Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, 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("33.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 162x^{12} + 10041x^{10} + 298396x^{8} + 4418856x^{6} + 32113344x^{4} + 102865552x^{2} + 102193344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{9}\cdot 11^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.9 | ||
Root | \(2.36054i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.5.b.a.23.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36054i | 0.590134i | 0.955477 | + | 0.295067i | \(0.0953420\pi\) | ||||
−0.955477 | + | 0.295067i | \(0.904658\pi\) | |||||||
\(3\) | 7.81446 | + | 4.46478i | 0.868273 | + | 0.496087i | ||||
\(4\) | 10.4279 | 0.651742 | ||||||||
\(5\) | − | 9.92884i | − | 0.397154i | −0.980085 | − | 0.198577i | \(-0.936368\pi\) | ||
0.980085 | − | 0.198577i | \(-0.0636319\pi\) | |||||||
\(6\) | −10.5393 | + | 18.4463i | −0.292758 | + | 0.512397i | ||||
\(7\) | −13.3317 | −0.272075 | −0.136037 | − | 0.990704i | \(-0.543437\pi\) | ||||
−0.136037 | + | 0.990704i | \(0.543437\pi\) | |||||||
\(8\) | 62.3839i | 0.974749i | ||||||||
\(9\) | 41.1315 | + | 69.7797i | 0.507796 | + | 0.861478i | ||||
\(10\) | 23.4374 | 0.234374 | ||||||||
\(11\) | − | 36.4829i | − | 0.301511i | ||||||
\(12\) | 81.4881 | + | 46.5582i | 0.565890 | + | 0.323321i | ||||
\(13\) | −138.667 | −0.820515 | −0.410257 | − | 0.911970i | \(-0.634561\pi\) | ||||
−0.410257 | + | 0.911970i | \(0.634561\pi\) | |||||||
\(14\) | − | 31.4699i | − | 0.160561i | ||||||
\(15\) | 44.3301 | − | 77.5885i | 0.197023 | − | 0.344838i | ||||
\(16\) | 19.5864 | 0.0765092 | ||||||||
\(17\) | − | 445.449i | − | 1.54135i | −0.637231 | − | 0.770673i | \(-0.719920\pi\) | ||
0.637231 | − | 0.770673i | \(-0.280080\pi\) | |||||||
\(18\) | −164.717 | + | 97.0923i | −0.508387 | + | 0.299668i | ||||
\(19\) | −151.893 | −0.420756 | −0.210378 | − | 0.977620i | \(-0.567470\pi\) | ||||
−0.210378 | + | 0.977620i | \(0.567470\pi\) | |||||||
\(20\) | − | 103.537i | − | 0.258842i | ||||||
\(21\) | −104.180 | − | 59.5229i | −0.236235 | − | 0.134973i | ||||
\(22\) | 86.1191 | 0.177932 | ||||||||
\(23\) | − | 661.969i | − | 1.25136i | −0.780080 | − | 0.625680i | \(-0.784822\pi\) | ||
0.780080 | − | 0.625680i | \(-0.215178\pi\) | |||||||
\(24\) | −278.531 | + | 487.497i | −0.483560 | + | 0.846348i | ||||
\(25\) | 526.418 | 0.842269 | ||||||||
\(26\) | − | 327.328i | − | 0.484214i | ||||||
\(27\) | 9.86893 | + | 728.933i | 0.0135376 | + | 0.999908i | ||||
\(28\) | −139.021 | −0.177322 | ||||||||
\(29\) | 130.511i | 0.155186i | 0.996985 | + | 0.0775929i | \(0.0247234\pi\) | ||||
−0.996985 | + | 0.0775929i | \(0.975277\pi\) | |||||||
\(30\) | 183.150 | + | 104.643i | 0.203500 | + | 0.116270i | ||||
\(31\) | −1039.18 | −1.08135 | −0.540677 | − | 0.841230i | \(-0.681832\pi\) | ||||
−0.540677 | + | 0.841230i | \(0.681832\pi\) | |||||||
\(32\) | 1044.38i | 1.01990i | ||||||||
\(33\) | 162.888 | − | 285.094i | 0.149576 | − | 0.261794i | ||||
\(34\) | 1051.50 | 0.909601 | ||||||||
\(35\) | 132.368i | 0.108055i | ||||||||
\(36\) | 428.913 | + | 727.653i | 0.330952 | + | 0.561461i | ||||
\(37\) | 1110.44 | 0.811135 | 0.405568 | − | 0.914065i | \(-0.367074\pi\) | ||||
0.405568 | + | 0.914065i | \(0.367074\pi\) | |||||||
\(38\) | − | 358.549i | − | 0.248303i | ||||||
\(39\) | −1083.61 | − | 619.118i | −0.712431 | − | 0.407046i | ||||
\(40\) | 619.400 | 0.387125 | ||||||||
\(41\) | 1278.11i | 0.760326i | 0.924919 | + | 0.380163i | \(0.124132\pi\) | ||||
−0.924919 | + | 0.380163i | \(0.875868\pi\) | |||||||
\(42\) | 140.506 | − | 245.920i | 0.0796520 | − | 0.139410i | ||||
\(43\) | −1137.18 | −0.615023 | −0.307511 | − | 0.951544i | \(-0.599496\pi\) | ||||
−0.307511 | + | 0.951544i | \(0.599496\pi\) | |||||||
\(44\) | − | 380.439i | − | 0.196508i | ||||||
\(45\) | 692.831 | − | 408.388i | 0.342139 | − | 0.201673i | ||||
\(46\) | 1562.60 | 0.738470 | ||||||||
\(47\) | 915.602i | 0.414487i | 0.978289 | + | 0.207244i | \(0.0664493\pi\) | ||||
−0.978289 | + | 0.207244i | \(0.933551\pi\) | |||||||
\(48\) | 153.057 | + | 87.4488i | 0.0664309 | + | 0.0379552i | ||||
\(49\) | −2223.27 | −0.925975 | ||||||||
\(50\) | 1242.63i | 0.497052i | ||||||||
\(51\) | 1988.83 | − | 3480.94i | 0.764642 | − | 1.33831i | ||||
\(52\) | −1446.00 | −0.534764 | ||||||||
\(53\) | − | 1306.79i | − | 0.465217i | −0.972570 | − | 0.232609i | \(-0.925274\pi\) | ||
0.972570 | − | 0.232609i | \(-0.0747261\pi\) | |||||||
\(54\) | −1720.67 | + | 23.2960i | −0.590080 | + | 0.00798902i | ||||
\(55\) | −362.233 | −0.119746 | ||||||||
\(56\) | − | 831.681i | − | 0.265205i | ||||||
\(57\) | −1186.96 | − | 678.169i | −0.365331 | − | 0.208732i | ||||
\(58\) | −308.077 | −0.0915804 | ||||||||
\(59\) | 1578.92i | 0.453581i | 0.973944 | + | 0.226791i | \(0.0728233\pi\) | ||||
−0.973944 | + | 0.226791i | \(0.927177\pi\) | |||||||
\(60\) | 462.268 | − | 809.082i | 0.128408 | − | 0.224745i | ||||
\(61\) | −5837.50 | −1.56880 | −0.784400 | − | 0.620255i | \(-0.787029\pi\) | ||||
−0.784400 | + | 0.620255i | \(0.787029\pi\) | |||||||
\(62\) | − | 2453.03i | − | 0.638144i | ||||||
\(63\) | −548.351 | − | 930.279i | −0.138158 | − | 0.234386i | ||||
\(64\) | −2151.91 | −0.525368 | ||||||||
\(65\) | 1376.80i | 0.325870i | ||||||||
\(66\) | 672.974 | + | 384.503i | 0.154494 | + | 0.0882698i | ||||
\(67\) | 7204.60 | 1.60494 | 0.802472 | − | 0.596689i | \(-0.203518\pi\) | ||||
0.802472 | + | 0.596689i | \(0.203518\pi\) | |||||||
\(68\) | − | 4645.08i | − | 1.00456i | ||||||
\(69\) | 2955.55 | − | 5172.93i | 0.620783 | − | 1.08652i | ||||
\(70\) | −312.459 | −0.0637672 | ||||||||
\(71\) | 9590.85i | 1.90257i | 0.308314 | + | 0.951285i | \(0.400235\pi\) | ||||
−0.308314 | + | 0.951285i | \(0.599765\pi\) | |||||||
\(72\) | −4353.13 | + | 2565.94i | −0.839724 | + | 0.494973i | ||||
\(73\) | 10547.4 | 1.97924 | 0.989621 | − | 0.143704i | \(-0.0459013\pi\) | ||||
0.989621 | + | 0.143704i | \(0.0459013\pi\) | |||||||
\(74\) | 2621.24i | 0.478679i | ||||||||
\(75\) | 4113.67 | + | 2350.34i | 0.731319 | + | 0.417839i | ||||
\(76\) | −1583.92 | −0.274225 | ||||||||
\(77\) | 486.377i | 0.0820336i | ||||||||
\(78\) | 1461.45 | − | 2557.89i | 0.240212 | − | 0.420430i | ||||
\(79\) | 1913.70 | 0.306634 | 0.153317 | − | 0.988177i | \(-0.451004\pi\) | ||||
0.153317 | + | 0.988177i | \(0.451004\pi\) | |||||||
\(80\) | − | 194.470i | − | 0.0303859i | ||||||
\(81\) | −3177.41 | + | 5740.28i | −0.484287 | + | 0.874909i | ||||
\(82\) | −3017.02 | −0.448694 | ||||||||
\(83\) | 10896.6i | 1.58173i | 0.611988 | + | 0.790867i | \(0.290370\pi\) | ||||
−0.611988 | + | 0.790867i | \(0.709630\pi\) | |||||||
\(84\) | −1086.37 | − | 620.697i | −0.153964 | − | 0.0879673i | ||||
\(85\) | −4422.79 | −0.612151 | ||||||||
\(86\) | − | 2684.35i | − | 0.362946i | ||||||
\(87\) | −582.704 | + | 1019.87i | −0.0769856 | + | 0.134744i | ||||
\(88\) | 2275.95 | 0.293898 | ||||||||
\(89\) | − | 6029.55i | − | 0.761211i | −0.924737 | − | 0.380606i | \(-0.875716\pi\) | ||
0.924737 | − | 0.380606i | \(-0.124284\pi\) | |||||||
\(90\) | 964.014 | + | 1635.45i | 0.119014 | + | 0.201908i | ||||
\(91\) | 1848.66 | 0.223241 | ||||||||
\(92\) | − | 6902.93i | − | 0.815564i | ||||||
\(93\) | −8120.64 | − | 4639.72i | −0.938911 | − | 0.536446i | ||||
\(94\) | −2161.31 | −0.244603 | ||||||||
\(95\) | 1508.12i | 0.167105i | ||||||||
\(96\) | −4662.92 | + | 8161.24i | −0.505959 | + | 0.885551i | ||||
\(97\) | −199.952 | −0.0212512 | −0.0106256 | − | 0.999944i | \(-0.503382\pi\) | ||||
−0.0106256 | + | 0.999944i | \(0.503382\pi\) | |||||||
\(98\) | − | 5248.10i | − | 0.546450i | ||||||
\(99\) | 2545.76 | − | 1500.59i | 0.259745 | − | 0.153106i | ||||
\(100\) | 5489.42 | 0.548942 | ||||||||
\(101\) | 493.281i | 0.0483561i | 0.999708 | + | 0.0241781i | \(0.00769687\pi\) | ||||
−0.999708 | + | 0.0241781i | \(0.992303\pi\) | |||||||
\(102\) | 8216.89 | + | 4694.71i | 0.789782 | + | 0.451241i | ||||
\(103\) | −1079.74 | −0.101775 | −0.0508877 | − | 0.998704i | \(-0.516205\pi\) | ||||
−0.0508877 | + | 0.998704i | \(0.516205\pi\) | |||||||
\(104\) | − | 8650.59i | − | 0.799796i | ||||||
\(105\) | −590.994 | + | 1034.38i | −0.0536049 | + | 0.0938216i | ||||
\(106\) | 3084.74 | 0.274540 | ||||||||
\(107\) | − | 9363.76i | − | 0.817867i | −0.912564 | − | 0.408934i | \(-0.865901\pi\) | ||
0.912564 | − | 0.408934i | \(-0.134099\pi\) | |||||||
\(108\) | 102.912 | + | 7601.22i | 0.00882304 | + | 0.651682i | ||||
\(109\) | −10122.9 | −0.852027 | −0.426014 | − | 0.904717i | \(-0.640082\pi\) | ||||
−0.426014 | + | 0.904717i | \(0.640082\pi\) | |||||||
\(110\) | − | 855.063i | − | 0.0706664i | ||||||
\(111\) | 8677.52 | + | 4957.89i | 0.704287 | + | 0.402393i | ||||
\(112\) | −261.119 | −0.0208162 | ||||||||
\(113\) | − | 22239.7i | − | 1.74169i | −0.491555 | − | 0.870846i | \(-0.663571\pi\) | ||
0.491555 | − | 0.870846i | \(-0.336429\pi\) | |||||||
\(114\) | 1600.84 | − | 2801.87i | 0.123180 | − | 0.215595i | ||||
\(115\) | −6572.59 | −0.496982 | ||||||||
\(116\) | 1360.95i | 0.101141i | ||||||||
\(117\) | −5703.57 | − | 9676.14i | −0.416654 | − | 0.706855i | ||||
\(118\) | −3727.09 | −0.267674 | ||||||||
\(119\) | 5938.57i | 0.419361i | ||||||||
\(120\) | 4840.27 | + | 2765.49i | 0.336130 | + | 0.192048i | ||||
\(121\) | −1331.00 | −0.0909091 | ||||||||
\(122\) | − | 13779.6i | − | 0.925802i | ||||||
\(123\) | −5706.48 | + | 9987.72i | −0.377188 | + | 0.660171i | ||||
\(124\) | −10836.5 | −0.704764 | ||||||||
\(125\) | − | 11432.2i | − | 0.731664i | ||||||
\(126\) | 2195.96 | − | 1294.40i | 0.138319 | − | 0.0815319i | ||||
\(127\) | −1308.71 | −0.0811402 | −0.0405701 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405701 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(128\) | 11630.4i | 0.709862i | ||||||||
\(129\) | −8886.42 | − | 5077.25i | −0.534007 | − | 0.305105i | ||||
\(130\) | −3249.99 | −0.192307 | ||||||||
\(131\) | 23314.1i | 1.35855i | 0.733882 | + | 0.679277i | \(0.237707\pi\) | ||||
−0.733882 | + | 0.679277i | \(0.762293\pi\) | |||||||
\(132\) | 1698.58 | − | 2972.92i | 0.0974848 | − | 0.170622i | ||||
\(133\) | 2024.99 | 0.114477 | ||||||||
\(134\) | 17006.7i | 0.947132i | ||||||||
\(135\) | 7237.46 | − | 97.9870i | 0.397117 | − | 0.00537652i | ||||
\(136\) | 27788.9 | 1.50243 | ||||||||
\(137\) | 19507.7i | 1.03936i | 0.854361 | + | 0.519680i | \(0.173949\pi\) | ||||
−0.854361 | + | 0.519680i | \(0.826051\pi\) | |||||||
\(138\) | 12210.9 | + | 6976.68i | 0.641194 | + | 0.366345i | ||||
\(139\) | 18786.5 | 0.972335 | 0.486167 | − | 0.873866i | \(-0.338395\pi\) | ||||
0.486167 | + | 0.873866i | \(0.338395\pi\) | |||||||
\(140\) | 1380.32i | 0.0704242i | ||||||||
\(141\) | −4087.96 | + | 7154.93i | −0.205622 | + | 0.359888i | ||||
\(142\) | −22639.6 | −1.12277 | ||||||||
\(143\) | 5058.97i | 0.247394i | ||||||||
\(144\) | 805.615 | + | 1366.73i | 0.0388510 | + | 0.0659110i | ||||
\(145\) | 1295.83 | 0.0616326 | ||||||||
\(146\) | 24897.5i | 1.16802i | ||||||||
\(147\) | −17373.6 | − | 9926.40i | −0.803999 | − | 0.459364i | ||||
\(148\) | 11579.6 | 0.528651 | ||||||||
\(149\) | − | 27456.7i | − | 1.23673i | −0.785890 | − | 0.618366i | \(-0.787795\pi\) | ||
0.785890 | − | 0.618366i | \(-0.212205\pi\) | |||||||
\(150\) | −5548.07 | + | 9710.47i | −0.246581 | + | 0.431576i | ||||
\(151\) | 32397.6 | 1.42089 | 0.710443 | − | 0.703755i | \(-0.248495\pi\) | ||||
0.710443 | + | 0.703755i | \(0.248495\pi\) | |||||||
\(152\) | − | 9475.69i | − | 0.410132i | ||||||
\(153\) | 31083.3 | − | 18322.0i | 1.32784 | − | 0.782689i | ||||
\(154\) | −1148.11 | −0.0484108 | ||||||||
\(155\) | 10317.9i | 0.429464i | ||||||||
\(156\) | −11299.7 | − | 6456.08i | −0.464321 | − | 0.265289i | ||||
\(157\) | −34439.8 | −1.39721 | −0.698604 | − | 0.715509i | \(-0.746195\pi\) | ||||
−0.698604 | + | 0.715509i | \(0.746195\pi\) | |||||||
\(158\) | 4517.37i | 0.180955i | ||||||||
\(159\) | 5834.55 | − | 10211.9i | 0.230788 | − | 0.403935i | ||||
\(160\) | 10369.5 | 0.405057 | ||||||||
\(161\) | 8825.15i | 0.340463i | ||||||||
\(162\) | −13550.1 | − | 7500.38i | −0.516314 | − | 0.285794i | ||||
\(163\) | 5011.87 | 0.188636 | 0.0943181 | − | 0.995542i | \(-0.469933\pi\) | ||||
0.0943181 | + | 0.995542i | \(0.469933\pi\) | |||||||
\(164\) | 13327.9i | 0.495536i | ||||||||
\(165\) | −2830.65 | − | 1617.29i | −0.103972 | − | 0.0594046i | ||||
\(166\) | −25721.7 | −0.933435 | ||||||||
\(167\) | − | 40070.8i | − | 1.43680i | −0.695633 | − | 0.718398i | \(-0.744876\pi\) | ||
0.695633 | − | 0.718398i | \(-0.255124\pi\) | |||||||
\(168\) | 3713.28 | − | 6499.14i | 0.131564 | − | 0.230270i | ||||
\(169\) | −9332.47 | −0.326756 | ||||||||
\(170\) | − | 10440.2i | − | 0.361251i | ||||||
\(171\) | −6247.58 | − | 10599.1i | −0.213658 | − | 0.362472i | ||||
\(172\) | −11858.3 | −0.400836 | ||||||||
\(173\) | 10613.1i | 0.354609i | 0.984156 | + | 0.177305i | \(0.0567378\pi\) | ||||
−0.984156 | + | 0.177305i | \(0.943262\pi\) | |||||||
\(174\) | −2407.45 | − | 1375.49i | −0.0795168 | − | 0.0454318i | ||||
\(175\) | −7018.03 | −0.229160 | ||||||||
\(176\) | − | 714.567i | − | 0.0230684i | ||||||
\(177\) | −7049.51 | + | 12338.4i | −0.225016 | + | 0.393832i | ||||
\(178\) | 14233.0 | 0.449217 | ||||||||
\(179\) | 17343.3i | 0.541285i | 0.962680 | + | 0.270643i | \(0.0872362\pi\) | ||||
−0.962680 | + | 0.270643i | \(0.912764\pi\) | |||||||
\(180\) | 7224.75 | − | 4258.61i | 0.222986 | − | 0.131439i | ||||
\(181\) | 27555.1 | 0.841096 | 0.420548 | − | 0.907270i | \(-0.361838\pi\) | ||||
0.420548 | + | 0.907270i | \(0.361838\pi\) | |||||||
\(182\) | 4363.83i | 0.131742i | ||||||||
\(183\) | −45616.9 | − | 26063.2i | −1.36215 | − | 0.778261i | ||||
\(184\) | 41296.3 | 1.21976 | ||||||||
\(185\) | − | 11025.4i | − | 0.322145i | ||||||
\(186\) | 10952.2 | − | 19169.1i | 0.316575 | − | 0.554083i | ||||
\(187\) | −16251.3 | −0.464733 | ||||||||
\(188\) | 9547.78i | 0.270139i | ||||||||
\(189\) | −131.569 | − | 9717.89i | −0.00368325 | − | 0.272050i | ||||
\(190\) | −3559.98 | −0.0986143 | ||||||||
\(191\) | 44039.3i | 1.20719i | 0.797293 | + | 0.603593i | \(0.206265\pi\) | ||||
−0.797293 | + | 0.603593i | \(0.793735\pi\) | |||||||
\(192\) | −16816.0 | − | 9607.80i | −0.456163 | − | 0.260628i | ||||
\(193\) | −5801.01 | −0.155736 | −0.0778680 | − | 0.996964i | \(-0.524811\pi\) | ||||
−0.0778680 | + | 0.996964i | \(0.524811\pi\) | |||||||
\(194\) | − | 471.995i | − | 0.0125410i | ||||||
\(195\) | −6147.12 | + | 10759.0i | −0.161660 | + | 0.282944i | ||||
\(196\) | −23183.9 | −0.603497 | ||||||||
\(197\) | − | 63465.5i | − | 1.63533i | −0.575694 | − | 0.817665i | \(-0.695268\pi\) | ||
0.575694 | − | 0.817665i | \(-0.304732\pi\) | |||||||
\(198\) | 3542.21 | + | 6009.37i | 0.0903532 | + | 0.153285i | ||||
\(199\) | −71174.9 | −1.79730 | −0.898650 | − | 0.438666i | \(-0.855451\pi\) | ||||
−0.898650 | + | 0.438666i | \(0.855451\pi\) | |||||||
\(200\) | 32840.0i | 0.821001i | ||||||||
\(201\) | 56300.0 | + | 32166.9i | 1.39353 | + | 0.796192i | ||||
\(202\) | −1164.41 | −0.0285366 | ||||||||
\(203\) | − | 1739.93i | − | 0.0422221i | ||||||
\(204\) | 20739.3 | − | 36298.8i | 0.498349 | − | 0.872232i | ||||
\(205\) | 12690.1 | 0.301966 | ||||||||
\(206\) | − | 2548.76i | − | 0.0600612i | ||||||
\(207\) | 46192.0 | − | 27227.8i | 1.07802 | − | 0.635435i | ||||
\(208\) | −2715.98 | −0.0627769 | ||||||||
\(209\) | 5541.50i | 0.126863i | ||||||||
\(210\) | −2441.70 | − | 1395.06i | −0.0553673 | − | 0.0316341i | ||||
\(211\) | 44163.4 | 0.991969 | 0.495984 | − | 0.868331i | \(-0.334807\pi\) | ||||
0.495984 | + | 0.868331i | \(0.334807\pi\) | |||||||
\(212\) | − | 13627.1i | − | 0.303201i | ||||||
\(213\) | −42821.1 | + | 74947.3i | −0.943840 | + | 1.65195i | ||||
\(214\) | 22103.5 | 0.482651 | ||||||||
\(215\) | 11290.8i | 0.244258i | ||||||||
\(216\) | −45473.7 | + | 615.663i | −0.974660 | + | 0.0131958i | ||||
\(217\) | 13854.0 | 0.294209 | ||||||||
\(218\) | − | 23895.6i | − | 0.502810i | ||||||
\(219\) | 82422.0 | + | 47091.7i | 1.71852 | + | 0.981876i | ||||
\(220\) | −3777.31 | −0.0780437 | ||||||||
\(221\) | 61769.1i | 1.26470i | ||||||||
\(222\) | −11703.3 | + | 20483.6i | −0.237466 | + | 0.415624i | ||||
\(223\) | −51860.1 | −1.04285 | −0.521427 | − | 0.853296i | \(-0.674600\pi\) | ||||
−0.521427 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(224\) | − | 13923.3i | − | 0.277489i | ||||||
\(225\) | 21652.3 | + | 36733.3i | 0.427701 | + | 0.725596i | ||||
\(226\) | 52497.6 | 1.02783 | ||||||||
\(227\) | 7471.89i | 0.145004i | 0.997368 | + | 0.0725018i | \(0.0230983\pi\) | ||||
−0.997368 | + | 0.0725018i | \(0.976902\pi\) | |||||||
\(228\) | −12377.5 | − | 7071.86i | −0.238102 | − | 0.136039i | ||||
\(229\) | 9715.01 | 0.185256 | 0.0926280 | − | 0.995701i | \(-0.470473\pi\) | ||||
0.0926280 | + | 0.995701i | \(0.470473\pi\) | |||||||
\(230\) | − | 15514.8i | − | 0.293286i | ||||||
\(231\) | −2171.57 | + | 3800.77i | −0.0406958 | + | 0.0712276i | ||||
\(232\) | −8141.81 | −0.151267 | ||||||||
\(233\) | − | 46529.7i | − | 0.857075i | −0.903524 | − | 0.428537i | \(-0.859029\pi\) | ||
0.903524 | − | 0.428537i | \(-0.140971\pi\) | |||||||
\(234\) | 22840.9 | − | 13463.5i | 0.417139 | − | 0.245882i | ||||
\(235\) | 9090.87 | 0.164615 | ||||||||
\(236\) | 16464.7i | 0.295618i | ||||||||
\(237\) | 14954.5 | + | 8544.27i | 0.266242 | + | 0.152117i | ||||
\(238\) | −14018.2 | −0.247479 | ||||||||
\(239\) | − | 35203.7i | − | 0.616301i | −0.951338 | − | 0.308150i | \(-0.900290\pi\) | ||
0.951338 | − | 0.308150i | \(-0.0997100\pi\) | |||||||
\(240\) | 868.265 | − | 1519.68i | 0.0150740 | − | 0.0263833i | ||||
\(241\) | 39215.8 | 0.675192 | 0.337596 | − | 0.941291i | \(-0.390386\pi\) | ||||
0.337596 | + | 0.941291i | \(0.390386\pi\) | |||||||
\(242\) | − | 3141.87i | − | 0.0536485i | ||||||
\(243\) | −50458.8 | + | 30670.7i | −0.854524 | + | 0.519412i | ||||
\(244\) | −60872.7 | −1.02245 | ||||||||
\(245\) | 22074.5i | 0.367754i | ||||||||
\(246\) | −23576.4 | − | 13470.3i | −0.389589 | − | 0.222591i | ||||
\(247\) | 21062.6 | 0.345237 | ||||||||
\(248\) | − | 64828.3i | − | 1.05405i | ||||||
\(249\) | −48650.8 | + | 85150.7i | −0.784677 | + | 1.37338i | ||||
\(250\) | 26986.2 | 0.431780 | ||||||||
\(251\) | − | 26453.8i | − | 0.419894i | −0.977713 | − | 0.209947i | \(-0.932671\pi\) | ||
0.977713 | − | 0.209947i | \(-0.0673292\pi\) | |||||||
\(252\) | −5718.13 | − | 9700.83i | −0.0900436 | − | 0.152759i | ||||
\(253\) | −24150.5 | −0.377299 | ||||||||
\(254\) | − | 3089.26i | − | 0.0478836i | ||||||
\(255\) | −34561.7 | − | 19746.8i | −0.531514 | − | 0.303680i | ||||
\(256\) | −61884.5 | −0.944282 | ||||||||
\(257\) | − | 51258.5i | − | 0.776068i | −0.921645 | − | 0.388034i | \(-0.873154\pi\) | ||
0.921645 | − | 0.388034i | \(-0.126846\pi\) | |||||||
\(258\) | 11985.0 | − | 20976.7i | 0.180053 | − | 0.315136i | ||||
\(259\) | −14804.1 | −0.220689 | ||||||||
\(260\) | 14357.1i | 0.212383i | ||||||||
\(261\) | −9107.03 | + | 5368.12i | −0.133689 | + | 0.0788027i | ||||
\(262\) | −55033.9 | −0.801729 | ||||||||
\(263\) | − | 16153.1i | − | 0.233531i | −0.993160 | − | 0.116765i | \(-0.962747\pi\) | ||
0.993160 | − | 0.116765i | \(-0.0372525\pi\) | |||||||
\(264\) | 17785.3 | + | 10161.6i | 0.255184 | + | 0.145799i | ||||
\(265\) | −12975.0 | −0.184763 | ||||||||
\(266\) | 4780.05i | 0.0675569i | ||||||||
\(267\) | 26920.6 | − | 47117.7i | 0.377627 | − | 0.660939i | ||||
\(268\) | 75128.6 | 1.04601 | ||||||||
\(269\) | − | 132830.i | − | 1.83565i | −0.396984 | − | 0.917826i | \(-0.629943\pi\) | ||
0.396984 | − | 0.917826i | \(-0.370057\pi\) | |||||||
\(270\) | 231.302 | + | 17084.3i | 0.00317287 | + | 0.234352i | ||||
\(271\) | 52870.0 | 0.719898 | 0.359949 | − | 0.932972i | \(-0.382794\pi\) | ||||
0.359949 | + | 0.932972i | \(0.382794\pi\) | |||||||
\(272\) | − | 8724.72i | − | 0.117927i | ||||||
\(273\) | 14446.3 | + | 8253.87i | 0.193834 | + | 0.110747i | ||||
\(274\) | −46048.7 | −0.613361 | ||||||||
\(275\) | − | 19205.2i | − | 0.253954i | ||||||
\(276\) | 30820.1 | − | 53942.6i | 0.404590 | − | 0.708132i | ||||
\(277\) | 113328. | 1.47699 | 0.738495 | − | 0.674259i | \(-0.235537\pi\) | ||||
0.738495 | + | 0.674259i | \(0.235537\pi\) | |||||||
\(278\) | 44346.2i | 0.573808i | ||||||||
\(279\) | −42743.1 | − | 72513.8i | −0.549107 | − | 0.931563i | ||||
\(280\) | −8257.63 | −0.105327 | ||||||||
\(281\) | 41838.0i | 0.529857i | 0.964268 | + | 0.264928i | \(0.0853483\pi\) | ||||
−0.964268 | + | 0.264928i | \(0.914652\pi\) | |||||||
\(282\) | −16889.5 | − | 9649.79i | −0.212382 | − | 0.121344i | ||||
\(283\) | 7318.14 | 0.0913751 | 0.0456875 | − | 0.998956i | \(-0.485452\pi\) | ||||
0.0456875 | + | 0.998956i | \(0.485452\pi\) | |||||||
\(284\) | 100012.i | 1.23998i | ||||||||
\(285\) | −6733.44 | + | 11785.2i | −0.0828986 | + | 0.145093i | ||||
\(286\) | −11941.9 | −0.145996 | ||||||||
\(287\) | − | 17039.3i | − | 0.206866i | ||||||
\(288\) | −72876.3 | + | 42956.8i | −0.878621 | + | 0.517901i | ||||
\(289\) | −114904. | −1.37575 | ||||||||
\(290\) | 3058.84i | 0.0363715i | ||||||||
\(291\) | −1562.52 | − | 892.743i | −0.0184518 | − | 0.0105424i | ||||
\(292\) | 109987. | 1.28995 | ||||||||
\(293\) | − | 41007.6i | − | 0.477671i | −0.971060 | − | 0.238836i | \(-0.923234\pi\) | ||
0.971060 | − | 0.238836i | \(-0.0767657\pi\) | |||||||
\(294\) | 23431.6 | − | 41011.1i | 0.271086 | − | 0.474467i | ||||
\(295\) | 15676.8 | 0.180141 | ||||||||
\(296\) | 69273.9i | 0.790653i | ||||||||
\(297\) | 26593.6 | − | 360.047i | 0.301484 | − | 0.00408175i | ||||
\(298\) | 64812.5 | 0.729837 | ||||||||
\(299\) | 91793.3i | 1.02676i | ||||||||
\(300\) | 42896.8 | + | 24509.1i | 0.476631 | + | 0.272323i | ||||
\(301\) | 15160.5 | 0.167332 | ||||||||
\(302\) | 76475.7i | 0.838513i | ||||||||
\(303\) | −2202.39 | + | 3854.72i | −0.0239888 | + | 0.0419863i | ||||
\(304\) | −2975.03 | −0.0321917 | ||||||||
\(305\) | 57959.6i | 0.623054i | ||||||||
\(306\) | 43249.7 | + | 73373.2i | 0.461891 | + | 0.783601i | ||||
\(307\) | −117657. | −1.24836 | −0.624180 | − | 0.781280i | \(-0.714567\pi\) | ||||
−0.624180 | + | 0.781280i | \(0.714567\pi\) | |||||||
\(308\) | 5071.88i | 0.0534647i | ||||||||
\(309\) | −8437.55 | − | 4820.79i | −0.0883689 | − | 0.0504895i | ||||
\(310\) | −24355.7 | −0.253441 | ||||||||
\(311\) | − | 90102.0i | − | 0.931566i | −0.884899 | − | 0.465783i | \(-0.845773\pi\) | ||
0.884899 | − | 0.465783i | \(-0.154227\pi\) | |||||||
\(312\) | 38623.0 | − | 67599.7i | 0.396768 | − | 0.694441i | ||||
\(313\) | −47224.3 | −0.482033 | −0.241016 | − | 0.970521i | \(-0.577481\pi\) | ||||
−0.241016 | + | 0.970521i | \(0.577481\pi\) | |||||||
\(314\) | − | 81296.3i | − | 0.824540i | ||||||
\(315\) | −9236.59 | + | 5444.48i | −0.0930873 | + | 0.0548701i | ||||
\(316\) | 19955.8 | 0.199846 | ||||||||
\(317\) | 148932.i | 1.48208i | 0.671463 | + | 0.741038i | \(0.265666\pi\) | ||||
−0.671463 | + | 0.741038i | \(0.734334\pi\) | |||||||
\(318\) | 24105.5 | + | 13772.7i | 0.238376 | + | 0.136196i | ||||
\(319\) | 4761.43 | 0.0467903 | ||||||||
\(320\) | 21366.0i | 0.208652i | ||||||||
\(321\) | 41807.2 | − | 73172.7i | 0.405733 | − | 0.710132i | ||||
\(322\) | −20832.1 | −0.200919 | ||||||||
\(323\) | 67660.6i | 0.648531i | ||||||||
\(324\) | −33133.6 | + | 59858.9i | −0.315630 | + | 0.570215i | ||||
\(325\) | −72996.8 | −0.691094 | ||||||||
\(326\) | 11830.7i | 0.111321i | ||||||||
\(327\) | −79105.3 | − | 45196.7i | −0.739792 | − | 0.422680i | ||||
\(328\) | −79733.4 | −0.741127 | ||||||||
\(329\) | − | 12206.5i | − | 0.112771i | ||||||
\(330\) | 3817.67 | − | 6681.85i | 0.0350567 | − | 0.0613577i | ||||
\(331\) | 20576.1 | 0.187805 | 0.0939027 | − | 0.995581i | \(-0.470066\pi\) | ||||
0.0939027 | + | 0.995581i | \(0.470066\pi\) | |||||||
\(332\) | 113628.i | 1.03088i | ||||||||
\(333\) | 45674.2 | + | 77486.4i | 0.411891 | + | 0.698775i | ||||
\(334\) | 94588.5 | 0.847902 | ||||||||
\(335\) | − | 71533.3i | − | 0.637409i | ||||||
\(336\) | −2040.50 | − | 1165.84i | −0.0180742 | − | 0.0103267i | ||||
\(337\) | 195633. | 1.72259 | 0.861297 | − | 0.508102i | \(-0.169653\pi\) | ||||
0.861297 | + | 0.508102i | \(0.169653\pi\) | |||||||
\(338\) | − | 22029.6i | − | 0.192830i | ||||||
\(339\) | 99295.3 | − | 173791.i | 0.864031 | − | 1.51226i | ||||
\(340\) | −46120.3 | −0.398964 | ||||||||
\(341\) | 37912.3i | 0.326041i | ||||||||
\(342\) | 25019.4 | − | 14747.6i | 0.213907 | − | 0.126087i | ||||
\(343\) | 61649.1 | 0.524009 | ||||||||
\(344\) | − | 70941.6i | − | 0.599493i | ||||||
\(345\) | −51361.2 | − | 29345.2i | −0.431516 | − | 0.246546i | ||||
\(346\) | −25052.6 | −0.209267 | ||||||||
\(347\) | 211691.i | 1.75810i | 0.476730 | + | 0.879050i | \(0.341822\pi\) | ||||
−0.476730 | + | 0.879050i | \(0.658178\pi\) | |||||||
\(348\) | −6076.36 | + | 10635.1i | −0.0501748 | + | 0.0878181i | ||||
\(349\) | −73946.3 | −0.607108 | −0.303554 | − | 0.952814i | \(-0.598173\pi\) | ||||
−0.303554 | + | 0.952814i | \(0.598173\pi\) | |||||||
\(350\) | − | 16566.3i | − | 0.135235i | ||||||
\(351\) | −1368.49 | − | 101079.i | −0.0111078 | − | 0.820439i | ||||
\(352\) | 38101.9 | 0.307511 | ||||||||
\(353\) | − | 124295.i | − | 0.997479i | −0.866752 | − | 0.498740i | \(-0.833796\pi\) | ||
0.866752 | − | 0.498740i | \(-0.166204\pi\) | |||||||
\(354\) | −29125.2 | − | 16640.6i | −0.232414 | − | 0.132789i | ||||
\(355\) | 95226.0 | 0.755612 | ||||||||
\(356\) | − | 62875.4i | − | 0.496113i | ||||||
\(357\) | −26514.4 | + | 46406.7i | −0.208040 | + | 0.364120i | ||||
\(358\) | −40939.5 | −0.319431 | ||||||||
\(359\) | − | 56677.7i | − | 0.439768i | −0.975526 | − | 0.219884i | \(-0.929432\pi\) | ||
0.975526 | − | 0.219884i | \(-0.0705678\pi\) | |||||||
\(360\) | 25476.8 | + | 43221.5i | 0.196580 | + | 0.333500i | ||||
\(361\) | −107249. | −0.822964 | ||||||||
\(362\) | 65044.9i | 0.496359i | ||||||||
\(363\) | −10401.0 | − | 5942.62i | −0.0789339 | − | 0.0450988i | ||||
\(364\) | 19277.6 | 0.145496 | ||||||||
\(365\) | − | 104723.i | − | 0.786063i | ||||||
\(366\) | 61523.1 | − | 107680.i | 0.459278 | − | 0.803849i | ||||
\(367\) | −151562. | −1.12527 | −0.562637 | − | 0.826704i | \(-0.690213\pi\) | ||||
−0.562637 | + | 0.826704i | \(0.690213\pi\) | |||||||
\(368\) | − | 12965.6i | − | 0.0957406i | ||||||
\(369\) | −89186.0 | + | 52570.5i | −0.655004 | + | 0.386090i | ||||
\(370\) | 26025.9 | 0.190109 | ||||||||
\(371\) | 17421.7i | 0.126574i | ||||||||
\(372\) | −84681.0 | − | 48382.4i | −0.611928 | − | 0.349624i | ||||
\(373\) | 43144.4 | 0.310104 | 0.155052 | − | 0.987906i | \(-0.450446\pi\) | ||||
0.155052 | + | 0.987906i | \(0.450446\pi\) | |||||||
\(374\) | − | 38361.7i | − | 0.274255i | ||||||
\(375\) | 51042.5 | − | 89336.8i | 0.362969 | − | 0.635284i | ||||
\(376\) | −57118.9 | −0.404021 | ||||||||
\(377\) | − | 18097.6i | − | 0.127332i | ||||||
\(378\) | 22939.4 | − | 310.574i | 0.160546 | − | 0.00217361i | ||||
\(379\) | −58997.4 | −0.410728 | −0.205364 | − | 0.978686i | \(-0.565838\pi\) | ||||
−0.205364 | + | 0.978686i | \(0.565838\pi\) | |||||||
\(380\) | 15726.5i | 0.108909i | ||||||||
\(381\) | −10226.9 | − | 5843.10i | −0.0704518 | − | 0.0402526i | ||||
\(382\) | −103956. | −0.712401 | ||||||||
\(383\) | − | 76112.7i | − | 0.518871i | −0.965760 | − | 0.259435i | \(-0.916464\pi\) | ||
0.965760 | − | 0.259435i | \(-0.0835365\pi\) | |||||||
\(384\) | −51927.1 | + | 90885.1i | −0.352153 | + | 0.616354i | ||||
\(385\) | 4829.16 | 0.0325799 | ||||||||
\(386\) | − | 13693.5i | − | 0.0919051i | ||||||
\(387\) | −46773.7 | − | 79351.8i | −0.312306 | − | 0.529828i | ||||
\(388\) | −2085.08 | −0.0138503 | ||||||||
\(389\) | 148021.i | 0.978189i | 0.872231 | + | 0.489094i | \(0.162673\pi\) | ||||
−0.872231 | + | 0.489094i | \(0.837327\pi\) | |||||||
\(390\) | −25396.9 | − | 14510.5i | −0.166975 | − | 0.0954010i | ||||
\(391\) | −294874. | −1.92878 | ||||||||
\(392\) | − | 138696.i | − | 0.902594i | ||||||
\(393\) | −104093. | + | 182187.i | −0.673961 | + | 1.17960i | ||||
\(394\) | 149813. | 0.965064 | ||||||||
\(395\) | − | 19000.8i | − | 0.121781i | ||||||
\(396\) | 26546.9 | − | 15648.0i | 0.169287 | − | 0.0997857i | ||||
\(397\) | 235920. | 1.49687 | 0.748433 | − | 0.663211i | \(-0.230807\pi\) | ||||
0.748433 | + | 0.663211i | \(0.230807\pi\) | |||||||
\(398\) | − | 168011.i | − | 1.06065i | ||||||
\(399\) | 15824.2 | + | 9041.12i | 0.0993974 | + | 0.0567906i | ||||
\(400\) | 10310.6 | 0.0644413 | ||||||||
\(401\) | 161186.i | 1.00239i | 0.865333 | + | 0.501197i | \(0.167107\pi\) | ||||
−0.865333 | + | 0.501197i | \(0.832893\pi\) | |||||||
\(402\) | −75931.2 | + | 132898.i | −0.469860 | + | 0.822369i | ||||
\(403\) | 144100. | 0.887267 | ||||||||
\(404\) | 5143.87i | 0.0315157i | ||||||||
\(405\) | 56994.3 | + | 31548.0i | 0.347473 | + | 0.192336i | ||||
\(406\) | 4107.17 | 0.0249167 | ||||||||
\(407\) | − | 40512.2i | − | 0.244566i | ||||||
\(408\) | 217155. | + | 124071.i | 1.30452 | + | 0.745334i | ||||
\(409\) | 147844. | 0.883808 | 0.441904 | − | 0.897062i | \(-0.354303\pi\) | ||||
0.441904 | + | 0.897062i | \(0.354303\pi\) | |||||||
\(410\) | 29955.5i | 0.178201i | ||||||||
\(411\) | −87097.8 | + | 152442.i | −0.515612 | + | 0.902448i | ||||
\(412\) | −11259.3 | −0.0663313 | ||||||||
\(413\) | − | 21049.6i | − | 0.123408i | ||||||
\(414\) | 64272.1 | + | 109038.i | 0.374992 | + | 0.636175i | ||||
\(415\) | 108190. | 0.628191 | ||||||||
\(416\) | − | 144821.i | − | 0.836843i | ||||||
\(417\) | 146806. | + | 83877.5i | 0.844252 | + | 0.482362i | ||||
\(418\) | −13080.9 | −0.0748661 | ||||||||
\(419\) | 154410.i | 0.879525i | 0.898114 | + | 0.439762i | \(0.144937\pi\) | ||||
−0.898114 | + | 0.439762i | \(0.855063\pi\) | |||||||
\(420\) | −6162.81 | + | 10786.4i | −0.0349365 | + | 0.0611475i | ||||
\(421\) | 186090. | 1.04993 | 0.524963 | − | 0.851125i | \(-0.324079\pi\) | ||||
0.524963 | + | 0.851125i | \(0.324079\pi\) | |||||||
\(422\) | 104249.i | 0.585395i | ||||||||
\(423\) | −63890.4 | + | 37660.1i | −0.357071 | + | 0.210475i | ||||
\(424\) | 81523.0 | 0.453470 | ||||||||
\(425\) | − | 234492.i | − | 1.29823i | ||||||
\(426\) | −176916. | − | 101081.i | −0.974872 | − | 0.556992i | ||||
\(427\) | 77823.6 | 0.426831 | ||||||||
\(428\) | − | 97644.1i | − | 0.533038i | ||||||
\(429\) | −22587.2 | + | 39533.1i | −0.122729 | + | 0.214806i | ||||
\(430\) | −26652.4 | −0.144145 | ||||||||
\(431\) | 155392.i | 0.836514i | 0.908329 | + | 0.418257i | \(0.137359\pi\) | ||||
−0.908329 | + | 0.418257i | \(0.862641\pi\) | |||||||
\(432\) | 193.296 | + | 14277.1i | 0.00103575 | + | 0.0765022i | ||||
\(433\) | 33432.8 | 0.178319 | 0.0891593 | − | 0.996017i | \(-0.471582\pi\) | ||||
0.0891593 | + | 0.996017i | \(0.471582\pi\) | |||||||
\(434\) | 32702.9i | 0.173623i | ||||||||
\(435\) | 10126.2 | + | 5785.58i | 0.0535139 | + | 0.0305751i | ||||
\(436\) | −105561. | −0.555302 | ||||||||
\(437\) | 100549.i | 0.526518i | ||||||||
\(438\) | −111162. | + | 194560.i | −0.579438 | + | 1.01416i | ||||
\(439\) | −166902. | −0.866030 | −0.433015 | − | 0.901387i | \(-0.642550\pi\) | ||||
−0.433015 | + | 0.901387i | \(0.642550\pi\) | |||||||
\(440\) | − | 22597.5i | − | 0.116723i | ||||||
\(441\) | −91446.2 | − | 155139.i | −0.470206 | − | 0.797707i | ||||
\(442\) | −145808. | −0.746341 | ||||||||
\(443\) | 25594.0i | 0.130416i | 0.997872 | + | 0.0652079i | \(0.0207711\pi\) | ||||
−0.997872 | + | 0.0652079i | \(0.979229\pi\) | |||||||
\(444\) | 90488.0 | + | 51700.2i | 0.459013 | + | 0.262257i | ||||
\(445\) | −59866.5 | −0.302318 | ||||||||
\(446\) | − | 122418.i | − | 0.615424i | ||||||
\(447\) | 122588. | − | 214559.i | 0.613526 | − | 1.07382i | ||||
\(448\) | 28688.5 | 0.142939 | ||||||||
\(449\) | − | 32470.8i | − | 0.161065i | −0.996752 | − | 0.0805323i | \(-0.974338\pi\) | ||
0.996752 | − | 0.0805323i | \(-0.0256620\pi\) | |||||||
\(450\) | −86710.3 | + | 51111.1i | −0.428199 | + | 0.252401i | ||||
\(451\) | 46629.1 | 0.229247 | ||||||||
\(452\) | − | 231912.i | − | 1.13513i | ||||||
\(453\) | 253170. | + | 144648.i | 1.23372 | + | 0.704882i | ||||
\(454\) | −17637.7 | −0.0855715 | ||||||||
\(455\) | − | 18355.1i | − | 0.0886610i | ||||||
\(456\) | 42306.9 | − | 74047.4i | 0.203461 | − | 0.356107i | ||||
\(457\) | −234589. | −1.12325 | −0.561624 | − | 0.827392i | \(-0.689823\pi\) | ||||
−0.561624 | + | 0.827392i | \(0.689823\pi\) | |||||||
\(458\) | 22932.6i | 0.109326i | ||||||||
\(459\) | 324703. | − | 4396.11i | 1.54120 | − | 0.0208662i | ||||
\(460\) | −68538.1 | −0.323904 | ||||||||
\(461\) | − | 96803.3i | − | 0.455500i | −0.973720 | − | 0.227750i | \(-0.926863\pi\) | ||
0.973720 | − | 0.227750i | \(-0.0731369\pi\) | |||||||
\(462\) | −8971.86 | − | 5126.06i | −0.0420338 | − | 0.0240160i | ||||
\(463\) | −3642.95 | −0.0169938 | −0.00849691 | − | 0.999964i | \(-0.502705\pi\) | ||||
−0.00849691 | + | 0.999964i | \(0.502705\pi\) | |||||||
\(464\) | 2556.24i | 0.0118731i | ||||||||
\(465\) | −46067.0 | + | 80628.5i | −0.213051 | + | 0.372892i | ||||
\(466\) | 109835. | 0.505789 | ||||||||
\(467\) | 182139.i | 0.835159i | 0.908640 | + | 0.417579i | \(0.137121\pi\) | ||||
−0.908640 | + | 0.417579i | \(0.862879\pi\) | |||||||
\(468\) | −59476.1 | − | 100901.i | −0.271551 | − | 0.460687i | ||||
\(469\) | −96049.2 | −0.436665 | ||||||||
\(470\) | 21459.3i | 0.0971450i | ||||||||
\(471\) | −269128. | − | 153766.i | −1.21316 | − | 0.693136i | ||||
\(472\) | −98499.0 | −0.442128 | ||||||||
\(473\) | 41487.5i | 0.185436i | ||||||||
\(474\) | −20169.0 | + | 35300.8i | −0.0897695 | + | 0.157118i | ||||
\(475\) | −79959.3 | −0.354390 | ||||||||
\(476\) | 61926.7i | 0.273315i | ||||||||
\(477\) | 91187.7 | − | 53750.4i | 0.400774 | − | 0.236235i | ||||
\(478\) | 83099.6 | 0.363700 | ||||||||
\(479\) | 35229.6i | 0.153545i | 0.997049 | + | 0.0767727i | \(0.0244616\pi\) | ||||
−0.997049 | + | 0.0767727i | \(0.975538\pi\) | |||||||
\(480\) | 81031.6 | + | 46297.3i | 0.351700 | + | 0.200943i | ||||
\(481\) | −153982. | −0.665548 | ||||||||
\(482\) | 92570.4i | 0.398454i | ||||||||
\(483\) | −39402.4 | + | 68963.8i | −0.168899 | + | 0.295615i | ||||
\(484\) | −13879.5 | −0.0592493 | ||||||||
\(485\) | 1985.29i | 0.00843998i | ||||||||
\(486\) | −72399.4 | − | 119110.i | −0.306522 | − | 0.504284i | ||||
\(487\) | 175239. | 0.738880 | 0.369440 | − | 0.929255i | \(-0.379550\pi\) | ||||
0.369440 | + | 0.929255i | \(0.379550\pi\) | |||||||
\(488\) | − | 364167.i | − | 1.52919i | ||||||
\(489\) | 39165.1 | + | 22376.9i | 0.163788 | + | 0.0935799i | ||||
\(490\) | −52107.6 | −0.217024 | ||||||||
\(491\) | 224892.i | 0.932847i | 0.884562 | + | 0.466423i | \(0.154458\pi\) | ||||
−0.884562 | + | 0.466423i | \(0.845542\pi\) | |||||||
\(492\) | −59506.4 | + | 104151.i | −0.245829 | + | 0.430261i | ||||
\(493\) | 58136.1 | 0.239195 | ||||||||
\(494\) | 49718.9i | 0.203736i | ||||||||
\(495\) | −14899.2 | − | 25276.5i | −0.0608067 | − | 0.103159i | ||||
\(496\) | −20353.8 | −0.0827336 | ||||||||
\(497\) | − | 127862.i | − | 0.517641i | ||||||
\(498\) | −201001. | − | 114842.i | −0.810476 | − | 0.463065i | ||||
\(499\) | −94767.9 | −0.380592 | −0.190296 | − | 0.981727i | \(-0.560945\pi\) | ||||
−0.190296 | + | 0.981727i | \(0.560945\pi\) | |||||||
\(500\) | − | 119214.i | − | 0.476856i | ||||||
\(501\) | 178907. | − | 313131.i | 0.712775 | − | 1.24753i | ||||
\(502\) | 62445.1 | 0.247794 | ||||||||
\(503\) | − | 233674.i | − | 0.923579i | −0.886990 | − | 0.461789i | \(-0.847208\pi\) | ||
0.886990 | − | 0.461789i | \(-0.152792\pi\) | |||||||
\(504\) | 58034.5 | − | 34208.3i | 0.228468 | − | 0.134670i | ||||
\(505\) | 4897.71 | 0.0192048 | ||||||||
\(506\) | − | 57008.2i | − | 0.222657i | ||||||
\(507\) | −72928.2 | − | 41667.5i | −0.283713 | − | 0.162099i | ||||
\(508\) | −13647.1 | −0.0528824 | ||||||||
\(509\) | 152655.i | 0.589216i | 0.955618 | + | 0.294608i | \(0.0951891\pi\) | ||||
−0.955618 | + | 0.294608i | \(0.904811\pi\) | |||||||
\(510\) | 46613.0 | − | 81584.2i | 0.179212 | − | 0.313665i | ||||
\(511\) | −140614. | −0.538501 | ||||||||
\(512\) | 40005.5i | 0.152609i | ||||||||
\(513\) | −1499.02 | − | 110720.i | −0.00569605 | − | 0.420718i | ||||
\(514\) | 120998. | 0.457984 | ||||||||
\(515\) | 10720.5i | 0.0404205i | ||||||||
\(516\) | −92666.4 | − | 52944.9i | −0.348035 | − | 0.198849i | ||||
\(517\) | 33403.8 | 0.124973 | ||||||||
\(518\) | − | 34945.5i | − | 0.130236i | ||||||
\(519\) | −47385.1 | + | 82935.6i | −0.175917 | + | 0.307897i | ||||
\(520\) | −85890.3 | −0.317642 | ||||||||
\(521\) | − | 282155.i | − | 1.03947i | −0.854328 | − | 0.519735i | \(-0.826031\pi\) | ||
0.854328 | − | 0.519735i | \(-0.173969\pi\) | |||||||
\(522\) | −12671.6 | − | 21497.5i | −0.0465042 | − | 0.0788945i | ||||
\(523\) | 403375. | 1.47471 | 0.737354 | − | 0.675507i | \(-0.236075\pi\) | ||||
0.737354 | + | 0.675507i | \(0.236075\pi\) | |||||||
\(524\) | 243117.i | 0.885427i | ||||||||
\(525\) | −54842.1 | − | 31334.0i | −0.198973 | − | 0.113683i | ||||
\(526\) | 38129.9 | 0.137814 | ||||||||
\(527\) | 462903.i | 1.66674i | ||||||||
\(528\) | 3190.38 | − | 5583.95i | 0.0114439 | − | 0.0200297i | ||||
\(529\) | −158363. | −0.565902 | ||||||||
\(530\) | − | 30627.8i | − | 0.109035i | ||||||
\(531\) | −110176. | + | 64943.1i | −0.390750 | + | 0.230327i | ||||
\(532\) | 21116.3 | 0.0746096 | ||||||||
\(533\) | − | 177231.i | − | 0.623859i | ||||||
\(534\) | 111223. | + | 63547.1i | 0.390043 | + | 0.222850i | ||||
\(535\) | −92971.3 | −0.324819 | ||||||||
\(536\) | 449451.i | 1.56442i | ||||||||
\(537\) | −77434.1 | + | 135529.i | −0.268524 | + | 0.469983i | ||||
\(538\) | 313549. | 1.08328 | ||||||||
\(539\) | 81111.2i | 0.279192i | ||||||||
\(540\) | 75471.3 | − | 1021.80i | 0.258818 | − | 0.00350410i | ||||
\(541\) | −299826. | −1.02441 | −0.512207 | − | 0.858862i | \(-0.671172\pi\) | ||||
−0.512207 | + | 0.858862i | \(0.671172\pi\) | |||||||
\(542\) | 124802.i | 0.424836i | ||||||||
\(543\) | 215328. | + | 123028.i | 0.730301 | + | 0.417256i | ||||
\(544\) | 465217. | 1.57202 | ||||||||
\(545\) | 100509.i | 0.338386i | ||||||||
\(546\) | −19483.5 | + | 34101.0i | −0.0653556 | + | 0.114388i | ||||
\(547\) | 6015.08 | 0.0201033 | 0.0100516 | − | 0.999949i | \(-0.496800\pi\) | ||||
0.0100516 | + | 0.999949i | \(0.496800\pi\) | |||||||
\(548\) | 203424.i | 0.677394i | ||||||||
\(549\) | −240105. | − | 407339.i | −0.796630 | − | 1.35149i | ||||
\(550\) | 45334.7 | 0.149867 | ||||||||
\(551\) | − | 19823.8i | − | 0.0652954i | ||||||
\(552\) | 322708. | + | 184379.i | 1.05909 | + | 0.605108i | ||||
\(553\) | −25512.8 | −0.0834274 | ||||||||
\(554\) | 267515.i | 0.871622i | ||||||||
\(555\) | 49226.1 | − | 86157.7i | 0.159812 | − | 0.279710i | ||||
\(556\) | 195903. | 0.633711 | ||||||||
\(557\) | 342983.i | 1.10551i | 0.833344 | + | 0.552755i | \(0.186423\pi\) | ||||
−0.833344 | + | 0.552755i | \(0.813577\pi\) | |||||||
\(558\) | 171171. | − | 100897.i | 0.549747 | − | 0.324047i | ||||
\(559\) | 157689. | 0.504635 | ||||||||
\(560\) | 2592.60i | 0.00826723i | ||||||||
\(561\) | −126995. | − | 72558.3i | −0.403515 | − | 0.230548i | ||||
\(562\) | −98760.2 | −0.312687 | ||||||||
\(563\) | 451877.i | 1.42562i | 0.701357 | + | 0.712810i | \(0.252578\pi\) | ||||
−0.701357 | + | 0.712810i | \(0.747422\pi\) | |||||||
\(564\) | −42628.8 | + | 74610.7i | −0.134012 | + | 0.234554i | ||||
\(565\) | −220814. | −0.691719 | ||||||||
\(566\) | 17274.7i | 0.0539235i | ||||||||
\(567\) | 42360.1 | − | 76527.4i | 0.131762 | − | 0.238041i | ||||
\(568\) | −598315. | −1.85453 | ||||||||
\(569\) | − | 476722.i | − | 1.47245i | −0.676737 | − | 0.736225i | \(-0.736606\pi\) | ||
0.676737 | − | 0.736225i | \(-0.263394\pi\) | |||||||
\(570\) | −27819.3 | − | 15894.5i | −0.0856241 | − | 0.0489213i | ||||
\(571\) | 484795. | 1.48692 | 0.743458 | − | 0.668783i | \(-0.233184\pi\) | ||||
0.743458 | + | 0.668783i | \(0.233184\pi\) | |||||||
\(572\) | 52754.3i | 0.161237i | ||||||||
\(573\) | −196626. | + | 344143.i | −0.598869 | + | 1.04817i | ||||
\(574\) | 40221.9 | 0.122078 | ||||||||
\(575\) | − | 348473.i | − | 1.05398i | ||||||
\(576\) | −88511.1 | − | 150160.i | −0.266780 | − | 0.452593i | ||||
\(577\) | −57731.0 | −0.173403 | −0.0867016 | − | 0.996234i | \(-0.527633\pi\) | ||||
−0.0867016 | + | 0.996234i | \(0.527633\pi\) | |||||||
\(578\) | − | 271235.i | − | 0.811876i | ||||||
\(579\) | −45331.7 | − | 25900.2i | −0.135221 | − | 0.0772586i | ||||
\(580\) | 13512.7 | 0.0401685 | ||||||||
\(581\) | − | 145269.i | − | 0.430350i | ||||||
\(582\) | 2107.35 | − | 3688.38i | 0.00622144 | − | 0.0108890i | ||||
\(583\) | −47675.6 | −0.140268 | ||||||||
\(584\) | 657987.i | 1.92926i | ||||||||
\(585\) | −96072.8 | + | 56629.9i | −0.280730 | + | 0.165476i | ||||
\(586\) | 96799.9 | 0.281890 | ||||||||
\(587\) | 197193.i | 0.572289i | 0.958186 | + | 0.286144i | \(0.0923737\pi\) | ||||
−0.958186 | + | 0.286144i | \(0.907626\pi\) | |||||||
\(588\) | −181170. | − | 103511.i | −0.524000 | − | 0.299387i | ||||
\(589\) | 157845. | 0.454987 | ||||||||
\(590\) | 37005.7i | 0.106308i | ||||||||
\(591\) | 283360. | − | 495949.i | 0.811266 | − | 1.41991i | ||||
\(592\) | 21749.6 | 0.0620593 | ||||||||
\(593\) | − | 298456.i | − | 0.848733i | −0.905490 | − | 0.424367i | \(-0.860497\pi\) | ||
0.905490 | − | 0.424367i | \(-0.139503\pi\) | |||||||
\(594\) | 849.904 | + | 62775.1i | 0.00240878 | + | 0.177916i | ||||
\(595\) | 58963.2 | 0.166551 | ||||||||
\(596\) | − | 286315.i | − | 0.806030i | ||||||
\(597\) | −556193. | − | 317780.i | −1.56055 | − | 0.891617i | ||||
\(598\) | −216681. | −0.605925 | ||||||||
\(599\) | − | 193343.i | − | 0.538859i | −0.963020 | − | 0.269429i | \(-0.913165\pi\) | ||
0.963020 | − | 0.269429i | \(-0.0868351\pi\) | |||||||
\(600\) | −146624. | + | 256627.i | −0.407288 | + | 0.712853i | ||||
\(601\) | −386484. | −1.07000 | −0.534998 | − | 0.844853i | \(-0.679688\pi\) | ||||
−0.534998 | + | 0.844853i | \(0.679688\pi\) | |||||||
\(602\) | 35786.8i | 0.0987483i | ||||||||
\(603\) | 296335. | + | 502734.i | 0.814984 | + | 1.38262i | ||||
\(604\) | 337838. | 0.926050 | ||||||||
\(605\) | 13215.3i | 0.0361049i | ||||||||
\(606\) | −9099.21 | − | 5198.82i | −0.0247776 | − | 0.0141566i | ||||
\(607\) | −191097. | −0.518653 | −0.259327 | − | 0.965790i | \(-0.583501\pi\) | ||||
−0.259327 | + | 0.965790i | \(0.583501\pi\) | |||||||
\(608\) | − | 158634.i | − | 0.429129i | ||||||
\(609\) | 7768.41 | − | 13596.6i | 0.0209458 | − | 0.0366603i | ||||
\(610\) | −136816. | −0.367686 | ||||||||
\(611\) | − | 126964.i | − | 0.340093i | ||||||
\(612\) | 324132. | − | 191059.i | 0.865406 | − | 0.510111i | ||||
\(613\) | −369401. | −0.983053 | −0.491526 | − | 0.870863i | \(-0.663561\pi\) | ||||
−0.491526 | + | 0.870863i | \(0.663561\pi\) | |||||||
\(614\) | − | 277733.i | − | 0.736700i | ||||||
\(615\) | 99166.5 | + | 56658.7i | 0.262189 | + | 0.149802i | ||||
\(616\) | −30342.1 | −0.0799622 | ||||||||
\(617\) | − | 429337.i | − | 1.12779i | −0.825847 | − | 0.563895i | \(-0.809302\pi\) | ||
0.825847 | − | 0.563895i | \(-0.190698\pi\) | |||||||
\(618\) | 11379.6 | − | 19917.1i | 0.0297956 | − | 0.0521495i | ||||
\(619\) | 297690. | 0.776932 | 0.388466 | − | 0.921463i | \(-0.373005\pi\) | ||||
0.388466 | + | 0.921463i | \(0.373005\pi\) | |||||||
\(620\) | 107593.i | 0.279900i | ||||||||
\(621\) | 482531. | − | 6532.93i | 1.25125 | − | 0.0169404i | ||||
\(622\) | 212689. | 0.549749 | ||||||||
\(623\) | 80383.9i | 0.207106i | ||||||||
\(624\) | −21223.9 | − | 12126.3i | −0.0545075 | − | 0.0311428i | ||||
\(625\) | 215502. | 0.551686 | ||||||||
\(626\) | − | 111475.i | − | 0.284464i | ||||||
\(627\) | −24741.6 | + | 43303.8i | −0.0629350 | + | 0.110152i | ||||
\(628\) | −359133. | −0.910618 | ||||||||
\(629\) | − | 494646.i | − | 1.25024i | ||||||
\(630\) | −12851.9 | − | 21803.3i | −0.0323807 | − | 0.0549340i | ||||
\(631\) | −238825. | −0.599821 | −0.299911 | − | 0.953967i | \(-0.596957\pi\) | ||||
−0.299911 | + | 0.953967i | \(0.596957\pi\) | |||||||
\(632\) | 119384.i | 0.298891i | ||||||||
\(633\) | 345113. | + | 197180.i | 0.861300 | + | 0.492103i | ||||
\(634\) | −351560. | −0.874623 | ||||||||
\(635\) | 12994.0i | 0.0322251i | ||||||||
\(636\) | 60841.9 | − | 106488.i | 0.150414 | − | 0.263262i | ||||
\(637\) | 308294. | 0.759776 | ||||||||
\(638\) | 11239.5i | 0.0276125i | ||||||||
\(639\) | −669247. | + | 394486.i | −1.63902 | + | 0.966117i | ||||
\(640\) | 115476. | 0.281924 | ||||||||
\(641\) | − | 88451.4i | − | 0.215273i | −0.994190 | − | 0.107636i | \(-0.965672\pi\) | ||
0.994190 | − | 0.107636i | \(-0.0343282\pi\) | |||||||
\(642\) | 172727. | + | 98687.3i | 0.419073 | + | 0.239437i | ||||
\(643\) | −107915. | −0.261012 | −0.130506 | − | 0.991448i | \(-0.541660\pi\) | ||||
−0.130506 | + | 0.991448i | \(0.541660\pi\) | |||||||
\(644\) | 92027.5i | 0.221894i | ||||||||
\(645\) | −50411.2 | + | 88231.8i | −0.121173 | + | 0.212083i | ||||
\(646\) | −159715. | −0.382720 | ||||||||
\(647\) | − | 293113.i | − | 0.700207i | −0.936711 | − | 0.350103i | \(-0.886146\pi\) | ||
0.936711 | − | 0.350103i | \(-0.113854\pi\) | |||||||
\(648\) | −358101. | − | 198219.i | −0.852817 | − | 0.472058i | ||||
\(649\) | 57603.4 | 0.136760 | ||||||||
\(650\) | − | 172312.i | − | 0.407838i | ||||||
\(651\) | 108262. | + | 61855.2i | 0.255454 | + | 0.145953i | ||||
\(652\) | 52263.2 | 0.122942 | ||||||||
\(653\) | − | 167595.i | − | 0.393038i | −0.980500 | − | 0.196519i | \(-0.937036\pi\) | ||
0.980500 | − | 0.196519i | \(-0.0629637\pi\) | |||||||
\(654\) | 106688. | − | 186731.i | 0.249438 | − | 0.436577i | ||||
\(655\) | 231482. | 0.539555 | ||||||||
\(656\) | 25033.5i | 0.0581720i | ||||||||
\(657\) | 433829. | + | 735993.i | 1.00505 | + | 1.70507i | ||||
\(658\) | 28813.9 | 0.0665503 | ||||||||
\(659\) | − | 322012.i | − | 0.741482i | −0.928736 | − | 0.370741i | \(-0.879104\pi\) | ||
0.928736 | − | 0.370741i | \(-0.120896\pi\) | |||||||
\(660\) | −29517.7 | − | 16864.9i | −0.0677632 | − | 0.0387164i | ||||
\(661\) | −166204. | −0.380399 | −0.190200 | − | 0.981745i | \(-0.560913\pi\) | ||||
−0.190200 | + | 0.981745i | \(0.560913\pi\) | |||||||
\(662\) | 48570.7i | 0.110830i | ||||||||
\(663\) | −275785. | + | 482692.i | −0.627400 | + | 1.09810i | ||||
\(664\) | −679770. | −1.54179 | ||||||||
\(665\) | − | 20105.8i | − | 0.0454650i | ||||||
\(666\) | −182910. | + | 107816.i | −0.412371 | + | 0.243071i | ||||
\(667\) | 86394.5 | 0.194193 | ||||||||
\(668\) | − | 417853.i | − | 0.936420i | ||||||
\(669\) | −405258. | − | 231544.i | −0.905482 | − | 0.517346i | ||||
\(670\) | 168857. | 0.376157 | ||||||||
\(671\) | 212969.i | 0.473011i | ||||||||
\(672\) | 62164.4 | − | 108803.i | 0.137659 | − | 0.240936i | ||||
\(673\) | 354661. | 0.783040 | 0.391520 | − | 0.920170i | \(-0.371949\pi\) | ||||
0.391520 | + | 0.920170i | \(0.371949\pi\) | |||||||
\(674\) | 461799.i | 1.01656i | ||||||||
\(675\) | 5195.18 | + | 383724.i | 0.0114023 | + | 0.842192i | ||||
\(676\) | −97317.8 | −0.212960 | ||||||||
\(677\) | 222358.i | 0.485150i | 0.970133 | + | 0.242575i | \(0.0779921\pi\) | ||||
−0.970133 | + | 0.242575i | \(0.922008\pi\) | |||||||
\(678\) | 410240. | + | 234390.i | 0.892439 | + | 0.509894i | ||||
\(679\) | 2665.70 | 0.00578191 | ||||||||
\(680\) | − | 275911.i | − | 0.596694i | ||||||
\(681\) | −33360.4 | + | 58388.8i | −0.0719344 | + | 0.125903i | ||||
\(682\) | −89493.4 | −0.192408 | ||||||||
\(683\) | 438076.i | 0.939092i | 0.882908 | + | 0.469546i | \(0.155582\pi\) | ||||
−0.882908 | + | 0.469546i | \(0.844418\pi\) | |||||||
\(684\) | −65149.0 | − | 110526.i | −0.139250 | − | 0.236238i | ||||
\(685\) | 193689. | 0.412785 | ||||||||
\(686\) | 145525.i | 0.309236i | ||||||||
\(687\) | 75917.6 | + | 43375.4i | 0.160853 | + | 0.0919031i | ||||
\(688\) | −22273.1 | −0.0470549 | ||||||||
\(689\) | 181209.i | 0.381717i | ||||||||
\(690\) | 69270.3 | − | 121240.i | 0.145495 | − | 0.254652i | ||||
\(691\) | −47579.0 | −0.0996458 | −0.0498229 | − | 0.998758i | \(-0.515866\pi\) | ||||
−0.0498229 | + | 0.998758i | \(0.515866\pi\) | |||||||
\(692\) | 110672.i | 0.231114i | ||||||||
\(693\) | −33939.2 | + | 20005.4i | −0.0706701 | + | 0.0416563i | ||||
\(694\) | −499704. | −1.03751 | ||||||||
\(695\) | − | 186528.i | − | 0.386166i | ||||||
\(696\) | −63623.8 | − | 36351.4i | −0.131341 | − | 0.0750417i | ||||
\(697\) | 569332. | 1.17193 | ||||||||
\(698\) | − | 174553.i | − | 0.358275i | ||||||
\(699\) | 207745. | − | 363605.i | 0.425184 | − | 0.744175i | ||||
\(700\) | −73183.1 | −0.149353 | ||||||||
\(701\) | 316760.i | 0.644607i | 0.946636 | + | 0.322303i | \(0.104457\pi\) | ||||
−0.946636 | + | 0.322303i | \(0.895543\pi\) | |||||||
\(702\) | 238601. | − | 3230.38i | 0.484169 | − | 0.00655510i | ||||
\(703\) | −168669. | −0.341290 | ||||||||
\(704\) | 78507.8i | 0.158405i | ||||||||
\(705\) | 71040.2 | + | 40588.7i | 0.142931 | + | 0.0816634i | ||||
\(706\) | 293403. | 0.588647 | ||||||||
\(707\) | − | 6576.25i | − | 0.0131565i | ||||||
\(708\) | −73511.4 | + | 128663.i | −0.146652 | + | 0.256677i | ||||
\(709\) | 455144. | 0.905433 | 0.452716 | − | 0.891655i | \(-0.350455\pi\) | ||||
0.452716 | + | 0.891655i | \(0.350455\pi\) | |||||||
\(710\) | 224784.i | 0.445912i | ||||||||
\(711\) | 78713.4 | + | 133538.i | 0.155707 | + | 0.264158i | ||||
\(712\) | 376147. | 0.741990 | ||||||||
\(713\) | 687907.i | 1.35316i | ||||||||
\(714\) | −109545. | − | 62588.3i | −0.214880 | − | 0.122771i | ||||
\(715\) | 50229.7 | 0.0982536 | ||||||||
\(716\) | 180854.i | 0.352778i | ||||||||
\(717\) | 157177. | − | 275098.i | 0.305739 | − | 0.535117i | ||||
\(718\) | 133790. | 0.259522 | ||||||||
\(719\) | − | 496408.i | − | 0.960243i | −0.877202 | − | 0.480121i | \(-0.840593\pi\) | ||
0.877202 | − | 0.480121i | \(-0.159407\pi\) | |||||||
\(720\) | 13570.0 | − | 7998.82i | 0.0261768 | − | 0.0154298i | ||||
\(721\) | 14394.7 | 0.0276905 | ||||||||
\(722\) | − | 253166.i | − | 0.485659i | ||||||
\(723\) | 306450. | + | 175090.i | 0.586251 | + | 0.334954i | ||||
\(724\) | 287341. | 0.548177 | ||||||||
\(725\) | 68703.5i | 0.130708i | ||||||||
\(726\) | 14027.8 | − | 24552.0i | 0.0266143 | − | 0.0465816i | ||||
\(727\) | 684607. | 1.29531 | 0.647654 | − | 0.761935i | \(-0.275750\pi\) | ||||
0.647654 | + | 0.761935i | \(0.275750\pi\) | |||||||
\(728\) | 115327.i | 0.217604i | ||||||||
\(729\) | −531246. | + | 14387.6i | −0.999633 | + | 0.0270728i | ||||
\(730\) | 247203. | 0.463882 | ||||||||
\(731\) | 506554.i | 0.947963i | ||||||||
\(732\) | −475687. | − | 271783.i | −0.887768 | − | 0.507225i | ||||
\(733\) | −645792. | −1.20194 | −0.600972 | − | 0.799270i | \(-0.705220\pi\) | ||||
−0.600972 | + | 0.799270i | \(0.705220\pi\) | |||||||
\(734\) | − | 357768.i | − | 0.664062i | ||||||
\(735\) | −98557.6 | + | 172500.i | −0.182438 | + | 0.319311i | ||||
\(736\) | 691346. | 1.27626 | ||||||||
\(737\) | − | 262844.i | − | 0.483909i | ||||||
\(738\) | −124094. | − | 210527.i | −0.227845 | − | 0.386540i | ||||
\(739\) | −963549. | −1.76435 | −0.882176 | − | 0.470920i | \(-0.843922\pi\) | ||||
−0.882176 | + | 0.470920i | \(0.843922\pi\) | |||||||
\(740\) | − | 114972.i | − | 0.209956i | ||||||
\(741\) | 164592. | + | 94039.7i | 0.299760 | + | 0.171267i | ||||
\(742\) | −41124.6 | −0.0746955 | ||||||||
\(743\) | − | 618795.i | − | 1.12091i | −0.828186 | − | 0.560453i | \(-0.810627\pi\) | ||
0.828186 | − | 0.560453i | \(-0.189373\pi\) | |||||||
\(744\) | 289444. | − | 506598.i | 0.522900 | − | 0.915203i | ||||
\(745\) | −272613. | −0.491172 | ||||||||
\(746\) | 101844.i | 0.183003i | ||||||||
\(747\) | −760359. | + | 448191.i | −1.36263 | + | 0.803198i | ||||
\(748\) | −169466. | −0.302886 | ||||||||
\(749\) | 124835.i | 0.222521i | ||||||||
\(750\) | 210883. | + | 120488.i | 0.374903 | + | 0.214200i | ||||
\(751\) | 261213. | 0.463143 | 0.231571 | − | 0.972818i | \(-0.425613\pi\) | ||||
0.231571 | + | 0.972818i | \(0.425613\pi\) | |||||||
\(752\) | 17933.3i | 0.0317121i | ||||||||
\(753\) | 118110. | − | 206722.i | 0.208304 | − | 0.364583i | ||||
\(754\) | 42720.0 | 0.0751431 | ||||||||
\(755\) | − | 321671.i | − | 0.564310i | ||||||
\(756\) | −1371.99 | − | 101337.i | −0.00240053 | − | 0.177306i | ||||
\(757\) | −536053. | −0.935439 | −0.467720 | − | 0.883877i | \(-0.654924\pi\) | ||||
−0.467720 | + | 0.883877i | \(0.654924\pi\) | |||||||
\(758\) | − | 139265.i | − | 0.242385i | ||||||
\(759\) | −188723. | − | 107827.i | −0.327599 | − | 0.187173i | ||||
\(760\) | −94082.6 | −0.162885 | ||||||||
\(761\) | 565879.i | 0.977135i | 0.872526 | + | 0.488568i | \(0.162480\pi\) | ||||
−0.872526 | + | 0.488568i | \(0.837520\pi\) | |||||||
\(762\) | 13792.9 | − | 24140.9i | 0.0237544 | − | 0.0415760i | ||||
\(763\) | 134956. | 0.231815 | ||||||||
\(764\) | 459236.i | 0.786773i | ||||||||
\(765\) | −181916. | − | 308621.i | −0.310848 | − | 0.527354i | ||||
\(766\) | 179667. | 0.306203 | ||||||||
\(767\) | − | 218943.i | − | 0.372170i | ||||||
\(768\) | −483593. | − | 276301.i | −0.819895 | − | 0.468446i | ||||
\(769\) | −171758. | −0.290445 | −0.145223 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145223 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(770\) | 11399.4i | 0.0192265i | ||||||||
\(771\) | 228858. | − | 400558.i | 0.384997 | − | 0.673839i | ||||
\(772\) | −60492.2 | −0.101500 | ||||||||
\(773\) | 148705.i | 0.248867i | 0.992228 | + | 0.124433i | \(0.0397113\pi\) | ||||
−0.992228 | + | 0.124433i | \(0.960289\pi\) | |||||||
\(774\) | 187313. | − | 110411.i | 0.312670 | − | 0.184302i | ||||
\(775\) | −547044. | −0.910792 | ||||||||
\(776\) | − | 12473.8i | − | 0.0207146i | ||||||
\(777\) | −115686. | − | 66096.9i | −0.191619 | − | 0.109481i | ||||
\(778\) | −349408. | −0.577263 | ||||||||
\(779\) | − | 194136.i | − | 0.319912i | ||||||
\(780\) | −64101.4 | + | 112193.i | −0.105361 | + | 0.184407i | ||||
\(781\) | 349902. | 0.573646 | ||||||||
\(782\) | − | 696060.i | − | 1.13824i | ||||||
\(783\) | −95134.0 | + | 1288.01i | −0.155172 | + | 0.00210085i | ||||
\(784\) | −43545.7 | −0.0708456 | ||||||||
\(785\) | 341947.i | 0.554906i | ||||||||
\(786\) | −430060. | − | 245714.i | −0.696120 | − | 0.397727i | ||||
\(787\) | −781097. | −1.26112 | −0.630559 | − | 0.776141i | \(-0.717174\pi\) | ||||
−0.630559 | + | 0.776141i | \(0.717174\pi\) | |||||||
\(788\) | − | 661810.i | − | 1.06581i | ||||||
\(789\) | 72119.9 | − | 126227.i | 0.115851 | − | 0.202768i | ||||
\(790\) | 44852.2 | 0.0718670 | ||||||||
\(791\) | 296492.i | 0.473870i | ||||||||
\(792\) | 93612.9 | + | 158815.i | 0.149240 | + | 0.253186i | ||||
\(793\) | 809469. | 1.28722 | ||||||||
\(794\) | 556897.i | 0.883351i | ||||||||
\(795\) | −101392. | − | 57930.3i | −0.160424 | − | 0.0916583i | ||||
\(796\) | −742202. | −1.17138 | ||||||||
\(797\) | − | 69274.9i | − | 0.109058i | −0.998512 | − | 0.0545292i | \(-0.982634\pi\) | ||
0.998512 | − | 0.0545292i | \(-0.0173658\pi\) | |||||||
\(798\) | −21341.9 | + | 37353.5i | −0.0335141 | + | 0.0586578i | ||||
\(799\) | 407854. | 0.638868 | ||||||||
\(800\) | 549779.i | 0.859030i | ||||||||
\(801\) | 420740. | − | 248004.i | 0.655766 | − | 0.386540i | ||||
\(802\) | −380486. | −0.591547 | ||||||||
\(803\) | − | 384799.i | − | 0.596764i | ||||||
\(804\) | 587089. | + | 335433.i | 0.908222 | + | 0.518911i | ||||
\(805\) | 87623.5 | 0.135216 | ||||||||
\(806\) | 340154.i | 0.523607i | ||||||||
\(807\) | 593055. | − | 1.03799e6i | 0.910642 | − | 1.59385i | ||||
\(808\) | −30772.8 | −0.0471351 | ||||||||
\(809\) | − | 497706.i | − | 0.760459i | −0.924892 | − | 0.380230i | \(-0.875845\pi\) | ||
0.924892 | − | 0.380230i | \(-0.124155\pi\) | |||||||
\(810\) | −74470.1 | + | 134537.i | −0.113504 | + | 0.205056i | ||||
\(811\) | −346897. | −0.527422 | −0.263711 | − | 0.964602i | \(-0.584947\pi\) | ||||
−0.263711 | + | 0.964602i | \(0.584947\pi\) | |||||||
\(812\) | − | 18143.8i | − | 0.0275179i | ||||||
\(813\) | 413151. | + | 236053.i | 0.625068 | + | 0.357132i | ||||
\(814\) | 95630.5 | 0.144327 | ||||||||
\(815\) | − | 49762.1i | − | 0.0749175i | ||||||
\(816\) | 38954.0 | − | 68179.0i | 0.0585021 | − | 0.102393i | ||||
\(817\) | 172729. | 0.258775 | ||||||||
\(818\) | 348992.i | 0.521565i | ||||||||
\(819\) | 76038.1 | + | 128999.i | 0.113361 | + | 0.192317i | ||||
\(820\) | 132331. | 0.196804 | ||||||||
\(821\) | 921375.i | 1.36694i | 0.729977 | + | 0.683471i | \(0.239531\pi\) | ||||
−0.729977 | + | 0.683471i | \(0.760469\pi\) | |||||||
\(822\) | −359846. | − | 205597.i | −0.532565 | − | 0.304280i | ||||
\(823\) | −329225. | −0.486064 | −0.243032 | − | 0.970018i | \(-0.578142\pi\) | ||||
−0.243032 | + | 0.970018i | \(0.578142\pi\) | |||||||
\(824\) | − | 67358.2i | − | 0.0992055i | ||||||
\(825\) | 85747.2 | − | 150079.i | 0.125983 | − | 0.220501i | ||||
\(826\) | 49688.3 | 0.0728272 | ||||||||
\(827\) | − | 350069.i | − | 0.511850i | −0.966697 | − | 0.255925i | \(-0.917620\pi\) | ||
0.966697 | − | 0.255925i | \(-0.0823799\pi\) | |||||||
\(828\) | 481684. | − | 283928.i | 0.702590 | − | 0.414140i | ||||
\(829\) | 707766. | 1.02987 | 0.514933 | − | 0.857231i | \(-0.327817\pi\) | ||||
0.514933 | + | 0.857231i | \(0.327817\pi\) | |||||||
\(830\) | 255387.i | 0.370717i | ||||||||
\(831\) | 885597. | + | 505985.i | 1.28243 | + | 0.732715i | ||||
\(832\) | 298399. | 0.431072 | ||||||||
\(833\) | 990352.i | 1.42725i | ||||||||
\(834\) | −197996. | + | 346541.i | −0.284658 | + | 0.498222i | ||||
\(835\) | −397856. | −0.570628 | ||||||||
\(836\) | 57786.0i | 0.0826818i | ||||||||
\(837\) | −10255.6 | − | 757494.i | −0.0146390 | − | 1.08126i | ||||
\(838\) | −364491. | −0.519038 | ||||||||
\(839\) | 260427.i | 0.369966i | 0.982742 | + | 0.184983i | \(0.0592231\pi\) | ||||
−0.982742 | + | 0.184983i | \(0.940777\pi\) | |||||||
\(840\) | −64528.9 | − | 36868.5i | −0.0914525 | − | 0.0522513i | ||||
\(841\) | 690248. | 0.975917 | ||||||||
\(842\) | 439272.i | 0.619597i | ||||||||
\(843\) | −186798. | + | 326941.i | −0.262855 | + | 0.460060i | ||||
\(844\) | 460531. | 0.646508 | ||||||||
\(845\) | 92660.6i | 0.129772i | ||||||||
\(846\) | −88897.9 | − | 150816.i | −0.124208 | − | 0.210720i | ||||
\(847\) | 17744.4 | 0.0247341 | ||||||||
\(848\) | − | 25595.3i | − | 0.0355934i | ||||||
\(849\) | 57187.3 | + | 32673.9i | 0.0793385 | + | 0.0453300i | ||||
\(850\) | 553528. | 0.766129 | ||||||||
\(851\) | − | 735080.i | − | 1.01502i | ||||||
\(852\) | −446532. | + | 781541.i | −0.615140 | + | 1.07664i | ||||
\(853\) | −851668. | −1.17050 | −0.585251 | − | 0.810852i | \(-0.699004\pi\) | ||||
−0.585251 | + | 0.810852i | \(0.699004\pi\) | |||||||
\(854\) | 183705.i | 0.251887i | ||||||||
\(855\) | −105236. | + | 62031.3i | −0.143957 | + | 0.0848552i | ||||
\(856\) | 584149. | 0.797216 | ||||||||
\(857\) | 1.34625e6i | 1.83301i | 0.400022 | + | 0.916505i | \(0.369002\pi\) | ||||
−0.400022 | + | 0.916505i | \(0.630998\pi\) | |||||||
\(858\) | −93319.3 | − | 53317.9i | −0.126764 | − | 0.0724266i | ||||
\(859\) | 901853. | 1.22222 | 0.611110 | − | 0.791546i | \(-0.290723\pi\) | ||||
0.611110 | + | 0.791546i | \(0.290723\pi\) | |||||||
\(860\) | 117739.i | 0.159193i | ||||||||
\(861\) | 76076.8 | − | 133153.i | 0.102623 | − | 0.179616i | ||||
\(862\) | −366808. | −0.493655 | ||||||||
\(863\) | − | 593241.i | − | 0.796543i | −0.917268 | − | 0.398272i | \(-0.869610\pi\) | ||
0.917268 | − | 0.398272i | \(-0.130390\pi\) | |||||||
\(864\) | −761281. | + | 10306.9i | −1.01981 | + | 0.0138070i | ||||
\(865\) | 105376. | 0.140834 | ||||||||
\(866\) | 78919.3i | 0.105232i | ||||||||
\(867\) | −897911. | − | 513021.i | −1.19452 | − | 0.682491i | ||||
\(868\) | 144468. | 0.191748 | ||||||||
\(869\) | − | 69817.4i | − | 0.0924536i | ||||||
\(870\) | −13657.1 | + | 23903.2i | −0.0180434 | + | 0.0315804i | ||||
\(871\) | −999039. | −1.31688 | ||||||||
\(872\) | − | 631509.i | − | 0.830513i | ||||||
\(873\) | −8224.33 | − | 13952.6i | −0.0107913 | − | 0.0183074i | ||||
\(874\) | −237349. | −0.310716 | ||||||||
\(875\) | 152411.i | 0.199067i | ||||||||
\(876\) | 859486. | + | 491066.i | 1.12003 | + | 0.639929i | ||||
\(877\) | −745074. | −0.968724 | −0.484362 | − | 0.874868i | \(-0.660948\pi\) | ||||
−0.484362 | + | 0.874868i | \(0.660948\pi\) | |||||||
\(878\) | − | 393979.i | − | 0.511074i | ||||||
\(879\) | 183090. | − | 320452.i | 0.236966 | − | 0.414749i | ||||
\(880\) | −7094.82 | −0.00916169 | ||||||||
\(881\) | 95207.0i | 0.122664i | 0.998117 | + | 0.0613320i | \(0.0195348\pi\) | ||||
−0.998117 | + | 0.0613320i | \(0.980465\pi\) | |||||||
\(882\) | 366211. | − | 215862.i | 0.470754 | − | 0.277485i | ||||
\(883\) | 789087. | 1.01205 | 0.506027 | − | 0.862518i | \(-0.331114\pi\) | ||||
0.506027 | + | 0.862518i | \(0.331114\pi\) | |||||||
\(884\) | 644120.i | 0.824256i | ||||||||
\(885\) | 122506. | + | 69993.5i | 0.156412 | + | 0.0893657i | ||||
\(886\) | −60415.5 | −0.0769628 | ||||||||
\(887\) | − | 1.06364e6i | − | 1.35190i | −0.736946 | − | 0.675951i | \(-0.763733\pi\) | ||
0.736946 | − | 0.675951i | \(-0.236267\pi\) | |||||||
\(888\) | −309293. | + | 541338.i | −0.392233 | + | 0.686503i | ||||
\(889\) | 17447.3 | 0.0220762 | ||||||||
\(890\) | − | 141317.i | − | 0.178408i | ||||||
\(891\) | 209422. | + | 115921.i | 0.263795 | + | 0.146018i | ||||
\(892\) | −540790. | −0.679672 | ||||||||
\(893\) | − | 139074.i | − | 0.174398i | ||||||
\(894\) | 506474. | + | 289374.i | 0.633698 | + | 0.362063i | ||||
\(895\) | 172199. | 0.214973 | ||||||||
\(896\) | − | 155052.i | − | 0.193135i | ||||||
\(897\) | −409837. | + | 717315.i | −0.509362 | + | 0.891507i | ||||
\(898\) | 76648.5 | 0.0950497 | ||||||||
\(899\) | − | 135625.i | − | 0.167811i | ||||||
\(900\) | 225788. | + | 383050.i | 0.278750 | + | 0.472901i | ||||
\(901\) | −582110. | −0.717061 | ||||||||
\(902\) | 110070.i | 0.135286i | ||||||||
\(903\) | 118471. | + | 67688.1i | 0.145290 | + | 0.0830112i | ||||
\(904\) | 1.38740e6 | 1.69771 | ||||||||
\(905\) | − | 273591.i | − | 0.334044i | ||||||
\(906\) | −341447. | + | 597616.i | −0.415975 | + | 0.728058i | ||||
\(907\) | −1.32897e6 | −1.61548 | −0.807740 | − | 0.589539i | \(-0.799310\pi\) | ||||
−0.807740 | + | 0.589539i | \(0.799310\pi\) | |||||||
\(908\) | 77915.9i | 0.0945049i | ||||||||
\(909\) | −34421.0 | + | 20289.4i | −0.0416577 | + | 0.0245550i | ||||
\(910\) | 43327.8 | 0.0523219 | ||||||||
\(911\) | 1.12314e6i | 1.35331i | 0.736302 | + | 0.676653i | \(0.236570\pi\) | ||||
−0.736302 | + | 0.676653i | \(0.763430\pi\) | |||||||
\(912\) | −23248.3 | − | 13282.9i | −0.0279512 | − | 0.0159699i | ||||
\(913\) | 397538. | 0.476911 | ||||||||
\(914\) | − | 553757.i | − | 0.662867i | ||||||
\(915\) | −258777. | + | 452923.i | −0.309089 | + | 0.540981i | ||||
\(916\) | 101307. | 0.120739 | ||||||||
\(917\) | − | 310816.i | − | 0.369628i | ||||||
\(918\) | 10377.2 | + | 766472.i | 0.0123138 | + | 0.909518i | ||||
\(919\) | −154862. | −0.183364 | −0.0916821 | − | 0.995788i | \(-0.529224\pi\) | ||||
−0.0916821 | + | 0.995788i | \(0.529224\pi\) | |||||||
\(920\) | − | 410024.i | − | 0.484433i | ||||||
\(921\) | −919424. | − | 525312.i | −1.08392 | − | 0.619295i | ||||
\(922\) | 228508. | 0.268806 | ||||||||
\(923\) | − | 1.32993e6i | − | 1.56109i | ||||||
\(924\) | −22644.8 | + | 39634.0i | −0.0265231 | + | 0.0464220i | ||||
\(925\) | 584558. | 0.683194 | ||||||||
\(926\) | − | 8599.31i | − | 0.0100286i | ||||||
\(927\) | −44411.1 | − | 75343.6i | −0.0516811 | − | 0.0876773i | ||||
\(928\) | −136303. | −0.158274 | ||||||||
\(929\) | − | 992052.i | − | 1.14948i | −0.818335 | − | 0.574742i | \(-0.805102\pi\) | ||
0.818335 | − | 0.574742i | \(-0.194898\pi\) | |||||||
\(930\) | −190327. | − | 108743.i | −0.220056 | − | 0.125729i | ||||
\(931\) | 337699. | 0.389610 | ||||||||
\(932\) | − | 485206.i | − | 0.558592i | ||||||
\(933\) | 402286. | − | 704098.i | 0.462138 | − | 0.808853i | ||||
\(934\) | −429945. | −0.492856 | ||||||||
\(935\) | 161356.i | 0.184571i | ||||||||
\(936\) | 603635. | − | 355811.i | 0.689006 | − | 0.406133i | ||||
\(937\) | 294602. | 0.335550 | 0.167775 | − | 0.985825i | \(-0.446342\pi\) | ||||
0.167775 | + | 0.985825i | \(0.446342\pi\) | |||||||
\(938\) | − | 226728.i | − | 0.257691i | ||||||
\(939\) | −369032. | − | 210846.i | −0.418536 | − | 0.239130i | ||||
\(940\) | 94798.4 | 0.107287 | ||||||||
\(941\) | 1.13953e6i | 1.28690i | 0.765488 | + | 0.643451i | \(0.222498\pi\) | ||||
−0.765488 | + | 0.643451i | \(0.777502\pi\) | |||||||
\(942\) | 362970. | − | 635286.i | 0.409043 | − | 0.715925i | ||||
\(943\) | 846069. | 0.951442 | ||||||||
\(944\) | 30925.2i | 0.0347031i | ||||||||
\(945\) | −96487.4 | + | 1306.33i | −0.108046 | + | 0.00146281i | ||||
\(946\) | −97932.7 | −0.109432 | ||||||||
\(947\) | − | 1.04095e6i | − | 1.16073i | −0.814356 | − | 0.580366i | \(-0.802910\pi\) | ||
0.814356 | − | 0.580366i | \(-0.197090\pi\) | |||||||
\(948\) | 155944. | + | 89098.5i | 0.173521 | + | 0.0991411i | ||||
\(949\) | −1.46257e6 | −1.62400 | ||||||||
\(950\) | − | 188747.i | − | 0.209138i | ||||||
\(951\) | −664950. | + | 1.16382e6i | −0.735238 | + | 1.28685i | ||||
\(952\) | −370472. | −0.408772 | ||||||||
\(953\) | − | 1.41370e6i | − | 1.55658i | −0.627905 | − | 0.778290i | \(-0.716087\pi\) | ||
0.627905 | − | 0.778290i | \(-0.283913\pi\) | |||||||
\(954\) | 126880. | + | 215252.i | 0.139410 | + | 0.236510i | ||||
\(955\) | 437259. | 0.479438 | ||||||||
\(956\) | − | 367100.i | − | 0.401669i | ||||||
\(957\) | 37208.0 | + | 21258.7i | 0.0406267 | + | 0.0232120i | ||||
\(958\) | −83160.7 | −0.0906123 | ||||||||
\(959\) | − | 260070.i | − | 0.282783i | ||||||
\(960\) | −95394.3 | + | 166963.i | −0.103509 | + | 0.181167i | ||||
\(961\) | 156378. | 0.169328 | ||||||||
\(962\) | − | 363480.i | − | 0.392763i | ||||||
\(963\) | 653400. | − | 385145.i | 0.704574 | − | 0.415310i | ||||
\(964\) | 408938. | 0.440051 | ||||||||
\(965\) | 57597.3i | 0.0618511i | ||||||||
\(966\) | −162791. | − | 93010.7i | −0.174453 | − | 0.0996733i | ||||
\(967\) | −1.01698e6 | −1.08758 | −0.543788 | − | 0.839222i | \(-0.683011\pi\) | ||||
−0.543788 | + | 0.839222i | \(0.683011\pi\) | |||||||
\(968\) | − | 83033.0i | − | 0.0886136i | ||||||
\(969\) | −302090. | + | 528731.i | −0.321728 | + | 0.563102i | ||||
\(970\) | −4686.36 | −0.00498072 | ||||||||
\(971\) | − | 1.67536e6i | − | 1.77693i | −0.458944 | − | 0.888465i | \(-0.651772\pi\) | ||
0.458944 | − | 0.888465i | \(-0.348228\pi\) | |||||||
\(972\) | −526178. | + | 319830.i | −0.556929 | + | 0.338522i | ||||
\(973\) | −250455. | −0.264548 | ||||||||
\(974\) | 413659.i | 0.436038i | ||||||||
\(975\) | −570430. | − | 325915.i | −0.600058 | − | 0.342843i | ||||
\(976\) | −114335. | −0.120028 | ||||||||
\(977\) | 468877.i | 0.491213i | 0.969370 | + | 0.245607i | \(0.0789871\pi\) | ||||
−0.969370 | + | 0.245607i | \(0.921013\pi\) | |||||||
\(978\) | −52821.5 | + | 92450.5i | −0.0552247 | + | 0.0966567i | ||||
\(979\) | −219975. | −0.229514 | ||||||||
\(980\) | 230190.i | 0.239681i | ||||||||
\(981\) | −416371. | − | 706375.i | −0.432656 | − | 0.734003i | ||||
\(982\) | −530865. | −0.550505 | ||||||||
\(983\) | 1.72528e6i | 1.78547i | 0.450580 | + | 0.892736i | \(0.351217\pi\) | ||||
−0.450580 | + | 0.892736i | \(0.648783\pi\) | |||||||
\(984\) | −623074. | − | 355992.i | −0.643501 | − | 0.367664i | ||||
\(985\) | −630139. | −0.649477 | ||||||||
\(986\) | 137232.i | 0.141157i | ||||||||
\(987\) | 54499.3 | − | 95387.1i | 0.0559444 | − | 0.0979164i | ||||
\(988\) | 219638. | 0.225005 | ||||||||
\(989\) | 752776.i | 0.769615i | ||||||||
\(990\) | 59666.0 | − | 35170.0i | 0.0608775 | − | 0.0358841i | ||||
\(991\) | 724559. | 0.737779 | 0.368889 | − | 0.929473i | \(-0.379738\pi\) | ||||
0.368889 | + | 0.929473i | \(0.379738\pi\) | |||||||
\(992\) | − | 1.08530e6i | − | 1.10287i | ||||||
\(993\) | 160791. | + | 91868.0i | 0.163066 | + | 0.0931678i | ||||
\(994\) | 301823. | 0.305478 | ||||||||
\(995\) | 706684.i | 0.713804i | ||||||||
\(996\) | −507324. | + | 887940.i | −0.511407 | + | 0.895087i | ||||
\(997\) | 1.67803e6 | 1.68814 | 0.844071 | − | 0.536232i | \(-0.180153\pi\) | ||||
0.844071 | + | 0.536232i | \(0.180153\pi\) | |||||||
\(998\) | − | 223703.i | − | 0.224601i | ||||||
\(999\) | 10958.9 | + | 809440.i | 0.0109808 | + | 0.811061i |
(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 | 33.5.b.a.23.9 | yes | 14 | |
3.2 | odd | 2 | inner | 33.5.b.a.23.6 | ✓ | 14 | |
4.3 | odd | 2 | 528.5.i.d.353.1 | 14 | |||
12.11 | even | 2 | 528.5.i.d.353.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.b.a.23.6 | ✓ | 14 | 3.2 | odd | 2 | inner | |
33.5.b.a.23.9 | yes | 14 | 1.1 | even | 1 | trivial | |
528.5.i.d.353.1 | 14 | 4.3 | odd | 2 | |||
528.5.i.d.353.2 | 14 | 12.11 | even | 2 |