Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(31,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.bb (of order \(6\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.31 |
Dual form | 1344.2.bb.a.607.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | + | 4.50000i | −0.783349 | + | 1.35680i | 0.146631 | + | 0.989191i | \(0.453157\pi\) |
−0.929980 | + | 0.367610i | \(0.880176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.00000i | − | 0.774597i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.92820 | + | 4.00000i | −1.58944 | + | 0.917663i | −0.596040 | + | 0.802955i | \(0.703260\pi\) |
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19615 | − | 3.00000i | 1.08347 | − | 0.625543i | 0.151642 | − | 0.988436i | \(-0.451544\pi\) |
0.931831 | + | 0.362892i | \(0.118211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.19615i | − | 0.964901i | −0.875923 | − | 0.482451i | \(-0.839747\pi\) | ||
0.875923 | − | 0.482451i | \(-0.160253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.33013 | + | 7.50000i | −0.777714 | + | 1.34704i | 0.155543 | + | 0.987829i | \(0.450287\pi\) |
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | + | 2.59808i | −0.783349 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.19615 | − | 6.00000i | 0.878310 | − | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | + | 3.46410i | −0.986394 | + | 0.569495i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73205 | + | 1.00000i | 0.277350 | + | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 1.62301i | 0.584349 | + | 0.811503i | \(0.301350\pi\) | ||||
−0.584349 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.50000 | − | 2.59808i | 0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.50000 | − | 2.59808i | −0.618123 | − | 0.356873i | 0.158015 | − | 0.987437i | \(-0.449491\pi\) |
−0.776138 | + | 0.630563i | \(0.782824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.5885 | 2.10195 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.79423 | + | 4.50000i | 1.01472 | + | 0.585850i | 0.912571 | − | 0.408919i | \(-0.134094\pi\) |
0.102151 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | + | 2.00000i | −0.218218 | + | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | + | 3.00000i | −0.211604 | + | 0.366508i | −0.952217 | − | 0.305424i | \(-0.901202\pi\) |
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000 | + | 6.92820i | 1.40449 | + | 0.810885i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.46410 | + | 2.00000i | −0.400000 | + | 0.230940i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.5000 | − | 2.59808i | −1.53847 | − | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.33013 | − | 2.50000i | 0.487177 | − | 0.281272i | −0.236225 | − | 0.971698i | \(-0.575910\pi\) |
0.723403 | + | 0.690426i | \(0.242577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.00000i | − | 0.987878i | −0.869496 | − | 0.493939i | \(-0.835557\pi\) | ||
0.869496 | − | 0.493939i | \(-0.164443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59808 | − | 4.50000i | 0.278543 | − | 0.482451i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.73205 | + | 5.00000i | 0.181568 | + | 0.524142i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.50000 | + | 4.33013i | −0.777714 | + | 0.449013i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.7846 | + | 12.0000i | 2.13246 | + | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.19615i | 0.527589i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) | ||||
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.19615 | −0.522233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | − | 3.00000i | −0.170664 | − | 0.295599i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.50000 | − | 2.59808i | 0.731925 | − | 0.253546i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.59808 | − | 4.50000i | −0.251166 | − | 0.435031i | 0.712681 | − | 0.701488i | \(-0.247481\pi\) |
−0.963847 | + | 0.266456i | \(0.914147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | + | 1.73205i | 0.287348 | + | 0.165900i | 0.636745 | − | 0.771074i | \(-0.280280\pi\) |
−0.349397 | + | 0.936975i | \(0.613614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92820 | −0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.5885 | − | 9.00000i | −1.45363 | − | 0.839254i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | + | 1.73205i | 0.0924500 | + | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | − | 13.8564i | −0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.19615 | + | 9.00000i | −0.468521 | + | 0.811503i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0000i | − | 1.50851i | −0.656584 | − | 0.754253i | \(-0.727999\pi\) | ||
0.656584 | − | 0.754253i | \(-0.272001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | + | 1.73205i | 0.264135 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59808 | + | 1.50000i | −0.226995 | + | 0.131056i | −0.609185 | − | 0.793028i | \(-0.708503\pi\) |
0.382190 | + | 0.924084i | \(0.375170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.0000 | − | 13.8564i | −1.38738 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.59808 | − | 1.50000i | 0.223607 | − | 0.129099i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000i | 1.69638i | 0.529694 | + | 0.848189i | \(0.322307\pi\) | ||||
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.19615 | + | 9.00000i | −0.434524 | + | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5000 | + | 7.79423i | −1.12111 | + | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.92820 | + | 1.00000i | −0.571429 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7224 | − | 8.50000i | −1.19809 | − | 0.691720i | −0.237964 | − | 0.971274i | \(-0.576480\pi\) |
−0.960130 | + | 0.279554i | \(0.909814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.9808 | 2.08683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.59808 | − | 4.50000i | −0.206041 | − | 0.356873i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | + | 10.3923i | 0.945732 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.19615 | − | 9.00000i | −0.406994 | − | 0.704934i | 0.587557 | − | 0.809183i | \(-0.300090\pi\) |
−0.994551 | + | 0.104248i | \(0.966756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.5000 | + | 7.79423i | 1.05097 | + | 0.606780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.3923 | −0.804181 | −0.402090 | − | 0.915600i | \(-0.631716\pi\) | ||||
−0.402090 | + | 0.915600i | \(0.631716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.92820 | − | 4.00000i | −0.529813 | − | 0.305888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.3923 | − | 2.00000i | −0.785584 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50000 | + | 7.79423i | 0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.19615 | − | 9.00000i | 0.388379 | − | 0.672692i | −0.603853 | − | 0.797096i | \(-0.706369\pi\) |
0.992232 | + | 0.124404i | \(0.0397019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.0000 | + | 10.3923i | 1.32339 | + | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | + | 0.866025i | −0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3923 | − | 6.00000i | 0.751961 | − | 0.434145i | −0.0744412 | − | 0.997225i | \(-0.523717\pi\) |
0.826402 | + | 0.563081i | \(0.190384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | − | 9.52628i | 0.395899 | − | 0.685717i | −0.597317 | − | 0.802005i | \(-0.703766\pi\) |
0.993215 | + | 0.116289i | \(0.0370998\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.00000i | − | 0.429669i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.19615 | + | 9.00000i | −0.368345 | + | 0.637993i | −0.989307 | − | 0.145848i | \(-0.953409\pi\) |
0.620962 | + | 0.783841i | \(0.286742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | + | 1.73205i | −0.211604 | + | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9904 | − | 4.50000i | 0.911746 | − | 0.315838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.0000 | − | 15.5885i | 1.88576 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.19615 | + | 3.00000i | 0.361158 | + | 0.208514i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 41.5692i | − | 2.87540i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7846 | 1.43087 | 0.715436 | − | 0.698679i | \(-0.246228\pi\) | ||||
0.715436 | + | 0.698679i | \(0.246228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | + | 10.3923i | −0.411113 | + | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.19615 | − | 9.00000i | −0.354375 | − | 0.613795i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.5000 | − | 4.33013i | −1.52740 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.92820 | + | 12.0000i | 0.468165 | + | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.19615 | 0.347960 | 0.173980 | − | 0.984749i | \(-0.444337\pi\) | ||||
0.173980 | + | 0.984749i | \(0.444337\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.59808 | − | 1.50000i | −0.172440 | − | 0.0995585i | 0.411296 | − | 0.911502i | \(-0.365076\pi\) |
−0.583736 | + | 0.811943i | \(0.698410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3923 | − | 9.00000i | −0.683763 | − | 0.592157i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | + | 20.7846i | 0.786146 | + | 1.36165i | 0.928312 | + | 0.371802i | \(0.121260\pi\) |
−0.142166 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.00000 | 0.324785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | + | 2.59808i | 0.289870 | + | 0.167357i | 0.637883 | − | 0.770133i | \(-0.279810\pi\) |
−0.348013 | + | 0.937490i | \(0.613143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.5000 | + | 7.79423i | 1.24581 | + | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8564 | + | 8.00000i | −0.881662 | + | 0.509028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.50000 | − | 7.79423i | 0.285176 | − | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00000i | 0.189358i | 0.995508 | + | 0.0946792i | \(0.0301825\pi\) | ||||
−0.995508 | + | 0.0946792i | \(0.969817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.1769i | 1.96008i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | − | 10.3923i | 1.12281 | − | 0.648254i | 0.180693 | − | 0.983540i | \(-0.442166\pi\) |
0.942117 | + | 0.335285i | \(0.108833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.8564 | − | 12.0000i | −0.860995 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | − | 2.59808i | 0.278543 | − | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.19615 | + | 3.00000i | 0.320408 | + | 0.184988i | 0.651575 | − | 0.758585i | \(-0.274109\pi\) |
−0.331166 | + | 0.943572i | \(0.607442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.5885i | 0.957591i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.50000 | + | 12.9904i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486418i | \(-0.984511\pi\) |
0.541533 | + | 0.840679i | \(0.317844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.79423 | − | 13.5000i | −0.473466 | − | 0.820067i | 0.526073 | − | 0.850439i | \(-0.323664\pi\) |
−0.999539 | + | 0.0303728i | \(0.990331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.00000 | + | 5.19615i | −0.0605228 | + | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.3923 | − | 18.0000i | −0.626680 | − | 1.08544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0000 | + | 13.8564i | 1.44202 | + | 0.832551i | 0.997984 | − | 0.0634583i | \(-0.0202130\pi\) |
0.444036 | + | 0.896009i | \(0.353546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.66025 | −0.518476 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.0000 | −1.78965 | −0.894825 | − | 0.446417i | \(-0.852700\pi\) | ||||
−0.894825 | + | 0.446417i | \(0.852700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.73205 | + | 1.00000i | 0.102960 | + | 0.0594438i | 0.550596 | − | 0.834772i | \(-0.314401\pi\) |
−0.447636 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | + | 20.7846i | 0.710819 | + | 1.23117i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.9808 | + | 9.00000i | −1.53360 | + | 0.531253i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.50000 | − | 14.7224i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.59808 | + | 4.50000i | −0.152302 | + | 0.263795i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.00000 | −0.175262 | −0.0876309 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876309 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 27.0000i | − | 1.57200i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50000 | − | 2.59808i | −0.261116 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3923 | − | 6.00000i | 0.601003 | − | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | + | 8.66025i | 0.172917 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.19615 | − | 3.00000i | 0.298511 | − | 0.172345i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | − | 20.7846i | 0.687118 | − | 1.19012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.0000i | − | 0.570730i | −0.958419 | − | 0.285365i | \(-0.907885\pi\) | ||
0.958419 | − | 0.285365i | \(-0.0921148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.46410i | − | 0.197066i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5885 | + | 27.0000i | −0.883940 | + | 1.53103i | −0.0370169 | + | 0.999315i | \(0.511786\pi\) |
−0.846923 | + | 0.531715i | \(0.821548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5000 | − | 14.7224i | 1.44135 | − | 0.832161i | 0.443406 | − | 0.896321i | \(-0.353770\pi\) |
0.997940 | + | 0.0641600i | \(0.0204368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.79423 | + | 1.50000i | 0.439155 | + | 0.0845154i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5000 | − | 12.9904i | 1.26373 | − | 0.729612i | 0.289933 | − | 0.957047i | \(-0.406367\pi\) |
0.973793 | + | 0.227435i | \(0.0730338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.3827 | + | 13.5000i | 1.30918 | + | 0.755855i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.19615i | − | 0.290021i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | + | 6.92820i | −0.221880 | + | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.73205 | + | 3.00000i | 0.0957826 | + | 0.165900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8564 | + | 24.0000i | 0.761617 | + | 1.31916i | 0.942017 | + | 0.335566i | \(0.108928\pi\) |
−0.180400 | + | 0.983593i | \(0.557739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | − | 3.46410i | −0.328798 | − | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3923 | 0.567792 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0000 | 1.36184 | 0.680918 | − | 0.732359i | \(-0.261581\pi\) | ||||
0.680918 | + | 0.732359i | \(0.261581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.19615 | − | 3.00000i | −0.282216 | − | 0.162938i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.5000 | − | 38.9711i | −1.21844 | − | 2.11041i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.00000 | − | 15.5885i | −0.484544 | − | 0.839254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.19615 | + | 9.00000i | −0.278944 | + | 0.483145i | −0.971123 | − | 0.238581i | \(-0.923318\pi\) |
0.692179 | + | 0.721726i | \(0.256651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000i | 0.106752i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.1769 | − | 18.0000i | 1.65470 | − | 0.955341i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.19615 | − | 3.00000i | 0.274242 | − | 0.158334i | −0.356572 | − | 0.934268i | \(-0.616054\pi\) |
0.630814 | + | 0.775934i | \(0.282721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5000 | − | 38.9711i | 1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 16.0000i | − | 0.839782i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 41.5692i | − | 2.17583i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.33013 | + | 7.50000i | −0.226031 | + | 0.391497i | −0.956628 | − | 0.291312i | \(-0.905908\pi\) |
0.730597 | + | 0.682808i | \(0.239242\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | + | 5.19615i | −0.468521 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.59808 | − | 13.5000i | 0.134885 | − | 0.700885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0000 | + | 8.66025i | −0.776671 | + | 0.448411i | −0.835249 | − | 0.549872i | \(-0.814677\pi\) |
0.0585785 | + | 0.998283i | \(0.481343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.59808 | − | 1.50000i | −0.134164 | − | 0.0774597i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10.3923i | − | 0.535231i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.2487 | −1.24557 | −0.622786 | − | 0.782392i | \(-0.713999\pi\) | ||||
−0.622786 | + | 0.782392i | \(0.713999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.50000 | − | 14.7224i | 0.435468 | − | 0.754253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3923 | − | 18.0000i | −0.531022 | − | 0.919757i | −0.999345 | − | 0.0361995i | \(-0.988475\pi\) |
0.468323 | − | 0.883558i | \(-0.344859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5000 | + | 38.9711i | 0.688024 | + | 1.98615i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73205 | + | 3.00000i | 0.0880451 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00000 | −0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9904 | − | 7.50000i | −0.653617 | − | 0.377366i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | − | 6.92820i | −0.200754 | − | 0.347717i | 0.748017 | − | 0.663679i | \(-0.231006\pi\) |
−0.948772 | + | 0.315963i | \(0.897673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | − | 20.0000i | −0.346844 | − | 1.00125i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.66025 | + | 15.0000i | −0.431398 | + | 0.747203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.00000 | 0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.0000i | − | 1.78445i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50000 | + | 0.866025i | 0.0741702 | + | 0.0428222i | 0.536626 | − | 0.843820i | \(-0.319698\pi\) |
−0.462456 | + | 0.886642i | \(0.653032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.5885 | − | 9.00000i | 0.768922 | − | 0.443937i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.50000 | + | 23.3827i | −0.221431 | + | 1.15059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.3827 | + | 13.5000i | −1.14781 | + | 0.662689i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | + | 17.3205i | −0.489702 | + | 0.848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 12.0000i | − | 0.586238i | −0.956076 | − | 0.293119i | \(-0.905307\pi\) | ||
0.956076 | − | 0.293119i | \(-0.0946933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 13.8564i | − | 0.675320i | −0.941268 | − | 0.337660i | \(-0.890365\pi\) | ||
0.941268 | − | 0.337660i | \(-0.109635\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8564 | + | 16.0000i | −0.670559 | + | 0.774294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.00000 | + | 5.19615i | −0.434524 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5885 | − | 9.00000i | −0.750870 | − | 0.433515i | 0.0751385 | − | 0.997173i | \(-0.476060\pi\) |
−0.826008 | + | 0.563658i | \(0.809393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.92820i | 0.332948i | 0.986046 | + | 0.166474i | \(0.0532382\pi\) | ||||
−0.986046 | + | 0.166474i | \(0.946762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.5885 | −0.747409 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.0000 | + | 41.5692i | −1.14808 | + | 1.98853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.79423 | + | 13.5000i | 0.371998 | + | 0.644320i | 0.989873 | − | 0.141957i | \(-0.0453394\pi\) |
−0.617875 | + | 0.786277i | \(0.712006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.1865 | + | 31.5000i | 0.864068 | + | 1.49661i | 0.867969 | + | 0.496618i | \(0.165425\pi\) |
−0.00390106 | + | 0.999992i | \(0.501242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −46.7654 | − | 27.0000i | −2.20210 | − | 1.27138i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.50000 | − | 14.7224i | −0.399365 | − | 0.691720i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.3923 | − | 12.0000i | 0.487199 | − | 0.562569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | − | 19.9186i | −0.537947 | − | 0.931752i | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.0000i | − | 0.929479i | −0.885448 | − | 0.464739i | \(-0.846148\pi\) | ||
0.885448 | − | 0.464739i | \(-0.153852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.5000 | + | 12.9904i | 1.04341 | + | 0.602414i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.00000 | − | 1.73205i | −0.415581 | − | 0.0799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.46410 | + | 2.00000i | −0.159617 | + | 0.0921551i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | + | 15.5885i | −0.413820 | + | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 32.0000i | − | 1.46826i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.19615i | − | 0.237915i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.19615 | − | 9.00000i | 0.237418 | − | 0.411220i | −0.722554 | − | 0.691314i | \(-0.757032\pi\) |
0.959973 | + | 0.280094i | \(0.0903655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | + | 6.92820i | −0.547153 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.19615 | + | 15.0000i | 0.236433 | + | 0.682524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.5000 | − | 7.79423i | 0.613003 | − | 0.353918i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0429 | + | 18.5000i | 1.45200 | + | 0.838315i | 0.998595 | − | 0.0529875i | \(-0.0168744\pi\) |
0.453409 | + | 0.891303i | \(0.350208\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10.3923i | − | 0.469956i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5885 | 0.703497 | 0.351749 | − | 0.936094i | \(-0.385587\pi\) | ||||
0.351749 | + | 0.936094i | \(0.385587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.79423 | + | 13.5000i | 0.350325 | + | 0.606780i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.0000 | + | 10.3923i | −1.34568 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8564 | + | 24.0000i | 0.620298 | + | 1.07439i | 0.989430 | + | 0.145011i | \(0.0463216\pi\) |
−0.369132 | + | 0.929377i | \(0.620345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | − | 5.19615i | −0.402090 | − | 0.232147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7846 | 0.926740 | 0.463370 | − | 0.886165i | \(-0.346640\pi\) | ||||
0.463370 | + | 0.886165i | \(0.346640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | − | 4.50000i | −0.346154 | − | 0.199852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5000 | + | 23.3827i | 0.598377 | + | 1.03642i | 0.993061 | + | 0.117602i | \(0.0375208\pi\) |
−0.394684 | + | 0.918817i | \(0.629146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.92820 | + | 36.0000i | −0.306486 | + | 1.59255i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | − | 6.92820i | −0.176604 | − | 0.305888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.19615 | + | 9.00000i | −0.228970 | + | 0.396587i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.0000i | − | 0.790112i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | + | 5.19615i | 0.394297 | + | 0.227648i | 0.684020 | − | 0.729463i | \(-0.260230\pi\) |
−0.289723 | + | 0.957110i | \(0.593563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.66025 | − | 5.00000i | 0.378686 | − | 0.218635i | −0.298560 | − | 0.954391i | \(-0.596506\pi\) |
0.677247 | + | 0.735756i | \(0.263173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.00000 | − | 6.92820i | −0.349149 | − | 0.302372i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.00000i | 0.390567i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.7846i | 0.900281i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.79423 | + | 13.5000i | −0.336974 | + | 0.583656i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.00000 | − | 5.19615i | 0.388379 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.19615 | − | 36.0000i | −0.223814 | − | 1.55063i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | + | 1.73205i | −0.128980 | + | 0.0744667i | −0.563102 | − | 0.826388i | \(-0.690392\pi\) |
0.434122 | + | 0.900854i | \(0.357059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.66025 | + | 5.00000i | 0.371647 | + | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 10.3923i | − | 0.445157i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7846 | + | 36.0000i | 0.885454 | + | 1.53365i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | + | 8.66025i | 0.425243 | + | 0.368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.3923 | + | 18.0000i | 0.441129 | + | 0.764057i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50000 | + | 2.59808i | 0.190671 | + | 0.110084i | 0.592297 | − | 0.805720i | \(-0.298221\pi\) |
−0.401626 | + | 0.915804i | \(0.631555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.92820 | 0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.1865 | + | 10.5000i | 0.766471 | + | 0.442522i | 0.831614 | − | 0.555354i | \(-0.187417\pi\) |
−0.0651433 | + | 0.997876i | \(0.520750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | + | 15.5885i | 0.378633 | + | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.59808 | − | 0.500000i | −0.109109 | − | 0.0209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000 | + | 31.1769i | 0.754599 | + | 1.30700i | 0.945573 | + | 0.325409i | \(0.105502\pi\) |
−0.190974 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46410 | − | 6.00000i | 0.144968 | − | 0.251092i | −0.784393 | − | 0.620264i | \(-0.787025\pi\) |
0.929361 | + | 0.369172i | \(0.120359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000i | 1.00087i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.50000 | + | 0.866025i | 0.0624458 | + | 0.0360531i | 0.530898 | − | 0.847436i | \(-0.321855\pi\) |
−0.468452 | + | 0.883489i | \(0.655188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52628 | − | 5.50000i | 0.395899 | − | 0.228572i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5000 | − | 7.79423i | 0.933457 | − | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.3827 | − | 13.5000i | 0.968412 | − | 0.559113i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 5.19615i | 0.124035 | − | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.0000i | 1.60970i | 0.593477 | + | 0.804851i | \(0.297755\pi\) | ||||
−0.593477 | + | 0.804851i | \(0.702245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 69.2820i | − | 2.85472i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.0000 | + | 15.5885i | −1.10876 | + | 0.640141i | −0.938507 | − | 0.345260i | \(-0.887791\pi\) |
−0.170250 | + | 0.985401i | \(0.554458\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.00000 | + | 5.19615i | −0.368345 | + | 0.212664i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5885 | + | 9.00000i | 0.636927 | + | 0.367730i | 0.783430 | − | 0.621480i | \(-0.213468\pi\) |
−0.146503 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73205i | 0.0706518i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) | ||||
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.46410 | −0.141069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.0000 | + | 41.5692i | −0.975739 | + | 1.69003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.33013 | + | 7.50000i | 0.175754 | + | 0.304416i | 0.940422 | − | 0.340009i | \(-0.110430\pi\) |
−0.764668 | + | 0.644425i | \(0.777097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.5000 | + | 2.59808i | 0.547048 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0000 | + | 15.5885i | 1.09052 | + | 0.629612i | 0.933715 | − | 0.358018i | \(-0.116547\pi\) |
0.156805 | + | 0.987630i | \(0.449881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.1769 | 1.25717 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6410 | + | 20.0000i | 1.39234 | + | 0.803868i | 0.993574 | − | 0.113185i | \(-0.0361052\pi\) |
0.398766 | + | 0.917053i | \(0.369439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.7846 | − | 36.0000i | 0.830057 | − | 1.43770i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000i | 0.278666i | 0.990246 | + | 0.139333i | \(0.0444958\pi\) | ||||
−0.990246 | + | 0.139333i | \(0.955504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0000 | + | 10.3923i | 0.715436 | + | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.1673 | + | 25.5000i | −1.75273 | + | 1.01194i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0000 | + | 8.66025i | −0.435836 | + | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.3923 | + | 6.00000i | −0.411113 | + | 0.237356i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | − | 20.7846i | 0.473972 | − | 0.820943i | −0.525584 | − | 0.850741i | \(-0.676153\pi\) |
0.999556 | + | 0.0297987i | \(0.00948663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.0000i | 1.34083i | 0.741987 | + | 0.670415i | \(0.233884\pi\) | ||||
−0.741987 | + | 0.670415i | \(0.766116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.3923i | − | 0.409197i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | + | 36.0000i | −0.817127 | + | 1.41531i | 0.0906629 | + | 0.995882i | \(0.471101\pi\) |
−0.907790 | + | 0.419424i | \(0.862232\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.5000 | + | 23.3827i | −1.58976 | + | 0.917851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3205 | − | 15.0000i | −0.678844 | − | 0.587896i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.5000 | − | 18.1865i | 1.23269 | − | 0.711694i | 0.265100 | − | 0.964221i | \(-0.414595\pi\) |
0.967590 | + | 0.252527i | \(0.0812616\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.79423 | + | 4.50000i | 0.304546 | + | 0.175830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.8564i | 0.540590i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1769 | −1.21448 | −0.607240 | − | 0.794518i | \(-0.707723\pi\) | ||||
−0.607240 | + | 0.794518i | \(0.707723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | − | 29.4449i | 0.661223 | − | 1.14527i | −0.319071 | − | 0.947731i | \(-0.603371\pi\) |
0.980294 | − | 0.197542i | \(-0.0632958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | + | 62.3538i | −0.465340 | + | 2.41798i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.5885 | − | 27.0000i | −0.603587 | − | 1.04544i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.50000 | + | 2.59808i | 0.173980 | + | 0.100447i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.5692 | −1.60476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.0000 | −1.19496 | −0.597481 | − | 0.801883i | \(-0.703832\pi\) | ||||
−0.597481 | + | 0.801883i | \(0.703832\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.46410 | − | 2.00000i | −0.133333 | − | 0.0769800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.5000 | − | 38.9711i | −0.864745 | − | 1.49778i | −0.867300 | − | 0.497786i | \(-0.834147\pi\) |
0.00255466 | − | 0.999997i | \(-0.499187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.9904 | + | 4.50000i | −0.498525 | + | 0.172694i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.50000 | − | 2.59808i | −0.0574801 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.9904 | + | 22.5000i | −0.497063 | + | 0.860939i | −0.999994 | − | 0.00338791i | \(-0.998922\pi\) |
0.502931 | + | 0.864326i | \(0.332255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.0000 | −2.06323 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | − | 5.19615i | −0.342873 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1244 | − | 7.00000i | 0.461232 | − | 0.266293i | −0.251330 | − | 0.967901i | \(-0.580868\pi\) |
0.712562 | + | 0.701609i | \(0.247535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.50000 | − | 12.9904i | −0.170941 | − | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 51.9615 | − | 30.0000i | 1.97101 | − | 1.13796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.0000i | 0.907763i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7654i | 1.76630i | 0.469087 | + | 0.883152i | \(0.344583\pi\) | ||||
−0.469087 | + | 0.883152i | \(0.655417\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.7128 | − | 48.0000i | 1.04521 | − | 1.81035i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.5885 | + | 3.00000i | 0.586264 | + | 0.112827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | + | 10.3923i | −0.676004 | + | 0.390291i | −0.798348 | − | 0.602197i | \(-0.794292\pi\) |
0.122344 | + | 0.992488i | \(0.460959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.33013 | + | 2.50000i | 0.162392 | + | 0.0937573i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.9615i | 1.94597i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.1769 | 1.16595 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.00000 | − | 5.19615i | 0.112037 | − | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.3923 | − | 18.0000i | −0.387568 | − | 0.671287i | 0.604554 | − | 0.796564i | \(-0.293351\pi\) |
−0.992122 | + | 0.125277i | \(0.960018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | − | 6.92820i | 0.223452 | − | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.59808 | + | 4.50000i | 0.0966235 | + | 0.167357i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.0000 | + | 10.3923i | 0.668503 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.66025 | 0.321191 | 0.160596 | − | 0.987020i | \(-0.448659\pi\) | ||||
0.160596 | + | 0.987020i | \(0.448659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.00000 | − | 1.73205i | −0.0369358 | − | 0.0639748i | 0.846967 | − | 0.531646i | \(-0.178426\pi\) |
−0.883902 | + | 0.467671i | \(0.845093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.9904 | + | 16.5000i | 0.479157 | + | 0.608612i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.00000 | − | 15.5885i | −0.331519 | − | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8564 | + | 24.0000i | −0.509716 | + | 0.882854i | 0.490221 | + | 0.871598i | \(0.336916\pi\) |
−0.999937 | + | 0.0112558i | \(0.996417\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.0000 | −0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.0000i | − | 0.660356i | −0.943919 | − | 0.330178i | \(-0.892891\pi\) | ||
0.943919 | − | 0.330178i | \(-0.107109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.79423 | − | 4.50000i | 0.285176 | − | 0.164646i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.00000 | − | 10.3923i | 0.328853 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.06218 | − | 3.50000i | 0.221212 | − | 0.127717i | −0.385299 | − | 0.922792i | \(-0.625902\pi\) |
0.606511 | + | 0.795075i | \(0.292568\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.50000 | + | 2.59808i | −0.0546630 | + | 0.0946792i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.0000i | 1.85608i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.5885 | + | 27.0000i | −0.565825 | + | 0.980038i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.0000 | − | 15.5885i | 0.978749 | − | 0.565081i | 0.0768569 | − | 0.997042i | \(-0.475512\pi\) |
0.901892 | + | 0.431961i | \(0.142178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.73205 | + | 9.00000i | −0.0627044 | + | 0.325822i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5885 | + | 9.00000i | 0.562867 | + | 0.324971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.73205i | − | 0.0624593i | −0.999512 | − | 0.0312297i | \(-0.990058\pi\) | ||
0.999512 | − | 0.0312297i | \(-0.00994233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.7846 | 0.748539 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3205 | − | 30.0000i | −0.622171 | − | 1.07763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.00000 | − | 17.3205i | −0.215249 | − | 0.621370i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.5692 | − | 72.0000i | −1.48937 | − | 2.57967i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | − | 31.1769i | −1.93227 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.19615 | 0.185695 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | 0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.46410 | + | 2.00000i | 0.123482 | + | 0.0712923i | 0.560469 | − | 0.828176i | \(-0.310621\pi\) |
−0.436987 | + | 0.899468i | \(0.643954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | + | 5.19615i | 0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.19615 | − | 15.0000i | −0.184754 | − | 0.533339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | + | 13.8564i | 0.284088 | + | 0.492055i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.79423 | + | 13.5000i | −0.276433 | + | 0.478796i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0000 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62.3538 | + | 36.0000i | −2.20042 | + | 1.27041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.00000 | − | 46.7654i | 0.317208 | − | 1.64826i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.9904 | + | 7.50000i | −0.457283 | + | 0.264013i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0000 | + | 31.1769i | −0.632846 | + | 1.09612i | 0.354121 | + | 0.935200i | \(0.384780\pi\) |
−0.986967 | + | 0.160922i | \(0.948553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.00000i | − | 0.0702295i | −0.999383 | − | 0.0351147i | \(-0.988820\pi\) | ||
0.999383 | − | 0.0351147i | \(-0.0111797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.5885i | − | 0.546711i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.5885 | + | 27.0000i | −0.546040 | + | 0.945769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0000 | + | 13.8564i | −0.839654 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.46410 | + | 4.00000i | −0.121046 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50000 | − | 2.59808i | 0.157051 | − | 0.0906735i | −0.419415 | − | 0.907795i | \(-0.637765\pi\) |
0.576466 | + | 0.817121i | \(0.304431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7128 | + | 16.0000i | 0.966008 | + | 0.557725i | 0.898017 | − | 0.439961i | \(-0.145008\pi\) |
0.0679910 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 20.7846i | − | 0.723627i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.3731 | −1.26482 | −0.632408 | − | 0.774636i | \(-0.717933\pi\) | ||||
−0.632408 | + | 0.774636i | \(0.717933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | + | 24.2487i | −0.486240 | + | 0.842193i | −0.999875 | − | 0.0158163i | \(-0.994965\pi\) |
0.513635 | + | 0.858009i | \(0.328299\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.8564 | + | 24.0000i | 0.480673 | + | 0.832551i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5885 | + | 27.0000i | 0.539461 | + | 0.934374i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.50000 | − | 4.33013i | −0.259238 | − | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.5692 | −1.43513 | −0.717564 | − | 0.696492i | \(-0.754743\pi\) | ||||
−0.717564 | + | 0.696492i | \(0.754743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | 0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9808 | − | 15.0000i | −0.894825 | − | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.5000 | + | 23.3827i | 0.464414 | + | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7128 | − | 32.0000i | 0.952224 | − | 1.09953i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00000 | + | 1.73205i | 0.0343199 | + | 0.0594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.7846 | + | 36.0000i | −0.712487 | + | 1.23406i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0000 | 0.753266 | 0.376633 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376633 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.0000i | 0.820783i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1244 | − | 7.00000i | 0.413678 | − | 0.238837i | −0.278691 | − | 0.960381i | \(-0.589901\pi\) |
0.692369 | + | 0.721544i | \(0.256567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.0000 | − | 5.19615i | −0.920158 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.5692 | − | 24.0000i | 1.41503 | − | 0.816970i | 0.419176 | − | 0.907905i | \(-0.362319\pi\) |
0.995857 | + | 0.0909355i | \(0.0289857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0000 | + | 46.7654i | −0.918028 | + | 1.59007i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 17.0000i | − | 0.577350i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9808i | 0.881337i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.46410 | + | 6.00000i | −0.117377 | + | 0.203302i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.50000 | + | 2.59808i | −0.152302 | + | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.59808 | − | 7.50000i | −0.0878310 | − | 0.253546i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0000 | − | 10.3923i | 0.607817 | − | 0.350923i | −0.164294 | − | 0.986411i | \(-0.552534\pi\) |
0.772111 | + | 0.635488i | \(0.219201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.59808 | − | 1.50000i | −0.0876309 | − | 0.0505937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 31.1769i | − | 1.05038i | −0.850986 | − | 0.525188i | \(-0.823995\pi\) | ||
0.850986 | − | 0.525188i | \(-0.176005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2487 | 0.816034 | 0.408017 | − | 0.912974i | \(-0.366220\pi\) | ||||
0.408017 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | − | 23.3827i | 0.453798 | − | 0.786000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.9808 | − | 45.0000i | −0.872349 | − | 1.51095i | −0.859561 | − | 0.511034i | \(-0.829263\pi\) |
−0.0127881 | − | 0.999918i | \(-0.504071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.5000 | − | 14.7224i | 1.42540 | − | 0.493775i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.59808 | − | 4.50000i | −0.0870388 | − | 0.150756i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.1769 | −1.04213 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.9711 | + | 22.5000i | 1.29976 | + | 0.750417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.73205 | + | 9.00000i | −0.0576390 | + | 0.299501i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0000 | − | 25.9808i | −0.498617 | − | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5167 | − | 39.0000i | 0.747653 | − | 1.29497i | −0.201291 | − | 0.979531i | \(-0.564514\pi\) |
0.948945 | − | 0.315442i | \(-0.102153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000i | 0.397578i | 0.980042 | + | 0.198789i | \(0.0637008\pi\) | ||||
−0.980042 | + | 0.198789i | \(0.936299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.5000 | + | 23.3827i | 1.34035 | + | 0.773854i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.7846 | − | 12.0000i | 0.687118 | − | 0.396708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.00000 | − | 5.19615i | −0.198137 | − | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.92820 | − | 4.00000i | 0.228540 | − | 0.131948i | −0.381358 | − | 0.924427i | \(-0.624544\pi\) |
0.609898 | + | 0.792480i | \(0.291210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.00000 | − | 8.66025i | 0.164756 | − | 0.285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000i | 0.789970i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 27.7128i | − | 0.911192i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.73205 | − | 3.00000i | 0.0568880 | − | 0.0985329i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | + | 5.19615i | −0.295280 | + | 0.170480i | −0.640321 | − | 0.768108i | \(-0.721199\pi\) |
0.345040 | + | 0.938588i | \(0.387865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.7846 | − | 52.0000i | 0.681188 | − | 1.70423i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.0000 | + | 15.5885i | −0.883940 | + | 0.510343i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.6936i | − | 1.75409i | −0.480406 | − | 0.877046i | \(-0.659511\pi\) | ||
0.480406 | − | 0.877046i | \(-0.340489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.4449 | 0.960897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.5000 | − | 49.3634i | 0.929073 | − | 1.60920i | 0.144198 | − | 0.989549i | \(-0.453940\pi\) |
0.784875 | − | 0.619654i | \(-0.212727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.1769 | + | 54.0000i | 1.01526 | + | 1.75848i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.00000 | + | 5.19615i | 0.195180 | + | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5885 | − | 27.0000i | −0.506557 | − | 0.877382i | −0.999971 | − | 0.00758776i | \(-0.997585\pi\) |
0.493414 | − | 0.869794i | \(-0.335749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | + | 13.8564i | 0.779073 | + | 0.449798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9808 | 0.842484 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.1769 | − | 18.0000i | −1.00886 | − | 0.582466i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.5000 | + | 23.3827i | 0.436393 | + | 0.755855i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.7654 | + | 9.00000i | 1.51013 | + | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | − | 38.1051i | −0.709677 | − | 1.22920i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.59808 | − | 4.50000i | 0.0837218 | − | 0.145010i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.0000 | −1.06231 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0000i | 0.932577i | 0.884633 | + | 0.466289i | \(0.154409\pi\) | ||||
−0.884633 | + | 0.466289i | \(0.845591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9904 | + | 7.50000i | −0.416881 | + | 0.240686i | −0.693742 | − | 0.720224i | \(-0.744039\pi\) |
0.276861 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.0000 | + | 17.3205i | −1.60293 | + | 0.555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.92820 | + | 4.00000i | −0.221880 | + | 0.128103i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.46410i | 0.110600i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.19615 | + | 9.00000i | −0.165732 | + | 0.287055i | −0.936915 | − | 0.349558i | \(-0.886332\pi\) |
0.771183 | + | 0.636613i | \(0.219665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000 | − | 10.3923i | 0.572367 | − | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.7224 | + | 8.50000i | 0.467673 | + | 0.270011i | 0.715265 | − | 0.698853i | \(-0.246306\pi\) |
−0.247592 | + | 0.968864i | \(0.579639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.7128i | 0.879440i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.1769 | 0.988375 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | − | 12.1244i | 0.221692 | − | 0.383982i | −0.733630 | − | 0.679549i | \(-0.762175\pi\) |
0.955322 | + | 0.295567i | \(0.0955086\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.46410 | − | 6.00000i | −0.109599 | − | 0.189832i |
(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 | 1344.2.bb.a.31.2 | yes | 4 | |
4.3 | odd | 2 | inner | 1344.2.bb.a.31.1 | ✓ | 4 | |
7.5 | odd | 6 | 1344.2.bb.d.607.2 | yes | 4 | ||
8.3 | odd | 2 | 1344.2.bb.d.31.2 | yes | 4 | ||
8.5 | even | 2 | 1344.2.bb.d.31.1 | yes | 4 | ||
28.19 | even | 6 | 1344.2.bb.d.607.1 | yes | 4 | ||
56.5 | odd | 6 | inner | 1344.2.bb.a.607.1 | yes | 4 | |
56.19 | even | 6 | inner | 1344.2.bb.a.607.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.bb.a.31.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
1344.2.bb.a.31.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1344.2.bb.a.607.1 | yes | 4 | 56.5 | odd | 6 | inner | |
1344.2.bb.a.607.2 | yes | 4 | 56.19 | even | 6 | inner | |
1344.2.bb.d.31.1 | yes | 4 | 8.5 | even | 2 | ||
1344.2.bb.d.31.2 | yes | 4 | 8.3 | odd | 2 | ||
1344.2.bb.d.607.1 | yes | 4 | 28.19 | even | 6 | ||
1344.2.bb.d.607.2 | yes | 4 | 7.5 | odd | 6 |