Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,6,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, 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("882.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(141.458529075\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{9601}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 2400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-48.4923\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 75.4923 | 1.35045 | 0.675224 | − | 0.737613i | \(-0.264047\pi\) | ||||
0.675224 | + | 0.737613i | \(0.264047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −301.969 | −0.954911 | ||||||||
\(11\) | 149.462 | 0.372433 | 0.186217 | − | 0.982509i | \(-0.440377\pi\) | ||||
0.186217 | + | 0.982509i | \(0.440377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 349.416 | 0.573435 | 0.286717 | − | 0.958015i | \(-0.407436\pi\) | ||||
0.286717 | + | 0.958015i | \(0.407436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1149.85 | 0.964979 | 0.482489 | − | 0.875902i | \(-0.339733\pi\) | ||||
0.482489 | + | 0.875902i | \(0.339733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2795.20 | −1.77635 | −0.888176 | − | 0.459503i | \(-0.848028\pi\) | ||||
−0.888176 | + | 0.459503i | \(0.848028\pi\) | |||||||
\(20\) | 1207.88 | 0.675224 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −597.847 | −0.263350 | ||||||||
\(23\) | −1813.97 | −0.715007 | −0.357504 | − | 0.933912i | \(-0.616372\pi\) | ||||
−0.357504 | + | 0.933912i | \(0.616372\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2574.09 | 0.823710 | ||||||||
\(26\) | −1397.66 | −0.405480 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 759.033 | 0.167597 | 0.0837984 | − | 0.996483i | \(-0.473295\pi\) | ||||
0.0837984 | + | 0.996483i | \(0.473295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9031.74 | 1.68798 | 0.843990 | − | 0.536359i | \(-0.180201\pi\) | ||||
0.843990 | + | 0.536359i | \(0.180201\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4599.39 | −0.682343 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7794.89 | 0.936064 | 0.468032 | − | 0.883711i | \(-0.344963\pi\) | ||||
0.468032 | + | 0.883711i | \(0.344963\pi\) | |||||||
\(38\) | 11180.8 | 1.25607 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4831.51 | −0.477456 | ||||||||
\(41\) | −7640.49 | −0.709842 | −0.354921 | − | 0.934896i | \(-0.615492\pi\) | ||||
−0.354921 | + | 0.934896i | \(0.615492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12188.8 | 1.00529 | 0.502645 | − | 0.864493i | \(-0.332360\pi\) | ||||
0.502645 | + | 0.864493i | \(0.332360\pi\) | |||||||
\(44\) | 2391.39 | 0.186217 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7255.88 | 0.505586 | ||||||||
\(47\) | −24598.8 | −1.62431 | −0.812156 | − | 0.583441i | \(-0.801706\pi\) | ||||
−0.812156 | + | 0.583441i | \(0.801706\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10296.4 | −0.582451 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5590.65 | 0.286717 | ||||||||
\(53\) | −13596.2 | −0.664858 | −0.332429 | − | 0.943128i | \(-0.607868\pi\) | ||||
−0.332429 | + | 0.943128i | \(0.607868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11283.2 | 0.502952 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3036.13 | −0.118509 | ||||||||
\(59\) | 26358.8 | 0.985816 | 0.492908 | − | 0.870081i | \(-0.335934\pi\) | ||||
0.492908 | + | 0.870081i | \(0.335934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35321.8 | 1.21540 | 0.607698 | − | 0.794168i | \(-0.292093\pi\) | ||||
0.607698 | + | 0.794168i | \(0.292093\pi\) | |||||||
\(62\) | −36127.0 | −1.19358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 26378.2 | 0.774394 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54371.9 | 1.47975 | 0.739874 | − | 0.672746i | \(-0.234885\pi\) | ||||
0.739874 | + | 0.672746i | \(0.234885\pi\) | |||||||
\(68\) | 18397.6 | 0.482489 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70145.7 | 1.65141 | 0.825706 | − | 0.564101i | \(-0.190777\pi\) | ||||
0.825706 | + | 0.564101i | \(0.190777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44468.8 | −0.976671 | −0.488335 | − | 0.872656i | \(-0.662396\pi\) | ||||
−0.488335 | + | 0.872656i | \(0.662396\pi\) | |||||||
\(74\) | −31179.6 | −0.661897 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −44723.2 | −0.888176 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61612.5 | 1.11071 | 0.555355 | − | 0.831613i | \(-0.312582\pi\) | ||||
0.555355 | + | 0.831613i | \(0.312582\pi\) | |||||||
\(80\) | 19326.0 | 0.337612 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 30562.0 | 0.501934 | ||||||||
\(83\) | 87142.0 | 1.38846 | 0.694228 | − | 0.719755i | \(-0.255746\pi\) | ||||
0.694228 | + | 0.719755i | \(0.255746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 86804.6 | 1.30315 | ||||||||
\(86\) | −48755.3 | −0.710847 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9565.55 | −0.131675 | ||||||||
\(89\) | −98569.4 | −1.31907 | −0.659534 | − | 0.751675i | \(-0.729246\pi\) | ||||
−0.659534 | + | 0.751675i | \(0.729246\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −29023.5 | −0.357504 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 98395.2 | 1.14856 | ||||||||
\(95\) | −211016. | −2.39887 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 32342.3 | 0.349013 | 0.174507 | − | 0.984656i | \(-0.444167\pi\) | ||||
0.174507 | + | 0.984656i | \(0.444167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 41185.5 | 0.411855 | ||||||||
\(101\) | −31346.4 | −0.305763 | −0.152881 | − | 0.988245i | \(-0.548855\pi\) | ||||
−0.152881 | + | 0.988245i | \(0.548855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 99332.9 | 0.922572 | 0.461286 | − | 0.887252i | \(-0.347388\pi\) | ||||
0.461286 | + | 0.887252i | \(0.347388\pi\) | |||||||
\(104\) | −22362.6 | −0.202740 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 54384.9 | 0.470125 | ||||||||
\(107\) | 145268. | 1.22662 | 0.613310 | − | 0.789842i | \(-0.289837\pi\) | ||||
0.613310 | + | 0.789842i | \(0.289837\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −180851. | −1.45799 | −0.728994 | − | 0.684520i | \(-0.760012\pi\) | ||||
−0.728994 | + | 0.684520i | \(0.760012\pi\) | |||||||
\(110\) | −45132.9 | −0.355640 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −197832. | −1.45748 | −0.728738 | − | 0.684793i | \(-0.759893\pi\) | ||||
−0.728738 | + | 0.684793i | \(0.759893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −136941. | −0.965580 | ||||||||
\(116\) | 12144.5 | 0.0837984 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −105435. | −0.697077 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −138712. | −0.861294 | ||||||||
\(122\) | −141287. | −0.859415 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 144508. | 0.843990 | ||||||||
\(125\) | −41589.2 | −0.238070 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −33517.2 | −0.184399 | −0.0921996 | − | 0.995741i | \(-0.529390\pi\) | ||||
−0.0921996 | + | 0.995741i | \(0.529390\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −105513. | −0.547579 | ||||||||
\(131\) | 10808.9 | 0.0550305 | 0.0275153 | − | 0.999621i | \(-0.491241\pi\) | ||||
0.0275153 | + | 0.999621i | \(0.491241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −217488. | −1.04634 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −73590.2 | −0.341171 | ||||||||
\(137\) | 18932.0 | 0.0861778 | 0.0430889 | − | 0.999071i | \(-0.486280\pi\) | ||||
0.0430889 | + | 0.999071i | \(0.486280\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −168897. | −0.741457 | −0.370729 | − | 0.928741i | \(-0.620892\pi\) | ||||
−0.370729 | + | 0.928741i | \(0.620892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −280583. | −1.16772 | ||||||||
\(143\) | 52224.3 | 0.213566 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 57301.2 | 0.226331 | ||||||||
\(146\) | 177875. | 0.690611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 124718. | 0.468032 | ||||||||
\(149\) | −264002. | −0.974186 | −0.487093 | − | 0.873350i | \(-0.661943\pi\) | ||||
−0.487093 | + | 0.873350i | \(0.661943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 279175. | 0.996400 | 0.498200 | − | 0.867062i | \(-0.333994\pi\) | ||||
0.498200 | + | 0.867062i | \(0.333994\pi\) | |||||||
\(152\) | 178893. | 0.628035 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 681828. | 2.27953 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 188602. | 0.610658 | 0.305329 | − | 0.952247i | \(-0.401234\pi\) | ||||
0.305329 | + | 0.952247i | \(0.401234\pi\) | |||||||
\(158\) | −246450. | −0.785391 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −77304.2 | −0.238728 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 89717.4 | 0.264489 | 0.132244 | − | 0.991217i | \(-0.457782\pi\) | ||||
0.132244 | + | 0.991217i | \(0.457782\pi\) | |||||||
\(164\) | −122248. | −0.354921 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −348568. | −0.981787 | ||||||||
\(167\) | −529411. | −1.46893 | −0.734467 | − | 0.678645i | \(-0.762568\pi\) | ||||
−0.734467 | + | 0.678645i | \(0.762568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −249202. | −0.671172 | ||||||||
\(170\) | −347219. | −0.921469 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 195021. | 0.502645 | ||||||||
\(173\) | −33838.3 | −0.0859594 | −0.0429797 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429797 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 38262.2 | 0.0931083 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 394278. | 0.932722 | ||||||||
\(179\) | 247744. | 0.577923 | 0.288962 | − | 0.957341i | \(-0.406690\pi\) | ||||
0.288962 | + | 0.957341i | \(0.406690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 369470. | 0.838268 | 0.419134 | − | 0.907924i | \(-0.362334\pi\) | ||||
0.419134 | + | 0.907924i | \(0.362334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 116094. | 0.252793 | ||||||||
\(185\) | 588455. | 1.26411 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 171858. | 0.359390 | ||||||||
\(188\) | −393581. | −0.812156 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 844065. | 1.69626 | ||||||||
\(191\) | 485225. | 0.962408 | 0.481204 | − | 0.876609i | \(-0.340200\pi\) | ||||
0.481204 | + | 0.876609i | \(0.340200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −330817. | −0.639285 | −0.319643 | − | 0.947538i | \(-0.603563\pi\) | ||||
−0.319643 | + | 0.947538i | \(0.603563\pi\) | |||||||
\(194\) | −129369. | −0.246790 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 161963. | 0.297337 | 0.148669 | − | 0.988887i | \(-0.452501\pi\) | ||||
0.148669 | + | 0.988887i | \(0.452501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 55396.2 | 0.0991625 | 0.0495813 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495813 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(200\) | −164742. | −0.291226 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 125386. | 0.216207 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −576799. | −0.958605 | ||||||||
\(206\) | −397332. | −0.652357 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 89450.4 | 0.143359 | ||||||||
\(209\) | −417776. | −0.661572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 481748. | 0.744926 | 0.372463 | − | 0.928047i | \(-0.378513\pi\) | ||||
0.372463 | + | 0.928047i | \(0.378513\pi\) | |||||||
\(212\) | −217540. | −0.332429 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −581072. | −0.867352 | ||||||||
\(215\) | 920164. | 1.35759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 723403. | 1.03095 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 180531. | 0.251476 | ||||||||
\(221\) | 401775. | 0.553353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 638779. | 0.860178 | 0.430089 | − | 0.902787i | \(-0.358482\pi\) | ||||
0.430089 | + | 0.902787i | \(0.358482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 791330. | 1.03059 | ||||||||
\(227\) | 525682. | 0.677109 | 0.338554 | − | 0.940947i | \(-0.390062\pi\) | ||||
0.338554 | + | 0.940947i | \(0.390062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 932686. | 1.17529 | 0.587647 | − | 0.809117i | \(-0.300054\pi\) | ||||
0.587647 | + | 0.809117i | \(0.300054\pi\) | |||||||
\(230\) | 547763. | 0.682768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −48578.1 | −0.0592544 | ||||||||
\(233\) | 707793. | 0.854115 | 0.427058 | − | 0.904224i | \(-0.359550\pi\) | ||||
0.427058 | + | 0.904224i | \(0.359550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.85702e6 | −2.19355 | ||||||||
\(236\) | 421741. | 0.492908 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 500614. | 0.566902 | 0.283451 | − | 0.958987i | \(-0.408521\pi\) | ||||
0.283451 | + | 0.958987i | \(0.408521\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.20822e6 | 1.33999 | 0.669997 | − | 0.742364i | \(-0.266295\pi\) | ||||
0.669997 | + | 0.742364i | \(0.266295\pi\) | |||||||
\(242\) | 554849. | 0.609027 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 565148. | 0.607698 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −976688. | −1.01862 | ||||||||
\(248\) | −578032. | −0.596791 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 166357. | 0.168341 | ||||||||
\(251\) | −97826.7 | −0.0980106 | −0.0490053 | − | 0.998799i | \(-0.515605\pi\) | ||||
−0.0490053 | + | 0.998799i | \(0.515605\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −271119. | −0.266292 | ||||||||
\(254\) | 134069. | 0.130390 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.10791e6 | 1.04634 | 0.523170 | − | 0.852228i | \(-0.324749\pi\) | ||||
0.523170 | + | 0.852228i | \(0.324749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 422052. | 0.387197 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −43235.6 | −0.0389125 | ||||||||
\(263\) | −1.50685e6 | −1.34333 | −0.671663 | − | 0.740856i | \(-0.734420\pi\) | ||||
−0.671663 | + | 0.740856i | \(0.734420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.02641e6 | −0.897856 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 869951. | 0.739874 | ||||||||
\(269\) | 2.13502e6 | 1.79896 | 0.899481 | − | 0.436960i | \(-0.143945\pi\) | ||||
0.899481 | + | 0.436960i | \(0.143945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.22860e6 | 1.01622 | 0.508108 | − | 0.861293i | \(-0.330345\pi\) | ||||
0.508108 | + | 0.861293i | \(0.330345\pi\) | |||||||
\(272\) | 294361. | 0.241245 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −75728.1 | −0.0609369 | ||||||||
\(275\) | 384729. | 0.306777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.84682e6 | −1.44619 | −0.723097 | − | 0.690747i | \(-0.757282\pi\) | ||||
−0.723097 | + | 0.690747i | \(0.757282\pi\) | |||||||
\(278\) | 675590. | 0.524289 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.28326e6 | 1.72500 | 0.862500 | − | 0.506056i | \(-0.168897\pi\) | ||||
0.862500 | + | 0.506056i | \(0.168897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.33693e6 | 0.992296 | 0.496148 | − | 0.868238i | \(-0.334747\pi\) | ||||
0.496148 | + | 0.868238i | \(0.334747\pi\) | |||||||
\(284\) | 1.12233e6 | 0.825706 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −208897. | −0.151014 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97709.0 | −0.0688161 | ||||||||
\(290\) | −229205. | −0.160040 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −711501. | −0.488335 | ||||||||
\(293\) | 2.23033e6 | 1.51775 | 0.758875 | − | 0.651236i | \(-0.225749\pi\) | ||||
0.758875 | + | 0.651236i | \(0.225749\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98989e6 | 1.33129 | ||||||||
\(296\) | −498873. | −0.330949 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.05601e6 | 0.688853 | ||||||||
\(299\) | −633830. | −0.410010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.11670e6 | −0.704561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −715572. | −0.444088 | ||||||||
\(305\) | 2.66652e6 | 1.64133 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.77782e6 | 1.07657 | 0.538284 | − | 0.842763i | \(-0.319073\pi\) | ||||
0.538284 | + | 0.842763i | \(0.319073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.72731e6 | −1.61187 | ||||||||
\(311\) | −1.40272e6 | −0.822373 | −0.411187 | − | 0.911551i | \(-0.634886\pi\) | ||||
−0.411187 | + | 0.911551i | \(0.634886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.21894e6 | 0.703271 | 0.351636 | − | 0.936137i | \(-0.385626\pi\) | ||||
0.351636 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(314\) | −754409. | −0.431800 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 985799. | 0.555355 | ||||||||
\(317\) | −2.68001e6 | −1.49792 | −0.748961 | − | 0.662615i | \(-0.769447\pi\) | ||||
−0.748961 | + | 0.662615i | \(0.769447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 113446. | 0.0624186 | ||||||||
\(320\) | 309217. | 0.168806 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.21405e6 | −1.71414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 899429. | 0.472344 | ||||||||
\(326\) | −358869. | −0.187022 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 488992. | 0.250967 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 142560. | 0.0715202 | 0.0357601 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357601 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(332\) | 1.39427e6 | 0.694228 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.11765e6 | 1.03869 | ||||||||
\(335\) | 4.10466e6 | 1.99832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.21206e6 | −0.581367 | −0.290683 | − | 0.956819i | \(-0.593883\pi\) | ||||
−0.290683 | + | 0.956819i | \(0.593883\pi\) | |||||||
\(338\) | 996806. | 0.474591 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.38887e6 | 0.651577 | ||||||||
\(341\) | 1.34990e6 | 0.628660 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −780085. | −0.355423 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 135353. | 0.0607825 | ||||||||
\(347\) | −3.46853e6 | −1.54640 | −0.773199 | − | 0.634163i | \(-0.781345\pi\) | ||||
−0.773199 | + | 0.634163i | \(0.781345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.01692e6 | 0.446911 | 0.223456 | − | 0.974714i | \(-0.428266\pi\) | ||||
0.223456 | + | 0.974714i | \(0.428266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −153049. | −0.0658375 | ||||||||
\(353\) | −1.56385e6 | −0.667974 | −0.333987 | − | 0.942578i | \(-0.608394\pi\) | ||||
−0.333987 | + | 0.942578i | \(0.608394\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.29547e6 | 2.23015 | ||||||||
\(356\) | −1.57711e6 | −0.659534 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −990975. | −0.408653 | ||||||||
\(359\) | −49553.1 | −0.0202925 | −0.0101462 | − | 0.999949i | \(-0.503230\pi\) | ||||
−0.0101462 | + | 0.999949i | \(0.503230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.33705e6 | 2.15543 | ||||||||
\(362\) | −1.47788e6 | −0.592745 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.35705e6 | −1.31894 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.54831e6 | 1.37517 | 0.687585 | − | 0.726104i | \(-0.258671\pi\) | ||||
0.687585 | + | 0.726104i | \(0.258671\pi\) | |||||||
\(368\) | −464376. | −0.178752 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.35382e6 | −0.893858 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.25573e6 | −0.839490 | −0.419745 | − | 0.907642i | \(-0.637880\pi\) | ||||
−0.419745 | + | 0.907642i | \(0.637880\pi\) | |||||||
\(374\) | −687432. | −0.254127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.57432e6 | 0.574281 | ||||||||
\(377\) | 265218. | 0.0961059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.39503e6 | 1.57168 | 0.785840 | − | 0.618430i | \(-0.212231\pi\) | ||||
0.785840 | + | 0.618430i | \(0.212231\pi\) | |||||||
\(380\) | −3.37626e6 | −1.19944 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.94090e6 | −0.680525 | ||||||||
\(383\) | 1.22781e6 | 0.427694 | 0.213847 | − | 0.976867i | \(-0.431401\pi\) | ||||
0.213847 | + | 0.976867i | \(0.431401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.32327e6 | 0.452043 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 517477. | 0.174507 | ||||||||
\(389\) | −2.05424e6 | −0.688300 | −0.344150 | − | 0.938915i | \(-0.611833\pi\) | ||||
−0.344150 | + | 0.938915i | \(0.611833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.08579e6 | −0.689967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −647851. | −0.210249 | ||||||||
\(395\) | 4.65127e6 | 1.49996 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.80367e6 | −1.21123 | −0.605615 | − | 0.795758i | \(-0.707073\pi\) | ||||
−0.605615 | + | 0.795758i | \(0.707073\pi\) | |||||||
\(398\) | −221585. | −0.0701185 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 658968. | 0.205928 | ||||||||
\(401\) | −1.18524e6 | −0.368084 | −0.184042 | − | 0.982918i | \(-0.558918\pi\) | ||||
−0.184042 | + | 0.982918i | \(0.558918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.15583e6 | 0.967947 | ||||||||
\(404\) | −501543. | −0.152881 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.16504e6 | 0.348621 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.30393e6 | −1.27220 | −0.636102 | − | 0.771605i | \(-0.719454\pi\) | ||||
−0.636102 | + | 0.771605i | \(0.719454\pi\) | |||||||
\(410\) | 2.30720e6 | 0.677836 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.58933e6 | 0.461286 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.57855e6 | 1.87504 | ||||||||
\(416\) | −357802. | −0.101370 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.67110e6 | 0.467802 | ||||||||
\(419\) | 113725. | 0.0316461 | 0.0158230 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158230 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 443417. | 0.121929 | 0.0609645 | − | 0.998140i | \(-0.480582\pi\) | ||||
0.0609645 | + | 0.998140i | \(0.480582\pi\) | |||||||
\(422\) | −1.92699e6 | −0.526743 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 870158. | 0.235063 | ||||||||
\(425\) | 2.95981e6 | 0.794863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.32429e6 | 0.613310 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.68065e6 | −0.959962 | ||||||||
\(431\) | −4.63310e6 | −1.20138 | −0.600688 | − | 0.799484i | \(-0.705107\pi\) | ||||
−0.600688 | + | 0.799484i | \(0.705107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.57955e6 | 1.68646 | 0.843231 | − | 0.537552i | \(-0.180651\pi\) | ||||
0.843231 | + | 0.537552i | \(0.180651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.89361e6 | −0.728994 | ||||||||
\(437\) | 5.07041e6 | 1.27010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.82070e6 | −0.450896 | −0.225448 | − | 0.974255i | \(-0.572385\pi\) | ||||
−0.225448 | + | 0.974255i | \(0.572385\pi\) | |||||||
\(440\) | −722126. | −0.177820 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.60710e6 | −0.391279 | ||||||||
\(443\) | 2.06990e6 | 0.501119 | 0.250559 | − | 0.968101i | \(-0.419385\pi\) | ||||
0.250559 | + | 0.968101i | \(0.419385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.44123e6 | −1.78133 | ||||||||
\(446\) | −2.55511e6 | −0.608238 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.72581e6 | −1.34036 | −0.670180 | − | 0.742199i | \(-0.733783\pi\) | ||||
−0.670180 | + | 0.742199i | \(0.733783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.14196e6 | −0.264369 | ||||||||
\(452\) | −3.16532e6 | −0.728738 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.10273e6 | −0.478788 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 318676. | 0.0713771 | 0.0356886 | − | 0.999363i | \(-0.488638\pi\) | ||||
0.0356886 | + | 0.999363i | \(0.488638\pi\) | |||||||
\(458\) | −3.73074e6 | −0.831059 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.19105e6 | −0.482790 | ||||||||
\(461\) | 3.42470e6 | 0.750535 | 0.375267 | − | 0.926917i | \(-0.377551\pi\) | ||||
0.375267 | + | 0.926917i | \(0.377551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.82945e6 | 0.830201 | 0.415101 | − | 0.909775i | \(-0.363746\pi\) | ||||
0.415101 | + | 0.909775i | \(0.363746\pi\) | |||||||
\(464\) | 194312. | 0.0418992 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.83117e6 | −0.603951 | ||||||||
\(467\) | −2.84462e6 | −0.603576 | −0.301788 | − | 0.953375i | \(-0.597583\pi\) | ||||
−0.301788 | + | 0.953375i | \(0.597583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.42809e6 | 1.55107 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.68696e6 | −0.348539 | ||||||||
\(473\) | 1.82176e6 | 0.374403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.19511e6 | −1.46320 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.00246e6 | −0.400860 | ||||||||
\(479\) | −1.30365e6 | −0.259611 | −0.129806 | − | 0.991539i | \(-0.541435\pi\) | ||||
−0.129806 | + | 0.991539i | \(0.541435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.72366e6 | 0.536772 | ||||||||
\(482\) | −4.83287e6 | −0.947519 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.21940e6 | −0.430647 | ||||||||
\(485\) | 2.44160e6 | 0.471324 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.23624e6 | 1.19152 | 0.595759 | − | 0.803164i | \(-0.296852\pi\) | ||||
0.595759 | + | 0.803164i | \(0.296852\pi\) | |||||||
\(488\) | −2.26059e6 | −0.429707 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.93928e6 | 0.737417 | 0.368709 | − | 0.929545i | \(-0.379800\pi\) | ||||
0.368709 | + | 0.929545i | \(0.379800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 872772. | 0.161727 | ||||||||
\(494\) | 3.90675e6 | 0.720275 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.31213e6 | 0.421995 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.97571e6 | 1.43390 | 0.716948 | − | 0.697126i | \(-0.245538\pi\) | ||||
0.716948 | + | 0.697126i | \(0.245538\pi\) | |||||||
\(500\) | −665427. | −0.119035 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 391307. | 0.0693040 | ||||||||
\(503\) | 2.70777e6 | 0.477190 | 0.238595 | − | 0.971119i | \(-0.423313\pi\) | ||||
0.238595 | + | 0.971119i | \(0.423313\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.36641e6 | −0.412917 | ||||||||
\(506\) | 1.08448e6 | 0.188297 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −536276. | −0.0921996 | ||||||||
\(509\) | −3.90049e6 | −0.667306 | −0.333653 | − | 0.942696i | \(-0.608281\pi\) | ||||
−0.333653 | + | 0.942696i | \(0.608281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.43165e6 | −0.739874 | ||||||||
\(515\) | 7.49887e6 | 1.24589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.67658e6 | −0.604947 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.68821e6 | −0.273790 | ||||||||
\(521\) | −7.00063e6 | −1.12991 | −0.564954 | − | 0.825122i | \(-0.691106\pi\) | ||||
−0.564954 | + | 0.825122i | \(0.691106\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.11208e6 | −0.337641 | −0.168821 | − | 0.985647i | \(-0.553996\pi\) | ||||
−0.168821 | + | 0.985647i | \(0.553996\pi\) | |||||||
\(524\) | 172943. | 0.0275153 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.02741e6 | 0.949875 | ||||||||
\(527\) | 1.03851e7 | 1.62887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.14586e6 | −0.488765 | ||||||||
\(530\) | 4.10564e6 | 0.634880 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.66971e6 | −0.407048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.09666e7 | 1.65649 | ||||||||
\(536\) | −3.47980e6 | −0.523170 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.54009e6 | −1.27206 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.70567e6 | 0.838134 | 0.419067 | − | 0.907955i | \(-0.362357\pi\) | ||||
0.419067 | + | 0.907955i | \(0.362357\pi\) | |||||||
\(542\) | −4.91439e6 | −0.718574 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.17744e6 | −0.170586 | ||||||||
\(545\) | −1.36528e7 | −1.96894 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.28054e6 | 0.325888 | 0.162944 | − | 0.986635i | \(-0.447901\pi\) | ||||
0.162944 | + | 0.986635i | \(0.447901\pi\) | |||||||
\(548\) | 302912. | 0.0430889 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.53891e6 | −0.216924 | ||||||||
\(551\) | −2.12165e6 | −0.297711 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.38730e6 | 1.02261 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.70236e6 | −0.370729 | ||||||||
\(557\) | 6.73941e6 | 0.920415 | 0.460208 | − | 0.887811i | \(-0.347775\pi\) | ||||
0.460208 | + | 0.887811i | \(0.347775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.25897e6 | 0.576468 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.13304e6 | −1.21976 | ||||||||
\(563\) | 9.66820e6 | 1.28551 | 0.642754 | − | 0.766073i | \(-0.277792\pi\) | ||||
0.642754 | + | 0.766073i | \(0.277792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.49348e7 | −1.96825 | ||||||||
\(566\) | −5.34770e6 | −0.701659 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.48933e6 | −0.583862 | ||||||||
\(569\) | 1.39587e7 | 1.80744 | 0.903719 | − | 0.428125i | \(-0.140826\pi\) | ||||
0.903719 | + | 0.428125i | \(0.140826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.35841e6 | −0.302711 | −0.151355 | − | 0.988479i | \(-0.548364\pi\) | ||||
−0.151355 | + | 0.988479i | \(0.548364\pi\) | |||||||
\(572\) | 835589. | 0.106783 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.66933e6 | −0.588959 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.01098e6 | 0.626589 | 0.313295 | − | 0.949656i | \(-0.398567\pi\) | ||||
0.313295 | + | 0.949656i | \(0.398567\pi\) | |||||||
\(578\) | 390836. | 0.0486603 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 916819. | 0.113165 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.03211e6 | −0.247615 | ||||||||
\(584\) | 2.84600e6 | 0.345305 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.92132e6 | −1.07321 | ||||||||
\(587\) | −3.95106e6 | −0.473280 | −0.236640 | − | 0.971597i | \(-0.576046\pi\) | ||||
−0.236640 | + | 0.971597i | \(0.576046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.52455e7 | −2.99845 | ||||||||
\(590\) | −7.95955e6 | −0.941367 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.99549e6 | 0.234016 | ||||||||
\(593\) | 2.53680e6 | 0.296244 | 0.148122 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148122 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.22403e6 | −0.487093 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.53532e6 | 0.289921 | ||||||||
\(599\) | −7.17714e6 | −0.817305 | −0.408652 | − | 0.912690i | \(-0.634001\pi\) | ||||
−0.408652 | + | 0.912690i | \(0.634001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.12527e7 | 1.27078 | 0.635392 | − | 0.772190i | \(-0.280838\pi\) | ||||
0.635392 | + | 0.772190i | \(0.280838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.46680e6 | 0.498200 | ||||||||
\(605\) | −1.04717e7 | −1.16313 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.40370e7 | −1.54633 | −0.773167 | − | 0.634202i | \(-0.781329\pi\) | ||||
−0.773167 | + | 0.634202i | \(0.781329\pi\) | |||||||
\(608\) | 2.86229e6 | 0.314018 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.06661e7 | −1.16059 | ||||||||
\(611\) | −8.59521e6 | −0.931437 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.62872e6 | −0.819975 | −0.409988 | − | 0.912091i | \(-0.634467\pi\) | ||||
−0.409988 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(614\) | −7.11128e6 | −0.761249 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.41080e6 | 0.466450 | 0.233225 | − | 0.972423i | \(-0.425072\pi\) | ||||
0.233225 | + | 0.972423i | \(0.425072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.04355e6 | −0.948664 | −0.474332 | − | 0.880346i | \(-0.657310\pi\) | ||||
−0.474332 | + | 0.880346i | \(0.657310\pi\) | |||||||
\(620\) | 1.09092e7 | 1.13977 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.61087e6 | 0.581506 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.11837e7 | −1.14521 | ||||||||
\(626\) | −4.87578e6 | −0.497288 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.01764e6 | 0.305329 | ||||||||
\(629\) | 8.96293e6 | 0.903282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.33039e6 | −0.732916 | −0.366458 | − | 0.930435i | \(-0.619430\pi\) | ||||
−0.366458 | + | 0.930435i | \(0.619430\pi\) | |||||||
\(632\) | −3.94320e6 | −0.392695 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.07201e7 | 1.05919 | ||||||||
\(635\) | −2.53030e6 | −0.249022 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −453786. | −0.0441366 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.23687e6 | −0.119364 | ||||||||
\(641\) | −3.68824e6 | −0.354547 | −0.177273 | − | 0.984162i | \(-0.556728\pi\) | ||||
−0.177273 | + | 0.984162i | \(0.556728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.17584e7 | −1.12155 | −0.560776 | − | 0.827968i | \(-0.689497\pi\) | ||||
−0.560776 | + | 0.827968i | \(0.689497\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.28562e7 | 1.21208 | ||||||||
\(647\) | 9.94050e6 | 0.933572 | 0.466786 | − | 0.884370i | \(-0.345412\pi\) | ||||
0.466786 | + | 0.884370i | \(0.345412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.93963e6 | 0.367151 | ||||||||
\(650\) | −3.59772e6 | −0.333998 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.43548e6 | 0.132244 | ||||||||
\(653\) | 1.02620e6 | 0.0941778 | 0.0470889 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470889 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 815990. | 0.0743159 | ||||||||
\(656\) | −1.95597e6 | −0.177461 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.00207e7 | −0.898846 | −0.449423 | − | 0.893319i | \(-0.648370\pi\) | ||||
−0.449423 | + | 0.893319i | \(0.648370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.62826e6 | 0.233972 | 0.116986 | − | 0.993134i | \(-0.462677\pi\) | ||||
0.116986 | + | 0.993134i | \(0.462677\pi\) | |||||||
\(662\) | −570241. | −0.0505724 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.57709e6 | −0.490893 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.37686e6 | −0.119833 | ||||||||
\(668\) | −8.47058e6 | −0.734467 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.64187e7 | −1.41303 | ||||||||
\(671\) | 5.27925e6 | 0.452654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.50220e7 | −1.27847 | −0.639233 | − | 0.769013i | \(-0.720748\pi\) | ||||
−0.639233 | + | 0.769013i | \(0.720748\pi\) | |||||||
\(674\) | 4.84825e6 | 0.411088 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.98723e6 | −0.335586 | ||||||||
\(677\) | 6.03310e6 | 0.505905 | 0.252953 | − | 0.967479i | \(-0.418598\pi\) | ||||
0.252953 | + | 0.967479i | \(0.418598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.55550e6 | −0.460734 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.39960e6 | −0.444530 | ||||||||
\(683\) | −1.10720e7 | −0.908187 | −0.454093 | − | 0.890954i | \(-0.650037\pi\) | ||||
−0.454093 | + | 0.890954i | \(0.650037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.42922e6 | 0.116379 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.12034e6 | 0.251322 | ||||||||
\(689\) | −4.75073e6 | −0.381253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.05548e7 | −0.840919 | −0.420460 | − | 0.907311i | \(-0.638131\pi\) | ||||
−0.420460 | + | 0.907311i | \(0.638131\pi\) | |||||||
\(692\) | −541413. | −0.0429797 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.38741e7 | 1.09347 | ||||||||
\(695\) | −1.27505e7 | −1.00130 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.78540e6 | −0.684983 | ||||||||
\(698\) | −4.06766e6 | −0.316014 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.20675e6 | 0.553917 | 0.276958 | − | 0.960882i | \(-0.410674\pi\) | ||||
0.276958 | + | 0.960882i | \(0.410674\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.17883e7 | −1.66278 | ||||||||
\(704\) | 612195. | 0.0465541 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.25542e6 | 0.472329 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69373e6 | 0.201252 | 0.100626 | − | 0.994924i | \(-0.467916\pi\) | ||||
0.100626 | + | 0.994924i | \(0.467916\pi\) | |||||||
\(710\) | −2.11819e7 | −1.57695 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.30844e6 | 0.466361 | ||||||||
\(713\) | −1.63833e7 | −1.20692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.94253e6 | 0.288410 | ||||||||
\(716\) | 3.96390e6 | 0.288962 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 198213. | 0.0143489 | ||||||||
\(719\) | −6.92550e6 | −0.499608 | −0.249804 | − | 0.968296i | \(-0.580366\pi\) | ||||
−0.249804 | + | 0.968296i | \(0.580366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.13482e7 | −1.52412 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.91152e6 | 0.419134 | ||||||||
\(725\) | 1.95382e6 | 0.138051 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.11366e6 | 0.288664 | 0.144332 | − | 0.989529i | \(-0.453897\pi\) | ||||
0.144332 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.34282e7 | 0.932634 | ||||||||
\(731\) | 1.40153e7 | 0.970083 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.92038e6 | 0.544485 | 0.272243 | − | 0.962229i | \(-0.412235\pi\) | ||||
0.272243 | + | 0.962229i | \(0.412235\pi\) | |||||||
\(734\) | −1.41932e7 | −0.972392 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.85750e6 | 0.126397 | ||||||||
\(737\) | 8.12652e6 | 0.551107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.60410e7 | 1.08049 | 0.540245 | − | 0.841508i | \(-0.318332\pi\) | ||||
0.540245 | + | 0.841508i | \(0.318332\pi\) | |||||||
\(740\) | 9.41527e6 | 0.632053 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.53453e7 | −1.01977 | −0.509887 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509887 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.99301e7 | −1.31559 | ||||||||
\(746\) | 9.02293e6 | 0.593609 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.74973e6 | 0.179695 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.24976e7 | 1.45558 | 0.727790 | − | 0.685800i | \(-0.240547\pi\) | ||||
0.727790 | + | 0.685800i | \(0.240547\pi\) | |||||||
\(752\) | −6.29729e6 | −0.406078 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.06087e6 | −0.0679571 | ||||||||
\(755\) | 2.10756e7 | 1.34559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.30349e7 | 1.46099 | 0.730494 | − | 0.682919i | \(-0.239290\pi\) | ||||
0.730494 | + | 0.682919i | \(0.239290\pi\) | |||||||
\(758\) | −1.75801e7 | −1.11135 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.35050e7 | 0.848129 | ||||||||
\(761\) | −5.40735e6 | −0.338472 | −0.169236 | − | 0.985576i | \(-0.554130\pi\) | ||||
−0.169236 | + | 0.985576i | \(0.554130\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.76359e6 | 0.481204 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.91123e6 | −0.302426 | ||||||||
\(767\) | 9.21019e6 | 0.565301 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.93100e6 | −0.483629 | −0.241814 | − | 0.970323i | \(-0.577742\pi\) | ||||
−0.241814 | + | 0.970323i | \(0.577742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.29307e6 | −0.319643 | ||||||||
\(773\) | −269579. | −0.0162270 | −0.00811349 | − | 0.999967i | \(-0.502583\pi\) | ||||
−0.00811349 | + | 0.999967i | \(0.502583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32486e7 | 1.39041 | ||||||||
\(776\) | −2.06991e6 | −0.123395 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.21698e6 | 0.486702 | ||||||||
\(779\) | 2.13567e7 | 1.26093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.04841e7 | 0.615041 | ||||||||
\(782\) | 8.34315e6 | 0.487880 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.42380e7 | 0.824662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.98621e6 | −0.517177 | −0.258589 | − | 0.965988i | \(-0.583257\pi\) | ||||
−0.258589 | + | 0.965988i | \(0.583257\pi\) | |||||||
\(788\) | 2.59140e6 | 0.148669 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.86051e7 | −1.06063 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.23420e7 | 0.696950 | ||||||||
\(794\) | 1.52147e7 | 0.856469 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 886340. | 0.0495813 | ||||||||
\(797\) | 2.65558e7 | 1.48086 | 0.740429 | − | 0.672135i | \(-0.234622\pi\) | ||||
0.740429 | + | 0.672135i | \(0.234622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.82849e7 | −1.56743 | ||||||||
\(800\) | −2.63587e6 | −0.145613 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.74098e6 | 0.260275 | ||||||||
\(803\) | −6.64638e6 | −0.363745 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.26233e7 | −0.684442 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.00617e6 | 0.108103 | ||||||||
\(809\) | −2.52557e7 | −1.35671 | −0.678356 | − | 0.734733i | \(-0.737307\pi\) | ||||
−0.678356 | + | 0.734733i | \(0.737307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.76866e6 | −0.254592 | −0.127296 | − | 0.991865i | \(-0.540630\pi\) | ||||
−0.127296 | + | 0.991865i | \(0.540630\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.66015e6 | −0.246513 | ||||||||
\(815\) | 6.77297e6 | 0.357179 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.40702e7 | −1.78575 | ||||||||
\(818\) | 1.72157e7 | 0.899585 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.22878e6 | −0.479303 | ||||||||
\(821\) | 5.95534e6 | 0.308353 | 0.154177 | − | 0.988043i | \(-0.450727\pi\) | ||||
0.154177 | + | 0.988043i | \(0.450727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.06659e7 | 0.548907 | 0.274453 | − | 0.961600i | \(-0.411503\pi\) | ||||
0.274453 | + | 0.961600i | \(0.411503\pi\) | |||||||
\(824\) | −6.35731e6 | −0.326178 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.52356e6 | 0.433369 | 0.216684 | − | 0.976242i | \(-0.430476\pi\) | ||||
0.216684 | + | 0.976242i | \(0.430476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.87458e6 | 0.195811 | 0.0979057 | − | 0.995196i | \(-0.468786\pi\) | ||||
0.0979057 | + | 0.995196i | \(0.468786\pi\) | |||||||
\(830\) | −2.63142e7 | −1.32585 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.43121e6 | 0.0716794 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.99665e7 | −1.98372 | ||||||||
\(836\) | −6.68441e6 | −0.330786 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −454899. | −0.0223772 | ||||||||
\(839\) | −2.13769e7 | −1.04843 | −0.524215 | − | 0.851586i | \(-0.675641\pi\) | ||||
−0.524215 | + | 0.851586i | \(0.675641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99350e7 | −0.971911 | ||||||||
\(842\) | −1.77367e6 | −0.0862168 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.70796e6 | 0.372463 | ||||||||
\(845\) | −1.88128e7 | −0.906383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.48063e6 | −0.166214 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.18393e7 | −0.562053 | ||||||||
\(851\) | −1.41397e7 | −0.669293 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −85930.0 | −0.00404364 | −0.00202182 | − | 0.999998i | \(-0.500644\pi\) | ||||
−0.00202182 | + | 0.999998i | \(0.500644\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.29715e6 | −0.433676 | ||||||||
\(857\) | 1.85664e7 | 0.863528 | 0.431764 | − | 0.901987i | \(-0.357891\pi\) | ||||
0.431764 | + | 0.901987i | \(0.357891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.92215e7 | 1.81360 | 0.906799 | − | 0.421564i | \(-0.138519\pi\) | ||||
0.906799 | + | 0.421564i | \(0.138519\pi\) | |||||||
\(860\) | 1.47226e7 | 0.678795 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.85324e7 | 0.849501 | ||||||||
\(863\) | −1.83642e7 | −0.839352 | −0.419676 | − | 0.907674i | \(-0.637856\pi\) | ||||
−0.419676 | + | 0.907674i | \(0.637856\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.55453e6 | −0.116084 | ||||||||
\(866\) | −2.63182e7 | −1.19251 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.20870e6 | 0.413665 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.89984e7 | 0.848539 | ||||||||
\(872\) | 1.15744e7 | 0.515477 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.02816e7 | −0.898100 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.42578e6 | −0.413826 | −0.206913 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206913 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(878\) | 7.28278e6 | 0.318831 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.88850e6 | 0.125738 | ||||||||
\(881\) | −1.32820e7 | −0.576534 | −0.288267 | − | 0.957550i | \(-0.593079\pi\) | ||||
−0.288267 | + | 0.957550i | \(0.593079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.88897e7 | 0.815309 | 0.407655 | − | 0.913136i | \(-0.366347\pi\) | ||||
0.407655 | + | 0.913136i | \(0.366347\pi\) | |||||||
\(884\) | 6.42840e6 | 0.276676 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.27961e6 | −0.354345 | ||||||||
\(887\) | −4.17083e7 | −1.77997 | −0.889987 | − | 0.455985i | \(-0.849287\pi\) | ||||
−0.889987 | + | 0.455985i | \(0.849287\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.97649e7 | 1.25959 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.02205e7 | 0.430089 | ||||||||
\(893\) | 6.87586e7 | 2.88535 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.87028e7 | 0.780455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.29033e7 | 0.947777 | ||||||||
\(899\) | 6.85539e6 | 0.282900 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.56336e7 | −0.641573 | ||||||||
\(902\) | 4.56785e6 | 0.186937 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.26613e7 | 0.515295 | ||||||||
\(905\) | 2.78922e7 | 1.13204 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.60801e7 | 1.85993 | 0.929963 | − | 0.367654i | \(-0.119839\pi\) | ||||
0.929963 | + | 0.367654i | \(0.119839\pi\) | |||||||
\(908\) | 8.41091e6 | 0.338554 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.25527e7 | −0.900334 | −0.450167 | − | 0.892944i | \(-0.648636\pi\) | ||||
−0.450167 | + | 0.892944i | \(0.648636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.30244e7 | 0.517107 | ||||||||
\(914\) | −1.27470e6 | −0.0504712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.49230e7 | 0.587647 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.25898e7 | −1.27290 | −0.636448 | − | 0.771319i | \(-0.719597\pi\) | ||||
−0.636448 | + | 0.771319i | \(0.719597\pi\) | |||||||
\(920\) | 8.76421e6 | 0.341384 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.36988e7 | −0.530708 | ||||||||
\(923\) | 2.45100e7 | 0.946977 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00648e7 | 0.771046 | ||||||||
\(926\) | −1.53178e7 | −0.587041 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −777250. | −0.0296272 | ||||||||
\(929\) | 4.56149e7 | 1.73407 | 0.867036 | − | 0.498246i | \(-0.166022\pi\) | ||||
0.867036 | + | 0.498246i | \(0.166022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.13247e7 | 0.427058 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.13785e7 | 0.426792 | ||||||||
\(935\) | 1.29740e7 | 0.485338 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.60574e6 | 0.134167 | 0.0670835 | − | 0.997747i | \(-0.478631\pi\) | ||||
0.0670835 | + | 0.997747i | \(0.478631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.97123e7 | −1.09677 | ||||||||
\(941\) | 4.40826e6 | 0.162290 | 0.0811452 | − | 0.996702i | \(-0.474142\pi\) | ||||
0.0811452 | + | 0.996702i | \(0.474142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.38596e7 | 0.507542 | ||||||||
\(944\) | 6.74786e6 | 0.246454 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.28706e6 | −0.264743 | ||||||||
\(947\) | −7.36278e6 | −0.266788 | −0.133394 | − | 0.991063i | \(-0.542588\pi\) | ||||
−0.133394 | + | 0.991063i | \(0.542588\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.55381e7 | −0.560057 | ||||||||
\(950\) | 2.87804e7 | 1.03464 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.73903e7 | −1.33360 | −0.666802 | − | 0.745235i | \(-0.732337\pi\) | ||||
−0.666802 | + | 0.745235i | \(0.732337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.66307e7 | 1.29968 | ||||||||
\(956\) | 8.00982e6 | 0.283451 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.21462e6 | 0.183573 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.29433e7 | 1.84928 | ||||||||
\(962\) | −1.08946e7 | −0.379555 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.93315e7 | 0.669997 | ||||||||
\(965\) | −2.49742e7 | −0.863322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.30730e7 | 0.449582 | 0.224791 | − | 0.974407i | \(-0.427830\pi\) | ||||
0.224791 | + | 0.974407i | \(0.427830\pi\) | |||||||
\(968\) | 8.87758e6 | 0.304513 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.76640e6 | −0.333277 | ||||||||
\(971\) | 1.52454e7 | 0.518908 | 0.259454 | − | 0.965755i | \(-0.416457\pi\) | ||||
0.259454 | + | 0.965755i | \(0.416457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.49450e7 | −0.842530 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.04237e6 | 0.303849 | ||||||||
\(977\) | −3.08690e6 | −0.103463 | −0.0517316 | − | 0.998661i | \(-0.516474\pi\) | ||||
−0.0517316 | + | 0.998661i | \(0.516474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.47324e7 | −0.491264 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.57571e7 | −0.521433 | ||||||||
\(983\) | −1.70201e7 | −0.561796 | −0.280898 | − | 0.959738i | \(-0.590632\pi\) | ||||
−0.280898 | + | 0.959738i | \(0.590632\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.22269e7 | 0.401539 | ||||||||
\(986\) | −3.49109e6 | −0.114359 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.56270e7 | −0.509311 | ||||||||
\(989\) | −2.21102e7 | −0.718789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.34672e7 | −1.40597 | −0.702987 | − | 0.711203i | \(-0.748151\pi\) | ||||
−0.702987 | + | 0.711203i | \(0.748151\pi\) | |||||||
\(992\) | −9.24851e6 | −0.298396 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.18199e6 | 0.133914 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.46672e7 | −0.785926 | −0.392963 | − | 0.919554i | \(-0.628550\pi\) | ||||
−0.392963 | + | 0.919554i | \(0.628550\pi\) | |||||||
\(998\) | −3.19028e7 | −1.01392 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.6.a.bh.1.2 | 2 | ||
3.2 | odd | 2 | 294.6.a.r.1.1 | 2 | |||
7.2 | even | 3 | 126.6.g.h.109.1 | 4 | |||
7.4 | even | 3 | 126.6.g.h.37.1 | 4 | |||
7.6 | odd | 2 | 882.6.a.bb.1.1 | 2 | |||
21.2 | odd | 6 | 42.6.e.c.25.2 | ✓ | 4 | ||
21.5 | even | 6 | 294.6.e.s.67.1 | 4 | |||
21.11 | odd | 6 | 42.6.e.c.37.2 | yes | 4 | ||
21.17 | even | 6 | 294.6.e.s.79.1 | 4 | |||
21.20 | even | 2 | 294.6.a.w.1.2 | 2 | |||
84.11 | even | 6 | 336.6.q.f.289.2 | 4 | |||
84.23 | even | 6 | 336.6.q.f.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.e.c.25.2 | ✓ | 4 | 21.2 | odd | 6 | ||
42.6.e.c.37.2 | yes | 4 | 21.11 | odd | 6 | ||
126.6.g.h.37.1 | 4 | 7.4 | even | 3 | |||
126.6.g.h.109.1 | 4 | 7.2 | even | 3 | |||
294.6.a.r.1.1 | 2 | 3.2 | odd | 2 | |||
294.6.a.w.1.2 | 2 | 21.20 | even | 2 | |||
294.6.e.s.67.1 | 4 | 21.5 | even | 6 | |||
294.6.e.s.79.1 | 4 | 21.17 | even | 6 | |||
336.6.q.f.193.2 | 4 | 84.23 | even | 6 | |||
336.6.q.f.289.2 | 4 | 84.11 | even | 6 | |||
882.6.a.bb.1.1 | 2 | 7.6 | odd | 2 | |||
882.6.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial |