Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (of order \(3\), degree \(2\), 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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1445900625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 77x^{4} + 36x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(-0.342371 - 0.593004i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.289 |
Dual form | 2016.2.s.x.865.4 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.46040 | − | 2.52950i | 0.653113 | − | 1.13122i | −0.329250 | − | 0.944243i | \(-0.606796\pi\) |
0.982363 | − | 0.186982i | \(-0.0598706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80278 | − | 1.93649i | −0.681385 | − | 0.731925i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.26556 | + | 3.92407i | 0.683093 | + | 1.18315i | 0.974032 | + | 0.226411i | \(0.0726991\pi\) |
−0.290939 | + | 0.956742i | \(0.593968\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53113 | 1.53406 | 0.767030 | − | 0.641612i | \(-0.221734\pi\) | ||||
0.767030 | + | 0.641612i | \(0.221734\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.23607 | − | 3.87298i | −0.542326 | − | 0.939336i | −0.998770 | − | 0.0495842i | \(-0.984210\pi\) |
0.456444 | − | 0.889752i | \(-0.349123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.342371 | − | 0.593004i | 0.0785453 | − | 0.136044i | −0.824077 | − | 0.566477i | \(-0.808306\pi\) |
0.902622 | + | 0.430433i | \(0.141639\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76556 | − | 3.05805i | −0.353113 | − | 0.611609i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29029 | 0.796687 | 0.398344 | − | 0.917236i | \(-0.369585\pi\) | ||||
0.398344 | + | 0.917236i | \(0.369585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.03884 | + | 6.99548i | 0.725398 | + | 1.25643i | 0.958810 | + | 0.284048i | \(0.0916775\pi\) |
−0.233412 | + | 0.972378i | \(0.574989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.53113 | + | 1.73205i | −1.27299 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.76556 | − | 4.79010i | 0.454656 | − | 0.787487i | −0.544012 | − | 0.839077i | \(-0.683096\pi\) |
0.998668 | + | 0.0515899i | \(0.0164289\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.73897 | 0.427755 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.78739 | −0.577572 | −0.288786 | − | 0.957394i | \(-0.593252\pi\) | ||||
−0.288786 | + | 0.957394i | \(0.593252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.53113 | − | 9.58020i | 0.806798 | − | 1.39742i | −0.108272 | − | 0.994121i | \(-0.534532\pi\) |
0.915070 | − | 0.403294i | \(-0.132135\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 6.98212i | −0.0714286 | + | 0.997446i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.93254 | − | 10.2755i | −0.814897 | − | 1.41144i | −0.909402 | − | 0.415919i | \(-0.863460\pi\) |
0.0945046 | − | 0.995524i | \(-0.469873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2346 | 1.78455 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.734436 | + | 1.27208i | 0.0956154 | + | 0.165611i | 0.909865 | − | 0.414904i | \(-0.136185\pi\) |
−0.814250 | + | 0.580515i | \(0.802851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.53113 | + | 9.58020i | −0.708188 | + | 1.22662i | 0.257340 | + | 0.966321i | \(0.417154\pi\) |
−0.965528 | + | 0.260298i | \(0.916179\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.07769 | − | 13.9910i | 1.00191 | − | 1.73537i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.18399 | − | 10.7110i | −0.755495 | − | 1.30856i | −0.945128 | − | 0.326700i | \(-0.894063\pi\) |
0.189633 | − | 0.981855i | \(-0.439270\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.06226 | −0.838136 | −0.419068 | − | 0.907955i | \(-0.637643\pi\) | ||||
−0.419068 | + | 0.907955i | \(0.637643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.76556 | − | 4.79010i | −0.323685 | − | 0.560639i | 0.657560 | − | 0.753402i | \(-0.271588\pi\) |
−0.981245 | + | 0.192763i | \(0.938255\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.51463 | − | 11.4615i | 0.400529 | − | 1.30616i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.32914 | + | 14.4265i | −0.937101 | + | 1.62311i | −0.166257 | + | 0.986082i | \(0.553168\pi\) |
−0.770844 | + | 0.637024i | \(0.780165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.46887 | −0.161230 | −0.0806148 | − | 0.996745i | \(-0.525688\pi\) | ||||
−0.0806148 | + | 0.996745i | \(0.525688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0623 | −1.41680 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.76243 | − | 15.1770i | 0.928816 | − | 1.60876i | 0.143509 | − | 0.989649i | \(-0.454161\pi\) |
0.785307 | − | 0.619107i | \(-0.212505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.97138 | − | 10.7110i | −1.04529 | − | 1.12282i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.46887 | −0.149141 | −0.0745706 | − | 0.997216i | \(-0.523759\pi\) | ||||
−0.0745706 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.55133 | − | 2.68698i | −0.154363 | − | 0.267364i | 0.778464 | − | 0.627689i | \(-0.215999\pi\) |
−0.932827 | + | 0.360325i | \(0.882666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.89370 | − | 3.27998i | 0.186592 | − | 0.323186i | −0.757520 | − | 0.652812i | \(-0.773589\pi\) |
0.944112 | + | 0.329626i | \(0.106923\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.26556 | − | 12.5843i | 0.702389 | − | 1.21657i | −0.265237 | − | 0.964183i | \(-0.585450\pi\) |
0.967626 | − | 0.252390i | \(-0.0812164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.76556 | − | 8.25420i | −0.456458 | − | 0.790609i | 0.542312 | − | 0.840177i | \(-0.317549\pi\) |
−0.998771 | + | 0.0495679i | \(0.984216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.57479 | −0.712576 | −0.356288 | − | 0.934376i | \(-0.615958\pi\) | ||||
−0.356288 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.92081 | − | 5.05899i | −0.272367 | − | 0.471753i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.46887 | + | 11.3122i | −0.317991 | + | 1.03699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.76556 | + | 8.25420i | −0.433233 | + | 0.750382i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.29029 | 0.383735 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6525 | 1.38893 | 0.694466 | − | 0.719525i | \(-0.255641\pi\) | ||||
0.694466 | + | 0.719525i | \(0.255641\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.79669 | + | 8.30812i | −0.419089 | + | 0.725884i | −0.995848 | − | 0.0910308i | \(-0.970984\pi\) |
0.576759 | + | 0.816914i | \(0.304317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.76556 | + | 0.406054i | −0.153094 | + | 0.0352094i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.29029 | + | 7.43101i | 0.366544 | + | 0.634874i | 0.989023 | − | 0.147763i | \(-0.0472074\pi\) |
−0.622478 | + | 0.782637i | \(0.713874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.79319 | 0.406553 | 0.203277 | − | 0.979121i | \(-0.434841\pi\) | ||||
0.203277 | + | 0.979121i | \(0.434841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5311 | + | 21.7046i | 1.04791 | + | 1.81503i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.26556 | − | 10.8523i | 0.520327 | − | 0.901232i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.29029 | − | 7.43101i | 0.351474 | − | 0.608772i | −0.635034 | − | 0.772485i | \(-0.719014\pi\) |
0.986508 | + | 0.163713i | \(0.0523471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.14515 | + | 3.71550i | 0.174570 | + | 0.302363i | 0.940012 | − | 0.341141i | \(-0.110813\pi\) |
−0.765443 | + | 0.643504i | \(0.777480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.5934 | 1.89507 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.53113 | + | 9.58020i | 0.441432 | + | 0.764583i | 0.997796 | − | 0.0663559i | \(-0.0211373\pi\) |
−0.556364 | + | 0.830939i | \(0.687804\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.15688 | + | 1.18601i | −0.406419 | + | 0.0934705i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.8651 | + | 20.5509i | −0.929345 | + | 1.60967i | −0.144925 | + | 0.989443i | \(0.546294\pi\) |
−0.784420 | + | 0.620230i | \(0.787039\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0000 | −1.08335 | −0.541676 | − | 0.840587i | \(-0.682210\pi\) | ||||
−0.541676 | + | 0.840587i | \(0.682210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.5934 | 1.35334 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.60555 | + | 6.24500i | −0.274125 | + | 0.474798i | −0.969914 | − | 0.243448i | \(-0.921722\pi\) |
0.695789 | + | 0.718246i | \(0.255055\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.73897 | + | 8.93197i | −0.207046 | + | 0.675194i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.53113 | − | 16.5084i | −0.712390 | − | 1.23390i | −0.963958 | − | 0.266056i | \(-0.914279\pi\) |
0.251568 | − | 0.967840i | \(-0.419054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.46887 | 0.629486 | 0.314743 | − | 0.949177i | \(-0.398082\pi\) | ||||
0.314743 | + | 0.949177i | \(0.398082\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.07769 | − | 13.9910i | −0.593883 | − | 1.02864i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1319 | − | 17.5490i | 0.740919 | − | 1.28331i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.46887 | − | 4.27621i | 0.178641 | − | 0.309416i | −0.762774 | − | 0.646665i | \(-0.776163\pi\) |
0.941415 | + | 0.337249i | \(0.109497\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.03113 | + | 15.6424i | 0.650075 | + | 1.12596i | 0.983104 | + | 0.183046i | \(0.0585958\pi\) |
−0.333029 | + | 0.942916i | \(0.608071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1554 | 1.15102 | 0.575511 | − | 0.817794i | \(-0.304803\pi\) | ||||
0.575511 | + | 0.817794i | \(0.304803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.21110 | + | 12.4900i | 0.511182 | + | 0.885392i | 0.999916 | + | 0.0129598i | \(0.00412534\pi\) |
−0.488735 | + | 0.872433i | \(0.662541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.73444 | − | 8.30812i | −0.542851 | − | 0.583115i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | − | 6.92820i | 0.279372 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.10265 | 0.214615 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.53113 | + | 9.58020i | −0.377220 | + | 0.653364i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.26556 | − | 20.4325i | 0.425334 | − | 1.38705i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.3680 | − | 21.4220i | −0.831960 | − | 1.44100i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.4956 | 0.702837 | 0.351419 | − | 0.936218i | \(-0.385699\pi\) | ||||
0.351419 | + | 0.936218i | \(0.385699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.73444 | + | 13.3964i | 0.513353 | + | 0.889153i | 0.999880 | + | 0.0154874i | \(0.00492999\pi\) |
−0.486528 | + | 0.873665i | \(0.661737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.82782 | − | 11.8261i | 0.451195 | − | 0.781493i | −0.547265 | − | 0.836959i | \(-0.684331\pi\) |
0.998461 | + | 0.0554661i | \(0.0176645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.07769 | + | 13.9910i | −0.529187 | + | 0.916579i | 0.470234 | + | 0.882542i | \(0.344170\pi\) |
−0.999421 | + | 0.0340366i | \(0.989164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1554 | − | 27.9819i | −1.05386 | − | 1.82534i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0623 | 1.36240 | 0.681202 | − | 0.732095i | \(-0.261457\pi\) | ||||
0.681202 | + | 0.732095i | \(0.261457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.734436 | + | 1.27208i | 0.0473092 | + | 0.0819419i | 0.888710 | − | 0.458469i | \(-0.151602\pi\) |
−0.841401 | + | 0.540411i | \(0.818269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.9310 | + | 11.4615i | 1.08168 | + | 0.732246i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.89370 | − | 3.27998i | 0.120493 | − | 0.208700i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.5934 | −1.48920 | −0.744601 | − | 0.667510i | \(-0.767360\pi\) | ||||
−0.744601 | + | 0.667510i | \(0.767360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.06226 | 0.569739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.60555 | − | 6.24500i | 0.224908 | − | 0.389552i | −0.731384 | − | 0.681966i | \(-0.761125\pi\) |
0.956292 | + | 0.292414i | \(0.0944585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2617 | + | 3.27998i | −0.886178 | + | 0.203808i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0623 | − | 26.0886i | −0.928779 | − | 1.60869i | −0.785369 | − | 0.619028i | \(-0.787527\pi\) |
−0.143410 | − | 0.989663i | \(-0.545807\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.6556 | −2.12888 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.16861 | + | 14.1484i | 0.498049 | + | 0.862646i | 0.999997 | − | 0.00225151i | \(-0.000716679\pi\) |
−0.501949 | + | 0.864897i | \(0.667383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.43544 | + | 11.1465i | −0.390925 | + | 0.677102i | −0.992572 | − | 0.121660i | \(-0.961178\pi\) |
0.601647 | + | 0.798762i | \(0.294512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.00000 | − | 13.8564i | 0.482418 | − | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.82782 | + | 11.8261i | 0.410244 | + | 0.710564i | 0.994916 | − | 0.100706i | \(-0.0321102\pi\) |
−0.584672 | + | 0.811270i | \(0.698777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00580 | −0.0600008 | −0.0300004 | − | 0.999550i | \(-0.509551\pi\) | ||||
−0.0300004 | + | 0.999550i | \(0.509551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.05057 | − | 12.2120i | −0.419113 | − | 0.725925i | 0.576737 | − | 0.816930i | \(-0.304326\pi\) |
−0.995850 | + | 0.0910044i | \(0.970992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.93774 | − | 5.30399i | −0.291466 | − | 0.313084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.50000 | + | 2.59808i | −0.0882353 | + | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.7594 | −1.79698 | −0.898492 | − | 0.438989i | \(-0.855337\pi\) | ||||
−0.898492 | + | 0.438989i | \(0.855337\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.29029 | 0.249791 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.53113 | − | 9.58020i | 0.319873 | − | 0.554037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.82782 | + | 7.33426i | 0.393549 | + | 0.422740i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.1554 | + | 27.9819i | 0.925054 | + | 1.60224i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7375 | −0.784038 | −0.392019 | − | 0.919957i | \(-0.628223\pi\) | ||||
−0.392019 | + | 0.919957i | \(0.628223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0000 | + | 24.2487i | 0.793867 | + | 1.37502i | 0.923556 | + | 0.383464i | \(0.125269\pi\) |
−0.129689 | + | 0.991555i | \(0.541398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.03113 | + | 3.51802i | −0.114806 | + | 0.198850i | −0.917702 | − | 0.397269i | \(-0.869958\pi\) |
0.802896 | + | 0.596119i | \(0.203291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.7257 | + | 18.5775i | −0.602417 | + | 1.04342i | 0.390037 | + | 0.920799i | \(0.372462\pi\) |
−0.992454 | + | 0.122618i | \(0.960871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.71994 | + | 16.8354i | 0.544212 | + | 0.942603i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.06226 | −0.170389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.76556 | − | 16.9145i | −0.541696 | − | 0.938245i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.5234 | + | 6.55996i | −1.57254 | + | 0.361662i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2617 | − | 24.7019i | 0.783893 | − | 1.35774i | −0.145766 | − | 0.989319i | \(-0.546565\pi\) |
0.929658 | − | 0.368423i | \(-0.120102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.1245 | −1.97369 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.1245 | −0.714938 | −0.357469 | − | 0.933925i | \(-0.616360\pi\) | ||||
−0.357469 | + | 0.933925i | \(0.616360\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.3005 | + | 31.6974i | −0.991029 | + | 1.71651i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4222 | − | 11.6190i | 0.778726 | − | 0.627364i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.53113 | + | 2.65199i | 0.0821953 | + | 0.142366i | 0.904193 | − | 0.427125i | \(-0.140474\pi\) |
−0.821997 | + | 0.569491i | \(0.807140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.12452 | −0.434895 | −0.217448 | − | 0.976072i | \(-0.569773\pi\) | ||||
−0.217448 | + | 0.976072i | \(0.569773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1011 | + | 24.4239i | 0.750528 | + | 1.29995i | 0.947567 | + | 0.319558i | \(0.103534\pi\) |
−0.197038 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3138 | + | 17.8639i | −0.547397 | + | 0.948120i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.5311 | − | 32.0969i | 0.978036 | − | 1.69401i | 0.308505 | − | 0.951223i | \(-0.400171\pi\) |
0.669530 | − | 0.742785i | \(-0.266495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.26556 | + | 16.0484i | 0.487661 | + | 0.844654i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.1554 | −0.845611 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.90543 | + | 8.49645i | 0.256061 | + | 0.443511i | 0.965183 | − | 0.261575i | \(-0.0842418\pi\) |
−0.709122 | + | 0.705086i | \(0.750908\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.20331 | + | 30.0127i | −0.477812 | + | 1.55818i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8278 | + | 18.7543i | −0.560643 | + | 0.971063i | 0.436797 | + | 0.899560i | \(0.356113\pi\) |
−0.997440 | + | 0.0715027i | \(0.977221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.7302 | 1.22217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3622 | −0.583636 | −0.291818 | − | 0.956474i | \(-0.594260\pi\) | ||||
−0.291818 | + | 0.956474i | \(0.594260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00000 | − | 12.1244i | 0.357683 | − | 0.619526i | −0.629890 | − | 0.776684i | \(-0.716900\pi\) |
0.987573 | + | 0.157159i | \(0.0502334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.8590 | − | 25.6286i | −1.21596 | − | 1.30616i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6525 | + | 27.1109i | 0.793612 | + | 1.37458i | 0.923717 | + | 0.383076i | \(0.125135\pi\) |
−0.130105 | + | 0.991500i | \(0.541531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94427 | −0.452331 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.3278 | + | 42.1370i | 1.22407 | + | 2.12014i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.76556 | + | 16.9145i | −0.490120 | + | 0.848912i | −0.999935 | − | 0.0113715i | \(-0.996380\pi\) |
0.509816 | + | 0.860284i | \(0.329714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.78739 | + | 6.55996i | −0.189133 | + | 0.327589i | −0.944962 | − | 0.327181i | \(-0.893901\pi\) |
0.755828 | + | 0.654770i | \(0.227235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.3394 | + | 38.6929i | 1.11280 | + | 1.92743i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0623 | 1.24229 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0934 | + | 22.6784i | 0.647426 | + | 1.12138i | 0.983735 | + | 0.179624i | \(0.0574880\pi\) |
−0.336309 | + | 0.941752i | \(0.609179\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.13935 | − | 3.71550i | 0.0560637 | − | 0.182828i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.14515 | + | 3.71550i | −0.105301 | + | 0.182387i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.87548 | −0.287036 | −0.143518 | − | 0.989648i | \(-0.545842\pi\) | ||||
−0.143518 | + | 0.989648i | \(0.545842\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.59339 | 0.126394 | 0.0631970 | − | 0.998001i | \(-0.479870\pi\) | ||||
0.0631970 | + | 0.998001i | \(0.479870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.89584 | + | 13.6760i | −0.383005 | + | 0.663384i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.5234 | − | 6.55996i | 1.38034 | − | 0.317459i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.59339 | + | 11.4201i | 0.317592 | + | 0.550086i | 0.979985 | − | 0.199071i | \(-0.0637923\pi\) |
−0.662393 | + | 0.749157i | \(0.730459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.4066 | −0.548167 | −0.274083 | − | 0.961706i | \(-0.588374\pi\) | ||||
−0.274083 | + | 0.961706i | \(0.588374\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.684742 | − | 1.18601i | −0.0327556 | − | 0.0567344i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.98677 | − | 13.8335i | 0.381188 | − | 0.660236i | −0.610045 | − | 0.792367i | \(-0.708849\pi\) |
0.991232 | + | 0.132131i | \(0.0421819\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.32782 | + | 4.03191i | −0.110598 | + | 0.191562i | −0.916012 | − | 0.401152i | \(-0.868610\pi\) |
0.805413 | + | 0.592713i | \(0.201943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.5934 | − | 44.3290i | −1.21324 | − | 2.10140i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.3165 | −1.57231 | −0.786153 | − | 0.618033i | \(-0.787930\pi\) | ||||
−0.786153 | + | 0.618033i | \(0.787930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.20531 | + | 10.7479i | 0.292196 | + | 0.506099i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −41.6556 | + | 9.58020i | −1.95285 | + | 0.449127i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.96887 | + | 3.41018i | −0.0920999 | + | 0.159522i | −0.908395 | − | 0.418114i | \(-0.862691\pi\) |
0.816295 | + | 0.577636i | \(0.196025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.30796 | 0.433515 | 0.216757 | − | 0.976225i | \(-0.430452\pi\) | ||||
0.216757 | + | 0.976225i | \(0.430452\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.5234 | −1.32559 | −0.662796 | − | 0.748800i | \(-0.730630\pi\) | ||||
−0.662796 | + | 0.748800i | \(0.730630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.53113 | − | 9.58020i | 0.255950 | − | 0.443319i | −0.709203 | − | 0.705004i | \(-0.750945\pi\) |
0.965153 | + | 0.261686i | \(0.0842784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.59339 | + | 31.2847i | −0.442981 | + | 1.44460i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.58059 | − | 14.8620i | −0.394536 | − | 0.683356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.41791 | −0.110941 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.59339 | − | 4.49188i | −0.118495 | − | 0.205239i | 0.800677 | − | 0.599097i | \(-0.204474\pi\) |
−0.919171 | + | 0.393858i | \(0.871140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2967 | − | 26.4947i | 0.697469 | − | 1.20805i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.14515 | + | 3.71550i | −0.0974061 | + | 0.168712i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6136 | − | 20.1154i | −0.526264 | − | 0.911516i | −0.999532 | − | 0.0305973i | \(-0.990259\pi\) |
0.473268 | − | 0.880919i | \(-0.343074\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.6556 | −0.480882 | −0.240441 | − | 0.970664i | \(-0.577292\pi\) | ||||
−0.240441 | + | 0.970664i | \(0.577292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.59339 | − | 16.6162i | −0.432064 | − | 0.748357i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7317 | + | 13.6760i | 0.571093 | + | 0.613453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7588 | − | 23.8309i | 0.615928 | − | 1.06682i | −0.374293 | − | 0.927310i | \(-0.622115\pi\) |
0.990221 | − | 0.139507i | \(-0.0445519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.3113 | 1.84198 | 0.920990 | − | 0.389587i | \(-0.127382\pi\) | ||||
0.920990 | + | 0.389587i | \(0.127382\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.06226 | −0.403265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.03519 | + | 15.6494i | −0.400478 | + | 0.693648i | −0.993784 | − | 0.111329i | \(-0.964489\pi\) |
0.593306 | + | 0.804977i | \(0.297823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.29029 | + | 13.9910i | −0.189791 | + | 0.618924i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.53113 | − | 9.58020i | −0.243731 | − | 0.422154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.1245 | 2.20447 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3138 | + | 17.8639i | 0.451854 | + | 0.782634i | 0.998501 | − | 0.0547291i | \(-0.0174295\pi\) |
−0.546647 | + | 0.837363i | \(0.684096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.18399 | + | 10.7110i | −0.270407 | + | 0.468359i | −0.968966 | − | 0.247194i | \(-0.920492\pi\) |
0.698559 | + | 0.715552i | \(0.253825\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.0623 | − | 31.2847i | 0.786804 | − | 1.36279i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.1496 | 0.656201 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.2213 | − | 36.7564i | −0.917478 | − | 1.58912i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.5311 | + | 13.8564i | −1.22892 | + | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.76556 | − | 16.9145i | 0.419854 | − | 0.727209i | −0.576070 | − | 0.817400i | \(-0.695414\pi\) |
0.995924 | + | 0.0901912i | \(0.0287478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.8386 | −1.19248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.7418 | −1.10064 | −0.550319 | − | 0.834954i | \(-0.685494\pi\) | ||||
−0.550319 | + | 0.834954i | \(0.685494\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.46887 | − | 2.54416i | 0.0625760 | − | 0.108385i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.9523 | − | 9.87842i | 1.82652 | − | 0.420073i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.14515 | + | 3.71550i | 0.0908928 | + | 0.157431i | 0.907887 | − | 0.419215i | \(-0.137695\pi\) |
−0.816994 | + | 0.576646i | \(0.804361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.9486 | −0.886030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.7344 | + | 25.5208i | 0.620982 | + | 1.07557i | 0.989303 | + | 0.145874i | \(0.0465995\pi\) |
−0.368321 | + | 0.929699i | \(0.620067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.0623 | + | 19.1604i | −0.465393 | + | 0.806084i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.4457 | + | 35.4129i | −0.857127 | + | 1.48459i | 0.0175307 | + | 0.999846i | \(0.494420\pi\) |
−0.874658 | + | 0.484741i | \(0.838914\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.4743 | + | 18.1420i | 0.438335 | + | 0.759219i | 0.997561 | − | 0.0697965i | \(-0.0222350\pi\) |
−0.559226 | + | 0.829015i | \(0.688902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.06226 | −0.294517 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5000 | + | 18.1865i | 0.437121 | + | 0.757115i | 0.997466 | − | 0.0711438i | \(-0.0226649\pi\) |
−0.560345 | + | 0.828259i | \(0.689332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.64805 | + | 2.84446i | 0.109859 | + | 0.118008i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.8811 | − | 46.5594i | 1.11330 | − | 1.92830i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.5934 | −1.55165 | −0.775823 | − | 0.630951i | \(-0.782665\pi\) | ||||
−0.775823 | + | 0.630951i | \(0.782665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.53113 | 0.227906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.76243 | + | 15.1770i | −0.359830 | + | 0.623244i | −0.987932 | − | 0.154887i | \(-0.950499\pi\) |
0.628102 | + | 0.778131i | \(0.283832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.5483 | + | 25.2950i | 0.965387 | + | 1.03699i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.53113 | + | 14.7763i | 0.348572 | + | 0.603745i | 0.985996 | − | 0.166768i | \(-0.0533332\pi\) |
−0.637424 | + | 0.770514i | \(0.720000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2490 | 0.948348 | 0.474174 | − | 0.880431i | \(-0.342747\pi\) | ||||
0.474174 | + | 0.880431i | \(0.342747\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.9193 | + | 24.1089i | 0.565900 | + | 0.980168i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.4553 | + | 30.2334i | −0.708487 | + | 1.22714i | 0.256932 | + | 0.966430i | \(0.417289\pi\) |
−0.965418 | + | 0.260706i | \(0.916045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.5934 | − | 52.9893i | 1.23768 | − | 2.14372i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.00000 | − | 8.66025i | −0.201948 | − | 0.349784i | 0.747208 | − | 0.664590i | \(-0.231394\pi\) |
−0.949156 | + | 0.314806i | \(0.898061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.1612 | 0.690883 | 0.345441 | − | 0.938440i | \(-0.387729\pi\) | ||||
0.345441 | + | 0.938440i | \(0.387729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.46849 | − | 16.3999i | −0.380571 | − | 0.659168i | 0.610573 | − | 0.791960i | \(-0.290939\pi\) |
−0.991144 | + | 0.132792i | \(0.957606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.1868 | + | 10.3923i | −1.81037 | + | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0934 | − | 26.1425i | 0.603735 | − | 1.04570i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.7360 | −0.986287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.4515 | 0.853969 | 0.426985 | − | 0.904259i | \(-0.359576\pi\) | ||||
0.426985 | + | 0.904259i | \(0.359576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.8590 | − | 39.5929i | 0.907130 | − | 1.57119i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.76556 | + | 38.6190i | −0.109576 | + | 1.53014i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3680 | + | 21.4220i | 0.488506 | + | 0.846117i | 0.999913 | − | 0.0132218i | \(-0.00420876\pi\) |
−0.511407 | + | 0.859339i | \(0.670875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5849 | −0.811788 | −0.405894 | − | 0.913920i | \(-0.633040\pi\) | ||||
−0.405894 | + | 0.913920i | \(0.633040\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.93774 | + | 5.08832i | 0.115495 | + | 0.200042i | 0.917977 | − | 0.396633i | \(-0.129821\pi\) |
−0.802483 | + | 0.596675i | \(0.796488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.32782 | + | 5.76396i | −0.130628 | + | 0.226255i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.42964 | + | 9.40442i | −0.212478 | + | 0.368023i | −0.952490 | − | 0.304571i | \(-0.901487\pi\) |
0.740011 | + | 0.672595i | \(0.234820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.0102 | + | 24.2664i | 0.547425 | + | 0.948168i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9377 | 0.503983 | 0.251991 | − | 0.967729i | \(-0.418915\pi\) | ||||
0.251991 | + | 0.967729i | \(0.418915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.76556 | − | 16.9145i | −0.379836 | − | 0.657896i | 0.611202 | − | 0.791475i | \(-0.290686\pi\) |
−0.991038 | + | 0.133579i | \(0.957353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.55133 | + | 5.05899i | −0.0601579 | + | 0.196179i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.29029 | − | 7.43101i | 0.166121 | − | 0.287730i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.1245 | −1.93504 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.93774 | 0.383072 | 0.191536 | − | 0.981486i | \(-0.438653\pi\) | ||||
0.191536 | + | 0.981486i | \(0.438653\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.8226 | − | 22.2094i | 0.492812 | − | 0.853576i | −0.507154 | − | 0.861856i | \(-0.669302\pi\) |
0.999966 | + | 0.00828010i | \(0.00263567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.64805 | + | 2.84446i | 0.101623 | + | 0.109160i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.7344 | − | 18.5926i | −0.410742 | − | 0.711426i | 0.584229 | − | 0.811589i | \(-0.301397\pi\) |
−0.994971 | + | 0.100163i | \(0.968064\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.0623 | 0.957580 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.8136 | − | 56.8349i | −1.25010 | − | 2.16524i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.89949 | + | 5.02207i | −0.110302 | + | 0.191049i | −0.915892 | − | 0.401425i | \(-0.868515\pi\) |
0.805590 | + | 0.592473i | \(0.201848\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.00000 | − | 12.1244i | 0.265525 | − | 0.459903i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.12452 | − | 10.6080i | −0.231983 | − | 0.401806i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8651 | 0.448138 | 0.224069 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224069 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.89370 | − | 3.27998i | −0.0714221 | − | 0.123707i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.40661 | + | 7.84815i | −0.0905100 | + | 0.295160i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.1245 | − | 33.1246i | 0.718236 | − | 1.24402i | −0.243462 | − | 0.969910i | \(-0.578283\pi\) |
0.961698 | − | 0.274111i | \(-0.0883836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1554 | 0.605024 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 73.2021 | 2.73760 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.5311 | + | 21.7046i | −0.467332 | + | 0.809443i | −0.999303 | − | 0.0373193i | \(-0.988118\pi\) |
0.531971 | + | 0.846762i | \(0.321451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.76556 | + | 2.24594i | −0.363689 | + | 0.0836431i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.57479 | − | 13.1199i | −0.281321 | − | 0.487262i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.8021 | −1.14238 | −0.571192 | − | 0.820816i | \(-0.693519\pi\) | ||||
−0.571192 | + | 0.820816i | \(0.693519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.46887 | + | 14.6685i | 0.313233 | + | 0.542535i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.23444 | + | 7.33426i | −0.156402 | + | 0.270897i | −0.933569 | − | 0.358398i | \(-0.883323\pi\) |
0.777166 | + | 0.629295i | \(0.216656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.0205 | − | 48.5329i | 1.03215 | − | 1.78773i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.17819 | + | 8.96889i | 0.190483 | + | 0.329926i | 0.945410 | − | 0.325882i | \(-0.105661\pi\) |
−0.754927 | + | 0.655808i | \(0.772328\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0623 | 0.772699 | 0.386350 | − | 0.922352i | \(-0.373736\pi\) | ||||
0.386350 | + | 0.922352i | \(0.373736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5311 | − | 21.7046i | −0.459105 | − | 0.795193i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.4676 | + | 8.61701i | −1.36904 | + | 0.314859i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.754348 | − | 1.30657i | 0.0275265 | − | 0.0476774i | −0.851934 | − | 0.523649i | \(-0.824570\pi\) |
0.879461 | + | 0.475972i | \(0.157904\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5311 | 0.456054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.0623 | −0.983594 | −0.491797 | − | 0.870710i | \(-0.663660\pi\) | ||||
−0.491797 | + | 0.870710i | \(0.663660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1861 | − | 21.1070i | 0.441747 | − | 0.765128i | −0.556072 | − | 0.831134i | \(-0.687692\pi\) |
0.997819 | + | 0.0660056i | \(0.0210255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.39295 | + | 24.1089i | −0.267643 | + | 0.872802i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.06226 | + | 7.03604i | 0.146680 | + | 0.254057i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0623 | −1.66105 | −0.830524 | − | 0.556983i | \(-0.811959\pi\) | ||||
−0.830524 | + | 0.556983i | \(0.811959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6040 | − | 25.2950i | −0.525271 | − | 0.909796i | −0.999567 | − | 0.0294306i | \(-0.990631\pi\) |
0.474296 | − | 0.880366i | \(-0.342703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.2617 | − | 24.7019i | 0.512295 | − | 0.887320i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.937742 | − | 1.62422i | 0.0335981 | − | 0.0581936i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | − | 27.7128i | −0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.3107 | 1.15322 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.7360 | + | 42.8439i | 0.881742 | + | 1.52722i | 0.849403 | + | 0.527745i | \(0.176962\pi\) |
0.0323386 | + | 0.999477i | \(0.489705\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6556 | + | 14.6685i | 0.485539 | + | 0.521552i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.5934 | + | 52.9893i | −1.08640 | + | 1.88171i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.3458 | 1.42912 | 0.714561 | − | 0.699573i | \(-0.246627\pi\) | ||||
0.714561 | + | 0.699573i | \(0.246627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.4719 | −1.75019 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.5311 | − | 21.7046i | 0.442214 | − | 0.765937i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.53113 | + | 14.7763i | −0.159701 | + | 0.520798i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.3680 | − | 21.4220i | −0.434835 | − | 0.753156i | 0.562447 | − | 0.826833i | \(-0.309860\pi\) |
−0.997282 | + | 0.0736769i | \(0.976527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.58059 | −0.301305 | −0.150653 | − | 0.988587i | \(-0.548137\pi\) | ||||
−0.150653 | + | 0.988587i | \(0.548137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.6556 | + | 60.0253i | 1.21393 | + | 2.10260i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.29669 | + | 2.24594i | −0.0453656 | + | 0.0785754i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2228 | − | 17.7065i | 0.356779 | − | 0.617960i | −0.630641 | − | 0.776074i | \(-0.717208\pi\) |
0.987421 | + | 0.158114i | \(0.0505415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1554 | − | 27.9819i | −0.563141 | − | 0.975389i | −0.997220 | − | 0.0745139i | \(-0.976259\pi\) |
0.434079 | − | 0.900875i | \(-0.357074\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.53113 | 0.0880160 | 0.0440080 | − | 0.999031i | \(-0.485987\pi\) | ||||
0.0440080 | + | 0.999031i | \(0.485987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.3590 | + | 33.5307i | 0.672364 | + | 1.16457i | 0.977232 | + | 0.212174i | \(0.0680544\pi\) |
−0.304868 | + | 0.952395i | \(0.598612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.1597 | − | 13.6760i | 0.975675 | − | 0.473845i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.4457 | + | 35.4129i | −0.707551 | + | 1.22552i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.0623 | −0.865245 | −0.432623 | − | 0.901575i | \(-0.642412\pi\) | ||||
−0.432623 | + | 0.901575i | \(0.642412\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5934 | −0.365289 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.6935 | − | 44.5024i | 0.883882 | − | 1.53093i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.5754 | − | 5.65199i | 0.844422 | − | 0.194205i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.53113 | − | 9.58020i | −0.189605 | − | 0.328405i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.5934 | 1.52685 | 0.763424 | − | 0.645897i | \(-0.223517\pi\) | ||||
0.763424 | + | 0.645897i | \(0.223517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.0028 | + | 39.8420i | 0.785760 | + | 1.36098i | 0.928544 | + | 0.371223i | \(0.121061\pi\) |
−0.142783 | + | 0.989754i | \(0.545605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.8885 | − | 30.9839i | 0.610349 | − | 1.05716i | −0.380832 | − | 0.924644i | \(-0.624362\pi\) |
0.991181 | − | 0.132512i | \(-0.0423042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.6556 | + | 21.9202i | −0.430803 | + | 0.746173i | −0.996943 | − | 0.0781365i | \(-0.975103\pi\) |
0.566140 | + | 0.824309i | \(0.308436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5311 | + | 18.2405i | 0.358069 | + | 0.620194i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −75.4808 | −2.56051 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.2044 | − | 59.2438i | −1.15897 | − | 2.00740i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.73444 | − | 8.30812i | −0.261472 | − | 0.280866i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.40661 | − | 2.43633i | 0.0474980 | − | 0.0822689i | −0.841299 | − | 0.540570i | \(-0.818209\pi\) |
0.888797 | + | 0.458301i | \(0.151542\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0439 | −1.14697 | −0.573484 | − | 0.819216i | \(-0.694409\pi\) | ||||
−0.573484 | + | 0.819216i | \(0.694409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9370 | 0.637280 | 0.318640 | − | 0.947876i | \(-0.396774\pi\) | ||||
0.318640 | + | 0.947876i | \(0.396774\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.46887 | − | 2.54416i | 0.0493199 | − | 0.0854245i | −0.840312 | − | 0.542104i | \(-0.817628\pi\) |
0.889631 | + | 0.456679i | \(0.150961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.2179 | − | 30.3109i | −0.946398 | − | 1.01659i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.78739 | − | 6.55996i | −0.126740 | − | 0.219521i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.6772 | −1.86108 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.3278 | + | 30.0127i | 0.577915 | + | 1.00098i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.5311 | + | 45.9533i | −0.883880 | + | 1.53093i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.3680 | − | 21.4220i | 0.411126 | − | 0.712090i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.9772 | + | 19.0130i | 0.364491 | + | 0.631318i | 0.988694 | − | 0.149945i | \(-0.0479095\pi\) |
−0.624203 | + | 0.781262i | \(0.714576\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1868 | 1.23205 | 0.616026 | − | 0.787726i | \(-0.288741\pi\) | ||||
0.616026 | + | 0.787726i | \(0.288741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.32782 | − | 5.76396i | −0.110135 | − | 0.190759i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.7360 | − | 5.68891i | 0.816853 | − | 0.187864i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2617 | − | 24.7019i | 0.470449 | − | 0.814842i | −0.528980 | − | 0.848635i | \(-0.677425\pi\) |
0.999429 | + | 0.0337924i | \(0.0107585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.0623 | −1.28575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.5311 | −0.642180 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8401 | + | 29.1679i | −0.552506 | + | 0.956969i | 0.445587 | + | 0.895239i | \(0.352995\pi\) |
−0.998093 | + | 0.0617301i | \(0.980338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.96924 | + | 2.68698i | 0.130086 | + | 0.0880621i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.5934 | − | 51.2572i | −0.967807 | − | 1.67629i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.1245 | −1.40882 | −0.704408 | − | 0.709795i | \(-0.748788\pi\) | ||||
−0.704408 | + | 0.709795i | \(0.748788\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.9560 | − | 20.7084i | −0.389755 | − | 0.675075i | 0.602662 | − | 0.797997i | \(-0.294107\pi\) |
−0.992416 | + | 0.122922i | \(0.960773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.73897 | − | 4.74403i | 0.0891930 | − | 0.154487i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2967 | − | 26.4947i | −0.496552 | − | 0.860053i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.58638 | 0.310533 | 0.155267 | − | 0.987873i | \(-0.450376\pi\) | ||||
0.155267 | + | 0.987873i | \(0.450376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.21110 | − | 12.4900i | −0.233346 | − | 0.404167i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.65564 | − | 21.7046i | 0.214922 | − | 0.700877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.1245 | + | 29.6605i | −0.552404 | + | 0.956791i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.7564 | 1.69829 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6525 | −0.503350 | −0.251675 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251675 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8590 | + | 39.5929i | −0.733579 | + | 1.27060i | 0.221765 | + | 0.975100i | \(0.428818\pi\) |
−0.955344 | + | 0.295495i | \(0.904515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.64105 | − | 9.28198i | −0.277019 | − | 0.297566i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.7302 | − | 41.1018i | −0.759195 | − | 1.31496i | −0.943262 | − | 0.332051i | \(-0.892259\pi\) |
0.184066 | − | 0.982914i | \(-0.441074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 79.4074 | 2.53787 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.5311 | + | 33.8289i | 0.622946 | + | 1.07897i | 0.988934 | + | 0.148355i | \(0.0473978\pi\) |
−0.365988 | + | 0.930620i | \(0.619269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.5934 | − | 40.8649i | 0.751748 | − | 1.30207i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.78739 | + | 6.55996i | −0.120432 | + | 0.208595i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1165 | − | 20.9864i | −0.384894 | − | 0.666656i | 0.606860 | − | 0.794809i | \(-0.292429\pi\) |
−0.991755 | + | 0.128152i | \(0.959095\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.1245 | 1.33544 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2344 | − | 19.4586i | −0.355798 | − | 0.616260i | 0.631456 | − | 0.775412i | \(-0.282458\pi\) |
−0.987254 | + | 0.159151i | \(0.949124\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2016.2.s.x.289.4 | yes | 8 | |
3.2 | odd | 2 | 2016.2.s.w.289.1 | ✓ | 8 | ||
4.3 | odd | 2 | 2016.2.s.w.289.4 | yes | 8 | ||
7.4 | even | 3 | inner | 2016.2.s.x.865.4 | yes | 8 | |
12.11 | even | 2 | inner | 2016.2.s.x.289.1 | yes | 8 | |
21.11 | odd | 6 | 2016.2.s.w.865.1 | yes | 8 | ||
28.11 | odd | 6 | 2016.2.s.w.865.4 | yes | 8 | ||
84.11 | even | 6 | inner | 2016.2.s.x.865.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.s.w.289.1 | ✓ | 8 | 3.2 | odd | 2 | ||
2016.2.s.w.289.4 | yes | 8 | 4.3 | odd | 2 | ||
2016.2.s.w.865.1 | yes | 8 | 21.11 | odd | 6 | ||
2016.2.s.w.865.4 | yes | 8 | 28.11 | odd | 6 | ||
2016.2.s.x.289.1 | yes | 8 | 12.11 | even | 2 | inner | |
2016.2.s.x.289.4 | yes | 8 | 1.1 | even | 1 | trivial | |
2016.2.s.x.865.1 | yes | 8 | 84.11 | even | 6 | inner | |
2016.2.s.x.865.4 | yes | 8 | 7.4 | even | 3 | inner |