Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,6,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (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: | \(22.1329671342\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.2 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.6.d.a.137.4 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.00000i | − | 0.707107i | ||||||
\(3\) | −11.7474 | + | 10.2469i | −0.753597 | + | 0.657337i | ||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 107.494 | 1.92291 | 0.961457 | − | 0.274954i | \(-0.0886627\pi\) | ||||
0.961457 | + | 0.274954i | \(0.0886627\pi\) | |||||||
\(6\) | 40.9875 | + | 46.9896i | 0.464808 | + | 0.532873i | ||||
\(7\) | 192.413i | 1.48419i | 0.670295 | + | 0.742094i | \(0.266167\pi\) | ||||
−0.670295 | + | 0.742094i | \(0.733833\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 33.0032 | − | 240.748i | 0.135816 | − | 0.990734i | ||||
\(10\) | − | 429.977i | − | 1.35971i | ||||||
\(11\) | 525.803 | 1.31021 | 0.655106 | − | 0.755537i | \(-0.272624\pi\) | ||||
0.655106 | + | 0.755537i | \(0.272624\pi\) | |||||||
\(12\) | 187.959 | − | 163.950i | 0.376798 | − | 0.328669i | ||||
\(13\) | −1096.97 | −1.80026 | −0.900132 | − | 0.435617i | \(-0.856530\pi\) | ||||
−0.900132 | + | 0.435617i | \(0.856530\pi\) | |||||||
\(14\) | 769.652 | 1.04948 | ||||||||
\(15\) | −1262.78 | + | 1101.48i | −1.44910 | + | 1.26400i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −665.814 | −0.558767 | −0.279384 | − | 0.960180i | \(-0.590130\pi\) | ||||
−0.279384 | + | 0.960180i | \(0.590130\pi\) | |||||||
\(18\) | −962.994 | − | 132.013i | −0.700555 | − | 0.0960361i | ||||
\(19\) | 365.592i | 0.232334i | 0.993230 | + | 0.116167i | \(0.0370608\pi\) | ||||
−0.993230 | + | 0.116167i | \(0.962939\pi\) | |||||||
\(20\) | −1719.91 | −0.961457 | ||||||||
\(21\) | −1971.63 | − | 2260.35i | −0.975613 | − | 1.11848i | ||||
\(22\) | − | 2103.21i | − | 0.926459i | ||||||
\(23\) | 1075.29 | + | 2297.85i | 0.423843 | + | 0.905736i | ||||
\(24\) | −655.800 | − | 751.834i | −0.232404 | − | 0.266437i | ||||
\(25\) | 8430.00 | 2.69760 | ||||||||
\(26\) | 4387.88i | 1.27298i | ||||||||
\(27\) | 2079.22 | + | 3166.35i | 0.548896 | + | 0.835890i | ||||
\(28\) | − | 3078.61i | − | 0.742094i | ||||||
\(29\) | − | 2165.14i | − | 0.478069i | −0.971011 | − | 0.239035i | \(-0.923169\pi\) | ||
0.971011 | − | 0.239035i | \(-0.0768310\pi\) | |||||||
\(30\) | 4405.92 | + | 5051.11i | 0.893785 | + | 1.02467i | ||||
\(31\) | −4020.58 | −0.751424 | −0.375712 | − | 0.926737i | \(-0.622602\pi\) | ||||
−0.375712 | + | 0.926737i | \(0.622602\pi\) | |||||||
\(32\) | − | 1024.00i | − | 0.176777i | ||||||
\(33\) | −6176.82 | + | 5387.84i | −0.987371 | + | 0.861251i | ||||
\(34\) | 2663.26i | 0.395108i | ||||||||
\(35\) | 20683.3i | 2.85397i | ||||||||
\(36\) | −528.051 | + | 3851.97i | −0.0679078 | + | 0.495367i | ||||
\(37\) | 11723.5i | 1.40784i | 0.710281 | + | 0.703918i | \(0.248568\pi\) | ||||
−0.710281 | + | 0.703918i | \(0.751432\pi\) | |||||||
\(38\) | 1462.37 | 0.164285 | ||||||||
\(39\) | 12886.6 | − | 11240.5i | 1.35667 | − | 1.18338i | ||||
\(40\) | 6879.63i | 0.679853i | ||||||||
\(41\) | 10135.8i | 0.941665i | 0.882223 | + | 0.470832i | \(0.156046\pi\) | ||||
−0.882223 | + | 0.470832i | \(0.843954\pi\) | |||||||
\(42\) | −9041.41 | + | 7886.52i | −0.790885 | + | 0.689862i | ||||
\(43\) | 3679.94i | 0.303508i | 0.988418 | + | 0.151754i | \(0.0484921\pi\) | ||||
−0.988418 | + | 0.151754i | \(0.951508\pi\) | |||||||
\(44\) | −8412.85 | −0.655106 | ||||||||
\(45\) | 3547.65 | − | 25879.1i | 0.261162 | − | 1.90510i | ||||
\(46\) | 9191.39 | − | 4301.15i | 0.640452 | − | 0.299702i | ||||
\(47\) | 8076.34i | 0.533298i | 0.963794 | + | 0.266649i | \(0.0859164\pi\) | ||||
−0.963794 | + | 0.266649i | \(0.914084\pi\) | |||||||
\(48\) | −3007.34 | + | 2623.20i | −0.188399 | + | 0.164334i | ||||
\(49\) | −20215.7 | −1.20282 | ||||||||
\(50\) | − | 33720.0i | − | 1.90749i | ||||||
\(51\) | 7821.59 | − | 6822.52i | 0.421085 | − | 0.367298i | ||||
\(52\) | 17551.5 | 0.900132 | ||||||||
\(53\) | 12175.6 | 0.595388 | 0.297694 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297694 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(54\) | 12665.4 | − | 8316.87i | 0.591064 | − | 0.388128i | ||||
\(55\) | 56520.8 | 2.51942 | ||||||||
\(56\) | −12314.4 | −0.524740 | ||||||||
\(57\) | −3746.18 | − | 4294.76i | −0.152722 | − | 0.175086i | ||||
\(58\) | −8660.56 | −0.338046 | ||||||||
\(59\) | − | 3846.00i | − | 0.143840i | −0.997410 | − | 0.0719199i | \(-0.977087\pi\) | ||
0.997410 | − | 0.0719199i | \(-0.0229126\pi\) | |||||||
\(60\) | 20204.5 | − | 17623.7i | 0.724551 | − | 0.632002i | ||||
\(61\) | 20774.9i | 0.714848i | 0.933942 | + | 0.357424i | \(0.116345\pi\) | ||||
−0.933942 | + | 0.357424i | \(0.883655\pi\) | |||||||
\(62\) | 16082.3i | 0.531337i | ||||||||
\(63\) | 46323.1 | + | 6350.24i | 1.47044 | + | 0.201576i | ||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | −117918. | −3.46176 | ||||||||
\(66\) | 21551.3 | + | 24707.3i | 0.608996 | + | 0.698176i | ||||
\(67\) | 20138.2i | 0.548067i | 0.961720 | + | 0.274034i | \(0.0883580\pi\) | ||||
−0.961720 | + | 0.274034i | \(0.911642\pi\) | |||||||
\(68\) | 10653.0 | 0.279384 | ||||||||
\(69\) | −36177.6 | − | 15975.4i | −0.914780 | − | 0.403952i | ||||
\(70\) | 82733.1 | 2.01806 | ||||||||
\(71\) | − | 57543.7i | − | 1.35473i | −0.735649 | − | 0.677363i | \(-0.763122\pi\) | ||
0.735649 | − | 0.677363i | \(-0.236878\pi\) | |||||||
\(72\) | 15407.9 | + | 2112.20i | 0.350277 | + | 0.0480181i | ||||
\(73\) | −34442.0 | −0.756452 | −0.378226 | − | 0.925713i | \(-0.623466\pi\) | ||||
−0.378226 | + | 0.925713i | \(0.623466\pi\) | |||||||
\(74\) | 46893.9 | 0.995491 | ||||||||
\(75\) | −99030.7 | + | 86381.2i | −2.03290 | + | 1.77323i | ||||
\(76\) | − | 5849.48i | − | 0.116167i | ||||||
\(77\) | 101171.i | 1.94460i | ||||||||
\(78\) | −44962.0 | − | 51546.2i | −0.836777 | − | 0.959313i | ||||
\(79\) | − | 13257.0i | − | 0.238989i | −0.992835 | − | 0.119495i | \(-0.961873\pi\) | ||
0.992835 | − | 0.119495i | \(-0.0381274\pi\) | |||||||
\(80\) | 27518.5 | 0.480729 | ||||||||
\(81\) | −56870.6 | − | 15890.9i | −0.963108 | − | 0.269114i | ||||
\(82\) | 40543.0 | 0.665858 | ||||||||
\(83\) | 7450.77 | 0.118715 | 0.0593576 | − | 0.998237i | \(-0.481095\pi\) | ||||
0.0593576 | + | 0.998237i | \(0.481095\pi\) | |||||||
\(84\) | 31546.1 | + | 36165.7i | 0.487806 | + | 0.559240i | ||||
\(85\) | −71571.2 | −1.07446 | ||||||||
\(86\) | 14719.8 | 0.214612 | ||||||||
\(87\) | 22185.9 | + | 25434.8i | 0.314253 | + | 0.360271i | ||||
\(88\) | 33651.4i | 0.463230i | ||||||||
\(89\) | 18913.7 | 0.253106 | 0.126553 | − | 0.991960i | \(-0.459609\pi\) | ||||
0.126553 | + | 0.991960i | \(0.459609\pi\) | |||||||
\(90\) | −103516. | − | 14190.6i | −1.34711 | − | 0.184669i | ||||
\(91\) | − | 211071.i | − | 2.67193i | ||||||
\(92\) | −17204.6 | − | 36765.6i | −0.211921 | − | 0.452868i | ||||
\(93\) | 47231.4 | − | 41198.4i | 0.566270 | − | 0.493939i | ||||
\(94\) | 32305.4 | 0.377099 | ||||||||
\(95\) | 39299.1i | 0.446759i | ||||||||
\(96\) | 10492.8 | + | 12029.3i | 0.116202 | + | 0.133218i | ||||
\(97\) | 41309.0i | 0.445775i | 0.974844 | + | 0.222887i | \(0.0715482\pi\) | ||||
−0.974844 | + | 0.222887i | \(0.928452\pi\) | |||||||
\(98\) | 80863.0i | 0.850520i | ||||||||
\(99\) | 17353.2 | − | 126586.i | 0.177947 | − | 1.29807i | ||||
\(100\) | −134880. | −1.34880 | ||||||||
\(101\) | 112029.i | 1.09277i | 0.837535 | + | 0.546384i | \(0.183996\pi\) | ||||
−0.837535 | + | 0.546384i | \(0.816004\pi\) | |||||||
\(102\) | −27290.1 | − | 31286.4i | −0.259719 | − | 0.297752i | ||||
\(103\) | 92392.1i | 0.858107i | 0.903279 | + | 0.429054i | \(0.141153\pi\) | ||||
−0.903279 | + | 0.429054i | \(0.858847\pi\) | |||||||
\(104\) | − | 70206.1i | − | 0.636490i | ||||||
\(105\) | −211939. | − | 242975.i | −1.87602 | − | 2.15074i | ||||
\(106\) | − | 48702.4i | − | 0.421003i | ||||||
\(107\) | 105386. | 0.889862 | 0.444931 | − | 0.895565i | \(-0.353228\pi\) | ||||
0.444931 | + | 0.895565i | \(0.353228\pi\) | |||||||
\(108\) | −33267.5 | − | 50661.6i | −0.274448 | − | 0.417945i | ||||
\(109\) | − | 67041.1i | − | 0.540474i | −0.962794 | − | 0.270237i | \(-0.912898\pi\) | ||
0.962794 | − | 0.270237i | \(-0.0871021\pi\) | |||||||
\(110\) | − | 226083.i | − | 1.78150i | ||||||
\(111\) | −120129. | − | 137721.i | −0.925423 | − | 1.06094i | ||||
\(112\) | 49257.7i | 0.371047i | ||||||||
\(113\) | −191967. | −1.41426 | −0.707131 | − | 0.707082i | \(-0.750011\pi\) | ||||
−0.707131 | + | 0.707082i | \(0.750011\pi\) | |||||||
\(114\) | −17179.1 | + | 14984.7i | −0.123805 | + | 0.107991i | ||||
\(115\) | 115587. | + | 247005.i | 0.815013 | + | 1.74165i | ||||
\(116\) | 34642.2i | 0.239035i | ||||||||
\(117\) | −36203.5 | + | 264094.i | −0.244504 | + | 1.78358i | ||||
\(118\) | −15384.0 | −0.101710 | ||||||||
\(119\) | − | 128111.i | − | 0.829316i | ||||||
\(120\) | −70494.7 | − | 80817.8i | −0.446893 | − | 0.512335i | ||||
\(121\) | 115418. | 0.716653 | ||||||||
\(122\) | 83099.4 | 0.505474 | ||||||||
\(123\) | −103860. | − | 119069.i | −0.618991 | − | 0.709636i | ||||
\(124\) | 64329.3 | 0.375712 | ||||||||
\(125\) | 570257. | 3.26434 | ||||||||
\(126\) | 25401.0 | − | 185292.i | 0.142536 | − | 1.03976i | ||||
\(127\) | 130291. | 0.716809 | 0.358405 | − | 0.933566i | \(-0.383321\pi\) | ||||
0.358405 | + | 0.933566i | \(0.383321\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −37707.9 | − | 43229.8i | −0.199507 | − | 0.228722i | ||||
\(130\) | 471672.i | 2.44783i | ||||||||
\(131\) | − | 131558.i | − | 0.669791i | −0.942255 | − | 0.334895i | \(-0.891299\pi\) | ||
0.942255 | − | 0.334895i | \(-0.108701\pi\) | |||||||
\(132\) | 98829.1 | − | 86205.4i | 0.493685 | − | 0.430625i | ||||
\(133\) | −70344.7 | −0.344828 | ||||||||
\(134\) | 80552.9 | 0.387542 | ||||||||
\(135\) | 223504. | + | 340364.i | 1.05548 | + | 1.60735i | ||||
\(136\) | − | 42612.1i | − | 0.197554i | ||||||
\(137\) | 133840. | 0.609233 | 0.304616 | − | 0.952475i | \(-0.401472\pi\) | ||||
0.304616 | + | 0.952475i | \(0.401472\pi\) | |||||||
\(138\) | −63901.7 | + | 144710.i | −0.285637 | + | 0.646847i | ||||
\(139\) | −87285.3 | −0.383181 | −0.191590 | − | 0.981475i | \(-0.561365\pi\) | ||||
−0.191590 | + | 0.981475i | \(0.561365\pi\) | |||||||
\(140\) | − | 330932.i | − | 1.42698i | ||||||
\(141\) | −82757.2 | − | 94876.0i | −0.350557 | − | 0.401891i | ||||
\(142\) | −230175. | −0.957937 | ||||||||
\(143\) | −576790. | −2.35873 | ||||||||
\(144\) | 8448.82 | − | 61631.6i | 0.0339539 | − | 0.247684i | ||||
\(145\) | − | 232740.i | − | 0.919287i | ||||||
\(146\) | 137768.i | 0.534893i | ||||||||
\(147\) | 237483. | − | 207148.i | 0.906439 | − | 0.790656i | ||||
\(148\) | − | 187576.i | − | 0.703918i | ||||||
\(149\) | 271122. | 1.00046 | 0.500230 | − | 0.865893i | \(-0.333249\pi\) | ||||
0.500230 | + | 0.865893i | \(0.333249\pi\) | |||||||
\(150\) | 345525. | + | 396123.i | 1.25387 | + | 1.43748i | ||||
\(151\) | 95889.0 | 0.342237 | 0.171118 | − | 0.985250i | \(-0.445262\pi\) | ||||
0.171118 | + | 0.985250i | \(0.445262\pi\) | |||||||
\(152\) | −23397.9 | −0.0821426 | ||||||||
\(153\) | −21974.0 | + | 160294.i | −0.0758893 | + | 0.553590i | ||||
\(154\) | 404685. | 1.37504 | ||||||||
\(155\) | −432189. | −1.44492 | ||||||||
\(156\) | −206185. | + | 179848.i | −0.678337 | + | 0.591690i | ||||
\(157\) | − | 542326.i | − | 1.75595i | −0.478710 | − | 0.877973i | \(-0.658895\pi\) | ||
0.478710 | − | 0.877973i | \(-0.341105\pi\) | |||||||
\(158\) | −53028.1 | −0.168991 | ||||||||
\(159\) | −143032. | + | 124762.i | −0.448683 | + | 0.391371i | ||||
\(160\) | − | 110074.i | − | 0.339926i | ||||||
\(161\) | −442136. | + | 206899.i | −1.34428 | + | 0.629062i | ||||
\(162\) | −63563.7 | + | 227482.i | −0.190293 | + | 0.681020i | ||||
\(163\) | 535276. | 1.57801 | 0.789004 | − | 0.614388i | \(-0.210597\pi\) | ||||
0.789004 | + | 0.614388i | \(0.210597\pi\) | |||||||
\(164\) | − | 162172.i | − | 0.470832i | ||||||
\(165\) | −663972. | + | 579161.i | −1.89863 | + | 1.65611i | ||||
\(166\) | − | 29803.1i | − | 0.0839443i | ||||||
\(167\) | − | 195562.i | − | 0.542616i | −0.962493 | − | 0.271308i | \(-0.912544\pi\) | ||
0.962493 | − | 0.271308i | \(-0.0874562\pi\) | |||||||
\(168\) | 144663. | − | 126184.i | 0.395442 | − | 0.344931i | ||||
\(169\) | 832050. | 2.24095 | ||||||||
\(170\) | 286285.i | 0.759759i | ||||||||
\(171\) | 88015.8 | + | 12065.7i | 0.230181 | + | 0.0315546i | ||||
\(172\) | − | 58879.1i | − | 0.151754i | ||||||
\(173\) | − | 700856.i | − | 1.78038i | −0.455585 | − | 0.890192i | \(-0.650570\pi\) | ||
0.455585 | − | 0.890192i | \(-0.349430\pi\) | |||||||
\(174\) | 101739. | − | 88743.7i | 0.254750 | − | 0.222210i | ||||
\(175\) | 1.62204e6i | 4.00375i | ||||||||
\(176\) | 134606. | 0.327553 | ||||||||
\(177\) | 39409.4 | + | 45180.5i | 0.0945512 | + | 0.108397i | ||||
\(178\) | − | 75654.8i | − | 0.178973i | ||||||
\(179\) | 460655.i | 1.07459i | 0.843394 | + | 0.537296i | \(0.180554\pi\) | ||||
−0.843394 | + | 0.537296i | \(0.819446\pi\) | |||||||
\(180\) | −56762.4 | + | 414065.i | −0.130581 | + | 0.952549i | ||||
\(181\) | − | 517198.i | − | 1.17344i | −0.809791 | − | 0.586719i | \(-0.800419\pi\) | ||
0.809791 | − | 0.586719i | \(-0.199581\pi\) | |||||||
\(182\) | −844285. | −1.88934 | ||||||||
\(183\) | −212877. | − | 244051.i | −0.469896 | − | 0.538707i | ||||
\(184\) | −147062. | + | 68818.3i | −0.320226 | + | 0.149851i | ||||
\(185\) | 1.26021e6i | 2.70715i | ||||||||
\(186\) | −164794. | − | 188926.i | −0.349267 | − | 0.400413i | ||||
\(187\) | −350087. | −0.732103 | ||||||||
\(188\) | − | 129221.i | − | 0.266649i | ||||||
\(189\) | −609247. | + | 400068.i | −1.24062 | + | 0.814666i | ||||
\(190\) | 157196. | 0.315906 | ||||||||
\(191\) | 451349. | 0.895219 | 0.447609 | − | 0.894229i | \(-0.352276\pi\) | ||||
0.447609 | + | 0.894229i | \(0.352276\pi\) | |||||||
\(192\) | 48117.4 | − | 41971.2i | 0.0941996 | − | 0.0821672i | ||||
\(193\) | −360534. | −0.696712 | −0.348356 | − | 0.937362i | \(-0.613260\pi\) | ||||
−0.348356 | + | 0.937362i | \(0.613260\pi\) | |||||||
\(194\) | 165236. | 0.315210 | ||||||||
\(195\) | 1.38523e6 | − | 1.20829e6i | 2.60877 | − | 2.27554i | ||||
\(196\) | 323452. | 0.601408 | ||||||||
\(197\) | − | 241803.i | − | 0.443911i | −0.975057 | − | 0.221955i | \(-0.928756\pi\) | ||
0.975057 | − | 0.221955i | \(-0.0712439\pi\) | |||||||
\(198\) | −506345. | − | 69412.7i | −0.917875 | − | 0.125828i | ||||
\(199\) | 314759.i | 0.563438i | 0.959497 | + | 0.281719i | \(0.0909046\pi\) | ||||
−0.959497 | + | 0.281719i | \(0.909095\pi\) | |||||||
\(200\) | 539520.i | 0.953746i | ||||||||
\(201\) | −206354. | − | 236572.i | −0.360265 | − | 0.413022i | ||||
\(202\) | 448117. | 0.772704 | ||||||||
\(203\) | 416601. | 0.709545 | ||||||||
\(204\) | −125145. | + | 109160.i | −0.210543 | + | 0.183649i | ||||
\(205\) | 1.08953e6i | 1.81074i | ||||||||
\(206\) | 369568. | 0.606773 | ||||||||
\(207\) | 588691. | − | 183037.i | 0.954908 | − | 0.296902i | ||||
\(208\) | −280824. | −0.450066 | ||||||||
\(209\) | 192230.i | 0.304407i | ||||||||
\(210\) | −971899. | + | 847756.i | −1.52080 | + | 1.32655i | ||||
\(211\) | 214122. | 0.331098 | 0.165549 | − | 0.986202i | \(-0.447060\pi\) | ||||
0.165549 | + | 0.986202i | \(0.447060\pi\) | |||||||
\(212\) | −194809. | −0.297694 | ||||||||
\(213\) | 589643. | + | 675989.i | 0.890512 | + | 1.02092i | ||||
\(214\) | − | 421543.i | − | 0.629228i | ||||||
\(215\) | 395572.i | 0.583620i | ||||||||
\(216\) | −202646. | + | 133070.i | −0.295532 | + | 0.194064i | ||||
\(217\) | − | 773612.i | − | 1.11525i | ||||||
\(218\) | −268164. | −0.382173 | ||||||||
\(219\) | 404605. | − | 352923.i | 0.570060 | − | 0.497244i | ||||
\(220\) | −904332. | −1.25971 | ||||||||
\(221\) | 730378. | 1.00593 | ||||||||
\(222\) | −550882. | + | 480516.i | −0.750199 | + | 0.654373i | ||||
\(223\) | 160098. | 0.215588 | 0.107794 | − | 0.994173i | \(-0.465621\pi\) | ||||
0.107794 | + | 0.994173i | \(0.465621\pi\) | |||||||
\(224\) | 197031. | 0.262370 | ||||||||
\(225\) | 278217. | − | 2.02951e6i | 0.366376 | − | 2.67260i | ||||
\(226\) | 767867.i | 1.00003i | ||||||||
\(227\) | −420238. | −0.541291 | −0.270645 | − | 0.962679i | \(-0.587237\pi\) | ||||
−0.270645 | + | 0.962679i | \(0.587237\pi\) | |||||||
\(228\) | 59938.9 | + | 68716.2i | 0.0763610 | + | 0.0875432i | ||||
\(229\) | 100486.i | 0.126625i | 0.997994 | + | 0.0633124i | \(0.0201664\pi\) | ||||
−0.997994 | + | 0.0633124i | \(0.979834\pi\) | |||||||
\(230\) | 988021. | − | 462348.i | 1.23153 | − | 0.576301i | ||||
\(231\) | −1.03669e6 | − | 1.18850e6i | −1.27826 | − | 1.46544i | ||||
\(232\) | 138569. | 0.169023 | ||||||||
\(233\) | − | 1.34829e6i | − | 1.62703i | −0.581546 | − | 0.813514i | \(-0.697552\pi\) | ||
0.581546 | − | 0.813514i | \(-0.302448\pi\) | |||||||
\(234\) | 1.05638e6 | + | 144814.i | 1.26118 | + | 0.172890i | ||||
\(235\) | 868159.i | 1.02549i | ||||||||
\(236\) | 61535.9i | 0.0719199i | ||||||||
\(237\) | 135843. | + | 155736.i | 0.157097 | + | 0.180101i | ||||
\(238\) | −512445. | −0.586415 | ||||||||
\(239\) | − | 539225.i | − | 0.610626i | −0.952252 | − | 0.305313i | \(-0.901239\pi\) | ||
0.952252 | − | 0.305313i | \(-0.0987611\pi\) | |||||||
\(240\) | −323271. | + | 281979.i | −0.362275 | + | 0.316001i | ||||
\(241\) | − | 1.51483e6i | − | 1.68005i | −0.542548 | − | 0.840025i | \(-0.682540\pi\) | ||
0.542548 | − | 0.840025i | \(-0.317460\pi\) | |||||||
\(242\) | − | 461671.i | − | 0.506750i | ||||||
\(243\) | 830914. | − | 396068.i | 0.902694 | − | 0.430283i | ||||
\(244\) | − | 332398.i | − | 0.357424i | ||||||
\(245\) | −2.17307e6 | −2.31291 | ||||||||
\(246\) | −476275. | + | 415439.i | −0.501788 | + | 0.437693i | ||||
\(247\) | − | 401044.i | − | 0.418263i | ||||||
\(248\) | − | 257317.i | − | 0.265668i | ||||||
\(249\) | −87527.3 | + | 76347.1i | −0.0894633 | + | 0.0780359i | ||||
\(250\) | − | 2.28103e6i | − | 2.30824i | ||||||
\(251\) | 30311.8 | 0.0303688 | 0.0151844 | − | 0.999885i | \(-0.495166\pi\) | ||||
0.0151844 | + | 0.999885i | \(0.495166\pi\) | |||||||
\(252\) | −741170. | − | 101604.i | −0.735218 | − | 0.100788i | ||||
\(253\) | 565389. | + | 1.20821e6i | 0.555323 | + | 1.18671i | ||||
\(254\) | − | 521162.i | − | 0.506861i | ||||||
\(255\) | 840776. | − | 733381.i | 0.809711 | − | 0.706284i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.54379e6i | 1.45799i | 0.684517 | + | 0.728997i | \(0.260013\pi\) | ||||
−0.684517 | + | 0.728997i | \(0.739987\pi\) | |||||||
\(258\) | −172919. | + | 150832.i | −0.161731 | + | 0.141073i | ||||
\(259\) | −2.25575e6 | −2.08950 | ||||||||
\(260\) | 1.88669e6 | 1.73088 | ||||||||
\(261\) | −521254. | − | 71456.5i | −0.473640 | − | 0.0649293i | ||||
\(262\) | −526232. | −0.473613 | ||||||||
\(263\) | −635855. | −0.566851 | −0.283425 | − | 0.958994i | \(-0.591471\pi\) | ||||
−0.283425 | + | 0.958994i | \(0.591471\pi\) | |||||||
\(264\) | −344821. | − | 395317.i | −0.304498 | − | 0.349088i | ||||
\(265\) | 1.30880e6 | 1.14488 | ||||||||
\(266\) | 281379.i | 0.243830i | ||||||||
\(267\) | −222187. | + | 193806.i | −0.190740 | + | 0.166376i | ||||
\(268\) | − | 322211.i | − | 0.274034i | ||||||
\(269\) | 702799.i | 0.592176i | 0.955161 | + | 0.296088i | \(0.0956821\pi\) | ||||
−0.955161 | + | 0.296088i | \(0.904318\pi\) | |||||||
\(270\) | 1.36146e6 | − | 894015.i | 1.13657 | − | 0.746337i | ||||
\(271\) | −1.07699e6 | −0.890817 | −0.445409 | − | 0.895327i | \(-0.646942\pi\) | ||||
−0.445409 | + | 0.895327i | \(0.646942\pi\) | |||||||
\(272\) | −170448. | −0.139692 | ||||||||
\(273\) | 2.16282e6 | + | 2.47954e6i | 1.75636 | + | 2.01356i | ||||
\(274\) | − | 535358.i | − | 0.430793i | ||||||
\(275\) | 4.43252e6 | 3.53443 | ||||||||
\(276\) | 578841. | + | 255607.i | 0.457390 | + | 0.201976i | ||||
\(277\) | −301096. | −0.235779 | −0.117890 | − | 0.993027i | \(-0.537613\pi\) | ||||
−0.117890 | + | 0.993027i | \(0.537613\pi\) | |||||||
\(278\) | 349141.i | 0.270950i | ||||||||
\(279\) | −132692. | + | 967949.i | −0.102055 | + | 0.744461i | ||||
\(280\) | −1.32373e6 | −1.00903 | ||||||||
\(281\) | −337816. | −0.255220 | −0.127610 | − | 0.991824i | \(-0.540731\pi\) | ||||
−0.127610 | + | 0.991824i | \(0.540731\pi\) | |||||||
\(282\) | −379504. | + | 331029.i | −0.284180 | + | 0.247881i | ||||
\(283\) | − | 1.49769e6i | − | 1.11162i | −0.831309 | − | 0.555811i | \(-0.812408\pi\) | ||
0.831309 | − | 0.555811i | \(-0.187592\pi\) | |||||||
\(284\) | 920699.i | 0.677363i | ||||||||
\(285\) | −402693. | − | 461662.i | −0.293671 | − | 0.336676i | ||||
\(286\) | 2.30716e6i | 1.66787i | ||||||||
\(287\) | −1.95025e6 | −1.39761 | ||||||||
\(288\) | −246526. | − | 33795.3i | −0.175139 | − | 0.0240090i | ||||
\(289\) | −976548. | −0.687779 | ||||||||
\(290\) | −930960. | −0.650034 | ||||||||
\(291\) | −423288. | − | 485274.i | −0.293024 | − | 0.335934i | ||||
\(292\) | 551073. | 0.378226 | ||||||||
\(293\) | 10578.7 | 0.00719883 | 0.00359942 | − | 0.999994i | \(-0.498854\pi\) | ||||
0.00359942 | + | 0.999994i | \(0.498854\pi\) | |||||||
\(294\) | −828592. | − | 949930.i | −0.559078 | − | 0.640949i | ||||
\(295\) | − | 413422.i | − | 0.276591i | ||||||
\(296\) | −750303. | −0.497745 | ||||||||
\(297\) | 1.09326e6 | + | 1.66488e6i | 0.719170 | + | 1.09519i | ||||
\(298\) | − | 1.08449e6i | − | 0.707432i | ||||||
\(299\) | −1.17956e6 | − | 2.52067e6i | −0.763029 | − | 1.63056i | ||||
\(300\) | 1.58449e6 | − | 1.38210e6i | 1.01645 | − | 0.886617i | ||||
\(301\) | −708069. | −0.450463 | ||||||||
\(302\) | − | 383556.i | − | 0.241998i | ||||||
\(303\) | −1.14795e6 | − | 1.31605e6i | −0.718317 | − | 0.823506i | ||||
\(304\) | 93591.7i | 0.0580836i | ||||||||
\(305\) | 2.23318e6i | 1.37459i | ||||||||
\(306\) | 641175. | + | 87896.0i | 0.391447 | + | 0.0536618i | ||||
\(307\) | 532300. | 0.322337 | 0.161169 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161169 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(308\) | − | 1.61874e6i | − | 0.972300i | ||||||
\(309\) | −946730. | − | 1.08537e6i | −0.564066 | − | 0.646667i | ||||
\(310\) | 1.72876e6i | 1.02172i | ||||||||
\(311\) | − | 1.02100e6i | − | 0.598586i | −0.954161 | − | 0.299293i | \(-0.903249\pi\) | ||
0.954161 | − | 0.299293i | \(-0.0967507\pi\) | |||||||
\(312\) | 719393. | + | 824739.i | 0.418388 | + | 0.479656i | ||||
\(313\) | − | 2.58546e6i | − | 1.49168i | −0.666123 | − | 0.745842i | \(-0.732047\pi\) | ||
0.666123 | − | 0.745842i | \(-0.267953\pi\) | |||||||
\(314\) | −2.16930e6 | −1.24164 | ||||||||
\(315\) | 4.97946e6 | + | 682614.i | 2.82752 | + | 0.387613i | ||||
\(316\) | 212112.i | 0.119495i | ||||||||
\(317\) | 1.88233e6i | 1.05208i | 0.850460 | + | 0.526039i | \(0.176324\pi\) | ||||
−0.850460 | + | 0.526039i | \(0.823676\pi\) | |||||||
\(318\) | 499047. | + | 572126.i | 0.276741 | + | 0.317266i | ||||
\(319\) | − | 1.13844e6i | − | 0.626372i | ||||||
\(320\) | −440296. | −0.240364 | ||||||||
\(321\) | −1.23801e6 | + | 1.07988e6i | −0.670597 | + | 0.584940i | ||||
\(322\) | 827596. | + | 1.76854e6i | 0.444814 | + | 0.950552i | ||||
\(323\) | − | 243417.i | − | 0.129821i | ||||||
\(324\) | 909929. | + | 254255.i | 0.481554 | + | 0.134557i | ||||
\(325\) | −9.24746e6 | −4.85639 | ||||||||
\(326\) | − | 2.14111e6i | − | 1.11582i | ||||||
\(327\) | 686962. | + | 787559.i | 0.355274 | + | 0.407299i | ||||
\(328\) | −648688. | −0.332929 | ||||||||
\(329\) | −1.55399e6 | −0.791515 | ||||||||
\(330\) | 2.31664e6 | + | 2.65589e6i | 1.17105 | + | 1.34253i | ||||
\(331\) | 2.81060e6 | 1.41003 | 0.705016 | − | 0.709191i | \(-0.250940\pi\) | ||||
0.705016 | + | 0.709191i | \(0.250940\pi\) | |||||||
\(332\) | −119212. | −0.0593576 | ||||||||
\(333\) | 2.82241e6 | + | 386912.i | 1.39479 | + | 0.191206i | ||||
\(334\) | −782246. | −0.383687 | ||||||||
\(335\) | 2.16474e6i | 1.05389i | ||||||||
\(336\) | −504738. | − | 578650.i | −0.243903 | − | 0.279620i | ||||
\(337\) | − | 1.28117e6i | − | 0.614516i | −0.951626 | − | 0.307258i | \(-0.900588\pi\) | ||
0.951626 | − | 0.307258i | \(-0.0994115\pi\) | |||||||
\(338\) | − | 3.32820e6i | − | 1.58459i | ||||||
\(339\) | 2.25511e6 | − | 1.96706e6i | 1.06578 | − | 0.929648i | ||||
\(340\) | 1.14514e6 | 0.537231 | ||||||||
\(341\) | −2.11403e6 | −0.984523 | ||||||||
\(342\) | 48262.9 | − | 352063.i | 0.0223125 | − | 0.162763i | ||||
\(343\) | − | 655886.i | − | 0.301018i | ||||||
\(344\) | −235516. | −0.107306 | ||||||||
\(345\) | −3.88888e6 | − | 1.71727e6i | −1.75904 | − | 0.776765i | ||||
\(346\) | −2.80343e6 | −1.25892 | ||||||||
\(347\) | 2.57596e6i | 1.14846i | 0.818694 | + | 0.574230i | \(0.194699\pi\) | ||||
−0.818694 | + | 0.574230i | \(0.805301\pi\) | |||||||
\(348\) | −354975. | − | 406957.i | −0.157126 | − | 0.180136i | ||||
\(349\) | −26106.9 | −0.0114734 | −0.00573669 | − | 0.999984i | \(-0.501826\pi\) | ||||
−0.00573669 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(350\) | 6.48817e6 | 2.83108 | ||||||||
\(351\) | −2.28084e6 | − | 3.47339e6i | −0.988159 | − | 1.50482i | ||||
\(352\) | − | 538422.i | − | 0.231615i | ||||||
\(353\) | − | 1.49802e6i | − | 0.639853i | −0.947442 | − | 0.319927i | \(-0.896342\pi\) | ||
0.947442 | − | 0.319927i | \(-0.103658\pi\) | |||||||
\(354\) | 180722. | − | 157638.i | 0.0766483 | − | 0.0668578i | ||||
\(355\) | − | 6.18561e6i | − | 2.60502i | ||||||
\(356\) | −302619. | −0.126553 | ||||||||
\(357\) | 1.31274e6 | + | 1.50498e6i | 0.545140 | + | 0.624970i | ||||
\(358\) | 1.84262e6 | 0.759851 | ||||||||
\(359\) | 2.55014e6 | 1.04430 | 0.522152 | − | 0.852852i | \(-0.325129\pi\) | ||||
0.522152 | + | 0.852852i | \(0.325129\pi\) | |||||||
\(360\) | 1.65626e6 | + | 227050.i | 0.673554 | + | 0.0923346i | ||||
\(361\) | 2.34244e6 | 0.946021 | ||||||||
\(362\) | −2.06879e6 | −0.829746 | ||||||||
\(363\) | −1.35586e6 | + | 1.18267e6i | −0.540067 | + | 0.471083i | ||||
\(364\) | 3.37714e6i | 1.33597i | ||||||||
\(365\) | −3.70232e6 | −1.45459 | ||||||||
\(366\) | −976203. | + | 851509.i | −0.380923 | + | 0.332267i | ||||
\(367\) | 4.09525e6i | 1.58714i | 0.608479 | + | 0.793570i | \(0.291780\pi\) | ||||
−0.608479 | + | 0.793570i | \(0.708220\pi\) | |||||||
\(368\) | 275273. | + | 588249.i | 0.105961 | + | 0.226434i | ||||
\(369\) | 2.44017e6 | + | 334512.i | 0.932940 | + | 0.127893i | ||||
\(370\) | 5.04082e6 | 1.91424 | ||||||||
\(371\) | 2.34274e6i | 0.883669i | ||||||||
\(372\) | −755703. | + | 659174.i | −0.283135 | + | 0.246969i | ||||
\(373\) | − | 1.56014e6i | − | 0.580620i | −0.956933 | − | 0.290310i | \(-0.906242\pi\) | ||
0.956933 | − | 0.290310i | \(-0.0937584\pi\) | |||||||
\(374\) | 1.40035e6i | 0.517675i | ||||||||
\(375\) | −6.69904e6 | + | 5.84335e6i | −2.46000 | + | 2.14577i | ||||
\(376\) | −516886. | −0.188549 | ||||||||
\(377\) | 2.37509e6i | 0.860652i | ||||||||
\(378\) | 1.60027e6 | + | 2.43699e6i | 0.576056 | + | 0.877250i | ||||
\(379\) | 4.72690e6i | 1.69036i | 0.534485 | + | 0.845178i | \(0.320506\pi\) | ||||
−0.534485 | + | 0.845178i | \(0.679494\pi\) | |||||||
\(380\) | − | 628785.i | − | 0.223379i | ||||||
\(381\) | −1.53058e6 | + | 1.33507e6i | −0.540185 | + | 0.471185i | ||||
\(382\) | − | 1.80540e6i | − | 0.633015i | ||||||
\(383\) | 3.06184e6 | 1.06656 | 0.533281 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533281 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(384\) | −167885. | − | 192470.i | −0.0581009 | − | 0.0666092i | ||||
\(385\) | 1.08753e7i | 3.73930i | ||||||||
\(386\) | 1.44214e6i | 0.492650i | ||||||||
\(387\) | 885940. | + | 121450.i | 0.300696 | + | 0.0412211i | ||||
\(388\) | − | 660944.i | − | 0.222887i | ||||||
\(389\) | 5.71202e6 | 1.91389 | 0.956943 | − | 0.290276i | \(-0.0937471\pi\) | ||||
0.956943 | + | 0.290276i | \(0.0937471\pi\) | |||||||
\(390\) | −4.83316e6 | − | 5.54092e6i | −1.60905 | − | 1.84468i | ||||
\(391\) | −715941. | − | 1.52994e6i | −0.236829 | − | 0.506095i | ||||
\(392\) | − | 1.29381e6i | − | 0.425260i | ||||||
\(393\) | 1.34806e6 | + | 1.54547e6i | 0.440278 | + | 0.504752i | ||||
\(394\) | −967211. | −0.313892 | ||||||||
\(395\) | − | 1.42505e6i | − | 0.459556i | ||||||
\(396\) | −277651. | + | 2.02538e6i | −0.0889736 | + | 0.649035i | ||||
\(397\) | 2.66168e6 | 0.847578 | 0.423789 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423789 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(398\) | 1.25904e6 | 0.398411 | ||||||||
\(399\) | 826368. | − | 720813.i | 0.259861 | − | 0.226668i | ||||
\(400\) | 2.15808e6 | 0.674400 | ||||||||
\(401\) | 1.16925e6 | 0.363117 | 0.181559 | − | 0.983380i | \(-0.441886\pi\) | ||||
0.181559 | + | 0.983380i | \(0.441886\pi\) | |||||||
\(402\) | −946287. | + | 825415.i | −0.292050 | + | 0.254746i | ||||
\(403\) | 4.41046e6 | 1.35276 | ||||||||
\(404\) | − | 1.79247e6i | − | 0.546384i | ||||||
\(405\) | −6.11326e6 | − | 1.70818e6i | −1.85197 | − | 0.517484i | ||||
\(406\) | − | 1.66640e6i | − | 0.501724i | ||||||
\(407\) | 6.16424e6i | 1.84456i | ||||||||
\(408\) | 436641. | + | 500582.i | 0.129860 | + | 0.148876i | ||||
\(409\) | −2.01066e6 | −0.594333 | −0.297166 | − | 0.954826i | \(-0.596042\pi\) | ||||
−0.297166 | + | 0.954826i | \(0.596042\pi\) | |||||||
\(410\) | 4.35814e6 | 1.28039 | ||||||||
\(411\) | −1.57227e6 | + | 1.37144e6i | −0.459116 | + | 0.400471i | ||||
\(412\) | − | 1.47827e6i | − | 0.429054i | ||||||
\(413\) | 740019. | 0.213485 | ||||||||
\(414\) | −732149. | − | 2.35476e6i | −0.209942 | − | 0.675222i | ||||
\(415\) | 800915. | 0.228279 | ||||||||
\(416\) | 1.12330e6i | 0.318245i | ||||||||
\(417\) | 1.02538e6 | − | 894401.i | 0.288764 | − | 0.251879i | ||||
\(418\) | 768918. | 0.215248 | ||||||||
\(419\) | −2.01268e6 | −0.560068 | −0.280034 | − | 0.959990i | \(-0.590346\pi\) | ||||
−0.280034 | + | 0.959990i | \(0.590346\pi\) | |||||||
\(420\) | 3.39102e6 | + | 3.88760e6i | 0.938010 | + | 1.07537i | ||||
\(421\) | − | 5.38411e6i | − | 1.48050i | −0.672332 | − | 0.740250i | \(-0.734707\pi\) | ||
0.672332 | − | 0.740250i | \(-0.265293\pi\) | |||||||
\(422\) | − | 856490.i | − | 0.234121i | ||||||
\(423\) | 1.94437e6 | + | 266545.i | 0.528356 | + | 0.0724302i | ||||
\(424\) | 779238.i | 0.210502i | ||||||||
\(425\) | −5.61282e6 | −1.50733 | ||||||||
\(426\) | 2.70396e6 | − | 2.35857e6i | 0.721898 | − | 0.629687i | ||||
\(427\) | −3.99735e6 | −1.06097 | ||||||||
\(428\) | −1.68617e6 | −0.444931 | ||||||||
\(429\) | 6.77579e6 | − | 5.91029e6i | 1.77753 | − | 1.55048i | ||||
\(430\) | 1.58229e6 | 0.412681 | ||||||||
\(431\) | −1.98569e6 | −0.514893 | −0.257447 | − | 0.966293i | \(-0.582881\pi\) | ||||
−0.257447 | + | 0.966293i | \(0.582881\pi\) | |||||||
\(432\) | 532279. | + | 810585.i | 0.137224 | + | 0.208973i | ||||
\(433\) | − | 3.71038e6i | − | 0.951041i | −0.879705 | − | 0.475520i | \(-0.842260\pi\) | ||
0.879705 | − | 0.475520i | \(-0.157740\pi\) | |||||||
\(434\) | −3.09445e6 | −0.788604 | ||||||||
\(435\) | 2.38486e6 | + | 2.73409e6i | 0.604281 | + | 0.692771i | ||||
\(436\) | 1.07266e6i | 0.270237i | ||||||||
\(437\) | −840076. | + | 393117.i | −0.210433 | + | 0.0984731i | ||||
\(438\) | −1.41169e6 | − | 1.61842e6i | −0.351605 | − | 0.403093i | ||||
\(439\) | 3.27132e6 | 0.810143 | 0.405071 | − | 0.914285i | \(-0.367247\pi\) | ||||
0.405071 | + | 0.914285i | \(0.367247\pi\) | |||||||
\(440\) | 3.61733e6i | 0.890751i | ||||||||
\(441\) | −667184. | + | 4.86691e6i | −0.163361 | + | 1.19167i | ||||
\(442\) | − | 2.92151e6i | − | 0.711299i | ||||||
\(443\) | 505087.i | 0.122280i | 0.998129 | + | 0.0611402i | \(0.0194737\pi\) | ||||
−0.998129 | + | 0.0611402i | \(0.980526\pi\) | |||||||
\(444\) | 1.92206e6 | + | 2.20353e6i | 0.462712 | + | 0.530470i | ||||
\(445\) | 2.03311e6 | 0.486700 | ||||||||
\(446\) | − | 640392.i | − | 0.152443i | ||||||
\(447\) | −3.18498e6 | + | 2.77816e6i | −0.753943 | + | 0.657639i | ||||
\(448\) | − | 788123.i | − | 0.185524i | ||||||
\(449\) | − | 5.18927e6i | − | 1.21476i | −0.794412 | − | 0.607380i | \(-0.792221\pi\) | ||
0.794412 | − | 0.607380i | \(-0.207779\pi\) | |||||||
\(450\) | −8.11804e6 | − | 1.11287e6i | −1.88982 | − | 0.259067i | ||||
\(451\) | 5.32941e6i | 1.23378i | ||||||||
\(452\) | 3.07147e6 | 0.707131 | ||||||||
\(453\) | −1.12645e6 | + | 982563.i | −0.257908 | + | 0.224965i | ||||
\(454\) | 1.68095e6i | 0.382750i | ||||||||
\(455\) | − | 2.26889e7i | − | 5.13790i | ||||||
\(456\) | 274865. | − | 239756.i | 0.0619024 | − | 0.0539954i | ||||
\(457\) | 2.63136e6i | 0.589373i | 0.955594 | + | 0.294686i | \(0.0952152\pi\) | ||||
−0.955594 | + | 0.294686i | \(0.904785\pi\) | |||||||
\(458\) | 401946. | 0.0895372 | ||||||||
\(459\) | −1.38437e6 | − | 2.10820e6i | −0.306705 | − | 0.467068i | ||||
\(460\) | −1.84939e6 | − | 3.95208e6i | −0.407506 | − | 0.870826i | ||||
\(461\) | 1.70117e6i | 0.372817i | 0.982472 | + | 0.186408i | \(0.0596848\pi\) | ||||
−0.982472 | + | 0.186408i | \(0.940315\pi\) | |||||||
\(462\) | −4.75400e6 | + | 4.14676e6i | −1.03623 | + | 0.903865i | ||||
\(463\) | 7.14600e6 | 1.54921 | 0.774605 | − | 0.632445i | \(-0.217949\pi\) | ||||
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(464\) | − | 554276.i | − | 0.119517i | ||||||
\(465\) | 5.07710e6 | − | 4.42859e6i | 1.08889 | − | 0.949802i | ||||
\(466\) | −5.39318e6 | −1.15048 | ||||||||
\(467\) | −6.75731e6 | −1.43378 | −0.716889 | − | 0.697187i | \(-0.754435\pi\) | ||||
−0.716889 | + | 0.697187i | \(0.754435\pi\) | |||||||
\(468\) | 579256. | − | 4.22550e6i | 0.122252 | − | 0.891792i | ||||
\(469\) | −3.87485e6 | −0.813436 | ||||||||
\(470\) | 3.47264e6 | 0.725128 | ||||||||
\(471\) | 5.55714e6 | + | 6.37092e6i | 1.15425 | + | 1.32328i | ||||
\(472\) | 246144. | 0.0508550 | ||||||||
\(473\) | 1.93492e6i | 0.397659i | ||||||||
\(474\) | 622943. | − | 543372.i | 0.127351 | − | 0.111084i | ||||
\(475\) | 3.08195e6i | 0.626745i | ||||||||
\(476\) | 2.04978e6i | 0.414658i | ||||||||
\(477\) | 401833. | − | 2.93125e6i | 0.0808630 | − | 0.589871i | ||||
\(478\) | −2.15690e6 | −0.431778 | ||||||||
\(479\) | 6.70521e6 | 1.33528 | 0.667642 | − | 0.744483i | \(-0.267304\pi\) | ||||
0.667642 | + | 0.744483i | \(0.267304\pi\) | |||||||
\(480\) | 1.12791e6 | + | 1.29308e6i | 0.223446 | + | 0.256167i | ||||
\(481\) | − | 1.28603e7i | − | 2.53448i | ||||||
\(482\) | −6.05933e6 | −1.18797 | ||||||||
\(483\) | 3.07388e6 | − | 6.96103e6i | 0.599541 | − | 1.35771i | ||||
\(484\) | −1.84668e6 | −0.358327 | ||||||||
\(485\) | 4.44048e6i | 0.857186i | ||||||||
\(486\) | −1.58427e6 | − | 3.32366e6i | −0.304256 | − | 0.638301i | ||||
\(487\) | −9.22373e6 | −1.76232 | −0.881159 | − | 0.472820i | \(-0.843236\pi\) | ||||
−0.881159 | + | 0.472820i | \(0.843236\pi\) | |||||||
\(488\) | −1.32959e6 | −0.252737 | ||||||||
\(489\) | −6.28811e6 | + | 5.48491e6i | −1.18918 | + | 1.03728i | ||||
\(490\) | 8.69230e6i | 1.63548i | ||||||||
\(491\) | − | 2.94821e6i | − | 0.551893i | −0.961173 | − | 0.275946i | \(-0.911009\pi\) | ||
0.961173 | − | 0.275946i | \(-0.0889912\pi\) | |||||||
\(492\) | 1.66176e6 | + | 1.90510e6i | 0.309496 | + | 0.354818i | ||||
\(493\) | 1.44158e6i | 0.267130i | ||||||||
\(494\) | −1.60418e6 | −0.295757 | ||||||||
\(495\) | 1.86537e6 | − | 1.36073e7i | 0.342177 | − | 2.49608i | ||||
\(496\) | −1.02927e6 | −0.187856 | ||||||||
\(497\) | 1.10721e7 | 2.01067 | ||||||||
\(498\) | 305389. | + | 350109.i | 0.0551797 | + | 0.0632601i | ||||
\(499\) | 1.69625e6 | 0.304958 | 0.152479 | − | 0.988307i | \(-0.451274\pi\) | ||||
0.152479 | + | 0.988307i | \(0.451274\pi\) | |||||||
\(500\) | −9.12411e6 | −1.63217 | ||||||||
\(501\) | 2.00390e6 | + | 2.29734e6i | 0.356682 | + | 0.408913i | ||||
\(502\) | − | 121247.i | − | 0.0214740i | ||||||
\(503\) | 3.24172e6 | 0.571288 | 0.285644 | − | 0.958336i | \(-0.407793\pi\) | ||||
0.285644 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(504\) | −406415. | + | 2.96468e6i | −0.0712679 | + | 0.519878i | ||||
\(505\) | 1.20425e7i | 2.10130i | ||||||||
\(506\) | 4.83286e6 | − | 2.26155e6i | 0.839127 | − | 0.392673i | ||||
\(507\) | −9.77443e6 | + | 8.52591e6i | −1.68877 | + | 1.47306i | ||||
\(508\) | −2.08465e6 | −0.358405 | ||||||||
\(509\) | − | 3.32600e6i | − | 0.569021i | −0.958673 | − | 0.284511i | \(-0.908169\pi\) | ||
0.958673 | − | 0.284511i | \(-0.0918311\pi\) | |||||||
\(510\) | −2.93352e6 | − | 3.36310e6i | −0.499418 | − | 0.572552i | ||||
\(511\) | − | 6.62709e6i | − | 1.12272i | ||||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | −1.15759e6 | + | 760146.i | −0.194206 | + | 0.127527i | ||||
\(514\) | 6.17516e6 | 1.03096 | ||||||||
\(515\) | 9.93161e6i | 1.65007i | ||||||||
\(516\) | 603326. | + | 691677.i | 0.0997535 | + | 0.114361i | ||||
\(517\) | 4.24656e6i | 0.698733i | ||||||||
\(518\) | 9.02300e6i | 1.47750i | ||||||||
\(519\) | 7.18159e6 | + | 8.23325e6i | 1.17031 | + | 1.34169i | ||||
\(520\) | − | 7.54675e6i | − | 1.22392i | ||||||
\(521\) | −944343. | −0.152418 | −0.0762089 | − | 0.997092i | \(-0.524282\pi\) | ||||
−0.0762089 | + | 0.997092i | \(0.524282\pi\) | |||||||
\(522\) | −285826. | + | 2.08502e6i | −0.0459119 | + | 0.334914i | ||||
\(523\) | − | 759859.i | − | 0.121473i | −0.998154 | − | 0.0607364i | \(-0.980655\pi\) | ||
0.998154 | − | 0.0607364i | \(-0.0193449\pi\) | |||||||
\(524\) | 2.10493e6i | 0.334895i | ||||||||
\(525\) | −1.66209e7 | − | 1.90548e7i | −2.63181 | − | 3.01721i | ||||
\(526\) | 2.54342e6i | 0.400824i | ||||||||
\(527\) | 2.67696e6 | 0.419871 | ||||||||
\(528\) | −1.58127e6 | + | 1.37929e6i | −0.246843 | + | 0.215313i | ||||
\(529\) | −4.12386e6 | + | 4.94169e6i | −0.640715 | + | 0.767779i | ||||
\(530\) | − | 5.23522e6i | − | 0.809553i | ||||||
\(531\) | −925917. | − | 126930.i | −0.142507 | − | 0.0195357i | ||||
\(532\) | 1.12552e6 | 0.172414 | ||||||||
\(533\) | − | 1.11186e7i | − | 1.69525i | ||||||
\(534\) | 775226. | + | 888748.i | 0.117645 | + | 0.134873i | ||||
\(535\) | 1.13284e7 | 1.71113 | ||||||||
\(536\) | −1.28885e6 | −0.193771 | ||||||||
\(537\) | −4.72028e6 | − | 5.41151e6i | −0.706369 | − | 0.809809i | ||||
\(538\) | 2.81120e6 | 0.418731 | ||||||||
\(539\) | −1.06295e7 | −1.57594 | ||||||||
\(540\) | −3.57606e6 | − | 5.44583e6i | −0.527740 | − | 0.803673i | ||||
\(541\) | −6.37429e6 | −0.936350 | −0.468175 | − | 0.883636i | \(-0.655088\pi\) | ||||
−0.468175 | + | 0.883636i | \(0.655088\pi\) | |||||||
\(542\) | 4.30796e6i | 0.629903i | ||||||||
\(543\) | 5.29966e6 | + | 6.07573e6i | 0.771344 | + | 0.884299i | ||||
\(544\) | 681794.i | 0.0987770i | ||||||||
\(545\) | − | 7.20653e6i | − | 1.03929i | ||||||
\(546\) | 9.91816e6 | − | 8.65128e6i | 1.42380 | − | 1.24193i | ||||
\(547\) | 7.43194e6 | 1.06202 | 0.531012 | − | 0.847364i | \(-0.321812\pi\) | ||||
0.531012 | + | 0.847364i | \(0.321812\pi\) | |||||||
\(548\) | −2.14143e6 | −0.304616 | ||||||||
\(549\) | 5.00151e6 | + | 685637.i | 0.708224 | + | 0.0970875i | ||||
\(550\) | − | 1.77301e7i | − | 2.49922i | ||||||
\(551\) | 791559. | 0.111072 | ||||||||
\(552\) | 1.02243e6 | − | 2.31536e6i | 0.142819 | − | 0.323424i | ||||
\(553\) | 2.55082e6 | 0.354705 | ||||||||
\(554\) | 1.20438e6i | 0.166721i | ||||||||
\(555\) | −1.29132e7 | − | 1.48042e7i | −1.77951 | − | 2.04010i | ||||
\(556\) | 1.39656e6 | 0.191590 | ||||||||
\(557\) | −6.53039e6 | −0.891869 | −0.445935 | − | 0.895066i | \(-0.647129\pi\) | ||||
−0.445935 | + | 0.895066i | \(0.647129\pi\) | |||||||
\(558\) | 3.87180e6 | + | 530768.i | 0.526413 | + | 0.0721638i | ||||
\(559\) | − | 4.03679e6i | − | 0.546394i | ||||||
\(560\) | 5.29492e6i | 0.713492i | ||||||||
\(561\) | 4.11262e6 | − | 3.58730e6i | 0.551710 | − | 0.481239i | ||||
\(562\) | 1.35126e6i | 0.180468i | ||||||||
\(563\) | −8.07931e6 | −1.07425 | −0.537123 | − | 0.843504i | \(-0.680489\pi\) | ||||
−0.537123 | + | 0.843504i | \(0.680489\pi\) | |||||||
\(564\) | 1.32412e6 | + | 1.51802e6i | 0.175278 | + | 0.200946i | ||||
\(565\) | −2.06353e7 | −2.71951 | ||||||||
\(566\) | −5.99078e6 | −0.786035 | ||||||||
\(567\) | 3.05762e6 | − | 1.09426e7i | 0.399416 | − | 1.42943i | ||||
\(568\) | 3.68280e6 | 0.478968 | ||||||||
\(569\) | 8.11855e6 | 1.05123 | 0.525615 | − | 0.850723i | \(-0.323835\pi\) | ||||
0.525615 | + | 0.850723i | \(0.323835\pi\) | |||||||
\(570\) | −1.84665e6 | + | 1.61077e6i | −0.238066 | + | 0.207657i | ||||
\(571\) | 1.43018e7i | 1.83569i | 0.396937 | + | 0.917846i | \(0.370073\pi\) | ||||
−0.396937 | + | 0.917846i | \(0.629927\pi\) | |||||||
\(572\) | 9.22864e6 | 1.17936 | ||||||||
\(573\) | −5.30218e6 | + | 4.62492e6i | −0.674634 | + | 0.588461i | ||||
\(574\) | 7.80100e6i | 0.988259i | ||||||||
\(575\) | 9.06467e6 | + | 1.93709e7i | 1.14336 | + | 2.44331i | ||||
\(576\) | −135181. | + | 986105.i | −0.0169769 | + | 0.123842i | ||||
\(577\) | 1.23884e7 | 1.54908 | 0.774541 | − | 0.632524i | \(-0.217981\pi\) | ||||
0.774541 | + | 0.632524i | \(0.217981\pi\) | |||||||
\(578\) | 3.90619e6i | 0.486333i | ||||||||
\(579\) | 4.23534e6 | − | 3.69435e6i | 0.525040 | − | 0.457975i | ||||
\(580\) | 3.72384e6i | 0.459643i | ||||||||
\(581\) | 1.43363e6i | 0.176196i | ||||||||
\(582\) | −1.94109e6 | + | 1.69315e6i | −0.237541 | + | 0.207199i | ||||
\(583\) | 6.40196e6 | 0.780084 | ||||||||
\(584\) | − | 2.20429e6i | − | 0.267446i | ||||||
\(585\) | −3.89167e6 | + | 2.83885e7i | −0.470160 | + | 3.42968i | ||||
\(586\) | − | 42314.7i | − | 0.00509034i | ||||||
\(587\) | − | 7.01309e6i | − | 0.840068i | −0.907508 | − | 0.420034i | \(-0.862018\pi\) | ||
0.907508 | − | 0.420034i | \(-0.137982\pi\) | |||||||
\(588\) | −3.79972e6 | + | 3.31437e6i | −0.453219 | + | 0.395328i | ||||
\(589\) | − | 1.46989e6i | − | 0.174581i | ||||||
\(590\) | −1.65369e6 | −0.195580 | ||||||||
\(591\) | 2.47772e6 | + | 2.84056e6i | 0.291799 | + | 0.334530i | ||||
\(592\) | 3.00121e6i | 0.351959i | ||||||||
\(593\) | − | 374140.i | − | 0.0436915i | −0.999761 | − | 0.0218458i | \(-0.993046\pi\) | ||
0.999761 | − | 0.0218458i | \(-0.00695427\pi\) | |||||||
\(594\) | 6.65950e6 | − | 4.37303e6i | 0.774418 | − | 0.508530i | ||||
\(595\) | − | 1.37712e7i | − | 1.59470i | ||||||
\(596\) | −4.33796e6 | −0.500230 | ||||||||
\(597\) | −3.22530e6 | − | 3.69761e6i | −0.370369 | − | 0.424605i | ||||
\(598\) | −1.00827e7 | + | 4.71823e6i | −1.15298 | + | 0.539543i | ||||
\(599\) | − | 2.30047e6i | − | 0.261969i | −0.991384 | − | 0.130984i | \(-0.958186\pi\) | ||
0.991384 | − | 0.130984i | \(-0.0418137\pi\) | |||||||
\(600\) | −5.52839e6 | − | 6.33796e6i | −0.626933 | − | 0.718740i | ||||
\(601\) | −8.31550e6 | −0.939079 | −0.469539 | − | 0.882912i | \(-0.655580\pi\) | ||||
−0.469539 | + | 0.882912i | \(0.655580\pi\) | |||||||
\(602\) | 2.83227e6i | 0.318525i | ||||||||
\(603\) | 4.84824e6 | + | 664625.i | 0.542989 | + | 0.0744361i | ||||
\(604\) | −1.53422e6 | −0.171118 | ||||||||
\(605\) | 1.24067e7 | 1.37806 | ||||||||
\(606\) | −5.26421e6 | + | 4.59180e6i | −0.582307 | + | 0.507927i | ||||
\(607\) | 1.58877e7 | 1.75021 | 0.875103 | − | 0.483937i | \(-0.160794\pi\) | ||||
0.875103 | + | 0.483937i | \(0.160794\pi\) | |||||||
\(608\) | 374367. | 0.0410713 | ||||||||
\(609\) | −4.89398e6 | + | 4.26886e6i | −0.534711 | + | 0.466411i | ||||
\(610\) | 8.93271e6 | 0.971983 | ||||||||
\(611\) | − | 8.85950e6i | − | 0.960077i | ||||||
\(612\) | 351584. | − | 2.56470e6i | 0.0379446 | − | 0.276795i | ||||
\(613\) | 1.65539e7i | 1.77930i | 0.456648 | + | 0.889648i | \(0.349050\pi\) | ||||
−0.456648 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(614\) | − | 2.12920e6i | − | 0.227927i | ||||||
\(615\) | −1.11643e7 | − | 1.27992e7i | −1.19027 | − | 1.36457i | ||||
\(616\) | −6.47496e6 | −0.687520 | ||||||||
\(617\) | 2.54420e6 | 0.269053 | 0.134527 | − | 0.990910i | \(-0.457049\pi\) | ||||
0.134527 | + | 0.990910i | \(0.457049\pi\) | |||||||
\(618\) | −4.34147e6 | + | 3.78692e6i | −0.457262 | + | 0.398855i | ||||
\(619\) | − | 3.65132e6i | − | 0.383021i | −0.981491 | − | 0.191511i | \(-0.938661\pi\) | ||
0.981491 | − | 0.191511i | \(-0.0613387\pi\) | |||||||
\(620\) | 6.91503e6 | 0.722462 | ||||||||
\(621\) | −5.04003e6 | + | 8.18245e6i | −0.524450 | + | 0.851441i | ||||
\(622\) | −4.08401e6 | −0.423264 | ||||||||
\(623\) | 3.63924e6i | 0.375657i | ||||||||
\(624\) | 3.29896e6 | − | 2.87757e6i | 0.339168 | − | 0.295845i | ||||
\(625\) | 3.49555e7 | 3.57945 | ||||||||
\(626\) | −1.03418e7 | −1.05478 | ||||||||
\(627\) | −1.96975e6 | − | 2.25820e6i | −0.200098 | − | 0.229400i | ||||
\(628\) | 8.67721e6i | 0.877973i | ||||||||
\(629\) | − | 7.80566e6i | − | 0.786653i | ||||||
\(630\) | 2.73046e6 | − | 1.99179e7i | 0.274084 | − | 1.99936i | ||||
\(631\) | − | 1.41202e7i | − | 1.41178i | −0.708319 | − | 0.705892i | \(-0.750546\pi\) | ||
0.708319 | − | 0.705892i | \(-0.249454\pi\) | |||||||
\(632\) | 848450. | 0.0844955 | ||||||||
\(633\) | −2.51538e6 | + | 2.19409e6i | −0.249514 | + | 0.217643i | ||||
\(634\) | 7.52933e6 | 0.743932 | ||||||||
\(635\) | 1.40055e7 | 1.37836 | ||||||||
\(636\) | 2.28851e6 | − | 1.99619e6i | 0.224341 | − | 0.195685i | ||||
\(637\) | 2.21761e7 | 2.16539 | ||||||||
\(638\) | −4.55375e6 | −0.442912 | ||||||||
\(639\) | −1.38535e7 | − | 1.89912e6i | −1.34217 | − | 0.183993i | ||||
\(640\) | 1.76118e6i | 0.169963i | ||||||||
\(641\) | 1.70992e7 | 1.64373 | 0.821865 | − | 0.569682i | \(-0.192934\pi\) | ||||
0.821865 | + | 0.569682i | \(0.192934\pi\) | |||||||
\(642\) | 4.31950e6 | + | 4.95204e6i | 0.413615 | + | 0.474184i | ||||
\(643\) | 8.69003e6i | 0.828884i | 0.910076 | + | 0.414442i | \(0.136023\pi\) | ||||
−0.910076 | + | 0.414442i | \(0.863977\pi\) | |||||||
\(644\) | 7.07417e6 | − | 3.31038e6i | 0.672142 | − | 0.314531i | ||||
\(645\) | −4.05338e6 | − | 4.64695e6i | −0.383635 | − | 0.439814i | ||||
\(646\) | −973667. | −0.0917971 | ||||||||
\(647\) | 1.20680e7i | 1.13338i | 0.823932 | + | 0.566689i | \(0.191776\pi\) | ||||
−0.823932 | + | 0.566689i | \(0.808224\pi\) | |||||||
\(648\) | 1.01702e6 | − | 3.63972e6i | 0.0951463 | − | 0.340510i | ||||
\(649\) | − | 2.02224e6i | − | 0.188460i | ||||||
\(650\) | 3.69898e7i | 3.43399i | ||||||||
\(651\) | 7.92711e6 | + | 9.08794e6i | 0.733098 | + | 0.840452i | ||||
\(652\) | −8.56442e6 | −0.789004 | ||||||||
\(653\) | − | 8.02078e6i | − | 0.736094i | −0.929807 | − | 0.368047i | \(-0.880026\pi\) | ||
0.929807 | − | 0.368047i | \(-0.119974\pi\) | |||||||
\(654\) | 3.15024e6 | − | 2.74785e6i | 0.288004 | − | 0.251216i | ||||
\(655\) | − | 1.41417e7i | − | 1.28795i | ||||||
\(656\) | 2.59475e6i | 0.235416i | ||||||||
\(657\) | −1.13670e6 | + | 8.29186e6i | −0.102738 | + | 0.749443i | ||||
\(658\) | 6.21597e6i | 0.559685i | ||||||||
\(659\) | −1.74345e7 | −1.56386 | −0.781928 | − | 0.623369i | \(-0.785763\pi\) | ||||
−0.781928 | + | 0.623369i | \(0.785763\pi\) | |||||||
\(660\) | 1.06236e7 | − | 9.26658e6i | 0.949315 | − | 0.828056i | ||||
\(661\) | − | 1.41203e6i | − | 0.125702i | −0.998023 | − | 0.0628509i | \(-0.979981\pi\) | ||
0.998023 | − | 0.0628509i | \(-0.0200193\pi\) | |||||||
\(662\) | − | 1.12424e7i | − | 0.997044i | ||||||
\(663\) | −8.58005e6 | + | 7.48409e6i | −0.758065 | + | 0.661234i | ||||
\(664\) | 476850.i | 0.0419721i | ||||||||
\(665\) | −7.56165e6 | −0.663075 | ||||||||
\(666\) | 1.54765e6 | − | 1.12896e7i | 0.135203 | − | 0.986267i | ||||
\(667\) | 4.97516e6 | − | 2.32815e6i | 0.433005 | − | 0.202626i | ||||
\(668\) | 3.12899e6i | 0.271308i | ||||||||
\(669\) | −1.88074e6 | + | 1.64050e6i | −0.162466 | + | 0.141714i | ||||
\(670\) | 8.65897e6 | 0.745211 | ||||||||
\(671\) | 1.09235e7i | 0.936601i | ||||||||
\(672\) | −2.31460e6 | + | 2.01895e6i | −0.197721 | + | 0.172466i | ||||
\(673\) | −9.62733e6 | −0.819347 | −0.409674 | − | 0.912232i | \(-0.634357\pi\) | ||||
−0.409674 | + | 0.912232i | \(0.634357\pi\) | |||||||
\(674\) | −5.12470e6 | −0.434529 | ||||||||
\(675\) | 1.75278e7 | + | 2.66923e7i | 1.48070 | + | 2.25490i | ||||
\(676\) | −1.33128e7 | −1.12048 | ||||||||
\(677\) | −8.02836e6 | −0.673217 | −0.336609 | − | 0.941645i | \(-0.609280\pi\) | ||||
−0.336609 | + | 0.941645i | \(0.609280\pi\) | |||||||
\(678\) | −7.86824e6 | − | 9.02045e6i | −0.657360 | − | 0.753623i | ||||
\(679\) | −7.94838e6 | −0.661614 | ||||||||
\(680\) | − | 4.58056e6i | − | 0.379880i | ||||||
\(681\) | 4.93671e6 | − | 4.30613e6i | 0.407915 | − | 0.355811i | ||||
\(682\) | 8.45614e6i | 0.696163i | ||||||||
\(683\) | − | 7.90761e6i | − | 0.648625i | −0.945950 | − | 0.324312i | \(-0.894867\pi\) | ||
0.945950 | − | 0.324312i | \(-0.105133\pi\) | |||||||
\(684\) | −1.40825e6 | − | 193051.i | −0.115091 | − | 0.0157773i | ||||
\(685\) | 1.43870e7 | 1.17150 | ||||||||
\(686\) | −2.62354e6 | −0.212852 | ||||||||
\(687\) | −1.02967e6 | − | 1.18045e6i | −0.0832352 | − | 0.0954240i | ||||
\(688\) | 942065.i | 0.0758770i | ||||||||
\(689\) | −1.33563e7 | −1.07186 | ||||||||
\(690\) | −6.86906e6 | + | 1.55555e7i | −0.549256 | + | 1.24383i | ||||
\(691\) | −3.74097e6 | −0.298050 | −0.149025 | − | 0.988833i | \(-0.547613\pi\) | ||||
−0.149025 | + | 0.988833i | \(0.547613\pi\) | |||||||
\(692\) | 1.12137e7i | 0.890192i | ||||||||
\(693\) | 2.43568e7 | + | 3.33898e6i | 1.92658 | + | 0.264107i | ||||
\(694\) | 1.03039e7 | 0.812084 | ||||||||
\(695\) | −9.38266e6 | −0.736824 | ||||||||
\(696\) | −1.62783e6 | + | 1.41990e6i | −0.127375 | + | 0.111105i | ||||
\(697\) | − | 6.74853e6i | − | 0.526171i | ||||||
\(698\) | 104427.i | 0.00811290i | ||||||||
\(699\) | 1.38158e7 | + | 1.58390e7i | 1.06951 | + | 1.22612i | ||||
\(700\) | − | 2.59527e7i | − | 2.00187i | ||||||
\(701\) | 9.94431e6 | 0.764328 | 0.382164 | − | 0.924095i | \(-0.375179\pi\) | ||||
0.382164 | + | 0.924095i | \(0.375179\pi\) | |||||||
\(702\) | −1.38936e7 | + | 9.12335e6i | −1.06407 | + | 0.698734i | ||||
\(703\) | −4.28602e6 | −0.327089 | ||||||||
\(704\) | −2.15369e6 | −0.163776 | ||||||||
\(705\) | −8.89592e6 | − | 1.01986e7i | −0.674090 | − | 0.772803i | ||||
\(706\) | −5.99207e6 | −0.452445 | ||||||||
\(707\) | −2.15559e7 | −1.62187 | ||||||||
\(708\) | −630551. | − | 722888.i | −0.0472756 | − | 0.0541986i | ||||
\(709\) | 1.32750e7i | 0.991786i | 0.868384 | + | 0.495893i | \(0.165159\pi\) | ||||
−0.868384 | + | 0.495893i | \(0.834841\pi\) | |||||||
\(710\) | −2.47424e7 | −1.84203 | ||||||||
\(711\) | −3.19161e6 | − | 437524.i | −0.236775 | − | 0.0324585i | ||||
\(712\) | 1.21048e6i | 0.0894863i | ||||||||
\(713\) | −4.32328e6 | − | 9.23869e6i | −0.318485 | − | 0.680591i | ||||
\(714\) | 6.01990e6 | − | 5.25096e6i | 0.441920 | − | 0.385472i | ||||
\(715\) | −6.20016e7 | −4.53563 | ||||||||
\(716\) | − | 7.37049e6i | − | 0.537296i | ||||||
\(717\) | 5.52537e6 | + | 6.33449e6i | 0.401387 | + | 0.460166i | ||||
\(718\) | − | 1.02005e7i | − | 0.738435i | ||||||
\(719\) | 1.73762e7i | 1.25352i | 0.779212 | + | 0.626760i | \(0.215620\pi\) | ||||
−0.779212 | + | 0.626760i | \(0.784380\pi\) | |||||||
\(720\) | 908199. | − | 6.62504e6i | 0.0652904 | − | 0.476274i | ||||
\(721\) | −1.77774e7 | −1.27359 | ||||||||
\(722\) | − | 9.36976e6i | − | 0.668938i | ||||||
\(723\) | 1.55223e7 | + | 1.77954e7i | 1.10436 | + | 1.26608i | ||||
\(724\) | 8.27516e6i | 0.586719i | ||||||||
\(725\) | − | 1.82521e7i | − | 1.28964i | ||||||
\(726\) | 4.73068e6 | + | 5.42344e6i | 0.333106 | + | 0.381885i | ||||
\(727\) | 2.23406e7i | 1.56769i | 0.620958 | + | 0.783844i | \(0.286744\pi\) | ||||
−0.620958 | + | 0.783844i | \(0.713256\pi\) | |||||||
\(728\) | 1.35086e7 | 0.944671 | ||||||||
\(729\) | −5.70263e6 | + | 1.31670e7i | −0.397426 | + | 0.917634i | ||||
\(730\) | 1.48093e7i | 1.02855i | ||||||||
\(731\) | − | 2.45016e6i | − | 0.169590i | ||||||
\(732\) | 3.40604e6 | + | 3.90481e6i | 0.234948 | + | 0.269353i | ||||
\(733\) | 3.81239e6i | 0.262082i | 0.991377 | + | 0.131041i | \(0.0418320\pi\) | ||||
−0.991377 | + | 0.131041i | \(0.958168\pi\) | |||||||
\(734\) | 1.63810e7 | 1.12228 | ||||||||
\(735\) | 2.55280e7 | − | 2.22672e7i | 1.74300 | − | 1.52036i | ||||
\(736\) | 2.35300e6 | − | 1.10109e6i | 0.160113 | − | 0.0749255i | ||||
\(737\) | 1.05887e7i | 0.718084i | ||||||||
\(738\) | 1.33805e6 | − | 9.76067e6i | 0.0904339 | − | 0.659688i | ||||
\(739\) | −2.01949e7 | −1.36029 | −0.680143 | − | 0.733079i | \(-0.738082\pi\) | ||||
−0.680143 | + | 0.733079i | \(0.738082\pi\) | |||||||
\(740\) | − | 2.01633e7i | − | 1.35357i | ||||||
\(741\) | 4.10945e6 | + | 4.71123e6i | 0.274940 | + | 0.315202i | ||||
\(742\) | 9.37096e6 | 0.624848 | ||||||||
\(743\) | 3.71077e6 | 0.246599 | 0.123300 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123300 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(744\) | 2.63670e6 | + | 3.02281e6i | 0.174634 | + | 0.200207i | ||||
\(745\) | 2.91441e7 | 1.92380 | ||||||||
\(746\) | −6.24057e6 | −0.410560 | ||||||||
\(747\) | 245899. | − | 1.79376e6i | 0.0161234 | − | 0.117615i | ||||
\(748\) | 5.60139e6 | 0.366051 | ||||||||
\(749\) | 2.02776e7i | 1.32072i | ||||||||
\(750\) | 2.33734e7 | + | 2.67962e7i | 1.51729 | + | 1.73948i | ||||
\(751\) | 2.64124e7i | 1.70886i | 0.519564 | + | 0.854432i | \(0.326095\pi\) | ||||
−0.519564 | + | 0.854432i | \(0.673905\pi\) | |||||||
\(752\) | 2.06754e6i | 0.133324i | ||||||||
\(753\) | −356085. | + | 310601.i | −0.0228858 | + | 0.0199625i | ||||
\(754\) | 9.50037e6 | 0.608573 | ||||||||
\(755\) | 1.03075e7 | 0.658092 | ||||||||
\(756\) | 9.74794e6 | − | 6.40109e6i | 0.620310 | − | 0.407333i | ||||
\(757\) | 1.30839e7i | 0.829846i | 0.909856 | + | 0.414923i | \(0.136192\pi\) | ||||
−0.909856 | + | 0.414923i | \(0.863808\pi\) | |||||||
\(758\) | 1.89076e7 | 1.19526 | ||||||||
\(759\) | −1.90223e7 | − | 8.39993e6i | −1.19856 | − | 0.529262i | ||||
\(760\) | −2.51514e6 | −0.157953 | ||||||||
\(761\) | 2.38346e7i | 1.49192i | 0.665989 | + | 0.745962i | \(0.268010\pi\) | ||||
−0.665989 | + | 0.745962i | \(0.731990\pi\) | |||||||
\(762\) | 5.34028e6 | + | 6.12230e6i | 0.333178 | + | 0.381968i | ||||
\(763\) | 1.28996e7 | 0.802166 | ||||||||
\(764\) | −7.22159e6 | −0.447609 | ||||||||
\(765\) | −2.36208e6 | + | 1.72306e7i | −0.145929 | + | 1.06451i | ||||
\(766\) | − | 1.22474e7i | − | 0.754173i | ||||||
\(767\) | 4.21894e6i | 0.258950i | ||||||||
\(768\) | −769878. | + | 671539.i | −0.0470998 | + | 0.0410836i | ||||
\(769\) | − | 2.74943e7i | − | 1.67659i | −0.545219 | − | 0.838294i | \(-0.683553\pi\) | ||
0.545219 | − | 0.838294i | \(-0.316447\pi\) | |||||||
\(770\) | 4.35013e7 | 2.64409 | ||||||||
\(771\) | −1.58190e7 | − | 1.81355e7i | −0.958393 | − | 1.09874i | ||||
\(772\) | 5.76855e6 | 0.348356 | ||||||||
\(773\) | −2.30897e7 | −1.38985 | −0.694927 | − | 0.719081i | \(-0.744563\pi\) | ||||
−0.694927 | + | 0.719081i | \(0.744563\pi\) | |||||||
\(774\) | 485799. | − | 3.54376e6i | 0.0291477 | − | 0.212624i | ||||
\(775\) | −3.38935e7 | −2.02704 | ||||||||
\(776\) | −2.64378e6 | −0.157605 | ||||||||
\(777\) | 2.64992e7 | − | 2.31144e7i | 1.57464 | − | 1.37350i | ||||
\(778\) | − | 2.28481e7i | − | 1.35332i | ||||||
\(779\) | −3.70556e6 | −0.218781 | ||||||||
\(780\) | −2.21637e7 | + | 1.93326e7i | −1.30438 | + | 1.13777i | ||||
\(781\) | − | 3.02566e7i | − | 1.77498i | ||||||
\(782\) | −6.11976e6 | + | 2.86376e6i | −0.357864 | + | 0.167464i | ||||
\(783\) | 6.85559e6 | − | 4.50179e6i | 0.399614 | − | 0.262411i | ||||
\(784\) | −5.17523e6 | −0.300704 | ||||||||
\(785\) | − | 5.82969e7i | − | 3.37653i | ||||||
\(786\) | 6.18186e6 | − | 5.39223e6i | 0.356913 | − | 0.311324i | ||||
\(787\) | − | 1.46279e7i | − | 0.841869i | −0.907091 | − | 0.420935i | \(-0.861702\pi\) | ||
0.907091 | − | 0.420935i | \(-0.138298\pi\) | |||||||
\(788\) | 3.86884e6i | 0.221955i | ||||||||
\(789\) | 7.46965e6 | − | 6.51553e6i | 0.427177 | − | 0.372612i | ||||
\(790\) | −5.70021e6 | −0.324955 | ||||||||
\(791\) | − | 3.69369e7i | − | 2.09903i | ||||||
\(792\) | 8.10152e6 | + | 1.11060e6i | 0.458937 | + | 0.0629138i | ||||
\(793\) | − | 2.27894e7i | − | 1.28692i | ||||||
\(794\) | − | 1.06467e7i | − | 0.599328i | ||||||
\(795\) | −1.53751e7 | + | 1.34112e7i | −0.862778 | + | 0.752573i | ||||
\(796\) | − | 5.03615e6i | − | 0.281719i | ||||||
\(797\) | 7.24279e6 | 0.403887 | 0.201943 | − | 0.979397i | \(-0.435274\pi\) | ||||
0.201943 | + | 0.979397i | \(0.435274\pi\) | |||||||
\(798\) | −2.88325e6 | − | 3.30547e6i | −0.160279 | − | 0.183750i | ||||
\(799\) | − | 5.37734e6i | − | 0.297989i | ||||||
\(800\) | − | 8.63232e6i | − | 0.476873i | ||||||
\(801\) | 624213. | − | 4.55345e6i | 0.0343757 | − | 0.250760i | ||||
\(802\) | − | 4.67701e6i | − | 0.256763i | ||||||
\(803\) | −1.81097e7 | −0.991112 | ||||||||
\(804\) | 3.30166e6 | + | 3.78515e6i | 0.180133 | + | 0.206511i | ||||
\(805\) | −4.75270e7 | + | 2.22404e7i | −2.58494 | + | 1.20963i | ||||
\(806\) | − | 1.76418e7i | − | 0.956547i | ||||||
\(807\) | −7.20149e6 | − | 8.25607e6i | −0.389259 | − | 0.446262i | ||||
\(808\) | −7.16987e6 | −0.386352 | ||||||||
\(809\) | − | 5.10431e6i | − | 0.274199i | −0.990557 | − | 0.137099i | \(-0.956222\pi\) | ||
0.990557 | − | 0.137099i | \(-0.0437780\pi\) | |||||||
\(810\) | −6.83273e6 | + | 2.44530e7i | −0.365916 | + | 1.30954i | ||||
\(811\) | −2.82748e7 | −1.50955 | −0.754775 | − | 0.655984i | \(-0.772254\pi\) | ||||
−0.754775 | + | 0.655984i | \(0.772254\pi\) | |||||||
\(812\) | −6.66561e6 | −0.354773 | ||||||||
\(813\) | 1.26518e7 | − | 1.10358e7i | 0.671317 | − | 0.585567i | ||||
\(814\) | 2.46570e7 | 1.30430 | ||||||||
\(815\) | 5.75391e7 | 3.03437 | ||||||||
\(816\) | 2.00233e6 | − | 1.74656e6i | 0.105271 | − | 0.0918246i | ||||
\(817\) | −1.34536e6 | −0.0705153 | ||||||||
\(818\) | 8.04263e6i | 0.420257i | ||||||||
\(819\) | −5.08151e7 | − | 6.96602e6i | −2.64718 | − | 0.362890i | ||||
\(820\) | − | 1.74326e7i | − | 0.905371i | ||||||
\(821\) | − | 7.74746e6i | − | 0.401145i | −0.979679 | − | 0.200572i | \(-0.935720\pi\) | ||
0.979679 | − | 0.200572i | \(-0.0642802\pi\) | |||||||
\(822\) | 5.48575e6 | + | 6.28907e6i | 0.283176 | + | 0.324644i | ||||
\(823\) | 2.24967e7 | 1.15776 | 0.578882 | − | 0.815412i | \(-0.303489\pi\) | ||||
0.578882 | + | 0.815412i | \(0.303489\pi\) | |||||||
\(824\) | −5.91309e6 | −0.303387 | ||||||||
\(825\) | −5.20706e7 | + | 4.54195e7i | −2.66353 | + | 2.32331i | ||||
\(826\) | − | 2.96008e6i | − | 0.150957i | ||||||
\(827\) | −1.29376e7 | −0.657794 | −0.328897 | − | 0.944366i | \(-0.606677\pi\) | ||||
−0.328897 | + | 0.944366i | \(0.606677\pi\) | |||||||
\(828\) | −9.41905e6 | + | 2.92859e6i | −0.477454 | + | 0.148451i | ||||
\(829\) | −2.87039e7 | −1.45062 | −0.725311 | − | 0.688421i | \(-0.758304\pi\) | ||||
−0.725311 | + | 0.688421i | \(0.758304\pi\) | |||||||
\(830\) | − | 3.20366e6i | − | 0.161418i | ||||||
\(831\) | 3.53710e6 | − | 3.08529e6i | 0.177682 | − | 0.154986i | ||||
\(832\) | 4.49319e6 | 0.225033 | ||||||||
\(833\) | 1.34599e7 | 0.672094 | ||||||||
\(834\) | −3.57760e6 | − | 4.10150e6i | −0.178105 | − | 0.204187i | ||||
\(835\) | − | 2.10217e7i | − | 1.04340i | ||||||
\(836\) | − | 3.07567e6i | − | 0.152203i | ||||||
\(837\) | −8.35966e6 | − | 1.27306e7i | −0.412454 | − | 0.628108i | ||||
\(838\) | 8.05074e6i | 0.396028i | ||||||||
\(839\) | 5.07889e6 | 0.249095 | 0.124547 | − | 0.992214i | \(-0.460252\pi\) | ||||
0.124547 | + | 0.992214i | \(0.460252\pi\) | |||||||
\(840\) | 1.55504e7 | − | 1.35641e7i | 0.760402 | − | 0.663273i | ||||
\(841\) | 1.58233e7 | 0.771450 | ||||||||
\(842\) | −2.15364e7 | −1.04687 | ||||||||
\(843\) | 3.96846e6 | − | 3.46156e6i | 0.192333 | − | 0.167765i | ||||
\(844\) | −3.42596e6 | −0.165549 | ||||||||
\(845\) | 8.94406e7 | 4.30916 | ||||||||
\(846\) | 1.06618e6 | − | 7.77746e6i | 0.0512159 | − | 0.373604i | ||||
\(847\) | 2.22079e7i | 1.06365i | ||||||||
\(848\) | 3.11695e6 | 0.148847 | ||||||||
\(849\) | 1.53467e7 | + | 1.75940e7i | 0.730710 | + | 0.837714i | ||||
\(850\) | 2.24513e7i | 1.06584i | ||||||||
\(851\) | −2.69388e7 | + | 1.26061e7i | −1.27513 | + | 0.596701i | ||||
\(852\) | −9.43428e6 | − | 1.08158e7i | −0.445256 | − | 0.510459i | ||||
\(853\) | 1.78715e7 | 0.840987 | 0.420494 | − | 0.907296i | \(-0.361857\pi\) | ||||
0.420494 | + | 0.907296i | \(0.361857\pi\) | |||||||
\(854\) | 1.59894e7i | 0.750218i | ||||||||
\(855\) | 9.46119e6 | + | 1.29699e6i | 0.442619 | + | 0.0606768i | ||||
\(856\) | 6.74469e6i | 0.314614i | ||||||||
\(857\) | − | 1.84032e7i | − | 0.855938i | −0.903793 | − | 0.427969i | \(-0.859229\pi\) | ||
0.903793 | − | 0.427969i | \(-0.140771\pi\) | |||||||
\(858\) | −2.36412e7 | − | 2.71032e7i | −1.09635 | − | 1.25690i | ||||
\(859\) | −1.83557e7 | −0.848765 | −0.424383 | − | 0.905483i | \(-0.639509\pi\) | ||||
−0.424383 | + | 0.905483i | \(0.639509\pi\) | |||||||
\(860\) | − | 6.32916e6i | − | 0.291810i | ||||||
\(861\) | 2.29104e7 | − | 1.99840e7i | 1.05323 | − | 0.918700i | ||||
\(862\) | 7.94274e6i | 0.364085i | ||||||||
\(863\) | − | 4.87260e6i | − | 0.222707i | −0.993781 | − | 0.111353i | \(-0.964481\pi\) | ||
0.993781 | − | 0.111353i | \(-0.0355185\pi\) | |||||||
\(864\) | 3.24234e6 | − | 2.12912e6i | 0.147766 | − | 0.0970321i | ||||
\(865\) | − | 7.53380e7i | − | 3.42353i | ||||||
\(866\) | −1.48415e7 | −0.672487 | ||||||||
\(867\) | 1.14719e7 | − | 1.00066e7i | 0.518308 | − | 0.452103i | ||||
\(868\) | 1.23778e7i | 0.557627i | ||||||||
\(869\) | − | 6.97058e6i | − | 0.313126i | ||||||
\(870\) | 1.09364e7 | − | 9.53943e6i | 0.489863 | − | 0.427291i | ||||
\(871\) | − | 2.20910e7i | − | 0.986666i | ||||||
\(872\) | 4.29063e6 | 0.191086 | ||||||||
\(873\) | 9.94507e6 | + | 1.36333e6i | 0.441644 | + | 0.0605431i | ||||
\(874\) | 1.57247e6 | + | 3.36030e6i | 0.0696310 | + | 0.148799i | ||||
\(875\) | 1.09725e8i | 4.84490i | ||||||||
\(876\) | −6.47367e6 | + | 5.64677e6i | −0.285030 | + | 0.248622i | ||||
\(877\) | 2.14525e7 | 0.941842 | 0.470921 | − | 0.882175i | \(-0.343922\pi\) | ||||
0.470921 | + | 0.882175i | \(0.343922\pi\) | |||||||
\(878\) | − | 1.30853e7i | − | 0.572857i | ||||||
\(879\) | −124272. | + | 108398.i | −0.00542501 | + | 0.00473206i | ||||
\(880\) | 1.44693e7 | 0.629856 | ||||||||
\(881\) | 2.89857e7 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283427\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283427\pi\) | |||||||
\(882\) | 1.94676e7 | + | 2.66874e6i | 0.842639 | + | 0.115514i | ||||
\(883\) | −1.65402e7 | −0.713904 | −0.356952 | − | 0.934123i | \(-0.616184\pi\) | ||||
−0.356952 | + | 0.934123i | \(0.616184\pi\) | |||||||
\(884\) | −1.16861e7 | −0.502964 | ||||||||
\(885\) | 4.23629e6 | + | 4.85664e6i | 0.181814 | + | 0.208438i | ||||
\(886\) | 2.02035e6 | 0.0864654 | ||||||||
\(887\) | − | 636415.i | − | 0.0271601i | −0.999908 | − | 0.0135801i | \(-0.995677\pi\) | ||
0.999908 | − | 0.0135801i | \(-0.00432280\pi\) | |||||||
\(888\) | 8.81411e6 | − | 7.68826e6i | 0.375099 | − | 0.327187i | ||||
\(889\) | 2.50696e7i | 1.06388i | ||||||||
\(890\) | − | 8.13246e6i | − | 0.344149i | ||||||
\(891\) | −2.99027e7 | − | 8.35550e6i | −1.26188 | − | 0.352597i | ||||
\(892\) | −2.56157e6 | −0.107794 | ||||||||
\(893\) | −2.95265e6 | −0.123903 | ||||||||
\(894\) | 1.11126e7 | + | 1.27399e7i | 0.465021 | + | 0.533118i | ||||
\(895\) | 4.95178e7i | 2.06635i | ||||||||
\(896\) | −3.15249e6 | −0.131185 | ||||||||
\(897\) | 3.96857e7 | + | 1.75246e7i | 1.64685 | + | 0.727221i | ||||
\(898\) | −2.07571e7 | −0.858965 | ||||||||
\(899\) | 8.70512e6i | 0.359233i | ||||||||
\(900\) | −4.45147e6 | + | 3.24721e7i | −0.183188 | + | 1.33630i | ||||
\(901\) | −8.10668e6 | −0.332683 | ||||||||
\(902\) | 2.13176e7 | 0.872414 | ||||||||
\(903\) | 8.31797e6 | − | 7.25549e6i | 0.339467 | − | 0.296106i | ||||
\(904\) | − | 1.22859e7i | − | 0.500017i | ||||||
\(905\) | − | 5.55957e7i | − | 2.25642i | ||||||
\(906\) | 3.93025e6 | + | 4.50579e6i | 0.159074 | + | 0.182369i | ||||
\(907\) | − | 1.04906e7i | − | 0.423432i | −0.977331 | − | 0.211716i | \(-0.932095\pi\) | ||
0.977331 | − | 0.211716i | \(-0.0679051\pi\) | |||||||
\(908\) | 6.72381e6 | 0.270645 | ||||||||
\(909\) | 2.69709e7 | + | 3.69732e6i | 1.08264 | + | 0.148415i | ||||
\(910\) | −9.07557e7 | −3.63304 | ||||||||
\(911\) | −4.44172e7 | −1.77319 | −0.886595 | − | 0.462547i | \(-0.846936\pi\) | ||||
−0.886595 | + | 0.462547i | \(0.846936\pi\) | |||||||
\(912\) | −959022. | − | 1.09946e6i | −0.0381805 | − | 0.0437716i | ||||
\(913\) | 3.91764e6 | 0.155542 | ||||||||
\(914\) | 1.05254e7 | 0.416749 | ||||||||
\(915\) | −2.28831e7 | − | 2.62340e7i | −0.903570 | − | 1.03589i | ||||
\(916\) | − | 1.60778e6i | − | 0.0633124i | ||||||
\(917\) | 2.53135e7 | 0.994096 | ||||||||
\(918\) | −8.43280e6 | + | 5.53749e6i | −0.330267 | + | 0.216873i | ||||
\(919\) | − | 2.84538e7i | − | 1.11135i | −0.831399 | − | 0.555676i | \(-0.812459\pi\) | ||
0.831399 | − | 0.555676i | \(-0.187541\pi\) | |||||||
\(920\) | −1.58083e7 | + | 7.39757e6i | −0.615767 | + | 0.288151i | ||||
\(921\) | −6.25315e6 | + | 5.45441e6i | −0.242912 | + | 0.211884i | ||||
\(922\) | 6.80468e6 | 0.263621 | ||||||||
\(923\) | 6.31237e7i | 2.43887i | ||||||||
\(924\) | 1.65870e7 | + | 1.90160e7i | 0.639129 | + | 0.732722i | ||||
\(925\) | 9.88290e7i | 3.79778i | ||||||||
\(926\) | − | 2.85840e7i | − | 1.09546i | ||||||
\(927\) | 2.22432e7 | + | 3.04923e6i | 0.850156 | + | 0.116544i | ||||
\(928\) | −2.21710e6 | −0.0845115 | ||||||||
\(929\) | 2.38380e7i | 0.906214i | 0.891456 | + | 0.453107i | \(0.149684\pi\) | ||||
−0.891456 | + | 0.453107i | \(0.850316\pi\) | |||||||
\(930\) | −1.77144e7 | − | 2.03084e7i | −0.671611 | − | 0.769961i | ||||
\(931\) | − | 7.39072e6i | − | 0.279456i | ||||||
\(932\) | 2.15727e7i | 0.813514i | ||||||||
\(933\) | 1.04621e7 | + | 1.19941e7i | 0.393473 | + | 0.451092i | ||||
\(934\) | 2.70293e7i | 1.01383i | ||||||||
\(935\) | −3.76323e7 | −1.40777 | ||||||||
\(936\) | −1.69020e7 | − | 2.31702e6i | −0.630592 | − | 0.0864452i | ||||
\(937\) | − | 1.48633e6i | − | 0.0553052i | −0.999618 | − | 0.0276526i | \(-0.991197\pi\) | ||
0.999618 | − | 0.0276526i | \(-0.00880322\pi\) | |||||||
\(938\) | 1.54994e7i | 0.575186i | ||||||||
\(939\) | 2.64929e7 | + | 3.03724e7i | 0.980539 | + | 1.12413i | ||||
\(940\) | − | 1.38906e7i | − | 0.512743i | ||||||
\(941\) | −4.67537e7 | −1.72124 | −0.860620 | − | 0.509247i | \(-0.829924\pi\) | ||||
−0.860620 | + | 0.509247i | \(0.829924\pi\) | |||||||
\(942\) | 2.54837e7 | − | 2.22286e7i | 0.935697 | − | 0.816177i | ||||
\(943\) | −2.32904e7 | + | 1.08988e7i | −0.852900 | + | 0.399118i | ||||
\(944\) | − | 984575.i | − | 0.0359599i | ||||||
\(945\) | −6.54905e7 | + | 4.30050e7i | −2.38561 | + | 1.56653i | ||||
\(946\) | 7.73970e6 | 0.281188 | ||||||||
\(947\) | − | 5.39020e7i | − | 1.95313i | −0.215233 | − | 0.976563i | \(-0.569051\pi\) | ||
0.215233 | − | 0.976563i | \(-0.430949\pi\) | |||||||
\(948\) | −2.17349e6 | − | 2.49177e6i | −0.0785483 | − | 0.0900507i | ||||
\(949\) | 3.77819e7 | 1.36181 | ||||||||
\(950\) | 1.23278e7 | 0.443176 | ||||||||
\(951\) | −1.92880e7 | − | 2.21125e7i | −0.691570 | − | 0.792843i | ||||
\(952\) | 8.19912e6 | 0.293207 | ||||||||
\(953\) | −5.48502e7 | −1.95635 | −0.978173 | − | 0.207791i | \(-0.933373\pi\) | ||||
−0.978173 | + | 0.207791i | \(0.933373\pi\) | |||||||
\(954\) | −1.17250e7 | − | 1.60733e6i | −0.417102 | − | 0.0571788i | ||||
\(955\) | 4.85174e7 | 1.72143 | ||||||||
\(956\) | 8.62760e6i | 0.305313i | ||||||||
\(957\) | 1.16654e7 | + | 1.33737e7i | 0.411738 | + | 0.472032i | ||||
\(958\) | − | 2.68208e7i | − | 0.944188i | ||||||
\(959\) | 2.57525e7i | 0.904216i | ||||||||
\(960\) | 5.17234e6 | − | 4.51166e6i | 0.181138 | − | 0.158000i | ||||
\(961\) | −1.24641e7 | −0.435363 | ||||||||
\(962\) | −5.14412e7 | −1.79215 | ||||||||
\(963\) | 3.47807e6 | − | 2.53715e7i | 0.120857 | − | 0.881617i | ||||
\(964\) | 2.42373e7i | 0.840025i | ||||||||
\(965\) | −3.87553e7 | −1.33972 | ||||||||
\(966\) | −2.78441e7 | − | 1.22955e7i | −0.960044 | − | 0.423940i | ||||
\(967\) | 2.46542e7 | 0.847860 | 0.423930 | − | 0.905695i | \(-0.360650\pi\) | ||||
0.423930 | + | 0.905695i | \(0.360650\pi\) | |||||||
\(968\) | 7.38673e6i | 0.253375i | ||||||||
\(969\) | 2.49426e6 | + | 2.85952e6i | 0.0853360 | + | 0.0978325i | ||||
\(970\) | 1.77619e7 | 0.606122 | ||||||||
\(971\) | 3.70476e7 | 1.26099 | 0.630496 | − | 0.776193i | \(-0.282852\pi\) | ||||
0.630496 | + | 0.776193i | \(0.282852\pi\) | |||||||
\(972\) | −1.32946e7 | + | 6.33709e6i | −0.451347 | + | 0.215142i | ||||
\(973\) | − | 1.67948e7i | − | 0.568713i | ||||||
\(974\) | 3.68949e7i | 1.24615i | ||||||||
\(975\) | 1.08634e8 | − | 9.47575e7i | 3.65976 | − | 3.19229i | ||||
\(976\) | 5.31836e6i | 0.178712i | ||||||||
\(977\) | −1.33333e7 | −0.446891 | −0.223446 | − | 0.974716i | \(-0.571731\pi\) | ||||
−0.223446 | + | 0.974716i | \(0.571731\pi\) | |||||||
\(978\) | 2.19396e7 | + | 2.51524e7i | 0.733470 | + | 0.840878i | ||||
\(979\) | 9.94488e6 | 0.331622 | ||||||||
\(980\) | 3.47692e7 | 1.15646 | ||||||||
\(981\) | −1.61400e7 | − | 2.21257e6i | −0.535466 | − | 0.0734048i | ||||
\(982\) | −1.17928e7 | −0.390247 | ||||||||
\(983\) | −6.57597e6 | −0.217058 | −0.108529 | − | 0.994093i | \(-0.534614\pi\) | ||||
−0.108529 | + | 0.994093i | \(0.534614\pi\) | |||||||
\(984\) | 7.62041e6 | − | 6.64703e6i | 0.250894 | − | 0.218847i | ||||
\(985\) | − | 2.59924e7i | − | 0.853602i | ||||||
\(986\) | 5.76633e6 | 0.188889 | ||||||||
\(987\) | 1.82554e7 | − | 1.59236e7i | 0.596483 | − | 0.520292i | ||||
\(988\) | 6.41670e6i | 0.209132i | ||||||||
\(989\) | −8.45595e6 | + | 3.95699e6i | −0.274898 | + | 0.128640i | ||||
\(990\) | −5.44291e7 | − | 7.46146e6i | −1.76499 | − | 0.241956i | ||||
\(991\) | −2.76808e6 | −0.0895352 | −0.0447676 | − | 0.998997i | \(-0.514255\pi\) | ||||
−0.0447676 | + | 0.998997i | \(0.514255\pi\) | |||||||
\(992\) | 4.11708e6i | 0.132834i | ||||||||
\(993\) | −3.30173e7 | + | 2.87999e7i | −1.06260 | + | 0.926867i | ||||
\(994\) | − | 4.42886e7i | − | 1.42176i | ||||||
\(995\) | 3.38348e7i | 1.08344i | ||||||||
\(996\) | 1.40044e6 | − | 1.22155e6i | 0.0447317 | − | 0.0390179i | ||||
\(997\) | 1.59147e7 | 0.507060 | 0.253530 | − | 0.967328i | \(-0.418408\pi\) | ||||
0.253530 | + | 0.967328i | \(0.418408\pi\) | |||||||
\(998\) | − | 6.78502e6i | − | 0.215638i | ||||||
\(999\) | −3.71206e7 | + | 2.43757e7i | −1.17680 | + | 0.772756i |
(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 | 138.6.d.a.137.2 | yes | 40 | |
3.2 | odd | 2 | inner | 138.6.d.a.137.3 | yes | 40 | |
23.22 | odd | 2 | inner | 138.6.d.a.137.1 | ✓ | 40 | |
69.68 | even | 2 | inner | 138.6.d.a.137.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.6.d.a.137.1 | ✓ | 40 | 23.22 | odd | 2 | inner | |
138.6.d.a.137.2 | yes | 40 | 1.1 | even | 1 | trivial | |
138.6.d.a.137.3 | yes | 40 | 3.2 | odd | 2 | inner | |
138.6.d.a.137.4 | yes | 40 | 69.68 | even | 2 | inner |