Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1585,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3744.1585");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.m (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: | \(29.8959905168\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 936) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1585.3 | ||
Root | \(0.752864 + 0.902863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1585 |
Dual form | 3744.2.m.h.1585.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3744\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(2017\) | \(2081\) | \(2341\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.68999 | −1.20300 | −0.601501 | − | 0.798872i | \(-0.705430\pi\) | ||||
−0.601501 | + | 0.798872i | \(0.705430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.15163i | 1.56917i | 0.620021 | + | 0.784585i | \(0.287124\pi\) | ||||
−0.620021 | + | 0.784585i | \(0.712876\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.35250 | −1.31233 | −0.656164 | − | 0.754618i | \(-0.727822\pi\) | ||||
−0.656164 | + | 0.754618i | \(0.727822\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.53159 | − | 0.726543i | −0.979487 | − | 0.201507i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.87130 | 1.42400 | 0.711999 | − | 0.702180i | \(-0.247790\pi\) | ||||
0.711999 | + | 0.702180i | \(0.247790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.71423 | −1.31094 | −0.655468 | − | 0.755223i | \(-0.727528\pi\) | ||||
−0.655468 | + | 0.755223i | \(0.727528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.62866 | −0.756628 | −0.378314 | − | 0.925677i | \(-0.623496\pi\) | ||||
−0.378314 | + | 0.925677i | \(0.623496\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23607 | 0.447214 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.08672i | 0.573190i | 0.958052 | + | 0.286595i | \(0.0925234\pi\) | ||||
−0.958052 | + | 0.286595i | \(0.907477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.28334i | 1.66734i | 0.552266 | + | 0.833668i | \(0.313763\pi\) | ||||
−0.552266 | + | 0.833668i | \(0.686237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 11.1679i | − | 1.88771i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.69790 | 0.443531 | 0.221766 | − | 0.975100i | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.1074i | − | 1.73468i | −0.497715 | − | 0.867340i | \(-0.665828\pi\) | ||
0.497715 | − | 0.867340i | \(-0.334172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.80423i | 0.580139i | 0.957006 | + | 0.290070i | \(0.0936784\pi\) | ||||
−0.957006 | + | 0.290070i | \(0.906322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.91034i | − | 0.716247i | −0.933674 | − | 0.358123i | \(-0.883417\pi\) | ||
0.933674 | − | 0.358123i | \(-0.116583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.2361 | −1.46230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.17902i | − | 0.161951i | −0.996716 | − | 0.0809757i | \(-0.974196\pi\) | ||
0.996716 | − | 0.0809757i | \(-0.0258036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7082 | 1.57873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.29753 | −0.299113 | −0.149556 | − | 0.988753i | \(-0.547785\pi\) | ||||
−0.149556 | + | 0.988753i | \(0.547785\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.05342i | 0.903098i | 0.892246 | + | 0.451549i | \(0.149128\pi\) | ||||
−0.892246 | + | 0.451549i | \(0.850872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.49996 | + | 1.95440i | 1.17832 | + | 0.242413i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0795 | 1.23141 | 0.615705 | − | 0.787977i | \(-0.288871\pi\) | ||||
0.615705 | + | 0.787977i | \(0.288871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.08191i | − | 0.247078i | −0.992340 | − | 0.123539i | \(-0.960576\pi\) | ||
0.992340 | − | 0.123539i | \(-0.0394244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.4350i | − | 1.57244i | −0.617944 | − | 0.786222i | \(-0.712034\pi\) | ||
0.617944 | − | 0.786222i | \(-0.287966\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 18.0700i | − | 2.05927i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9443 | −1.23133 | −0.615663 | − | 0.788009i | \(-0.711112\pi\) | ||||
−0.615663 | + | 0.788009i | \(0.711112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.73249 | 1.06828 | 0.534140 | − | 0.845396i | \(-0.320636\pi\) | ||||
0.534140 | + | 0.845396i | \(0.320636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.7938 | −1.71307 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1877i | 1.29190i | 0.763381 | + | 0.645949i | \(0.223538\pi\) | ||||
−0.763381 | + | 0.645949i | \(0.776462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01634 | − | 14.6619i | 0.316198 | − | 1.53698i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.3713 | 1.57706 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.13170i | − | 0.521045i | −0.965468 | − | 0.260523i | \(-0.916105\pi\) | ||
0.965468 | − | 0.260523i | \(-0.0838949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.9833i | − | 1.49089i | −0.666566 | − | 0.745446i | \(-0.732237\pi\) | ||
0.666566 | − | 0.745446i | \(-0.267763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.70820 | −0.168314 | −0.0841572 | − | 0.996452i | \(-0.526820\pi\) | ||||
−0.0841572 | + | 0.996452i | \(0.526820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.99442i | − | 0.482829i | −0.970422 | − | 0.241415i | \(-0.922389\pi\) | ||
0.970422 | − | 0.241415i | \(-0.0776114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.73057 | 0.836237 | 0.418119 | − | 0.908392i | \(-0.362690\pi\) | ||||
0.418119 | + | 0.908392i | \(0.362690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.87130 | 0.552325 | 0.276163 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276163 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.76108 | 0.910225 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.3755i | 2.23450i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.94427 | 0.722207 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.43496 | 0.665003 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.80982i | 0.769718i | 0.922975 | + | 0.384859i | \(0.125750\pi\) | ||||
−0.922975 | + | 0.384859i | \(0.874250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 23.7234i | − | 2.05708i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4397i | 0.891922i | 0.895052 | + | 0.445961i | \(0.147138\pi\) | ||||
−0.895052 | + | 0.445961i | \(0.852862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3188i | 1.21451i | 0.794507 | + | 0.607254i | \(0.207729\pi\) | ||||
−0.794507 | + | 0.607254i | \(0.792271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.3713 | + | 3.16228i | 1.28541 | + | 0.264443i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.30327i | − | 0.689549i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.635021 | 0.0520230 | 0.0260115 | − | 0.999662i | \(-0.491719\pi\) | ||||
0.0260115 | + | 0.999662i | \(0.491719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.15163i | − | 0.337855i | −0.985628 | − | 0.168928i | \(-0.945970\pi\) | ||
0.985628 | − | 0.168928i | \(-0.0540304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 24.9721i | − | 2.00581i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1150i | 1.28611i | 0.765818 | + | 0.643057i | \(0.222334\pi\) | ||||
−0.765818 | + | 0.643057i | \(0.777666\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 15.0649i | − | 1.18728i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0795 | 0.789489 | 0.394745 | − | 0.918791i | \(-0.370833\pi\) | ||||
0.394745 | + | 0.918791i | \(0.370833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 24.2967i | − | 1.88013i | −0.340992 | − | 0.940066i | \(-0.610763\pi\) | ||
0.340992 | − | 0.940066i | \(-0.389237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9443 | + | 5.13170i | 0.918790 | + | 0.394746i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.17902i | − | 0.0896395i | −0.998995 | − | 0.0448198i | \(-0.985729\pi\) | ||
0.998995 | − | 0.0448198i | \(-0.0142714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.28334i | 0.701754i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.7987i | − | 1.40508i | −0.711645 | − | 0.702539i | \(-0.752049\pi\) | ||
0.711645 | − | 0.702539i | \(-0.247951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2088i | − | 0.981802i | −0.871215 | − | 0.490901i | \(-0.836668\pi\) | ||
0.871215 | − | 0.490901i | \(-0.163332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.25732 | −0.533569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.5548 | −1.86875 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.3713 | 1.11223 | 0.556113 | − | 0.831107i | \(-0.312292\pi\) | ||||
0.556113 | + | 0.831107i | \(0.312292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.4350i | − | 0.967070i | −0.875325 | − | 0.483535i | \(-0.839353\pi\) | ||
0.875325 | − | 0.483535i | \(-0.160647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6101 | −0.755936 | −0.377968 | − | 0.925819i | \(-0.623377\pi\) | ||||
−0.377968 | + | 0.925819i | \(0.623377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.8149 | −0.899433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.8788i | 2.08682i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.8712 | 1.72038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.0130i | − | 1.17122i | −0.810591 | − | 0.585612i | \(-0.800854\pi\) | ||
0.810591 | − | 0.585612i | \(-0.199146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 10.2333i | − | 0.697908i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.5410 | −2.61633 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.7350 | − | 4.26575i | −1.39479 | − | 0.286945i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.28334i | − | 0.621658i | −0.950466 | − | 0.310829i | \(-0.899393\pi\) | ||
0.950466 | − | 0.310829i | \(-0.100607\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.02749 | −0.0681967 | −0.0340983 | − | 0.999418i | \(-0.510856\pi\) | ||||
−0.0340983 | + | 0.999418i | \(0.510856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4917 | 1.22196 | 0.610981 | − | 0.791645i | \(-0.290775\pi\) | ||||
0.610981 | + | 0.791645i | \(0.290775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.25732 | −0.475443 | −0.237722 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237722 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.2088i | 0.861646i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.07107i | − | 0.457389i | −0.973498 | − | 0.228695i | \(-0.926554\pi\) | ||
0.973498 | − | 0.228695i | \(-0.0734457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5667i | 1.19598i | 0.801502 | + | 0.597992i | \(0.204035\pi\) | ||||
−0.801502 | + | 0.597992i | \(0.795965\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.5350 | 1.75914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.1803 | + | 4.15163i | 1.28404 | + | 0.264162i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.35805i | − | 0.148839i | −0.997227 | − | 0.0744193i | \(-0.976290\pi\) | ||
0.997227 | − | 0.0744193i | \(-0.0237103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.7938 | 0.992945 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.2572 | −1.63788 | −0.818941 | − | 0.573878i | \(-0.805438\pi\) | ||||
−0.818941 | + | 0.573878i | \(0.805438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.2007i | 0.695976i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.25732 | −0.447506 | −0.223753 | − | 0.974646i | \(-0.571831\pi\) | ||||
−0.223753 | + | 0.974646i | \(0.571831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.17157i | 0.194828i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 19.2490i | − | 1.17363i | −0.809720 | − | 0.586817i | \(-0.800381\pi\) | ||
0.809720 | − | 0.586817i | \(-0.199619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.28334i | − | 0.563923i | −0.959426 | − | 0.281961i | \(-0.909015\pi\) | ||
0.959426 | − | 0.281961i | \(-0.0909850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.73249 | −0.586891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.7153i | − | 1.30475i | −0.757898 | − | 0.652373i | \(-0.773774\pi\) | ||
0.757898 | − | 0.652373i | \(-0.226226\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.35931i | − | 0.558330i | −0.960243 | − | 0.279165i | \(-0.909942\pi\) | ||
0.960243 | − | 0.279165i | \(-0.0900576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.3107i | − | 0.731797i | −0.930655 | − | 0.365899i | \(-0.880762\pi\) | ||
0.930655 | − | 0.365899i | \(-0.119238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.1138 | 2.72201 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.4721 | 1.02777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.4800 | −1.48856 | −0.744278 | − | 0.667869i | \(-0.767206\pi\) | ||||
−0.744278 | + | 0.667869i | \(0.767206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.18034 | 0.359833 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8149 | + | 2.63638i | 0.741108 | + | 0.152466i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.7938 | −0.910337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 18.9737i | − | 1.08643i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.04684 | 0.230966 | 0.115483 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115483 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8860 | −0.617288 | −0.308644 | − | 0.951178i | \(-0.599875\pi\) | ||||
−0.308644 | + | 0.951178i | \(0.599875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47214 | −0.139733 | −0.0698667 | − | 0.997556i | \(-0.522257\pi\) | ||||
−0.0698667 | + | 0.997556i | \(0.522257\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2349 | −0.799512 | −0.399756 | − | 0.916622i | \(-0.630905\pi\) | ||||
−0.399756 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 13.4350i | − | 0.752214i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.5500 | −1.86677 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.89688 | − | 1.62460i | −0.438040 | − | 0.0901165i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.3859 | 1.12391 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.01634 | −0.165793 | −0.0828965 | − | 0.996558i | \(-0.526417\pi\) | ||||
−0.0828965 | + | 0.996558i | \(0.526417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.1139 | −1.48139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4721 | 0.788347 | 0.394174 | − | 0.919036i | \(-0.371031\pi\) | ||||
0.394174 | + | 0.919036i | \(0.371031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 40.4057i | − | 2.18809i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.4350i | − | 0.725420i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.5092i | 1.53045i | 0.643761 | + | 0.765227i | \(0.277373\pi\) | ||||
−0.643761 | + | 0.765227i | \(0.722627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.76108 | −0.522499 | −0.261249 | − | 0.965271i | \(-0.584134\pi\) | ||||
−0.261249 | + | 0.965271i | \(0.584134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.86629i | 0.418680i | 0.977843 | + | 0.209340i | \(0.0671316\pi\) | ||||
−0.977843 | + | 0.209340i | \(0.932868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.60034i | 0.297235i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.1406i | 0.693533i | 0.937951 | + | 0.346767i | \(0.112720\pi\) | ||||
−0.937951 | + | 0.346767i | \(0.887280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.6525 | 0.718551 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.1400i | 1.89165i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.12461 | 0.476301 | 0.238150 | − | 0.971228i | \(-0.423459\pi\) | ||||
0.238150 | + | 0.971228i | \(0.423459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.89487 | 0.254129 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.343027i | 0.0177613i | 0.999961 | + | 0.00888063i | \(0.00282683\pi\) | ||||
−0.999961 | + | 0.00888063i | \(0.997173\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.24264 | − | 10.9010i | 0.115502 | − | 0.561432i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8101 | −0.966210 | −0.483105 | − | 0.875563i | \(-0.660491\pi\) | ||||
−0.483105 | + | 0.875563i | \(0.660491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.2241i | − | 0.829010i | −0.910047 | − | 0.414505i | \(-0.863955\pi\) | ||
0.910047 | − | 0.414505i | \(-0.136045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 48.6082i | 2.47730i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6182i | 0.589067i | 0.955641 | + | 0.294534i | \(0.0951643\pi\) | ||||
−0.955641 | + | 0.294534i | \(0.904836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.3050 | −1.07744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.4400 | 1.48129 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.5243 | 1.23084 | 0.615420 | − | 0.788199i | \(-0.288986\pi\) | ||||
0.615420 | + | 0.788199i | \(0.288986\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3438i | 1.16574i | 0.812567 | + | 0.582868i | \(0.198069\pi\) | ||||
−0.812567 | + | 0.582868i | \(0.801931\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.74474 | − | 32.7849i | 0.335979 | − | 1.63313i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.7426 | −0.582059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3951i | 0.761239i | 0.924732 | + | 0.380620i | \(0.124289\pi\) | ||||
−0.924732 | + | 0.380620i | \(0.875711\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.53850i | − | 0.469359i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.1803 | −1.28514 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 14.9833i | − | 0.731981i | −0.930619 | − | 0.365990i | \(-0.880730\pi\) | ||
0.930619 | − | 0.365990i | \(-0.119270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7938 | −0.769741 | −0.384870 | − | 0.922971i | \(-0.625754\pi\) | ||||
−0.384870 | + | 0.922971i | \(0.625754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.1286 | 0.636832 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.2832 | −1.41711 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.8005i | − | 1.00193i | −0.865468 | − | 0.500963i | \(-0.832979\pi\) | ||
0.865468 | − | 0.500963i | \(-0.167021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1803 | 0.681464 | 0.340732 | − | 0.940161i | \(-0.389325\pi\) | ||||
0.340732 | + | 0.940161i | \(0.389325\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7350 | 0.991891 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.1803 | −1.15406 | −0.577032 | − | 0.816721i | \(-0.695789\pi\) | ||||
−0.577032 | + | 0.816721i | \(0.695789\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.17902i | − | 0.0560171i | −0.999608 | − | 0.0280086i | \(-0.991083\pi\) | ||
0.999608 | − | 0.0280086i | \(-0.00891656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 32.7849i | − | 1.55416i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.3221i | 1.57257i | 0.617865 | + | 0.786284i | \(0.287998\pi\) | ||||
−0.617865 | + | 0.786284i | \(0.712002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.3449i | 2.27647i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.11393 | + | 39.4404i | −0.380387 | + | 1.84899i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.3448i | 1.79369i | 0.442342 | + | 0.896847i | \(0.354148\pi\) | ||||
−0.442342 | + | 0.896847i | \(0.645852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6951 | 1.15016 | 0.575082 | − | 0.818096i | \(-0.304970\pi\) | ||||
0.575082 | + | 0.818096i | \(0.304970\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.15163i | 0.192943i | 0.995336 | + | 0.0964714i | \(0.0307556\pi\) | ||||
−0.995336 | + | 0.0964714i | \(0.969244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.17345i | 0.285673i | 0.989746 | + | 0.142837i | \(0.0456223\pi\) | ||||
−0.989746 | + | 0.142837i | \(0.954378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.8465i | 1.93229i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 16.5579i | − | 0.761333i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7774 | −0.586268 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3122i | 0.471174i | 0.971853 | + | 0.235587i | \(0.0757013\pi\) | ||||
−0.971853 | + | 0.235587i | \(0.924299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.52786 | − | 1.96014i | −0.434433 | − | 0.0893745i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8042i | 0.626819i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.5866i | − | 0.796925i | −0.917185 | − | 0.398463i | \(-0.869544\pi\) | ||
0.917185 | − | 0.398463i | \(-0.130456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.1511i | − | 1.18018i | −0.807336 | − | 0.590092i | \(-0.799091\pi\) | ||
0.807336 | − | 0.590092i | \(-0.200909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1231i | 0.816222i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.64335 | 0.387707 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.3628 | 1.76212 | 0.881059 | − | 0.473006i | \(-0.156831\pi\) | ||||
0.881059 | + | 0.473006i | \(0.156831\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9999 | −0.847164 | −0.423582 | − | 0.905858i | \(-0.639228\pi\) | ||||
−0.423582 | + | 0.905858i | \(0.639228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.3049i | 1.79355i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.5350 | 1.22047 | 0.610233 | − | 0.792222i | \(-0.291076\pi\) | ||||
0.610233 | + | 0.792222i | \(0.291076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 55.7771 | 2.46743 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.59506 | 0.202482 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.3723i | 0.939951i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8712 | 1.08963 | 0.544814 | − | 0.838557i | \(-0.316600\pi\) | ||||
0.544814 | + | 0.838557i | \(0.316600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.9273i | 0.958814i | 0.877593 | + | 0.479407i | \(0.159148\pi\) | ||||
−0.877593 | + | 0.479407i | \(0.840852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54.5052i | 2.37429i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.83282 | −0.427514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.06998 | + | 39.2267i | −0.349550 | + | 1.69910i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4350i | 0.580844i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.5525 | 1.91901 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.3486 | −1.77771 | −0.888857 | − | 0.458184i | \(-0.848500\pi\) | ||||
−0.888857 | + | 0.458184i | \(0.848500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.4852 | −1.00600 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.212002i | − | 0.00906456i | −0.999990 | − | 0.00453228i | \(-0.998557\pi\) | ||
0.999990 | − | 0.00453228i | \(-0.00144267\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 17.6383i | − | 0.751415i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 45.4366i | − | 1.93216i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.47492 | 0.147237 | 0.0736186 | − | 0.997286i | \(-0.476545\pi\) | ||||
0.0736186 | + | 0.997286i | \(0.476545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.76393 | − | 13.4350i | 0.116902 | − | 0.568239i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1567i | 0.891649i | 0.895120 | + | 0.445825i | \(0.147090\pi\) | ||||
−0.895120 | + | 0.445825i | \(0.852910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.7938 | −0.664448 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.48527 | −0.188032 | −0.0940162 | − | 0.995571i | \(-0.529971\pi\) | ||||
−0.0940162 | + | 0.995571i | \(0.529971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.81234i | 0.243239i | 0.992577 | + | 0.121619i | \(0.0388087\pi\) | ||||
−0.992577 | + | 0.121619i | \(0.961191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.11393 | −0.338374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.6464i | − | 0.609738i | −0.952394 | − | 0.304869i | \(-0.901387\pi\) | ||
0.952394 | − | 0.304869i | \(-0.0986126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.4057i | 1.67631i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.13170i | 0.212533i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.0875 | −1.03547 | −0.517736 | − | 0.855540i | \(-0.673225\pi\) | ||||
−0.517736 | + | 0.855540i | \(0.673225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 53.0472i | − | 2.18577i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 17.1769i | − | 0.705370i | −0.935742 | − | 0.352685i | \(-0.885269\pi\) | ||
0.935742 | − | 0.352685i | \(-0.114731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 65.5699i | − | 2.68810i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.9705 | −1.14284 | −0.571421 | − | 0.820657i | \(-0.693608\pi\) | ||||
−0.571421 | + | 0.820657i | \(0.693608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.41641 | −0.302522 | −0.151261 | − | 0.988494i | \(-0.548333\pi\) | ||||
−0.151261 | + | 0.988494i | \(0.548333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.3700 | −0.868816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.29180 | −0.0930211 | −0.0465106 | − | 0.998918i | \(-0.514810\pi\) | ||||
−0.0465106 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.56757 | + | 17.3413i | −0.144329 | + | 0.701555i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.2854 | 1.38477 | 0.692387 | − | 0.721526i | \(-0.256559\pi\) | ||||
0.692387 | + | 0.721526i | \(0.256559\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.53089i | − | 0.262924i | −0.991321 | − | 0.131462i | \(-0.958033\pi\) | ||
0.991321 | − | 0.131462i | \(-0.0419671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.2996 | −1.29823 | −0.649115 | − | 0.760691i | \(-0.724860\pi\) | ||||
−0.649115 | + | 0.760691i | \(0.724860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50.5990 | −2.02721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1803 | −1.24721 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8401 | 0.631588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.32320i | − | 0.291532i | −0.989319 | − | 0.145766i | \(-0.953435\pi\) | ||
0.989319 | − | 0.145766i | \(-0.0465647\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1400 | −0.640495 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.1496 | + | 7.43694i | 1.43230 | + | 0.294662i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.6433 | −1.09184 | −0.545922 | − | 0.837836i | \(-0.683820\pi\) | ||||
−0.545922 | + | 0.837836i | \(0.683820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.9691 | 1.53679 | 0.768396 | − | 0.639974i | \(-0.221055\pi\) | ||||
0.768396 | + | 0.639974i | \(0.221055\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2279 | 0.637983 | 0.318992 | − | 0.947758i | \(-0.396656\pi\) | ||||
0.318992 | + | 0.947758i | \(0.396656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | 0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.7694i | 1.47803i | 0.673689 | + | 0.739015i | \(0.264709\pi\) | ||||
−0.673689 | + | 0.739015i | \(0.735291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 23.6984i | − | 0.925972i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.45735i | 0.0567704i | 0.999597 | + | 0.0283852i | \(0.00903651\pi\) | ||||
−0.999597 | + | 0.0283852i | \(0.990963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.4938 | 0.913804 | 0.456902 | − | 0.889517i | \(-0.348959\pi\) | ||||
0.456902 | + | 0.889517i | \(0.348959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 63.8158i | 2.47467i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.2007i | − | 0.433692i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 30.7000i | − | 1.18516i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6525 | 0.719000 | 0.359500 | − | 0.933145i | \(-0.382947\pi\) | ||||
0.359500 | + | 0.933145i | \(0.382947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.5036i | − | 1.28765i | −0.765173 | − | 0.643824i | \(-0.777347\pi\) | ||
0.765173 | − | 0.643824i | \(-0.222653\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3050 | 0.817609 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.0875 | −0.959947 | −0.479974 | − | 0.877283i | \(-0.659354\pi\) | ||||
−0.479974 | + | 0.877283i | \(0.659354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 28.0827i | − | 1.07298i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.856611 | + | 4.16383i | −0.0326343 | + | 0.158629i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.34895 | 0.0513164 | 0.0256582 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256582 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 38.5176i | − | 1.46106i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 65.2147i | − | 2.47018i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.44477i | − | 0.205646i | −0.994700 | − | 0.102823i | \(-0.967212\pi\) | ||
0.994700 | − | 0.102823i | \(-0.0327876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4164 | −0.581441 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 62.2051 | 2.33946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7938 | 0.593147 | 0.296573 | − | 0.955010i | \(-0.404156\pi\) | ||||
0.296573 | + | 0.955010i | \(0.404156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 33.6861i | − | 1.26155i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.3486 | − | 8.50651i | −1.54635 | − | 0.318125i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.1139 | 1.01118 | 0.505588 | − | 0.862775i | \(-0.331276\pi\) | ||||
0.505588 | + | 0.862775i | \(0.331276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.09184i | − | 0.264114i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.90212i | 0.256338i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.3607 | −0.829312 | −0.414656 | − | 0.909978i | \(-0.636098\pi\) | ||||
−0.414656 | + | 0.909978i | \(0.636098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.3357i | 0.826117i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9179 | 0.920365 | 0.460183 | − | 0.887824i | \(-0.347784\pi\) | ||||
0.460183 | + | 0.887824i | \(0.347784\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.8711 | −1.61601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.6017 | 1.08892 | 0.544458 | − | 0.838788i | \(-0.316736\pi\) | ||||
0.544458 | + | 0.838788i | \(0.316736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.31990i | − | 0.121795i | −0.998144 | − | 0.0608977i | \(-0.980604\pi\) | ||
0.998144 | − | 0.0608977i | \(-0.0193963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.70820 | −0.0625837 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.7350 | 0.757641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5410 | −0.457628 | −0.228814 | − | 0.973470i | \(-0.573485\pi\) | ||||
−0.228814 | + | 0.973470i | \(0.573485\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.1679i | 0.406440i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.25731i | − | 0.191080i | −0.995426 | − | 0.0955401i | \(-0.969542\pi\) | ||
0.995426 | − | 0.0955401i | \(-0.0304578\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.2681i | − | 0.480968i | −0.970653 | − | 0.240484i | \(-0.922694\pi\) | ||
0.970653 | − | 0.240484i | \(-0.0773062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.2461i | 1.31220i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.11393 | + | 1.66925i | 0.292977 | + | 0.0602732i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 46.6480i | − | 1.68217i | −0.540902 | − | 0.841086i | \(-0.681917\pi\) | ||
0.540902 | − | 0.841086i | \(-0.318083\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.0249 | −1.33169 | −0.665846 | − | 0.746089i | \(-0.731929\pi\) | ||||
−0.665846 | + | 0.746089i | \(0.731929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7582i | 0.745656i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.4702i | 2.27405i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.06154i | 0.324247i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 43.3491i | − | 1.54720i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.07735 | 0.180988 | 0.0904940 | − | 0.995897i | \(-0.471155\pi\) | ||||
0.0904940 | + | 0.995897i | \(0.471155\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.3755i | 0.866692i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.12461 | − | 24.9098i | 0.181980 | − | 0.884573i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.4336i | 0.546687i | 0.961917 | + | 0.273343i | \(0.0881295\pi\) | ||||
−0.961917 | + | 0.273343i | \(0.911870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 28.8301i | − | 1.01993i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.4757i | 2.06356i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40.5244i | 1.42830i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3859 | −0.716732 | −0.358366 | − | 0.933581i | \(-0.616666\pi\) | ||||
−0.358366 | + | 0.933581i | \(0.616666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6365 | 1.42694 | 0.713471 | − | 0.700685i | \(-0.247122\pi\) | ||||
0.713471 | + | 0.700685i | \(0.247122\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.1139 | −0.949757 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21.7382i | − | 0.760525i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0750 | −1.04963 | −0.524813 | − | 0.851217i | \(-0.675865\pi\) | ||||
−0.524813 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.18034 | 0.285149 | 0.142574 | − | 0.989784i | \(-0.454462\pi\) | ||||
0.142574 | + | 0.989784i | \(0.454462\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.7424 | −1.41675 | −0.708376 | − | 0.705836i | \(-0.750572\pi\) | ||||
−0.708376 | + | 0.705836i | \(0.750572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.84953i | − | 0.307357i | −0.988121 | − | 0.153679i | \(-0.950888\pi\) | ||
0.988121 | − | 0.153679i | \(-0.0491120\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −60.0990 | −2.08231 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.3579i | 2.26180i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.8763i | 1.06597i | 0.846126 | + | 0.532984i | \(0.178929\pi\) | ||||
−0.846126 | + | 0.532984i | \(0.821071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4721 | 0.671453 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.1300 | − | 13.8042i | −1.10531 | − | 0.474881i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.9817i | 1.13327i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.78975 | −0.335588 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.09369 | −0.277123 | −0.138561 | − | 0.990354i | \(-0.544248\pi\) | ||||
−0.138561 | + | 0.990354i | \(0.544248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.9998 | −1.29805 | −0.649025 | − | 0.760767i | \(-0.724823\pi\) | ||||
−0.649025 | + | 0.760767i | \(0.724823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.49839i | − | 0.221722i | −0.993836 | − | 0.110861i | \(-0.964639\pi\) | ||
0.993836 | − | 0.110861i | \(-0.0353609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.7093i | − | 0.841115i | −0.907266 | − | 0.420558i | \(-0.861834\pi\) | ||
0.907266 | − | 0.420558i | \(-0.138166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.17157i | 0.107836i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.6350 | 1.61591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.5967 | − | 7.32320i | −1.20615 | − | 0.248137i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.8672i | 1.04350i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.4444 | −1.83846 | −0.919229 | − | 0.393723i | \(-0.871187\pi\) | ||||
−0.919229 | + | 0.393723i | \(0.871187\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7426 | 0.395618 | 0.197809 | − | 0.980241i | \(-0.436617\pi\) | ||||
0.197809 | + | 0.980241i | \(0.436617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 17.0130i | − | 0.572534i | −0.958150 | − | 0.286267i | \(-0.907586\pi\) | ||
0.958150 | − | 0.286267i | \(-0.0924144\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.8859 | 1.00347 | 0.501735 | − | 0.865021i | \(-0.332695\pi\) | ||||
0.501735 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.9098i | 0.835448i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.0588i | 0.938953i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.5683i | 1.69031i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.6551 | −0.955701 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.92240i | − | 0.230619i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.5316i | 1.18111i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.6215i | − | 0.817542i | −0.912637 | − | 0.408771i | \(-0.865957\pi\) | ||
0.912637 | − | 0.408771i | \(-0.134043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.1433 | −0.601115 | −0.300557 | − | 0.953764i | \(-0.597173\pi\) | ||||
−0.300557 | + | 0.953764i | \(0.597173\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.3607 | −1.40193 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.5752 | −1.20782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.4164 | 0.706462 | 0.353231 | − | 0.935536i | \(-0.385083\pi\) | ||||
0.353231 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.51260 | + | 7.35247i | −0.0497878 | + | 0.242010i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.03268 | 0.198353 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.62210i | − | 0.0860282i | −0.999074 | − | 0.0430141i | \(-0.986304\pi\) | ||
0.999074 | − | 0.0430141i | \(-0.0136960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58.4913 | 1.91697 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 68.7424 | 2.24812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.652476 | 0.0213155 | 0.0106577 | − | 0.999943i | \(-0.496607\pi\) | ||||
0.0106577 | + | 0.999943i | \(0.496607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.9099 | −0.355652 | −0.177826 | − | 0.984062i | \(-0.556906\pi\) | ||||
−0.177826 | + | 0.984062i | \(0.556906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.3049i | 1.31251i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.59735 | −0.0844024 | −0.0422012 | − | 0.999109i | \(-0.513437\pi\) | ||||
−0.0422012 | + | 0.999109i | \(0.513437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.76108 | + | 47.4468i | −0.316858 | + | 1.54019i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.5146 | 0.470176 | 0.235088 | − | 0.971974i | \(-0.424462\pi\) | ||||
0.235088 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −41.3486 | −1.33801 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43.3417 | −1.39958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −55.1803 | −1.78001 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.1400i | 1.16339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0216i | 0.997587i | 0.866721 | + | 0.498793i | \(0.166223\pi\) | ||||
−0.866721 | + | 0.498793i | \(0.833777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 52.3023i | − | 1.67846i | −0.543776 | − | 0.839230i | \(-0.683006\pi\) | ||
0.543776 | − | 0.839230i | \(-0.316994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.4466 | −1.90577 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.8909i | 1.43619i | 0.695947 | + | 0.718093i | \(0.254985\pi\) | ||||
−0.695947 | + | 0.718093i | \(0.745015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 53.0472i | − | 1.69539i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 43.4280i | − | 1.38514i | −0.721352 | − | 0.692568i | \(-0.756479\pi\) | ||
0.721352 | − | 0.692568i | \(-0.243521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.5410 | 0.909393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.8042i | − | 0.438950i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1803 | −0.386921 | −0.193461 | − | 0.981108i | \(-0.561971\pi\) | ||||
−0.193461 | + | 0.981108i | \(0.561971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.4199 | 1.53501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 55.0553i | − | 1.74362i | −0.489846 | − | 0.871809i | \(-0.662947\pi\) | ||
0.489846 | − | 0.871809i | \(-0.337053\pi\) | |||||||
\(998\) | 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 | 3744.2.m.h.1585.3 | 16 | ||
3.2 | odd | 2 | inner | 3744.2.m.h.1585.15 | 16 | ||
4.3 | odd | 2 | 936.2.m.h.181.11 | yes | 16 | ||
8.3 | odd | 2 | 936.2.m.h.181.7 | yes | 16 | ||
8.5 | even | 2 | inner | 3744.2.m.h.1585.16 | 16 | ||
12.11 | even | 2 | 936.2.m.h.181.5 | ✓ | 16 | ||
13.12 | even | 2 | inner | 3744.2.m.h.1585.14 | 16 | ||
24.5 | odd | 2 | inner | 3744.2.m.h.1585.4 | 16 | ||
24.11 | even | 2 | 936.2.m.h.181.9 | yes | 16 | ||
39.38 | odd | 2 | inner | 3744.2.m.h.1585.2 | 16 | ||
52.51 | odd | 2 | 936.2.m.h.181.6 | yes | 16 | ||
104.51 | odd | 2 | 936.2.m.h.181.10 | yes | 16 | ||
104.77 | even | 2 | inner | 3744.2.m.h.1585.1 | 16 | ||
156.155 | even | 2 | 936.2.m.h.181.12 | yes | 16 | ||
312.77 | odd | 2 | inner | 3744.2.m.h.1585.13 | 16 | ||
312.155 | even | 2 | 936.2.m.h.181.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
936.2.m.h.181.5 | ✓ | 16 | 12.11 | even | 2 | ||
936.2.m.h.181.6 | yes | 16 | 52.51 | odd | 2 | ||
936.2.m.h.181.7 | yes | 16 | 8.3 | odd | 2 | ||
936.2.m.h.181.8 | yes | 16 | 312.155 | even | 2 | ||
936.2.m.h.181.9 | yes | 16 | 24.11 | even | 2 | ||
936.2.m.h.181.10 | yes | 16 | 104.51 | odd | 2 | ||
936.2.m.h.181.11 | yes | 16 | 4.3 | odd | 2 | ||
936.2.m.h.181.12 | yes | 16 | 156.155 | even | 2 | ||
3744.2.m.h.1585.1 | 16 | 104.77 | even | 2 | inner | ||
3744.2.m.h.1585.2 | 16 | 39.38 | odd | 2 | inner | ||
3744.2.m.h.1585.3 | 16 | 1.1 | even | 1 | trivial | ||
3744.2.m.h.1585.4 | 16 | 24.5 | odd | 2 | inner | ||
3744.2.m.h.1585.13 | 16 | 312.77 | odd | 2 | inner | ||
3744.2.m.h.1585.14 | 16 | 13.12 | even | 2 | inner | ||
3744.2.m.h.1585.15 | 16 | 3.2 | odd | 2 | inner | ||
3744.2.m.h.1585.16 | 16 | 8.5 | even | 2 | inner |