |
−0.945056 | + | 0.326910i | \(0.893993\pi\) | |||||||
\(24\) | −1517.58 | −0.537803 | ||||||||
\(25\) | −2878.80 | + | 1215.78i | −0.921217 | + | 0.389049i | ||||
\(26\) | 236.342 | 0.0685659 | ||||||||
\(27\) | 2356.70 | − | 2356.70i | 0.622151 | − | 0.622151i | ||||
\(28\) | 1593.12 | − | 1593.12i | 0.384019 | − | 0.384019i | ||||
\(29\) | 477.232 | 0.105374 | 0.0526871 | − | 0.998611i | \(-0.483221\pi\) | ||||
0.0526871 | + | 0.998611i | \(0.483221\pi\) | |||||||
\(30\) | −1755.78 | + | 355.548i | −0.356178 | + | 0.0721266i | ||||
\(31\) | 8126.11 | 1.51872 | 0.759362 | − | 0.650669i | \(-0.225511\pi\) | ||||
0.759362 | + | 0.650669i | \(0.225511\pi\) | |||||||
\(32\) | 3515.44 | + | 3515.44i | 0.606884 | + | 0.606884i | ||||
\(33\) | 130.928 | − | 3149.60i | 0.0209289 | − | 0.503467i | ||||
\(34\) | 4339.19i | 0.643742i | ||||||||
\(35\) | 4533.01 | − | 6835.06i | 0.625484 | − | 0.943131i | ||||
\(36\) | −2784.09 | −0.358036 | ||||||||
\(37\) | −971.434 | + | 971.434i | −0.116657 | + | 0.116657i | −0.763025 | − | 0.646369i | \(-0.776287\pi\) |
0.646369 | + | 0.763025i | \(0.276287\pi\) | |||||||
\(38\) | 6732.40 | + | 6732.40i | 0.756330 | + | 0.756330i | ||||
\(39\) | −455.058 | −0.0479077 | ||||||||
\(40\) | 9000.59 | + | 5969.19i | 0.889449 | + | 0.589883i | ||||
\(41\) | − | 2223.10i | − | 0.206538i | −0.994653 | − | 0.103269i | \(-0.967070\pi\) | ||
0.994653 | − | 0.103269i | \(-0.0329302\pi\) | |||||||
\(42\) | 3324.53 | − | 3324.53i | 0.290809 | − | 0.290809i | ||||
\(43\) | 10296.0 | − | 10296.0i | 0.849179 | − | 0.849179i | −0.140852 | − | 0.990031i | \(-0.544984\pi\) |
0.990031 | + | 0.140852i | \(0.0449840\pi\) | |||||||
\(44\) | −4534.92 | + | 4172.94i | −0.353133 | + | 0.324945i | ||||
\(45\) | −9933.26 | + | 2011.50i | −0.731241 | + | 0.148077i | ||||
\(46\) | 9047.93i | 0.630456i | ||||||||
\(47\) | 3963.20 | − | 3963.20i | 0.261698 | − | 0.261698i | −0.564045 | − | 0.825744i | \(-0.690756\pi\) |
0.825744 | + | 0.564045i | \(0.190756\pi\) | |||||||
\(48\) | 1648.40 | + | 1648.40i | 0.103266 | + | 0.103266i | ||||
\(49\) | 4718.17i | 0.280727i | ||||||||
\(50\) | 11811.9 | + | 4797.42i | 0.668179 | + | 0.271383i | ||||
\(51\) | − | 8354.77i | − | 0.449789i | ||||||
\(52\) | 629.061 | + | 629.061i | 0.0322615 | + | 0.0322615i | ||||
\(53\) | 11691.1 | + | 11691.1i | 0.571697 | + | 0.571697i | 0.932602 | − | 0.360906i | \(-0.117532\pi\) |
−0.360906 | + | 0.932602i | \(0.617532\pi\) | |||||||
\(54\) | −13597.0 | −0.634540 | ||||||||
\(55\) | −13165.1 | + | 18165.0i | −0.586835 | + | 0.809707i | ||||
\(56\) | −28344.9 | −1.20783 | ||||||||
\(57\) | −12962.7 | − | 12962.7i | −0.528456 | − | 0.528456i | ||||
\(58\) | −1376.69 | − | 1376.69i | −0.0537363 | − | 0.0537363i | ||||
\(59\) | − | 2379.92i | − | 0.0890087i | −0.999009 | − | 0.0445043i | \(-0.985829\pi\) | ||
0.999009 | − | 0.0445043i | \(-0.0141709\pi\) | |||||||
\(60\) | −5619.63 | − | 3726.94i | −0.201525 | − | 0.133652i | ||||
\(61\) | 34132.7i | 1.17448i | 0.809413 | + | 0.587240i | \(0.199786\pi\) | ||||
−0.809413 | + | 0.587240i | \(0.800214\pi\) | |||||||
\(62\) | −23441.8 | − | 23441.8i | −0.774484 | − | 0.774484i | ||||
\(63\) | 18808.4 | − | 18808.4i | 0.597036 | − | 0.597036i | ||||
\(64\) | − | 29779.2i | − | 0.908789i | ||||||
\(65\) | 2698.90 | + | 1789.91i | 0.0792325 | + | 0.0525470i | ||||
\(66\) | −9463.52 | + | 8708.13i | −0.267419 | + | 0.246074i | ||||
\(67\) | 31275.3 | − | 31275.3i | 0.851167 | − | 0.851167i | −0.139110 | − | 0.990277i | \(-0.544424\pi\) |
0.990277 | + | 0.139110i | \(0.0444240\pi\) | |||||||
\(68\) | −11549.4 | + | 11549.4i | −0.302892 | + | 0.302892i | ||||
\(69\) | − | 17421.1i | − | 0.440506i | ||||||
\(70\) | −32794.0 | + | 6640.83i | −0.799926 | + | 0.161986i | ||||
\(71\) | 34239.7 | 0.806091 | 0.403046 | − | 0.915180i | \(-0.367952\pi\) | ||||
0.403046 | + | 0.915180i | \(0.367952\pi\) | |||||||
\(72\) | 24767.4 | + | 24767.4i | 0.563053 | + | 0.563053i | ||||
\(73\) | −6013.88 | + | 6013.88i | −0.132083 | + | 0.132083i | −0.770058 | − | 0.637974i | \(-0.779773\pi\) |
0.637974 | + | 0.770058i | \(0.279773\pi\) | |||||||
\(74\) | 5604.69 | 0.118980 | ||||||||
\(75\) | −22742.8 | − | 9237.05i | −0.466864 | − | 0.189618i | ||||
\(76\) | 35838.6i | 0.711734i | ||||||||
\(77\) | 2445.43 | − | 58827.5i | 0.0470033 | − | 1.13072i | ||||
\(78\) | 1312.73 | + | 1312.73i | 0.0244309 | + | 0.0244309i | ||||
\(79\) | −97400.0 | −1.75587 | −0.877933 | − | 0.478784i | \(-0.841078\pi\) | ||||
−0.877933 | + | 0.478784i | \(0.841078\pi\) | |||||||
\(80\) | −3292.71 | − | 16260.2i | −0.0575213 | − | 0.284054i | ||||
\(81\) | −17875.5 | −0.302723 | ||||||||
\(82\) | −6413.09 | + | 6413.09i | −0.105325 | + | 0.105325i | ||||
\(83\) | 58184.5 | − | 58184.5i | 0.927069 | − | 0.927069i | −0.0704462 | − | 0.997516i | \(-0.522442\pi\) |
0.997516 | + | 0.0704462i | \(0.0224423\pi\) | |||||||
\(84\) | 17697.5 | 0.273662 | ||||||||
\(85\) | −32862.4 | + | 49551.2i | −0.493346 | + | 0.743887i | ||||
\(86\) | −59403.1 | −0.866090 | ||||||||
\(87\) | 2650.72 | + | 2650.72i | 0.0375461 | + | 0.0375461i | ||||
\(88\) | 77465.6 | + | 3220.21i | 1.06636 | + | 0.0443279i | ||||
\(89\) | − | 109220.i | − | 1.46159i | −0.682596 | − | 0.730796i | \(-0.739149\pi\) | ||
0.682596 | − | 0.730796i | \(-0.260851\pi\) | |||||||
\(90\) | 34457.6 | + | 22852.3i | 0.448414 | + | 0.297388i | ||||
\(91\) | −8499.46 | −0.107594 | ||||||||
\(92\) | −24082.4 | + | 24082.4i | −0.296641 | + | 0.296641i | ||||
\(93\) | 45135.4 | + | 45135.4i | 0.541140 | + | 0.541140i | ||||
\(94\) | −22865.7 | −0.266910 | ||||||||
\(95\) | 25893.3 | + | 127867.i | 0.294360 | + | 1.45362i | ||||
\(96\) | 39052.1i | 0.432480i | ||||||||
\(97\) | −36525.4 | + | 36525.4i | −0.394154 | + | 0.394154i | −0.876165 | − | 0.482011i | \(-0.839906\pi\) |
0.482011 | + | 0.876165i | \(0.339906\pi\) | |||||||
\(98\) | 13610.8 | − | 13610.8i | 0.143158 | − | 0.143158i | ||||
\(99\) | −53539.4 | + | 49265.8i | −0.549017 | + | 0.505194i | ||||
\(100\) | 18670.0 | + | 44208.1i | 0.186700 | + | 0.442081i | ||||
\(101\) | − | 152382.i | − | 1.48638i | −0.669080 | − | 0.743190i | \(-0.733312\pi\) | ||
0.669080 | − | 0.743190i | \(-0.266688\pi\) | |||||||
\(102\) | −24101.4 | + | 24101.4i | −0.229373 | + | 0.229373i | ||||
\(103\) | 76493.8 | + | 76493.8i | 0.710450 | + | 0.710450i | 0.966629 | − | 0.256180i | \(-0.0824639\pi\) |
−0.256180 | + | 0.966629i | \(0.582464\pi\) | |||||||
\(104\) | − | 11192.3i | − | 0.101470i | ||||||
\(105\) | 63142.3 | − | 12786.4i | 0.558917 | − | 0.113181i | ||||
\(106\) | − | 67451.8i | − | 0.583081i | ||||||
\(107\) | −160384. | − | 160384.i | −1.35426 | − | 1.35426i | −0.880831 | − | 0.473431i | \(-0.843015\pi\) |
−0.473431 | − | 0.880831i | \(-0.656985\pi\) | |||||||
\(108\) | −36190.5 | − | 36190.5i | −0.298563 | − | 0.298563i | ||||
\(109\) | 230522. | 1.85843 | 0.929214 | − | 0.369543i | \(-0.120486\pi\) | ||||
0.929214 | + | 0.369543i | \(0.120486\pi\) | |||||||
\(110\) | 90379.3 | − | 14423.5i | 0.712176 | − | 0.113655i | ||||
\(111\) | −10791.4 | −0.0831323 | ||||||||
\(112\) | 30788.3 | + | 30788.3i | 0.231922 | + | 0.231922i | ||||
\(113\) | 117467. | + | 117467.i | 0.865409 | + | 0.865409i | 0.991960 | − | 0.126551i | \(-0.0403908\pi\) |
−0.126551 | + | 0.991960i | \(0.540391\pi\) | |||||||
\(114\) | 74788.4i | 0.538979i | ||||||||
\(115\) | −68523.4 | + | 103322.i | −0.483164 | + | 0.728534i | ||||
\(116\) | − | 7328.56i | − | 0.0505678i | ||||||
\(117\) | 7426.71 | + | 7426.71i | 0.0501570 | + | 0.0501570i | ||||
\(118\) | −6865.48 | + | 6865.48i | −0.0453906 | + | 0.0453906i | ||||
\(119\) | − | 156048.i | − | 1.01016i | ||||||
\(120\) | 16837.5 | + | 83147.6i | 0.106739 | + | 0.527104i | ||||
\(121\) | −13366.5 | + | 160495.i | −0.0829956 | + | 0.996550i | ||||
\(122\) | 98464.3 | − | 98464.3i | 0.598934 | − | 0.598934i | ||||
\(123\) | 12347.9 | − | 12347.9i | 0.0735919 | − | 0.0735919i | ||||
\(124\) | − | 124788.i | − | 0.728817i | ||||||
\(125\) | 98552.2 | + | 144240.i | 0.564146 | + | 0.825675i | ||||
\(126\) | −108515. | −0.608925 | ||||||||
\(127\) | 131960. | + | 131960.i | 0.725992 | + | 0.725992i | 0.969819 | − | 0.243827i | \(-0.0784029\pi\) |
−0.243827 | + | 0.969819i | \(0.578403\pi\) | |||||||
\(128\) | 26588.7 | − | 26588.7i | 0.143440 | − | 0.143440i | ||||
\(129\) | 114376. | 0.605146 | ||||||||
\(130\) | −2622.21 | − | 12949.1i | −0.0136085 | − | 0.0672018i | ||||
\(131\) | − | 5606.55i | − | 0.0285442i | −0.999898 | − | 0.0142721i | \(-0.995457\pi\) | ||
0.999898 | − | 0.0142721i | \(-0.00454310\pi\) | |||||||
\(132\) | −48366.6 | − | 2010.58i | −0.241608 | − | 0.0100435i | ||||
\(133\) | −242114. | − | 242114.i | −1.18684 | − | 1.18684i | ||||
\(134\) | −180443. | −0.868117 | ||||||||
\(135\) | −155270. | − | 102975.i | −0.733254 | − | 0.486294i | ||||
\(136\) | 205489. | 0.952666 | ||||||||
\(137\) | −51214.1 | + | 51214.1i | −0.233125 | + | 0.233125i | −0.813996 | − | 0.580871i | \(-0.802712\pi\) |
0.580871 | + | 0.813996i | \(0.302712\pi\) | |||||||
\(138\) | −50255.4 | + | 50255.4i | −0.224639 | + | 0.224639i | ||||
\(139\) | 29167.4 | 0.128044 | 0.0640222 | − | 0.997948i | \(-0.479607\pi\) | ||||
0.0640222 | + | 0.997948i | \(0.479607\pi\) | |||||||
\(140\) | −104962. | − | 69610.8i | −0.452597 | − | 0.300162i | ||||
\(141\) | 44026.0 | 0.186493 | ||||||||
\(142\) | −98773.1 | − | 98773.1i | −0.411072 | − | 0.411072i | ||||
\(143\) | 23228.7 | + | 965.606i | 0.0949915 | + | 0.00394875i | ||||
\(144\) | − | 53804.8i | − | 0.216230i | ||||||
\(145\) | −5294.87 | − | 26147.3i | −0.0209139 | − | 0.103278i | ||||
\(146\) | 34697.1 | 0.134714 | ||||||||
\(147\) | −26206.4 | + | 26206.4i | −0.100026 | + | 0.100026i | ||||
\(148\) | 14917.7 | + | 14917.7i | 0.0559821 | + | 0.0559821i | ||||
\(149\) | −313510. | −1.15687 | −0.578436 | − | 0.815728i | \(-0.696337\pi\) | ||||
−0.578436 | + | 0.815728i | \(0.696337\pi\) | |||||||
\(150\) | 38960.7 | + | 92253.9i | 0.141383 | + | 0.334778i | ||||
\(151\) | 173899.i | 0.620662i | 0.950629 | + | 0.310331i | \(0.100440\pi\) | ||||
−0.950629 | + | 0.310331i | \(0.899560\pi\) | |||||||
\(152\) | 318823. | − | 318823.i | 1.11928 | − | 1.11928i | ||||
\(153\) | −136353. | + | 136353.i | −0.470907 | + | 0.470907i | ||||
\(154\) | −176757. | + | 162648.i | −0.600586 | + | 0.552646i | ||||
\(155\) | −90158.9 | − | 445227.i | −0.301425 | − | 1.48851i | ||||
\(156\) | 6988.06i | 0.0229903i | ||||||||
\(157\) | −161370. | + | 161370.i | −0.522484 | + | 0.522484i | −0.918321 | − | 0.395837i | \(-0.870455\pi\) |
0.395837 | + | 0.918321i | \(0.370455\pi\) | |||||||
\(158\) | 280975. | + | 280975.i | 0.895416 | + | 0.895416i | ||||
\(159\) | 129873.i | 0.407405i | ||||||||
\(160\) | 153606. | − | 231614.i | 0.474361 | − | 0.715260i | ||||
\(161\) | − | 325386.i | − | 0.989314i | ||||||
\(162\) | 51566.3 | + | 51566.3i | 0.154376 | + | 0.154376i | ||||
\(163\) | −442373. | − | 442373.i | −1.30413 | − | 1.30413i | −0.925585 | − | 0.378540i | \(-0.876426\pi\) |
−0.378540 | − | 0.925585i | \(-0.623574\pi\) | |||||||
\(164\) | −34138.8 | −0.0991149 | ||||||||
\(165\) | −174018. | + | 27771.3i | −0.497605 | + | 0.0794119i | ||||
\(166\) | −335696. | −0.945531 | ||||||||
\(167\) | 197052. | + | 197052.i | 0.546751 | + | 0.546751i | 0.925500 | − | 0.378749i | \(-0.123646\pi\) |
−0.378749 | + | 0.925500i | \(0.623646\pi\) | |||||||
\(168\) | −157438. | − | 157438.i | −0.430364 | − | 0.430364i | ||||
\(169\) | 367937.i | 0.990961i | ||||||||
\(170\) | 237743. | − | 48143.2i | 0.630935 | − | 0.127765i | ||||
\(171\) | 423112.i | 1.10653i | ||||||||
\(172\) | −158110. | − | 158110.i | −0.407511 | − | 0.407511i | ||||
\(173\) | 38967.4 | − | 38967.4i | 0.0989888 | − | 0.0989888i | −0.655878 | − | 0.754867i | \(-0.727701\pi\) |
0.754867 | + | 0.655878i | \(0.227701\pi\) | |||||||
\(174\) | − | 15293.3i | − | 0.0382938i | ||||||
\(175\) | −424784. | − | 172527.i | −1.04851 | − | 0.425856i | ||||
\(176\) | −80645.5 | − | 87641.1i | −0.196245 | − | 0.213268i | ||||
\(177\) | 13218.9 | − | 13218.9i | 0.0317149 | − | 0.0317149i | ||||
\(178\) | −315072. | + | 315072.i | −0.745349 | + | 0.745349i | ||||
\(179\) | 334650.i | 0.780653i | 0.920676 | + | 0.390327i | \(0.127638\pi\) | ||||
−0.920676 | + | 0.390327i | \(0.872362\pi\) | |||||||
\(180\) | 30889.4 | + | 152539.i | 0.0710604 | + | 0.350914i | ||||
\(181\) | 102496. | 0.232547 | 0.116273 | − | 0.993217i | \(-0.462905\pi\) | ||||
0.116273 | + | 0.993217i | \(0.462905\pi\) | |||||||
\(182\) | 24518.8 | + | 24518.8i | 0.0548683 | + | 0.0548683i | ||||
\(183\) | −189585. | + | 189585.i | −0.418482 | + | 0.418482i | ||||
\(184\) | 428477. | 0.933003 | ||||||||
\(185\) | 64002.5 | + | 42446.5i | 0.137489 | + | 0.0911827i | ||||
\(186\) | − | 260409.i | − | 0.551916i | ||||||
\(187\) | −17728.3 | + | 426474.i | −0.0370735 | + | 0.891843i | ||||
\(188\) | −60860.5 | − | 60860.5i | −0.125586 | − | 0.125586i | ||||
\(189\) | 488983. | 0.995724 | ||||||||
\(190\) | 294170. | − | 443562.i | 0.591173 | − | 0.891395i | ||||
\(191\) | 565974. | 1.12257 | 0.561284 | − | 0.827623i | \(-0.310307\pi\) | ||||
0.561284 | + | 0.827623i | \(0.310307\pi\) | |||||||
\(192\) | 165404. | − | 165404.i | 0.323813 | − | 0.323813i | ||||
\(193\) | 364829. | − | 364829.i | 0.705011 | − | 0.705011i | −0.260471 | − | 0.965482i | \(-0.583878\pi\) |
0.965482 | + | 0.260471i | \(0.0838779\pi\) | |||||||
\(194\) | 210734. | 0.402003 | ||||||||
\(195\) | 5048.85 | + | 24932.5i | 0.00950837 | + | 0.0469546i | ||||
\(196\) | 72454.2 | 0.134717 | ||||||||
\(197\) | 235641. | + | 235641.i | 0.432598 | + | 0.432598i | 0.889511 | − | 0.456913i | \(-0.151045\pi\) |
−0.456913 | + | 0.889511i | \(0.651045\pi\) | |||||||
\(198\) | 296568. | + | 12328.2i | 0.537602 | + | 0.0223479i | ||||
\(199\) | − | 767403.i | − | 1.37370i | −0.726801 | − | 0.686848i | \(-0.758994\pi\) | ||
0.726801 | − | 0.686848i | \(-0.241006\pi\) | |||||||
\(200\) | 227189. | − | 559367.i | 0.401616 | − | 0.988830i | ||||
\(201\) | 347429. | 0.606563 | ||||||||
\(202\) | −439584. | + | 439584.i | −0.757990 | + | 0.757990i | ||||
\(203\) | 49509.4 | + | 49509.4i | 0.0843233 | + | 0.0843233i | ||||
\(204\) | −128299. | −0.215848 | ||||||||
\(205\) | −121803. | + | 24665.2i | −0.202429 | + | 0.0409921i | ||||
\(206\) | − | 441331.i | − | 0.724597i | ||||||
\(207\) | −284318. | + | 284318.i | −0.461188 | + | 0.461188i | ||||
\(208\) | −12157.1 | + | 12157.1i | −0.0194837 | + | 0.0194837i | ||||
\(209\) | 634182. | + | 689195.i | 1.00427 | + | 1.09138i | ||||
\(210\) | −219036. | − | 145264.i | −0.342741 | − | 0.227306i | ||||
\(211\) | 218175.i | 0.337364i | 0.985671 | + | 0.168682i | \(0.0539511\pi\) | ||||
−0.985671 | + | 0.168682i | \(0.946049\pi\) | |||||||
\(212\) | 179533. | − | 179533.i | 0.274350 | − | 0.274350i | ||||
\(213\) | 190180. | + | 190180.i | 0.287220 | + | 0.287220i | ||||
\(214\) | 925338.i | 1.38123i | ||||||||
\(215\) | −678351. | − | 449882.i | −1.00082 | − | 0.663747i | ||||
\(216\) | 643906.i | 0.939049i | ||||||||
\(217\) | 843027. | + | 843027.i | 1.21532 | + | 1.21532i | ||||
\(218\) | −664998. | − | 664998.i | −0.947718 | − | 0.947718i | ||||
\(219\) | −66806.5 | −0.0941258 | ||||||||
\(220\) | 278949. | + | 202168.i | 0.388568 | + | 0.281615i | ||||
\(221\) | 61617.4 | 0.0848638 | ||||||||
\(222\) | 31130.5 | + | 31130.5i | 0.0423939 | + | 0.0423939i | ||||
\(223\) | 34654.9 | + | 34654.9i | 0.0466661 | + | 0.0466661i | 0.730055 | − | 0.683389i | \(-0.239495\pi\) |
−0.683389 | + | 0.730055i | \(0.739495\pi\) | |||||||
\(224\) | 729405.i | 0.971289i | ||||||||
\(225\) | 220418. | + | 521922.i | 0.290263 | + | 0.687304i | ||||
\(226\) | − | 677729.i | − | 0.882642i | ||||||
\(227\) | −136425. | − | 136425.i | −0.175724 | − | 0.175724i | 0.613765 | − | 0.789489i | \(-0.289654\pi\) |
−0.789489 | + | 0.613765i | \(0.789654\pi\) | |||||||
\(228\) | −199061. | + | 199061.i | −0.253600 | + | 0.253600i | ||||
\(229\) | − | 582233.i | − | 0.733682i | −0.930284 | − | 0.366841i | \(-0.880439\pi\) | ||
0.930284 | − | 0.366841i | \(-0.119561\pi\) | |||||||
\(230\) | 495732. | − | 100386.i | 0.617913 | − | 0.125128i | ||||
\(231\) | 340332. | − | 313166.i | 0.419636 | − | 0.386140i | ||||
\(232\) | −65195.3 | + | 65195.3i | −0.0795237 | + | 0.0795237i | ||||
\(233\) | 283442. | − | 283442.i | 0.342038 | − | 0.342038i | −0.515095 | − | 0.857133i | \(-0.672243\pi\) |
0.857133 | + | 0.515095i | \(0.172243\pi\) | |||||||
\(234\) | − | 42848.4i | − | 0.0511558i | ||||||
\(235\) | −261113. | − | 173170.i | −0.308432 | − | 0.204552i | ||||
\(236\) | −36547.0 | −0.0427142 | ||||||||
\(237\) | −540995. | − | 540995.i | −0.625637 | − | 0.625637i | ||||
\(238\) | −450160. | + | 450160.i | −0.515139 | + | 0.515139i | ||||
\(239\) | −1.58918e6 | −1.79960 | −0.899802 | − | 0.436298i | \(-0.856289\pi\) | ||||
−0.899802 | + | 0.436298i | \(0.856289\pi\) | |||||||
\(240\) | 72026.1 | − | 108604.i | 0.0807164 | − | 0.121708i | ||||
\(241\) | − | 519927.i | − | 0.576633i | −0.957535 | − | 0.288317i | \(-0.906904\pi\) | ||
0.957535 | − | 0.288317i | \(-0.0930956\pi\) | |||||||
\(242\) | 501548. | − | 424430.i | 0.550522 | − | 0.465873i | ||||
\(243\) | −671966. | − | 671966.i | −0.730015 | − | 0.730015i | ||||
\(244\) | 524156. | 0.563619 | ||||||||
\(245\) | 258507. | − | 52347.9i | 0.275142 | − | 0.0557166i | ||||
\(246\) | −71241.2 | −0.0750574 | ||||||||
\(247\) | 95601.5 | − | 95601.5i | 0.0997062 | − | 0.0997062i | ||||
\(248\) | −1.11012e6 | + | 1.11012e6i | −1.14615 | + | 1.14615i | ||||
\(249\) | 646356. | 0.660653 | ||||||||
\(250\) | 131797. | − | 700394.i | 0.133369 | − | 0.708749i | ||||
\(251\) | −70673.7 | −0.0708066 | −0.0354033 | − | 0.999373i | \(-0.511272\pi\) | ||||
−0.0354033 | + | 0.999373i | \(0.511272\pi\) | |||||||
\(252\) | −288829. | − | 288829.i | −0.286510 | − | 0.286510i | ||||
\(253\) | −36966.4 | + | 889267.i | −0.0363083 | + | 0.873436i | ||||
\(254\) | − | 761342.i | − | 0.740449i | ||||||
\(255\) | −457755. | + | 92695.9i | −0.440841 | + | 0.0892709i | ||||
\(256\) | −1.10634e6 | −1.05509 | ||||||||
\(257\) | −1.20806e6 | + | 1.20806e6i | −1.14092 | + | 1.14092i | −0.152640 | + | 0.988282i | \(0.548777\pi\) |
−0.988282 | + | 0.152640i | \(0.951223\pi\) | |||||||
\(258\) | −329946. | − | 329946.i | −0.308598 | − | 0.308598i | ||||
\(259\) | −201559. | −0.186703 | ||||||||
\(260\) | 27486.6 | − | 41445.4i | 0.0252167 | − | 0.0380227i | ||||
\(261\) | − | 86521.2i | − | 0.0786179i | ||||||
\(262\) | −16173.5 | + | 16173.5i | −0.0145563 | + | 0.0145563i | ||||
\(263\) | −893794. | + | 893794.i | −0.796798 | + | 0.796798i | −0.982589 | − | 0.185792i | \(-0.940515\pi\) |
0.185792 | + | 0.982589i | \(0.440515\pi\) | |||||||
\(264\) | 412386. | + | 448158.i | 0.364161 | + | 0.395751i | ||||
\(265\) | 510839. | − | 770263.i | 0.446857 | − | 0.673790i | ||||
\(266\) | 1.39688e6i | 1.21047i | ||||||||
\(267\) | 606646. | − | 606646.i | 0.520784 | − | 0.520784i | ||||
\(268\) | −480277. | − | 480277.i | −0.408465 | − | 0.408465i | ||||
\(269\) | − | 969842.i | − | 0.817184i | −0.912717 | − | 0.408592i | \(-0.866020\pi\) | ||
0.912717 | − | 0.408592i | \(-0.133980\pi\) | |||||||
\(270\) | 150858. | + | 744975.i | 0.125939 | + | 0.621917i | ||||
\(271\) | − | 1.10341e6i | − | 0.912669i | −0.889808 | − | 0.456334i | \(-0.849162\pi\) | ||
0.889808 | − | 0.456334i | \(-0.150838\pi\) | |||||||
\(272\) | −223202. | − | 223202.i | −0.182926 | − | 0.182926i | ||||
\(273\) | −47209.0 | − | 47209.0i | −0.0383370 | − | 0.0383370i | ||||
\(274\) | 295480. | 0.237767 | ||||||||
\(275\) | 1.14132e6 | + | 519769.i | 0.910069 | + | 0.414456i | ||||
\(276\) | −267525. | −0.211394 | ||||||||
\(277\) | 170236. | + | 170236.i | 0.133307 | + | 0.133307i | 0.770612 | − | 0.637305i | \(-0.219951\pi\) |
−0.637305 | + | 0.770612i | \(0.719951\pi\) | |||||||
\(278\) | −84140.6 | − | 84140.6i | −0.0652971 | − | 0.0652971i | ||||
\(279\) | − | 1.47325e6i | − | 1.13309i | ||||||
\(280\) | 314486. | + | 1.55301e6i | 0.239721 | + | 1.18380i | ||||
\(281\) | − | 14924.1i | − | 0.0112751i | −0.999984 | − | 0.00563756i | \(-0.998205\pi\) | ||
0.999984 | − | 0.00563756i | \(-0.00179450\pi\) | |||||||
\(282\) | −127004. | − | 127004.i | −0.0951032 | − | 0.0951032i | ||||
\(283\) | 66100.1 | − | 66100.1i | 0.0490610 | − | 0.0490610i | −0.682151 | − | 0.731212i | \(-0.738955\pi\) |
0.731212 | + | 0.682151i | \(0.238955\pi\) | |||||||
\(284\) | − | 525799.i | − | 0.386833i | ||||||
\(285\) | −566401. | + | 854043.i | −0.413059 | + | 0.622827i | ||||
\(286\) | −64223.5 | − | 69794.5i | −0.0464279 | − | 0.0504552i | ||||
\(287\) | 230631. | − | 230631.i | 0.165277 | − | 0.165277i | ||||
\(288\) | 637344. | − | 637344.i | 0.452785 | − | 0.452785i | ||||
\(289\) | − | 288575.i | − | 0.203242i | ||||||
\(290\) | −60154.2 | + | 90702.9i | −0.0420021 | + | 0.0633325i | ||||
\(291\) | −405751. | −0.280884 | ||||||||
\(292\) | 92351.7 | + | 92351.7i | 0.0633852 | + | 0.0633852i | ||||
\(293\) | 1.59914e6 | − | 1.59914e6i | 1.08822 | − | 1.08822i | 0.0925065 | − | 0.995712i | \(-0.470512\pi\) |
0.995712 | − | 0.0925065i | \(-0.0294879\pi\) | |||||||
\(294\) | 151198. | 0.102018 | ||||||||
\(295\) | −130395. | + | 26405.1i | −0.0872380 | + | 0.0176658i | ||||
\(296\) | − | 265418.i | − | 0.176076i | ||||||
\(297\) | −1.33637e6 | − | 55552.3i | −0.879095 | − | 0.0365436i | ||||
\(298\) | 904398. | + | 904398.i | 0.589955 | + | 0.589955i | ||||
\(299\) | 128482. | 0.0831123 | ||||||||
\(300\) | −141848. | + | 349247.i | −0.0909955 | + | 0.224042i | ||||
\(301\) | 2.13628e6 | 1.35907 | ||||||||
\(302\) | 501656. | − | 501656.i | 0.316511 | − | 0.316511i | ||||
\(303\) | 846384. | − | 846384.i | 0.529616 | − | 0.529616i | ||||
\(304\) | −692611. | −0.429839 | ||||||||
\(305\) | 1.87012e6 | − | 378701.i | 1.15112 | − | 0.233102i | ||||
\(306\) | 786688. | 0.480285 | ||||||||
\(307\) | −1.02898e6 | − | 1.02898e6i | −0.623107 | − | 0.623107i | 0.323218 | − | 0.946325i | \(-0.395235\pi\) |
−0.946325 | + | 0.323218i | \(0.895235\pi\) | |||||||
\(308\) | −903379. | − | 37553.0i | −0.542617 | − | 0.0225563i | ||||
\(309\) | 849748.i | 0.506284i | ||||||||
\(310\) | −1.02428e6 | + | 1.54445e6i | −0.605362 | + | 0.912790i | ||||
\(311\) | −1.96307e6 | −1.15089 | −0.575446 | − | 0.817840i | \(-0.695171\pi\) | ||||
−0.575446 | + | 0.817840i | \(0.695171\pi\) | |||||||
\(312\) | 62166.2 | − | 62166.2i | 0.0361549 | − | 0.0361549i | ||||
\(313\) | 1.41211e6 | + | 1.41211e6i | 0.814719 | + | 0.814719i | 0.985337 | − | 0.170618i | \(-0.0545764\pi\) |
−0.170618 | + | 0.985337i | \(0.554576\pi\) | |||||||
\(314\) | 931023. | 0.532889 | ||||||||
\(315\) | −1.23918e6 | − | 821826.i | −0.703654 | − | 0.466663i | ||||
\(316\) | 1.49571e6i | 0.842619i | ||||||||
\(317\) | −527387. | + | 527387.i | −0.294769 | + | 0.294769i | −0.838961 | − | 0.544192i | \(-0.816836\pi\) |
0.544192 | + | 0.838961i | \(0.316836\pi\) | |||||||
\(318\) | 374652. | − | 374652.i | 0.207759 | − | 0.207759i | ||||
\(319\) | −129683. | − | 140932.i | −0.0713518 | − | 0.0775412i | ||||
\(320\) | −1.63159e6 | + | 330399.i | −0.890709 | + | 0.180370i | ||||
\(321\) | − | 1.78167e6i | − | 0.965081i | ||||||
\(322\) | −938658. | + | 938658.i | −0.504508 | + | 0.504508i | ||||
\(323\) | 1.75522e6 | + | 1.75522e6i | 0.936108 | + | 0.936108i | ||||
\(324\) | 274503.i | 0.145273i | ||||||||
\(325\) | 68124.3 | − | 167731.i | 0.0357761 | − | 0.0880854i | ||||
\(326\) | 2.55227e6i | 1.33010i | ||||||||
\(327\) | 1.28040e6 | + | 1.28040e6i | 0.662181 | + | 0.662181i | ||||
\(328\) | 303701. | + | 303701.i | 0.155870 | + | 0.155870i | ||||
\(329\) | 822307. | 0.418836 | ||||||||
\(330\) | 582112. | + | 421886.i | 0.294254 | + | 0.213260i | ||||
\(331\) | 103664. | 0.0520067 | 0.0260034 | − | 0.999662i | \(-0.491722\pi\) | ||||
0.0260034 | + | 0.999662i | \(0.491722\pi\) | |||||||
\(332\) | −893506. | − | 893506.i | −0.444889 | − | 0.444889i | ||||
\(333\) | 176119. | + | 176119.i | 0.0870355 | + | 0.0870355i | ||||
\(334\) | − | 1.13689e6i | − | 0.557639i | ||||||
\(335\) | −2.06056e6 | − | 1.36656e6i | −1.00317 | − | 0.665301i | ||||
\(336\) | 342019.i | 0.165273i | ||||||||
\(337\) | 1.47688e6 | + | 1.47688e6i | 0.708387 | + | 0.708387i | 0.966196 | − | 0.257809i | \(-0.0830006\pi\) |
−0.257809 | + | 0.966196i | \(0.583001\pi\) | |||||||
\(338\) | 1.06141e6 | − | 1.06141e6i | 0.505347 | − | 0.505347i | ||||
\(339\) | 1.30491e6i | 0.616712i | ||||||||
\(340\) | 760929. | + | 504648.i | 0.356982 | + | 0.236751i | ||||
\(341\) | −2.20818e6 | − | 2.39973e6i | −1.02837 | − | 1.11758i | ||||
\(342\) | 1.22057e6 | − | 1.22057e6i | 0.564285 | − | 0.564285i | ||||
\(343\) | 1.25413e6 | − | 1.25413e6i | 0.575582 | − | 0.575582i | ||||
\(344\) | 2.81312e6i | 1.28172i | ||||||||
\(345\) | −954493. | + | 193286.i | −0.431743 | + | 0.0874284i | ||||
\(346\) | −224823. | −0.100960 | ||||||||
\(347\) | 1.35556e6 | + | 1.35556e6i | 0.604358 | + | 0.604358i | 0.941466 | − | 0.337108i | \(-0.109449\pi\) |
−0.337108 | + | 0.941466i | \(0.609449\pi\) | |||||||
\(348\) | 40705.5 | − | 40705.5i | 0.0180179 | − | 0.0180179i | ||||
\(349\) | −3.89080e6 | −1.70992 | −0.854960 | − | 0.518695i | \(-0.826418\pi\) | ||||
−0.854960 | + | 0.518695i | \(0.826418\pi\) | |||||||
\(350\) | 727697. | + | 1.72309e6i | 0.317527 | + | 0.751863i | ||||
\(351\) | 193080.i | 0.0836508i | ||||||||
\(352\) | 82866.2 | − | 1.99343e6i | 0.0356468 | − | 0.857522i | ||||
\(353\) | 2.14991e6 | + | 2.14991e6i | 0.918299 | + | 0.918299i | 0.996906 | − | 0.0786071i | \(-0.0250473\pi\) |
−0.0786071 | + | 0.996906i | \(0.525047\pi\) | |||||||
\(354\) | −76266.7 | −0.0323465 | ||||||||
\(355\) | −379888. | − | 1.87598e6i | −0.159987 | − | 0.790055i | ||||
\(356\) | −1.67722e6 | −0.701401 | ||||||||
\(357\) | 866748. | − | 866748.i | 0.359933 | − | 0.359933i | ||||
\(358\) | 965382. | − | 965382.i | 0.398100 | − | 0.398100i | ||||
\(359\) | −2.36885e6 | −0.970067 | −0.485033 | − | 0.874496i | \(-0.661193\pi\) | ||||
−0.485033 | + | 0.874496i | \(0.661193\pi\) | |||||||
\(360\) | 1.08220e6 | − | 1.63179e6i | 0.440101 | − | 0.663603i | ||||
\(361\) | 2.97048e6 | 1.19966 | ||||||||
\(362\) | −295675. | − | 295675.i | −0.118589 | − | 0.118589i | ||||
\(363\) | −965692. | + | 817206.i | −0.384655 | + | 0.325511i | ||||
\(364\) | 130521.i | 0.0516330i | ||||||||
\(365\) | 396222. | + | 262774.i | 0.155671 | + | 0.103241i | ||||
\(366\) | 1.09381e6 | 0.426816 | ||||||||
\(367\) | 2.46073e6 | − | 2.46073e6i | 0.953672 | − | 0.953672i | −0.0453010 | − | 0.998973i | \(-0.514425\pi\) |
0.998973 | + | 0.0453010i | \(0.0144247\pi\) | |||||||
\(368\) | −465413. | − | 465413.i | −0.179151 | − | 0.179151i | ||||
\(369\) | −403044. | −0.154094 | ||||||||
\(370\) | −62183.9 | − | 307079.i | −0.0236142 | − | 0.116613i | ||||
\(371\) | 2.42574e6i | 0.914974i | ||||||||
\(372\) | 693117. | − | 693117.i | 0.259687 | − | 0.259687i | ||||
\(373\) | 2.21059e6 | − | 2.21059e6i | 0.822690 | − | 0.822690i | −0.163803 | − | 0.986493i | \(-0.552376\pi\) |
0.986493 | + | 0.163803i | \(0.0523760\pi\) | |||||||
\(374\) | 1.28141e6 | − | 1.17913e6i | 0.473707 | − | 0.435895i | ||||
\(375\) | −253764. | + | 1.34855e6i | −0.0931862 | + | 0.495210i | ||||
\(376\) | 1.08284e6i | 0.394996i | ||||||||
\(377\) | −19549.3 | + | 19549.3i | −0.00708400 | + | 0.00708400i | ||||
\(378\) | −1.41059e6 | − | 1.41059e6i | −0.507776 | − | 0.507776i | ||||
\(379\) | − | 1.51410e6i | − | 0.541447i | −0.962657 | − | 0.270724i | \(-0.912737\pi\) | ||
0.962657 | − | 0.270724i | \(-0.0872630\pi\) | |||||||
\(380\) | 1.96359e6 | − | 397628.i | 0.697575 | − | 0.141260i | ||||
\(381\) | 1.46590e6i | 0.517360i | ||||||||
\(382\) | −1.63269e6 | − | 1.63269e6i | −0.572462 | − | 0.572462i | ||||
\(383\) | −1.34885e6 | − | 1.34885e6i | −0.469857 | − | 0.469857i | 0.432011 | − | 0.901868i | \(-0.357804\pi\) |
−0.901868 | + | 0.432011i | \(0.857804\pi\) | |||||||
\(384\) | 295366. | 0.102219 | ||||||||
\(385\) | −3.25027e6 | + | 518704.i | −1.11755 | + | 0.178348i | ||||
\(386\) | −2.10488e6 | −0.719050 | ||||||||
\(387\) | −1.86665e6 | − | 1.86665e6i | −0.633558 | − | 0.633558i | ||||
\(388\) | 560900. | + | 560900.i | 0.189150 | + | 0.189150i | ||||
\(389\) | − | 1.61439e6i | − | 0.540921i | −0.962731 | − | 0.270461i | \(-0.912824\pi\) | ||
0.962731 | − | 0.270461i | \(-0.0871760\pi\) | |||||||
\(390\) | 57359.3 | − | 86488.6i | 0.0190960 | − | 0.0287937i | ||||
\(391\) | 2.35891e6i | 0.780313i | ||||||||
\(392\) | −644557. | − | 644557.i | −0.211859 | − | 0.211859i | ||||
\(393\) | 31140.8 | − | 31140.8i | 0.0101707 | − | 0.0101707i | ||||
\(394\) | − | 1.35953e6i | − | 0.441213i | ||||||
\(395\) | 1.08065e6 | + | 5.33651e6i | 0.348491 | + | 1.72094i | ||||
\(396\) | 756546. | + | 822173.i | 0.242436 | + | 0.263466i | ||||
\(397\) | −1.63341e6 | + | 1.63341e6i | −0.520137 | + | 0.520137i | −0.917613 | − | 0.397476i | \(-0.869886\pi\) |
0.397476 | + | 0.917613i | \(0.369886\pi\) | |||||||
\(398\) | −2.21377e6 | + | 2.21377e6i | −0.700526 | + | 0.700526i | ||||
\(399\) | − | 2.68958e6i | − | 0.845769i | ||||||
\(400\) | −854358. | + | 360813.i | −0.266987 | + | 0.112754i | ||||
\(401\) | −3.39398e6 | −1.05402 | −0.527010 | − | 0.849859i | \(-0.676687\pi\) | ||||
−0.527010 | + | 0.849859i | \(0.676687\pi\) | |||||||
\(402\) | −1.00225e6 | − | 1.00225e6i | −0.309321 | − | 0.309321i | ||||
\(403\) | −332879. | + | 332879.i | −0.102099 | + | 0.102099i | ||||
\(404\) | −2.34004e6 | −0.713296 | ||||||||
\(405\) | 198328. | + | 979391.i | 0.0600822 | + | 0.296701i | ||||
\(406\) | − | 285645.i | − | 0.0860025i | ||||||
\(407\) | 550852. | + | 22898.7i | 0.164835 | + | 0.00685211i | ||||
\(408\) | 1.14136e6 | + | 1.14136e6i | 0.339446 | + | 0.339446i | ||||
\(409\) | −4.46788e6 | −1.32067 | −0.660333 | − | 0.750973i | \(-0.729585\pi\) | ||||
−0.660333 | + | 0.750973i | \(0.729585\pi\) | |||||||
\(410\) | 422524. | + | 280218.i | 0.124134 | + | 0.0823258i | ||||
\(411\) | −568923. | −0.166130 | ||||||||
\(412\) | 1.17467e6 | − | 1.17467e6i | 0.340936 | − | 0.340936i | ||||
\(413\) | 246900. | − | 246900.i | 0.0712271 | − | 0.0712271i | ||||
\(414\) | 1.64037e6 | 0.470372 | ||||||||
\(415\) | −3.83346e6 | − | 2.54235e6i | −1.09262 | − | 0.724629i | ||||
\(416\) | −288014. | −0.0815981 | ||||||||
\(417\) | 162006. | + | 162006.i | 0.0456238 | + | 0.0456238i | ||||
\(418\) | 158696. | − | 3.81761e6i | 0.0444249 | − | 1.06869i | ||||
\(419\) | 3.51858e6i | 0.979112i | 0.871972 | + | 0.489556i | \(0.162841\pi\) | ||||
−0.871972 | + | 0.489556i | \(0.837159\pi\) | |||||||
\(420\) | −196353. | − | 969640.i | −0.0543144 | − | 0.268218i | ||||
\(421\) | 5.31362e6 | 1.46112 | 0.730559 | − | 0.682849i | \(-0.239259\pi\) | ||||
0.730559 | + | 0.682849i | \(0.239259\pi\) | |||||||
\(422\) | 629381. | − | 629381.i | 0.172041 | − | 0.172041i | ||||
\(423\) | −718520. | − | 718520.i | −0.195249 | − | 0.195249i | ||||
\(424\) | −3.19428e6 | −0.862895 | ||||||||
\(425\) | 3.07950e6 | + | 1.25075e6i | 0.827004 | + | 0.335890i | ||||
\(426\) | − | 1.09724e6i | − | 0.292940i | ||||||
\(427\) | −3.54102e6 | + | 3.54102e6i | −0.939851 | + | 0.939851i | ||||
\(428\) | −2.46293e6 | + | 2.46293e6i | −0.649894 | + | 0.649894i | ||||
\(429\) | 123657. | + | 134384.i | 0.0324396 | + | 0.0352536i | ||||
\(430\) | 659075. | + | 3.25467e6i | 0.171895 | + | 0.848860i | ||||
\(431\) | − | 1.57613e6i | − | 0.408694i | −0.978898 | − | 0.204347i | \(-0.934493\pi\) | ||
0.978898 | − | 0.204347i | \(-0.0655071\pi\) | |||||||
\(432\) | 699412. | − | 699412.i | 0.180312 | − | 0.180312i | ||||
\(433\) | −3.29284e6 | − | 3.29284e6i | −0.844017 | − | 0.844017i | 0.145361 | − | 0.989379i | \(-0.453566\pi\) |
−0.989379 | + | 0.145361i | \(0.953566\pi\) | |||||||
\(434\) | − | 4.86385e6i | − | 1.23953i | ||||||
\(435\) | 115822. | − | 174641.i | 0.0293473 | − | 0.0442511i | ||||
\(436\) | − | 3.53999e6i | − | 0.891837i | ||||||
\(437\) | 3.65993e6 | + | 3.65993e6i | 0.916788 | + | 0.916788i | ||||
\(438\) | 192720. | + | 192720.i | 0.0480001 | + | 0.0480001i | ||||
\(439\) | 4.51196e6 | 1.11739 | 0.558694 | − | 0.829374i | \(-0.311302\pi\) | ||||
0.558694 | + | 0.829374i | \(0.311302\pi\) | |||||||
\(440\) | −683044. | − | 4.28004e6i | −0.168197 | − | 1.05394i | ||||
\(441\) | 855396. | 0.209445 | ||||||||
\(442\) | −177751. | − | 177751.i | −0.0432769 | − | 0.0432769i | ||||
\(443\) | 4.03065e6 | + | 4.03065e6i | 0.975812 | + | 0.975812i | 0.999714 | − | 0.0239020i | \(-0.00760897\pi\) |
−0.0239020 | + | 0.999714i | \(0.507609\pi\) | |||||||
\(444\) | 165717.i | 0.0398942i | ||||||||
\(445\) | −5.98411e6 | + | 1.21179e6i | −1.43252 | + | 0.290086i | ||||
\(446\) | − | 199941.i | − | 0.0475954i | ||||||
\(447\) | −1.74135e6 | − | 1.74135e6i | −0.412208 | − | 0.412208i | ||||
\(448\) | 3.08938e6 | − | 3.08938e6i | 0.727237 | − | 0.727237i | ||||
\(449\) | 7.25561e6i | 1.69847i | 0.528014 | + | 0.849235i | \(0.322937\pi\) | ||||
−0.528014 | + | 0.849235i | \(0.677063\pi\) | |||||||
\(450\) | 869763. | − | 2.14147e6i | 0.202474 | − | 0.498517i | ||||
\(451\) | −656506. | + | 604103.i | −0.151984 | + | 0.139852i | ||||
\(452\) | 1.80388e6 | − | 1.80388e6i | 0.415299 | − | 0.415299i | ||||
\(453\) | −965899. | + | 965899.i | −0.221150 | + | 0.221150i | ||||
\(454\) | 787107.i | 0.179223i | ||||||||
\(455\) | 94301.2 | + | 465682.i | 0.0213545 | + | 0.105453i | ||||
\(456\) | 3.54171e6 | 0.797629 | ||||||||
\(457\) | 3.32290e6 | + | 3.32290e6i | 0.744265 | + | 0.744265i | 0.973396 | − | 0.229131i | \(-0.0735884\pi\) |
−0.229131 | + | 0.973396i | \(0.573588\pi\) | |||||||
\(458\) | −1.67960e6 | + | 1.67960e6i | −0.374146 | + | 0.374146i | ||||
\(459\) | −3.54491e6 | −0.785369 | ||||||||
\(460\) | 1.58666e6 | + | 1.05227e6i | 0.349615 | + | 0.231864i | ||||
\(461\) | − | 748252.i | − | 0.163982i | −0.996633 | − | 0.0819909i | \(-0.973872\pi\) | ||
0.996633 | − | 0.0819909i | \(-0.0261278\pi\) | |||||||
\(462\) | −1.88518e6 | − | 78366.0i | −0.410911 | − | 0.0170814i | ||||
\(463\) | 4.39822e6 | + | 4.39822e6i | 0.953509 | + | 0.953509i | 0.998966 | − | 0.0454573i | \(-0.0144745\pi\) |
−0.0454573 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(464\) | 141631. | 0.0305395 | ||||||||
\(465\) | 1.97217e6 | − | 2.97372e6i | 0.422973 | − | 0.637776i | ||||
\(466\) | −1.63532e6 | −0.348850 | ||||||||
\(467\) | −694029. | + | 694029.i | −0.147260 | + | 0.147260i | −0.776893 | − | 0.629633i | \(-0.783205\pi\) |
0.629633 | + | 0.776893i | \(0.283205\pi\) | |||||||
\(468\) | 114048. | − | 114048.i | 0.0240697 | − | 0.0240697i | ||||
\(469\) | 6.48919e6 | 1.36225 | ||||||||
\(470\) | 253694. | + | 1.25280e6i | 0.0529743 | + | 0.261600i | ||||
\(471\) | −1.79261e6 | −0.372335 | ||||||||
\(472\) | 325124. | + | 325124.i | 0.0671730 | + | 0.0671730i | ||||
\(473\) | −5.83838e6 | − | 242699.i | −1.19988 | − | 0.0498786i | ||||
\(474\) | 3.12127e6i | 0.638095i | ||||||||
\(475\) | 6.71852e6 | − | 2.83737e6i | 1.36628 | − | 0.577008i | ||||
\(476\) | −2.39634e6 | −0.484765 | ||||||||
\(477\) | 2.11958e6 | − | 2.11958e6i | 0.426533 | − | 0.426533i | ||||
\(478\) | 4.58438e6 | + | 4.58438e6i | 0.917721 | + | 0.917721i | ||||
\(479\) | 4.12849e6 | 0.822153 | 0.411076 | − | 0.911601i | \(-0.365153\pi\) | ||||
0.411076 | + | 0.911601i | \(0.365153\pi\) | |||||||
\(480\) | 2.13965e6 | − | 433281.i | 0.423877 | − | 0.0858355i | ||||
\(481\) | − | 79587.8i | − | 0.0156850i | ||||||
\(482\) | −1.49986e6 | + | 1.49986e6i | −0.294058 | + | 0.294058i | ||||
\(483\) | 1.80731e6 | − | 1.80731e6i | 0.352505 | − | 0.352505i | ||||
\(484\) | 2.46463e6 | + | 205262.i | 0.478232 | + | 0.0398286i | ||||
\(485\) | 2.40646e6 | + | 1.59597e6i | 0.464542 | + | 0.308084i | ||||
\(486\) | 3.87691e6i | 0.744552i | ||||||||
\(487\) | −2.14733e6 | + | 2.14733e6i | −0.410277 | + | 0.410277i | −0.881835 | − | 0.471558i | \(-0.843692\pi\) |
0.471558 | + | 0.881835i | \(0.343692\pi\) | |||||||
\(488\) | −4.66292e6 | − | 4.66292e6i | −0.886356 | − | 0.886356i | ||||
\(489\) | − | 4.91419e6i | − | 0.929352i | ||||||
\(490\) | −896739. | − | 594717.i | −0.168724 | − | 0.111897i | ||||
\(491\) | − | 8.67245e6i | − | 1.62345i | −0.584042 | − | 0.811723i | \(-0.698530\pi\) | ||
0.584042 | − | 0.811723i | \(-0.301470\pi\) | |||||||
\(492\) | −189619. | − | 189619.i | −0.0353159 | − | 0.0353159i | ||||
\(493\) | −358922. | − | 358922.i | −0.0665093 | − | 0.0665093i | ||||
\(494\) | −551573. | −0.101692 | ||||||||
\(495\) | 3.29327e6 | + | 2.38680e6i | 0.604108 | + | 0.437828i | ||||
\(496\) | 2.41163e6 | 0.440156 | ||||||||
\(497\) | 3.55213e6 | + | 3.55213e6i | 0.645056 | + | 0.645056i | ||||
\(498\) | −1.86458e6 | − | 1.86458e6i | −0.336904 | − | 0.336904i | ||||
\(499\) | − | 5.93754e6i | − | 1.06747i | −0.845652 | − | 0.533735i | \(-0.820788\pi\) | ||
0.845652 | − | 0.533735i | \(-0.179212\pi\) | |||||||
\(500\) | 2.21500e6 | − | 1.51341e6i | 0.396232 | − | 0.270727i | ||||
\(501\) | 2.18899e6i | 0.389628i | ||||||||
\(502\) | 203876. | + | 203876.i | 0.0361083 | + | 0.0361083i | ||||
\(503\) | 977755. | − | 977755.i | 0.172310 | − | 0.172310i | −0.615684 | − | 0.787993i | \(-0.711120\pi\) |
0.787993 | + | 0.615684i | \(0.211120\pi\) | |||||||
\(504\) | 5.13889e6i | 0.901141i | ||||||||
\(505\) | −8.34895e6 | + | 1.69067e6i | −1.45681 | + | 0.295006i | ||||
\(506\) | 2.67195e6 | − | 2.45868e6i | 0.463930 | − | 0.426899i | ||||
\(507\) | −2.04365e6 | + | 2.04365e6i | −0.353092 | + | 0.353092i | ||||
\(508\) | 2.02643e6 | − | 2.02643e6i | 0.348395 | − | 0.348395i | ||||
\(509\) | 5.91467e6i | 1.01190i | 0.862564 | + | 0.505948i | \(0.168857\pi\) | ||||
−0.862564 | + | 0.505948i | \(0.831143\pi\) | |||||||
\(510\) | 1.58791e6 | + | 1.05310e6i | 0.270334 | + | 0.179286i | ||||
\(511\) | −1.24779e6 | −0.211393 | ||||||||
\(512\) | 2.34067e6 | + | 2.34067e6i | 0.394608 | + | 0.394608i | ||||
\(513\) | −5.50005e6 | + | 5.50005e6i | −0.922728 | + | 0.922728i | ||||
\(514\) | 6.96991e6 | 1.16364 | ||||||||
\(515\) | 3.34237e6 | − | 5.03976e6i | 0.555311 | − | 0.837321i | ||||
\(516\) | − | 1.75640e6i | − | 0.290402i | ||||||
\(517\) | −2.24733e6 | − | 93420.6i | −0.369778 | − | 0.0153715i | ||||
\(518\) | 581447. | + | 581447.i | 0.0952107 | + | 0.0952107i | ||||
\(519\) | 432878. | 0.0705419 | ||||||||
\(520\) | −613223. | + | 124178.i | −0.0994512 | + | 0.0201390i | ||||
\(521\) | −3.44763e6 | −0.556451 | −0.278225 | − | 0.960516i | \(-0.589746\pi\) | ||||
−0.278225 | + | 0.960516i | \(0.589746\pi\) | |||||||
\(522\) | −249592. | + | 249592.i | −0.0400917 | + | 0.0400917i | ||||
\(523\) | 179722. | − | 179722.i | 0.0287308 | − | 0.0287308i | −0.692595 | − | 0.721326i | \(-0.743533\pi\) |
0.721326 | + | 0.692595i | \(0.243533\pi\) | |||||||
\(524\) | −86096.6 | −0.0136980 | ||||||||
\(525\) | −1.40112e6 | − | 3.31768e6i | −0.221860 | − | 0.525335i | ||||
\(526\) | 5.15675e6 | 0.812665 | ||||||||
\(527\) | −6.11158e6 | − | 6.11158e6i | −0.958577 | − | 0.958577i | ||||
\(528\) | 38856.1 | − | 934725.i | 0.00606560 | − | 0.145915i | ||||
\(529\) | − | 1.51763e6i | − | 0.235791i | ||||||
\(530\) | −3.69566e6 | + | 748376.i | −0.571482 | + | 0.115726i | ||||
\(531\) | −431475. | −0.0664079 | ||||||||
\(532\) | −3.71800e6 | + | 3.71800e6i | −0.569549 | + | 0.569549i | ||||
\(533\) | 91067.1 | + | 91067.1i | 0.0138849 | + | 0.0138849i | ||||
\(534\) | −3.50005e6 | −0.531154 | ||||||||
\(535\) | −7.00794e6 | + | 1.05669e7i | −1.05854 | + | 1.59610i | ||||
\(536\) | 8.54514e6i | 1.28472i | ||||||||
\(537\) | −1.85877e6 | + | 1.85877e6i | −0.278156 | + | 0.278156i | ||||
\(538\) | −2.79775e6 | + | 2.79775e6i | −0.416729 | + | 0.416729i | ||||
\(539\) | 1.39333e6 | − | 1.28211e6i | 0.206577 | − | 0.190088i | ||||
\(540\) | −1.58133e6 | + | 2.38440e6i | −0.233367 | + | 0.351880i | ||||
\(541\) | − | 1.06366e7i | − | 1.56247i | −0.624237 | − | 0.781235i | \(-0.714590\pi\) | ||
0.624237 | − | 0.781235i | \(-0.285410\pi\) | |||||||
\(542\) | −3.18306e6 | + | 3.18306e6i | −0.465422 | + | 0.465422i | ||||
\(543\) | 569299. | + | 569299.i | 0.0828592 | + | 0.0828592i | ||||
\(544\) | − | 5.28787e6i | − | 0.766097i | ||||||
\(545\) | −2.55763e6 | − | 1.26302e7i | −0.368847 | − | 1.82146i | ||||
\(546\) | 272373.i | 0.0391005i | ||||||||
\(547\) | 2.27156e6 | + | 2.27156e6i | 0.324606 | + | 0.324606i | 0.850531 | − | 0.525925i | \(-0.176281\pi\) |
−0.525925 | + | 0.850531i | \(0.676281\pi\) | |||||||
\(548\) | 786465. | + | 786465.i | 0.111874 | + | 0.111874i | ||||
\(549\) | 6.18819e6 | 0.876260 | ||||||||
\(550\) | −1.79301e6 | − | 4.79182e6i | −0.252741 | − | 0.675451i | ||||
\(551\) | −1.11376e6 | −0.156283 | ||||||||
\(552\) | 2.37992e6 | + | 2.37992e6i | 0.332441 | + | 0.332441i | ||||
\(553\) | −1.01046e7 | − | 1.01046e7i | −1.40509 | − | 1.40509i | ||||
\(554\) | − | 982178.i | − | 0.135962i | ||||||
\(555\) | 119730. | + | 591256.i | 0.0164995 | + | 0.0814785i | ||||
\(556\) | − | 447906.i | − | 0.0614469i | ||||||
\(557\) | −3.46671e6 | − | 3.46671e6i | −0.473456 | − | 0.473456i | 0.429575 | − | 0.903031i | \(-0.358663\pi\) |
−0.903031 | + | 0.429575i | \(0.858663\pi\) | |||||||
\(558\) | −4.24996e6 | + | 4.24996e6i | −0.577829 | + | 0.577829i | ||||
\(559\) | 843535.i | 0.114176i | ||||||||
\(560\) | 1.34529e6 | − | 2.02848e6i | 0.181278 | − | 0.273338i | ||||
\(561\) | −2.46726e6 | + | 2.27032e6i | −0.330984 | + | 0.304565i | ||||
\(562\) | −43052.2 | + | 43052.2i | −0.00574983 | + | 0.00574983i | ||||
\(563\) | −3.54634e6 | + | 3.54634e6i | −0.471530 | + | 0.471530i | −0.902409 | − | 0.430880i | \(-0.858203\pi\) |
0.430880 | + | 0.902409i | \(0.358203\pi\) | |||||||
\(564\) | − | 676082.i | − | 0.0894956i | ||||||
\(565\) | 5.13270e6 | − | 7.73929e6i | 0.676433 | − | 1.01995i | ||||
\(566\) | −381365. | −0.0500379 | ||||||||
\(567\) | −1.85445e6 | − | 1.85445e6i | −0.242247 | − | 0.242247i | ||||
\(568\) | −4.67754e6 | + | 4.67754e6i | −0.608340 | + | 0.608340i | ||||
\(569\) | 3.69527e6 | 0.478482 | 0.239241 | − | 0.970960i | \(-0.423101\pi\) | ||||
0.239241 | + | 0.970960i | \(0.423101\pi\) | |||||||
\(570\) | 4.09763e6 | − | 829774.i | 0.528257 | − | 0.106973i | ||||
\(571\) | 57926.4i | 0.00743509i | 0.999993 | + | 0.00371754i | \(0.00118333\pi\) | ||||
−0.999993 | + | 0.00371754i | \(0.998817\pi\) | |||||||
\(572\) | 14828.2 | − | 356709.i | 0.00189496 | − | 0.0455853i | ||||
\(573\) | 3.14362e6 | + | 3.14362e6i | 0.399985 | + | 0.399985i | ||||
\(574\) | −1.33062e6 | −0.168568 | ||||||||
\(575\) | 6.42126e6 | + | 2.60801e6i | 0.809935 | + | 0.328958i | ||||
\(576\) | −5.39891e6 | −0.678032 | ||||||||
\(577\) | −4.07236e6 | + | 4.07236e6i | −0.509222 | + | 0.509222i | −0.914288 | − | 0.405066i | \(-0.867249\pi\) |
0.405066 | + | 0.914288i | \(0.367249\pi\) | |||||||
\(578\) | −832467. | + | 832467.i | −0.103645 | + | 0.103645i | ||||
\(579\) | 4.05278e6 | 0.502408 | ||||||||
\(580\) | −401529. | + | 81310.2i | −0.0495618 | + | 0.0100363i | ||||
\(581\) | 1.20725e7 | 1.48373 | ||||||||
\(582\) | 1.17049e6 | + | 1.17049e6i | 0.143239 | + | 0.143239i | ||||
\(583\) | 275583. | − | 6.62945e6i | 0.0335800 | − | 0.807804i | ||||
\(584\) | − | 1.64313e6i | − | 0.199361i | ||||||
\(585\) | 324507. | − | 489305.i | 0.0392044 | − | 0.0591140i | ||||
\(586\) | −9.22622e6 | −1.10989 | ||||||||
\(587\) | 9.28769e6 | − | 9.28769e6i | 1.11253 | − | 1.11253i | 0.119725 | − | 0.992807i | \(-0.461799\pi\) |
0.992807 | − | 0.119725i | \(-0.0382013\pi\) | |||||||
\(588\) | 402437. | + | 402437.i | 0.0480014 | + | 0.0480014i | ||||
\(589\) | −1.89646e7 | −2.25246 | ||||||||
\(590\) | 452329. | + | 299985.i | 0.0534964 | + | 0.0354788i | ||||
\(591\) | 2.61767e6i | 0.308280i | ||||||||
\(592\) | −288298. | + | 288298.i | −0.0338094 | + | 0.0338094i | ||||
\(593\) | −8.14113e6 | + | 8.14113e6i | −0.950710 | + | 0.950710i | −0.998841 | − | 0.0481307i | \(-0.984674\pi\) |
0.0481307 | + | 0.998841i | \(0.484674\pi\) | |||||||
\(594\) | 3.69484e6 | + | 4.01535e6i | 0.429665 | + | 0.466936i | ||||
\(595\) | −8.54982e6 | + | 1.73135e6i | −0.990067 | + | 0.200490i | ||||
\(596\) | 4.81439e6i | 0.555169i | ||||||||
\(597\) | 4.26243e6 | − | 4.26243e6i | 0.489465 | − | 0.489465i | ||||
\(598\) | −370640. | − | 370640.i | −0.0423837 | − | 0.0423837i | ||||
\(599\) | 9.35621e6i | 1.06545i | 0.846288 | + | 0.532725i | \(0.178832\pi\) | ||||
−0.846288 | + | 0.532725i | \(0.821168\pi\) | |||||||
\(600\) | 4.36881e6 | − | 1.84504e6i | 0.495433 | − | 0.209232i | ||||
\(601\) | − | 3.08695e6i | − | 0.348612i | −0.984692 | − | 0.174306i | \(-0.944232\pi\) | ||
0.984692 | − | 0.174306i | \(-0.0557682\pi\) | |||||||
\(602\) | −6.16265e6 | − | 6.16265e6i | −0.693068 | − | 0.693068i | ||||
\(603\) | −5.67016e6 | − | 5.67016e6i | −0.635042 | − | 0.635042i | ||||
\(604\) | 2.67047e6 | 0.297848 | ||||||||
\(605\) | 8.94178e6 | − | 1.04834e6i | 0.993197 | − | 0.116443i | ||||
\(606\) | −4.88322e6 | −0.540162 | ||||||||
\(607\) | 8.54411e6 | + | 8.54411e6i | 0.941229 | + | 0.941229i | 0.998366 | − | 0.0571376i | \(-0.0181974\pi\) |
−0.0571376 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(608\) | −8.20431e6 | − | 8.20431e6i | −0.900084 | − | 0.900084i | ||||
\(609\) | 549986.i | 0.0600908i | ||||||||
\(610\) | −6.48728e6 | − | 4.30236e6i | −0.705892 | − | 0.468147i | ||||
\(611\) | 324697.i | 0.0351864i | ||||||||
\(612\) | 2.09389e6 | + | 2.09389e6i | 0.225983 | + | 0.225983i | ||||
\(613\) | −795336. | + | 795336.i | −0.0854868 | + | 0.0854868i | −0.748557 | − | 0.663070i | \(-0.769253\pi\) |
0.663070 | + | 0.748557i | \(0.269253\pi\) | |||||||
\(614\) | 5.93673e6i | 0.635516i | ||||||||
\(615\) | −813536. | − | 539537.i | −0.0867339 | − | 0.0575219i | ||||
\(616\) | 7.70243e6 | + | 8.37058e6i | 0.817855 | + | 0.888800i | ||||
\(617\) | 8.54656e6 | − | 8.54656e6i | 0.903813 | − | 0.903813i | −0.0919506 | − | 0.995764i | \(-0.529310\pi\) |
0.995764 | + | 0.0919506i | \(0.0293102\pi\) | |||||||
\(618\) | 2.45131e6 | − | 2.45131e6i | 0.258183 | − | 0.258183i | ||||
\(619\) | 1.12492e7i | 1.18003i | 0.807392 | + | 0.590016i | \(0.200879\pi\) | ||||
−0.807392 | + | 0.590016i | \(0.799121\pi\) | |||||||
\(620\) | −6.83709e6 | + | 1.38452e6i | −0.714318 | + | 0.144650i | ||||
\(621\) | −7.39172e6 | −0.769160 | ||||||||
\(622\) | 5.66297e6 | + | 5.66297e6i | 0.586905 | + | 0.586905i | ||||
\(623\) | 1.13308e7 | − | 1.13308e7i | 1.16961 | − | 1.16961i | ||||
\(624\) | −135050. | −0.0138846 | ||||||||
\(625\) | 6.80940e6 | − | 6.99997e6i | 0.697282 | − | 0.716797i | ||||
\(626\) | − | 8.14718e6i | − | 0.830944i | ||||||
\(627\) | −305557. | + | 7.35051e6i | −0.0310402 | + | 0.746704i | ||||
\(628\) | 2.47806e6 | + | 2.47806e6i | 0.250734 | + | 0.250734i | ||||
\(629\) | 1.46121e6 | 0.147261 | ||||||||
\(630\) | 1.20397e6 | + | 5.94550e6i | 0.120855 | + | 0.596811i | ||||
\(631\) | 1.09646e7 | 1.09628 | 0.548139 | − | 0.836387i | \(-0.315337\pi\) | ||||
0.548139 | + | 0.836387i | \(0.315337\pi\) | |||||||
\(632\) | 1.33060e7 | − | 1.33060e7i | 1.32512 | − | 1.32512i | ||||
\(633\) | −1.21182e6 | + | 1.21182e6i | −0.120207 | + | 0.120207i | ||||
\(634\) | 3.04276e6 | 0.300639 | ||||||||
\(635\) | 5.76593e6 | − | 8.69410e6i | 0.567460 | − | 0.855639i | ||||
\(636\) | 1.99439e6 | 0.195509 | ||||||||
\(637\) | −193275. | − | 193275.i | −0.0188724 | − | 0.0188724i | ||||
\(638\) | −32451.5 | + | 780655.i | −0.00315633 | + | 0.0759290i | ||||
\(639\) | − | 6.20760e6i | − | 0.601411i | ||||||
\(640\) | −1.75178e6 | − | 1.16178e6i | −0.169056 | − | 0.112118i | ||||
\(641\) | 1.14621e7 | 1.10184 | 0.550922 | − | 0.834557i | \(-0.314276\pi\) | ||||
0.550922 | + | 0.834557i | \(0.314276\pi\) | |||||||
\(642\) | −5.13966e6 | + | 5.13966e6i | −0.492149 | + | 0.492149i | ||||
\(643\) | 1.26161e7 | + | 1.26161e7i | 1.20337 | + | 1.20337i | 0.973135 | + | 0.230235i | \(0.0739496\pi\) |
0.230235 | + | 0.973135i | \(0.426050\pi\) | |||||||
\(644\) | −4.99676e6 | −0.474760 | ||||||||
\(645\) | −1.26900e6 | − | 6.26661e6i | −0.120105 | − | 0.593108i | ||||
\(646\) | − | 1.01268e7i | − | 0.954749i | ||||||
\(647\) | −1.04760e7 | + | 1.04760e7i | −0.983863 | + | 0.983863i | −0.999872 | − | 0.0160092i | \(-0.994904\pi\) |
0.0160092 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(648\) | 2.44200e6 | − | 2.44200e6i | 0.228459 | − | 0.228459i | ||||
\(649\) | −702817. | + | 646718.i | −0.0654984 | + | 0.0602703i | ||||
\(650\) | −680383. | + | 287340.i | −0.0631640 | + | 0.0266755i | ||||
\(651\) | 9.36495e6i | 0.866070i | ||||||||
\(652\) | −6.79326e6 | + | 6.79326e6i | −0.625834 | + | 0.625834i | ||||
\(653\) | 7.16606e6 | + | 7.16606e6i | 0.657654 | + | 0.657654i | 0.954824 | − | 0.297170i | \(-0.0960429\pi\) |
−0.297170 | + | 0.954824i | \(0.596043\pi\) | |||||||
\(654\) | − | 7.38728e6i | − | 0.675367i | ||||||
\(655\) | −307181. | + | 62204.5i | −0.0279764 | + | 0.00566524i | ||||
\(656\) | − | 659761.i | − | 0.0598587i | ||||||
\(657\) | 1.09031e6 | + | 1.09031e6i | 0.0985451 | + | 0.0985451i | ||||
\(658\) | −2.37215e6 | − | 2.37215e6i | −0.213588 | − | 0.213588i | ||||
\(659\) | 3.23080e6 | 0.289799 | 0.144900 | − | 0.989446i | \(-0.453714\pi\) | ||||
0.144900 | + | 0.989446i | \(0.453714\pi\) | |||||||
\(660\) | 426467. | + | 2.67229e6i | 0.0381088 | + | 0.238795i | ||||
\(661\) | −933367. | −0.0830900 | −0.0415450 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415450 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(662\) | −299046. | − | 299046.i | −0.0265212 | − | 0.0265212i | ||||
\(663\) | 342245. | + | 342245.i | 0.0302380 | + | 0.0302380i | ||||
\(664\) | 1.58973e7i | 1.39928i | ||||||||
\(665\) | −1.05791e7 | + | 1.59516e7i | −0.927672 | + | 1.39878i | ||||
\(666\) | − | 1.01612e6i | − | 0.0887687i | ||||||
\(667\) | −748410. | − | 748410.i | −0.0651366 | − | 0.0651366i | ||||
\(668\) | 3.02601e6 | − | 3.02601e6i | 0.262379 | − | 0.262379i | ||||
\(669\) | 384971.i | 0.0332554i | ||||||||
\(670\) | 2.00201e6 | + | 9.88641e6i | 0.172298 | + | 0.850847i | ||||
\(671\) | 1.00798e7 | − | 9.27519e6i | 0.864260 | − | 0.795274i | ||||
\(672\) | −4.05138e6 | + | 4.05138e6i | −0.346082 | + | 0.346082i | ||||
\(673\) | 1.28117e6 | − | 1.28117e6i | 0.109036 | − | 0.109036i | −0.650484 | − | 0.759520i | \(-0.725434\pi\) |
0.759520 | + | 0.650484i | \(0.225434\pi\) | |||||||
\(674\) | − | 8.52086e6i | − | 0.722493i | ||||||
\(675\) | −3.91926e6 | + | 9.64972e6i | −0.331089 | + | 0.815183i | ||||
\(676\) | 5.65019e6 | 0.475550 | ||||||||
\(677\) | −9.10030e6 | − | 9.10030e6i | −0.763105 | − | 0.763105i | 0.213778 | − | 0.976882i | \(-0.431423\pi\) |
−0.976882 | + | 0.213778i | \(0.931423\pi\) | |||||||
\(678\) | 3.76435e6 | − | 3.76435e6i | 0.314496 | − | 0.314496i | ||||
\(679\) | −7.57851e6 | −0.630825 | ||||||||
\(680\) | −2.27989e6 | − | 1.12586e7i | −0.189078 | − | 0.933714i | ||||
\(681\) | − | 1.51551e6i | − | 0.125225i | ||||||
\(682\) | −552571. | + | 1.32927e7i | −0.0454912 | + | 1.09434i | ||||
\(683\) | −2.56185e6 | − | 2.56185e6i | −0.210136 | − | 0.210136i | 0.594189 | − | 0.804325i | \(-0.297473\pi\) |
−0.804325 | + | 0.594189i | \(0.797473\pi\) | |||||||
\(684\) | 6.49748e6 | 0.531012 | ||||||||
\(685\) | 3.37422e6 | + | 2.23778e6i | 0.274756 | + | 0.182218i | ||||
\(686\) | −7.23571e6 | −0.587044 | ||||||||
\(687\) | 3.23393e6 | − | 3.23393e6i | 0.261420 | − | 0.261420i | ||||
\(688\) | 3.05561e6 | − | 3.05561e6i | 0.246109 | − | 0.246109i | ||||
\(689\) | −957829. | −0.0768670 | ||||||||
\(690\) | 3.31106e6 | + | 2.19589e6i | 0.264755 | + | 0.175585i | ||||
\(691\) | −1.42077e7 | −1.13195 | −0.565977 | − | 0.824421i | \(-0.691501\pi\) | ||||
−0.565977 | + | 0.824421i | \(0.691501\pi\) | |||||||
\(692\) | −598399. | − | 598399.i | −0.0475035 | − | 0.0475035i | ||||
\(693\) | −1.06653e7 | − | 443352.i | −0.843608 | − | 0.0350684i | ||||
\(694\) | − | 7.82089e6i | − | 0.616393i | ||||||
\(695\) | −323611. | − | 1.59807e6i | −0.0254133 | − | 0.125497i | ||||
\(696\) | −724237. | −0.0566705 | ||||||||
\(697\) | −1.67197e6 | + | 1.67197e6i | −0.130361 | + | 0.130361i | ||||
\(698\) | 1.12240e7 | + | 1.12240e7i | 0.871985 | + | 0.871985i | ||||
\(699\) | 3.14868e6 | 0.243745 | ||||||||
\(700\) | −2.64940e6 | + | 6.52315e6i | −0.204363 | + | 0.503167i | ||||
\(701\) | 5.09542e6i | 0.391638i | 0.980640 | + | 0.195819i | \(0.0627365\pi\) | ||||
−0.980640 | + | 0.195819i | \(0.937264\pi\) | |||||||
\(702\) | 556989. | − | 556989.i | 0.0426583 | − | 0.0426583i | ||||
\(703\) | 2.26712e6 | − | 2.26712e6i | 0.173016 | − | 0.173016i | ||||
\(704\) | −8.79413e6 | + | 8.09217e6i | −0.668746 | + | 0.615366i | ||||
\(705\) | −488467. | − | 2.41217e6i | −0.0370137 | − | 0.182783i | ||||
\(706\) | − | 1.24039e7i | − | 0.936585i | ||||||
\(707\) | 1.58085e7 | − | 1.58085e7i | 1.18944 | − | 1.18944i | ||||
\(708\) | −202995. | − | 202995.i | −0.0152196 | − | 0.0152196i | ||||
\(709\) | − | 1.06450e7i | − | 0.795298i | −0.917538 | − | 0.397649i | \(-0.869826\pi\) | ||
0.917538 | − | 0.397649i | \(-0.130174\pi\) | |||||||
\(710\) | −4.31586e6 | + | 6.50762e6i | −0.321308 | + | 0.484481i | ||||
\(711\) | 1.76584e7i | 1.31002i | ||||||||
\(712\) | 1.49207e7 | + | 1.49207e7i | 1.10303 | + | 1.10303i | ||||
\(713\) | −1.27436e7 | − | 1.27436e7i | −0.938793 | − | 0.938793i | ||||
\(714\) | −5.00071e6 | −0.367101 | ||||||||
\(715\) | −204816. | − | 1.28340e6i | −0.0149830 | − | 0.0938855i | ||||
\(716\) | 5.13902e6 | 0.374626 | ||||||||
\(717\) | −8.82685e6 | − | 8.82685e6i | −0.641221 | − | 0.641221i | ||||
\(718\) | 6.83355e6 | + | 6.83355e6i | 0.494692 | + | 0.494692i | ||||
\(719\) | − | 1.91481e6i | − | 0.138135i | −0.997612 | − | 0.0690675i | \(-0.977998\pi\) | ||
0.997612 | − | 0.0690675i | \(-0.0220024\pi\) | |||||||
\(720\) | −2.94795e6 | + | 596963.i | −0.211928 | + | 0.0429157i | ||||
\(721\) | 1.58714e7i | 1.13704i | ||||||||
\(722\) | −8.56909e6 | − | 8.56909e6i | −0.611775 | − | 0.611775i | ||||
\(723\) | 2.88786e6 | − | 2.88786e6i | 0.205462 | − | 0.205462i | ||||
\(724\) | − | 1.57397e6i | − | 0.111596i | ||||||
\(725\) | −1.37386e6 | + | 580207.i | −0.0970725 | + | 0.0409957i | ||||
\(726\) | 5.14322e6 | + | 428343.i | 0.362154 | + | 0.0301613i | ||||
\(727\) | 2.86558e6 | − | 2.86558e6i | 0.201084 | − | 0.201084i | −0.599380 | − | 0.800464i | \(-0.704586\pi\) |
0.800464 | + | 0.599380i | \(0.204586\pi\) | |||||||
\(728\) | 1.16112e6 | − | 1.16112e6i | 0.0811989 | − | 0.0811989i | ||||
\(729\) | − | 3.12094e6i | − | 0.217504i | ||||||
\(730\) | −384963. | − | 1.90104e6i | −0.0267370 | − | 0.132034i | ||||
\(731\) | −1.54871e7 | −1.07196 | ||||||||
\(732\) | 2.91135e6 | + | 2.91135e6i | 0.200824 | + | 0.200824i | ||||
\(733\) | −3.71404e6 | + | 3.71404e6i | −0.255321 | + | 0.255321i | −0.823148 | − | 0.567827i | \(-0.807784\pi\) |
0.567827 | + | 0.823148i | \(0.307784\pi\) | |||||||
\(734\) | −1.41972e7 | −0.972664 | ||||||||
\(735\) | 1.72660e6 | + | 1.14508e6i | 0.117889 | + | 0.0781840i | ||||
\(736\) | − | 1.10261e7i | − | 0.750285i | ||||||
\(737\) | −1.77347e7 | − | 737223.i | −1.20269 | − | 0.0499954i | ||||
\(738\) | 1.16268e6 | + | 1.16268e6i | 0.0785814 | + | 0.0785814i | ||||
\(739\) | −361202. | −0.0243298 | −0.0121649 | − | 0.999926i | \(-0.503872\pi\) | ||||
−0.0121649 | + | 0.999926i | \(0.503872\pi\) | |||||||
\(740\) | 651826. | − | 982849.i | 0.0437575 | − | 0.0659793i | ||||
\(741\) | 1.06201e6 | 0.0710531 | ||||||||
\(742\) | 6.99765e6 | − | 6.99765e6i | 0.466597 | − | 0.466597i | ||||
\(743\) | 1.41219e7 | − | 1.41219e7i | 0.938471 | − | 0.938471i | −0.0597430 | − | 0.998214i | \(-0.519028\pi\) |
0.998214 | + | 0.0597430i | \(0.0190281\pi\) | |||||||
\(744\) | −1.23320e7 | −0.816774 | ||||||||
\(745\) | 3.47838e6 | + | 1.71771e7i | 0.229608 | + | 1.13386i | ||||
\(746\) | −1.27540e7 | −0.839073 | ||||||||
\(747\) | −1.05487e7 | − | 1.05487e7i | −0.691671 | − | 0.691671i | ||||
\(748\) | 6.54911e6 | + | 272243.i | 0.427985 | + | 0.0177911i | ||||
\(749\) | − | 3.32775e7i | − | 2.16743i | ||||||
\(750\) | 4.62229e6 | − | 3.15819e6i | 0.300057 | − | 0.205015i | ||||
\(751\) | 1.69707e7 | 1.09800 | 0.548998 | − | 0.835824i | \(-0.315009\pi\) | ||||
0.548998 | + | 0.835824i | \(0.315009\pi\) | |||||||
\(752\) | 1.17618e6 | − | 1.17618e6i | 0.0758453 | − | 0.0758453i | ||||
\(753\) | −392547. | − | 392547.i | −0.0252293 | − | 0.0252293i | ||||
\(754\) | 112790. | 0.00722507 | ||||||||
\(755\) | 9.52787e6 | − | 1.92941e6i | 0.608315 | − | 0.123184i | ||||
\(756\) | − | 7.50902e6i | − | 0.477836i | ||||||
\(757\) | 8.98692e6 | − | 8.98692e6i | 0.569995 | − | 0.569995i | −0.362132 | − | 0.932127i | \(-0.617951\pi\) |
0.932127 | + | 0.362132i | \(0.117951\pi\) | |||||||
\(758\) | −4.36780e6 | + | 4.36780e6i | −0.276115 | + | 0.276115i | ||||
\(759\) | −5.14464e6 | + | 4.73399e6i | −0.324153 | + | 0.298279i | ||||
\(760\) | −2.10055e7 | − | 1.39308e7i | −1.31916 | − | 0.874870i | ||||
\(761\) | 2.69339e7i | 1.68592i | 0.537973 | + | 0.842962i | \(0.319190\pi\) | ||||
−0.537973 | + | 0.842962i | \(0.680810\pi\) | |||||||
\(762\) | 4.22877e6 | − | 4.22877e6i | 0.263831 | − | 0.263831i | ||||
\(763\) | 2.39150e7 | + | 2.39150e7i | 1.48716 | + | 1.48716i | ||||
\(764\) | − | 8.69133e6i | − | 0.538707i | ||||||
\(765\) | 8.98354e6 | + | 5.95789e6i | 0.555001 | + | 0.368077i | ||||
\(766\) | 7.78218e6i | 0.479214i | ||||||||
\(767\) | 97491.2 | + | 97491.2i | 0.00598380 | + | 0.00598380i | ||||
\(768\) | −6.14500e6 | − | 6.14500e6i | −0.375940 | − | 0.375940i | ||||
\(769\) | −202443. | −0.0123449 | −0.00617243 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617243 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(770\) | 1.08725e7 | + | 7.87988e6i | 0.660852 | + | 0.478953i | ||||
\(771\) | −1.34200e7 | −0.813049 | ||||||||
\(772\) | −5.60246e6 | − | 5.60246e6i | −0.338326 | − | 0.338326i | ||||
\(773\) | −1.15495e7 | − | 1.15495e7i | −0.695208 | − | 0.695208i | 0.268165 | − | 0.963373i | \(-0.413583\pi\) |
−0.963373 | + | 0.268165i | \(0.913583\pi\) | |||||||
\(774\) | 1.07697e7i | 0.646175i | ||||||||
\(775\) | −2.33935e7 | + | 9.87955e6i | −1.39907 | + | 0.590858i | ||||
\(776\) | − | 9.97959e6i | − | 0.594920i | ||||||
\(777\) | −1.11953e6 | − | 1.11953e6i | −0.0665247 | − | 0.0665247i | ||||
\(778\) | −4.65711e6 | + | 4.65711e6i | −0.275847 | + | 0.275847i | ||||
\(779\) | 5.18825e6i | 0.306321i | ||||||||
\(780\) | 382873. | − | 77532.3i | 0.0225330 | − | 0.00456295i | ||||
\(781\) | −9.30427e6 | − | 1.01114e7i | −0.545827 | − | 0.593175i | ||||
\(782\) | 6.80486e6 | − | 6.80486e6i | 0.397926 | − | 0.397926i | ||||
\(783\) | 1.12469e6 | − | 1.12469e6i | 0.0655586 | − | 0.0655586i | ||||
\(784\) | 1.40024e6i | 0.0813601i | ||||||||
\(785\) | 1.06318e7 | + | 7.05099e6i | 0.615789 | + | 0.408391i | ||||
\(786\) | −179667. | −0.0103732 | ||||||||
\(787\) | 4.00932e6 | + | 4.00932e6i | 0.230746 | + | 0.230746i | 0.813004 | − | 0.582258i | \(-0.197831\pi\) |
−0.582258 | + | 0.813004i | \(0.697831\pi\) | |||||||
\(788\) | 3.61860e6 | − | 3.61860e6i | 0.207599 | − | 0.207599i | ||||
\(789\) | −9.92891e6 | −0.567818 | ||||||||
\(790\) | 1.22771e7 | − | 1.85119e7i | 0.699887 | − | 1.05532i | ||||
\(791\) | 2.43728e7i | 1.38505i | ||||||||
\(792\) | 583818. | − | 1.40444e7i | 0.0330723 | − | 0.795590i | ||||
\(793\) | −1.39821e6 | − | 1.39821e6i | −0.0789569 | − | 0.0789569i | ||||
\(794\) | 9.42394e6 | 0.530495 | ||||||||
\(795\) | 7.11570e6 | − | 1.44094e6i | 0.399300 | − | 0.0808588i | ||||
\(796\) | −1.17846e7 | −0.659220 | ||||||||
\(797\) | −3.11217e6 | + | 3.11217e6i | −0.173547 | + | 0.173547i | −0.788536 | − | 0.614989i | \(-0.789160\pi\) |
0.614989 | + | 0.788536i | \(0.289160\pi\) | |||||||
\(798\) | −7.75876e6 | + | 7.75876e6i | −0.431306 | + | 0.431306i | ||||
\(799\) | −5.96137e6 | −0.330354 | ||||||||
\(800\) | −1.43943e7 | − | 5.84628e6i | −0.795179 | − | 0.322964i | ||||
\(801\) | −1.98014e7 | −1.09047 | ||||||||
\(802\) | 9.79080e6 | + | 9.79080e6i | 0.537505 | + | 0.537505i | ||||
\(803\) | 3.41018e6 | + | 141759.i | 0.186633 | + | 0.00775824i | ||||
\(804\) | − | 5.33526e6i | − | 0.291082i | ||||||
\(805\) | −1.78278e7 | + | 3.61015e6i | −0.969633 | + | 0.196352i | ||||
\(806\) | 1.92054e6 | 0.104133 | ||||||||
\(807\) | 5.38685e6 | − | 5.38685e6i | 0.291173 | − | 0.291173i | ||||
\(808\) | 2.08171e7 | + | 2.08171e7i | 1.12174 | + | 1.12174i | ||||
\(809\) | 3.41033e7 | 1.83200 | 0.915998 | − | 0.401182i | \(-0.131400\pi\) | ||||
0.915998 | + | 0.401182i | \(0.131400\pi\) | |||||||
\(810\) | 2.25317e6 | − | 3.39743e6i | 0.120665 | − | 0.181944i | ||||
\(811\) | − | 1.41485e7i | − | 0.755367i | −0.925935 | − | 0.377683i | \(-0.876721\pi\) | ||
0.925935 | − | 0.377683i | \(-0.123279\pi\) | |||||||
\(812\) | 760286. | − | 760286.i | 0.0404657 | − | 0.0404657i | ||||
\(813\) | 6.12873e6 | − | 6.12873e6i | 0.325195 | − | 0.325195i | ||||
\(814\) | −1.52302e6 | − | 1.65513e6i | −0.0805644 | − | 0.0875530i | ||||
\(815\) | −1.93293e7 | + | 2.91455e7i | −1.01935 | + | 1.53701i | ||||
\(816\) | − | 2.47949e6i | − | 0.130358i | ||||||
\(817\) | −2.40288e7 | + | 2.40288e7i | −1.25944 | + | 1.25944i | ||||
\(818\) | 1.28887e7 | + | 1.28887e7i | 0.673483 | + | 0.673483i | ||||
\(819\) | 1.54094e6i | 0.0802740i | ||||||||
\(820\) | 378769. | + | 1.87045e6i | 0.0196716 | + | 0.0971432i | ||||
\(821\) | − | 426503.i | − | 0.0220833i | −0.999939 | − | 0.0110416i | \(-0.996485\pi\) | ||
0.999939 | − | 0.0110416i | \(-0.00351474\pi\) | |||||||
\(822\) | 1.64120e6 | + | 1.64120e6i | 0.0847193 | + | 0.0847193i | ||||
\(823\) | −1.23191e7 | − | 1.23191e7i | −0.633985 | − | 0.633985i | 0.315080 | − | 0.949065i | \(-0.397969\pi\) |
−0.949065 | + | 0.315080i | \(0.897969\pi\) | |||||||
\(824\) | −2.08999e7 | −1.07232 | ||||||||
\(825\) | 3.45230e6 | + | 9.22627e6i | 0.176593 | + | 0.471945i | ||||
\(826\) | −1.42449e6 | −0.0726456 | ||||||||
\(827\) | −2.45123e7 | − | 2.45123e7i | −1.24630 | − | 1.24630i | −0.957344 | − | 0.288951i | \(-0.906693\pi\) |
−0.288951 | − | 0.957344i | \(-0.593307\pi\) | |||||||
\(828\) | 4.36610e6 | + | 4.36610e6i | 0.221319 | + | 0.221319i | ||||
\(829\) | 3.31255e6i | 0.167408i | 0.996491 | + | 0.0837039i | \(0.0266750\pi\) | ||||
−0.996491 | + | 0.0837039i | \(0.973325\pi\) | |||||||
\(830\) | 3.72453e6 | + | 1.83926e7i | 0.187662 | + | 0.926721i | ||||
\(831\) | 1.89111e6i | 0.0949978i | ||||||||
\(832\) | 1.21988e6 | + | 1.21988e6i | 0.0610952 | + | 0.0610952i | ||||
\(833\) | 3.54850e6 | − | 3.54850e6i | 0.177187 | − | 0.177187i | ||||
\(834\) | − | 934695.i | − | 0.0465323i | ||||||
\(835\) | 8.61011e6 | − | 1.29827e7i | 0.427359 | − | 0.644389i | ||||
\(836\) | 1.05836e7 | − | 9.73877e6i | 0.523740 | − | 0.481935i | ||||
\(837\) | 1.91509e7 | − | 1.91509e7i | 0.944875 | − | 0.944875i | ||||
\(838\) | 1.01502e7 | − | 1.01502e7i | 0.499305 | − | 0.499305i | ||||
\(839\) | − | 7.51942e6i | − | 0.368790i | −0.982852 | − | 0.184395i | \(-0.940967\pi\) | ||
0.982852 | − | 0.184395i | \(-0.0590326\pi\) | |||||||
\(840\) | −6.87920e6 | + | 1.03727e7i | −0.336387 | + | 0.507219i | ||||
\(841\) | −2.02834e7 | −0.988896 | ||||||||
\(842\) | −1.53285e7 | − | 1.53285e7i | −0.745108 | − | 0.745108i | ||||
\(843\) | 82893.7 | − | 82893.7i | 0.00401747 | − | 0.00401747i | ||||
\(844\) | 3.35039e6 | 0.161897 | ||||||||
\(845\) | 2.01591e7 | − | 4.08225e6i | 0.971247 | − | 0.196679i | ||||
\(846\) | 4.14550e6i | 0.199137i | ||||||||
\(847\) | −1.80369e7 | + | 1.52636e7i | −0.863882 | + | 0.731051i | ||||
\(848\) | 3.46963e6 | + | 3.46963e6i | 0.165689 | + | 0.165689i | ||||
\(849\) | 734287. | 0.0349620 | ||||||||
\(850\) | −5.27549e6 | − | 1.24917e7i | −0.250447 | − | 0.593026i | ||||
\(851\) | 3.04687e6 | 0.144222 | ||||||||
\(852\) | 2.92048e6 | − | 2.92048e6i | 0.137834 | − | 0.137834i | ||||
\(853\) | −4.14004e6 | + | 4.14004e6i | −0.194820 | + | 0.194820i | −0.797775 | − | 0.602955i | \(-0.793990\pi\) |
0.602955 | + | 0.797775i | \(0.293990\pi\) | |||||||
\(854\) | 2.04299e7 | 0.958567 | ||||||||
\(855\) | 2.31821e7 | − | 4.69441e6i | 1.08452 | − | 0.219617i | ||||
\(856\) | 4.38207e7 | 2.04407 | ||||||||
\(857\) | 2.93533e7 | + | 2.93533e7i | 1.36523 | + | 1.36523i | 0.867108 | + | 0.498120i | \(0.165976\pi\) |
0.498120 | + | 0.867108i | \(0.334024\pi\) | |||||||
\(858\) | 30943.7 | − | 744384.i | 0.00143501 | − | 0.0345206i | ||||
\(859\) | − | 3.26018e7i | − | 1.50750i | −0.657160 | − | 0.753751i | \(-0.728242\pi\) | ||
0.657160 | − | 0.753751i | \(-0.271758\pi\) | |||||||
\(860\) | −6.90858e6 | + | 1.04170e7i | −0.318524 | + | 0.480284i | ||||
\(861\) | 2.56201e6 | 0.117780 | ||||||||
\(862\) | −4.54674e6 | + | 4.54674e6i | −0.208417 | + | 0.208417i | ||||
\(863\) | 1.82172e7 | + | 1.82172e7i | 0.832636 | + | 0.832636i | 0.987877 | − | 0.155241i | \(-0.0496153\pi\) |
−0.155241 | + | 0.987877i | \(0.549615\pi\) | |||||||
\(864\) | 1.65697e7 | 0.755146 | ||||||||
\(865\) | −2.56735e6 | − | 1.70267e6i | −0.116666 | − | 0.0773730i | ||||
\(866\) | 1.89981e7i | 0.860825i | ||||||||
\(867\) | 1.60285e6 | − | 1.60285e6i | 0.0724177 | − | 0.0724177i | ||||
\(868\) | 1.29459e7 | − | 1.29459e7i | 0.583219 | − | 0.583219i | ||||
\(869\) | 2.64674e7 | + | 2.87633e7i | 1.18895 | + | 1.29208i | ||||
\(870\) | −837915. | + | 169679.i | −0.0375320 | + | 0.00760028i | ||||
\(871\) | 2.56233e6i | 0.114443i | ||||||||
\(872\) | −3.14919e7 | + | 3.14919e7i | −1.40252 | + | 1.40252i | ||||
\(873\) | 6.62199e6 | + | 6.62199e6i | 0.294072 | + | 0.294072i | ||||
\(874\) | − | 2.11160e7i | − | 0.935044i | ||||||
\(875\) | −4.73974e6 | + | 2.51879e7i | −0.209283 | + | 1.11217i | ||||
\(876\) | 1.02591e6i | 0.0451698i | ||||||||
\(877\) | −2.48426e7 | − | 2.48426e7i | −1.09068 | − | 1.09068i | −0.995456 | − | 0.0952252i | \(-0.969643\pi\) |
−0.0952252 | − | 0.995456i | \(-0.530357\pi\) | |||||||
\(878\) | −1.30159e7 | − | 1.30159e7i | −0.569820 | − | 0.569820i | ||||
\(879\) | 1.77643e7 | 0.775491 | ||||||||
\(880\) | −3.90706e6 | + | 5.39091e6i | −0.170076 | + | 0.234669i | ||||
\(881\) | −2.11393e7 | −0.917597 | −0.458798 | − | 0.888540i | \(-0.651720\pi\) | ||||
−0.458798 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(882\) | −2.46761e6 | − | 2.46761e6i | −0.106808 | − | 0.106808i | ||||
\(883\) | −1.39827e7 | − | 1.39827e7i | −0.603516 | − | 0.603516i | 0.337728 | − | 0.941244i | \(-0.390342\pi\) |
−0.941244 | + | 0.337728i | \(0.890342\pi\) | |||||||
\(884\) | − | 946222.i | − | 0.0407251i | ||||||
\(885\) | −870924. | − | 577597.i | −0.0373785 | − | 0.0247894i | ||||
\(886\) | − | 2.32549e7i | − | 0.995244i | ||||||
\(887\) | 2.11639e7 | + | 2.11639e7i | 0.903205 | + | 0.903205i | 0.995712 | − | 0.0925066i | \(-0.0294879\pi\) |
−0.0925066 | + | 0.995712i | \(0.529488\pi\) | |||||||
\(888\) | 1.47423e6 | − | 1.47423e6i | 0.0627382 | − | 0.0627382i | ||||
\(889\) | 2.73797e7i | 1.16192i | ||||||||
\(890\) | 2.07584e7 | + | 1.37670e7i | 0.878453 | + | 0.582590i | ||||
\(891\) | 4.85747e6 | + | 5.27883e6i | 0.204982 | + | 0.222763i | ||||
\(892\) | 532174. | − | 532174.i | 0.0223945 | − | 0.0223945i | ||||
\(893\) | −9.24927e6 | + | 9.24927e6i | −0.388131 | + | 0.388131i | ||||
\(894\) | 1.00467e7i | 0.420416i | ||||||||
\(895\) | 1.83353e7 | − | 3.71293e6i | 0.765123 | − | 0.154938i | ||||
\(896\) | 5.51677e6 | 0.229570 | ||||||||
\(897\) | 713637. | + | 713637.i | 0.0296139 | + | 0.0296139i | ||||
\(898\) | 2.09306e7 | − | 2.09306e7i | 0.866147 | − | 0.866147i | ||||
\(899\) | 3.87804e6 | 0.160034 | ||||||||
\(900\) | 8.01485e6 | − | 3.38483e6i | 0.329829 | − | 0.139294i | ||||
\(901\) | − | 1.75855e7i | − | 0.721679i | ||||||
\(902\) | 3.63655e6 | + | 151170.i | 0.148824 | + | 0.00618654i | ||||
\(903\) | 1.18657e7 | + | 1.18657e7i | 0.484254 | + | 0.484254i | ||||
\(904\) | −3.20948e7 | −1.30621 | ||||||||
\(905\) | −1.13719e6 | − | 5.61571e6i | −0.0461541 | − | 0.227920i | ||||
\(906\) | 5.57276e6 | 0.225554 | ||||||||
\(907\) | 1.80897e7 | − | 1.80897e7i | 0.730152 | − | 0.730152i | −0.240498 | − | 0.970650i | \(-0.577311\pi\) |
0.970650 | + | 0.240498i | \(0.0773107\pi\) | |||||||
\(908\) | −2.09501e6 | + | 2.09501e6i | −0.0843277 | + | 0.0843277i | ||||
\(909\) | −2.76266e7 | −1.10896 | ||||||||
\(910\) | 1.07134e6 | − | 1.61541e6i | 0.0428869 | − | 0.0646666i | ||||
\(911\) | −5.34182e6 | −0.213252 | −0.106626 | − | 0.994299i | \(-0.534005\pi\) | ||||
−0.106626 | + | 0.994299i | \(0.534005\pi\) | |||||||
\(912\) | −3.84701e6 | − | 3.84701e6i | −0.153157 | − | 0.153157i | ||||
\(913\) | −3.29936e7 | − | 1.37153e6i | −1.30994 | − | 0.0544537i | ||||
\(914\) | − | 1.91715e7i | − | 0.759086i | ||||||
\(915\) | 1.24907e7 | + | 8.28386e6i | 0.493214 | + | 0.327100i | ||||
\(916\) | −8.94101e6 | −0.352085 | ||||||||
\(917\) | 581640. | − | 581640.i | 0.0228418 | − | 0.0228418i | ||||
\(918\) | 1.02262e7 | + | 1.02262e7i | 0.400504 | + | 0.400504i | ||||
\(919\) | −2.14327e6 | −0.0837121 | −0.0418561 | − | 0.999124i | \(-0.513327\pi\) | ||||
−0.0418561 | + | 0.999124i | \(0.513327\pi\) | |||||||
\(920\) | −4.75394e6 | − | 2.34761e7i | −0.185176 | − | 0.914443i | ||||
\(921\) | − | 1.14307e7i | − | 0.444042i | ||||||
\(922\) | −2.15852e6 | + | 2.15852e6i | −0.0836237 | + | 0.0836237i | ||||
\(923\) | −1.40260e6 | + | 1.40260e6i | −0.0541912 | + | 0.0541912i | ||||
\(924\) | −4.80911e6 | − | 5.22627e6i | −0.185304 | − | 0.201378i | ||||
\(925\) | 1.61552e6 | − | 3.97762e6i | 0.0620809 | − | 0.152851i | ||||
\(926\) | − | 2.53756e7i | − | 0.972497i | ||||||
\(927\) | 1.38682e7 | − | 1.38682e7i | 0.530054 | − | 0.530054i | ||||
\(928\) | 1.67768e6 | + | 1.67768e6i | 0.0639498 | + | 0.0639498i | ||||
\(929\) | 1.07564e7i | 0.408909i | 0.978876 | + | 0.204454i | \(0.0655420\pi\) | ||||
−0.978876 | + | 0.204454i | \(0.934458\pi\) | |||||||
\(930\) | −1.42677e7 | + | 2.88922e6i | −0.540937 | + | 0.109540i | ||||
\(931\) | − | 1.10112e7i | − | 0.416353i | ||||||
\(932\) | −4.35266e6 | − | 4.35266e6i | −0.164140 | − | 0.164140i | ||||
\(933\) | −1.09036e7 | − | 1.09036e7i | −0.410077 | − | 0.410077i | ||||
\(934\) | 4.00420e6 | 0.150193 | ||||||||
\(935\) | 2.35630e7 | − | 3.76038e6i | 0.881459 | − | 0.140670i | ||||
\(936\) | −2.02915e6 | −0.0757049 | ||||||||
\(937\) | 2.67520e7 | + | 2.67520e7i | 0.995424 | + | 0.995424i | 0.999990 | − | 0.00456603i | \(-0.00145342\pi\) |
−0.00456603 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(938\) | −1.87197e7 | − | 1.87197e7i | −0.694691 | − | 0.694691i | ||||
\(939\) | 1.56867e7i | 0.580589i | ||||||||
\(940\) | −2.65928e6 | + | 4.00977e6i | −0.0981621 | + | 0.148013i | ||||
\(941\) | 1.84090e7i | 0.677730i | 0.940835 | + | 0.338865i | \(0.110043\pi\) | ||||
−0.940835 | + | 0.338865i | \(0.889957\pi\) | |||||||
\(942\) | 5.17124e6 | + | 5.17124e6i | 0.189875 | + | 0.189875i | ||||
\(943\) | −3.48634e6 | + | 3.48634e6i | −0.127670 | + | 0.127670i | ||||
\(944\) | − | 706302.i | − | 0.0257965i | ||||||
\(945\) | −5.42524e6 | − | 2.67912e7i | −0.197624 | − | 0.975916i | ||||
\(946\) | 1.61421e7 | + | 1.75424e7i | 0.586453 | + | 0.637325i | ||||
\(947\) | 1.48200e7 | − | 1.48200e7i | 0.537000 | − | 0.537000i | −0.385647 | − | 0.922646i | \(-0.626022\pi\) |
0.922646 | + | 0.385647i | \(0.126022\pi\) | |||||||
\(948\) | −8.30774e6 | + | 8.30774e6i | −0.300235 | + | 0.300235i | ||||
\(949\) | − | 492706.i | − | 0.0177592i | ||||||
\(950\) | −2.75664e7 | − | 1.11962e7i | −0.990993 | − | 0.402495i | ||||
\(951\) | −5.85860e6 | −0.210059 | ||||||||
\(952\) | 2.13180e7 | + | 2.13180e7i | 0.762349 | + | 0.762349i | ||||
\(953\) | −2.44828e7 | + | 2.44828e7i | −0.873230 | + | 0.873230i | −0.992823 | − | 0.119593i | \(-0.961841\pi\) |
0.119593 | + | 0.992823i | \(0.461841\pi\) | |||||||
\(954\) | −1.22289e7 | −0.435027 | ||||||||
\(955\) | −6.27946e6 | − | 3.10095e7i | −0.222799 | − | 1.10024i | ||||
\(956\) | 2.44040e7i | 0.863609i | ||||||||
\(957\) | 62482.7 | − | 1.50309e6i | 0.00220536 | − | 0.0530524i | ||||
\(958\) | −1.19097e7 | − | 1.19097e7i | −0.419262 | − | 0.419262i | ||||
\(959\) | −1.06262e7 | −0.373105 | ||||||||
\(960\) | −1.08976e7 | − | 7.22728e6i | −0.381639 | − | 0.253103i | ||||
\(961\) | 3.74046e7 | 1.30652 | ||||||||
\(962\) | −229591. | + | 229591.i | −0.00799866 | + | 0.00799866i | ||||
\(963\) | −2.90774e7 | + | 2.90774e7i | −1.01039 | + | 1.01039i | ||||
\(964\) | −7.98421e6 | −0.276719 | ||||||||
\(965\) | −2.40366e7 | − | 1.59411e7i | −0.830911 | − | 0.551060i | ||||
\(966\) | −1.04273e7 | −0.359525 | ||||||||
\(967\) | −1.53148e7 | − | 1.53148e7i | −0.526679 | − | 0.526679i | 0.392901 | − | 0.919581i | \(-0.371471\pi\) |
−0.919581 | + | 0.392901i | \(0.871471\pi\) | |||||||
\(968\) | −2.00995e7 | − | 2.37515e7i | −0.689440 | − | 0.814710i | ||||
\(969\) | 1.94983e7i | 0.667094i | ||||||||
\(970\) | −2.33808e6 | − | 1.15460e7i | −0.0797867 | − | 0.394006i | ||||
\(971\) | 2.59371e7 | 0.882823 | 0.441412 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441412 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(972\) | −1.03190e7 | + | 1.03190e7i | −0.350325 | + | 0.350325i | ||||
\(973\) | 3.02591e6 | + | 3.02591e6i | 0.102465 | + | 0.102465i | ||||
\(974\) | 1.23891e7 | 0.418447 | ||||||||
\(975\) | 1.31002e6 | − | 553249.i | 0.0441334 | − | 0.0186384i | ||||
\(976\) | 1.01297e7i | 0.340388i | ||||||||
\(977\) | −2.89552e7 | + | 2.89552e7i | −0.970488 | + | 0.970488i | −0.999577 | − | 0.0290887i | \(-0.990739\pi\) |
0.0290887 | + | 0.999577i | \(0.490739\pi\) | |||||||
\(978\) | −1.41762e7 | + | 1.41762e7i | −0.473929 | + | 0.473929i | ||||
\(979\) | −3.22538e7 | + | 2.96793e7i | −1.07554 | + | 0.989685i | ||||
\(980\) | −803877. | − | 3.96974e6i | −0.0267377 | − | 0.132037i | ||||
\(981\) | − | 4.17932e7i | − | 1.38654i | ||||||
\(982\) | −2.50179e7 | + | 2.50179e7i | −0.827888 | + | 0.827888i | ||||
\(983\) | −3.40565e7 | − | 3.40565e7i | −1.12413 | − | 1.12413i | −0.991114 | − | 0.133014i | \(-0.957535\pi\) |
−0.133014 | − | 0.991114i | \(-0.542465\pi\) | |||||||
\(984\) | 3.37373e6i | 0.111077i | ||||||||
\(985\) | 1.02962e7 | − | 1.55251e7i | 0.338133 | − | 0.509851i | ||||
\(986\) | 2.07080e6i | 0.0678337i | ||||||||
\(987\) | 4.56739e6 | + | 4.56739e6i | 0.149236 | + | 0.149236i | ||||
\(988\) | −1.46810e6 | − | 1.46810e6i | −0.0478478 | − | 0.0478478i | ||||
\(989\) | −3.22932e7 | −1.04983 | ||||||||
\(990\) | −2.61495e6 | − | 1.63856e7i | −0.0847960 | − | 0.531342i | ||||
\(991\) | −1.26497e7 | −0.409162 | −0.204581 | − | 0.978850i | \(-0.565583\pi\) | ||||
−0.204581 | + | 0.978850i | \(0.565583\pi\) | |||||||
\(992\) | 2.85669e7 | + | 2.85669e7i | 0.921688 | + | 0.921688i | ||||
\(993\) | 575789. | + | 575789.i | 0.0185306 | + | 0.0185306i | ||||
\(994\) | − | 2.04940e7i | − | 0.657902i | ||||||
\(995\) | −4.20457e7 | + | 8.51430e6i | −1.34637 | + | 0.272641i | ||||
\(996\) | − | 9.92570e6i | − | 0.317039i | ||||||
\(997\) | 1.08845e7 | + | 1.08845e7i | 0.346793 | + | 0.346793i | 0.858913 | − | 0.512121i | \(-0.171140\pi\) |
−0.512121 | + | 0.858913i | \(0.671140\pi\) | |||||||
\(998\) | −1.71283e7 | + | 1.71283e7i | −0.544363 | + | 0.544363i | ||||
\(999\) | 4.57877e6i | 0.145156i |
(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 | 55.6.e.b.43.10 | yes | 52 | |
5.2 | odd | 4 | inner | 55.6.e.b.32.17 | yes | 52 | |
11.10 | odd | 2 | inner | 55.6.e.b.43.17 | yes | 52 | |
55.32 | even | 4 | inner | 55.6.e.b.32.10 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.6.e.b.32.10 | ✓ | 52 | 55.32 | even | 4 | inner | |
55.6.e.b.32.17 | yes | 52 | 5.2 | odd | 4 | inner | |
55.6.e.b.43.10 | yes | 52 | 1.1 | even | 1 | trivial | |
55.6.e.b.43.17 | yes | 52 | 11.10 | odd | 2 | inner |