Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.500000 - 2.22827i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.97 |
Dual form | 432.2.u.c.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.986166 | + | 1.42389i | 0.569363 | + | 0.822086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.52129 | + | 0.917674i | 1.12755 | + | 0.410396i | 0.837404 | − | 0.546585i | \(-0.184072\pi\) |
0.290150 | + | 0.956981i | \(0.406295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.168844 | + | 0.957561i | −0.0638170 | + | 0.361924i | 0.936130 | + | 0.351653i | \(0.114380\pi\) |
−0.999947 | + | 0.0102706i | \(0.996731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.05495 | + | 2.80839i | −0.351651 | + | 0.936131i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.297791 | + | 0.108387i | −0.0897872 | + | 0.0326799i | −0.386523 | − | 0.922280i | \(-0.626324\pi\) |
0.296736 | + | 0.954960i | \(0.404102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.15981 | + | 0.973200i | −0.321675 | + | 0.269917i | −0.789297 | − | 0.614011i | \(-0.789555\pi\) |
0.467623 | + | 0.883928i | \(0.345111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.17974 | + | 4.49503i | 0.304607 | + | 1.16061i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.587342 | − | 1.01731i | −0.142451 | − | 0.246733i | 0.785968 | − | 0.618267i | \(-0.212165\pi\) |
−0.928419 | + | 0.371534i | \(0.878832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11040 | − | 5.38737i | 0.713575 | − | 1.23595i | −0.249931 | − | 0.968264i | \(-0.580408\pi\) |
0.963507 | − | 0.267685i | \(-0.0862586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.52997 | + | 0.703898i | −0.333868 | + | 0.153603i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.375556 | − | 2.12988i | −0.0783089 | − | 0.444112i | −0.998601 | − | 0.0528796i | \(-0.983160\pi\) |
0.920292 | − | 0.391232i | \(-0.127951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.68454 | + | 1.41350i | 0.336909 | + | 0.282700i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.03922 | + | 1.26740i | −0.969797 | + | 0.243912i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.37436 | − | 2.83142i | −0.626602 | − | 0.525782i | 0.273269 | − | 0.961938i | \(-0.411895\pi\) |
−0.899871 | + | 0.436156i | \(0.856340\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50609 | + | 8.54146i | 0.270502 | + | 1.53409i | 0.752897 | + | 0.658138i | \(0.228656\pi\) |
−0.482395 | + | 0.875954i | \(0.660233\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.448003 | − | 0.317135i | −0.0779872 | − | 0.0552061i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.30443 | + | 2.25934i | −0.220489 | + | 0.381899i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.23332 | + | 3.86823i | 0.367156 | + | 0.635933i | 0.989120 | − | 0.147113i | \(-0.0469982\pi\) |
−0.621964 | + | 0.783046i | \(0.713665\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.52950 | − | 0.691717i | −0.405045 | − | 0.110763i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47767 | − | 3.75721i | 0.699295 | − | 0.586778i | −0.222278 | − | 0.974983i | \(-0.571349\pi\) |
0.921573 | + | 0.388205i | \(0.126905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.25381 | − | 1.91223i | 0.801199 | − | 0.291613i | 0.0912158 | − | 0.995831i | \(-0.470925\pi\) |
0.709983 | + | 0.704219i | \(0.248702\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.23703 | + | 6.11267i | −0.780690 | + | 0.911223i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.429965 | − | 2.43845i | 0.0627168 | − | 0.355685i | −0.937258 | − | 0.348636i | \(-0.886645\pi\) |
0.999975 | − | 0.00704911i | \(-0.00224382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.68943 | + | 2.07078i | 0.812776 | + | 0.295826i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.869320 | − | 1.83955i | 0.121729 | − | 0.257588i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8920 | −1.49613 | −0.748063 | − | 0.663628i | \(-0.769016\pi\) | ||||
−0.748063 | + | 0.663628i | \(0.769016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.850279 | −0.114652 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.7384 | − | 0.883963i | 1.42234 | − | 0.117084i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.62023 | − | 0.589715i | −0.210936 | − | 0.0767743i | 0.234391 | − | 0.972142i | \(-0.424690\pi\) |
−0.445327 | + | 0.895368i | \(0.646913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.176214 | − | 0.999361i | 0.0225619 | − | 0.127955i | −0.971446 | − | 0.237259i | \(-0.923751\pi\) |
0.994008 | + | 0.109304i | \(0.0348621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.51109 | − | 1.48436i | −0.316367 | − | 0.187012i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.81731 | + | 1.38939i | −0.473478 | + | 0.172332i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.656156 | + | 0.550580i | −0.0801622 | + | 0.0672641i | −0.681988 | − | 0.731363i | \(-0.738884\pi\) |
0.601826 | + | 0.798627i | \(0.294440\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.66237 | − | 2.63517i | 0.320512 | − | 0.317238i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.79788 | − | 8.31018i | −0.569404 | − | 0.986237i | −0.996625 | − | 0.0820894i | \(-0.973841\pi\) |
0.427221 | − | 0.904147i | \(-0.359493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.62091 | − | 13.1998i | 0.891960 | − | 1.54492i | 0.0544385 | − | 0.998517i | \(-0.482663\pi\) |
0.837522 | − | 0.546404i | \(-0.184004\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.351434 | + | 3.79256i | −0.0405802 | + | 0.437927i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0535070 | − | 0.303453i | −0.00609768 | − | 0.0345817i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59024 | + | 7.20807i | 0.966478 | + | 0.810971i | 0.981995 | − | 0.188908i | \(-0.0604949\pi\) |
−0.0155168 | + | 0.999880i | \(0.504939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.77415 | − | 5.92544i | −0.752684 | − | 0.658382i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.58886 | − | 3.01141i | −0.393929 | − | 0.330546i | 0.424212 | − | 0.905563i | \(-0.360551\pi\) |
−0.818141 | + | 0.575017i | \(0.804995\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.547303 | − | 3.10391i | −0.0593633 | − | 0.336666i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.703969 | − | 7.59698i | 0.0754734 | − | 0.814482i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.74976 | − | 13.4230i | 0.821473 | − | 1.42283i | −0.0831130 | − | 0.996540i | \(-0.526486\pi\) |
0.904586 | − | 0.426292i | \(-0.140180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.736071 | − | 1.27491i | −0.0771612 | − | 0.133647i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6769 | + | 10.5678i | −1.10714 | + | 1.09583i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.7861 | − | 10.7288i | 1.31182 | − | 1.10075i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.21481 | − | 1.89804i | 0.529484 | − | 0.192716i | −0.0634241 | − | 0.997987i | \(-0.520202\pi\) |
0.592908 | + | 0.805270i | \(0.297980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.00976156 | − | 0.950656i | 0.000981074 | − | 0.0955445i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.76063 | + | 9.98501i | −0.175189 | + | 0.993546i | 0.762737 | + | 0.646709i | \(0.223855\pi\) |
−0.937926 | + | 0.346836i | \(0.887256\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.25906 | − | 3.37002i | −0.912323 | − | 0.332058i | −0.157143 | − | 0.987576i | \(-0.550228\pi\) |
−0.755180 | + | 0.655518i | \(0.772451\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.50345 | + | 0.370714i | −0.439492 | + | 0.0361780i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.17080 | −0.499880 | −0.249940 | − | 0.968261i | \(-0.580411\pi\) | ||||
−0.249940 | + | 0.968261i | \(0.580411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.31065 | −0.700234 | −0.350117 | − | 0.936706i | \(-0.613858\pi\) | ||||
−0.350117 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.30552 | + | 6.99473i | −0.313746 | + | 0.663911i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.74991 | − | 3.54868i | −0.917195 | − | 0.333832i | −0.160073 | − | 0.987105i | \(-0.551173\pi\) |
−0.757122 | + | 0.653274i | \(0.773395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00765 | − | 5.71469i | 0.0939642 | − | 0.532898i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50958 | − | 4.28390i | −0.139561 | − | 0.396046i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.07330 | − | 0.390650i | 0.0983894 | − | 0.0358108i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.34956 | + | 7.00611i | −0.759051 | + | 0.636919i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.76560 | + | 2.67050i | 0.880535 | + | 0.240790i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.75766 | − | 6.50846i | −0.336095 | − | 0.582134i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.61372 | − | 4.52709i | 0.231930 | − | 0.401714i | −0.726446 | − | 0.687223i | \(-0.758829\pi\) |
0.958376 | + | 0.285509i | \(0.0921627\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.90395 | + | 5.59510i | 0.695904 | + | 0.492621i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25622 | + | 7.12440i | 0.109757 | + | 0.622461i | 0.989213 | + | 0.146482i | \(0.0467951\pi\) |
−0.879457 | + | 0.475979i | \(0.842094\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.63357 | + | 3.88802i | 0.401781 | + | 0.337134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.8684 | − | 1.42887i | −1.19360 | − | 0.122977i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.61748 | + | 7.23092i | 0.736241 | + | 0.617779i | 0.931825 | − | 0.362907i | \(-0.118216\pi\) |
−0.195584 | + | 0.980687i | \(0.562660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.62885 | − | 9.23766i | −0.138157 | − | 0.783528i | −0.972609 | − | 0.232447i | \(-0.925327\pi\) |
0.834452 | − | 0.551081i | \(-0.185784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89612 | − | 1.79249i | 0.328112 | − | 0.150955i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.239900 | − | 0.415518i | 0.0200614 | − | 0.0347474i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.90940 | − | 10.2354i | −0.490749 | − | 0.850003i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.66215 | + | 10.1433i | 0.219570 | + | 0.836605i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5941 | − | 12.2459i | 1.19560 | − | 1.00322i | 0.195851 | − | 0.980634i | \(-0.437253\pi\) |
0.999745 | − | 0.0225899i | \(-0.00719121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.77193 | − | 1.37287i | 0.306955 | − | 0.111723i | −0.183950 | − | 0.982936i | \(-0.558888\pi\) |
0.490905 | + | 0.871213i | \(0.336666\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.47661 | − | 0.576279i | 0.281068 | − | 0.0465894i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.04099 | + | 22.9176i | −0.324580 | + | 1.84078i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.83713 | − | 2.48851i | −0.545662 | − | 0.198605i | 0.0544560 | − | 0.998516i | \(-0.482658\pi\) |
−0.600118 | + | 0.799911i | \(0.704880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7413 | − | 15.5090i | −0.851839 | − | 1.22994i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.10290 | 0.165732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4492 | −0.975094 | −0.487547 | − | 0.873097i | \(-0.662108\pi\) | ||||
−0.487547 | + | 0.873097i | \(0.662108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.838517 | − | 1.21071i | −0.0652785 | − | 0.0942535i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.19126 | − | 0.797553i | −0.169565 | − | 0.0617165i | 0.255843 | − | 0.966718i | \(-0.417647\pi\) |
−0.425408 | + | 0.905002i | \(0.639869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.85937 | + | 10.5450i | −0.143029 | + | 0.811157i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8485 | + | 14.4187i | 0.906081 | + | 1.10262i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.36623 | − | 1.22521i | 0.255930 | − | 0.0931509i | −0.210869 | − | 0.977514i | \(-0.567629\pi\) |
0.466799 | + | 0.884363i | \(0.345407\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.63794 | + | 1.37439i | −0.123816 | + | 0.103894i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.758123 | − | 2.88859i | −0.0569840 | − | 0.217120i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.99785 | − | 17.3168i | −0.747275 | − | 1.29432i | −0.949124 | − | 0.314901i | \(-0.898029\pi\) |
0.201850 | − | 0.979416i | \(-0.435305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.86616 | + | 8.42844i | −0.361699 | + | 0.626481i | −0.988241 | − | 0.152907i | \(-0.951136\pi\) |
0.626542 | + | 0.779388i | \(0.284470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.59676 | − | 0.734626i | 0.118036 | − | 0.0543051i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.08108 | + | 11.8024i | 0.153004 | + | 0.867728i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.285168 | + | 0.239284i | 0.0208535 | + | 0.0174982i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.362776 | − | 5.03935i | −0.0263881 | − | 0.366559i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6023 | + | 11.4137i | 0.984227 | + | 0.825864i | 0.984722 | − | 0.174135i | \(-0.0557130\pi\) |
−0.000494763 | 1.00000i | \(0.500157\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.83795 | + | 10.4235i | 0.132299 | + | 0.750303i | 0.976703 | + | 0.214596i | \(0.0688435\pi\) |
−0.844404 | + | 0.535706i | \(0.820045\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.74284 | − | 4.06528i | −0.411253 | − | 0.291120i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.07945 | + | 12.2620i | −0.504390 | + | 0.873628i | 0.495597 | + | 0.868552i | \(0.334949\pi\) |
−0.999987 | + | 0.00507615i | \(0.998384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.77010 | + | 6.53000i | 0.267255 | + | 0.462899i | 0.968152 | − | 0.250363i | \(-0.0805501\pi\) |
−0.700897 | + | 0.713263i | \(0.747217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.43105 | − | 0.391333i | −0.100938 | − | 0.0276025i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.28100 | − | 2.75308i | 0.230281 | − | 0.193229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7374 | − | 5.36397i | 1.02930 | − | 0.374636i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.37775 | + | 1.19222i | 0.443284 | + | 0.0828648i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.342328 | + | 1.94144i | −0.0236793 | + | 0.134292i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89922 | + | 1.78317i | 0.337276 | + | 0.122758i | 0.505106 | − | 0.863058i | \(-0.331454\pi\) |
−0.167829 | + | 0.985816i | \(0.553676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.10131 | − | 15.0269i | 0.486573 | − | 1.02963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.0012 | 1.02307 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.43326 | −0.572487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.3106 | − | 2.16583i | 1.77791 | − | 0.146353i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.67125 | + | 0.608285i | 0.112420 | + | 0.0409177i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.07250 | + | 17.4250i | −0.205750 | + | 1.16686i | 0.690506 | + | 0.723326i | \(0.257388\pi\) |
−0.896256 | + | 0.443537i | \(0.853723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.74677 | + | 3.23969i | −0.383118 | + | 0.215979i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.8208 | + | 5.39434i | −0.983692 | + | 0.358035i | −0.783275 | − | 0.621676i | \(-0.786452\pi\) |
−0.200418 | + | 0.979711i | \(0.564230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.35350 | + | 1.13572i | −0.0894415 | + | 0.0750504i | −0.686412 | − | 0.727213i | \(-0.740815\pi\) |
0.596971 | + | 0.802263i | \(0.296371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.379318 | − | 0.375443i | 0.0249573 | − | 0.0247024i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.94920 | + | 12.0364i | 0.455257 | + | 0.788529i | 0.998703 | − | 0.0509157i | \(-0.0162140\pi\) |
−0.543446 | + | 0.839444i | \(0.682881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.32177 | − | 5.75347i | 0.216688 | − | 0.375315i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.79212 | + | 19.3400i | −0.116411 | + | 1.25627i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.44391 | + | 19.5314i | 0.222768 | + | 1.26338i | 0.866906 | + | 0.498471i | \(0.166105\pi\) |
−0.644138 | + | 0.764909i | \(0.722784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8419 | + | 12.4538i | 0.956050 | + | 0.802221i | 0.980306 | − | 0.197485i | \(-0.0632773\pi\) |
−0.0242563 | + | 0.999706i | \(0.507722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.75676 | − | 15.4892i | 0.112696 | − | 0.993629i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.4444 | + | 10.4421i | 0.795043 | + | 0.667120i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.63550 | + | 9.27540i | 0.104065 | + | 0.590179i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.748720 | − | 8.07992i | 0.0474482 | − | 0.512044i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.73786 | + | 4.74212i | −0.172812 | + | 0.299320i | −0.939402 | − | 0.342818i | \(-0.888619\pi\) |
0.766590 | + | 0.642137i | \(0.221952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.342689 | + | 0.593554i | 0.0215447 | + | 0.0373164i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.87991 | − | 3.84027i | 0.242969 | − | 0.240487i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.85943 | + | 7.43395i | −0.552636 | + | 0.463717i | −0.875833 | − | 0.482615i | \(-0.839687\pi\) |
0.323196 | + | 0.946332i | \(0.395243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.08115 | + | 1.48542i | −0.253590 | + | 0.0922993i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.5115 | − | 6.48951i | 0.712546 | − | 0.401691i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.12488 | + | 6.37952i | −0.0693632 | + | 0.393378i | 0.930285 | + | 0.366839i | \(0.119560\pi\) |
−0.999648 | + | 0.0265395i | \(0.991551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.4618 | − | 9.99526i | −1.68696 | − | 0.614004i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.7554 | − | 2.20245i | 1.63741 | − | 0.134788i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8387 | −0.843758 | −0.421879 | − | 0.906652i | \(-0.638629\pi\) | ||||
−0.421879 | + | 0.906652i | \(0.638629\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.94536 | −0.118172 | −0.0590860 | − | 0.998253i | \(-0.518819\pi\) | ||||
−0.0590860 | + | 0.998253i | \(0.518819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.08945 | − | 2.30536i | 0.0659366 | − | 0.139527i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.654846 | − | 0.238344i | −0.0394887 | − | 0.0143727i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.16586 | − | 12.2832i | 0.130134 | − | 0.738026i | −0.847991 | − | 0.530010i | \(-0.822188\pi\) |
0.978125 | − | 0.208016i | \(-0.0667007\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.5766 | − | 4.78114i | −1.53123 | − | 0.286239i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.16752 | + | 3.33670i | −0.546888 | + | 0.199051i | −0.600663 | − | 0.799502i | \(-0.705097\pi\) |
0.0537751 | + | 0.998553i | \(0.482875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.3547 | + | 17.0797i | −1.20996 | + | 1.01528i | −0.210676 | + | 0.977556i | \(0.567567\pi\) |
−0.999288 | + | 0.0377246i | \(0.987989\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27.8858 | + | 7.62565i | 1.65181 | + | 0.451704i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.84173 | + | 4.92202i | 0.167742 | + | 0.290538i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.81006 | − | 13.5274i | 0.459415 | − | 0.795730i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.84527 | + | 5.55356i | 0.459898 | + | 0.325556i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.12849 | + | 12.0712i | 0.124347 | + | 0.705210i | 0.981693 | + | 0.190469i | \(0.0610008\pi\) |
−0.857346 | + | 0.514741i | \(0.827888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.54389 | − | 2.97368i | −0.206334 | − | 0.173134i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.36326 | − | 0.923606i | 0.0791044 | − | 0.0535930i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.50838 | + | 2.10478i | 0.145063 | + | 0.121723i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.944004 | + | 5.35371i | 0.0544115 | + | 0.308583i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.9539 | + | 7.33993i | −0.916526 | + | 0.421668i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.36137 | − | 2.35797i | 0.0779521 | − | 0.135017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2370 | − | 22.9271i | −0.755475 | − | 1.30852i | −0.945138 | − | 0.326671i | \(-0.894073\pi\) |
0.189663 | − | 0.981849i | \(-0.439260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.33242 | − | 16.5073i | −0.246463 | − | 0.939070i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5280 | − | 11.3513i | 0.767100 | − | 0.643673i | −0.172865 | − | 0.984946i | \(-0.555302\pi\) |
0.939964 | + | 0.341272i | \(0.110858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.06541 | + | 3.29954i | −0.512407 | + | 0.186501i | −0.585266 | − | 0.810841i | \(-0.699010\pi\) |
0.0728589 | + | 0.997342i | \(0.476788\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.96901 | − | 6.04686i | −0.279972 | − | 0.340702i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.644320 | + | 3.65412i | −0.0361886 | + | 0.205236i | −0.997541 | − | 0.0700850i | \(-0.977673\pi\) |
0.961352 | + | 0.275321i | \(0.0887841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.31174 | + | 0.477435i | 0.0734434 | + | 0.0267312i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.09927 | − | 7.36268i | −0.284614 | − | 0.410945i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.30748 | −0.406599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.32937 | −0.184680 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.20952 | − | 10.4096i | −0.398687 | − | 0.575652i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.26237 | + | 0.823435i | 0.124728 | + | 0.0453974i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.245329 | − | 1.39133i | 0.0134845 | − | 0.0764745i | −0.977323 | − | 0.211755i | \(-0.932082\pi\) |
0.990807 | + | 0.135280i | \(0.0431934\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.2196 | + | 2.19126i | −0.724427 | + | 0.120080i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.15961 | + | 0.786034i | −0.117992 | + | 0.0429456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.95097 | + | 8.34986i | −0.542064 | + | 0.454846i | −0.872243 | − | 0.489073i | \(-0.837335\pi\) |
0.330179 | + | 0.943918i | \(0.392891\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.56209 | − | 17.3824i | −0.247779 | − | 0.944084i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.37428 | − | 2.38033i | −0.0744215 | − | 0.128902i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.34669 | + | 10.9928i | −0.342689 | + | 0.593555i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.13083 | − | 4.20084i | 0.491587 | − | 0.226166i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.833591 | + | 4.72753i | 0.0447495 | + | 0.253787i | 0.998973 | − | 0.0453070i | \(-0.0144266\pi\) |
−0.954224 | + | 0.299094i | \(0.903316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2954 | − | 14.5126i | −0.925803 | − | 0.776841i | 0.0492565 | − | 0.998786i | \(-0.484315\pi\) |
−0.975059 | + | 0.221946i | \(0.928759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.61112 | − | 6.37412i | 0.246123 | − | 0.340225i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.7565 | − | 19.0950i | −1.21121 | − | 1.01632i | −0.999237 | − | 0.0390490i | \(-0.987567\pi\) |
−0.211972 | − | 0.977276i | \(-0.567988\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.47081 | − | 25.3552i | −0.237286 | − | 1.34572i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.61470 | + | 1.14302i | 0.0854589 | + | 0.0604952i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.70991 | − | 11.6219i | 0.354136 | − | 0.613381i | −0.632834 | − | 0.774288i | \(-0.718108\pi\) |
0.986970 | + | 0.160906i | \(0.0514418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.84920 | − | 17.0593i | −0.518379 | − | 0.897858i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.2100 | − | 4.97970i | −0.955778 | − | 0.261366i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.3276 | − | 26.2870i | 1.63976 | − | 1.37592i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.47054 | + | 2.71905i | −0.389959 | + | 0.141933i | −0.529556 | − | 0.848275i | \(-0.677641\pi\) |
0.139597 | + | 0.990208i | \(0.455419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.82801 | + | 16.5387i | 0.303394 | + | 0.860973i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.83904 | − | 10.4297i | 0.0954782 | − | 0.541484i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.7318 | + | 3.90604i | 0.555670 | + | 0.202247i | 0.604564 | − | 0.796557i | \(-0.293347\pi\) |
−0.0488939 | + | 0.998804i | \(0.515570\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.56168 | − | 11.7689i | 0.287204 | − | 0.607745i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.66917 | 0.343480 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1705 | 1.24155 | 0.620777 | − | 0.783987i | \(-0.286817\pi\) | ||||
0.620777 | + | 0.783987i | \(0.286817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.02366 | − | 0.742807i | 0.462296 | − | 0.0380551i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.87378 | + | 3.22979i | 0.453429 | + | 0.165035i | 0.558631 | − | 0.829416i | \(-0.311327\pi\) |
−0.105202 | + | 0.994451i | \(0.533549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.143564 | − | 0.814194i | 0.00731672 | − | 0.0414952i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.172220 | + | 16.7721i | −0.00875442 | + | 0.852573i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.39406 | − | 0.871367i | 0.121384 | − | 0.0441801i | −0.280614 | − | 0.959821i | \(-0.590538\pi\) |
0.401998 | + | 0.915641i | \(0.368316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.94617 | + | 1.63303i | −0.0984218 | + | 0.0825857i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.90554 | + | 8.81457i | −0.449225 | + | 0.444636i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0438 | + | 26.0567i | 0.756937 | + | 1.31105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.83759 | + | 3.18279i | −0.0922258 | + | 0.159740i | −0.908447 | − | 0.417999i | \(-0.862731\pi\) |
0.816222 | + | 0.577739i | \(0.196065\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.966669 | + | 10.4319i | −0.0483940 | + | 0.522251i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.80420 | + | 15.9034i | 0.140035 | + | 0.794177i | 0.971220 | + | 0.238182i | \(0.0765516\pi\) |
−0.831186 | + | 0.555995i | \(0.812337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0593 | − | 8.44078i | −0.501091 | − | 0.420465i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.6420 | − | 21.1562i | −0.578494 | − | 1.05126i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.08433 | − | 0.909859i | −0.0537481 | − | 0.0451000i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.59443 | + | 9.04248i | 0.0788396 | + | 0.447122i | 0.998517 | + | 0.0544462i | \(0.0173393\pi\) |
−0.919677 | + | 0.392676i | \(0.871550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.79780 | + | 19.4013i | −0.0886792 | + | 0.956994i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.838253 | − | 1.45190i | 0.0412477 | − | 0.0714432i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.28506 | − | 10.8860i | −0.308522 | − | 0.534375i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.5471 | − | 11.4292i | 0.565466 | − | 0.559689i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.34613 | − | 4.48594i | 0.261176 | − | 0.219152i | −0.502791 | − | 0.864408i | \(-0.667694\pi\) |
0.763967 | + | 0.645256i | \(0.223249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.9525 | + | 10.5379i | −1.41106 | + | 0.513584i | −0.931441 | − | 0.363894i | \(-0.881447\pi\) |
−0.479619 | + | 0.877477i | \(0.659225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.39454 | + | 3.77996i | 0.310913 | + | 0.183788i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.448559 | − | 2.54390i | 0.0217583 | − | 0.123397i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.927196 | + | 0.337472i | 0.0448702 | + | 0.0163314i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.828236 | − | 0.0681784i | 0.0399876 | − | 0.00329169i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.8971 | −1.34376 | −0.671879 | − | 0.740661i | \(-0.734513\pi\) | ||||
−0.671879 | + | 0.740661i | \(0.734513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.1706 | 0.921278 | 0.460639 | − | 0.887588i | \(-0.347620\pi\) | ||||
0.460639 | + | 0.887588i | \(0.347620\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.74646 | − | 18.5082i | 0.419361 | − | 0.887398i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.6426 | − | 4.60154i | −0.604778 | − | 0.220121i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.12397 | − | 23.3882i | 0.196826 | − | 1.11626i | −0.712968 | − | 0.701197i | \(-0.752649\pi\) |
0.909794 | − | 0.415060i | \(-0.136239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.8177 | + | 13.7936i | −0.562746 | + | 0.656838i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9496 | − | 7.98900i | 1.04286 | − | 0.379569i | 0.236894 | − | 0.971536i | \(-0.423871\pi\) |
0.805962 | + | 0.591967i | \(0.201648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.8573 | − | 26.7314i | 1.51018 | − | 1.26719i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.8291 | + | 8.70396i | 1.50546 | + | 0.411683i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.40953 | − | 4.17343i | −0.113713 | − | 0.196956i | 0.803552 | − | 0.595235i | \(-0.202941\pi\) |
−0.917264 | + | 0.398279i | \(0.869608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.926176 | + | 1.60418i | −0.0436119 | + | 0.0755380i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.67457 | + | 4.01695i | 0.266615 | + | 0.188733i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.685893 | − | 3.88989i | −0.0321552 | − | 0.182361i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.74872 | − | 3.14555i | −0.175358 | − | 0.147142i | 0.550885 | − | 0.834581i | \(-0.314290\pi\) |
−0.726242 | + | 0.687439i | \(0.758735\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.24908 | + | 4.38203i | 0.198330 | + | 0.204535i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4419 | + | 17.9919i | 0.998650 | + | 0.837967i | 0.986797 | − | 0.161963i | \(-0.0517824\pi\) |
0.0118535 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.77104 | + | 27.0579i | 0.221729 | + | 1.25749i | 0.868840 | + | 0.495093i | \(0.164866\pi\) |
−0.647111 | + | 0.762396i | \(0.724023\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −36.6173 | + | 16.8466i | −1.69809 | + | 0.781243i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.6232 | + | 18.4000i | −0.491585 | + | 0.851450i | −0.999953 | − | 0.00968963i | \(-0.996916\pi\) |
0.508368 | + | 0.861140i | \(0.330249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.416426 | − | 0.721272i | −0.0192288 | − | 0.0333052i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.19917 | − | 12.1894i | −0.147410 | − | 0.561659i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.35728 | + | 1.13889i | −0.0624076 | + | 0.0523662i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.8547 | − | 4.67871i | 0.589812 | − | 0.214674i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4905 | − | 30.5889i | 0.526113 | − | 1.40057i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.23745 | − | 41.0456i | 0.330688 | − | 1.87542i | −0.135560 | − | 0.990769i | \(-0.543283\pi\) |
0.466248 | − | 0.884654i | \(-0.345606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.35480 | − | 2.31296i | −0.289754 | − | 0.105462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.07381 | + | 2.99431i | 0.0943618 | + | 0.136246i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.8898 | 0.676112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.02801 | −0.182527 | −0.0912634 | − | 0.995827i | \(-0.529091\pi\) | ||||
−0.0912634 | + | 0.995827i | \(0.529091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2769 | − | 17.7263i | −0.555183 | − | 0.801611i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.2922 | − | 13.2093i | −1.63784 | − | 0.596126i | −0.651184 | − | 0.758920i | \(-0.725727\pi\) |
−0.986660 | + | 0.162793i | \(0.947950\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.898521 | + | 5.09577i | −0.0404674 | + | 0.229502i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.897004 | − | 2.38792i | 0.0403173 | − | 0.107329i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.76759 | − | 3.19114i | 0.393280 | − | 0.143142i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.11922 | − | 2.61734i | 0.139636 | − | 0.117168i | −0.570295 | − | 0.821440i | \(-0.693171\pi\) |
0.709930 | + | 0.704272i | \(0.248726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.02531 | − | 3.90664i | −0.0458076 | − | 0.174536i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.71297 | − | 2.96695i | −0.0763775 | − | 0.132290i | 0.825307 | − | 0.564684i | \(-0.191002\pi\) |
−0.901684 | + | 0.432395i | \(0.857669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.6020 | + | 23.5594i | −0.605282 | + | 1.04838i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.8487 | + | 7.75161i | −0.748276 | + | 0.344261i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.12952 | − | 12.0771i | −0.0943893 | − | 0.535308i | −0.994933 | − | 0.100542i | \(-0.967942\pi\) |
0.900543 | − | 0.434766i | \(-0.143169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.3529 | + | 9.52619i | 0.502222 | + | 0.421414i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.84601 | + | 31.0903i | −0.390561 | + | 1.37267i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.2522 | − | 16.9936i | −0.892418 | − | 0.748827i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.136257 | + | 0.772750i | 0.00599257 | + | 0.0339855i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.06423 | + | 3.58490i | 0.222295 | + | 0.157360i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.04117 | + | 12.1957i | −0.308479 | + | 0.534302i | −0.978030 | − | 0.208465i | \(-0.933153\pi\) |
0.669551 | + | 0.742766i | \(0.266487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.88956 | + | 8.46897i | 0.213806 | + | 0.370322i | 0.952902 | − | 0.303277i | \(-0.0980808\pi\) |
−0.739097 | + | 0.673599i | \(0.764747\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.57227 | − | 0.976870i | −0.155906 | − | 0.0426341i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.80469 | − | 6.54892i | 0.339978 | − | 0.285275i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.2176 | − | 6.26668i | 0.748590 | − | 0.272464i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.36541 | − | 3.92812i | 0.146047 | − | 0.170466i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.53675 | + | 8.71534i | −0.0665640 | + | 0.377503i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0371 | − | 4.74511i | −0.563642 | − | 0.205149i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7977 | − | 31.3131i | 0.638569 | − | 1.35126i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.91871 | −0.0826445 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.9454 | 1.76038 | 0.880189 | − | 0.474623i | \(-0.157416\pi\) | ||||
0.880189 | + | 0.474623i | \(0.157416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.8001 | + | 1.38294i | −0.720959 | + | 0.0593477i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4323 | − | 6.70879i | −0.789551 | − | 0.287373i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.192798 | + | 1.09341i | −0.00824343 | + | 0.0467508i | −0.988652 | − | 0.150224i | \(-0.952001\pi\) |
0.980409 | + | 0.196975i | \(0.0631117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.62070 | + | 1.54916i | 0.111849 | + | 0.0661164i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.7495 | + | 9.37206i | −1.09697 | + | 0.399263i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.35257 | + | 7.00864i | −0.355188 | + | 0.298038i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.7531 | + | 14.6023i | −0.626232 | + | 0.619835i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5201 | − | 30.3458i | −0.742352 | − | 1.28579i | −0.951422 | − | 0.307890i | \(-0.900377\pi\) |
0.209070 | − | 0.977901i | \(-0.432956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.23247 | + | 7.33084i | −0.179014 | + | 0.310062i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0594925 | + | 0.642022i | −0.00251178 | + | 0.0271062i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.73255 | + | 38.1822i | 0.283743 | + | 1.60919i | 0.709741 | + | 0.704463i | \(0.248812\pi\) |
−0.425998 | + | 0.904724i | \(0.640077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.3258 | − | 17.8945i | −0.897183 | − | 0.752826i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.81774 | − | 5.48619i | 0.286318 | − | 0.230398i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.0213 | − | 21.8344i | −1.09087 | − | 0.915347i | −0.0940904 | − | 0.995564i | \(-0.529994\pi\) |
−0.996777 | + | 0.0802169i | \(0.974439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.75191 | − | 9.93559i | −0.0733153 | − | 0.415792i | −0.999272 | − | 0.0381610i | \(-0.987850\pi\) |
0.925956 | − | 0.377631i | \(-0.123261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.83775 | + | 30.6240i | −0.118549 | + | 1.27934i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.37795 | − | 4.11873i | 0.0991674 | − | 0.171763i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.06615 | + | 10.5069i | 0.252537 | + | 0.437407i | 0.964224 | − | 0.265090i | \(-0.0854017\pi\) |
−0.711687 | + | 0.702497i | \(0.752068\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0295 | + | 12.8964i | −0.541487 | + | 0.535956i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.48957 | − | 2.92810i | 0.144772 | − | 0.121478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.24352 | − | 1.18055i | 0.134333 | − | 0.0488932i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.125131 | − | 12.1862i | 0.00517353 | − | 0.503839i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.51319 | + | 31.2669i | −0.227554 | + | 1.29052i | 0.630189 | + | 0.776442i | \(0.282977\pi\) |
−0.857743 | + | 0.514079i | \(0.828134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.7006 | + | 18.4535i | 2.08908 | + | 0.760363i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.4412 | + | 2.01195i | −1.00538 | + | 0.0827605i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.4906 | 0.553993 | 0.276996 | − | 0.960871i | \(-0.410661\pi\) | ||||
0.276996 | + | 0.960871i | \(0.410661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.06459 | 0.125636 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.58009 | + | 11.8079i | −0.228378 | + | 0.483265i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.8715 | − | 14.5120i | −1.62911 | − | 0.592946i | −0.644020 | − | 0.765009i | \(-0.722735\pi\) |
−0.985086 | + | 0.172063i | \(0.944957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.43906 | + | 19.5039i | −0.140282 | + | 0.795579i | 0.830753 | + | 0.556641i | \(0.187910\pi\) |
−0.971035 | + | 0.238938i | \(0.923201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.854034 | − | 2.42358i | −0.0347789 | − | 0.0986958i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.4810 | + | 10.0022i | −1.11726 | + | 0.406649i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.5769 | − | 23.1397i | 1.11931 | − | 0.939213i | 0.120741 | − | 0.992684i | \(-0.461473\pi\) |
0.998569 | + | 0.0534715i | \(0.0170286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.15571 | + | 1.95680i | 0.289964 | + | 0.0792934i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.87442 | + | 3.24659i | 0.0758310 | + | 0.131343i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.2314 | + | 22.9175i | −0.534411 | + | 0.925627i | 0.464780 | + | 0.885426i | \(0.346133\pi\) |
−0.999192 | + | 0.0402013i | \(0.987200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.1712 | + | 15.6947i | 0.894031 | + | 0.632872i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.52903 | + | 48.3705i | 0.343366 | + | 1.94732i | 0.319425 | + | 0.947611i | \(0.396510\pi\) |
0.0239406 | + | 0.999713i | \(0.492379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5430 | + | 15.5595i | 0.745307 | + | 0.625387i | 0.934257 | − | 0.356600i | \(-0.116064\pi\) |
−0.188950 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.59193 | + | 10.2570i | 0.184268 | + | 0.411598i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5448 | + | 9.68725i | 0.462533 | + | 0.388111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.41077 | − | 30.6860i | −0.216431 | − | 1.22744i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.10199 | + | 1.42714i | −0.123882 | + | 0.0569945i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.62345 | − | 4.54395i | 0.104604 | − | 0.181179i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.84842 | + | 15.3259i | 0.352250 | + | 0.610115i | 0.986643 | − | 0.162895i | \(-0.0520833\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.29240 | + | 8.73447i | 0.0911147 | + | 0.347164i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7443 | − | 9.01555i | 0.426375 | − | 0.357771i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.61398 | + | 3.13523i | −0.341298 | + | 0.124222i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.3998 | − | 4.70751i | 1.12348 | − | 0.186226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.60738 | − | 37.4723i | 0.260976 | − | 1.48007i | −0.519278 | − | 0.854605i | \(-0.673799\pi\) |
0.780254 | − | 0.625463i | \(-0.215090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.1115 | + | 16.0553i | 1.73959 | + | 0.633158i | 0.999237 | − | 0.0390615i | \(-0.0124368\pi\) |
0.740352 | + | 0.672220i | \(0.234659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.7937 | + | 21.3601i | 0.582500 | + | 0.841053i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2333 | 1.10997 | 0.554983 | − | 0.831862i | \(-0.312725\pi\) | ||||
0.554983 | + | 0.831862i | \(0.312725\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.546406 | 0.0214483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.31660 | − | 12.0081i | −0.325953 | − | 0.470634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.1779 | − | 12.0758i | −1.29835 | − | 0.472562i | −0.401893 | − | 0.915687i | \(-0.631647\pi\) |
−0.896460 | + | 0.443125i | \(0.853870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.37057 | + | 19.1155i | −0.131699 | + | 0.746902i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.0306 | + | 35.3277i | 1.13259 | + | 1.37826i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.1793 | − | 14.2601i | 1.52621 | − | 0.555494i | 0.563519 | − | 0.826103i | \(-0.309447\pi\) |
0.962689 | + | 0.270609i | \(0.0872250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.975874 | − | 0.818856i | 0.0379571 | − | 0.0318498i | −0.623612 | − | 0.781734i | \(-0.714335\pi\) |
0.661569 | + | 0.749884i | \(0.269891\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.781997 | + | 2.97956i | 0.0303702 | + | 0.115716i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.11461 | + | 14.0549i | 0.314671 | + | 0.545027i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.76334 | + | 8.25035i | −0.184437 | + | 0.319455i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.8413 | + | 12.8090i | −1.07641 | + | 0.495226i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0558427 | + | 0.316700i | 0.00215578 | + | 0.0122261i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2963 | + | 22.9043i | 1.05219 | + | 0.882896i | 0.993323 | − | 0.115370i | \(-0.0368053\pi\) |
0.0588715 | + | 0.998266i | \(0.481250\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.2802 | − | 4.98793i | −0.395687 | − | 0.191986i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7902 | + | 11.5714i | 0.530002 | + | 0.444725i | 0.868102 | − | 0.496386i | \(-0.165340\pi\) |
−0.338100 | + | 0.941110i | \(0.609784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.936996 | + | 5.31397i | 0.0359586 | + | 0.203931i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.2968 | − | 15.7836i | −0.854414 | − | 0.604828i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.8807 | − | 34.4344i | 0.760715 | − | 1.31760i | −0.181768 | − | 0.983341i | \(-0.558182\pi\) |
0.942483 | − | 0.334255i | \(-0.108485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0915 | + | 26.1393i | 0.576617 | + | 0.998730i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.95192 | − | 0.807229i | −0.112623 | − | 0.0307977i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.6327 | − | 10.6001i | 0.481266 | − | 0.403830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.8251 | + | 5.75986i | −0.602015 | + | 0.219115i | −0.625006 | − | 0.780620i | \(-0.714903\pi\) |
0.0229909 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.908663 | + | 0.169860i | 0.0345173 | + | 0.00645244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.37036 | − | 24.7855i | 0.165777 | − | 0.940169i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.45216 | − | 2.34839i | −0.244393 | − | 0.0889518i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.2854 | + | 21.7648i | −0.389031 | + | 0.823220i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.96921 | −0.338762 | −0.169381 | − | 0.985551i | \(-0.554177\pi\) | ||||
−0.169381 | + | 0.985551i | \(0.554177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.7861 | 1.04797 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.4682 | − | 0.944032i | 0.431916 | − | 0.0355543i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.26398 | − | 3.37181i | −0.348408 | − | 0.126810i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.15026 | − | 17.8660i | 0.118311 | − | 0.670973i | −0.866747 | − | 0.498748i | \(-0.833793\pi\) |
0.985058 | − | 0.172225i | \(-0.0550955\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.3054 | + | 16.5206i | −1.09904 | + | 0.619572i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.6267 | − | 6.41560i | 0.660125 | − | 0.240266i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.986166 | − | 0.827492i | 0.0368805 | − | 0.0309464i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.4144 | + | 24.1650i | −0.911771 | + | 0.902457i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.7860 | + | 27.3421i | 0.588718 | + | 1.01969i | 0.994401 | + | 0.105675i | \(0.0337004\pi\) |
−0.405683 | + | 0.914014i | \(0.632966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.79034 | − | 8.29711i | 0.178402 | − | 0.309001i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.09636 | + | 33.4148i | −0.115155 | + | 1.24271i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.68204 | − | 9.53930i | −0.0624693 | − | 0.354281i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.4232 | − | 24.6890i | −1.09125 | − | 0.915664i | −0.0944407 | − | 0.995530i | \(-0.530106\pi\) |
−0.996806 | + | 0.0798662i | \(0.974551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.7874 | − | 12.7734i | 0.881014 | − | 0.473090i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.03111 | − | 4.22160i | −0.186082 | − | 0.156142i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.26680 | − | 29.8695i | −0.194534 | − | 1.10326i | −0.913081 | − | 0.407778i | \(-0.866304\pi\) |
0.718547 | − | 0.695478i | \(-0.244807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.59619 | + | 28.0171i | −0.0957618 | + | 1.03343i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.135721 | − | 0.235076i | 0.00499936 | − | 0.00865915i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00127 | + | 8.66245i | 0.183975 | + | 0.318653i | 0.943230 | − | 0.332139i | \(-0.107770\pi\) |
−0.759256 | + | 0.650792i | \(0.774437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.5943 | + | 11.4759i | −0.425928 | + | 0.421577i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.7873 | + | 23.3163i | −1.01942 | + | 0.855394i | −0.989554 | − | 0.144160i | \(-0.953952\pi\) |
−0.0298642 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.0337 | − | 17.4828i | 1.75982 | − | 0.640521i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2433 | − | 6.90205i | 0.447960 | − | 0.252533i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.873058 | − | 4.95136i | 0.0319008 | − | 0.180919i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6766 | − | 4.97788i | −0.499067 | − | 0.181646i | 0.0802073 | − | 0.996778i | \(-0.474442\pi\) |
−0.579274 | + | 0.815133i | \(0.696664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.45226 | + | 0.778089i | −0.344460 | + | 0.0283551i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.7700 | 0.391959 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.5754 | −1.65646 | −0.828232 | − | 0.560385i | \(-0.810653\pi\) | ||||
−0.828232 | + | 0.560385i | \(0.810653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.507211 | + | 1.07330i | −0.0184106 | + | 0.0389582i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.9040 | − | 7.60843i | −0.757769 | − | 0.275805i | −0.0658978 | − | 0.997826i | \(-0.520991\pi\) |
−0.691871 | + | 0.722021i | \(0.743213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.23436 | − | 7.00040i | 0.0446868 | − | 0.253431i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.29438 | + | 1.73743i | 0.336039 | + | 0.0628170i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.45307 | − | 0.892846i | 0.0885754 | − | 0.0322388i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.4679 | − | 8.78365i | 0.377484 | − | 0.316747i | −0.434230 | − | 0.900802i | \(-0.642979\pi\) |
0.811714 | + | 0.584056i | \(0.198535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3220 | − | 5.28379i | −0.695866 | − | 0.190291i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.3270 | + | 17.8869i | 0.371436 | + | 0.643345i | 0.989787 | − | 0.142557i | \(-0.0455323\pi\) |
−0.618351 | + | 0.785902i | \(0.712199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.53628 | + | 16.5173i | −0.342553 | + | 0.593319i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.13977 | − | 4.34626i | −0.220263 | − | 0.155921i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.31415 | − | 35.8093i | −0.226228 | − | 1.28300i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.32948 | + | 1.95466i | 0.0833553 | + | 0.0699434i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.5927 | + | 9.99147i | 0.735922 | + | 0.357066i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.9547 | − | 12.5485i | −0.533757 | − | 0.447875i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.28970 | + | 24.3281i | 0.152911 | + | 0.867202i | 0.960671 | + | 0.277690i | \(0.0895689\pi\) |
−0.807759 | + | 0.589512i | \(0.799320\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.1931 | + | 4.68956i | −0.362884 | + | 0.166953i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.04429 | − | 8.73696i | 0.179354 | − | 0.310651i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.768202 | + | 1.33057i | 0.0272797 | + | 0.0472498i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.8497 | − | 48.9596i | −0.455731 | − | 1.73642i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.4148 | + | 19.6473i | −0.829393 | + | 0.695943i | −0.955152 | − | 0.296117i | \(-0.904308\pi\) |
0.125758 | + | 0.992061i | \(0.459864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.73319 | + | 0.994799i | −0.0966933 | + | 0.0351935i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.5214 | + | 35.9250i | 1.04309 | + | 1.26935i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.838750 | + | 4.75679i | −0.0295988 | + | 0.167863i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.30203 | + | 1.92978i | 0.186872 | + | 0.0680158i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.6472 | − | 19.7048i | −0.480405 | − | 0.693642i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.8599 | 1.64751 | 0.823753 | − | 0.566949i | \(-0.191876\pi\) | ||||
0.823753 | + | 0.566949i | \(0.191876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.9984 | −0.386206 | −0.193103 | − | 0.981178i | \(-0.561855\pi\) | ||||
−0.193103 | + | 0.981178i | \(0.561855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.91845 | − | 2.76999i | −0.0672829 | − | 0.0971476i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.3879 | − | 11.4243i | −1.09947 | − | 0.400175i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.03956 | − | 34.2521i | 0.211298 | − | 1.19833i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.35697 | − | 0.722206i | 0.152245 | − | 0.0252359i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.8133 | − | 12.3070i | 1.18009 | − | 0.429518i | 0.323857 | − | 0.946106i | \(-0.395020\pi\) |
0.856234 | + | 0.516588i | \(0.172798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.5259 | − | 31.4880i | 1.30807 | − | 1.09760i | 0.319383 | − | 0.947626i | \(-0.396524\pi\) |
0.988689 | − | 0.149977i | \(-0.0479200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.306410 | − | 1.16748i | −0.0106678 | − | 0.0406464i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.80533 | − | 13.5192i | −0.271418 | − | 0.470109i | 0.697807 | − | 0.716286i | \(-0.254159\pi\) |
−0.969225 | + | 0.246176i | \(0.920826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.73541 | + | 9.93401i | −0.199199 | + | 0.345023i | −0.948269 | − | 0.317468i | \(-0.897167\pi\) |
0.749070 | + | 0.662491i | \(0.230501\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.6259 | − | 9.02932i | 0.680814 | − | 0.313224i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.23502 | − | 7.00416i | −0.0427910 | − | 0.242680i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.79290 | − | 4.02172i | −0.165865 | − | 0.139177i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.4150 | − | 41.1334i | −0.636515 | − | 1.42178i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.517329 | + | 0.434090i | 0.0178602 | + | 0.0149865i | 0.651674 | − | 0.758499i | \(-0.274067\pi\) |
−0.633814 | + | 0.773486i | \(0.718511\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.66646 | − | 9.45097i | −0.0574642 | − | 0.325895i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.7918 | − | 9.76304i | −0.475015 | − | 0.336257i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.3649 | + | 24.8808i | −0.494168 | + | 0.855925i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.29901 | − | 9.17815i | −0.182076 | − | 0.315365i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.3928 | − | 12.1396i | −1.52356 | − | 0.416631i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.40014 | − | 6.20946i | 0.253674 | − | 0.212857i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.9823 | + | 13.4605i | −1.26625 | + | 0.460877i | −0.885862 | − | 0.463949i | \(-0.846432\pi\) |
−0.380388 | + | 0.924827i | \(0.624210\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.6420 | + | 47.2267i | 0.569143 | + | 1.61512i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.67172 | − | 32.1659i | 0.193742 | − | 1.09877i | −0.720457 | − | 0.693500i | \(-0.756068\pi\) |
0.914199 | − | 0.405266i | \(-0.132821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1946 | − | 11.3539i | −1.06435 | − | 0.387391i | −0.250287 | − | 0.968172i | \(-0.580525\pi\) |
−0.814060 | + | 0.580781i | \(0.802747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.20602 | + | 8.90026i | −0.143341 | + | 0.303320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.6796 | −0.772024 | −0.386012 | − | 0.922494i | \(-0.626148\pi\) | ||||
−0.386012 | + | 0.922494i | \(0.626148\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.61158 | 0.326804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.9636 | − | 2.21958i | 0.915733 | − | 0.0753810i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.33935 | − | 1.21543i | −0.113280 | − | 0.0412305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.225195 | − | 1.27714i | 0.00763043 | − | 0.0432743i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.170941 | + | 16.6476i | −0.00578549 | + | 0.563435i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.86670 | − | 2.49927i | 0.232137 | − | 0.0844909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.08113 | − | 5.94178i | 0.239113 | − | 0.200640i | −0.515354 | − | 0.856977i | \(-0.672340\pi\) |
0.754467 | + | 0.656338i | \(0.227895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.0891 | + | 14.9350i | −0.508944 | + | 0.503745i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.89378 | − | 6.74422i | −0.131185 | − | 0.227219i | 0.792949 | − | 0.609288i | \(-0.208545\pi\) |
−0.924134 | + | 0.382070i | \(0.875211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.2309 | + | 28.1127i | −0.546213 | + | 0.946068i | 0.452317 | + | 0.891857i | \(0.350598\pi\) |
−0.998530 | + | 0.0542106i | \(0.982736\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.739338 | − | 7.97868i | 0.0248526 | − | 0.268200i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.87759 | + | 33.3334i | 0.197350 | + | 1.11923i | 0.909032 | + | 0.416726i | \(0.136823\pi\) |
−0.711682 | + | 0.702502i | \(0.752066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.89365 | + | 3.26716i | 0.130589 | + | 0.109577i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.65952 | + | 1.03031i | 0.0890972 | + | 0.0345167i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.7995 | − | 9.90095i | −0.394855 | − | 0.331323i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.31630 | − | 52.8354i | −0.311410 | − | 1.76609i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.523306 | + | 5.64733i | −0.0174727 | + | 0.188559i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.1024 | − | 33.0863i | 0.637101 | − | 1.10349i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.39731 | + | 11.0805i | 0.213125 | + | 0.369144i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.69218 | + | 6.62382i | −0.222702 | + | 0.220427i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0035 | + | 16.7850i | −0.664940 | + | 0.557951i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.3929 | + | 3.78269i | −0.345089 | + | 0.125602i | −0.508750 | − | 0.860915i | \(-0.669892\pi\) |
0.163660 | + | 0.986517i | \(0.447670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.1845 | − | 15.4782i | −0.868484 | − | 0.513381i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.17845 | + | 12.3546i | −0.0721751 | + | 0.409325i | 0.927219 | + | 0.374520i | \(0.122192\pi\) |
−0.999394 | + | 0.0348058i | \(0.988919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.39513 | + | 0.507785i | 0.0461720 | + | 0.0168052i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.70004 | − | 0.386897i | 0.155379 | − | 0.0127904i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.03415 | −0.232288 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.92909 | 0.195583 | 0.0977913 | − | 0.995207i | \(-0.468822\pi\) | ||||
0.0977913 | + | 0.995207i | \(0.468822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5920 | − | 41.4580i | 0.645577 | − | 1.36609i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.6521 | + | 4.96897i | 0.449365 | + | 0.163555i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.70561 | + | 9.67300i | −0.0560801 | + | 0.318046i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.2322 | − | 22.4479i | 0.631669 | − | 0.737285i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.42772 | − | 3.43141i | 0.309314 | − | 0.112581i | −0.182699 | − | 0.983169i | \(-0.558483\pi\) |
0.492013 | + | 0.870588i | \(0.336261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.8525 | − | 24.2101i | 0.945603 | − | 0.793455i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.5039 | + | 8.06811i | 0.965913 | + | 0.264138i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.499405 | + | 0.864995i | 0.0163323 | + | 0.0282883i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.7671 | − | 20.3811i | 0.384413 | − | 0.665823i | −0.607274 | − | 0.794492i | \(-0.707737\pi\) |
0.991688 | + | 0.128669i | \(0.0410705\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.6382 | − | 9.65429i | −0.445066 | − | 0.315056i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.08781 | − | 28.8544i | −0.165858 | − | 0.940627i | −0.948175 | − | 0.317747i | \(-0.897074\pi\) |
0.782317 | − | 0.622880i | \(-0.214038\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.68405 | − | 8.12588i | −0.315356 | − | 0.264615i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.70981 | − | 13.0386i | 0.120680 | − | 0.424144i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.1074 | − | 34.4932i | −1.33581 | − | 1.12088i | −0.982681 | − | 0.185304i | \(-0.940673\pi\) |
−0.353130 | − | 0.935574i | \(-0.614883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00721 | + | 22.7260i | 0.130079 | + | 0.737717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.83849 | + | 2.68613i | −0.189326 | + | 0.0871036i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.44828 | − | 4.24055i | 0.0793076 | − | 0.137365i | −0.823644 | − | 0.567108i | \(-0.808062\pi\) |
0.902951 | + | 0.429743i | \(0.141396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.8212 | + | 41.2596i | 0.770837 | + | 1.33513i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.613778 | + | 2.33861i | 0.0198406 | + | 0.0755965i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.37906 | + | 7.03086i | −0.270574 | + | 0.227038i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −41.5578 | + | 15.1258i | −1.34057 | + | 0.487929i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.45495 | − | 14.5216i | 0.175783 | − | 0.467954i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.93140 | + | 27.9674i | −0.158747 | + | 0.900302i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9683 | + | 5.81200i | 0.513507 | + | 0.186901i | 0.585759 | − | 0.810485i | \(-0.300796\pi\) |
−0.0722523 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.20639 | − | 10.4051i | −0.231503 | − | 0.334259i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.68374 | 0.0861253 | 0.0430627 | − | 0.999072i | \(-0.486288\pi\) | ||||
0.0430627 | + | 0.999072i | \(0.486288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.12064 | 0.292394 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.28332 | − | 4.74068i | −0.105150 | − | 0.151823i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.3301 | − | 3.75984i | −0.330488 | − | 0.120288i | 0.171446 | − | 0.985193i | \(-0.445156\pi\) |
−0.501935 | + | 0.864906i | \(0.667378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.852930 | + | 4.83721i | −0.0272598 | + | 0.154598i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.71239 | − | 20.5312i | 0.246238 | − | 0.655511i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.8944 | + | 16.3402i | −1.43191 | + | 0.521172i | −0.937478 | − | 0.348044i | \(-0.886846\pi\) |
−0.494431 | + | 0.869217i | \(0.664624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.1018 | + | 24.4193i | −0.927260 | + | 0.778064i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.05859 | + | 4.03342i | 0.0336952 | + | 0.128385i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.04594 | − | 10.4719i | −0.192250 | − | 0.332986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7503 | − | 48.0649i | 0.881517 | − | 1.52683i | 0.0318627 | − | 0.999492i | \(-0.489856\pi\) |
0.849654 | − | 0.527340i | \(-0.176811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.22305 | − | 1.02276i | 0.0705462 | − | 0.0324564i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.51309 | + | 19.9237i | 0.111372 | + | 0.631624i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5078 | − | 28.9555i | −1.09287 | − | 0.917029i | −0.0959472 | − | 0.995386i | \(-0.530588\pi\) |
−0.996925 | + | 0.0783575i | \(0.975032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.1568 | − | 16.6623i | −0.511179 | − | 0.527172i |
(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 | 432.2.u.c.97.2 | 12 | ||
4.3 | odd | 2 | 27.2.e.a.16.1 | ✓ | 12 | ||
12.11 | even | 2 | 81.2.e.a.46.2 | 12 | |||
20.3 | even | 4 | 675.2.u.b.124.1 | 24 | |||
20.7 | even | 4 | 675.2.u.b.124.4 | 24 | |||
20.19 | odd | 2 | 675.2.l.c.151.2 | 12 | |||
27.22 | even | 9 | inner | 432.2.u.c.49.2 | 12 | ||
36.7 | odd | 6 | 243.2.e.d.217.1 | 12 | |||
36.11 | even | 6 | 243.2.e.a.217.2 | 12 | |||
36.23 | even | 6 | 243.2.e.b.55.1 | 12 | |||
36.31 | odd | 6 | 243.2.e.c.55.2 | 12 | |||
108.7 | odd | 18 | 729.2.a.a.1.2 | 6 | |||
108.11 | even | 18 | 729.2.c.b.487.2 | 12 | |||
108.23 | even | 18 | 243.2.e.a.28.2 | 12 | |||
108.31 | odd | 18 | 243.2.e.d.28.1 | 12 | |||
108.43 | odd | 18 | 729.2.c.e.487.5 | 12 | |||
108.47 | even | 18 | 729.2.a.d.1.5 | 6 | |||
108.59 | even | 18 | 81.2.e.a.37.2 | 12 | |||
108.67 | odd | 18 | 243.2.e.c.190.2 | 12 | |||
108.79 | odd | 18 | 729.2.c.e.244.5 | 12 | |||
108.83 | even | 18 | 729.2.c.b.244.2 | 12 | |||
108.95 | even | 18 | 243.2.e.b.190.1 | 12 | |||
108.103 | odd | 18 | 27.2.e.a.22.1 | yes | 12 | ||
540.103 | even | 36 | 675.2.u.b.49.4 | 24 | |||
540.319 | odd | 18 | 675.2.l.c.76.2 | 12 | |||
540.427 | even | 36 | 675.2.u.b.49.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.16.1 | ✓ | 12 | 4.3 | odd | 2 | ||
27.2.e.a.22.1 | yes | 12 | 108.103 | odd | 18 | ||
81.2.e.a.37.2 | 12 | 108.59 | even | 18 | |||
81.2.e.a.46.2 | 12 | 12.11 | even | 2 | |||
243.2.e.a.28.2 | 12 | 108.23 | even | 18 | |||
243.2.e.a.217.2 | 12 | 36.11 | even | 6 | |||
243.2.e.b.55.1 | 12 | 36.23 | even | 6 | |||
243.2.e.b.190.1 | 12 | 108.95 | even | 18 | |||
243.2.e.c.55.2 | 12 | 36.31 | odd | 6 | |||
243.2.e.c.190.2 | 12 | 108.67 | odd | 18 | |||
243.2.e.d.28.1 | 12 | 108.31 | odd | 18 | |||
243.2.e.d.217.1 | 12 | 36.7 | odd | 6 | |||
432.2.u.c.49.2 | 12 | 27.22 | even | 9 | inner | ||
432.2.u.c.97.2 | 12 | 1.1 | even | 1 | trivial | ||
675.2.l.c.76.2 | 12 | 540.319 | odd | 18 | |||
675.2.l.c.151.2 | 12 | 20.19 | odd | 2 | |||
675.2.u.b.49.1 | 24 | 540.427 | even | 36 | |||
675.2.u.b.49.4 | 24 | 540.103 | even | 36 | |||
675.2.u.b.124.1 | 24 | 20.3 | even | 4 | |||
675.2.u.b.124.4 | 24 | 20.7 | even | 4 | |||
729.2.a.a.1.2 | 6 | 108.7 | odd | 18 | |||
729.2.a.d.1.5 | 6 | 108.47 | even | 18 | |||
729.2.c.b.244.2 | 12 | 108.83 | even | 18 | |||
729.2.c.b.487.2 | 12 | 108.11 | even | 18 | |||
729.2.c.e.244.5 | 12 | 108.79 | odd | 18 | |||
729.2.c.e.487.5 | 12 | 108.43 | odd | 18 |