Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.a.1889.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.73205i | − | 0.397360i | −0.980064 | − | 0.198680i | \(-0.936335\pi\) | ||
0.980064 | − | 0.198680i | \(-0.0636654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.19615i | − | 1.08347i | −0.840548 | − | 0.541736i | \(-0.817767\pi\) | ||
0.840548 | − | 0.541736i | \(-0.182233\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3923i | 1.92980i | 0.262613 | + | 0.964901i | \(0.415416\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.19615i | − | 0.933257i | −0.884454 | − | 0.466628i | \(-0.845469\pi\) | ||
0.884454 | − | 0.466628i | \(-0.154531\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00000 | + | 5.19615i | 1.01419 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.5885i | − | 2.10195i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.8564i | − | 1.77413i | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||
0.461644 | − | 0.887066i | \(-0.347260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.3923i | − | 1.28901i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.19615i | − | 0.616670i | −0.951278 | − | 0.308335i | \(-0.900228\pi\) | ||
0.951278 | − | 0.308335i | \(-0.0997717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.46410i | − | 0.405442i | −0.979236 | − | 0.202721i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | − | 10.3923i | 1.02565 | − | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0000 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.0000 | −1.95237 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 6.92820i | 0.628971 | − | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.19615i | 0.533114i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.92820i | − | 0.703452i | −0.936103 | − | 0.351726i | \(-0.885595\pi\) | ||
0.936103 | − | 0.351726i | \(-0.114405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025i | 0.853320i | 0.904412 | + | 0.426660i | \(0.140310\pi\) | ||||
−0.904412 | + | 0.426660i | \(0.859690\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.3923i | − | 1.00466i | −0.864675 | − | 0.502331i | \(-0.832476\pi\) | ||
0.864675 | − | 0.502331i | \(-0.167524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.5885i | 1.45363i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | − | 10.3923i | −1.10004 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 3.46410i | −0.260133 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923i | 0.887875i | 0.896058 | + | 0.443937i | \(0.146419\pi\) | ||||
−0.896058 | + | 0.443937i | \(0.853581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.3205i | − | 1.46911i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||
0.678551 | − | 0.734553i | \(-0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.0000 | −1.50524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 31.1769i | − | 2.58910i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.5885i | 1.25210i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.3923i | − | 0.829396i | −0.909959 | − | 0.414698i | \(-0.863887\pi\) | ||
0.909959 | − | 0.414698i | \(-0.136113\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | + | 10.3923i | −0.709299 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | − | 6.92820i | −0.604743 | − | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.1769i | 2.27988i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.19615i | − | 0.375980i | −0.982171 | − | 0.187990i | \(-0.939803\pi\) | ||
0.982171 | − | 0.187990i | \(-0.0601973\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.7846i | − | 1.48084i | −0.672143 | − | 0.740421i | \(-0.734626\pi\) | ||
0.672143 | − | 0.740421i | \(-0.265374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.73205i | 0.122782i | 0.998114 | + | 0.0613909i | \(0.0195536\pi\) | ||||
−0.998114 | + | 0.0613909i | \(0.980446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0000 | − | 20.7846i | 1.26335 | − | 1.45879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000 | 0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.0000 | 2.04598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | + | 10.3923i | −0.610960 | + | 0.705476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.7846i | 1.39812i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.9808i | − | 1.73980i | −0.493228 | − | 0.869900i | \(-0.664183\pi\) | ||
0.493228 | − | 0.869900i | \(-0.335817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.7846i | − | 1.37349i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||
0.726900 | − | 0.686743i | \(-0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.7846i | − | 1.36165i | −0.732448 | − | 0.680823i | \(-0.761622\pi\) | ||
0.732448 | − | 0.680823i | \(-0.238378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0000 | 1.17419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.46410i | − | 0.223142i | −0.993756 | − | 0.111571i | \(-0.964412\pi\) | ||
0.993756 | − | 0.111571i | \(-0.0355883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 20.7846i | −0.191663 | − | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | −0.561405 | −0.280702 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280702 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | − | 1.73205i | −0.124274 | − | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.19615i | − | 0.320408i | −0.987084 | − | 0.160204i | \(-0.948785\pi\) | ||
0.987084 | − | 0.160204i | \(-0.0512153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.0000 | 1.28039 | 0.640196 | − | 0.768211i | \(-0.278853\pi\) | ||||
0.640196 | + | 0.768211i | \(0.278853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.46410i | − | 0.210429i | −0.994450 | − | 0.105215i | \(-0.966447\pi\) | ||
0.994450 | − | 0.105215i | \(-0.0335529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.7846i | 1.25336i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.0000 | −1.14160 | −0.570800 | − | 0.821089i | \(-0.693367\pi\) | ||||
−0.570800 | + | 0.821089i | \(0.693367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.3923i | − | 0.619953i | −0.950744 | − | 0.309976i | \(-0.899679\pi\) | ||
0.950744 | − | 0.309976i | \(-0.100321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3923i | 0.617758i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) | ||||
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | − | 5.19615i | −0.354169 | − | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.0000 | −1.04800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0000 | 1.04097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | + | 17.3205i | 1.15278 | + | 0.998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.5692i | 2.38025i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.5885i | − | 0.889680i | −0.895610 | − | 0.444840i | \(-0.853260\pi\) | ||
0.895610 | − | 0.444840i | \(-0.146740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46410i | 0.195803i | 0.995196 | + | 0.0979013i | \(0.0312129\pi\) | ||||
−0.995196 | + | 0.0979013i | \(0.968787\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.1769i | 1.75107i | 0.483155 | + | 0.875535i | \(0.339491\pi\) | ||||
−0.483155 | + | 0.875535i | \(0.660509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −54.0000 | −3.02342 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.3923i | − | 0.578243i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8564i | 0.768615i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 10.3923i | 0.661581 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.00000 | 0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.0000 | −1.57973 | −0.789865 | − | 0.613280i | \(-0.789850\pi\) | ||||
−0.789865 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.0000 | 1.46213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.19615i | 0.278944i | 0.990226 | + | 0.139472i | \(0.0445405\pi\) | ||||
−0.990226 | + | 0.139472i | \(0.955459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7128i | 1.48343i | 0.670714 | + | 0.741716i | \(0.265988\pi\) | ||||
−0.670714 | + | 0.741716i | \(0.734012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | 0.798369 | 0.399185 | − | 0.916871i | \(-0.369293\pi\) | ||||
0.399185 | + | 0.916871i | \(0.369293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5885i | 0.827349i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3923i | 0.548485i | 0.961661 | + | 0.274242i | \(0.0884271\pi\) | ||||
−0.961661 | + | 0.274242i | \(0.911573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3923i | 0.543958i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73205i | 0.0904123i | 0.998978 | + | 0.0452062i | \(0.0143945\pi\) | ||||
−0.998978 | + | 0.0452062i | \(0.985606\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0000 | 1.50156 | 0.750782 | − | 0.660551i | \(-0.229677\pi\) | ||||
0.750782 | + | 0.660551i | \(0.229677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.0000 | −1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.0000 | + | 31.1769i | −1.37605 | + | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 20.7846i | − | 1.05382i | −0.849921 | − | 0.526911i | \(-0.823350\pi\) | ||
0.849921 | − | 0.526911i | \(-0.176650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 31.1769i | − | 1.57668i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 42.0000 | 2.11325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.7846i | − | 1.04315i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.3923i | − | 0.518967i | −0.965748 | − | 0.259483i | \(-0.916448\pi\) | ||
0.965748 | − | 0.259483i | \(-0.0835523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | 0.896644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.19615i | 0.257564i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3205i | 0.856444i | 0.903674 | + | 0.428222i | \(0.140860\pi\) | ||||
−0.903674 | + | 0.428222i | \(0.859140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | − | 10.3923i | −0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | −0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | 0.243685 | 0.121843 | − | 0.992549i | \(-0.461120\pi\) | ||||
0.121843 | + | 0.992549i | \(0.461120\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.0000 | 1.16417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.0000 | + | 27.7128i | −1.16144 | + | 1.34112i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.3731i | 1.75203i | 0.482285 | + | 0.876014i | \(0.339807\pi\) | ||||
−0.482285 | + | 0.876014i | \(0.660193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.00000 | −0.430528 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.1769i | − | 1.48799i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||
0.668184 | − | 0.743996i | \(-0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.5885i | − | 0.740630i | −0.928906 | − | 0.370315i | \(-0.879250\pi\) | ||
0.928906 | − | 0.370315i | \(-0.120750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.0000 | 1.27992 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7846i | 0.980886i | 0.871473 | + | 0.490443i | \(0.163165\pi\) | ||||
−0.871473 | + | 0.490443i | \(0.836835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.5885i | 0.734032i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.0000 | + | 20.7846i | −0.843853 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | −0.795226 | −0.397613 | − | 0.917553i | \(-0.630161\pi\) | ||||
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | −0.698620 | −0.349310 | − | 0.937007i | \(-0.613584\pi\) | ||||
−0.349310 | + | 0.937007i | \(0.613584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0000 | −0.832941 | −0.416470 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416470 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | + | 3.46410i | 0.184703 | + | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 51.9615i | − | 2.38919i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.92820i | − | 0.317888i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.46410i | 0.157949i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.7846i | 0.943781i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.0000 | 1.17817 | 0.589086 | − | 0.808070i | \(-0.299488\pi\) | ||||
0.589086 | + | 0.808070i | \(0.299488\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.5885i | − | 0.703497i | −0.936094 | − | 0.351749i | \(-0.885587\pi\) | ||
0.936094 | − | 0.351749i | \(-0.114413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 62.3538i | 2.80828i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.00000 | + | 10.3923i | −0.403705 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.0000 | 2.40297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.0000 | −1.86162 | −0.930809 | − | 0.365507i | \(-0.880896\pi\) | ||||
−0.930809 | + | 0.365507i | \(0.880896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 6.92820i | −0.265424 | + | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 25.9808i | − | 1.14485i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 31.1769i | − | 1.37116i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0000 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1244i | 0.530161i | 0.964226 | + | 0.265081i | \(0.0853985\pi\) | ||||
−0.964226 | + | 0.265081i | \(0.914601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 31.1769i | − | 1.35809i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3923i | 0.450141i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.1769i | 1.34790i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.0000 | + | 5.19615i | −1.55063 | + | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.0000 | 1.41356 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000 | 1.71028 | 0.855138 | − | 0.518400i | \(-0.173472\pi\) | ||||
0.855138 | + | 0.518400i | \(0.173472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.0000 | 0.766826 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | + | 24.2487i | 1.19068 | + | 1.03116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.7846i | − | 0.880672i | −0.897833 | − | 0.440336i | \(-0.854859\pi\) | ||
0.897833 | − | 0.440336i | \(-0.145141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.6410i | − | 1.46516i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 41.5692i | − | 1.74267i | −0.490687 | − | 0.871336i | \(-0.663254\pi\) | ||
0.490687 | − | 0.871336i | \(-0.336746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 20.7846i | − | 0.866778i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | \(-0.743654\pi\) | ||
0.692870 | − | 0.721062i | \(-0.256346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | − | 10.3923i | −0.497844 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.0000 | −1.48588 | −0.742940 | − | 0.669359i | \(-0.766569\pi\) | ||||
−0.742940 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.0000 | 1.60154 | 0.800769 | − | 0.598973i | \(-0.204424\pi\) | ||||
0.800769 | + | 0.598973i | \(0.204424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.0000 | + | 31.1769i | 1.47586 | + | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.9808i | − | 1.06155i | −0.847514 | − | 0.530773i | \(-0.821902\pi\) | ||
0.847514 | − | 0.530773i | \(-0.178098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.3923i | − | 0.423911i | −0.977279 | − | 0.211955i | \(-0.932017\pi\) | ||
0.977279 | − | 0.211955i | \(-0.0679832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 48.0000 | 1.95148 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3205i | 0.703018i | 0.936185 | + | 0.351509i | \(0.114331\pi\) | ||||
−0.936185 | + | 0.351509i | \(0.885669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 20.7846i | − | 0.840855i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | −0.767403 | −0.383701 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383701 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1769i | 1.25514i | 0.778562 | + | 0.627568i | \(0.215949\pi\) | ||||
−0.778562 | + | 0.627568i | \(0.784051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9090i | 1.32272i | 0.750067 | + | 0.661361i | \(0.230021\pi\) | ||||
−0.750067 | + | 0.661361i | \(0.769979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | + | 15.5885i | 0.721155 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0000 | −1.03504 | −0.517522 | − | 0.855670i | \(-0.673145\pi\) | ||||
−0.517522 | + | 0.855670i | \(0.673145\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.00000 | 0.238103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0000 | + | 3.46410i | −0.950915 | + | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.7846i | − | 0.820943i | −0.911873 | − | 0.410471i | \(-0.865364\pi\) | ||
0.911873 | − | 0.410471i | \(-0.134636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.7654i | 1.84425i | 0.386897 | + | 0.922123i | \(0.373547\pi\) | ||||
−0.386897 | + | 0.922123i | \(0.626453\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0000 | −0.707653 | −0.353827 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353827 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.1769i | 1.22380i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3923i | 0.406682i | 0.979108 | + | 0.203341i | \(0.0651801\pi\) | ||||
−0.979108 | + | 0.203341i | \(0.934820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.0000 | 2.10995 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.3731i | − | 1.41689i | −0.705764 | − | 0.708447i | \(-0.749396\pi\) | ||
0.705764 | − | 0.708447i | \(-0.250604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.2487i | 0.943166i | 0.881822 | + | 0.471583i | \(0.156317\pi\) | ||||
−0.881822 | + | 0.471583i | \(0.843683\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.00000 | − | 10.3923i | 0.349005 | − | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000 | 2.09089 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 72.0000 | 2.77953 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.0000 | −1.03769 | −0.518847 | − | 0.854867i | \(-0.673639\pi\) | ||||
−0.518847 | + | 0.854867i | \(0.673639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 13.8564i | −0.460518 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.5885i | − | 0.596476i | −0.954492 | − | 0.298238i | \(-0.903601\pi\) | ||
0.954492 | − | 0.298238i | \(-0.0963989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.1769i | − | 1.19121i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.3923i | 0.395342i | 0.980268 | + | 0.197671i | \(0.0633378\pi\) | ||||
−0.980268 | + | 0.197671i | \(0.936662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 51.9615i | 1.97101i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | 0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.1769i | − | 1.17754i | −0.808302 | − | 0.588768i | \(-0.799613\pi\) | ||
0.808302 | − | 0.588768i | \(-0.200387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.73205i | − | 0.0653255i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.0000 | + | 31.1769i | 1.35392 | + | 1.17253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0000 | −0.863783 | −0.431892 | − | 0.901926i | \(-0.642154\pi\) | ||||
−0.431892 | + | 0.901926i | \(0.642154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.0000 | −1.01116 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 54.0000 | 2.01949 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | − | 17.3205i | 0.558629 | − | 0.645049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.5692i | 1.54384i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1769i | 1.15629i | 0.815935 | + | 0.578144i | \(0.196223\pi\) | ||||
−0.815935 | + | 0.578144i | \(0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.0000 | −2.21918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3923i | 0.383849i | 0.981410 | + | 0.191924i | \(0.0614728\pi\) | ||||
−0.981410 | + | 0.191924i | \(0.938527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.3923i | − | 0.382805i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0000 | 0.588570 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.3731i | 1.33440i | 0.744879 | + | 0.667199i | \(0.232507\pi\) | ||||
−0.744879 | + | 0.667199i | \(0.767493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 20.7846i | −0.657706 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | 0.0729810 | 0.0364905 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364905 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0000 | + | 19.0526i | 0.796453 | + | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7846i | 0.750489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.46410i | − | 0.124919i | −0.998048 | − | 0.0624593i | \(-0.980106\pi\) | ||
0.998048 | − | 0.0624593i | \(-0.0198944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.0000 | −1.40273 | −0.701366 | − | 0.712801i | \(-0.747426\pi\) | ||||
−0.701366 | + | 0.712801i | \(0.747426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20.7846i | − | 0.746605i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.19615i | − | 0.186171i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | 0.966136 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.1769i | 1.11275i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.1051i | 1.35830i | 0.733999 | + | 0.679150i | \(0.237652\pi\) | ||||
−0.733999 | + | 0.679150i | \(0.762348\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.0000 | 1.59398 | 0.796991 | − | 0.603991i | \(-0.206424\pi\) | ||||
0.796991 | + | 0.603991i | \(0.206424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.0000 | −1.27359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0000 | 0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.0000 | − | 31.1769i | 0.951625 | − | 1.09884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.1769i | − | 1.09612i | −0.836438 | − | 0.548061i | \(-0.815366\pi\) | ||
0.836438 | − | 0.548061i | \(-0.184634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.19615i | 0.182462i | 0.995830 | + | 0.0912308i | \(0.0290801\pi\) | ||||
−0.995830 | + | 0.0912308i | \(0.970920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.0000 | −1.05085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3205i | 0.605968i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1769i | 1.08808i | 0.839059 | + | 0.544041i | \(0.183106\pi\) | ||||
−0.839059 | + | 0.544041i | \(0.816894\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.7654i | 1.62619i | 0.582130 | + | 0.813096i | \(0.302219\pi\) | ||||
−0.582130 | + | 0.813096i | \(0.697781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0333i | 1.56407i | 0.623233 | + | 0.782036i | \(0.285819\pi\) | ||||
−0.623233 | + | 0.782036i | \(0.714181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000 | + | 41.5692i | 0.207888 | + | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | −1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.0000 | −1.45000 | −0.725001 | − | 0.688748i | \(-0.758161\pi\) | ||||
−0.725001 | + | 0.688748i | \(0.758161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −79.0000 | −2.72414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.0000 | + | 27.7128i | 1.09953 | + | 0.952224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.19615i | − | 0.178122i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 48.4974i | − | 1.66052i | −0.557376 | − | 0.830260i | \(-0.688192\pi\) | ||
0.557376 | − | 0.830260i | \(-0.311808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | −0.717346 | −0.358673 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358673 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 29.4449i | − | 1.00465i | −0.864680 | − | 0.502323i | \(-0.832479\pi\) | ||
0.864680 | − | 0.502323i | \(-0.167521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.3923i | 0.353758i | 0.984233 | + | 0.176879i | \(0.0566002\pi\) | ||||
−0.984233 | + | 0.176879i | \(0.943400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0000 | −0.918028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 72.7461i | − | 2.46774i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.92820i | − | 0.234753i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.00000 | − | 5.19615i | −0.202837 | − | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000 | 0.0675352 | 0.0337676 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337676 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.0000 | −1.41022 | −0.705111 | − | 0.709097i | \(-0.749103\pi\) | ||||
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 3.46410i | 0.134156 | + | 0.116182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3923i | 0.347765i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.1769i | − | 1.04213i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54.0000 | 1.80100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7846i | 0.690904i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0000 | 1.06254 | 0.531271 | − | 0.847202i | \(-0.321714\pi\) | ||||
0.531271 | + | 0.847202i | \(0.321714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.3923i | − | 0.344312i | −0.985070 | − | 0.172156i | \(-0.944927\pi\) | ||
0.985070 | − | 0.172156i | \(-0.0550734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.1769i | 1.03181i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.0000 | + | 31.1769i | 1.18882 | + | 1.02955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | − | 1.73205i | 0.393284 | − | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 93.5307i | − | 3.05878i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 55.4256i | − | 1.81068i | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||
0.424691 | − | 0.905338i | \(-0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | 0.684580 | 0.342290 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342290 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.5885i | − | 0.507630i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.9808i | 0.844261i | 0.906535 | + | 0.422131i | \(0.138718\pi\) | ||||
−0.906535 | + | 0.422131i | \(0.861282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1769i | 1.00992i | 0.863143 | + | 0.504960i | \(0.168493\pi\) | ||||
−0.863143 | + | 0.504960i | \(0.831507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.5885i | 0.504431i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0000 | − | 20.7846i | 0.581250 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00000 | 0.129032 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.00000 | 0.193147 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | 0.192549 | 0.0962746 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962746 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.0000 | + | 34.6410i | −0.961756 | + | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 41.5692i | − | 1.32992i | −0.746880 | − | 0.664959i | \(-0.768449\pi\) | ||
0.746880 | − | 0.664959i | \(-0.231551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 46.7654i | − | 1.49463i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.0000 | 1.33959 | 0.669796 | − | 0.742545i | \(-0.266382\pi\) | ||||
0.669796 | + | 0.742545i | \(0.266382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 62.3538i | 1.98676i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.9615i | 1.65228i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | −0.317660 | −0.158830 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158830 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.19615i | − | 0.164729i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 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 | 3024.2.k.a.1889.1 | 2 | ||
3.2 | odd | 2 | 3024.2.k.d.1889.1 | 2 | |||
4.3 | odd | 2 | 756.2.f.a.377.2 | yes | 2 | ||
7.6 | odd | 2 | 3024.2.k.d.1889.2 | 2 | |||
12.11 | even | 2 | 756.2.f.c.377.2 | yes | 2 | ||
21.20 | even | 2 | inner | 3024.2.k.a.1889.2 | 2 | ||
28.27 | even | 2 | 756.2.f.c.377.1 | yes | 2 | ||
36.7 | odd | 6 | 2268.2.x.h.377.1 | 2 | |||
36.11 | even | 6 | 2268.2.x.b.377.1 | 2 | |||
36.23 | even | 6 | 2268.2.x.a.1889.1 | 2 | |||
36.31 | odd | 6 | 2268.2.x.g.1889.1 | 2 | |||
84.83 | odd | 2 | 756.2.f.a.377.1 | ✓ | 2 | ||
252.83 | odd | 6 | 2268.2.x.g.377.1 | 2 | |||
252.139 | even | 6 | 2268.2.x.b.1889.1 | 2 | |||
252.167 | odd | 6 | 2268.2.x.h.1889.1 | 2 | |||
252.223 | even | 6 | 2268.2.x.a.377.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.f.a.377.1 | ✓ | 2 | 84.83 | odd | 2 | ||
756.2.f.a.377.2 | yes | 2 | 4.3 | odd | 2 | ||
756.2.f.c.377.1 | yes | 2 | 28.27 | even | 2 | ||
756.2.f.c.377.2 | yes | 2 | 12.11 | even | 2 | ||
2268.2.x.a.377.1 | 2 | 252.223 | even | 6 | |||
2268.2.x.a.1889.1 | 2 | 36.23 | even | 6 | |||
2268.2.x.b.377.1 | 2 | 36.11 | even | 6 | |||
2268.2.x.b.1889.1 | 2 | 252.139 | even | 6 | |||
2268.2.x.g.377.1 | 2 | 252.83 | odd | 6 | |||
2268.2.x.g.1889.1 | 2 | 36.31 | odd | 6 | |||
2268.2.x.h.377.1 | 2 | 36.7 | odd | 6 | |||
2268.2.x.h.1889.1 | 2 | 252.167 | odd | 6 | |||
3024.2.k.a.1889.1 | 2 | 1.1 | even | 1 | trivial | ||
3024.2.k.a.1889.2 | 2 | 21.20 | even | 2 | inner | ||
3024.2.k.d.1889.1 | 2 | 3.2 | odd | 2 | |||
3024.2.k.d.1889.2 | 2 | 7.6 | odd | 2 |