Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [676,6,Mod(337,676)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(676, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("676.337");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 676 = 2^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 676.d (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: | \(108.419462194\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 676.337 |
Dual form | 676.6.d.a.337.1 |
$q$-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 \(\left(\mathbb{Z}/676\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(509\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −12.0000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 54.0000i | 0.965981i | 0.875625 | + | 0.482991i | \(0.160450\pi\) | ||||
−0.875625 | + | 0.482991i | \(0.839550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 88.0000i | 0.678793i | 0.940643 | + | 0.339397i | \(0.110223\pi\) | ||||
−0.940643 | + | 0.339397i | \(0.889777\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −99.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 540.000i | − 1.34559i | −0.739830 | − | 0.672794i | \(-0.765094\pi\) | ||||
0.739830 | − | 0.672794i | \(-0.234906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 648.000i | − 0.743613i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −594.000 | −0.498499 | −0.249249 | − | 0.968439i | \(-0.580184\pi\) | ||||
−0.249249 | + | 0.968439i | \(0.580184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 836.000i | 0.531279i | 0.964072 | + | 0.265639i | \(0.0855830\pi\) | ||||
−0.964072 | + | 0.265639i | \(0.914417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1056.00i | − 0.522535i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4104.00 | 1.61766 | 0.808831 | − | 0.588041i | \(-0.200101\pi\) | ||||
0.808831 | + | 0.588041i | \(0.200101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 209.000 | 0.0668800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4104.00 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −594.000 | −0.131157 | −0.0655785 | − | 0.997847i | \(-0.520889\pi\) | ||||
−0.0655785 | + | 0.997847i | \(0.520889\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4256.00i | 0.795422i | 0.917511 | + | 0.397711i | \(0.130195\pi\) | ||||
−0.917511 | + | 0.397711i | \(0.869805\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6480.00i | 1.03583i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4752.00 | −0.655702 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 298.000i | 0.0357859i | 0.999840 | + | 0.0178930i | \(0.00569581\pi\) | ||||
−0.999840 | + | 0.0178930i | \(0.994304\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17226.0i | 1.60039i | 0.599742 | + | 0.800193i | \(0.295270\pi\) | ||||
−0.599742 | + | 0.800193i | \(0.704730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12100.0 | 0.997963 | 0.498981 | − | 0.866613i | \(-0.333708\pi\) | ||||
0.498981 | + | 0.866613i | \(0.333708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 5346.00i | − 0.393548i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1296.00i | 0.0855777i | 0.999084 | + | 0.0427888i | \(0.0136243\pi\) | ||||
−0.999084 | + | 0.0427888i | \(0.986376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9063.00 | 0.539240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7128.00 | 0.383745 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19494.0 | 0.953260 | 0.476630 | − | 0.879104i | \(-0.341858\pi\) | ||||
0.476630 | + | 0.879104i | \(0.341858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29160.0 | 1.29981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 10032.0i | − 0.408978i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7668.00i | 0.286782i | 0.989666 | + | 0.143391i | \(0.0458007\pi\) | ||||
−0.989666 | + | 0.143391i | \(0.954199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34738.0 | −1.19531 | −0.597655 | − | 0.801754i | \(-0.703901\pi\) | ||||
−0.597655 | + | 0.801754i | \(0.703901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 8712.00i | − 0.276545i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21812.0i | 0.593620i | 0.954937 | + | 0.296810i | \(0.0959228\pi\) | ||||
−0.954937 | + | 0.296810i | \(0.904077\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −49248.0 | −1.24528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 46872.0i | − 1.10349i | −0.834014 | − | 0.551744i | \(-0.813963\pi\) | ||||
0.834014 | − | 0.551744i | \(-0.186037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 67562.0i | − 1.48387i | −0.670473 | − | 0.741934i | \(-0.733909\pi\) | ||||
0.670473 | − | 0.741934i | \(-0.266091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2508.00 | −0.0514842 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 47520.0 | 0.913376 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −76912.0 | −1.38652 | −0.693260 | − | 0.720687i | \(-0.743826\pi\) | ||||
−0.693260 | + | 0.720687i | \(0.743826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25191.0 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 67716.0i | 1.07894i | 0.842006 | + | 0.539468i | \(0.181375\pi\) | ||||
−0.842006 | + | 0.539468i | \(0.818625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 32076.0i | − 0.481541i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7128.00 | 0.100965 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 29754.0i | − 0.398172i | −0.979982 | − | 0.199086i | \(-0.936203\pi\) | ||||
0.979982 | − | 0.199086i | \(-0.0637973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 51072.0i | − 0.612316i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −45144.0 | −0.513205 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 122398.i | − 1.32082i | −0.750903 | − | 0.660412i | \(-0.770382\pi\) | ||||
0.750903 | − | 0.660412i | \(-0.229618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 53460.0i | 0.548202i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11286.0 | −0.110087 | −0.0550436 | − | 0.998484i | \(-0.517530\pi\) | ||||
−0.0550436 | + | 0.998484i | \(0.517530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27256.0 | 0.253145 | 0.126572 | − | 0.991957i | \(-0.459602\pi\) | ||||
0.126572 | + | 0.991957i | \(0.459602\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 57024.0 | 0.504759 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 122364. | 1.03322 | 0.516612 | − | 0.856220i | \(-0.327193\pi\) | ||||
0.516612 | + | 0.856220i | \(0.327193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 99902.0i | 0.805393i | 0.915334 | + | 0.402697i | \(0.131927\pi\) | ||||
−0.915334 | + | 0.402697i | \(0.868073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 3576.00i | − 0.0275480i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −29646.0 | −0.218409 | −0.109204 | − | 0.994019i | \(-0.534830\pi\) | ||||
−0.109204 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 221616.i | 1.56263i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 52272.0i | − 0.338378i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −130549. | −0.810607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 206712.i | − 1.23198i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 180036.i | 1.03059i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −336512. | −1.85136 | −0.925681 | − | 0.378305i | \(-0.876507\pi\) | ||||
−0.925681 | + | 0.378305i | \(0.876507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −145200. | −0.768232 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 100980. | 0.514111 | 0.257056 | − | 0.966397i | \(-0.417248\pi\) | ||||
0.257056 | + | 0.966397i | \(0.417248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73568.0 | −0.360628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 221616.i | 1.04657i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 317142.i | 1.44362i | 0.692092 | + | 0.721809i | \(0.256689\pi\) | ||||
−0.692092 | + | 0.721809i | \(0.743311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −148324. | −0.651140 | −0.325570 | − | 0.945518i | \(-0.605556\pi\) | ||||
−0.325570 | + | 0.945518i | \(0.605556\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 15552.0i | − 0.0658777i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 32076.0i | − 0.126695i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −108756. | −0.415107 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 196614.i | 0.725519i | 0.931883 | + | 0.362759i | \(0.118165\pi\) | ||||
−0.931883 | + | 0.362759i | \(0.881835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 74360.0i | − 0.265398i | −0.991156 | − | 0.132699i | \(-0.957636\pi\) | ||||
0.991156 | − | 0.132699i | \(-0.0423643\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 58806.0 | 0.203092 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −229824. | −0.768362 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 120878. | 0.391380 | 0.195690 | − | 0.980666i | \(-0.437305\pi\) | ||||
0.195690 | + | 0.980666i | \(0.437305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −233928. | −0.733820 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 361152.i | 1.09806i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111340.i | 0.328233i | 0.986441 | + | 0.164116i | \(0.0524773\pi\) | ||||
−0.986441 | + | 0.164116i | \(0.947523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −349920. | −1.00060 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 491832.i | 1.36466i | 0.731043 | + | 0.682332i | \(0.239034\pi\) | ||||
−0.731043 | + | 0.682332i | \(0.760966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 82764.0i | − 0.216447i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −707454. | −1.79714 | −0.898572 | − | 0.438826i | \(-0.855395\pi\) | ||||
−0.898572 | + | 0.438826i | \(0.855395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18392.0i | 0.0453977i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 92016.0i | − 0.220765i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −493668. | −1.15160 | −0.575801 | − | 0.817590i | \(-0.695310\pi\) | ||||
−0.575801 | + | 0.817590i | \(0.695310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 559450. | 1.26930 | 0.634651 | − | 0.772799i | \(-0.281144\pi\) | ||||
0.634651 | + | 0.772799i | \(0.281144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 416856. | 0.920149 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16092.0 | −0.0345685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 320760.i | 0.670774i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 361152.i | 0.735420i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −724032. | −1.43607 | −0.718033 | − | 0.696009i | \(-0.754957\pi\) | ||||
−0.718033 | + | 0.696009i | \(0.754957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 7106.00i | − 0.0137319i | −0.999976 | − | 0.00686597i | \(-0.997814\pi\) | ||||
0.999976 | − | 0.00686597i | \(-0.00218552\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 530442.i | − 0.973806i | −0.873456 | − | 0.486903i | \(-0.838127\pi\) | ||||
0.873456 | − | 0.486903i | \(-0.161873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −56168.0 | −0.100544 | −0.0502720 | − | 0.998736i | \(-0.516009\pi\) | ||||
−0.0502720 | + | 0.998736i | \(0.516009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 261744.i | − 0.456969i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 52272.0i | − 0.0890285i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −930204. | −1.54594 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −406296. | −0.659047 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 451440. | 0.714882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −339196. | −0.524499 | −0.262249 | − | 0.965000i | \(-0.584464\pi\) | ||||
−0.262249 | + | 0.965000i | \(0.584464\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 562464.i | 0.849465i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 653400.i | 0.964013i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −374528. | −0.539927 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 810744.i | 1.14228i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 779360.i | 1.04948i | 0.851261 | + | 0.524742i | \(0.175838\pi\) | ||||
−0.851261 | + | 0.524742i | \(0.824162\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20691.0 | −0.0272474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 744876.i | − 0.959443i | −0.877421 | − | 0.479722i | \(-0.840738\pi\) | ||||
0.877421 | − | 0.479722i | \(-0.159262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 272746.i | 0.343692i | 0.985124 | + | 0.171846i | \(0.0549732\pi\) | ||||
−0.985124 | + | 0.171846i | \(0.945027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −570240. | −0.703117 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 153846. | 0.185651 | 0.0928253 | − | 0.995682i | \(-0.470410\pi\) | ||||
0.0928253 | + | 0.995682i | \(0.470410\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69984.0 | −0.0826664 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 922944. | 1.06734 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.15474e6i | 1.30764i | 0.756650 | + | 0.653820i | \(0.226834\pi\) | ||||
−0.756650 | + | 0.653820i | \(0.773166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 657074.i | − 0.728738i | −0.931255 | − | 0.364369i | \(-0.881285\pi\) | ||||
0.931255 | − | 0.364369i | \(-0.118715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −694980. | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 489402.i | 0.520895i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 812592.i | − 0.830566i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.34190e6 | −1.34442 | −0.672211 | − | 0.740359i | \(-0.734655\pi\) | ||||
−0.672211 | + | 0.740359i | \(0.734655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.21616e6i | − 2.17671i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 384912.i | 0.370690i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −132354. | −0.124998 | −0.0624992 | − | 0.998045i | \(-0.519907\pi\) | ||||
−0.0624992 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26224.0 | −0.0242912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 58806.0 | 0.0534343 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 943272. | 0.840906 | 0.420453 | − | 0.907314i | \(-0.361871\pi\) | ||||
0.420453 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.05268e6i | 0.920831i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 357048.i | 0.306513i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 967518. | 0.815227 | 0.407613 | − | 0.913155i | \(-0.366361\pi\) | ||||
0.407613 | + | 0.913155i | \(0.366361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 518320.i | 0.428721i | 0.976755 | + | 0.214360i | \(0.0687667\pi\) | ||||
−0.976755 | + | 0.214360i | \(0.931233\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 112860.i | − 0.0899929i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.22273e6 | −1.74055 | −0.870275 | − | 0.492566i | \(-0.836059\pi\) | ||||
−0.870275 | + | 0.492566i | \(0.836059\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 421344.i | − 0.324061i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196614.i | 0.148542i | 0.997238 | + | 0.0742709i | \(0.0236629\pi\) | ||||
−0.997238 | + | 0.0742709i | \(0.976337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.55228e6 | 1.15213 | 0.576067 | − | 0.817403i | \(-0.304587\pi\) | ||||
0.576067 | + | 0.817403i | \(0.304587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 541728. | 0.395066 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51589e6 | −1.08633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06702e6 | −0.751499 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.46878e6i | 1.01677i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.07217e6i | 0.729616i | 0.931083 | + | 0.364808i | \(0.118865\pi\) | ||||
−0.931083 | + | 0.364808i | \(0.881135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −414072. | −0.277026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.21616e6i | − 1.45784i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.06480e6i | 0.677410i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 135432. | 0.0847451 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1.87585e6i | − 1.15465i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.58589e6i | − 0.960346i | −0.877174 | − | 0.480173i | \(-0.840574\pi\) | ||||
0.877174 | − | 0.480173i | \(-0.159426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −327072. | −0.194871 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 730728. | 0.428405 | 0.214203 | − | 0.976789i | \(-0.431285\pi\) | ||||
0.214203 | + | 0.976789i | \(0.431285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 584858. | 0.337435 | 0.168717 | − | 0.985664i | \(-0.446038\pi\) | ||||
0.168717 | + | 0.985664i | \(0.446038\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 470448. | 0.267138 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.48287e6i | − 1.38773i | −0.720105 | − | 0.693865i | \(-0.755906\pi\) | ||||
0.720105 | − | 0.693865i | \(-0.244094\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 320760.i | 0.176483i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.46837e6 | −0.795376 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 496584.i | − 0.264842i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.19882e6i | − 0.619992i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −114048. | −0.0580895 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 377948.i | 0.189610i | 0.995496 | + | 0.0948052i | \(0.0302228\pi\) | ||||
−0.995496 | + | 0.0948052i | \(0.969777\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 29502.0i | − 0.0145794i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.17785e6 | −0.573426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −639122. | −0.306555 | −0.153278 | − | 0.988183i | \(-0.548983\pi\) | ||||
−0.153278 | + | 0.988183i | \(0.548983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 355752. | 0.168131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29824e6 | 1.07031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.27656e6i | 1.04483i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 2.65939e6i | − 1.20291i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.90466e6 | −1.29501 | −0.647503 | − | 0.762063i | \(-0.724187\pi\) | ||||
−0.647503 | + | 0.762063i | \(0.724187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.99157e6i | 1.75420i | 0.480304 | + | 0.877102i | \(0.340526\pi\) | ||||
−0.480304 | + | 0.877102i | \(0.659474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.42922e6i | 0.610466i | 0.952278 | + | 0.305233i | \(0.0987344\pi\) | ||||
−0.952278 | + | 0.305233i | \(0.901266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53109e6 | 1.06595 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 627264.i | 0.260483i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 1.16186e6i | − 0.475794i | −0.971290 | − | 0.237897i | \(-0.923542\pi\) | ||||
0.971290 | − | 0.237897i | \(-0.0764581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.77720e6 | 0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.56659e6 | 0.624005 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64835e6 | 1.43339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.08923e6 | −0.422139 | −0.211069 | − | 0.977471i | \(-0.567695\pi\) | ||||
−0.211069 | + | 0.977471i | \(0.567695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 1.70537e6i | − 0.652009i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.71547e6i | 0.647066i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50577e6 | 1.30470 | 0.652350 | − | 0.757918i | \(-0.273783\pi\) | ||||
0.652350 | + | 0.757918i | \(0.273783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 2.16043e6i | − 0.793346i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.04385e6i | 1.44610i | 0.690798 | + | 0.723048i | \(0.257260\pi\) | ||||
−0.690798 | + | 0.723048i | \(0.742740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.03814e6 | 1.42518 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.18746e6i | 1.80700i | 0.428591 | + | 0.903499i | \(0.359010\pi\) | ||||
−0.428591 | + | 0.903499i | \(0.640990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.56608e6i | 0.882304i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.19790e6 | −0.406577 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 950346. | 0.318425 | 0.159213 | − | 0.987244i | \(-0.449104\pi\) | ||||
0.159213 | + | 0.987244i | \(0.449104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.43778e6 | −0.806403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.21176e6 | −0.395763 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.15325e6i | − 1.33935i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 520738.i | 0.165822i | 0.996557 | + | 0.0829112i | \(0.0264218\pi\) | ||||
−0.996557 | + | 0.0829112i | \(0.973578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 882816. | 0.277612 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 764370.i | − 0.237379i | −0.992931 | − | 0.118690i | \(-0.962131\pi\) | ||||
0.992931 | − | 0.118690i | \(-0.0378693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.36031e6i | − 0.412099i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 160920. | 0.0481531 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.64051e6i | 0.780511i | 0.920707 | + | 0.390255i | \(0.127613\pi\) | ||||
−0.920707 | + | 0.390255i | \(0.872387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 3.80570e6i | − 1.11130i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −674784. | −0.194666 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.65666e6 | −1.04223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.77989e6 | 0.501248 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.98020e6 | −1.38584 | −0.692918 | − | 0.721016i | \(-0.743675\pi\) | ||||
−0.692918 | + | 0.721016i | \(0.743675\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 237994.i | − 0.0654426i | −0.999465 | − | 0.0327213i | \(-0.989583\pi\) | ||||
0.999465 | − | 0.0327213i | \(-0.0104174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 128304.i | − 0.0348650i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −124146. | −0.0333396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.05694e6i | − 0.811368i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.88238e6i | − 1.00671i | −0.864079 | − | 0.503356i | \(-0.832098\pi\) | ||||
0.864079 | − | 0.503356i | \(-0.167902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 66958.0 | 0.0171626 | 0.00858129 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858129 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 384912.i | 0.0975300i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.43094e6i | 0.859429i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.50135e6 | 1.61006 | 0.805031 | − | 0.593233i | \(-0.202149\pi\) | ||||
0.805031 | + | 0.593233i | \(0.202149\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −897237. | −0.219690 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.60760e6 | −1.11549 | −0.557745 | − | 0.830012i | \(-0.688333\pi\) | ||||
−0.557745 | + | 0.830012i | \(0.688333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.60672e6 | 0.384626 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.35937e6i | − 0.558505i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 3.77671e6i | − 0.884092i | −0.896992 | − | 0.442046i | \(-0.854253\pi\) | ||||
0.896992 | − | 0.442046i | \(-0.145747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.30204e6 | 2.15346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 892320.i | 0.204303i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 3.18069e6i | − 0.712412i | −0.934407 | − | 0.356206i | \(-0.884070\pi\) | ||||
0.934407 | − | 0.356206i | \(-0.115930\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.43778e6 | −0.540085 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.68547e6i | 1.46514i | 0.680691 | + | 0.732571i | \(0.261680\pi\) | ||||
−0.680691 | + | 0.732571i | \(0.738320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.35122e6i | 0.943318i | 0.881781 | + | 0.471659i | \(0.156345\pi\) | ||||
−0.881781 | + | 0.471659i | \(0.843655\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.75789e6 | 0.591486 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.07994e6 | −1.50223 | −0.751117 | − | 0.660170i | \(-0.770484\pi\) | ||||
−0.751117 | + | 0.660170i | \(0.770484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91946e6 | −0.402945 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.45054e6 | −0.301284 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.53400e6i | − 1.34285i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 174724.i | 0.0355319i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.92991e6 | −0.388365 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 3.22186e6i | − 0.641604i | −0.947146 | − | 0.320802i | \(-0.896048\pi\) | ||||
0.947146 | − | 0.320802i | \(-0.103952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.33382e6i | − 0.845286i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.60949e6 | 1.27589 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29710e6i | 0.438891i | 0.975625 | + | 0.219446i | \(0.0704248\pi\) | ||||
−0.975625 | + | 0.219446i | \(0.929575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 1.33608e6i | − 0.252674i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.82150e6 | −0.528173 | −0.264087 | − | 0.964499i | \(-0.585070\pi\) | ||||
−0.264087 | + | 0.964499i | \(0.585070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 352836. | 0.0653816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.88684e6 | −0.529553 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.12474e6 | 0.749040 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.13628e6i | − 0.743634i | −0.928306 | − | 0.371817i | \(-0.878735\pi\) | ||||
0.928306 | − | 0.371817i | \(-0.121265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.90198e6i | − 1.05052i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.33263e6 | 1.46846 | 0.734230 | − | 0.678901i | \(-0.237543\pi\) | ||||
0.734230 | + | 0.678901i | \(0.237543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 609444.i | − 0.106342i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.34101e6i | 0.742670i | 0.928499 | + | 0.371335i | \(0.121100\pi\) | ||||
−0.928499 | + | 0.371335i | \(0.878900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.94546e6 | 1.00724 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.43094e6i | 0.575599i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.47182e6i | 0.244533i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 699840. | 0.115152 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.48945e6 | 1.38344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.74185e6 | −1.08814 | −0.544070 | − | 0.839040i | \(-0.683117\pi\) | ||||
−0.544070 | + | 0.839040i | \(0.683117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.72196e6 | −1.23445 | −0.617224 | − | 0.786787i | \(-0.711743\pi\) | ||||
−0.617224 | + | 0.786787i | \(0.711743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 220704.i | − 0.0349472i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.52806e6i | − 0.396517i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.04065e7 | 1.61683 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 759132.i | − 0.116837i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.60766e6i | 0.998075i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.92402e6 | 0.886504 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.89402e6i | − 0.725594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 682066.i | 0.100192i | 0.998744 | + | 0.0500960i | \(0.0159527\pi\) | ||||
−0.998744 | + | 0.0500960i | \(0.984047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.71340e6 | −0.977109 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.39471e6 | −0.777995 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.15772e6 | 0.308337 | 0.154169 | − | 0.988045i | \(-0.450730\pi\) | ||||
0.154169 | + | 0.988045i | \(0.450730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.43906e6 | 0.486978 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 496584.i | − 0.0696809i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6.76826e6i | − 0.941161i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 193104. | 0.0266109 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.67597e6i | 0.365463i | 0.983163 | + | 0.182731i | \(0.0584939\pi\) | ||||
−0.983163 | + | 0.182731i | \(0.941506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − 3.84912e6i | − 0.516362i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.55331e6 | 0.472457 | 0.236228 | − | 0.971698i | \(-0.424089\pi\) | ||||
0.236228 | + | 0.971698i | \(0.424089\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.60088e6i | − 0.210979i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2.21681e6i | − 0.289581i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.29225e7 | 1.67327 | 0.836633 | − | 0.547764i | \(-0.184521\pi\) | ||||
0.836633 | + | 0.547764i | \(0.184521\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.08357e6 | 0.780851 | 0.390426 | − | 0.920634i | \(-0.372328\pi\) | ||||
0.390426 | + | 0.920634i | \(0.372328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.68838e6 | 1.10548 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 857736. | 0.108189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.58241e7i | − 1.97869i | −0.145579 | − | 0.989347i | \(-0.546505\pi\) | ||||
0.145579 | − | 0.989347i | \(-0.453495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 85272.0i | 0.0105709i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.95901e6 | −0.732375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.05268e7i | − 1.28269i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.60220e6i | 0.551278i | 0.961261 | + | 0.275639i | \(0.0888894\pi\) | ||||
−0.961261 | + | 0.275639i | \(0.911111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.55802e6 | −0.422590 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.36530e6i | 0.749636i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 8.61122e6i | − 1.00561i | −0.864401 | − | 0.502803i | \(-0.832302\pi\) | ||||
0.864401 | − | 0.502803i | \(-0.167698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.82269e6 | 0.326867 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 674016. | 0.0773988 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.98228e6 | −0.908992 | −0.454496 | − | 0.890749i | \(-0.650181\pi\) | ||||
−0.454496 | + | 0.890749i | \(0.650181\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.01740e7 | 1.14896 | 0.574481 | − | 0.818518i | \(-0.305204\pi\) | ||||
0.574481 | + | 0.818518i | \(0.305204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.15939e6i | − 0.241845i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.04965e6i | − 0.783031i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.95843e6 | −1.09703 | −0.548516 | − | 0.836140i | \(-0.684807\pi\) | ||||
−0.548516 | + | 0.836140i | \(0.684807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 627264.i | 0.0685342i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.19586e6i | 0.450993i | 0.974244 | + | 0.225497i | \(0.0724005\pi\) | ||||
−0.974244 | + | 0.225497i | \(0.927600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11624e7 | 1.19007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.12551e6i | 0.965038i | 0.875885 | + | 0.482519i | \(0.160278\pi\) | ||||
−0.875885 | + | 0.482519i | \(0.839722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 6.45734e6i | − 0.677372i | −0.940900 | − | 0.338686i | \(-0.890018\pi\) | ||||
0.940900 | − | 0.338686i | \(-0.109982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.68428e7 | 1.75261 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.61835e6 | 0.270276 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.06882e6 | −0.928647 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.41728e6 | −0.550316 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 177012.i | − 0.0178392i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.40514e7i | 1.40490i | 0.711733 | + | 0.702450i | \(0.247910\pi\) | ||||
−0.711733 | + | 0.702450i | \(0.752090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.07035e6 | 0.403759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.81716e7i | − 1.78838i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.64033e6i | 0.449569i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.47168e6 | −0.814375 | −0.407188 | − | 0.913345i | \(-0.633490\pi\) | ||||
−0.407188 | + | 0.913345i | \(0.633490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 488564.i | 0.0466009i | 0.999729 | + | 0.0233004i | \(0.00741743\pi\) | ||||
−0.999729 | + | 0.0233004i | \(0.992583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 7.84080e6i | − 0.742098i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.48119e6 | −0.233023 | −0.116512 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116512 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.14072e6 | 0.385891 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.49434e6 | 0.415636 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.29130e6 | −0.485601 | −0.242800 | − | 0.970076i | \(-0.578066\pi\) | ||||
−0.242800 | + | 0.970076i | \(0.578066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.45292e6i | 0.496622i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.68864e6i | 0.604539i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.72468e6 | 0.423798 | 0.211899 | − | 0.977292i | \(-0.432035\pi\) | ||||
0.211899 | + | 0.977292i | \(0.432035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.17420e6i | 0.549639i | 0.961496 | + | 0.274819i | \(0.0886180\pi\) | ||||
−0.961496 | + | 0.274819i | \(0.911382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 3.97267e6i | − 0.348360i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.43778e6 | −0.212168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 9.35232e6i | − 0.807893i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.87585e7i | 1.60839i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.40925e6 | 0.800787 | 0.400394 | − | 0.916343i | \(-0.368873\pi\) | ||||
0.400394 | + | 0.916343i | \(0.368873\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 857736. | 0.0724593 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.50086e7 | 1.25854 | 0.629272 | − | 0.777185i | \(-0.283353\pi\) | ||||
0.629272 | + | 0.777185i | \(0.283353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.07710e7 | 0.896567 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.93851e6i | 0.738580i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.29707e7i | 1.06393i | 0.846768 | + | 0.531963i | \(0.178545\pi\) | ||||
−0.846768 | + | 0.531963i | \(0.821455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.71257e7 | −1.39451 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.27295e6i | − 0.264574i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.26556e7i | 1.80501i | 0.430677 | + | 0.902506i | \(0.358275\pi\) | ||||
−0.430677 | + | 0.902506i | \(0.641725\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.70448e6 | −0.372116 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 8.00950e6i | − 0.628989i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.02322e7i | − 0.797791i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.84615e6 | −0.142914 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.90169e7 | −1.46166 | −0.730828 | − | 0.682562i | \(-0.760866\pi\) | ||||
−0.730828 | + | 0.682562i | \(0.760866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −249128. | −0.0190123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 839808. | 0.0636366 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 993168.i | − 0.0747264i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.51311e7i | − 1.13046i | −0.824933 | − | 0.565231i | \(-0.808787\pi\) | ||||
0.824933 | − | 0.565231i | \(-0.191213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.61429e6 | 0.564879 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74666e7i | 1.28672i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.38568e7i | − 1.00662i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.50323e7 | 1.08443 | 0.542217 | − | 0.840238i | \(-0.317585\pi\) | ||||
0.542217 | + | 0.840238i | \(0.317585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39853e6i | 0.171833i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.88489e6i | 0.560983i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −124146. | −0.00877178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.41230e6 | 0.520136 | 0.260068 | − | 0.965590i | \(-0.416255\pi\) | ||||
0.260068 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.44612e7 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.18740e6 | −0.497483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.77928e6i | − 0.191061i | −0.995426 | − | 0.0955306i | \(-0.969545\pi\) | ||||
0.995426 | − | 0.0955306i | \(-0.0304548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 5.87282e6i | − 0.400985i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17785e7 | 0.798768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.21046e7i | 0.815342i | 0.913129 | + | 0.407671i | \(0.133659\pi\) | ||||
−0.913129 | + | 0.407671i | \(0.866341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.46926e6i | 0.297005i | 0.988912 | + | 0.148502i | \(0.0474452\pi\) | ||||
−0.988912 | + | 0.148502i | \(0.952555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.06172e7 | −0.700838 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.70388e6i | − 0.439567i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.07680e7i | 0.701345i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.88463e7 | −1.86634 | −0.933168 | − | 0.359442i | \(-0.882967\pi\) | ||||
−0.933168 | + | 0.359442i | \(0.882967\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.61028e7 | 1.03494 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.01544e6 | 0.256369 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.60868e6 | 0.609430 | 0.304715 | − | 0.952444i | \(-0.401439\pi\) | ||||
0.304715 | + | 0.952444i | \(0.401439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.65939e7i | 1.67563i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 4.54588e6i | − 0.284549i | −0.989827 | − | 0.142274i | \(-0.954558\pi\) | ||||
0.989827 | − | 0.142274i | \(-0.0454415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.79138e6 | −0.546696 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.17552e6i | 0.196183i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 2.15923e7i | − 1.31669i | −0.752716 | − | 0.658345i | \(-0.771257\pi\) | ||||
0.752716 | − | 0.658345i | \(-0.228743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58825e6 | 0.0962238 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.48400e7i | − 0.893276i | −0.894715 | − | 0.446638i | \(-0.852621\pi\) | ||||
0.894715 | − | 0.446638i | \(-0.147379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 889504.i | 0.0531978i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 314688. | 0.0186994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.44009e7 | −0.850251 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.53109e7 | −1.48484 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.43778e6 | −0.142098 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.52741e6i | 0.378065i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.48785e7i | 1.43182i | 0.698194 | + | 0.715909i | \(0.253987\pi\) | ||||
−0.698194 | + | 0.715909i | \(0.746013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.13193e7 | −0.647330 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 2.60885e6i | − 0.148254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.26321e7i | − 0.708856i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.16080e7 | −1.76259 | −0.881294 | − | 0.472568i | \(-0.843327\pi\) | ||||
−0.881294 | + | 0.472568i | \(0.843327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 769824.i | − 0.0426604i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.94565e6i | 0.162218i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.64835e7 | −1.99668 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.95022e7 | −1.06070 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.16102e7 | −0.627562 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.10009e6 | −0.166534 | −0.0832669 | − | 0.996527i | \(-0.526535\pi\) | ||||
−0.0832669 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87180e6i | 0.0999328i | 0.998751 | + | 0.0499664i | \(0.0159114\pi\) | ||||
−0.998751 | + | 0.0499664i | \(0.984089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.21984e6i | − 0.330030i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.01236e6 | −0.317067 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01156e7i | 0.530196i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.00184e7i | − 1.03650i | −0.855228 | − | 0.518252i | \(-0.826583\pi\) | ||||
0.855228 | − | 0.518252i | \(-0.173417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.53118e7 | −0.787999 | −0.394000 | − | 0.919111i | \(-0.628909\pi\) | ||||
−0.394000 | + | 0.919111i | \(0.628909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.35432e6i | 0.0692766i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.59310e6i | − 0.487748i | −0.969807 | − | 0.243874i | \(-0.921582\pi\) | ||||
0.969807 | − | 0.243874i | \(-0.0784183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.52209e7 | −1.27460 | −0.637302 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637302 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.66727e7 | 1.33988 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.38342e6 | −0.268810 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.65589e7 | −1.31824 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.74666e7i | 0.861778i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.77623e7i | 0.871154i | 0.900151 | + | 0.435577i | \(0.143456\pi\) | ||||
−0.900151 | + | 0.435577i | \(0.856544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01583e7 | −0.982798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.35937e6i | − 0.114348i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.14883e7i | − 0.550234i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.86273e7 | −0.886913 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.22299e6i | 0.0578895i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 486970.i | 0.0229155i | 0.999934 | + | 0.0114578i | \(0.00364720\pi\) | ||||
−0.999934 | + | 0.0114578i | \(0.996353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.46926e6 | 0.209084 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.92634e6 | 0.0895945 | 0.0447972 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447972 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.23538e7 | 1.03364 | 0.516820 | − | 0.856094i | \(-0.327116\pi\) | ||||
0.516820 | + | 0.856094i | \(0.327116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81907e7 | 0.836258 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.85838e7i | 0.849390i | 0.905337 | + | 0.424695i | \(0.139619\pi\) | ||||
−0.905337 | + | 0.424695i | \(0.860381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 3.82025e7i | − 1.73601i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.28043e7 | 0.578504 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.15325e7i | 1.86569i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.21174e7i | 0.538114i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.58432e7 | −0.699555 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.91048e7i | − 1.27781i | −0.769286 | − | 0.638905i | \(-0.779388\pi\) | ||||
0.769286 | − | 0.638905i | \(-0.220612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1.28660e7i | − 0.561659i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.14696e6 | 0.136600 | 0.0683001 | − | 0.997665i | \(-0.478242\pi\) | ||||
0.0683001 | + | 0.997665i | \(0.478242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59995e7 | −0.690566 | −0.345283 | − | 0.938499i | \(-0.612217\pi\) | ||||
−0.345283 | + | 0.938499i | \(0.612217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.96886e6 | 0.213255 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.45874e7 | −1.47608 | −0.738039 | − | 0.674758i | \(-0.764248\pi\) | ||||
−0.738039 | + | 0.674758i | \(0.764248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − 2.96131e7i | − 1.25669i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.36031e7i | 0.574044i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.08346e6 | −0.0454656 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.66581e7i | − 1.11243i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.52806e6i | − 0.104325i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.15794e7 | −0.475199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.27776e7i | − 0.521471i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.02103e7i | 1.22612i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.74396e7 | −0.703914 | −0.351957 | − | 0.936016i | \(-0.614484\pi\) | ||||
−0.351957 | + | 0.936016i | \(0.614484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.11731e6 | 0.0448503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.59589e6 | −0.103631 | −0.0518155 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518155 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.65666e7 | 1.45180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.25102e7i | 0.888847i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.88624e6i | 0.348975i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.76411e7 | −0.689028 | −0.344514 | − | 0.938781i | \(-0.611956\pi\) | ||||
−0.344514 | + | 0.938781i | \(0.611956\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.90307e7i | 0.739275i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62282.0i | 0.00239336i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.69834e6 | −0.103133 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96785e7i | 1.50840i | 0.656646 | + | 0.754199i | \(0.271975\pi\) | ||||
−0.656646 | + | 0.754199i | \(0.728025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.57667e6i | 0.286486i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.76874e6 | −0.329787 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.73210e7 | −0.647955 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.93413e7 | 1.46386 | 0.731930 | − | 0.681380i | \(-0.238620\pi\) | ||||
0.731930 | + | 0.681380i | \(0.238620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.01830e6 | −0.259757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.62506e7i | 1.70272i | 0.524581 | + | 0.851361i | \(0.324222\pi\) | ||||
−0.524581 | + | 0.851361i | \(0.675778\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.06955e7i | 2.58888i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.95022e7 | −0.710402 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.79025e7i | 1.37339i | 0.726947 | + | 0.686693i | \(0.240938\pi\) | ||||
−0.726947 | + | 0.686693i | \(0.759062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97944e7i | 1.06828i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.66462e7 | 0.950394 | 0.475197 | − | 0.879879i | \(-0.342377\pi\) | ||||
0.475197 | + | 0.879879i | \(0.342377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 3.90977e7i | − 1.38721i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 3.84912e6i | − 0.135857i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.79085e7 | −0.979918 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.05156e7 | 0.367304 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.21140e7 | −0.420943 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 383724. | 0.0132648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.09790e7i | 1.40927i | 0.709568 | + | 0.704637i | \(0.248890\pi\) | ||||
−0.709568 | + | 0.704637i | \(0.751110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.95901e6i | 0.203875i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.72034e7 | −0.925922 | −0.462961 | − | 0.886379i | \(-0.653213\pi\) | ||||
−0.462961 | + | 0.886379i | \(0.653213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.30525e7i | − 0.441990i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.53555e7i | 0.849839i | 0.905231 | + | 0.424919i | \(0.139698\pi\) | ||||
−0.905231 | + | 0.424919i | \(0.860302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.60672e7 | −0.535775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.89030e6i | − 0.328123i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.19139e7i | − 0.393252i | −0.980479 | − | 0.196626i | \(-0.937002\pi\) | ||||
0.980479 | − | 0.196626i | \(-0.0629984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.86439e7 | 0.940678 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.36858e6 | 0.0447173 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.96584e7 | 1.61437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91931e7 | 0.944268 | 0.472134 | − | 0.881527i | \(-0.343484\pi\) | ||||
0.472134 | + | 0.881527i | \(0.343484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 4.53538e6i | − 0.145962i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.03307e6i | − 0.0971237i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.73001e7 | −0.551201 | −0.275601 | − | 0.961272i | \(-0.588877\pi\) | ||||
−0.275601 | + | 0.961272i | \(0.588877\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.22299e6i | 0.0387713i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))