Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(1215,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.h (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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14453810176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 6x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1215.1 | ||
Root | \(-0.331077 - 1.37491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1215 |
Dual form | 1216.2.h.d.1215.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.35829 | −1.36156 | −0.680781 | − | 0.732487i | \(-0.738359\pi\) | ||||
−0.680781 | + | 0.732487i | \(0.738359\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56155 | 1.14556 | 0.572781 | − | 0.819709i | \(-0.305865\pi\) | ||||
0.572781 | + | 0.819709i | \(0.305865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.15286i | − | 1.56963i | −0.619729 | − | 0.784816i | \(-0.712757\pi\) | ||
0.619729 | − | 0.784816i | \(-0.287243\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.56155 | 0.853851 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.33205i | − | 0.703139i | −0.936162 | − | 0.351569i | \(-0.885648\pi\) | ||
0.936162 | − | 0.351569i | \(-0.114352\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.29400i | − | 1.19094i | −0.803377 | − | 0.595471i | \(-0.796966\pi\) | ||
0.803377 | − | 0.595471i | \(-0.203034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.04090 | −1.55975 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.68260 | + | 2.33205i | −0.844847 | + | 0.535008i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.79366i | 2.13715i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.82081i | 0.379665i | 0.981817 | + | 0.189832i | \(0.0607944\pi\) | ||||
−0.981817 | + | 0.189832i | \(0.939206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.03399 | 0.198991 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.20565i | − | 0.223884i | −0.993715 | − | 0.111942i | \(-0.964293\pi\) | ||
0.993715 | − | 0.111942i | \(-0.0357071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.32431 | −0.237853 | −0.118926 | − | 0.992903i | \(-0.537945\pi\) | ||||
−0.118926 | + | 0.992903i | \(0.537945\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.49966i | 0.957367i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 10.6378i | − | 1.79811i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.49966i | 0.904138i | 0.891983 | + | 0.452069i | \(0.149314\pi\) | ||||
−0.891983 | + | 0.452069i | \(0.850686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.1265i | 1.62154i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.49966i | 0.858902i | 0.903090 | + | 0.429451i | \(0.141293\pi\) | ||||
−0.903090 | + | 0.429451i | \(0.858707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.30957i | 0.199707i | 0.995002 | + | 0.0998536i | \(0.0318375\pi\) | ||||
−0.995002 | + | 0.0998536i | \(0.968163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.56155 | 0.978139 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.99614i | − | 1.02049i | −0.860028 | − | 0.510246i | \(-0.829554\pi\) | ||
0.860028 | − | 0.510246i | \(-0.170446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.2462 | −1.46374 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.35829 | 0.330227 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.79366i | − | 1.34526i | −0.739978 | − | 0.672631i | \(-0.765164\pi\) | ||
0.739978 | − | 0.672631i | \(-0.234836\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.97366i | − | 0.805489i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.68466 | − | 5.49966i | 1.15031 | − | 0.728447i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.33122 | −0.824254 | −0.412127 | − | 0.911126i | \(-0.635214\pi\) | ||||
−0.412127 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6847 | −1.49607 | −0.748034 | − | 0.663661i | \(-0.769002\pi\) | ||||
−0.748034 | + | 0.663661i | \(0.769002\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 10.6378i | − | 1.34023i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.9993i | − | 1.36430i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.290319 | 0.0354681 | 0.0177341 | − | 0.999843i | \(-0.494355\pi\) | ||||
0.0177341 | + | 0.999843i | \(0.494355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4.29400i | − | 0.516937i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.06798 | 0.245423 | 0.122712 | − | 0.992442i | \(-0.460841\pi\) | ||||
0.122712 | + | 0.992442i | \(0.460841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.123106 | −0.0144084 | −0.00720421 | − | 0.999974i | \(-0.502293\pi\) | ||||
−0.00720421 | + | 0.999974i | \(0.502293\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.68260 | −0.425230 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.68466 | −1.10367 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4061 | −1.50830 | −0.754152 | − | 0.656700i | \(-0.771952\pi\) | ||||
−0.754152 | + | 0.656700i | \(0.771952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1231 | −1.12479 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.9473i | 1.31139i | 0.755026 | + | 0.655695i | \(0.227624\pi\) | ||||
−0.755026 | + | 0.655695i | \(0.772376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.56155 | −0.277839 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.84329i | 0.304832i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.0877i | − | 1.49329i | −0.665223 | − | 0.746644i | \(-0.731664\pi\) | ||
0.665223 | − | 0.746644i | \(-0.268336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.8324 | −1.86934 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.12311 | 0.323851 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.43318 | + | 5.97366i | −0.967824 | + | 0.612885i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.41131i | − | 0.244831i | −0.992479 | − | 0.122416i | \(-0.960936\pi\) | ||
0.992479 | − | 0.122416i | \(-0.0390641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.97366i | − | 0.600376i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.24621 | 0.820529 | 0.410264 | − | 0.911967i | \(-0.365436\pi\) | ||||
0.410264 | + | 0.911967i | \(0.365436\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0818 | 1.19045 | 0.595227 | − | 0.803557i | \(-0.297062\pi\) | ||||
0.595227 | + | 0.803557i | \(0.297062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 25.0870i | 2.44824i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.75058 | 0.555929 | 0.277965 | − | 0.960591i | \(-0.410340\pi\) | ||||
0.277965 | + | 0.960591i | \(0.410340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.2050i | − | 1.16902i | −0.811385 | − | 0.584512i | \(-0.801286\pi\) | ||
0.811385 | − | 0.584512i | \(-0.198714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 12.9698i | − | 1.23104i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.49966i | − | 0.517364i | −0.965963 | − | 0.258682i | \(-0.916712\pi\) | ||
0.965963 | − | 0.258682i | \(-0.0832882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.66410i | 0.434929i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.9993i | − | 1.01689i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.15286i | 0.380692i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.56155 | 0.505596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 12.9698i | − | 1.16945i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.80776 | −0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.04090 | 0.536043 | 0.268021 | − | 0.963413i | \(-0.413630\pi\) | ||||
0.268021 | + | 0.963413i | \(0.413630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.08835i | − | 0.271914i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.97366i | − | 0.521921i | −0.965349 | − | 0.260961i | \(-0.915961\pi\) | ||
0.965349 | − | 0.260961i | \(-0.0840393\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.68466 | + | 15.2933i | 0.839766 | + | 1.32610i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.64861 | 0.227956 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.1231 | −1.03575 | −0.517873 | − | 0.855457i | \(-0.673276\pi\) | ||||
−0.517873 | + | 0.855457i | \(0.673276\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.9435i | − | 1.60676i | −0.595464 | − | 0.803382i | \(-0.703032\pi\) | ||
0.595464 | − | 0.803382i | \(-0.296968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4990i | 1.38946i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0138 | −0.837397 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.08835i | − | 0.256473i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.1636 | 1.99298 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.80776 | −0.230021 | −0.115010 | − | 0.993364i | \(-0.536690\pi\) | ||||
−0.115010 | + | 0.993364i | \(0.536690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.85254 | −0.720409 | −0.360205 | − | 0.932873i | \(-0.617293\pi\) | ||||
−0.360205 | + | 0.932873i | \(0.617293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.56155 | −0.207089 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39228 | −0.272475 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.0963i | 1.83166i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.56155 | 0.595934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6339i | 1.38119i | 0.723240 | + | 0.690597i | \(0.242652\pi\) | ||||
−0.723240 | + | 0.690597i | \(0.757348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.0877i | 1.09672i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7575 | −0.832439 | −0.416220 | − | 0.909264i | \(-0.636645\pi\) | ||||
−0.416220 | + | 0.909264i | \(0.636645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.43845 | −0.418342 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.43318 | + | 5.97366i | −0.721373 | + | 0.456817i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.41131i | 0.183328i | 0.995790 | + | 0.0916642i | \(0.0292186\pi\) | ||||
−0.995790 | + | 0.0916642i | \(0.970781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.48490i | − | 0.490213i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.9309 | 1.12227 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.10887 | 0.606085 | 0.303043 | − | 0.952977i | \(-0.401998\pi\) | ||||
0.303043 | + | 0.952977i | \(0.401998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.5873i | − | 1.45591i | −0.685623 | − | 0.727957i | \(-0.740470\pi\) | ||
0.685623 | − | 0.727957i | \(-0.259530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.5559 | 2.03699 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.0877i | 1.03575i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.33205i | 0.170536i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 4.29400i | − | 0.312343i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.79447i | − | 0.563988i | −0.959416 | − | 0.281994i | \(-0.909004\pi\) | ||
0.959416 | − | 0.281994i | \(-0.0909959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.49966i | 0.395874i | 0.980215 | + | 0.197937i | \(0.0634241\pi\) | ||||
−0.980215 | + | 0.197937i | \(0.936576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.9396i | 1.85757i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4924 | 1.60252 | 0.801259 | − | 0.598317i | \(-0.204164\pi\) | ||||
0.801259 | + | 0.598317i | \(0.204164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.17534i | 0.366870i | 0.983032 | + | 0.183435i | \(0.0587217\pi\) | ||||
−0.983032 | + | 0.183435i | \(0.941278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.684658 | −0.0482921 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00691 | −0.351416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0877i | 0.983925i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.66410i | 0.324177i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.43845 | + | 8.58800i | 0.376185 | + | 0.594045i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.1976 | 1.73467 | 0.867336 | − | 0.497723i | \(-0.165830\pi\) | ||||
0.867336 | + | 0.497723i | \(0.165830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.87689 | −0.334159 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.35453i | 0.228777i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.49966i | 0.373341i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.290319 | 0.0196180 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.29400i | 0.288846i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2586 | 1.49055 | 0.745274 | − | 0.666758i | \(-0.232319\pi\) | ||||
0.745274 | + | 0.666758i | \(0.232319\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.6169 | −1.63388 | −0.816942 | − | 0.576720i | \(-0.804332\pi\) | ||||
−0.816942 | + | 0.576720i | \(0.804332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.56155 | 0.433600 | 0.216800 | − | 0.976216i | \(-0.430438\pi\) | ||||
0.216800 | + | 0.976216i | \(0.430438\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.8393 | 1.50271 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8078 | 0.708040 | 0.354020 | − | 0.935238i | \(-0.384814\pi\) | ||||
0.354020 | + | 0.935238i | \(0.384814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 17.9210i | − | 1.16904i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 31.6155 | 2.05365 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.83943i | − | 0.636460i | −0.948014 | − | 0.318230i | \(-0.896912\pi\) | ||
0.948014 | − | 0.318230i | \(-0.103088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6757i | 1.46067i | 0.683090 | + | 0.730334i | \(0.260635\pi\) | ||||
−0.683090 | + | 0.730334i | \(0.739365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.7713 | 1.33248 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.2462 | −1.67681 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0138 | + | 15.8131i | 0.637164 | + | 1.00616i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 28.1753i | − | 1.78554i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5626i | 1.36102i | 0.732739 | + | 0.680510i | \(0.238242\pi\) | ||||
−0.732739 | + | 0.680510i | \(0.761758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.24621 | 0.266957 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.04090 | 0.378296 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.1760i | − | 1.07141i | −0.844405 | − | 0.535705i | \(-0.820046\pi\) | ||
0.844405 | − | 0.535705i | \(-0.179954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.8393 | 1.41916 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 3.08835i | − | 0.191164i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.2794i | − | 0.880504i | −0.897874 | − | 0.440252i | \(-0.854889\pi\) | ||
0.897874 | − | 0.440252i | \(-0.145111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 25.0870i | − | 1.54108i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.2228i | 2.03321i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.49966i | − | 0.335320i | −0.985845 | − | 0.167660i | \(-0.946379\pi\) | ||
0.985845 | − | 0.167660i | \(-0.0536211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0738i | 1.34089i | 0.741959 | + | 0.670445i | \(0.233897\pi\) | ||||
−0.741959 | + | 0.670445i | \(0.766103\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 42.0540 | 2.54522 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.64162i | − | 0.219598i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0540 | −0.784337 | −0.392169 | − | 0.919893i | \(-0.628275\pi\) | ||||
−0.392169 | + | 0.919893i | \(0.628275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.39228 | −0.203091 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.1753i | 1.68080i | 0.541968 | + | 0.840399i | \(0.317679\pi\) | ||||
−0.541968 | + | 0.840399i | \(0.682321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.97366i | − | 0.355097i | −0.984112 | − | 0.177549i | \(-0.943183\pi\) | ||
0.984112 | − | 0.177549i | \(-0.0568167\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 22.2462 | − | 14.0877i | 1.31775 | − | 0.834481i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.8393 | 1.34816 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.68658i | 0.333353i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.29400i | 0.250858i | 0.992103 | + | 0.125429i | \(0.0400308\pi\) | ||||
−0.992103 | + | 0.125429i | \(0.959969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.2177 | −0.944233 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.41131i | − | 0.139918i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.81855 | 0.452159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.43845 | 0.313467 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.4470 | −1.11720 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.9309 | −1.71384 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4061 | 0.765126 | 0.382563 | − | 0.923929i | \(-0.375041\pi\) | ||||
0.382563 | + | 0.923929i | \(0.375041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.4924 | −1.62088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.15286i | − | 0.235487i | −0.993044 | − | 0.117743i | \(-0.962434\pi\) | ||
0.993044 | − | 0.117743i | \(-0.0375660\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.438447 | −0.0247825 | −0.0123913 | − | 0.999923i | \(-0.503944\pi\) | ||||
−0.0123913 | + | 0.999923i | \(0.503944\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 27.2492i | − | 1.53532i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.29400i | − | 0.241175i | −0.992703 | − | 0.120588i | \(-0.961522\pi\) | ||
0.992703 | − | 0.120588i | \(-0.0384779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81164 | −0.157422 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5616 | −0.756932 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.68260 | − | 2.33205i | 0.204905 | − | 0.129759i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.70531i | − | 0.371944i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.7829i | 1.59170i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.0540 | −1.60180 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8733 | 1.31219 | 0.656097 | − | 0.754677i | \(-0.272206\pi\) | ||||
0.656097 | + | 0.754677i | \(0.272206\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0877i | 0.771999i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.743668 | 0.0406309 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.17669i | − | 0.336466i | −0.985747 | − | 0.168233i | \(-0.946194\pi\) | ||
0.985747 | − | 0.168233i | \(-0.0538061\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9698i | 0.704423i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.08835i | 0.167243i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4810i | 0.727908i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 10.9993i | − | 0.592183i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 29.8683i | − | 1.60342i | −0.597716 | − | 0.801708i | \(-0.703925\pi\) | ||
0.597716 | − | 0.801708i | \(-0.296075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.05398 | −0.484648 | −0.242324 | − | 0.970195i | \(-0.577910\pi\) | ||||
−0.242324 | + | 0.970195i | \(0.577910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.43994i | − | 0.236987i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.6847 | 0.994484 | 0.497242 | − | 0.867612i | \(-0.334346\pi\) | ||||
0.497242 | + | 0.867612i | \(0.334346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.29723 | 0.281148 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 9.79366i | − | 0.518335i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.19782i | − | 0.327108i | −0.986534 | − | 0.163554i | \(-0.947704\pi\) | ||
0.986534 | − | 0.163554i | \(-0.0522958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.12311 | − | 17.1760i | 0.427532 | − | 0.904000i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.1158 | −0.688400 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.315342 | −0.0165057 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.02248i | − | 0.0533730i | −0.999644 | − | 0.0266865i | \(-0.991504\pi\) | ||
0.999644 | − | 0.0266865i | \(-0.00849559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0877i | 0.733374i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.6716 | −2.11157 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.70531i | − | 0.347188i | −0.984817 | − | 0.173594i | \(-0.944462\pi\) | ||
0.984817 | − | 0.173594i | \(-0.0555380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.7713 | 1.07263 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.17708 | −0.266633 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7644 | −0.809762 | −0.404881 | − | 0.914369i | \(-0.632687\pi\) | ||||
−0.404881 | + | 0.914369i | \(0.632687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.2462 | −0.729856 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.2586 | −1.13736 | −0.568682 | − | 0.822558i | \(-0.692546\pi\) | ||||
−0.568682 | + | 0.822558i | \(0.692546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.8078 | −1.26432 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.35453i | 0.170520i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.8078 | −0.750783 | −0.375392 | − | 0.926866i | \(-0.622492\pi\) | ||||
−0.375392 | + | 0.926866i | \(0.622492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.82081i | − | 0.0920822i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.0877i | 0.710628i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −34.3404 | −1.72785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.93087 | 0.197285 | 0.0986423 | − | 0.995123i | \(-0.468550\pi\) | ||||
0.0986423 | + | 0.995123i | \(0.468550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.8393 | − | 36.0661i | −1.14339 | − | 1.80557i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.91096i | 0.395055i | 0.980297 | + | 0.197527i | \(0.0632911\pi\) | ||||
−0.980297 | + | 0.197527i | \(0.936709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.68658i | 0.283269i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.9309 | −1.28852 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8255 | 0.635734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.4983i | − | 1.35970i | −0.733350 | − | 0.679851i | \(-0.762044\pi\) | ||
0.733350 | − | 0.679851i | \(-0.237956\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.5899 | 1.41023 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.2926i | 1.29378i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.6037i | 1.50228i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 44.6743i | 2.18771i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 39.9319i | − | 1.95080i | −0.220440 | − | 0.975401i | \(-0.570749\pi\) | ||
0.220440 | − | 0.975401i | \(-0.429251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2043i | 1.13091i | 0.824780 | + | 0.565454i | \(0.191299\pi\) | ||||
−0.824780 | + | 0.565454i | \(0.808701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 17.9210i | − | 0.871348i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.56155 | −0.0757464 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.5247i | 2.34827i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.6155 | 1.14017 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.29723 | −0.255158 | −0.127579 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127579 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.9103i | − | 0.908770i | −0.890805 | − | 0.454385i | \(-0.849859\pi\) | ||
0.890805 | − | 0.454385i | \(-0.150141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.28323i | 0.349204i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.24621 | − | 6.70531i | −0.203124 | − | 0.320758i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.6100 | 0.935935 | 0.467968 | − | 0.883746i | \(-0.344986\pi\) | ||||
0.467968 | + | 0.883746i | \(0.344986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.2462 | −1.24982 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.2344i | 0.581275i | 0.956833 | + | 0.290637i | \(0.0938673\pi\) | ||||
−0.956833 | + | 0.290637i | \(0.906133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 36.0863i | − | 1.71065i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.62153 | 0.313188 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.7647i | 0.696789i | 0.937348 | + | 0.348395i | \(0.113273\pi\) | ||||
−0.937348 | + | 0.348395i | \(0.886727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8255 | 0.603927 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.8769 | 0.980882 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.6786 | −2.14144 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.87689 | 0.181353 | 0.0906767 | − | 0.995880i | \(-0.471097\pi\) | ||||
0.0906767 | + | 0.995880i | \(0.471097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.03399 | −0.0482624 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.6847 | −1.47570 | −0.737851 | − | 0.674964i | \(-0.764159\pi\) | ||||
−0.737851 | + | 0.674964i | \(0.764159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.3243i | − | 0.758656i | −0.925262 | − | 0.379328i | \(-0.876155\pi\) | ||
0.925262 | − | 0.379328i | \(-0.123845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | 0.370991 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.33205i | − | 0.107914i | −0.998543 | − | 0.0539572i | \(-0.982817\pi\) | ||
0.998543 | − | 0.0539572i | \(-0.0171834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.20565i | − | 0.0556719i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1498 | 0.651987 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.05398 | 0.140422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.75058 | + | 3.64162i | −0.263855 | + | 0.167089i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 25.0870i | − | 1.14865i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 41.5286i | − | 1.89749i | −0.316045 | − | 0.948744i | \(-0.602355\pi\) | ||
0.316045 | − | 0.948744i | \(-0.397645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.6155 | 1.07678 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.8324 | −0.811401 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 6.17669i | − | 0.280469i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8664 | 0.854916 | 0.427458 | − | 0.904035i | \(-0.359409\pi\) | ||||
0.427458 | + | 0.904035i | \(0.359409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 41.5859i | − | 1.88058i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.2755i | − | 0.960151i | −0.877227 | − | 0.480075i | \(-0.840609\pi\) | ||
0.877227 | − | 0.480075i | \(-0.159391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.20565i | 0.0542999i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 15.3019i | − | 0.687767i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.58800i | − | 0.385225i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.30957i | 0.0586243i | 0.999570 | + | 0.0293122i | \(0.00933169\pi\) | ||||
−0.999570 | + | 0.0293122i | \(0.990668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.3693 | 1.13342 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.3873i | 0.730672i | 0.930876 | + | 0.365336i | \(0.119046\pi\) | ||||
−0.930876 | + | 0.365336i | \(0.880954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.1231 | 0.939966 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8255 | 0.569599 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.58800i | 0.380657i | 0.981721 | + | 0.190328i | \(0.0609552\pi\) | ||||
−0.981721 | + | 0.190328i | \(0.939045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.511240i | 0.0226159i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.80776 | + | 2.41131i | −0.168117 | + | 0.106462i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.9481 | 1.36374 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.3153 | −0.717548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.68658i | − | 0.249613i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.6757i | − | 0.993439i | −0.867911 | − | 0.496719i | \(-0.834538\pi\) | ||
0.867911 | − | 0.496719i | \(-0.165462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.19526 | −0.0959922 | −0.0479961 | − | 0.998848i | \(-0.515284\pi\) | ||||
−0.0479961 | + | 0.998848i | \(0.515284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.2933i | 0.667455i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.32431 | 0.0576877 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6847 | 0.855855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.2177 | −0.703790 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.6155 | 1.02290 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7304 | 0.636851 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.1231 | −0.825223 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.8947i | 1.02922i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.8078 | 1.41052 | 0.705258 | − | 0.708951i | \(-0.250831\pi\) | ||||
0.705258 | + | 0.708951i | \(0.250831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.1927i | 1.98232i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 31.2637i | − | 1.33919i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.580639 | −0.0248263 | −0.0124132 | − | 0.999923i | \(-0.503951\pi\) | ||||
−0.0124132 | + | 0.999923i | \(0.503951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.9309 | −1.27742 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.81164 | + | 4.43994i | 0.119780 | + | 0.189148i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.6736i | 2.36748i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 33.2228i | − | 1.41023i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.93087 | −0.420784 | −0.210392 | − | 0.977617i | \(-0.567474\pi\) | ||||
−0.210392 | + | 0.977617i | \(0.567474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.62329 | 0.237840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.49966i | − | 0.232196i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.3519 | −0.899877 | −0.449938 | − | 0.893060i | \(-0.648554\pi\) | ||||
−0.449938 | + | 0.893060i | \(0.648554\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.0877i | − | 0.592672i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.0398i | 1.76551i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.5859i | 1.74337i | 0.490064 | + | 0.871687i | \(0.336973\pi\) | ||||
−0.490064 | + | 0.871687i | \(0.663027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.5889i | − | 0.652377i | −0.945305 | − | 0.326188i | \(-0.894236\pi\) | ||
0.945305 | − | 0.326188i | \(-0.105764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.3817i | 0.767905i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.84329i | 0.118573i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0000 | 1.12402 | 0.562012 | − | 0.827129i | \(-0.310027\pi\) | ||||
0.562012 | + | 0.827129i | \(0.310027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 12.9698i | − | 0.539007i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 49.6155 | 2.05840 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.8393 | −0.945906 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 28.1753i | − | 1.16491i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 5.97366i | − | 0.246559i | −0.992372 | − | 0.123280i | \(-0.960659\pi\) | ||
0.992372 | − | 0.123280i | \(-0.0393412\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.87689 | − | 3.08835i | 0.200949 | − | 0.127253i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −53.0438 | −2.18193 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.7386 | 0.523113 | 0.261556 | − | 0.965188i | \(-0.415764\pi\) | ||||
0.261556 | + | 0.965188i | \(0.415764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.6378i | 0.436106i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 12.2050i | − | 0.499516i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.9073 | −1.01768 | −0.508841 | − | 0.860860i | \(-0.669926\pi\) | ||||
−0.508841 | + | 0.860860i | \(0.669926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.4092i | 1.44437i | 0.691698 | + | 0.722187i | \(0.256863\pi\) | ||||
−0.691698 | + | 0.722187i | \(0.743137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.743668 | 0.0302845 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.2462 | 0.579191 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.5288 | 1.27971 | 0.639857 | − | 0.768494i | \(-0.278994\pi\) | ||||
0.639857 | + | 0.768494i | \(0.278994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.8078 | 0.478475 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.0414 | −1.21535 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3002 | 1.18342 | 0.591712 | − | 0.806150i | \(-0.298452\pi\) | ||||
0.591712 | + | 0.806150i | \(0.298452\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 33.2228i | − | 1.33967i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.5464 | 1.67259 | 0.836297 | − | 0.548276i | \(-0.184716\pi\) | ||||
0.836297 | + | 0.548276i | \(0.184716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.70906i | − | 0.269660i | −0.990869 | − | 0.134830i | \(-0.956951\pi\) | ||
0.990869 | − | 0.134830i | \(-0.0430488\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.88269i | 0.0755499i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −58.5040 | −2.34391 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.8255 | − | 20.2530i | −0.512200 | − | 0.808828i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.49966i | − | 0.219286i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.61528i | 0.382778i | 0.981514 | + | 0.191389i | \(0.0612992\pi\) | ||||
−0.981514 | + | 0.191389i | \(0.938701\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.4233 | −2.36186 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4741 | 0.614070 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.9972i | 1.74323i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.29723 | 0.209555 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 26.8212i | − | 1.05938i | −0.848193 | − | 0.529688i | \(-0.822309\pi\) | ||
0.848193 | − | 0.529688i | \(-0.177691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2794i | 0.563124i | 0.959543 | + | 0.281562i | \(0.0908524\pi\) | ||||
−0.959543 | + | 0.281562i | \(0.909148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.91096i | − | 0.311494i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.1374i | − | 1.26345i | −0.775191 | − | 0.631726i | \(-0.782347\pi\) | ||
0.775191 | − | 0.631726i | \(-0.217653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7647i | 0.579565i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 12.9698i | − | 0.508327i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.1922 | 0.985848 | 0.492924 | − | 0.870072i | \(-0.335928\pi\) | ||||
0.492924 | + | 0.870072i | \(0.335928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 15.3019i | − | 0.597893i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.315342 | −0.0123026 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.9960 | −1.63593 | −0.817965 | − | 0.575268i | \(-0.804898\pi\) | ||||
−0.817965 | + | 0.575268i | \(0.804898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.2919i | 1.45049i | 0.688492 | + | 0.725244i | \(0.258273\pi\) | ||||
−0.688492 | + | 0.725244i | \(0.741727\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 10.1265i | − | 0.393281i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.8078 | + | 39.1746i | 0.962004 | + | 1.51913i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.19526 | 0.0850010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.4924 | −2.02947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.2492i | 1.05194i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4099i | 0.940934i | 0.882418 | + | 0.470467i | \(0.155914\pi\) | ||||
−0.882418 | + | 0.470467i | \(0.844086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.61463 | 0.0621470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.3803i | 1.55194i | 0.630770 | + | 0.775970i | \(0.282739\pi\) | ||||
−0.630770 | + | 0.775970i | \(0.717261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0138 | −0.384295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 58.0540 | 2.22463 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5288 | 1.20642 | 0.603208 | − | 0.797584i | \(-0.293889\pi\) | ||||
0.603208 | + | 0.797584i | \(0.293889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.0540 | −1.18651 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.4741 | −0.590373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.0540 | −1.60213 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.01862i | − | 0.305043i | −0.988300 | − | 0.152521i | \(-0.951261\pi\) | ||
0.988300 | − | 0.152521i | \(-0.0487393\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.8078 | −0.942369 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 48.5247i | − | 1.84065i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.49966i | − | 0.208314i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4879 | −0.964041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.63068 | −0.174898 | −0.0874492 | − | 0.996169i | \(-0.527872\pi\) | ||||
−0.0874492 | + | 0.996169i | \(0.527872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.8255 | − | 20.2530i | −0.483721 | − | 0.763858i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 42.2630i | 1.59172i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 34.2453i | − | 1.28793i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6307 | −0.474355 | −0.237178 | − | 0.971466i | \(-0.576222\pi\) | ||||
−0.237178 | + | 0.971466i | \(0.576222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.3404 | −1.28787 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.41131i | − | 0.0903042i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.6509 | −0.959290 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.2043i | 0.866580i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 26.4509i | − | 0.986450i | −0.869902 | − | 0.493225i | \(-0.835818\pi\) | ||
0.869902 | − | 0.493225i | \(-0.164182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 50.1739i | − | 1.86858i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 53.4759i | − | 1.98879i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.88269i | − | 0.0699215i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 44.6589i | − | 1.65631i | −0.560500 | − | 0.828154i | \(-0.689391\pi\) | ||
0.560500 | − | 0.828154i | \(-0.310609\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.6155 | −0.689464 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.30957i | − | 0.0484361i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.12311 | 0.189226 | 0.0946131 | − | 0.995514i | \(-0.469839\pi\) | ||||
0.0946131 | + | 0.995514i | \(0.469839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 61.8963 | 2.28308 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.677039i | − | 0.0249390i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.2042i | 0.927152i | 0.886057 | + | 0.463576i | \(0.153434\pi\) | ||||
−0.886057 | + | 0.463576i | \(0.846566\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.6155 | − | 37.2919i | −0.867538 | − | 1.36995i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.9188 | −0.437257 | −0.218628 | − | 0.975808i | \(-0.570158\pi\) | ||||
−0.218628 | + | 0.975808i | \(0.570158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.19224 | −0.263503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.6037i | 1.11973i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 23.8813i | − | 0.872604i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.6647 | 1.30142 | 0.650712 | − | 0.759324i | \(-0.274470\pi\) | ||||
0.650712 | + | 0.759324i | \(0.274470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 50.8510i | − | 1.85311i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.6762 | −0.825273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.8078 | 1.62857 | 0.814283 | − | 0.580468i | \(-0.197130\pi\) | ||||
0.814283 | + | 0.580468i | \(0.197130\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.0138 | −0.363479 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6155 | 1.10981 | 0.554906 | − | 0.831913i | \(-0.312754\pi\) | ||||
0.554906 | + | 0.831913i | \(0.312754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.6855 | −1.83494 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.56155 | −0.237233 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.1862i | 0.981638i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2311 | −1.01804 | −0.509019 | − | 0.860755i | \(-0.669992\pi\) | ||||
−0.509019 | + | 0.860755i | \(0.669992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.5061i | 1.45879i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 41.0573i | − | 1.47673i | −0.674402 | − | 0.738365i | \(-0.735598\pi\) | ||
0.674402 | − | 0.738365i | \(-0.264402\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.06798 | −0.0742839 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −53.8617 | −1.93228 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.8255 | − | 20.2530i | −0.459520 | − | 0.725640i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.82262i | − | 0.172567i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.24663i | − | 0.0445510i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.3693 | −0.548554 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3588 | 0.939591 | 0.469796 | − | 0.882775i | \(-0.344328\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344328\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 33.6750i | 1.19886i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.8393 | −0.812071 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.1739i | 1.78173i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 59.1625i | 2.09828i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 23.2043i | − | 0.821938i | −0.911649 | − | 0.410969i | \(-0.865191\pi\) | ||
0.911649 | − | 0.410969i | \(-0.134809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.99614i | 0.247506i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 36.0863i | − | 1.27505i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.287088i | 0.0101311i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.3693 | 0.682679 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.9698i | 0.456559i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.3693 | 1.55994 | 0.779971 | − | 0.625816i | \(-0.215234\pi\) | ||||
0.779971 | + | 0.625816i | \(0.215234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9142 | 1.05043 | 0.525214 | − | 0.850970i | \(-0.323985\pi\) | ||||
0.525214 | + | 0.850970i | \(0.323985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 52.0566i | − | 1.82571i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.1702i | 1.58224i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.05398 | − | 4.82262i | −0.106845 | − | 0.168722i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.6786 | −1.59614 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.4233 | 0.991980 | 0.495990 | − | 0.868328i | \(-0.334805\pi\) | ||||
0.495990 | + | 0.868328i | \(0.334805\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.1150i | 1.08460i | 0.840185 | + | 0.542299i | \(0.182446\pi\) | ||||
−0.840185 | + | 0.542299i | \(0.817554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.58800i | 0.298996i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.5242 | 1.72212 | 0.861062 | − | 0.508499i | \(-0.169800\pi\) | ||||
0.861062 | + | 0.508499i | \(0.169800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.4686i | − | 1.50973i | −0.655881 | − | 0.754864i | \(-0.727703\pi\) | ||
0.655881 | − | 0.754864i | \(-0.272297\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.7851 | 1.06792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.2462 | 0.355010 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.5559 | −0.953610 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.36932 | −0.0473305 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.8917 | −0.548642 | −0.274321 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274321 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.5464 | 0.949876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 66.4457i | − | 2.28851i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.9309 | −0.479236 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 23.0963i | − | 0.793599i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.0877i | 0.483487i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0138 | −0.343269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.3693 | −1.07406 | −0.537032 | − | 0.843562i | \(-0.680455\pi\) | ||||
−0.537032 | + | 0.843562i | \(0.680455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.1636 | + | 15.3019i | −0.826377 | + | 0.523312i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 39.1746i | − | 1.33818i | −0.743181 | − | 0.669090i | \(-0.766684\pi\) | ||
0.743181 | − | 0.669090i | \(-0.233316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.9056i | 1.56628i | 0.621847 | + | 0.783139i | \(0.286383\pi\) | ||||
−0.621847 | + | 0.783139i | \(0.713617\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −53.8617 | −1.83560 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.4199 | 0.797223 | 0.398612 | − | 0.917120i | \(-0.369492\pi\) | ||||
0.398612 | + | 0.917120i | \(0.369492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.17669i | 0.210014i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.7327 | 1.28147 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2637i | 1.06055i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.24663i | − | 0.0422405i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.17669i | − | 0.209049i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.5774i | 1.23654i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.8820i | 0.434994i | 0.976061 | + | 0.217497i | \(0.0697893\pi\) | ||||
−0.976061 | + | 0.217497i | \(0.930211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.1265i | − | 0.341559i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.1771 | −0.342875 | −0.171437 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171437 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.5247i | − | 1.63299i | −0.577355 | − | 0.816493i | \(-0.695915\pi\) | ||
0.577355 | − | 0.816493i | \(-0.304085\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.2462 | 1.28563 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.0023 | −0.772342 | −0.386171 | − | 0.922427i | \(-0.626203\pi\) | ||||
−0.386171 | + | 0.922427i | \(0.626203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 25.0870i | − | 0.841390i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.6076i | 0.790883i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.3153 | + | 25.7640i | 0.545972 | + | 0.862160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.7713 | 0.694308 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.4384 | −0.615642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.59666i | 0.0532515i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.79366i | 0.326274i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.8255 | −0.426805 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 50.1739i | − | 1.66784i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0345 | 0.831258 | 0.415629 | − | 0.909534i | \(-0.363561\pi\) | ||||
0.415629 | + | 0.909534i | \(0.363561\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.1231 | 0.700609 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3813 | 1.33789 | 0.668946 | − | 0.743311i | \(-0.266746\pi\) | ||||
0.668946 | + | 0.743311i | \(0.266746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.8617 | 0.922089 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 70.5858 | 2.33349 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.8078 | −0.819225 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.1188i | − | 0.795606i | −0.917471 | − | 0.397803i | \(-0.869773\pi\) | ||
0.917471 | − | 0.397803i | \(-0.130227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6155 | −1.04177 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.87989i | − | 0.292285i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.58800i | 0.282372i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.9481 | 1.01647 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.3153 | −0.436862 | −0.218431 | − | 0.975852i | \(-0.570094\pi\) | ||||
−0.218431 | + | 0.975852i | \(0.570094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.7327 | − | 23.8947i | 1.23664 | − | 0.783116i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.79366i | 0.320630i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.97366i | 0.195360i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8769 | −0.453338 | −0.226669 | − | 0.973972i | \(-0.572784\pi\) | ||||
−0.226669 | + | 0.973972i | \(0.572784\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.03399 | 0.0337429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 48.2912i | − | 1.57425i | −0.616794 | − | 0.787125i | \(-0.711569\pi\) | ||
0.616794 | − | 0.787125i | \(-0.288431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0138 | −0.326095 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 10.9993i | − | 0.357808i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 21.2755i | − | 0.691361i | −0.938352 | − | 0.345681i | \(-0.887648\pi\) | ||
0.938352 | − | 0.345681i | \(-0.112352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.528616i | 0.0171596i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.1265i | 0.328375i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.2637i | − | 1.01273i | −0.862319 | − | 0.506365i | \(-0.830989\pi\) | ||
0.862319 | − | 0.506365i | \(-0.169011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 19.9660i | − | 0.646083i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.63068 | 0.214340 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.3455i | 1.62574i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2462 | −0.943426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7304 | 0.474681 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0877i | 0.453498i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3507i | 0.332855i | 0.986054 | + | 0.166428i | \(0.0532232\pi\) | ||||
−0.986054 | + | 0.166428i | \(0.946777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.68466 | + | 5.49966i | −0.278991 | + | 0.176674i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.580639 | 0.0186336 | 0.00931679 | − | 0.999957i | \(-0.497034\pi\) | ||||
0.00931679 | + | 0.999957i | \(0.497034\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −78.6695 | −2.52203 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.8131i | 0.506424i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.8510i | 1.62687i | 0.581658 | + | 0.813433i | \(0.302404\pi\) | ||||
−0.581658 | + | 0.813433i | \(0.697596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.8531 | −1.04999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 31.2637i | − | 0.998172i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.78456 | −0.216394 | −0.108197 | − | 0.994129i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994129i | \(0.534508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.6155 | 1.83578 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 68.5178 | 2.18095 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.38447 | −0.0758218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.417609 | 0.0132658 | 0.00663289 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663289 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.3002 | −1.78663 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.2569i | 0.420272i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.5464 | −1.31579 | −0.657894 | − | 0.753111i | \(-0.728552\pi\) | ||||
−0.657894 | + | 0.753111i | \(0.728552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.68658i | 0.179915i |
(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 | 1216.2.h.d.1215.1 | 8 | ||
4.3 | odd | 2 | inner | 1216.2.h.d.1215.8 | 8 | ||
8.3 | odd | 2 | 76.2.d.a.75.4 | yes | 8 | ||
8.5 | even | 2 | 76.2.d.a.75.6 | yes | 8 | ||
19.18 | odd | 2 | inner | 1216.2.h.d.1215.7 | 8 | ||
24.5 | odd | 2 | 684.2.f.b.379.3 | 8 | |||
24.11 | even | 2 | 684.2.f.b.379.5 | 8 | |||
76.75 | even | 2 | inner | 1216.2.h.d.1215.2 | 8 | ||
152.37 | odd | 2 | 76.2.d.a.75.3 | ✓ | 8 | ||
152.75 | even | 2 | 76.2.d.a.75.5 | yes | 8 | ||
456.227 | odd | 2 | 684.2.f.b.379.4 | 8 | |||
456.341 | even | 2 | 684.2.f.b.379.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.d.a.75.3 | ✓ | 8 | 152.37 | odd | 2 | ||
76.2.d.a.75.4 | yes | 8 | 8.3 | odd | 2 | ||
76.2.d.a.75.5 | yes | 8 | 152.75 | even | 2 | ||
76.2.d.a.75.6 | yes | 8 | 8.5 | even | 2 | ||
684.2.f.b.379.3 | 8 | 24.5 | odd | 2 | |||
684.2.f.b.379.4 | 8 | 456.227 | odd | 2 | |||
684.2.f.b.379.5 | 8 | 24.11 | even | 2 | |||
684.2.f.b.379.6 | 8 | 456.341 | even | 2 | |||
1216.2.h.d.1215.1 | 8 | 1.1 | even | 1 | trivial | ||
1216.2.h.d.1215.2 | 8 | 76.75 | even | 2 | inner | ||
1216.2.h.d.1215.7 | 8 | 19.18 | odd | 2 | inner | ||
1216.2.h.d.1215.8 | 8 | 4.3 | odd | 2 | inner |