Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(577,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1153.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1153 |
Dual form | 1728.2.i.l.577.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 1.50000i | −0.327327 | + | 0.566947i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.866025 | − | 1.50000i | 0.261116 | − | 0.452267i | −0.705422 | − | 0.708787i | \(-0.749243\pi\) |
0.966539 | + | 0.256520i | \(0.0825760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 2.59808i | −0.416025 | − | 0.720577i | 0.579510 | − | 0.814965i | \(-0.303244\pi\) |
−0.995535 | + | 0.0943882i | \(0.969911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.33013 | + | 7.50000i | 0.902894 | + | 1.56386i | 0.823720 | + | 0.566997i | \(0.191895\pi\) |
0.0791743 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.59808 | + | 4.50000i | 0.466628 | + | 0.808224i | 0.999273 | − | 0.0381148i | \(-0.0121353\pi\) |
−0.532645 | + | 0.846339i | \(0.678802\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | −0.292770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | + | 4.33013i | 0.390434 | + | 0.676252i | 0.992507 | − | 0.122189i | \(-0.0389915\pi\) |
−0.602072 | + | 0.798441i | \(0.705658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.33013 | − | 7.50000i | 0.660338 | − | 1.14374i | −0.320189 | − | 0.947354i | \(-0.603746\pi\) |
0.980527 | − | 0.196385i | \(-0.0629204\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.06218 | + | 10.5000i | −0.884260 | + | 1.53158i | −0.0376995 | + | 0.999289i | \(0.512003\pi\) |
−0.846560 | + | 0.532293i | \(0.821330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | + | 3.46410i | 0.285714 | + | 0.494872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.866025 | + | 1.50000i | 0.112747 | + | 0.195283i | 0.916877 | − | 0.399170i | \(-0.130702\pi\) |
−0.804130 | + | 0.594454i | \(0.797368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.50000 | − | 2.59808i | 0.186052 | − | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | + | 7.50000i | 0.529009 | + | 0.916271i | 0.999428 | + | 0.0338274i | \(0.0107696\pi\) |
−0.470418 | + | 0.882443i | \(0.655897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410 | 0.411113 | 0.205557 | − | 0.978645i | \(-0.434100\pi\) | ||||
0.205557 | + | 0.978645i | \(0.434100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | + | 2.59808i | 0.170941 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59808 | + | 4.50000i | −0.292306 | + | 0.506290i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) |
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.33013 | + | 7.50000i | −0.475293 | + | 0.823232i | −0.999600 | − | 0.0282978i | \(-0.990991\pi\) |
0.524306 | + | 0.851530i | \(0.324325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 3.46410i | −0.216930 | − | 0.375735i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.19615 | 0.544705 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.46410 | + | 6.00000i | 0.355409 | + | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | − | 2.59808i | 0.152302 | − | 0.263795i | −0.779771 | − | 0.626064i | \(-0.784665\pi\) |
0.932073 | + | 0.362270i | \(0.117998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50000 | − | 11.2583i | 0.646774 | − | 1.12025i | −0.337115 | − | 0.941464i | \(-0.609451\pi\) |
0.983889 | − | 0.178782i | \(-0.0572157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.866025 | + | 1.50000i | 0.0853320 | + | 0.147799i | 0.905533 | − | 0.424277i | \(-0.139472\pi\) |
−0.820201 | + | 0.572076i | \(0.806138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820 | 0.669775 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.500000 | − | 0.866025i | −0.0470360 | − | 0.0814688i | 0.841549 | − | 0.540181i | \(-0.181644\pi\) |
−0.888585 | + | 0.458712i | \(0.848311\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.33013 | + | 7.50000i | −0.403786 | + | 0.699379i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46410 | − | 6.00000i | 0.317554 | − | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.00000 | + | 6.92820i | 0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8564 | 1.22956 | 0.614779 | − | 0.788700i | \(-0.289245\pi\) | ||||
0.614779 | + | 0.788700i | \(0.289245\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.79423 | + | 13.5000i | 0.680985 | + | 1.17950i | 0.974681 | + | 0.223602i | \(0.0717814\pi\) |
−0.293696 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 10.3923i | −0.520266 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.50000 | − | 11.2583i | 0.555332 | − | 0.961864i | −0.442545 | − | 0.896746i | \(-0.645924\pi\) |
0.997878 | − | 0.0651178i | \(-0.0207423\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.866025 | − | 1.50000i | −0.0734553 | − | 0.127228i | 0.826958 | − | 0.562263i | \(-0.190069\pi\) |
−0.900414 | + | 0.435035i | \(0.856736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.19615 | −0.434524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.50000 | + | 9.52628i | 0.450578 | + | 0.780423i | 0.998422 | − | 0.0561570i | \(-0.0178847\pi\) |
−0.547844 | + | 0.836580i | \(0.684551\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2583 | − | 19.5000i | 0.916190 | − | 1.58689i | 0.111040 | − | 0.993816i | \(-0.464582\pi\) |
0.805150 | − | 0.593072i | \(-0.202085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59808 | + | 4.50000i | −0.208683 | + | 0.361449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.50000 | − | 14.7224i | −0.678374 | − | 1.17498i | −0.975470 | − | 0.220131i | \(-0.929352\pi\) |
0.297097 | − | 0.954847i | \(-0.403982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.0000 | −1.18217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | −0.542659 | −0.271329 | − | 0.962487i | \(-0.587463\pi\) | ||||
−0.271329 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.79423 | − | 13.5000i | −0.603136 | − | 1.04466i | −0.992343 | − | 0.123511i | \(-0.960584\pi\) |
0.389208 | − | 0.921150i | \(-0.372749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | − | 3.46410i | 0.153846 | − | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.50000 | − | 11.2583i | 0.494186 | − | 0.855955i | −0.505792 | − | 0.862656i | \(-0.668800\pi\) |
0.999978 | + | 0.00670064i | \(0.00213290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | + | 6.00000i | 0.261861 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | + | 6.00000i | −0.253320 | + | 0.438763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.866025 | − | 1.50000i | 0.0626634 | − | 0.108536i | −0.832992 | − | 0.553285i | \(-0.813374\pi\) |
0.895655 | + | 0.444749i | \(0.146707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410 | 0.245564 | 0.122782 | − | 0.992434i | \(-0.460818\pi\) | ||||
0.122782 | + | 0.992434i | \(0.460818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.866025 | − | 1.50000i | −0.0607831 | − | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.50000 | + | 4.33013i | −0.174608 | + | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | − | 10.3923i | 0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.33013 | + | 7.50000i | 0.298098 | + | 0.516321i | 0.975701 | − | 0.219107i | \(-0.0703144\pi\) |
−0.677603 | + | 0.735428i | \(0.736981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.66025 | 0.590624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | −0.610960 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.866025 | + | 1.50000i | −0.0579934 | + | 0.100447i | −0.893565 | − | 0.448935i | \(-0.851804\pi\) |
0.835571 | + | 0.549382i | \(0.185137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.06218 | + | 10.5000i | −0.402361 | + | 0.696909i | −0.994010 | − | 0.109286i | \(-0.965144\pi\) |
0.591649 | + | 0.806195i | \(0.298477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.50000 | + | 12.9904i | 0.495614 | + | 0.858429i | 0.999987 | − | 0.00505719i | \(-0.00160976\pi\) |
−0.504373 | + | 0.863486i | \(0.668276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1244 | −0.790906 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.52628 | − | 16.5000i | −0.616204 | − | 1.06730i | −0.990172 | − | 0.139855i | \(-0.955336\pi\) |
0.373968 | − | 0.927442i | \(-0.377997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | − | 7.79423i | 0.289870 | − | 0.502070i | −0.683908 | − | 0.729568i | \(-0.739721\pi\) |
0.973779 | + | 0.227498i | \(0.0730544\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.00000 | + | 3.46410i | −0.127775 | + | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3923 | − | 18.0000i | −0.661247 | − | 1.14531i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7846 | 1.31191 | 0.655956 | − | 0.754799i | \(-0.272265\pi\) | ||||
0.655956 | + | 0.754799i | \(0.272265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5000 | + | 26.8468i | 0.966863 | + | 1.67466i | 0.704523 | + | 0.709681i | \(0.251161\pi\) |
0.262341 | + | 0.964975i | \(0.415506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.92820 | + | 12.0000i | −0.430498 | + | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.52628 | − | 16.5000i | 0.587416 | − | 1.01743i | −0.407154 | − | 0.913360i | \(-0.633479\pi\) |
0.994570 | − | 0.104074i | \(-0.0331879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | − | 6.92820i | −0.245718 | − | 0.425596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0000 | −0.975537 | −0.487769 | − | 0.872973i | \(-0.662189\pi\) | ||||
−0.487769 | + | 0.872973i | \(0.662189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8564 | −0.841717 | −0.420858 | − | 0.907126i | \(-0.638271\pi\) | ||||
−0.420858 | + | 0.907126i | \(0.638271\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | − | 6.00000i | −0.208893 | − | 0.361814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5000 | − | 23.3827i | 0.811136 | − | 1.40493i | −0.100933 | − | 0.994893i | \(-0.532183\pi\) |
0.912069 | − | 0.410036i | \(-0.134484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50000 | + | 16.4545i | −0.566722 | + | 0.981592i | 0.430165 | + | 0.902750i | \(0.358455\pi\) |
−0.996887 | + | 0.0788417i | \(0.974878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7224 | − | 25.5000i | −0.875158 | − | 1.51582i | −0.856595 | − | 0.515990i | \(-0.827424\pi\) |
−0.0185631 | − | 0.999828i | \(-0.505909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.66025 | −0.511199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.50000 | − | 6.06218i | −0.204472 | − | 0.354156i | 0.745492 | − | 0.666514i | \(-0.232214\pi\) |
−0.949964 | + | 0.312358i | \(0.898881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.866025 | + | 1.50000i | −0.0504219 | + | 0.0873334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9904 | − | 22.5000i | 0.751253 | − | 1.30121i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.50000 | + | 12.9904i | 0.432293 | + | 0.748753i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.92820 | −0.395413 | −0.197707 | − | 0.980261i | \(-0.563349\pi\) | ||||
−0.197707 | + | 0.980261i | \(0.563349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.59808 | − | 4.50000i | −0.147323 | − | 0.255172i | 0.782914 | − | 0.622130i | \(-0.213732\pi\) |
−0.930237 | + | 0.366958i | \(0.880399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.50000 | + | 14.7224i | −0.477408 | + | 0.826894i | −0.999665 | − | 0.0258939i | \(-0.991757\pi\) |
0.522257 | + | 0.852788i | \(0.325090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.866025 | + | 1.50000i | 0.0484881 | + | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.7128 | −1.54198 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | −0.665640 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5000 | − | 18.1865i | −0.578884 | − | 1.00266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.06218 | − | 10.5000i | 0.333207 | − | 0.577132i | −0.649931 | − | 0.759993i | \(-0.725202\pi\) |
0.983139 | + | 0.182861i | \(0.0585357\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.33013 | + | 7.50000i | −0.236580 | + | 0.409769i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.50000 | − | 12.9904i | −0.408551 | − | 0.707631i | 0.586177 | − | 0.810183i | \(-0.300632\pi\) |
−0.994728 | + | 0.102552i | \(0.967299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.00000 | 0.487377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0526 | −1.02874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.2583 | − | 19.5000i | −0.604379 | − | 1.04681i | −0.992149 | − | 0.125059i | \(-0.960088\pi\) |
0.387770 | − | 0.921756i | \(-0.373245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.50000 | − | 9.52628i | 0.294408 | − | 0.509930i | −0.680439 | − | 0.732805i | \(-0.738211\pi\) |
0.974847 | + | 0.222875i | \(0.0715441\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5000 | − | 25.1147i | 0.771757 | − | 1.33672i | −0.164842 | − | 0.986320i | \(-0.552711\pi\) |
0.936599 | − | 0.350403i | \(-0.113955\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73205 | + | 3.00000i | 0.0919277 | + | 0.159223i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | − | 10.3923i | −0.314054 | − | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4545 | + | 28.5000i | −0.858917 | + | 1.48769i | 0.0140459 | + | 0.999901i | \(0.495529\pi\) |
−0.872963 | + | 0.487787i | \(0.837804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.92820 | − | 12.0000i | 0.359694 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.00000 | 0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3923 | −0.533817 | −0.266908 | − | 0.963722i | \(-0.586002\pi\) | ||||
−0.266908 | + | 0.963722i | \(0.586002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.9904 | + | 22.5000i | 0.663777 | + | 1.14970i | 0.979615 | + | 0.200883i | \(0.0643811\pi\) |
−0.315838 | + | 0.948813i | \(0.602286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.50000 | + | 2.59808i | −0.0764471 | + | 0.132410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.5000 | − | 25.1147i | 0.735179 | − | 1.27337i | −0.219465 | − | 0.975620i | \(-0.570431\pi\) |
0.954645 | − | 0.297747i | \(-0.0962353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3205 | − | 30.0000i | −0.875936 | − | 1.51717i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.19615 | −0.261447 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.00000 | −0.401508 | −0.200754 | − | 0.979642i | \(-0.564339\pi\) | ||||
−0.200754 | + | 0.979642i | \(0.564339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.50000 | + | 11.2583i | 0.324595 | + | 0.562214i | 0.981430 | − | 0.191820i | \(-0.0614388\pi\) |
−0.656836 | + | 0.754034i | \(0.728105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.79423 | − | 13.5000i | 0.388258 | − | 0.672483i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.92820 | − | 12.0000i | 0.343418 | − | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50000 | + | 7.79423i | 0.222511 | + | 0.385400i | 0.955570 | − | 0.294765i | \(-0.0952414\pi\) |
−0.733059 | + | 0.680165i | \(0.761908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.00000 | −0.147620 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.66025 | −0.425115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2583 | − | 19.5000i | −0.550005 | − | 0.952637i | −0.998273 | − | 0.0587381i | \(-0.981292\pi\) |
0.448268 | − | 0.893899i | \(-0.352041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.50000 | + | 12.9904i | −0.365528 | + | 0.633112i | −0.988861 | − | 0.148844i | \(-0.952445\pi\) |
0.623333 | + | 0.781956i | \(0.285778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | + | 13.8564i | −0.388057 | + | 0.672134i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.06218 | − | 10.5000i | −0.293369 | − | 0.508131i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7128 | −1.33488 | −0.667440 | − | 0.744664i | \(-0.732610\pi\) | ||||
−0.667440 | + | 0.744664i | \(0.732610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.0000 | + | 51.9615i | 1.43509 | + | 2.48566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.59808 | + | 4.50000i | −0.123999 | + | 0.214773i | −0.921341 | − | 0.388755i | \(-0.872905\pi\) |
0.797342 | + | 0.603528i | \(0.206239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.4545 | − | 28.5000i | 0.781776 | − | 1.35408i | −0.149130 | − | 0.988818i | \(-0.547647\pi\) |
0.930906 | − | 0.365258i | \(-0.119019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0000 | −0.943858 | −0.471929 | − | 0.881636i | \(-0.656442\pi\) | ||||
−0.471929 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.66025 | 0.407795 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.59808 | + | 4.50000i | 0.121800 | + | 0.210963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5000 | + | 18.1865i | −0.491169 | + | 0.850730i | −0.999948 | − | 0.0101670i | \(-0.996764\pi\) |
0.508779 | + | 0.860897i | \(0.330097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.500000 | + | 0.866025i | −0.0232873 | + | 0.0403348i | −0.877434 | − | 0.479697i | \(-0.840747\pi\) |
0.854147 | + | 0.520032i | \(0.174080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.4545 | + | 28.5000i | 0.764705 | + | 1.32451i | 0.940403 | + | 0.340063i | \(0.110448\pi\) |
−0.175698 | + | 0.984444i | \(0.556218\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.92820 | −0.320599 | −0.160300 | − | 0.987068i | \(-0.551246\pi\) | ||||
−0.160300 | + | 0.987068i | \(0.551246\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.50000 | − | 12.9904i | −0.344850 | − | 0.597298i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8564 | − | 24.0000i | 0.635776 | − | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.33013 | + | 7.50000i | −0.197849 | + | 0.342684i | −0.947831 | − | 0.318774i | \(-0.896729\pi\) |
0.749982 | + | 0.661458i | \(0.230062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | − | 20.7846i | −0.547153 | − | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00000 | 0.136223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | −1.25579 | −0.627894 | − | 0.778299i | \(-0.716083\pi\) | ||||
−0.627894 | + | 0.778299i | \(0.716083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.866025 | + | 1.50000i | 0.0390832 | + | 0.0676941i | 0.884905 | − | 0.465771i | \(-0.154223\pi\) |
−0.845822 | + | 0.533465i | \(0.820890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | − | 3.46410i | 0.0900755 | − | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.866025 | − | 1.50000i | −0.0387686 | − | 0.0671492i | 0.845990 | − | 0.533199i | \(-0.179010\pi\) |
−0.884759 | + | 0.466049i | \(0.845677\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2487 | 1.08120 | 0.540598 | − | 0.841281i | \(-0.318198\pi\) | ||||
0.540598 | + | 0.841281i | \(0.318198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0000 | 0.578492 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5000 | − | 32.0429i | −0.819998 | − | 1.42028i | −0.905683 | − | 0.423956i | \(-0.860641\pi\) |
0.0856847 | − | 0.996322i | \(-0.472692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3923 | − | 18.0000i | 0.459728 | − | 0.796273i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.866025 | + | 1.50000i | −0.0381616 | + | 0.0660979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5000 | + | 18.1865i | 0.461789 | + | 0.799843i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0000 | 1.13908 | 0.569540 | − | 0.821963i | \(-0.307121\pi\) | ||||
0.569540 | + | 0.821963i | \(0.307121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3923 | 0.454424 | 0.227212 | − | 0.973845i | \(-0.427039\pi\) | ||||
0.227212 | + | 0.973845i | \(0.427039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3923 | − | 18.0000i | −0.452696 | − | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.0000 | + | 45.0333i | −1.13043 | + | 1.95797i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.50000 | − | 12.9904i | 0.324861 | − | 0.562676i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.46410 | + | 6.00000i | 0.149766 | + | 0.259403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.92820 | 0.298419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.79423 | + | 13.5000i | −0.333257 | + | 0.577218i | −0.983148 | − | 0.182809i | \(-0.941481\pi\) |
0.649891 | + | 0.760027i | \(0.274814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46410 | + | 6.00000i | −0.147576 | + | 0.255609i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 7.79423i | −0.191359 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0000 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9808 | −1.09887 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2583 | − | 19.5000i | −0.474482 | − | 0.821827i | 0.525091 | − | 0.851046i | \(-0.324031\pi\) |
−0.999573 | + | 0.0292191i | \(0.990698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.500000 | − | 0.866025i | 0.0210352 | − | 0.0364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5000 | − | 26.8468i | 0.649794 | − | 1.12548i | −0.333378 | − | 0.942793i | \(-0.608189\pi\) |
0.983172 | − | 0.182683i | \(-0.0584781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.33013 | + | 7.50000i | 0.181210 | + | 0.313865i | 0.942293 | − | 0.334790i | \(-0.108665\pi\) |
−0.761083 | + | 0.648655i | \(0.775332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.6410 | 1.44463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.50000 | − | 12.9904i | −0.311152 | − | 0.538932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.92820 | + | 12.0000i | −0.286937 | + | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.59808 | − | 4.50000i | 0.107234 | − | 0.185735i | −0.807415 | − | 0.589984i | \(-0.799134\pi\) |
0.914649 | + | 0.404249i | \(0.132467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | + | 31.1769i | 0.741677 | + | 1.28462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0000 | 0.821302 | 0.410651 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410651 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.92820 | 0.284029 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.866025 | − | 1.50000i | −0.0353848 | − | 0.0612883i | 0.847791 | − | 0.530331i | \(-0.177932\pi\) |
−0.883175 | + | 0.469043i | \(0.844599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50000 | − | 9.52628i | 0.224350 | − | 0.388585i | −0.731774 | − | 0.681547i | \(-0.761308\pi\) |
0.956124 | + | 0.292962i | \(0.0946409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.00000 | + | 6.92820i | −0.162623 | + | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.06218 | − | 10.5000i | −0.246056 | − | 0.426182i | 0.716372 | − | 0.697719i | \(-0.245801\pi\) |
−0.962428 | + | 0.271537i | \(0.912468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.3731 | 1.47150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.00000 | −0.323117 | −0.161558 | − | 0.986863i | \(-0.551652\pi\) | ||||
−0.161558 | + | 0.986863i | \(0.551652\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.50000 | + | 4.33013i | 0.100646 | + | 0.174324i | 0.911951 | − | 0.410299i | \(-0.134576\pi\) |
−0.811305 | + | 0.584623i | \(0.801242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.79423 | + | 13.5000i | −0.313276 | + | 0.542611i | −0.979070 | − | 0.203526i | \(-0.934760\pi\) |
0.665793 | + | 0.746136i | \(0.268093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.46410 | + | 6.00000i | −0.138786 | + | 0.240385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.0000 | −1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.5692 | 1.65484 | 0.827422 | − | 0.561580i | \(-0.189806\pi\) | ||||
0.827422 | + | 0.561580i | \(0.189806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.92820 | + | 12.0000i | 0.274937 | + | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | − | 10.3923i | 0.237729 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.50000 | − | 6.06218i | 0.138242 | − | 0.239442i | −0.788589 | − | 0.614920i | \(-0.789188\pi\) |
0.926831 | + | 0.375478i | \(0.122522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.59808 | − | 4.50000i | −0.102458 | − | 0.177463i | 0.810239 | − | 0.586100i | \(-0.199337\pi\) |
−0.912697 | + | 0.408637i | \(0.866004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.8564 | −0.544752 | −0.272376 | − | 0.962191i | \(-0.587809\pi\) | ||||
−0.272376 | + | 0.962191i | \(0.587809\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | 0.117760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.500000 | + | 0.866025i | 0.0195665 | + | 0.0338902i | 0.875643 | − | 0.482959i | \(-0.160438\pi\) |
−0.856076 | + | 0.516849i | \(0.827105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.79423 | + | 13.5000i | −0.304546 | + | 0.527489i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9186 | + | 34.5000i | −0.775918 | + | 1.34393i | 0.158359 | + | 0.987382i | \(0.449380\pi\) |
−0.934277 | + | 0.356548i | \(0.883954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.50000 | − | 14.7224i | −0.330612 | − | 0.572636i | 0.652020 | − | 0.758202i | \(-0.273922\pi\) |
−0.982632 | + | 0.185565i | \(0.940588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | −0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.66025 | −0.335326 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.06218 | + | 10.5000i | 0.234028 | + | 0.405348i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.50000 | + | 4.33013i | −0.0963679 | + | 0.166914i | −0.910179 | − | 0.414216i | \(-0.864056\pi\) |
0.813811 | + | 0.581130i | \(0.197389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.50000 | + | 9.52628i | −0.211382 | + | 0.366125i | −0.952147 | − | 0.305639i | \(-0.901130\pi\) |
0.740765 | + | 0.671764i | \(0.234463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.59808 | + | 4.50000i | 0.0997050 | + | 0.172694i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.6410 | −1.32550 | −0.662751 | − | 0.748840i | \(-0.730611\pi\) | ||||
−0.662751 | + | 0.748840i | \(0.730611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.0000 | 0.496704 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.52628 | + | 16.5000i | −0.362397 | + | 0.627690i | −0.988355 | − | 0.152167i | \(-0.951375\pi\) |
0.625958 | + | 0.779857i | \(0.284708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.866025 | − | 1.50000i | 0.0328502 | − | 0.0568982i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0000 | − | 17.3205i | −0.378777 | − | 0.656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.4256 | 2.09042 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.2583 | + | 19.5000i | 0.423413 | + | 0.733373i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | − | 23.3827i | 0.507003 | − | 0.878155i | −0.492964 | − | 0.870050i | \(-0.664087\pi\) |
0.999967 | − | 0.00810550i | \(-0.00258009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.5000 | + | 38.9711i | −0.842632 | + | 1.45948i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.59808 | − | 4.50000i | −0.0971625 | − | 0.168290i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.5692 | −1.55027 | −0.775135 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775135 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | + | 3.46410i | 0.0742781 | + | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2583 | − | 19.5000i | 0.417548 | − | 0.723215i | −0.578144 | − | 0.815935i | \(-0.696223\pi\) |
0.995692 | + | 0.0927199i | \(0.0295561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.3205 | + | 30.0000i | −0.640622 | + | 1.10959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5000 | + | 18.1865i | 0.387826 | + | 0.671735i | 0.992157 | − | 0.124999i | \(-0.0398927\pi\) |
−0.604331 | + | 0.796734i | \(0.706559\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0000 | 0.552532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.46410 | −0.127429 | −0.0637145 | − | 0.997968i | \(-0.520295\pi\) | ||||
−0.0637145 | + | 0.997968i | \(0.520295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.866025 | − | 1.50000i | −0.0317714 | − | 0.0550297i | 0.849703 | − | 0.527262i | \(-0.176782\pi\) |
−0.881474 | + | 0.472233i | \(0.843448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.50000 | + | 9.52628i | −0.201504 | + | 0.349016i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9904 | − | 22.5000i | −0.474026 | − | 0.821037i | 0.525532 | − | 0.850774i | \(-0.323866\pi\) |
−0.999558 | + | 0.0297372i | \(0.990533\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.5167 | 0.819465 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00000 | −0.218074 | −0.109037 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109037 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.5000 | − | 37.2391i | −0.779374 | − | 1.34992i | −0.932303 | − | 0.361679i | \(-0.882204\pi\) |
0.152928 | − | 0.988237i | \(-0.451130\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.59808 | − | 4.50000i | 0.0938111 | − | 0.162486i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | + | 0.866025i | 0.0180305 | + | 0.0312297i | 0.874900 | − | 0.484304i | \(-0.160927\pi\) |
−0.856869 | + | 0.515534i | \(0.827594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.0000 | 1.43870 | 0.719350 | − | 0.694648i | \(-0.244440\pi\) | ||||
0.719350 | + | 0.694648i | \(0.244440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7846 | 0.746605 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.3205 | + | 30.0000i | 0.620572 | + | 1.07486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | − | 5.19615i | 0.107348 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.50000 | − | 14.7224i | 0.303378 | − | 0.525466i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9904 | + | 22.5000i | 0.463057 | + | 0.802038i | 0.999112 | − | 0.0421450i | \(-0.0134192\pi\) |
−0.536054 | + | 0.844183i | \(0.680086\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.73205 | 0.0615846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.0000 | 0.745732 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.5000 | − | 25.1147i | −0.513616 | − | 0.889610i | −0.999875 | − | 0.0157948i | \(-0.994972\pi\) |
0.486259 | − | 0.873815i | \(-0.338361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.2487 | − | 42.0000i | 0.857858 | − | 1.48585i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3923 | + | 18.0000i | −0.366736 | + | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.50000 | − | 12.9904i | −0.264340 | − | 0.457851i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.00000 | 0.140633 | 0.0703163 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703163 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7846 | 0.729846 | 0.364923 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364923 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.46410 | − | 6.00000i | −0.121342 | − | 0.210171i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | − | 51.9615i | 1.04957 | − | 1.81790i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.50000 | − | 6.06218i | 0.122151 | − | 0.211571i | −0.798465 | − | 0.602042i | \(-0.794354\pi\) |
0.920616 | + | 0.390470i | \(0.127687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3827 | + | 40.5000i | 0.815069 | + | 1.41174i | 0.909278 | + | 0.416189i | \(0.136634\pi\) |
−0.0942090 | + | 0.995552i | \(0.530032\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.92820 | −0.240917 | −0.120459 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120459 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0000 | −0.833554 | −0.416777 | − | 0.909009i | \(-0.636840\pi\) | ||||
−0.416777 | + | 0.909009i | \(0.636840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.00000 | − | 13.8564i | −0.277184 | − | 0.480096i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.79423 | − | 13.5000i | 0.269730 | − | 0.467187i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9904 | + | 22.5000i | −0.448478 | + | 0.776786i | −0.998287 | − | 0.0585039i | \(-0.981367\pi\) |
0.549809 | + | 0.835290i | \(0.314700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00000 | 0.137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.8564 | −0.476112 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.6410 | + | 60.0000i | 1.18748 | + | 2.05677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5000 | + | 19.9186i | −0.393753 | + | 0.681999i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.5000 | + | 37.2391i | −0.734426 | + | 1.27206i | 0.220549 | + | 0.975376i | \(0.429215\pi\) |
−0.954975 | + | 0.296687i | \(0.904118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.1865 | + | 31.5000i | 0.620517 | + | 1.07477i | 0.989390 | + | 0.145286i | \(0.0464103\pi\) |
−0.368873 | + | 0.929480i | \(0.620256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.4256 | 1.88671 | 0.943355 | − | 0.331785i | \(-0.107651\pi\) | ||||
0.943355 | + | 0.331785i | \(0.107651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0000 | 0.442013 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.50000 | + | 7.79423i | 0.152652 | + | 0.264401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9904 | − | 22.5000i | 0.440162 | − | 0.762383i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.79423 | + | 13.5000i | −0.263493 | + | 0.456383i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.5000 | − | 37.2391i | −0.726003 | − | 1.25747i | −0.958560 | − | 0.284892i | \(-0.908042\pi\) |
0.232556 | − | 0.972583i | \(-0.425291\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.0000 | −1.75192 | −0.875962 | − | 0.482380i | \(-0.839773\pi\) | ||||
−0.875962 | + | 0.482380i | \(0.839773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.7846 | −0.699458 | −0.349729 | − | 0.936851i | \(-0.613726\pi\) | ||||
−0.349729 | + | 0.936851i | \(0.613726\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.59808 | − | 4.50000i | −0.0872349 | − | 0.151095i | 0.819106 | − | 0.573641i | \(-0.194470\pi\) |
−0.906341 | + | 0.422546i | \(0.861136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | + | 20.7846i | −0.402467 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.0000 | + | 72.7461i | −1.40548 | + | 2.43436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.46410 | − | 6.00000i | −0.115792 | − | 0.200558i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.19615 | −0.173301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000 | 1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4545 | + | 28.5000i | −0.546362 | + | 0.946327i | 0.452158 | + | 0.891938i | \(0.350654\pi\) |
−0.998520 | + | 0.0543890i | \(0.982679\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.4545 | − | 28.5000i | 0.545161 | − | 0.944247i | −0.453435 | − | 0.891289i | \(-0.649802\pi\) |
0.998597 | − | 0.0529580i | \(-0.0168649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.50000 | + | 12.9904i | 0.248214 | + | 0.429919i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.0000 | −0.891619 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8564 | 0.457081 | 0.228540 | − | 0.973534i | \(-0.426605\pi\) | ||||
0.228540 | + | 0.973534i | \(0.426605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.19615 | − | 9.00000i | −0.171033 | − | 0.296239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | − | 27.7128i | 0.526077 | − | 0.911192i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.5000 | + | 30.3109i | −0.574156 | + | 0.994468i | 0.421976 | + | 0.906607i | \(0.361337\pi\) |
−0.996133 | + | 0.0878612i | \(0.971997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8564 | + | 24.0000i | 0.454125 | + | 0.786568i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.92820 | −0.226576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00000 | 0.130674 | 0.0653372 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653372 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.50000 | − | 6.06218i | −0.114097 | − | 0.197621i | 0.803322 | − | 0.595545i | \(-0.203064\pi\) |
−0.917418 | + | 0.397924i | \(0.869731\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.6506 | + | 37.5000i | −0.705042 | + | 1.22117i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.79423 | − | 13.5000i | 0.253278 | − | 0.438691i | −0.711148 | − | 0.703042i | \(-0.751824\pi\) |
0.964426 | + | 0.264351i | \(0.0851578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | + | 31.1769i | 0.584305 | + | 1.01205i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0000 | 1.42530 | 0.712650 | − | 0.701520i | \(-0.247495\pi\) | ||||
0.712650 | + | 0.701520i | \(0.247495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.73205 | 0.0560478 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2583 | + | 19.5000i | 0.363550 | + | 0.629688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.00000 | − | 3.46410i | 0.0645161 | − | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.50000 | + | 9.52628i | −0.177051 | + | 0.306662i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4545 | + | 28.5000i | 0.529140 | + | 0.916498i | 0.999422 | + | 0.0339820i | \(0.0108189\pi\) |
−0.470282 | + | 0.882516i | \(0.655848\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.1051 | 1.22285 | 0.611426 | − | 0.791302i | \(-0.290596\pi\) | ||||
0.611426 | + | 0.791302i | \(0.290596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00000 | 0.0961756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.5000 | − | 21.6506i | −0.399910 | − | 0.692665i | 0.593804 | − | 0.804610i | \(-0.297625\pi\) |
−0.993714 | + | 0.111945i | \(0.964292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46410 | − | 6.00000i | 0.110713 | − | 0.191761i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.33013 | + | 7.50000i | −0.138110 | + | 0.239213i | −0.926781 | − | 0.375602i | \(-0.877436\pi\) |
0.788671 | + | 0.614815i | \(0.210769\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0000 | − | 19.0526i | −0.350489 | − | 0.607065i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75.0000 | 2.38486 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.4256 | 1.76065 | 0.880327 | − | 0.474368i | \(-0.157323\pi\) | ||||
0.880327 | + | 0.474368i | \(0.157323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.73205 | + | 3.00000i | 0.0549097 | + | 0.0951064i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.50000 | + | 11.2583i | −0.205857 | + | 0.356555i | −0.950405 | − | 0.311014i | \(-0.899332\pi\) |
0.744548 | + | 0.667568i | \(0.232665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.i.l.1153.1 | 4 | ||
3.2 | odd | 2 | 576.2.i.k.385.1 | 4 | |||
4.3 | odd | 2 | inner | 1728.2.i.l.1153.2 | 4 | ||
8.3 | odd | 2 | 864.2.i.d.289.2 | 4 | |||
8.5 | even | 2 | 864.2.i.d.289.1 | 4 | |||
9.2 | odd | 6 | 5184.2.a.bx.1.2 | 2 | |||
9.4 | even | 3 | inner | 1728.2.i.l.577.1 | 4 | ||
9.5 | odd | 6 | 576.2.i.k.193.1 | 4 | |||
9.7 | even | 3 | 5184.2.a.bl.1.2 | 2 | |||
12.11 | even | 2 | 576.2.i.k.385.2 | 4 | |||
24.5 | odd | 2 | 288.2.i.d.97.2 | yes | 4 | ||
24.11 | even | 2 | 288.2.i.d.97.1 | ✓ | 4 | ||
36.7 | odd | 6 | 5184.2.a.bl.1.1 | 2 | |||
36.11 | even | 6 | 5184.2.a.bx.1.1 | 2 | |||
36.23 | even | 6 | 576.2.i.k.193.2 | 4 | |||
36.31 | odd | 6 | inner | 1728.2.i.l.577.2 | 4 | ||
72.5 | odd | 6 | 288.2.i.d.193.2 | yes | 4 | ||
72.11 | even | 6 | 2592.2.a.l.1.1 | 2 | |||
72.13 | even | 6 | 864.2.i.d.577.1 | 4 | |||
72.29 | odd | 6 | 2592.2.a.l.1.2 | 2 | |||
72.43 | odd | 6 | 2592.2.a.p.1.1 | 2 | |||
72.59 | even | 6 | 288.2.i.d.193.1 | yes | 4 | ||
72.61 | even | 6 | 2592.2.a.p.1.2 | 2 | |||
72.67 | odd | 6 | 864.2.i.d.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.d.97.1 | ✓ | 4 | 24.11 | even | 2 | ||
288.2.i.d.97.2 | yes | 4 | 24.5 | odd | 2 | ||
288.2.i.d.193.1 | yes | 4 | 72.59 | even | 6 | ||
288.2.i.d.193.2 | yes | 4 | 72.5 | odd | 6 | ||
576.2.i.k.193.1 | 4 | 9.5 | odd | 6 | |||
576.2.i.k.193.2 | 4 | 36.23 | even | 6 | |||
576.2.i.k.385.1 | 4 | 3.2 | odd | 2 | |||
576.2.i.k.385.2 | 4 | 12.11 | even | 2 | |||
864.2.i.d.289.1 | 4 | 8.5 | even | 2 | |||
864.2.i.d.289.2 | 4 | 8.3 | odd | 2 | |||
864.2.i.d.577.1 | 4 | 72.13 | even | 6 | |||
864.2.i.d.577.2 | 4 | 72.67 | odd | 6 | |||
1728.2.i.l.577.1 | 4 | 9.4 | even | 3 | inner | ||
1728.2.i.l.577.2 | 4 | 36.31 | odd | 6 | inner | ||
1728.2.i.l.1153.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.i.l.1153.2 | 4 | 4.3 | odd | 2 | inner | ||
2592.2.a.l.1.1 | 2 | 72.11 | even | 6 | |||
2592.2.a.l.1.2 | 2 | 72.29 | odd | 6 | |||
2592.2.a.p.1.1 | 2 | 72.43 | odd | 6 | |||
2592.2.a.p.1.2 | 2 | 72.61 | even | 6 | |||
5184.2.a.bl.1.1 | 2 | 36.7 | odd | 6 | |||
5184.2.a.bl.1.2 | 2 | 9.7 | even | 3 | |||
5184.2.a.bx.1.1 | 2 | 36.11 | even | 6 | |||
5184.2.a.bx.1.2 | 2 | 9.2 | odd | 6 |