Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 616) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.h.177.2 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.20711 | − | 2.09077i | 0.696923 | − | 1.20711i | −0.272605 | − | 0.962126i | \(-0.587885\pi\) |
0.969528 | − | 0.244981i | \(-0.0787816\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | + | 1.22474i | 0.316228 | + | 0.547723i | 0.979698 | − | 0.200480i | \(-0.0642503\pi\) |
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | − | 2.09077i | 0.612801 | − | 0.790237i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.82843 | −1.06181 | −0.530907 | − | 0.847430i | \(-0.678149\pi\) | ||||
−0.530907 | + | 0.847430i | \(0.678149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70711 | − | 4.68885i | −0.621053 | − | 1.07570i | −0.989290 | − | 0.145963i | \(-0.953372\pi\) |
0.368237 | − | 0.929732i | \(-0.379961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.41421 | − | 5.91359i | −0.526825 | − | 1.29045i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.29289 | + | 2.23936i | 0.269587 | + | 0.466938i | 0.968755 | − | 0.248019i | \(-0.0797795\pi\) |
−0.699168 | + | 0.714957i | \(0.746446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | − | 1.43488i | 0.148790 | − | 0.257712i | −0.781991 | − | 0.623290i | \(-0.785796\pi\) |
0.930780 | + | 0.365579i | \(0.119129\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.20711 | − | 2.09077i | −0.210130 | − | 0.363956i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.70711 | + | 0.507306i | 0.626615 | + | 0.0857504i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.53553 | − | 4.39167i | −0.416839 | − | 0.721987i | 0.578780 | − | 0.815483i | \(-0.303529\pi\) |
−0.995620 | + | 0.0934968i | \(0.970196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.62132 | + | 8.00436i | −0.740003 | + | 1.28172i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.24264 | −0.350242 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | − | 3.46410i | 0.298142 | − | 0.516398i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.414214 | − | 0.717439i | −0.0604193 | − | 0.104649i | 0.834234 | − | 0.551411i | \(-0.185910\pi\) |
−0.894653 | + | 0.446762i | \(0.852577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | − | 6.77962i | −0.248949 | − | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | − | 4.18154i | −0.338058 | − | 0.585533i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.70711 | + | 4.68885i | −0.371850 | + | 0.644063i | −0.989850 | − | 0.142115i | \(-0.954610\pi\) |
0.618000 | + | 0.786178i | \(0.287943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.0711 | −1.73131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.792893 | − | 1.37333i | 0.103226 | − | 0.178793i | −0.809786 | − | 0.586725i | \(-0.800417\pi\) |
0.913012 | + | 0.407933i | \(0.133750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.91421 | + | 11.9758i | 0.885274 | + | 1.53334i | 0.845399 | + | 0.534135i | \(0.179363\pi\) |
0.0398754 | + | 0.999205i | \(0.487304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.41421 | − | 1.01461i | −0.934103 | − | 0.127829i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.70711 | − | 4.68885i | −0.335775 | − | 0.581580i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.03553 | + | 5.25770i | −0.370849 | + | 0.642330i | −0.989696 | − | 0.143181i | \(-0.954267\pi\) |
0.618847 | + | 0.785512i | \(0.287600\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.24264 | 0.751526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2426 | 1.69029 | 0.845145 | − | 0.534537i | \(-0.179514\pi\) | ||||
0.845145 | + | 0.534537i | \(0.179514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.292893 | − | 0.507306i | 0.0342806 | − | 0.0593757i | −0.848376 | − | 0.529394i | \(-0.822419\pi\) |
0.882657 | + | 0.470018i | \(0.155753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.62132 | − | 6.27231i | −0.418154 | − | 0.724264i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | − | 2.44949i | −0.113961 | − | 0.279145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.03553 | − | 5.25770i | −0.341524 | − | 0.591537i | 0.643192 | − | 0.765705i | \(-0.277610\pi\) |
−0.984716 | + | 0.174168i | \(0.944276\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.48528 | −0.711852 | −0.355926 | − | 0.934514i | \(-0.615835\pi\) | ||||
−0.355926 | + | 0.934514i | \(0.615835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.20711 | − | 2.09077i | 0.129415 | − | 0.224154i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.41421 | + | 12.8418i | 0.785905 | + | 1.36123i | 0.928457 | + | 0.371440i | \(0.121136\pi\) |
−0.142552 | + | 0.989787i | \(0.545531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.20711 | + | 8.00436i | −0.650682 | + | 0.839085i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.82843 | − | 6.63103i | 0.392788 | − | 0.680329i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1716 | −1.03277 | −0.516383 | − | 0.856358i | \(-0.672722\pi\) | ||||
−0.516383 | + | 0.856358i | \(0.672722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74264 | + | 8.21449i | −0.471910 | + | 0.817373i | −0.999483 | − | 0.0321369i | \(-0.989769\pi\) |
0.527573 | + | 0.849510i | \(0.323102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.94975 | + | 3.37706i | 0.192114 | + | 0.332752i | 0.945951 | − | 0.324310i | \(-0.105132\pi\) |
−0.753836 | + | 0.657062i | \(0.771799\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.53553 | − | 7.13834i | 0.540213 | − | 0.696630i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.77817 | − | 15.2042i | −0.848618 | − | 1.46985i | −0.882442 | − | 0.470422i | \(-0.844102\pi\) |
0.0338234 | − | 0.999428i | \(-0.489232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24264 | + | 7.34847i | −0.406371 | + | 0.703856i | −0.994480 | − | 0.104926i | \(-0.966539\pi\) |
0.588109 | + | 0.808782i | \(0.299873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.2426 | −1.16202 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.48528 | 0.892300 | 0.446150 | − | 0.894958i | \(-0.352795\pi\) | ||||
0.446150 | + | 0.894958i | \(0.352795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.82843 | + | 3.16693i | −0.170502 | + | 0.295318i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.41421 | + | 9.37769i | 0.500544 | + | 0.866968i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | − | 4.89898i | −0.183340 | − | 0.449089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.70711 | + | 4.68885i | −0.244092 | + | 0.422779i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.58579 | −0.318187 | −0.159094 | − | 0.987264i | \(-0.550857\pi\) | ||||
−0.159094 | + | 0.987264i | \(0.550857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.65685 | − | 16.7262i | 0.850239 | − | 1.47266i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.53553 | − | 16.5160i | −0.833123 | − | 1.44301i | −0.895549 | − | 0.444963i | \(-0.853217\pi\) |
0.0624257 | − | 0.998050i | \(-0.480116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.1924 | − | 1.94218i | −1.23064 | − | 0.168409i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.292893 | + | 0.507306i | 0.0252082 | + | 0.0436619i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.50000 | + | 14.7224i | −0.726204 | + | 1.25782i | 0.232273 | + | 0.972651i | \(0.425384\pi\) |
−0.958477 | + | 0.285171i | \(0.907949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.3137 | −1.63817 | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||||
−0.819084 | + | 0.573674i | \(0.805518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.91421 | + | 3.31552i | −0.160075 | + | 0.277257i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.707107 | + | 1.22474i | 0.0587220 | + | 0.101710i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.2782 | − | 4.54026i | −1.34260 | − | 0.374474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.00000 | + | 13.8564i | 0.655386 | + | 1.13516i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) |
−0.326411 | + | 0.945228i | \(0.605840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.20711 | − | 7.28692i | 0.342369 | − | 0.593001i | −0.642503 | − | 0.766283i | \(-0.722104\pi\) |
0.984872 | + | 0.173282i | \(0.0554372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.65685 | −0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.34315 | 0.188206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.65685 | + | 13.2621i | −0.611083 | + | 1.05843i | 0.379975 | + | 0.924997i | \(0.375933\pi\) |
−0.991058 | + | 0.133431i | \(0.957401\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.53553 | + | 11.3199i | 0.518302 | + | 0.897725i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.77817 | + | 0.927572i | 0.534195 | + | 0.0731029i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4497 | + | 21.5636i | 0.975139 | + | 1.68899i | 0.679474 | + | 0.733700i | \(0.262208\pi\) |
0.295665 | + | 0.955292i | \(0.404459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.70711 | − | 2.95680i | 0.132898 | − | 0.230186i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.7279 | 1.99089 | 0.995443 | − | 0.0953565i | \(-0.0303991\pi\) | ||||
0.995443 | + | 0.0953565i | \(0.0303991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.65685 | + | 13.2621i | −0.585534 | + | 1.01418i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.91421 | − | 6.77962i | −0.297592 | − | 0.515445i | 0.677992 | − | 0.735069i | \(-0.262850\pi\) |
−0.975585 | + | 0.219624i | \(0.929517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | − | 7.34847i | −0.226779 | − | 0.555492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.91421 | − | 3.31552i | −0.143881 | − | 0.249209i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.449747 | + | 0.778985i | −0.0336157 | + | 0.0582241i | −0.882344 | − | 0.470605i | \(-0.844036\pi\) |
0.848728 | + | 0.528829i | \(0.177369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.31371 | 0.692283 | 0.346141 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.3848 | 2.46787 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.58579 | − | 6.21076i | 0.263632 | − | 0.456624i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.671573 | − | 0.866025i | 0.0488497 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.24264 | + | 9.08052i | 0.379344 | + | 0.657043i | 0.990967 | − | 0.134106i | \(-0.0428163\pi\) |
−0.611623 | + | 0.791150i | \(0.709483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.60660 | − | 16.6391i | 0.691498 | − | 1.19771i | −0.279849 | − | 0.960044i | \(-0.590284\pi\) |
0.971347 | − | 0.237666i | \(-0.0763824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.0711 | −0.936039 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1421 | 1.22133 | 0.610663 | − | 0.791890i | \(-0.290903\pi\) | ||||
0.610663 | + | 0.791890i | \(0.290903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0208 | + | 20.8207i | −0.852133 | + | 1.47594i | 0.0271465 | + | 0.999631i | \(0.491358\pi\) |
−0.879279 | + | 0.476306i | \(0.841975\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.32843 | + | 12.6932i | 0.516907 | + | 0.895310i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.62132 | − | 2.09077i | 0.113794 | − | 0.146743i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58579 | − | 2.74666i | −0.110756 | − | 0.191835i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.65685 | − | 6.33386i | 0.254169 | − | 0.440234i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.41421 | −0.374509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0711 | 1.31291 | 0.656453 | − | 0.754367i | \(-0.272056\pi\) | ||||
0.656453 | + | 0.754367i | \(0.272056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.1924 | − | 29.7781i | 1.17800 | − | 2.04036i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | + | 9.79796i | 0.385794 | + | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.65685 | − | 4.05845i | −0.112475 | − | 0.275505i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.707107 | − | 1.22474i | −0.0477818 | − | 0.0827606i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.82843 | + | 6.63103i | −0.257528 | + | 0.446051i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5563 | 0.773870 | 0.386935 | − | 0.922107i | \(-0.373534\pi\) | ||||
0.386935 | + | 0.922107i | \(0.373534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.48528 | −0.565685 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.0710678 | − | 0.123093i | 0.00471694 | − | 0.00816997i | −0.863657 | − | 0.504079i | \(-0.831832\pi\) |
0.868374 | + | 0.495909i | \(0.165165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.32843 | − | 0.866025i | −0.416380 | − | 0.0569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.19239 | + | 14.1896i | 0.536701 | + | 0.929594i | 0.999079 | + | 0.0429107i | \(0.0136631\pi\) |
−0.462378 | + | 0.886683i | \(0.653004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.585786 | − | 1.01461i | 0.0382125 | − | 0.0661860i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.6569 | −0.952065 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7279 | −0.887985 | −0.443993 | − | 0.896030i | \(-0.646438\pi\) | ||||
−0.443993 | + | 0.896030i | \(0.646438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.36396 | + | 2.36245i | −0.0878605 | + | 0.152179i | −0.906607 | − | 0.421977i | \(-0.861336\pi\) |
0.818746 | + | 0.574156i | \(0.194670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.8284 | − | 18.7554i | −0.694644 | − | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.07107 | − | 6.92820i | 0.451754 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3640 | + | 17.9509i | 0.659443 | + | 1.14219i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.82843 | + | 13.5592i | −0.496106 | + | 0.859282i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4853 | 1.04054 | 0.520271 | − | 0.854001i | \(-0.325831\pi\) | ||||
0.520271 | + | 0.854001i | \(0.325831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58579 | 0.162567 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.41421 | − | 5.91359i | 0.213806 | − | 0.370323i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.25736 | + | 2.17781i | 0.0784319 | + | 0.135848i | 0.902574 | − | 0.430536i | \(-0.141675\pi\) |
−0.824142 | + | 0.566384i | \(0.808342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.2929 | − | 1.81909i | −0.825980 | − | 0.113033i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41421 | − | 2.44949i | −0.0875376 | − | 0.151620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5208 | − | 21.6867i | 0.772067 | − | 1.33726i | −0.164362 | − | 0.986400i | \(-0.552557\pi\) |
0.936429 | − | 0.350858i | \(-0.114110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.65685 | −0.470357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.7990 | 2.19086 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.17157 | − | 2.02922i | 0.0714321 | − | 0.123724i | −0.828097 | − | 0.560585i | \(-0.810576\pi\) |
0.899529 | + | 0.436861i | \(0.143910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.03553 | + | 12.1859i | 0.427378 | + | 0.740241i | 0.996639 | − | 0.0819160i | \(-0.0261039\pi\) |
−0.569261 | + | 0.822157i | \(0.692771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.24264 | + | 22.6398i | 0.559390 | + | 1.37022i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.39949 | + | 12.8163i | −0.444593 | + | 0.770057i | −0.998024 | − | 0.0628380i | \(-0.979985\pi\) |
0.553431 | + | 0.832895i | \(0.313318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.68629 | −0.280561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.89949 | 0.471244 | 0.235622 | − | 0.971845i | \(-0.424287\pi\) | ||||
0.235622 | + | 0.971845i | \(0.424287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.77817 | + | 3.07989i | −0.105702 | + | 0.183080i | −0.914025 | − | 0.405659i | \(-0.867042\pi\) |
0.808323 | + | 0.588739i | \(0.200375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.24264 | − | 16.0087i | −0.547487 | − | 0.948275i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.63604 | + | 4.68885i | −0.214629 | + | 0.276774i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2782 | + | 21.2664i | −0.719759 | + | 1.24666i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8284 | −1.09997 | −0.549984 | − | 0.835175i | \(-0.685366\pi\) | ||||
−0.549984 | + | 0.835175i | \(0.685366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.24264 | 0.130572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.207107 | − | 0.358719i | 0.0120176 | − | 0.0208150i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.94975 | − | 8.57321i | −0.286251 | − | 0.495802i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9706 | − | 16.7262i | 0.747611 | − | 0.964080i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4497 | + | 19.8315i | 0.657771 | + | 1.13929i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.77817 | + | 16.9363i | −0.559897 | + | 0.969769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4142 | −0.651444 | −0.325722 | − | 0.945466i | \(-0.605607\pi\) | ||||
−0.325722 | + | 0.945466i | \(0.605607\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.41421 | 0.535556 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.60660 | − | 13.1750i | 0.431331 | − | 0.747087i | −0.565657 | − | 0.824640i | \(-0.691378\pi\) |
0.996988 | + | 0.0775535i | \(0.0247109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3284 | + | 17.8894i | 0.583797 | + | 1.01117i | 0.995024 | + | 0.0996335i | \(0.0317670\pi\) |
−0.411227 | + | 0.911533i | \(0.634900\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | − | 9.79796i | −0.225374 | − | 0.552052i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.48528 | + | 11.2328i | 0.364250 | + | 0.630899i | 0.988655 | − | 0.150201i | \(-0.0479921\pi\) |
−0.624406 | + | 0.781100i | \(0.714659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.3848 | −2.36569 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.8284 | −0.602510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.74264 | + | 9.94655i | −0.318544 | + | 0.551735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.2426 | + | 17.7408i | 0.566419 | + | 0.981067i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.17157 | − | 0.297173i | −0.119723 | − | 0.0163837i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6924 | + | 27.1800i | 0.862532 | + | 1.49395i | 0.869477 | + | 0.493973i | \(0.164456\pi\) |
−0.00694571 | + | 0.999976i | \(0.502211\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.17157 | + | 12.4215i | −0.393000 | + | 0.680696i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.58579 | −0.469092 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.24264 | 0.340058 | 0.170029 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170029 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.4497 | − | 19.8315i | 0.621865 | − | 1.07710i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.828427 | − | 1.43488i | −0.0448618 | − | 0.0777030i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.41421 | + | 7.64564i | 0.237653 | + | 0.411628i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.70711 | + | 9.88500i | −0.306374 | + | 0.530655i | −0.977566 | − | 0.210628i | \(-0.932449\pi\) |
0.671193 | + | 0.741283i | \(0.265782\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.2843 | −1.72814 | −0.864069 | − | 0.503374i | \(-0.832092\pi\) | ||||
−0.864069 | + | 0.503374i | \(0.832092\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.58579 | −0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.6569 | − | 21.9223i | 0.673656 | − | 1.16681i | −0.303203 | − | 0.952926i | \(-0.598056\pi\) |
0.976860 | − | 0.213881i | \(-0.0686105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0711 | + | 17.4436i | 0.534517 | + | 0.925810i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.6569 | − | 1.73205i | −0.669872 | − | 0.0916698i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0355 | + | 24.3103i | 0.740767 | + | 1.28305i | 0.952146 | + | 0.305642i | \(0.0988711\pi\) |
−0.211379 | + | 0.977404i | \(0.567796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.15685 | + | 8.93193i | −0.271413 | + | 0.470102i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.41421 | −0.126713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.828427 | 0.0433619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.121320 | + | 0.210133i | −0.00633287 | + | 0.0109689i | −0.869174 | − | 0.494506i | \(-0.835349\pi\) |
0.862842 | + | 0.505474i | \(0.168682\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.17157 | + | 5.49333i | 0.165105 | + | 0.285971i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.41421 | + | 13.2621i | 0.281092 | + | 0.688532i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8137 | − | 27.3901i | −0.818803 | − | 1.41821i | −0.906565 | − | 0.422067i | \(-0.861305\pi\) |
0.0877621 | − | 0.996141i | \(-0.472028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.6569 | − | 23.6544i | 0.705237 | − | 1.22151i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.82843 | −0.197174 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3848 | −1.50939 | −0.754697 | − | 0.656073i | \(-0.772216\pi\) | ||||
−0.754697 | + | 0.656073i | \(0.772216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.32843 | + | 7.49706i | −0.221752 | + | 0.384086i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.9497 | − | 24.1617i | −0.712799 | − | 1.23460i | −0.963802 | − | 0.266618i | \(-0.914094\pi\) |
0.251004 | − | 0.967986i | \(-0.419239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.29289 | − | 2.95680i | 0.116857 | − | 0.150692i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3137 | − | 19.5959i | −0.575108 | − | 0.996116i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.60660 | − | 7.97887i | 0.233564 | − | 0.404545i | −0.725290 | − | 0.688443i | \(-0.758295\pi\) |
0.958854 | + | 0.283898i | \(0.0916278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.17157 | 0.261538 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.0416 | −2.32249 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.29289 | − | 7.43551i | 0.215999 | − | 0.374121i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1716 | − | 21.0818i | −0.610874 | − | 1.05806i | −0.991093 | − | 0.133168i | \(-0.957485\pi\) |
0.380220 | − | 0.924896i | \(-0.375848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.1924 | + | 27.3286i | −1.06095 | + | 1.36814i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.5000 | + | 21.6506i | 0.624220 | + | 1.08118i | 0.988691 | + | 0.149966i | \(0.0479165\pi\) |
−0.364471 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.17157 | + | 5.49333i | −0.157987 | + | 0.273642i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.4142 | 0.666558 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.07107 | −0.251363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.05025 | − | 12.2114i | 0.348613 | − | 0.603815i | −0.637391 | − | 0.770541i | \(-0.719986\pi\) |
0.986003 | + | 0.166726i | \(0.0533196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.5208 | + | 35.5431i | 1.01222 | + | 1.75321i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.58579 | − | 3.88437i | −0.0780314 | − | 0.191137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.58579 | − | 7.94282i | −0.225107 | − | 0.389897i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.3137 | + | 40.3805i | −1.14168 | + | 1.97744i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4558 | −1.24360 | −0.621800 | − | 0.783176i | \(-0.713598\pi\) | ||||
−0.621800 | + | 0.783176i | \(0.713598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65685 | −0.0807501 | −0.0403751 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403751 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.17157 | + | 2.02922i | −0.0569638 | + | 0.0986642i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 5.19615i | −0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.2487 | + | 4.96053i | 1.75420 | + | 0.240057i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.62132 | + | 8.00436i | 0.223119 | + | 0.386454i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.86396 | + | 15.3528i | −0.426962 | + | 0.739520i | −0.996601 | − | 0.0823749i | \(-0.973750\pi\) |
0.569639 | + | 0.821895i | \(0.307083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4558 | 1.80001 | 0.900006 | − | 0.435876i | \(-0.143562\pi\) | ||||
0.900006 | + | 0.435876i | \(0.143562\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.41421 | 0.163699 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.00000 | − | 12.1244i | 0.334855 | − | 0.579987i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.03553 | + | 13.9180i | 0.383515 | + | 0.664268i | 0.991562 | − | 0.129633i | \(-0.0413801\pi\) |
−0.608047 | + | 0.793901i | \(0.708047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1421 | + | 13.8564i | −0.673435 | + | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.65685 | − | 14.9941i | −0.411300 | − | 0.712392i | 0.583733 | − | 0.811946i | \(-0.301592\pi\) |
−0.995032 | + | 0.0995543i | \(0.968258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4853 | + | 18.1610i | −0.497050 | + | 0.860916i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.6274 | 1.82701 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12132 | + | 1.94218i | −0.0528009 | + | 0.0914539i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.1569 | − | 17.5922i | −0.477211 | − | 0.826553i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.1924 | − | 1.94218i | −0.665349 | − | 0.0910510i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.34315 | − | 5.79050i | −0.156386 | − | 0.270868i | 0.777177 | − | 0.629282i | \(-0.216651\pi\) |
−0.933563 | + | 0.358414i | \(0.883318\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.414214 | − | 0.717439i | 0.0193338 | − | 0.0334872i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0000 | −0.605470 | −0.302735 | − | 0.953075i | \(-0.597900\pi\) | ||||
−0.302735 | + | 0.953075i | \(0.597900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7990 | −1.19898 | −0.599490 | − | 0.800382i | \(-0.704630\pi\) | ||||
−0.599490 | + | 0.800382i | \(0.704630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.82843 | − | 4.89898i | 0.131165 | − | 0.227185i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.9706 | − | 27.6618i | −0.739030 | − | 1.28004i | −0.952933 | − | 0.303182i | \(-0.901951\pi\) |
0.213903 | − | 0.976855i | \(-0.431382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.07107 | + | 14.8710i | 0.280336 | + | 0.686680i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4853 | + | 32.0174i | 0.851757 | + | 1.47529i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.2426 | −0.745263 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3137 | 0.701167 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.0355339 | + | 0.0615465i | −0.00162359 | + | 0.00281213i | −0.866836 | − | 0.498593i | \(-0.833850\pi\) |
0.865212 | + | 0.501405i | \(0.167183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.70711 | + | 16.8132i | 0.442606 | + | 0.766616i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1213 | − | 13.0519i | 0.460536 | − | 0.593883i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.19239 | − | 12.4576i | −0.326590 | − | 0.565670i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.343146 | + | 0.594346i | −0.0155494 | + | 0.0269324i | −0.873695 | − | 0.486473i | \(-0.838283\pi\) |
0.858146 | + | 0.513406i | \(0.171616\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 60.1127 | 2.71839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.82843 | −0.217904 | −0.108952 | − | 0.994047i | \(-0.534749\pi\) | ||||
−0.108952 | + | 0.994047i | \(0.534749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00000 | − | 1.73205i | 0.0450377 | − | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | − | 3.46410i | −0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0919 | − | 29.7781i | 1.03581 | − | 1.33573i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.89949 | + | 13.6823i | 0.353630 | + | 0.612505i | 0.986883 | − | 0.161440i | \(-0.0516139\pi\) |
−0.633253 | + | 0.773945i | \(0.718281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.0563 | − | 53.7912i | 1.38750 | − | 2.40321i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.72792 | −0.255395 | −0.127698 | − | 0.991813i | \(-0.540759\pi\) | ||||
−0.127698 | + | 0.991813i | \(0.540759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4142 | −0.596925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.00000 | − | 3.46410i | 0.0888231 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.1716 | − | 21.0818i | −0.539495 | − | 0.934434i | −0.998931 | − | 0.0462225i | \(-0.985282\pi\) |
0.459436 | − | 0.888211i | \(-0.348052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.585786 | − | 1.43488i | −0.0259137 | − | 0.0634753i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12132 | − | 1.94218i | −0.0495075 | − | 0.0857495i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.75736 | + | 4.77589i | −0.121504 | + | 0.210451i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.828427 | −0.0364342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8995 | −0.829596 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | + | 10.3923i | −0.262865 | + | 0.455295i | −0.967002 | − | 0.254769i | \(-0.918001\pi\) |
0.704137 | + | 0.710064i | \(0.251334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.535534 | + | 0.927572i | 0.0234173 | + | 0.0405599i | 0.877497 | − | 0.479583i | \(-0.159212\pi\) |
−0.854079 | + | 0.520143i | \(0.825879\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.9853 | − | 2.59808i | −0.828586 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.65685 | − | 2.86976i | −0.0721737 | − | 0.125009i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.15685 | − | 14.1281i | 0.354646 | − | 0.614265i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.48528 | −0.194645 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.58579 | 0.371892 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.4142 | − | 21.5020i | 0.536713 | − | 0.929615i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.08579 | + | 1.88064i | 0.0468551 | + | 0.0811555i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.74264 | − | 1.88064i | −0.290426 | − | 0.0810048i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5711 | + | 32.1660i | 0.798433 | + | 1.38293i | 0.920637 | + | 0.390421i | \(0.127670\pi\) |
−0.122204 | + | 0.992505i | \(0.538996\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2426 | − | 19.4728i | 0.482468 | − | 0.835659i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6985 | −0.671219 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.5563 | − | 33.8726i | 0.834645 | − | 1.44565i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.70711 | − | 4.68885i | −0.115327 | − | 0.199752i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.9142 | − | 2.17781i | −0.676741 | − | 0.0926099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.65685 | − | 14.9941i | −0.367463 | − | 0.636465i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.58579 | − | 11.4069i | 0.279049 | − | 0.483327i | −0.692100 | − | 0.721802i | \(-0.743314\pi\) |
0.971149 | + | 0.238475i | \(0.0766476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.6274 | −1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.82843 | −0.203856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6066 | − | 39.1558i | 0.952755 | − | 1.65022i | 0.213330 | − | 0.976980i | \(-0.431569\pi\) |
0.739425 | − | 0.673239i | \(-0.235098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.70711 | + | 11.6170i | 0.282170 | + | 0.488733i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.48528 | − | 23.2341i | −0.398344 | − | 0.975740i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.4853 | − | 18.1610i | −0.439566 | − | 0.761350i | 0.558090 | − | 0.829780i | \(-0.311534\pi\) |
−0.997656 | + | 0.0684300i | \(0.978201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.29289 | − | 3.97141i | 0.0959546 | − | 0.166198i | −0.814052 | − | 0.580792i | \(-0.802743\pi\) |
0.910007 | + | 0.414594i | \(0.136076\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.3137 | 1.05750 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.75736 | 0.323504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.98528 | − | 15.5630i | 0.374062 | − | 0.647895i | −0.616124 | − | 0.787649i | \(-0.711298\pi\) |
0.990186 | + | 0.139754i | \(0.0446313\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.1924 | − | 40.1704i | −0.963843 | − | 1.66942i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5147 | + | 13.5592i | −0.436224 | + | 0.562532i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.70711 | + | 4.68885i | 0.112117 | + | 0.194192i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.65685 | + | 13.2621i | −0.316572 | + | 0.548319i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.2132 | 1.08193 | 0.540967 | − | 0.841044i | \(-0.318058\pi\) | ||||
0.540967 | + | 0.841044i | \(0.318058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.97056 | −0.369626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.6924 | − | 35.8403i | 0.851171 | − | 1.47427i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.70711 | + | 11.6170i | 0.275428 | + | 0.477055i | 0.970243 | − | 0.242133i | \(-0.0778471\pi\) |
−0.694815 | + | 0.719188i | \(0.744514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.58579 | − | 5.91359i | 0.187999 | − | 0.242434i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.0208 | + | 50.2655i | 1.18774 | + | 2.05723i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.51472 | − | 9.55177i | 0.225325 | − | 0.390275i | −0.731092 | − | 0.682279i | \(-0.760989\pi\) |
0.956417 | + | 0.292004i | \(0.0943222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3431 | −0.503487 | −0.251744 | − | 0.967794i | \(-0.581004\pi\) | ||||
−0.251744 | + | 0.967794i | \(0.581004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1716 | 0.699281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.707107 | − | 1.22474i | 0.0287480 | − | 0.0497930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1421 | − | 29.6910i | −0.695778 | − | 1.20512i | −0.969918 | − | 0.243433i | \(-0.921726\pi\) |
0.274140 | − | 0.961690i | \(-0.411607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.41421 | − | 5.91359i | −0.0978289 | − | 0.239631i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.58579 | + | 2.74666i | 0.0641541 | + | 0.111118i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.31371 | − | 14.3998i | 0.335788 | − | 0.581601i | −0.647848 | − | 0.761769i | \(-0.724331\pi\) |
0.983636 | + | 0.180168i | \(0.0576643\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.65685 | −0.308754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6274 | −0.468102 | −0.234051 | − | 0.972224i | \(-0.575198\pi\) | ||||
−0.234051 | + | 0.972224i | \(0.575198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6569 | − | 20.1903i | 0.468529 | − | 0.811515i | −0.530824 | − | 0.847482i | \(-0.678118\pi\) |
0.999353 | + | 0.0359666i | \(0.0114510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.535534 | + | 0.927572i | 0.0214902 | + | 0.0372222i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.8701 | + | 5.31925i | 1.55730 | + | 0.213111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.53553 | + | 11.3199i | −0.261004 | + | 0.452072i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1421 | −0.404393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3848 | −1.28922 | −0.644609 | − | 0.764513i | \(-0.722980\pi\) | ||||
−0.644609 | + | 0.764513i | \(0.722980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.0208 | − | 39.8732i | 0.914995 | − | 1.58482i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.53553 | − | 4.39167i | −0.100620 | − | 0.174278i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.67157 | + | 25.9553i | 0.264337 | + | 1.02839i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.1421 | − | 34.8872i | −0.796811 | − | 1.38012i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.1274 | − | 40.0579i | 0.913478 | − | 1.58219i | 0.104364 | − | 0.994539i | \(-0.466719\pi\) |
0.809114 | − | 0.587651i | \(-0.199947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.4142 | −1.51491 | −0.757454 | − | 0.652888i | \(-0.773557\pi\) | ||||
−0.757454 | + | 0.652888i | \(0.773557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.3137 | 1.07548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.535534 | − | 0.927572i | 0.0210540 | − | 0.0364666i | −0.855306 | − | 0.518122i | \(-0.826631\pi\) |
0.876360 | + | 0.481656i | \(0.159964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.792893 | − | 1.37333i | −0.0311238 | − | 0.0539080i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4853 | − | 1.43488i | −0.410951 | − | 0.0562373i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.4645 | + | 30.2493i | 0.683437 | + | 1.18375i | 0.973925 | + | 0.226870i | \(0.0728491\pi\) |
−0.290488 | + | 0.956879i | \(0.593818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.4853 | − | 23.3572i | 0.526914 | − | 0.912641i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.65685 | −0.0646400 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.68629 | −0.338370 | −0.169185 | − | 0.985584i | \(-0.554114\pi\) | ||||
−0.169185 | + | 0.985584i | \(0.554114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.3137 | + | 35.1844i | −0.790112 | + | 1.36851i | 0.135786 | + | 0.990738i | \(0.456644\pi\) |
−0.925897 | + | 0.377775i | \(0.876689\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.24264 | + | 16.0087i | 0.358954 | + | 0.621727i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.65685 | − | 18.7554i | −0.296920 | − | 0.727303i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29289 | + | 2.23936i | 0.0500610 | + | 0.0867082i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.9497 | − | 24.1617i | 0.539328 | − | 0.934144i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.8284 | 0.533841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.75736 | 0.299024 | 0.149512 | − | 0.988760i | \(-0.452230\pi\) | ||||
0.149512 | + | 0.988760i | \(0.452230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.621320 | − | 1.07616i | 0.0239146 | − | 0.0414214i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.1421 | + | 41.8154i | 0.927858 | + | 1.60710i | 0.786900 | + | 0.617081i | \(0.211685\pi\) |
0.140958 | + | 0.990016i | \(0.454982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.4914 | + | 21.2664i | −0.632881 | + | 0.816130i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.171573 | − | 0.297173i | −0.00657469 | − | 0.0113877i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.44975 | + | 4.24309i | −0.0937370 | + | 0.162357i | −0.909081 | − | 0.416620i | \(-0.863215\pi\) |
0.815344 | + | 0.578977i | \(0.196548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0416 | −0.918583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.65685 | 0.368432 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.3640 | − | 17.9509i | 0.394835 | − | 0.683875i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.69239 | − | 6.39540i | −0.140465 | − | 0.243293i | 0.787207 | − | 0.616689i | \(-0.211526\pi\) |
−0.927672 | + | 0.373397i | \(0.878193\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.58579 | + | 5.91359i | −0.174200 | + | 0.224639i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.6569 | − | 23.6544i | −0.518034 | − | 0.897261i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.24264 | + | 3.88437i | −0.0849461 | + | 0.147131i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.5563 | 1.49616 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.45584 | −0.319373 | −0.159686 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159686 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.7279 | + | 23.7775i | −0.517758 | + | 0.896784i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.41421 | − | 2.44949i | −0.0532624 | − | 0.0922531i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.48528 | + | 23.2341i | 0.356731 | + | 0.873808i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.5355 | − | 28.6404i | −0.621005 | − | 1.07561i | −0.989299 | − | 0.145903i | \(-0.953391\pi\) |
0.368294 | − | 0.929709i | \(-0.379942\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.58579 | + | 14.8710i | −0.321992 | + | 0.557707i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.28427 | 0.160447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.41421 | −0.202480 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.5711 | + | 28.7019i | −0.618858 | + | 1.07189i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5858 | + | 20.0672i | 0.432077 | + | 0.748379i | 0.997052 | − | 0.0767288i | \(-0.0244476\pi\) |
−0.564975 | + | 0.825108i | \(0.691114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2218 | + | 1.39882i | 0.380681 | + | 0.0520950i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.29289 | + | 5.70346i | 0.122464 | + | 0.212114i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | − | 2.59808i | 0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.7990 | −0.956832 | −0.478416 | − | 0.878133i | \(-0.658789\pi\) | ||||
−0.478416 | + | 0.878133i | \(0.658789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | − | 13.8564i | 0.295891 | − | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.67157 | − | 15.0196i | −0.320292 | − | 0.554762i | 0.660256 | − | 0.751040i | \(-0.270448\pi\) |
−0.980548 | + | 0.196279i | \(0.937114\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.94975 | − | 23.1471i | −0.219460 | − | 0.853792i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.03553 | + | 5.25770i | 0.111815 | + | 0.193670i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.2132 | + | 41.9385i | −0.890697 | + | 1.54273i | −0.0516557 | + | 0.998665i | \(0.516450\pi\) |
−0.839041 | + | 0.544068i | \(0.816883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.0416 | 1.83833 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0000 | −1.24734 | −0.623670 | − | 0.781688i | \(-0.714359\pi\) | ||||
−0.623670 | + | 0.781688i | \(0.714359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.3137 | + | 19.5959i | −0.414502 | + | 0.717939i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.17157 | + | 15.8856i | 0.335570 | + | 0.581225i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.0208 | − | 6.29780i | −1.68156 | − | 0.230117i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.65685 | − | 9.79796i | −0.206422 | − | 0.357533i | 0.744163 | − | 0.667998i | \(-0.232848\pi\) |
−0.950585 | + | 0.310465i | \(0.899515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.8995 | − | 34.4669i | 0.725178 | − | 1.25604i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8995 | 0.433067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.31371 | −0.193130 | −0.0965650 | − | 0.995327i | \(-0.530786\pi\) | ||||
−0.0965650 | + | 0.995327i | \(0.530786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.12132 | − | 5.40629i | 0.113297 | − | 0.196236i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.9706 | − | 34.5900i | −0.723932 | − | 1.25389i | −0.959412 | − | 0.282008i | \(-0.908999\pi\) |
0.235480 | − | 0.971879i | \(-0.424334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.48528 | + | 20.7846i | 0.307188 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | − | 6.92820i | −0.144620 | − | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.03553 | + | 5.25770i | −0.109607 | + | 0.189845i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.97056 | −0.107121 | −0.0535606 | − | 0.998565i | \(-0.517057\pi\) | ||||
−0.0535606 | + | 0.998565i | \(0.517057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.07107 | 0.218644 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.31371 | − | 9.20361i | 0.191121 | − | 0.331031i | −0.754501 | − | 0.656299i | \(-0.772121\pi\) |
0.945622 | + | 0.325268i | \(0.105454\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.48528 | − | 4.30463i | −0.0892739 | − | 0.154627i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.8492 | + | 25.5965i | −0.712088 | + | 0.918271i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.07107 | + | 10.5154i | 0.217519 | + | 0.376753i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.12132 | − | 12.3345i | 0.254821 | − | 0.441363i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.414214 | 0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6569 | −0.772966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.1924 | − | 36.7063i | 0.755427 | − | 1.30844i | −0.189735 | − | 0.981835i | \(-0.560763\pi\) |
0.945162 | − | 0.326603i | \(-0.105904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.2279 | − | 52.3563i | −1.07614 | − | 1.86393i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.3787 | − | 19.8315i | 0.546803 | − | 0.705129i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.4706 | − | 45.8484i | −0.939997 | − | 1.62812i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.24264 | + | 16.0087i | −0.327803 | + | 0.567771i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3137 | −0.471596 | −0.235798 | − | 0.971802i | \(-0.575770\pi\) | ||||
−0.235798 | + | 0.971802i | \(0.575770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65685 | −0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.9706 | − | 36.3221i | 0.740958 | − | 1.28338i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.292893 | − | 0.507306i | −0.0103360 | − | 0.0179024i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.65685 | + | 8.95743i | 0.128887 | + | 0.315708i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.82843 | − | 4.89898i | −0.0995654 | − | 0.172452i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.00000 | − | 6.92820i | 0.140633 | − | 0.243583i | −0.787102 | − | 0.616822i | \(-0.788420\pi\) |
0.927735 | + | 0.373240i | \(0.121753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3431 | −1.34641 | −0.673205 | − | 0.739456i | \(-0.735083\pi\) | ||||
−0.673205 | + | 0.739456i | \(0.735083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.9706 | 1.19140 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.6066 | + | 30.4955i | −0.616732 | + | 1.06821i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.6569 | − | 37.5108i | −0.757677 | − | 1.31234i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.3848 | + | 3.88437i | 0.991844 | + | 0.135731i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9142 | + | 24.1001i | 0.485609 | + | 0.841100i | 0.999863 | − | 0.0165379i | \(-0.00526441\pi\) |
−0.514254 | + | 0.857638i | \(0.671931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4142 | + | 28.4303i | −0.572164 | + | 0.991016i | 0.424180 | + | 0.905578i | \(0.360562\pi\) |
−0.996343 | + | 0.0854384i | \(0.972771\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.24264 | −0.252156 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5269 | 1.13107 | 0.565536 | − | 0.824724i | \(-0.308669\pi\) | ||||
0.565536 | + | 0.824724i | \(0.308669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2929 | + | 29.9522i | −0.600607 | + | 1.04028i | 0.392122 | + | 0.919913i | \(0.371741\pi\) |
−0.992729 | + | 0.120369i | \(0.961592\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8640 | + | 30.9413i | 0.619694 | + | 1.07334i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.4853 | − | 3.76127i | −0.467237 | − | 0.130320i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.1924 | + | 31.5101i | 0.629574 | + | 1.09045i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.343146 | − | 0.594346i | 0.0118609 | − | 0.0205436i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.51472 | −0.328485 | −0.164242 | − | 0.986420i | \(-0.552518\pi\) | ||||
−0.164242 | + | 0.986420i | \(0.552518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.53553 | − | 16.5160i | 0.328421 | − | 0.568842i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.17157 | + | 2.02922i | 0.0403033 | + | 0.0698074i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.62132 | − | 0.358719i | −0.0900696 | − | 0.0123257i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.29289 | + | 7.43551i | 0.147332 | + | 0.255186i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.55635 | − | 11.3559i | 0.224749 | − | 0.389276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.0000 | −1.71197 | −0.855984 | − | 0.517003i | \(-0.827048\pi\) | ||||
−0.855984 | + | 0.517003i | \(0.827048\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.6569 | −0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.14214 | + | 7.17439i | −0.141493 | + | 0.245072i | −0.928059 | − | 0.372433i | \(-0.878523\pi\) |
0.786566 | + | 0.617506i | \(0.211857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.79289 | − | 8.30153i | −0.163531 | − | 0.283245i | 0.772601 | − | 0.634891i | \(-0.218955\pi\) |
−0.936133 | + | 0.351647i | \(0.885622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.41421 | + | 13.2621i | 0.184516 | + | 0.451970i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.19239 | + | 8.99348i | 0.176751 | + | 0.306142i | 0.940766 | − | 0.339057i | \(-0.110108\pi\) |
−0.764015 | + | 0.645199i | \(0.776775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.53553 | − | 9.58783i | 0.188214 | − | 0.325996i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.3848 | 1.06588 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.07107 | −0.205947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6213 | − | 20.1287i | 0.393773 | − | 0.682036i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.3848 | + | 24.9152i | 0.486851 | + | 0.843251i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.3431 | − | 23.6544i | 0.620112 | − | 0.799664i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6421 | + | 37.4853i | 0.730803 | + | 1.26579i | 0.956540 | + | 0.291600i | \(0.0941875\pi\) |
−0.225737 | + | 0.974188i | \(0.572479\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.7279 | + | 39.3659i | −0.766594 | + | 1.32778i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1716 | 0.477452 | 0.238726 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238726 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.6690 | 1.80611 | 0.903054 | − | 0.429528i | \(-0.141320\pi\) | ||||
0.903054 | + | 0.429528i | \(0.141320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.70711 | − | 4.68885i | 0.0909984 | − | 0.157614i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.13604 | − | 5.43178i | −0.105298 | − | 0.182381i | 0.808562 | − | 0.588411i | \(-0.200246\pi\) |
−0.913860 | + | 0.406030i | \(0.866913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.81371 | + | 7.49706i | −0.194986 | + | 0.251443i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.74264 | − | 8.21449i | −0.158884 | − | 0.275196i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.24264 | + | 3.88437i | −0.0750471 | + | 0.129985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27208 | −0.0425209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.8995 | −0.797981 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.828427 | − | 1.43488i | 0.0276296 | − | 0.0478559i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.41421 | + | 9.37769i | 0.180374 | + | 0.312416i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.3137 | − | 47.3087i | −0.642720 | − | 1.57434i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.58579 | + | 11.4069i | 0.218919 | + | 0.379179i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3137 | − | 28.2562i | 0.541688 | − | 0.938231i | −0.457120 | − | 0.889405i | \(-0.651119\pi\) |
0.998807 | − | 0.0488255i | \(-0.0155478\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.8284 | 0.889843 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5147 | −0.712814 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.24264 | + | 5.61642i | −0.107316 | + | 0.185876i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.6066 | + | 40.8878i | 0.780410 | + | 1.35171i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.9914 | − | 6.84116i | −1.65086 | − | 0.225915i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.7279 | − | 39.3659i | −0.749725 | − | 1.29856i | −0.947954 | − | 0.318406i | \(-0.896852\pi\) |
0.198229 | − | 0.980156i | \(-0.436481\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.7782 | + | 23.8645i | −0.454006 | + | 0.786362i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.5269 | −1.79478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2132 | −0.500207 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.51472 | − | 9.55177i | 0.181127 | − | 0.313721i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.7132 | − | 37.6084i | −0.712387 | − | 1.23389i | −0.963959 | − | 0.266052i | \(-0.914281\pi\) |
0.251572 | − | 0.967839i | \(-0.419053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.0711 | + | 26.5241i | −0.887218 | + | 0.869293i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3640 | − | 31.8073i | −0.601209 | − | 1.04132i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.41421 | − | 2.44949i | 0.0462497 | − | 0.0801069i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5858 | −0.607171 | −0.303586 | − | 0.952804i | \(-0.598184\pi\) | ||||
−0.303586 | + | 0.952804i | \(0.598184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.8701 | 1.62745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.47056 | + | 14.6714i | −0.276132 | + | 0.478275i | −0.970420 | − | 0.241422i | \(-0.922386\pi\) |
0.694288 | + | 0.719698i | \(0.255720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.89949 | − | 5.02207i | −0.0944205 | − | 0.163541i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.53553 | + | 0.210133i | 0.0499509 | + | 0.00683563i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.8995 | + | 34.4669i | 0.646647 | + | 1.12002i | 0.983919 | + | 0.178618i | \(0.0571625\pi\) |
−0.337272 | + | 0.941407i | \(0.609504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.12132 | + | 1.94218i | −0.0363996 | + | 0.0630460i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.3137 | 1.01542 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.3848 | 1.76170 | 0.880848 | − | 0.473399i | \(-0.156973\pi\) | ||||
0.880848 | + | 0.473399i | \(0.156973\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.41421 | + | 12.8418i | −0.239918 | + | 0.415551i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.20711 | − | 2.09077i | −0.0390202 | − | 0.0675850i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.0000 | + | 41.6413i | 0.548959 | + | 1.34467i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1274 | + | 24.4694i | 0.455723 | + | 0.789336i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.8284 | + | 43.0041i | −0.800085 | + | 1.38579i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.1716 | 0.874684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6569 | 0.953700 | 0.476850 | − | 0.878985i | \(-0.341778\pi\) | ||||
0.476850 | + | 0.878985i | \(0.341778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.0711 | + | 22.6398i | −0.419903 | + | 0.727294i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.10660 | − | 10.5769i | −0.195970 | − | 0.339430i | 0.751248 | − | 0.660020i | \(-0.229452\pi\) |
−0.947218 | + | 0.320590i | \(0.896119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.3137 | + | 40.3805i | −1.00387 | + | 1.29454i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.8640 | + | 24.0131i | 0.444002 | + | 0.769034i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.4853 | + | 32.0174i | −0.591397 | + | 1.02433i | 0.402648 | + | 0.915355i | \(0.368090\pi\) |
−0.994045 | + | 0.108974i | \(0.965243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8284 | 0.473919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.0000 | 0.766261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.2426 | + | 40.2574i | −0.741325 | + | 1.28401i | 0.210567 | + | 0.977579i | \(0.432469\pi\) |
−0.951892 | + | 0.306433i | \(0.900864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1213 | + | 20.9947i | 0.386217 | + | 0.668948i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.24264 | + | 4.18154i | −0.103214 | + | 0.133100i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3431 | + | 17.9149i | 0.328893 | + | 0.569659i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.94975 | − | 17.2335i | 0.316064 | − | 0.547439i | −0.663599 | − | 0.748088i | \(-0.730972\pi\) |
0.979663 | + | 0.200649i | \(0.0643052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 75.7696 | 2.40447 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0000 | −1.07787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.72792 | − | 8.18900i | 0.149735 | − | 0.259348i | −0.781395 | − | 0.624037i | \(-0.785491\pi\) |
0.931129 | + | 0.364689i | \(0.118825\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.05025 | − | 1.81909i | −0.0332285 | − | 0.0575535i |
(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 | 1232.2.q.h.529.2 | 4 | ||
4.3 | odd | 2 | 616.2.q.b.529.1 | yes | 4 | ||
7.2 | even | 3 | inner | 1232.2.q.h.177.2 | 4 | ||
7.3 | odd | 6 | 8624.2.a.cd.1.2 | 2 | |||
7.4 | even | 3 | 8624.2.a.bg.1.1 | 2 | |||
28.3 | even | 6 | 4312.2.a.m.1.1 | 2 | |||
28.11 | odd | 6 | 4312.2.a.u.1.2 | 2 | |||
28.23 | odd | 6 | 616.2.q.b.177.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.q.b.177.1 | ✓ | 4 | 28.23 | odd | 6 | ||
616.2.q.b.529.1 | yes | 4 | 4.3 | odd | 2 | ||
1232.2.q.h.177.2 | 4 | 7.2 | even | 3 | inner | ||
1232.2.q.h.529.2 | 4 | 1.1 | even | 1 | trivial | ||
4312.2.a.m.1.1 | 2 | 28.3 | even | 6 | |||
4312.2.a.u.1.2 | 2 | 28.11 | odd | 6 | |||
8624.2.a.bg.1.1 | 2 | 7.4 | even | 3 | |||
8624.2.a.cd.1.2 | 2 | 7.3 | odd | 6 |