Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(97,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.y (of order \(9\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Character | \(\chi\) | \(=\) | 864.193 |
Dual form | 864.2.y.a.385.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0827900 | + | 1.73007i | −0.0477988 | + | 0.998857i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.532774 | + | 3.02151i | −0.238264 | + | 1.35126i | 0.597366 | + | 0.801969i | \(0.296214\pi\) |
−0.835630 | + | 0.549293i | \(0.814897\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.03971 | + | 1.71152i | −0.770938 | + | 0.646894i | −0.940949 | − | 0.338549i | \(-0.890064\pi\) |
0.170011 | + | 0.985442i | \(0.445620\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98629 | − | 0.286465i | −0.995431 | − | 0.0954883i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.900636 | − | 5.10776i | −0.271552 | − | 1.54005i | −0.749706 | − | 0.661771i | \(-0.769805\pi\) |
0.478154 | − | 0.878276i | \(-0.341306\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.525472 | + | 0.191256i | −0.145740 | + | 0.0530449i | −0.413860 | − | 0.910340i | \(-0.635820\pi\) |
0.268120 | + | 0.963385i | \(0.413598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.18332 | − | 1.17189i | −1.33833 | − | 0.302580i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.47022 | + | 4.27855i | −0.599117 | + | 1.03770i | 0.393834 | + | 0.919181i | \(0.371148\pi\) |
−0.992952 | + | 0.118520i | \(0.962185\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.14343 | − | 1.98047i | −0.262320 | − | 0.454351i | 0.704538 | − | 0.709666i | \(-0.251154\pi\) |
−0.966858 | + | 0.255315i | \(0.917821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.79218 | − | 3.67054i | −0.609304 | − | 0.800977i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.60649 | + | 1.34801i | 0.334977 | + | 0.281079i | 0.794724 | − | 0.606971i | \(-0.207616\pi\) |
−0.459747 | + | 0.888050i | \(0.652060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.14723 | − | 1.50947i | −0.829446 | − | 0.301893i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.742840 | − | 5.14278i | 0.142960 | − | 0.989729i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.83081 | + | 2.85018i | 1.45414 | + | 0.529265i | 0.943746 | − | 0.330672i | \(-0.107275\pi\) |
0.510399 | + | 0.859938i | \(0.329498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.35148 | − | 1.13403i | −0.242734 | − | 0.203678i | 0.513302 | − | 0.858208i | \(-0.328422\pi\) |
−0.756036 | + | 0.654530i | \(0.772866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.91135 | − | 1.13529i | 1.55127 | − | 0.197629i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.08467 | − | 7.07486i | −0.690436 | − | 1.19587i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.54909 | − | 6.14721i | 0.583468 | − | 1.01060i | −0.411597 | − | 0.911366i | \(-0.635029\pi\) |
0.995065 | − | 0.0992295i | \(-0.0316378\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.287383 | − | 0.924938i | −0.0460181 | − | 0.148109i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.72625 | + | 3.17609i | −1.36281 | + | 0.496023i | −0.916922 | − | 0.399066i | \(-0.869334\pi\) |
−0.445888 | + | 0.895089i | \(0.647112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.25426 | − | 7.11326i | −0.191273 | − | 1.08476i | −0.917627 | − | 0.397442i | \(-0.869898\pi\) |
0.726355 | − | 0.687320i | \(-0.241213\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.45658 | − | 8.87050i | 0.366205 | − | 1.32234i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.318115 | − | 0.266930i | 0.0464018 | − | 0.0389357i | −0.619292 | − | 0.785161i | \(-0.712580\pi\) |
0.665694 | + | 0.746225i | \(0.268136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0155785 | − | 0.0883500i | 0.00222550 | − | 0.0126214i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.19769 | − | 4.62788i | −1.00788 | − | 0.648033i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.35868 | 0.598711 | 0.299356 | − | 0.954142i | \(-0.403228\pi\) | ||||
0.299356 | + | 0.954142i | \(0.403228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.9130 | 2.14571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.52102 | − | 1.81424i | 0.466371 | − | 0.240303i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.47724 | + | 8.37782i | −0.192320 | + | 1.09070i | 0.723864 | + | 0.689942i | \(0.242364\pi\) |
−0.916184 | + | 0.400757i | \(0.868747\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.90191 | + | 6.63049i | −1.01174 | + | 0.848947i | −0.988567 | − | 0.150784i | \(-0.951820\pi\) |
−0.0231695 | + | 0.999732i | \(0.507376\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.58146 | − | 4.52679i | 0.829186 | − | 0.570322i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.297925 | − | 1.68962i | −0.0369531 | − | 0.209571i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.91918 | + | 2.88234i | −0.967482 | + | 0.352134i | −0.776961 | − | 0.629549i | \(-0.783240\pi\) |
−0.190521 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.46515 | + | 2.66774i | −0.296769 | + | 0.321159i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.71642 | + | 11.6332i | −0.797092 | + | 1.38060i | 0.124411 | + | 0.992231i | \(0.460296\pi\) |
−0.921502 | + | 0.388373i | \(0.873037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03573 | − | 1.79394i | −0.121223 | − | 0.209964i | 0.799027 | − | 0.601295i | \(-0.205348\pi\) |
−0.920250 | + | 0.391330i | \(0.872015\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.95483 | − | 7.05003i | 0.341195 | − | 0.814067i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.5791 | + | 8.87689i | 1.20560 | + | 1.01162i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8150 | − | 5.39221i | −1.66681 | − | 0.606671i | −0.675402 | − | 0.737449i | \(-0.736030\pi\) |
−0.991412 | + | 0.130779i | \(0.958252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.83588 | + | 1.71094i | 0.981764 | + | 0.190104i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3743 | − | 5.23180i | −1.57778 | − | 0.574265i | −0.603060 | − | 0.797696i | \(-0.706052\pi\) |
−0.974720 | + | 0.223431i | \(0.928274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6116 | − | 9.74332i | −1.25946 | − | 1.05681i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.57933 | + | 13.3119i | −0.598167 | + | 1.42718i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.58615 | + | 7.94345i | 0.486131 | + | 0.842004i | 0.999873 | − | 0.0159407i | \(-0.00507430\pi\) |
−0.513742 | + | 0.857945i | \(0.671741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.744472 | − | 1.28946i | 0.0780418 | − | 0.135172i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07384 | − | 2.24428i | 0.215047 | − | 0.232721i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.59321 | − | 2.39973i | 0.676449 | − | 0.246207i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.972374 | − | 5.51461i | −0.0987297 | − | 0.559924i | −0.993540 | − | 0.113478i | \(-0.963801\pi\) |
0.894811 | − | 0.446445i | \(-0.147310\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.22637 | + | 15.5113i | 0.123254 | + | 1.55894i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.67776 | + | 3.92511i | −0.465455 | + | 0.390563i | −0.845133 | − | 0.534555i | \(-0.820479\pi\) |
0.379678 | + | 0.925119i | \(0.376035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.00832028 | − | 0.0471867i | 0.000819822 | − | 0.00464944i | −0.984395 | − | 0.175972i | \(-0.943693\pi\) |
0.985215 | + | 0.171323i | \(0.0548042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.5782 | − | 6.48105i | 1.22750 | − | 0.632485i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6768 | 1.41886 | 0.709430 | − | 0.704776i | \(-0.248952\pi\) | ||||
0.709430 | + | 0.704776i | \(0.248952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6691 | −1.50083 | −0.750415 | − | 0.660967i | \(-0.770146\pi\) | ||||
−0.750415 | + | 0.660967i | \(0.770146\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3413 | + | 6.64911i | 0.981551 | + | 0.631106i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.01820 | − | 17.1170i | 0.283928 | − | 1.61024i | −0.425162 | − | 0.905117i | \(-0.639783\pi\) |
0.709090 | − | 0.705118i | \(-0.249106\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.92892 | + | 4.13585i | −0.459624 | + | 0.385670i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.62400 | − | 0.420618i | 0.150139 | − | 0.0388861i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.28429 | − | 12.9548i | −0.209400 | − | 1.18757i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.9414 | + | 5.43824i | −1.35831 | + | 0.494385i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.77242 | − | 15.3600i | −0.430315 | − | 1.38496i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.899900 | + | 1.55867i | −0.0804895 | + | 0.139412i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.93670 | + | 6.81857i | 0.349326 | + | 0.605050i | 0.986130 | − | 0.165976i | \(-0.0530773\pi\) |
−0.636804 | + | 0.771026i | \(0.719744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4103 | − | 1.58105i | 1.09266 | − | 0.139204i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6635 | + | 11.4650i | 1.19378 | + | 1.00170i | 0.999786 | + | 0.0207005i | \(0.00658966\pi\) |
0.193997 | + | 0.981002i | \(0.437855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.72187 | + | 2.08259i | 0.496149 | + | 0.180584i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.1432 | + | 4.98444i | 1.30332 | + | 0.428992i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.71051 | − | 2.07845i | −0.487881 | − | 0.177574i | 0.0863540 | − | 0.996265i | \(-0.472478\pi\) |
−0.574235 | + | 0.818690i | \(0.694701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.52743 | − | 7.15537i | −0.723288 | − | 0.606910i | 0.205005 | − | 0.978761i | \(-0.434279\pi\) |
−0.928293 | + | 0.371851i | \(0.878723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.435471 | + | 0.572460i | 0.0366733 | + | 0.0482098i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.45015 | + | 2.51173i | 0.121268 | + | 0.210042i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.7839 | + | 22.1424i | −1.06165 | + | 1.83883i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.151562 | + | 0.0342664i | 0.0125006 | + | 0.00282624i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.28459 | + | 3.01534i | −0.678700 | + | 0.247027i | −0.658289 | − | 0.752765i | \(-0.728720\pi\) |
−0.0204107 | + | 0.999792i | \(0.506497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.13116 | + | 17.7577i | 0.254810 | + | 1.44510i | 0.796560 | + | 0.604559i | \(0.206651\pi\) |
−0.541750 | + | 0.840540i | \(0.682238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.60246 | − | 12.0694i | 0.695468 | − | 0.975751i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.14652 | − | 3.47934i | 0.333057 | − | 0.279468i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.20456 | − | 6.83139i | 0.0961343 | − | 0.545205i | −0.898260 | − | 0.439465i | \(-0.855168\pi\) |
0.994394 | − | 0.105739i | \(-0.0337209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.360855 | + | 7.54083i | −0.0286177 | + | 0.598027i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.58392 | −0.440074 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.6705 | 1.54071 | 0.770356 | − | 0.637614i | \(-0.220079\pi\) | ||||
0.770356 | + | 0.637614i | \(0.220079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.31744 | + | 27.5306i | −0.102562 | + | 2.14325i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.47684 | + | 8.37558i | −0.114281 | + | 0.648121i | 0.872822 | + | 0.488038i | \(0.162287\pi\) |
−0.987104 | + | 0.160083i | \(0.948824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.71904 | + | 8.15524i | −0.747618 | + | 0.627326i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.84727 | + | 6.24182i | 0.217736 | + | 0.477324i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.77597 | + | 15.7433i | 0.211053 | + | 1.19694i | 0.887625 | + | 0.460566i | \(0.152354\pi\) |
−0.676572 | + | 0.736376i | \(0.736535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0426 | − | 4.01919i | 0.834744 | − | 0.303822i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.3719 | − | 3.24932i | −1.08026 | − | 0.244234i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.83560 | − | 17.0358i | 0.735147 | − | 1.27331i | −0.219511 | − | 0.975610i | \(-0.570446\pi\) |
0.954659 | − | 0.297703i | \(-0.0962204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.55489 | − | 9.62135i | −0.412892 | − | 0.715149i | 0.582313 | − | 0.812965i | \(-0.302148\pi\) |
−0.995205 | + | 0.0978154i | \(0.968815\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8170 | − | 14.2198i | −0.799617 | − | 1.05116i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.6830 | + | 13.9987i | 1.22656 | + | 1.02921i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0786 | + | 8.76389i | 1.76080 | + | 0.640879i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.28679 | + | 11.7612i | 0.530036 | + | 0.855499i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.46078 | − | 0.895652i | −0.178056 | − | 0.0648071i | 0.251454 | − | 0.967869i | \(-0.419091\pi\) |
−0.429510 | + | 0.903062i | \(0.641314\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.35123 | + | 1.97292i | 0.169245 | + | 0.142014i | 0.723476 | − | 0.690349i | \(-0.242543\pi\) |
−0.554231 | + | 0.832363i | \(0.686988\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.94782 | − | 0.375548i | 0.211098 | − | 0.0268936i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.74770 | + | 15.1515i | 0.623248 | + | 1.07950i | 0.988877 | + | 0.148737i | \(0.0475206\pi\) |
−0.365629 | + | 0.930761i | \(0.619146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.97489 | + | 3.42060i | −0.139996 | + | 0.242480i | −0.927495 | − | 0.373836i | \(-0.878042\pi\) |
0.787499 | + | 0.616316i | \(0.211376\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.33103 | − | 13.9394i | −0.305488 | − | 0.983207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.8507 | + | 7.58904i | −1.46343 | + | 0.532646i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.94749 | − | 28.0586i | −0.345548 | − | 1.95970i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.41130 | − | 4.48575i | −0.306606 | − | 0.311781i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.08596 | + | 7.62403i | −0.628489 | + | 0.527365i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.13238 | − | 12.0934i | 0.146799 | − | 0.832541i | −0.819105 | − | 0.573643i | \(-0.805530\pi\) |
0.965905 | − | 0.258898i | \(-0.0833592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.5702 | − | 12.5830i | −1.34093 | − | 0.862172i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.1610 | 1.51137 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.69755 | 0.318890 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.18939 | − | 1.64337i | 0.215519 | − | 0.111048i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.479734 | − | 2.72071i | 0.0322704 | − | 0.183015i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.2447 | + | 14.4700i | −1.15479 | + | 0.968983i | −0.999821 | − | 0.0189364i | \(-0.993972\pi\) |
−0.154968 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.9524 | + | 5.69575i | 0.796828 | + | 0.379716i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.58146 | + | 20.3115i | 0.237710 | + | 1.34812i | 0.836831 | + | 0.547461i | \(0.184406\pi\) |
−0.599122 | + | 0.800658i | \(0.704483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0027 | − | 6.91642i | 1.25573 | − | 0.457050i | 0.373399 | − | 0.927671i | \(-0.378192\pi\) |
0.882336 | + | 0.470621i | \(0.155970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.2335 | + | 17.5676i | −1.06808 | + | 1.15586i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.10859 | − | 7.11628i | 0.269163 | − | 0.466203i | −0.699483 | − | 0.714649i | \(-0.746586\pi\) |
0.968646 | + | 0.248446i | \(0.0799198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.637049 | + | 1.10340i | 0.0415565 | + | 0.0719779i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.5554 | − | 25.1845i | 0.685649 | − | 1.63591i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.20425 | + | 2.68869i | 0.207266 | + | 0.173917i | 0.740511 | − | 0.672044i | \(-0.234583\pi\) |
−0.533246 | + | 0.845961i | \(0.679028\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.2957 | + | 6.29514i | 1.11412 | + | 0.405505i | 0.832502 | − | 0.554022i | \(-0.186908\pi\) |
0.281615 | + | 0.959528i | \(0.409130\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.69156 | + | 15.1450i | −0.236814 | + | 0.971555i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.258651 | + | 0.0941412i | 0.0165246 | + | 0.00601446i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.979616 | + | 0.821995i | 0.0623315 | + | 0.0523023i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2414 | − | 24.4353i | 0.649024 | − | 1.54853i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.77483 | − | 6.53819i | −0.238265 | − | 0.412687i | 0.721952 | − | 0.691944i | \(-0.243245\pi\) |
−0.960217 | + | 0.279257i | \(0.909912\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.43843 | − | 9.41964i | 0.341911 | − | 0.592207i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.8180 | − | 19.2823i | 1.11580 | − | 1.20750i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.31085 | + | 3.02490i | −0.518417 | + | 0.188688i | −0.587959 | − | 0.808891i | \(-0.700068\pi\) |
0.0695423 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.28195 | + | 18.6129i | 0.203931 | + | 1.15655i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.5686 | − | 10.7547i | −1.39696 | − | 0.665701i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.7407 | + | 14.8862i | −1.09394 | + | 0.917922i | −0.997003 | − | 0.0773688i | \(-0.975348\pi\) |
−0.0969342 | + | 0.995291i | \(0.530904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.32219 | + | 13.1698i | −0.142651 | + | 0.809016i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.1224 | + | 7.27673i | −0.864278 | + | 0.445329i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.10407 | −0.0673162 | −0.0336581 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336581 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0358 | 1.09560 | 0.547798 | − | 0.836611i | \(-0.315466\pi\) | ||||
0.547798 | + | 0.836611i | \(0.315466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.16923 | + | 1.39474i | 0.131288 | + | 0.0844137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.97485 | + | 22.5425i | −0.239693 | + | 1.35936i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1340 | − | 13.5381i | 0.969400 | − | 0.813424i | −0.0130562 | − | 0.999915i | \(-0.504156\pi\) |
0.982457 | + | 0.186491i | \(0.0597116\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.71107 | + | 3.77370i | 0.222176 | + | 0.225925i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.68697 | + | 9.56727i | 0.100636 | + | 0.570735i | 0.992874 | + | 0.119170i | \(0.0380233\pi\) |
−0.892238 | + | 0.451566i | \(0.850866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.69898 | − | 3.53014i | 0.576545 | − | 0.209845i | −0.0372566 | − | 0.999306i | \(-0.511862\pi\) |
0.613801 | + | 0.789461i | \(0.289640\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.60585 | + | 11.6054i | 0.213592 | + | 0.687444i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.3631 | − | 21.4134i | 0.729768 | − | 1.26400i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.70401 | − | 6.41554i | −0.217883 | − | 0.377385i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.62117 | − | 1.22572i | 0.564003 | − | 0.0718531i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.64392 | + | 7.25311i | 0.504983 | + | 0.423731i | 0.859360 | − | 0.511372i | \(-0.170862\pi\) |
−0.354376 | + | 0.935103i | \(0.615307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.5267 | − | 8.92698i | −1.42800 | − | 0.519749i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.9371 | + | 0.837525i | −1.56305 | + | 0.0485981i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.10198 | − | 0.401089i | −0.0637292 | − | 0.0231955i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.7328 | + | 12.3623i | 0.849185 | + | 0.712550i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.40345 | − | 8.41783i | −0.367869 | − | 0.483591i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.8242 | − | 27.4083i | −0.906090 | − | 1.56939i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.3776 | + | 26.6348i | −0.877646 | + | 1.52013i | −0.0237280 | + | 0.999718i | \(0.507554\pi\) |
−0.853918 | + | 0.520408i | \(0.825780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0809475 | + | 0.0183013i | 0.00460494 | + | 0.00104112i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.97071 | + | 2.17316i | −0.338568 | + | 0.123229i | −0.505709 | − | 0.862704i | \(-0.668769\pi\) |
0.167140 | + | 0.985933i | \(0.446547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.271566 | + | 1.54013i | 0.0153498 | + | 0.0870532i | 0.991520 | − | 0.129952i | \(-0.0414823\pi\) |
−0.976170 | + | 0.217005i | \(0.930371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.1713 | + | 22.2977i | 0.573089 | + | 1.25633i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4451 | − | 12.9600i | 0.867482 | − | 0.727903i | −0.0960847 | − | 0.995373i | \(-0.530632\pi\) |
0.963566 | + | 0.267470i | \(0.0861875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50533 | − | 42.5649i | 0.420218 | − | 2.38317i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.21509 | + | 25.3919i | −0.0678198 | + | 1.41724i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.2981 | 0.628641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.46795 | 0.136897 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.29725 | − | 27.1087i | 0.0717378 | − | 1.49911i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.192006 | + | 1.08892i | −0.0105856 | + | 0.0600340i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.64629 | + | 3.05960i | −0.200418 | + | 0.168171i | −0.737473 | − | 0.675376i | \(-0.763981\pi\) |
0.537055 | + | 0.843547i | \(0.319537\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.3596 | + | 17.3407i | −0.677302 | + | 0.950263i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.48991 | − | 25.4635i | −0.245310 | − | 1.39122i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05863 | − | 0.749279i | 0.112141 | − | 0.0408158i | −0.285340 | − | 0.958426i | \(-0.592107\pi\) |
0.397481 | + | 0.917610i | \(0.369884\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.3638 | + | 6.63881i | 1.59482 | + | 0.360571i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.57516 | + | 7.92440i | −0.247759 | + | 0.429130i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.19984 | − | 15.9346i | −0.496745 | − | 0.860387i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.74725 | − | 8.86978i | −0.363260 | − | 0.477533i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3974 | − | 10.4026i | −0.665525 | − | 0.558442i | 0.246212 | − | 0.969216i | \(-0.420814\pi\) |
−0.911737 | + | 0.410774i | \(0.865258\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.64114 | − | 2.78115i | −0.409021 | − | 0.148871i | 0.129311 | − | 0.991604i | \(-0.458723\pi\) |
−0.538332 | + | 0.842733i | \(0.680946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.593247 | + | 2.84446i | 0.0316652 | + | 0.151826i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6117 | − | 4.59029i | −0.671254 | − | 0.244317i | −0.0161666 | − | 0.999869i | \(-0.505146\pi\) |
−0.655088 | + | 0.755553i | \(0.727368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.5714 | − | 26.4916i | −1.67564 | − | 1.40603i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.6019 | − | 2.87945i | 1.19622 | − | 0.152397i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.5614 | + | 21.7570i | 0.662967 | + | 1.14829i | 0.979832 | + | 0.199822i | \(0.0640363\pi\) |
−0.316866 | + | 0.948470i | \(0.602630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.88516 | − | 11.9254i | 0.362377 | − | 0.627655i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.17153 | − | 26.3000i | −0.428894 | − | 1.38039i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.97221 | − | 2.17371i | 0.312600 | − | 0.113777i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.83795 | + | 16.0948i | 0.148140 | + | 0.840144i | 0.964792 | + | 0.263013i | \(0.0847163\pi\) |
−0.816652 | + | 0.577130i | \(0.804173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.9690 | − | 6.98498i | 1.40395 | − | 0.363623i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.89045 | + | 7.45997i | −0.461569 | + | 0.387302i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.483980 | − | 2.74478i | 0.0250595 | − | 0.142120i | −0.969711 | − | 0.244255i | \(-0.921457\pi\) |
0.994770 | + | 0.102136i | \(0.0325676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.62211 | − | 1.68593i | −0.135405 | − | 0.0870612i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.65999 | −0.240002 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6950 | −1.16577 | −0.582883 | − | 0.812556i | \(-0.698075\pi\) | ||||
−0.582883 | + | 0.812556i | \(0.698075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.1225 | + | 6.24626i | −0.621056 | + | 0.320006i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.42329 | − | 13.7431i | 0.123824 | − | 0.702242i | −0.858175 | − | 0.513357i | \(-0.828402\pi\) |
0.981999 | − | 0.188885i | \(-0.0604873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −32.4579 | + | 27.2354i | −1.65421 | + | 1.38804i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.70788 | + | 21.6016i | 0.0868166 | + | 1.09807i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.00646381 | + | 0.0366581i | 0.000327728 | + | 0.00185864i | 0.984971 | − | 0.172719i | \(-0.0552552\pi\) |
−0.984643 | + | 0.174577i | \(0.944144\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.73591 | + | 3.54358i | −0.492366 | + | 0.179207i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.9665 | + | 22.6896i | −1.05762 | + | 1.14454i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.1857 | − | 41.8908i | 1.21691 | − | 2.10775i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4223 | + | 31.9084i | 0.924591 | + | 1.60144i | 0.792217 | + | 0.610239i | \(0.208927\pi\) |
0.132374 | + | 0.991200i | \(0.457740\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.07674 | + | 9.72683i | −0.204092 | + | 0.486950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.48227 | − | 2.08287i | −0.123959 | − | 0.104014i | 0.578701 | − | 0.815540i | \(-0.303560\pi\) |
−0.702660 | + | 0.711526i | \(0.748004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.927058 | + | 0.337421i | 0.0461800 | + | 0.0168082i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.87714 | + | 25.7862i | −0.490799 | + | 1.28132i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.5949 | − | 12.5915i | −1.71481 | − | 0.624138i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.18837 | + | 7.70996i | 0.454336 | + | 0.381233i | 0.841042 | − | 0.540970i | \(-0.181943\pi\) |
−0.386706 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.06865 | − | 9.70751i | 0.200691 | − | 0.478836i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3257 | − | 19.6166i | −0.557300 | − | 0.965272i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.4662 | − | 40.6446i | 1.15191 | − | 1.99517i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0853 | − | 14.1607i | 0.640789 | − | 0.693451i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.84461 | + | 2.49124i | −0.334381 | + | 0.121705i | −0.503754 | − | 0.863847i | \(-0.668048\pi\) |
0.169373 | + | 0.985552i | \(0.445826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.14577 | − | 12.1693i | −0.104578 | − | 0.593093i | −0.991388 | − | 0.130958i | \(-0.958195\pi\) |
0.886810 | − | 0.462135i | \(-0.152917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.02645 | + | 0.706002i | −0.0499077 | + | 0.0343270i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.7029 | − | 14.0154i | 0.810211 | − | 0.679847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.76939 | − | 27.0486i | 0.230807 | − | 1.30897i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.46553 | + | 2.30092i | −0.215598 | + | 0.111089i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.3428 | −0.835373 | −0.417686 | − | 0.908591i | \(-0.637159\pi\) | ||||
−0.417686 | + | 0.908591i | \(0.637159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6172 | 0.894683 | 0.447342 | − | 0.894363i | \(-0.352371\pi\) | ||||
0.447342 | + | 0.894363i | \(0.352371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.2495 | − | 23.9502i | −1.78598 | − | 1.14833i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.832785 | − | 4.72296i | 0.0398375 | − | 0.225930i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.430130 | − | 0.360922i | 0.0205290 | − | 0.0172259i | −0.632465 | − | 0.774589i | \(-0.717957\pi\) |
0.652994 | + | 0.757363i | \(0.273513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0718311 | + | 0.259376i | −0.00342053 | + | 0.0123512i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.461911 | − | 2.61963i | −0.0219461 | − | 0.124462i | 0.971867 | − | 0.235532i | \(-0.0756833\pi\) |
−0.993813 | + | 0.111070i | \(0.964572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.4446 | + | 9.62506i | −1.25360 | + | 0.456271i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.53088 | − | 14.5826i | −0.214303 | − | 0.689732i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.46856 | − | 11.2039i | 0.305270 | − | 0.528743i | −0.672051 | − | 0.740504i | \(-0.734587\pi\) |
0.977321 | + | 0.211761i | \(0.0679200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0819 | + | 41.7110i | 1.13397 | + | 1.96410i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.9813 | + | 3.94697i | −1.45563 | + | 0.185445i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.49949 | + | 2.93642i | 0.164059 | + | 0.137662i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.6300 | + | 13.3322i | 1.71348 | + | 0.623655i | 0.997243 | − | 0.0742028i | \(-0.0236412\pi\) |
0.716236 | + | 0.697858i | \(0.245863\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.1687 | + | 15.8821i | 0.941393 | + | 0.741313i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.23220 | − | 0.812453i | −0.103964 | − | 0.0378397i | 0.289515 | − | 0.957174i | \(-0.406506\pi\) |
−0.393478 | + | 0.919334i | \(0.628728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.40962 | − | 7.05651i | −0.390828 | − | 0.327944i | 0.426108 | − | 0.904672i | \(-0.359884\pi\) |
−0.816936 | + | 0.576729i | \(0.804329\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.67622 | + | 7.46183i | 0.263229 | + | 0.346034i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.88903 | + | 15.3963i | 0.411335 | + | 0.712454i | 0.995036 | − | 0.0995151i | \(-0.0317291\pi\) |
−0.583701 | + | 0.811969i | \(0.698396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2196 | − | 19.4330i | 0.518074 | − | 0.897331i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7191 | + | 2.64954i | 0.539986 | + | 0.122085i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.2032 | + | 12.8129i | −1.61864 | + | 0.589138i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.75259 | + | 9.93943i | 0.0804143 | + | 0.456052i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.0163 | − | 1.24861i | −0.595975 | − | 0.0571699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2453 | + | 17.8269i | −0.970723 | + | 0.814533i | −0.982664 | − | 0.185395i | \(-0.940643\pi\) |
0.0119409 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.689258 | + | 3.90898i | −0.0314275 | + | 0.178234i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.462292 | − | 9.66057i | 0.0210350 | − | 0.439571i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.1805 | 0.780127 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.27190 | −0.420150 | −0.210075 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210075 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.62852 | + | 34.0313i | −0.0736442 | + | 1.53895i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.35740 | + | 30.3833i | −0.241776 | + | 1.37118i | 0.586086 | + | 0.810249i | \(0.300668\pi\) |
−0.827862 | + | 0.560932i | \(0.810443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.5385 | + | 26.4639i | −1.42042 | + | 1.19188i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −47.5208 | − | 4.55851i | −2.13590 | − | 0.204890i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.21087 | − | 35.2236i | −0.278595 | − | 1.57999i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.56790 | + | 2.39052i | −0.294020 | + | 0.107014i | −0.484819 | − | 0.874615i | \(-0.661114\pi\) |
0.190799 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3681 | − | 3.24845i | −0.641918 | − | 0.145130i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.24640 | − | 7.35498i | 0.189338 | − | 0.327942i | −0.755692 | − | 0.654927i | \(-0.772699\pi\) |
0.945030 | + | 0.326985i | \(0.106033\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.36758 | − | 16.2251i | −0.416852 | − | 0.722009i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.3045 | − | 17.4898i | −0.590874 | − | 0.776749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3394 | − | 24.6187i | −1.30045 | − | 1.09121i | −0.990068 | − | 0.140592i | \(-0.955099\pi\) |
−0.310380 | − | 0.950613i | \(-0.600456\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.18295 | + | 1.88644i | 0.229280 | + | 0.0834511i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.0345 | + | 4.40921i | −0.487186 | + | 0.194672i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.138142 | + | 0.0502797i | 0.00608728 | + | 0.00221559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.64992 | − | 1.38445i | −0.0725633 | − | 0.0608879i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.4669 | + | 3.49924i | −1.20566 | + | 0.153600i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00838 | − | 10.4068i | −0.263232 | − | 0.455931i | 0.703867 | − | 0.710332i | \(-0.251455\pi\) |
−0.967099 | + | 0.254401i | \(0.918122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.71235 | − | 8.16204i | 0.206057 | − | 0.356901i | −0.744412 | − | 0.667720i | \(-0.767270\pi\) |
0.950469 | + | 0.310820i | \(0.100603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.03926 | + | 19.4373i | 0.263575 | + | 0.848312i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.19048 | − | 2.98109i | 0.356783 | − | 0.129858i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.23021 | − | 18.3195i | −0.140444 | − | 0.796498i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.81141 | − | 24.5954i | 0.295590 | − | 1.06735i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.97795 | − | 3.33790i | 0.172304 | − | 0.144580i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.81942 | + | 44.3462i | −0.338063 | + | 1.91725i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.6588 | + | 18.4267i | 1.23672 | + | 0.795170i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.465301 | −0.0200419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1872 | −0.609956 | −0.304978 | − | 0.952359i | \(-0.598649\pi\) | ||||
−0.304978 | + | 0.952359i | \(0.598649\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.1055 | − | 8.81380i | 0.734068 | − | 0.378236i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.34810 | − | 47.3444i | 0.357593 | − | 2.02801i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5517 | + | 11.3712i | −0.579428 | + | 0.486198i | −0.884759 | − | 0.466048i | \(-0.845677\pi\) |
0.305331 | + | 0.952246i | \(0.401233\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.4968 | − | 17.5370i | 1.08818 | − | 0.748459i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.30925 | − | 18.7677i | −0.140979 | − | 0.799529i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.4471 | − | 14.3576i | 1.67746 | − | 0.610546i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.5999 | + | 27.7038i | −1.08666 | + | 1.17596i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.84820 | − | 8.39732i | 0.205425 | − | 0.355806i | −0.744843 | − | 0.667239i | \(-0.767476\pi\) |
0.950268 | + | 0.311433i | \(0.100809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.01953 | + | 3.49793i | 0.0854171 | + | 0.147947i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.1556 | + | 40.9321i | −0.724311 | + | 1.72815i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.3908 | − | 9.55804i | −0.480066 | − | 0.402823i | 0.370384 | − | 0.928879i | \(-0.379226\pi\) |
−0.850450 | + | 0.526055i | \(0.823670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.1113 | + | 18.2390i | 2.10820 | + | 0.767322i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.9509 | + | 11.6330i | −0.879856 | + | 0.488538i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0880 | + | 6.21952i | 0.716365 | + | 0.260736i | 0.674382 | − | 0.738383i | \(-0.264410\pi\) |
0.0419833 | + | 0.999118i | \(0.486632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.494303 | + | 0.414769i | 0.0206859 | + | 0.0173576i | 0.653072 | − | 0.757296i | \(-0.273480\pi\) |
−0.632386 | + | 0.774653i | \(0.717924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75327 | − | 4.18318i | 0.0732439 | − | 0.174755i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.62772 | − | 8.01544i | −0.192989 | − | 0.334267i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.8016 | + | 34.2974i | −0.824351 | + | 1.42782i | 0.0780633 | + | 0.996948i | \(0.475126\pi\) |
−0.902414 | + | 0.430869i | \(0.858207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.60795 | + | 3.90446i | −0.149941 | + | 0.162264i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.2736 | − | 13.9305i | 1.58786 | − | 0.577933i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.92559 | − | 22.2631i | −0.162581 | − | 0.922043i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.405675 | + | 5.13104i | 0.0167726 | + | 0.212142i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.1865 | − | 27.0077i | 1.32848 | − | 1.11473i | 0.344050 | − | 0.938951i | \(-0.388201\pi\) |
0.984430 | − | 0.175776i | \(-0.0562434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.700592 | + | 3.97326i | −0.0288674 | + | 0.163715i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.9373 | + | 13.8798i | −1.10805 | + | 0.570937i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.58469 | −0.0650756 | −0.0325378 | − | 0.999471i | \(-0.510359\pi\) | ||||
−0.0325378 | + | 0.999471i | \(0.510359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.3602 | 1.65461 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.75439 | − | 3.69988i | −0.235511 | − | 0.151426i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.447444 | + | 2.53758i | −0.0182821 | + | 0.103683i | −0.992583 | − | 0.121566i | \(-0.961208\pi\) |
0.974301 | + | 0.225249i | \(0.0723195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6975 | − | 9.81540i | 0.477152 | − | 0.400378i | −0.372243 | − | 0.928135i | \(-0.621411\pi\) |
0.849396 | + | 0.527757i | \(0.176967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.4747 | − | 6.33896i | 0.996685 | − | 0.258142i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.47129 | − | 48.0431i | −0.344407 | − | 1.95323i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6374 | − | 5.69156i | 0.634704 | − | 0.231013i | −0.00457324 | − | 0.999990i | \(-0.501456\pi\) |
0.639278 | + | 0.768976i | \(0.279233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.4033 | − | 36.7015i | −0.462087 | − | 1.48722i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.116108 | + | 0.201106i | −0.00469724 | + | 0.00813586i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0896 | + | 38.2603i | 0.892190 | + | 1.54532i | 0.837244 | + | 0.546829i | \(0.184165\pi\) |
0.0549457 | + | 0.998489i | \(0.482501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.9530 | − | 6.23654i | 1.97397 | − | 0.251481i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.32615 | − | 6.14737i | −0.294940 | − | 0.247484i | 0.483295 | − | 0.875458i | \(-0.339440\pi\) |
−0.778234 | + | 0.627974i | \(0.783884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.76827 | − | 3.55536i | −0.392620 | − | 0.142902i | 0.138164 | − | 0.990409i | \(-0.455880\pi\) |
−0.530783 | + | 0.847507i | \(0.678102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.12587 | − | 7.26048i | 0.326080 | − | 0.291353i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.9498 | − | 8.35304i | −0.919464 | − | 0.334658i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1344 | − | 17.7338i | −0.845374 | − | 0.709353i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.4379 | − | 16.3505i | −0.496721 | − | 0.652978i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.5341 | + | 30.3700i | 0.699131 | + | 1.21093i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.77581 | − | 11.7361i | 0.269741 | − | 0.467205i | −0.699054 | − | 0.715069i | \(-0.746395\pi\) |
0.968795 | + | 0.247864i | \(0.0797286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7458 | + | 4.69038i | 0.824572 | + | 0.186426i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6998 | + | 8.26204i | −0.900812 | + | 0.327869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.00871143 | + | 0.0494050i | 0.000345159 | + | 0.00195750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.3897 | − | 32.8160i | 0.925281 | − | 1.29818i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.27616 | + | 6.10542i | −0.287391 | + | 0.241150i | −0.775073 | − | 0.631872i | \(-0.782287\pi\) |
0.487682 | + | 0.873021i | \(0.337843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.88450 | − | 39.0439i | 0.271498 | − | 1.53974i | −0.478372 | − | 0.878158i | \(-0.658773\pi\) |
0.749870 | − | 0.661585i | \(-0.230116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.83471 | + | 38.3402i | −0.0722417 | + | 1.50964i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5044 | 0.766798 | 0.383399 | − | 0.923583i | \(-0.374753\pi\) | ||||
0.383399 | + | 0.923583i | \(0.374753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.1223 | 1.73195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.388910 | + | 8.12709i | −0.0152426 | + | 0.318526i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.18031 | + | 6.69386i | −0.0461890 | + | 0.261951i | −0.999154 | − | 0.0411302i | \(-0.986904\pi\) |
0.952965 | + | 0.303081i | \(0.0980153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.9212 | + | 35.1761i | −1.63800 | + | 1.37444i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.57909 | + | 5.65392i | 0.100620 | + | 0.220580i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.88196 | + | 16.3444i | 0.112265 | + | 0.636687i | 0.988068 | + | 0.154018i | \(0.0492215\pi\) |
−0.875803 | + | 0.482669i | \(0.839667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.88894 | + | 2.14340i | −0.229053 | + | 0.0833686i | −0.453997 | − | 0.891003i | \(-0.650002\pi\) |
0.224944 | + | 0.974372i | \(0.427780\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.66730 | + | 1.05522i | 0.181263 | + | 0.0409814i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.34104 | + | 16.1792i | −0.362230 | + | 0.627401i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.73807 | + | 15.1348i | 0.338339 | + | 0.586021i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.6064 | − | 31.0325i | −0.912678 | − | 1.19979i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.9837 | + | 34.3894i | 1.58216 | + | 1.32759i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8172 | + | 8.66874i | 0.918084 | + | 0.334155i | 0.757476 | − | 0.652863i | \(-0.226432\pi\) |
0.160608 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.8436 | + | 20.2070i | −0.417370 | + | 0.777767i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.3294 | − | 8.12724i | −0.858189 | − | 0.312355i | −0.124815 | − | 0.992180i | \(-0.539834\pi\) |
−0.733375 | + | 0.679825i | \(0.762056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4217 | + | 9.58396i | 0.438325 | + | 0.367799i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.4368 | + | 4.51459i | −1.35794 | + | 0.173000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6068 | − | 21.8356i | −0.482386 | − | 0.835517i | 0.517409 | − | 0.855738i | \(-0.326896\pi\) |
−0.999796 | + | 0.0202207i | \(0.993563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.32249 | − | 16.1470i | 0.356194 | − | 0.616946i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.3927 | + | 33.4486i | 0.396505 | + | 1.27615i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.29037 | + | 0.833625i | −0.0872560 | + | 0.0317586i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.95664 | − | 22.4392i | −0.150518 | − | 0.853629i | −0.962770 | − | 0.270323i | \(-0.912870\pi\) |
0.812252 | − | 0.583307i | \(-0.198241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −29.0492 | − | 29.5395i | −1.10349 | − | 1.12211i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.1632 | − | 21.9536i | 0.992428 | − | 0.832746i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.96669 | − | 45.1814i | 0.301760 | − | 1.71137i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.9715 | + | 7.69731i | 0.452805 | + | 0.291139i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.53279 | −0.322279 | −0.161140 | − | 0.986932i | \(-0.551517\pi\) | ||||
−0.161140 | + | 0.986932i | \(0.551517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.2325 | −0.612221 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.96170 | + | 1.01079i | −0.0738820 | + | 0.0380685i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.82338 | − | 16.0122i | 0.106184 | − | 0.602200i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.7053 | + | 13.1783i | −0.589825 | + | 0.494922i | −0.888157 | − | 0.459541i | \(-0.848014\pi\) |
0.298332 | + | 0.954462i | \(0.403570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.6971 | + | 20.3467i | 1.60127 | + | 0.763060i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.642469 | − | 3.64362i | −0.0240606 | − | 0.136455i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.36183 | + | 3.04346i | −0.312715 | + | 0.113819i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.91690 | + | 5.32099i | −0.183625 | + | 0.198716i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.72008 | − | 4.71132i | 0.101442 | − | 0.175703i | −0.810837 | − | 0.585272i | \(-0.800988\pi\) |
0.912279 | + | 0.409569i | \(0.134321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0637900 | + | 0.110487i | 0.00237566 | + | 0.00411477i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.3229 | + | 29.4017i | −0.458295 | + | 1.09346i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.1739 | − | 23.6407i | −1.04635 | − | 0.877994i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7417 | + | 6.09349i | 0.620917 | + | 0.225995i | 0.633273 | − | 0.773929i | \(-0.281711\pi\) |
−0.0123564 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8964 | − | 7.64052i | −0.959125 | − | 0.282982i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.5328 | + | 12.2049i | 1.24025 | + | 0.451415i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.10760 | + | 5.12488i | 0.225589 | + | 0.189292i | 0.748576 | − | 0.663049i | \(-0.230738\pi\) |
−0.522987 | + | 0.852341i | \(0.675182\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.184285 | + | 0.439690i | −0.00679744 | + | 0.0162182i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.8546 | + | 37.8533i | 0.805025 | + | 1.39434i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.56787 | + | 2.71563i | −0.0576749 | + | 0.0998959i | −0.893421 | − | 0.449220i | \(-0.851702\pi\) |
0.835746 | + | 0.549116i | \(0.185035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.50321 | + | 1.62675i | −0.0552219 | + | 0.0597602i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.7743 | − | 12.6568i | 1.27574 | − | 0.464333i | 0.386722 | − | 0.922196i | \(-0.373607\pi\) |
0.889023 | + | 0.457863i | \(0.151385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.69708 | − | 26.6385i | −0.172088 | − | 0.975959i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.4270 | + | 19.7414i | 1.51573 | + | 0.722300i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.9364 | + | 25.1196i | −1.09385 | + | 0.917852i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.20695 | + | 40.8726i | −0.262985 | + | 1.49146i | 0.511726 | + | 0.859149i | \(0.329006\pi\) |
−0.774711 | + | 0.632315i | \(0.782105\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.6241 | − | 5.98942i | 0.423604 | − | 0.218267i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.3232 | −2.01342 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5894 | 0.457571 | 0.228786 | − | 0.973477i | \(-0.426525\pi\) | ||||
0.228786 | + | 0.973477i | \(0.426525\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.8464 | + | 10.1887i | 0.575188 | + | 0.369827i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.38353 | + | 13.5177i | −0.0864029 | + | 0.490015i | 0.910642 | + | 0.413196i | \(0.135588\pi\) |
−0.997045 | + | 0.0768194i | \(0.975524\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.9604 | − | 26.8180i | 1.15705 | − | 0.970877i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.8846 | + | 32.4227i | 1.15279 | + | 1.17225i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.826064 | − | 4.68484i | −0.0298275 | − | 0.169160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.8589 | − | 7.59201i | 0.752190 | − | 0.273775i | 0.0626629 | − | 0.998035i | \(-0.480041\pi\) |
0.689527 | + | 0.724260i | \(0.257818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.54524 | − | 14.6288i | −0.163693 | − | 0.526843i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4098 | − | 19.7623i | 0.410381 | − | 0.710800i | −0.584550 | − | 0.811357i | \(-0.698729\pi\) |
0.994931 | + | 0.100557i | \(0.0320625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.89313 | + | 6.74310i | 0.139845 | + | 0.242219i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.4733 | + | 4.13705i | −1.16497 | + | 0.148416i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.2680 | + | 13.6505i | 0.582861 | + | 0.489078i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65.4685 | + | 23.8286i | 2.34265 | + | 0.852653i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.4749 | − | 38.1549i | 0.731713 | − | 1.36354i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.9994 | + | 7.27918i | 0.713809 | + | 0.259805i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.65334 | − | 4.74371i | −0.201520 | − | 0.169095i | 0.536443 | − | 0.843936i | \(-0.319768\pi\) |
−0.737963 | + | 0.674841i | \(0.764212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.2854 | − | 31.9251i | −0.864584 | − | 1.13656i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1399 | + | 40.0795i | 0.822760 | + | 1.42506i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.88411 | − | 4.99543i | 0.102418 | − | 0.177393i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.5925 | − | 5.10789i | −0.801272 | − | 0.181158i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.4935 | − | 12.1906i | 1.18640 | − | 0.431815i | 0.327943 | − | 0.944698i | \(-0.393645\pi\) |
0.858459 | + | 0.512883i | \(0.171422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.356259 | + | 2.02045i | 0.0126035 | + | 0.0714783i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4201 | − | 25.0352i | −0.403508 | − | 0.884577i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.23018 | + | 6.90594i | −0.290437 | + | 0.243705i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.97497 | − | 16.8719i | 0.104854 | − | 0.594655i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0914057 | − | 1.91011i | 0.00321763 | − | 0.0672392i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.09426 | −0.0384721 | −0.0192360 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192360 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.6255 | −0.970063 | −0.485031 | − | 0.874497i | \(-0.661192\pi\) | ||||
−0.485031 | + | 0.874497i | \(0.661192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.49318 | + | 31.2032i | −0.0523681 | + | 1.09434i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4799 | + | 59.4346i | −0.367096 | + | 2.08190i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.6535 | + | 10.6175i | −0.442688 | + | 0.371460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.59260 | + | 3.63745i | −0.0905926 | + | 0.127103i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.69214 | + | 37.9530i | 0.233557 | + | 1.32457i | 0.845631 | + | 0.533769i | \(0.179225\pi\) |
−0.612073 | + | 0.790801i | \(0.709664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3783 | + | 5.96120i | −0.570911 | + | 0.207794i | −0.611313 | − | 0.791389i | \(-0.709358\pi\) |
0.0404023 | + | 0.999183i | \(0.487136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.6711 | − | 8.74307i | −1.34635 | − | 0.304395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.4085 | + | 45.7409i | −0.918313 | + | 1.59057i | −0.116337 | + | 0.993210i | \(0.537115\pi\) |
−0.801976 | + | 0.597356i | \(0.796218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4297 | − | 26.7250i | −0.535895 | − | 0.928197i | −0.999119 | − | 0.0419562i | \(-0.986641\pi\) |
0.463225 | − | 0.886241i | \(-0.346692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0861 | + | 29.0338i | 0.766158 | + | 1.00717i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.339528 | + | 0.284898i | 0.0117639 | + | 0.00987112i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.5201 | − | 8.92458i | −0.848553 | − | 0.308848i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.83600 | + | 6.10798i | −0.236287 | + | 0.211123i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.8026 | − | 15.2149i | −1.44318 | − | 0.525276i | −0.502505 | − | 0.864574i | \(-0.667588\pi\) |
−0.940679 | + | 0.339298i | \(0.889811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.9827 | + | 25.9976i | 1.06837 | + | 0.896469i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6917 | + | 2.12650i | −0.574893 | + | 0.0732406i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.4631 | − | 33.7111i | −0.669551 | − | 1.15970i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.1685 | − | 36.6650i | 0.727359 | − | 1.25982i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.30442 | + | 17.0722i | 0.182047 | + | 0.585916i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.9881 | − | 5.09124i | 0.479505 | − | 0.174526i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.75590 | − | 21.3007i | −0.128599 | − | 0.729324i | −0.979105 | − | 0.203357i | \(-0.934815\pi\) |
0.850505 | − | 0.525967i | \(-0.176296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.3767 | + | 5.27757i | −0.696868 | + | 0.180489i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.87094 | + | 4.08720i | −0.166388 | + | 0.139616i | −0.722180 | − | 0.691705i | \(-0.756860\pi\) |
0.555792 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.47386 | + | 8.35865i | −0.0502873 | + | 0.285193i | −0.999573 | − | 0.0292214i | \(-0.990697\pi\) |
0.949286 | + | 0.314415i | \(0.101808\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0232 | + | 23.1618i | 1.22767 | + | 0.789352i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.56354 | 0.325547 | 0.162773 | − | 0.986663i | \(-0.447956\pi\) | ||||
0.162773 | + | 0.986663i | \(0.447956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.0476 | −1.66767 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.4060 | − | 5.87706i | 0.387368 | − | 0.199596i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.1992 | + | 80.5277i | −0.481675 | + | 2.73171i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.61004 | − | 3.02918i | 0.122322 | − | 0.102640i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.32405 | + | 16.7468i | 0.0448123 | + | 0.566793i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.832164 | − | 4.71944i | −0.0281323 | − | 0.159546i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.10266 | − | 0.401336i | 0.0372343 | − | 0.0135522i | −0.323336 | − | 0.946284i | \(-0.604804\pi\) |
0.360570 | + | 0.932732i | \(0.382582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.2640 | + | 14.3541i | −0.447385 | + | 0.484152i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.60086 | − | 4.50483i | 0.0876253 | − | 0.151772i | −0.818882 | − | 0.573963i | \(-0.805406\pi\) |
0.906507 | + | 0.422191i | \(0.138739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.30273 | + | 16.1128i | 0.313062 | + | 0.542239i | 0.979024 | − | 0.203747i | \(-0.0653120\pi\) |
−0.665962 | + | 0.745986i | \(0.731979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.4749 | − | 41.6938i | 0.587411 | − | 1.40152i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.01393 | + | 5.88539i | 0.235505 | + | 0.197612i | 0.752901 | − | 0.658134i | \(-0.228654\pi\) |
−0.517396 | + | 0.855746i | \(0.673098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.6998 | − | 7.17015i | −0.660711 | − | 0.240479i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.781144 | − | 46.6724i | 0.0261693 | − | 1.56359i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.892387 | − | 0.324802i | −0.0298626 | − | 0.0108691i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.2336 | + | 38.7946i | 1.54542 | + | 1.29676i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.785145 | − | 1.87330i | 0.0262152 | − | 0.0625477i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.35102 | − | 12.7323i | −0.245170 | − | 0.424648i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7669 | + | 18.6489i | −0.358698 | + | 0.621284i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.6074 | + | 24.4653i | −0.752326 | + | 0.814155i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.0305 | − | 11.6582i | 1.06473 | − | 0.387530i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.57026 | + | 48.6044i | 0.284571 | + | 1.61388i | 0.706815 | + | 0.707399i | \(0.250132\pi\) |
−0.422244 | + | 0.906482i | \(0.638757\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.0936 | − | 10.3815i | 0.500622 | − | 0.344333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.3464 | + | 22.1073i | −0.872895 | + | 0.732446i | −0.964706 | − | 0.263330i | \(-0.915179\pi\) |
0.0918103 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7768 | + | 78.1322i | −0.455946 | + | 2.58580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.7284 | − | 25.1078i | 1.61091 | − | 0.830039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.4921 | −1.56833 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.3599 | 1.89213 | 0.946063 | − | 0.323981i | \(-0.105022\pi\) | ||||
0.946063 | + | 0.323981i | \(0.105022\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.8069 | − | 28.8094i | −1.47644 | − | 0.949303i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.30437 | − | 7.39746i | 0.0429339 | − | 0.243491i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9979 | + | 20.1366i | −0.789047 | + | 0.662089i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0383641 | + | 0.138530i | −0.00126004 | + | 0.00454991i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.83992 | + | 21.7773i | 0.125984 | + | 0.714490i | 0.980719 | + | 0.195425i | \(0.0626086\pi\) |
−0.854735 | + | 0.519065i | \(0.826280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.192788 | + | 0.0701689i | −0.00631836 | + | 0.00229969i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.26541 | − | 10.5097i | −0.106905 | − | 0.344071i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.3087 | + | 68.0846i | −1.28553 | + | 2.22660i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.37383 | + | 7.57569i | 0.142887 | + | 0.247487i | 0.928583 | − | 0.371126i | \(-0.121028\pi\) |
−0.785696 | + | 0.618613i | \(0.787695\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.68701 | + | 0.342322i | −0.0876874 | + | 0.0111712i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.9702 | − | 35.2172i | −1.36819 | − | 1.14805i | −0.973357 | − | 0.229295i | \(-0.926358\pi\) |
−0.394833 | − | 0.918753i | \(-0.629197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.3000 | − | 6.66067i | −0.595931 | − | 0.216901i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −39.4187 | + | 15.7511i | −1.28229 | + | 0.512383i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.3653 | + | 14.6918i | 1.31170 | + | 0.477418i | 0.900788 | − | 0.434259i | \(-0.142990\pi\) |
0.410907 | + | 0.911677i | \(0.365212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.887349 | + | 0.744574i | 0.0288046 | + | 0.0241699i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.1429 | + | 27.7940i | 0.685607 | + | 0.901283i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.95900 | + | 3.39309i | 0.0634583 | + | 0.109913i | 0.896009 | − | 0.444036i | \(-0.146454\pi\) |
−0.832551 | + | 0.553949i | \(0.813120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.01727 | − | 6.95811i | 0.129996 | − | 0.225159i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 73.0189 | + | 16.5087i | 2.36036 | + | 0.533650i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2051 | − | 5.53420i | 0.490998 | − | 0.178709i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.84261 | − | 27.4638i | −0.156213 | − | 0.885929i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.8292 | − | 4.20439i | −1.41238 | − | 0.135485i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.21388 | + | 6.05316i | −0.232223 | + | 0.194858i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.22038 | + | 35.2775i | −0.200034 | + | 1.13445i | 0.705031 | + | 0.709176i | \(0.250933\pi\) |
−0.905065 | + | 0.425273i | \(0.860178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.935367 | + | 19.5465i | −0.0300483 | + | 0.627923i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.1246 | 1.51230 | 0.756150 | − | 0.654398i | \(-0.227078\pi\) | ||||
0.756150 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6400 | 0.950216 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.204321 | + | 4.26973i | −0.00654352 | + | 0.136741i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.15880 | + | 40.5996i | −0.229030 | + | 1.29890i | 0.625798 | + | 0.779985i | \(0.284773\pi\) |
−0.854828 | + | 0.518911i | \(0.826338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.4428 | − | 30.5791i | 1.16472 | − | 0.977313i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.7926 | + | 4.48865i | 1.49397 | + | 0.143312i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.72372 | − | 32.4608i | −0.182558 | − | 1.03534i | −0.929053 | − | 0.369947i | \(-0.879376\pi\) |
0.746494 | − | 0.665392i | \(-0.231735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.4409 | + | 18.3590i | −1.60718 | + | 0.584966i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.86801 | − | 0.422335i | −0.0594594 | − | 0.0134431i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.57376 | − | 13.1181i | 0.240832 | − | 0.417133i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.46511 | + | 7.73379i | 0.141839 | + | 0.245672i | 0.928189 | − | 0.372109i | \(-0.121365\pi\) |
−0.786350 | + | 0.617781i | \(0.788032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.99145 | − | 6.56165i | −0.158399 | − | 0.208228i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.28323 | − | 7.78955i | −0.294298 | − | 0.246945i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.4876 | − | 12.5525i | −1.09223 | − | 0.397541i | −0.267786 | − | 0.963478i | \(-0.586292\pi\) |
−0.824448 | + | 0.565937i | \(0.808514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.9774 | − | 22.8186i | −0.916803 | − | 0.721949i |
(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 | 864.2.y.a.193.4 | ✓ | 48 | |
4.3 | odd | 2 | inner | 864.2.y.a.193.5 | yes | 48 | |
27.7 | even | 9 | inner | 864.2.y.a.385.4 | yes | 48 | |
108.7 | odd | 18 | inner | 864.2.y.a.385.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.y.a.193.4 | ✓ | 48 | 1.1 | even | 1 | trivial | |
864.2.y.a.193.5 | yes | 48 | 4.3 | odd | 2 | inner | |
864.2.y.a.385.4 | yes | 48 | 27.7 | even | 9 | inner | |
864.2.y.a.385.5 | yes | 48 | 108.7 | odd | 18 | inner |