Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [528,6,Mod(1,528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(528, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("528.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.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: | \(84.6826568613\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 528.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 46.0000 | 0.822873 | 0.411437 | − | 0.911438i | \(-0.365027\pi\) | ||||
0.411437 | + | 0.911438i | \(0.365027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −148.000 | −1.14161 | −0.570803 | − | 0.821087i | \(-0.693368\pi\) | ||||
−0.570803 | + | 0.821087i | \(0.693368\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 574.000 | 0.942006 | 0.471003 | − | 0.882132i | \(-0.343892\pi\) | ||||
0.471003 | + | 0.882132i | \(0.343892\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 414.000 | 0.475086 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −722.000 | −0.605919 | −0.302960 | − | 0.953003i | \(-0.597975\pi\) | ||||
−0.302960 | + | 0.953003i | \(0.597975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2160.00 | −1.37268 | −0.686341 | − | 0.727280i | \(-0.740784\pi\) | ||||
−0.686341 | + | 0.727280i | \(0.740784\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1332.00 | −0.659107 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2536.00 | 0.999608 | 0.499804 | − | 0.866139i | \(-0.333405\pi\) | ||||
0.499804 | + | 0.866139i | \(0.333405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1009.00 | −0.322880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4650.00 | 1.02673 | 0.513367 | − | 0.858169i | \(-0.328398\pi\) | ||||
0.513367 | + | 0.858169i | \(0.328398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5032.00 | −0.940451 | −0.470226 | − | 0.882546i | \(-0.655828\pi\) | ||||
−0.470226 | + | 0.882546i | \(0.655828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6808.00 | −0.939398 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8118.00 | 0.974866 | 0.487433 | − | 0.873161i | \(-0.337933\pi\) | ||||
0.487433 | + | 0.873161i | \(0.337933\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5166.00 | 0.543867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5138.00 | −0.477347 | −0.238674 | − | 0.971100i | \(-0.576713\pi\) | ||||
−0.238674 | + | 0.971100i | \(0.576713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −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 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −24728.0 | −1.63284 | −0.816421 | − | 0.577457i | \(-0.804045\pi\) | ||||
−0.816421 | + | 0.577457i | \(0.804045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5097.00 | 0.303266 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6498.00 | −0.349828 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28746.0 | −1.40568 | −0.702842 | − | 0.711346i | \(-0.748086\pi\) | ||||
−0.702842 | + | 0.711346i | \(0.748086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5566.00 | −0.248106 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19440.0 | −0.792518 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5860.00 | 0.219163 | 0.109582 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109582 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53658.0 | −1.84633 | −0.923166 | − | 0.384401i | \(-0.874408\pi\) | ||||
−0.923166 | + | 0.384401i | \(0.874408\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11988.0 | −0.380536 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26404.0 | 0.775151 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −30908.0 | −0.841170 | −0.420585 | − | 0.907253i | \(-0.638175\pi\) | ||||
−0.420585 | + | 0.907253i | \(0.638175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22824.0 | 0.577124 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 69648.0 | 1.63969 | 0.819847 | − | 0.572583i | \(-0.194058\pi\) | ||||
0.819847 | + | 0.572583i | \(0.194058\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18446.0 | −0.405131 | −0.202565 | − | 0.979269i | \(-0.564928\pi\) | ||||
−0.202565 | + | 0.979269i | \(0.564928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9081.00 | −0.186415 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17908.0 | 0.344207 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25300.0 | 0.456092 | 0.228046 | − | 0.973650i | \(-0.426766\pi\) | ||||
0.228046 | + | 0.973650i | \(0.426766\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17556.0 | 0.279724 | 0.139862 | − | 0.990171i | \(-0.455334\pi\) | ||||
0.139862 | + | 0.990171i | \(0.455334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33212.0 | −0.498595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 41850.0 | 0.592785 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 132570. | 1.77407 | 0.887034 | − | 0.461704i | \(-0.152762\pi\) | ||||
0.887034 | + | 0.461704i | \(0.152762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −84952.0 | −1.07540 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −45288.0 | −0.542970 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −99360.0 | −1.12954 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70658.0 | 0.762486 | 0.381243 | − | 0.924475i | \(-0.375496\pi\) | ||||
0.381243 | + | 0.924475i | \(0.375496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −101998. | −0.994920 | −0.497460 | − | 0.867487i | \(-0.665734\pi\) | ||||
−0.497460 | + | 0.867487i | \(0.665734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −130904. | −1.21579 | −0.607897 | − | 0.794016i | \(-0.707987\pi\) | ||||
−0.607897 | + | 0.794016i | \(0.707987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −61272.0 | −0.542361 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 141612. | 1.19575 | 0.597875 | − | 0.801589i | \(-0.296012\pi\) | ||||
0.597875 | + | 0.801589i | \(0.296012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −239810. | −1.93331 | −0.966654 | − | 0.256086i | \(-0.917567\pi\) | ||||
−0.966654 | + | 0.256086i | \(0.917567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 73062.0 | 0.562839 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −42726.0 | −0.314772 | −0.157386 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157386 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 116656. | 0.822550 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 46494.0 | 0.314002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 106856. | 0.691722 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −46242.0 | −0.275597 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −190164. | −1.08856 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −51788.0 | −0.284918 | −0.142459 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142459 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −74736.0 | −0.395417 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 33534.0 | 0.158362 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −228862. | −1.04177 | −0.520886 | − | 0.853627i | \(-0.674398\pi\) | ||||
−0.520886 | + | 0.853627i | \(0.674398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −374920. | −1.64589 | −0.822947 | − | 0.568119i | \(-0.807671\pi\) | ||||
−0.822947 | + | 0.568119i | \(0.807671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −222552. | −0.942722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −69454.0 | −0.284025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 213900. | 0.844872 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 45873.0 | 0.175091 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −65830.0 | −0.242917 | −0.121459 | − | 0.992597i | \(-0.538757\pi\) | ||||
−0.121459 | + | 0.992597i | \(0.538757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −154052. | −0.549826 | −0.274913 | − | 0.961469i | \(-0.588649\pi\) | ||||
−0.274913 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −58482.0 | −0.201973 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −231472. | −0.773872 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 287678. | 0.931446 | 0.465723 | − | 0.884931i | \(-0.345794\pi\) | ||||
0.465723 | + | 0.884931i | \(0.345794\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −258714. | −0.811572 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −375328. | −1.14116 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −105124. | −0.309908 | −0.154954 | − | 0.987922i | \(-0.549523\pi\) | ||||
−0.154954 | + | 0.987922i | \(0.549523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −50094.0 | −0.143244 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −150528. | −0.417663 | −0.208832 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208832 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −41817.0 | −0.112625 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −174960. | −0.457560 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2166.00 | −0.00550229 | −0.00275114 | − | 0.999996i | \(-0.500876\pi\) | ||||
−0.00275114 | + | 0.999996i | \(0.500876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 149332. | 0.368602 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 52740.0 | 0.126534 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −672780. | −1.56942 | −0.784712 | − | 0.619860i | \(-0.787189\pi\) | ||||
−0.784712 | + | 0.619860i | \(0.787189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −526778. | −1.19517 | −0.597587 | − | 0.801804i | \(-0.703874\pi\) | ||||
−0.597587 | + | 0.801804i | \(0.703874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −482922. | −1.06598 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 373428. | 0.802191 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 87362.0 | 0.182692 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −107892. | −0.219702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 305608. | 0.606152 | 0.303076 | − | 0.952966i | \(-0.401986\pi\) | ||||
0.303076 | + | 0.952966i | \(0.401986\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 116434. | 0.225002 | 0.112501 | − | 0.993652i | \(-0.464114\pi\) | ||||
0.112501 | + | 0.993652i | \(0.464114\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 237636. | 0.447534 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −247742. | −0.454814 | −0.227407 | − | 0.973800i | \(-0.573025\pi\) | ||||
−0.227407 | + | 0.973800i | \(0.573025\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 513360. | 0.918945 | 0.459472 | − | 0.888192i | \(-0.348039\pi\) | ||||
0.459472 | + | 0.888192i | \(0.348039\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −278172. | −0.485650 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −688200. | −1.17213 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −236348. | −0.392796 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 205416. | 0.333203 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 261360. | 0.413879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 620688. | 0.959770 | 0.479885 | − | 0.877331i | \(-0.340678\pi\) | ||||
0.479885 | + | 0.877331i | \(0.340678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 626832. | 0.946678 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −381984. | −0.563571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 744736. | 1.07363 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −166014. | −0.233902 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −414428. | −0.570780 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.31802e6 | 1.77484 | 0.887419 | − | 0.460964i | \(-0.152496\pi\) | ||||
0.887419 | + | 0.460964i | \(0.152496\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −81729.0 | −0.107627 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 887412. | 1.14304 | 0.571519 | − | 0.820589i | \(-0.306354\pi\) | ||||
0.571519 | + | 0.820589i | \(0.306354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −237450. | −0.299215 | −0.149608 | − | 0.988745i | \(-0.547801\pi\) | ||||
−0.149608 | + | 0.988745i | \(0.547801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 161172. | 0.198728 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −914706. | −1.10380 | −0.551902 | − | 0.833909i | \(-0.686098\pi\) | ||||
−0.551902 | + | 0.833909i | \(0.686098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.13749e6 | −1.34362 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 227700. | 0.263325 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.40892e6 | −1.59548 | −0.797740 | − | 0.603001i | \(-0.793971\pi\) | ||||
−0.797740 | + | 0.603001i | \(0.793971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −826358. | −0.916486 | −0.458243 | − | 0.888827i | \(-0.651521\pi\) | ||||
−0.458243 | + | 0.888827i | \(0.651521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 234462. | 0.249550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23984e6 | −1.29307 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 158004. | 0.161499 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.60387e6 | 1.60688 | 0.803442 | − | 0.595384i | \(-0.203000\pi\) | ||||
0.803442 | + | 0.595384i | \(0.203000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −306856. | −0.301393 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −298908. | −0.287864 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 397618. | 0.375520 | 0.187760 | − | 0.982215i | \(-0.439877\pi\) | ||||
0.187760 | + | 0.982215i | \(0.439877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.20146e6 | −1.11291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 376650. | 0.342245 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.19313e6 | 1.02426 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −725810. | −0.611564 | −0.305782 | − | 0.952101i | \(-0.598918\pi\) | ||||
−0.305782 | + | 0.952101i | \(0.598918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46787e6 | 1.21413 | 0.607063 | − | 0.794654i | \(-0.292348\pi\) | ||||
0.607063 | + | 0.794654i | \(0.292348\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −764568. | −0.620883 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 122089. | 0.0973520 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.52100e6 | 1.19105 | 0.595524 | − | 0.803338i | \(-0.296944\pi\) | ||||
0.595524 | + | 0.803338i | \(0.296944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −407592. | −0.313484 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 464382. | 0.350840 | 0.175420 | − | 0.984494i | \(-0.443872\pi\) | ||||
0.175420 | + | 0.984494i | \(0.443872\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 415136. | 0.308123 | 0.154062 | − | 0.988061i | \(-0.450765\pi\) | ||||
0.154062 | + | 0.988061i | \(0.450765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −894240. | −0.652142 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 760424. | 0.544943 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −898573. | −0.632862 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 635922. | 0.440222 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.59321e6 | −1.76469 | −0.882344 | − | 0.470605i | \(-0.844036\pi\) | ||||
−0.882344 | + | 0.470605i | \(0.844036\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 269560. | 0.180343 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.45566e6 | 0.941636 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22899e6 | 0.781867 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −917982. | −0.574417 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.46827e6 | −1.51930 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 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 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.48527e6 | −1.45704 | −0.728522 | − | 0.685022i | \(-0.759793\pi\) | ||||
−0.728522 | + | 0.685022i | \(0.759793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31719e6 | 0.759957 | 0.379978 | − | 0.924995i | \(-0.375931\pi\) | ||||
0.379978 | + | 0.924995i | \(0.375931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −551448. | −0.313133 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.25540e6 | 1.26059 | 0.630297 | − | 0.776354i | \(-0.282933\pi\) | ||||
0.630297 | + | 0.776354i | \(0.282933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −562650. | −0.309572 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.27451e6 | 0.690367 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.55952e6 | 0.831734 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −579166. | −0.304155 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.15829e6 | −1.11620 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.65974e6 | 1.86406 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.17071e6 | 1.59069 | 0.795346 | − | 0.606155i | \(-0.207289\pi\) | ||||
0.795346 | + | 0.606155i | \(0.207289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 657558. | 0.324955 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.42177e6 | −0.692176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.27630e6 | 0.612177 | 0.306089 | − | 0.952003i | \(-0.400980\pi\) | ||||
0.306089 | + | 0.952003i | \(0.400980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −384534. | −0.181734 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 608872. | 0.283557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.73308e6 | 0.795396 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.04990e6 | 0.474900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.69303e6 | −1.64649 | −0.823245 | − | 0.567687i | \(-0.807838\pi\) | ||||
−0.823245 | + | 0.567687i | \(0.807838\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.70919e6 | 0.751150 | 0.375575 | − | 0.926792i | \(-0.377445\pi\) | ||||
0.375575 | + | 0.926792i | \(0.377445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 418446. | 0.181289 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.36859e6 | 1.86597 | 0.932986 | − | 0.359914i | \(-0.117194\pi\) | ||||
0.932986 | + | 0.359914i | \(0.117194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.20381e6 | 1.34926 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 961704. | 0.399366 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.51284e6 | 1.43854 | 0.719271 | − | 0.694730i | \(-0.244476\pi\) | ||||
0.719271 | + | 0.694730i | \(0.244476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.18950e6 | 0.884254 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −848516. | −0.333371 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.15259e6 | 0.834251 | 0.417125 | − | 0.908849i | \(-0.363038\pi\) | ||||
0.417125 | + | 0.908849i | \(0.363038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −416178. | −0.159116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.25441e6 | 1.60474 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.24247e6 | −0.834553 | −0.417276 | − | 0.908780i | \(-0.637015\pi\) | ||||
−0.417276 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.71148e6 | −0.628482 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.66910e6 | 0.967189 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.40986e6 | 0.861775 | 0.430887 | − | 0.902406i | \(-0.358201\pi\) | ||||
0.430887 | + | 0.902406i | \(0.358201\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −466092. | −0.164497 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.01066e6 | 0.352052 | 0.176026 | − | 0.984386i | \(-0.443676\pi\) | ||||
0.176026 | + | 0.984386i | \(0.443676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 823768. | 0.283239 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −672624. | −0.228294 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.27779e6 | 0.428140 | 0.214070 | − | 0.976818i | \(-0.431328\pi\) | ||||
0.214070 | + | 0.976818i | \(0.431328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.83099e6 | −0.605682 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −482868. | −0.157706 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.16380e6 | 0.375306 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.45400e6 | 1.73676 | 0.868378 | − | 0.495903i | \(-0.165163\pi\) | ||||
0.868378 | + | 0.495903i | \(0.165163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.87712e6 | 0.904744 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.48980e6 | −0.462665 | −0.231332 | − | 0.972875i | \(-0.574308\pi\) | ||||
−0.231332 | + | 0.972875i | \(0.574308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.88837e6 | −0.885911 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 301806. | 0.0914303 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −982278. | −0.293933 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.39899e6 | −1.30030 | −0.650152 | − | 0.759804i | \(-0.725295\pi\) | ||||
−0.650152 | + | 0.759804i | \(0.725295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.05976e6 | −0.601467 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −867280. | −0.250198 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 807576. | 0.230178 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.37428e6 | −0.950257 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 280420. | 0.0780322 | 0.0390161 | − | 0.999239i | \(-0.487578\pi\) | ||||
0.0390161 | + | 0.999239i | \(0.487578\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 817462. | 0.224782 | 0.112391 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112391 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00297e6 | −0.544281 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 728498. | 0.195639 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.94138e6 | 2.10779 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −625086. | −0.163982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.88599e6 | −0.489043 | −0.244521 | − | 0.969644i | \(-0.578631\pi\) | ||||
−0.244521 | + | 0.969644i | \(0.578631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.84067e6 | 1.49707 | 0.748537 | − | 0.663093i | \(-0.230757\pi\) | ||||
0.748537 | + | 0.663093i | \(0.230757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.92510e6 | 0.487787 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.47776e6 | −1.37214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 509540. | 0.126188 | 0.0630938 | − | 0.998008i | \(-0.479903\pi\) | ||||
0.0630938 | + | 0.998008i | \(0.479903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 412857. | 0.101089 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.10268e6 | −0.993250 | −0.496625 | − | 0.867965i | \(-0.665428\pi\) | ||||
−0.496625 | + | 0.867965i | \(0.665428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.09822e6 | 1.45983 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −592470. | −0.140248 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 513410. | 0.120185 | 0.0600923 | − | 0.998193i | \(-0.480861\pi\) | ||||
0.0600923 | + | 0.998193i | \(0.480861\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 621698. | 0.143926 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.38647e6 | −0.317442 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.90779e6 | −0.884918 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.22738e6 | 0.274908 | 0.137454 | − | 0.990508i | \(-0.456108\pi\) | ||||
0.137454 | + | 0.990508i | \(0.456108\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −526338. | −0.116609 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.41000e6 | −1.40477 | −0.702386 | − | 0.711797i | \(-0.747882\pi\) | ||||
−0.702386 | + | 0.711797i | \(0.747882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.63030e6 | −1.43741 | −0.718705 | − | 0.695315i | \(-0.755265\pi\) | ||||
−0.718705 | + | 0.695315i | \(0.755265\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.08325e6 | −0.446795 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.14769e6 | 0.880064 | 0.440032 | − | 0.897982i | \(-0.354967\pi\) | ||||
0.440032 | + | 0.897982i | \(0.354967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.57438e6 | 0.960286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.58910e6 | 0.537770 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00478e6 | 0.206500 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.17944e6 | 0.443211 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.32843e6 | −0.468561 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.05132e6 | 1.00593 | 0.502963 | − | 0.864308i | \(-0.332243\pi\) | ||||
0.502963 | + | 0.864308i | \(0.332243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.65973e6 | 0.918329 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.37795e6 | −0.658849 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.25027e6 | 0.627429 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.66221e6 | −0.508651 | −0.254325 | − | 0.967119i | \(-0.581853\pi\) | ||||
−0.254325 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −946116. | −0.178925 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.54659e6 | 1.03830 | 0.519149 | − | 0.854684i | \(-0.326249\pi\) | ||||
0.519149 | + | 0.854684i | \(0.326249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.35730e6 | −0.622118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −450846. | −0.0827018 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.03079e7 | −1.87189 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6820.00 | 0.00122612 | 0.000613060 | − | 1.00000i | \(-0.499805\pi\) | ||||
0.000613060 | 1.00000i | \(0.499805\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.35475e6 | −0.241138 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 451136. | 0.0795037 | 0.0397519 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397519 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.69191e6 | −0.818693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −376353. | −0.0650243 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 393390. | 0.0673021 | 0.0336511 | − | 0.999434i | \(-0.489287\pi\) | ||||
0.0336511 | + | 0.999434i | \(0.489287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.73001e6 | 0.462500 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.57464e6 | −0.264173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.02158e6 | −1.00044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.99209e6 | 0.492321 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19494.0 | −0.00317675 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.28432e6 | 0.530092 | 0.265046 | − | 0.964236i | \(-0.414613\pi\) | ||||
0.265046 | + | 0.964236i | \(0.414613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.68266e6 | 0.268993 | 0.134497 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134497 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.34399e6 | 0.212812 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.63310e6 | 0.569838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5047.00 | −0.000784141 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 474660. | 0.0730544 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.94921e6 | −0.449664 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.51415e6 | 0.983951 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.05502e6 | −0.906108 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −616737. | −0.0914383 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.48158e6 | 1.39280 | 0.696398 | − | 0.717656i | \(-0.254785\pi\) | ||||
0.696398 | + | 0.717656i | \(0.254785\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.74100e6 | −0.690034 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.10313e7 | −1.59087 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.09239e6 | 0.870602 | 0.435301 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435301 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.34630e6 | −0.615444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00440e7 | −1.40938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.74440e6 | −0.520678 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.36085e6 | 0.463145 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.49594e6 | 1.16031 | 0.580154 | − | 0.814507i | \(-0.302992\pi\) | ||||
0.580154 | + | 0.814507i | \(0.302992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.76650e6 | −0.645163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 786258. | 0.105477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.02216e6 | 0.933683 | 0.466842 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466842 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.96540e6 | −0.259017 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −971028. | −0.126845 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.41847e6 | 1.21955 | 0.609775 | − | 0.792574i | \(-0.291260\pi\) | ||||
0.609775 | + | 0.792574i | \(0.291260\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.55882e6 | −0.322753 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.29590e6 | −0.412131 | −0.206065 | − | 0.978538i | \(-0.566066\pi\) | ||||
−0.206065 | + | 0.978538i | \(0.566066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.04791e6 | 0.129905 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.59829e6 | −0.319335 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.47827e6 | 0.423830 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.13872e6 | 0.258384 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.39827e6 | −0.526849 | −0.263425 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263425 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.08691e7 | 1.29094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.22968e6 | −0.262587 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.21781e6 | 1.07644 | 0.538222 | − | 0.842803i | \(-0.319096\pi\) | ||||
0.538222 | + | 0.842803i | \(0.319096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.91538e6 | 0.569199 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.62024e6 | 0.530553 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.77140e6 | −0.429473 | −0.214736 | − | 0.976672i | \(-0.568889\pi\) | ||||
−0.214736 | + | 0.976672i | \(0.568889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.19724e6 | 0.473999 | 0.237000 | − | 0.971510i | \(-0.423836\pi\) | ||||
0.237000 | + | 0.971510i | \(0.423836\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.50355e6 | −0.280390 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 673486. | 0.0748066 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.00133e6 | 0.110308 | 0.0551539 | − | 0.998478i | \(-0.482435\pi\) | ||||
0.0551539 | + | 0.998478i | \(0.482435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.19380e6 | −0.676728 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.41939e7 | −1.53815 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.38239e6 | −0.793498 | −0.396749 | − | 0.917927i | \(-0.629862\pi\) | ||||
−0.396749 | + | 0.917927i | \(0.629862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.12713e6 | −0.226781 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.54025e7 | −1.62884 | −0.814418 | − | 0.580279i | \(-0.802944\pi\) | ||||
−0.814418 | + | 0.580279i | \(0.802944\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.12402e6 | 0.747306 | 0.373653 | − | 0.927569i | \(-0.378105\pi\) | ||||
0.373653 | + | 0.927569i | \(0.378105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.84874e6 | 0.192375 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.96204e7 | −2.02529 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.59442e6 | −0.572869 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.35224e6 | 0.238953 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.86120e6 | −0.590690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.16696e7 | −1.16677 | −0.583383 | − | 0.812197i | \(-0.698271\pi\) | ||||
−0.583383 | + | 0.812197i | \(0.698271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.58619e6 | 0.554124 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.38225e6 | −0.234451 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.92568e6 | 0.285679 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.64149e6 | 0.546565 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.10271e7 | −1.06003 | −0.530014 | − | 0.847989i | \(-0.677813\pi\) | ||||
−0.530014 | + | 0.847989i | \(0.677813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.56024e6 | 0.911887 | 0.455944 | − | 0.890009i | \(-0.349302\pi\) | ||||
0.455944 | + | 0.890009i | \(0.349302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.43786e6 | −0.325378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.09942e7 | 1.03253 | 0.516263 | − | 0.856430i | \(-0.327323\pi\) | ||||
0.516263 | + | 0.856430i | \(0.327323\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −709060. | −0.0660802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.70262e6 | 0.619858 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −295346. | −0.0271049 | −0.0135525 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135525 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.46799e6 | −0.224771 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.49413e6 | −0.135044 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.472047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.72985e6 | −0.329540 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.47053e7 | 1.28949 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17924e7 | 1.02633 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.18621e7 | 1.02470 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.49262e6 | 0.556690 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.63733e6 | −0.139347 | −0.0696735 | − | 0.997570i | \(-0.522196\pi\) | ||||
−0.0696735 | + | 0.997570i | \(0.522196\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −735561. | −0.0621383 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.35878e6 | −0.533215 | −0.266607 | − | 0.963805i | \(-0.585903\pi\) | ||||
−0.266607 | + | 0.963805i | \(0.585903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.04574e7 | −0.870460 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.98671e6 | 0.659933 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.11033e7 | −0.910751 | −0.455376 | − | 0.890299i | \(-0.650495\pi\) | ||||
−0.455376 | + | 0.890299i | \(0.650495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.05277e7 | −0.857245 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.13705e6 | −0.172752 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.65002e7 | −1.32416 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.70189e7 | −1.35592 | −0.677962 | − | 0.735097i | \(-0.737136\pi\) | ||||
−0.677962 | + | 0.735097i | \(0.737136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.45055e6 | 0.114736 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.72463e7 | −1.35436 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.70964e6 | 0.289234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.23235e6 | −0.637281 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.58021e7 | 1.21456 | 0.607280 | − | 0.794488i | \(-0.292260\pi\) | ||||
0.607280 | + | 0.794488i | \(0.292260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.75349e7 | −1.33818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.02374e7 | −0.775741 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.50957e7 | 1.13581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.24834e7 | 0.932643 | 0.466322 | − | 0.884615i | \(-0.345579\pi\) | ||||
0.466322 | + | 0.884615i | \(0.345579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.04930e6 | 0.152031 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.27612e7 | −0.940083 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.19488e6 | −0.233717 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.26803e7 | −0.921151 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.00724e6 | −0.144803 | −0.0724014 | − | 0.997376i | \(-0.523066\pi\) | ||||
−0.0724014 | + | 0.997376i | \(0.523066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.93738e7 | 1.38796 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.43722e6 | −0.529133 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.69185e6 | −0.331512 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.97301e6 | −0.489310 | −0.244655 | − | 0.969610i | \(-0.578675\pi\) | ||||
−0.244655 | + | 0.969610i | \(0.578675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.99549e6 | 0.414984 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.34965e7 | −1.61527 | −0.807633 | − | 0.589685i | \(-0.799252\pi\) | ||||
−0.807633 | + | 0.589685i | \(0.799252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.11016e6 | 0.144078 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.73987e6 | 0.253622 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.39901e7 | 0.942346 | 0.471173 | − | 0.882041i | \(-0.343831\pi\) | ||||
0.471173 | + | 0.882041i | \(0.343831\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.11586e7 | −0.746556 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.42745e7 | −1.61316 | −0.806582 | − | 0.591123i | \(-0.798685\pi\) | ||||
−0.806582 | + | 0.591123i | \(0.798685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.02818e6 | −0.199890 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.42204e6 | 0.0932415 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09586e7 | −1.36508 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.53660e7 | −0.994170 | −0.497085 | − | 0.867702i | \(-0.665596\pi\) | ||||
−0.497085 | + | 0.867702i | \(0.665596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.44348e7 | 0.927734 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.08639e6 | −0.452437 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.07605e7 | 1.31674 | 0.658368 | − | 0.752697i | \(-0.271247\pi\) | ||||
0.658368 | + | 0.752697i | \(0.271247\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.76170e6 | −0.174009 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.83810e6 | 0.365435 | 0.182717 | − | 0.983165i | \(-0.441511\pi\) | ||||
0.182717 | + | 0.983165i | \(0.441511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.54919e7 | 2.20708 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.69017e6 | −0.166198 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.36364e6 | 0.206453 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.39197e7 | −0.848818 | −0.424409 | − | 0.905471i | \(-0.639518\pi\) | ||||
−0.424409 | + | 0.905471i | \(0.639518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.57856e6 | 0.216807 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.17883e6 | −0.251539 | −0.125770 | − | 0.992059i | \(-0.540140\pi\) | ||||
−0.125770 | + | 0.992059i | \(0.540140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.07729e6 | 0.303653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.08132e7 | −0.642541 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.10981e7 | 0.655246 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.42741e6 | −0.494386 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.38985e6 | 0.197595 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32332e7 | 0.766461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.66705e6 | −0.556361 | −0.278181 | − | 0.960529i | \(-0.589731\pi\) | ||||
−0.278181 | + | 0.960529i | \(0.589731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.91850e7 | −1.09716 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.32345e6 | 0.359346 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.07997e7 | −1.73926 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.19008e7 | −0.667821 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.79884e6 | −0.323367 | −0.161683 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161683 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.78536e7 | 0.989371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.07382e7 | 0.591356 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.23197e6 | 0.122151 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.72651e7 | −0.939029 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.53229e6 | −0.353087 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.92543e7 | −1.03433 | −0.517163 | − | 0.855887i | \(-0.673012\pi\) | ||||
−0.517163 | + | 0.855887i | \(0.673012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.31938e7 | 0.704396 | 0.352198 | − | 0.935926i | \(-0.385434\pi\) | ||||
0.352198 | + | 0.935926i | \(0.385434\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.32108e7 | 0.700976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.83570e6 | −0.255015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.79366e7 | 0.940126 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.88111e6 | −0.358467 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.33779e7 | 0.692677 | 0.346338 | − | 0.938110i | \(-0.387425\pi\) | ||||
0.346338 | + | 0.938110i | \(0.387425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.88613e7 | 0.970673 | 0.485336 | − | 0.874327i | \(-0.338697\pi\) | ||||
0.485336 | + | 0.874327i | \(0.338697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.09880e6 | 0.0562062 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.62680e7 | −0.827123 | −0.413561 | − | 0.910476i | \(-0.635715\pi\) | ||||
−0.413561 | + | 0.910476i | \(0.635715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.18098e7 | −1.10221 | −0.551107 | − | 0.834435i | \(-0.685794\pi\) | ||||
−0.551107 | + | 0.834435i | \(0.685794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.36890e7 | 0.687652 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.68003e6 | −0.183755 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.92429e6 | −0.343684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.66833e6 | −0.180990 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.17771e7 | −0.577607 | −0.288804 | − | 0.957388i | \(-0.593257\pi\) | ||||
−0.288804 | + | 0.957388i | \(0.593257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.11135e6 | 0.0541828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.17944e6 | 0.202558 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.92358e6 | −0.0926764 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.16687e6 | −0.103782 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.73622e6 | 0.177895 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.05872e7 | 0.974483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.43993e7 | −0.677591 | −0.338796 | − | 0.940860i | \(-0.610020\pi\) | ||||
−0.338796 | + | 0.940860i | \(0.610020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.04816e6 | −0.376514 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.27604e6 | 0.291900 | 0.145950 | − | 0.989292i | \(-0.453376\pi\) | ||||
0.145950 | + | 0.989292i | \(0.453376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.71738e6 | 0.218131 | 0.109066 | − | 0.994035i | \(-0.465214\pi\) | ||||
0.109066 | + | 0.994035i | \(0.465214\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.84382e6 | 0.314623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.53926e6 | −0.344589 | −0.172295 | − | 0.985045i | \(-0.555118\pi\) | ||||
−0.172295 | + | 0.985045i | \(0.555118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −99636.0 | −0.00452768 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.08716e6 | −0.365383 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.06130e6 | −0.137517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.77412e7 | −0.792387 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.72330e6 | 0.254162 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.81443e7 | 1.24271 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.04331e7 | −0.458051 | −0.229025 | − | 0.973420i | \(-0.573554\pi\) | ||||
−0.229025 | + | 0.973420i | \(0.573554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.33389e7 | −1.01884 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.91076e7 | 1.69755 | 0.848774 | − | 0.528756i | \(-0.177342\pi\) | ||||
0.848774 | + | 0.528756i | \(0.177342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.29282e7 | −0.558003 | −0.279001 | − | 0.960291i | \(-0.590003\pi\) | ||||
−0.279001 | + | 0.960291i | \(0.590003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.42604e6 | 0.104121 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.36466e7 | −1.43592 | −0.717962 | − | 0.696082i | \(-0.754925\pi\) | ||||
−0.717962 | + | 0.696082i | \(0.754925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.66462e6 | 0.325264 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.34125e7 | 2.24137 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.09479e7 | −1.29144 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.31010e7 | 0.543654 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.33988e7 | −0.965594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.07546e7 | 0.851731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.10609e7 | 0.451411 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.42318e7 | −0.983477 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.19629e7 | 1.69374 | 0.846872 | − | 0.531797i | \(-0.178483\pi\) | ||||
0.846872 | + | 0.531797i | \(0.178483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.26184e6 | −0.331640 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.92521e6 | 0.0768567 | 0.0384283 | − | 0.999261i | \(-0.487765\pi\) | ||||
0.0384283 | + | 0.999261i | \(0.487765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12428e6 | −0.0843401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.22144e7 | −0.877167 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.94050e6 | 0.311835 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.72481e7 | 0.673678 | 0.336839 | − | 0.941562i | \(-0.390642\pi\) | ||||
0.336839 | + | 0.941562i | \(0.390642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.37749e6 | 0.325435 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.99780e7 | 1.54460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.19106e6 | −0.314765 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.06032e7 | −0.405265 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.51145e6 | 0.0954740 | 0.0477370 | − | 0.998860i | \(-0.484799\pi\) | ||||
0.0477370 | + | 0.998860i | \(0.484799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.10095e7 | −0.416288 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.23674e7 | −0.841225 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.01865e6 | 0.150332 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.79853e7 | 0.669221 | 0.334611 | − | 0.942357i | \(-0.391395\pi\) | ||||
0.334611 | + | 0.942357i | \(0.391395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.18547e7 | 0.438761 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.22586e7 | −1.18760 | −0.593802 | − | 0.804611i | \(-0.702374\pi\) | ||||
−0.593802 | + | 0.804611i | \(0.702374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.30300e7 | −0.477160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.96303e6 | −0.180787 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.41659e7 | −1.60034 | −0.800169 | − | 0.599774i | \(-0.795257\pi\) | ||||
−0.800169 | + | 0.599774i | \(0.795257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.05880e7 | −0.381635 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.02986e7 | 0.727804 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.87488e7 | 0.668714 | 0.334357 | − | 0.942446i | \(-0.391481\pi\) | ||||
0.334357 | + | 0.942446i | \(0.391481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.40580e7 | 0.498786 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.06385e6 | −0.178731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.38716e7 | 1.18929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.30813e6 | −0.115551 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.14706e7 | 0.398584 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.35596e6 | 0.185148 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.79123e7 | 1.63079 | 0.815397 | − | 0.578902i | \(-0.196519\pi\) | ||||
0.815397 | + | 0.578902i | \(0.196519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.54882e7 | 1.87896 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.21249e6 | −0.175604 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.01385e7 | 1.34532 | 0.672658 | − | 0.739954i | \(-0.265153\pi\) | ||||
0.672658 | + | 0.739954i | \(0.265153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.60410e7 | −0.534902 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.94246e7 | −0.644436 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.22682e6 | −0.106510 | −0.0532551 | − | 0.998581i | \(-0.516960\pi\) | ||||
−0.0532551 | + | 0.998581i | \(0.516960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.13961e7 | −0.374254 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.29377e7 | 1.07622 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.10589e7 | −0.684614 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.95345e6 | 0.192568 | 0.0962841 | − | 0.995354i | \(-0.469304\pi\) | ||||
0.0962841 | + | 0.995354i | \(0.469304\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.85364e7 | 0.918387 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.36146e7 | 0.756175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.20783e7 | 1.02205 | 0.511027 | − | 0.859565i | \(-0.329265\pi\) | ||||
0.511027 | + | 0.859565i | \(0.329265\pi\) | |||||||
\(998\) | 0 | 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 | 528.6.a.i.1.1 | 1 | ||
4.3 | odd | 2 | 33.6.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 99.6.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 825.6.a.b.1.1 | 1 | |||
44.43 | even | 2 | 363.6.a.c.1.1 | 1 | |||
132.131 | odd | 2 | 1089.6.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
99.6.a.b.1.1 | 1 | 12.11 | even | 2 | |||
363.6.a.c.1.1 | 1 | 44.43 | even | 2 | |||
528.6.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
825.6.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
1089.6.a.d.1.1 | 1 | 132.131 | odd | 2 |