Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(961,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.i (of order \(3\), degree \(2\), 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: | \(12.5205430369\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1537 |
Dual form | 1568.2.i.j.961.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 5.19615i | 0.688247 | + | 1.19208i | 0.972404 | + | 0.233301i | \(0.0749529\pi\) |
−0.284157 | + | 0.958778i | \(0.591714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | + | 6.92820i | 0.696311 | + | 1.20605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 8.66025i | −0.821995 | − | 1.42374i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
0.0821995 | − | 0.996616i | \(-0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | − | 6.92820i | 0.640513 | − | 1.10940i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | − | 3.46410i | −0.291730 | − | 0.505291i | 0.682489 | − | 0.730896i | \(-0.260898\pi\) |
−0.974219 | + | 0.225605i | \(0.927564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | + | 3.46410i | 0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0000 | 1.58944 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00000 | + | 8.66025i | −0.650945 | + | 1.12747i | 0.331949 | + | 0.943297i | \(0.392294\pi\) |
−0.982894 | + | 0.184172i | \(0.941040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.0000 | 1.92617 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 5.19615i | −0.351123 | + | 0.608164i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | − | 8.66025i | −0.577350 | − | 1.00000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | − | 13.8564i | −0.900070 | − | 1.55897i | −0.827401 | − | 0.561611i | \(-0.810182\pi\) |
−0.0726692 | − | 0.997356i | \(-0.523152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | − | 3.46410i | 0.214423 | − | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | + | 15.5885i | 0.953998 | + | 1.65237i | 0.736644 | + | 0.676280i | \(0.236409\pi\) |
0.217354 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | − | 13.8564i | −0.773389 | − | 1.33955i | −0.935695 | − | 0.352809i | \(-0.885227\pi\) |
0.162306 | − | 0.986740i | \(-0.448107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0000 | −1.89832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 3.46410i | −0.184900 | − | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.0000 | − | 17.3205i | 0.901670 | − | 1.56174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.00000 | − | 12.1244i | 0.598050 | − | 1.03585i | −0.395058 | − | 0.918656i | \(-0.629276\pi\) |
0.993109 | − | 0.117198i | \(-0.0373911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | + | 13.8564i | −0.668994 | + | 1.15873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | + | 13.8564i | −0.651031 | + | 1.12762i | 0.331842 | + | 0.943335i | \(0.392330\pi\) |
−0.982873 | + | 0.184284i | \(0.941004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | − | 10.3923i | 0.478852 | − | 0.829396i | −0.520854 | − | 0.853646i | \(-0.674386\pi\) |
0.999706 | + | 0.0242497i | \(0.00771967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | − | 3.46410i | −0.158610 | − | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | + | 3.46410i | 0.156652 | + | 0.271329i | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.0000 | 1.54765 | 0.773823 | − | 0.633402i | \(-0.218342\pi\) | ||||
0.773823 | + | 0.633402i | \(0.218342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | − | 10.3923i | −0.456172 | − | 0.790112i | 0.542583 | − | 0.840002i | \(-0.317446\pi\) |
−0.998755 | + | 0.0498898i | \(0.984113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0000 | + | 17.3205i | 0.751646 | + | 1.30189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0000 | 0.891953 | 0.445976 | − | 0.895045i | \(-0.352856\pi\) | ||||
0.445976 | + | 0.895045i | \(0.352856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.0000 | −1.18275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | − | 6.92820i | −0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | + | 13.8564i | 0.564276 | + | 0.977356i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | − | 6.92820i | 0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 10.3923i | 0.405442 | + | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | + | 6.92820i | −0.269069 | + | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0000 | − | 19.0526i | 0.730096 | − | 1.26456i | −0.226746 | − | 0.973954i | \(-0.572809\pi\) |
0.956842 | − | 0.290609i | \(-0.0938578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.0000 | −2.07862 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | − | 12.1244i | 0.450910 | − | 0.780998i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.998443 | + | 0.0557856i | \(0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.00000 | − | 3.46410i | 0.126745 | − | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0000 | −0.631194 | −0.315597 | − | 0.948893i | \(-0.602205\pi\) | ||||
−0.315597 | + | 0.948893i | \(0.602205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.00000 | + | 1.73205i | 0.0623783 | + | 0.108042i | 0.895528 | − | 0.445005i | \(-0.146798\pi\) |
−0.833150 | + | 0.553047i | \(0.813465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | − | 1.73205i | −0.0618984 | − | 0.107211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | + | 13.8564i | −0.493301 | + | 0.854423i | −0.999970 | − | 0.00771799i | \(-0.997543\pi\) |
0.506669 | + | 0.862141i | \(0.330877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.0000 | 2.20316 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0000 | + | 17.3205i | 0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.00000 | + | 8.66025i | −0.297219 | + | 0.514799i | −0.975499 | − | 0.220005i | \(-0.929393\pi\) |
0.678280 | + | 0.734804i | \(0.262726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | − | 3.46410i | 0.117242 | − | 0.203069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.00000 | −0.467365 | −0.233682 | − | 0.972313i | \(-0.575078\pi\) | ||||
−0.233682 | + | 0.972313i | \(0.575078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.00000 | + | 13.8564i | −0.464207 | + | 0.804030i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.0000 | + | 27.7128i | 0.925304 | + | 1.60267i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | − | 22.5167i | −0.734803 | − | 1.27272i | −0.954810 | − | 0.297218i | \(-0.903941\pi\) |
0.220006 | − | 0.975499i | \(-0.429392\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0000 | + | 29.4449i | 0.954815 | + | 1.65379i | 0.734791 | + | 0.678294i | \(0.237280\pi\) |
0.220024 | + | 0.975494i | \(0.429386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.0000 | −1.78607 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0000 | − | 17.3205i | 0.554700 | − | 0.960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | + | 17.3205i | 0.553001 | + | 0.957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | − | 10.3923i | −0.329790 | − | 0.571213i | 0.652680 | − | 0.757634i | \(-0.273645\pi\) |
−0.982470 | + | 0.186421i | \(0.940311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | + | 8.66025i | −0.273998 | + | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | −0.980522 | −0.490261 | − | 0.871576i | \(-0.663099\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | − | 10.3923i | 0.325875 | − | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | + | 13.8564i | 0.433224 | + | 0.750366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | − | 13.8564i | −0.422224 | − | 0.731313i | 0.573933 | − | 0.818902i | \(-0.305417\pi\) |
−0.996157 | + | 0.0875892i | \(0.972084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.00000 | − | 8.66025i | −0.260290 | − | 0.450835i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | − | 5.19615i | −0.155334 | − | 0.269047i | 0.777847 | − | 0.628454i | \(-0.216312\pi\) |
−0.933181 | + | 0.359408i | \(0.882979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000 | − | 27.7128i | 0.819705 | − | 1.41977i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0000 | − | 17.3205i | −0.510976 | − | 0.885037i | −0.999919 | − | 0.0127209i | \(-0.995951\pi\) |
0.488943 | − | 0.872316i | \(-0.337383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | + | 3.46410i | 0.101666 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | − | 24.2487i | −0.702640 | − | 1.21701i | −0.967537 | − | 0.252731i | \(-0.918671\pi\) |
0.264897 | − | 0.964277i | \(-0.414662\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | + | 1.73205i | 0.0499376 | + | 0.0864945i | 0.889914 | − | 0.456129i | \(-0.150764\pi\) |
−0.839976 | + | 0.542623i | \(0.817431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | − | 13.8564i | 0.398508 | − | 0.690237i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0000 | 1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | + | 1.73205i | −0.0494468 | + | 0.0856444i | −0.889689 | − | 0.456566i | \(-0.849079\pi\) |
0.840243 | + | 0.542211i | \(0.182412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.0000 | − | 24.2487i | −0.690569 | − | 1.19610i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | + | 17.3205i | −0.489702 | + | 0.848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00000 | + | 3.46410i | −0.0972433 | + | 0.168430i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.00000 | + | 8.66025i | 0.242536 | + | 0.420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.0000 | + | 27.7128i | 0.772487 | + | 1.33799i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.00000 | − | 6.92820i | 0.192673 | − | 0.333720i | −0.753462 | − | 0.657491i | \(-0.771618\pi\) |
0.946135 | + | 0.323772i | \(0.104951\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.0000 | + | 41.5692i | −1.14808 | + | 1.98853i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | + | 34.6410i | −0.941763 | + | 1.63118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000 | + | 27.7128i | 0.751746 | + | 1.30206i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | − | 19.0526i | −0.514558 | − | 0.891241i | −0.999857 | − | 0.0168929i | \(-0.994623\pi\) |
0.485299 | − | 0.874348i | \(-0.338711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | + | 6.92820i | −0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.00000 | − | 15.5885i | −0.416470 | − | 0.721348i | 0.579111 | − | 0.815249i | \(-0.303400\pi\) |
−0.995582 | + | 0.0939008i | \(0.970066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0000 | − | 20.7846i | −0.552931 | − | 0.957704i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | − | 13.8564i | 0.367840 | − | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.0000 | 1.37649 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | − | 34.6410i | −0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | − | 20.7846i | 0.543772 | − | 0.941841i | −0.454911 | − | 0.890537i | \(-0.650329\pi\) |
0.998683 | − | 0.0513038i | \(-0.0163377\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | + | 3.46410i | −0.0900755 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | − | 6.92820i | −0.179065 | − | 0.310149i | 0.762496 | − | 0.646993i | \(-0.223974\pi\) |
−0.941560 | + | 0.336844i | \(0.890640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0000 | − | 34.6410i | 0.893534 | − | 1.54765i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | − | 5.19615i | 0.133235 | − | 0.230769i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.0000 | + | 17.3205i | 0.443242 | + | 0.767718i | 0.997928 | − | 0.0643419i | \(-0.0204948\pi\) |
−0.554686 | + | 0.832060i | \(0.687161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.0000 | + | 20.7846i | 0.529813 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.0000 | − | 32.9090i | 0.832405 | − | 1.44177i | −0.0637207 | − | 0.997968i | \(-0.520297\pi\) |
0.896126 | − | 0.443800i | \(-0.146370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.00000 | + | 12.1244i | 0.306089 | + | 0.530161i | 0.977503 | − | 0.210921i | \(-0.0676463\pi\) |
−0.671414 | + | 0.741082i | \(0.734313\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | + | 6.92820i | 0.174243 | + | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.0000 | 1.73259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | − | 25.9808i | −0.644900 | − | 1.11700i | −0.984325 | − | 0.176367i | \(-0.943566\pi\) |
0.339424 | − | 0.940633i | \(-0.389768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0000 | − | 20.7846i | 0.514969 | − | 0.891953i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | + | 25.9808i | −0.635570 | + | 1.10084i | 0.350824 | + | 0.936442i | \(0.385902\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0000 | −0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.0000 | + | 39.8372i | −0.969334 | + | 1.67894i | −0.271846 | + | 0.962341i | \(0.587634\pi\) |
−0.697489 | + | 0.716596i | \(0.745699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.0000 | 1.66812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | + | 12.1244i | −0.291414 | + | 0.504744i | −0.974144 | − | 0.225927i | \(-0.927459\pi\) |
0.682730 | + | 0.730670i | \(0.260792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0000 | + | 24.2487i | 0.581820 | + | 1.00774i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | + | 6.92820i | 0.165663 | + | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | − | 10.3923i | 0.246807 | − | 0.427482i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00000 | − | 5.19615i | −0.123195 | − | 0.213380i | 0.797831 | − | 0.602881i | \(-0.205981\pi\) |
−0.921026 | + | 0.389501i | \(0.872647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.00000 | + | 6.92820i | 0.163709 | + | 0.283552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.0000 | 1.87638 | 0.938190 | − | 0.346122i | \(-0.112502\pi\) | ||||
0.938190 | + | 0.346122i | \(0.112502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | − | 41.5692i | −0.974130 | − | 1.68724i | −0.682777 | − | 0.730627i | \(-0.739228\pi\) |
−0.291353 | − | 0.956616i | \(-0.594105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | − | 13.8564i | −0.323645 | − | 0.560570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | − | 19.0526i | 0.444286 | − | 0.769526i | −0.553716 | − | 0.832705i | \(-0.686791\pi\) |
0.998002 | + | 0.0631797i | \(0.0201241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0000 | − | 19.0526i | 0.442127 | − | 0.765787i | −0.555720 | − | 0.831370i | \(-0.687557\pi\) |
0.997847 | + | 0.0655827i | \(0.0208906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | + | 27.7128i | 0.642058 | + | 1.11208i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.0000 | + | 41.5692i | −0.958468 | + | 1.66011i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | + | 13.8564i | −0.317971 | + | 0.550743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0000 | − | 29.4449i | 0.671460 | − | 1.16300i | −0.306031 | − | 0.952022i | \(-0.599001\pi\) |
0.977490 | − | 0.210981i | \(-0.0676657\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.0000 | −1.34083 | −0.670415 | − | 0.741987i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741987i | \(0.733884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | − | 10.3923i | 0.235884 | − | 0.408564i | −0.723645 | − | 0.690172i | \(-0.757535\pi\) |
0.959529 | + | 0.281609i | \(0.0908680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | − | 34.6410i | −0.785069 | − | 1.35978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | + | 32.9090i | 0.743527 | + | 1.28783i | 0.950880 | + | 0.309561i | \(0.100182\pi\) |
−0.207352 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000 | − | 20.7846i | 0.466746 | − | 0.808428i | −0.532533 | − | 0.846410i | \(-0.678760\pi\) |
0.999278 | + | 0.0379819i | \(0.0120929\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.00000 | + | 13.8564i | 0.310694 | + | 0.538138i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | + | 13.8564i | 0.309761 | + | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | − | 41.5692i | 0.927894 | − | 1.60716i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000 | 1.23535 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | − | 17.3205i | 0.384900 | − | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | + | 31.1769i | 0.691796 | + | 1.19823i | 0.971249 | + | 0.238067i | \(0.0765137\pi\) |
−0.279453 | + | 0.960159i | \(0.590153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.0000 | − | 38.1051i | −0.843042 | − | 1.46019i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | + | 20.7846i | −0.459167 | + | 0.795301i | −0.998917 | − | 0.0465244i | \(-0.985185\pi\) |
0.539750 | + | 0.841825i | \(0.318519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.0000 | −1.52610 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000 | − | 6.92820i | 0.152388 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | + | 19.0526i | 0.418460 | + | 0.724793i | 0.995785 | − | 0.0917209i | \(-0.0292368\pi\) |
−0.577325 | + | 0.816514i | \(0.695903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0000 | + | 17.3205i | −0.378777 | + | 0.656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0000 | − | 51.9615i | 1.13147 | − | 1.95977i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | − | 22.5167i | −0.488225 | − | 0.845631i | 0.511683 | − | 0.859174i | \(-0.329022\pi\) |
−0.999908 | + | 0.0135434i | \(0.995689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | + | 13.8564i | −0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.0000 | 1.19841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0000 | + | 41.5692i | −0.896296 | + | 1.55243i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0000 | − | 24.2487i | −0.520666 | − | 0.901819i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.00000 | − | 8.66025i | 0.185695 | − | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.00000 | + | 6.92820i | 0.147743 | + | 0.255899i | 0.930393 | − | 0.366563i | \(-0.119466\pi\) |
−0.782650 | + | 0.622462i | \(0.786132\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | − | 27.7128i | −0.589368 | − | 1.02081i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | − | 3.46410i | 0.0735712 | − | 0.127429i | −0.826893 | − | 0.562360i | \(-0.809894\pi\) |
0.900464 | + | 0.434930i | \(0.143227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.0000 | 1.76332 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.00000 | − | 1.73205i | −0.0365881 | − | 0.0633724i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | + | 20.7846i | 0.437886 | + | 0.758441i | 0.997526 | − | 0.0702946i | \(-0.0223939\pi\) |
−0.559640 | + | 0.828736i | \(0.689061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.0000 | + | 17.3205i | −0.364420 | + | 0.631194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.0000 | + | 55.4256i | −1.16153 | + | 2.01182i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.0000 | + | 34.6410i | −0.722158 | + | 1.25081i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.00000 | 0.144056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.0000 | + | 20.7846i | −0.431610 | + | 0.747570i | −0.997012 | − | 0.0772449i | \(-0.975388\pi\) |
0.565402 | + | 0.824815i | \(0.308721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0000 | − | 17.3205i | −0.359211 | − | 0.622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | + | 51.9615i | 1.07486 | + | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0000 | − | 39.8372i | 0.819861 | − | 1.42004i | −0.0859225 | − | 0.996302i | \(-0.527384\pi\) |
0.905784 | − | 0.423740i | \(-0.139283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | + | 27.7128i | 0.569615 | + | 0.986602i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0000 | − | 27.7128i | −0.568177 | − | 0.984111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.0000 | −0.708436 | −0.354218 | − | 0.935163i | \(-0.615253\pi\) | ||||
−0.354218 | + | 0.935163i | \(0.615253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00000 | − | 15.5885i | 0.317999 | − | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | − | 20.7846i | −0.423471 | − | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.0000 | + | 20.7846i | 0.422420 | + | 0.731653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0000 | − | 22.5167i | 0.457056 | − | 0.791644i | −0.541748 | − | 0.840541i | \(-0.682237\pi\) |
0.998804 | + | 0.0488972i | \(0.0155707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0000 | 1.19390 | 0.596951 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596951 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0000 | 1.12229 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | − | 20.7846i | −0.419827 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.00000 | + | 1.73205i | 0.0349002 | + | 0.0604490i | 0.882948 | − | 0.469471i | \(-0.155555\pi\) |
−0.848048 | + | 0.529920i | \(0.822222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | − | 6.92820i | 0.139431 | − | 0.241502i | −0.787850 | − | 0.615867i | \(-0.788806\pi\) |
0.927281 | + | 0.374365i | \(0.122139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 40.0000 | 1.39262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0000 | − | 20.7846i | 0.416777 | − | 0.721879i | −0.578836 | − | 0.815444i | \(-0.696493\pi\) |
0.995613 | + | 0.0935647i | \(0.0298262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | + | 24.2487i | 0.485655 | + | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | − | 13.8564i | 0.276520 | − | 0.478947i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.0000 | −1.79524 | −0.897620 | − | 0.440771i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440771i | \(0.854705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00000 | + | 10.3923i | −0.206651 | + | 0.357930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0000 | + | 17.3205i | 0.343199 | + | 0.594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.0000 | − | 69.2820i | 1.37118 | − | 2.37496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0000 | 1.23262 | 0.616308 | − | 0.787505i | \(-0.288628\pi\) | ||||
0.616308 | + | 0.787505i | \(0.288628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.00000 | + | 15.5885i | −0.307434 | + | 0.532492i | −0.977800 | − | 0.209539i | \(-0.932804\pi\) |
0.670366 | + | 0.742030i | \(0.266137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | + | 22.5167i | 0.443554 | + | 0.768259i | 0.997950 | − | 0.0639945i | \(-0.0203840\pi\) |
−0.554396 | + | 0.832253i | \(0.687051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000 | + | 41.5692i | 0.816970 | + | 1.41503i | 0.907905 | + | 0.419176i | \(0.137681\pi\) |
−0.0909355 | + | 0.995857i | \(0.528986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.0000 | 0.883006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.0000 | 2.17105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | + | 27.7128i | −0.542139 | + | 0.939013i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.00000 | − | 1.73205i | −0.0338449 | − | 0.0586210i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.00000 | + | 12.1244i | 0.236373 | + | 0.409410i | 0.959671 | − | 0.281126i | \(-0.0907079\pi\) |
−0.723298 | + | 0.690536i | \(0.757375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.00000 | + | 13.8564i | −0.269833 | + | 0.467365i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.0000 | 1.28025 | 0.640126 | − | 0.768270i | \(-0.278882\pi\) | ||||
0.640126 | + | 0.768270i | \(0.278882\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0000 | − | 24.2487i | −0.470074 | − | 0.814192i | 0.529340 | − | 0.848410i | \(-0.322439\pi\) |
−0.999414 | + | 0.0342175i | \(0.989106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.0000 | + | 38.1051i | 0.737028 | + | 1.27657i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 64.0000 | 2.13690 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | − | 6.92820i | 0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.00000 | + | 3.46410i | 0.0666297 | + | 0.115406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0000 | − | 27.7128i | 0.531271 | − | 0.920189i | −0.468063 | − | 0.883695i | \(-0.655048\pi\) |
0.999334 | − | 0.0364935i | \(-0.0116188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | + | 6.92820i | −0.132381 | + | 0.229290i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | − | 34.6410i | −0.659739 | − | 1.14270i | −0.980683 | − | 0.195603i | \(-0.937333\pi\) |
0.320944 | − | 0.947098i | \(-0.396000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000 | − | 17.3205i | 0.329511 | − | 0.570730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.0000 | −1.64399 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | − | 15.5885i | −0.295280 | − | 0.511441i | 0.679770 | − | 0.733426i | \(-0.262080\pi\) |
−0.975050 | + | 0.221985i | \(0.928746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | − | 41.5692i | −0.785725 | − | 1.36092i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.0000 | −1.69696 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0000 | + | 34.6410i | −0.651981 | + | 1.12926i | 0.330660 | + | 0.943750i | \(0.392729\pi\) |
−0.982641 | + | 0.185515i | \(0.940605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000 | + | 69.2820i | 1.30258 | + | 2.25613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.00000 | − | 3.46410i | −0.0649913 | − | 0.112568i | 0.831699 | − | 0.555227i | \(-0.187369\pi\) |
−0.896690 | + | 0.442659i | \(0.854035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | + | 20.7846i | −0.389536 | + | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 68.0000 | 2.20505 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.0000 | −0.712650 | −0.356325 | − | 0.934362i | \(-0.615970\pi\) | ||||
−0.356325 | + | 0.934362i | \(0.615970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.00000 | + | 13.8564i | 0.258603 | + | 0.447914i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.00000 | + | 13.8564i | −0.257796 | + | 0.446516i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | + | 20.7846i | −0.385496 | + | 0.667698i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0000 | − | 36.3731i | −0.673922 | − | 1.16727i | −0.976783 | − | 0.214232i | \(-0.931275\pi\) |
0.302861 | − | 0.953035i | \(-0.402058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.0000 | − | 34.6410i | −0.640513 | − | 1.10940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.0000 | + | 22.5167i | −0.415907 | + | 0.720372i | −0.995523 | − | 0.0945177i | \(-0.969869\pi\) |
0.579616 | + | 0.814890i | \(0.303202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −72.0000 | −2.30113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | − | 31.1769i | 0.574111 | − | 0.994389i | −0.422027 | − | 0.906583i | \(-0.638681\pi\) |
0.996138 | − | 0.0878058i | \(-0.0279855\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | + | 34.6410i | −0.635321 | + | 1.10041i | 0.351126 | + | 0.936328i | \(0.385799\pi\) |
−0.986447 | + | 0.164080i | \(0.947534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0000 | −0.761617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.00000 | − | 6.92820i | 0.126681 | − | 0.219418i | −0.795708 | − | 0.605681i | \(-0.792901\pi\) |
0.922389 | + | 0.386263i | \(0.126234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.0000 | − | 34.6410i | −0.632772 | − | 1.09599i |
(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 | 1568.2.i.j.1537.1 | 2 | ||
4.3 | odd | 2 | 1568.2.i.c.1537.1 | 2 | |||
7.2 | even | 3 | inner | 1568.2.i.j.961.1 | 2 | ||
7.3 | odd | 6 | 224.2.a.b.1.1 | yes | 1 | ||
7.4 | even | 3 | 1568.2.a.b.1.1 | 1 | |||
7.5 | odd | 6 | 1568.2.i.b.961.1 | 2 | |||
7.6 | odd | 2 | 1568.2.i.b.1537.1 | 2 | |||
21.17 | even | 6 | 2016.2.a.g.1.1 | 1 | |||
28.3 | even | 6 | 224.2.a.a.1.1 | ✓ | 1 | ||
28.11 | odd | 6 | 1568.2.a.h.1.1 | 1 | |||
28.19 | even | 6 | 1568.2.i.k.961.1 | 2 | |||
28.23 | odd | 6 | 1568.2.i.c.961.1 | 2 | |||
28.27 | even | 2 | 1568.2.i.k.1537.1 | 2 | |||
35.24 | odd | 6 | 5600.2.a.c.1.1 | 1 | |||
56.3 | even | 6 | 448.2.a.f.1.1 | 1 | |||
56.11 | odd | 6 | 3136.2.a.f.1.1 | 1 | |||
56.45 | odd | 6 | 448.2.a.b.1.1 | 1 | |||
56.53 | even | 6 | 3136.2.a.y.1.1 | 1 | |||
84.59 | odd | 6 | 2016.2.a.e.1.1 | 1 | |||
112.3 | even | 12 | 1792.2.b.f.897.1 | 2 | |||
112.45 | odd | 12 | 1792.2.b.b.897.2 | 2 | |||
112.59 | even | 12 | 1792.2.b.f.897.2 | 2 | |||
112.101 | odd | 12 | 1792.2.b.b.897.1 | 2 | |||
140.59 | even | 6 | 5600.2.a.t.1.1 | 1 | |||
168.59 | odd | 6 | 4032.2.a.p.1.1 | 1 | |||
168.101 | even | 6 | 4032.2.a.z.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.a.1.1 | ✓ | 1 | 28.3 | even | 6 | ||
224.2.a.b.1.1 | yes | 1 | 7.3 | odd | 6 | ||
448.2.a.b.1.1 | 1 | 56.45 | odd | 6 | |||
448.2.a.f.1.1 | 1 | 56.3 | even | 6 | |||
1568.2.a.b.1.1 | 1 | 7.4 | even | 3 | |||
1568.2.a.h.1.1 | 1 | 28.11 | odd | 6 | |||
1568.2.i.b.961.1 | 2 | 7.5 | odd | 6 | |||
1568.2.i.b.1537.1 | 2 | 7.6 | odd | 2 | |||
1568.2.i.c.961.1 | 2 | 28.23 | odd | 6 | |||
1568.2.i.c.1537.1 | 2 | 4.3 | odd | 2 | |||
1568.2.i.j.961.1 | 2 | 7.2 | even | 3 | inner | ||
1568.2.i.j.1537.1 | 2 | 1.1 | even | 1 | trivial | ||
1568.2.i.k.961.1 | 2 | 28.19 | even | 6 | |||
1568.2.i.k.1537.1 | 2 | 28.27 | even | 2 | |||
1792.2.b.b.897.1 | 2 | 112.101 | odd | 12 | |||
1792.2.b.b.897.2 | 2 | 112.45 | odd | 12 | |||
1792.2.b.f.897.1 | 2 | 112.3 | even | 12 | |||
1792.2.b.f.897.2 | 2 | 112.59 | even | 12 | |||
2016.2.a.e.1.1 | 1 | 84.59 | odd | 6 | |||
2016.2.a.g.1.1 | 1 | 21.17 | even | 6 | |||
3136.2.a.f.1.1 | 1 | 56.11 | odd | 6 | |||
3136.2.a.y.1.1 | 1 | 56.53 | even | 6 | |||
4032.2.a.p.1.1 | 1 | 168.59 | odd | 6 | |||
4032.2.a.z.1.1 | 1 | 168.101 | even | 6 | |||
5600.2.a.c.1.1 | 1 | 35.24 | odd | 6 | |||
5600.2.a.t.1.1 | 1 | 140.59 | even | 6 |