Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.10 | ||
Root | \(-0.987688 - 0.156434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.d.3025.7 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0549306i | 0.0245657i | 0.999925 | + | 0.0122828i | \(0.00390985\pi\) | ||||
−0.999925 | + | 0.0122828i | \(0.996090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.63506i | 0.794502i | 0.917710 | + | 0.397251i | \(0.130036\pi\) | ||||
−0.917710 | + | 0.397251i | \(0.869964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.67853i | 1.02024i | 0.860103 | + | 0.510121i | \(0.170399\pi\) | ||||
−0.860103 | + | 0.510121i | \(0.829601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16228 | −0.766965 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07768i | 0.706069i | 0.935610 | + | 0.353035i | \(0.114850\pi\) | ||||
−0.935610 | + | 0.353035i | \(0.885150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.86834 | 0.598090 | 0.299045 | − | 0.954239i | \(-0.403332\pi\) | ||||
0.299045 | + | 0.954239i | \(0.403332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99698 | 0.999397 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1898i | 1.89219i | 0.323890 | + | 0.946095i | \(0.395009\pi\) | ||||
−0.323890 | + | 0.946095i | \(0.604991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.32437 | −1.67471 | −0.837353 | − | 0.546662i | \(-0.815898\pi\) | ||||
−0.837353 | + | 0.546662i | \(0.815898\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0549306i | 0.00928496i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.774554i | − 0.127336i | −0.997971 | − | 0.0636679i | \(-0.979720\pi\) | ||||
0.997971 | − | 0.0636679i | \(-0.0202798\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.36183 | −0.993551 | −0.496775 | − | 0.867879i | \(-0.665483\pi\) | ||||
−0.496775 | + | 0.867879i | \(0.665483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.98927i | − 1.52335i | −0.647960 | − | 0.761674i | \(-0.724378\pi\) | ||||
0.647960 | − | 0.761674i | \(-0.275622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3126 | −1.79598 | −0.897990 | − | 0.440015i | \(-0.854973\pi\) | ||||
−0.897990 | + | 0.440015i | \(0.854973\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.39291i | − 0.466052i | −0.972470 | − | 0.233026i | \(-0.925137\pi\) | ||||
0.972470 | − | 0.233026i | \(-0.0748628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.144746 | −0.0195175 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.93263i | − 0.902552i | −0.892384 | − | 0.451276i | \(-0.850969\pi\) | ||||
0.892384 | − | 0.451276i | \(-0.149031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.35114i | 1.06925i | 0.845088 | + | 0.534627i | \(0.179548\pi\) | ||||
−0.845088 | + | 0.534627i | \(0.820452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.202064 | −0.0250629 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.93584i | − 1.09169i | −0.837887 | − | 0.545843i | \(-0.816209\pi\) | ||||
0.837887 | − | 0.545843i | \(-0.183791\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.28255 | 0.508245 | 0.254123 | − | 0.967172i | \(-0.418213\pi\) | ||||
0.254123 | + | 0.967172i | \(0.418213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.38081 | 0.980900 | 0.490450 | − | 0.871469i | \(-0.336832\pi\) | ||||
0.490450 | + | 0.871469i | \(0.336832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.63506i | 0.300293i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.03186 | 0.341111 | 0.170556 | − | 0.985348i | \(-0.445444\pi\) | ||||
0.170556 | + | 0.985348i | \(0.445444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 10.3255i | − 1.13338i | −0.823932 | − | 0.566688i | \(-0.808224\pi\) | ||||
0.823932 | − | 0.566688i | \(-0.191776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.173706i | − 0.0188410i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.8155 | −1.35844 | −0.679222 | − | 0.733933i | \(-0.737683\pi\) | ||||
−0.679222 | + | 0.733933i | \(0.737683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.67853i | 0.385615i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.169059 | −0.0173451 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1803 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.02749i | 0.102239i | 0.998693 | + | 0.0511194i | \(0.0162789\pi\) | ||||
−0.998693 | + | 0.0511194i | \(0.983721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.72905 | −0.170368 | −0.0851842 | − | 0.996365i | \(-0.527148\pi\) | ||||
−0.0851842 | + | 0.996365i | \(0.527148\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 6.11985i | − 0.591629i | −0.955245 | − | 0.295814i | \(-0.904409\pi\) | ||||
0.955245 | − | 0.295814i | \(-0.0955910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.85597i | 0.848248i | 0.905604 | + | 0.424124i | \(0.139418\pi\) | ||||
−0.905604 | + | 0.424124i | \(0.860582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.02383 | −0.848891 | −0.424445 | − | 0.905454i | \(-0.639531\pi\) | ||||
−0.424445 | + | 0.905454i | \(0.639531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.157559i | 0.0146925i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.05644 | 0.368767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.549140i | 0.0491166i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.2656 | −1.62081 | −0.810406 | − | 0.585868i | \(-0.800754\pi\) | ||||
−0.810406 | + | 0.585868i | \(0.800754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4470i | 1.52435i | 0.647373 | + | 0.762174i | \(0.275868\pi\) | ||||
−0.647373 | + | 0.762174i | \(0.724132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.07768i | 0.266869i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.73613 | −0.660942 | −0.330471 | − | 0.943816i | \(-0.607208\pi\) | ||||
−0.330471 | + | 0.943816i | \(0.607208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.802034i | 0.0680276i | 0.999421 | + | 0.0340138i | \(0.0108290\pi\) | ||||
−0.999421 | + | 0.0340138i | \(0.989171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.69316 | −0.810583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.559729 | −0.0464829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.7165i | 1.28755i | 0.765215 | + | 0.643775i | \(0.222633\pi\) | ||||
−0.765215 | + | 0.643775i | \(0.777367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.58129 | −0.210062 | −0.105031 | − | 0.994469i | \(-0.533494\pi\) | ||||
−0.105031 | + | 0.994469i | \(0.533494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.512193i | − 0.0411403i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.680724i | 0.0543277i | 0.999631 | + | 0.0271638i | \(0.00864758\pi\) | ||||
−0.999631 | + | 0.0271638i | \(0.991352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.86834 | 0.226057 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 21.8339i | − 1.71016i | −0.518494 | − | 0.855081i | \(-0.673507\pi\) | ||||
0.518494 | − | 0.855081i | \(-0.326493\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.2203 | −1.33255 | −0.666274 | − | 0.745707i | \(-0.732112\pi\) | ||||
−0.666274 | + | 0.745707i | \(0.732112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.531594 | −0.0408918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.57218i | 0.195559i | 0.995208 | + | 0.0977797i | \(0.0311741\pi\) | ||||
−0.995208 | + | 0.0977797i | \(0.968826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.99698 | 0.377736 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.26703i | 0.393676i | 0.980436 | + | 0.196838i | \(0.0630673\pi\) | ||||
−0.980436 | + | 0.196838i | \(0.936933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.0189i | − 1.19068i | −0.803475 | − | 0.595339i | \(-0.797018\pi\) | ||||
0.803475 | − | 0.595339i | \(-0.202982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0425467 | 0.00312809 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.33280i | − 0.609355i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.83730 | −0.132943 | −0.0664713 | − | 0.997788i | \(-0.521174\pi\) | ||||
−0.0664713 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3429 | 1.10441 | 0.552204 | − | 0.833709i | \(-0.313787\pi\) | ||||
0.552204 | + | 0.833709i | \(0.313787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.02447i | − 0.357979i | −0.983851 | − | 0.178989i | \(-0.942717\pi\) | ||||
0.983851 | − | 0.178989i | \(-0.0572828\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0333 | 1.56190 | 0.780949 | − | 0.624595i | \(-0.214736\pi\) | ||||
0.780949 | + | 0.624595i | \(0.214736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1898i | 0.715180i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.349459i | − 0.0244073i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.10989 | −0.560973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.50651i | 0.585612i | 0.956172 | + | 0.292806i | \(0.0945890\pi\) | ||||
−0.956172 | + | 0.292806i | \(0.905411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.548716 | 0.0374221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.32437 | −0.632980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 11.6325i | − 0.782489i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5574 | 0.907872 | 0.453936 | − | 0.891034i | \(-0.350019\pi\) | ||||
0.453936 | + | 0.891034i | \(0.350019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0721i | 1.06674i | 0.845882 | + | 0.533370i | \(0.179075\pi\) | ||||
−0.845882 | + | 0.533370i | \(0.820925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.50870i | 0.364025i | 0.983296 | + | 0.182013i | \(0.0582612\pi\) | ||||
−0.983296 | + | 0.182013i | \(0.941739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.6599 | −1.87757 | −0.938787 | − | 0.344498i | \(-0.888049\pi\) | ||||
−0.938787 | + | 0.344498i | \(0.888049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 0.676339i | − 0.0441195i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.82998 | 0.247741 | 0.123870 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123870 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.72834 | −0.111332 | −0.0556660 | − | 0.998449i | \(-0.517728\pi\) | ||||
−0.0556660 | + | 0.998449i | \(0.517728\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0549306i | 0.00350938i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3214 | −0.720361 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 0.245657i | − 0.0155057i | −0.999970 | − | 0.00775286i | \(-0.997532\pi\) | ||||
0.999970 | − | 0.00775286i | \(-0.00246784\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.55825i | 0.475183i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.2120 | 1.01128 | 0.505638 | − | 0.862746i | \(-0.331257\pi\) | ||||
0.505638 | + | 0.862746i | \(0.331257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.774554i | − 0.0481284i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3265 | −1.43837 | −0.719187 | − | 0.694817i | \(-0.755485\pi\) | ||||
−0.719187 | + | 0.694817i | \(0.755485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.186375 | 0.0114489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 23.6947i | − 1.44469i | −0.691534 | − | 0.722344i | \(-0.743065\pi\) | ||||
0.691534 | − | 0.722344i | \(-0.256935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.52786 | −0.214302 | −0.107151 | − | 0.994243i | \(-0.534173\pi\) | ||||
−0.107151 | + | 0.994243i | \(0.534173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1674i | 0.794022i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6014i | 1.71849i | 0.511561 | + | 0.859247i | \(0.329068\pi\) | ||||
−0.511561 | + | 0.859247i | \(0.670932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.6546 | 1.53043 | 0.765214 | − | 0.643776i | \(-0.222633\pi\) | ||||
0.765214 | + | 0.643776i | \(0.222633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8539i | 0.882974i | 0.897268 | + | 0.441487i | \(0.145549\pi\) | ||||
−0.897268 | + | 0.441487i | \(0.854451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.36183 | −0.375527 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6946i | 1.26741i | 0.773574 | + | 0.633706i | \(0.218467\pi\) | ||||
−0.773574 | + | 0.633706i | \(0.781533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.380813 | 0.0221718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.5513i | 0.610195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 9.98927i | − 0.575772i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.458733 | −0.0262670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.422903i | − 0.0241363i | −0.999927 | − | 0.0120682i | \(-0.996158\pi\) | ||||
0.999927 | − | 0.0120682i | \(-0.00384151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6732 | −0.775338 | −0.387669 | − | 0.921799i | \(-0.626720\pi\) | ||||
−0.387669 | + | 0.921799i | \(0.626720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.68665 | −0.434475 | −0.217237 | − | 0.976119i | \(-0.569705\pi\) | ||||
−0.217237 | + | 0.976119i | \(0.569705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2068i | 1.35959i | 0.733401 | + | 0.679796i | \(0.237932\pi\) | ||||
−0.733401 | + | 0.679796i | \(0.762068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.8506 | −1.50335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.73249i | − 0.541530i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.3816i | 1.01963i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3126 | −0.678817 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.15756i | 0.503345i | 0.967812 | + | 0.251672i | \(0.0809806\pi\) | ||||
−0.967812 | + | 0.251672i | \(0.919019\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.490851 | 0.0268180 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.2441 | 1.81092 | 0.905460 | − | 0.424432i | \(-0.139526\pi\) | ||||
0.905460 | + | 0.424432i | \(0.139526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 24.5703i | − 1.33056i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.03418i | 0.431297i | 0.976471 | + | 0.215649i | \(0.0691866\pi\) | ||||
−0.976471 | + | 0.215649i | \(0.930813\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5.46493i | − 0.292531i | −0.989245 | − | 0.146265i | \(-0.953275\pi\) | ||||
0.989245 | − | 0.146265i | \(-0.0467254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.85159 | 0.417898 | 0.208949 | − | 0.977927i | \(-0.432996\pi\) | ||||
0.208949 | + | 0.977927i | \(0.432996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.235243i | 0.0124854i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.4616 | −1.60770 | −0.803851 | − | 0.594831i | \(-0.797219\pi\) | ||||
−0.803851 | + | 0.594831i | \(0.797219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.52786 | 0.501467 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.460363i | 0.0240965i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.97241 | −0.468356 | −0.234178 | − | 0.972194i | \(-0.575240\pi\) | ||||
−0.234178 | + | 0.972194i | \(0.575240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 3.39291i | − 0.176151i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 19.6614i | − 1.01803i | −0.860759 | − | 0.509013i | \(-0.830010\pi\) | ||||
0.860759 | − | 0.509013i | \(-0.169990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.4833 | −1.93049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9871i | 1.28350i | 0.766914 | + | 0.641750i | \(0.221791\pi\) | ||||
−0.766914 | + | 0.641750i | \(0.778209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.3323 | −1.03893 | −0.519465 | − | 0.854492i | \(-0.673869\pi\) | ||||
−0.519465 | + | 0.854492i | \(0.673869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.144746 | −0.00737691 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.92753i | 0.148432i | 0.997242 | + | 0.0742159i | \(0.0236454\pi\) | ||||
−0.997242 | + | 0.0742159i | \(0.976355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.07048 | −0.458714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.166542i | 0.00837964i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.20287i | − 0.411690i | −0.978585 | − | 0.205845i | \(-0.934006\pi\) | ||||
0.978585 | − | 0.205845i | \(-0.0659943\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.5590 | −1.82567 | −0.912834 | − | 0.408332i | \(-0.866111\pi\) | ||||
−0.912834 | + | 0.408332i | \(0.866111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 34.3000i | − 1.70860i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.04100 | 0.101169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.01783 | −0.297562 | −0.148781 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148781 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6.93263i | − 0.341133i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.567188 | 0.0278422 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.25247i | − 0.110040i | −0.998485 | − | 0.0550201i | \(-0.982478\pi\) | ||||
0.998485 | − | 0.0550201i | \(-0.0175223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.87431i | 0.140085i | 0.997544 | + | 0.0700425i | \(0.0223135\pi\) | ||||
−0.997544 | + | 0.0700425i | \(0.977686\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.8018 | −0.766502 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.35114i | 0.404140i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.7211 | −0.757261 | −0.378630 | − | 0.925548i | \(-0.623605\pi\) | ||||
−0.378630 | + | 0.925548i | \(0.623605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.44027 | −0.165329 | −0.0826644 | − | 0.996577i | \(-0.526343\pi\) | ||||
−0.0826644 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.82783i | 0.422292i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2955 | 0.586833 | 0.293417 | − | 0.955985i | \(-0.405208\pi\) | ||||
0.293417 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 15.8932i | − 0.755107i | −0.925988 | − | 0.377553i | \(-0.876765\pi\) | ||||
0.925988 | − | 0.377553i | \(-0.123235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 0.703964i | − 0.0333711i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.97450 | −0.423533 | −0.211766 | − | 0.977320i | \(-0.567922\pi\) | ||||
−0.211766 | + | 0.977320i | \(0.567922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 16.7638i | − 0.789377i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.202064 | −0.00947290 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0037 | −0.701845 | −0.350922 | − | 0.936405i | \(-0.614132\pi\) | ||||
−0.350922 | + | 0.936405i | \(0.614132\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.69884i | − 0.405145i | −0.979267 | − | 0.202573i | \(-0.935070\pi\) | ||||
0.979267 | − | 0.202573i | \(-0.0649303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.34522 | 0.434309 | 0.217155 | − | 0.976137i | \(-0.430322\pi\) | ||||
0.217155 | + | 0.976137i | \(0.430322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 9.23326i | − 0.427265i | −0.976914 | − | 0.213632i | \(-0.931471\pi\) | ||||
0.976914 | − | 0.213632i | \(-0.0685294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.93584i | − 0.412619i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.3223 | 1.21030 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.3791i | 0.705643i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.66050 | 0.395708 | 0.197854 | − | 0.980231i | \(-0.436603\pi\) | ||||
0.197854 | + | 0.980231i | \(0.436603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.84922 | 0.129913 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.559212i | − 0.0253925i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1424 | −0.504912 | −0.252456 | − | 0.967608i | \(-0.581238\pi\) | ||||
−0.252456 | + | 0.967608i | \(0.581238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.4479i | 1.14845i | 0.818698 | + | 0.574224i | \(0.194696\pi\) | ||||
−0.818698 | + | 0.574224i | \(0.805304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 32.2228i | − 1.45124i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.28255 | 0.192099 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.17422i | − 0.186864i | −0.995626 | − | 0.0934318i | \(-0.970216\pi\) | ||||
0.995626 | − | 0.0934318i | \(-0.0297837\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.6106 | −0.473105 | −0.236552 | − | 0.971619i | \(-0.576017\pi\) | ||||
−0.236552 | + | 0.971619i | \(0.576017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0564404 | −0.00251156 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.1111i | 1.06871i | 0.845262 | + | 0.534353i | \(0.179445\pi\) | ||||
−0.845262 | + | 0.534353i | \(0.820555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.38081 | 0.370745 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 0.0949777i | − 0.00418522i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 32.4445i | − 1.42691i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.5642 | 1.42666 | 0.713331 | − | 0.700827i | \(-0.247185\pi\) | ||||
0.713331 | + | 0.700827i | \(0.247185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.6166i | − 0.814046i | −0.913418 | − | 0.407023i | \(-0.866567\pi\) | ||||
0.913418 | − | 0.407023i | \(-0.133433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4863 | 1.28444 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7726 | −0.642289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 23.4022i | − 1.01366i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.336167 | 0.0145338 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.63506i | 0.113500i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.3556i | 1.77802i | 0.457891 | + | 0.889008i | \(0.348605\pi\) | ||||
−0.457891 | + | 0.889008i | \(0.651395\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.486463 | −0.0208378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 18.8135i | − 0.804408i | −0.915550 | − | 0.402204i | \(-0.868244\pi\) | ||||
0.915550 | − | 0.402204i | \(-0.131756\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.3608 | −1.33602 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.03186 | 0.128928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.05808i | − 0.171946i | −0.996297 | − | 0.0859731i | \(-0.972600\pi\) | ||||
0.996297 | − | 0.0859731i | \(-0.0273999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.7458 | 1.55418 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.2454i | 1.90687i | 0.301605 | + | 0.953433i | \(0.402478\pi\) | ||||
−0.301605 | + | 0.953433i | \(0.597522\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 0.495684i | − 0.0208536i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6255 | −0.571212 | −0.285606 | − | 0.958347i | \(-0.592195\pi\) | ||||
−0.285606 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9574i | 1.29553i | 0.761842 | + | 0.647763i | \(0.224295\pi\) | ||||
−0.761842 | + | 0.647763i | \(0.775705\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.3330 | 0.597729 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4675 | −1.60142 | −0.800712 | − | 0.599049i | \(-0.795545\pi\) | ||||
−0.800712 | + | 0.599049i | \(0.795545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 10.3255i | − 0.428376i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.94054 | 0.370279 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.6131i | 1.18099i | 0.807041 | + | 0.590495i | \(0.201068\pi\) | ||||
−0.807041 | + | 0.590495i | \(0.798932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 28.6975i | − 1.18246i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.5554 | −0.926239 | −0.463119 | − | 0.886296i | \(-0.653270\pi\) | ||||
−0.463119 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 0.173706i | − 0.00712124i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.1743 | 1.72319 | 0.861597 | − | 0.507593i | \(-0.169465\pi\) | ||||
0.861597 | + | 0.507593i | \(0.169465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0155 | −0.571705 | −0.285853 | − | 0.958274i | \(-0.592277\pi\) | ||||
−0.285853 | + | 0.958274i | \(0.592277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.222823i | 0.00905902i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5893 | 0.876282 | 0.438141 | − | 0.898906i | \(-0.355637\pi\) | ||||
0.438141 | + | 0.898906i | \(0.355637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 45.2924i | − 1.83233i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.788508i | 0.0318475i | 0.999873 | + | 0.0159238i | \(0.00506891\pi\) | ||||
−0.999873 | + | 0.0159238i | \(0.994931\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.4936 | 1.38866 | 0.694331 | − | 0.719656i | \(-0.255701\pi\) | ||||
0.694331 | + | 0.719656i | \(0.255701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.8005i | 1.92127i | 0.277822 | + | 0.960633i | \(0.410388\pi\) | ||||
−0.277822 | + | 0.960633i | \(0.589612\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.8155 | −0.513443 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9547 | 0.998190 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.44935i | 0.0976621i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7200 | 0.864659 | 0.432330 | − | 0.901716i | \(-0.357692\pi\) | ||||
0.432330 | + | 0.901716i | \(0.357692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.00334i | − 0.0398164i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.67853i | 0.145749i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0166 | −0.672117 | −0.336058 | − | 0.941841i | \(-0.609094\pi\) | ||||
−0.336058 | + | 0.941841i | \(0.609094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4170i | 1.51502i | 0.652824 | + | 0.757509i | \(0.273584\pi\) | ||||
−0.652824 | + | 0.757509i | \(0.726416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7497 | 0.894382 | 0.447191 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447191 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.2679 | 0.717079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.9198i | 0.505591i | 0.967520 | + | 0.252795i | \(0.0813499\pi\) | ||||
−0.967520 | + | 0.252795i | \(0.918650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.958371 | −0.0374466 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 47.1905i | − 1.83828i | −0.393932 | − | 0.919140i | \(-0.628885\pi\) | ||||
0.393932 | − | 0.919140i | \(-0.371115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 31.5648i | − 1.22773i | −0.789412 | − | 0.613864i | \(-0.789614\pi\) | ||||
0.789412 | − | 0.613864i | \(-0.210386\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.169059 | −0.00655582 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.2276i | 1.13170i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.0058 | −0.849524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1186 | −1.43082 | −0.715408 | − | 0.698707i | \(-0.753759\pi\) | ||||
−0.715408 | + | 0.698707i | \(0.753759\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8912i | 0.610750i | 0.952232 | + | 0.305375i | \(0.0987818\pi\) | ||||
−0.952232 | + | 0.305375i | \(0.901218\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1803 | −0.390686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 27.4319i | − 1.04965i | −0.851210 | − | 0.524826i | \(-0.824131\pi\) | ||||
0.851210 | − | 0.524826i | \(-0.175869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 0.424950i | − 0.0162365i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.4809 | 0.475486 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.57770i | 0.250227i | 0.992142 | + | 0.125114i | \(0.0399296\pi\) | ||||
−0.992142 | + | 0.125114i | \(0.960070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0440562 | −0.00167115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.1179 | 0.762018 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9.07153i | − 0.342627i | −0.985217 | − | 0.171314i | \(-0.945199\pi\) | ||||
0.985217 | − | 0.171314i | \(-0.0548011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.38383 | 0.0899079 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02749i | 0.0386426i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6.16889i | − 0.231678i | −0.993268 | − | 0.115839i | \(-0.963044\pi\) | ||||
0.993268 | − | 0.115839i | \(-0.0369556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.7454 | −1.00162 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.532451i | − 0.0199125i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.5440 | −1.13910 | −0.569550 | − | 0.821956i | \(-0.692883\pi\) | ||||
−0.569550 | + | 0.821956i | \(0.692883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.72905 | −0.0643932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 50.9180i | 1.89105i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.3429 | 0.791565 | 0.395782 | − | 0.918344i | \(-0.370473\pi\) | ||||
0.395782 | + | 0.918344i | \(0.370473\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5888i | 1.16836i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1235i | 0.558599i | 0.960204 | + | 0.279300i | \(0.0901023\pi\) | ||||
−0.960204 | + | 0.279300i | \(0.909898\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.5465 | 0.867347 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 38.7212i | − 1.42438i | −0.701985 | − | 0.712192i | \(-0.747703\pi\) | ||||
0.701985 | − | 0.712192i | \(-0.252297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7258 | 1.45740 | 0.728698 | − | 0.684835i | \(-0.240126\pi\) | ||||
0.728698 | + | 0.684835i | \(0.240126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.863319 | −0.0316296 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.11985i | − 0.223615i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.96814 | 0.108309 | 0.0541544 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541544 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 0.141792i | − 0.00516032i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.1588i | − 1.71401i | −0.515305 | − | 0.857007i | \(-0.672321\pi\) | ||||
0.515305 | − | 0.857007i | \(-0.327679\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.8000 | −1.47900 | −0.739499 | − | 0.673158i | \(-0.764937\pi\) | ||||
−0.739499 | + | 0.673158i | \(0.764937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.85597i | 0.320608i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.5019 | 0.920821 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.9121 | −1.90806 | −0.954029 | − | 0.299714i | \(-0.903109\pi\) | ||||
−0.954029 | + | 0.299714i | \(0.903109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 39.0168i | − 1.40334i | −0.712503 | − | 0.701669i | \(-0.752439\pi\) | ||||
0.712503 | − | 0.701669i | \(-0.247561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.5937 | −1.67370 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 19.5797i | − 0.701515i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2848i | 0.403802i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0373925 | −0.00133460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.01675i | 0.0362431i | 0.999836 | + | 0.0181215i | \(0.00576858\pi\) | ||||
−0.999836 | + | 0.0181215i | \(0.994231\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.02383 | −0.320851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7199 | −1.09090 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.9667i | 1.80533i | 0.430339 | + | 0.902667i | \(0.358394\pi\) | ||||
−0.430339 | + | 0.902667i | \(0.641606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.9359 | 1.37745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0840i | 0.779327i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.157559i | 0.00555324i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.3800 | 0.716522 | 0.358261 | − | 0.933622i | \(-0.383370\pi\) | ||||
0.358261 | + | 0.933622i | \(0.383370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7638i | 1.43141i | 0.698402 | + | 0.715706i | \(0.253895\pi\) | ||||
−0.698402 | + | 0.715706i | \(0.746105\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.19935 | 0.0420113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.7438 | 1.07559 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.8394i | 1.25080i | 0.780303 | + | 0.625402i | \(0.215065\pi\) | ||||
−0.780303 | + | 0.625402i | \(0.784935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.8745 | −1.21565 | −0.607824 | − | 0.794071i | \(-0.707958\pi\) | ||||
−0.607824 | + | 0.794071i | \(0.707958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 42.4727i | − 1.47692i | −0.674296 | − | 0.738461i | \(-0.735553\pi\) | ||||
0.674296 | − | 0.738461i | \(-0.264447\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 33.1210i | − 1.15034i | −0.818034 | − | 0.575169i | \(-0.804936\pi\) | ||||
0.818034 | − | 0.575169i | \(-0.195064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.16228 | −0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 0.945922i | − 0.0327350i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.5817 | 1.50461 | 0.752304 | − | 0.658817i | \(-0.228943\pi\) | ||||
0.752304 | + | 0.658817i | \(0.228943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −74.8311 | −2.58038 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 0.0292007i | − 0.00100454i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.05644 | 0.139381 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.22168i | − 0.0761582i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8928i | 1.26319i | 0.775300 | + | 0.631593i | \(0.217599\pi\) | ||||
−0.775300 | + | 0.631593i | \(0.782401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.2607 | 0.657933 | 0.328967 | − | 0.944342i | \(-0.393300\pi\) | ||||
0.328967 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 19.4667i | − 0.664195i | −0.943245 | − | 0.332098i | \(-0.892244\pi\) | ||||
0.943245 | − | 0.332098i | \(-0.107756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.4715 | 0.730898 | 0.365449 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365449 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.141291 | −0.00480405 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.98916i | 0.271014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.8708 | 1.11378 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.549140i | 0.0185643i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8421i | 0.805091i | 0.915400 | + | 0.402545i | \(0.131874\pi\) | ||||
−0.915400 | + | 0.402545i | \(0.868126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.81134 | 0.296862 | 0.148431 | − | 0.988923i | \(-0.452578\pi\) | ||||
0.148431 | + | 0.988923i | \(0.452578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0935i | 1.01273i | 0.862320 | + | 0.506363i | \(0.169011\pi\) | ||||
−0.862320 | + | 0.506363i | \(0.830989\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0549 | 0.438340 | 0.219170 | − | 0.975687i | \(-0.429665\pi\) | ||||
0.219170 | + | 0.975687i | \(0.429665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.2656 | −0.612609 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 37.8944i | − 1.26809i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.289321 | −0.00967092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 95.0131i | − 3.16886i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7293i | 0.357446i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.879929 | 0.0292498 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 35.8987i | − 1.19200i | −0.802985 | − | 0.595999i | \(-0.796756\pi\) | ||||
0.802985 | − | 0.595999i | \(-0.203244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.3926 | 1.53705 | 0.768527 | − | 0.639817i | \(-0.220990\pi\) | ||||
0.768527 | + | 0.639817i | \(0.220990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2085 | 0.900469 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.4470i | 0.576149i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.87878 | 0.325871 | 0.162935 | − | 0.986637i | \(-0.447904\pi\) | ||||
0.162935 | + | 0.986637i | \(0.447904\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.7535i | 0.518533i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 3.87043i | − 0.127259i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.21688 | 0.105543 | 0.0527713 | − | 0.998607i | \(-0.483195\pi\) | ||||
0.0527713 | + | 0.998607i | \(0.483195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07768i | 0.100867i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.457725 | 0.0149692 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7874 | 1.78983 | 0.894913 | − | 0.446241i | \(-0.147237\pi\) | ||||
0.894913 | + | 0.446241i | \(0.147237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.31449i | 0.271045i | 0.990774 | + | 0.135522i | \(0.0432713\pi\) | ||||
−0.990774 | + | 0.135522i | \(0.956729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.2479 | −0.594232 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.2157i | 0.396958i | 0.980105 | + | 0.198479i | \(0.0636001\pi\) | ||||
−0.980105 | + | 0.198479i | \(0.936400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.8291i | 1.00075i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.2955 | 1.62923 | 0.814615 | − | 0.580002i | \(-0.196948\pi\) | ||||
0.814615 | + | 0.580002i | \(0.196948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 0.100924i | − 0.00326583i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.73613 | −0.249813 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.9439 | 1.80464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.842795i | 0.0271305i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.17661 | −0.198626 | −0.0993132 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993132 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.74342i | − 0.120132i | −0.998194 | − | 0.0600660i | \(-0.980869\pi\) | ||||
0.998194 | − | 0.0600660i | \(-0.0191311\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.802034i | 0.0257120i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.1012 | 1.37893 | 0.689464 | − | 0.724320i | \(-0.257846\pi\) | ||||
0.689464 | + | 0.724320i | \(0.257846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 33.7697i | − 1.07929i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.8079 | 1.49294 | 0.746470 | − | 0.665419i | \(-0.231747\pi\) | ||||
0.746470 | + | 0.665419i | \(0.231747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.275997 | 0.00879399 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 28.6526i | − 0.911099i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6923 | 1.41970 | 0.709850 | − | 0.704353i | \(-0.248763\pi\) | ||||
0.709850 | + | 0.704353i | \(0.248763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.21030i | 0.0383691i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 41.1361i | − 1.30279i | −0.758737 | − | 0.651397i | \(-0.774183\pi\) | ||||
0.758737 | − | 0.651397i | \(-0.225817\pi\) | |||||||
\(998\) | 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 | 6048.2.c.d.3025.10 | 16 | ||
3.2 | odd | 2 | inner | 6048.2.c.d.3025.8 | 16 | ||
4.3 | odd | 2 | 1512.2.c.d.757.7 | yes | 16 | ||
8.3 | odd | 2 | 1512.2.c.d.757.6 | ✓ | 16 | ||
8.5 | even | 2 | inner | 6048.2.c.d.3025.7 | 16 | ||
12.11 | even | 2 | 1512.2.c.d.757.10 | yes | 16 | ||
24.5 | odd | 2 | inner | 6048.2.c.d.3025.9 | 16 | ||
24.11 | even | 2 | 1512.2.c.d.757.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.6 | ✓ | 16 | 8.3 | odd | 2 | ||
1512.2.c.d.757.7 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.c.d.757.10 | yes | 16 | 12.11 | even | 2 | ||
1512.2.c.d.757.11 | yes | 16 | 24.11 | even | 2 | ||
6048.2.c.d.3025.7 | 16 | 8.5 | even | 2 | inner | ||
6048.2.c.d.3025.8 | 16 | 3.2 | odd | 2 | inner | ||
6048.2.c.d.3025.9 | 16 | 24.5 | odd | 2 | inner | ||
6048.2.c.d.3025.10 | 16 | 1.1 | even | 1 | trivial |