Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.6140289600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 32x^{4} + 116x^{3} + 256x^{2} + 2778x + 7605 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(0.844467 + 4.86464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.j.449.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.755735i | − 0.0484804i | −0.999706 | − | 0.0242402i | \(-0.992283\pi\) | ||||
0.999706 | − | 0.0242402i | \(-0.00771666\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 172.424i | 1.33001i | 0.746841 | + | 0.665003i | \(0.231570\pi\) | ||||
−0.746841 | + | 0.665003i | \(0.768430\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 242.429 | 0.997650 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 391.540 | 0.975651 | 0.487825 | − | 0.872941i | \(-0.337790\pi\) | ||||
0.487825 | + | 0.872941i | \(0.337790\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 149.245i | 0.244930i | 0.992473 | + | 0.122465i | \(0.0390800\pi\) | ||||
−0.992473 | + | 0.122465i | \(0.960920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1187.74i | − 0.996776i | −0.866954 | − | 0.498388i | \(-0.833925\pi\) | ||||
0.866954 | − | 0.498388i | \(-0.166075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −685.033 | −0.435339 | −0.217670 | − | 0.976023i | \(-0.569845\pi\) | ||||
−0.217670 | + | 0.976023i | \(0.569845\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 130.307 | 0.0644792 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 996.236i | 0.392684i | 0.980536 | + | 0.196342i | \(0.0629062\pi\) | ||||
−0.980536 | + | 0.196342i | \(0.937094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 366.856i | − 0.0968469i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8769.13 | 1.93625 | 0.968125 | − | 0.250466i | \(-0.0805839\pi\) | ||||
0.968125 | + | 0.250466i | \(0.0805839\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9525.61 | 1.78028 | 0.890140 | − | 0.455686i | \(-0.150606\pi\) | ||||
0.890140 | + | 0.455686i | \(0.150606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 295.901i | − 0.0473000i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 10226.8i | − 1.22811i | −0.789264 | − | 0.614054i | \(-0.789538\pi\) | ||||
0.789264 | − | 0.614054i | \(-0.210462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 112.790 | 0.0118743 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.6496 | 0.00303332 | 0.00151666 | − | 0.999999i | \(-0.499517\pi\) | ||||
0.00151666 | + | 0.999999i | \(0.499517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10321.5i | 0.851279i | 0.904893 | + | 0.425639i | \(0.139951\pi\) | ||||
−0.904893 | + | 0.425639i | \(0.860049\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 16931.7i | − 1.11804i | −0.829156 | − | 0.559018i | \(-0.811178\pi\) | ||||
0.829156 | − | 0.559018i | \(-0.188822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12923.1 | −0.768914 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −897.614 | −0.0483242 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 22287.0i | − 1.08984i | −0.838489 | − | 0.544919i | \(-0.816561\pi\) | ||||
0.838489 | − | 0.544919i | \(-0.183439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 517.704i | 0.0211054i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44251.2 | −1.65499 | −0.827494 | − | 0.561474i | \(-0.810234\pi\) | ||||
−0.827494 | + | 0.561474i | \(0.810234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21743.1 | −0.748165 | −0.374083 | − | 0.927395i | \(-0.622042\pi\) | ||||
−0.374083 | + | 0.927395i | \(0.622042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 41800.6i | 1.32688i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 20709.0i | − 0.563600i | −0.959473 | − | 0.281800i | \(-0.909068\pi\) | ||||
0.959473 | − | 0.281800i | \(-0.0909315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 752.891 | 0.0190375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15379.5 | 0.362073 | 0.181037 | − | 0.983476i | \(-0.442055\pi\) | ||||
0.181037 | + | 0.983476i | \(0.442055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57995.4i | 1.27376i | 0.770964 | + | 0.636878i | \(0.219775\pi\) | ||||
−0.770964 | + | 0.636878i | \(0.780225\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 67511.0i | 1.29762i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62466.5 | 1.12611 | 0.563054 | − | 0.826420i | \(-0.309626\pi\) | ||||
0.563054 | + | 0.826420i | \(0.309626\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 58633.0 | 0.992954 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 43578.7i | − 0.694351i | −0.937800 | − | 0.347175i | \(-0.887141\pi\) | ||||
0.937800 | − | 0.347175i | \(-0.112859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 6627.14i | − 0.0938703i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −66297.9 | −0.887207 | −0.443603 | − | 0.896223i | \(-0.646300\pi\) | ||||
−0.443603 | + | 0.896223i | \(0.646300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25733.5 | −0.325758 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7198.84i | − 0.0863088i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12264.3i | 0.132346i | 0.997808 | + | 0.0661732i | \(0.0210790\pi\) | ||||
−0.997808 | + | 0.0661732i | \(0.978921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 94920.6 | 0.973358 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37376.8 | −0.364584 | −0.182292 | − | 0.983244i | \(-0.558352\pi\) | ||||
−0.182292 | + | 0.983244i | \(0.558352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41642.9i | 0.386765i | 0.981123 | + | 0.193383i | \(0.0619459\pi\) | ||||
−0.981123 | + | 0.193383i | \(0.938054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 69664.7i | 0.588239i | 0.955769 | + | 0.294119i | \(0.0950263\pi\) | ||||
−0.955769 | + | 0.294119i | \(0.904974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 88554.2 | 0.713909 | 0.356954 | − | 0.934122i | \(-0.383815\pi\) | ||||
0.356954 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7728.78 | −0.0595392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 77809.3i | 0.573239i | 0.958045 | + | 0.286619i | \(0.0925315\pi\) | ||||
−0.958045 | + | 0.286619i | \(0.907469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36181.4i | 0.244355i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 204795. | 1.32572 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7747.38 | −0.0481051 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 24.6744i | 0 0.000147057i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 294580.i | 1.62067i | 0.585970 | + | 0.810333i | \(0.300714\pi\) | ||||
−0.585970 | + | 0.810333i | \(0.699286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7800.32 | 0.0412704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 173565. | 0.883658 | 0.441829 | − | 0.897099i | \(-0.354330\pi\) | ||||
0.441829 | + | 0.897099i | \(0.354330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 118116.i | − 0.579003i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 346072.i | − 1.57531i | −0.616119 | − | 0.787653i | \(-0.711296\pi\) | ||||
0.616119 | − | 0.787653i | \(-0.288704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 329344. | 1.44581 | 0.722907 | − | 0.690945i | \(-0.242805\pi\) | ||||
0.722907 | + | 0.690945i | \(0.242805\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12795.9 | −0.0542029 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 58435.5i | 0.238966i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9766.47i | 0.0372773i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −83495.2 | −0.308103 | −0.154052 | − | 0.988063i | \(-0.549232\pi\) | ||||
−0.154052 | + | 0.988063i | \(0.549232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −155105. | −0.553585 | −0.276792 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 287941.i | − 0.994433i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60634.6i | 0.196323i | 0.995170 | + | 0.0981615i | \(0.0312962\pi\) | ||||
−0.995170 | + | 0.0981615i | \(0.968704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16843.1 | −0.0528358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −171775. | −0.522271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 528292.i | 1.55742i | 0.627387 | + | 0.778708i | \(0.284125\pi\) | ||||
−0.627387 | + | 0.778708i | \(0.715875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 681927.i | − 1.89211i | −0.324002 | − | 0.946056i | \(-0.605029\pi\) | ||||
0.324002 | − | 0.946056i | \(-0.394971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 349019. | 0.940009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −166072. | −0.434316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 148111.i | − 0.376245i | −0.982146 | − | 0.188122i | \(-0.939760\pi\) | ||||
0.982146 | − | 0.188122i | \(-0.0602402\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33442.2i | 0.0802346i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 650289. | 1.51696 | 0.758480 | − | 0.651697i | \(-0.225942\pi\) | ||||
0.758480 | + | 0.651697i | \(0.225942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 315052. | 0.714803 | 0.357401 | − | 0.933951i | \(-0.383663\pi\) | ||||
0.357401 | + | 0.933951i | \(0.383663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16432.1i | 0.0362714i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 465046.i | − 0.972506i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 63254.8 | 0.128807 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 851610. | 1.68911 | 0.844554 | − | 0.535471i | \(-0.179866\pi\) | ||||
0.844554 | + | 0.535471i | \(0.179866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 916910.i | 1.77188i | 0.463804 | + | 0.885938i | \(0.346484\pi\) | ||||
−0.463804 | + | 0.885938i | \(0.653516\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 595345.i | − 1.09296i | −0.837473 | − | 0.546479i | \(-0.815968\pi\) | ||||
0.837473 | − | 0.546479i | \(-0.184032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 159504. | 0.285522 | 0.142761 | − | 0.989757i | \(-0.454402\pi\) | ||||
0.142761 | + | 0.989757i | \(0.454402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15650.5 | −0.0273236 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.51201e6i | 2.57522i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 241516.i | 0.391761i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −268218. | −0.424739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 776648. | 1.20093 | 0.600466 | − | 0.799650i | \(-0.294982\pi\) | ||||
0.600466 | + | 0.799650i | \(0.294982\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 11622.8i | − 0.0175535i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.64245e6i | 2.36778i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 43829.2 | 0.0617523 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 177264. | 0.244141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 969846.i | 1.30599i | 0.757361 | + | 0.652996i | \(0.226488\pi\) | ||||
−0.757361 | + | 0.652996i | \(0.773512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 32926.6i | − 0.0424113i | −0.999775 | − | 0.0212057i | \(-0.993250\pi\) | ||||
0.999775 | − | 0.0212057i | \(-0.00675048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −730255. | −0.920208 | −0.460104 | − | 0.887865i | \(-0.652188\pi\) | ||||
−0.460104 | + | 0.887865i | \(0.652188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 51020.5 | 0.0629092 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 550888.i | − 0.664774i | −0.943143 | − | 0.332387i | \(-0.892146\pi\) | ||||
0.943143 | − | 0.332387i | \(-0.107854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 47208.2i | − 0.0545942i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 996266. | 1.12819 | 0.564093 | − | 0.825711i | \(-0.309226\pi\) | ||||
0.564093 | + | 0.825711i | \(0.309226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −953235. | −1.05720 | −0.528600 | − | 0.848871i | \(-0.677283\pi\) | ||||
−0.528600 | + | 0.848871i | \(0.677283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 133457.i | − 0.144986i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 102238.i | − 0.106628i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32933.9 | −0.0336624 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 780609. | 0.782077 | 0.391038 | − | 0.920374i | \(-0.372116\pi\) | ||||
0.391038 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 390066.i | 0.383122i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 340539.i | 0.321614i | 0.986986 | + | 0.160807i | \(0.0514096\pi\) | ||||
−0.986986 | + | 0.160807i | \(0.948590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.76335e6 | 1.63339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.12589e6 | 1.93170 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.05298e6i | 1.83018i | 0.403246 | + | 0.915092i | \(0.367882\pi\) | ||||
−0.403246 | + | 0.915092i | \(0.632118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 50103.7i | 0.0430122i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −98629.8 | −0.0831050 | −0.0415525 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415525 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17220e6 | 0.969565 | 0.484783 | − | 0.874635i | \(-0.338899\pi\) | ||||
0.484783 | + | 0.874635i | \(0.338899\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19447.7i | 0.0157929i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.13901e6i | − 0.891923i | −0.895052 | − | 0.445962i | \(-0.852862\pi\) | ||||
0.895052 | − | 0.445962i | \(-0.147138\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.30928e6 | 1.77610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.33128e6 | −1.00578 | −0.502889 | − | 0.864351i | \(-0.667730\pi\) | ||||
−0.502889 | + | 0.864351i | \(0.667730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 921840.i | − 0.684210i | −0.939662 | − | 0.342105i | \(-0.888860\pi\) | ||||
0.939662 | − | 0.342105i | \(-0.111140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5629.58i | 0.00403433i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9140.20 | 0.00643741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9268.54 | 0.00641621 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.64240e6i | − 1.11766i | −0.829281 | − | 0.558831i | \(-0.811250\pi\) | ||||
0.829281 | − | 0.558831i | \(-0.188750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 143639.i | − 0.0944888i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −148684. | −0.0961801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77968e6 | −1.13221 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28246.9i | 0.0176752i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 810866.i | 0.491025i | 0.969393 | + | 0.245512i | \(0.0789562\pi\) | ||||
−0.969393 | + | 0.245512i | \(0.921044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31471.0 | 0.0187506 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.67678e6 | −0.983050 | −0.491525 | − | 0.870864i | \(-0.663560\pi\) | ||||
−0.491525 | + | 0.870864i | \(0.663560\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.43902e6i | 0.830242i | 0.909766 | + | 0.415121i | \(0.136261\pi\) | ||||
−0.909766 | + | 0.415121i | \(0.863739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 783839.i | − 0.438105i | −0.975713 | − | 0.219053i | \(-0.929703\pi\) | ||||
0.975713 | − | 0.219053i | \(-0.0702967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.43347e6 | 1.88910 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 52648.1 | 0.0285181 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 813639.i | 0.433936i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 66923.5i | − 0.0346106i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.91943e6 | 1.48699 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.30343e6 | −1.65728 | −0.828638 | − | 0.559785i | \(-0.810884\pi\) | ||||
−0.828638 | + | 0.559785i | \(0.810884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.47928e6i | − 1.22522i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.17037e6i | − 1.04102i | −0.853856 | − | 0.520510i | \(-0.825742\pi\) | ||||
0.853856 | − | 0.520510i | \(-0.174258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 58803.2 | 0.0277909 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.72966e6 | 1.73693 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 669673.i | 0.307346i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.26327e6i | − 0.563215i | −0.959530 | − | 0.281607i | \(-0.909132\pi\) | ||||
0.959530 | − | 0.281607i | \(-0.0908676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.84682e6 | 0.811636 | 0.405818 | − | 0.913954i | \(-0.366987\pi\) | ||||
0.405818 | + | 0.913954i | \(0.366987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54751.5 | 0.0237207 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.82123e6i | 1.63217i | 0.577929 | + | 0.816087i | \(0.303861\pi\) | ||||
−0.577929 | + | 0.816087i | \(0.696139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 154770.i | − 0.0642714i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.71131e6 | −0.700798 | −0.350399 | − | 0.936600i | \(-0.613954\pi\) | ||||
−0.350399 | + | 0.936600i | \(0.613954\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.00683e6 | −0.810480 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5854.97i | 0.00233216i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.72599e6i | 0.668919i | 0.942410 | + | 0.334460i | \(0.108554\pi\) | ||||
−0.942410 | + | 0.334460i | \(0.891446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7915.20 | 0.00302619 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.84282e6 | 1.44949 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 732009.i | 0.272423i | 0.990680 | + | 0.136212i | \(0.0434927\pi\) | ||||
−0.990680 | + | 0.136212i | \(0.956507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.30875e6i | 0.474246i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.07751e6 | 1.10053 | 0.550264 | − | 0.834991i | \(-0.314527\pi\) | ||||
0.550264 | + | 0.834991i | \(0.314527\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 222624. | 0.0785706 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.26468e6i | 0.440540i | 0.975439 | + | 0.220270i | \(0.0706938\pi\) | ||||
−0.975439 | + | 0.220270i | \(0.929306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.50223e6i | 0.849278i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.65533e6 | −1.22476 | −0.612382 | − | 0.790562i | \(-0.709788\pi\) | ||||
−0.612382 | + | 0.790562i | \(0.709788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.18327e6 | 0.391418 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 131169.i | − 0.0428401i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.99465e6i | 1.59048i | 0.606294 | + | 0.795241i | \(0.292655\pi\) | ||||
−0.606294 | + | 0.795241i | \(0.707345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −89264.7 | −0.0280703 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 298037. | 0.0925570 | 0.0462785 | − | 0.998929i | \(-0.485264\pi\) | ||||
0.0462785 | + | 0.998929i | \(0.485264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.42165e6i | 0.436045i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.00421e6i | − 1.19821i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.26110e6 | −0.963954 | −0.481977 | − | 0.876184i | \(-0.660081\pi\) | ||||
−0.481977 | + | 0.876184i | \(0.660081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −261539. | −0.0763715 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.62998e6i | − 2.20114i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 248897.i | − 0.0700937i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.24623e6 | −0.346786 | −0.173393 | − | 0.984853i | \(-0.555473\pi\) | ||||
−0.173393 | + | 0.984853i | \(0.555473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.88625e6 | −0.518674 | −0.259337 | − | 0.965787i | \(-0.583504\pi\) | ||||
−0.259337 | + | 0.965787i | \(0.583504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4.10473e6i | − 1.11541i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.74905e6i | − 0.995064i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44161.8 | 0.0115852 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.30534e6 | 0.857082 | 0.428541 | − | 0.903522i | \(-0.359028\pi\) | ||||
0.428541 | + | 0.903522i | \(0.359028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.61270e6i | 1.95128i | 0.219384 | + | 0.975639i | \(0.429595\pi\) | ||||
−0.219384 | + | 0.975639i | \(0.570405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 682455.i | − 0.170951i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.45916e6 | −1.35196 | −0.675982 | − | 0.736918i | \(-0.736280\pi\) | ||||
−0.675982 | + | 0.736918i | \(0.736280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.13294e6 | −0.767107 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.09261e6i | 1.23291i | 0.787391 | + | 0.616454i | \(0.211431\pi\) | ||||
−0.787391 | + | 0.616454i | \(0.788569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 63100.3i | 0.0149370i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.83842e6 | −1.36672 | −0.683360 | − | 0.730082i | \(-0.739482\pi\) | ||||
−0.683360 | + | 0.730082i | \(0.739482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12783.6 | 0.00295946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 117219.i | 0.0268380i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.06917e6i | 1.13539i | 0.823238 | + | 0.567697i | \(0.192165\pi\) | ||||
−0.823238 | + | 0.567697i | \(0.807835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −435728. | −0.0965347 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.10777e6 | 1.33854 | 0.669269 | − | 0.743021i | \(-0.266608\pi\) | ||||
0.669269 | + | 0.743021i | \(0.266608\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.29238e6i | − 0.930563i | −0.885163 | − | 0.465282i | \(-0.845953\pi\) | ||||
0.885163 | − | 0.465282i | \(-0.154047\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.64461e6i | 0.348957i | 0.984661 | + | 0.174478i | \(0.0558239\pi\) | ||||
−0.984661 | + | 0.174478i | \(0.944176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.57073e6 | 0.749591 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45823.7 | 0.00951783 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.04128e6i | 0.830551i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.40301e6i | − 1.08728i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.11578e6 | −1.61619 | −0.808093 | − | 0.589055i | \(-0.799500\pi\) | ||||
−0.808093 | + | 0.589055i | \(0.799500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.52631e6 | 0.300801 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 129817.i | 0.0253199i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.11681e6i | 1.16870i | 0.811502 | + | 0.584350i | \(0.198650\pi\) | ||||
−0.811502 | + | 0.584350i | \(0.801350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 399249. | 0.0755042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.78707e6 | 1.27051 | 0.635256 | − | 0.772301i | \(-0.280895\pi\) | ||||
0.635256 | + | 0.772301i | \(0.280895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.04154e7i | − 1.93001i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.65180e6i | 0.481560i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.07689e6 | −1.09252 | −0.546260 | − | 0.837615i | \(-0.683949\pi\) | ||||
−0.546260 | + | 0.837615i | \(0.683949\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −515357. | −0.0917305 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.89757e6i | 0.334410i | 0.985922 | + | 0.167205i | \(0.0534741\pi\) | ||||
−0.985922 | + | 0.167205i | \(0.946526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 263766.i | − 0.0455721i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.07101e6 | 1.20973 | 0.604863 | − | 0.796330i | \(-0.293228\pi\) | ||||
0.604863 | + | 0.796330i | \(0.293228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.99982e6 | −1.69410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 251308.i | 0.0421613i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.62944e6i | − 1.09081i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −111932. | −0.0182405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.99273e6 | −1.29003 | −0.645017 | − | 0.764169i | \(-0.723150\pi\) | ||||
−0.645017 | + | 0.764169i | \(0.723150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.04897e7i | − 1.67691i | −0.544974 | − | 0.838453i | \(-0.683460\pi\) | ||||
0.544974 | − | 0.838453i | \(-0.316540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.13139e7i | − 1.77454i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.44386e6 | 0.845800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07278e7 | −1.65110 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4872.79i | 0 0.000742951i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 491447.i | − 0.0735429i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.05992e6 | −0.750191 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.56741e6 | 0.964719 | 0.482359 | − | 0.875973i | \(-0.339780\pi\) | ||||
0.482359 | + | 0.875973i | \(0.339780\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 238096.i | − 0.0346540i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.90324e6i | − 0.843573i | −0.906695 | − | 0.421786i | \(-0.861403\pi\) | ||||
0.906695 | − | 0.421786i | \(-0.138597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.27116e6 | −0.746407 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00715e6 | −0.842926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.07707e7i | 1.49773i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.34903e6i | − 0.457384i | −0.973499 | − | 0.228692i | \(-0.926555\pi\) | ||||
0.973499 | − | 0.228692i | \(-0.0734448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.54044e6 | −0.208504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −351452. | −0.0471475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.34193e7i | − 1.78426i | −0.451774 | − | 0.892132i | \(-0.649209\pi\) | ||||
0.451774 | − | 0.892132i | \(-0.350791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.01097e7i | 1.32063i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.38493e7 | 1.79327 | 0.896635 | − | 0.442770i | \(-0.146004\pi\) | ||||
0.896635 | + | 0.442770i | \(0.146004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.24337e6 | −1.05807 | −0.529035 | − | 0.848600i | \(-0.677446\pi\) | ||||
−0.529035 | + | 0.848600i | \(0.677446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 643592.i | − 0.0818887i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9.90608e6i | − 1.23869i | −0.785119 | − | 0.619345i | \(-0.787398\pi\) | ||||
0.785119 | − | 0.619345i | \(-0.212602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 692941. | 0.0859013 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.51402e6 | 0.923490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 8.72625e6i | − 1.06330i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.29572e7i | 1.55209i | 0.630679 | + | 0.776044i | \(0.282776\pi\) | ||||
−0.630679 | + | 0.776044i | \(0.717224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.52536e6 | −0.775026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −449923. | −0.0529871 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 5.95284e6i | − 0.695164i | −0.937650 | − | 0.347582i | \(-0.887003\pi\) | ||||
0.937650 | − | 0.347582i | \(-0.112997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 120543.i | − 0.0138423i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.48855e6 | −0.283387 | −0.141694 | − | 0.989911i | \(-0.545255\pi\) | ||||
−0.141694 | + | 0.989911i | \(0.545255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.34152e7 | −1.51499 | −0.757497 | − | 0.652838i | \(-0.773578\pi\) | ||||
−0.757497 | + | 0.652838i | \(0.773578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.02045e6i | − 0.562276i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.49423e6i | 0.935734i | 0.883799 | + | 0.467867i | \(0.154977\pi\) | ||||
−0.883799 | + | 0.467867i | \(0.845023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.14268e6 | 0.124848 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.52698e6 | 0.273841 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.36612e7i | − 1.46837i | −0.678948 | − | 0.734187i | \(-0.737564\pi\) | ||||
0.678948 | − | 0.734187i | \(-0.262436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43013e7i | 1.51238i | 0.654351 | + | 0.756191i | \(0.272942\pi\) | ||||
−0.654351 | + | 0.756191i | \(0.727058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.03774e7 | −1.08858 | −0.544292 | − | 0.838896i | \(-0.683202\pi\) | ||||
−0.544292 | + | 0.838896i | \(0.683202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 365475. | 0.0380302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.14314e7i | − 1.17999i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 202702.i | 0.0205915i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.21468e7 | −1.22415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.91347e6 | 0.791214 | 0.395607 | − | 0.918420i | \(-0.370534\pi\) | ||||
0.395607 | + | 0.918420i | \(0.370534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 586941.i | − 0.0582217i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.92872e6i | − 0.188330i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.72844e6 | 0.361222 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.70174e6 | −0.548103 | −0.274052 | − | 0.961715i | \(-0.588364\pi\) | ||||
−0.274052 | + | 0.961715i | \(0.588364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.06376e6i | − 0.292232i | −0.989267 | − | 0.146116i | \(-0.953323\pi\) | ||||
0.989267 | − | 0.146116i | \(-0.0466773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1.36482e6i | − 0.128178i | −0.997944 | − | 0.0640890i | \(-0.979586\pi\) | ||||
0.997944 | − | 0.0640890i | \(-0.0204141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.73261e7 | −1.61469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.24125e6 | 0.114791 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.58212e6i | 0.787610i | 0.919194 | + | 0.393805i | \(0.128842\pi\) | ||||
−0.919194 | + | 0.393805i | \(0.871158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.40598e7i | 1.27076i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.84222e7 | −1.65245 | −0.826224 | − | 0.563342i | \(-0.809515\pi\) | ||||
−0.826224 | + | 0.563342i | \(0.809515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69479e7 | 1.50873 | 0.754367 | − | 0.656453i | \(-0.227944\pi\) | ||||
0.754367 | + | 0.656453i | \(0.227944\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 133965.i | − 0.0118360i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.73613e6i | 0.760334i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 732947. | 0.0633151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.51331e6 | −0.729948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.18245e6i | 0.100634i | 0.998733 | + | 0.0503172i | \(0.0160232\pi\) | ||||
−0.998733 | + | 0.0503172i | \(0.983977\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.34424e6i | 0.364285i | 0.983272 | + | 0.182143i | \(0.0583033\pi\) | ||||
−0.983272 | + | 0.182143i | \(0.941697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.11466e6 | −0.176021 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24883.8 | −0.00205612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.03260e7i | − 0.846991i | −0.905898 | − | 0.423495i | \(-0.860803\pi\) | ||||
0.905898 | − | 0.423495i | \(-0.139197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 551880.i | 0.0446121i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.32623e6 | 0.266934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.07013e7 | −1.64931 | −0.824656 | − | 0.565635i | \(-0.808631\pi\) | ||||
−0.824656 | + | 0.565635i | \(0.808631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.63666e7i | 1.29457i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 38779.1i | − 0.00302354i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −416326. | −0.0322285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.75116e6 | −0.211457 | −0.105728 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105728 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00572e6i | 0.534643i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6.44466e6i | − 0.484899i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.07210e6 | 0.304230 | 0.152115 | − | 0.988363i | \(-0.451392\pi\) | ||||
0.152115 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.51437e7 | 1.12346 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.48976e6i | 0.699087i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 752914.i | − 0.0546950i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.75553e7 | −1.26645 | −0.633223 | − | 0.773970i | \(-0.718268\pi\) | ||||
−0.633223 | + | 0.773970i | \(0.718268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.18024e6 | −0.514400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 720394.i | 0.0512536i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.46241e7i | − 1.02620i | −0.858328 | − | 0.513101i | \(-0.828496\pi\) | ||||
0.858328 | − | 0.513101i | \(-0.171504\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.41470e7 | 0.985925 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.22592e7 | 0.848534 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.54961e7i | − 1.06528i | −0.846342 | − | 0.532639i | \(-0.821200\pi\) | ||||
0.846342 | − | 0.532639i | \(-0.178800\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 8.10839e6i | − 0.549877i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.39408e6 | −0.228619 | −0.114309 | − | 0.993445i | \(-0.536465\pi\) | ||||
−0.114309 | + | 0.993445i | \(0.536465\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −77264.9 | −0.00516936 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 3.94591e6i | − 0.262225i | −0.991367 | − | 0.131113i | \(-0.958145\pi\) | ||||
0.991367 | − | 0.131113i | \(-0.0418550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.05647e7i | − 0.692719i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.20119e7 | −0.782360 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −824656. | −0.0533547 | −0.0266774 | − | 0.999644i | \(-0.508493\pi\) | ||||
−0.0266774 | + | 0.999644i | \(0.508493\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 589934.i | − 0.0379154i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.53800e7i | 0.975474i | 0.872991 | + | 0.487737i | \(0.162177\pi\) | ||||
−0.872991 | + | 0.487737i | \(0.837823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 294787. | 0.0185739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.06295e6 | 0.504699 | 0.252349 | − | 0.967636i | \(-0.418797\pi\) | ||||
0.252349 | + | 0.967636i | \(0.418797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52689e7i | 0.949502i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 6.60429e6i | − 0.405357i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.12351e7 | 0.685110 | 0.342555 | − | 0.939498i | \(-0.388708\pi\) | ||||
0.342555 | + | 0.939498i | \(0.388708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 257358. | 0.0155920 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 554517.i | 0.0333784i | 0.999861 | + | 0.0166892i | \(0.00531259\pi\) | ||||
−0.999861 | + | 0.0166892i | \(0.994687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.33263e6i | − 0.0791875i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22366.0 | −0.00132052 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.02169e6 | 0.353257 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.21701e6i | − 0.187520i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.56812e7i | − 0.902492i | −0.892400 | − | 0.451246i | \(-0.850980\pi\) | ||||
0.892400 | − | 0.451246i | \(-0.149020\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.55151e6 | 0.0887281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34162e7 | −0.762410 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 3.24506e6i | − 0.183248i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.44267e7i | − 1.91977i | −0.280393 | − | 0.959885i | \(-0.590465\pi\) | ||||
0.280393 | − | 0.959885i | \(-0.409535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.01104e7 | −1.11443 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60725e7 | −0.885122 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.27075e7i | 1.24274i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 74538.0i | 0.00402897i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.20856e7 | −0.649230 | −0.324615 | − | 0.945846i | \(-0.605235\pi\) | ||||
−0.324615 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.20419e6 | 0.331232 | 0.165616 | − | 0.986190i | \(-0.447039\pi\) | ||||
0.165616 | + | 0.986190i | \(0.447039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 885870.i | − 0.0470050i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 7.07057e6i | − 0.370595i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.23855e6 | −0.324993 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.59426e7 | −1.34325 | −0.671624 | − | 0.740892i | \(-0.734403\pi\) | ||||
−0.671624 | + | 0.740892i | \(0.734403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 7.30743e6i | − 0.376067i | −0.982163 | − | 0.188034i | \(-0.939789\pi\) | ||||
0.982163 | − | 0.188034i | \(-0.0602114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.22800e7i | 0.624357i | 0.950023 | + | 0.312179i | \(0.101059\pi\) | ||||
−0.950023 | + | 0.312179i | \(0.898941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.21244e7 | 1.62349 | 0.811743 | − | 0.584014i | \(-0.198519\pi\) | ||||
0.811743 | + | 0.584014i | \(0.198519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −860789. | −0.0432408 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.53493e7i | 0.766435i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.49452e6i | − 0.172415i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.36956e6 | 0.312395 | 0.156198 | − | 0.987726i | \(-0.450076\pi\) | ||||
0.156198 | + | 0.987726i | \(0.450076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.63865e7 | 2.74907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.00609e6i | 0.0487606i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.33584e6i | − 0.0639801i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −696667. | −0.0331708 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.01883e7 | 0.482258 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.05840e7i | − 1.90978i | −0.296964 | − | 0.954889i | \(-0.595974\pi\) | ||||
0.296964 | − | 0.954889i | \(-0.404026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.30412e6i | − 0.153675i | −0.997044 | − | 0.0768376i | \(-0.975518\pi\) | ||||
0.997044 | − | 0.0768376i | \(-0.0244823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.45392e7 | 0.672292 | 0.336146 | − | 0.941810i | \(-0.390876\pi\) | ||||
0.336146 | + | 0.941810i | \(0.390876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4254.47 | 0.000195586 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.28020e7i | 1.04219i | 0.853499 | + | 0.521094i | \(0.174476\pi\) | ||||
−0.853499 | + | 0.521094i | \(0.825524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6907.58i | 0 0.000312089i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.44582e7 | 1.09869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.09072e6 | 0.138043 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.97321e6i | 0.132035i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.93150e6i | 0.348222i | 0.984726 | + | 0.174111i | \(0.0557052\pi\) | ||||
−0.984726 | + | 0.174111i | \(0.944295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.24122e6 | −0.0541848 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.31349e7 | −1.43829 | −0.719144 | − | 0.694861i | \(-0.755466\pi\) | ||||
−0.719144 | + | 0.694861i | \(0.755466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.25079e7i | − 0.971479i | −0.874104 | − | 0.485740i | \(-0.838550\pi\) | ||||
0.874104 | − | 0.485740i | \(-0.161450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.66717e7i | 1.56503i | 0.622632 | + | 0.782515i | \(0.286063\pi\) | ||||
−0.622632 | + | 0.782515i | \(0.713937\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.07927e7 | −2.15549 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.29572e7 | 0.968777 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.15988e7i | 0.486725i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 112365.i | 0.00466285i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.35313e7 | 3.44707 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.64711e7 | −1.08632 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.34497e6i | 0.0548898i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.40388e6i | 0.0970274i | 0.998823 | + | 0.0485137i | \(0.0154485\pi\) | ||||
−0.998823 | + | 0.0485137i | \(0.984552\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.06120e6 | −0.363728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 467873. | 0.0186781 | 0.00933904 | − | 0.999956i | \(-0.497027\pi\) | ||||
0.00933904 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.70628e7i | − 0.677444i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.99268e7i | 1.17527i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.59601e7 | 1.01395 | 0.506976 | − | 0.861960i | \(-0.330763\pi\) | ||||
0.506976 | + | 0.861960i | \(0.330763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 612800. | 0.0238051 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.29532e6i | 0.0886827i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.00954e7i | 0.385856i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.52441e6 | 0.171998 | 0.0859989 | − | 0.996295i | \(-0.472592\pi\) | ||||
0.0859989 | + | 0.996295i | \(0.472592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.85278e6 | 0.334738 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.26720e6i | 0.0476587i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.69269e7i | − 1.00193i | −0.865468 | − | 0.500964i | \(-0.832979\pi\) | ||||
0.865468 | − | 0.500964i | \(-0.167021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.08751e6 | 0.0402505 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.38789e6 | −0.0510953 | −0.0255477 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255477 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32526.7i | 0.00119113i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.10208e7i | 0.399335i | 0.979864 | + | 0.199667i | \(0.0639862\pi\) | ||||
−0.979864 | + | 0.199667i | \(0.936014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.65555e6 | −0.311982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −592375. | −0.0212396 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.09536e7i | − 0.390683i | −0.980735 | − | 0.195342i | \(-0.937418\pi\) | ||||
0.980735 | − | 0.195342i | \(-0.0625815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.59479e6i | − 0.0915847i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.96712e7 | 2.09517 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.21081e7 | 2.16940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68887e7i | 0.586856i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.52685e7i | − 1.21289i | −0.795127 | − | 0.606443i | \(-0.792596\pi\) | ||||
0.795127 | − | 0.606443i | \(-0.207404\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 614895. | 0.0210374 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.58480e7 | −1.22016 | −0.610079 | − | 0.792340i | \(-0.708862\pi\) | ||||
−0.610079 | + | 0.792340i | \(0.708862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.67869e7i | 1.92294i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.95941e6i | 0.300292i | 0.988664 | + | 0.150146i | \(0.0479743\pi\) | ||||
−0.988664 | + | 0.150146i | \(0.952026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.59583e7 | −0.865604 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.14681e7 | 0.712231 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.94666e6i | 0.229294i | 0.993406 | + | 0.114647i | \(0.0365737\pi\) | ||||
−0.993406 | + | 0.114647i | \(0.963426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.20632e6i | − 0.0720901i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.02827e7 | −0.334283 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.72743e6 | −0.249949 | −0.124974 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124974 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.49652e6i | 0.0803455i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.32625e7i | 1.37840i | 0.724573 | + | 0.689198i | \(0.242037\pi\) | ||||
−0.724573 | + | 0.689198i | \(0.757963\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.75177e6 | −0.118939 |
(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 | 800.6.c.j.449.3 | 6 | ||
4.3 | odd | 2 | 800.6.c.k.449.4 | 6 | |||
5.2 | odd | 4 | 160.6.a.g.1.2 | yes | 3 | ||
5.3 | odd | 4 | 800.6.a.n.1.2 | 3 | |||
5.4 | even | 2 | inner | 800.6.c.j.449.4 | 6 | ||
20.3 | even | 4 | 800.6.a.o.1.2 | 3 | |||
20.7 | even | 4 | 160.6.a.f.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 800.6.c.k.449.3 | 6 | |||
40.27 | even | 4 | 320.6.a.y.1.2 | 3 | |||
40.37 | odd | 4 | 320.6.a.x.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.2 | ✓ | 3 | 20.7 | even | 4 | ||
160.6.a.g.1.2 | yes | 3 | 5.2 | odd | 4 | ||
320.6.a.x.1.2 | 3 | 40.37 | odd | 4 | |||
320.6.a.y.1.2 | 3 | 40.27 | even | 4 | |||
800.6.a.n.1.2 | 3 | 5.3 | odd | 4 | |||
800.6.a.o.1.2 | 3 | 20.3 | even | 4 | |||
800.6.c.j.449.3 | 6 | 1.1 | even | 1 | trivial | ||
800.6.c.j.449.4 | 6 | 5.4 | even | 2 | inner | ||
800.6.c.k.449.3 | 6 | 20.19 | odd | 2 | |||
800.6.c.k.449.4 | 6 | 4.3 | odd | 2 |