Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 253.2 | ||
Root | \(1.20201 + 1.24706i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.253 |
Dual form | 324.2.i.a.73.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.46957 | − | 1.23312i | −0.657212 | − | 0.551467i | 0.252038 | − | 0.967717i | \(-0.418899\pi\) |
−0.909250 | + | 0.416251i | \(0.863344\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.86125 | − | 1.40538i | −1.45941 | − | 0.531184i | −0.514211 | − | 0.857664i | \(-0.671915\pi\) |
−0.945204 | + | 0.326480i | \(0.894137\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.34920 | + | 3.64942i | −1.31133 | + | 1.10034i | −0.323269 | + | 0.946307i | \(0.604782\pi\) |
−0.988066 | + | 0.154033i | \(0.950774\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.251022 | + | 1.42362i | −0.0696210 | + | 0.394840i | 0.930006 | + | 0.367543i | \(0.119801\pi\) |
−0.999627 | + | 0.0272969i | \(0.991310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.36924 | + | 2.37159i | −0.332089 | + | 0.575195i | −0.982921 | − | 0.184026i | \(-0.941087\pi\) |
0.650832 | + | 0.759222i | \(0.274420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.54610 | − | 4.40998i | −0.584116 | − | 1.01172i | −0.994985 | − | 0.100025i | \(-0.968108\pi\) |
0.410869 | − | 0.911695i | \(-0.365226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.42643 | − | 1.61109i | 0.922974 | − | 0.335935i | 0.163553 | − | 0.986535i | \(-0.447705\pi\) |
0.759421 | + | 0.650600i | \(0.225482\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.229178 | − | 1.29973i | −0.0458356 | − | 0.259947i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.768745 | − | 4.35977i | −0.142752 | − | 0.809589i | −0.969144 | − | 0.246494i | \(-0.920722\pi\) |
0.826392 | − | 0.563095i | \(-0.190390\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.06475 | + | 0.387538i | −0.191235 | + | 0.0696039i | −0.435862 | − | 0.900013i | \(-0.643557\pi\) |
0.244627 | + | 0.969617i | \(0.421334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.94138 | + | 6.82668i | 0.666215 | + | 1.15392i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.97441 | − | 3.41977i | 0.324590 | − | 0.562207i | −0.656839 | − | 0.754031i | \(-0.728107\pi\) |
0.981429 | + | 0.191824i | \(0.0614403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0493888 | − | 0.280098i | 0.00771323 | − | 0.0437439i | −0.980708 | − | 0.195477i | \(-0.937374\pi\) |
0.988421 | + | 0.151733i | \(0.0484855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.90028 | + | 4.11182i | −0.747286 | + | 0.627047i | −0.934784 | − | 0.355218i | \(-0.884407\pi\) |
0.187498 | + | 0.982265i | \(0.439962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.79555 | − | 2.10941i | −0.845368 | − | 0.307689i | −0.117218 | − | 0.993106i | \(-0.537398\pi\) |
−0.728150 | + | 0.685417i | \(0.759620\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.57184 | + | 6.35352i | 1.08169 | + | 0.907646i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.16159 | 1.12108 | 0.560540 | − | 0.828127i | \(-0.310594\pi\) | ||||
0.560540 | + | 0.828127i | \(0.310594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8916 | 1.46863 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8951 | − | 9.14210i | −1.41843 | − | 1.19020i | −0.952177 | − | 0.305546i | \(-0.901161\pi\) |
−0.466248 | − | 0.884654i | \(-0.654395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76413 | + | 1.00606i | 0.353910 | + | 0.128813i | 0.512856 | − | 0.858475i | \(-0.328587\pi\) |
−0.158946 | + | 0.987287i | \(0.550810\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.12438 | − | 1.78257i | 0.263497 | − | 0.221100i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.14911 | + | 12.1882i | −0.262556 | + | 1.48903i | 0.513350 | + | 0.858179i | \(0.328404\pi\) |
−0.775906 | + | 0.630848i | \(0.782707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.15719 | − | 5.46842i | 0.374690 | − | 0.648982i | −0.615591 | − | 0.788066i | \(-0.711082\pi\) |
0.990281 | + | 0.139084i | \(0.0444158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.36669 | + | 4.09923i | 0.277000 | + | 0.479779i | 0.970638 | − | 0.240545i | \(-0.0773263\pi\) |
−0.693637 | + | 0.720324i | \(0.743993\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.9222 | − | 7.97902i | 2.49826 | − | 0.909293i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.09121 | − | 6.18856i | −0.122771 | − | 0.696267i | −0.982607 | − | 0.185697i | \(-0.940546\pi\) |
0.859836 | − | 0.510570i | \(-0.170566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.82134 | + | 16.0006i | 0.309683 | + | 1.75630i | 0.600600 | + | 0.799550i | \(0.294929\pi\) |
−0.290917 | + | 0.956748i | \(0.593960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.93664 | − | 1.79679i | 0.535454 | − | 0.194889i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.02796 | − | 1.78048i | −0.108963 | − | 0.188730i | 0.806387 | − | 0.591388i | \(-0.201420\pi\) |
−0.915351 | + | 0.402658i | \(0.868086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.96998 | − | 5.14416i | 0.311338 | − | 0.539254i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69634 | + | 9.62043i | −0.174041 | + | 0.987035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.00867542 | − | 0.00727954i | 0.000880855 | − | 0.000739125i | −0.642347 | − | 0.766414i | \(-0.722039\pi\) |
0.643228 | + | 0.765675i | \(0.277595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.55554 | − | 0.930139i | −0.254285 | − | 0.0925523i | 0.211732 | − | 0.977328i | \(-0.432089\pi\) |
−0.466018 | + | 0.884775i | \(0.654312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.93683 | − | 2.46429i | −0.289374 | − | 0.242814i | 0.486531 | − | 0.873663i | \(-0.338262\pi\) |
−0.775905 | + | 0.630850i | \(0.782706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.63565 | −0.254798 | −0.127399 | − | 0.991852i | \(-0.540663\pi\) | ||||
−0.127399 | + | 0.991852i | \(0.540663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3548 | −1.37494 | −0.687470 | − | 0.726212i | \(-0.741279\pi\) | ||||
−0.687470 | + | 0.726212i | \(0.741279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.23122 | − | 1.03312i | −0.115824 | − | 0.0971877i | 0.583036 | − | 0.812446i | \(-0.301865\pi\) |
−0.698860 | + | 0.715258i | \(0.746309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.49161 | − | 3.09069i | −0.791846 | − | 0.288209i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.61996 | − | 7.23300i | 0.790190 | − | 0.663048i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.68721 | − | 20.9112i | 0.335201 | − | 1.90102i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.06190 | + | 10.4995i | −0.542193 | + | 0.939106i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55302 | + | 9.61811i | 0.492751 | + | 0.853469i | 0.999965 | − | 0.00835083i | \(-0.00265818\pi\) |
−0.507215 | + | 0.861820i | \(0.669325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.47367 | + | 1.62828i | −0.390866 | + | 0.142264i | −0.529975 | − | 0.848014i | \(-0.677799\pi\) |
0.139109 | + | 0.990277i | \(0.455576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.63344 | + | 20.6063i | 0.315059 | + | 1.78679i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.59714 | − | 14.7291i | −0.221888 | − | 1.25839i | −0.868545 | − | 0.495610i | \(-0.834945\pi\) |
0.646657 | − | 0.762781i | \(-0.276167\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.09109 | + | 1.12507i | −0.262183 | + | 0.0954269i | −0.469767 | − | 0.882790i | \(-0.655662\pi\) |
0.207584 | + | 0.978217i | \(0.433440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.10362 | − | 7.10768i | −0.343162 | − | 0.594374i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.24638 | + | 7.35494i | −0.352642 | + | 0.610795i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.09732 | + | 23.2371i | −0.335666 | + | 1.90366i | 0.0848922 | + | 0.996390i | \(0.472945\pi\) |
−0.420558 | + | 0.907266i | \(0.638166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5314 | − | 11.3542i | 1.10117 | − | 0.923992i | 0.103667 | − | 0.994612i | \(-0.466942\pi\) |
0.997503 | + | 0.0706202i | \(0.0224978\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.04261 | + | 0.743449i | 0.164066 | + | 0.0597152i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5813 | − | 9.71789i | −0.924291 | − | 0.775572i | 0.0504927 | − | 0.998724i | \(-0.483921\pi\) |
−0.974784 | + | 0.223152i | \(0.928365\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.3557 | −1.52544 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.2428 | −1.11558 | −0.557789 | − | 0.829983i | \(-0.688350\pi\) | ||||
−0.557789 | + | 0.829983i | \(0.688350\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.9620 | − | 10.0373i | −0.925644 | − | 0.776708i | 0.0493862 | − | 0.998780i | \(-0.484273\pi\) |
−0.975030 | + | 0.222072i | \(0.928718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2523 | + | 3.73154i | 0.788641 | + | 0.287042i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.1113 | + | 8.48440i | −0.768749 | + | 0.645057i | −0.940388 | − | 0.340103i | \(-0.889538\pi\) |
0.171640 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.941705 | + | 5.34067i | −0.0711862 | + | 0.403717i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.82046 | − | 10.0813i | 0.435042 | − | 0.753514i | −0.562257 | − | 0.826962i | \(-0.690067\pi\) |
0.997299 | + | 0.0734481i | \(0.0234003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.69794 | − | 15.0653i | −0.646513 | − | 1.11979i | −0.983950 | − | 0.178445i | \(-0.942893\pi\) |
0.337437 | − | 0.941348i | \(-0.390440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.11851 | + | 2.59092i | −0.523363 | + | 0.190489i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.69982 | − | 15.3115i | −0.197431 | − | 1.11968i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.890593 | + | 5.05080i | 0.0644410 | + | 0.365463i | 0.999927 | + | 0.0120989i | \(0.00385130\pi\) |
−0.935486 | + | 0.353364i | \(0.885038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6739 | + | 4.24897i | −0.840309 | + | 0.305847i | −0.726083 | − | 0.687607i | \(-0.758661\pi\) |
−0.114226 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.45190 | − | 7.71091i | −0.317185 | − | 0.549380i | 0.662715 | − | 0.748872i | \(-0.269404\pi\) |
−0.979899 | + | 0.199492i | \(0.936071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.393080 | + | 0.680834i | −0.0278647 | + | 0.0482631i | −0.879621 | − | 0.475674i | \(-0.842204\pi\) |
0.851757 | + | 0.523937i | \(0.175537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.15881 | + | 17.9145i | −0.221705 | + | 1.25735i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.417973 | + | 0.350721i | −0.0291925 | + | 0.0244954i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.1674 | + | 9.88812i | 1.87921 | + | 0.683976i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.35690 | − | 1.97768i | −0.162256 | − | 0.136149i | 0.558045 | − | 0.829811i | \(-0.311552\pi\) |
−0.720301 | + | 0.693662i | \(0.755996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.2717 | 0.836921 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.65591 | 0.316064 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.03253 | − | 2.54459i | −0.203990 | − | 0.171168i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1923 | + | 4.43765i | 0.816459 | + | 0.297167i | 0.716289 | − | 0.697804i | \(-0.245839\pi\) |
0.100170 | + | 0.994970i | \(0.468061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.67917 | − | 3.08719i | 0.244195 | − | 0.204904i | −0.512473 | − | 0.858704i | \(-0.671270\pi\) |
0.756668 | + | 0.653799i | \(0.226826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.52222 | − | 8.63293i | 0.100591 | − | 0.570480i | −0.892299 | − | 0.451445i | \(-0.850909\pi\) |
0.992890 | − | 0.119035i | \(-0.0379801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.99833 | − | 3.46120i | 0.130915 | − | 0.226751i | −0.793115 | − | 0.609072i | \(-0.791542\pi\) |
0.924029 | + | 0.382321i | \(0.124875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.91583 | + | 10.2465i | 0.385906 | + | 0.668409i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.08212 | − | 2.57768i | 0.458105 | − | 0.166736i | −0.102652 | − | 0.994717i | \(-0.532733\pi\) |
0.560756 | + | 0.827981i | \(0.310510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.67523 | − | 9.50068i | −0.107911 | − | 0.611993i | −0.990018 | − | 0.140943i | \(-0.954986\pi\) |
0.882107 | − | 0.471049i | \(-0.156125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.29272 | − | 18.6739i | −0.210364 | − | 1.19303i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.91725 | − | 2.51767i | 0.440134 | − | 0.160196i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.24195 | − | 2.15112i | −0.0783912 | − | 0.135778i | 0.824165 | − | 0.566350i | \(-0.191645\pi\) |
−0.902556 | + | 0.430573i | \(0.858312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.3719 | + | 23.1608i | −0.840684 | + | 1.45611i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.72311 | + | 15.4435i | −0.169863 | + | 0.963340i | 0.774045 | + | 0.633131i | \(0.218230\pi\) |
−0.943908 | + | 0.330209i | \(0.892881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4297 | + | 10.4298i | −0.772347 | + | 0.648076i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2643 | + | 4.09987i | 0.694586 | + | 0.252809i | 0.665098 | − | 0.746756i | \(-0.268390\pi\) |
0.0294886 | + | 0.999565i | \(0.490612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.9940 | − | 10.0642i | −0.736788 | − | 0.618238i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.7528 | −1.20435 | −0.602174 | − | 0.798365i | \(-0.705699\pi\) | ||||
−0.602174 | + | 0.798365i | \(0.705699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.61217 | 0.401661 | 0.200830 | − | 0.979626i | \(-0.435636\pi\) | ||||
0.200830 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.74001 | + | 4.81644i | 0.346135 | + | 0.290442i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0116 | + | 5.46379i | 0.901962 | + | 0.328287i | 0.751039 | − | 0.660258i | \(-0.229553\pi\) |
0.150923 | + | 0.988545i | \(0.451775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.34624 | − | 5.32513i | 0.378585 | − | 0.317671i | −0.433562 | − | 0.901124i | \(-0.642743\pi\) |
0.812147 | + | 0.583453i | \(0.198299\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.99620 | − | 16.9923i | 0.178106 | − | 1.01009i | −0.756392 | − | 0.654118i | \(-0.773040\pi\) |
0.934498 | − | 0.355969i | \(-0.115849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.584346 | + | 1.01212i | −0.0344928 | + | 0.0597434i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.75037 | + | 8.22788i | 0.279434 | + | 0.483993i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0989 | − | 3.67569i | 0.589983 | − | 0.214736i | −0.0297390 | − | 0.999558i | \(-0.509468\pi\) |
0.619722 | + | 0.784821i | \(0.287245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.73789 | + | 26.8699i | 0.275851 | + | 1.56443i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.18244 | + | 6.70595i | 0.0683823 | + | 0.387815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.6999 | − | 8.99002i | 1.42368 | − | 0.518176i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.82149 | − | 4.88696i | −0.161558 | − | 0.279827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.32872 | + | 2.30142i | −0.0758343 | + | 0.131349i | −0.901449 | − | 0.432886i | \(-0.857495\pi\) |
0.825614 | + | 0.564235i | \(0.190829\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.98755 | − | 33.9571i | 0.339523 | − | 1.92553i | −0.0374342 | − | 0.999299i | \(-0.511918\pi\) |
0.376957 | − | 0.926231i | \(-0.376970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.70435 | − | 8.14292i | 0.548522 | − | 0.460265i | −0.325918 | − | 0.945398i | \(-0.605673\pi\) |
0.874440 | + | 0.485133i | \(0.161229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.26564 | − | 3.00845i | −0.464244 | − | 0.168971i | 0.0992989 | − | 0.995058i | \(-0.468340\pi\) |
−0.563543 | + | 0.826087i | \(0.690562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2540 | + | 16.1561i | 1.07802 | + | 0.904565i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9449 | 0.775915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.90785 | 0.105828 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.4135 | + | 16.2899i | 1.07030 | + | 0.898091i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1353 | + | 4.05290i | 0.612049 | + | 0.222768i | 0.629400 | − | 0.777082i | \(-0.283301\pi\) |
−0.0173504 | + | 0.999849i | \(0.505523\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.1878 | − | 15.2613i | 0.993704 | − | 0.833816i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.26880 | + | 18.5383i | −0.178063 | + | 1.00984i | 0.756486 | + | 0.654009i | \(0.226914\pi\) |
−0.934549 | + | 0.355834i | \(0.884197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.21654 | − | 5.57120i | 0.174185 | − | 0.301698i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.92593 | − | 10.2640i | −0.319970 | − | 0.554205i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.61122 | − | 1.31438i | 0.193861 | − | 0.0705595i | −0.243265 | − | 0.969960i | \(-0.578219\pi\) |
0.437126 | + | 0.899400i | \(0.355996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.642364 | − | 3.64303i | −0.0343850 | − | 0.195007i | 0.962777 | − | 0.270298i | \(-0.0871224\pi\) |
−0.997162 | + | 0.0752915i | \(0.976011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.34505 | + | 13.2995i | 0.124815 | + | 0.707859i | 0.981418 | + | 0.191883i | \(0.0614595\pi\) |
−0.856603 | + | 0.515976i | \(0.827429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.3829 | + | 4.14304i | −0.604143 | + | 0.219890i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.38794 | − | 14.5283i | −0.442699 | − | 0.766777i | 0.555190 | − | 0.831724i | \(-0.312646\pi\) |
−0.997889 | + | 0.0649470i | \(0.979312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.46530 | + | 6.00207i | −0.182384 | + | 0.315898i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.57681 | − | 8.94252i | 0.0825339 | − | 0.468073i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8640 | − | 11.6333i | 0.723695 | − | 0.607252i | −0.204710 | − | 0.978823i | \(-0.565625\pi\) |
0.928405 | + | 0.371570i | \(0.121181\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.5139 | − | 11.4701i | −1.63612 | − | 0.595499i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1258 | + | 8.49660i | 0.524297 | + | 0.439937i | 0.866127 | − | 0.499825i | \(-0.166602\pi\) |
−0.341830 | + | 0.939762i | \(0.611047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.39961 | 0.329597 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.8219 | 1.63458 | 0.817289 | − | 0.576227i | \(-0.195476\pi\) | ||||
0.817289 | + | 0.576227i | \(0.195476\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.16826 | − | 3.49758i | −0.212988 | − | 0.178718i | 0.530052 | − | 0.847965i | \(-0.322172\pi\) |
−0.743040 | + | 0.669247i | \(0.766617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −42.0553 | − | 15.3069i | −2.14333 | − | 0.780110i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.9094 | + | 9.99317i | −0.603831 | + | 0.506674i | −0.892674 | − | 0.450702i | \(-0.851174\pi\) |
0.288844 | + | 0.957376i | \(0.406729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23999 | + | 12.7036i | −0.113281 | + | 0.642450i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.02761 | + | 10.4401i | −0.303282 | + | 0.525299i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.11698 | − | 15.7911i | −0.457568 | − | 0.792531i | 0.541264 | − | 0.840853i | \(-0.317946\pi\) |
−0.998832 | + | 0.0483217i | \(0.984613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.0083 | + | 12.0140i | −1.64836 | + | 0.599953i | −0.988471 | − | 0.151413i | \(-0.951618\pi\) |
−0.659886 | + | 0.751366i | \(0.729395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.284429 | − | 1.61308i | −0.0141684 | − | 0.0803532i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.89307 | + | 22.0787i | 0.192972 | + | 1.09440i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.1161 | + | 11.3253i | −1.53859 | + | 0.560001i | −0.965707 | − | 0.259636i | \(-0.916398\pi\) |
−0.572884 | + | 0.819637i | \(0.694175\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.2207 | + | 50.6117i | 1.43786 | + | 2.49044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.5845 | − | 26.9931i | 0.765012 | − | 1.32504i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.567077 | − | 3.21606i | 0.0277035 | − | 0.157115i | −0.967818 | − | 0.251652i | \(-0.919026\pi\) |
0.995521 | + | 0.0945375i | \(0.0301372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0256 | + | 14.2861i | −0.829775 | + | 0.696264i | −0.955239 | − | 0.295835i | \(-0.904402\pi\) |
0.125465 | + | 0.992098i | \(0.459958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.39623 | + | 1.23613i | 0.164742 | + | 0.0599610i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.25908 | − | 7.76929i | −0.448078 | − | 0.375982i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.4064 | 1.12744 | 0.563722 | − | 0.825964i | \(-0.309369\pi\) | ||||
0.563722 | + | 0.825964i | \(0.309369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.5736 | −0.988706 | −0.494353 | − | 0.869261i | \(-0.664595\pi\) | ||||
−0.494353 | + | 0.869261i | \(0.664595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.3750 | − | 15.4185i | −0.878996 | − | 0.737565i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.1780 | − | 11.7118i | −1.53577 | − | 0.558975i | −0.570745 | − | 0.821127i | \(-0.693346\pi\) |
−0.965027 | + | 0.262152i | \(0.915568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.36729 | + | 1.98639i | −0.112473 | + | 0.0943762i | −0.697290 | − | 0.716789i | \(-0.745611\pi\) |
0.584817 | + | 0.811166i | \(0.301166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.684877 | + | 3.88413i | −0.0324663 | + | 0.184125i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.22660 | − | 3.85659i | 0.105080 | − | 0.182004i | −0.808691 | − | 0.588234i | \(-0.799824\pi\) |
0.913771 | + | 0.406230i | \(0.133157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.807391 | + | 1.39844i | 0.0380186 | + | 0.0658501i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7079 | + | 3.89737i | −0.501996 | + | 0.182712i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.27178 | − | 7.21262i | −0.0594913 | − | 0.337392i | 0.940506 | − | 0.339778i | \(-0.110352\pi\) |
−0.999997 | + | 0.00238542i | \(0.999241\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58659 | − | 14.6693i | −0.120470 | − | 0.683217i | −0.983896 | − | 0.178742i | \(-0.942797\pi\) |
0.863426 | − | 0.504475i | \(-0.168314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59572 | − | 2.76462i | 0.353003 | − | 0.128483i | −0.159431 | − | 0.987209i | \(-0.550966\pi\) |
0.512434 | + | 0.858726i | \(0.328744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.02480 | + | 6.97116i | 0.186246 | + | 0.322587i | 0.943996 | − | 0.329958i | \(-0.107035\pi\) |
−0.757750 | + | 0.652545i | \(0.773701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.4273 | − | 44.0414i | 1.17412 | − | 2.03364i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.30657 | − | 35.7663i | 0.289976 | − | 1.64454i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.14829 | + | 4.31993i | −0.236220 | + | 0.198212i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.2766 | − | 14.6595i | −1.84029 | − | 0.669809i | −0.989545 | − | 0.144224i | \(-0.953931\pi\) |
−0.850741 | − | 0.525585i | \(-0.823846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.37282 | + | 3.66923i | 0.199384 | + | 0.167303i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0217257 | −0.000986511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.79142 | −0.217120 | −0.108560 | − | 0.994090i | \(-0.534624\pi\) | ||||
−0.108560 | + | 0.994090i | \(0.534624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.1356 | + | 16.0567i | 0.863576 | + | 0.724627i | 0.962735 | − | 0.270445i | \(-0.0871708\pi\) |
−0.0991590 | + | 0.995072i | \(0.531615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3922 | + | 4.14641i | 0.513078 | + | 0.186745i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.8759 | + | 16.6779i | −0.891557 | + | 0.748105i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.04732 | + | 5.93966i | −0.0468845 | + | 0.265895i | −0.999235 | − | 0.0391108i | \(-0.987547\pi\) |
0.952350 | + | 0.305006i | \(0.0986586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.74621 | + | 15.1489i | −0.389974 | + | 0.675455i | −0.992446 | − | 0.122685i | \(-0.960849\pi\) |
0.602472 | + | 0.798140i | \(0.294183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.60857 | + | 4.51818i | 0.116080 | + | 0.201056i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1790 | − | 4.06882i | 0.495500 | − | 0.180347i | −0.0821690 | − | 0.996618i | \(-0.526185\pi\) |
0.577669 | + | 0.816271i | \(0.303963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.37741 | − | 19.1543i | −0.149408 | − | 0.847334i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.27712 | + | 7.24290i | 0.0562766 | + | 0.319160i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.9041 | − | 11.9761i | 1.44712 | − | 0.526710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.51200 | − | 9.54706i | −0.241485 | − | 0.418264i | 0.719652 | − | 0.694334i | \(-0.244301\pi\) |
−0.961138 | + | 0.276070i | \(0.910968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.7734 | + | 30.7844i | −0.777175 | + | 1.34611i | 0.156388 | + | 0.987696i | \(0.450015\pi\) |
−0.933564 | + | 0.358412i | \(0.883318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.538818 | − | 3.05579i | 0.0234713 | − | 0.133112i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.621378 | + | 0.521398i | −0.0270164 | + | 0.0226695i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.386354 | + | 0.140621i | 0.0167349 | + | 0.00609099i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.87328 | + | 3.25007i | 0.167456 | + | 0.140513i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −56.1181 | −2.41718 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1225 | −0.607173 | −0.303586 | − | 0.952804i | \(-0.598184\pi\) | ||||
−0.303586 | + | 0.952804i | \(0.598184\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0954 | + | 17.7011i | 0.903628 | + | 0.758234i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.14230 | − | 3.32752i | −0.390896 | − | 0.142275i | 0.139092 | − | 0.990279i | \(-0.455582\pi\) |
−0.529989 | + | 0.848005i | \(0.677804\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.2692 | + | 14.4906i | −0.735692 | + | 0.617319i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.48384 | + | 25.4291i | −0.190672 | + | 1.08136i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0204 | + | 19.0878i | −0.466948 | + | 0.808777i | −0.999287 | − | 0.0377541i | \(-0.987980\pi\) |
0.532340 | + | 0.846531i | \(0.321313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.62358 | − | 8.00828i | −0.195557 | − | 0.338714i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.7726 | + | 5.37678i | −0.622590 | + | 0.226604i | −0.634003 | − | 0.773331i | \(-0.718589\pi\) |
0.0114132 | + | 0.999935i | \(0.496367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.535414 | + | 3.03649i | 0.0225251 | + | 0.127746i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.99337 | − | 33.9901i | −0.251255 | − | 1.42494i | −0.805505 | − | 0.592589i | \(-0.798106\pi\) |
0.554250 | − | 0.832350i | \(-0.313005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.9253 | + | 9.43603i | −1.08494 | + | 0.394885i | −0.821744 | − | 0.569857i | \(-0.806999\pi\) |
−0.263195 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.10842 | − | 5.38395i | −0.129630 | − | 0.224526i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3911 | − | 35.3184i | 0.848893 | − | 1.47033i | −0.0333036 | − | 0.999445i | \(-0.510603\pi\) |
0.882197 | − | 0.470881i | \(-0.156064\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.5931 | − | 65.7475i | 0.480961 | − | 2.72767i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.4964 | + | 29.7850i | −1.47011 | + | 1.23357i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.6219 | + | 4.23001i | 0.479685 | + | 0.174591i | 0.570535 | − | 0.821274i | \(-0.306736\pi\) |
−0.0908495 | + | 0.995865i | \(0.528958\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.42000 | + | 3.70882i | 0.182123 | + | 0.152819i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9594 | 1.27135 | 0.635674 | − | 0.771957i | \(-0.280722\pi\) | ||||
0.635674 | + | 0.771957i | \(0.280722\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.5868 | −0.884971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6214 | + | 18.9816i | 0.924286 | + | 0.775568i | 0.974783 | − | 0.223157i | \(-0.0716361\pi\) |
−0.0504971 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9678 | + | 6.53974i | 0.732922 | + | 0.266762i | 0.681401 | − | 0.731910i | \(-0.261371\pi\) |
0.0515206 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.2046 | + | 26.1838i | −1.26865 | + | 1.06452i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.26774 | − | 29.8748i | 0.213811 | − | 1.21258i | −0.669147 | − | 0.743130i | \(-0.733340\pi\) |
0.882958 | − | 0.469452i | \(-0.155549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.45780 | − | 7.72113i | 0.180343 | − | 0.312364i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.9327 | + | 34.5245i | 0.805075 | + | 1.39443i | 0.916240 | + | 0.400629i | \(0.131208\pi\) |
−0.111165 | + | 0.993802i | \(0.535458\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4318 | + | 5.98068i | −0.661519 | + | 0.240773i | −0.650892 | − | 0.759170i | \(-0.725605\pi\) |
−0.0106270 | + | 0.999944i | \(0.503383\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.81674 | − | 21.6458i | −0.153408 | − | 0.870019i | −0.960227 | − | 0.279220i | \(-0.909924\pi\) |
0.806819 | − | 0.590798i | \(-0.201187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.46696 | + | 8.31953i | 0.0587724 | + | 0.333315i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6546 | − | 5.69780i | 0.626183 | − | 0.227912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.40686 | + | 9.36496i | 0.215586 | + | 0.373406i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.224323 | − | 0.388538i | 0.00893014 | − | 0.0154675i | −0.861526 | − | 0.507714i | \(-0.830491\pi\) |
0.870456 | + | 0.492246i | \(0.163824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.69969 | − | 20.9820i | 0.146818 | − | 0.832646i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9457 | + | 9.18452i | −0.433684 | + | 0.363904i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.4938 | + | 15.4665i | 1.67840 | + | 0.610889i | 0.993089 | − | 0.117360i | \(-0.0374430\pi\) |
0.685313 | + | 0.728248i | \(0.259665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.4317 | + | 17.1442i | 0.805747 | + | 0.676102i | 0.949589 | − | 0.313499i | \(-0.101501\pi\) |
−0.143842 | + | 0.989601i | \(0.545946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.1104 | 1.34102 | 0.670508 | − | 0.741902i | \(-0.266076\pi\) | ||||
0.670508 | + | 0.741902i | \(0.266076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 80.7485 | 3.16965 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.14784 | + | 1.80225i | 0.0840514 | + | 0.0705275i | 0.683845 | − | 0.729627i | \(-0.260306\pi\) |
−0.599794 | + | 0.800155i | \(0.704751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.58223 | + | 3.12368i | 0.335336 | + | 0.122052i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.6755 | − | 28.2571i | 1.31181 | − | 1.10074i | 0.323840 | − | 0.946112i | \(-0.395026\pi\) |
0.987972 | − | 0.154630i | \(-0.0494185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.685986 | − | 3.89042i | 0.0266818 | − | 0.151320i | −0.968556 | − | 0.248795i | \(-0.919965\pi\) |
0.995238 | + | 0.0974750i | \(0.0310766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.0703 | − | 34.7629i | 0.778295 | − | 1.34805i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4268 | − | 18.0597i | −0.403726 | − | 0.699273i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.6933 | + | 5.71188i | −0.605832 | + | 0.220505i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.65507 | − | 9.38639i | −0.0637984 | − | 0.361819i | −0.999948 | − | 0.0102164i | \(-0.996748\pi\) |
0.936149 | − | 0.351603i | \(-0.114363\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.22825 | − | 6.96575i | −0.0472055 | − | 0.267716i | 0.952065 | − | 0.305894i | \(-0.0989555\pi\) |
−0.999271 | + | 0.0381788i | \(0.987844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0437284 | + | 0.0159159i | −0.00167814 | + | 0.000610794i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.9236 | + | 37.9729i | 0.838885 | + | 1.45299i | 0.890828 | + | 0.454341i | \(0.150125\pi\) |
−0.0519432 | + | 0.998650i | \(0.516541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.3460 | + | 24.8480i | −0.548133 | + | 0.949394i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.04874 | + | 11.6190i | −0.0780507 | + | 0.442648i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5288 | − | 23.9385i | 1.08529 | − | 0.910663i | 0.0889369 | − | 0.996037i | \(-0.471653\pi\) |
0.996349 | + | 0.0853743i | \(0.0272086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.92992 | + | 2.15832i | 0.224935 | + | 0.0818696i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.596652 | + | 0.500651i | 0.0225998 | + | 0.0189635i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.6893 | 1.34797 | 0.673984 | − | 0.738746i | \(-0.264582\pi\) | ||||
0.673984 | + | 0.738746i | \(0.264582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.1082 | −0.758394 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.56036 | + | 7.18299i | 0.321945 | + | 0.270144i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.6583 | − | 16.9822i | −1.75229 | − | 0.637781i | −0.752507 | − | 0.658585i | \(-0.771155\pi\) |
−0.999784 | + | 0.0208033i | \(0.993378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.08869 | + | 3.43082i | −0.153123 | + | 0.128485i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.73404 | + | 15.5055i | −0.102247 | + | 0.579873i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.92100 | + | 15.4516i | −0.332697 | + | 0.576248i | −0.983040 | − | 0.183393i | \(-0.941292\pi\) |
0.650343 | + | 0.759641i | \(0.274625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.87655 | + | 13.6426i | 0.293338 | + | 0.508077i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.49035 | + | 1.99833i | −0.203907 | + | 0.0742160i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.88271 | + | 44.7051i | 0.292354 | + | 1.65802i | 0.677768 | + | 0.735276i | \(0.262947\pi\) |
−0.385414 | + | 0.922744i | \(0.625941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.04191 | − | 17.2515i | −0.112509 | − | 0.638071i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.0003 | + | 13.1031i | −1.32970 | + | 0.483972i | −0.906555 | − | 0.422088i | \(-0.861297\pi\) |
−0.423148 | + | 0.906061i | \(0.639075\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.1329 | − | 60.8520i | −1.29414 | − | 2.24151i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0715 | − | 17.4443i | 0.370485 | − | 0.641698i | −0.619156 | − | 0.785268i | \(-0.712525\pi\) |
0.989640 | + | 0.143570i | \(0.0458583\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.0950690 | + | 0.539163i | −0.00348774 | + | 0.0197800i | −0.986502 | − | 0.163749i | \(-0.947641\pi\) |
0.983014 | + | 0.183529i | \(0.0587523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.6753 | − | 29.0961i | 1.27041 | − | 1.06600i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1769 | + | 3.70409i | 0.371856 | + | 0.135345i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.4772 | − | 23.0561i | −1.00266 | − | 0.841328i | −0.0153056 | − | 0.999883i | \(-0.504872\pi\) |
−0.987350 | + | 0.158555i | \(0.949317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.8864 | −1.23325 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.7777 | −0.682486 | −0.341243 | − | 0.939975i | \(-0.610848\pi\) | ||||
−0.341243 | + | 0.939975i | \(0.610848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.66973 | − | 3.91837i | −0.169278 | − | 0.142041i | 0.554213 | − | 0.832375i | \(-0.313019\pi\) |
−0.723491 | + | 0.690334i | \(0.757464\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 55.4275 | + | 20.1739i | 2.00661 | + | 0.730346i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.7498 | − | 13.2156i | 0.568691 | − | 0.477188i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.30566 | + | 47.1037i | −0.299510 | + | 1.69860i | 0.348776 | + | 0.937206i | \(0.386597\pi\) |
−0.648285 | + | 0.761397i | \(0.724514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.33612 | − | 16.1706i | 0.335797 | − | 0.581617i | −0.647841 | − | 0.761776i | \(-0.724328\pi\) |
0.983638 | + | 0.180159i | \(0.0576611\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.747714 | + | 1.29508i | 0.0268587 | + | 0.0465206i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.36097 | + | 0.495354i | −0.0487620 | + | 0.0177479i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.22526 | + | 35.3052i | 0.222757 | + | 1.26332i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.03630 | + | 28.5623i | 0.179753 | + | 1.01943i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.9691 | − | 14.1836i | 1.38910 | − | 0.505591i | 0.464176 | − | 0.885743i | \(-0.346351\pi\) |
0.924924 | + | 0.380152i | \(0.124128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.30214 | + | 5.71947i | 0.117410 | + | 0.203361i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.12610 | + | 3.68251i | −0.0755000 | + | 0.130770i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.10235 | + | 17.5943i | −0.109891 | + | 0.623222i | 0.879263 | + | 0.476337i | \(0.158036\pi\) |
−0.989154 | + | 0.146885i | \(0.953075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9381 | − | 10.8564i | 0.457719 | − | 0.384072i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.2530 | − | 9.19135i | −0.891160 | − | 0.324356i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.4446 | + | 23.8679i | 1.00254 | + | 0.841232i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.9533 | −0.842153 | −0.421076 | − | 0.907025i | \(-0.638348\pi\) | ||||
−0.421076 | + | 0.907025i | \(0.638348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0602 | −0.669294 | −0.334647 | − | 0.942344i | \(-0.608617\pi\) | ||||
−0.334647 | + | 0.942344i | \(0.608617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.9307 | + | 17.5630i | 0.733172 | + | 0.615204i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.6097 | + | 11.1410i | 1.07090 | + | 0.389775i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4864 | − | 15.5119i | 0.645178 | − | 0.541369i | −0.260425 | − | 0.965494i | \(-0.583863\pi\) |
0.905604 | + | 0.424125i | \(0.139418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.74245 | − | 49.5809i | 0.304743 | − | 1.72828i | −0.319972 | − | 0.947427i | \(-0.603673\pi\) |
0.624714 | − | 0.780854i | \(-0.285216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.21235 | + | 3.83190i | −0.0769310 | + | 0.133248i | −0.901924 | − | 0.431894i | \(-0.857845\pi\) |
0.824993 | + | 0.565142i | \(0.191179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.40772 | − | 16.2947i | −0.326744 | − | 0.565937i | 0.655120 | − | 0.755525i | \(-0.272618\pi\) |
−0.981864 | + | 0.189588i | \(0.939285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.4356 | + | 9.25781i | −0.881292 | + | 0.320764i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.20182 | + | 29.5010i | 0.180016 | + | 1.02092i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.78845 | − | 27.1567i | −0.165316 | − | 0.937553i | −0.948738 | − | 0.316063i | \(-0.897639\pi\) |
0.783422 | − | 0.621490i | \(-0.213472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.83448 | − | 3.21549i | 0.304637 | − | 0.110879i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4651 | − | 18.1261i | −0.360011 | − | 0.623556i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.6254 | + | 75.5615i | −1.49899 | + | 2.59632i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.23001 | − | 18.3183i | 0.110723 | − | 0.627943i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0781 | − | 13.4911i | 0.550504 | − | 0.461928i | −0.324608 | − | 0.945849i | \(-0.605232\pi\) |
0.875112 | + | 0.483921i | \(0.160788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.88556 | + | 2.14217i | 0.201047 | + | 0.0731751i | 0.440581 | − | 0.897713i | \(-0.354772\pi\) |
−0.239534 | + | 0.970888i | \(0.576995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9084 | − | 18.3833i | −0.747505 | − | 0.627232i | 0.187336 | − | 0.982296i | \(-0.440015\pi\) |
−0.934842 | + | 0.355064i | \(0.884459\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.0721 | −1.63639 | −0.818196 | − | 0.574940i | \(-0.805026\pi\) | ||||
−0.818196 | + | 0.574940i | \(0.805026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.3215 | 0.860958 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.3305 | + | 22.9330i | 0.927125 | + | 0.777950i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8119 | − | 6.11902i | −0.569649 | − | 0.207335i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.1623 | − | 32.0220i | 1.29012 | − | 1.08254i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.92997 | − | 50.6444i | 0.301544 | − | 1.71014i | −0.337800 | − | 0.941218i | \(-0.609683\pi\) |
0.639344 | − | 0.768921i | \(-0.279206\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.25145 | − | 7.36372i | 0.143235 | − | 0.248090i | −0.785478 | − | 0.618889i | \(-0.787583\pi\) |
0.928713 | + | 0.370799i | \(0.120916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.2957 | − | 21.2968i | −0.413784 | − | 0.716695i | 0.581516 | − | 0.813535i | \(-0.302460\pi\) |
−0.995300 | + | 0.0968398i | \(0.969127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.4921 | + | 7.82247i | −0.721633 | + | 0.262653i | −0.676619 | − | 0.736333i | \(-0.736555\pi\) |
−0.0450141 | + | 0.998986i | \(0.514333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.92449 | − | 44.9420i | −0.265779 | − | 1.50731i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.45363 | + | 30.9291i | 0.182499 | + | 1.03500i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.9850 | + | 7.63793i | −0.701453 | + | 0.255308i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.50810 | + | 4.34415i | 0.0836497 | + | 0.144886i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1752 | + | 19.3560i | −0.372299 | + | 0.644840i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.79500 | + | 32.8651i | −0.192632 | + | 1.09247i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8226 | + | 22.5069i | −0.890631 | + | 0.747328i | −0.968337 | − | 0.249648i | \(-0.919685\pi\) |
0.0777056 | + | 0.996976i | \(0.475241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.2243 | − | 9.90882i | −0.901980 | − | 0.328294i | −0.150934 | − | 0.988544i | \(-0.548228\pi\) |
−0.751046 | + | 0.660250i | \(0.770450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −70.6636 | − | 59.2938i | −2.33862 | − | 1.96234i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.5623 | 0.646004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8729 | −1.21632 | −0.608162 | − | 0.793813i | \(-0.708093\pi\) | ||||
−0.608162 | + | 0.793813i | \(0.708093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.99241 | + | 5.86733i | 0.230158 | + | 0.193125i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.89728 | − | 1.78246i | −0.161022 | − | 0.0586070i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.3030 | − | 17.0363i | 0.666121 | − | 0.558942i | −0.245793 | − | 0.969322i | \(-0.579048\pi\) |
0.911915 | + | 0.410380i | \(0.134604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.74025 | − | 49.5684i | 0.286450 | − | 1.62454i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.9132 | + | 25.8305i | −0.487715 | + | 0.844747i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.51461 | + | 6.08749i | 0.114817 | + | 0.198870i | 0.917707 | − | 0.397259i | \(-0.130038\pi\) |
−0.802889 | + | 0.596128i | \(0.796705\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.9101 | + | 9.06653i | −0.812045 | + | 0.295560i | −0.714468 | − | 0.699668i | \(-0.753331\pi\) |
−0.0975769 | + | 0.995228i | \(0.531109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.232646 | − | 1.31940i | −0.00757600 | − | 0.0429656i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.94224 | + | 33.7001i | 0.193097 | + | 1.09511i | 0.915103 | + | 0.403220i | \(0.132109\pi\) |
−0.722006 | + | 0.691887i | \(0.756780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.42983 | + | 2.34027i | −0.208721 | + | 0.0759682i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.88821 | − | 6.73458i | −0.125952 | − | 0.218155i | 0.796153 | − | 0.605095i | \(-0.206865\pi\) |
−0.922105 | + | 0.386941i | \(0.873532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.91944 | − | 8.52072i | 0.159189 | − | 0.275724i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.6718 | + | 60.5226i | −0.344609 | + | 1.95438i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7639 | + | 19.1012i | −0.734318 | + | 0.616166i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.3952 | + | 8.15117i | 0.720926 | + | 0.262396i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.86408 | + | 1.56415i | 0.0599447 | + | 0.0502996i | 0.672268 | − | 0.740308i | \(-0.265320\pi\) |
−0.612323 | + | 0.790608i | \(0.709765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.2097 | −0.905293 | −0.452647 | − | 0.891690i | \(-0.649520\pi\) | ||||
−0.452647 | + | 0.891690i | \(0.649520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.5166 | 0.433323 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.0040 | − | 30.2110i | −1.15187 | − | 0.966534i | −0.152109 | − | 0.988364i | \(-0.548606\pi\) |
−0.999762 | + | 0.0218295i | \(0.993051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.9685 | + | 3.99221i | 0.350555 | + | 0.127592i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.7166 | + | 24.9352i | −0.947812 | + | 0.795309i | −0.978928 | − | 0.204207i | \(-0.934538\pi\) |
0.0311156 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.96607 | + | 16.8214i | −0.0945070 | + | 0.535976i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.0662 | + | 26.0955i | −0.479078 | + | 0.829788i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3763 | + | 17.9722i | 0.329613 | + | 0.570906i | 0.982435 | − | 0.186605i | \(-0.0597484\pi\) |
−0.652822 | + | 0.757511i | \(0.726415\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.41721 | − | 0.515821i | 0.0449285 | − | 0.0163526i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.72919 | − | 49.5057i | −0.276456 | − | 1.56786i | −0.734298 | − | 0.678827i | \(-0.762488\pi\) |
0.457842 | − | 0.889034i | \(-0.348623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.2.i.a.253.2 | 18 | ||
3.2 | odd | 2 | 108.2.i.a.13.2 | ✓ | 18 | ||
9.2 | odd | 6 | 972.2.i.a.109.2 | 18 | |||
9.4 | even | 3 | 972.2.i.b.433.2 | 18 | |||
9.5 | odd | 6 | 972.2.i.c.433.2 | 18 | |||
9.7 | even | 3 | 972.2.i.d.109.2 | 18 | |||
12.11 | even | 2 | 432.2.u.d.337.2 | 18 | |||
27.2 | odd | 18 | 108.2.i.a.25.2 | yes | 18 | ||
27.4 | even | 9 | 2916.2.e.d.1945.6 | 18 | |||
27.5 | odd | 18 | 2916.2.a.d.1.6 | 9 | |||
27.7 | even | 9 | 972.2.i.d.865.2 | 18 | |||
27.11 | odd | 18 | 972.2.i.c.541.2 | 18 | |||
27.13 | even | 9 | 2916.2.e.d.973.6 | 18 | |||
27.14 | odd | 18 | 2916.2.e.c.973.4 | 18 | |||
27.16 | even | 9 | 972.2.i.b.541.2 | 18 | |||
27.20 | odd | 18 | 972.2.i.a.865.2 | 18 | |||
27.22 | even | 9 | 2916.2.a.c.1.4 | 9 | |||
27.23 | odd | 18 | 2916.2.e.c.1945.4 | 18 | |||
27.25 | even | 9 | inner | 324.2.i.a.73.2 | 18 | ||
108.83 | even | 18 | 432.2.u.d.241.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.13.2 | ✓ | 18 | 3.2 | odd | 2 | ||
108.2.i.a.25.2 | yes | 18 | 27.2 | odd | 18 | ||
324.2.i.a.73.2 | 18 | 27.25 | even | 9 | inner | ||
324.2.i.a.253.2 | 18 | 1.1 | even | 1 | trivial | ||
432.2.u.d.241.2 | 18 | 108.83 | even | 18 | |||
432.2.u.d.337.2 | 18 | 12.11 | even | 2 | |||
972.2.i.a.109.2 | 18 | 9.2 | odd | 6 | |||
972.2.i.a.865.2 | 18 | 27.20 | odd | 18 | |||
972.2.i.b.433.2 | 18 | 9.4 | even | 3 | |||
972.2.i.b.541.2 | 18 | 27.16 | even | 9 | |||
972.2.i.c.433.2 | 18 | 9.5 | odd | 6 | |||
972.2.i.c.541.2 | 18 | 27.11 | odd | 18 | |||
972.2.i.d.109.2 | 18 | 9.7 | even | 3 | |||
972.2.i.d.865.2 | 18 | 27.7 | even | 9 | |||
2916.2.a.c.1.4 | 9 | 27.22 | even | 9 | |||
2916.2.a.d.1.6 | 9 | 27.5 | odd | 18 | |||
2916.2.e.c.973.4 | 18 | 27.14 | odd | 18 | |||
2916.2.e.c.1945.4 | 18 | 27.23 | odd | 18 | |||
2916.2.e.d.973.6 | 18 | 27.13 | even | 9 | |||
2916.2.e.d.1945.6 | 18 | 27.4 | even | 9 |