Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.19 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.19 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01287 | + | 5.28662i | 0.355828 | + | 0.934552i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −23.8967 | + | 21.2825i | −0.746773 | + | 0.665079i | ||||
\(5\) | 78.5398 | − | 45.3450i | 1.40496 | − | 0.811155i | 0.410066 | − | 0.912056i | \(-0.365506\pi\) |
0.994897 | + | 0.100901i | \(0.0321724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −69.6792 | − | 40.2293i | −0.537475 | − | 0.310311i | 0.206580 | − | 0.978430i | \(-0.433767\pi\) |
−0.744055 | + | 0.668118i | \(0.767100\pi\) | |||||||
\(8\) | −160.614 | − | 83.4942i | −0.887273 | − | 0.461245i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 397.812 | + | 323.937i | 1.25799 | + | 1.02438i | ||||
\(11\) | 275.903 | − | 477.878i | 0.687503 | − | 1.19079i | −0.285140 | − | 0.958486i | \(-0.592040\pi\) |
0.972643 | − | 0.232304i | \(-0.0746265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −307.186 | − | 532.062i | −0.504131 | − | 0.873180i | −0.999989 | − | 0.00477646i | \(-0.998480\pi\) |
0.495858 | − | 0.868404i | \(-0.334854\pi\) | |||||||
\(14\) | 72.4223 | − | 449.344i | 0.0987534 | − | 0.612715i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 118.109 | − | 1017.17i | 0.115341 | − | 0.993326i | ||||
\(17\) | − | 482.387i | − | 0.404830i | −0.979300 | − | 0.202415i | \(-0.935121\pi\) | ||
0.979300 | − | 0.202415i | \(-0.0648791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 453.989i | − | 0.288510i | −0.989541 | − | 0.144255i | \(-0.953921\pi\) | ||
0.989541 | − | 0.144255i | \(-0.0460786\pi\) | |||||||
\(20\) | −911.790 | + | 2755.12i | −0.509706 | + | 1.54016i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3081.72 | + | 496.691i | 1.35749 | + | 0.218791i | ||||
\(23\) | 310.876 | + | 538.452i | 0.122537 | + | 0.212240i | 0.920767 | − | 0.390112i | \(-0.127564\pi\) |
−0.798231 | + | 0.602352i | \(0.794230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2549.83 | − | 4416.44i | 0.815946 | − | 1.41326i | ||||
\(26\) | 2194.49 | − | 2694.95i | 0.636648 | − | 0.781838i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2521.29 | − | 521.599i | 0.607753 | − | 0.125731i | ||||
\(29\) | 7777.18 | + | 4490.16i | 1.71723 | + | 0.991440i | 0.923893 | + | 0.382652i | \(0.124989\pi\) |
0.793332 | + | 0.608789i | \(0.208344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −650.730 | + | 375.699i | −0.121618 | + | 0.0702159i | −0.559575 | − | 0.828780i | \(-0.689035\pi\) |
0.437957 | + | 0.898996i | \(0.355702\pi\) | |||||||
\(32\) | 5615.11 | − | 1423.02i | 0.969356 | − | 0.245661i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2550.20 | − | 970.980i | 0.378335 | − | 0.144050i | ||||
\(35\) | −7296.79 | −1.00684 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4221.49 | −0.506946 | −0.253473 | − | 0.967342i | \(-0.581573\pi\) | ||||
−0.253473 | + | 0.967342i | \(0.581573\pi\) | |||||||
\(38\) | 2400.07 | − | 913.819i | 0.269628 | − | 0.102660i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16400.6 | + | 725.399i | −1.62073 | + | 0.0716848i | ||||
\(41\) | −11012.8 | + | 6358.24i | −1.02315 | + | 0.590714i | −0.915014 | − | 0.403422i | \(-0.867821\pi\) |
−0.108133 | + | 0.994136i | \(0.534487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13956.9 | + | 8058.04i | 1.15112 | + | 0.664597i | 0.949159 | − | 0.314797i | \(-0.101937\pi\) |
0.201957 | + | 0.979394i | \(0.435270\pi\) | |||||||
\(44\) | 3577.26 | + | 17291.6i | 0.278560 | + | 1.34649i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2220.84 | + | 2727.31i | −0.154747 | + | 0.190038i | ||||
\(47\) | 9570.02 | − | 16575.8i | 0.631929 | − | 1.09453i | −0.355228 | − | 0.934780i | \(-0.615597\pi\) |
0.987157 | − | 0.159753i | \(-0.0510697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5166.71 | − | 8949.00i | −0.307414 | − | 0.532457i | ||||
\(50\) | 28480.5 | + | 4590.30i | 1.61110 | + | 0.259667i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18664.4 | + | 6176.86i | 0.957205 | + | 0.316781i | ||||
\(53\) | − | 8422.39i | − | 0.411856i | −0.978567 | − | 0.205928i | \(-0.933979\pi\) | ||
0.978567 | − | 0.205928i | \(-0.0660213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 50043.2i | − | 2.23069i | ||||||
\(56\) | 7832.51 | + | 12279.2i | 0.333757 | + | 0.523238i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8083.35 | + | 50153.1i | −0.315516 | + | 1.95762i | ||||
\(59\) | −2693.87 | − | 4665.91i | −0.100750 | − | 0.174505i | 0.811244 | − | 0.584708i | \(-0.198791\pi\) |
−0.911994 | + | 0.410204i | \(0.865458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5910.89 | + | 10238.0i | −0.203390 | + | 0.352281i | −0.949618 | − | 0.313408i | \(-0.898529\pi\) |
0.746229 | + | 0.665689i | \(0.231862\pi\) | |||||||
\(62\) | −3296.01 | − | 2683.93i | −0.108895 | − | 0.0886731i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 18825.4 | + | 26820.6i | 0.574507 | + | 0.818500i | ||||
\(65\) | −48252.7 | − | 27858.7i | −1.41657 | − | 0.817857i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 27131.6 | − | 15664.5i | 0.738395 | − | 0.426313i | −0.0830902 | − | 0.996542i | \(-0.526479\pi\) |
0.821486 | + | 0.570229i | \(0.193146\pi\) | |||||||
\(68\) | 10266.4 | + | 11527.5i | 0.269244 | + | 0.302317i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −14687.4 | − | 38575.3i | −0.358262 | − | 0.940946i | ||||
\(71\) | −68895.9 | −1.62199 | −0.810994 | − | 0.585054i | \(-0.801073\pi\) | ||||
−0.810994 | + | 0.585054i | \(0.801073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −23822.3 | −0.523210 | −0.261605 | − | 0.965175i | \(-0.584252\pi\) | ||||
−0.261605 | + | 0.965175i | \(0.584252\pi\) | |||||||
\(74\) | −8497.30 | − | 22317.4i | −0.180385 | − | 0.473767i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9662.03 | + | 10848.9i | 0.191882 | + | 0.215452i | ||||
\(77\) | −38449.4 | + | 22198.8i | −0.739031 | + | 0.426680i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19337.5 | − | 11164.5i | −0.348604 | − | 0.201267i | 0.315466 | − | 0.948937i | \(-0.397839\pi\) |
−0.664070 | + | 0.747670i | \(0.731172\pi\) | |||||||
\(80\) | −36847.1 | − | 85243.6i | −0.643692 | − | 1.48914i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −55780.9 | − | 45422.2i | −0.916117 | − | 0.745991i | ||||
\(83\) | 39320.2 | − | 68104.6i | 0.626499 | − | 1.08513i | −0.361750 | − | 0.932275i | \(-0.617821\pi\) |
0.988249 | − | 0.152853i | \(-0.0488461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21873.8 | − | 37886.6i | −0.328380 | − | 0.568772i | ||||
\(86\) | −14506.4 | + | 90004.8i | −0.211501 | + | 1.31226i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −84213.8 | + | 53717.4i | −1.15925 | + | 0.739449i | ||||
\(89\) | 87925.1i | 1.17662i | 0.808634 | + | 0.588312i | \(0.200207\pi\) | ||||
−0.808634 | + | 0.588312i | \(0.799793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49431.5i | 0.625750i | ||||||||
\(92\) | −18888.5 | − | 6251.04i | −0.232664 | − | 0.0769986i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 106893. | + | 17228.3i | 1.24775 | + | 0.201105i | ||||
\(95\) | −20586.1 | − | 35656.2i | −0.234027 | − | 0.405346i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39159.6 | + | 67826.3i | −0.422580 | + | 0.731929i | −0.996191 | − | 0.0871983i | \(-0.972209\pi\) |
0.573611 | + | 0.819128i | \(0.305542\pi\) | |||||||
\(98\) | 36910.1 | − | 45327.5i | 0.388222 | − | 0.476757i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 33060.2 | + | 159805.i | 0.330602 | + | 1.59805i | ||||
\(101\) | 22486.3 | + | 12982.5i | 0.219339 | + | 0.126635i | 0.605644 | − | 0.795736i | \(-0.292916\pi\) |
−0.386305 | + | 0.922371i | \(0.626249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −21490.3 | + | 12407.4i | −0.199595 | + | 0.115236i | −0.596466 | − | 0.802638i | \(-0.703429\pi\) |
0.396872 | + | 0.917874i | \(0.370096\pi\) | |||||||
\(104\) | 4914.16 | + | 111105.i | 0.0445519 | + | 1.00728i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 44526.0 | − | 16953.1i | 0.384901 | − | 0.146550i | ||||
\(107\) | 105956. | 0.894680 | 0.447340 | − | 0.894364i | \(-0.352371\pi\) | ||||
0.447340 | + | 0.894364i | \(0.352371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −24092.4 | −0.194229 | −0.0971146 | − | 0.995273i | \(-0.530961\pi\) | ||||
−0.0971146 | + | 0.995273i | \(0.530961\pi\) | |||||||
\(110\) | 264560. | − | 100730.i | 2.08469 | − | 0.793740i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −49149.6 | + | 66123.9i | −0.370233 | + | 0.498096i | ||||
\(113\) | −7844.35 | + | 4528.94i | −0.0577911 | + | 0.0333657i | −0.528617 | − | 0.848860i | \(-0.677289\pi\) |
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48832.2 | + | 28193.3i | 0.344320 | + | 0.198793i | ||||
\(116\) | −281411. | + | 58217.8i | −1.94176 | + | 0.401709i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 19244.5 | − | 23633.3i | 0.127234 | − | 0.156250i | ||||
\(119\) | −19406.1 | + | 33612.3i | −0.125623 | + | 0.217586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −71719.4 | − | 124222.i | −0.445321 | − | 0.771318i | ||||
\(122\) | −66022.1 | − | 10641.0i | −0.401596 | − | 0.0647267i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7554.50 | − | 22827.1i | 0.0441216 | − | 0.133321i | ||||
\(125\) | − | 179082.i | − | 1.02513i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 195212.i | − | 1.07398i | −0.843587 | − | 0.536992i | \(-0.819561\pi\) | ||
0.843587 | − | 0.536992i | \(-0.180439\pi\) | |||||||
\(128\) | −103897. | + | 153509.i | −0.560505 | + | 0.828151i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 50152.2 | − | 311169.i | 0.260275 | − | 1.61487i | ||||
\(131\) | 126871. | + | 219747.i | 0.645929 | + | 1.11878i | 0.984086 | + | 0.177693i | \(0.0568632\pi\) |
−0.338157 | + | 0.941090i | \(0.609803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18263.7 | + | 31633.6i | −0.0895280 | + | 0.155067i | ||||
\(134\) | 137424. | + | 111904.i | 0.661153 | + | 0.538375i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −40276.5 | + | 77477.9i | −0.186726 | + | 0.359195i | ||||
\(137\) | 108349. | + | 62555.1i | 0.493199 | + | 0.284748i | 0.725900 | − | 0.687800i | \(-0.241423\pi\) |
−0.232702 | + | 0.972548i | \(0.574757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −155476. | + | 89764.4i | −0.682539 | + | 0.394064i | −0.800811 | − | 0.598917i | \(-0.795598\pi\) |
0.118272 | + | 0.992981i | \(0.462265\pi\) | |||||||
\(140\) | 174369. | − | 155294.i | 0.751883 | − | 0.669629i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −138678. | − | 364227.i | −0.577149 | − | 1.51583i | ||||
\(143\) | −339014. | −1.38637 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 814424. | 3.21685 | ||||||||
\(146\) | −47951.1 | − | 125939.i | −0.186173 | − | 0.488967i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 100880. | − | 89844.0i | 0.378574 | − | 0.337159i | ||||
\(149\) | 395679. | − | 228445.i | 1.46008 | − | 0.842978i | 0.461067 | − | 0.887366i | \(-0.347467\pi\) |
0.999014 | + | 0.0443874i | \(0.0141336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 189659. | + | 109500.i | 0.676909 | + | 0.390814i | 0.798690 | − | 0.601743i | \(-0.205527\pi\) |
−0.121780 | + | 0.992557i | \(0.538860\pi\) | |||||||
\(152\) | −37905.4 | + | 72916.8i | −0.133074 | + | 0.255987i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −194750. | − | 158584.i | −0.661722 | − | 0.538838i | ||||
\(155\) | −34072.1 | + | 59014.6i | −0.113912 | + | 0.197301i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 113832. | + | 197163.i | 0.368566 | + | 0.638375i | 0.989342 | − | 0.145614i | \(-0.0465156\pi\) |
−0.620776 | + | 0.783988i | \(0.713182\pi\) | |||||||
\(158\) | 20098.8 | − | 124703.i | 0.0640511 | − | 0.397405i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 376483. | − | 366381.i | 1.16264 | − | 1.13144i | ||||
\(161\) | − | 50025.3i | − | 0.152098i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 460735.i | 1.35826i | 0.734020 | + | 0.679128i | \(0.237642\pi\) | ||||
−0.734020 | + | 0.679128i | \(0.762358\pi\) | |||||||
\(164\) | 127851. | − | 386321.i | 0.371187 | − | 1.12160i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 439189. | + | 70785.6i | 1.23703 | + | 0.199377i | ||||
\(167\) | 286572. | + | 496357.i | 0.795137 | + | 1.37722i | 0.922752 | + | 0.385395i | \(0.125935\pi\) |
−0.127614 | + | 0.991824i | \(0.540732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3080.17 | + | 5335.01i | −0.00829579 | + | 0.0143687i | ||||
\(170\) | 156263. | − | 191899.i | 0.414699 | − | 0.509273i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −505021. | + | 104478.i | −1.30163 | + | 0.269279i | ||||
\(173\) | 283930. | + | 163927.i | 0.721268 | + | 0.416424i | 0.815219 | − | 0.579153i | \(-0.196617\pi\) |
−0.0939514 | + | 0.995577i | \(0.529950\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −355340. | + | 205156.i | −0.877101 | + | 0.506394i | ||||
\(176\) | −453495. | − | 337081.i | −1.10355 | − | 0.820261i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −464827. | + | 176981.i | −1.09962 | + | 0.418676i | ||||
\(179\) | 123110. | 0.287185 | 0.143592 | − | 0.989637i | \(-0.454135\pi\) | ||||
0.143592 | + | 0.989637i | \(0.454135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −311888. | −0.707622 | −0.353811 | − | 0.935317i | \(-0.615114\pi\) | ||||
−0.353811 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(182\) | −261326. | + | 99499.0i | −0.584795 | + | 0.222659i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4973.19 | − | 112439.i | −0.0108290 | − | 0.244835i | ||||
\(185\) | −331555. | + | 191423.i | −0.712240 | + | 0.411212i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −230522. | − | 133092.i | −0.482068 | − | 0.278322i | ||||
\(188\) | 124082. | + | 599781.i | 0.256043 | + | 1.23765i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 147064. | − | 180602.i | 0.295544 | − | 0.362943i | ||||
\(191\) | 97915.9 | − | 169595.i | 0.194209 | − | 0.336380i | −0.752432 | − | 0.658670i | \(-0.771119\pi\) |
0.946641 | + | 0.322290i | \(0.104453\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −296774. | − | 514028.i | −0.573499 | − | 0.993330i | −0.996203 | − | 0.0870619i | \(-0.972252\pi\) |
0.422704 | − | 0.906268i | \(-0.361081\pi\) | |||||||
\(194\) | −437395. | − | 70496.5i | −0.834391 | − | 0.134482i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 313925. | + | 103891.i | 0.583694 | + | 0.193170i | ||||
\(197\) | − | 100175.i | − | 0.183905i | −0.995763 | − | 0.0919523i | \(-0.970689\pi\) | ||
0.995763 | − | 0.0919523i | \(-0.0293107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 402805.i | − | 0.721045i | −0.932751 | − | 0.360522i | \(-0.882598\pi\) | ||
0.932751 | − | 0.360522i | \(-0.117402\pi\) | |||||||
\(200\) | −778285. | + | 496444.i | −1.37583 | + | 0.877597i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23371.6 | + | 145009.i | −0.0403004 | + | 0.250044i | ||||
\(203\) | −361272. | − | 625741.i | −0.615310 | − | 1.06575i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −576628. | + | 998750.i | −0.958322 | + | 1.65986i | ||||
\(206\) | −108850. | − | 88636.5i | −0.178715 | − | 0.145527i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −577477. | + | 249618.i | −0.925499 | + | 0.400053i | ||||
\(209\) | −216951. | − | 125257.i | −0.343555 | − | 0.198352i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −538419. | + | 310856.i | −0.832557 | + | 0.480677i | −0.854728 | − | 0.519077i | \(-0.826276\pi\) |
0.0221701 | + | 0.999754i | \(0.492942\pi\) | |||||||
\(212\) | 179250. | + | 201268.i | 0.273917 | + | 0.307563i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 213276. | + | 560152.i | 0.318352 | + | 0.836125i | ||||
\(215\) | 1.46157e6 | 2.15637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 60456.4 | 0.0871552 | ||||||||
\(218\) | −48494.9 | − | 127368.i | −0.0691122 | − | 0.181517i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.06505e6 | + | 1.19587e6i | 1.48358 | + | 1.66582i | ||||
\(221\) | −256660. | + | 148183.i | −0.353490 | + | 0.204088i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.11763e6 | + | 645261.i | 1.50499 | + | 0.868907i | 0.999983 | + | 0.00579252i | \(0.00184383\pi\) |
0.505008 | + | 0.863115i | \(0.331490\pi\) | |||||||
\(224\) | −448503. | − | 126737.i | −0.597236 | − | 0.168765i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −39732.4 | − | 32354.0i | −0.0517456 | − | 0.0421363i | ||||
\(227\) | −435023. | + | 753483.i | −0.560335 | + | 0.970529i | 0.437132 | + | 0.899398i | \(0.355994\pi\) |
−0.997467 | + | 0.0711316i | \(0.977339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 55144.9 | + | 95513.7i | 0.0694891 | + | 0.120359i | 0.898677 | − | 0.438612i | \(-0.144530\pi\) |
−0.829187 | + | 0.558971i | \(0.811196\pi\) | |||||||
\(230\) | −50754.6 | + | 314907.i | −0.0632639 | + | 0.392521i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −874219. | − | 1.37053e6i | −1.06635 | − | 1.67174i | ||||
\(233\) | 352716.i | 0.425633i | 0.977092 | + | 0.212817i | \(0.0682637\pi\) | ||||
−0.977092 | + | 0.212817i | \(0.931736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.73581e6i | − | 2.05037i | ||||||
\(236\) | 163677. | + | 54167.9i | 0.191297 | + | 0.0633085i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −216758. | − | 34935.6i | −0.248046 | − | 0.0399784i | ||||
\(239\) | −345720. | − | 598804.i | −0.391498 | − | 0.678094i | 0.601150 | − | 0.799137i | \(-0.294710\pi\) |
−0.992647 | + | 0.121043i | \(0.961376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37478.3 | + | 64914.3i | −0.0415659 | + | 0.0719942i | −0.886060 | − | 0.463571i | \(-0.846568\pi\) |
0.844494 | + | 0.535565i | \(0.179901\pi\) | |||||||
\(242\) | 512351. | − | 629195.i | 0.562379 | − | 0.690632i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −76638.6 | − | 370453.i | −0.0824087 | − | 0.398344i | ||||
\(245\) | −811584. | − | 468568.i | −0.863810 | − | 0.498721i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −241550. | + | 139459.i | −0.251921 | + | 0.145447i | ||||
\(248\) | 135885. | − | 6010.18i | 0.140295 | − | 0.00620524i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 946739. | − | 360468.i | 0.958033 | − | 0.364768i | ||||
\(251\) | −1.33103e6 | −1.33353 | −0.666767 | − | 0.745266i | \(-0.732322\pi\) | ||||
−0.666767 | + | 0.745266i | \(0.732322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 343086. | 0.336978 | ||||||||
\(254\) | 1.03201e6 | − | 392936.i | 1.00369 | − | 0.382153i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.02068e6 | − | 240273.i | −0.973393 | − | 0.229142i | ||||
\(257\) | 185992. | − | 107383.i | 0.175656 | − | 0.101415i | −0.409594 | − | 0.912268i | \(-0.634330\pi\) |
0.585250 | + | 0.810853i | \(0.300996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 294150. | + | 169828.i | 0.272471 | + | 0.157311i | ||||
\(260\) | 1.74598e6 | − | 361206.i | 1.60180 | − | 0.331377i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −906347. | + | 1.11304e6i | −0.815720 | + | 1.00175i | ||||
\(263\) | −327806. | + | 567776.i | −0.292232 | + | 0.506160i | −0.974337 | − | 0.225094i | \(-0.927731\pi\) |
0.682106 | + | 0.731254i | \(0.261064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −381913. | − | 661492.i | −0.334079 | − | 0.578642i | ||||
\(266\) | −203997. | − | 32878.9i | −0.176775 | − | 0.0284914i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −314979. | + | 951759.i | −0.267882 | + | 0.809450i | ||||
\(269\) | 424539.i | 0.357715i | 0.983875 | + | 0.178857i | \(0.0572401\pi\) | ||||
−0.983875 | + | 0.178857i | \(0.942760\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 276579.i | 0.228769i | 0.993437 | + | 0.114384i | \(0.0364895\pi\) | ||||
−0.993437 | + | 0.114384i | \(0.963510\pi\) | |||||||
\(272\) | −490667. | − | 56974.2i | −0.402129 | − | 0.0466934i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −112614. | + | 698713.i | −0.0906183 | + | 0.562241i | ||||
\(275\) | −1.40701e6 | − | 2.43702e6i | −1.12193 | − | 1.94324i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 758444. | − | 1.31366e6i | 0.593915 | − | 1.02869i | −0.399784 | − | 0.916609i | \(-0.630915\pi\) |
0.993699 | − | 0.112081i | \(-0.0357517\pi\) | |||||||
\(278\) | −787503. | − | 641262.i | −0.611140 | − | 0.497649i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.17196e6 | + | 609239.i | 0.893344 | + | 0.464401i | ||||
\(281\) | −831581. | − | 480113.i | −0.628259 | − | 0.362725i | 0.151819 | − | 0.988408i | \(-0.451487\pi\) |
−0.780077 | + | 0.625683i | \(0.784820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 780527. | − | 450638.i | 0.579325 | − | 0.334473i | −0.181540 | − | 0.983384i | \(-0.558108\pi\) |
0.760865 | + | 0.648910i | \(0.224775\pi\) | |||||||
\(284\) | 1.64639e6 | − | 1.46628e6i | 1.21126 | − | 1.07875i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −682390. | − | 1.79224e6i | −0.493307 | − | 1.29563i | ||||
\(287\) | 1.02315e6 | 0.733221 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.18716e6 | 0.836112 | ||||||||
\(290\) | 1.63933e6 | + | 4.30555e6i | 1.14464 | + | 3.00631i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 569275. | − | 506998.i | 0.390719 | − | 0.347976i | ||||
\(293\) | 1.02663e6 | − | 592723.i | 0.698623 | − | 0.403350i | −0.108211 | − | 0.994128i | \(-0.534512\pi\) |
0.806835 | + | 0.590778i | \(0.201179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −423151. | − | 244307.i | −0.283101 | − | 0.163448i | ||||
\(296\) | 678029. | + | 352470.i | 0.449800 | + | 0.233826i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00415e6 | + | 1.63197e6i | 1.30734 | + | 1.06457i | ||||
\(299\) | 190993. | − | 330810.i | 0.123549 | − | 0.213994i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −648339. | − | 1.12296e6i | −0.412464 | − | 0.714408i | ||||
\(302\) | −197125. | + | 1.22306e6i | −0.124373 | + | 0.771669i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −461782. | − | 53620.1i | −0.286585 | − | 0.0332770i | ||||
\(305\) | 1.07212e6i | 0.659922i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 740939.i | − | 0.448680i | −0.974511 | − | 0.224340i | \(-0.927977\pi\) | ||
0.974511 | − | 0.224340i | \(-0.0720226\pi\) | |||||||
\(308\) | 446370. | − | 1.34878e6i | 0.268113 | − | 0.810147i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −380571. | − | 61337.9i | −0.224921 | − | 0.0362514i | ||||
\(311\) | 1.37781e6 | + | 2.38644e6i | 0.807771 | + | 1.39910i | 0.914404 | + | 0.404802i | \(0.132660\pi\) |
−0.106633 | + | 0.994298i | \(0.534007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.36134e6 | + | 2.35791e6i | −0.785427 | + | 1.36040i | 0.143317 | + | 0.989677i | \(0.454223\pi\) |
−0.928744 | + | 0.370722i | \(0.879110\pi\) | |||||||
\(314\) | −813196. | + | 998648.i | −0.465448 | + | 0.571595i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 699713. | − | 144755.i | 0.394187 | − | 0.0815486i | ||||
\(317\) | 731344. | + | 422242.i | 0.408765 | + | 0.236001i | 0.690259 | − | 0.723562i | \(-0.257497\pi\) |
−0.281494 | + | 0.959563i | \(0.590830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.29149e6 | − | 2.47770e6i | 2.36119 | − | 1.36324i | ||||
\(320\) | 2.69472e6 | + | 1.25285e6i | 1.47109 | + | 0.683947i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 264465. | − | 100694.i | 0.142144 | − | 0.0541208i | ||||
\(323\) | −218998. | −0.116798 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.13309e6 | −1.64537 | ||||||||
\(326\) | −2.43573e6 | + | 927397.i | −1.26936 | + | 0.483305i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.29968e6 | − | 101715.i | 1.18027 | − | 0.0522036i | ||||
\(329\) | −1.33366e6 | + | 769990.i | −0.679291 | + | 0.392189i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52485e6 | − | 880372.i | −0.764992 | − | 0.441668i | 0.0660935 | − | 0.997813i | \(-0.478946\pi\) |
−0.831085 | + | 0.556145i | \(0.812280\pi\) | |||||||
\(332\) | 509812. | + | 2.46431e6i | 0.253843 | + | 1.22702i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.04722e6 | + | 2.51410e6i | −1.00415 | + | 1.23315i | ||||
\(335\) | 1.42061e6 | − | 2.46057e6i | 0.691612 | − | 1.19791i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.23174e6 | − | 2.13344e6i | −0.590806 | − | 1.02331i | −0.994124 | − | 0.108246i | \(-0.965477\pi\) |
0.403318 | − | 0.915060i | \(-0.367857\pi\) | |||||||
\(338\) | −34404.1 | − | 5545.03i | −0.0163802 | − | 0.00264005i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.32903e6 | + | 439836.i | 0.623504 | + | 0.206345i | ||||
\(341\) | 414626.i | 0.193095i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.18368e6i | 1.00220i | ||||||||
\(344\) | −1.56887e6 | − | 2.45955e6i | −0.714812 | − | 1.12063i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −295108. | + | 1.83100e6i | −0.132523 | + | 0.822237i | ||||
\(347\) | −473354. | − | 819874.i | −0.211039 | − | 0.365530i | 0.741001 | − | 0.671504i | \(-0.234351\pi\) |
−0.952040 | + | 0.305974i | \(0.901018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.96690e6 | − | 3.40677e6i | 0.864408 | − | 1.49720i | −0.00322519 | − | 0.999995i | \(-0.501027\pi\) |
0.867633 | − | 0.497204i | \(-0.165640\pi\) | |||||||
\(350\) | −1.79983e6 | − | 1.46560e6i | −0.785349 | − | 0.639507i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 869195. | − | 3.07595e6i | 0.373904 | − | 1.32319i | ||||
\(353\) | 3.34675e6 | + | 1.93225e6i | 1.42951 | + | 0.825327i | 0.997082 | − | 0.0763423i | \(-0.0243242\pi\) |
0.432426 | + | 0.901669i | \(0.357658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.41107e6 | + | 3.12408e6i | −2.27883 | + | 1.31568i | ||||
\(356\) | −1.87127e6 | − | 2.10112e6i | −0.782548 | − | 0.878672i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 247804. | + | 650837.i | 0.102188 | + | 0.268389i | ||||
\(359\) | −1.23588e6 | −0.506106 | −0.253053 | − | 0.967452i | \(-0.581435\pi\) | ||||
−0.253053 | + | 0.967452i | \(0.581435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.26999e6 | 0.916762 | ||||||||
\(362\) | −627788. | − | 1.64883e6i | −0.251792 | − | 0.661310i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.05203e6 | − | 1.18125e6i | −0.416173 | − | 0.467293i | ||||
\(365\) | −1.87100e6 | + | 1.08022e6i | −0.735091 | + | 0.424405i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 435715. | + | 251560.i | 0.168864 | + | 0.0974937i | 0.582050 | − | 0.813153i | \(-0.302251\pi\) |
−0.413186 | + | 0.910647i | \(0.635584\pi\) | |||||||
\(368\) | 584413. | − | 252616.i | 0.224957 | − | 0.0972392i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.67936e6 | − | 1.36750e6i | −0.637734 | − | 0.519305i | ||||
\(371\) | −338827. | + | 586865.i | −0.127804 | + | 0.221362i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28143e6 | + | 3.95156e6i | 0.849055 | + | 1.47061i | 0.882052 | + | 0.471151i | \(0.156161\pi\) |
−0.0329973 | + | 0.999455i | \(0.510505\pi\) | |||||||
\(374\) | 239597. | − | 1.48658e6i | 0.0885732 | − | 0.549552i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.92105e6 | + | 1.86325e6i | −1.06554 | + | 0.679675i | ||||
\(377\) | − | 5.51726e6i | − | 1.99926i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.52082e6i | 1.25906i | 0.776977 | + | 0.629529i | \(0.216752\pi\) | ||||
−0.776977 | + | 0.629529i | \(0.783248\pi\) | |||||||
\(380\) | 1.25079e6 | + | 413943.i | 0.444352 | + | 0.147055i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.09368e6 | + | 176272.i | 0.383470 | + | 0.0618051i | ||||
\(383\) | 598408. | + | 1.03647e6i | 0.208449 | + | 0.361045i | 0.951226 | − | 0.308494i | \(-0.0998250\pi\) |
−0.742777 | + | 0.669539i | \(0.766492\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.01320e6 | + | 3.48697e6i | −0.692207 | + | 1.19894i | ||||
\(386\) | 2.12011e6 | − | 2.60360e6i | 0.724251 | − | 0.889419i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −507729. | − | 2.45424e6i | −0.171219 | − | 0.827634i | ||||
\(389\) | −1.22413e6 | − | 706752.i | −0.410160 | − | 0.236806i | 0.280698 | − | 0.959796i | \(-0.409434\pi\) |
−0.690859 | + | 0.722990i | \(0.742767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 259742. | − | 149962.i | 0.0859213 | − | 0.0496067i | ||||
\(392\) | 82653.6 | + | 1.86872e6i | 0.0271673 | + | 0.614227i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 529586. | − | 201638.i | 0.171868 | − | 0.0654383i | ||||
\(395\) | −2.02502e6 | −0.653035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.97577e6 | 0.629160 | 0.314580 | − | 0.949231i | \(-0.398136\pi\) | ||||
0.314580 | + | 0.949231i | \(0.398136\pi\) | |||||||
\(398\) | 2.12948e6 | − | 810792.i | 0.673854 | − | 0.256568i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.19109e6 | − | 3.11522e6i | −1.30972 | − | 0.973507i | ||||
\(401\) | 650613. | − | 375632.i | 0.202052 | − | 0.116654i | −0.395561 | − | 0.918440i | \(-0.629450\pi\) |
0.597612 | + | 0.801785i | \(0.296116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 399790. | + | 230819.i | 0.122622 | + | 0.0707960i | ||||
\(404\) | −813650. | + | 168327.i | −0.248019 | + | 0.0513097i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.58087e6 | − | 3.16944e6i | 0.777052 | − | 0.954262i | ||||
\(407\) | −1.16472e6 | + | 2.01736e6i | −0.348527 | + | 0.603666i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.22030e6 | + | 2.11362e6i | 0.360710 | + | 0.624768i | 0.988078 | − | 0.153955i | \(-0.0492011\pi\) |
−0.627368 | + | 0.778723i | \(0.715868\pi\) | |||||||
\(410\) | −6.44069e6 | − | 1.03807e6i | −1.89222 | − | 0.304976i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 249487. | − | 753864.i | 0.0724109 | − | 0.218801i | ||||
\(413\) | 433490.i | 0.125056i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.13189e6i | − | 2.03275i | ||||||
\(416\) | −2.48202e6 | − | 2.55045e6i | −0.703189 | − | 0.722577i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 225492. | − | 1.39906e6i | 0.0631234 | − | 0.391649i | ||||
\(419\) | 3.49913e6 | + | 6.06068e6i | 0.973701 | + | 1.68650i | 0.684158 | + | 0.729334i | \(0.260170\pi\) |
0.289543 | + | 0.957165i | \(0.406497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 575740. | − | 997211.i | 0.158315 | − | 0.274209i | −0.775946 | − | 0.630799i | \(-0.782727\pi\) |
0.934261 | + | 0.356590i | \(0.116061\pi\) | |||||||
\(422\) | −2.72714e6 | − | 2.22071e6i | −0.745465 | − | 0.607030i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −703220. | + | 1.35275e6i | −0.189966 | + | 0.365429i | ||||
\(425\) | −2.13043e6 | − | 1.23001e6i | −0.572131 | − | 0.330320i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 823733. | − | 475582.i | 0.218633 | − | 0.126228i | ||||
\(428\) | −2.53201e6 | + | 2.25502e6i | −0.668123 | + | 0.595033i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.94194e6 | + | 7.72675e6i | 0.767295 | + | 2.01524i | ||||
\(431\) | −61287.6 | −0.0158920 | −0.00794601 | − | 0.999968i | \(-0.502529\pi\) | ||||
−0.00794601 | + | 0.999968i | \(0.502529\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.42481e6 | −1.64680 | −0.823399 | − | 0.567462i | \(-0.807925\pi\) | ||||
−0.823399 | + | 0.567462i | \(0.807925\pi\) | |||||||
\(434\) | 121691. | + | 319610.i | 0.0310122 | + | 0.0814510i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 575731. | − | 512748.i | 0.145045 | − | 0.129178i | ||||
\(437\) | 244451. | − | 141134.i | 0.0612335 | − | 0.0353532i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.53160e6 | − | 884268.i | −0.379301 | − | 0.218989i | 0.298213 | − | 0.954499i | \(-0.403609\pi\) |
−0.677514 | + | 0.735510i | \(0.736943\pi\) | |||||||
\(440\) | −4.17832e6 | + | 8.03762e6i | −1.02889 | + | 1.97923i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.30001e6 | − | 1.05859e6i | −0.316512 | − | 0.257735i | ||||
\(443\) | 3.28943e6 | − | 5.69747e6i | 0.796364 | − | 1.37934i | −0.125605 | − | 0.992080i | \(-0.540087\pi\) |
0.921969 | − | 0.387263i | \(-0.126579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.98696e6 | + | 6.90562e6i | 0.954425 | + | 1.65311i | ||||
\(446\) | −1.16162e6 | + | 7.20729e6i | −0.276521 | + | 1.71567i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −232767. | − | 2.62617e6i | −0.0547931 | − | 0.618199i | ||||
\(449\) | − | 974339.i | − | 0.228084i | −0.993476 | − | 0.114042i | \(-0.963620\pi\) | ||
0.993476 | − | 0.114042i | \(-0.0363798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.01703e6i | 1.62447i | ||||||||
\(452\) | 91067.2 | − | 275174.i | 0.0209660 | − | 0.0633522i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.85902e6 | − | 783145.i | −1.10639 | − | 0.178321i | ||||
\(455\) | 2.24147e6 | + | 3.88234e6i | 0.507580 | + | 0.879155i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.33316e6 | − | 4.04116e6i | 0.522583 | − | 0.905140i | −0.477072 | − | 0.878864i | \(-0.658302\pi\) |
0.999655 | − | 0.0262754i | \(-0.00836468\pi\) | |||||||
\(458\) | −393946. | + | 483787.i | −0.0877552 | + | 0.107768i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.76696e6 | + | 365545.i | −0.389342 | + | 0.0805463i | ||||
\(461\) | −2.23506e6 | − | 1.29041e6i | −0.489820 | − | 0.282798i | 0.234680 | − | 0.972073i | \(-0.424596\pi\) |
−0.724500 | + | 0.689275i | \(0.757929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00581e6 | − | 1.15806e6i | 0.434849 | − | 0.251060i | −0.266561 | − | 0.963818i | \(-0.585887\pi\) |
0.701410 | + | 0.712758i | \(0.252554\pi\) | |||||||
\(464\) | 5.48579e6 | − | 7.38036e6i | 1.18289 | − | 1.59141i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.86468e6 | + | 709970.i | −0.397776 | + | 0.151452i | ||||
\(467\) | 26296.7 | 0.00557969 | 0.00278984 | − | 0.999996i | \(-0.499112\pi\) | ||||
0.00278984 | + | 0.999996i | \(0.499112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.52068e6 | −0.529159 | ||||||||
\(470\) | 9.17656e6 | − | 3.49395e6i | 1.91618 | − | 0.729578i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 43094.7 | + | 974331.i | 0.00890367 | + | 0.201304i | ||||
\(473\) | 7.70152e6 | − | 4.44648e6i | 1.58279 | − | 0.913825i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00501e6 | − | 1.15760e6i | −0.407740 | − | 0.235409i | ||||
\(476\) | −251613. | − | 1.21624e6i | −0.0508997 | − | 0.246037i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.46976e6 | − | 3.03300e6i | 0.494408 | − | 0.607159i | ||||
\(479\) | −3.17700e6 | + | 5.50272e6i | −0.632671 | + | 1.09582i | 0.354332 | + | 0.935120i | \(0.384708\pi\) |
−0.987003 | + | 0.160699i | \(0.948625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.29678e6 | + | 2.24610e6i | 0.255567 | + | 0.442655i | ||||
\(482\) | −418616. | − | 67469.7i | −0.0820726 | − | 0.0132279i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.35761e6 | + | 1.44212e6i | 0.845541 | + | 0.279827i | ||||
\(485\) | 7.10276e6i | 1.37111i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.12992e6i | 1.36227i | 0.732159 | + | 0.681134i | \(0.238513\pi\) | ||||
−0.732159 | + | 0.681134i | \(0.761487\pi\) | |||||||
\(488\) | 1.80418e6 | − | 1.15083e6i | 0.342950 | − | 0.218757i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 843534. | − | 5.23370e6i | 0.158713 | − | 0.984734i | ||||
\(491\) | −4.12052e6 | − | 7.13694e6i | −0.771343 | − | 1.33601i | −0.936827 | − | 0.349793i | \(-0.886252\pi\) |
0.165483 | − | 0.986213i | \(-0.447082\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.16599e6 | − | 3.75161e6i | 0.401365 | − | 0.695185i | ||||
\(494\) | −1.22348e6 | − | 996273.i | −0.225568 | − | 0.183680i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 305291. | + | 706273.i | 0.0557199 | + | 0.128905i | ||||
\(497\) | 4.80061e6 | + | 2.77164e6i | 0.871778 | + | 0.503321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.31706e6 | + | 4.22451e6i | −1.31548 | + | 0.759495i | −0.982998 | − | 0.183614i | \(-0.941220\pi\) |
−0.332485 | + | 0.943109i | \(0.607887\pi\) | |||||||
\(500\) | 3.81132e6 | + | 4.27948e6i | 0.681789 | + | 0.765536i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.67919e6 | − | 7.03666e6i | −0.474508 | − | 1.24626i | ||||
\(503\) | 6.32200e6 | 1.11413 | 0.557063 | − | 0.830470i | \(-0.311928\pi\) | ||||
0.557063 | + | 0.830470i | \(0.311928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35476e6 | 0.410883 | ||||||||
\(506\) | 690586. | + | 1.81377e6i | 0.119906 | + | 0.314923i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.15461e6 | + | 4.66494e6i | 0.714284 | + | 0.802023i | ||||
\(509\) | 194691. | − | 112405.i | 0.0333082 | − | 0.0192305i | −0.483253 | − | 0.875481i | \(-0.660545\pi\) |
0.516562 | + | 0.856250i | \(0.327212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65992e6 | + | 958354.i | 0.281212 | + | 0.162358i | ||||
\(512\) | −784254. | − | 5.87957e6i | −0.132215 | − | 0.991221i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 942070. | + | 767124.i | 0.157281 | + | 0.128073i | ||||
\(515\) | −1.12523e6 | + | 1.94895e6i | −0.186949 | + | 0.323805i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.28079e6 | − | 9.14660e6i | −0.868906 | − | 1.50499i | ||||
\(518\) | −305730. | + | 1.89690e6i | −0.0500627 | + | 0.310614i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.42399e6 | + | 8.50330e6i | 0.879652 | + | 1.37905i | ||||
\(521\) | 5.59008e6i | 0.902243i | 0.892462 | + | 0.451122i | \(0.148976\pi\) | ||||
−0.892462 | + | 0.451122i | \(0.851024\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 193807.i | 0.0309825i | 0.999880 | + | 0.0154912i | \(0.00493121\pi\) | ||||
−0.999880 | + | 0.0154912i | \(0.995069\pi\) | |||||||
\(524\) | −7.70859e6 | − | 2.55111e6i | −1.22644 | − | 0.405883i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.66145e6 | − | 590128.i | −0.577017 | − | 0.0929997i | ||||
\(527\) | 181232. | + | 313903.i | 0.0284255 | + | 0.0492345i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.02488e6 | − | 5.23925e6i | 0.469969 | − | 0.814011i | ||||
\(530\) | 2.72832e6 | − | 3.35052e6i | 0.421896 | − | 0.518111i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −236800. | − | 1.14464e6i | −0.0362747 | − | 0.175343i | ||||
\(533\) | 6.76596e6 | + | 3.90633e6i | 1.03160 | + | 0.595594i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.32179e6 | − | 4.80459e6i | 1.25699 | − | 0.725725i | ||||
\(536\) | −5.66560e6 | + | 250590.i | −0.851793 | + | 0.0376748i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.24438e6 | + | 854540.i | −0.334303 | + | 0.127285i | ||||
\(539\) | −5.70204e6 | −0.845392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.08637e6 | 0.453373 | 0.226686 | − | 0.973968i | \(-0.427211\pi\) | ||||
0.226686 | + | 0.973968i | \(0.427211\pi\) | |||||||
\(542\) | −1.46217e6 | + | 556717.i | −0.213796 | + | 0.0814022i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −686447. | − | 2.70865e6i | −0.0994511 | − | 0.392425i | ||||
\(545\) | −1.89222e6 | + | 1.09247e6i | −0.272885 | + | 0.157550i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.05052e6 | − | 1.18387e6i | −0.293018 | − | 0.169174i | 0.346284 | − | 0.938130i | \(-0.387443\pi\) |
−0.639302 | + | 0.768955i | \(0.720777\pi\) | |||||||
\(548\) | −3.92051e6 | + | 811068.i | −0.557688 | + | 0.115373i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00515e7 | − | 1.23437e7i | 1.41685 | − | 1.73996i | ||||
\(551\) | 2.03848e6 | − | 3.53075e6i | 0.286041 | − | 0.495437i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 898281. | + | 1.55587e6i | 0.124911 | + | 0.216352i | ||||
\(554\) | 8.47149e6 | + | 1.36538e6i | 1.17270 | + | 0.189007i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.80497e6 | − | 5.45401e6i | 0.247618 | − | 0.748219i | ||||
\(557\) | − | 1.20970e7i | − | 1.65211i | −0.563589 | − | 0.826056i | \(-0.690580\pi\) | ||
0.563589 | − | 0.826056i | \(-0.309420\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.90128e6i | − | 1.34018i | ||||||
\(560\) | −861815. | + | 7.42204e6i | −0.116130 | + | 1.00012i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 864318. | − | 5.36266e6i | 0.115434 | − | 0.716208i | ||||
\(563\) | −2.49691e6 | − | 4.32478e6i | −0.331996 | − | 0.575033i | 0.650907 | − | 0.759157i | \(-0.274389\pi\) |
−0.982903 | + | 0.184124i | \(0.941055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −410729. | + | 711403.i | −0.0541295 | + | 0.0937551i | ||||
\(566\) | 3.95345e6 | + | 3.21928e6i | 0.518722 | + | 0.422394i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.10656e7 | + | 5.75241e6i | 1.43915 | + | 0.748134i | ||||
\(569\) | −5.38818e6 | − | 3.11087e6i | −0.697688 | − | 0.402810i | 0.108798 | − | 0.994064i | \(-0.465300\pi\) |
−0.806486 | + | 0.591253i | \(0.798633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.67863e6 | − | 5.01061e6i | 1.11394 | − | 0.643132i | 0.174091 | − | 0.984730i | \(-0.444301\pi\) |
0.939846 | + | 0.341597i | \(0.110968\pi\) | |||||||
\(572\) | 8.10134e6 | − | 7.21508e6i | 1.03530 | − | 0.922042i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.05946e6 | + | 5.40901e6i | 0.260900 | + | 0.685233i | ||||
\(575\) | 3.17072e6 | 0.399934 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.84784e6 | −0.856276 | −0.428138 | − | 0.903713i | \(-0.640830\pi\) | ||||
−0.428138 | + | 0.903713i | \(0.640830\pi\) | |||||||
\(578\) | 2.38959e6 | + | 6.27607e6i | 0.297512 | + | 0.781390i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.94621e7 | + | 1.73330e7i | −2.40226 | + | 2.13946i | ||||
\(581\) | −5.47960e6 | + | 3.16365e6i | −0.673455 | + | 0.388819i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.02487e6 | − | 2.32376e6i | −0.490434 | − | 0.283152i | ||||
\(584\) | 3.82618e6 | + | 1.98902e6i | 0.464230 | + | 0.241328i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.19996e6 | + | 4.23431e6i | 0.625541 | + | 0.509376i | ||||
\(587\) | 636726. | − | 1.10284e6i | 0.0762706 | − | 0.132105i | −0.825368 | − | 0.564596i | \(-0.809032\pi\) |
0.901638 | + | 0.432491i | \(0.142365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 170563. | + | 295424.i | 0.0202580 | + | 0.0350879i | ||||
\(590\) | 439810. | − | 2.72880e6i | 0.0520157 | − | 0.322731i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −498596. | + | 4.29396e6i | −0.0584715 | + | 0.503563i | ||||
\(593\) | − | 1.18555e6i | − | 0.138447i | −0.997601 | − | 0.0692233i | \(-0.977948\pi\) | ||
0.997601 | − | 0.0692233i | \(-0.0220521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.51987e6i | 0.407600i | ||||||||
\(596\) | −4.59354e6 | + | 1.38801e7i | −0.529703 | + | 1.60058i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.13331e6 | + | 343833.i | 0.243950 | + | 0.0393183i | ||||
\(599\) | 124447. | + | 215548.i | 0.0141715 | + | 0.0245458i | 0.873024 | − | 0.487677i | \(-0.162156\pi\) |
−0.858853 | + | 0.512223i | \(0.828822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.20084e6 | + | 3.81197e6i | −0.248544 | + | 0.430491i | −0.963122 | − | 0.269065i | \(-0.913285\pi\) |
0.714578 | + | 0.699556i | \(0.246619\pi\) | |||||||
\(602\) | 4.63163e6 | − | 5.68788e6i | 0.520885 | − | 0.639675i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.86265e6 | + | 1.41973e6i | −0.765420 | + | 0.158349i | ||||
\(605\) | −1.12656e7 | − | 6.50422e6i | −1.25132 | − | 0.722449i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.35875e6 | − | 3.09387e6i | 0.590325 | − | 0.340824i | −0.174901 | − | 0.984586i | \(-0.555960\pi\) |
0.765226 | + | 0.643762i | \(0.222627\pi\) | |||||||
\(608\) | −646036. | − | 2.54920e6i | −0.0708758 | − | 0.279669i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.66788e6 | + | 2.15803e6i | −0.616731 | + | 0.234819i | ||||
\(611\) | −1.17591e7 | −1.27430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.13948e7 | −1.22478 | −0.612389 | − | 0.790557i | \(-0.709791\pi\) | ||||
−0.612389 | + | 0.790557i | \(0.709791\pi\) | |||||||
\(614\) | 3.91707e6 | − | 1.49141e6i | 0.419314 | − | 0.159653i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.02896e6 | − | 355121.i | 0.852526 | − | 0.0377073i | ||||
\(617\) | −1.05792e7 | + | 6.10788e6i | −1.11876 | + | 0.645918i | −0.941085 | − | 0.338170i | \(-0.890192\pi\) |
−0.177678 | + | 0.984089i | \(0.556859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.02681e7 | − | 5.92826e6i | −1.07711 | − | 0.621872i | −0.146997 | − | 0.989137i | \(-0.546961\pi\) |
−0.930116 | + | 0.367265i | \(0.880294\pi\) | |||||||
\(620\) | −441767. | − | 2.13540e6i | −0.0461545 | − | 0.223100i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.84284e6 | + | 1.20875e7i | −1.02010 | + | 1.25274i | ||||
\(623\) | 3.53717e6 | − | 6.12655e6i | 0.365120 | − | 0.632406i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −152246. | − | 263699.i | −0.0155900 | − | 0.0270027i | ||||
\(626\) | −1.52056e7 | − | 2.45073e6i | −1.55084 | − | 0.249954i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.91633e6 | − | 2.28892e6i | −0.699804 | − | 0.231596i | ||||
\(629\) | 2.03639e6i | 0.205227i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.84995e6i | − | 0.284947i | −0.989799 | − | 0.142474i | \(-0.954494\pi\) | ||
0.989799 | − | 0.142474i | \(-0.0455056\pi\) | |||||||
\(632\) | 2.17369e6 | + | 3.40774e6i | 0.216474 | + | 0.339371i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −760135. | + | 4.71626e6i | −0.0751048 | + | 0.465987i | ||||
\(635\) | −8.85189e6 | − | 1.53319e7i | −0.871168 | − | 1.50891i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.17428e6 | + | 5.49802e6i | −0.309954 | + | 0.536856i | ||||
\(638\) | 2.17368e7 | + | 1.77002e7i | 2.11419 | + | 1.72158i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.19920e6 | + | 1.67678e7i | −0.115729 | + | 1.61818i | ||||
\(641\) | −174871. | − | 100962.i | −0.0168102 | − | 0.00970538i | 0.491571 | − | 0.870837i | \(-0.336423\pi\) |
−0.508382 | + | 0.861132i | \(0.669756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.06513e6 | − | 1.76965e6i | 0.292362 | − | 0.168795i | −0.346644 | − | 0.937997i | \(-0.612679\pi\) |
0.639007 | + | 0.769201i | \(0.279346\pi\) | |||||||
\(644\) | 1.06466e6 | + | 1.19544e6i | 0.101157 | + | 0.113583i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −440814. | − | 1.15776e6i | −0.0415599 | − | 0.109154i | ||||
\(647\) | 1.88702e7 | 1.77221 | 0.886106 | − | 0.463482i | \(-0.153400\pi\) | ||||
0.886106 | + | 0.463482i | \(0.153400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.97298e6 | −0.277064 | ||||||||
\(650\) | −6.30649e6 | − | 1.65635e7i | −0.585470 | − | 1.53769i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.80559e6 | − | 1.10101e7i | −0.903347 | − | 1.01431i | ||||
\(653\) | −7.69628e6 | + | 4.44345e6i | −0.706314 | + | 0.407790i | −0.809695 | − | 0.586851i | \(-0.800367\pi\) |
0.103381 | + | 0.994642i | \(0.467034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.99289e7 | + | 1.15059e7i | 1.81501 | + | 1.04790i | ||||
\(656\) | 5.16668e6 | + | 1.19528e7i | 0.468761 | + | 1.08445i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.75513e6 | − | 5.50068e6i | −0.608232 | − | 0.495281i | ||||
\(659\) | −3.43642e6 | + | 5.95205e6i | −0.308242 | + | 0.533892i | −0.977978 | − | 0.208708i | \(-0.933074\pi\) |
0.669736 | + | 0.742600i | \(0.266407\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −219686. | − | 380507.i | −0.0195568 | − | 0.0338734i | 0.856081 | − | 0.516841i | \(-0.172892\pi\) |
−0.875638 | + | 0.482968i | \(0.839559\pi\) | |||||||
\(662\) | 1.58488e6 | − | 9.83337e6i | 0.140556 | − | 0.872082i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.20017e7 | + | 7.65551e6i | −1.05639 | + | 0.673835i | ||||
\(665\) | 3.31266e6i | 0.290484i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.58352e6i | 0.485952i | ||||||||
\(668\) | −1.74119e7 | − | 5.76234e6i | −1.50975 | − | 0.499641i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.58676e7 | + | 2.55743e6i | 1.36560 | + | 0.220098i | ||||
\(671\) | 3.26167e6 | + | 5.64937e6i | 0.279662 | + | 0.484388i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.79543e6 | + | 8.30592e6i | −0.408122 | + | 0.706887i | −0.994679 | − | 0.103020i | \(-0.967149\pi\) |
0.586558 | + | 0.809908i | \(0.300483\pi\) | |||||||
\(674\) | 8.79935e6 | − | 1.08061e7i | 0.746107 | − | 0.916259i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39936.4 | − | 193043.i | −0.00336126 | − | 0.0162475i | ||||
\(677\) | 4.71537e6 | + | 2.72242e6i | 0.395407 | + | 0.228288i | 0.684500 | − | 0.729013i | \(-0.260020\pi\) |
−0.289093 | + | 0.957301i | \(0.593354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.45721e6 | − | 3.15072e6i | 0.454252 | − | 0.262262i | ||||
\(680\) | 349923. | + | 7.91143e6i | 0.0290202 | + | 0.656119i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.19197e6 | + | 834586.i | −0.180457 | + | 0.0687084i | ||||
\(683\) | −1.41906e7 | −1.16399 | −0.581995 | − | 0.813193i | \(-0.697728\pi\) | ||||
−0.581995 | + | 0.813193i | \(0.697728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.13462e7 | 0.923901 | ||||||||
\(686\) | −1.15443e7 | + | 4.39545e6i | −0.936606 | + | 0.356610i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.84480e6 | − | 1.32448e7i | 0.792932 | − | 1.06678i | ||||
\(689\) | −4.48123e6 | + | 2.58724e6i | −0.359625 | + | 0.207629i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.74007e7 | − | 1.00463e7i | −1.38634 | − | 0.800406i | −0.393443 | − | 0.919349i | \(-0.628716\pi\) |
−0.992901 | + | 0.118943i | \(0.962049\pi\) | |||||||
\(692\) | −1.02738e7 | + | 2.12542e6i | −0.815578 | + | 0.168725i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.38156e6 | − | 4.15274e6i | 0.266513 | − | 0.327293i | ||||
\(695\) | −8.14072e6 | + | 1.41001e7i | −0.639295 | + | 1.10729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.06713e6 | + | 5.31243e6i | 0.239139 | + | 0.414201i | ||||
\(698\) | 2.19694e7 | + | 3.54089e6i | 1.70679 | + | 0.275089i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.12525e6 | − | 1.24651e7i | 0.318203 | − | 0.961503i | ||||
\(701\) | 1.36721e7i | 1.05085i | 0.850841 | + | 0.525423i | \(0.176093\pi\) | ||||
−0.850841 | + | 0.525423i | \(0.823907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.91651e6i | 0.146259i | ||||||||
\(704\) | 1.80110e7 | − | 1.59637e6i | 1.36964 | − | 0.121396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.47850e6 | + | 2.15824e7i | −0.262652 | + | 1.62962i | ||||
\(707\) | −1.04455e6 | − | 1.80922e6i | −0.0785927 | − | 0.136126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00757e6 | + | 1.74517e6i | −0.0752767 | + | 0.130383i | −0.901207 | − | 0.433390i | \(-0.857317\pi\) |
0.825930 | + | 0.563773i | \(0.190651\pi\) | |||||||
\(710\) | −2.74076e7 | − | 2.23179e7i | −2.04045 | − | 1.66153i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.34124e6 | − | 1.41220e7i | 0.542712 | − | 1.04399i | ||||
\(713\) | −404592. | − | 233591.i | −0.0298053 | − | 0.0172081i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.66261e7 | + | 1.53726e7i | −1.94779 | + | 1.12456i | ||||
\(716\) | −2.94193e6 | + | 2.62009e6i | −0.214462 | + | 0.191000i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.48767e6 | − | 6.53365e6i | −0.180087 | − | 0.472982i | ||||
\(719\) | 1.07956e7 | 0.778796 | 0.389398 | − | 0.921070i | \(-0.372683\pi\) | ||||
0.389398 | + | 0.921070i | \(0.372683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.99657e6 | 0.143036 | ||||||||
\(722\) | 4.56919e6 | + | 1.20006e7i | 0.326209 | + | 0.856761i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.45310e6 | − | 6.63775e6i | 0.528433 | − | 0.470625i | ||||
\(725\) | 3.96610e7 | − | 2.28983e7i | 2.80233 | − | 1.61792i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00659e7 | + | 1.15851e7i | 1.40807 | + | 0.812947i | 0.995202 | − | 0.0978454i | \(-0.0311951\pi\) |
0.412864 | + | 0.910793i | \(0.364528\pi\) | |||||||
\(728\) | 4.12725e6 | − | 7.93938e6i | 0.288624 | − | 0.555211i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.47678e6 | − | 7.71691e6i | −0.658194 | − | 0.535965i | ||||
\(731\) | 3.88709e6 | − | 6.73265e6i | 0.269049 | − | 0.466007i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.96332e6 | − | 6.86468e6i | −0.272458 | − | 0.471911i | 0.697033 | − | 0.717039i | \(-0.254503\pi\) |
−0.969491 | + | 0.245128i | \(0.921170\pi\) | |||||||
\(734\) | −452868. | + | 2.80982e6i | −0.0310264 | + | 0.192503i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.51183e6 | + | 2.58109e6i | 0.170921 | + | 0.175634i | ||||
\(737\) | − | 1.72875e7i | − | 1.17237i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.45640e7i | − | 1.65458i | −0.561776 | − | 0.827289i | \(-0.689882\pi\) | ||
0.561776 | − | 0.827289i | \(-0.310118\pi\) | |||||||
\(740\) | 3.84912e6 | − | 1.16307e7i | 0.258394 | − | 0.780778i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.78455e6 | − | 609968.i | −0.252350 | − | 0.0406722i | ||||
\(743\) | −2.79240e6 | − | 4.83658e6i | −0.185569 | − | 0.321415i | 0.758199 | − | 0.652023i | \(-0.226080\pi\) |
−0.943768 | + | 0.330608i | \(0.892746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.07177e7 | − | 3.58841e7i | 1.36757 | − | 2.36871i | ||||
\(746\) | −1.62982e7 | + | 2.00150e7i | −1.07224 | + | 1.31677i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.34126e6 | − | 1.72562e6i | 0.545102 | − | 0.112770i | ||||
\(749\) | −7.38296e6 | − | 4.26255e6i | −0.480868 | − | 0.277629i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.13834e7 | + | 6.57223e6i | −0.736501 | + | 0.425219i | −0.820796 | − | 0.571222i | \(-0.806470\pi\) |
0.0842946 | + | 0.996441i | \(0.473136\pi\) | |||||||
\(752\) | −1.57300e7 | − | 1.16920e7i | −1.01434 | − | 0.753955i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.91677e7 | − | 1.11055e7i | 1.86841 | − | 0.711393i | ||||
\(755\) | 1.98610e7 | 1.26804 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.33312e7 | 0.845528 | 0.422764 | − | 0.906240i | \(-0.361060\pi\) | ||||
0.422764 | + | 0.906240i | \(0.361060\pi\) | |||||||
\(758\) | −1.86132e7 | + | 7.08694e6i | −1.17666 | + | 0.448008i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 329323. | + | 7.44569e6i | 0.0206818 | + | 0.467596i | ||||
\(761\) | −9.74299e6 | + | 5.62512e6i | −0.609861 | + | 0.352103i | −0.772911 | − | 0.634515i | \(-0.781200\pi\) |
0.163050 | + | 0.986618i | \(0.447867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.67874e6 | + | 969222.i | 0.104393 | + | 0.0602715i | ||||
\(764\) | 1.26954e6 | + | 6.13667e6i | 0.0786891 | + | 0.380364i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.27493e6 | + | 5.24984e6i | −0.263243 | + | 0.323276i | ||||
\(767\) | −1.65504e6 | + | 2.86661e6i | −0.101583 | + | 0.175946i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05229e7 | − | 1.82262e7i | −0.641680 | − | 1.11142i | −0.985058 | − | 0.172225i | \(-0.944904\pi\) |
0.343378 | − | 0.939197i | \(-0.388429\pi\) | |||||||
\(770\) | −2.24866e7 | − | 3.62424e6i | −1.36678 | − | 0.220288i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.80317e7 | + | 5.96749e6i | 1.08892 | + | 0.360370i | ||||
\(773\) | 5.93037e6i | 0.356971i | 0.983943 | + | 0.178486i | \(0.0571198\pi\) | ||||
−0.983943 | + | 0.178486i | \(0.942880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.83188e6i | 0.229170i | ||||||||
\(776\) | 1.19527e7 | − | 7.62423e6i | 0.712542 | − | 0.454508i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.27232e6 | − | 7.89411e6i | 0.0753612 | − | 0.467578i | ||||
\(779\) | 2.88657e6 | + | 4.99969e6i | 0.170427 | + | 0.295188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.90086e7 | + | 3.29239e7i | −1.11512 | + | 1.93145i | ||||
\(782\) | 1.31562e6 | + | 1.07131e6i | 0.0769332 | + | 0.0626465i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.71285e6 | + | 4.19844e6i | −0.564360 | + | 0.243948i | ||||
\(785\) | 1.78807e7 | + | 1.03234e7i | 1.03564 | + | 0.597928i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.15888e6 | + | 3.55583e6i | −0.354458 | + | 0.204646i | −0.666647 | − | 0.745374i | \(-0.732271\pi\) |
0.312189 | + | 0.950020i | \(0.398938\pi\) | |||||||
\(788\) | 2.13197e6 | + | 2.39385e6i | 0.122311 | + | 0.137335i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.07609e6 | − | 1.07055e7i | −0.232368 | − | 0.610295i | ||||
\(791\) | 728784. | 0.0414150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.26298e6 | 0.410140 | ||||||||
\(794\) | 3.97697e6 | + | 1.04452e7i | 0.223872 | + | 0.587982i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.57271e6 | + | 9.62573e6i | 0.479552 | + | 0.538457i | ||||
\(797\) | 2.88348e7 | − | 1.66478e7i | 1.60795 | − | 0.928348i | 0.618116 | − | 0.786087i | \(-0.287896\pi\) |
0.989829 | − | 0.142261i | \(-0.0454371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.99593e6 | − | 4.61645e6i | −0.443100 | − | 0.255824i | ||||
\(800\) | 8.03290e6 | − | 2.84272e7i | 0.443759 | − | 1.57040i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.29542e6 | + | 2.68345e6i | 0.180915 | + | 0.147319i | ||||
\(803\) | −6.57264e6 | + | 1.13841e7i | −0.359709 | + | 0.623034i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.26839e6 | − | 3.92897e6i | −0.123375 | − | 0.213692i | ||||
\(806\) | −415529. | + | 2.57815e6i | −0.0225301 | + | 0.139788i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.52765e6 | − | 3.96264e6i | −0.136203 | − | 0.213529i | ||||
\(809\) | 5.88004e6i | 0.315871i | 0.987449 | + | 0.157935i | \(0.0504838\pi\) | ||||
−0.987449 | + | 0.157935i | \(0.949516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.76658e6i | 0.361258i | 0.983551 | + | 0.180629i | \(0.0578133\pi\) | ||||
−0.983551 | + | 0.180629i | \(0.942187\pi\) | |||||||
\(812\) | 2.19506e7 | + | 7.26440e6i | 1.16830 | + | 0.386643i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.30094e7 | − | 2.09678e6i | −0.688173 | − | 0.110915i | ||||
\(815\) | 2.08920e7 | + | 3.61860e7i | 1.10176 | + | 1.90830i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.65826e6 | − | 6.33630e6i | 0.191743 | − | 0.332109i | ||||
\(818\) | −8.71761e6 | + | 1.07057e7i | −0.455527 | + | 0.559412i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.47637e6 | − | 3.61390e7i | −0.388290 | − | 1.87690i | ||||
\(821\) | 8.96822e6 | + | 5.17780e6i | 0.464353 | + | 0.268094i | 0.713873 | − | 0.700275i | \(-0.246939\pi\) |
−0.249520 | + | 0.968370i | \(0.580273\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.37906e7 | + | 7.96198e6i | −0.709712 | + | 0.409752i | −0.810954 | − | 0.585109i | \(-0.801052\pi\) |
0.101242 | + | 0.994862i | \(0.467718\pi\) | |||||||
\(824\) | 4.48758e6 | − | 198486.i | 0.230247 | − | 0.0101838i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.29170e6 | + | 872556.i | −0.116871 | + | 0.0444983i | ||||
\(827\) | −4.35492e6 | −0.221420 | −0.110710 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110710 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.45459e7 | 0.735112 | 0.367556 | − | 0.930001i | \(-0.380195\pi\) | ||||
0.367556 | + | 0.930001i | \(0.380195\pi\) | |||||||
\(830\) | 3.77036e7 | − | 1.43555e7i | 1.89971 | − | 0.723310i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.48731e6 | − | 1.82552e7i | 0.425071 | − | 0.914279i | ||||
\(833\) | −4.31688e6 | + | 2.49235e6i | −0.215555 | + | 0.124451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.50146e7 | + | 2.59892e7i | 2.23428 | + | 1.28996i | ||||
\(836\) | 7.85021e6 | − | 1.62404e6i | 0.388477 | − | 0.0803675i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.49972e7 | + | 3.06979e7i | −1.22965 | + | 1.51008i | ||||
\(839\) | 6.07367e6 | − | 1.05199e7i | 0.297884 | − | 0.515949i | −0.677768 | − | 0.735276i | \(-0.737053\pi\) |
0.975652 | + | 0.219326i | \(0.0703860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00675e7 | + | 5.20784e7i | 1.46591 | + | 2.53903i | ||||
\(842\) | 6.43076e6 | + | 1.03647e6i | 0.312595 | + | 0.0503820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.25066e6 | − | 1.88874e7i | 0.302043 | − | 0.912673i | ||||
\(845\) | 558680.i | 0.0269167i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.15409e7i | 0.552752i | ||||||||
\(848\) | −8.56696e6 | − | 994758.i | −0.409107 | − | 0.0475037i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.21430e6 | − | 1.37386e7i | 0.105121 | − | 0.652223i | ||||
\(851\) | −1.31236e6 | − | 2.27307e6i | −0.0621196 | − | 0.107594i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.85932e6 | + | 1.18807e7i | −0.322782 | + | 0.559074i | −0.981061 | − | 0.193700i | \(-0.937951\pi\) |
0.658279 | + | 0.752774i | \(0.271285\pi\) | |||||||
\(854\) | 4.17229e6 | + | 3.39748e6i | 0.195763 | + | 0.159409i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.70180e7 | − | 8.84675e6i | −0.793826 | − | 0.412667i | ||||
\(857\) | −4.68499e6 | − | 2.70488e6i | −0.217900 | − | 0.125804i | 0.387078 | − | 0.922047i | \(-0.373485\pi\) |
−0.604977 | + | 0.796243i | \(0.706818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.58659e6 | + | 1.49337e6i | −0.119604 | + | 0.0690532i | −0.558608 | − | 0.829432i | \(-0.688664\pi\) |
0.439005 | + | 0.898485i | \(0.355331\pi\) | |||||||
\(860\) | −3.49267e7 | + | 3.11058e7i | −1.61032 | + | 1.43415i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −123364. | − | 324004.i | −0.00565482 | − | 0.0148519i | ||||
\(863\) | −2.98138e7 | −1.36267 | −0.681334 | − | 0.731973i | \(-0.738600\pi\) | ||||
−0.681334 | + | 0.731973i | \(0.738600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.97331e7 | 1.35114 | ||||||||
\(866\) | −1.29323e7 | − | 3.39655e7i | −0.585977 | − | 1.53902i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.44471e6 | + | 1.28666e6i | −0.0650851 | + | 0.0579650i | ||||
\(869\) | −1.06706e7 | + | 6.16065e6i | −0.479333 | + | 0.276743i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.66689e7 | − | 9.62381e6i | −0.744496 | − | 0.429835i | ||||
\(872\) | 3.86957e6 | + | 2.01158e6i | 0.172334 | + | 0.0895872i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.23817e6 | + | 1.00824e6i | 0.0548279 | + | 0.0446462i | ||||
\(875\) | −7.20435e6 | + | 1.24783e7i | −0.318108 | + | 0.550979i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.54476e7 | − | 2.67561e7i | −0.678207 | − | 1.17469i | −0.975520 | − | 0.219910i | \(-0.929424\pi\) |
0.297313 | − | 0.954780i | \(-0.403910\pi\) | |||||||
\(878\) | 1.59189e6 | − | 9.87689e6i | 0.0696911 | − | 0.432398i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.09023e7 | − | 5.91055e6i | −2.21580 | − | 0.257289i | ||||
\(881\) | − | 1.23151e7i | − | 0.534563i | −0.963618 | − | 0.267282i | \(-0.913875\pi\) | ||
0.963618 | − | 0.267282i | \(-0.0861254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.12796e7i | 0.486845i | 0.969920 | + | 0.243422i | \(0.0782701\pi\) | ||||
−0.969920 | + | 0.243422i | \(0.921730\pi\) | |||||||
\(884\) | 2.97963e6 | − | 9.00345e6i | 0.128243 | − | 0.387506i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.67415e7 | + | 5.92176e6i | 1.57244 | + | 0.253435i | ||||
\(887\) | −5.21370e6 | − | 9.03039e6i | −0.222504 | − | 0.385388i | 0.733064 | − | 0.680160i | \(-0.238090\pi\) |
−0.955568 | + | 0.294772i | \(0.904756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.85325e6 | + | 1.36022e7i | −0.333269 | + | 0.577239i | ||||
\(890\) | −2.84822e7 | + | 3.49776e7i | −1.20531 | + | 1.48018i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.04404e7 | + | 8.36624e6i | −1.70178 | + | 0.352061i | ||||
\(893\) | −7.52521e6 | − | 4.34468e6i | −0.315784 | − | 0.182318i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.66904e6 | − | 5.58242e6i | 0.403484 | − | 0.232951i | ||||
\(896\) | 1.34151e7 | − | 6.51668e6i | 0.558242 | − | 0.271179i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.15096e6 | − | 1.96121e6i | 0.213156 | − | 0.0811585i | ||||
\(899\) | −6.74779e6 | −0.278460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.06285e6 | −0.166732 | ||||||||
\(902\) | −3.70964e7 | + | 1.41243e7i | −1.51815 | + | 0.578032i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.63805e6 | − | 72451.0i | 0.0666662 | − | 0.00294865i | ||||
\(905\) | −2.44956e7 | + | 1.41425e7i | −0.994183 | + | 0.573992i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24643e7 | − | 1.29698e7i | −0.906723 | − | 0.523497i | −0.0273474 | − | 0.999626i | \(-0.508706\pi\) |
−0.879375 | + | 0.476129i | \(0.842039\pi\) | |||||||
\(908\) | −5.64036e6 | − | 2.72642e7i | −0.227035 | − | 1.09743i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.60127e7 | + | 1.96644e7i | −0.641004 | + | 0.787188i | ||||
\(911\) | 5.68513e6 | − | 9.84694e6i | 0.226958 | − | 0.393102i | −0.729947 | − | 0.683503i | \(-0.760455\pi\) |
0.956905 | + | 0.290401i | \(0.0937888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.16971e7 | − | 3.75805e7i | −0.861440 | − | 1.49206i | ||||
\(914\) | 2.60604e7 | + | 4.20025e6i | 1.03185 | + | 0.166307i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.35056e6 | − | 1.10885e6i | −0.131941 | − | 0.0436649i | ||||
\(917\) | − | 2.04158e7i | − | 0.801756i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.39949e7i | − | 1.71836i | −0.511675 | − | 0.859179i | \(-0.670975\pi\) | ||
0.511675 | − | 0.859179i | \(-0.329025\pi\) | |||||||
\(920\) | −5.48914e6 | − | 8.60543e6i | −0.213813 | − | 0.335199i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.32304e6 | − | 1.44133e7i | 0.0899975 | − | 0.558389i | ||||
\(923\) | 2.11639e7 | + | 3.66569e7i | 0.817694 | + | 1.41629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.07641e7 | + | 1.86440e7i | −0.413641 | + | 0.716447i | ||||
\(926\) | 1.01596e7 | + | 8.27297e6i | 0.389360 | + | 0.317054i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.00593e7 | + | 1.41456e7i | 1.90816 | + | 0.539203i | ||||
\(929\) | 2.15711e7 | + | 1.24541e7i | 0.820037 | + | 0.473449i | 0.850429 | − | 0.526089i | \(-0.176342\pi\) |
−0.0303922 | + | 0.999538i | \(0.509676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.06275e6 | + | 2.34563e6i | −0.153619 | + | 0.0886921i | ||||
\(932\) | −7.50669e6 | − | 8.42877e6i | −0.283080 | − | 0.317852i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 52931.8 | + | 139021.i | 0.00198541 | + | 0.00521451i | ||||
\(935\) | −2.41402e7 | −0.903050 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.28010e7 | −1.22050 | −0.610250 | − | 0.792209i | \(-0.708931\pi\) | ||||
−0.610250 | + | 0.792209i | \(0.708931\pi\) | |||||||
\(938\) | −5.07379e6 | − | 1.33259e7i | −0.188289 | − | 0.494526i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.69424e7 | + | 4.14802e7i | 1.36366 | + | 1.53116i | ||||
\(941\) | −3.67890e7 | + | 2.12402e7i | −1.35439 | + | 0.781959i | −0.988861 | − | 0.148841i | \(-0.952446\pi\) |
−0.365531 | + | 0.930799i | \(0.619112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.84722e6 | − | 3.95325e6i | −0.250747 | − | 0.144769i | ||||
\(944\) | −5.06418e6 | + | 2.18902e6i | −0.184960 | + | 0.0799504i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.90090e7 | + | 3.17649e7i | 1.41722 | + | 1.15404i | ||||
\(947\) | 2.36823e7 | − | 4.10190e7i | 0.858123 | − | 1.48631i | −0.0155950 | − | 0.999878i | \(-0.504964\pi\) |
0.873718 | − | 0.486433i | \(-0.161702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.31788e6 | + | 1.26749e7i | 0.263766 | + | 0.456857i | ||||
\(950\) | 2.08395e6 | − | 1.29298e7i | 0.0749165 | − | 0.464819i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.92332e6 | − | 3.77830e6i | 0.211823 | − | 0.135115i | ||||
\(953\) | − | 3.03620e7i | − | 1.08293i | −0.840725 | − | 0.541463i | \(-0.817871\pi\) | ||
0.840725 | − | 0.541463i | \(-0.182129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.77600e7i | − | 0.630135i | ||||||
\(956\) | 2.10056e7 | + | 6.95168e6i | 0.743346 | + | 0.246006i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.54857e7 | − | 5.71935e6i | −1.24922 | − | 0.201341i | ||||
\(959\) | −5.03310e6 | − | 8.71758e6i | −0.176721 | − | 0.306090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40323e7 | + | 2.43046e7i | −0.490139 | + | 0.848946i | ||||
\(962\) | −9.26401e6 | + | 1.13767e7i | −0.322746 | + | 0.396350i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −485930. | − | 2.34887e6i | −0.0168415 | − | 0.0814079i | ||||
\(965\) | −4.66172e7 | − | 2.69144e7i | −1.61149 | − | 0.930394i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41777e7 | − | 1.39590e7i | 0.831475 | − | 0.480052i | −0.0228826 | − | 0.999738i | \(-0.507284\pi\) |
0.854357 | + | 0.519686i | \(0.173951\pi\) | |||||||
\(968\) | 1.14732e6 | + | 2.59398e7i | 0.0393546 | + | 0.889772i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.75496e7 | + | 1.42969e7i | −1.28137 | + | 0.487879i | ||||
\(971\) | 2.50332e7 | 0.852057 | 0.426028 | − | 0.904710i | \(-0.359912\pi\) | ||||
0.426028 | + | 0.904710i | \(0.359912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.44446e7 | 0.489130 | ||||||||
\(974\) | −3.76932e7 | + | 1.43516e7i | −1.27311 | + | 0.484733i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.71558e6 | + | 7.22155e6i | 0.326471 | + | 0.242664i | ||||
\(977\) | 2.16546e7 | − | 1.25023e7i | 0.725793 | − | 0.419037i | −0.0910880 | − | 0.995843i | \(-0.529034\pi\) |
0.816881 | + | 0.576806i | \(0.195701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.20175e7 | + | 2.42588e7i | 1.40111 | + | 0.808933i | ||||
\(980\) | 2.93665e7 | − | 6.07529e6i | 0.976759 | − | 0.202070i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.94363e7 | − | 3.61493e7i | 0.974101 | − | 1.19625i | ||||
\(983\) | 1.95719e7 | − | 3.38995e7i | 0.646025 | − | 1.11895i | −0.338039 | − | 0.941132i | \(-0.609764\pi\) |
0.984064 | − | 0.177816i | \(-0.0569031\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.54242e6 | − | 7.86770e6i | −0.149175 | − | 0.258379i | ||||
\(986\) | 2.41932e7 | + | 3.89930e6i | 0.792503 | + | 0.127730i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.80422e6 | − | 8.47342e6i | 0.0913946 | − | 0.276163i | ||||
\(989\) | 1.00202e7i | 0.325751i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.82027e7i | 0.588779i | 0.955686 | + | 0.294389i | \(0.0951163\pi\) | ||||
−0.955686 | + | 0.294389i | \(0.904884\pi\) | |||||||
\(992\) | −3.11929e6 | + | 3.03559e6i | −0.100641 | + | 0.0979409i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.98960e6 | + | 3.09580e7i | −0.160177 | + | 0.993817i | ||||
\(995\) | −1.82652e7 | − | 3.16362e7i | −0.584879 | − | 1.01304i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.16083e7 | − | 3.74266e7i | 0.688466 | − | 1.19246i | −0.283868 | − | 0.958863i | \(-0.591618\pi\) |
0.972334 | − | 0.233594i | \(-0.0750488\pi\) | |||||||
\(998\) | −3.70616e7 | − | 3.01792e7i | −1.17787 | − | 0.959138i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.h.a.35.19 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.10 | yes | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.28 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.1 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.28 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.1 | ✓ | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.19 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.10 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.1 | ✓ | 56 | 12.11 | even | 2 | ||
36.6.h.a.11.10 | yes | 56 | 3.2 | odd | 2 | ||
36.6.h.a.23.1 | yes | 56 | 9.4 | even | 3 | ||
36.6.h.a.23.10 | yes | 56 | 36.31 | odd | 6 | ||
108.6.h.a.35.19 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.35.28 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.71.19 | 56 | 36.23 | even | 6 | inner | ||
108.6.h.a.71.28 | 56 | 9.5 | odd | 6 | inner |