Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.3 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.76 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.49534i | − | 1.87384i | −0.349550 | − | 0.936918i | \(-0.613666\pi\) | ||
0.349550 | − | 0.936918i | \(-0.386334\pi\) | |||||||
\(3\) | −6.13251 | + | 6.58728i | −0.681390 | + | 0.731920i | ||||
\(4\) | −40.1801 | −2.51126 | ||||||||
\(5\) | − | 24.9668i | − | 0.998670i | −0.866409 | − | 0.499335i | \(-0.833578\pi\) | ||
0.866409 | − | 0.499335i | \(-0.166422\pi\) | |||||||
\(6\) | 49.3739 | + | 45.9653i | 1.37150 | + | 1.27681i | ||||
\(7\) | −52.3496 | −1.06836 | −0.534179 | − | 0.845371i | \(-0.679379\pi\) | ||||
−0.534179 | + | 0.845371i | \(0.679379\pi\) | |||||||
\(8\) | 181.238i | 2.83185i | ||||||||
\(9\) | −5.78454 | − | 80.7932i | −0.0714141 | − | 0.997447i | ||||
\(10\) | −187.134 | −1.87134 | ||||||||
\(11\) | 127.308i | 1.05213i | 0.850445 | + | 0.526064i | \(0.176333\pi\) | ||||
−0.850445 | + | 0.526064i | \(0.823667\pi\) | |||||||
\(12\) | 246.405 | − | 264.678i | 1.71115 | − | 1.83804i | ||||
\(13\) | −56.9103 | −0.336747 | −0.168374 | − | 0.985723i | \(-0.553851\pi\) | ||||
−0.168374 | + | 0.985723i | \(0.553851\pi\) | |||||||
\(14\) | 392.378i | 2.00193i | ||||||||
\(15\) | 164.463 | + | 153.109i | 0.730947 | + | 0.680484i | ||||
\(16\) | 715.561 | 2.79516 | ||||||||
\(17\) | 227.481i | 0.787133i | 0.919296 | + | 0.393566i | \(0.128759\pi\) | ||||
−0.919296 | + | 0.393566i | \(0.871241\pi\) | |||||||
\(18\) | −605.572 | + | 43.3571i | −1.86905 | + | 0.133818i | ||||
\(19\) | −187.501 | −0.519392 | −0.259696 | − | 0.965690i | \(-0.583622\pi\) | ||||
−0.259696 | + | 0.965690i | \(0.583622\pi\) | |||||||
\(20\) | 1003.17i | 2.50792i | ||||||||
\(21\) | 321.035 | − | 344.841i | 0.727970 | − | 0.781953i | ||||
\(22\) | 954.213 | 1.97151 | ||||||||
\(23\) | − | 905.445i | − | 1.71162i | −0.517294 | − | 0.855808i | \(-0.673061\pi\) | ||
0.517294 | − | 0.855808i | \(-0.326939\pi\) | |||||||
\(24\) | −1193.87 | − | 1111.45i | −2.07269 | − | 1.92959i | ||||
\(25\) | 1.66106 | 0.00265769 | ||||||||
\(26\) | 426.562i | 0.631009i | ||||||||
\(27\) | 567.681 | + | 457.361i | 0.778712 | + | 0.627381i | ||||
\(28\) | 2103.41 | 2.68293 | ||||||||
\(29\) | − | 1371.77i | − | 1.63111i | −0.578678 | − | 0.815556i | \(-0.696431\pi\) | ||
0.578678 | − | 0.815556i | \(-0.303569\pi\) | |||||||
\(30\) | 1147.60 | − | 1232.71i | 1.27512 | − | 1.36967i | ||||
\(31\) | 812.896 | 0.845885 | 0.422943 | − | 0.906157i | \(-0.360997\pi\) | ||||
0.422943 | + | 0.906157i | \(0.360997\pi\) | |||||||
\(32\) | − | 2463.56i | − | 2.40582i | ||||||
\(33\) | −838.610 | − | 780.715i | −0.770074 | − | 0.716910i | ||||
\(34\) | 1705.05 | 1.47496 | ||||||||
\(35\) | 1307.00i | 1.06694i | ||||||||
\(36\) | 232.424 | + | 3246.28i | 0.179339 | + | 2.50485i | ||||
\(37\) | 253.452 | 0.185136 | 0.0925682 | − | 0.995706i | \(-0.470492\pi\) | ||||
0.0925682 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(38\) | 1405.38i | 0.973255i | ||||||||
\(39\) | 349.003 | − | 374.884i | 0.229456 | − | 0.246472i | ||||
\(40\) | 4524.93 | 2.82808 | ||||||||
\(41\) | 1746.31i | 1.03885i | 0.854515 | + | 0.519427i | \(0.173854\pi\) | ||||
−0.854515 | + | 0.519427i | \(0.826146\pi\) | |||||||
\(42\) | −2584.70 | − | 2406.26i | −1.46525 | − | 1.36409i | ||||
\(43\) | 1428.74 | 0.772708 | 0.386354 | − | 0.922350i | \(-0.373734\pi\) | ||||
0.386354 | + | 0.922350i | \(0.373734\pi\) | |||||||
\(44\) | − | 5115.23i | − | 2.64217i | ||||||
\(45\) | −2017.14 | + | 144.421i | −0.996120 | + | 0.0713192i | ||||
\(46\) | −6786.61 | −3.20728 | ||||||||
\(47\) | 1935.60i | 0.876233i | 0.898918 | + | 0.438117i | \(0.144354\pi\) | ||||
−0.898918 | + | 0.438117i | \(0.855646\pi\) | |||||||
\(48\) | −4388.19 | + | 4713.60i | −1.90459 | + | 2.04583i | ||||
\(49\) | 339.479 | 0.141391 | ||||||||
\(50\) | − | 12.4502i | − | 0.00498008i | ||||||
\(51\) | −1498.48 | − | 1395.03i | −0.576118 | − | 0.536345i | ||||
\(52\) | 2286.66 | 0.845659 | ||||||||
\(53\) | 4446.72i | 1.58303i | 0.611152 | + | 0.791513i | \(0.290706\pi\) | ||||
−0.611152 | + | 0.791513i | \(0.709294\pi\) | |||||||
\(54\) | 3428.08 | − | 4254.96i | 1.17561 | − | 1.45918i | ||||
\(55\) | 3178.46 | 1.05073 | ||||||||
\(56\) | − | 9487.75i | − | 3.02543i | ||||||
\(57\) | 1149.85 | − | 1235.12i | 0.353909 | − | 0.380154i | ||||
\(58\) | −10281.8 | −3.05644 | ||||||||
\(59\) | − | 453.188i | − | 0.130189i | ||||||
\(60\) | −6608.15 | − | 6151.94i | −1.83560 | − | 1.70887i | ||||
\(61\) | −2336.04 | −0.627798 | −0.313899 | − | 0.949456i | \(-0.601635\pi\) | ||||
−0.313899 | + | 0.949456i | \(0.601635\pi\) | |||||||
\(62\) | − | 6092.93i | − | 1.58505i | ||||||
\(63\) | 302.819 | + | 4229.49i | 0.0762959 | + | 1.06563i | ||||
\(64\) | −7016.24 | −1.71295 | ||||||||
\(65\) | 1420.86i | 0.336299i | ||||||||
\(66\) | −5851.73 | + | 6285.67i | −1.34337 | + | 1.44299i | ||||
\(67\) | 4913.00 | 1.09445 | 0.547227 | − | 0.836984i | \(-0.315683\pi\) | ||||
0.547227 | + | 0.836984i | \(0.315683\pi\) | |||||||
\(68\) | − | 9140.23i | − | 1.97669i | ||||||
\(69\) | 5964.42 | + | 5552.65i | 1.25277 | + | 1.16628i | ||||
\(70\) | 9796.41 | 1.99927 | ||||||||
\(71\) | 8307.66i | 1.64802i | 0.566577 | + | 0.824009i | \(0.308267\pi\) | ||||
−0.566577 | + | 0.824009i | \(0.691733\pi\) | |||||||
\(72\) | 14642.8 | − | 1048.38i | 2.82462 | − | 0.202234i | ||||
\(73\) | −3769.78 | −0.707408 | −0.353704 | − | 0.935357i | \(-0.615078\pi\) | ||||
−0.353704 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(74\) | − | 1899.71i | − | 0.346915i | ||||||
\(75\) | −10.1865 | + | 10.9419i | −0.00181093 | + | 0.00194522i | ||||
\(76\) | 7533.80 | 1.30433 | ||||||||
\(77\) | − | 6664.50i | − | 1.12405i | ||||||
\(78\) | −2809.88 | − | 2615.90i | −0.461848 | − | 0.429963i | ||||
\(79\) | 2128.79 | 0.341097 | 0.170549 | − | 0.985349i | \(-0.445446\pi\) | ||||
0.170549 | + | 0.985349i | \(0.445446\pi\) | |||||||
\(80\) | − | 17865.2i | − | 2.79144i | ||||||
\(81\) | −6494.08 | + | 934.704i | −0.989800 | + | 0.142464i | ||||
\(82\) | 13089.2 | 1.94664 | ||||||||
\(83\) | 7492.96i | 1.08767i | 0.839192 | + | 0.543835i | \(0.183028\pi\) | ||||
−0.839192 | + | 0.543835i | \(0.816972\pi\) | |||||||
\(84\) | −12899.2 | + | 13855.8i | −1.82812 | + | 1.96369i | ||||
\(85\) | 5679.47 | 0.786086 | ||||||||
\(86\) | − | 10708.9i | − | 1.44793i | ||||||
\(87\) | 9036.20 | + | 8412.37i | 1.19384 | + | 1.11142i | ||||
\(88\) | −23073.0 | −2.97947 | ||||||||
\(89\) | − | 10955.2i | − | 1.38306i | −0.722349 | − | 0.691529i | \(-0.756937\pi\) | ||
0.722349 | − | 0.691529i | \(-0.243063\pi\) | |||||||
\(90\) | 1082.49 | + | 15119.2i | 0.133640 | + | 1.86657i | ||||
\(91\) | 2979.23 | 0.359767 | ||||||||
\(92\) | 36380.9i | 4.29831i | ||||||||
\(93\) | −4985.09 | + | 5354.77i | −0.576378 | + | 0.619120i | ||||
\(94\) | 14508.0 | 1.64192 | ||||||||
\(95\) | 4681.28i | 0.518702i | ||||||||
\(96\) | 16228.2 | + | 15107.8i | 1.76087 | + | 1.63930i | ||||
\(97\) | −16012.3 | −1.70181 | −0.850906 | − | 0.525318i | \(-0.823946\pi\) | ||||
−0.850906 | + | 0.525318i | \(0.823946\pi\) | |||||||
\(98\) | − | 2544.51i | − | 0.264943i | ||||||
\(99\) | 10285.6 | − | 736.416i | 1.04944 | − | 0.0751368i | ||||
\(100\) | −66.7416 | −0.00667416 | ||||||||
\(101\) | 13426.8i | 1.31622i | 0.752920 | + | 0.658112i | \(0.228645\pi\) | ||||
−0.752920 | + | 0.658112i | \(0.771355\pi\) | |||||||
\(102\) | −10456.2 | + | 11231.6i | −1.00502 | + | 1.07955i | ||||
\(103\) | 16881.8 | 1.59127 | 0.795635 | − | 0.605777i | \(-0.207138\pi\) | ||||
0.795635 | + | 0.605777i | \(0.207138\pi\) | |||||||
\(104\) | − | 10314.3i | − | 0.953617i | ||||||
\(105\) | −8609.57 | − | 8015.19i | −0.780914 | − | 0.727002i | ||||
\(106\) | 33329.7 | 2.96633 | ||||||||
\(107\) | 8103.84i | 0.707820i | 0.935279 | + | 0.353910i | \(0.115148\pi\) | ||||
−0.935279 | + | 0.353910i | \(0.884852\pi\) | |||||||
\(108\) | −22809.5 | − | 18376.8i | −1.95555 | − | 1.57552i | ||||
\(109\) | 4896.71 | 0.412146 | 0.206073 | − | 0.978537i | \(-0.433932\pi\) | ||||
0.206073 | + | 0.978537i | \(0.433932\pi\) | |||||||
\(110\) | − | 23823.6i | − | 1.96889i | ||||||
\(111\) | −1554.30 | + | 1669.56i | −0.126150 | + | 0.135505i | ||||
\(112\) | −37459.3 | −2.98623 | ||||||||
\(113\) | 11924.9i | 0.933897i | 0.884284 | + | 0.466949i | \(0.154647\pi\) | ||||
−0.884284 | + | 0.466949i | \(0.845353\pi\) | |||||||
\(114\) | −9257.64 | − | 8618.52i | −0.712345 | − | 0.663167i | ||||
\(115\) | −22606.0 | −1.70934 | ||||||||
\(116\) | 55117.7i | 4.09614i | ||||||||
\(117\) | 329.200 | + | 4597.96i | 0.0240485 | + | 0.335887i | ||||
\(118\) | −3396.80 | −0.243953 | ||||||||
\(119\) | − | 11908.6i | − | 0.840940i | ||||||
\(120\) | −27749.2 | + | 29807.0i | −1.92703 | + | 2.06993i | ||||
\(121\) | −1566.21 | −0.106974 | ||||||||
\(122\) | 17509.4i | 1.17639i | ||||||||
\(123\) | −11503.4 | − | 10709.3i | −0.760357 | − | 0.707865i | ||||
\(124\) | −32662.2 | −2.12424 | ||||||||
\(125\) | − | 15645.7i | − | 1.00132i | ||||||
\(126\) | 31701.5 | − | 2269.73i | 1.99682 | − | 0.142966i | ||||
\(127\) | 22268.1 | 1.38063 | 0.690313 | − | 0.723510i | \(-0.257473\pi\) | ||||
0.690313 | + | 0.723510i | \(0.257473\pi\) | |||||||
\(128\) | 13172.2i | 0.803965i | ||||||||
\(129\) | −8761.76 | + | 9411.50i | −0.526516 | + | 0.565561i | ||||
\(130\) | 10649.9 | 0.630169 | ||||||||
\(131\) | − | 13648.9i | − | 0.795343i | −0.917528 | − | 0.397672i | \(-0.869818\pi\) | ||
0.917528 | − | 0.397672i | \(-0.130182\pi\) | |||||||
\(132\) | 33695.5 | + | 31369.2i | 1.93385 | + | 1.80035i | ||||
\(133\) | 9815.58 | 0.554897 | ||||||||
\(134\) | − | 36824.6i | − | 2.05083i | ||||||
\(135\) | 11418.8 | − | 14173.2i | 0.626547 | − | 0.777677i | ||||
\(136\) | −41228.3 | −2.22904 | ||||||||
\(137\) | − | 33762.7i | − | 1.79885i | −0.437070 | − | 0.899427i | \(-0.643984\pi\) | ||
0.437070 | − | 0.899427i | \(-0.356016\pi\) | |||||||
\(138\) | 41619.0 | − | 44705.3i | 2.18541 | − | 2.34748i | ||||
\(139\) | 9781.52 | 0.506264 | 0.253132 | − | 0.967432i | \(-0.418539\pi\) | ||||
0.253132 | + | 0.967432i | \(0.418539\pi\) | |||||||
\(140\) | − | 52515.4i | − | 2.67936i | ||||||
\(141\) | −12750.3 | − | 11870.1i | −0.641333 | − | 0.597057i | ||||
\(142\) | 62268.7 | 3.08811 | ||||||||
\(143\) | − | 7245.10i | − | 0.354301i | ||||||
\(144\) | −4139.19 | − | 57812.4i | −0.199614 | − | 2.78802i | ||||
\(145\) | −34248.5 | −1.62894 | ||||||||
\(146\) | 28255.8i | 1.32557i | ||||||||
\(147\) | −2081.86 | + | 2236.25i | −0.0963424 | + | 0.103487i | ||||
\(148\) | −10183.7 | −0.464925 | ||||||||
\(149\) | 43389.2i | 1.95438i | 0.212363 | + | 0.977191i | \(0.431884\pi\) | ||||
−0.212363 | + | 0.977191i | \(0.568116\pi\) | |||||||
\(150\) | 82.0130 | + | 76.3511i | 0.00364502 | + | 0.00339338i | ||||
\(151\) | −15713.3 | −0.689148 | −0.344574 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344574 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(152\) | − | 33982.3i | − | 1.47084i | ||||||
\(153\) | 18378.9 | − | 1315.88i | 0.785123 | − | 0.0562124i | ||||
\(154\) | −49952.7 | −2.10629 | ||||||||
\(155\) | − | 20295.4i | − | 0.844760i | ||||||
\(156\) | −14023.0 | + | 15062.9i | −0.576224 | + | 0.618955i | ||||
\(157\) | −14305.3 | −0.580361 | −0.290181 | − | 0.956972i | \(-0.593715\pi\) | ||||
−0.290181 | + | 0.956972i | \(0.593715\pi\) | |||||||
\(158\) | − | 15956.0i | − | 0.639160i | ||||||
\(159\) | −29291.8 | − | 27269.6i | −1.15865 | − | 1.07866i | ||||
\(160\) | −61507.1 | −2.40262 | ||||||||
\(161\) | 47399.6i | 1.82862i | ||||||||
\(162\) | 7005.92 | + | 48675.3i | 0.266953 | + | 1.85472i | ||||
\(163\) | −11045.1 | −0.415713 | −0.207857 | − | 0.978159i | \(-0.566649\pi\) | ||||
−0.207857 | + | 0.978159i | \(0.566649\pi\) | |||||||
\(164\) | − | 70167.0i | − | 2.60883i | ||||||
\(165\) | −19491.9 | + | 20937.4i | −0.715957 | + | 0.769050i | ||||
\(166\) | 56162.3 | 2.03812 | ||||||||
\(167\) | 36094.9i | 1.29424i | 0.762390 | + | 0.647118i | \(0.224026\pi\) | ||||
−0.762390 | + | 0.647118i | \(0.775974\pi\) | |||||||
\(168\) | 62498.5 | + | 58183.8i | 2.21437 | + | 2.06150i | ||||
\(169\) | −25322.2 | −0.886601 | ||||||||
\(170\) | − | 42569.6i | − | 1.47300i | ||||||
\(171\) | 1084.61 | + | 15148.8i | 0.0370919 | + | 0.518066i | ||||
\(172\) | −57406.9 | −1.94047 | ||||||||
\(173\) | 36096.8i | 1.20608i | 0.797711 | + | 0.603040i | \(0.206044\pi\) | ||||
−0.797711 | + | 0.603040i | \(0.793956\pi\) | |||||||
\(174\) | 63053.6 | − | 67729.4i | 2.08263 | − | 2.23707i | ||||
\(175\) | −86.9558 | −0.00283937 | ||||||||
\(176\) | 91096.3i | 2.94087i | ||||||||
\(177\) | 2985.27 | + | 2779.18i | 0.0952879 | + | 0.0887095i | ||||
\(178\) | −82113.0 | −2.59162 | ||||||||
\(179\) | 4409.95i | 0.137635i | 0.997629 | + | 0.0688174i | \(0.0219226\pi\) | ||||
−0.997629 | + | 0.0688174i | \(0.978077\pi\) | |||||||
\(180\) | 81049.1 | − | 5802.87i | 2.50152 | − | 0.179101i | ||||
\(181\) | −43407.5 | −1.32497 | −0.662487 | − | 0.749074i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749074i | \(0.730499\pi\) | |||||||
\(182\) | − | 22330.3i | − | 0.674144i | ||||||
\(183\) | 14325.8 | − | 15388.1i | 0.427776 | − | 0.459498i | ||||
\(184\) | 164101. | 4.84704 | ||||||||
\(185\) | − | 6327.87i | − | 0.184890i | ||||||
\(186\) | 40135.8 | + | 37365.0i | 1.16013 | + | 1.08004i | ||||
\(187\) | −28960.1 | −0.828165 | ||||||||
\(188\) | − | 77772.6i | − | 2.20045i | ||||||
\(189\) | −29717.9 | − | 23942.7i | −0.831944 | − | 0.670268i | ||||
\(190\) | 35087.8 | 0.971961 | ||||||||
\(191\) | 40966.2i | 1.12295i | 0.827495 | + | 0.561473i | \(0.189765\pi\) | ||||
−0.827495 | + | 0.561473i | \(0.810235\pi\) | |||||||
\(192\) | 43027.2 | − | 46217.9i | 1.16719 | − | 1.25374i | ||||
\(193\) | 37461.5 | 1.00571 | 0.502853 | − | 0.864372i | \(-0.332284\pi\) | ||||
0.502853 | + | 0.864372i | \(0.332284\pi\) | |||||||
\(194\) | 120018.i | 3.18891i | ||||||||
\(195\) | −9359.63 | − | 8713.47i | −0.246144 | − | 0.229151i | ||||
\(196\) | −13640.3 | −0.355069 | ||||||||
\(197\) | − | 60634.8i | − | 1.56239i | −0.624287 | − | 0.781195i | \(-0.714611\pi\) | ||
0.624287 | − | 0.781195i | \(-0.285389\pi\) | |||||||
\(198\) | −5519.69 | − | 77093.9i | −0.140794 | − | 1.96648i | ||||
\(199\) | −37712.7 | −0.952317 | −0.476159 | − | 0.879359i | \(-0.657971\pi\) | ||||
−0.476159 | + | 0.879359i | \(0.657971\pi\) | |||||||
\(200\) | 301.048i | 0.00752619i | ||||||||
\(201\) | −30129.1 | + | 32363.3i | −0.745751 | + | 0.801053i | ||||
\(202\) | 100638. | 2.46639 | ||||||||
\(203\) | 71811.4i | 1.74261i | ||||||||
\(204\) | 60209.3 | + | 56052.6i | 1.44678 | + | 1.34690i | ||||
\(205\) | 43599.7 | 1.03747 | ||||||||
\(206\) | − | 126535.i | − | 2.98178i | ||||||
\(207\) | −73153.7 | + | 5237.58i | −1.70725 | + | 0.122234i | ||||
\(208\) | −40722.7 | −0.941262 | ||||||||
\(209\) | − | 23870.2i | − | 0.546467i | ||||||
\(210\) | −60076.6 | + | 64531.7i | −1.36228 | + | 1.46330i | ||||
\(211\) | 44136.4 | 0.991362 | 0.495681 | − | 0.868505i | \(-0.334919\pi\) | ||||
0.495681 | + | 0.868505i | \(0.334919\pi\) | |||||||
\(212\) | − | 178670.i | − | 3.97539i | ||||||
\(213\) | −54724.9 | − | 50946.8i | −1.20622 | − | 1.12294i | ||||
\(214\) | 60741.0 | 1.32634 | ||||||||
\(215\) | − | 35671.0i | − | 0.771681i | ||||||
\(216\) | −82891.3 | + | 102886.i | −1.77665 | + | 2.20520i | ||||
\(217\) | −42554.7 | −0.903709 | ||||||||
\(218\) | − | 36702.5i | − | 0.772293i | ||||||
\(219\) | 23118.2 | − | 24832.6i | 0.482021 | − | 0.517767i | ||||
\(220\) | −127711. | −2.63865 | ||||||||
\(221\) | − | 12946.0i | − | 0.265065i | ||||||
\(222\) | 12513.9 | + | 11650.0i | 0.253914 | + | 0.236385i | ||||
\(223\) | 44232.6 | 0.889473 | 0.444736 | − | 0.895662i | \(-0.353297\pi\) | ||||
0.444736 | + | 0.895662i | \(0.353297\pi\) | |||||||
\(224\) | 128966.i | 2.57028i | ||||||||
\(225\) | −9.60847 | − | 134.202i | −0.000189797 | − | 0.00265091i | ||||
\(226\) | 89381.4 | 1.74997 | ||||||||
\(227\) | − | 18920.9i | − | 0.367190i | −0.983002 | − | 0.183595i | \(-0.941227\pi\) | ||
0.983002 | − | 0.183595i | \(-0.0587735\pi\) | |||||||
\(228\) | −46201.1 | + | 49627.2i | −0.888757 | + | 0.954664i | ||||
\(229\) | 32265.4 | 0.615271 | 0.307635 | − | 0.951504i | \(-0.400462\pi\) | ||||
0.307635 | + | 0.951504i | \(0.400462\pi\) | |||||||
\(230\) | 169440.i | 3.20302i | ||||||||
\(231\) | 43900.9 | + | 40870.1i | 0.822715 | + | 0.765917i | ||||
\(232\) | 248616. | 4.61906 | ||||||||
\(233\) | − | 22096.7i | − | 0.407019i | −0.979073 | − | 0.203509i | \(-0.934765\pi\) | ||
0.979073 | − | 0.203509i | \(-0.0652348\pi\) | |||||||
\(234\) | 34463.3 | − | 2467.47i | 0.629397 | − | 0.0450629i | ||||
\(235\) | 48325.6 | 0.875068 | ||||||||
\(236\) | 18209.1i | 0.326938i | ||||||||
\(237\) | −13054.8 | + | 14022.9i | −0.232420 | + | 0.249656i | ||||
\(238\) | −89258.7 | −1.57578 | ||||||||
\(239\) | − | 24979.4i | − | 0.437307i | −0.975803 | − | 0.218654i | \(-0.929834\pi\) | ||
0.975803 | − | 0.218654i | \(-0.0701665\pi\) | |||||||
\(240\) | 117683. | + | 109559.i | 2.04311 | + | 1.90206i | ||||
\(241\) | 32935.6 | 0.567064 | 0.283532 | − | 0.958963i | \(-0.408494\pi\) | ||||
0.283532 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(242\) | 11739.2i | 0.200452i | ||||||||
\(243\) | 33667.9 | − | 48510.4i | 0.570168 | − | 0.821528i | ||||
\(244\) | 93862.3 | 1.57656 | ||||||||
\(245\) | − | 8475.70i | − | 0.141203i | ||||||
\(246\) | −80269.7 | + | 86222.3i | −1.32642 | + | 1.42478i | ||||
\(247\) | 10670.7 | 0.174904 | ||||||||
\(248\) | 147328.i | 2.39542i | ||||||||
\(249\) | −49358.3 | − | 45950.7i | −0.796088 | − | 0.741128i | ||||
\(250\) | −117270. | −1.87632 | ||||||||
\(251\) | 15587.0i | 0.247409i | 0.992319 | + | 0.123705i | \(0.0394776\pi\) | ||||
−0.992319 | + | 0.123705i | \(0.960522\pi\) | |||||||
\(252\) | −12167.3 | − | 169941.i | −0.191599 | − | 2.67607i | ||||
\(253\) | 115270. | 1.80084 | ||||||||
\(254\) | − | 166907.i | − | 2.58707i | ||||||
\(255\) | −34829.4 | + | 37412.3i | −0.535631 | + | 0.575352i | ||||
\(256\) | −13530.0 | −0.206451 | ||||||||
\(257\) | 7399.34i | 0.112028i | 0.998430 | + | 0.0560140i | \(0.0178392\pi\) | ||||
−0.998430 | + | 0.0560140i | \(0.982161\pi\) | |||||||
\(258\) | 70542.4 | + | 65672.3i | 1.05977 | + | 0.986604i | ||||
\(259\) | −13268.1 | −0.197792 | ||||||||
\(260\) | − | 57090.5i | − | 0.844534i | ||||||
\(261\) | −110829. | + | 7935.04i | −1.62695 | + | 0.116484i | ||||
\(262\) | −102303. | −1.49034 | ||||||||
\(263\) | 111995.i | 1.61916i | 0.587013 | + | 0.809578i | \(0.300304\pi\) | ||||
−0.587013 | + | 0.809578i | \(0.699696\pi\) | |||||||
\(264\) | 141495. | − | 151988.i | 2.03018 | − | 2.18073i | ||||
\(265\) | 111020. | 1.58092 | ||||||||
\(266\) | − | 73571.1i | − | 1.03979i | ||||||
\(267\) | 72165.0 | + | 67182.9i | 1.01229 | + | 0.942403i | ||||
\(268\) | −197405. | −2.74846 | ||||||||
\(269\) | − | 21091.5i | − | 0.291475i | −0.989323 | − | 0.145738i | \(-0.953444\pi\) | ||
0.989323 | − | 0.145738i | \(-0.0465556\pi\) | |||||||
\(270\) | −106233. | − | 85587.9i | −1.45724 | − | 1.17405i | ||||
\(271\) | −71615.9 | −0.975148 | −0.487574 | − | 0.873082i | \(-0.662118\pi\) | ||||
−0.487574 | + | 0.873082i | \(0.662118\pi\) | |||||||
\(272\) | 162777.i | 2.20016i | ||||||||
\(273\) | −18270.2 | + | 19625.0i | −0.245142 | + | 0.263321i | ||||
\(274\) | −253063. | −3.37076 | ||||||||
\(275\) | 211.465i | 0.00279624i | ||||||||
\(276\) | −239651. | − | 223106.i | −3.14602 | − | 2.92883i | ||||
\(277\) | 90722.5 | 1.18238 | 0.591188 | − | 0.806534i | \(-0.298659\pi\) | ||||
0.591188 | + | 0.806534i | \(0.298659\pi\) | |||||||
\(278\) | − | 73315.8i | − | 0.948655i | ||||||
\(279\) | −4702.23 | − | 65676.4i | −0.0604081 | − | 0.843725i | ||||
\(280\) | −236878. | −3.02141 | ||||||||
\(281\) | − | 44079.6i | − | 0.558246i | −0.960255 | − | 0.279123i | \(-0.909956\pi\) | ||
0.960255 | − | 0.279123i | \(-0.0900436\pi\) | |||||||
\(282\) | −88970.4 | + | 95568.1i | −1.11879 | + | 1.20175i | ||||
\(283\) | 4240.96 | 0.0529530 | 0.0264765 | − | 0.999649i | \(-0.491571\pi\) | ||||
0.0264765 | + | 0.999649i | \(0.491571\pi\) | |||||||
\(284\) | − | 333803.i | − | 4.13860i | ||||||
\(285\) | −30836.9 | − | 28708.0i | −0.379648 | − | 0.353438i | ||||
\(286\) | −54304.5 | −0.663902 | ||||||||
\(287\) | − | 91418.7i | − | 1.10987i | ||||||
\(288\) | −199039. | + | 14250.6i | −2.39968 | + | 0.171809i | ||||
\(289\) | 31773.2 | 0.380422 | ||||||||
\(290\) | 256704.i | 3.05237i | ||||||||
\(291\) | 98195.9 | − | 105478.i | 1.15960 | − | 1.24559i | ||||
\(292\) | 151470. | 1.77649 | ||||||||
\(293\) | 11551.5i | 0.134556i | 0.997734 | + | 0.0672778i | \(0.0214314\pi\) | ||||
−0.997734 | + | 0.0672778i | \(0.978569\pi\) | |||||||
\(294\) | 16761.4 | + | 15604.3i | 0.193917 | + | 0.180530i | ||||
\(295\) | −11314.6 | −0.130016 | ||||||||
\(296\) | 45935.2i | 0.524278i | ||||||||
\(297\) | −58225.5 | + | 72270.1i | −0.660086 | + | 0.819305i | ||||
\(298\) | 325217. | 3.66219 | ||||||||
\(299\) | 51529.1i | 0.576381i | ||||||||
\(300\) | 409.294 | − | 439.646i | 0.00454771 | − | 0.00488495i | ||||
\(301\) | −74793.8 | −0.825530 | ||||||||
\(302\) | 117776.i | 1.29135i | ||||||||
\(303\) | −88446.1 | − | 82340.1i | −0.963371 | − | 0.896863i | ||||
\(304\) | −134168. | −1.45178 | ||||||||
\(305\) | 58323.3i | 0.626964i | ||||||||
\(306\) | −9862.94 | − | 137756.i | −0.105333 | − | 1.47119i | ||||
\(307\) | −13202.7 | −0.140084 | −0.0700418 | − | 0.997544i | \(-0.522313\pi\) | ||||
−0.0700418 | + | 0.997544i | \(0.522313\pi\) | |||||||
\(308\) | 267780.i | 2.82278i | ||||||||
\(309\) | −103528. | + | 111205.i | −1.08428 | + | 1.16468i | ||||
\(310\) | −152121. | −1.58294 | ||||||||
\(311\) | − | 68017.1i | − | 0.703230i | −0.936145 | − | 0.351615i | \(-0.885633\pi\) | ||
0.936145 | − | 0.351615i | \(-0.114367\pi\) | |||||||
\(312\) | 67943.3 | + | 63252.7i | 0.697971 | + | 0.649785i | ||||
\(313\) | 10627.8 | 0.108481 | 0.0542404 | − | 0.998528i | \(-0.482726\pi\) | ||||
0.0542404 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(314\) | 107223.i | 1.08750i | ||||||||
\(315\) | 105597. | − | 7560.40i | 1.06421 | − | 0.0761945i | ||||
\(316\) | −85534.9 | −0.856583 | ||||||||
\(317\) | 123218.i | 1.22619i | 0.790010 | + | 0.613094i | \(0.210075\pi\) | ||||
−0.790010 | + | 0.613094i | \(0.789925\pi\) | |||||||
\(318\) | −204395. | + | 219552.i | −2.02123 | + | 2.17112i | ||||
\(319\) | 174636. | 1.71614 | ||||||||
\(320\) | 175173.i | 1.71067i | ||||||||
\(321\) | −53382.3 | − | 49696.9i | −0.518068 | − | 0.482302i | ||||
\(322\) | 355277. | 3.42653 | ||||||||
\(323\) | − | 42652.9i | − | 0.408831i | ||||||
\(324\) | 260933. | − | 37556.5i | 2.48564 | − | 0.357763i | ||||
\(325\) | −94.5313 | −0.000894971 | ||||||||
\(326\) | 82786.7i | 0.778978i | ||||||||
\(327\) | −30029.1 | + | 32256.0i | −0.280832 | + | 0.301658i | ||||
\(328\) | −316499. | −2.94187 | ||||||||
\(329\) | − | 101328.i | − | 0.936132i | ||||||
\(330\) | 156933. | + | 146099.i | 1.44107 | + | 1.34159i | ||||
\(331\) | −142152. | −1.29747 | −0.648734 | − | 0.761015i | \(-0.724701\pi\) | ||||
−0.648734 | + | 0.761015i | \(0.724701\pi\) | |||||||
\(332\) | − | 301068.i | − | 2.73142i | ||||||
\(333\) | −1466.10 | − | 20477.2i | −0.0132214 | − | 0.184664i | ||||
\(334\) | 270544. | 2.42518 | ||||||||
\(335\) | − | 122662.i | − | 1.09300i | ||||||
\(336\) | 229720. | − | 246755.i | 2.03479 | − | 2.18568i | ||||
\(337\) | −115078. | −1.01328 | −0.506642 | − | 0.862156i | \(-0.669114\pi\) | ||||
−0.506642 | + | 0.862156i | \(0.669114\pi\) | |||||||
\(338\) | 189799.i | 1.66134i | ||||||||
\(339\) | −78552.9 | − | 73129.8i | −0.683538 | − | 0.636349i | ||||
\(340\) | −228202. | −1.97406 | ||||||||
\(341\) | 103488.i | 0.889980i | ||||||||
\(342\) | 113545. | − | 8129.49i | 0.970770 | − | 0.0695042i | ||||
\(343\) | 107920. | 0.917303 | ||||||||
\(344\) | 258942.i | 2.18819i | ||||||||
\(345\) | 138632. | − | 148912.i | 1.16473 | − | 1.25110i | ||||
\(346\) | 270558. | 2.26000 | ||||||||
\(347\) | 155553.i | 1.29188i | 0.763390 | + | 0.645938i | \(0.223533\pi\) | ||||
−0.763390 | + | 0.645938i | \(0.776467\pi\) | |||||||
\(348\) | −363076. | − | 338010.i | −2.99805 | − | 2.79107i | ||||
\(349\) | −71293.8 | −0.585330 | −0.292665 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292665 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(350\) | 651.763i | 0.00532052i | ||||||||
\(351\) | −32306.9 | − | 26028.5i | −0.262229 | − | 0.211269i | ||||
\(352\) | 313630. | 2.53123 | ||||||||
\(353\) | 64338.5i | 0.516323i | 0.966102 | + | 0.258162i | \(0.0831167\pi\) | ||||
−0.966102 | + | 0.258162i | \(0.916883\pi\) | |||||||
\(354\) | 20830.9 | − | 22375.6i | 0.166227 | − | 0.178554i | ||||
\(355\) | 207415. | 1.64583 | ||||||||
\(356\) | 440182.i | 3.47322i | ||||||||
\(357\) | 78445.0 | + | 73029.4i | 0.615501 | + | 0.573009i | ||||
\(358\) | 33054.1 | 0.257905 | ||||||||
\(359\) | − | 38102.5i | − | 0.295641i | −0.989014 | − | 0.147821i | \(-0.952774\pi\) | ||
0.989014 | − | 0.147821i | \(-0.0472258\pi\) | |||||||
\(360\) | −26174.7 | − | 365584.i | −0.201965 | − | 2.82086i | ||||
\(361\) | −95164.5 | −0.730232 | ||||||||
\(362\) | 325354.i | 2.48278i | ||||||||
\(363\) | 9604.78 | − | 10317.0i | 0.0728910 | − | 0.0782964i | ||||
\(364\) | −119706. | −0.903467 | ||||||||
\(365\) | 94119.2i | 0.706468i | ||||||||
\(366\) | −115339. | − | 107377.i | −0.861024 | − | 0.801582i | ||||
\(367\) | 170699. | 1.26736 | 0.633679 | − | 0.773596i | \(-0.281544\pi\) | ||||
0.633679 | + | 0.773596i | \(0.281544\pi\) | |||||||
\(368\) | − | 647901.i | − | 4.78424i | ||||||
\(369\) | 141090. | − | 10101.6i | 1.03620 | − | 0.0741888i | ||||
\(370\) | −47429.5 | −0.346454 | ||||||||
\(371\) | − | 232784.i | − | 1.69124i | ||||||
\(372\) | 200302. | − | 215155.i | 1.44743 | − | 1.55477i | ||||
\(373\) | 63737.6 | 0.458118 | 0.229059 | − | 0.973412i | \(-0.426435\pi\) | ||||
0.229059 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(374\) | 217066.i | 1.55184i | ||||||||
\(375\) | 103063. | + | 95947.4i | 0.732889 | + | 0.682293i | ||||
\(376\) | −350805. | −2.48136 | ||||||||
\(377\) | 78067.5i | 0.549272i | ||||||||
\(378\) | −179458. | + | 222746.i | −1.25597 | + | 1.55893i | ||||
\(379\) | −278735. | −1.94050 | −0.970249 | − | 0.242111i | \(-0.922160\pi\) | ||||
−0.970249 | + | 0.242111i | \(0.922160\pi\) | |||||||
\(380\) | − | 188095.i | − | 1.30259i | ||||||
\(381\) | −136560. | + | 146686.i | −0.940746 | + | 1.01051i | ||||
\(382\) | 307056. | 2.10422 | ||||||||
\(383\) | 82161.9i | 0.560110i | 0.959984 | + | 0.280055i | \(0.0903527\pi\) | ||||
−0.959984 | + | 0.280055i | \(0.909647\pi\) | |||||||
\(384\) | −86768.8 | − | 80778.5i | −0.588438 | − | 0.547814i | ||||
\(385\) | −166391. | −1.12256 | ||||||||
\(386\) | − | 280787.i | − | 1.88453i | ||||||
\(387\) | −8264.60 | − | 115432.i | −0.0551823 | − | 0.770736i | ||||
\(388\) | 643378. | 4.27369 | ||||||||
\(389\) | − | 101073.i | − | 0.667939i | −0.942584 | − | 0.333969i | \(-0.891612\pi\) | ||
0.942584 | − | 0.333969i | \(-0.108388\pi\) | |||||||
\(390\) | −65310.4 | + | 70153.6i | −0.429391 | + | 0.461234i | ||||
\(391\) | 205972. | 1.34727 | ||||||||
\(392\) | 61526.7i | 0.400398i | ||||||||
\(393\) | 89909.0 | + | 83702.0i | 0.582128 | + | 0.541939i | ||||
\(394\) | −454478. | −2.92766 | ||||||||
\(395\) | − | 53148.9i | − | 0.340643i | ||||||
\(396\) | −413276. | + | 29589.3i | −2.63542 | + | 0.188688i | ||||
\(397\) | 60367.3 | 0.383019 | 0.191510 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(398\) | 282670.i | 1.78449i | ||||||||
\(399\) | −60194.2 | + | 64658.0i | −0.378102 | + | 0.406141i | ||||
\(400\) | 1188.59 | 0.00742868 | ||||||||
\(401\) | − | 91315.9i | − | 0.567881i | −0.958842 | − | 0.283941i | \(-0.908358\pi\) | ||
0.958842 | − | 0.283941i | \(-0.0916419\pi\) | |||||||
\(402\) | 242574. | + | 225828.i | 1.50104 | + | 1.39741i | ||||
\(403\) | −46262.1 | −0.284849 | ||||||||
\(404\) | − | 539491.i | − | 3.30538i | ||||||
\(405\) | 23336.5 | + | 162136.i | 0.142274 | + | 0.988484i | ||||
\(406\) | 538251. | 3.26537 | ||||||||
\(407\) | 32266.3i | 0.194787i | ||||||||
\(408\) | 252833. | − | 271583.i | 1.51885 | − | 1.63148i | ||||
\(409\) | 23670.6 | 0.141502 | 0.0707510 | − | 0.997494i | \(-0.477460\pi\) | ||||
0.0707510 | + | 0.997494i | \(0.477460\pi\) | |||||||
\(410\) | − | 326795.i | − | 1.94405i | ||||||
\(411\) | 222404. | + | 207050.i | 1.31662 | + | 1.22572i | ||||
\(412\) | −678312. | −3.99609 | ||||||||
\(413\) | 23724.2i | 0.139088i | ||||||||
\(414\) | 39257.5 | + | 548312.i | 0.229045 | + | 3.19910i | ||||
\(415\) | 187075. | 1.08622 | ||||||||
\(416\) | 140202.i | 0.810153i | ||||||||
\(417\) | −59985.3 | + | 64433.6i | −0.344963 | + | 0.370545i | ||||
\(418\) | −178916. | −1.02399 | ||||||||
\(419\) | 116387.i | 0.662946i | 0.943465 | + | 0.331473i | \(0.107546\pi\) | ||||
−0.943465 | + | 0.331473i | \(0.892454\pi\) | |||||||
\(420\) | 345934. | + | 322051.i | 1.96108 | + | 1.82569i | ||||
\(421\) | 321783. | 1.81551 | 0.907755 | − | 0.419500i | \(-0.137795\pi\) | ||||
0.907755 | + | 0.419500i | \(0.137795\pi\) | |||||||
\(422\) | − | 330818.i | − | 1.85765i | ||||||
\(423\) | 156383. | − | 11196.6i | 0.873996 | − | 0.0625754i | ||||
\(424\) | −805916. | −4.48289 | ||||||||
\(425\) | 377.860i | 0.00209196i | ||||||||
\(426\) | −381864. | + | 410182.i | −2.10421 | + | 2.26025i | ||||
\(427\) | 122291. | 0.670714 | ||||||||
\(428\) | − | 325613.i | − | 1.77752i | ||||||
\(429\) | 47725.5 | + | 44430.7i | 0.259320 | + | 0.241417i | ||||
\(430\) | −267366. | −1.44600 | ||||||||
\(431\) | 300041.i | 1.61520i | 0.589732 | + | 0.807599i | \(0.299233\pi\) | ||||
−0.589732 | + | 0.807599i | \(0.700767\pi\) | |||||||
\(432\) | 406210. | + | 327270.i | 2.17662 | + | 1.75363i | ||||
\(433\) | 41166.3 | 0.219566 | 0.109783 | − | 0.993956i | \(-0.464984\pi\) | ||||
0.109783 | + | 0.993956i | \(0.464984\pi\) | |||||||
\(434\) | 318962.i | 1.69340i | ||||||||
\(435\) | 210030. | − | 225605.i | 1.10995 | − | 1.19226i | ||||
\(436\) | −196750. | −1.03500 | ||||||||
\(437\) | 169771.i | 0.889000i | ||||||||
\(438\) | −186129. | − | 173279.i | −0.970209 | − | 0.903229i | ||||
\(439\) | −132293. | −0.686450 | −0.343225 | − | 0.939253i | \(-0.611519\pi\) | ||||
−0.343225 | + | 0.939253i | \(0.611519\pi\) | |||||||
\(440\) | 576058.i | 2.97551i | ||||||||
\(441\) | −1963.73 | − | 27427.6i | −0.0100973 | − | 0.141030i | ||||
\(442\) | −97034.8 | −0.496687 | ||||||||
\(443\) | 125977.i | 0.641926i | 0.947092 | + | 0.320963i | \(0.104007\pi\) | ||||
−0.947092 | + | 0.320963i | \(0.895993\pi\) | |||||||
\(444\) | 62451.8 | − | 67083.0i | 0.316796 | − | 0.340288i | ||||
\(445\) | −273516. | −1.38122 | ||||||||
\(446\) | − | 331538.i | − | 1.66673i | ||||||
\(447\) | −285817. | − | 266085.i | −1.43045 | − | 1.33170i | ||||
\(448\) | 367297. | 1.83004 | ||||||||
\(449\) | − | 129881.i | − | 0.644246i | −0.946698 | − | 0.322123i | \(-0.895604\pi\) | ||
0.946698 | − | 0.322123i | \(-0.104396\pi\) | |||||||
\(450\) | −1005.89 | + | 72.0188i | −0.00496737 | + | 0.000355648i | ||||
\(451\) | −222319. | −1.09301 | ||||||||
\(452\) | − | 479145.i | − | 2.34526i | ||||||
\(453\) | 96361.8 | − | 103508.i | 0.469579 | − | 0.504401i | ||||
\(454\) | −141819. | −0.688053 | ||||||||
\(455\) | − | 74381.7i | − | 0.359288i | ||||||
\(456\) | 223851. | + | 208397.i | 1.07654 | + | 1.00222i | ||||
\(457\) | −63515.2 | −0.304120 | −0.152060 | − | 0.988371i | \(-0.548591\pi\) | ||||
−0.152060 | + | 0.988371i | \(0.548591\pi\) | |||||||
\(458\) | − | 241840.i | − | 1.15292i | ||||||
\(459\) | −104041. | + | 129137.i | −0.493832 | + | 0.612950i | ||||
\(460\) | 908313. | 4.29259 | ||||||||
\(461\) | − | 75639.2i | − | 0.355914i | −0.984038 | − | 0.177957i | \(-0.943051\pi\) | ||
0.984038 | − | 0.177957i | \(-0.0569488\pi\) | |||||||
\(462\) | 306335. | − | 329052.i | 1.43520 | − | 1.54163i | ||||
\(463\) | −180512. | −0.842062 | −0.421031 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421031 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(464\) | − | 981581.i | − | 4.55922i | ||||||
\(465\) | 133691. | + | 124462.i | 0.618297 | + | 0.575612i | ||||
\(466\) | −165622. | −0.762686 | ||||||||
\(467\) | 57521.3i | 0.263752i | 0.991266 | + | 0.131876i | \(0.0421000\pi\) | ||||
−0.991266 | + | 0.131876i | \(0.957900\pi\) | |||||||
\(468\) | −13227.3 | − | 184747.i | −0.0603920 | − | 0.843500i | ||||
\(469\) | −257194. | −1.16927 | ||||||||
\(470\) | − | 362217.i | − | 1.63973i | ||||||
\(471\) | 87727.6 | − | 94233.2i | 0.395453 | − | 0.424778i | ||||
\(472\) | 82135.0 | 0.368675 | ||||||||
\(473\) | 181889.i | 0.812988i | ||||||||
\(474\) | 105107. | + | 97850.3i | 0.467814 | + | 0.435517i | ||||
\(475\) | −311.450 | −0.00138039 | ||||||||
\(476\) | 478487.i | 2.11182i | ||||||||
\(477\) | 359265. | − | 25722.2i | 1.57898 | − | 0.113050i | ||||
\(478\) | −187229. | −0.819441 | ||||||||
\(479\) | − | 337448.i | − | 1.47074i | −0.677666 | − | 0.735370i | \(-0.737008\pi\) | ||
0.677666 | − | 0.735370i | \(-0.262992\pi\) | |||||||
\(480\) | 377193. | − | 405164.i | 1.63712 | − | 1.75853i | ||||
\(481\) | −14424.0 | −0.0623441 | ||||||||
\(482\) | − | 246864.i | − | 1.06258i | ||||||
\(483\) | −312235. | − | 290679.i | −1.33840 | − | 1.24600i | ||||
\(484\) | 62930.4 | 0.268639 | ||||||||
\(485\) | 399776.i | 1.69955i | ||||||||
\(486\) | −363602. | − | 252352.i | −1.53941 | − | 1.06840i | ||||
\(487\) | −118967. | −0.501615 | −0.250807 | − | 0.968037i | \(-0.580696\pi\) | ||||
−0.250807 | + | 0.968037i | \(0.580696\pi\) | |||||||
\(488\) | − | 423380.i | − | 1.77783i | ||||||
\(489\) | 67734.1 | − | 72757.1i | 0.283263 | − | 0.304269i | ||||
\(490\) | −63528.3 | −0.264591 | ||||||||
\(491\) | − | 250334.i | − | 1.03838i | −0.854658 | − | 0.519191i | \(-0.826233\pi\) | ||
0.854658 | − | 0.519191i | \(-0.173767\pi\) | |||||||
\(492\) | 462210. | + | 430300.i | 1.90945 | + | 1.77763i | ||||
\(493\) | 312051. | 1.28390 | ||||||||
\(494\) | − | 79980.6i | − | 0.327741i | ||||||
\(495\) | −18385.9 | − | 256798.i | −0.0750369 | − | 1.04805i | ||||
\(496\) | 581676. | 2.36438 | ||||||||
\(497\) | − | 434902.i | − | 1.76067i | ||||||
\(498\) | −344416. | + | 369957.i | −1.38875 | + | 1.49174i | ||||
\(499\) | 163877. | 0.658140 | 0.329070 | − | 0.944306i | \(-0.393265\pi\) | ||||
0.329070 | + | 0.944306i | \(0.393265\pi\) | |||||||
\(500\) | 628646.i | 2.51458i | ||||||||
\(501\) | −237767. | − | 221353.i | −0.947277 | − | 0.881879i | ||||
\(502\) | 116830. | 0.463605 | ||||||||
\(503\) | 151110.i | 0.597253i | 0.954370 | + | 0.298626i | \(0.0965285\pi\) | ||||
−0.954370 | + | 0.298626i | \(0.903472\pi\) | |||||||
\(504\) | −766546. | + | 54882.3i | −3.01771 | + | 0.216059i | ||||
\(505\) | 335224. | 1.31447 | ||||||||
\(506\) | − | 863987.i | − | 3.37448i | ||||||
\(507\) | 155289. | − | 166805.i | 0.604122 | − | 0.648921i | ||||
\(508\) | −894736. | −3.46711 | ||||||||
\(509\) | 493716.i | 1.90564i | 0.303533 | + | 0.952821i | \(0.401834\pi\) | ||||
−0.303533 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(510\) | 280418. | + | 261058.i | 1.07812 | + | 1.00369i | ||||
\(511\) | 197346. | 0.755766 | ||||||||
\(512\) | 312166.i | 1.19082i | ||||||||
\(513\) | −106441. | − | 85755.5i | −0.404457 | − | 0.325857i | ||||
\(514\) | 55460.6 | 0.209922 | ||||||||
\(515\) | − | 421483.i | − | 1.58915i | ||||||
\(516\) | 352048. | − | 378155.i | 1.32222 | − | 1.42027i | ||||
\(517\) | −246416. | −0.921910 | ||||||||
\(518\) | 99448.9i | 0.370630i | ||||||||
\(519\) | −237780. | − | 221364.i | −0.882754 | − | 0.821811i | ||||
\(520\) | −257515. | −0.952349 | ||||||||
\(521\) | 212011.i | 0.781056i | 0.920591 | + | 0.390528i | \(0.127708\pi\) | ||||
−0.920591 | + | 0.390528i | \(0.872292\pi\) | |||||||
\(522\) | 59475.8 | + | 830703.i | 0.218273 | + | 3.04863i | ||||
\(523\) | 59345.3 | 0.216962 | 0.108481 | − | 0.994099i | \(-0.465401\pi\) | ||||
0.108481 | + | 0.994099i | \(0.465401\pi\) | |||||||
\(524\) | 548414.i | 1.99731i | ||||||||
\(525\) | 533.257 | − | 572.802i | 0.00193472 | − | 0.00207819i | ||||
\(526\) | 839443. | 3.03403 | ||||||||
\(527\) | 184919.i | 0.665824i | ||||||||
\(528\) | −600077. | − | 558649.i | −2.15248 | − | 2.00388i | ||||
\(529\) | −539989. | −1.92963 | ||||||||
\(530\) | − | 832134.i | − | 2.96239i | ||||||
\(531\) | −36614.5 | + | 2621.48i | −0.129857 | + | 0.00929733i | ||||
\(532\) | −394391. | −1.39349 | ||||||||
\(533\) | − | 99383.1i | − | 0.349831i | ||||||
\(534\) | 503559. | − | 540901.i | 1.76591 | − | 1.89686i | ||||
\(535\) | 202327. | 0.706879 | ||||||||
\(536\) | 890425.i | 3.09933i | ||||||||
\(537\) | −29049.6 | − | 27044.1i | −0.100738 | − | 0.0937830i | ||||
\(538\) | −158088. | −0.546177 | ||||||||
\(539\) | 43218.3i | 0.148761i | ||||||||
\(540\) | −458810. | + | 569479.i | −1.57342 | + | 1.95295i | ||||
\(541\) | 87347.9 | 0.298440 | 0.149220 | − | 0.988804i | \(-0.452324\pi\) | ||||
0.149220 | + | 0.988804i | \(0.452324\pi\) | |||||||
\(542\) | 536785.i | 1.82727i | ||||||||
\(543\) | 266197. | − | 285937.i | 0.902824 | − | 0.969775i | ||||
\(544\) | 560414. | 1.89370 | ||||||||
\(545\) | − | 122255.i | − | 0.411598i | ||||||
\(546\) | 147096. | + | 136941.i | 0.493419 | + | 0.459355i | ||||
\(547\) | 224496. | 0.750298 | 0.375149 | − | 0.926964i | \(-0.377592\pi\) | ||||
0.375149 | + | 0.926964i | \(0.377592\pi\) | |||||||
\(548\) | 1.35659e6i | 4.51739i | ||||||||
\(549\) | 13512.9 | + | 188736.i | 0.0448337 | + | 0.626196i | ||||
\(550\) | 1585.00 | 0.00523969 | ||||||||
\(551\) | 257207.i | 0.847187i | ||||||||
\(552\) | −1.00635e6 | + | 1.08098e6i | −3.30272 | + | 3.54764i | ||||
\(553\) | −111441. | −0.364414 | ||||||||
\(554\) | − | 679996.i | − | 2.21558i | ||||||
\(555\) | 41683.4 | + | 38805.7i | 0.135325 | + | 0.125982i | ||||
\(556\) | −393023. | −1.27136 | ||||||||
\(557\) | − | 28993.3i | − | 0.0934518i | −0.998908 | − | 0.0467259i | \(-0.985121\pi\) | ||
0.998908 | − | 0.0467259i | \(-0.0148787\pi\) | |||||||
\(558\) | −492267. | + | 35244.8i | −1.58100 | + | 0.113195i | ||||
\(559\) | −81309.8 | −0.260207 | ||||||||
\(560\) | 935238.i | 2.98226i | ||||||||
\(561\) | 177598. | − | 190768.i | 0.564303 | − | 0.606150i | ||||
\(562\) | −330392. | −1.04606 | ||||||||
\(563\) | − | 398832.i | − | 1.25827i | −0.777297 | − | 0.629134i | \(-0.783410\pi\) | ||
0.777297 | − | 0.629134i | \(-0.216590\pi\) | |||||||
\(564\) | 512310. | + | 476942.i | 1.61055 | + | 1.49936i | ||||
\(565\) | 297727. | 0.932655 | ||||||||
\(566\) | − | 31787.4i | − | 0.0992253i | ||||||
\(567\) | 339962. | − | 48931.3i | 1.05746 | − | 0.152202i | ||||
\(568\) | −1.50567e6 | −4.66694 | ||||||||
\(569\) | 191717.i | 0.592155i | 0.955164 | + | 0.296078i | \(0.0956787\pi\) | ||||
−0.955164 | + | 0.296078i | \(0.904321\pi\) | |||||||
\(570\) | −215176. | + | 231133.i | −0.662285 | + | 0.711398i | ||||
\(571\) | 35119.6 | 0.107715 | 0.0538577 | − | 0.998549i | \(-0.482848\pi\) | ||||
0.0538577 | + | 0.998549i | \(0.482848\pi\) | |||||||
\(572\) | 291109.i | 0.889742i | ||||||||
\(573\) | −269856. | − | 251226.i | −0.821907 | − | 0.765165i | ||||
\(574\) | −685214. | −2.07971 | ||||||||
\(575\) | − | 1504.00i | − | 0.00454895i | ||||||
\(576\) | 40585.7 | + | 566864.i | 0.122329 | + | 1.70858i | ||||
\(577\) | −125393. | −0.376636 | −0.188318 | − | 0.982108i | \(-0.560303\pi\) | ||||
−0.188318 | + | 0.982108i | \(0.560303\pi\) | |||||||
\(578\) | − | 238151.i | − | 0.712848i | ||||||
\(579\) | −229733. | + | 246770.i | −0.685279 | + | 0.736097i | ||||
\(580\) | 1.37611e6 | 4.09070 | ||||||||
\(581\) | − | 392254.i | − | 1.16202i | ||||||
\(582\) | −790592. | − | 736012.i | −2.33403 | − | 2.17290i | ||||
\(583\) | −566101. | −1.66555 | ||||||||
\(584\) | − | 683229.i | − | 2.00327i | ||||||
\(585\) | 114796. | − | 8219.05i | 0.335441 | − | 0.0240165i | ||||
\(586\) | 86582.2 | 0.252135 | ||||||||
\(587\) | 241835.i | 0.701848i | 0.936404 | + | 0.350924i | \(0.114133\pi\) | ||||
−0.936404 | + | 0.350924i | \(0.885867\pi\) | |||||||
\(588\) | 83649.5 | − | 89852.7i | 0.241941 | − | 0.259882i | ||||
\(589\) | −152418. | −0.439346 | ||||||||
\(590\) | 84807.0i | 0.243628i | ||||||||
\(591\) | 399418. | + | 371844.i | 1.14354 | + | 1.06460i | ||||
\(592\) | 181360. | 0.517486 | ||||||||
\(593\) | 658549.i | 1.87275i | 0.351007 | + | 0.936373i | \(0.385839\pi\) | ||||
−0.351007 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(594\) | 541689. | + | 436420.i | 1.53524 | + | 1.23689i | ||||
\(595\) | −297318. | −0.839822 | ||||||||
\(596\) | − | 1.74338e6i | − | 4.90796i | ||||||
\(597\) | 231274. | − | 248424.i | 0.648900 | − | 0.697020i | ||||
\(598\) | 386228. | 1.08004 | ||||||||
\(599\) | 217294.i | 0.605611i | 0.953052 | + | 0.302805i | \(0.0979232\pi\) | ||||
−0.953052 | + | 0.302805i | \(0.902077\pi\) | |||||||
\(600\) | −1983.08 | − | 1846.18i | −0.00550857 | − | 0.00512827i | ||||
\(601\) | −103070. | −0.285353 | −0.142677 | − | 0.989769i | \(-0.545571\pi\) | ||||
−0.142677 | + | 0.989769i | \(0.545571\pi\) | |||||||
\(602\) | 560605.i | 1.54691i | ||||||||
\(603\) | −28419.5 | − | 396937.i | −0.0781595 | − | 1.09166i | ||||
\(604\) | 631361. | 1.73063 | ||||||||
\(605\) | 39103.1i | 0.106832i | ||||||||
\(606\) | −617167. | + | 662934.i | −1.68057 | + | 1.80520i | ||||
\(607\) | 405932. | 1.10173 | 0.550866 | − | 0.834594i | \(-0.314298\pi\) | ||||
0.550866 | + | 0.834594i | \(0.314298\pi\) | |||||||
\(608\) | 461919.i | 1.24956i | ||||||||
\(609\) | −473042. | − | 440384.i | −1.27545 | − | 1.18740i | ||||
\(610\) | 437153. | 1.17483 | ||||||||
\(611\) | − | 110155.i | − | 0.295069i | ||||||
\(612\) | −738468. | + | 52872.1i | −1.97165 | + | 0.141164i | ||||
\(613\) | −71073.7 | −0.189142 | −0.0945710 | − | 0.995518i | \(-0.530148\pi\) | ||||
−0.0945710 | + | 0.995518i | \(0.530148\pi\) | |||||||
\(614\) | 98959.0i | 0.262493i | ||||||||
\(615\) | −267376. | + | 287204.i | −0.706923 | + | 0.759346i | ||||
\(616\) | 1.20786e6 | 3.18314 | ||||||||
\(617\) | 442654.i | 1.16277i | 0.813628 | + | 0.581386i | \(0.197489\pi\) | ||||
−0.813628 | + | 0.581386i | \(0.802511\pi\) | |||||||
\(618\) | 833519. | + | 775975.i | 2.18242 | + | 2.03175i | ||||
\(619\) | −255374. | −0.666493 | −0.333246 | − | 0.942840i | \(-0.608144\pi\) | ||||
−0.333246 | + | 0.942840i | \(0.608144\pi\) | |||||||
\(620\) | 815470.i | 2.12141i | ||||||||
\(621\) | 414115. | − | 514004.i | 1.07384 | − | 1.33286i | ||||
\(622\) | −509812. | −1.31774 | ||||||||
\(623\) | 573500.i | 1.47760i | ||||||||
\(624\) | 249733. | − | 268252.i | 0.641367 | − | 0.688928i | ||||
\(625\) | −389584. | −0.997335 | ||||||||
\(626\) | − | 79658.6i | − | 0.203275i | ||||||
\(627\) | 157240. | + | 146385.i | 0.399970 | + | 0.372358i | ||||
\(628\) | 574790. | 1.45744 | ||||||||
\(629\) | 57655.5i | 0.145727i | ||||||||
\(630\) | −56667.7 | − | 791483.i | −0.142776 | − | 1.99416i | ||||
\(631\) | 200823. | 0.504376 | 0.252188 | − | 0.967678i | \(-0.418850\pi\) | ||||
0.252188 | + | 0.967678i | \(0.418850\pi\) | |||||||
\(632\) | 385818.i | 0.965935i | ||||||||
\(633\) | −270667. | + | 290739.i | −0.675505 | + | 0.725598i | ||||
\(634\) | 923564. | 2.29767 | ||||||||
\(635\) | − | 555963.i | − | 1.37879i | ||||||
\(636\) | 1.17695e6 | + | 1.09569e6i | 2.90967 | + | 2.70879i | ||||
\(637\) | −19319.9 | −0.0476130 | ||||||||
\(638\) | − | 1.30896e6i | − | 3.21576i | ||||||
\(639\) | 671202. | − | 48056.0i | 1.64381 | − | 0.117692i | ||||
\(640\) | 328866. | 0.802896 | ||||||||
\(641\) | − | 557807.i | − | 1.35759i | −0.734328 | − | 0.678794i | \(-0.762503\pi\) | ||
0.734328 | − | 0.678794i | \(-0.237497\pi\) | |||||||
\(642\) | −372495. | + | 400118.i | −0.903755 | + | 0.970774i | ||||
\(643\) | 117775. | 0.284859 | 0.142429 | − | 0.989805i | \(-0.454509\pi\) | ||||
0.142429 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(644\) | − | 1.90452e6i | − | 4.59214i | ||||||
\(645\) | 234975. | + | 218753.i | 0.564809 | + | 0.525816i | ||||
\(646\) | −319698. | −0.766081 | ||||||||
\(647\) | 179763.i | 0.429430i | 0.976677 | + | 0.214715i | \(0.0688823\pi\) | ||||
−0.976677 | + | 0.214715i | \(0.931118\pi\) | |||||||
\(648\) | −169404. | − | 1.17698e6i | −0.403435 | − | 2.80296i | ||||
\(649\) | 57694.2 | 0.136975 | ||||||||
\(650\) | 708.544i | 0.00167703i | ||||||||
\(651\) | 260968. | − | 280320.i | 0.615779 | − | 0.661443i | ||||
\(652\) | 443793. | 1.04396 | ||||||||
\(653\) | − | 369529.i | − | 0.866608i | −0.901248 | − | 0.433304i | \(-0.857348\pi\) | ||
0.901248 | − | 0.433304i | \(-0.142652\pi\) | |||||||
\(654\) | 241770. | + | 225078.i | 0.565257 | + | 0.526233i | ||||
\(655\) | −340768. | −0.794286 | ||||||||
\(656\) | 1.24959e6i | 2.90376i | ||||||||
\(657\) | 21806.5 | + | 304573.i | 0.0505190 | + | 0.705602i | ||||
\(658\) | −759487. | −1.75416 | ||||||||
\(659\) | − | 245142.i | − | 0.564477i | −0.959344 | − | 0.282239i | \(-0.908923\pi\) | ||
0.959344 | − | 0.282239i | \(-0.0910770\pi\) | |||||||
\(660\) | 783188. | − | 841267.i | 1.79795 | − | 1.93128i | ||||
\(661\) | −440649. | −1.00853 | −0.504266 | − | 0.863548i | \(-0.668237\pi\) | ||||
−0.504266 | + | 0.863548i | \(0.668237\pi\) | |||||||
\(662\) | 1.06548e6i | 2.43124i | ||||||||
\(663\) | 85279.1 | + | 79391.7i | 0.194006 | + | 0.180613i | ||||
\(664\) | −1.35801e6 | −3.08012 | ||||||||
\(665\) | − | 245063.i | − | 0.554160i | ||||||
\(666\) | −153483. | + | 10988.9i | −0.346029 | + | 0.0247746i | ||||
\(667\) | −1.24206e6 | −2.79184 | ||||||||
\(668\) | − | 1.45030e6i | − | 3.25016i | ||||||
\(669\) | −271257. | + | 291372.i | −0.606078 | + | 0.651023i | ||||
\(670\) | −919392. | −2.04810 | ||||||||
\(671\) | − | 297395.i | − | 0.660525i | ||||||
\(672\) | −849537. | − | 790888.i | −1.88124 | − | 1.75136i | ||||
\(673\) | 409414. | 0.903925 | 0.451963 | − | 0.892037i | \(-0.350724\pi\) | ||||
0.451963 | + | 0.892037i | \(0.350724\pi\) | |||||||
\(674\) | 862547.i | 1.89873i | ||||||||
\(675\) | 942.952 | + | 759.704i | 0.00206958 | + | 0.00166739i | ||||
\(676\) | 1.01745e6 | 2.22648 | ||||||||
\(677\) | 877372.i | 1.91429i | 0.289617 | + | 0.957143i | \(0.406472\pi\) | ||||
−0.289617 | + | 0.957143i | \(0.593528\pi\) | |||||||
\(678\) | −548133. | + | 588781.i | −1.19241 | + | 1.28084i | ||||
\(679\) | 838240. | 1.81815 | ||||||||
\(680\) | 1.02934e6i | 2.22608i | ||||||||
\(681\) | 124637. | + | 116033.i | 0.268754 | + | 0.250200i | ||||
\(682\) | 775676. | 1.66768 | ||||||||
\(683\) | 170253.i | 0.364967i | 0.983209 | + | 0.182483i | \(0.0584136\pi\) | ||||
−0.983209 | + | 0.182483i | \(0.941586\pi\) | |||||||
\(684\) | −43579.6 | − | 608680.i | −0.0931474 | − | 1.30100i | ||||
\(685\) | −842945. | −1.79646 | ||||||||
\(686\) | − | 808895.i | − | 1.71887i | ||||||
\(687\) | −197868. | + | 212541.i | −0.419239 | + | 0.450329i | ||||
\(688\) | 1.02235e6 | 2.15984 | ||||||||
\(689\) | − | 253064.i | − | 0.533079i | ||||||
\(690\) | −1.11615e6 | − | 1.03909e6i | −2.34435 | − | 2.18251i | ||||
\(691\) | −582038. | −1.21898 | −0.609488 | − | 0.792796i | \(-0.708625\pi\) | ||||
−0.609488 | + | 0.792796i | \(0.708625\pi\) | |||||||
\(692\) | − | 1.45037e6i | − | 3.02878i | ||||||
\(693\) | −538446. | + | 38551.1i | −1.12118 | + | 0.0802731i | ||||
\(694\) | 1.16593e6 | 2.42076 | ||||||||
\(695\) | − | 244213.i | − | 0.505591i | ||||||
\(696\) | −1.52464e6 | + | 1.63771e6i | −3.14739 | + | 3.38078i | ||||
\(697\) | −397253. | −0.817715 | ||||||||
\(698\) | 534372.i | 1.09681i | ||||||||
\(699\) | 145557. | + | 135508.i | 0.297905 | + | 0.277339i | ||||
\(700\) | 3493.89 | 0.00713040 | ||||||||
\(701\) | − | 441218.i | − | 0.897877i | −0.893563 | − | 0.448939i | \(-0.851802\pi\) | ||
0.893563 | − | 0.448939i | \(-0.148198\pi\) | |||||||
\(702\) | −195093. | + | 242151.i | −0.395883 | + | 0.491374i | ||||
\(703\) | −47522.3 | −0.0961584 | ||||||||
\(704\) | − | 893220.i | − | 1.80224i | ||||||
\(705\) | −296358. | + | 318335.i | −0.596263 | + | 0.640480i | ||||
\(706\) | 482239. | 0.967504 | ||||||||
\(707\) | − | 702888.i | − | 1.40620i | ||||||
\(708\) | −119949. | − | 111668.i | −0.239292 | − | 0.222772i | ||||
\(709\) | 338754. | 0.673895 | 0.336947 | − | 0.941523i | \(-0.390606\pi\) | ||||
0.336947 | + | 0.941523i | \(0.390606\pi\) | |||||||
\(710\) | − | 1.55465e6i | − | 3.08401i | ||||||
\(711\) | −12314.1 | − | 171991.i | −0.0243591 | − | 0.340226i | ||||
\(712\) | 1.98550e6 | 3.91661 | ||||||||
\(713\) | − | 736032.i | − | 1.44783i | ||||||
\(714\) | 547380. | − | 587972.i | 1.07372 | − | 1.15335i | ||||
\(715\) | −180887. | −0.353830 | ||||||||
\(716\) | − | 177193.i | − | 0.345636i | ||||||
\(717\) | 164546. | + | 153187.i | 0.320074 | + | 0.297977i | ||||
\(718\) | −285591. | −0.553982 | ||||||||
\(719\) | 380368.i | 0.735777i | 0.929870 | + | 0.367889i | \(0.119919\pi\) | ||||
−0.929870 | + | 0.367889i | \(0.880081\pi\) | |||||||
\(720\) | −1.44339e6 | + | 103342.i | −2.78432 | + | 0.199348i | ||||
\(721\) | −883754. | −1.70005 | ||||||||
\(722\) | 713291.i | 1.36833i | ||||||||
\(723\) | −201978. | + | 216956.i | −0.386392 | + | 0.415046i | ||||
\(724\) | 1.74412e6 | 3.32735 | ||||||||
\(725\) | − | 2278.58i | − | 0.00433500i | ||||||
\(726\) | −77329.7 | − | 71991.1i | −0.146715 | − | 0.136586i | ||||
\(727\) | −698672. | −1.32192 | −0.660959 | − | 0.750422i | \(-0.729850\pi\) | ||||
−0.660959 | + | 0.750422i | \(0.729850\pi\) | |||||||
\(728\) | 539950.i | 1.01881i | ||||||||
\(729\) | 113083. | + | 519270.i | 0.212786 | + | 0.977099i | ||||
\(730\) | 705455. | 1.32380 | ||||||||
\(731\) | 325011.i | 0.608224i | ||||||||
\(732\) | −575612. | + | 618297.i | −1.07426 | + | 1.15392i | ||||
\(733\) | 633385. | 1.17885 | 0.589427 | − | 0.807822i | \(-0.299354\pi\) | ||||
0.589427 | + | 0.807822i | \(0.299354\pi\) | |||||||
\(734\) | − | 1.27945e6i | − | 2.37482i | ||||||
\(735\) | 55831.8 | + | 51977.4i | 0.103349 | + | 0.0962143i | ||||
\(736\) | −2.23062e6 | −4.11784 | ||||||||
\(737\) | 625462.i | 1.15151i | ||||||||
\(738\) | −75715.1 | − | 1.05752e6i | −0.139018 | − | 1.94167i | ||||
\(739\) | 809388. | 1.48207 | 0.741034 | − | 0.671468i | \(-0.234336\pi\) | ||||
0.741034 | + | 0.671468i | \(0.234336\pi\) | |||||||
\(740\) | 254255.i | 0.464307i | ||||||||
\(741\) | −65438.3 | + | 70291.0i | −0.119178 | + | 0.128016i | ||||
\(742\) | −1.74479e6 | −3.16910 | ||||||||
\(743\) | 93385.4i | 0.169161i | 0.996417 | + | 0.0845807i | \(0.0269551\pi\) | ||||
−0.996417 | + | 0.0845807i | \(0.973045\pi\) | |||||||
\(744\) | −970490. | − | 903490.i | −1.75325 | − | 1.63222i | ||||
\(745\) | 1.08329e6 | 1.95178 | ||||||||
\(746\) | − | 477735.i | − | 0.858438i | ||||||
\(747\) | 605380. | − | 43343.4i | 1.08489 | − | 0.0776750i | ||||
\(748\) | 1.16362e6 | 2.07973 | ||||||||
\(749\) | − | 424233.i | − | 0.756206i | ||||||
\(750\) | 719159. | − | 772489.i | 1.27850 | − | 1.37331i | ||||
\(751\) | 728422. | 1.29153 | 0.645763 | − | 0.763538i | \(-0.276539\pi\) | ||||
0.645763 | + | 0.763538i | \(0.276539\pi\) | |||||||
\(752\) | 1.38504e6i | 2.44921i | ||||||||
\(753\) | −102676. | − | 95587.8i | −0.181084 | − | 0.168582i | ||||
\(754\) | 585143. | 1.02925 | ||||||||
\(755\) | 392309.i | 0.688232i | ||||||||
\(756\) | 1.19407e6 | + | 962019.i | 2.08923 | + | 1.68322i | ||||
\(757\) | 625905. | 1.09224 | 0.546118 | − | 0.837708i | \(-0.316105\pi\) | ||||
0.546118 | + | 0.837708i | \(0.316105\pi\) | |||||||
\(758\) | 2.08921e6i | 3.63617i | ||||||||
\(759\) | −706894. | + | 759315.i | −1.22707 | + | 1.31807i | ||||
\(760\) | −848428. | −1.46888 | ||||||||
\(761\) | 545569.i | 0.942064i | 0.882116 | + | 0.471032i | \(0.156118\pi\) | ||||
−0.882116 | + | 0.471032i | \(0.843882\pi\) | |||||||
\(762\) | 1.09946e6 | + | 1.02356e6i | 1.89353 | + | 1.76280i | ||||
\(763\) | −256341. | −0.440320 | ||||||||
\(764\) | − | 1.64603e6i | − | 2.82001i | ||||||
\(765\) | −32853.2 | − | 458863.i | −0.0561376 | − | 0.784079i | ||||
\(766\) | 615832. | 1.04955 | ||||||||
\(767\) | 25791.0i | 0.0438407i | ||||||||
\(768\) | 82972.7 | − | 89125.7i | 0.140674 | − | 0.151106i | ||||
\(769\) | −577208. | −0.976066 | −0.488033 | − | 0.872825i | \(-0.662285\pi\) | ||||
−0.488033 | + | 0.872825i | \(0.662285\pi\) | |||||||
\(770\) | 1.24716e6i | 2.10348i | ||||||||
\(771\) | −48741.5 | − | 45376.6i | −0.0819956 | − | 0.0763349i | ||||
\(772\) | −1.50521e6 | −2.52559 | ||||||||
\(773\) | 1.00968e6i | 1.68977i | 0.534951 | + | 0.844883i | \(0.320330\pi\) | ||||
−0.534951 | + | 0.844883i | \(0.679670\pi\) | |||||||
\(774\) | −865204. | + | 61946.0i | −1.44423 | + | 0.103403i | ||||
\(775\) | 1350.27 | 0.00224810 | ||||||||
\(776\) | − | 2.90205e6i | − | 4.81927i | ||||||
\(777\) | 81366.8 | − | 87400.7i | 0.134774 | − | 0.144768i | ||||
\(778\) | −757578. | −1.25161 | ||||||||
\(779\) | − | 327435.i | − | 0.539572i | ||||||
\(780\) | 376071. | + | 350108.i | 0.618132 | + | 0.575458i | ||||
\(781\) | −1.05763e6 | −1.73393 | ||||||||
\(782\) | − | 1.54383e6i | − | 2.52456i | ||||||
\(783\) | 627392. | − | 778725.i | 1.02333 | − | 1.27017i | ||||
\(784\) | 242918. | 0.395210 | ||||||||
\(785\) | 357158.i | 0.579590i | ||||||||
\(786\) | 627375. | − | 673899.i | 1.01550 | − | 1.09081i | ||||
\(787\) | −153315. | −0.247534 | −0.123767 | − | 0.992311i | \(-0.539498\pi\) | ||||
−0.123767 | + | 0.992311i | \(0.539498\pi\) | |||||||
\(788\) | 2.43631e6i | 3.92356i | ||||||||
\(789\) | −737745. | − | 686813.i | −1.18509 | − | 1.10328i | ||||
\(790\) | −398369. | −0.638310 | ||||||||
\(791\) | − | 624265.i | − | 0.997738i | ||||||
\(792\) | 133467. | + | 1.86414e6i | 0.212776 | + | 2.97186i | ||||
\(793\) | 132945. | 0.211409 | ||||||||
\(794\) | − | 452473.i | − | 0.717715i | ||||||
\(795\) | −680833. | + | 731321.i | −1.07722 | + | 1.15711i | ||||
\(796\) | 1.51530e6 | 2.39151 | ||||||||
\(797\) | − | 620724.i | − | 0.977197i | −0.872509 | − | 0.488598i | \(-0.837508\pi\) | ||
0.872509 | − | 0.488598i | \(-0.162492\pi\) | |||||||
\(798\) | 484634. | + | 451176.i | 0.761040 | + | 0.708500i | ||||
\(799\) | −440313. | −0.689712 | ||||||||
\(800\) | − | 4092.12i | − | 0.00639393i | ||||||
\(801\) | −885106. | + | 63370.9i | −1.37953 | + | 0.0987699i | ||||
\(802\) | −684444. | −1.06412 | ||||||||
\(803\) | − | 479921.i | − | 0.744284i | ||||||
\(804\) | 1.21059e6 | − | 1.30036e6i | 1.87277 | − | 2.01165i | ||||
\(805\) | 1.18342e6 | 1.82619 | ||||||||
\(806\) | 346750.i | 0.533761i | ||||||||
\(807\) | 138935. | + | 129344.i | 0.213337 | + | 0.198609i | ||||
\(808\) | −2.43345e6 | −3.72735 | ||||||||
\(809\) | 713419.i | 1.09005i | 0.838419 | + | 0.545027i | \(0.183480\pi\) | ||||
−0.838419 | + | 0.545027i | \(0.816520\pi\) | |||||||
\(810\) | 1.21527e6 | − | 174915.i | 1.85226 | − | 0.266598i | ||||
\(811\) | 1.03006e6 | 1.56610 | 0.783050 | − | 0.621959i | \(-0.213663\pi\) | ||||
0.783050 | + | 0.621959i | \(0.213663\pi\) | |||||||
\(812\) | − | 2.88539e6i | − | 4.37615i | ||||||
\(813\) | 439185. | − | 471754.i | 0.664457 | − | 0.713731i | ||||
\(814\) | 241847. | 0.364999 | ||||||||
\(815\) | 275760.i | 0.415160i | ||||||||
\(816\) | −1.07226e6 | − | 998231.i | −1.61034 | − | 1.49917i | ||||
\(817\) | −267889. | −0.401339 | ||||||||
\(818\) | − | 177419.i | − | 0.265152i | ||||||
\(819\) | −17233.5 | − | 240701.i | −0.0256924 | − | 0.358848i | ||||
\(820\) | −1.75184e6 | −2.60536 | ||||||||
\(821\) | − | 796533.i | − | 1.18173i | −0.806771 | − | 0.590864i | \(-0.798787\pi\) | ||
0.806771 | − | 0.590864i | \(-0.201213\pi\) | |||||||
\(822\) | 1.55191e6 | − | 1.66700e6i | 2.29680 | − | 2.46712i | ||||
\(823\) | −574913. | −0.848795 | −0.424397 | − | 0.905476i | \(-0.639514\pi\) | ||||
−0.424397 | + | 0.905476i | \(0.639514\pi\) | |||||||
\(824\) | 3.05962e6i | 4.50623i | ||||||||
\(825\) | −1392.98 | − | 1296.81i | −0.00204662 | − | 0.00190533i | ||||
\(826\) | 177821. | 0.260629 | ||||||||
\(827\) | 342178.i | 0.500312i | 0.968206 | + | 0.250156i | \(0.0804819\pi\) | ||||
−0.968206 | + | 0.250156i | \(0.919518\pi\) | |||||||
\(828\) | 2.93933e6 | − | 210447.i | 4.28733 | − | 0.306960i | ||||
\(829\) | −46861.3 | −0.0681876 | −0.0340938 | − | 0.999419i | \(-0.510855\pi\) | ||||
−0.0340938 | + | 0.999419i | \(0.510855\pi\) | |||||||
\(830\) | − | 1.40219e6i | − | 2.03541i | ||||||
\(831\) | −556357. | + | 597614.i | −0.805659 | + | 0.865404i | ||||
\(832\) | 399296. | 0.576831 | ||||||||
\(833\) | 77225.2i | 0.111293i | ||||||||
\(834\) | 482952. | + | 449610.i | 0.694340 | + | 0.646404i | ||||
\(835\) | 901173. | 1.29251 | ||||||||
\(836\) | 959109.i | 1.37232i | ||||||||
\(837\) | 461466. | + | 371787.i | 0.658701 | + | 0.530692i | ||||
\(838\) | 872363. | 1.24225 | ||||||||
\(839\) | 531080.i | 0.754460i | 0.926120 | + | 0.377230i | \(0.123123\pi\) | ||||
−0.926120 | + | 0.377230i | \(0.876877\pi\) | |||||||
\(840\) | 1.45266e6 | − | 1.56038e6i | 2.05876 | − | 2.21143i | ||||
\(841\) | −1.17446e6 | −1.66053 | ||||||||
\(842\) | − | 2.41187e6i | − | 3.40197i | ||||||
\(843\) | 290365. | + | 270319.i | 0.408591 | + | 0.380383i | ||||
\(844\) | −1.77341e6 | −2.48957 | ||||||||
\(845\) | 632214.i | 0.885422i | ||||||||
\(846\) | −83922.0 | − | 1.17215e6i | −0.117256 | − | 1.63772i | ||||
\(847\) | 81990.2 | 0.114287 | ||||||||
\(848\) | 3.18190e6i | 4.42481i | ||||||||
\(849\) | −26007.7 | + | 27936.4i | −0.0360817 | + | 0.0387574i | ||||
\(850\) | 2832.19 | 0.00391999 | ||||||||
\(851\) | − | 229486.i | − | 0.316882i | ||||||
\(852\) | 2.19885e6 | + | 2.04705e6i | 3.02912 | + | 2.82000i | ||||
\(853\) | 545553. | 0.749788 | 0.374894 | − | 0.927068i | \(-0.377679\pi\) | ||||
0.374894 | + | 0.927068i | \(0.377679\pi\) | |||||||
\(854\) | − | 916610.i | − | 1.25681i | ||||||
\(855\) | 378216. | − | 27079.1i | 0.517377 | − | 0.0370426i | ||||
\(856\) | −1.46873e6 | −2.00444 | ||||||||
\(857\) | 1.21696e6i | 1.65698i | 0.560007 | + | 0.828488i | \(0.310799\pi\) | ||||
−0.560007 | + | 0.828488i | \(0.689201\pi\) | |||||||
\(858\) | 333023. | − | 357719.i | 0.452376 | − | 0.485923i | ||||
\(859\) | −57401.7 | −0.0777926 | −0.0388963 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388963 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(860\) | 1.43326e6i | 1.93789i | ||||||||
\(861\) | 602201. | + | 560627.i | 0.812335 | + | 0.756253i | ||||
\(862\) | 2.24891e6 | 3.02661 | ||||||||
\(863\) | 157657.i | 0.211686i | 0.994383 | + | 0.105843i | \(0.0337540\pi\) | ||||
−0.994383 | + | 0.105843i | \(0.966246\pi\) | |||||||
\(864\) | 1.12674e6 | − | 1.39852e6i | 1.50937 | − | 1.87344i | ||||
\(865\) | 901219. | 1.20448 | ||||||||
\(866\) | − | 308555.i | − | 0.411431i | ||||||
\(867\) | −194850. | + | 209299.i | −0.259216 | + | 0.278439i | ||||
\(868\) | 1.70986e6 | 2.26945 | ||||||||
\(869\) | 271011.i | 0.358878i | ||||||||
\(870\) | −1.69098e6 | − | 1.57424e6i | −2.23409 | − | 2.07986i | ||||
\(871\) | −279600. | −0.368554 | ||||||||
\(872\) | 887471.i | 1.16713i | ||||||||
\(873\) | 92624.1 | + | 1.29369e6i | 0.121533 | + | 1.69747i | ||||
\(874\) | 1.27249e6 | 1.66584 | ||||||||
\(875\) | 819046.i | 1.06977i | ||||||||
\(876\) | −928893. | + | 997777.i | −1.21048 | + | 1.30025i | ||||
\(877\) | 949711. | 1.23479 | 0.617394 | − | 0.786654i | \(-0.288188\pi\) | ||||
0.617394 | + | 0.786654i | \(0.288188\pi\) | |||||||
\(878\) | 991583.i | 1.28629i | ||||||||
\(879\) | −76092.8 | − | 70839.5i | −0.0984840 | − | 0.0916849i | ||||
\(880\) | 2.27438e6 | 2.93696 | ||||||||
\(881\) | − | 175198.i | − | 0.225724i | −0.993611 | − | 0.112862i | \(-0.963998\pi\) | ||
0.993611 | − | 0.112862i | \(-0.0360018\pi\) | |||||||
\(882\) | −205579. | + | 14718.9i | −0.264267 | + | 0.0189207i | ||||
\(883\) | −700135. | −0.897967 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(884\) | 520173.i | 0.665646i | ||||||||
\(885\) | 69387.1 | − | 74532.6i | 0.0885915 | − | 0.0951612i | ||||
\(886\) | 944244. | 1.20286 | ||||||||
\(887\) | 693550.i | 0.881517i | 0.897626 | + | 0.440758i | \(0.145290\pi\) | ||||
−0.897626 | + | 0.440758i | \(0.854710\pi\) | |||||||
\(888\) | −302588. | − | 281698.i | −0.383730 | − | 0.357238i | ||||
\(889\) | −1.16573e6 | −1.47500 | ||||||||
\(890\) | 2.05009e6i | 2.58818i | ||||||||
\(891\) | −118995. | − | 826745.i | −0.149890 | − | 1.04140i | ||||
\(892\) | −1.77727e6 | −2.23370 | ||||||||
\(893\) | − | 362926.i | − | 0.455109i | ||||||
\(894\) | −1.99440e6 | + | 2.14230e6i | −2.49538 | + | 2.68043i | ||||
\(895\) | 110102. | 0.137452 | ||||||||
\(896\) | − | 689557.i | − | 0.858923i | ||||||
\(897\) | −339437. | − | 316003.i | −0.421865 | − | 0.392741i | ||||
\(898\) | −973499. | −1.20721 | ||||||||
\(899\) | − | 1.11510e6i | − | 1.37973i | ||||||
\(900\) | 386.070 | + | 5392.26i | 0.000476629 | + | 0.00665712i | ||||
\(901\) | −1.01155e6 | −1.24605 | ||||||||
\(902\) | 1.66635e6i | 2.04811i | ||||||||
\(903\) | 458674. | − | 492688.i | 0.562508 | − | 0.604222i | ||||
\(904\) | −2.16125e6 | −2.64466 | ||||||||
\(905\) | 1.08374e6i | 1.32321i | ||||||||
\(906\) | −775825. | − | 722265.i | −0.945165 | − | 0.879913i | ||||
\(907\) | 1.02333e6 | 1.24395 | 0.621974 | − | 0.783038i | \(-0.286331\pi\) | ||||
0.621974 | + | 0.783038i | \(0.286331\pi\) | |||||||
\(908\) | 760245.i | 0.922109i | ||||||||
\(909\) | 1.08479e6 | − | 77667.9i | 1.31286 | − | 0.0939970i | ||||
\(910\) | −557516. | −0.673247 | ||||||||
\(911\) | − | 199363.i | − | 0.240219i | −0.992761 | − | 0.120110i | \(-0.961675\pi\) | ||
0.992761 | − | 0.120110i | \(-0.0383246\pi\) | |||||||
\(912\) | 822788. | − | 883803.i | 0.989232 | − | 1.06259i | ||||
\(913\) | −953911. | −1.14437 | ||||||||
\(914\) | 476068.i | 0.569871i | ||||||||
\(915\) | −384192. | − | 357668.i | −0.458887 | − | 0.427207i | ||||
\(916\) | −1.29643e6 | −1.54510 | ||||||||
\(917\) | 714513.i | 0.849712i | ||||||||
\(918\) | 967925. | + | 779823.i | 1.14857 | + | 0.925360i | ||||
\(919\) | 174760. | 0.206924 | 0.103462 | − | 0.994633i | \(-0.467008\pi\) | ||||
0.103462 | + | 0.994633i | \(0.467008\pi\) | |||||||
\(920\) | − | 4.09708e6i | − | 4.84059i | ||||||
\(921\) | 80965.9 | − | 86970.1i | 0.0954516 | − | 0.102530i | ||||
\(922\) | −566941. | −0.666924 | ||||||||
\(923\) | − | 472791.i | − | 0.554965i | ||||||
\(924\) | −1.76394e6 | − | 1.64217e6i | −2.06605 | − | 1.92342i | ||||
\(925\) | 420.998 | 0.000492036 | ||||||||
\(926\) | 1.35300e6i | 1.57788i | ||||||||
\(927\) | −97653.4 | − | 1.36393e6i | −0.113639 | − | 1.58721i | ||||
\(928\) | −3.37942e6 | −3.92416 | ||||||||
\(929\) | 947396.i | 1.09774i | 0.835907 | + | 0.548871i | \(0.184942\pi\) | ||||
−0.835907 | + | 0.548871i | \(0.815058\pi\) | |||||||
\(930\) | 932882. | − | 1.00206e6i | 1.07860 | − | 1.15859i | ||||
\(931\) | −63652.6 | −0.0734373 | ||||||||
\(932\) | 887846.i | 1.02213i | ||||||||
\(933\) | 448048. | + | 417116.i | 0.514708 | + | 0.479174i | ||||
\(934\) | 431142. | 0.494227 | ||||||||
\(935\) | 723039.i | 0.827063i | ||||||||
\(936\) | −833327. | + | 59663.6i | −0.951182 | + | 0.0681017i | ||||
\(937\) | −393273. | −0.447935 | −0.223968 | − | 0.974597i | \(-0.571901\pi\) | ||||
−0.223968 | + | 0.974597i | \(0.571901\pi\) | |||||||
\(938\) | 1.92775e6i | 2.19102i | ||||||||
\(939\) | −65174.8 | + | 70008.0i | −0.0739178 | + | 0.0793993i | ||||
\(940\) | −1.94173e6 | −2.19752 | ||||||||
\(941\) | − | 211502.i | − | 0.238856i | −0.992843 | − | 0.119428i | \(-0.961894\pi\) | ||
0.992843 | − | 0.119428i | \(-0.0381060\pi\) | |||||||
\(942\) | −706310. | − | 657548.i | −0.795964 | − | 0.741013i | ||||
\(943\) | 1.58119e6 | 1.77812 | ||||||||
\(944\) | − | 324283.i | − | 0.363899i | ||||||
\(945\) | −597770. | + | 741959.i | −0.669377 | + | 0.830838i | ||||
\(946\) | 1.36332e6 | 1.52341 | ||||||||
\(947\) | − | 1.54738e6i | − | 1.72543i | −0.505687 | − | 0.862717i | \(-0.668761\pi\) | ||
0.505687 | − | 0.862717i | \(-0.331239\pi\) | |||||||
\(948\) | 524544. | − | 563443.i | 0.583667 | − | 0.626950i | ||||
\(949\) | 214539. | 0.238218 | ||||||||
\(950\) | 2334.42i | 0.00258662i | ||||||||
\(951\) | −811675. | − | 755639.i | −0.897472 | − | 0.835513i | ||||
\(952\) | 2.15829e6 | 2.38142 | ||||||||
\(953\) | − | 589681.i | − | 0.649279i | −0.945838 | − | 0.324640i | \(-0.894757\pi\) | ||
0.945838 | − | 0.324640i | \(-0.105243\pi\) | |||||||
\(954\) | −192797. | − | 2.69281e6i | −0.211838 | − | 2.95876i | ||||
\(955\) | 1.02279e6 | 1.12145 | ||||||||
\(956\) | 1.00368e6i | 1.09819i | ||||||||
\(957\) | −1.07096e6 | + | 1.15038e6i | −1.16936 | + | 1.25608i | ||||
\(958\) | −2.52929e6 | −2.75592 | ||||||||
\(959\) | 1.76746e6i | 1.92182i | ||||||||
\(960\) | −1.15391e6 | − | 1.07425e6i | −1.25207 | − | 1.16564i | ||||
\(961\) | −262722. | −0.284478 | ||||||||
\(962\) | 108113.i | 0.116823i | ||||||||
\(963\) | 654735. | − | 46877.0i | 0.706013 | − | 0.0505484i | ||||
\(964\) | −1.32336e6 | −1.42404 | ||||||||
\(965\) | − | 935293.i | − | 1.00437i | ||||||
\(966\) | −2.17874e6 | + | 2.34031e6i | −2.33481 | + | 2.50795i | ||||
\(967\) | −126892. | −0.135700 | −0.0678501 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678501 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(968\) | − | 283856.i | − | 0.302934i | ||||||
\(969\) | 280967. | + | 261569.i | 0.299231 | + | 0.278573i | ||||
\(970\) | 2.99646e6 | 3.18467 | ||||||||
\(971\) | 76870.5i | 0.0815308i | 0.999169 | + | 0.0407654i | \(0.0129796\pi\) | ||||
−0.999169 | + | 0.0407654i | \(0.987020\pi\) | |||||||
\(972\) | −1.35278e6 | + | 1.94915e6i | −1.43184 | + | 2.06307i | ||||
\(973\) | −512059. | −0.540871 | ||||||||
\(974\) | 891702.i | 0.939943i | ||||||||
\(975\) | 579.715 | − | 622.704i | 0.000609825 | − | 0.000655047i | ||||
\(976\) | −1.67158e6 | −1.75480 | ||||||||
\(977\) | − | 1.22620e6i | − | 1.28462i | −0.766447 | − | 0.642308i | \(-0.777977\pi\) | ||
0.766447 | − | 0.642308i | \(-0.222023\pi\) | |||||||
\(978\) | −545339. | − | 507690.i | −0.570150 | − | 0.530788i | ||||
\(979\) | 1.39468e6 | 1.45515 | ||||||||
\(980\) | 340555.i | 0.354597i | ||||||||
\(981\) | −28325.2 | − | 395620.i | −0.0294330 | − | 0.411094i | ||||
\(982\) | −1.87634e6 | −1.94576 | ||||||||
\(983\) | 1.20316e6i | 1.24514i | 0.782565 | + | 0.622569i | \(0.213911\pi\) | ||||
−0.782565 | + | 0.622569i | \(0.786089\pi\) | |||||||
\(984\) | 1.94093e6 | − | 2.08487e6i | 2.00457 | − | 2.15322i | ||||
\(985\) | −1.51385e6 | −1.56031 | ||||||||
\(986\) | − | 2.33893e6i | − | 2.40582i | ||||||
\(987\) | 667475. | + | 621394.i | 0.685174 | + | 0.637871i | ||||
\(988\) | −428750. | −0.439229 | ||||||||
\(989\) | − | 1.29364e6i | − | 1.32258i | ||||||
\(990\) | −1.92479e6 | + | 137809.i | −1.96387 | + | 0.140607i | ||||
\(991\) | −608943. | −0.620053 | −0.310027 | − | 0.950728i | \(-0.600338\pi\) | ||||
−0.310027 | + | 0.950728i | \(0.600338\pi\) | |||||||
\(992\) | − | 2.00262e6i | − | 2.03505i | ||||||
\(993\) | 871749. | − | 936395.i | 0.884083 | − | 0.949643i | ||||
\(994\) | −3.25974e6 | −3.29921 | ||||||||
\(995\) | 941564.i | 0.951051i | ||||||||
\(996\) | 1.98322e6 | + | 1.84631e6i | 1.99918 | + | 1.86116i | ||||
\(997\) | −741591. | −0.746060 | −0.373030 | − | 0.927819i | \(-0.621681\pi\) | ||||
−0.373030 | + | 0.927819i | \(0.621681\pi\) | |||||||
\(998\) | − | 1.22832e6i | − | 1.23325i | ||||||
\(999\) | 143880. | + | 115919.i | 0.144168 | + | 0.116151i |
(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 | 177.5.b.a.119.3 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.76 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.3 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.76 | yes | 78 | 3.2 | odd | 2 | inner |