Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), degree \(2\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1345.3 | ||
Root | \(0.500000 + 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1345 |
Dual form | 1792.2.m.d.449.3 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.23681 | + | 1.23681i | 0.714074 | + | 0.714074i | 0.967385 | − | 0.253311i | \(-0.0815195\pi\) |
−0.253311 | + | 0.967385i | \(0.581520\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.571717 | + | 0.571717i | −0.255680 | + | 0.255680i | −0.823294 | − | 0.567615i | \(-0.807866\pi\) |
0.567615 | + | 0.823294i | \(0.307866\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0594122i | 0.0198041i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.55765 | + | 4.55765i | −1.37418 | + | 1.37418i | −0.520041 | + | 0.854141i | \(0.674083\pi\) |
−0.854141 | + | 0.520041i | \(0.825917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.65103 | − | 3.65103i | −1.01261 | − | 1.01261i | −0.999919 | − | 0.0126931i | \(-0.995960\pi\) |
−0.0126931 | − | 0.999919i | \(-0.504040\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47363 | 0.599942 | 0.299971 | − | 0.953948i | \(-0.403023\pi\) | ||||
0.299971 | + | 0.953948i | \(0.403023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.54358 | − | 5.54358i | −1.27178 | − | 1.27178i | −0.945151 | − | 0.326633i | \(-0.894086\pi\) |
−0.326633 | − | 0.945151i | \(-0.605914\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.23681 | − | 1.23681i | 0.269895 | − | 0.269895i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.08402i | − | 0.851577i | −0.904823 | − | 0.425789i | \(-0.859997\pi\) | ||
0.904823 | − | 0.425789i | \(-0.140003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.34628i | 0.869256i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.63696 | − | 3.63696i | 0.699933 | − | 0.699933i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.30205 | − | 4.30205i | −0.798871 | − | 0.798871i | 0.184046 | − | 0.982918i | \(-0.441080\pi\) |
−0.982918 | + | 0.184046i | \(0.941080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02461 | −0.184025 | −0.0920126 | − | 0.995758i | \(-0.529330\pi\) | ||||
−0.0920126 | + | 0.995758i | \(0.529330\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.2739 | −1.96254 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.571717 | + | 0.571717i | 0.0966378 | + | 0.0966378i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.91245 | − | 5.91245i | 0.972001 | − | 0.972001i | −0.0276180 | − | 0.999619i | \(-0.508792\pi\) |
0.999619 | + | 0.0276180i | \(0.00879219\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 9.03127i | − | 1.44616i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.47010i | − | 0.854285i | −0.904184 | − | 0.427143i | \(-0.859520\pi\) | ||
0.904184 | − | 0.427143i | \(-0.140480\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.35480 | + | 4.35480i | −0.664101 | + | 0.664101i | −0.956344 | − | 0.292243i | \(-0.905598\pi\) |
0.292243 | + | 0.956344i | \(0.405598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0339670 | − | 0.0339670i | −0.00506349 | − | 0.00506349i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.47363 | 0.944275 | 0.472138 | − | 0.881525i | \(-0.343483\pi\) | ||||
0.472138 | + | 0.881525i | \(0.343483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05941 | + | 3.05941i | 0.428403 | + | 0.428403i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.94059 | + | 1.94059i | −0.266560 | + | 0.266560i | −0.827713 | − | 0.561152i | \(-0.810358\pi\) |
0.561152 | + | 0.827713i | \(0.310358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.21137i | − | 0.702701i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 13.7127i | − | 1.81630i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.90191 | + | 6.90191i | −0.898552 | + | 0.898552i | −0.995308 | − | 0.0967561i | \(-0.969153\pi\) |
0.0967561 | + | 0.995308i | \(0.469153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.84563 | − | 7.84563i | −1.00453 | − | 1.00453i | −0.999990 | − | 0.00454037i | \(-0.998555\pi\) |
−0.00454037 | − | 0.999990i | \(-0.501445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0594122 | 0.00748523 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.17471 | 0.517809 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88118 | + | 3.88118i | 0.474161 | + | 0.474161i | 0.903258 | − | 0.429097i | \(-0.141168\pi\) |
−0.429097 | + | 0.903258i | \(0.641168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.05117 | − | 5.05117i | 0.608089 | − | 0.608089i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.44196i | 1.12055i | 0.828305 | + | 0.560277i | \(0.189305\pi\) | ||||
−0.828305 | + | 0.560277i | \(0.810695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.06608i | − | 0.124775i | −0.998052 | − | 0.0623874i | \(-0.980129\pi\) | ||
0.998052 | − | 0.0623874i | \(-0.0198714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.37553 | + | 5.37553i | −0.620713 | + | 0.620713i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.55765 | + | 4.55765i | 0.519392 | + | 0.519392i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3400 | −1.38836 | −0.694179 | − | 0.719803i | \(-0.744232\pi\) | ||||
−0.694179 | + | 0.719803i | \(0.744232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.17471 | 1.01941 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.68230 | + | 5.68230i | 0.623713 | + | 0.623713i | 0.946479 | − | 0.322766i | \(-0.104613\pi\) |
−0.322766 | + | 0.946479i | \(0.604613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41421 | + | 1.41421i | −0.153393 | + | 0.153393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.6417i | − | 1.14091i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.81900i | − | 0.298814i | −0.988776 | − | 0.149407i | \(-0.952264\pi\) | ||
0.988776 | − | 0.149407i | \(-0.0477364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.65103 | + | 3.65103i | −0.382732 | + | 0.382732i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.26725 | − | 1.26725i | −0.131408 | − | 0.131408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.33871 | 0.650338 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.74754 | −0.177436 | −0.0887179 | − | 0.996057i | \(-0.528277\pi\) | ||||
−0.0887179 | + | 0.996057i | \(0.528277\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.270780 | − | 0.270780i | −0.0272144 | − | 0.0272144i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.10947 | + | 5.10947i | −0.508411 | + | 0.508411i | −0.914038 | − | 0.405628i | \(-0.867053\pi\) |
0.405628 | + | 0.914038i | \(0.367053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.35833i | − | 0.133840i | −0.997758 | − | 0.0669202i | \(-0.978683\pi\) | ||
0.997758 | − | 0.0669202i | \(-0.0213173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421i | 0.138013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.348138 | + | 0.348138i | −0.0336557 | + | 0.0336557i | −0.723734 | − | 0.690079i | \(-0.757576\pi\) |
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.70108 | − | 6.70108i | −0.641847 | − | 0.641847i | 0.309162 | − | 0.951009i | \(-0.399951\pi\) |
−0.951009 | + | 0.309162i | \(0.899951\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.6252 | 1.38816 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1747 | −1.33344 | −0.666722 | − | 0.745306i | \(-0.732303\pi\) | ||||
−0.666722 | + | 0.745306i | \(0.732303\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.33490 | + | 2.33490i | 0.217731 | + | 0.217731i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.216915 | − | 0.216915i | 0.0200538 | − | 0.0200538i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.47363i | − | 0.226757i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 30.5443i | − | 2.77675i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.76549 | − | 6.76549i | 0.610023 | − | 0.610023i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.34343 | − | 5.34343i | −0.477931 | − | 0.477931i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.457538 | −0.0405999 | −0.0203000 | − | 0.999794i | \(-0.506462\pi\) | ||||
−0.0203000 | + | 0.999794i | \(0.506462\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7721 | −0.948435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.75966 | + | 5.75966i | 0.503224 | + | 0.503224i | 0.912438 | − | 0.409215i | \(-0.134197\pi\) |
−0.409215 | + | 0.912438i | \(0.634197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.54358 | + | 5.54358i | −0.480689 | + | 0.480689i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.15862i | 0.357917i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.60764i | − | 0.479093i | −0.970885 | − | 0.239546i | \(-0.923001\pi\) | ||
0.970885 | − | 0.239546i | \(-0.0769987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.03239 | − | 7.03239i | 0.596479 | − | 0.596479i | −0.342894 | − | 0.939374i | \(-0.611407\pi\) |
0.939374 | + | 0.342894i | \(0.111407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00666 | + | 8.00666i | 0.674283 | + | 0.674283i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 33.2802 | 2.78303 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.91911 | 0.408510 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.23681 | − | 1.23681i | −0.102011 | − | 0.102011i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4947 | − | 11.4947i | 0.941683 | − | 0.941683i | −0.0567079 | − | 0.998391i | \(-0.518060\pi\) |
0.998391 | + | 0.0567079i | \(0.0180604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.863230i | − | 0.0702487i | −0.999383 | − | 0.0351243i | \(-0.988817\pi\) | ||
0.999383 | − | 0.0351243i | \(-0.0111827\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.146964i | 0.0118813i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.585786 | − | 0.585786i | 0.0470515 | − | 0.0470515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.83778 | − | 1.83778i | −0.146671 | − | 0.146671i | 0.629958 | − | 0.776629i | \(-0.283072\pi\) |
−0.776629 | + | 0.629958i | \(0.783072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.80029 | −0.380688 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08402 | −0.321866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.27078 | + | 4.27078i | 0.334513 | + | 0.334513i | 0.854298 | − | 0.519784i | \(-0.173988\pi\) |
−0.519784 | + | 0.854298i | \(0.673988\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.44549 | − | 6.44549i | 0.501780 | − | 0.501780i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.52637i | 0.118114i | 0.998255 | + | 0.0590572i | \(0.0188094\pi\) | ||||
−0.998255 | + | 0.0590572i | \(0.981191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.6600i | 1.05077i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.329356 | − | 0.329356i | 0.0251865 | − | 0.0251865i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.4232 | + | 18.4232i | 1.40069 | + | 1.40069i | 0.797905 | + | 0.602783i | \(0.205941\pi\) |
0.602783 | + | 0.797905i | \(0.294059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.34628 | 0.328548 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.0727 | −1.28327 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.23412 | − | 9.23412i | −0.690190 | − | 0.690190i | 0.272083 | − | 0.962274i | \(-0.412287\pi\) |
−0.962274 | + | 0.272083i | \(0.912287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7683 | + | 15.7683i | −1.17205 | + | 1.17205i | −0.190325 | + | 0.981721i | \(0.560954\pi\) |
−0.981721 | + | 0.190325i | \(0.939046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 19.4072i | − | 1.43462i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.76049i | 0.497041i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2739 | + | 11.2739i | −0.824430 | + | 0.824430i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.63696 | − | 3.63696i | −0.264550 | − | 0.264550i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.9178 | −1.87535 | −0.937674 | − | 0.347517i | \(-0.887025\pi\) | ||||
−0.937674 | + | 0.347517i | \(0.887025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4884 | −0.826954 | −0.413477 | − | 0.910515i | \(-0.635686\pi\) | ||||
−0.413477 | + | 0.910515i | \(0.635686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.16333 | + | 5.16333i | 0.369754 | + | 0.369754i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9241 | − | 17.9241i | 1.27704 | − | 1.27704i | 0.334723 | − | 0.942317i | \(-0.391357\pi\) |
0.942317 | − | 0.334723i | \(-0.108643\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.34538i | − | 0.166259i | −0.996539 | − | 0.0831297i | \(-0.973508\pi\) | ||
0.996539 | − | 0.0831297i | \(-0.0264916\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.60058i | 0.677172i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.30205 | + | 4.30205i | −0.301945 | + | 0.301945i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.12735 | + | 3.12735i | 0.218423 | + | 0.218423i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.242641 | 0.0168647 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 50.5313 | 3.49533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.94725 | + | 4.94725i | 0.340583 | + | 0.340583i | 0.856586 | − | 0.516004i | \(-0.172581\pi\) |
−0.516004 | + | 0.856586i | \(0.672581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6779 | + | 11.6779i | −0.800159 | + | 0.800159i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.97943i | − | 0.339594i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.02461i | 0.0695550i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.31854 | − | 1.31854i | 0.0890984 | − | 0.0890984i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.03127 | − | 9.03127i | −0.607509 | − | 0.607509i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.47233 | 0.366454 | 0.183227 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183227 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.258222 | −0.0172148 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.59986 | − | 5.59986i | −0.371675 | − | 0.371675i | 0.496412 | − | 0.868087i | \(-0.334651\pi\) |
−0.868087 | + | 0.496412i | \(0.834651\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.48888 | + | 8.48888i | −0.560961 | + | 0.560961i | −0.929580 | − | 0.368620i | \(-0.879831\pi\) |
0.368620 | + | 0.929580i | \(0.379831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.2739i | 0.741769i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.673711i | 0.0441363i | 0.999756 | + | 0.0220682i | \(0.00702508\pi\) | ||||
−0.999756 | + | 0.0220682i | \(0.992975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.70108 | + | 3.70108i | −0.241432 | + | 0.241432i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.2623 | − | 15.2623i | −0.991390 | − | 0.991390i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4603 | −1.12941 | −0.564706 | − | 0.825292i | \(-0.691010\pi\) | ||||
−0.564706 | + | 0.825292i | \(0.691010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.01519 | 0.451888 | 0.225944 | − | 0.974140i | \(-0.427453\pi\) | ||||
0.225944 | + | 0.974140i | \(0.427453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.436525 | + | 0.436525i | 0.0280031 | + | 0.0280031i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.571717 | − | 0.571717i | 0.0365257 | − | 0.0365257i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.4795i | 2.57565i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0559i | 0.890755i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.38248 | − | 8.38248i | 0.529097 | − | 0.529097i | −0.391206 | − | 0.920303i | \(-0.627942\pi\) |
0.920303 | + | 0.391206i | \(0.127942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.6135 | + | 18.6135i | 1.17022 | + | 1.17022i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.49824 | −0.219068 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.28724 | 0.579322 | 0.289661 | − | 0.957129i | \(-0.406457\pi\) | ||||
0.289661 | + | 0.957129i | \(0.406457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.91245 | − | 5.91245i | −0.367382 | − | 0.367382i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.255594 | − | 0.255594i | 0.0158209 | − | 0.0158209i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.8547i | 0.730993i | 0.930813 | + | 0.365496i | \(0.119101\pi\) | ||||
−0.930813 | + | 0.365496i | \(0.880899\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.21893i | − | 0.136308i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.48658 | − | 3.48658i | 0.213375 | − | 0.213375i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.902189 | + | 0.902189i | 0.0550074 | + | 0.0550074i | 0.734075 | − | 0.679068i | \(-0.237616\pi\) |
−0.679068 | + | 0.734075i | \(0.737616\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.2043 | −1.16658 | −0.583289 | − | 0.812264i | \(-0.698235\pi\) | ||||
−0.583289 | + | 0.812264i | \(0.698235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.03127 | −0.546598 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.8088 | − | 19.8088i | −1.19452 | − | 1.19452i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.0461 | + | 23.0461i | −1.38470 | + | 1.38470i | −0.548655 | + | 0.836049i | \(0.684860\pi\) |
−0.836049 | + | 0.548655i | \(0.815140\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.0608743i | − | 0.00364445i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.3459i | − | 1.15408i | −0.816716 | − | 0.577039i | \(-0.804208\pi\) | ||
0.816716 | − | 0.577039i | \(-0.195792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1935 | − | 12.1935i | 0.724828 | − | 0.724828i | −0.244757 | − | 0.969584i | \(-0.578708\pi\) |
0.969584 | + | 0.244757i | \(0.0787081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.83980 | + | 7.83980i | 0.464390 | + | 0.464390i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.47010 | −0.322890 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8812 | −0.640069 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.16138 | − | 2.16138i | −0.126702 | − | 0.126702i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.5139 | − | 14.5139i | 0.847909 | − | 0.847909i | −0.141963 | − | 0.989872i | \(-0.545341\pi\) |
0.989872 | + | 0.141963i | \(0.0453415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.89188i | − | 0.459483i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 33.1519i | 1.92367i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.9109 | + | 14.9109i | −0.862318 | + | 0.862318i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.35480 | + | 4.35480i | 0.251007 | + | 0.251007i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.6389 | −0.726086 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.97096 | 0.513676 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6975 | + | 12.6975i | 0.724684 | + | 0.724684i | 0.969555 | − | 0.244872i | \(-0.0787459\pi\) |
−0.244872 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.68000 | − | 1.68000i | 0.0955719 | − | 0.0955719i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7155i | 1.00455i | 0.864707 | + | 0.502277i | \(0.167504\pi\) | ||||
−0.864707 | + | 0.502277i | \(0.832496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7873i | 0.779306i | 0.920962 | + | 0.389653i | \(0.127405\pi\) | ||||
−0.920962 | + | 0.389653i | \(0.872595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0339670 | + | 0.0339670i | −0.00191382 | + | 0.00191382i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.95039 | − | 8.95039i | −0.502704 | − | 0.502704i | 0.409573 | − | 0.912277i | \(-0.365678\pi\) |
−0.912277 | + | 0.409573i | \(0.865678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.2145 | 2.19559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.861162 | −0.0480654 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.7127 | − | 13.7127i | −0.762997 | − | 0.762997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.8684 | − | 15.8684i | 0.880219 | − | 0.880219i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 16.5760i | − | 0.916653i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.47363i | − | 0.356903i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0509 | − | 12.0509i | 0.662377 | − | 0.662377i | −0.293563 | − | 0.955940i | \(-0.594841\pi\) |
0.955940 | + | 0.293563i | \(0.0948410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.351272 | + | 0.351272i | 0.0192496 | + | 0.0192496i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.43787 | −0.242467 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.50100 | −0.408605 | −0.204303 | − | 0.978908i | \(-0.565493\pi\) | ||||
−0.204303 | + | 0.978908i | \(0.565493\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.5315 | − | 17.5315i | −0.952178 | − | 0.952178i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.66981 | − | 4.66981i | 0.252884 | − | 0.252884i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.77568i | 0.310952i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.9589 | − | 16.9589i | 0.910402 | − | 0.910402i | −0.0859018 | − | 0.996304i | \(-0.527377\pi\) |
0.996304 | + | 0.0859018i | \(0.0273771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.4131 | − | 12.4131i | −0.664458 | − | 0.664458i | 0.291970 | − | 0.956428i | \(-0.405689\pi\) |
−0.956428 | + | 0.291970i | \(0.905689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.5573 | −1.41752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.71903 | 0.251168 | 0.125584 | − | 0.992083i | \(-0.459919\pi\) | ||||
0.125584 | + | 0.992083i | \(0.459919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.39813 | − | 5.39813i | −0.286503 | − | 0.286503i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.05941 | − | 3.05941i | 0.161921 | − | 0.161921i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.09029i | − | 0.321433i | −0.987001 | − | 0.160717i | \(-0.948619\pi\) | ||
0.987001 | − | 0.160717i | \(-0.0513805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.4625i | 2.23487i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.7776 | − | 37.7776i | 1.98281 | − | 1.98281i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.609494 | + | 0.609494i | 0.0319024 | + | 0.0319024i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0286 | −1.61968 | −0.809841 | − | 0.586649i | \(-0.800447\pi\) | ||||
−0.809841 | + | 0.586649i | \(0.800447\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.324990 | 0.0169183 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.94059 | + | 1.94059i | 0.100750 | + | 0.100750i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.96021 | − | 4.96021i | 0.256830 | − | 0.256830i | −0.566934 | − | 0.823763i | \(-0.691870\pi\) |
0.823763 | + | 0.566934i | \(0.191870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 13.2176i | − | 0.682556i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.4138i | 1.61789i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.6815 | + | 10.6815i | −0.548670 | + | 0.548670i | −0.926056 | − | 0.377386i | \(-0.876823\pi\) |
0.377386 | + | 0.926056i | \(0.376823\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.565889 | − | 0.565889i | −0.0289914 | − | 0.0289914i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.43030 | 0.481866 | 0.240933 | − | 0.970542i | \(-0.422547\pi\) | ||||
0.240933 | + | 0.970542i | \(0.422547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.21137 | −0.265596 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.258728 | − | 0.258728i | −0.0131519 | − | 0.0131519i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.33462 | + | 6.33462i | −0.321178 | + | 0.321178i | −0.849219 | − | 0.528041i | \(-0.822927\pi\) |
0.528041 | + | 0.849219i | \(0.322927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.1023i | − | 0.510897i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.2472i | 0.718678i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.05498 | − | 7.05498i | 0.354975 | − | 0.354975i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.6080 | + | 17.6080i | 0.883719 | + | 0.883719i | 0.993910 | − | 0.110191i | \(-0.0351463\pi\) |
−0.110191 | + | 0.993910i | \(0.535146\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.7127 | −0.686495 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.7529 | 1.23610 | 0.618051 | − | 0.786138i | \(-0.287923\pi\) | ||||
0.618051 | + | 0.786138i | \(0.287923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.74088 | + | 3.74088i | 0.186346 | + | 0.186346i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.24533 | + | 5.24533i | −0.260643 | + | 0.260643i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.8937i | 2.67141i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.6913i | − | 1.07256i | −0.844039 | − | 0.536282i | \(-0.819828\pi\) | ||
0.844039 | − | 0.536282i | \(-0.180172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.93560 | − | 6.93560i | 0.342108 | − | 0.342108i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.90191 | + | 6.90191i | 0.339621 | + | 0.339621i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.49733 | −0.318942 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.3955 | 0.851861 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.39320 | − | 7.39320i | −0.361181 | − | 0.361181i | 0.503066 | − | 0.864248i | \(-0.332205\pi\) |
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.59821 | + | 4.59821i | −0.224103 | + | 0.224103i | −0.810224 | − | 0.586121i | \(-0.800654\pi\) |
0.586121 | + | 0.810224i | \(0.300654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.384612i | 0.0187005i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.7511i | 0.521503i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.84563 | + | 7.84563i | −0.379677 | + | 0.379677i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.1614 | + | 41.1614i | 1.98729 | + | 1.98729i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3842 | 0.500190 | 0.250095 | − | 0.968221i | \(-0.419538\pi\) | ||||
0.250095 | + | 0.968221i | \(0.419538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.6476 | 1.32866 | 0.664329 | − | 0.747441i | \(-0.268718\pi\) | ||||
0.664329 | + | 0.747441i | \(0.268718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.08402 | + | 6.08402i | 0.291707 | + | 0.291707i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.6401 | + | 22.6401i | −1.08302 | + | 1.08302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.2404i | 1.58648i | 0.608911 | + | 0.793239i | \(0.291607\pi\) | ||||
−0.608911 | + | 0.793239i | \(0.708393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 0.0594122i | − | 0.00282915i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.8780 | + | 21.8780i | −1.03946 | + | 1.03946i | −0.0402671 | + | 0.999189i | \(0.512821\pi\) |
−0.999189 | + | 0.0402671i | \(0.987179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.61167 | + | 1.61167i | 0.0764006 | + | 0.0764006i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.4336 | 1.34486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.9670 | 0.753531 | 0.376765 | − | 0.926309i | \(-0.377036\pi\) | ||||
0.376765 | + | 0.926309i | \(0.377036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9308 | + | 24.9308i | 1.17394 | + | 1.17394i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.06765 | − | 1.06765i | 0.0501628 | − | 0.0501628i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.17471i | − | 0.195713i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.09512i | − | 0.378674i | −0.981912 | − | 0.189337i | \(-0.939366\pi\) | ||
0.981912 | − | 0.189337i | \(-0.0606338\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.99647 | − | 8.99647i | 0.419919 | − | 0.419919i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.240227 | + | 0.240227i | 0.0111885 | + | 0.0111885i | 0.712679 | − | 0.701490i | \(-0.247482\pi\) |
−0.701490 | + | 0.712679i | \(0.747482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7400 | −0.499129 | −0.249564 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249564 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.44902 | 0.0671965 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.77143 | − | 6.77143i | −0.313344 | − | 0.313344i | 0.532859 | − | 0.846204i | \(-0.321117\pi\) |
−0.846204 | + | 0.532859i | \(0.821117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.88118 | − | 3.88118i | 0.179216 | − | 0.179216i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4.54599i | − | 0.209468i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 39.6953i | − | 1.82519i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0939 | − | 24.0939i | 1.10551 | − | 1.10551i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.115295 | − | 0.115295i | −0.00527898 | − | 0.00527898i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.7472 | 0.947962 | 0.473981 | − | 0.880535i | \(-0.342816\pi\) | ||||
0.473981 | + | 0.880535i | \(0.342816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.1730 | −1.96852 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.05117 | − | 5.05117i | −0.229836 | − | 0.229836i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.999098 | − | 0.999098i | 0.0453667 | − | 0.0453667i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.57283i | 0.252529i | 0.991997 | + | 0.126265i | \(0.0402988\pi\) | ||||
−0.991997 | + | 0.126265i | \(0.959701\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.5643i | 0.477735i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4196 | + | 16.4196i | −0.741005 | + | 0.741005i | −0.972772 | − | 0.231766i | \(-0.925550\pi\) |
0.231766 | + | 0.972772i | \(0.425550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.6417 | − | 10.6417i | −0.479277 | − | 0.479277i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.309619 | 0.0139163 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.44196 | 0.423530 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.7731 | + | 17.7731i | 0.795631 | + | 0.795631i | 0.982403 | − | 0.186772i | \(-0.0598026\pi\) |
−0.186772 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.88784 | + | 1.88784i | −0.0843424 | + | 0.0843424i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.9839i | − | 0.935625i | −0.883828 | − | 0.467813i | \(-0.845042\pi\) | ||
0.883828 | − | 0.467813i | \(-0.154958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.84234i | − | 0.259981i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.8948 | + | 16.8948i | −0.750327 | + | 0.750327i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.90544 | + | 2.90544i | 0.128781 | + | 0.128781i | 0.768560 | − | 0.639778i | \(-0.220974\pi\) |
−0.639778 | + | 0.768560i | \(0.720974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.06608 | −0.0471604 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.3235 | −1.78033 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.776581 | + | 0.776581i | 0.0342202 | + | 0.0342202i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.5045 | + | 29.5045i | −1.29761 | + | 1.29761i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.5720i | 2.00039i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.02225i | − | 0.0447854i | −0.999749 | − | 0.0223927i | \(-0.992872\pi\) | ||
0.999749 | − | 0.0223927i | \(-0.00712841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2532 | − | 22.2532i | 0.973064 | − | 0.973064i | −0.0265830 | − | 0.999647i | \(-0.508463\pi\) |
0.999647 | + | 0.0265830i | \(0.00846262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.37553 | + | 5.37553i | 0.234608 | + | 0.234608i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.53450 | −0.110405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.32077 | 0.274816 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.410058 | − | 0.410058i | −0.0177950 | − | 0.0177950i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.9715 | + | 19.9715i | −0.865060 | + | 0.865060i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.398072i | − | 0.0172102i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 22.8418i | − | 0.985694i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.55765 | − | 4.55765i | 0.196312 | − | 0.196312i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1188 | + | 11.1188i | 0.478036 | + | 0.478036i | 0.904503 | − | 0.426467i | \(-0.140242\pi\) |
−0.426467 | + | 0.904503i | \(0.640242\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.0048 | −1.67386 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.66224 | 0.328214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7261 | − | 17.7261i | −0.757912 | − | 0.757912i | 0.218030 | − | 0.975942i | \(-0.430037\pi\) |
−0.975942 | + | 0.218030i | \(0.930037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.466126 | − | 0.466126i | 0.0198938 | − | 0.0198938i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.6975i | 2.03198i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3400i | 0.524750i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.36147 | + | 8.36147i | −0.354924 | + | 0.354924i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.1751 | + | 14.1751i | 0.600617 | + | 0.600617i | 0.940476 | − | 0.339859i | \(-0.110379\pi\) |
−0.339859 | + | 0.940476i | \(0.610379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7990 | 1.34495 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.8874 | −1.17741 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.484561 | + | 0.484561i | 0.0204218 | + | 0.0204218i | 0.717244 | − | 0.696822i | \(-0.245403\pi\) |
−0.696822 | + | 0.717244i | \(0.745403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.10392 | − | 8.10392i | 0.340934 | − | 0.340934i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 9.17471i | − | 0.385301i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.22040i | 0.386539i | 0.981146 | + | 0.193270i | \(0.0619092\pi\) | ||||
−0.981146 | + | 0.193270i | \(0.938091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.47325 | + | 1.47325i | −0.0616537 | + | 0.0616537i | −0.737261 | − | 0.675608i | \(-0.763881\pi\) |
0.675608 | + | 0.737261i | \(0.263881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.0555 | − | 32.0555i | −1.33914 | − | 1.33914i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.7503 | 0.740239 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.4518 | 1.68403 | 0.842014 | − | 0.539455i | \(-0.181370\pi\) | ||||
0.842014 | + | 0.539455i | \(0.181370\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.2090 | − | 14.2090i | −0.590507 | − | 0.590507i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.68230 | − | 5.68230i | 0.235742 | − | 0.235742i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 17.6890i | − | 0.732605i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.248028i | 0.0102547i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.58467 | + | 2.58467i | −0.106681 | + | 0.106681i | −0.758432 | − | 0.651752i | \(-0.774034\pi\) |
0.651752 | + | 0.758432i | \(0.274034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.68000 | + | 5.68000i | 0.234040 | + | 0.234040i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.3375 | 1.82380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.8610 | −1.55476 | −0.777382 | − | 0.629029i | \(-0.783453\pi\) | ||||
−0.777382 | + | 0.629029i | \(0.783453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.41421 | + | 1.41421i | 0.0579771 | + | 0.0579771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.90079 | − | 2.90079i | 0.118722 | − | 0.118722i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.42807i | 0.0583493i | 0.999574 | + | 0.0291747i | \(0.00928790\pi\) | ||||
−0.999574 | + | 0.0291747i | \(0.990712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.2990i | 1.43988i | 0.694038 | + | 0.719939i | \(0.255830\pi\) | ||||
−0.694038 | + | 0.719939i | \(0.744170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.230589 | + | 0.230589i | −0.00939032 | + | 0.00939032i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.4627 | + | 17.4627i | 0.709959 | + | 0.709959i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4364 | −0.951256 | −0.475628 | − | 0.879647i | \(-0.657779\pi\) | ||||
−0.475628 | + | 0.879647i | \(0.657779\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.6417 | −0.431222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.6354 | − | 23.6354i | −0.956185 | − | 0.956185i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4964 | − | 13.4964i | 0.545114 | − | 0.545114i | −0.379910 | − | 0.925023i | \(-0.624045\pi\) |
0.925023 | + | 0.379910i | \(0.124045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.73588i | 0.311941i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.504525i | 0.0203114i | 0.999948 | + | 0.0101557i | \(0.00323272\pi\) | ||||
−0.999948 | + | 0.0101557i | \(0.996767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.6377 | − | 23.6377i | 0.950078 | − | 0.950078i | −0.0487334 | − | 0.998812i | \(-0.515518\pi\) |
0.998812 | + | 0.0487334i | \(0.0155185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.8534 | − | 14.8534i | −0.596047 | − | 0.596047i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.81900 | −0.112941 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.6215 | −0.624862 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 62.4978 | + | 62.4978i | 2.49592 | + | 2.49592i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.6252 | − | 14.6252i | 0.583144 | − | 0.583144i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.0329i | − | 1.51407i | −0.653376 | − | 0.757033i | \(-0.726648\pi\) | ||
0.653376 | − | 0.757033i | \(-0.273352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2376i | 0.486403i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.261582 | − | 0.261582i | 0.0103806 | − | 0.0103806i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.65103 | + | 3.65103i | 0.144659 | + | 0.144659i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.560967 | −0.0221915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.2113 | 1.74624 | 0.873122 | − | 0.487503i | \(-0.162092\pi\) | ||||
0.873122 | + | 0.487503i | \(0.162092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.98280 | + | 7.98280i | 0.314811 | + | 0.314811i | 0.846770 | − | 0.531959i | \(-0.178544\pi\) |
−0.531959 | + | 0.846770i | \(0.678544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.15862 | − | 6.15862i | 0.242495 | − | 0.242495i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.5922i | − | 1.83173i | −0.401487 | − | 0.915865i | \(-0.631507\pi\) | ||
0.401487 | − | 0.915865i | \(-0.368493\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 62.9129i | − | 2.46955i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.26725 | + | 1.26725i | −0.0496674 | + | 0.0496674i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.1497 | + | 28.1497i | 1.10158 | + | 1.10158i | 0.994220 | + | 0.107363i | \(0.0342407\pi\) |
0.107363 | + | 0.994220i | \(0.465759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.58579 | −0.257328 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.0633379 | 0.00247105 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5741 | − | 12.5741i | −0.489819 | − | 0.489819i | 0.418430 | − | 0.908249i | \(-0.362580\pi\) |
−0.908249 | + | 0.418430i | \(0.862580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.13055 | − | 7.13055i | 0.277346 | − | 0.277346i | −0.554703 | − | 0.832049i | \(-0.687168\pi\) |
0.832049 | + | 0.554703i | \(0.187168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 22.3400i | − | 0.867613i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 6.33871i | − | 0.245805i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5697 | + | 17.5697i | −0.680301 | + | 0.680301i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.76825 | + | 6.76825i | 0.261675 | + | 0.261675i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 71.5152 | 2.76081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.0500 | −1.31253 | −0.656265 | − | 0.754531i | \(-0.727865\pi\) | ||||
−0.656265 | + | 0.754531i | \(0.727865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.8072 | + | 15.8072i | 0.608421 | + | 0.608421i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.7666 | − | 15.7666i | 0.605960 | − | 0.605960i | −0.335928 | − | 0.941888i | \(-0.609050\pi\) |
0.941888 | + | 0.335928i | \(0.109050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.74754i | 0.0670644i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 13.8519i | − | 0.530808i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.5756 | − | 30.5756i | 1.16994 | − | 1.16994i | 0.187719 | − | 0.982223i | \(-0.439891\pi\) |
0.982223 | − | 0.187719i | \(-0.0601094\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.20598 | + | 3.20598i | 0.122494 | + | 0.122494i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.9983 | −0.801135 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1703 | 0.539844 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.97140 | − | 3.97140i | −0.151079 | − | 0.151079i | 0.627521 | − | 0.778600i | \(-0.284070\pi\) |
−0.778600 | + | 0.627521i | \(0.784070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.270780 | + | 0.270780i | −0.0102861 | + | 0.0102861i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.04107i | 0.305015i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 13.5310i | − | 0.512522i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.833255 | + | 0.833255i | −0.0315166 | + | 0.0315166i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.4532 | + | 21.4532i | 0.810278 | + | 0.810278i | 0.984675 | − | 0.174398i | \(-0.0557978\pi\) |
−0.174398 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −65.5522 | −2.47235 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.15509 | −0.344801 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.10947 | + | 5.10947i | 0.192161 | + | 0.192161i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.30481 | + | 2.30481i | −0.0865591 | + | 0.0865591i | −0.749061 | − | 0.662502i | \(-0.769495\pi\) |
0.662502 | + | 0.749061i | \(0.269495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.733146i | − | 0.0274951i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.18453i | 0.156712i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.0268 | + | 19.0268i | −0.711564 | + | 0.711564i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.5951 | − | 21.5951i | −0.806484 | − | 0.806484i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8530 | 1.03874 | 0.519371 | − | 0.854549i | \(-0.326166\pi\) | ||||
0.519371 | + | 0.854549i | \(0.326166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.35833 | −0.0505869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.67647 | + | 8.67647i | 0.322681 | + | 0.322681i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.6979 | − | 18.6979i | 0.694423 | − | 0.694423i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.56027i | − | 0.169131i | −0.996418 | − | 0.0845656i | \(-0.973050\pi\) | ||
0.996418 | − | 0.0845656i | \(-0.0269503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 26.4443i | − | 0.979419i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.7721 | + | 10.7721i | −0.398422 | + | 0.398422i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.8784 | − | 29.8784i | −1.10358 | − | 1.10358i | −0.993975 | − | 0.109608i | \(-0.965041\pi\) |
−0.109608 | − | 0.993975i | \(-0.534959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.3781 | −1.30317 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9312 | − | 10.9312i | −0.402109 | − | 0.402109i | 0.476866 | − | 0.878976i | \(-0.341773\pi\) |
−0.878976 | + | 0.476866i | \(0.841773\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.0656 | + | 50.0656i | −1.83920 | + | 1.83920i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.5354i | − | 1.23029i | −0.788412 | − | 0.615147i | \(-0.789097\pi\) | ||
0.788412 | − | 0.615147i | \(-0.210903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1434i | 0.481538i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.337598 | + | 0.337598i | −0.0123521 | + | 0.0123521i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.348138 | + | 0.348138i | 0.0127207 | + | 0.0127207i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.7562 | −0.611442 | −0.305721 | − | 0.952121i | \(-0.598898\pi\) | ||||
−0.305721 | + | 0.952121i | \(0.598898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.7351 | 0.755630 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.493523 | + | 0.493523i | 0.0179611 | + | 0.0179611i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.2722 | + | 10.2722i | −0.373351 | + | 0.373351i | −0.868696 | − | 0.495345i | \(-0.835042\pi\) |
0.495345 | + | 0.868696i | \(0.335042\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.0429i | 1.67125i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.54207i | − | 0.0558998i | −0.999609 | − | 0.0279499i | \(-0.991102\pi\) | ||
0.999609 | − | 0.0279499i | \(-0.00889790\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.70108 | + | 6.70108i | −0.242595 | + | 0.242595i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0840215 | − | 0.0840215i | −0.00303780 | − | 0.00303780i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.3981 | 1.81977 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.1627 | 1.15982 | 0.579908 | − | 0.814682i | \(-0.303089\pi\) | ||||
0.579908 | + | 0.814682i | \(0.303089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4866 | + | 11.4866i | 0.413679 | + | 0.413679i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.9593 | − | 20.9593i | 0.753852 | − | 0.753852i | −0.221344 | − | 0.975196i | \(-0.571044\pi\) |
0.975196 | + | 0.221344i | \(0.0710443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.45324i | − | 0.159965i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.6252i | − | 0.524676i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.3239 | + | 30.3239i | −1.08647 | + | 1.08647i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.0331 | − | 43.0331i | −1.53985 | − | 1.53985i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.2928 | −1.11831 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.10139 | 0.0750016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.8158 | − | 14.8158i | −0.528127 | − | 0.528127i | 0.391887 | − | 0.920014i | \(-0.371823\pi\) |
−0.920014 | + | 0.391887i | \(0.871823\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.6621 | + | 14.6621i | −0.521983 | + | 0.521983i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.1747i | 0.503995i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.2892i | 2.03440i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.74441 | − | 2.74441i | 0.0973340 | − | 0.0973340i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.4119 | − | 35.4119i | −1.25435 | − | 1.25435i | −0.953749 | − | 0.300605i | \(-0.902811\pi\) |
−0.300605 | − | 0.953749i | \(-0.597189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0133 | 0.566511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.167483 | 0.00591773 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.85880 | + | 4.85880i | 0.171463 | + | 0.171463i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.33490 | − | 2.33490i | 0.0822946 | − | 0.0822946i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.23168i | 0.0785588i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.4359i | − | 0.613012i | −0.951869 | − | 0.306506i | \(-0.900840\pi\) | ||
0.951869 | − | 0.306506i | \(-0.0991599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.5546 | + | 38.5546i | −1.35383 | + | 1.35383i | −0.472506 | + | 0.881327i | \(0.656651\pi\) |
−0.881327 | + | 0.472506i | \(0.843349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.7521 | − | 23.7521i | −0.833024 | − | 0.833024i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.88335 | −0.171056 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.2824 | 1.68919 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.216915 | − | 0.216915i | −0.00757964 | − | 0.00757964i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1020 | + | 12.1020i | −0.422362 | + | 0.422362i | −0.886016 | − | 0.463655i | \(-0.846538\pi\) |
0.463655 | + | 0.886016i | \(0.346538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.3555i | − | 1.12784i | −0.825829 | − | 0.563921i | \(-0.809292\pi\) | ||
0.825829 | − | 0.563921i | \(-0.190708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 48.9996i | − | 1.70595i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2064 | + | 11.2064i | −0.389684 | + | 0.389684i | −0.874575 | − | 0.484891i | \(-0.838859\pi\) |
0.484891 | + | 0.874575i | \(0.338859\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.6494 | − | 23.6494i | −0.821379 | − | 0.821379i | 0.164927 | − | 0.986306i | \(-0.447261\pi\) |
−0.986306 | + | 0.164927i | \(0.947261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.0073 | −1.97756 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.47363 | −0.0857061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.872654 | − | 0.872654i | −0.0301994 | − | 0.0301994i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.72646 | + | 3.72646i | −0.128805 | + | 0.128805i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 28.6777i | − | 0.990066i | −0.868874 | − | 0.495033i | \(-0.835156\pi\) | ||
0.868874 | − | 0.495033i | \(-0.164844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.01532i | 0.276390i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.9272 | − | 23.9272i | 0.824098 | − | 0.824098i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.80965 | − | 7.80965i | −0.268660 | − | 0.268660i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.5443 | −1.04951 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.1621 | 1.03516 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.1466 | − | 24.1466i | −0.827734 | − | 0.827734i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0950 | − | 24.0950i | 0.824998 | − | 0.824998i | −0.161822 | − | 0.986820i | \(-0.551737\pi\) |
0.986820 | + | 0.161822i | \(0.0517370\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.376597i | 0.0128793i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 38.8652i | − | 1.32761i | −0.747906 | − | 0.663805i | \(-0.768941\pi\) | ||
0.747906 | − | 0.663805i | \(-0.231059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.2051 | + | 10.2051i | −0.348195 | + | 0.348195i | −0.859437 | − | 0.511242i | \(-0.829186\pi\) |
0.511242 | + | 0.859437i | \(0.329186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.76549 | − | 6.76549i | −0.230567 | − | 0.230567i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.8471 | 0.743684 | 0.371842 | − | 0.928296i | \(-0.378726\pi\) | ||||
0.371842 | + | 0.928296i | \(0.378726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0657 | −0.716255 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4580 | − | 13.4580i | −0.457057 | − | 0.457057i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.2413 | − | 56.2413i | 1.90786 | − | 1.90786i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.3405i | − | 0.960283i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.103825i | − | 0.00351395i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.34343 | + | 5.34343i | −0.180641 | + | 0.180641i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.6322 | − | 26.6322i | −0.899306 | − | 0.899306i | 0.0960685 | − | 0.995375i | \(-0.469373\pi\) |
−0.995375 | + | 0.0960685i | \(0.969373\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.9019 | 1.21094 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.11567 | −0.138660 | −0.0693302 | − | 0.997594i | \(-0.522086\pi\) | ||||
−0.0693302 | + | 0.997594i | \(0.522086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.315403 | + | 0.315403i | 0.0106141 | + | 0.0106141i | 0.712394 | − | 0.701780i | \(-0.247611\pi\) |
−0.701780 | + | 0.712394i | \(0.747611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.76077 | − | 9.76077i | 0.328105 | − | 0.328105i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5273i | 0.689240i | 0.938742 | + | 0.344620i | \(0.111992\pi\) | ||||
−0.938742 | + | 0.344620i | \(0.888008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.457538i | 0.0153453i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.8151 | + | 41.8151i | −1.40086 | + | 1.40086i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.8870 | − | 35.8870i | −1.20091 | − | 1.20091i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5586 | 0.352935 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.8839 | −1.23152 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.40792 | + | 4.40792i | 0.147012 | + | 0.147012i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.80029 | + | 4.80029i | −0.159921 | + | 0.159921i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.7721i | 0.358475i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.0300i | − | 0.599337i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.78157 | + | 6.78157i | −0.225178 | + | 0.225178i | −0.810675 | − | 0.585497i | \(-0.800900\pi\) |
0.585497 | + | 0.810675i | \(0.300900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.303565 | − | 0.303565i | −0.0100686 | − | 0.0100686i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.5756 | −1.01301 | −0.506507 | − | 0.862236i | \(-0.669064\pi\) | ||||
−0.506507 | + | 0.862236i | \(0.669064\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51.7958 | −1.71419 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.0954 | + | 11.0954i | 0.366803 | + | 0.366803i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.75966 | − | 5.75966i | 0.190201 | − | 0.190201i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.4777i | − | 0.741470i | −0.928739 | − | 0.370735i | \(-0.879106\pi\) | ||
0.928739 | − | 0.370735i | \(-0.120894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.4088i | 1.03496i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.4728 | − | 34.4728i | 1.13469 | − | 1.13469i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.6972 | + | 25.6972i | 0.844917 | + | 0.844917i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0807014 | 0.00265058 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3955 | 0.505111 | 0.252555 | − | 0.967582i | \(-0.418729\pi\) | ||||
0.252555 | + | 0.967582i | \(0.418729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.54358 | + | 5.54358i | 0.181683 | + | 0.181683i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.9108 | + | 21.9108i | −0.717326 | + | 0.717326i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.8910i | − | 0.421580i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4553i | 0.962262i | 0.876649 | + | 0.481131i | \(0.159774\pi\) | ||||
−0.876649 | + | 0.481131i | \(0.840226\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0524 | + | 17.0524i | −0.556482 | + | 0.556482i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.2529 | + | 10.2529i | 0.334235 | + | 0.334235i | 0.854192 | − | 0.519957i | \(-0.174052\pi\) |
−0.519957 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.3400 | −0.727490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.15862 | 0.135280 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.6627 | − | 31.6627i | −1.02890 | − | 1.02890i | −0.999570 | − | 0.0293306i | \(-0.990662\pi\) |
−0.0293306 | − | 0.999570i | \(-0.509338\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.89227 | + | 3.89227i | −0.126348 | + | 0.126348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 22.1399i | − | 0.717936i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7024i | 0.703008i | 0.936186 | + | 0.351504i | \(0.114330\pi\) | ||||
−0.936186 | + | 0.351504i | \(0.885670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.8177 | − | 14.8177i | 0.479488 | − | 0.479488i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 48.5010 | + | 48.5010i | 1.56781 | + | 1.56781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.60764 | −0.181080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9502 | −0.966135 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0206836 | − | 0.0206836i | −0.000666520 | − | 0.000666520i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.56812 | − | 6.56812i | 0.211435 | − | 0.211435i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.1725i | − | 0.520072i | −0.965599 | − | 0.260036i | \(-0.916266\pi\) | ||
0.965599 | − | 0.260036i | \(-0.0837344\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 33.9202i | − | 1.08967i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6139 | + | 19.6139i | −0.629439 | + | 0.629439i | −0.947927 | − | 0.318488i | \(-0.896825\pi\) |
0.318488 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.03239 | − | 7.03239i | −0.225448 | − | 0.225448i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.2524 | 1.25708 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.3566 | −1.57906 | −0.789529 | − | 0.613713i | \(-0.789675\pi\) | ||||
−0.789529 | + | 0.613713i | \(0.789675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8480 | + | 12.8480i | 0.410625 | + | 0.410625i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.398126 | − | 0.398126i | 0.0127112 | − | 0.0127112i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 0.208762i | − | 0.00665848i | −0.999994 | − | 0.00332924i | \(-0.998940\pi\) | ||
0.999994 | − | 0.00332924i | \(-0.00105973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.4950i | 0.653026i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00666 | − | 8.00666i | 0.254855 | − | 0.254855i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.7851 | + | 17.7851i | 0.565533 | + | 0.565533i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.4623 | −0.745306 | −0.372653 | − | 0.927971i | \(-0.621552\pi\) | ||||
−0.372653 | + | 0.927971i | \(0.621552\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.8094 | 0.945972 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.34089 | + | 1.34089i | 0.0425091 | + | 0.0425091i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7777 | − | 19.7777i | 0.626366 | − | 0.626366i | −0.320786 | − | 0.947152i | \(-0.603947\pi\) |
0.947152 | + | 0.320786i | \(0.103947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 43.0066i | − | 1.36067i |
(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 | 1792.2.m.d.1345.3 | yes | 8 | |
4.3 | odd | 2 | 1792.2.m.b.1345.2 | yes | 8 | ||
8.3 | odd | 2 | 1792.2.m.c.1345.3 | yes | 8 | ||
8.5 | even | 2 | 1792.2.m.a.1345.2 | yes | 8 | ||
16.3 | odd | 4 | 1792.2.m.c.449.3 | yes | 8 | ||
16.5 | even | 4 | inner | 1792.2.m.d.449.3 | yes | 8 | |
16.11 | odd | 4 | 1792.2.m.b.449.2 | yes | 8 | ||
16.13 | even | 4 | 1792.2.m.a.449.2 | ✓ | 8 | ||
32.5 | even | 8 | 7168.2.a.x.1.1 | 4 | |||
32.11 | odd | 8 | 7168.2.a.s.1.1 | 4 | |||
32.21 | even | 8 | 7168.2.a.t.1.4 | 4 | |||
32.27 | odd | 8 | 7168.2.a.w.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.a.449.2 | ✓ | 8 | 16.13 | even | 4 | ||
1792.2.m.a.1345.2 | yes | 8 | 8.5 | even | 2 | ||
1792.2.m.b.449.2 | yes | 8 | 16.11 | odd | 4 | ||
1792.2.m.b.1345.2 | yes | 8 | 4.3 | odd | 2 | ||
1792.2.m.c.449.3 | yes | 8 | 16.3 | odd | 4 | ||
1792.2.m.c.1345.3 | yes | 8 | 8.3 | odd | 2 | ||
1792.2.m.d.449.3 | yes | 8 | 16.5 | even | 4 | inner | |
1792.2.m.d.1345.3 | yes | 8 | 1.1 | even | 1 | trivial | |
7168.2.a.s.1.1 | 4 | 32.11 | odd | 8 | |||
7168.2.a.t.1.4 | 4 | 32.21 | even | 8 | |||
7168.2.a.w.1.4 | 4 | 32.27 | odd | 8 | |||
7168.2.a.x.1.1 | 4 | 32.5 | even | 8 |