Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.a (trivial) |
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: | yes |
Analytic conductor: | \(172.412606299\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(10.9591\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.95911 | −1.58376 | −0.791881 | − | 0.610675i | \(-0.790898\pi\) | ||||
−0.791881 | + | 0.610675i | \(0.790898\pi\) | |||||||
\(3\) | 25.1057 | 1.61053 | 0.805264 | − | 0.592916i | \(-0.202023\pi\) | ||||
0.805264 | + | 0.592916i | \(0.202023\pi\) | |||||||
\(4\) | 48.2657 | 1.50830 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −224.924 | −2.55070 | ||||||||
\(7\) | 166.001 | 1.28046 | 0.640230 | − | 0.768183i | \(-0.278839\pi\) | ||||
0.640230 | + | 0.768183i | \(0.278839\pi\) | |||||||
\(8\) | −145.726 | −0.805033 | ||||||||
\(9\) | 387.294 | 1.59380 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 607.827 | 1.51460 | 0.757301 | − | 0.653066i | \(-0.226518\pi\) | ||||
0.757301 | + | 0.653066i | \(0.226518\pi\) | |||||||
\(12\) | 1211.74 | 2.42917 | ||||||||
\(13\) | 1039.54 | 1.70602 | 0.853011 | − | 0.521894i | \(-0.174774\pi\) | ||||
0.853011 | + | 0.521894i | \(0.174774\pi\) | |||||||
\(14\) | −1487.22 | −2.02794 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −238.923 | −0.233323 | ||||||||
\(17\) | −1439.76 | −1.20828 | −0.604138 | − | 0.796880i | \(-0.706483\pi\) | ||||
−0.604138 | + | 0.796880i | \(0.706483\pi\) | |||||||
\(18\) | −3469.81 | −2.52421 | ||||||||
\(19\) | −1332.62 | −0.846881 | −0.423440 | − | 0.905924i | \(-0.639178\pi\) | ||||
−0.423440 | + | 0.905924i | \(0.639178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4167.57 | 2.06222 | ||||||||
\(22\) | −5445.59 | −2.39877 | ||||||||
\(23\) | 437.244 | 0.172347 | 0.0861737 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861737 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(24\) | −3658.56 | −1.29653 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9313.39 | −2.70193 | ||||||||
\(27\) | 3622.60 | 0.956336 | ||||||||
\(28\) | 8012.16 | 1.93132 | ||||||||
\(29\) | −87.2656 | −0.0192685 | −0.00963425 | − | 0.999954i | \(-0.503067\pi\) | ||||
−0.00963425 | + | 0.999954i | \(0.503067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2654.45 | 0.496101 | 0.248050 | − | 0.968747i | \(-0.420210\pi\) | ||||
0.248050 | + | 0.968747i | \(0.420210\pi\) | |||||||
\(32\) | 6803.79 | 1.17456 | ||||||||
\(33\) | 15259.9 | 2.43931 | ||||||||
\(34\) | 12898.9 | 1.91362 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 18693.0 | 2.40394 | ||||||||
\(37\) | 4671.70 | 0.561010 | 0.280505 | − | 0.959853i | \(-0.409498\pi\) | ||||
0.280505 | + | 0.959853i | \(0.409498\pi\) | |||||||
\(38\) | 11939.1 | 1.34126 | ||||||||
\(39\) | 26098.4 | 2.74760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9012.91 | −0.837347 | −0.418674 | − | 0.908137i | \(-0.637505\pi\) | ||||
−0.418674 | + | 0.908137i | \(0.637505\pi\) | |||||||
\(42\) | −37337.7 | −3.26606 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | 29337.2 | 2.28448 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3917.32 | −0.272957 | ||||||||
\(47\) | 8623.49 | 0.569427 | 0.284714 | − | 0.958613i | \(-0.408101\pi\) | ||||
0.284714 | + | 0.958613i | \(0.408101\pi\) | |||||||
\(48\) | −5998.32 | −0.375774 | ||||||||
\(49\) | 10749.4 | 0.639577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −36146.0 | −1.94596 | ||||||||
\(52\) | 50174.3 | 2.57320 | ||||||||
\(53\) | 28358.3 | 1.38672 | 0.693362 | − | 0.720590i | \(-0.256129\pi\) | ||||
0.693362 | + | 0.720590i | \(0.256129\pi\) | |||||||
\(54\) | −32455.3 | −1.51461 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −24190.8 | −1.03081 | ||||||||
\(57\) | −33456.3 | −1.36393 | ||||||||
\(58\) | 781.822 | 0.0305167 | ||||||||
\(59\) | 48066.0 | 1.79766 | 0.898832 | − | 0.438294i | \(-0.144417\pi\) | ||||
0.898832 | + | 0.438294i | \(0.144417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39750.4 | −1.36778 | −0.683891 | − | 0.729585i | \(-0.739713\pi\) | ||||
−0.683891 | + | 0.729585i | \(0.739713\pi\) | |||||||
\(62\) | −23781.5 | −0.785706 | ||||||||
\(63\) | 64291.2 | 2.04080 | ||||||||
\(64\) | −53310.4 | −1.62690 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −136715. | −3.86329 | ||||||||
\(67\) | −19233.9 | −0.523456 | −0.261728 | − | 0.965142i | \(-0.584292\pi\) | ||||
−0.261728 | + | 0.965142i | \(0.584292\pi\) | |||||||
\(68\) | −69490.8 | −1.82245 | ||||||||
\(69\) | 10977.3 | 0.277570 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17008.5 | 0.400424 | 0.200212 | − | 0.979753i | \(-0.435837\pi\) | ||||
0.200212 | + | 0.979753i | \(0.435837\pi\) | |||||||
\(72\) | −56439.0 | −1.28306 | ||||||||
\(73\) | −22236.4 | −0.488380 | −0.244190 | − | 0.969727i | \(-0.578522\pi\) | ||||
−0.244190 | + | 0.969727i | \(0.578522\pi\) | |||||||
\(74\) | −41854.3 | −0.888506 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −64319.9 | −1.27735 | ||||||||
\(77\) | 100900. | 1.93939 | ||||||||
\(78\) | −233819. | −4.35154 | ||||||||
\(79\) | 36951.1 | 0.666131 | 0.333066 | − | 0.942904i | \(-0.391917\pi\) | ||||
0.333066 | + | 0.942904i | \(0.391917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3164.77 | −0.0535957 | ||||||||
\(82\) | 80747.7 | 1.32616 | ||||||||
\(83\) | 117990. | 1.87997 | 0.939985 | − | 0.341216i | \(-0.110839\pi\) | ||||
0.939985 | + | 0.341216i | \(0.110839\pi\) | |||||||
\(84\) | 201151. | 3.11045 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16565.4 | −0.241522 | ||||||||
\(87\) | −2190.86 | −0.0310325 | ||||||||
\(88\) | −88576.5 | −1.21930 | ||||||||
\(89\) | 41537.6 | 0.555861 | 0.277931 | − | 0.960601i | \(-0.410351\pi\) | ||||
0.277931 | + | 0.960601i | \(0.410351\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 172565. | 2.18449 | ||||||||
\(92\) | 21103.9 | 0.259952 | ||||||||
\(93\) | 66641.7 | 0.798985 | ||||||||
\(94\) | −77258.8 | −0.901838 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 170814. | 1.89166 | ||||||||
\(97\) | −32593.9 | −0.351728 | −0.175864 | − | 0.984415i | \(-0.556272\pi\) | ||||
−0.175864 | + | 0.984415i | \(0.556272\pi\) | |||||||
\(98\) | −96304.8 | −1.01294 | ||||||||
\(99\) | 235408. | 2.41398 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7934.83 | −0.0773988 | −0.0386994 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386994 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(102\) | 323836. | 3.08194 | ||||||||
\(103\) | −132558. | −1.23116 | −0.615579 | − | 0.788075i | \(-0.711078\pi\) | ||||
−0.615579 | + | 0.788075i | \(0.711078\pi\) | |||||||
\(104\) | −151489. | −1.37340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −254065. | −2.19624 | ||||||||
\(107\) | −120642. | −1.01868 | −0.509342 | − | 0.860564i | \(-0.670111\pi\) | ||||
−0.509342 | + | 0.860564i | \(0.670111\pi\) | |||||||
\(108\) | 174847. | 1.44245 | ||||||||
\(109\) | 16769.1 | 0.135190 | 0.0675950 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675950 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 117286. | 0.903522 | ||||||||
\(112\) | −39661.5 | −0.298761 | ||||||||
\(113\) | 18201.6 | 0.134096 | 0.0670478 | − | 0.997750i | \(-0.478642\pi\) | ||||
0.0670478 | + | 0.997750i | \(0.478642\pi\) | |||||||
\(114\) | 299739. | 2.16013 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4211.94 | −0.0290628 | ||||||||
\(117\) | 402609. | 2.71906 | ||||||||
\(118\) | −430629. | −2.84707 | ||||||||
\(119\) | −239001. | −1.54715 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 208403. | 1.29402 | ||||||||
\(122\) | 356128. | 2.16624 | ||||||||
\(123\) | −226275. | −1.34857 | ||||||||
\(124\) | 128119. | 0.748271 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −575993. | −3.23214 | ||||||||
\(127\) | 155225. | 0.853987 | 0.426994 | − | 0.904255i | \(-0.359573\pi\) | ||||
0.426994 | + | 0.904255i | \(0.359573\pi\) | |||||||
\(128\) | 259892. | 1.40207 | ||||||||
\(129\) | 46420.4 | 0.245603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 206749. | 1.05261 | 0.526303 | − | 0.850297i | \(-0.323578\pi\) | ||||
0.526303 | + | 0.850297i | \(0.323578\pi\) | |||||||
\(132\) | 736530. | 3.67922 | ||||||||
\(133\) | −221216. | −1.08440 | ||||||||
\(134\) | 172319. | 0.829030 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 209810. | 0.972702 | ||||||||
\(137\) | 219188. | 0.997736 | 0.498868 | − | 0.866678i | \(-0.333749\pi\) | ||||
0.498868 | + | 0.866678i | \(0.333749\pi\) | |||||||
\(138\) | −98347.0 | −0.439606 | ||||||||
\(139\) | 83047.4 | 0.364577 | 0.182288 | − | 0.983245i | \(-0.441650\pi\) | ||||
0.182288 | + | 0.983245i | \(0.441650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 216498. | 0.917079 | ||||||||
\(142\) | −152381. | −0.634176 | ||||||||
\(143\) | 631863. | 2.58394 | ||||||||
\(144\) | −92533.5 | −0.371871 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 199219. | 0.773478 | ||||||||
\(147\) | 269870. | 1.03006 | ||||||||
\(148\) | 225483. | 0.846173 | ||||||||
\(149\) | −505431. | −1.86507 | −0.932537 | − | 0.361074i | \(-0.882410\pi\) | ||||
−0.932537 | + | 0.361074i | \(0.882410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −222212. | −0.793095 | −0.396548 | − | 0.918014i | \(-0.629792\pi\) | ||||
−0.396548 | + | 0.918014i | \(0.629792\pi\) | |||||||
\(152\) | 194198. | 0.681767 | ||||||||
\(153\) | −557609. | −1.92575 | ||||||||
\(154\) | −903974. | −3.07153 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.25966e6 | 4.14421 | ||||||||
\(157\) | −18138.1 | −0.0587275 | −0.0293638 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293638 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(158\) | −331049. | −1.05499 | ||||||||
\(159\) | 711953. | 2.23336 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72583.1 | 0.220684 | ||||||||
\(162\) | 28353.5 | 0.0848828 | ||||||||
\(163\) | 428372. | 1.26285 | 0.631425 | − | 0.775437i | \(-0.282470\pi\) | ||||
0.631425 | + | 0.775437i | \(0.282470\pi\) | |||||||
\(164\) | −435015. | −1.26297 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.05709e6 | −2.97743 | ||||||||
\(167\) | −590110. | −1.63735 | −0.818676 | − | 0.574256i | \(-0.805291\pi\) | ||||
−0.818676 | + | 0.574256i | \(0.805291\pi\) | |||||||
\(168\) | −607325. | −1.66015 | ||||||||
\(169\) | 709358. | 1.91051 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −516116. | −1.34976 | ||||||||
\(172\) | 89243.3 | 0.230014 | ||||||||
\(173\) | 194001. | 0.492821 | 0.246410 | − | 0.969166i | \(-0.420749\pi\) | ||||
0.246410 | + | 0.969166i | \(0.420749\pi\) | |||||||
\(174\) | 19628.2 | 0.0491481 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −145224. | −0.353392 | ||||||||
\(177\) | 1.20673e6 | 2.89519 | ||||||||
\(178\) | −372140. | −0.880353 | ||||||||
\(179\) | −434140. | −1.01274 | −0.506369 | − | 0.862317i | \(-0.669012\pi\) | ||||
−0.506369 | + | 0.862317i | \(0.669012\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −626829. | −1.42217 | −0.711087 | − | 0.703104i | \(-0.751797\pi\) | ||||
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(182\) | −1.54603e6 | −3.45972 | ||||||||
\(183\) | −997959. | −2.20285 | ||||||||
\(184\) | −63718.1 | −0.138745 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −597050. | −1.26540 | ||||||||
\(187\) | −875122. | −1.83006 | ||||||||
\(188\) | 416219. | 0.858870 | ||||||||
\(189\) | 601355. | 1.22455 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −109059. | −0.216310 | −0.108155 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108155 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(192\) | −1.33839e6 | −2.62017 | ||||||||
\(193\) | 31563.2 | 0.0609941 | 0.0304971 | − | 0.999535i | \(-0.490291\pi\) | ||||
0.0304971 | + | 0.999535i | \(0.490291\pi\) | |||||||
\(194\) | 292012. | 0.557053 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 518826. | 0.964676 | ||||||||
\(197\) | 276843. | 0.508238 | 0.254119 | − | 0.967173i | \(-0.418214\pi\) | ||||
0.254119 | + | 0.967173i | \(0.418214\pi\) | |||||||
\(198\) | −2.10905e6 | −3.82316 | ||||||||
\(199\) | −777649. | −1.39204 | −0.696019 | − | 0.718024i | \(-0.745047\pi\) | ||||
−0.696019 | + | 0.718024i | \(0.745047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −482879. | −0.843041 | ||||||||
\(202\) | 71089.0 | 0.122581 | ||||||||
\(203\) | −14486.2 | −0.0246725 | ||||||||
\(204\) | −1.74461e6 | −2.93511 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.18761e6 | 1.94986 | ||||||||
\(207\) | 169342. | 0.274688 | ||||||||
\(208\) | −248371. | −0.398055 | ||||||||
\(209\) | −810002. | −1.28269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −89486.6 | −0.138373 | −0.0691866 | − | 0.997604i | \(-0.522040\pi\) | ||||
−0.0691866 | + | 0.997604i | \(0.522040\pi\) | |||||||
\(212\) | 1.36873e6 | 2.09160 | ||||||||
\(213\) | 427009. | 0.644894 | ||||||||
\(214\) | 1.08085e6 | 1.61335 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −527908. | −0.769882 | ||||||||
\(217\) | 440641. | 0.635237 | ||||||||
\(218\) | −150237. | −0.214109 | ||||||||
\(219\) | −558260. | −0.786550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.49669e6 | −2.06135 | ||||||||
\(222\) | −1.05078e6 | −1.43096 | ||||||||
\(223\) | 952284. | 1.28234 | 0.641172 | − | 0.767398i | \(-0.278449\pi\) | ||||
0.641172 | + | 0.767398i | \(0.278449\pi\) | |||||||
\(224\) | 1.12944e6 | 1.50398 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −163071. | −0.212376 | ||||||||
\(227\) | 465809. | 0.599988 | 0.299994 | − | 0.953941i | \(-0.403015\pi\) | ||||
0.299994 | + | 0.953941i | \(0.403015\pi\) | |||||||
\(228\) | −1.61479e6 | −2.05721 | ||||||||
\(229\) | 477440. | 0.601631 | 0.300815 | − | 0.953682i | \(-0.402741\pi\) | ||||
0.300815 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.53316e6 | 3.12344 | ||||||||
\(232\) | 12716.9 | 0.0155118 | ||||||||
\(233\) | −743589. | −0.897312 | −0.448656 | − | 0.893705i | \(-0.648097\pi\) | ||||
−0.448656 | + | 0.893705i | \(0.648097\pi\) | |||||||
\(234\) | −3.60702e6 | −4.30635 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.31994e6 | 2.71142 | ||||||||
\(237\) | 927682. | 1.07282 | ||||||||
\(238\) | 2.14124e6 | 2.45032 | ||||||||
\(239\) | 1.27115e6 | 1.43947 | 0.719734 | − | 0.694250i | \(-0.244264\pi\) | ||||
0.719734 | + | 0.694250i | \(0.244264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −875960. | −0.971497 | −0.485749 | − | 0.874099i | \(-0.661453\pi\) | ||||
−0.485749 | + | 0.874099i | \(0.661453\pi\) | |||||||
\(242\) | −1.86710e6 | −2.04942 | ||||||||
\(243\) | −959745. | −1.04265 | ||||||||
\(244\) | −1.91858e6 | −2.06303 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.02722e6 | 2.13582 | ||||||||
\(247\) | −1.38532e6 | −1.44480 | ||||||||
\(248\) | −386823. | −0.399377 | ||||||||
\(249\) | 2.96222e6 | 3.02774 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.19674e6 | −1.19899 | −0.599494 | − | 0.800380i | \(-0.704631\pi\) | ||||
−0.599494 | + | 0.800380i | \(0.704631\pi\) | |||||||
\(252\) | 3.10306e6 | 3.07815 | ||||||||
\(253\) | 265769. | 0.261038 | ||||||||
\(254\) | −1.39068e6 | −1.35251 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −622474. | −0.593638 | ||||||||
\(257\) | 1.31630e6 | 1.24315 | 0.621573 | − | 0.783357i | \(-0.286494\pi\) | ||||
0.621573 | + | 0.783357i | \(0.286494\pi\) | |||||||
\(258\) | −415885. | −0.388977 | ||||||||
\(259\) | 775507. | 0.718350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33797.4 | −0.0307102 | ||||||||
\(262\) | −1.85229e6 | −1.66708 | ||||||||
\(263\) | −1.74612e6 | −1.55663 | −0.778314 | − | 0.627876i | \(-0.783925\pi\) | ||||
−0.778314 | + | 0.627876i | \(0.783925\pi\) | |||||||
\(264\) | −2.22377e6 | −1.96372 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.98190e6 | 1.71743 | ||||||||
\(267\) | 1.04283e6 | 0.895231 | ||||||||
\(268\) | −928338. | −0.789531 | ||||||||
\(269\) | −470733. | −0.396637 | −0.198319 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198319 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29459.5 | 0.0243670 | 0.0121835 | − | 0.999926i | \(-0.496122\pi\) | ||||
0.0121835 | + | 0.999926i | \(0.496122\pi\) | |||||||
\(272\) | 343991. | 0.281919 | ||||||||
\(273\) | 4.33237e6 | 3.51819 | ||||||||
\(274\) | −1.96373e6 | −1.58018 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 529828. | 0.418661 | ||||||||
\(277\) | −1.01172e6 | −0.792244 | −0.396122 | − | 0.918198i | \(-0.629644\pi\) | ||||
−0.396122 | + | 0.918198i | \(0.629644\pi\) | |||||||
\(278\) | −744031. | −0.577403 | ||||||||
\(279\) | 1.02805e6 | 0.790687 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −74592.9 | −0.0563549 | −0.0281775 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281775 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(282\) | −1.93963e6 | −1.45244 | ||||||||
\(283\) | 1.14789e6 | 0.851993 | 0.425996 | − | 0.904725i | \(-0.359924\pi\) | ||||
0.425996 | + | 0.904725i | \(0.359924\pi\) | |||||||
\(284\) | 820927. | 0.603961 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.66093e6 | −4.09235 | ||||||||
\(287\) | −1.49615e6 | −1.07219 | ||||||||
\(288\) | 2.63507e6 | 1.87202 | ||||||||
\(289\) | 653038. | 0.459932 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −818290. | −0.566467 | ||||||||
\(292\) | −1.07326e6 | −0.736625 | ||||||||
\(293\) | 1.30694e6 | 0.889376 | 0.444688 | − | 0.895686i | \(-0.353315\pi\) | ||||
0.444688 | + | 0.895686i | \(0.353315\pi\) | |||||||
\(294\) | −2.41780e6 | −1.63137 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −680790. | −0.451631 | ||||||||
\(297\) | 2.20191e6 | 1.44847 | ||||||||
\(298\) | 4.52821e6 | 2.95383 | ||||||||
\(299\) | 454535. | 0.294028 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 306936. | 0.195268 | ||||||||
\(302\) | 1.99082e6 | 1.25607 | ||||||||
\(303\) | −199209. | −0.124653 | ||||||||
\(304\) | 318394. | 0.197597 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.99568e6 | 3.04994 | ||||||||
\(307\) | 1.50999e6 | 0.914380 | 0.457190 | − | 0.889369i | \(-0.348856\pi\) | ||||
0.457190 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(308\) | 4.87001e6 | 2.92518 | ||||||||
\(309\) | −3.32796e6 | −1.98282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.69979e6 | 0.996539 | 0.498269 | − | 0.867022i | \(-0.333969\pi\) | ||||
0.498269 | + | 0.867022i | \(0.333969\pi\) | |||||||
\(312\) | −3.80323e6 | −2.21190 | ||||||||
\(313\) | −2.85190e6 | −1.64541 | −0.822703 | − | 0.568471i | \(-0.807535\pi\) | ||||
−0.822703 | + | 0.568471i | \(0.807535\pi\) | |||||||
\(314\) | 162501. | 0.0930104 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.78347e6 | 1.00473 | ||||||||
\(317\) | 158403. | 0.0885351 | 0.0442676 | − | 0.999020i | \(-0.485905\pi\) | ||||
0.0442676 | + | 0.999020i | \(0.485905\pi\) | |||||||
\(318\) | −6.37847e6 | −3.53711 | ||||||||
\(319\) | −53042.4 | −0.0291841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.02880e6 | −1.64062 | ||||||||
\(322\) | −650280. | −0.349511 | ||||||||
\(323\) | 1.91865e6 | 1.02327 | ||||||||
\(324\) | −152750. | −0.0808386 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.83783e6 | −2.00006 | ||||||||
\(327\) | 421000. | 0.217727 | ||||||||
\(328\) | 1.31342e6 | 0.674092 | ||||||||
\(329\) | 1.43151e6 | 0.729129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.38726e6 | 0.695968 | 0.347984 | − | 0.937501i | \(-0.386866\pi\) | ||||
0.347984 | + | 0.937501i | \(0.386866\pi\) | |||||||
\(332\) | 5.69488e6 | 2.83557 | ||||||||
\(333\) | 1.80932e6 | 0.894139 | ||||||||
\(334\) | 5.28687e6 | 2.59318 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −995728. | −0.481163 | ||||||||
\(337\) | −602990. | −0.289225 | −0.144612 | − | 0.989488i | \(-0.546193\pi\) | ||||
−0.144612 | + | 0.989488i | \(0.546193\pi\) | |||||||
\(338\) | −6.35522e6 | −3.02579 | ||||||||
\(339\) | 456964. | 0.215965 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.61345e6 | 0.751395 | ||||||||
\(342\) | 4.62394e6 | 2.13770 | ||||||||
\(343\) | −1.00557e6 | −0.461507 | ||||||||
\(344\) | −269448. | −0.122766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.73808e6 | −0.780511 | ||||||||
\(347\) | −1.38847e6 | −0.619030 | −0.309515 | − | 0.950895i | \(-0.600167\pi\) | ||||
−0.309515 | + | 0.950895i | \(0.600167\pi\) | |||||||
\(348\) | −105743. | −0.0468064 | ||||||||
\(349\) | 1.90607e6 | 0.837676 | 0.418838 | − | 0.908061i | \(-0.362437\pi\) | ||||
0.418838 | + | 0.908061i | \(0.362437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.76585e6 | 1.63153 | ||||||||
\(352\) | 4.13553e6 | 1.77899 | ||||||||
\(353\) | 2.53782e6 | 1.08399 | 0.541993 | − | 0.840383i | \(-0.317670\pi\) | ||||
0.541993 | + | 0.840383i | \(0.317670\pi\) | |||||||
\(354\) | −1.08112e7 | −4.58529 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00484e6 | 0.838408 | ||||||||
\(357\) | −6.00028e6 | −2.49173 | ||||||||
\(358\) | 3.88951e6 | 1.60394 | ||||||||
\(359\) | −589213. | −0.241288 | −0.120644 | − | 0.992696i | \(-0.538496\pi\) | ||||
−0.120644 | + | 0.992696i | \(0.538496\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −700223. | −0.282793 | ||||||||
\(362\) | 5.61583e6 | 2.25239 | ||||||||
\(363\) | 5.23209e6 | 2.08405 | ||||||||
\(364\) | 8.32900e6 | 3.29488 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.94083e6 | 3.48879 | ||||||||
\(367\) | −1.67673e6 | −0.649826 | −0.324913 | − | 0.945744i | \(-0.605335\pi\) | ||||
−0.324913 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(368\) | −104468. | −0.0402127 | ||||||||
\(369\) | −3.49065e6 | −1.33457 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.70750e6 | 1.77564 | ||||||||
\(372\) | 3.21651e6 | 1.20511 | ||||||||
\(373\) | −3.12665e6 | −1.16361 | −0.581804 | − | 0.813329i | \(-0.697653\pi\) | ||||
−0.581804 | + | 0.813329i | \(0.697653\pi\) | |||||||
\(374\) | 7.84032e6 | 2.89838 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25667e6 | −0.458408 | ||||||||
\(377\) | −90716.4 | −0.0328725 | ||||||||
\(378\) | −5.38761e6 | −1.93940 | ||||||||
\(379\) | −1.98431e6 | −0.709596 | −0.354798 | − | 0.934943i | \(-0.615450\pi\) | ||||
−0.354798 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.89702e6 | 1.37537 | ||||||||
\(382\) | 977069. | 0.342584 | ||||||||
\(383\) | −321813. | −0.112100 | −0.0560502 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560502 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(384\) | 6.52477e6 | 2.25807 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −282778. | −0.0966002 | ||||||||
\(387\) | 716107. | 0.243053 | ||||||||
\(388\) | −1.57317e6 | −0.530512 | ||||||||
\(389\) | −1.34564e6 | −0.450874 | −0.225437 | − | 0.974258i | \(-0.572381\pi\) | ||||
−0.225437 | + | 0.974258i | \(0.572381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −629525. | −0.208243 | ||||||||
\(392\) | −1.56647e6 | −0.514880 | ||||||||
\(393\) | 5.19057e6 | 1.69525 | ||||||||
\(394\) | −2.48026e6 | −0.804929 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.13621e7 | 3.64101 | ||||||||
\(397\) | −1.40299e6 | −0.446763 | −0.223382 | − | 0.974731i | \(-0.571710\pi\) | ||||
−0.223382 | + | 0.974731i | \(0.571710\pi\) | |||||||
\(398\) | 6.96704e6 | 2.20466 | ||||||||
\(399\) | −5.55378e6 | −1.74645 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.44258e6 | 1.06911 | 0.534556 | − | 0.845133i | \(-0.320479\pi\) | ||||
0.534556 | + | 0.845133i | \(0.320479\pi\) | |||||||
\(402\) | 4.32617e6 | 1.33518 | ||||||||
\(403\) | 2.75942e6 | 0.846359 | ||||||||
\(404\) | −382980. | −0.116741 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 129783. | 0.0390754 | ||||||||
\(407\) | 2.83958e6 | 0.849706 | ||||||||
\(408\) | 5.26743e6 | 1.56656 | ||||||||
\(409\) | 6.44614e6 | 1.90542 | 0.952711 | − | 0.303877i | \(-0.0982811\pi\) | ||||
0.952711 | + | 0.303877i | \(0.0982811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.50286e6 | 1.60688 | ||||||||
\(412\) | −6.39802e6 | −1.85696 | ||||||||
\(413\) | 7.97902e6 | 2.30184 | ||||||||
\(414\) | −1.51716e6 | −0.435040 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.07283e6 | 2.00383 | ||||||||
\(417\) | 2.08496e6 | 0.587161 | ||||||||
\(418\) | 7.25690e6 | 2.03147 | ||||||||
\(419\) | −1.77865e6 | −0.494943 | −0.247472 | − | 0.968895i | \(-0.579600\pi\) | ||||
−0.247472 | + | 0.968895i | \(0.579600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37157e6 | −0.927100 | −0.463550 | − | 0.886071i | \(-0.653425\pi\) | ||||
−0.463550 | + | 0.886071i | \(0.653425\pi\) | |||||||
\(422\) | 801721. | 0.219150 | ||||||||
\(423\) | 3.33983e6 | 0.907555 | ||||||||
\(424\) | −4.13255e6 | −1.11636 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.82562e6 | −1.02136 | ||||||||
\(427\) | −6.59861e6 | −1.75139 | ||||||||
\(428\) | −5.82288e6 | −1.53649 | ||||||||
\(429\) | 1.58633e7 | 4.16151 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.38644e6 | 0.359508 | 0.179754 | − | 0.983712i | \(-0.442470\pi\) | ||||
0.179754 | + | 0.983712i | \(0.442470\pi\) | |||||||
\(432\) | −865522. | −0.223136 | ||||||||
\(433\) | −5.74536e6 | −1.47264 | −0.736322 | − | 0.676632i | \(-0.763439\pi\) | ||||
−0.736322 | + | 0.676632i | \(0.763439\pi\) | |||||||
\(434\) | −3.94776e6 | −1.00606 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 809375. | 0.203908 | ||||||||
\(437\) | −582681. | −0.145958 | ||||||||
\(438\) | 5.00152e6 | 1.24571 | ||||||||
\(439\) | −5.14484e6 | −1.27412 | −0.637060 | − | 0.770814i | \(-0.719850\pi\) | ||||
−0.637060 | + | 0.770814i | \(0.719850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.16317e6 | 1.01936 | ||||||||
\(442\) | 1.34090e7 | 3.26468 | ||||||||
\(443\) | 5.65845e6 | 1.36990 | 0.684949 | − | 0.728591i | \(-0.259824\pi\) | ||||
0.684949 | + | 0.728591i | \(0.259824\pi\) | |||||||
\(444\) | 5.66090e6 | 1.36279 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.53162e6 | −2.03093 | ||||||||
\(447\) | −1.26892e7 | −3.00376 | ||||||||
\(448\) | −8.84958e6 | −2.08318 | ||||||||
\(449\) | −956361. | −0.223875 | −0.111938 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111938 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.47829e6 | −1.26825 | ||||||||
\(452\) | 878515. | 0.202257 | ||||||||
\(453\) | −5.57878e6 | −1.27730 | ||||||||
\(454\) | −4.17323e6 | −0.950239 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.87547e6 | 1.09800 | ||||||||
\(457\) | 5.50698e6 | 1.23345 | 0.616727 | − | 0.787177i | \(-0.288458\pi\) | ||||
0.616727 | + | 0.787177i | \(0.288458\pi\) | |||||||
\(458\) | −4.27744e6 | −0.952840 | ||||||||
\(459\) | −5.21565e6 | −1.15552 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.10202e6 | 0.460665 | 0.230333 | − | 0.973112i | \(-0.426019\pi\) | ||||
0.230333 | + | 0.973112i | \(0.426019\pi\) | |||||||
\(462\) | −2.26949e7 | −4.94678 | ||||||||
\(463\) | −2.36108e6 | −0.511868 | −0.255934 | − | 0.966694i | \(-0.582383\pi\) | ||||
−0.255934 | + | 0.966694i | \(0.582383\pi\) | |||||||
\(464\) | 20849.8 | 0.00449579 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.66190e6 | 1.42113 | ||||||||
\(467\) | 8.56485e6 | 1.81730 | 0.908652 | − | 0.417554i | \(-0.137113\pi\) | ||||
0.908652 | + | 0.417554i | \(0.137113\pi\) | |||||||
\(468\) | 1.94322e7 | 4.10117 | ||||||||
\(469\) | −3.19285e6 | −0.670264 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −455368. | −0.0945823 | ||||||||
\(472\) | −7.00450e6 | −1.44718 | ||||||||
\(473\) | 1.12387e6 | 0.230975 | ||||||||
\(474\) | −8.31121e6 | −1.69910 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.15356e7 | −2.33357 | ||||||||
\(477\) | 1.09830e7 | 2.21016 | ||||||||
\(478\) | −1.13884e7 | −2.27977 | ||||||||
\(479\) | 3.09570e6 | 0.616481 | 0.308241 | − | 0.951308i | \(-0.400260\pi\) | ||||
0.308241 | + | 0.951308i | \(0.400260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.85643e6 | 0.957095 | ||||||||
\(482\) | 7.84782e6 | 1.53862 | ||||||||
\(483\) | 1.82225e6 | 0.355418 | ||||||||
\(484\) | 1.00587e7 | 1.95177 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.59846e6 | 1.65132 | ||||||||
\(487\) | 4.69724e6 | 0.897471 | 0.448736 | − | 0.893665i | \(-0.351875\pi\) | ||||
0.448736 | + | 0.893665i | \(0.351875\pi\) | |||||||
\(488\) | 5.79268e6 | 1.10111 | ||||||||
\(489\) | 1.07546e7 | 2.03386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.40851e6 | 0.825255 | 0.412628 | − | 0.910900i | \(-0.364611\pi\) | ||||
0.412628 | + | 0.910900i | \(0.364611\pi\) | |||||||
\(492\) | −1.09213e7 | −2.03406 | ||||||||
\(493\) | 125641. | 0.0232817 | ||||||||
\(494\) | 1.24112e7 | 2.28821 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −634209. | −0.115752 | ||||||||
\(497\) | 2.82343e6 | 0.512726 | ||||||||
\(498\) | −2.65389e7 | −4.79523 | ||||||||
\(499\) | 3.52789e6 | 0.634255 | 0.317127 | − | 0.948383i | \(-0.397282\pi\) | ||||
0.317127 | + | 0.948383i | \(0.397282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.48151e7 | −2.63700 | ||||||||
\(502\) | 1.07217e7 | 1.89891 | ||||||||
\(503\) | −79054.9 | −0.0139319 | −0.00696593 | − | 0.999976i | \(-0.502217\pi\) | ||||
−0.00696593 | + | 0.999976i | \(0.502217\pi\) | |||||||
\(504\) | −9.36894e6 | −1.64291 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.38105e6 | −0.413422 | ||||||||
\(507\) | 1.78089e7 | 3.07693 | ||||||||
\(508\) | 7.49203e6 | 1.28807 | ||||||||
\(509\) | 155909. | 0.0266733 | 0.0133366 | − | 0.999911i | \(-0.495755\pi\) | ||||
0.0133366 | + | 0.999911i | \(0.495755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.69127e6 | −0.625351 | ||||||||
\(512\) | −2.73974e6 | −0.461885 | ||||||||
\(513\) | −4.82754e6 | −0.809903 | ||||||||
\(514\) | −1.17929e7 | −1.96885 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.24051e6 | 0.370444 | ||||||||
\(517\) | 5.24159e6 | 0.862456 | ||||||||
\(518\) | −6.94786e6 | −1.13770 | ||||||||
\(519\) | 4.87052e6 | 0.793702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.24897e6 | −0.685787 | −0.342893 | − | 0.939374i | \(-0.611407\pi\) | ||||
−0.342893 | + | 0.939374i | \(0.611407\pi\) | |||||||
\(522\) | 302795. | 0.0486377 | ||||||||
\(523\) | −1.30285e6 | −0.208276 | −0.104138 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104138 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(524\) | 9.97890e6 | 1.58765 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.56437e7 | 2.46533 | ||||||||
\(527\) | −3.82176e6 | −0.599427 | ||||||||
\(528\) | −3.64594e6 | −0.569148 | ||||||||
\(529\) | −6.24516e6 | −0.970296 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.86157e7 | 2.86512 | ||||||||
\(532\) | −1.06772e7 | −1.63560 | ||||||||
\(533\) | −9.36932e6 | −1.42853 | ||||||||
\(534\) | −9.34283e6 | −1.41783 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.80289e6 | 0.421399 | ||||||||
\(537\) | −1.08994e7 | −1.63104 | ||||||||
\(538\) | 4.21735e6 | 0.628179 | ||||||||
\(539\) | 6.53376e6 | 0.968704 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.58581e6 | 0.232948 | 0.116474 | − | 0.993194i | \(-0.462841\pi\) | ||||
0.116474 | + | 0.993194i | \(0.462841\pi\) | |||||||
\(542\) | −263931. | −0.0385915 | ||||||||
\(543\) | −1.57370e7 | −2.29045 | ||||||||
\(544\) | −9.79579e6 | −1.41919 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.88142e7 | −5.57197 | ||||||||
\(547\) | 5.60569e6 | 0.801052 | 0.400526 | − | 0.916285i | \(-0.368827\pi\) | ||||
0.400526 | + | 0.916285i | \(0.368827\pi\) | |||||||
\(548\) | 1.05793e7 | 1.50489 | ||||||||
\(549\) | −1.53951e7 | −2.17997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 116292. | 0.0163181 | ||||||||
\(552\) | −1.59968e6 | −0.223453 | ||||||||
\(553\) | 6.13393e6 | 0.852954 | ||||||||
\(554\) | 9.06408e6 | 1.25473 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00834e6 | 0.549892 | ||||||||
\(557\) | 44346.9 | 0.00605655 | 0.00302828 | − | 0.999995i | \(-0.499036\pi\) | ||||
0.00302828 | + | 0.999995i | \(0.499036\pi\) | |||||||
\(558\) | −9.21043e6 | −1.25226 | ||||||||
\(559\) | 1.92212e6 | 0.260166 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.19705e7 | −2.94736 | ||||||||
\(562\) | 668286. | 0.0892528 | ||||||||
\(563\) | −4.30007e6 | −0.571748 | −0.285874 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285874 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(564\) | 1.04495e7 | 1.38323 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.02841e7 | −1.34935 | ||||||||
\(567\) | −525355. | −0.0686271 | ||||||||
\(568\) | −2.47859e6 | −0.322354 | ||||||||
\(569\) | 6.54339e6 | 0.847271 | 0.423635 | − | 0.905833i | \(-0.360754\pi\) | ||||
0.423635 | + | 0.905833i | \(0.360754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.65292e6 | 1.11064 | 0.555319 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555319 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(572\) | 3.04973e7 | 3.89737 | ||||||||
\(573\) | −2.73799e6 | −0.348374 | ||||||||
\(574\) | 1.34042e7 | 1.69809 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.06468e7 | −2.59296 | ||||||||
\(577\) | −3.48407e6 | −0.435660 | −0.217830 | − | 0.975987i | \(-0.569898\pi\) | ||||
−0.217830 | + | 0.975987i | \(0.569898\pi\) | |||||||
\(578\) | −5.85064e6 | −0.728423 | ||||||||
\(579\) | 792415. | 0.0982328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.95865e7 | 2.40723 | ||||||||
\(582\) | 7.33116e6 | 0.897150 | ||||||||
\(583\) | 1.72369e7 | 2.10033 | ||||||||
\(584\) | 3.24044e6 | 0.393162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.17090e7 | −1.40856 | ||||||||
\(587\) | −6.56208e6 | −0.786043 | −0.393021 | − | 0.919529i | \(-0.628570\pi\) | ||||
−0.393021 | + | 0.919529i | \(0.628570\pi\) | |||||||
\(588\) | 1.30255e7 | 1.55364 | ||||||||
\(589\) | −3.53737e6 | −0.420138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.95032e6 | 0.818532 | ||||||||
\(592\) | −1.11618e6 | −0.130897 | ||||||||
\(593\) | −8.08785e6 | −0.944488 | −0.472244 | − | 0.881468i | \(-0.656556\pi\) | ||||
−0.472244 | + | 0.881468i | \(0.656556\pi\) | |||||||
\(594\) | −1.97272e7 | −2.29403 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.43950e7 | −2.81310 | ||||||||
\(597\) | −1.95234e7 | −2.24192 | ||||||||
\(598\) | −4.07223e6 | −0.465671 | ||||||||
\(599\) | −9.16029e6 | −1.04314 | −0.521569 | − | 0.853209i | \(-0.674653\pi\) | ||||
−0.521569 | + | 0.853209i | \(0.674653\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.25891e7 | −1.42171 | −0.710853 | − | 0.703341i | \(-0.751691\pi\) | ||||
−0.710853 | + | 0.703341i | \(0.751691\pi\) | |||||||
\(602\) | −2.74988e6 | −0.309259 | ||||||||
\(603\) | −7.44917e6 | −0.834285 | ||||||||
\(604\) | −1.07252e7 | −1.19623 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.78474e6 | 0.197421 | ||||||||
\(607\) | 1.05315e7 | 1.16017 | 0.580083 | − | 0.814558i | \(-0.303020\pi\) | ||||
0.580083 | + | 0.814558i | \(0.303020\pi\) | |||||||
\(608\) | −9.06686e6 | −0.994713 | ||||||||
\(609\) | −363685. | −0.0397358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.96450e6 | 0.971455 | ||||||||
\(612\) | −2.69134e7 | −2.90462 | ||||||||
\(613\) | −2.50815e6 | −0.269589 | −0.134794 | − | 0.990874i | \(-0.543037\pi\) | ||||
−0.134794 | + | 0.990874i | \(0.543037\pi\) | |||||||
\(614\) | −1.35281e7 | −1.44816 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.47038e7 | −1.56127 | ||||||||
\(617\) | −1.04940e7 | −1.10975 | −0.554876 | − | 0.831933i | \(-0.687234\pi\) | ||||
−0.554876 | + | 0.831933i | \(0.687234\pi\) | |||||||
\(618\) | 2.98156e7 | 3.14031 | ||||||||
\(619\) | −7.31973e6 | −0.767836 | −0.383918 | − | 0.923367i | \(-0.625426\pi\) | ||||
−0.383918 | + | 0.923367i | \(0.625426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.58396e6 | 0.164822 | ||||||||
\(622\) | −1.52286e7 | −1.57828 | ||||||||
\(623\) | 6.89529e6 | 0.711758 | ||||||||
\(624\) | −6.23552e6 | −0.641078 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.55505e7 | 2.60593 | ||||||||
\(627\) | −2.03356e7 | −2.06580 | ||||||||
\(628\) | −875446. | −0.0885789 | ||||||||
\(629\) | −6.72610e6 | −0.677855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.30990e6 | −0.630883 | −0.315442 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(632\) | −5.38476e6 | −0.536258 | ||||||||
\(633\) | −2.24662e6 | −0.222854 | ||||||||
\(634\) | −1.41915e6 | −0.140219 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.43629e7 | 3.36858 | ||||||||
\(637\) | 1.11744e7 | 1.09113 | ||||||||
\(638\) | 475213. | 0.0462207 | ||||||||
\(639\) | 6.58729e6 | 0.638196 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 176304. | 0.0169479 | 0.00847395 | − | 0.999964i | \(-0.497303\pi\) | ||||
0.00847395 | + | 0.999964i | \(0.497303\pi\) | |||||||
\(642\) | 2.71354e7 | 2.59835 | ||||||||
\(643\) | 4.73829e6 | 0.451954 | 0.225977 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225977 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(644\) | 3.50327e6 | 0.332858 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.71894e7 | −1.62061 | ||||||||
\(647\) | 1.27894e7 | 1.20113 | 0.600563 | − | 0.799577i | \(-0.294943\pi\) | ||||
0.600563 | + | 0.799577i | \(0.294943\pi\) | |||||||
\(648\) | 461191. | 0.0431463 | ||||||||
\(649\) | 2.92158e7 | 2.72274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.10626e7 | 1.02307 | ||||||||
\(652\) | 2.06757e7 | 1.90476 | ||||||||
\(653\) | −2.31597e6 | −0.212545 | −0.106272 | − | 0.994337i | \(-0.533892\pi\) | ||||
−0.106272 | + | 0.994337i | \(0.533892\pi\) | |||||||
\(654\) | −3.77179e6 | −0.344828 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.15339e6 | 0.195373 | ||||||||
\(657\) | −8.61203e6 | −0.778381 | ||||||||
\(658\) | −1.28250e7 | −1.15477 | ||||||||
\(659\) | −4.32880e6 | −0.388288 | −0.194144 | − | 0.980973i | \(-0.562193\pi\) | ||||
−0.194144 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.34429e7 | 1.19671 | 0.598355 | − | 0.801231i | \(-0.295821\pi\) | ||||
0.598355 | + | 0.801231i | \(0.295821\pi\) | |||||||
\(662\) | −1.24287e7 | −1.10225 | ||||||||
\(663\) | −3.75754e7 | −3.31986 | ||||||||
\(664\) | −1.71943e7 | −1.51344 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.62099e7 | −1.41610 | ||||||||
\(667\) | −38156.4 | −0.00332088 | ||||||||
\(668\) | −2.84821e7 | −2.46962 | ||||||||
\(669\) | 2.39077e7 | 2.06525 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.41614e7 | −2.07164 | ||||||||
\(672\) | 2.83552e7 | 2.42220 | ||||||||
\(673\) | 1.30893e7 | 1.11398 | 0.556991 | − | 0.830518i | \(-0.311956\pi\) | ||||
0.556991 | + | 0.830518i | \(0.311956\pi\) | |||||||
\(674\) | 5.40225e6 | 0.458063 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.42377e7 | 2.88163 | ||||||||
\(677\) | −1.26746e6 | −0.106283 | −0.0531415 | − | 0.998587i | \(-0.516923\pi\) | ||||
−0.0531415 | + | 0.998587i | \(0.516923\pi\) | |||||||
\(678\) | −4.09399e6 | −0.342037 | ||||||||
\(679\) | −5.41062e6 | −0.450373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16944e7 | 0.966298 | ||||||||
\(682\) | −1.44550e7 | −1.19003 | ||||||||
\(683\) | 1.77529e7 | 1.45619 | 0.728093 | − | 0.685479i | \(-0.240407\pi\) | ||||
0.728093 | + | 0.685479i | \(0.240407\pi\) | |||||||
\(684\) | −2.49107e7 | −2.03585 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.00905e6 | 0.730918 | ||||||||
\(687\) | 1.19864e7 | 0.968944 | ||||||||
\(688\) | −441769. | −0.0355815 | ||||||||
\(689\) | 2.94797e7 | 2.36578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.47133e6 | 0.435911 | 0.217955 | − | 0.975959i | \(-0.430061\pi\) | ||||
0.217955 | + | 0.975959i | \(0.430061\pi\) | |||||||
\(692\) | 9.36360e6 | 0.743323 | ||||||||
\(693\) | 3.90780e7 | 3.09100 | ||||||||
\(694\) | 1.24394e7 | 0.980396 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 319266. | 0.0249822 | ||||||||
\(697\) | 1.29764e7 | 1.01175 | ||||||||
\(698\) | −1.70767e7 | −1.32668 | ||||||||
\(699\) | −1.86683e7 | −1.44515 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.16242e7 | −0.893443 | −0.446721 | − | 0.894673i | \(-0.647408\pi\) | ||||
−0.446721 | + | 0.894673i | \(0.647408\pi\) | |||||||
\(702\) | −3.37387e7 | −2.58396 | ||||||||
\(703\) | −6.22560e6 | −0.475108 | ||||||||
\(704\) | −3.24035e7 | −2.46411 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.27366e7 | −1.71678 | ||||||||
\(707\) | −1.31719e6 | −0.0991060 | ||||||||
\(708\) | 5.82437e7 | 4.36682 | ||||||||
\(709\) | −4.30447e6 | −0.321591 | −0.160795 | − | 0.986988i | \(-0.551406\pi\) | ||||
−0.160795 | + | 0.986988i | \(0.551406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.43110e7 | 1.06168 | ||||||||
\(712\) | −6.05313e6 | −0.447487 | ||||||||
\(713\) | 1.16064e6 | 0.0855017 | ||||||||
\(714\) | 5.37572e7 | 3.94631 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.09541e7 | −1.52752 | ||||||||
\(717\) | 3.19130e7 | 2.31830 | ||||||||
\(718\) | 5.27883e6 | 0.382143 | ||||||||
\(719\) | 1.35107e7 | 0.974664 | 0.487332 | − | 0.873217i | \(-0.337970\pi\) | ||||
0.487332 | + | 0.873217i | \(0.337970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.20048e7 | −1.57645 | ||||||||
\(722\) | 6.27338e6 | 0.447877 | ||||||||
\(723\) | −2.19915e7 | −1.56462 | ||||||||
\(724\) | −3.02544e7 | −2.14507 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.68749e7 | −3.30064 | ||||||||
\(727\) | −2.62118e7 | −1.83934 | −0.919668 | − | 0.392697i | \(-0.871542\pi\) | ||||
−0.919668 | + | 0.392697i | \(0.871542\pi\) | |||||||
\(728\) | −2.51474e7 | −1.75859 | ||||||||
\(729\) | −2.33260e7 | −1.62563 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.66211e6 | −0.184260 | ||||||||
\(732\) | −4.81672e7 | −3.32257 | ||||||||
\(733\) | 2.19136e7 | 1.50644 | 0.753222 | − | 0.657766i | \(-0.228499\pi\) | ||||
0.753222 | + | 0.657766i | \(0.228499\pi\) | |||||||
\(734\) | 1.50220e7 | 1.02917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.97492e6 | 0.202433 | ||||||||
\(737\) | −1.16909e7 | −0.792827 | ||||||||
\(738\) | 3.12731e7 | 2.11364 | ||||||||
\(739\) | −2.72080e6 | −0.183267 | −0.0916337 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916337 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.47793e7 | −2.32689 | ||||||||
\(742\) | −4.21751e7 | −2.81220 | ||||||||
\(743\) | 5.79913e6 | 0.385381 | 0.192691 | − | 0.981260i | \(-0.438279\pi\) | ||||
0.192691 | + | 0.981260i | \(0.438279\pi\) | |||||||
\(744\) | −9.71146e6 | −0.643209 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.80120e7 | 1.84288 | ||||||||
\(747\) | 4.56969e7 | 2.99630 | ||||||||
\(748\) | −4.22384e7 | −2.76028 | ||||||||
\(749\) | −2.00267e7 | −1.30438 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.22708e6 | −0.144091 | −0.0720455 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720455 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(752\) | −2.06035e6 | −0.132861 | ||||||||
\(753\) | −3.00449e7 | −1.93100 | ||||||||
\(754\) | 812739. | 0.0520622 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.90248e7 | 1.84699 | ||||||||
\(757\) | −1.68706e7 | −1.07002 | −0.535009 | − | 0.844846i | \(-0.679692\pi\) | ||||
−0.535009 | + | 0.844846i | \(0.679692\pi\) | |||||||
\(758\) | 1.77776e7 | 1.12383 | ||||||||
\(759\) | 6.67231e6 | 0.420409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.73683e6 | −0.421691 | −0.210845 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210845 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(762\) | −3.49138e7 | −2.17826 | ||||||||
\(763\) | 2.78370e6 | 0.173105 | ||||||||
\(764\) | −5.26380e6 | −0.326261 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.88316e6 | 0.177540 | ||||||||
\(767\) | 4.99668e7 | 3.06685 | ||||||||
\(768\) | −1.56276e7 | −0.956071 | ||||||||
\(769\) | 2.99965e7 | 1.82917 | 0.914587 | − | 0.404390i | \(-0.132516\pi\) | ||||
0.914587 | + | 0.404390i | \(0.132516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.30466e7 | 2.00212 | ||||||||
\(772\) | 1.52342e6 | 0.0919977 | ||||||||
\(773\) | −2.03964e7 | −1.22773 | −0.613867 | − | 0.789409i | \(-0.710387\pi\) | ||||
−0.613867 | + | 0.789409i | \(0.710387\pi\) | |||||||
\(774\) | −6.41568e6 | −0.384938 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.74979e6 | 0.283152 | ||||||||
\(777\) | 1.94696e7 | 1.15692 | ||||||||
\(778\) | 1.20558e7 | 0.714078 | ||||||||
\(779\) | 1.20108e7 | 0.709133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03382e7 | 0.606482 | ||||||||
\(782\) | 5.63999e6 | 0.329808 | ||||||||
\(783\) | −316128. | −0.0184272 | ||||||||
\(784\) | −2.56827e6 | −0.149228 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.65029e7 | −2.68488 | ||||||||
\(787\) | 9.96285e6 | 0.573386 | 0.286693 | − | 0.958023i | \(-0.407444\pi\) | ||||
0.286693 | + | 0.958023i | \(0.407444\pi\) | |||||||
\(788\) | 1.33620e7 | 0.766578 | ||||||||
\(789\) | −4.38375e7 | −2.50699 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.02149e6 | 0.171704 | ||||||||
\(792\) | −3.43052e7 | −1.94333 | ||||||||
\(793\) | −4.13223e7 | −2.33346 | ||||||||
\(794\) | 1.25695e7 | 0.707567 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.75338e7 | −2.09961 | ||||||||
\(797\) | 4.33007e6 | 0.241462 | 0.120731 | − | 0.992685i | \(-0.461476\pi\) | ||||
0.120731 | + | 0.992685i | \(0.461476\pi\) | |||||||
\(798\) | 4.97570e7 | 2.76597 | ||||||||
\(799\) | −1.24157e7 | −0.688026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.60873e7 | 0.885933 | ||||||||
\(802\) | −3.08425e7 | −1.69322 | ||||||||
\(803\) | −1.35159e7 | −0.739701 | ||||||||
\(804\) | −2.33065e7 | −1.27156 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.47219e7 | −1.34043 | ||||||||
\(807\) | −1.18181e7 | −0.638796 | ||||||||
\(808\) | 1.15631e6 | 0.0623085 | ||||||||
\(809\) | 4.65045e6 | 0.249818 | 0.124909 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124909 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.23521e7 | −1.19334 | −0.596672 | − | 0.802486i | \(-0.703510\pi\) | ||||
−0.596672 | + | 0.802486i | \(0.703510\pi\) | |||||||
\(812\) | −699186. | −0.0372137 | ||||||||
\(813\) | 739599. | 0.0392437 | ||||||||
\(814\) | −2.54402e7 | −1.34573 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.63611e6 | 0.454039 | ||||||||
\(817\) | −2.46401e6 | −0.129148 | ||||||||
\(818\) | −5.77517e7 | −3.01774 | ||||||||
\(819\) | 6.68336e7 | 3.48165 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.86450e6 | 0.355427 | 0.177714 | − | 0.984082i | \(-0.443130\pi\) | ||||
0.177714 | + | 0.984082i | \(0.443130\pi\) | |||||||
\(822\) | −4.93008e7 | −2.54492 | ||||||||
\(823\) | 3.78159e7 | 1.94614 | 0.973072 | − | 0.230502i | \(-0.0740369\pi\) | ||||
0.973072 | + | 0.230502i | \(0.0740369\pi\) | |||||||
\(824\) | 1.93173e7 | 0.991123 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.14849e7 | −3.64556 | ||||||||
\(827\) | −3.11812e7 | −1.58536 | −0.792681 | − | 0.609637i | \(-0.791315\pi\) | ||||
−0.792681 | + | 0.609637i | \(0.791315\pi\) | |||||||
\(828\) | 8.17342e6 | 0.414313 | ||||||||
\(829\) | −7.56161e6 | −0.382145 | −0.191072 | − | 0.981576i | \(-0.561196\pi\) | ||||
−0.191072 | + | 0.981576i | \(0.561196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.53998e7 | −1.27593 | ||||||||
\(832\) | −5.54185e7 | −2.77553 | ||||||||
\(833\) | −1.54765e7 | −0.772786 | ||||||||
\(834\) | −1.86794e7 | −0.929924 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.90954e7 | −1.93468 | ||||||||
\(837\) | 9.61600e6 | 0.474439 | ||||||||
\(838\) | 1.59351e7 | 0.783873 | ||||||||
\(839\) | 1.20663e7 | 0.591792 | 0.295896 | − | 0.955220i | \(-0.404382\pi\) | ||||
0.295896 | + | 0.955220i | \(0.404382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05035e7 | −0.999629 | ||||||||
\(842\) | 3.02062e7 | 1.46831 | ||||||||
\(843\) | −1.87270e6 | −0.0907612 | ||||||||
\(844\) | −4.31914e6 | −0.208709 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.99219e7 | −1.43735 | ||||||||
\(847\) | 3.45951e7 | 1.65694 | ||||||||
\(848\) | −6.77544e6 | −0.323555 | ||||||||
\(849\) | 2.88186e7 | 1.37216 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.04267e6 | 0.0966886 | ||||||||
\(852\) | 2.06099e7 | 0.972696 | ||||||||
\(853\) | −2.73307e7 | −1.28611 | −0.643055 | − | 0.765820i | \(-0.722333\pi\) | ||||
−0.643055 | + | 0.765820i | \(0.722333\pi\) | |||||||
\(854\) | 5.91177e7 | 2.77378 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.75808e7 | 0.820074 | ||||||||
\(857\) | 3.10213e7 | 1.44280 | 0.721402 | − | 0.692516i | \(-0.243498\pi\) | ||||
0.721402 | + | 0.692516i | \(0.243498\pi\) | |||||||
\(858\) | −1.42121e8 | −6.59085 | ||||||||
\(859\) | 2.98878e7 | 1.38201 | 0.691006 | − | 0.722849i | \(-0.257168\pi\) | ||||
0.691006 | + | 0.722849i | \(0.257168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.75619e7 | −1.72679 | ||||||||
\(862\) | −1.24213e7 | −0.569375 | ||||||||
\(863\) | 2.37019e7 | 1.08332 | 0.541660 | − | 0.840598i | \(-0.317796\pi\) | ||||
0.541660 | + | 0.840598i | \(0.317796\pi\) | |||||||
\(864\) | 2.46474e7 | 1.12328 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.14733e7 | 2.33232 | ||||||||
\(867\) | 1.63949e7 | 0.740734 | ||||||||
\(868\) | 2.12679e7 | 0.958131 | ||||||||
\(869\) | 2.24599e7 | 1.00892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.99945e7 | −0.893027 | ||||||||
\(872\) | −2.44371e6 | −0.108832 | ||||||||
\(873\) | −1.26234e7 | −0.560584 | ||||||||
\(874\) | 5.22030e6 | 0.231162 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.69448e7 | −1.18636 | ||||||||
\(877\) | −3.85645e7 | −1.69312 | −0.846562 | − | 0.532290i | \(-0.821332\pi\) | ||||
−0.846562 | + | 0.532290i | \(0.821332\pi\) | |||||||
\(878\) | 4.60932e7 | 2.01790 | ||||||||
\(879\) | 3.28115e7 | 1.43237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.45951e7 | −1.50167 | −0.750836 | − | 0.660489i | \(-0.770349\pi\) | ||||
−0.750836 | + | 0.660489i | \(0.770349\pi\) | |||||||
\(882\) | −3.72983e7 | −1.61442 | ||||||||
\(883\) | 8.71550e6 | 0.376175 | 0.188088 | − | 0.982152i | \(-0.439771\pi\) | ||||
0.188088 | + | 0.982152i | \(0.439771\pi\) | |||||||
\(884\) | −7.22388e7 | −3.10914 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.06947e7 | −2.16959 | ||||||||
\(887\) | −4.58909e6 | −0.195847 | −0.0979237 | − | 0.995194i | \(-0.531220\pi\) | ||||
−0.0979237 | + | 0.995194i | \(0.531220\pi\) | |||||||
\(888\) | −1.70917e7 | −0.727365 | ||||||||
\(889\) | 2.57675e7 | 1.09350 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.92363e6 | −0.0811761 | ||||||||
\(892\) | 4.59627e7 | 1.93416 | ||||||||
\(893\) | −1.14918e7 | −0.482237 | ||||||||
\(894\) | 1.13684e8 | 4.75723 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.31424e7 | 1.79529 | ||||||||
\(897\) | 1.14114e7 | 0.473541 | ||||||||
\(898\) | 8.56815e6 | 0.354565 | ||||||||
\(899\) | −231642. | −0.00955912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.08290e7 | −1.67555 | ||||||||
\(902\) | 4.90807e7 | 2.00860 | ||||||||
\(903\) | 7.70583e6 | 0.314485 | ||||||||
\(904\) | −2.65246e6 | −0.107951 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.99809e7 | 2.02294 | ||||||||
\(907\) | −1.10880e7 | −0.447544 | −0.223772 | − | 0.974642i | \(-0.571837\pi\) | ||||
−0.223772 | + | 0.974642i | \(0.571837\pi\) | |||||||
\(908\) | 2.24826e7 | 0.904965 | ||||||||
\(909\) | −3.07311e6 | −0.123358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.54367e7 | 1.41468 | 0.707339 | − | 0.706875i | \(-0.249896\pi\) | ||||
0.707339 | + | 0.706875i | \(0.249896\pi\) | |||||||
\(912\) | 7.99348e6 | 0.318236 | ||||||||
\(913\) | 7.17177e7 | 2.84740 | ||||||||
\(914\) | −4.93377e7 | −1.95350 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.30440e7 | 0.907442 | ||||||||
\(917\) | 3.43206e7 | 1.34782 | ||||||||
\(918\) | 4.67276e7 | 1.83007 | ||||||||
\(919\) | 3.32990e7 | 1.30060 | 0.650298 | − | 0.759679i | \(-0.274644\pi\) | ||||
0.650298 | + | 0.759679i | \(0.274644\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.79092e7 | 1.47264 | ||||||||
\(922\) | −1.88323e7 | −0.729584 | ||||||||
\(923\) | 1.76811e7 | 0.683131 | ||||||||
\(924\) | 1.22265e8 | 4.71109 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.11532e7 | 0.810677 | ||||||||
\(927\) | −5.13390e7 | −1.96222 | ||||||||
\(928\) | −593736. | −0.0226320 | ||||||||
\(929\) | 3.43816e7 | 1.30703 | 0.653517 | − | 0.756912i | \(-0.273293\pi\) | ||||
0.653517 | + | 0.756912i | \(0.273293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.43248e7 | −0.541645 | ||||||||
\(932\) | −3.58899e7 | −1.35342 | ||||||||
\(933\) | 4.26743e7 | 1.60495 | ||||||||
\(934\) | −7.67335e7 | −2.87818 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.86708e7 | −2.18893 | ||||||||
\(937\) | −3.81989e7 | −1.42135 | −0.710677 | − | 0.703518i | \(-0.751611\pi\) | ||||
−0.710677 | + | 0.703518i | \(0.751611\pi\) | |||||||
\(938\) | 2.86051e7 | 1.06154 | ||||||||
\(939\) | −7.15988e7 | −2.64997 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.92661e7 | 1.07744 | 0.538718 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538718 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(942\) | 4.07969e6 | 0.149796 | ||||||||
\(943\) | −3.94085e6 | −0.144315 | ||||||||
\(944\) | −1.14841e7 | −0.419437 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.00689e7 | −0.365809 | ||||||||
\(947\) | −4.49447e6 | −0.162856 | −0.0814280 | − | 0.996679i | \(-0.525948\pi\) | ||||
−0.0814280 | + | 0.996679i | \(0.525948\pi\) | |||||||
\(948\) | 4.47753e7 | 1.61814 | ||||||||
\(949\) | −2.31157e7 | −0.833186 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.97681e6 | 0.142588 | ||||||||
\(952\) | 3.48288e7 | 1.24551 | ||||||||
\(953\) | 7.96508e6 | 0.284091 | 0.142046 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142046 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(954\) | −9.83978e7 | −3.50038 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.13529e7 | 2.17115 | ||||||||
\(957\) | −1.33166e6 | −0.0470018 | ||||||||
\(958\) | −2.77347e7 | −0.976360 | ||||||||
\(959\) | 3.63855e7 | 1.27756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.15831e7 | −0.753884 | ||||||||
\(962\) | −4.35094e7 | −1.51581 | ||||||||
\(963\) | −4.67240e7 | −1.62358 | ||||||||
\(964\) | −4.22788e7 | −1.46531 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.63257e7 | −0.562897 | ||||||||
\(967\) | −3.91114e6 | −0.134505 | −0.0672523 | − | 0.997736i | \(-0.521423\pi\) | ||||
−0.0672523 | + | 0.997736i | \(0.521423\pi\) | |||||||
\(968\) | −3.03698e7 | −1.04173 | ||||||||
\(969\) | 4.81689e7 | 1.64800 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.98964e7 | −1.01759 | −0.508793 | − | 0.860889i | \(-0.669908\pi\) | ||||
−0.508793 | + | 0.860889i | \(0.669908\pi\) | |||||||
\(972\) | −4.63228e7 | −1.57264 | ||||||||
\(973\) | 1.37860e7 | 0.466826 | ||||||||
\(974\) | −4.20831e7 | −1.42138 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.49728e6 | 0.319135 | ||||||||
\(977\) | 4.36187e7 | 1.46196 | 0.730981 | − | 0.682398i | \(-0.239063\pi\) | ||||
0.730981 | + | 0.682398i | \(0.239063\pi\) | |||||||
\(978\) | −9.63513e7 | −3.22115 | ||||||||
\(979\) | 2.52477e7 | 0.841909 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.49459e6 | 0.215466 | ||||||||
\(982\) | −3.94964e7 | −1.30701 | ||||||||
\(983\) | 1.95377e7 | 0.644895 | 0.322448 | − | 0.946587i | \(-0.395494\pi\) | ||||
0.322448 | + | 0.946587i | \(0.395494\pi\) | |||||||
\(984\) | 3.29743e7 | 1.08564 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.12563e6 | −0.0368727 | ||||||||
\(987\) | 3.59390e7 | 1.17428 | ||||||||
\(988\) | −6.68633e7 | −2.17919 | ||||||||
\(989\) | 808465. | 0.0262827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.45462e7 | 1.11742 | 0.558709 | − | 0.829364i | \(-0.311297\pi\) | ||||
0.558709 | + | 0.829364i | \(0.311297\pi\) | |||||||
\(992\) | 1.80603e7 | 0.582701 | ||||||||
\(993\) | 3.48282e7 | 1.12088 | ||||||||
\(994\) | −2.52954e7 | −0.812037 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.42974e8 | 4.56676 | ||||||||
\(997\) | −3.34457e7 | −1.06562 | −0.532810 | − | 0.846235i | \(-0.678864\pi\) | ||||
−0.532810 | + | 0.846235i | \(0.678864\pi\) | |||||||
\(998\) | −3.16068e7 | −1.00451 | ||||||||
\(999\) | 1.69237e7 | 0.536514 |
(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 | 1075.6.a.a.1.1 | 8 | ||
5.4 | even | 2 | 43.6.a.a.1.8 | ✓ | 8 | ||
15.14 | odd | 2 | 387.6.a.c.1.1 | 8 | |||
20.19 | odd | 2 | 688.6.a.e.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.8 | ✓ | 8 | 5.4 | even | 2 | ||
387.6.a.c.1.1 | 8 | 15.14 | odd | 2 | |||
688.6.a.e.1.7 | 8 | 20.19 | odd | 2 | |||
1075.6.a.a.1.1 | 8 | 1.1 | even | 1 | trivial |