Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(865,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.7 | ||
Root | \(2.40332 - 0.123797i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.865 |
Dual form | 2268.2.i.n.2053.7 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.15101 | − | 1.99360i | 0.514746 | − | 0.891566i | −0.485108 | − | 0.874454i | \(-0.661220\pi\) |
0.999854 | − | 0.0171118i | \(-0.00544711\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41508 | + | 1.08045i | 0.912816 | + | 0.408371i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23145 | − | 3.86499i | −0.672809 | − | 1.16534i | −0.977104 | − | 0.212761i | \(-0.931754\pi\) |
0.304295 | − | 0.952578i | \(-0.401579\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42148 | + | 2.46208i | 0.394248 | + | 0.682858i | 0.993005 | − | 0.118073i | \(-0.0376717\pi\) |
−0.598757 | + | 0.800931i | \(0.704338\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.115312 | + | 0.199726i | −0.0279673 | + | 0.0484408i | −0.879670 | − | 0.475584i | \(-0.842237\pi\) |
0.851703 | + | 0.524025i | \(0.175570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.49360 | − | 2.58700i | −0.342656 | − | 0.593498i | 0.642269 | − | 0.766479i | \(-0.277993\pi\) |
−0.984925 | + | 0.172982i | \(0.944660\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.400294 | − | 0.693329i | 0.0834670 | − | 0.144569i | −0.821270 | − | 0.570540i | \(-0.806734\pi\) |
0.904737 | + | 0.425971i | \(0.140067\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.149635 | − | 0.259175i | −0.0299269 | − | 0.0518349i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.82751 | − | 6.62944i | 0.710750 | − | 1.23106i | −0.253825 | − | 0.967250i | \(-0.581689\pi\) |
0.964576 | − | 0.263806i | \(-0.0849778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.28647 | 0.949479 | 0.474739 | − | 0.880126i | \(-0.342542\pi\) | ||||
0.474739 | + | 0.880126i | \(0.342542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.93376 | − | 3.57112i | 0.833958 | − | 0.603629i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.69333 | − | 2.93293i | −0.278382 | − | 0.482171i | 0.692601 | − | 0.721321i | \(-0.256465\pi\) |
−0.970983 | + | 0.239150i | \(0.923131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.899697 | − | 1.55832i | −0.140509 | − | 0.243369i | 0.787179 | − | 0.616724i | \(-0.211541\pi\) |
−0.927688 | + | 0.373355i | \(0.878207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.85860 | − | 8.41533i | 0.740929 | − | 1.28333i | −0.211144 | − | 0.977455i | \(-0.567719\pi\) |
0.952073 | − | 0.305871i | \(-0.0989478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.77636 | 0.842569 | 0.421284 | − | 0.906929i | \(-0.361579\pi\) | ||||
0.421284 | + | 0.906929i | \(0.361579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.66527 | + | 5.21874i | 0.666467 | + | 0.745535i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.31905 | + | 7.48081i | −0.593267 | + | 1.02757i | 0.400522 | + | 0.916287i | \(0.368829\pi\) |
−0.993789 | + | 0.111281i | \(0.964505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.2737 | −1.38530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.35585 | −1.08784 | −0.543920 | − | 0.839137i | \(-0.683060\pi\) | ||||
−0.543920 | + | 0.839137i | \(0.683060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1735 | −1.68669 | −0.843347 | − | 0.537370i | \(-0.819418\pi\) | ||||
−0.843347 | + | 0.537370i | \(0.819418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.54454 | 0.811751 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.53090 | −0.920046 | −0.460023 | − | 0.887907i | \(-0.652159\pi\) | ||||
−0.460023 | + | 0.887907i | \(0.652159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.59672 | 1.02024 | 0.510122 | − | 0.860102i | \(-0.329600\pi\) | ||||
0.510122 | + | 0.860102i | \(0.329600\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.29287 | + | 3.97137i | −0.268360 | + | 0.464814i | −0.968439 | − | 0.249252i | \(-0.919815\pi\) |
0.700078 | + | 0.714066i | \(0.253148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.21323 | − | 11.7453i | −0.138260 | − | 1.33850i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.67313 | 1.08831 | 0.544156 | − | 0.838984i | \(-0.316850\pi\) | ||||
0.544156 | + | 0.838984i | \(0.316850\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.46521 | − | 14.6622i | 0.929177 | − | 1.60938i | 0.144476 | − | 0.989508i | \(-0.453850\pi\) |
0.784701 | − | 0.619874i | \(-0.212816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.265450 | + | 0.459773i | 0.0287921 | + | 0.0498694i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.944450 | + | 1.63584i | 0.100111 | + | 0.173398i | 0.911730 | − | 0.410789i | \(-0.134747\pi\) |
−0.811619 | + | 0.584187i | \(0.801413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.772852 | + | 7.48196i | 0.0810169 | + | 0.784323i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.87659 | −0.705523 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.70796 | − | 13.3506i | 0.782624 | − | 1.35555i | −0.147784 | − | 0.989020i | \(-0.547214\pi\) |
0.930408 | − | 0.366525i | \(-0.119453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.40744 | + | 2.43775i | 0.140045 | + | 0.242566i | 0.927513 | − | 0.373790i | \(-0.121942\pi\) |
−0.787468 | + | 0.616355i | \(0.788609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.55832 | + | 4.43114i | −0.252079 | + | 0.436614i | −0.964098 | − | 0.265547i | \(-0.914448\pi\) |
0.712019 | + | 0.702160i | \(0.247781\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.29487 | − | 2.24278i | −0.125180 | − | 0.216818i | 0.796623 | − | 0.604476i | \(-0.206617\pi\) |
−0.921803 | + | 0.387658i | \(0.873284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.76728 | + | 15.1854i | −0.839753 | + | 1.45450i | 0.0503474 | + | 0.998732i | \(0.483967\pi\) |
−0.890101 | + | 0.455764i | \(0.849366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.21711 | − | 14.2325i | −0.773001 | − | 1.33888i | −0.935911 | − | 0.352236i | \(-0.885421\pi\) |
0.162910 | − | 0.986641i | \(-0.447912\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.921482 | − | 1.59605i | −0.0859286 | − | 0.148833i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.494282 | + | 0.357767i | −0.0453108 | + | 0.0327965i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.45878 | + | 7.72283i | −0.405344 | + | 0.702076i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8211 | 0.967873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.13145 | 0.721549 | 0.360775 | − | 0.932653i | \(-0.382512\pi\) | ||||
0.360775 | + | 0.932653i | \(0.382512\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.25591 | − | 10.8356i | 0.546582 | − | 0.946707i | −0.451924 | − | 0.892057i | \(-0.649262\pi\) |
0.998506 | − | 0.0546508i | \(-0.0174046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.812064 | − | 7.86157i | −0.0704148 | − | 0.681685i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.09668 | − | 14.0239i | −0.691746 | − | 1.19814i | −0.971265 | − | 0.237999i | \(-0.923508\pi\) |
0.279519 | − | 0.960140i | \(-0.409825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.07212 | + | 5.32107i | 0.260574 | + | 0.451327i | 0.966395 | − | 0.257063i | \(-0.0827549\pi\) |
−0.705821 | + | 0.708391i | \(0.749422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.34394 | − | 10.9880i | 0.530507 | − | 0.918866i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.81098 | − | 15.2611i | −0.731712 | − | 1.26736i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.85927 | + | 6.68446i | −0.316164 | + | 0.547612i | −0.979684 | − | 0.200546i | \(-0.935728\pi\) |
0.663520 | + | 0.748158i | \(0.269062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.45878 | + | 12.9190i | 0.606987 | + | 1.05133i | 0.991734 | + | 0.128310i | \(0.0409553\pi\) |
−0.384747 | + | 0.923022i | \(0.625711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.08477 | − | 10.5391i | 0.488740 | − | 0.846523i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.257220 | −0.0205284 | −0.0102642 | − | 0.999947i | \(-0.503267\pi\) | ||||
−0.0102642 | + | 0.999947i | \(0.503267\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.71585 | − | 1.24195i | 0.135228 | − | 0.0978795i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.28748 | − | 10.8902i | −0.492473 | − | 0.852989i | 0.507489 | − | 0.861658i | \(-0.330574\pi\) |
−0.999962 | + | 0.00866931i | \(0.997240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.8470 | + | 18.7875i | 0.839363 | + | 1.45382i | 0.890428 | + | 0.455123i | \(0.150405\pi\) |
−0.0510657 | + | 0.998695i | \(0.516262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.45878 | − | 4.25873i | 0.189137 | − | 0.327595i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7605 | 1.04619 | 0.523095 | − | 0.852275i | \(-0.324777\pi\) | ||||
0.523095 | + | 0.852275i | \(0.324777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0813555 | − | 0.787601i | −0.00614990 | − | 0.0595370i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.448262 | + | 0.776412i | −0.0335046 | + | 0.0580317i | −0.882292 | − | 0.470703i | \(-0.844000\pi\) |
0.848787 | + | 0.528735i | \(0.177334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4613 | −1.29788 | −0.648942 | − | 0.760838i | \(-0.724788\pi\) | ||||
−0.648942 | + | 0.760838i | \(0.724788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.79613 | −0.573183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.02925 | 0.0752665 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.46902 | −0.106295 | −0.0531474 | − | 0.998587i | \(-0.516925\pi\) | ||||
−0.0531474 | + | 0.998587i | \(0.516925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50330 | 0.468118 | 0.234059 | − | 0.972222i | \(-0.424799\pi\) | ||||
0.234059 | + | 0.972222i | \(0.424799\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9521 | −0.851552 | −0.425776 | − | 0.904828i | \(-0.639999\pi\) | ||||
−0.425776 | + | 0.904828i | \(0.639999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.73886 | − | 16.8682i | 0.690369 | − | 1.19575i | −0.281348 | − | 0.959606i | \(-0.590781\pi\) |
0.971717 | − | 0.236149i | \(-0.0758852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.4065 | − | 11.8752i | 1.15151 | − | 0.833478i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.14223 | −0.289306 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.66581 | + | 11.5455i | −0.461084 | + | 0.798621i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.43611 | + | 11.1477i | 0.443080 | + | 0.767437i | 0.997916 | − | 0.0645225i | \(-0.0205524\pi\) |
−0.554836 | + | 0.831960i | \(0.687219\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1846 | − | 19.3722i | −0.762780 | − | 1.32117i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.7673 | + | 5.71176i | 0.866700 | + | 0.387739i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.655656 | −0.0441042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.92331 | + | 8.52743i | −0.329690 | + | 0.571039i | −0.982450 | − | 0.186525i | \(-0.940277\pi\) |
0.652761 | + | 0.757564i | \(0.273611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2254 | − | 21.1750i | −0.811426 | − | 1.40543i | −0.911866 | − | 0.410489i | \(-0.865358\pi\) |
0.100439 | − | 0.994943i | \(-0.467975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0018 | − | 19.0557i | 0.727022 | − | 1.25924i | −0.231115 | − | 0.972926i | \(-0.574237\pi\) |
0.958136 | − | 0.286312i | \(-0.0924293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8179 | + | 18.7372i | 0.708706 | + | 1.22752i | 0.965337 | + | 0.261006i | \(0.0840542\pi\) |
−0.256631 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.64863 | − | 11.5158i | 0.433709 | − | 0.751206i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.86360 | − | 15.3522i | −0.573338 | − | 0.993051i | −0.996220 | − | 0.0868662i | \(-0.972315\pi\) |
0.422882 | − | 0.906185i | \(-0.361019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.15887 | − | 3.73927i | −0.139065 | − | 0.240868i | 0.788078 | − | 0.615575i | \(-0.211076\pi\) |
−0.927143 | + | 0.374708i | \(0.877743\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.7739 | − | 3.29388i | 1.00775 | − | 0.210438i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.24626 | − | 7.35473i | 0.270183 | − | 0.467971i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2938 | 0.649741 | 0.324870 | − | 0.945759i | \(-0.394679\pi\) | ||||
0.324870 | + | 0.945759i | \(0.394679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.57295 | −0.224629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.89568 | + | 10.2116i | −0.367763 | + | 0.636983i | −0.989215 | − | 0.146468i | \(-0.953209\pi\) |
0.621453 | + | 0.783452i | \(0.286543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.920654 | − | 8.91283i | −0.0572066 | − | 0.553816i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.59359 | − | 4.49223i | −0.159928 | − | 0.277003i | 0.774915 | − | 0.632066i | \(-0.217793\pi\) |
−0.934842 | + | 0.355063i | \(0.884459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.94251 | + | 17.2209i | 0.610763 | + | 1.05787i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.6103 | + | 25.3058i | −0.890805 | + | 1.54292i | −0.0518936 | + | 0.998653i | \(0.516526\pi\) |
−0.838912 | + | 0.544268i | \(0.816808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2801 | + | 17.8056i | 0.624470 | + | 1.08161i | 0.988643 | + | 0.150283i | \(0.0480184\pi\) |
−0.364173 | + | 0.931331i | \(0.618648\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.667805 | + | 1.15667i | −0.0402702 | + | 0.0697500i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.97833 | + | 10.3548i | 0.359203 | + | 0.622158i | 0.987828 | − | 0.155550i | \(-0.0497151\pi\) |
−0.628625 | + | 0.777709i | \(0.716382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9166 | + | 25.8363i | −0.889850 | + | 1.54126i | −0.0497975 | + | 0.998759i | \(0.515858\pi\) |
−0.840052 | + | 0.542506i | \(0.817476\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.57094 | −0.568933 | −0.284467 | − | 0.958686i | \(-0.591817\pi\) | ||||
−0.284467 | + | 0.958686i | \(0.591817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.489161 | − | 4.73555i | −0.0288742 | − | 0.279531i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.47341 | + | 14.6764i | 0.498436 | + | 0.863316i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.41014 | + | 12.8347i | 0.432905 | + | 0.749813i | 0.997122 | − | 0.0758132i | \(-0.0241553\pi\) |
−0.564217 | + | 0.825626i | \(0.690822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.61765 | + | 16.6583i | −0.559961 | + | 0.969881i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.27604 | 0.131627 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.8262 | − | 15.0743i | 1.20040 | − | 0.868867i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1628 | + | 26.2627i | −0.868219 | + | 1.50380i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.88207 | −0.335708 | −0.167854 | − | 0.985812i | \(-0.553684\pi\) | ||||
−0.167854 | + | 0.985812i | \(0.553684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2351 | 0.920606 | 0.460303 | − | 0.887762i | \(-0.347741\pi\) | ||||
0.460303 | + | 0.887762i | \(0.347741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.6896 | 0.999875 | 0.499937 | − | 0.866062i | \(-0.333356\pi\) | ||||
0.499937 | + | 0.866062i | \(0.333356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.28017 | −0.296564 | −0.148282 | − | 0.988945i | \(-0.547374\pi\) | ||||
−0.148282 | + | 0.988945i | \(0.547374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.1636 | −1.91280 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.688922 | 0.0383326 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.425406 | − | 0.736824i | 0.0235973 | − | 0.0408716i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.9504 | + | 6.24105i | 0.769110 | + | 0.344080i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6072 | −0.857847 | −0.428923 | − | 0.903341i | \(-0.641107\pi\) | ||||
−0.428923 | + | 0.903341i | \(0.641107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.66812 | + | 15.0136i | −0.473590 | + | 0.820282i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.77185 | − | 6.53303i | −0.205466 | − | 0.355877i | 0.744815 | − | 0.667271i | \(-0.232538\pi\) |
−0.950281 | + | 0.311394i | \(0.899204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7965 | − | 20.4322i | −0.638818 | − | 1.10646i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.62843 | + | 17.6443i | 0.303907 | + | 0.952702i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.9003 | −1.44408 | −0.722042 | − | 0.691849i | \(-0.756796\pi\) | ||||
−0.722042 | + | 0.691849i | \(0.756796\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00100 | − | 12.1261i | 0.374755 | − | 0.649095i | −0.615535 | − | 0.788109i | \(-0.711060\pi\) |
0.990290 | + | 0.139014i | \(0.0443934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1655 | + | 26.2675i | 0.807180 | + | 1.39808i | 0.914810 | + | 0.403885i | \(0.132341\pi\) |
−0.107630 | + | 0.994191i | \(0.534326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.89489 | − | 17.1384i | 0.525166 | − | 0.909614i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.99876 | + | 12.1222i | 0.369381 | + | 0.639786i | 0.989469 | − | 0.144746i | \(-0.0462366\pi\) |
−0.620088 | + | 0.784532i | \(0.712903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.03830 | − | 8.72659i | 0.265174 | − | 0.459294i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.27822 | + | 9.14215i | 0.276275 | + | 0.478522i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.25165 | + | 2.16792i | 0.0653356 | + | 0.113165i | 0.896843 | − | 0.442349i | \(-0.145855\pi\) |
−0.831507 | + | 0.555514i | \(0.812522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.5135 | + | 13.4003i | −0.961172 | + | 0.695708i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.80311 | + | 15.2474i | −0.455808 | + | 0.789482i | −0.998734 | − | 0.0502980i | \(-0.983983\pi\) |
0.542926 | + | 0.839780i | \(0.317316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.7629 | 1.12085 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.5474 | 0.541781 | 0.270891 | − | 0.962610i | \(-0.412682\pi\) | ||||
0.270891 | + | 0.962610i | \(0.412682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8418 | − | 18.7786i | 0.553992 | − | 0.959542i | −0.443989 | − | 0.896032i | \(-0.646437\pi\) |
0.997981 | − | 0.0635100i | \(-0.0202295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.8118 | − | 11.1002i | −1.26453 | − | 0.565717i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.96652 | + | 12.0664i | 0.353217 | + | 0.611790i | 0.986811 | − | 0.161876i | \(-0.0517545\pi\) |
−0.633594 | + | 0.773665i | \(0.718421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0923174 | + | 0.159898i | 0.00466869 | + | 0.00808641i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.1338 | − | 19.2844i | 0.560204 | − | 0.970303i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.9542 | + | 24.1694i | 0.700342 | + | 1.21303i | 0.968346 | + | 0.249610i | \(0.0803025\pi\) |
−0.268004 | + | 0.963418i | \(0.586364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.4525 | + | 30.2285i | −0.871534 | + | 1.50954i | −0.0111242 | + | 0.999938i | \(0.503541\pi\) |
−0.860410 | + | 0.509603i | \(0.829792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.51463 | + | 13.0157i | 0.374330 | + | 0.648359i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.55717 | + | 13.0894i | −0.374595 | + | 0.648818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.6739 | −1.02226 | −0.511128 | − | 0.859504i | \(-0.670772\pi\) | ||||
−0.511128 | + | 0.859504i | \(0.670772\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.1801 | − | 9.02806i | −0.992998 | − | 0.444242i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.4870 | − | 33.7525i | −0.956581 | − | 1.65685i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9859 | + | 34.6166i | 0.976376 | + | 1.69113i | 0.675316 | + | 0.737529i | \(0.264007\pi\) |
0.301061 | + | 0.953605i | \(0.402659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5082 | + | 21.6649i | −0.609614 | + | 1.05588i | 0.381690 | + | 0.924290i | \(0.375342\pi\) |
−0.991304 | + | 0.131592i | \(0.957991\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0690187 | 0.00334790 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.8151 | − | 14.2333i | −1.53964 | − | 0.688796i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.05181 | − | 12.2141i | 0.339674 | − | 0.588332i | −0.644698 | − | 0.764438i | \(-0.723017\pi\) |
0.984371 | + | 0.176106i | \(0.0563500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.58941 | 0.0763821 | 0.0381911 | − | 0.999270i | \(-0.487840\pi\) | ||||
0.0381911 | + | 0.999270i | \(0.487840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.39152 | −0.114402 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.3768 | −1.16344 | −0.581721 | − | 0.813389i | \(-0.697620\pi\) | ||||
−0.581721 | + | 0.813389i | \(0.697620\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.5640 | −0.882002 | −0.441001 | − | 0.897507i | \(-0.645376\pi\) | ||||
−0.441001 | + | 0.897507i | \(0.645376\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.34827 | 0.206128 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.4616 | −1.01284 | −0.506418 | − | 0.862288i | \(-0.669031\pi\) | ||||
−0.506418 | + | 0.862288i | \(0.669031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.01527 | + | 6.95465i | −0.189072 | + | 0.327482i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.8056 | + | 7.07103i | 0.740979 | + | 0.331495i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1274 | 0.707631 | 0.353816 | − | 0.935315i | \(-0.384884\pi\) | ||||
0.353816 | + | 0.935315i | \(0.384884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5385 | + | 28.6455i | −0.770273 | + | 1.33415i | 0.167140 | + | 0.985933i | \(0.446547\pi\) |
−0.937413 | + | 0.348219i | \(0.886787\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4223 | − | 23.2481i | −0.623788 | − | 1.08043i | −0.988774 | − | 0.149419i | \(-0.952260\pi\) |
0.364986 | − | 0.931013i | \(-0.381074\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.93579 | − | 10.2811i | −0.274675 | − | 0.475752i | 0.695378 | − | 0.718644i | \(-0.255237\pi\) |
−0.970053 | + | 0.242893i | \(0.921904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1878 | − | 8.13674i | −0.839833 | − | 0.375720i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.3669 | −1.99401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.446989 | + | 0.774208i | −0.0205093 | + | 0.0355231i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.71973 | − | 15.1030i | −0.398415 | − | 0.690075i | 0.595116 | − | 0.803640i | \(-0.297106\pi\) |
−0.993531 | + | 0.113565i | \(0.963773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.81407 | − | 8.33822i | 0.219503 | − | 0.380190i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.7438 | − | 30.7332i | −0.805706 | − | 1.39552i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3889 | − | 31.8504i | 0.833279 | − | 1.44328i | −0.0621458 | − | 0.998067i | \(-0.519794\pi\) |
0.895424 | − | 0.445214i | \(-0.146872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.54050 | + | 7.86437i | 0.204910 | + | 0.354914i | 0.950104 | − | 0.311933i | \(-0.100977\pi\) |
−0.745194 | + | 0.666847i | \(0.767643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.882716 | + | 1.52891i | 0.0397555 | + | 0.0688586i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.7618 | + | 9.28831i | 0.931294 | + | 0.416638i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.41261 | + | 5.91082i | −0.152769 | + | 0.264604i | −0.932245 | − | 0.361829i | \(-0.882153\pi\) |
0.779475 | + | 0.626433i | \(0.215486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.09211 | 0.182458 | 0.0912291 | − | 0.995830i | \(-0.470920\pi\) | ||||
0.0912291 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.47989 | 0.288351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3991 | − | 24.9400i | 0.638228 | − | 1.10544i | −0.347593 | − | 0.937646i | \(-0.613001\pi\) |
0.985821 | − | 0.167798i | \(-0.0536658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.82834 | + | 7.11387i | −0.434780 | + | 0.314699i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.88929 | + | 10.2006i | 0.259513 | + | 0.449490i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.8897 | − | 22.3256i | −0.566888 | − | 0.981878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.92170 | + | 10.2567i | −0.259434 | + | 0.449353i | −0.966090 | − | 0.258204i | \(-0.916869\pi\) |
0.706656 | + | 0.707557i | \(0.250203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.86664 | + | 11.8934i | 0.300257 | + | 0.520061i | 0.976194 | − | 0.216899i | \(-0.0695942\pi\) |
−0.675937 | + | 0.736959i | \(0.736261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.609594 | + | 1.05585i | −0.0265543 | + | 0.0459935i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1795 | + | 19.3635i | 0.486067 | + | 0.841892i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.55781 | − | 4.43025i | 0.110791 | − | 0.191896i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.96162 | −0.257743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.76008 | − | 29.6766i | 0.420396 | − | 1.27826i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7425 | + | 37.6592i | 0.934784 | + | 1.61909i | 0.775019 | + | 0.631938i | \(0.217740\pi\) |
0.159765 | + | 0.987155i | \(0.448926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.1824 | + | 34.9570i | 0.864519 | + | 1.49739i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.0307 | + | 19.1058i | −0.471640 | + | 0.816904i | −0.999474 | − | 0.0324437i | \(-0.989671\pi\) |
0.527834 | + | 0.849348i | \(0.323004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.8671 | −0.974171 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.3614 | + | 10.4513i | 0.993429 | + | 0.444435i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.0925 | + | 27.8730i | −0.681862 | + | 1.18102i | 0.292551 | + | 0.956250i | \(0.405496\pi\) |
−0.974412 | + | 0.224769i | \(0.927837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.6256 | 1.16844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.38738 | 0.142761 | 0.0713804 | − | 0.997449i | \(-0.477260\pi\) | ||||
0.0713804 | + | 0.997449i | \(0.477260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.8318 | −1.59160 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.3474 | −1.69145 | −0.845726 | − | 0.533618i | \(-0.820832\pi\) | ||||
−0.845726 | + | 0.533618i | \(0.820832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4386 | −0.436840 | −0.218420 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218420 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.239591 | −0.00999164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.55156 | − | 9.61559i | 0.231114 | − | 0.400302i | −0.727022 | − | 0.686614i | \(-0.759096\pi\) |
0.958136 | + | 0.286312i | \(0.0924295\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.2859 | − | 26.2642i | 1.50539 | − | 1.08962i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.5510 | 1.59662 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.3875 | + | 35.3122i | −0.841482 | + | 1.45749i | 0.0471601 | + | 0.998887i | \(0.484983\pi\) |
−0.888642 | + | 0.458602i | \(0.848350\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.89589 | − | 13.6761i | −0.325345 | − | 0.563513i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7930 | + | 25.6221i | 0.607474 | + | 1.05218i | 0.991655 | + | 0.128918i | \(0.0411503\pi\) |
−0.384182 | + | 0.923258i | \(0.625516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.144324 | + | 1.39720i | 0.00591669 | + | 0.0572794i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3552 | −0.749973 | −0.374987 | − | 0.927030i | \(-0.622353\pi\) | ||||
−0.374987 | + | 0.927030i | \(0.622353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9250 | − | 27.5828i | 0.649593 | − | 1.12513i | −0.333628 | − | 0.942705i | \(-0.608273\pi\) |
0.983220 | − | 0.182423i | \(-0.0583939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2642 | + | 17.7781i | 0.417298 | + | 0.722781i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8452 | + | 20.5164i | −0.480780 | + | 0.832736i | −0.999757 | − | 0.0220527i | \(-0.992980\pi\) |
0.518977 | + | 0.854788i | \(0.326313\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.21099 | + | 14.2219i | 0.332181 | + | 0.575354i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3159 | − | 23.0638i | 0.537824 | − | 0.931539i | −0.461197 | − | 0.887298i | \(-0.652580\pi\) |
0.999021 | − | 0.0442411i | \(-0.0140870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.72483 | + | 8.18364i | 0.190214 | + | 0.329461i | 0.945321 | − | 0.326141i | \(-0.105748\pi\) |
−0.755107 | + | 0.655602i | \(0.772415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0474 | + | 31.2589i | 0.725385 | + | 1.25640i | 0.958815 | + | 0.284030i | \(0.0916714\pi\) |
−0.233431 | + | 0.972373i | \(0.574995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.513492 | + | 4.97111i | 0.0205726 | + | 0.199163i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.2034 | − | 22.8689i | 0.528136 | − | 0.914758i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.781045 | 0.0311423 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0100579 | 0.000400401 | 0.000200200 | − | 1.00000i | \(-0.499936\pi\) | ||||
0.000200200 | 1.00000i | \(0.499936\pi\) | ||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.35935 | − | 16.2109i | 0.371415 | − | 0.643309i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.21737 | + | 18.9046i | −0.246341 | + | 0.749028i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.45227 | + | 4.24745i | 0.0968587 | + | 0.167764i | 0.910383 | − | 0.413767i | \(-0.135787\pi\) |
−0.813524 | + | 0.581531i | \(0.802454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0655 | + | 38.2186i | 0.870180 | + | 1.50720i | 0.861810 | + | 0.507231i | \(0.169331\pi\) |
0.00837033 | + | 0.999965i | \(0.497336\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.8813 | + | 43.0957i | −0.978186 | + | 1.69427i | −0.309192 | + | 0.950999i | \(0.600059\pi\) |
−0.668993 | + | 0.743268i | \(0.733275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6457 | + | 32.2953i | 0.731908 | + | 1.26770i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.98578 | + | 12.0997i | −0.273375 | + | 0.473499i | −0.969724 | − | 0.244205i | \(-0.921473\pi\) |
0.696349 | + | 0.717703i | \(0.254807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4012 | − | 24.9436i | −0.562702 | − | 0.974628i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9827 | − | 22.4867i | 0.505733 | − | 0.875956i | −0.494245 | − | 0.869323i | \(-0.664555\pi\) |
0.999978 | − | 0.00663317i | \(-0.00211142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5362 | 0.993244 | 0.496622 | − | 0.867967i | \(-0.334574\pi\) | ||||
0.496622 | + | 0.867967i | \(0.334574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.6075 | − | 7.42979i | −0.644013 | − | 0.288115i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.06425 | − | 5.30744i | −0.118648 | − | 0.205505i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3961 | + | 50.9155i | 1.13482 | + | 1.96557i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.71472 | − | 4.70203i | 0.104645 | − | 0.181250i | −0.808948 | − | 0.587880i | \(-0.799963\pi\) |
0.913593 | + | 0.406630i | \(0.133296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1514 | −0.543883 | −0.271942 | − | 0.962314i | \(-0.587666\pi\) | ||||
−0.271942 | + | 0.962314i | \(0.587666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.0400 | − | 23.9147i | 1.26796 | − | 0.917763i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.553330 | + | 0.958397i | −0.0211726 | + | 0.0366720i | −0.876418 | − | 0.481552i | \(-0.840073\pi\) |
0.855245 | + | 0.518224i | \(0.173407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.2773 | −1.42429 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.5578 | −0.935577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.9077 | 0.871450 | 0.435725 | − | 0.900080i | \(-0.356492\pi\) | ||||
0.435725 | + | 0.900080i | \(0.356492\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1441 | 0.536517 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.414984 | 0.0157186 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.4056 | −0.430782 | −0.215391 | − | 0.976528i | \(-0.569103\pi\) | ||||
−0.215391 | + | 0.976528i | \(0.569103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.05832 | + | 8.76127i | −0.190778 | + | 0.330438i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.765216 | + | 7.40805i | 0.0287789 | + | 0.278608i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0671 | −1.39208 | −0.696042 | − | 0.718001i | \(-0.745057\pi\) | ||||
−0.696042 | + | 0.718001i | \(0.745057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.11614 | − | 3.66527i | 0.0792502 | − | 0.137265i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.6038 | − | 25.2946i | −0.546153 | − | 0.945965i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.459342 | − | 0.795604i | −0.0171306 | − | 0.0296710i | 0.857333 | − | 0.514762i | \(-0.172120\pi\) |
−0.874464 | + | 0.485091i | \(0.838786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9662 | + | 7.93745i | −0.408402 | + | 0.295606i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.29091 | −0.0850822 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.34433 | − | 12.7208i | 0.272386 | − | 0.471787i | −0.697086 | − | 0.716987i | \(-0.745521\pi\) |
0.969472 | + | 0.245201i | \(0.0788538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.12051 | + | 1.94078i | 0.0414435 | + | 0.0717823i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4312 | − | 19.7994i | 0.422220 | − | 0.731307i | −0.573936 | − | 0.818900i | \(-0.694584\pi\) |
0.996156 | + | 0.0875931i | \(0.0279175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.8049 | + | 29.1069i | 0.619015 | + | 1.07217i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6692 | − | 34.0681i | 0.723544 | − | 1.25321i | −0.236027 | − | 0.971746i | \(-0.575845\pi\) |
0.959571 | − | 0.281468i | \(-0.0908212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8663 | + | 18.8210i | 0.398647 | + | 0.690477i | 0.993559 | − | 0.113314i | \(-0.0361465\pi\) |
−0.594912 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.88410 | + | 15.3877i | 0.325488 | + | 0.563762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.704014 | − | 6.81554i | −0.0257241 | − | 0.249034i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3071 | + | 17.8525i | −0.376113 | + | 0.651446i | −0.990493 | − | 0.137564i | \(-0.956073\pi\) |
0.614380 | + | 0.789010i | \(0.289406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.3404 | 1.24978 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8453 | 0.648600 | 0.324300 | − | 0.945954i | \(-0.394871\pi\) | ||||
0.324300 | + | 0.945954i | \(0.394871\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9714 | − | 29.3953i | 0.615211 | − | 1.06558i | −0.375136 | − | 0.926970i | \(-0.622404\pi\) |
0.990347 | − | 0.138607i | \(-0.0442626\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37.5807 | + | 27.2014i | −1.36051 | + | 0.984756i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.8777 | − | 20.5728i | −0.428879 | − | 0.742840i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3452 | + | 35.2389i | 0.733665 | + | 1.27075i | 0.955306 | + | 0.295617i | \(0.0955253\pi\) |
−0.221641 | + | 0.975128i | \(0.571141\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.17562 | − | 3.76829i | 0.0782517 | − | 0.135536i | −0.824244 | − | 0.566235i | \(-0.808400\pi\) |
0.902496 | + | 0.430699i | \(0.141733\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.791039 | − | 1.37012i | −0.0284150 | − | 0.0492162i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.68758 | + | 4.65503i | −0.0962926 | + | 0.166784i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1832 | − | 33.2263i | −0.686429 | − | 1.18893i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.296062 | + | 0.512795i | −0.0105669 | + | 0.0183024i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.6220 | 1.34108 | 0.670539 | − | 0.741874i | \(-0.266063\pi\) | ||||
0.670539 | + | 0.741874i | \(0.266063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.46760 | − | 43.2508i | −0.158850 | − | 1.53782i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7259 | − | 32.4342i | −0.664976 | − | 1.15177i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.1570 | − | 38.3771i | −0.784842 | − | 1.35939i | −0.929093 | − | 0.369845i | \(-0.879411\pi\) |
0.144251 | − | 0.989541i | \(-0.453923\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.666084 | + | 1.15369i | −0.0235644 | + | 0.0408147i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.4658 | 0.722221 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.501005 | − | 4.85022i | −0.0176581 | − | 0.170948i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.78609 | + | 16.9500i | −0.344061 | + | 0.595931i | −0.985183 | − | 0.171508i | \(-0.945136\pi\) |
0.641122 | + | 0.767439i | \(0.278469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.15430 | −0.145877 | −0.0729386 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729386 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.9477 | −1.01399 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0272 | −1.01553 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.7542 | 1.00353 | 0.501764 | − | 0.865005i | \(-0.332685\pi\) | ||||
0.501764 | + | 0.865005i | \(0.332685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.0881 | −0.735086 | −0.367543 | − | 0.930007i | \(-0.619801\pi\) | ||||
−0.367543 | + | 0.930007i | \(0.619801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −56.8422 | −1.97660 | −0.988299 | − | 0.152530i | \(-0.951258\pi\) | ||||
−0.988299 | + | 0.152530i | \(0.951258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.97588 | + | 15.5467i | −0.311745 | + | 0.539959i | −0.978740 | − | 0.205104i | \(-0.934247\pi\) |
0.666995 | + | 0.745062i | \(0.267580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.58028 | + | 0.329992i | −0.0547535 | + | 0.0114336i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.9397 | 1.72823 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.38469 | + | 7.59451i | −0.151376 | + | 0.262192i | −0.931734 | − | 0.363142i | \(-0.881704\pi\) |
0.780357 | + | 0.625334i | \(0.215037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7996 | − | 25.6337i | −0.510332 | − | 0.883921i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.66014 | − | 9.80366i | −0.194715 | − | 0.337256i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.1124 | + | 13.8338i | −0.656711 | + | 0.475336i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.71132 | −0.0929427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0519 | − | 27.8027i | 0.549607 | − | 0.951948i | −0.448694 | − | 0.893686i | \(-0.648111\pi\) |
0.998301 | − | 0.0582625i | \(-0.0185560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.25126 | + | 10.8275i | 0.213539 | + | 0.369861i | 0.952820 | − | 0.303537i | \(-0.0981676\pi\) |
−0.739281 | + | 0.673398i | \(0.764834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.78438 | + | 6.55474i | −0.129121 | + | 0.223645i | −0.923336 | − | 0.383992i | \(-0.874549\pi\) |
0.794215 | + | 0.607637i | \(0.207882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.268987 | + | 0.465899i | 0.00915642 | + | 0.0158594i | 0.870567 | − | 0.492049i | \(-0.163752\pi\) |
−0.861411 | + | 0.507909i | \(0.830419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.8384 | − | 27.4329i | 0.538522 | − | 0.932747i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.5852 | − | 37.3866i | −0.732226 | − | 1.26825i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.7050 | − | 18.5417i | −0.362726 | − | 0.628260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.1340 | + | 11.6917i | 0.883490 | + | 0.395251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3537 | + | 23.1292i | −0.450921 | + | 0.781019i | −0.998443 | − | 0.0557726i | \(-0.982238\pi\) |
0.547522 | + | 0.836791i | \(0.315571\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.6239 | 1.13282 | 0.566408 | − | 0.824125i | \(-0.308333\pi\) | ||||
0.566408 | + | 0.824125i | \(0.308333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.20109 | 0.242336 | 0.121168 | − | 0.992632i | \(-0.461336\pi\) | ||||
0.121168 | + | 0.992632i | \(0.461336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.39373 | − | 4.14606i | 0.0803736 | − | 0.139211i | −0.823037 | − | 0.567988i | \(-0.807722\pi\) |
0.903410 | + | 0.428777i | \(0.141055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.6381 | + | 8.78560i | 0.658642 | + | 0.294660i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.62759 | − | 14.9434i | −0.288711 | − | 0.500062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.03190 | + | 1.78731i | 0.0344928 | + | 0.0597432i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.2340 | − | 35.0464i | 0.674842 | − | 1.16886i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.996076 | − | 1.72525i | −0.0331841 | − | 0.0574766i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0980 | + | 34.8108i | −0.668081 | + | 1.15715i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4176 | + | 30.1681i | 0.578341 | + | 1.00172i | 0.995670 | + | 0.0929599i | \(0.0296328\pi\) |
−0.417329 | + | 0.908755i | \(0.637034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1584 | − | 50.5038i | 0.966060 | − | 1.67326i | 0.259319 | − | 0.965792i | \(-0.416502\pi\) |
0.706740 | − | 0.707473i | \(-0.250165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −75.5589 | −2.50063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.8158 | − | 19.4096i | 0.885536 | − | 0.640962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.113983 | − | 0.197424i | −0.00375995 | − | 0.00651242i | 0.864139 | − | 0.503253i | \(-0.167863\pi\) |
−0.867899 | + | 0.496740i | \(0.834530\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.2201 | + | 21.1658i | 0.402229 | + | 0.696681i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.506761 | + | 0.877736i | −0.0166622 | + | 0.0288598i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.8851 | −0.816453 | −0.408226 | − | 0.912881i | \(-0.633853\pi\) | ||||
−0.408226 | + | 0.912881i | \(0.633853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.53281 | − | 19.8638i | 0.214104 | − | 0.651008i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.18468 | − | 2.05192i | 0.0387432 | − | 0.0671051i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.3194 | −1.44785 | −0.723926 | − | 0.689878i | \(-0.757664\pi\) | ||||
−0.723926 | + | 0.689878i | \(0.757664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.2820 | 1.96514 | 0.982568 | − | 0.185904i | \(-0.0595215\pi\) | ||||
0.982568 | + | 0.185904i | \(0.0595215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.44057 | −0.0469115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.5977 | −0.474361 | −0.237180 | − | 0.971466i | \(-0.576223\pi\) | ||||
−0.237180 | + | 0.971466i | \(0.576223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.0371 | −0.423202 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9601 | 0.387427 | 0.193713 | − | 0.981058i | \(-0.437947\pi\) | ||||
0.193713 | + | 0.981058i | \(0.437947\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.69086 | + | 2.92865i | −0.0547148 | + | 0.0947688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.40212 | − | 42.6168i | −0.142152 | − | 1.37617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.05319 | −0.0984899 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.48535 | − | 12.9650i | 0.240962 | − | 0.417358i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8250 | + | 39.5340i | 0.734001 | + | 1.27133i | 0.955160 | + | 0.296090i | \(0.0956828\pi\) |
−0.221159 | + | 0.975238i | \(0.570984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.25397 | + | 2.17194i | 0.0402418 | + | 0.0697009i | 0.885445 | − | 0.464745i | \(-0.153854\pi\) |
−0.845203 | + | 0.534445i | \(0.820521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.67030 | + | 16.1701i | 0.0535472 | + | 0.518390i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.6201 | −1.84343 | −0.921715 | − | 0.387867i | \(-0.873212\pi\) | ||||
−0.921715 | + | 0.387867i | \(0.873212\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.21499 | − | 7.30058i | 0.134712 | − | 0.233328i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6868 | − | 51.4190i | −0.946862 | − | 1.64001i | −0.751980 | − | 0.659186i | \(-0.770901\pi\) |
−0.194881 | − | 0.980827i | \(-0.562432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.7570 | + | 23.8278i | −0.438333 | + | 0.759215i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.88973 | − | 6.73721i | −0.123686 | − | 0.214231i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2341 | + | 35.0465i | −0.642758 | + | 1.11329i | 0.342057 | + | 0.939679i | \(0.388877\pi\) |
−0.984814 | + | 0.173610i | \(0.944457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.4190 | − | 38.8308i | −0.710730 | − | 1.23102i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.07112 | + | 12.2475i | 0.223945 | + | 0.387883i | 0.956002 | − | 0.293359i | \(-0.0947732\pi\) |
−0.732058 | + | 0.681243i | \(0.761440\pi\) | |||||||
\(998\) | 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 | 2268.2.i.n.865.7 | 16 | ||
3.2 | odd | 2 | inner | 2268.2.i.n.865.2 | 16 | ||
7.2 | even | 3 | 2268.2.l.n.541.2 | 16 | |||
9.2 | odd | 6 | 2268.2.k.g.1621.2 | yes | 16 | ||
9.4 | even | 3 | 2268.2.l.n.109.2 | 16 | |||
9.5 | odd | 6 | 2268.2.l.n.109.7 | 16 | |||
9.7 | even | 3 | 2268.2.k.g.1621.7 | yes | 16 | ||
21.2 | odd | 6 | 2268.2.l.n.541.7 | 16 | |||
63.2 | odd | 6 | 2268.2.k.g.1297.2 | ✓ | 16 | ||
63.16 | even | 3 | 2268.2.k.g.1297.7 | yes | 16 | ||
63.23 | odd | 6 | inner | 2268.2.i.n.2053.2 | 16 | ||
63.58 | even | 3 | inner | 2268.2.i.n.2053.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.2 | 16 | 3.2 | odd | 2 | inner | ||
2268.2.i.n.865.7 | 16 | 1.1 | even | 1 | trivial | ||
2268.2.i.n.2053.2 | 16 | 63.23 | odd | 6 | inner | ||
2268.2.i.n.2053.7 | 16 | 63.58 | even | 3 | inner | ||
2268.2.k.g.1297.2 | ✓ | 16 | 63.2 | odd | 6 | ||
2268.2.k.g.1297.7 | yes | 16 | 63.16 | even | 3 | ||
2268.2.k.g.1621.2 | yes | 16 | 9.2 | odd | 6 | ||
2268.2.k.g.1621.7 | yes | 16 | 9.7 | even | 3 | ||
2268.2.l.n.109.2 | 16 | 9.4 | even | 3 | |||
2268.2.l.n.109.7 | 16 | 9.5 | odd | 6 | |||
2268.2.l.n.541.2 | 16 | 7.2 | even | 3 | |||
2268.2.l.n.541.7 | 16 | 21.2 | odd | 6 |