Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,6,Mod(1,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, 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("363.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.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: | \(58.2193265921\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 363.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.353553 | 0.176777 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176777 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | 46.0000 | 0.822873 | 0.411437 | − | 0.911438i | \(-0.365027\pi\) | ||||
0.411437 | + | 0.911438i | \(0.365027\pi\) | |||||||
\(6\) | −18.0000 | −0.204124 | ||||||||
\(7\) | −148.000 | −1.14161 | −0.570803 | − | 0.821087i | \(-0.693368\pi\) | ||||
−0.570803 | + | 0.821087i | \(0.693368\pi\) | |||||||
\(8\) | −120.000 | −0.662913 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 92.0000 | 0.290930 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 252.000 | 0.505181 | ||||||||
\(13\) | −574.000 | −0.942006 | −0.471003 | − | 0.882132i | \(-0.656108\pi\) | ||||
−0.471003 | + | 0.882132i | \(0.656108\pi\) | |||||||
\(14\) | −296.000 | −0.403619 | ||||||||
\(15\) | −414.000 | −0.475086 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | 722.000 | 0.605919 | 0.302960 | − | 0.953003i | \(-0.402025\pi\) | ||||
0.302960 | + | 0.953003i | \(0.402025\pi\) | |||||||
\(18\) | 162.000 | 0.117851 | ||||||||
\(19\) | −2160.00 | −1.37268 | −0.686341 | − | 0.727280i | \(-0.740784\pi\) | ||||
−0.686341 | + | 0.727280i | \(0.740784\pi\) | |||||||
\(20\) | −1288.00 | −0.720014 | ||||||||
\(21\) | 1332.00 | 0.659107 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2536.00 | −0.999608 | −0.499804 | − | 0.866139i | \(-0.666595\pi\) | ||||
−0.499804 | + | 0.866139i | \(0.666595\pi\) | |||||||
\(24\) | 1080.00 | 0.382733 | ||||||||
\(25\) | −1009.00 | −0.322880 | ||||||||
\(26\) | −1148.00 | −0.333049 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4144.00 | 0.998906 | ||||||||
\(29\) | −4650.00 | −1.02673 | −0.513367 | − | 0.858169i | \(-0.671602\pi\) | ||||
−0.513367 | + | 0.858169i | \(0.671602\pi\) | |||||||
\(30\) | −828.000 | −0.167968 | ||||||||
\(31\) | 5032.00 | 0.940451 | 0.470226 | − | 0.882546i | \(-0.344172\pi\) | ||||
0.470226 | + | 0.882546i | \(0.344172\pi\) | |||||||
\(32\) | 5152.00 | 0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1444.00 | 0.214225 | ||||||||
\(35\) | −6808.00 | −0.939398 | ||||||||
\(36\) | −2268.00 | −0.291667 | ||||||||
\(37\) | 8118.00 | 0.974866 | 0.487433 | − | 0.873161i | \(-0.337933\pi\) | ||||
0.487433 | + | 0.873161i | \(0.337933\pi\) | |||||||
\(38\) | −4320.00 | −0.485316 | ||||||||
\(39\) | 5166.00 | 0.543867 | ||||||||
\(40\) | −5520.00 | −0.545493 | ||||||||
\(41\) | 5138.00 | 0.477347 | 0.238674 | − | 0.971100i | \(-0.423287\pi\) | ||||
0.238674 | + | 0.971100i | \(0.423287\pi\) | |||||||
\(42\) | 2664.00 | 0.233030 | ||||||||
\(43\) | −8304.00 | −0.684883 | −0.342441 | − | 0.939539i | \(-0.611254\pi\) | ||||
−0.342441 | + | 0.939539i | \(0.611254\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3726.00 | 0.274291 | ||||||||
\(46\) | −5072.00 | −0.353415 | ||||||||
\(47\) | 24728.0 | 1.63284 | 0.816421 | − | 0.577457i | \(-0.195955\pi\) | ||||
0.816421 | + | 0.577457i | \(0.195955\pi\) | |||||||
\(48\) | −5904.00 | −0.369865 | ||||||||
\(49\) | 5097.00 | 0.303266 | ||||||||
\(50\) | −2018.00 | −0.114155 | ||||||||
\(51\) | −6498.00 | −0.349828 | ||||||||
\(52\) | 16072.0 | 0.824255 | ||||||||
\(53\) | −28746.0 | −1.40568 | −0.702842 | − | 0.711346i | \(-0.748086\pi\) | ||||
−0.702842 | + | 0.711346i | \(0.748086\pi\) | |||||||
\(54\) | −1458.00 | −0.0680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17760.0 | 0.756786 | ||||||||
\(57\) | 19440.0 | 0.792518 | ||||||||
\(58\) | −9300.00 | −0.363005 | ||||||||
\(59\) | −5860.00 | −0.219163 | −0.109582 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109582 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(60\) | 11592.0 | 0.415700 | ||||||||
\(61\) | 53658.0 | 1.84633 | 0.923166 | − | 0.384401i | \(-0.125592\pi\) | ||||
0.923166 | + | 0.384401i | \(0.125592\pi\) | |||||||
\(62\) | 10064.0 | 0.332500 | ||||||||
\(63\) | −11988.0 | −0.380536 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | −26404.0 | −0.775151 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30908.0 | 0.841170 | 0.420585 | − | 0.907253i | \(-0.361825\pi\) | ||||
0.420585 | + | 0.907253i | \(0.361825\pi\) | |||||||
\(68\) | −20216.0 | −0.530180 | ||||||||
\(69\) | 22824.0 | 0.577124 | ||||||||
\(70\) | −13616.0 | −0.332127 | ||||||||
\(71\) | −69648.0 | −1.63969 | −0.819847 | − | 0.572583i | \(-0.805942\pi\) | ||||
−0.819847 | + | 0.572583i | \(0.805942\pi\) | |||||||
\(72\) | −9720.00 | −0.220971 | ||||||||
\(73\) | 18446.0 | 0.405131 | 0.202565 | − | 0.979269i | \(-0.435072\pi\) | ||||
0.202565 | + | 0.979269i | \(0.435072\pi\) | |||||||
\(74\) | 16236.0 | 0.344667 | ||||||||
\(75\) | 9081.00 | 0.186415 | ||||||||
\(76\) | 60480.0 | 1.20110 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10332.0 | 0.192286 | ||||||||
\(79\) | 25300.0 | 0.456092 | 0.228046 | − | 0.973650i | \(-0.426766\pi\) | ||||
0.228046 | + | 0.973650i | \(0.426766\pi\) | |||||||
\(80\) | 30176.0 | 0.527153 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 10276.0 | 0.168768 | ||||||||
\(83\) | 17556.0 | 0.279724 | 0.139862 | − | 0.990171i | \(-0.455334\pi\) | ||||
0.139862 | + | 0.990171i | \(0.455334\pi\) | |||||||
\(84\) | −37296.0 | −0.576719 | ||||||||
\(85\) | 33212.0 | 0.498595 | ||||||||
\(86\) | −16608.0 | −0.242143 | ||||||||
\(87\) | 41850.0 | 0.592785 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 132570. | 1.77407 | 0.887034 | − | 0.461704i | \(-0.152762\pi\) | ||||
0.887034 | + | 0.461704i | \(0.152762\pi\) | |||||||
\(90\) | 7452.00 | 0.0969765 | ||||||||
\(91\) | 84952.0 | 1.07540 | ||||||||
\(92\) | 71008.0 | 0.874657 | ||||||||
\(93\) | −45288.0 | −0.542970 | ||||||||
\(94\) | 49456.0 | 0.577297 | ||||||||
\(95\) | −99360.0 | −1.12954 | ||||||||
\(96\) | −46368.0 | −0.513500 | ||||||||
\(97\) | 70658.0 | 0.762486 | 0.381243 | − | 0.924475i | \(-0.375496\pi\) | ||||
0.381243 | + | 0.924475i | \(0.375496\pi\) | |||||||
\(98\) | 10194.0 | 0.107221 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28252.0 | 0.282520 | ||||||||
\(101\) | 101998. | 0.994920 | 0.497460 | − | 0.867487i | \(-0.334266\pi\) | ||||
0.497460 | + | 0.867487i | \(0.334266\pi\) | |||||||
\(102\) | −12996.0 | −0.123683 | ||||||||
\(103\) | 130904. | 1.21579 | 0.607897 | − | 0.794016i | \(-0.292013\pi\) | ||||
0.607897 | + | 0.794016i | \(0.292013\pi\) | |||||||
\(104\) | 68880.0 | 0.624467 | ||||||||
\(105\) | 61272.0 | 0.542361 | ||||||||
\(106\) | −57492.0 | −0.496984 | ||||||||
\(107\) | 141612. | 1.19575 | 0.597875 | − | 0.801589i | \(-0.296012\pi\) | ||||
0.597875 | + | 0.801589i | \(0.296012\pi\) | |||||||
\(108\) | 20412.0 | 0.168394 | ||||||||
\(109\) | 239810. | 1.93331 | 0.966654 | − | 0.256086i | \(-0.0824330\pi\) | ||||
0.966654 | + | 0.256086i | \(0.0824330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −73062.0 | −0.562839 | ||||||||
\(112\) | −97088.0 | −0.731342 | ||||||||
\(113\) | −42726.0 | −0.314772 | −0.157386 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157386 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(114\) | 38880.0 | 0.280197 | ||||||||
\(115\) | −116656. | −0.822550 | ||||||||
\(116\) | 130200. | 0.898392 | ||||||||
\(117\) | −46494.0 | −0.314002 | ||||||||
\(118\) | −11720.0 | −0.0774859 | ||||||||
\(119\) | −106856. | −0.691722 | ||||||||
\(120\) | 49680.0 | 0.314940 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 107316. | 0.652777 | ||||||||
\(123\) | −46242.0 | −0.275597 | ||||||||
\(124\) | −140896. | −0.822895 | ||||||||
\(125\) | −190164. | −1.08856 | ||||||||
\(126\) | −23976.0 | −0.134540 | ||||||||
\(127\) | −51788.0 | −0.284918 | −0.142459 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142459 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(128\) | −186240. | −1.00473 | ||||||||
\(129\) | 74736.0 | 0.395417 | ||||||||
\(130\) | −52808.0 | −0.274057 | ||||||||
\(131\) | −53652.0 | −0.273154 | −0.136577 | − | 0.990629i | \(-0.543610\pi\) | ||||
−0.136577 | + | 0.990629i | \(0.543610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 319680. | 1.56706 | ||||||||
\(134\) | 61816.0 | 0.297399 | ||||||||
\(135\) | −33534.0 | −0.158362 | ||||||||
\(136\) | −86640.0 | −0.401672 | ||||||||
\(137\) | −228862. | −1.04177 | −0.520886 | − | 0.853627i | \(-0.674398\pi\) | ||||
−0.520886 | + | 0.853627i | \(0.674398\pi\) | |||||||
\(138\) | 45648.0 | 0.204044 | ||||||||
\(139\) | −374920. | −1.64589 | −0.822947 | − | 0.568119i | \(-0.807671\pi\) | ||||
−0.822947 | + | 0.568119i | \(0.807671\pi\) | |||||||
\(140\) | 190624. | 0.821973 | ||||||||
\(141\) | −222552. | −0.942722 | ||||||||
\(142\) | −139296. | −0.579719 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 53136.0 | 0.213542 | ||||||||
\(145\) | −213900. | −0.844872 | ||||||||
\(146\) | 36892.0 | 0.143235 | ||||||||
\(147\) | −45873.0 | −0.175091 | ||||||||
\(148\) | −227304. | −0.853007 | ||||||||
\(149\) | 65830.0 | 0.242917 | 0.121459 | − | 0.992597i | \(-0.461243\pi\) | ||||
0.121459 | + | 0.992597i | \(0.461243\pi\) | |||||||
\(150\) | 18162.0 | 0.0659076 | ||||||||
\(151\) | −154052. | −0.549826 | −0.274913 | − | 0.961469i | \(-0.588649\pi\) | ||||
−0.274913 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(152\) | 259200. | 0.909968 | ||||||||
\(153\) | 58482.0 | 0.201973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 231472. | 0.773872 | ||||||||
\(156\) | −144648. | −0.475884 | ||||||||
\(157\) | 287678. | 0.931446 | 0.465723 | − | 0.884931i | \(-0.345794\pi\) | ||||
0.465723 | + | 0.884931i | \(0.345794\pi\) | |||||||
\(158\) | 50600.0 | 0.161253 | ||||||||
\(159\) | 258714. | 0.811572 | ||||||||
\(160\) | 236992. | 0.731870 | ||||||||
\(161\) | 375328. | 1.14116 | ||||||||
\(162\) | 13122.0 | 0.0392837 | ||||||||
\(163\) | 105124. | 0.309908 | 0.154954 | − | 0.987922i | \(-0.450477\pi\) | ||||
0.154954 | + | 0.987922i | \(0.450477\pi\) | |||||||
\(164\) | −143864. | −0.417679 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35112.0 | 0.0988975 | ||||||||
\(167\) | −150528. | −0.417663 | −0.208832 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208832 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(168\) | −159840. | −0.436930 | ||||||||
\(169\) | −41817.0 | −0.112625 | ||||||||
\(170\) | 66424.0 | 0.176280 | ||||||||
\(171\) | −174960. | −0.457560 | ||||||||
\(172\) | 232512. | 0.599272 | ||||||||
\(173\) | 2166.00 | 0.00550229 | 0.00275114 | − | 0.999996i | \(-0.499124\pi\) | ||||
0.00275114 | + | 0.999996i | \(0.499124\pi\) | |||||||
\(174\) | 83700.0 | 0.209581 | ||||||||
\(175\) | 149332. | 0.368602 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 52740.0 | 0.126534 | ||||||||
\(178\) | 265140. | 0.627228 | ||||||||
\(179\) | 672780. | 1.56942 | 0.784712 | − | 0.619860i | \(-0.212811\pi\) | ||||
0.784712 | + | 0.619860i | \(0.212811\pi\) | |||||||
\(180\) | −104328. | −0.240005 | ||||||||
\(181\) | −526778. | −1.19517 | −0.597587 | − | 0.801804i | \(-0.703874\pi\) | ||||
−0.597587 | + | 0.801804i | \(0.703874\pi\) | |||||||
\(182\) | 169904. | 0.380211 | ||||||||
\(183\) | −482922. | −1.06598 | ||||||||
\(184\) | 304320. | 0.662653 | ||||||||
\(185\) | 373428. | 0.802191 | ||||||||
\(186\) | −90576.0 | −0.191969 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −692384. | −1.42874 | ||||||||
\(189\) | 107892. | 0.219702 | ||||||||
\(190\) | −198720. | −0.399354 | ||||||||
\(191\) | −305608. | −0.606152 | −0.303076 | − | 0.952966i | \(-0.598014\pi\) | ||||
−0.303076 | + | 0.952966i | \(0.598014\pi\) | |||||||
\(192\) | 96192.0 | 0.188315 | ||||||||
\(193\) | −116434. | −0.225002 | −0.112501 | − | 0.993652i | \(-0.535886\pi\) | ||||
−0.112501 | + | 0.993652i | \(0.535886\pi\) | |||||||
\(194\) | 141316. | 0.269580 | ||||||||
\(195\) | 237636. | 0.447534 | ||||||||
\(196\) | −142716. | −0.265358 | ||||||||
\(197\) | 247742. | 0.454814 | 0.227407 | − | 0.973800i | \(-0.426975\pi\) | ||||
0.227407 | + | 0.973800i | \(0.426975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −513360. | −0.918945 | −0.459472 | − | 0.888192i | \(-0.651961\pi\) | ||||
−0.459472 | + | 0.888192i | \(0.651961\pi\) | |||||||
\(200\) | 121080. | 0.214041 | ||||||||
\(201\) | −278172. | −0.485650 | ||||||||
\(202\) | 203996. | 0.351757 | ||||||||
\(203\) | 688200. | 1.17213 | ||||||||
\(204\) | 181944. | 0.306099 | ||||||||
\(205\) | 236348. | 0.392796 | ||||||||
\(206\) | 261808. | 0.429848 | ||||||||
\(207\) | −205416. | −0.333203 | ||||||||
\(208\) | −376544. | −0.603472 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 122544. | 0.191754 | ||||||||
\(211\) | 620688. | 0.959770 | 0.479885 | − | 0.877331i | \(-0.340678\pi\) | ||||
0.479885 | + | 0.877331i | \(0.340678\pi\) | |||||||
\(212\) | 804888. | 1.22997 | ||||||||
\(213\) | 626832. | 0.946678 | ||||||||
\(214\) | 283224. | 0.422762 | ||||||||
\(215\) | −381984. | −0.563571 | ||||||||
\(216\) | 87480.0 | 0.127578 | ||||||||
\(217\) | −744736. | −1.07363 | ||||||||
\(218\) | 479620. | 0.683528 | ||||||||
\(219\) | −166014. | −0.233902 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −414428. | −0.570780 | ||||||||
\(222\) | −146124. | −0.198994 | ||||||||
\(223\) | −1.31802e6 | −1.77484 | −0.887419 | − | 0.460964i | \(-0.847504\pi\) | ||||
−0.887419 | + | 0.460964i | \(0.847504\pi\) | |||||||
\(224\) | −762496. | −1.01535 | ||||||||
\(225\) | −81729.0 | −0.107627 | ||||||||
\(226\) | −85452.0 | −0.111289 | ||||||||
\(227\) | 887412. | 1.14304 | 0.571519 | − | 0.820589i | \(-0.306354\pi\) | ||||
0.571519 | + | 0.820589i | \(0.306354\pi\) | |||||||
\(228\) | −544320. | −0.693453 | ||||||||
\(229\) | −237450. | −0.299215 | −0.149608 | − | 0.988745i | \(-0.547801\pi\) | ||||
−0.149608 | + | 0.988745i | \(0.547801\pi\) | |||||||
\(230\) | −233312. | −0.290815 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 558000. | 0.680635 | ||||||||
\(233\) | 914706. | 1.10380 | 0.551902 | − | 0.833909i | \(-0.313902\pi\) | ||||
0.551902 | + | 0.833909i | \(0.313902\pi\) | |||||||
\(234\) | −92988.0 | −0.111016 | ||||||||
\(235\) | 1.13749e6 | 1.34362 | ||||||||
\(236\) | 164080. | 0.191768 | ||||||||
\(237\) | −227700. | −0.263325 | ||||||||
\(238\) | −213712. | −0.244561 | ||||||||
\(239\) | −1.40892e6 | −1.59548 | −0.797740 | − | 0.603001i | \(-0.793971\pi\) | ||||
−0.797740 | + | 0.603001i | \(0.793971\pi\) | |||||||
\(240\) | −271584. | −0.304352 | ||||||||
\(241\) | 826358. | 0.916486 | 0.458243 | − | 0.888827i | \(-0.348479\pi\) | ||||
0.458243 | + | 0.888827i | \(0.348479\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −1.50242e6 | −1.61554 | ||||||||
\(245\) | 234462. | 0.249550 | ||||||||
\(246\) | −92484.0 | −0.0974381 | ||||||||
\(247\) | 1.23984e6 | 1.29307 | ||||||||
\(248\) | −603840. | −0.623437 | ||||||||
\(249\) | −158004. | −0.161499 | ||||||||
\(250\) | −380328. | −0.384865 | ||||||||
\(251\) | −1.60387e6 | −1.60688 | −0.803442 | − | 0.595384i | \(-0.797000\pi\) | ||||
−0.803442 | + | 0.595384i | \(0.797000\pi\) | |||||||
\(252\) | 335664. | 0.332969 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −103576. | −0.100734 | ||||||||
\(255\) | −298908. | −0.287864 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | 397618. | 0.375520 | 0.187760 | − | 0.982215i | \(-0.439877\pi\) | ||||
0.187760 | + | 0.982215i | \(0.439877\pi\) | |||||||
\(258\) | 149472. | 0.139801 | ||||||||
\(259\) | −1.20146e6 | −1.11291 | ||||||||
\(260\) | 739312. | 0.678257 | ||||||||
\(261\) | −376650. | −0.342245 | ||||||||
\(262\) | −107304. | −0.0965745 | ||||||||
\(263\) | −2.13166e6 | −1.90033 | −0.950166 | − | 0.311745i | \(-0.899087\pi\) | ||||
−0.950166 | + | 0.311745i | \(0.899087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.32232e6 | −1.15670 | ||||||||
\(266\) | 639360. | 0.554040 | ||||||||
\(267\) | −1.19313e6 | −1.02426 | ||||||||
\(268\) | −865424. | −0.736024 | ||||||||
\(269\) | −725810. | −0.611564 | −0.305782 | − | 0.952101i | \(-0.598918\pi\) | ||||
−0.305782 | + | 0.952101i | \(0.598918\pi\) | |||||||
\(270\) | −67068.0 | −0.0559894 | ||||||||
\(271\) | 1.46787e6 | 1.21413 | 0.607063 | − | 0.794654i | \(-0.292348\pi\) | ||||
0.607063 | + | 0.794654i | \(0.292348\pi\) | |||||||
\(272\) | 473632. | 0.388167 | ||||||||
\(273\) | −764568. | −0.620883 | ||||||||
\(274\) | −457724. | −0.368322 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −639072. | −0.504983 | ||||||||
\(277\) | −1.52100e6 | −1.19105 | −0.595524 | − | 0.803338i | \(-0.703056\pi\) | ||||
−0.595524 | + | 0.803338i | \(0.703056\pi\) | |||||||
\(278\) | −749840. | −0.581911 | ||||||||
\(279\) | 407592. | 0.313484 | ||||||||
\(280\) | 816960. | 0.622738 | ||||||||
\(281\) | −464382. | −0.350840 | −0.175420 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175420 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(282\) | −445104. | −0.333303 | ||||||||
\(283\) | 415136. | 0.308123 | 0.154062 | − | 0.988061i | \(-0.450765\pi\) | ||||
0.154062 | + | 0.988061i | \(0.450765\pi\) | |||||||
\(284\) | 1.95014e6 | 1.43473 | ||||||||
\(285\) | 894240. | 0.652142 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −760424. | −0.544943 | ||||||||
\(288\) | 417312. | 0.296469 | ||||||||
\(289\) | −898573. | −0.632862 | ||||||||
\(290\) | −427800. | −0.298707 | ||||||||
\(291\) | −635922. | −0.440222 | ||||||||
\(292\) | −516488. | −0.354489 | ||||||||
\(293\) | 2.59321e6 | 1.76469 | 0.882344 | − | 0.470605i | \(-0.155964\pi\) | ||||
0.882344 | + | 0.470605i | \(0.155964\pi\) | |||||||
\(294\) | −91746.0 | −0.0619040 | ||||||||
\(295\) | −269560. | −0.180343 | ||||||||
\(296\) | −974160. | −0.646251 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 131660. | 0.0858842 | ||||||||
\(299\) | 1.45566e6 | 0.941636 | ||||||||
\(300\) | −254268. | −0.163113 | ||||||||
\(301\) | 1.22899e6 | 0.781867 | ||||||||
\(302\) | −308104. | −0.194393 | ||||||||
\(303\) | −917982. | −0.574417 | ||||||||
\(304\) | −1.41696e6 | −0.879374 | ||||||||
\(305\) | 2.46827e6 | 1.51930 | ||||||||
\(306\) | 116964. | 0.0714083 | ||||||||
\(307\) | 930832. | 0.563671 | 0.281835 | − | 0.959463i | \(-0.409057\pi\) | ||||
0.281835 | + | 0.959463i | \(0.409057\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17814e6 | −0.701939 | ||||||||
\(310\) | 462944. | 0.273605 | ||||||||
\(311\) | 2.48527e6 | 1.45704 | 0.728522 | − | 0.685022i | \(-0.240207\pi\) | ||||
0.728522 | + | 0.685022i | \(0.240207\pi\) | |||||||
\(312\) | −619920. | −0.360536 | ||||||||
\(313\) | 1.31719e6 | 0.759957 | 0.379978 | − | 0.924995i | \(-0.375931\pi\) | ||||
0.379978 | + | 0.924995i | \(0.375931\pi\) | |||||||
\(314\) | 575356. | 0.329316 | ||||||||
\(315\) | −551448. | −0.313133 | ||||||||
\(316\) | −708400. | −0.399081 | ||||||||
\(317\) | 2.25540e6 | 1.26059 | 0.630297 | − | 0.776354i | \(-0.282933\pi\) | ||||
0.630297 | + | 0.776354i | \(0.282933\pi\) | |||||||
\(318\) | 517428. | 0.286934 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −491648. | −0.268398 | ||||||||
\(321\) | −1.27451e6 | −0.690367 | ||||||||
\(322\) | 750656. | 0.403461 | ||||||||
\(323\) | −1.55952e6 | −0.831734 | ||||||||
\(324\) | −183708. | −0.0972222 | ||||||||
\(325\) | 579166. | 0.304155 | ||||||||
\(326\) | 210248. | 0.109569 | ||||||||
\(327\) | −2.15829e6 | −1.11620 | ||||||||
\(328\) | −616560. | −0.316440 | ||||||||
\(329\) | −3.65974e6 | −1.86406 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.17071e6 | −1.59069 | −0.795346 | − | 0.606155i | \(-0.792711\pi\) | ||||
−0.795346 | + | 0.606155i | \(0.792711\pi\) | |||||||
\(332\) | −491568. | −0.244759 | ||||||||
\(333\) | 657558. | 0.324955 | ||||||||
\(334\) | −301056. | −0.147666 | ||||||||
\(335\) | 1.42177e6 | 0.692176 | ||||||||
\(336\) | 873792. | 0.422240 | ||||||||
\(337\) | −1.27630e6 | −0.612177 | −0.306089 | − | 0.952003i | \(-0.599020\pi\) | ||||
−0.306089 | + | 0.952003i | \(0.599020\pi\) | |||||||
\(338\) | −83634.0 | −0.0398191 | ||||||||
\(339\) | 384534. | 0.181734 | ||||||||
\(340\) | −929936. | −0.436270 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −349920. | −0.161772 | ||||||||
\(343\) | 1.73308e6 | 0.795396 | ||||||||
\(344\) | 996480. | 0.454017 | ||||||||
\(345\) | 1.04990e6 | 0.474900 | ||||||||
\(346\) | 4332.00 | 0.00194535 | ||||||||
\(347\) | −3.69303e6 | −1.64649 | −0.823245 | − | 0.567687i | \(-0.807838\pi\) | ||||
−0.823245 | + | 0.567687i | \(0.807838\pi\) | |||||||
\(348\) | −1.17180e6 | −0.518687 | ||||||||
\(349\) | −1.70919e6 | −0.751150 | −0.375575 | − | 0.926792i | \(-0.622555\pi\) | ||||
−0.375575 | + | 0.926792i | \(0.622555\pi\) | |||||||
\(350\) | 298664. | 0.130321 | ||||||||
\(351\) | 418446. | 0.181289 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.36859e6 | 1.86597 | 0.932986 | − | 0.359914i | \(-0.117194\pi\) | ||||
0.932986 | + | 0.359914i | \(0.117194\pi\) | |||||||
\(354\) | 105480. | 0.0447365 | ||||||||
\(355\) | −3.20381e6 | −1.34926 | ||||||||
\(356\) | −3.71196e6 | −1.55231 | ||||||||
\(357\) | 961704. | 0.399366 | ||||||||
\(358\) | 1.34556e6 | 0.554875 | ||||||||
\(359\) | 3.51284e6 | 1.43854 | 0.719271 | − | 0.694730i | \(-0.244476\pi\) | ||||
0.719271 | + | 0.694730i | \(0.244476\pi\) | |||||||
\(360\) | −447120. | −0.181831 | ||||||||
\(361\) | 2.18950e6 | 0.884254 | ||||||||
\(362\) | −1.05356e6 | −0.422558 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.37866e6 | −0.940975 | ||||||||
\(365\) | 848516. | 0.333371 | ||||||||
\(366\) | −965844. | −0.376881 | ||||||||
\(367\) | −2.15259e6 | −0.834251 | −0.417125 | − | 0.908849i | \(-0.636962\pi\) | ||||
−0.417125 | + | 0.908849i | \(0.636962\pi\) | |||||||
\(368\) | −1.66362e6 | −0.640374 | ||||||||
\(369\) | 416178. | 0.159116 | ||||||||
\(370\) | 746856. | 0.283617 | ||||||||
\(371\) | 4.25441e6 | 1.60474 | ||||||||
\(372\) | 1.26806e6 | 0.475099 | ||||||||
\(373\) | 2.24247e6 | 0.834553 | 0.417276 | − | 0.908780i | \(-0.362985\pi\) | ||||
0.417276 | + | 0.908780i | \(0.362985\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.71148e6 | 0.628482 | ||||||||
\(376\) | −2.96736e6 | −1.08243 | ||||||||
\(377\) | 2.66910e6 | 0.967189 | ||||||||
\(378\) | 215784. | 0.0776765 | ||||||||
\(379\) | −2.40986e6 | −0.861775 | −0.430887 | − | 0.902406i | \(-0.641799\pi\) | ||||
−0.430887 | + | 0.902406i | \(0.641799\pi\) | |||||||
\(380\) | 2.78208e6 | 0.988350 | ||||||||
\(381\) | 466092. | 0.164497 | ||||||||
\(382\) | −611216. | −0.214307 | ||||||||
\(383\) | −1.01066e6 | −0.352052 | −0.176026 | − | 0.984386i | \(-0.556324\pi\) | ||||
−0.176026 | + | 0.984386i | \(0.556324\pi\) | |||||||
\(384\) | 1.67616e6 | 0.580079 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −232868. | −0.0795503 | ||||||||
\(387\) | −672624. | −0.228294 | ||||||||
\(388\) | −1.97842e6 | −0.667175 | ||||||||
\(389\) | 1.27779e6 | 0.428140 | 0.214070 | − | 0.976818i | \(-0.431328\pi\) | ||||
0.214070 | + | 0.976818i | \(0.431328\pi\) | |||||||
\(390\) | 475272. | 0.158227 | ||||||||
\(391\) | −1.83099e6 | −0.605682 | ||||||||
\(392\) | −611640. | −0.201039 | ||||||||
\(393\) | 482868. | 0.157706 | ||||||||
\(394\) | 495484. | 0.160801 | ||||||||
\(395\) | 1.16380e6 | 0.375306 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.45400e6 | 1.73676 | 0.868378 | − | 0.495903i | \(-0.165163\pi\) | ||||
0.868378 | + | 0.495903i | \(0.165163\pi\) | |||||||
\(398\) | −1.02672e6 | −0.324896 | ||||||||
\(399\) | −2.87712e6 | −0.904744 | ||||||||
\(400\) | −661904. | −0.206845 | ||||||||
\(401\) | −1.48980e6 | −0.462665 | −0.231332 | − | 0.972875i | \(-0.574308\pi\) | ||||
−0.231332 | + | 0.972875i | \(0.574308\pi\) | |||||||
\(402\) | −556344. | −0.171703 | ||||||||
\(403\) | −2.88837e6 | −0.885911 | ||||||||
\(404\) | −2.85594e6 | −0.870555 | ||||||||
\(405\) | 301806. | 0.0914303 | ||||||||
\(406\) | 1.37640e6 | 0.414409 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 779760. | 0.231905 | ||||||||
\(409\) | 4.39899e6 | 1.30030 | 0.650152 | − | 0.759804i | \(-0.274705\pi\) | ||||
0.650152 | + | 0.759804i | \(0.274705\pi\) | |||||||
\(410\) | 472696. | 0.138874 | ||||||||
\(411\) | 2.05976e6 | 0.601467 | ||||||||
\(412\) | −3.66531e6 | −1.06382 | ||||||||
\(413\) | 867280. | 0.250198 | ||||||||
\(414\) | −410832. | −0.117805 | ||||||||
\(415\) | 807576. | 0.230178 | ||||||||
\(416\) | −2.95725e6 | −0.837827 | ||||||||
\(417\) | 3.37428e6 | 0.950257 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −280420. | −0.0780322 | −0.0390161 | − | 0.999239i | \(-0.512422\pi\) | ||||
−0.0390161 | + | 0.999239i | \(0.512422\pi\) | |||||||
\(420\) | −1.71562e6 | −0.474566 | ||||||||
\(421\) | 817462. | 0.224782 | 0.112391 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112391 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(422\) | 1.24138e6 | 0.339330 | ||||||||
\(423\) | 2.00297e6 | 0.544281 | ||||||||
\(424\) | 3.44952e6 | 0.931846 | ||||||||
\(425\) | −728498. | −0.195639 | ||||||||
\(426\) | 1.25366e6 | 0.334701 | ||||||||
\(427\) | −7.94138e6 | −2.10779 | ||||||||
\(428\) | −3.96514e6 | −1.04628 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −763968. | −0.199253 | ||||||||
\(431\) | −1.88599e6 | −0.489043 | −0.244521 | − | 0.969644i | \(-0.578631\pi\) | ||||
−0.244521 | + | 0.969644i | \(0.578631\pi\) | |||||||
\(432\) | −478224. | −0.123288 | ||||||||
\(433\) | 5.84067e6 | 1.49707 | 0.748537 | − | 0.663093i | \(-0.230757\pi\) | ||||
0.748537 | + | 0.663093i | \(0.230757\pi\) | |||||||
\(434\) | −1.48947e6 | −0.379584 | ||||||||
\(435\) | 1.92510e6 | 0.487787 | ||||||||
\(436\) | −6.71468e6 | −1.69164 | ||||||||
\(437\) | 5.47776e6 | 1.37214 | ||||||||
\(438\) | −332028. | −0.0826969 | ||||||||
\(439\) | 509540. | 0.126188 | 0.0630938 | − | 0.998008i | \(-0.479903\pi\) | ||||
0.0630938 | + | 0.998008i | \(0.479903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 412857. | 0.101089 | ||||||||
\(442\) | −828856. | −0.201801 | ||||||||
\(443\) | 4.10268e6 | 0.993250 | 0.496625 | − | 0.867965i | \(-0.334572\pi\) | ||||
0.496625 | + | 0.867965i | \(0.334572\pi\) | |||||||
\(444\) | 2.04574e6 | 0.492484 | ||||||||
\(445\) | 6.09822e6 | 1.45983 | ||||||||
\(446\) | −2.63603e6 | −0.627500 | ||||||||
\(447\) | −592470. | −0.140248 | ||||||||
\(448\) | 1.58182e6 | 0.372360 | ||||||||
\(449\) | 513410. | 0.120185 | 0.0600923 | − | 0.998193i | \(-0.480861\pi\) | ||||
0.0600923 | + | 0.998193i | \(0.480861\pi\) | |||||||
\(450\) | −163458. | −0.0380518 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.19633e6 | 0.275426 | ||||||||
\(453\) | 1.38647e6 | 0.317442 | ||||||||
\(454\) | 1.77482e6 | 0.404125 | ||||||||
\(455\) | 3.90779e6 | 0.884918 | ||||||||
\(456\) | −2.33280e6 | −0.525370 | ||||||||
\(457\) | −1.22738e6 | −0.274908 | −0.137454 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137454 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(458\) | −474900. | −0.105789 | ||||||||
\(459\) | −526338. | −0.116609 | ||||||||
\(460\) | 3.26637e6 | 0.719732 | ||||||||
\(461\) | 6.41000e6 | 1.40477 | 0.702386 | − | 0.711797i | \(-0.252118\pi\) | ||||
0.702386 | + | 0.711797i | \(0.252118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.63030e6 | 1.43741 | 0.718705 | − | 0.695315i | \(-0.244735\pi\) | ||||
0.718705 | + | 0.695315i | \(0.244735\pi\) | |||||||
\(464\) | −3.05040e6 | −0.657751 | ||||||||
\(465\) | −2.08325e6 | −0.446795 | ||||||||
\(466\) | 1.82941e6 | 0.390253 | ||||||||
\(467\) | −4.14769e6 | −0.880064 | −0.440032 | − | 0.897982i | \(-0.645033\pi\) | ||||
−0.440032 | + | 0.897982i | \(0.645033\pi\) | |||||||
\(468\) | 1.30183e6 | 0.274752 | ||||||||
\(469\) | −4.57438e6 | −0.960286 | ||||||||
\(470\) | 2.27498e6 | 0.475042 | ||||||||
\(471\) | −2.58910e6 | −0.537770 | ||||||||
\(472\) | 703200. | 0.145286 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −455400. | −0.0930995 | ||||||||
\(475\) | 2.17944e6 | 0.443211 | ||||||||
\(476\) | 2.99197e6 | 0.605257 | ||||||||
\(477\) | −2.32843e6 | −0.468561 | ||||||||
\(478\) | −2.81784e6 | −0.564088 | ||||||||
\(479\) | 5.05132e6 | 1.00593 | 0.502963 | − | 0.864308i | \(-0.332243\pi\) | ||||
0.502963 | + | 0.864308i | \(0.332243\pi\) | |||||||
\(480\) | −2.13293e6 | −0.422545 | ||||||||
\(481\) | −4.65973e6 | −0.918329 | ||||||||
\(482\) | 1.65272e6 | 0.324027 | ||||||||
\(483\) | −3.37795e6 | −0.658849 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.25027e6 | 0.627429 | ||||||||
\(486\) | −118098. | −0.0226805 | ||||||||
\(487\) | 2.66221e6 | 0.508651 | 0.254325 | − | 0.967119i | \(-0.418147\pi\) | ||||
0.254325 | + | 0.967119i | \(0.418147\pi\) | |||||||
\(488\) | −6.43896e6 | −1.22396 | ||||||||
\(489\) | −946116. | −0.178925 | ||||||||
\(490\) | 468924. | 0.0882292 | ||||||||
\(491\) | 5.54659e6 | 1.03830 | 0.519149 | − | 0.854684i | \(-0.326249\pi\) | ||||
0.519149 | + | 0.854684i | \(0.326249\pi\) | |||||||
\(492\) | 1.29478e6 | 0.241147 | ||||||||
\(493\) | −3.35730e6 | −0.622118 | ||||||||
\(494\) | 2.47968e6 | 0.457171 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.30099e6 | 0.602477 | ||||||||
\(497\) | 1.03079e7 | 1.87189 | ||||||||
\(498\) | −316008. | −0.0570985 | ||||||||
\(499\) | −6820.00 | −0.00122612 | −0.000613060 | − | 1.00000i | \(-0.500195\pi\) | ||||
−0.000613060 | 1.00000i | \(0.500195\pi\) | ||||||||
\(500\) | 5.32459e6 | 0.952492 | ||||||||
\(501\) | 1.35475e6 | 0.241138 | ||||||||
\(502\) | −3.20774e6 | −0.568119 | ||||||||
\(503\) | 451136. | 0.0795037 | 0.0397519 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397519 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(504\) | 1.43856e6 | 0.252262 | ||||||||
\(505\) | 4.69191e6 | 0.818693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 376353. | 0.0650243 | ||||||||
\(508\) | 1.45006e6 | 0.249303 | ||||||||
\(509\) | 393390. | 0.0673021 | 0.0336511 | − | 0.999434i | \(-0.489287\pi\) | ||||
0.0336511 | + | 0.999434i | \(0.489287\pi\) | |||||||
\(510\) | −597816. | −0.101775 | ||||||||
\(511\) | −2.73001e6 | −0.462500 | ||||||||
\(512\) | 5.89875e6 | 0.994455 | ||||||||
\(513\) | 1.57464e6 | 0.264173 | ||||||||
\(514\) | 795236. | 0.132766 | ||||||||
\(515\) | 6.02158e6 | 1.00044 | ||||||||
\(516\) | −2.09261e6 | −0.345990 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.40293e6 | −0.393474 | ||||||||
\(519\) | −19494.0 | −0.00317675 | ||||||||
\(520\) | 3.16848e6 | 0.513857 | ||||||||
\(521\) | 3.28432e6 | 0.530092 | 0.265046 | − | 0.964236i | \(-0.414613\pi\) | ||||
0.265046 | + | 0.964236i | \(0.414613\pi\) | |||||||
\(522\) | −753300. | −0.121002 | ||||||||
\(523\) | 1.68266e6 | 0.268993 | 0.134497 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134497 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(524\) | 1.50226e6 | 0.239010 | ||||||||
\(525\) | −1.34399e6 | −0.212812 | ||||||||
\(526\) | −4.26333e6 | −0.671869 | ||||||||
\(527\) | 3.63310e6 | 0.569838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5047.00 | −0.000784141 0 | ||||||||
\(530\) | −2.64463e6 | −0.408955 | ||||||||
\(531\) | −474660. | −0.0730544 | ||||||||
\(532\) | −8.95104e6 | −1.37118 | ||||||||
\(533\) | −2.94921e6 | −0.449664 | ||||||||
\(534\) | −2.38626e6 | −0.362130 | ||||||||
\(535\) | 6.51415e6 | 0.983951 | ||||||||
\(536\) | −3.70896e6 | −0.557622 | ||||||||
\(537\) | −6.05502e6 | −0.906108 | ||||||||
\(538\) | −1.45162e6 | −0.216221 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 938952. | 0.138567 | ||||||||
\(541\) | −9.48158e6 | −1.39280 | −0.696398 | − | 0.717656i | \(-0.745215\pi\) | ||||
−0.696398 | + | 0.717656i | \(0.745215\pi\) | |||||||
\(542\) | 2.93574e6 | 0.429258 | ||||||||
\(543\) | 4.74100e6 | 0.690034 | ||||||||
\(544\) | 3.71974e6 | 0.538909 | ||||||||
\(545\) | 1.10313e7 | 1.59087 | ||||||||
\(546\) | −1.52914e6 | −0.219515 | ||||||||
\(547\) | 6.09239e6 | 0.870602 | 0.435301 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435301 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(548\) | 6.40814e6 | 0.911550 | ||||||||
\(549\) | 4.34630e6 | 0.615444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00440e7 | 1.40938 | ||||||||
\(552\) | −2.73888e6 | −0.382583 | ||||||||
\(553\) | −3.74440e6 | −0.520678 | ||||||||
\(554\) | −3.04200e6 | −0.421099 | ||||||||
\(555\) | −3.36085e6 | −0.463145 | ||||||||
\(556\) | 1.04978e7 | 1.44016 | ||||||||
\(557\) | −8.49594e6 | −1.16031 | −0.580154 | − | 0.814507i | \(-0.697008\pi\) | ||||
−0.580154 | + | 0.814507i | \(0.697008\pi\) | |||||||
\(558\) | 815184. | 0.110833 | ||||||||
\(559\) | 4.76650e6 | 0.645163 | ||||||||
\(560\) | −4.46605e6 | −0.601802 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −928764. | −0.124041 | ||||||||
\(563\) | 7.02216e6 | 0.933683 | 0.466842 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466842 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(564\) | 6.23146e6 | 0.824882 | ||||||||
\(565\) | −1.96540e6 | −0.259017 | ||||||||
\(566\) | 830272. | 0.108938 | ||||||||
\(567\) | −971028. | −0.126845 | ||||||||
\(568\) | 8.35776e6 | 1.08697 | ||||||||
\(569\) | −9.41847e6 | −1.21955 | −0.609775 | − | 0.792574i | \(-0.708740\pi\) | ||||
−0.609775 | + | 0.792574i | \(0.708740\pi\) | |||||||
\(570\) | 1.78848e6 | 0.230567 | ||||||||
\(571\) | −7.29699e6 | −0.936599 | −0.468299 | − | 0.883570i | \(-0.655133\pi\) | ||||
−0.468299 | + | 0.883570i | \(0.655133\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.75047e6 | 0.349962 | ||||||||
\(574\) | −1.52085e6 | −0.192666 | ||||||||
\(575\) | 2.55882e6 | 0.322753 | ||||||||
\(576\) | −865728. | −0.108724 | ||||||||
\(577\) | −3.29590e6 | −0.412131 | −0.206065 | − | 0.978538i | \(-0.566066\pi\) | ||||
−0.206065 | + | 0.978538i | \(0.566066\pi\) | |||||||
\(578\) | −1.79715e6 | −0.223750 | ||||||||
\(579\) | 1.04791e6 | 0.129905 | ||||||||
\(580\) | 5.98920e6 | 0.739263 | ||||||||
\(581\) | −2.59829e6 | −0.319335 | ||||||||
\(582\) | −1.27184e6 | −0.155642 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.21352e6 | −0.268566 | ||||||||
\(585\) | −2.13872e6 | −0.258384 | ||||||||
\(586\) | 5.18641e6 | 0.623911 | ||||||||
\(587\) | 4.39827e6 | 0.526849 | 0.263425 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263425 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(588\) | 1.28444e6 | 0.153205 | ||||||||
\(589\) | −1.08691e7 | −1.29094 | ||||||||
\(590\) | −539120. | −0.0637610 | ||||||||
\(591\) | −2.22968e6 | −0.262587 | ||||||||
\(592\) | 5.32541e6 | 0.624523 | ||||||||
\(593\) | −9.21781e6 | −1.07644 | −0.538222 | − | 0.842803i | \(-0.680904\pi\) | ||||
−0.538222 | + | 0.842803i | \(0.680904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.91538e6 | −0.569199 | ||||||||
\(596\) | −1.84324e6 | −0.212553 | ||||||||
\(597\) | 4.62024e6 | 0.530553 | ||||||||
\(598\) | 2.91133e6 | 0.332919 | ||||||||
\(599\) | 3.77140e6 | 0.429473 | 0.214736 | − | 0.976672i | \(-0.431111\pi\) | ||||
0.214736 | + | 0.976672i | \(0.431111\pi\) | |||||||
\(600\) | −1.08972e6 | −0.123577 | ||||||||
\(601\) | −4.19724e6 | −0.473999 | −0.237000 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.237000 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(602\) | 2.45798e6 | 0.276432 | ||||||||
\(603\) | 2.50355e6 | 0.280390 | ||||||||
\(604\) | 4.31346e6 | 0.481097 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.83596e6 | −0.203087 | ||||||||
\(607\) | 1.00133e6 | 0.110308 | 0.0551539 | − | 0.998478i | \(-0.482435\pi\) | ||||
0.0551539 | + | 0.998478i | \(0.482435\pi\) | |||||||
\(608\) | −1.11283e7 | −1.22087 | ||||||||
\(609\) | −6.19380e6 | −0.676728 | ||||||||
\(610\) | 4.93654e6 | 0.537153 | ||||||||
\(611\) | −1.41939e7 | −1.53815 | ||||||||
\(612\) | −1.63750e6 | −0.176727 | ||||||||
\(613\) | 7.38239e6 | 0.793498 | 0.396749 | − | 0.917927i | \(-0.370138\pi\) | ||||
0.396749 | + | 0.917927i | \(0.370138\pi\) | |||||||
\(614\) | 1.86166e6 | 0.199288 | ||||||||
\(615\) | −2.12713e6 | −0.226781 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.54025e7 | −1.62884 | −0.814418 | − | 0.580279i | \(-0.802944\pi\) | ||||
−0.814418 | + | 0.580279i | \(0.802944\pi\) | |||||||
\(618\) | −2.35627e6 | −0.248173 | ||||||||
\(619\) | −7.12402e6 | −0.747306 | −0.373653 | − | 0.927569i | \(-0.621895\pi\) | ||||
−0.373653 | + | 0.927569i | \(0.621895\pi\) | |||||||
\(620\) | −6.48122e6 | −0.677138 | ||||||||
\(621\) | 1.84874e6 | 0.192375 | ||||||||
\(622\) | 4.97054e6 | 0.515143 | ||||||||
\(623\) | −1.96204e7 | −2.02529 | ||||||||
\(624\) | 3.38890e6 | 0.348415 | ||||||||
\(625\) | −5.59442e6 | −0.572869 | ||||||||
\(626\) | 2.63439e6 | 0.268685 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.05498e6 | −0.815015 | ||||||||
\(629\) | 5.86120e6 | 0.590690 | ||||||||
\(630\) | −1.10290e6 | −0.110709 | ||||||||
\(631\) | 1.16696e7 | 1.16677 | 0.583383 | − | 0.812197i | \(-0.301729\pi\) | ||||
0.583383 | + | 0.812197i | \(0.301729\pi\) | |||||||
\(632\) | −3.03600e6 | −0.302349 | ||||||||
\(633\) | −5.58619e6 | −0.554124 | ||||||||
\(634\) | 4.51080e6 | 0.445687 | ||||||||
\(635\) | −2.38225e6 | −0.234451 | ||||||||
\(636\) | −7.24399e6 | −0.710126 | ||||||||
\(637\) | −2.92568e6 | −0.285679 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.64149e6 | −0.546565 | ||||||||
\(640\) | −8.56704e6 | −0.826763 | ||||||||
\(641\) | −1.10271e7 | −1.06003 | −0.530014 | − | 0.847989i | \(-0.677813\pi\) | ||||
−0.530014 | + | 0.847989i | \(0.677813\pi\) | |||||||
\(642\) | −2.54902e6 | −0.244082 | ||||||||
\(643\) | −9.56024e6 | −0.911887 | −0.455944 | − | 0.890009i | \(-0.650698\pi\) | ||||
−0.455944 | + | 0.890009i | \(0.650698\pi\) | |||||||
\(644\) | −1.05092e7 | −0.998514 | ||||||||
\(645\) | 3.43786e6 | 0.325378 | ||||||||
\(646\) | −3.11904e6 | −0.294063 | ||||||||
\(647\) | −1.09942e7 | −1.03253 | −0.516263 | − | 0.856430i | \(-0.672677\pi\) | ||||
−0.516263 | + | 0.856430i | \(0.672677\pi\) | |||||||
\(648\) | −787320. | −0.0736570 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.15833e6 | 0.107535 | ||||||||
\(651\) | 6.70262e6 | 0.619858 | ||||||||
\(652\) | −2.94347e6 | −0.271170 | ||||||||
\(653\) | −295346. | −0.0271049 | −0.0135525 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135525 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(654\) | −4.31658e6 | −0.394635 | ||||||||
\(655\) | −2.46799e6 | −0.224771 | ||||||||
\(656\) | 3.37053e6 | 0.305801 | ||||||||
\(657\) | 1.49413e6 | 0.135044 | ||||||||
\(658\) | −7.31949e6 | −0.659046 | ||||||||
\(659\) | 1.65613e7 | 1.48553 | 0.742766 | − | 0.669551i | \(-0.233514\pi\) | ||||
0.742766 | + | 0.669551i | \(0.233514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.97042e6 | 0.175411 | 0.0877053 | − | 0.996146i | \(-0.472047\pi\) | ||||
0.0877053 | + | 0.996146i | \(0.472047\pi\) | |||||||
\(662\) | −6.34142e6 | −0.562395 | ||||||||
\(663\) | 3.72985e6 | 0.329540 | ||||||||
\(664\) | −2.10672e6 | −0.185433 | ||||||||
\(665\) | 1.47053e7 | 1.28949 | ||||||||
\(666\) | 1.31512e6 | 0.114889 | ||||||||
\(667\) | 1.17924e7 | 1.02633 | ||||||||
\(668\) | 4.21478e6 | 0.365455 | ||||||||
\(669\) | 1.18621e7 | 1.02470 | ||||||||
\(670\) | 2.84354e6 | 0.244721 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.86246e6 | 0.586215 | ||||||||
\(673\) | 1.63733e6 | 0.139347 | 0.0696735 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696735 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(674\) | −2.55260e6 | −0.216437 | ||||||||
\(675\) | 735561. | 0.0621383 | ||||||||
\(676\) | 1.17088e6 | 0.0985472 | ||||||||
\(677\) | 6.35878e6 | 0.533215 | 0.266607 | − | 0.963805i | \(-0.414097\pi\) | ||||
0.266607 | + | 0.963805i | \(0.414097\pi\) | |||||||
\(678\) | 769068. | 0.0642526 | ||||||||
\(679\) | −1.04574e7 | −0.870460 | ||||||||
\(680\) | −3.98544e6 | −0.330525 | ||||||||
\(681\) | −7.98671e6 | −0.659933 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.11033e7 | 0.910751 | 0.455376 | − | 0.890299i | \(-0.349505\pi\) | ||||
0.455376 | + | 0.890299i | \(0.349505\pi\) | |||||||
\(684\) | 4.89888e6 | 0.400365 | ||||||||
\(685\) | −1.05277e7 | −0.857245 | ||||||||
\(686\) | 3.46616e6 | 0.281215 | ||||||||
\(687\) | 2.13705e6 | 0.172752 | ||||||||
\(688\) | −5.44742e6 | −0.438753 | ||||||||
\(689\) | 1.65002e7 | 1.32416 | ||||||||
\(690\) | 2.09981e6 | 0.167902 | ||||||||
\(691\) | 1.70189e7 | 1.35592 | 0.677962 | − | 0.735097i | \(-0.262864\pi\) | ||||
0.677962 | + | 0.735097i | \(0.262864\pi\) | |||||||
\(692\) | −60648.0 | −0.00481450 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.38606e6 | −0.582122 | ||||||||
\(695\) | −1.72463e7 | −1.35436 | ||||||||
\(696\) | −5.02200e6 | −0.392965 | ||||||||
\(697\) | 3.70964e6 | 0.289234 | ||||||||
\(698\) | −3.41838e6 | −0.265572 | ||||||||
\(699\) | −8.23235e6 | −0.637281 | ||||||||
\(700\) | −4.18130e6 | −0.322527 | ||||||||
\(701\) | −1.58021e7 | −1.21456 | −0.607280 | − | 0.794488i | \(-0.707740\pi\) | ||||
−0.607280 | + | 0.794488i | \(0.707740\pi\) | |||||||
\(702\) | 836892. | 0.0640954 | ||||||||
\(703\) | −1.75349e7 | −1.33818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.02374e7 | −0.775741 | ||||||||
\(706\) | 8.73719e6 | 0.659720 | ||||||||
\(707\) | −1.50957e7 | −1.13581 | ||||||||
\(708\) | −1.47672e6 | −0.110717 | ||||||||
\(709\) | 1.24834e7 | 0.932643 | 0.466322 | − | 0.884615i | \(-0.345579\pi\) | ||||
0.466322 | + | 0.884615i | \(0.345579\pi\) | |||||||
\(710\) | −6.40762e6 | −0.477035 | ||||||||
\(711\) | 2.04930e6 | 0.152031 | ||||||||
\(712\) | −1.59084e7 | −1.17605 | ||||||||
\(713\) | −1.27612e7 | −0.940083 | ||||||||
\(714\) | 1.92341e6 | 0.141197 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.88378e7 | −1.37325 | ||||||||
\(717\) | 1.26803e7 | 0.921151 | ||||||||
\(718\) | 7.02568e6 | 0.508601 | ||||||||
\(719\) | 2.00724e6 | 0.144803 | 0.0724014 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0724014 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(720\) | 2.44426e6 | 0.175718 | ||||||||
\(721\) | −1.93738e7 | −1.38796 | ||||||||
\(722\) | 4.37900e6 | 0.312631 | ||||||||
\(723\) | −7.43722e6 | −0.529133 | ||||||||
\(724\) | 1.47498e7 | 1.04578 | ||||||||
\(725\) | 4.69185e6 | 0.331512 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.97301e6 | 0.489310 | 0.244655 | − | 0.969610i | \(-0.421325\pi\) | ||||
0.244655 | + | 0.969610i | \(0.421325\pi\) | |||||||
\(728\) | −1.01942e7 | −0.712896 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.69703e6 | 0.117864 | ||||||||
\(731\) | −5.99549e6 | −0.414984 | ||||||||
\(732\) | 1.35218e7 | 0.932733 | ||||||||
\(733\) | 2.34965e7 | 1.61527 | 0.807633 | − | 0.589685i | \(-0.200748\pi\) | ||||
0.807633 | + | 0.589685i | \(0.200748\pi\) | |||||||
\(734\) | −4.30518e6 | −0.294952 | ||||||||
\(735\) | −2.11016e6 | −0.144078 | ||||||||
\(736\) | −1.30655e7 | −0.889059 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 832356. | 0.0562559 | ||||||||
\(739\) | 1.39901e7 | 0.942346 | 0.471173 | − | 0.882041i | \(-0.343831\pi\) | ||||
0.471173 | + | 0.882041i | \(0.343831\pi\) | |||||||
\(740\) | −1.04560e7 | −0.701917 | ||||||||
\(741\) | −1.11586e7 | −0.746556 | ||||||||
\(742\) | 8.50882e6 | 0.567361 | ||||||||
\(743\) | −2.42745e7 | −1.61316 | −0.806582 | − | 0.591123i | \(-0.798685\pi\) | ||||
−0.806582 | + | 0.591123i | \(0.798685\pi\) | |||||||
\(744\) | 5.43456e6 | 0.359942 | ||||||||
\(745\) | 3.02818e6 | 0.199890 | ||||||||
\(746\) | 4.48493e6 | 0.295059 | ||||||||
\(747\) | 1.42204e6 | 0.0932415 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09586e7 | −1.36508 | ||||||||
\(750\) | 3.42295e6 | 0.222202 | ||||||||
\(751\) | 1.53660e7 | 0.994170 | 0.497085 | − | 0.867702i | \(-0.334404\pi\) | ||||
0.497085 | + | 0.867702i | \(0.334404\pi\) | |||||||
\(752\) | 1.62216e7 | 1.04604 | ||||||||
\(753\) | 1.44348e7 | 0.927734 | ||||||||
\(754\) | 5.33820e6 | 0.341953 | ||||||||
\(755\) | −7.08639e6 | −0.452437 | ||||||||
\(756\) | −3.02098e6 | −0.192240 | ||||||||
\(757\) | 2.07605e7 | 1.31674 | 0.658368 | − | 0.752697i | \(-0.271247\pi\) | ||||
0.658368 | + | 0.752697i | \(0.271247\pi\) | |||||||
\(758\) | −4.81972e6 | −0.304683 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.19232e7 | 0.748788 | ||||||||
\(761\) | −5.83810e6 | −0.365435 | −0.182717 | − | 0.983165i | \(-0.558489\pi\) | ||||
−0.182717 | + | 0.983165i | \(0.558489\pi\) | |||||||
\(762\) | 932184. | 0.0581586 | ||||||||
\(763\) | −3.54919e7 | −2.20708 | ||||||||
\(764\) | 8.55702e6 | 0.530383 | ||||||||
\(765\) | 2.69017e6 | 0.166198 | ||||||||
\(766\) | −2.02131e6 | −0.124469 | ||||||||
\(767\) | 3.36364e6 | 0.206453 | ||||||||
\(768\) | 274176. | 0.0167736 | ||||||||
\(769\) | 1.39197e7 | 0.848818 | 0.424409 | − | 0.905471i | \(-0.360482\pi\) | ||||
0.424409 | + | 0.905471i | \(0.360482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.57856e6 | −0.216807 | ||||||||
\(772\) | 3.26015e6 | 0.196877 | ||||||||
\(773\) | −4.17883e6 | −0.251539 | −0.125770 | − | 0.992059i | \(-0.540140\pi\) | ||||
−0.125770 | + | 0.992059i | \(0.540140\pi\) | |||||||
\(774\) | −1.34525e6 | −0.0807142 | ||||||||
\(775\) | −5.07729e6 | −0.303653 | ||||||||
\(776\) | −8.47896e6 | −0.505462 | ||||||||
\(777\) | 1.08132e7 | 0.642541 | ||||||||
\(778\) | 2.55558e6 | 0.151370 | ||||||||
\(779\) | −1.10981e7 | −0.655246 | ||||||||
\(780\) | −6.65381e6 | −0.391592 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.66198e6 | −0.214141 | ||||||||
\(783\) | 3.38985e6 | 0.197595 | ||||||||
\(784\) | 3.34363e6 | 0.194280 | ||||||||
\(785\) | 1.32332e7 | 0.766461 | ||||||||
\(786\) | 965736. | 0.0557573 | ||||||||
\(787\) | −9.66705e6 | −0.556361 | −0.278181 | − | 0.960529i | \(-0.589731\pi\) | ||||
−0.278181 | + | 0.960529i | \(0.589731\pi\) | |||||||
\(788\) | −6.93678e6 | −0.397962 | ||||||||
\(789\) | 1.91850e7 | 1.09716 | ||||||||
\(790\) | 2.32760e6 | 0.132691 | ||||||||
\(791\) | 6.32345e6 | 0.359346 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.07997e7 | −1.73926 | ||||||||
\(794\) | 1.09080e7 | 0.614036 | ||||||||
\(795\) | 1.19008e7 | 0.667821 | ||||||||
\(796\) | 1.43741e7 | 0.804077 | ||||||||
\(797\) | −5.79884e6 | −0.323367 | −0.161683 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161683 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(798\) | −5.75424e6 | −0.319875 | ||||||||
\(799\) | 1.78536e7 | 0.989371 | ||||||||
\(800\) | −5.19837e6 | −0.287172 | ||||||||
\(801\) | 1.07382e7 | 0.591356 | ||||||||
\(802\) | −2.97960e6 | −0.163577 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.78882e6 | 0.424944 | ||||||||
\(805\) | 1.72651e7 | 0.939029 | ||||||||
\(806\) | −5.77674e6 | −0.313217 | ||||||||
\(807\) | 6.53229e6 | 0.353087 | ||||||||
\(808\) | −1.22398e7 | −0.659545 | ||||||||
\(809\) | 1.92543e7 | 1.03433 | 0.517163 | − | 0.855887i | \(-0.326988\pi\) | ||||
0.517163 | + | 0.855887i | \(0.326988\pi\) | |||||||
\(810\) | 603612. | 0.0323255 | ||||||||
\(811\) | 1.31938e7 | 0.704396 | 0.352198 | − | 0.935926i | \(-0.385434\pi\) | ||||
0.352198 | + | 0.935926i | \(0.385434\pi\) | |||||||
\(812\) | −1.92696e7 | −1.02561 | ||||||||
\(813\) | −1.32108e7 | −0.700976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.83570e6 | 0.255015 | ||||||||
\(816\) | −4.26269e6 | −0.224108 | ||||||||
\(817\) | 1.79366e7 | 0.940126 | ||||||||
\(818\) | 8.79798e6 | 0.459727 | ||||||||
\(819\) | 6.88111e6 | 0.358467 | ||||||||
\(820\) | −6.61774e6 | −0.343697 | ||||||||
\(821\) | −1.33779e7 | −0.692677 | −0.346338 | − | 0.938110i | \(-0.612575\pi\) | ||||
−0.346338 | + | 0.938110i | \(0.612575\pi\) | |||||||
\(822\) | 4.11952e6 | 0.212651 | ||||||||
\(823\) | −1.88613e7 | −0.970673 | −0.485336 | − | 0.874327i | \(-0.661303\pi\) | ||||
−0.485336 | + | 0.874327i | \(0.661303\pi\) | |||||||
\(824\) | −1.57085e7 | −0.805965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.73456e6 | 0.0884584 | ||||||||
\(827\) | −1.62680e7 | −0.827123 | −0.413561 | − | 0.910476i | \(-0.635715\pi\) | ||||
−0.413561 | + | 0.910476i | \(0.635715\pi\) | |||||||
\(828\) | 5.75165e6 | 0.291552 | ||||||||
\(829\) | −2.18098e7 | −1.10221 | −0.551107 | − | 0.834435i | \(-0.685794\pi\) | ||||
−0.551107 | + | 0.834435i | \(0.685794\pi\) | |||||||
\(830\) | 1.61515e6 | 0.0813801 | ||||||||
\(831\) | 1.36890e7 | 0.687652 | ||||||||
\(832\) | 6.13491e6 | 0.307256 | ||||||||
\(833\) | 3.68003e6 | 0.183755 | ||||||||
\(834\) | 6.74856e6 | 0.335967 | ||||||||
\(835\) | −6.92429e6 | −0.343684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.66833e6 | −0.180990 | ||||||||
\(838\) | −560840. | −0.0275886 | ||||||||
\(839\) | 1.17771e7 | 0.577607 | 0.288804 | − | 0.957388i | \(-0.406743\pi\) | ||||
0.288804 | + | 0.957388i | \(0.406743\pi\) | |||||||
\(840\) | −7.35264e6 | −0.359538 | ||||||||
\(841\) | 1.11135e6 | 0.0541828 | ||||||||
\(842\) | 1.63492e6 | 0.0794726 | ||||||||
\(843\) | 4.17944e6 | 0.202558 | ||||||||
\(844\) | −1.73793e7 | −0.839799 | ||||||||
\(845\) | −1.92358e6 | −0.0926764 | ||||||||
\(846\) | 4.00594e6 | 0.192432 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.88574e7 | −0.900516 | ||||||||
\(849\) | −3.73622e6 | −0.177895 | ||||||||
\(850\) | −1.45700e6 | −0.0691689 | ||||||||
\(851\) | −2.05872e7 | −0.974483 | ||||||||
\(852\) | −1.75513e7 | −0.828343 | ||||||||
\(853\) | 1.43993e7 | 0.677591 | 0.338796 | − | 0.940860i | \(-0.389980\pi\) | ||||
0.338796 | + | 0.940860i | \(0.389980\pi\) | |||||||
\(854\) | −1.58828e7 | −0.745215 | ||||||||
\(855\) | −8.04816e6 | −0.376514 | ||||||||
\(856\) | −1.69934e7 | −0.792678 | ||||||||
\(857\) | −6.27604e6 | −0.291900 | −0.145950 | − | 0.989292i | \(-0.546624\pi\) | ||||
−0.145950 | + | 0.989292i | \(0.546624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.71738e6 | −0.218131 | −0.109066 | − | 0.994035i | \(-0.534786\pi\) | ||||
−0.109066 | + | 0.994035i | \(0.534786\pi\) | |||||||
\(860\) | 1.06956e7 | 0.493125 | ||||||||
\(861\) | 6.84382e6 | 0.314623 | ||||||||
\(862\) | −3.77198e6 | −0.172903 | ||||||||
\(863\) | 7.53926e6 | 0.344589 | 0.172295 | − | 0.985045i | \(-0.444882\pi\) | ||||
0.172295 | + | 0.985045i | \(0.444882\pi\) | |||||||
\(864\) | −3.75581e6 | −0.171167 | ||||||||
\(865\) | 99636.0 | 0.00452768 | ||||||||
\(866\) | 1.16813e7 | 0.529296 | ||||||||
\(867\) | 8.08716e6 | 0.365383 | ||||||||
\(868\) | 2.08526e7 | 0.939423 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.85020e6 | 0.172459 | ||||||||
\(871\) | −1.77412e7 | −0.792387 | ||||||||
\(872\) | −2.87772e7 | −1.28161 | ||||||||
\(873\) | 5.72330e6 | 0.254162 | ||||||||
\(874\) | 1.09555e7 | 0.485126 | ||||||||
\(875\) | 2.81443e7 | 1.24271 | ||||||||
\(876\) | 4.64839e6 | 0.204664 | ||||||||
\(877\) | 1.04331e7 | 0.458051 | 0.229025 | − | 0.973420i | \(-0.426446\pi\) | ||||
0.229025 | + | 0.973420i | \(0.426446\pi\) | |||||||
\(878\) | 1.01908e6 | 0.0446141 | ||||||||
\(879\) | −2.33389e7 | −1.01884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.91076e7 | 1.69755 | 0.848774 | − | 0.528756i | \(-0.177342\pi\) | ||||
0.848774 | + | 0.528756i | \(0.177342\pi\) | |||||||
\(882\) | 825714. | 0.0357403 | ||||||||
\(883\) | 1.29282e7 | 0.558003 | 0.279001 | − | 0.960291i | \(-0.409997\pi\) | ||||
0.279001 | + | 0.960291i | \(0.409997\pi\) | |||||||
\(884\) | 1.16040e7 | 0.499432 | ||||||||
\(885\) | 2.42604e6 | 0.104121 | ||||||||
\(886\) | 8.20537e6 | 0.351167 | ||||||||
\(887\) | −3.36466e7 | −1.43592 | −0.717962 | − | 0.696082i | \(-0.754925\pi\) | ||||
−0.717962 | + | 0.696082i | \(0.754925\pi\) | |||||||
\(888\) | 8.76744e6 | 0.373113 | ||||||||
\(889\) | 7.66462e6 | 0.325264 | ||||||||
\(890\) | 1.21964e7 | 0.516129 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.69044e7 | 1.55298 | ||||||||
\(893\) | −5.34125e7 | −2.24137 | ||||||||
\(894\) | −1.18494e6 | −0.0495853 | ||||||||
\(895\) | 3.09479e7 | 1.29144 | ||||||||
\(896\) | 2.75635e7 | 1.14700 | ||||||||
\(897\) | −1.31010e7 | −0.543654 | ||||||||
\(898\) | 1.02682e6 | 0.0424916 | ||||||||
\(899\) | −2.33988e7 | −0.965594 | ||||||||
\(900\) | 2.28841e6 | 0.0941733 | ||||||||
\(901\) | −2.07546e7 | −0.851731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.10609e7 | −0.451411 | ||||||||
\(904\) | 5.12712e6 | 0.208666 | ||||||||
\(905\) | −2.42318e7 | −0.983477 | ||||||||
\(906\) | 2.77294e6 | 0.112233 | ||||||||
\(907\) | −4.19629e7 | −1.69374 | −0.846872 | − | 0.531797i | \(-0.821517\pi\) | ||||
−0.846872 | + | 0.531797i | \(0.821517\pi\) | |||||||
\(908\) | −2.48475e7 | −1.00016 | ||||||||
\(909\) | 8.26184e6 | 0.331640 | ||||||||
\(910\) | 7.81558e6 | 0.312866 | ||||||||
\(911\) | −1.92521e6 | −0.0768567 | −0.0384283 | − | 0.999261i | \(-0.512235\pi\) | ||||
−0.0384283 | + | 0.999261i | \(0.512235\pi\) | |||||||
\(912\) | 1.27526e7 | 0.507707 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.45476e6 | −0.0971948 | ||||||||
\(915\) | −2.22144e7 | −0.877167 | ||||||||
\(916\) | 6.64860e6 | 0.261813 | ||||||||
\(917\) | 7.94050e6 | 0.311835 | ||||||||
\(918\) | −1.05268e6 | −0.0412276 | ||||||||
\(919\) | 1.72481e7 | 0.673678 | 0.336839 | − | 0.941562i | \(-0.390642\pi\) | ||||
0.336839 | + | 0.941562i | \(0.390642\pi\) | |||||||
\(920\) | 1.39987e7 | 0.545279 | ||||||||
\(921\) | −8.37749e6 | −0.325435 | ||||||||
\(922\) | 1.28200e7 | 0.496662 | ||||||||
\(923\) | 3.99780e7 | 1.54460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.19106e6 | −0.314765 | ||||||||
\(926\) | 1.32606e7 | 0.508202 | ||||||||
\(927\) | 1.06032e7 | 0.405265 | ||||||||
\(928\) | −2.39568e7 | −0.913185 | ||||||||
\(929\) | 2.51145e6 | 0.0954740 | 0.0477370 | − | 0.998860i | \(-0.484799\pi\) | ||||
0.0477370 | + | 0.998860i | \(0.484799\pi\) | |||||||
\(930\) | −4.16650e6 | −0.157966 | ||||||||
\(931\) | −1.10095e7 | −0.416288 | ||||||||
\(932\) | −2.56118e7 | −0.965828 | ||||||||
\(933\) | −2.23674e7 | −0.841225 | ||||||||
\(934\) | −8.29538e6 | −0.311150 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.57928e6 | 0.208156 | ||||||||
\(937\) | −1.79853e7 | −0.669221 | −0.334611 | − | 0.942357i | \(-0.608605\pi\) | ||||
−0.334611 | + | 0.942357i | \(0.608605\pi\) | |||||||
\(938\) | −9.14877e6 | −0.339512 | ||||||||
\(939\) | −1.18547e7 | −0.438761 | ||||||||
\(940\) | −3.18497e7 | −1.17567 | ||||||||
\(941\) | 3.22586e7 | 1.18760 | 0.593802 | − | 0.804611i | \(-0.297626\pi\) | ||||
0.593802 | + | 0.804611i | \(0.297626\pi\) | |||||||
\(942\) | −5.17820e6 | −0.190131 | ||||||||
\(943\) | −1.30300e7 | −0.477160 | ||||||||
\(944\) | −3.84416e6 | −0.140401 | ||||||||
\(945\) | 4.96303e6 | 0.180787 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.41659e7 | 1.60034 | 0.800169 | − | 0.599774i | \(-0.204743\pi\) | ||||
0.800169 | + | 0.599774i | \(0.204743\pi\) | |||||||
\(948\) | 6.37560e6 | 0.230409 | ||||||||
\(949\) | −1.05880e7 | −0.381635 | ||||||||
\(950\) | 4.35888e6 | 0.156699 | ||||||||
\(951\) | −2.02986e7 | −0.727804 | ||||||||
\(952\) | 1.28227e7 | 0.458551 | ||||||||
\(953\) | −1.87488e7 | −0.668714 | −0.334357 | − | 0.942446i | \(-0.608519\pi\) | ||||
−0.334357 | + | 0.942446i | \(0.608519\pi\) | |||||||
\(954\) | −4.65685e6 | −0.165661 | ||||||||
\(955\) | −1.40580e7 | −0.498786 | ||||||||
\(956\) | 3.94498e7 | 1.39605 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.01026e7 | 0.355649 | ||||||||
\(959\) | 3.38716e7 | 1.18929 | ||||||||
\(960\) | 4.42483e6 | 0.154960 | ||||||||
\(961\) | −3.30813e6 | −0.115551 | ||||||||
\(962\) | −9.31946e6 | −0.324678 | ||||||||
\(963\) | 1.14706e7 | 0.398584 | ||||||||
\(964\) | −2.31380e7 | −0.801925 | ||||||||
\(965\) | −5.35596e6 | −0.185148 | ||||||||
\(966\) | −6.75590e6 | −0.232938 | ||||||||
\(967\) | −1.08673e7 | −0.373730 | −0.186865 | − | 0.982386i | \(-0.559833\pi\) | ||||
−0.186865 | + | 0.982386i | \(0.559833\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.40357e7 | 0.480202 | ||||||||
\(970\) | 6.50054e6 | 0.221830 | ||||||||
\(971\) | −4.79123e7 | −1.63079 | −0.815397 | − | 0.578902i | \(-0.803481\pi\) | ||||
−0.815397 | + | 0.578902i | \(0.803481\pi\) | |||||||
\(972\) | 1.65337e6 | 0.0561313 | ||||||||
\(973\) | 5.54882e7 | 1.87896 | ||||||||
\(974\) | 5.32442e6 | 0.179835 | ||||||||
\(975\) | −5.21249e6 | −0.175604 | ||||||||
\(976\) | 3.51996e7 | 1.18281 | ||||||||
\(977\) | 4.01385e7 | 1.34532 | 0.672658 | − | 0.739954i | \(-0.265153\pi\) | ||||
0.672658 | + | 0.739954i | \(0.265153\pi\) | |||||||
\(978\) | −1.89223e6 | −0.0632597 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.56494e6 | −0.218356 | ||||||||
\(981\) | 1.94246e7 | 0.644436 | ||||||||
\(982\) | 1.10932e7 | 0.367094 | ||||||||
\(983\) | 3.22682e6 | 0.106510 | 0.0532551 | − | 0.998581i | \(-0.483040\pi\) | ||||
0.0532551 | + | 0.998581i | \(0.483040\pi\) | |||||||
\(984\) | 5.54904e6 | 0.182696 | ||||||||
\(985\) | 1.13961e7 | 0.374254 | ||||||||
\(986\) | −6.71460e6 | −0.219952 | ||||||||
\(987\) | 3.29377e7 | 1.07622 | ||||||||
\(988\) | −3.47155e7 | −1.13144 | ||||||||
\(989\) | 2.10589e7 | 0.684614 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.95345e6 | −0.192568 | −0.0962841 | − | 0.995354i | \(-0.530696\pi\) | ||||
−0.0962841 | + | 0.995354i | \(0.530696\pi\) | |||||||
\(992\) | 2.59249e7 | 0.836445 | ||||||||
\(993\) | 2.85364e7 | 0.918387 | ||||||||
\(994\) | 2.06158e7 | 0.661812 | ||||||||
\(995\) | −2.36146e7 | −0.756175 | ||||||||
\(996\) | 4.42411e6 | 0.141312 | ||||||||
\(997\) | −3.20783e7 | −1.02205 | −0.511027 | − | 0.859565i | \(-0.670735\pi\) | ||||
−0.511027 | + | 0.859565i | \(0.670735\pi\) | |||||||
\(998\) | −13640.0 | −0.000433499 0 | ||||||||
\(999\) | −5.91802e6 | −0.187613 |
(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 | 363.6.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 1089.6.a.d.1.1 | 1 | |||
11.10 | odd | 2 | 33.6.a.a.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 99.6.a.b.1.1 | 1 | |||
44.43 | even | 2 | 528.6.a.i.1.1 | 1 | |||
55.54 | odd | 2 | 825.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.a.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
99.6.a.b.1.1 | 1 | 33.32 | even | 2 | |||
363.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
528.6.a.i.1.1 | 1 | 44.43 | even | 2 | |||
825.6.a.b.1.1 | 1 | 55.54 | odd | 2 | |||
1089.6.a.d.1.1 | 1 | 3.2 | odd | 2 |