Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(81,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.ba (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 81.3 | ||
Character | \(\chi\) | \(=\) | 448.81 |
Dual form | 448.2.ba.c.177.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.95279 | + | 0.523249i | −1.12744 | + | 0.302098i | −0.773893 | − | 0.633317i | \(-0.781693\pi\) |
−0.353552 | + | 0.935415i | \(0.615026\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.959072 | + | 0.256983i | 0.428910 | + | 0.114926i | 0.466814 | − | 0.884355i | \(-0.345402\pi\) |
−0.0379045 | + | 0.999281i | \(0.512068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.292831 | − | 2.62950i | −0.110680 | − | 0.993856i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.941530 | − | 0.543593i | 0.313843 | − | 0.181198i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.505816 | + | 1.88773i | 0.152509 | + | 0.569172i | 0.999306 | + | 0.0372551i | \(0.0118614\pi\) |
−0.846797 | + | 0.531917i | \(0.821472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.10314 | − | 2.10314i | −0.583307 | − | 0.583307i | 0.352504 | − | 0.935810i | \(-0.385330\pi\) |
−0.935810 | + | 0.352504i | \(0.885330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00733 | −0.518291 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.83885 | − | 4.91704i | 0.688523 | − | 1.19256i | −0.283792 | − | 0.958886i | \(-0.591593\pi\) |
0.972316 | − | 0.233672i | \(-0.0750741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.165210 | − | 0.616573i | 0.0379018 | − | 0.141451i | −0.944382 | − | 0.328850i | \(-0.893339\pi\) |
0.982284 | + | 0.187399i | \(0.0600056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.94772 | + | 4.98163i | 0.425027 | + | 1.08708i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.92691 | − | 3.42190i | 1.23585 | − | 0.713516i | 0.267604 | − | 0.963529i | \(-0.413768\pi\) |
0.968243 | + | 0.250013i | \(0.0804348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47635 | − | 2.00707i | −0.695270 | − | 0.401414i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.73445 | − | 2.73445i | 0.526245 | − | 0.526245i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.207295 | − | 0.207295i | −0.0384937 | − | 0.0384937i | 0.687598 | − | 0.726092i | \(-0.258665\pi\) |
−0.726092 | + | 0.687598i | \(0.758665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.94693 | − | 6.83628i | 0.708889 | − | 1.22783i | −0.256381 | − | 0.966576i | \(-0.582530\pi\) |
0.965270 | − | 0.261255i | \(-0.0841365\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.97551 | − | 3.42168i | −0.343891 | − | 0.595637i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.394889 | − | 2.59713i | 0.0667484 | − | 0.438995i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.60533 | + | 2.57374i | 1.57911 | + | 0.423120i | 0.938649 | − | 0.344873i | \(-0.112078\pi\) |
0.640457 | + | 0.767994i | \(0.278745\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.20747 | + | 3.00653i | 0.833862 | + | 0.481430i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.40202i | − | 0.375132i | −0.982252 | − | 0.187566i | \(-0.939940\pi\) | ||
0.982252 | − | 0.187566i | \(-0.0600599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.65586 | + | 3.65586i | −0.557514 | + | 0.557514i | −0.928599 | − | 0.371085i | \(-0.878986\pi\) |
0.371085 | + | 0.928599i | \(0.378986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.04269 | − | 0.279388i | 0.155435 | − | 0.0416486i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.144593 | + | 0.250442i | 0.0210910 | + | 0.0365307i | 0.876378 | − | 0.481623i | \(-0.159953\pi\) |
−0.855287 | + | 0.518154i | \(0.826619\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82850 | + | 1.53999i | −0.975500 | + | 0.219999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.97086 | + | 11.0874i | −0.416003 | + | 1.55254i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.04376 | − | 7.62740i | −0.280732 | − | 1.04770i | −0.951902 | − | 0.306402i | \(-0.900875\pi\) |
0.671171 | − | 0.741303i | \(-0.265792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.94045i | 0.261651i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.29048i | 0.170929i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.60507 | − | 13.4543i | −0.469340 | − | 1.75160i | −0.642084 | − | 0.766634i | \(-0.721930\pi\) |
0.172744 | − | 0.984967i | \(-0.444737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.969174 | + | 3.61701i | −0.124090 | + | 0.463110i | −0.999806 | − | 0.0197171i | \(-0.993723\pi\) |
0.875716 | + | 0.482827i | \(0.160390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.70508 | − | 2.31657i | −0.214820 | − | 0.291860i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.47659 | − | 2.55754i | −0.183149 | − | 0.317223i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0468 | + | 2.69202i | −1.22741 | + | 0.328883i | −0.813570 | − | 0.581467i | \(-0.802479\pi\) |
−0.413838 | + | 0.910350i | \(0.635812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.78352 | + | 9.78352i | −1.17780 | + | 1.17780i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5947i | 1.37603i | 0.725695 | + | 0.688017i | \(0.241518\pi\) | ||||
−0.725695 | + | 0.688017i | \(0.758482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.310772 | − | 0.179424i | −0.0363731 | − | 0.0210000i | 0.481703 | − | 0.876334i | \(-0.340018\pi\) |
−0.518076 | + | 0.855334i | \(0.673352\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.83878 | + | 2.10040i | 0.905145 | + | 0.242533i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.81566 | − | 1.88283i | 0.548795 | − | 0.214568i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.84953 | + | 6.66758i | 0.433106 | + | 0.750161i | 0.997139 | − | 0.0755910i | \(-0.0240843\pi\) |
−0.564033 | + | 0.825752i | \(0.690751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.53979 | + | 9.59520i | −0.615532 | + | 1.06613i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.424001 | + | 0.424001i | 0.0465402 | + | 0.0465402i | 0.729994 | − | 0.683454i | \(-0.239523\pi\) |
−0.683454 | + | 0.729994i | \(0.739523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.98626 | − | 3.98626i | 0.432371 | − | 0.432371i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.513270 | + | 0.296337i | 0.0550283 | + | 0.0317706i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2323 | + | 8.79437i | −1.61462 | + | 0.932201i | −0.626340 | + | 0.779550i | \(0.715448\pi\) |
−0.988280 | + | 0.152652i | \(0.951219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.91434 | + | 6.14607i | −0.515163 | + | 0.644283i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.13045 | + | 15.4150i | −0.428308 | + | 1.59847i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.316897 | − | 0.548881i | 0.0325129 | − | 0.0563140i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2678 | 1.24560 | 0.622802 | − | 0.782379i | \(-0.285994\pi\) | ||||
0.622802 | + | 0.782379i | \(0.285994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.50240 | + | 1.50240i | 0.150997 | + | 0.150997i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.313118 | − | 1.16857i | −0.0311564 | − | 0.116277i | 0.948596 | − | 0.316488i | \(-0.102504\pi\) |
−0.979753 | + | 0.200211i | \(0.935837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.06181 | + | 2.92244i | −0.498755 | + | 0.287956i | −0.728199 | − | 0.685365i | \(-0.759643\pi\) |
0.229444 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.587809 | + | 5.27828i | 0.0573643 | + | 0.515107i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.62492 | − | 0.971295i | −0.350435 | − | 0.0938987i | 0.0793079 | − | 0.996850i | \(-0.474729\pi\) |
−0.429742 | + | 0.902952i | \(0.641396\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.67656 | − | 2.59283i | 0.926846 | − | 0.248348i | 0.236337 | − | 0.971671i | \(-0.424053\pi\) |
0.690509 | + | 0.723323i | \(0.257386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.1039 | −1.90818 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07461 | 0.477379 | 0.238689 | − | 0.971096i | \(-0.423282\pi\) | ||||
0.238689 | + | 0.971096i | \(0.423282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.56370 | − | 1.75874i | 0.612069 | − | 0.164003i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12342 | − | 0.836919i | −0.288761 | − | 0.0773732i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.7606 | − | 6.02490i | −1.26144 | − | 0.552301i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.21861 | − | 3.59031i | 0.565328 | − | 0.326392i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.25685 | + | 4.69064i | 0.113327 | + | 0.422941i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.32873 | − | 6.32873i | −0.566059 | − | 0.566059i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1710 | 0.991270 | 0.495635 | − | 0.868531i | \(-0.334935\pi\) | ||||
0.495635 | + | 0.868531i | \(0.334935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.22621 | − | 9.05207i | 0.460142 | − | 0.796990i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.26332 | − | 12.1789i | 0.285118 | − | 1.06407i | −0.663636 | − | 0.748056i | \(-0.730988\pi\) |
0.948753 | − | 0.316017i | \(-0.102346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.66965 | − | 0.253868i | −0.144777 | − | 0.0220131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.32524 | − | 1.91983i | 0.286191 | − | 0.165233i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0325 | + | 8.10166i | 1.19888 | + | 0.692172i | 0.960305 | − | 0.278953i | \(-0.0899874\pi\) |
0.238572 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5018 | + | 10.5018i | −0.890748 | + | 0.890748i | −0.994593 | − | 0.103846i | \(-0.966885\pi\) |
0.103846 | + | 0.994593i | \(0.466885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.413403 | − | 0.413403i | −0.0348148 | − | 0.0348148i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.90636 | − | 5.03397i | 0.243042 | − | 0.420961i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.145539 | − | 0.252082i | −0.0120864 | − | 0.0209342i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.5288 | − | 6.58030i | 1.03336 | − | 0.542734i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.61931 | − | 2.57749i | −0.788045 | − | 0.211156i | −0.157716 | − | 0.987484i | \(-0.550413\pi\) |
−0.630329 | + | 0.776328i | \(0.717080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.97638 | − | 5.18252i | −0.730487 | − | 0.421747i | 0.0881130 | − | 0.996110i | \(-0.471916\pi\) |
−0.818600 | + | 0.574363i | \(0.805250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.17272i | − | 0.499035i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.54219 | − | 5.54219i | 0.445159 | − | 0.445159i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.98512 | − | 1.06781i | 0.318047 | − | 0.0852205i | −0.0962637 | − | 0.995356i | \(-0.530689\pi\) |
0.414311 | + | 0.910135i | \(0.364023\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.98206 | + | 13.8253i | 0.633019 | + | 1.09642i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7335 | − | 14.5828i | −0.845916 | − | 1.14928i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.13899 | + | 7.98280i | −0.167538 | + | 0.625261i | 0.830165 | + | 0.557518i | \(0.188246\pi\) |
−0.997703 | + | 0.0677429i | \(0.978420\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.01534 | − | 3.78930i | −0.0790442 | − | 0.294997i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.92669i | − | 0.690768i | −0.938462 | − | 0.345384i | \(-0.887749\pi\) | ||
0.938462 | − | 0.345384i | \(-0.112251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.15359i | − | 0.319507i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.179614 | − | 0.670329i | −0.0137354 | − | 0.0512613i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41044 | − | 5.26383i | 0.107234 | − | 0.400202i | −0.891355 | − | 0.453305i | \(-0.850245\pi\) |
0.998589 | + | 0.0531037i | \(0.0169114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.25960 | + | 9.72878i | −0.321996 | + | 0.735426i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.0799 | + | 24.3871i | 1.05831 | + | 1.83305i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.42440 | − | 2.52526i | 0.704413 | − | 0.188747i | 0.111207 | − | 0.993797i | \(-0.464528\pi\) |
0.593206 | + | 0.805050i | \(0.297862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.42976 | + | 8.42976i | −0.626579 | + | 0.626579i | −0.947206 | − | 0.320627i | \(-0.896106\pi\) |
0.320627 | + | 0.947206i | \(0.396106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.57038i | − | 0.559619i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.55080 | + | 4.93680i | 0.628667 | + | 0.362961i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7180 | + | 2.87187i | 0.783776 | + | 0.210012i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.99096 | − | 6.38950i | −0.581257 | − | 0.464767i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.46522 | − | 4.26989i | −0.178377 | − | 0.308958i | 0.762948 | − | 0.646460i | \(-0.223751\pi\) |
−0.941325 | + | 0.337502i | \(0.890418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9543 | + | 18.9735i | −0.788510 | + | 1.36574i | 0.138370 | + | 0.990381i | \(0.455814\pi\) |
−0.926880 | + | 0.375358i | \(0.877520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.22171 | + | 4.22171i | 0.302323 | + | 0.302323i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.61984 | − | 7.61984i | 0.542891 | − | 0.542891i | −0.381484 | − | 0.924375i | \(-0.624587\pi\) |
0.924375 | + | 0.381484i | \(0.124587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.09710 | + | 1.78811i | 0.219547 | + | 0.126756i | 0.605741 | − | 0.795662i | \(-0.292877\pi\) |
−0.386193 | + | 0.922418i | \(0.626210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.2106 | − | 10.5139i | 1.28448 | − | 0.741595i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.484378 | + | 0.605783i | −0.0339967 | + | 0.0425176i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.617276 | − | 2.30371i | 0.0431125 | − | 0.160898i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.72024 | − | 6.44365i | 0.258575 | − | 0.447865i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.24749 | 0.0862906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.33737 | − | 7.33737i | −0.505126 | − | 0.505126i | 0.407901 | − | 0.913026i | \(-0.366261\pi\) |
−0.913026 | + | 0.407901i | \(0.866261\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.06690 | − | 22.6420i | −0.415697 | − | 1.55140i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.44573 | + | 2.56674i | −0.303196 | + | 0.175050i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.1317 | − | 8.37655i | −1.29875 | − | 0.568637i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.700757 | + | 0.187767i | 0.0473528 | + | 0.0126881i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3117 | + | 4.37072i | −1.09725 | + | 0.294006i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.26037 | −0.285295 | −0.142648 | − | 0.989774i | \(-0.545562\pi\) | ||||
−0.142648 | + | 0.989774i | \(0.545562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.36411 | −0.290941 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.67340 | − | 1.25223i | 0.310184 | − | 0.0831136i | −0.100369 | − | 0.994950i | \(-0.532002\pi\) |
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9490 | + | 5.07737i | 1.25218 | + | 0.335522i | 0.823180 | − | 0.567781i | \(-0.192198\pi\) |
0.429005 | + | 0.903302i | \(0.358864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.41879 | + | 6.19656i | −0.553916 | + | 0.407703i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.38681 | − | 2.53273i | 0.287390 | − | 0.165925i | −0.349374 | − | 0.936983i | \(-0.613606\pi\) |
0.636764 | + | 0.771059i | \(0.280273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0743155 | + | 0.277349i | 0.00484781 | + | 0.0180923i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0061 | − | 11.0061i | −0.714925 | − | 0.714925i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.32494 | 0.603181 | 0.301590 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301590 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8663 | + | 22.2850i | −0.828789 | + | 1.43550i | 0.0702006 | + | 0.997533i | \(0.477636\pi\) |
−0.898989 | + | 0.437971i | \(0.855697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.79475 | − | 10.4301i | 0.179283 | − | 0.669093i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.94477 | − | 0.277839i | −0.443685 | − | 0.0177505i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.64420 | + | 0.949280i | −0.104618 | + | 0.0604012i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.04984 | − | 0.606128i | −0.0665312 | − | 0.0384118i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.64372 | − | 3.64372i | 0.229990 | − | 0.229990i | −0.582699 | − | 0.812688i | \(-0.698003\pi\) |
0.812688 | + | 0.582699i | \(0.198003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.45755 | + | 9.45755i | 0.594591 | + | 0.594591i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.69853 | + | 9.87014i | −0.356856 | + | 0.618092i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.87774 | + | 3.25234i | 0.117130 | + | 0.202875i | 0.918629 | − | 0.395121i | \(-0.129297\pi\) |
−0.801499 | + | 0.597996i | \(0.795964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.95490 | − | 26.0108i | 0.245746 | − | 1.61624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.307858 | − | 0.0824903i | −0.0190559 | − | 0.00510602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.3252 | + | 9.42534i | 1.00665 | + | 0.581191i | 0.910210 | − | 0.414147i | \(-0.135920\pi\) |
0.0964430 | + | 0.995339i | \(0.469253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.84044i | − | 0.481634i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.1439 | − | 25.1439i | 1.53878 | − | 1.53878i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5643 | − | 4.43839i | 1.00994 | − | 0.270614i | 0.284338 | − | 0.958724i | \(-0.408226\pi\) |
0.725606 | + | 0.688111i | \(0.241560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.65608 | + | 4.60046i | 0.161345 | + | 0.279458i | 0.935351 | − | 0.353720i | \(-0.115083\pi\) |
−0.774006 | + | 0.633178i | \(0.781750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.38076 | − | 14.5734i | 0.386181 | − | 0.882023i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.03042 | − | 7.57761i | 0.122439 | − | 0.456947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.93434 | − | 14.6832i | −0.236392 | − | 0.882226i | −0.977517 | − | 0.210859i | \(-0.932374\pi\) |
0.741125 | − | 0.671367i | \(-0.234293\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.58208i | − | 0.513795i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.15786i | 0.188382i | 0.995554 | + | 0.0941910i | \(0.0300264\pi\) | ||||
−0.995554 | + | 0.0941910i | \(0.969974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.65368 | + | 13.6357i | 0.217189 | + | 0.810559i | 0.985385 | + | 0.170344i | \(0.0544879\pi\) |
−0.768196 | + | 0.640215i | \(0.778845\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.331632 | + | 1.23767i | −0.0196442 | + | 0.0733131i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.31609 | + | 0.703385i | −0.372827 | + | 0.0415195i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.61819 | − | 13.1951i | −0.448129 | − | 0.776182i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.9564 | + | 6.41911i | −1.40435 | + | 0.376295i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.9335 | + | 10.9335i | −0.638743 | + | 0.638743i | −0.950245 | − | 0.311502i | \(-0.899168\pi\) |
0.311502 | + | 0.950245i | \(0.399168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.8301i | − | 0.805219i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.54503 | + | 3.77878i | 0.379781 | + | 0.219267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.6619 | − | 5.26839i | −1.13708 | − | 0.304679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.6836 | + | 8.54253i | 0.615794 | + | 0.492383i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.22291 | + | 2.11814i | 0.0702543 | + | 0.121684i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.85902 | + | 3.21991i | −0.106447 | + | 0.184371i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7735 | + | 14.7735i | 0.843170 | + | 0.843170i | 0.989270 | − | 0.146100i | \(-0.0466721\pi\) |
−0.146100 | + | 0.989270i | \(0.546672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.35550 | − | 8.35550i | 0.475328 | − | 0.475328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.56549 | + | 4.36794i | 0.429000 | + | 0.247683i | 0.698920 | − | 0.715199i | \(-0.253664\pi\) |
−0.269921 | + | 0.962883i | \(0.586998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.56615 | − | 2.05892i | 0.201571 | − | 0.116377i | −0.395817 | − | 0.918329i | \(-0.629539\pi\) |
0.597388 | + | 0.801952i | \(0.296205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.03998 | − | 2.65993i | −0.0585962 | − | 0.149870i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.32257 | − | 23.5962i | 0.355111 | − | 1.32529i | −0.525234 | − | 0.850958i | \(-0.676022\pi\) |
0.880345 | − | 0.474335i | \(-0.157311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.286463 | − | 0.496169i | 0.0160389 | − | 0.0277801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.58695 | 0.423462 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.56271 | − | 2.56271i | −0.142593 | − | 0.142593i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.09010 | + | 11.5324i | 0.171408 | + | 0.639703i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5396 | + | 10.1265i | −0.969943 | + | 0.559997i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.616194 | − | 0.453543i | 0.0339719 | − | 0.0250046i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.05503 | + | 1.89039i | 0.387780 | + | 0.103905i | 0.447441 | − | 0.894313i | \(-0.352335\pi\) |
−0.0596615 | + | 0.998219i | \(0.519002\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.4428 | − | 2.79813i | 0.572260 | − | 0.153337i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3274 | −0.564245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.53985 | −0.519669 | −0.259834 | − | 0.965653i | \(-0.583668\pi\) | ||||
−0.259834 | + | 0.965653i | \(0.583668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.90965 | + | 2.65528i | −0.538218 | + | 0.144215i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.9015 | + | 3.99283i | 0.806959 | + | 0.216224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.04901 | + | 17.5046i | 0.326616 | + | 0.945157i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.8973 | + | 6.86890i | −0.640528 | + | 0.369809i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.36483 | − | 8.82567i | −0.126951 | − | 0.473787i | 0.872951 | − | 0.487808i | \(-0.162203\pi\) |
−0.999902 | + | 0.0140212i | \(0.995537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4862 | + | 24.4862i | 1.31072 | + | 1.31072i | 0.920887 | + | 0.389831i | \(0.127467\pi\) |
0.389831 | + | 0.920887i | \(0.372533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.5019 | −0.613925 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0352 | − | 22.5776i | 0.693793 | − | 1.20168i | −0.276793 | − | 0.960930i | \(-0.589272\pi\) |
0.970586 | − | 0.240755i | \(-0.0773950\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.97963 | + | 11.1201i | −0.158142 | + | 0.590194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.0242 | + | 4.56513i | 1.58905 | + | 0.241612i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.01740 | − | 1.74210i | 0.159252 | − | 0.0919443i | −0.418256 | − | 0.908329i | \(-0.637358\pi\) |
0.577508 | + | 0.816385i | \(0.304025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1016 | + | 9.29627i | 0.847453 | + | 0.489277i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2650 | + | 10.2650i | −0.538773 | + | 0.538773i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.251944 | − | 0.251944i | −0.0131873 | − | 0.0131873i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2280 | − | 21.1796i | 0.638298 | − | 1.10556i | −0.347508 | − | 0.937677i | \(-0.612972\pi\) |
0.985806 | − | 0.167888i | \(-0.0536946\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.30572 | − | 2.26157i | −0.0679730 | − | 0.117733i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.4578 | + | 7.60759i | −1.01020 | + | 0.394966i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.4993 | − | 9.51200i | −1.83808 | − | 0.492513i | −0.839385 | − | 0.543537i | \(-0.817085\pi\) |
−0.998697 | + | 0.0510246i | \(0.983751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.6702 | + | 9.04719i | 0.809206 | + | 0.467195i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.871940i | 0.0449072i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5183 | + | 18.5183i | −0.951222 | + | 0.951222i | −0.998864 | − | 0.0476420i | \(-0.984829\pi\) |
0.0476420 | + | 0.998864i | \(0.484829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.8147 | + | 5.84524i | −1.11760 | + | 0.299461i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.89785 | − | 13.6795i | −0.403562 | − | 0.698989i | 0.590591 | − | 0.806971i | \(-0.298895\pi\) |
−0.994153 | + | 0.107982i | \(0.965561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.10242 | − | 0.568225i | 0.260043 | − | 0.0289594i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.45480 | + | 5.42940i | −0.0739519 | + | 0.275992i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.47562 | + | 5.50707i | 0.0748167 | + | 0.279220i | 0.993192 | − | 0.116492i | \(-0.0371648\pi\) |
−0.918375 | + | 0.395711i | \(0.870498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 38.8572i | − | 1.96509i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.4903i | 1.28582i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.97852 | + | 7.38395i | 0.0995503 | + | 0.371527i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.260427 | − | 0.971927i | 0.0130705 | − | 0.0487796i | −0.959083 | − | 0.283126i | \(-0.908628\pi\) |
0.972153 | + | 0.234347i | \(0.0752951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.39332 | − | 0.377894i | 0.169879 | − | 0.0189183i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.70318 | + | 15.0744i | 0.434616 | + | 0.752777i | 0.997264 | − | 0.0739192i | \(-0.0235507\pi\) |
−0.562648 | + | 0.826697i | \(0.690217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.6786 | + | 6.07671i | −1.12970 | + | 0.302703i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.77886 | + | 7.77886i | −0.386535 | + | 0.386535i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4341i | 0.963313i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.0605 | − | 19.0875i | −1.63474 | − | 0.943815i | −0.982605 | − | 0.185709i | \(-0.940542\pi\) |
−0.652131 | − | 0.758106i | \(-0.726125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.6417 | − | 8.47837i | −1.56077 | − | 0.418207i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.3224 | + | 13.4194i | −1.68889 | + | 0.660323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.297687 | + | 0.515608i | 0.0146129 | + | 0.0253102i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.0127 | − | 26.0028i | 0.735176 | − | 1.27336i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.0004 | + | 27.0004i | 1.31905 | + | 1.31905i | 0.914525 | + | 0.404529i | \(0.132565\pi\) |
0.404529 | + | 0.914525i | \(0.367435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1472 | + | 19.1472i | −0.933175 | + | 0.933175i | −0.997903 | − | 0.0647277i | \(-0.979382\pi\) |
0.0647277 | + | 0.997903i | \(0.479382\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.272276 | + | 0.157199i | 0.0132385 | + | 0.00764327i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.7377 | + | 11.3956i | −0.957419 | + | 0.552766i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.79471 | + | 1.48927i | 0.473999 | + | 0.0720708i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.04150 | + | 11.3510i | −0.146845 | + | 0.548033i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.628555 | − | 1.08869i | 0.0302764 | − | 0.0524403i | −0.850490 | − | 0.525991i | \(-0.823695\pi\) |
0.880767 | + | 0.473551i | \(0.157028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.16885 | −0.440627 | −0.220313 | − | 0.975429i | \(-0.570708\pi\) | ||||
−0.220313 | + | 0.975429i | \(0.570708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.416110 | + | 0.416110i | 0.0199509 | + | 0.0199509i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.13067 | − | 4.21971i | −0.0540871 | − | 0.201856i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.89864 | − | 3.98293i | 0.329254 | − | 0.190095i | −0.326256 | − | 0.945282i | \(-0.605787\pi\) |
0.655510 | + | 0.755187i | \(0.272454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.59211 | + | 5.16187i | −0.266291 | + | 0.245803i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.1691 | + | 6.47610i | 1.14831 | + | 0.307689i | 0.782288 | − | 0.622918i | \(-0.214053\pi\) |
0.366022 | + | 0.930606i | \(0.380719\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8689 | + | 4.52000i | −0.799661 | + | 0.214269i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.1332 | 0.952267 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.33038 | −0.393135 | −0.196567 | − | 0.980490i | \(-0.562979\pi\) | ||||
−0.196567 | + | 0.980490i | \(0.562979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.53436 | − | 1.21498i | 0.213515 | − | 0.0572111i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.2407 | + | 5.42349i | 0.950993 | + | 0.254818i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.29264 | + | 4.63162i | −0.295003 | + | 0.217134i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5338 | + | 7.23641i | −0.586308 | + | 0.338505i | −0.763636 | − | 0.645647i | \(-0.776588\pi\) |
0.177328 | + | 0.984152i | \(0.443255\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.68270 | − | 21.2081i | −0.265246 | − | 0.989910i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.23021 | − | 4.23021i | −0.197020 | − | 0.197020i | 0.601701 | − | 0.798721i | \(-0.294490\pi\) |
−0.798721 | + | 0.601701i | \(0.794490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1987 | 1.17108 | 0.585542 | − | 0.810642i | \(-0.300882\pi\) | ||||
0.585542 | + | 0.810642i | \(0.300882\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.92280 | + | 13.7227i | −0.367411 | + | 0.636374i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.97667 | + | 14.8411i | −0.184018 | + | 0.686766i | 0.810820 | + | 0.585295i | \(0.199021\pi\) |
−0.994839 | + | 0.101470i | \(0.967645\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0207 | + | 25.6296i | 0.462711 | + | 1.18347i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.22338 | + | 4.17042i | −0.332836 | + | 0.192163i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.75047 | − | 5.05209i | −0.402347 | − | 0.232295i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.81183 | + | 1.81183i | −0.0831326 | + | 0.0831326i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.07046 | − | 6.07046i | −0.277947 | − | 0.277947i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.4147 | + | 18.0387i | −0.475859 | + | 0.824211i | −0.999618 | − | 0.0276553i | \(-0.991196\pi\) |
0.523759 | + | 0.851867i | \(0.324529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7884 | − | 25.6143i | −0.674294 | − | 1.16791i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.5906 | + | 22.8608i | 1.30092 | + | 1.04020i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.7657 | + | 3.15261i | 0.534252 | + | 0.143152i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.192631 | + | 0.111216i | 0.00872895 | + | 0.00503966i | 0.504358 | − | 0.863495i | \(-0.331729\pi\) |
−0.495629 | + | 0.868534i | \(0.665062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 16.7080i | − | 0.755561i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1586 | + | 18.1586i | −0.819486 | + | 0.819486i | −0.986033 | − | 0.166547i | \(-0.946738\pi\) |
0.166547 | + | 0.986033i | \(0.446738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.60776 | + | 0.430797i | −0.0724097 | + | 0.0194021i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05482 | + | 1.82700i | 0.0474105 | + | 0.0821173i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.4881 | − | 3.39527i | 1.36758 | − | 0.152299i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.908747 | + | 3.39149i | −0.0406811 | + | 0.151824i | −0.983279 | − | 0.182107i | \(-0.941708\pi\) |
0.942598 | + | 0.333930i | \(0.108375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.67088 | + | 17.4320i | 0.208680 | + | 0.778802i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.65278i | − | 0.341220i | −0.985339 | − | 0.170610i | \(-0.945426\pi\) | ||
0.985339 | − | 0.170610i | \(-0.0545739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.20121i | − | 0.0534532i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.17336 | + | 8.11109i | 0.0965223 | + | 0.360226i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.27238 | + | 30.8730i | −0.366667 | + | 1.36842i | 0.498480 | + | 0.866901i | \(0.333892\pi\) |
−0.865147 | + | 0.501519i | \(0.832775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.380792 | + | 0.869715i | −0.0168452 | + | 0.0384739i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.23423 | − | 2.13775i | −0.0544925 | − | 0.0943838i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.60566 | + | 1.50203i | −0.247015 | + | 0.0661874i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.399629 | + | 0.399629i | −0.0175757 | + | 0.0175757i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0172i | 0.483600i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.39816 | + | 1.38458i | 0.105065 | + | 0.0606595i | 0.551612 | − | 0.834101i | \(-0.314013\pi\) |
−0.446547 | + | 0.894760i | \(0.647346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3583 | + | 5.72293i | 0.933932 | + | 0.250246i | 0.693530 | − | 0.720427i | \(-0.256054\pi\) |
0.240401 | + | 0.970674i | \(0.422721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.22754 | − | 21.2271i | 0.140862 | − | 0.926427i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.4095 | − | 38.8144i | −0.976173 | − | 1.69078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.9189 | − | 20.6441i | 0.518211 | − | 0.897568i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.7079 | − | 10.7079i | −0.464685 | − | 0.464685i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.05178 | + | 5.05178i | −0.218817 | + | 0.218817i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.22696 | − | 1.86308i | −0.139513 | − | 0.0805481i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.0826 | + | 9.86262i | −0.737167 | + | 0.425603i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.36106 | − | 12.1114i | −0.273990 | − | 0.521675i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.64497 | − | 32.2635i | 0.371676 | − | 1.38711i | −0.486465 | − | 0.873700i | \(-0.661714\pi\) |
0.858141 | − | 0.513414i | \(-0.171619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0507 | − | 20.8724i | 0.517145 | − | 0.895721i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.94683 | 0.426075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.45137 | − | 3.45137i | −0.147570 | − | 0.147570i | 0.629462 | − | 0.777032i | \(-0.283276\pi\) |
−0.777032 | + | 0.629462i | \(0.783276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.05367 | + | 3.93236i | 0.0449696 | + | 0.167829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.162059 | + | 0.0935651i | −0.00690396 | + | 0.00398601i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.4051 | − | 12.0748i | 0.697616 | − | 0.513472i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.2811 | − | 5.16636i | −0.818437 | − | 0.219300i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.3055 | − | 5.70879i | 0.902742 | − | 0.241889i | 0.222549 | − | 0.974922i | \(-0.428562\pi\) |
0.680194 | + | 0.733032i | \(0.261896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.3776 | 0.650403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.4327 | −0.947109 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.6690 | + | 7.14593i | −1.12396 | + | 0.301165i | −0.772486 | − | 0.635031i | \(-0.780987\pi\) |
−0.351477 | + | 0.936196i | \(0.614321\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.86691 | + | 1.30408i | 0.204752 | + | 0.0548633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.8528 | + | 11.7571i | 1.12771 | + | 0.493751i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.3657 | − | 17.5317i | 1.27300 | − | 0.734965i | 0.297446 | − | 0.954739i | \(-0.403865\pi\) |
0.975551 | + | 0.219773i | \(0.0705318\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.334280 | + | 1.24755i | 0.0139892 | + | 0.0522083i | 0.972568 | − | 0.232620i | \(-0.0747300\pi\) |
−0.958578 | + | 0.284829i | \(0.908063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.04827 | + | 7.04827i | 0.294446 | + | 0.294446i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.4720 | −1.14566 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.66470 | + | 13.2757i | −0.319086 | + | 0.552673i | −0.980298 | − | 0.197527i | \(-0.936709\pi\) |
0.661212 | + | 0.750199i | \(0.270042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4637 | − | 42.7830i | 0.476414 | − | 1.77800i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.990749 | − | 1.23907i | 0.0411032 | − | 0.0514053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.3647 | − | 7.71612i | 0.553510 | − | 0.319569i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.78051 | − | 1.60533i | −0.114960 | − | 0.0663722i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.8270 | − | 27.8270i | 1.14854 | − | 1.14854i | 0.161702 | − | 0.986840i | \(-0.448302\pi\) |
0.986840 | − | 0.161702i | \(-0.0516982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.56299 | − | 3.56299i | −0.146810 | − | 0.146810i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.8929 | + | 18.8670i | −0.448074 | + | 0.776087i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.89810 | − | 15.4120i | −0.365401 | − | 0.632894i | 0.623439 | − | 0.781872i | \(-0.285735\pi\) |
−0.988840 | + | 0.148978i | \(0.952402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.6492 | − | 9.31455i | −0.477569 | − | 0.381859i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.98361 | − | 1.87125i | −0.285820 | − | 0.0765853i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.6221 | + | 9.59676i | 0.679159 | + | 0.392113i | 0.799538 | − | 0.600615i | \(-0.205078\pi\) |
−0.120379 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9530i | 1.09944i | 0.835351 | + | 0.549718i | \(0.185265\pi\) | ||||
−0.835351 | + | 0.549718i | \(0.814735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.99597 | + | 7.99597i | −0.325621 | + | 0.325621i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.88674 | − | 1.84530i | 0.279986 | − | 0.0750219i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.7276 | − | 25.5089i | −0.597773 | − | 1.03537i | −0.993149 | − | 0.116854i | \(-0.962719\pi\) |
0.395376 | − | 0.918519i | \(-0.370614\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.628915 | − | 1.43642i | 0.0254849 | − | 0.0582066i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.222616 | − | 0.830813i | 0.00900607 | − | 0.0336111i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.46001 | − | 24.1091i | −0.260917 | − | 0.973756i | −0.964702 | − | 0.263343i | \(-0.915175\pi\) |
0.703785 | − | 0.710413i | \(-0.251492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.82165i | 0.194428i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.8407i | − | 0.436431i | −0.975901 | − | 0.218216i | \(-0.929976\pi\) | ||
0.975901 | − | 0.218216i | \(-0.0700236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.19721 | − | 19.3962i | −0.208893 | − | 0.779601i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.779334 | − | 0.626609i | \(-0.215558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.84982 | − | 25.5639i | 0.274874 | − | 1.02584i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.5853 | + | 37.4780i | 1.10518 | + | 1.50152i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.59202 | + | 9.68566i | 0.223681 | + | 0.387426i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.43609 | + | 0.652747i | −0.0972879 | + | 0.0260682i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.9233 | − | 39.9233i | 1.59185 | − | 1.59185i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.71697i | − | 0.227589i | −0.993504 | − | 0.113794i | \(-0.963699\pi\) | ||
0.993504 | − | 0.113794i | \(-0.0363005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1676 | + | 10.4891i | 0.722099 | + | 0.416904i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7138 | + | 2.87076i | 0.425166 | + | 0.113923i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6001 | + | 11.1225i | 0.697343 | + | 0.440689i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.30277 | + | 10.9167i | 0.249334 | + | 0.431859i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.8475 | + | 25.7166i | −0.586441 | + | 1.01575i | 0.408253 | + | 0.912869i | \(0.366138\pi\) |
−0.994694 | + | 0.102877i | \(0.967195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.53512 | − | 3.53512i | −0.139412 | − | 0.139412i | 0.633957 | − | 0.773368i | \(-0.281430\pi\) |
−0.773368 | + | 0.633957i | \(0.781430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.33854 | − | 7.33854i | 0.288955 | − | 0.288955i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7788 | − | 7.37782i | −0.502385 | − | 0.290052i | 0.227313 | − | 0.973822i | \(-0.427006\pi\) |
−0.729698 | + | 0.683770i | \(0.760339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.5746 | − | 13.6108i | 0.925384 | − | 0.534270i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.7433 | + | 6.34700i | 1.63605 | + | 0.248759i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.56350 | + | 9.56710i | −0.100317 | + | 0.374390i | −0.997772 | − | 0.0667174i | \(-0.978747\pi\) |
0.897455 | + | 0.441107i | \(0.145414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.25952 | − | 10.8418i | 0.244580 | − | 0.423624i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.390135 | −0.0152206 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.68205 | − | 5.68205i | −0.221341 | − | 0.221341i | 0.587722 | − | 0.809063i | \(-0.300025\pi\) |
−0.809063 | + | 0.587722i | \(0.800025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.48266 | − | 9.26542i | −0.0965643 | − | 0.360383i | 0.900688 | − | 0.434467i | \(-0.143063\pi\) |
−0.997252 | + | 0.0740843i | \(0.976397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.5665 | − | 17.0702i | 1.14827 | − | 0.662952i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.53608 | − | 0.672550i | −0.0595666 | − | 0.0260804i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.93796 | − | 0.519275i | −0.0750381 | − | 0.0201064i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.31961 | − | 2.22923i | 0.321655 | − | 0.0861871i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.31815 | −0.282514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.24280 | 0.125001 | 0.0625004 | − | 0.998045i | \(-0.480093\pi\) | ||||
0.0625004 | + | 0.998045i | \(0.480093\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.9941 | + | 4.01767i | −0.577125 | + | 0.154640i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.3879 | − | 8.67832i | −1.24477 | − | 0.333535i | −0.424455 | − | 0.905449i | \(-0.639534\pi\) |
−0.820314 | + | 0.571914i | \(0.806201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.59239 | − | 32.2581i | −0.137863 | − | 1.23795i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.47094 | + | 4.89070i | −0.324607 | + | 0.187412i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.81432 | − | 17.9673i | −0.184215 | − | 0.687499i | −0.994797 | − | 0.101874i | \(-0.967516\pi\) |
0.810583 | − | 0.585624i | \(-0.199151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3762 | + | 11.3762i | 0.434662 | + | 0.434662i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.6602 | −1.51313 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.7432 | + | 20.3398i | −0.447380 | + | 0.774886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.60826 | + | 20.9303i | −0.213348 | + | 0.796227i | 0.773393 | + | 0.633927i | \(0.218558\pi\) |
−0.986741 | + | 0.162300i | \(0.948109\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.51060 | − | 4.39049i | 0.133357 | − | 0.166781i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7707 | + | 7.37317i | −0.484421 | + | 0.279680i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.8108 | − | 6.81898i | −0.447367 | − | 0.258287i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.24128 | + | 7.24128i | −0.273891 | + | 0.273891i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.96023 | + | 4.96023i | 0.187345 | + | 0.187345i | 0.794547 | − | 0.607202i | \(-0.207708\pi\) |
−0.607202 | + | 0.794547i | \(0.707708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.17380 | − | 5.49718i | 0.119702 | − | 0.207330i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.290246 | − | 0.502720i | −0.0109313 | − | 0.0189335i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.98107 | + | 1.16554i | −0.112115 | + | 0.0438345i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.9774 | + | 3.74523i | 0.524932 | + | 0.140655i | 0.511547 | − | 0.859255i | \(-0.329073\pi\) |
0.0133851 | + | 0.999910i | \(0.495739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.24889 | + | 4.18515i | 0.271855 | + | 0.156955i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 54.0240i | − | 2.02321i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.08105 | − | 4.08105i | 0.152623 | − | 0.152623i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.2097 | + | 4.87927i | −0.680053 | + | 0.182220i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.5646 | + | 28.6908i | 0.617756 | + | 1.06998i | 0.989894 | + | 0.141808i | \(0.0452914\pi\) |
−0.372138 | + | 0.928177i | \(0.621375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.16680 | + | 12.4542i | 0.341389 | + | 0.463820i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.4645 | − | 50.2502i | 0.500751 | − | 1.86883i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.304573 | + | 1.13668i | 0.0113116 | + | 0.0422154i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5496i | 0.873406i | 0.899606 | + | 0.436703i | \(0.143854\pi\) | ||||
−0.899606 | + | 0.436703i | \(0.856146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 11.4085i | − | 0.422538i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.59756 | + | 28.3545i | 0.281006 | + | 1.04873i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.462947 | − | 1.72774i | 0.0170993 | − | 0.0638156i | −0.956849 | − | 0.290586i | \(-0.906150\pi\) |
0.973948 | + | 0.226770i | \(0.0728166\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.7071 | − | 3.09128i | 0.505593 | − | 0.114024i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.1636 | − | 17.6039i | −0.374382 | − | 0.648448i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6228 | − | 6.06175i | 0.832192 | − | 0.222985i | 0.182522 | − | 0.983202i | \(-0.441574\pi\) |
0.649670 | + | 0.760217i | \(0.274907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.71407 | − | 2.71407i | 0.0997039 | − | 0.0997039i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.9219i | − | 0.510747i | −0.966843 | − | 0.255373i | \(-0.917802\pi\) | ||
0.966843 | − | 0.255373i | \(-0.0821984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.56324 | − | 4.94399i | −0.313733 | − | 0.181134i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.629693 | + | 0.168726i | 0.0230393 | + | 0.00617336i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.49253 | + | 9.81615i | −0.0545358 | + | 0.358674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.53854 | − | 7.86098i | −0.165614 | − | 0.286851i | 0.771259 | − | 0.636521i | \(-0.219627\pi\) |
−0.936873 | + | 0.349670i | \(0.886294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.20885 | + | 9.02200i | −0.189821 | + | 0.328780i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.27718 | − | 7.27718i | −0.264844 | − | 0.264844i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.14043 | + | 1.14043i | −0.0414496 | + | 0.0414496i | −0.727528 | − | 0.686078i | \(-0.759331\pi\) |
0.686078 | + | 0.727528i | \(0.259331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.4173 | − | 13.5200i | −0.849994 | − | 0.490744i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.60476 | + | 4.39061i | −0.275672 | + | 0.159159i | −0.631463 | − | 0.775406i | \(-0.717545\pi\) |
0.355790 | + | 0.934566i | \(0.384212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.65142 | − | 24.6852i | −0.349405 | − | 0.893665i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.58628 | − | 5.92008i | 0.0573521 | − | 0.214041i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7143 | + | 35.8783i | −0.747951 | + | 1.29549i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.8204 | 1.07535 | 0.537676 | − | 0.843152i | \(-0.319303\pi\) | ||||
0.537676 | + | 0.843152i | \(0.319303\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.36862 | − | 5.36862i | −0.193346 | − | 0.193346i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9365 | + | 44.5476i | 0.429326 | + | 1.60227i | 0.754291 | + | 0.656540i | \(0.227981\pi\) |
−0.324965 | + | 0.945726i | \(0.605352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.4418 | + | 15.8435i | −0.985738 | + | 0.569116i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.88705 | + | 52.8632i | 0.211197 | + | 1.89646i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.48102 | − | 0.396838i | −0.0530630 | − | 0.0142182i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.8876 | + | 5.86476i | −0.783199 | + | 0.209858i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.13367 | −0.0405142 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.09643 | 0.146208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.3091 | − | 6.78154i | 0.902170 | − | 0.241736i | 0.222222 | − | 0.974996i | \(-0.428669\pi\) |
0.679948 | + | 0.733260i | \(0.262002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.8115 | − | 9.86360i | −1.31052 | − | 0.351153i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.48600 | − | 13.3437i | −0.0528361 | − | 0.474446i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.64539 | − | 5.56877i | 0.342518 | − | 0.197753i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.10250 | + | 15.3107i | 0.145501 | + | 0.543016i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.7419 | − | 16.7419i | −0.593028 | − | 0.593028i | 0.345420 | − | 0.938448i | \(-0.387736\pi\) |
−0.938448 | + | 0.345420i | \(0.887736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.64191 | 0.0580866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.56111 | + | 16.5603i | −0.337825 | + | 0.585130i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.181511 | − | 0.677409i | 0.00640540 | − | 0.0239053i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.54665 | − | 16.7442i | −0.230739 | − | 0.590156i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0243 | + | 17.3345i | −1.05690 | + | 0.610204i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.7720 | + | 17.7662i | 1.08189 | + | 0.624628i | 0.931405 | − | 0.363985i | \(-0.118584\pi\) |
0.150482 | + | 0.988613i | \(0.451917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.5602 | + | 29.5602i | −1.03800 | + | 1.03800i | −0.0387507 | + | 0.999249i | \(0.512338\pi\) |
−0.999249 | + | 0.0387507i | \(0.987662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.59395 | − | 7.59395i | −0.266331 | − | 0.266331i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.10288 | + | 7.10640i | −0.143718 | + | 0.248926i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.65012 | + | 2.85809i | 0.0577304 | + | 0.0999920i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.28604 | + | 8.45811i | −0.0449379 | + | 0.295550i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.63653 | − | 2.04620i | −0.266517 | − | 0.0714129i | 0.123086 | − | 0.992396i | \(-0.460721\pi\) |
−0.389602 | + | 0.920983i | \(0.627388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.2107 | − | 24.9477i | −1.50623 | − | 0.869623i | −0.999974 | − | 0.00724096i | \(-0.997695\pi\) |
−0.506258 | − | 0.862382i | \(-0.668972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.8599i | 0.552171i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.11672 | − | 8.11672i | 0.282246 | − | 0.282246i | −0.551758 | − | 0.834004i | \(-0.686043\pi\) |
0.834004 | + | 0.551758i | \(0.186043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.87035 | − | 1.84091i | 0.238617 | − | 0.0639373i | −0.137528 | − | 0.990498i | \(-0.543916\pi\) |
0.376146 | + | 0.926561i | \(0.377249\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.3659 | + | 26.6145i | 0.533037 | + | 0.923248i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.8129 | + | 37.9478i | −0.409293 | + | 1.31481i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29400 | − | 8.56133i | 0.0793872 | − | 0.296277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.90079 | − | 29.4861i | −0.273091 | − | 1.01919i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.57060i | − | 0.123271i | −0.998099 | − | 0.0616354i | \(-0.980368\pi\) | ||
0.998099 | − | 0.0616354i | \(-0.0196316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.9141i | − | 0.997036i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.65235 | − | 6.16664i | −0.0569098 | − | 0.212390i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.06740 | − | 3.98359i | 0.0367197 | − | 0.137040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.2617 | − | 15.3004i | −0.386957 | − | 0.525730i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.2697 | − | 24.7159i | −0.489736 | − | 0.848248i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 65.7370 | − | 17.6142i | 2.25344 | − | 0.603806i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8958 | − | 13.8958i | 0.475784 | − | 0.475784i | −0.427996 | − | 0.903780i | \(-0.640780\pi\) |
0.903780 | + | 0.427996i | \(0.140780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.689051i | − | 0.0235650i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.8241 | + | 20.1057i | 1.18957 | + | 0.686798i | 0.958209 | − | 0.286070i | \(-0.0923490\pi\) |
0.231360 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.0429 | + | 6.71022i | 0.854452 | + | 0.228950i | 0.659353 | − | 0.751834i | \(-0.270830\pi\) |
0.195099 | + | 0.980784i | \(0.437497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.9660 | − | 4.67845i | 0.407799 | − | 0.159441i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.22908 | + | 14.2532i | 0.280121 | + | 0.485184i | 0.971414 | − | 0.237390i | \(-0.0762920\pi\) |
−0.691293 | + | 0.722574i | \(0.742959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.70543 | − | 4.68593i | 0.0919872 | − | 0.159327i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.7811 | + | 21.7811i | 0.739724 | + | 0.739724i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.6394 | + | 10.6394i | −0.360918 | + | 0.360918i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.7915 | + | 15.4681i | 0.907795 | + | 0.524116i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5505 | − | 6.66868i | 0.390925 | − | 0.225700i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.7881 | + | 18.4946i | −0.499930 | + | 0.625232i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.90884 | − | 22.0521i | 0.199527 | − | 0.744646i | −0.791521 | − | 0.611142i | \(-0.790710\pi\) |
0.991048 | − | 0.133504i | \(-0.0426228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.6299 | − | 27.0718i | 0.527185 | − | 0.913111i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.29761 | 0.178481 | 0.0892405 | − | 0.996010i | \(-0.471556\pi\) | ||||
0.0892405 | + | 0.996010i | \(0.471556\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7426 | + | 30.7426i | 1.03457 | + | 1.03457i | 0.999381 | + | 0.0351900i | \(0.0112036\pi\) |
0.0351900 | + | 0.999381i | \(0.488796\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.23658 | + | 27.0073i | 0.243255 | + | 0.907840i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.04199 | + | 2.91100i | −0.169294 | + | 0.0977417i | −0.582253 | − | 0.813008i | \(-0.697829\pi\) |
0.412959 | + | 0.910750i | \(0.364495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.27123 | − | 29.3742i | −0.109713 | − | 0.985180i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.9153 | − | 5.60423i | −0.700688 | − | 0.187749i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.178304 | − | 0.0477763i | 0.00596671 | − | 0.00159877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.68763 | 0.323822 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 41.1522 | 1.37403 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.23530 | + | 0.598947i | −0.0745514 | + | 0.0199760i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.3062 | − | 11.6039i | −1.44274 | − | 0.386581i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.3328 | − | 11.0916i | −0.843022 | − | 0.369105i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.2510 | + | 5.91844i | −0.340756 | + | 0.196736i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.44791 | + | 20.3319i | 0.180895 | + | 0.675108i | 0.995472 | + | 0.0950536i | \(0.0303022\pi\) |
−0.814577 | + | 0.580055i | \(0.803031\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.930037 | − | 0.930037i | −0.0308474 | − | 0.0308474i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.3231 | 1.53475 | 0.767376 | − | 0.641197i | \(-0.221562\pi\) | ||||
0.767376 | + | 0.641197i | \(0.221562\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.585933 | + | 1.01487i | −0.0193916 | + | 0.0335872i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.94546 | − | 7.26054i | 0.0643148 | − | 0.240026i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.9799 | − | 5.01454i | −1.08909 | − | 0.165595i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8775 | + | 7.43484i | −0.424790 | + | 0.245253i | −0.697125 | − | 0.716950i | \(-0.745538\pi\) |
0.272335 | + | 0.962203i | \(0.412204\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.5799 | − | 21.1194i | −1.20535 | − | 0.695908i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.3852 | − | 24.3852i | 0.802649 | − | 0.802649i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.2258 | − | 28.2258i | −0.928058 | − | 0.928058i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.17723 | + | 5.50313i | −0.104354 | + | 0.180746i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.8504 | + | 44.7742i | 0.848124 | + | 1.46899i | 0.882881 | + | 0.469598i | \(0.155601\pi\) |
−0.0347569 | + | 0.999396i | \(0.511066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.178619 | + | 4.46469i | −0.00585399 | + | 0.146324i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.0593 | − | 4.57104i | −0.558498 | − | 0.149649i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.54129 | + | 5.50867i | 0.312034 | + | 0.180153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.1408i | 1.63803i | 0.573773 | + | 0.819014i | \(0.305479\pi\) | ||||
−0.573773 | + | 0.819014i | \(0.694521\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.88663 | + | 5.88663i | −0.192103 | + | 0.192103i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.3123 | + | 11.6055i | −1.41194 | + | 0.378328i | −0.882617 | − | 0.470093i | \(-0.844220\pi\) |
−0.529322 | + | 0.848421i | \(0.677554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.21947 | − | 14.2365i | −0.267663 | − | 0.463606i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.02192 | − | 8.18152i | −0.195893 | − | 0.266145i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.427149 | + | 1.59414i | −0.0138805 | + | 0.0518027i | −0.972519 | − | 0.232825i | \(-0.925203\pi\) |
0.958638 | + | 0.284627i | \(0.0918698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.276243 | + | 1.03095i | 0.00896723 | + | 0.0334661i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.3867i | 1.60147i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9510i | 1.32653i | 0.748384 | + | 0.663266i | \(0.230830\pi\) | ||||
−0.748384 | + | 0.663266i | \(0.769170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.26704 | − | 4.72865i | −0.0410003 | − | 0.153015i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.299783 | + | 1.11881i | −0.00969062 | + | 0.0361659i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.1941 | − | 39.2708i | 0.555228 | − | 1.26812i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.6564 | − | 27.1177i | −0.505046 | − | 0.874766i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.94096 | + | 1.05598i | −0.126996 | + | 0.0340284i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.3818 | + | 15.3818i | −0.495159 | + | 0.495159i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.6315i | 0.470518i | 0.971933 | + | 0.235259i | \(0.0755938\pi\) | ||||
−0.971933 | + | 0.235259i | \(0.924406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.34536 | + | 3.66350i | 0.203842 | + | 0.117688i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5944 | + | 6.32211i | 0.757181 | + | 0.202886i | 0.616701 | − | 0.787197i | \(-0.288469\pi\) |
0.140480 | + | 0.990084i | \(0.455135\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.6896 | + | 24.5391i | 0.983863 | + | 0.786687i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.0686 | − | 20.9035i | −0.386506 | − | 0.669448i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.85781 | − | 4.94988i | 0.0914295 | − | 0.158361i | −0.816683 | − | 0.577086i | \(-0.804190\pi\) |
0.908113 | + | 0.418725i | \(0.137523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.3061 | − | 24.3061i | −0.776827 | − | 0.776827i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.70133 | − | 7.70133i | 0.245885 | − | 0.245885i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.6714 | − | 10.7799i | −0.595525 | − | 0.343827i | 0.171754 | − | 0.985140i | \(-0.445057\pi\) |
−0.767279 | + | 0.641313i | \(0.778390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.26615 | − | 5.34981i | 0.295244 | − | 0.170459i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.965983 | + | 1.20810i | −0.0307476 | + | 0.0384542i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.15796 | + | 34.1780i | −0.291206 | + | 1.08680i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3811 | + | 30.1049i | −0.552128 | + | 0.956314i | 0.445993 | + | 0.895037i | \(0.352851\pi\) |
−0.998121 | + | 0.0612772i | \(0.980483\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.7661 | −0.468590 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.51082 | + | 2.51082i | 0.0795985 | + | 0.0795985i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32792 | + | 4.95586i | 0.0420556 | + | 0.156954i | 0.983760 | − | 0.179487i | \(-0.0574436\pi\) |
−0.941705 | + | 0.336440i | \(0.890777\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.3031 | − | 19.2275i | 1.05366 | − | 0.608332i |
(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 | 448.2.ba.c.81.3 | 48 | ||
4.3 | odd | 2 | 112.2.w.c.109.3 | yes | 48 | ||
7.2 | even | 3 | inner | 448.2.ba.c.401.10 | 48 | ||
8.3 | odd | 2 | 896.2.ba.f.417.3 | 48 | |||
8.5 | even | 2 | 896.2.ba.e.417.10 | 48 | |||
16.3 | odd | 4 | 896.2.ba.f.865.10 | 48 | |||
16.5 | even | 4 | inner | 448.2.ba.c.305.10 | 48 | ||
16.11 | odd | 4 | 112.2.w.c.53.7 | yes | 48 | ||
16.13 | even | 4 | 896.2.ba.e.865.3 | 48 | |||
28.3 | even | 6 | 784.2.m.k.589.10 | 24 | |||
28.11 | odd | 6 | 784.2.m.j.589.10 | 24 | |||
28.19 | even | 6 | 784.2.x.o.765.7 | 48 | |||
28.23 | odd | 6 | 112.2.w.c.93.7 | yes | 48 | ||
28.27 | even | 2 | 784.2.x.o.557.3 | 48 | |||
56.37 | even | 6 | 896.2.ba.e.289.3 | 48 | |||
56.51 | odd | 6 | 896.2.ba.f.289.10 | 48 | |||
112.11 | odd | 12 | 784.2.m.j.197.10 | 24 | |||
112.27 | even | 4 | 784.2.x.o.165.7 | 48 | |||
112.37 | even | 12 | inner | 448.2.ba.c.177.3 | 48 | ||
112.51 | odd | 12 | 896.2.ba.f.737.3 | 48 | |||
112.59 | even | 12 | 784.2.m.k.197.10 | 24 | |||
112.75 | even | 12 | 784.2.x.o.373.3 | 48 | |||
112.93 | even | 12 | 896.2.ba.e.737.10 | 48 | |||
112.107 | odd | 12 | 112.2.w.c.37.3 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.3 | ✓ | 48 | 112.107 | odd | 12 | ||
112.2.w.c.53.7 | yes | 48 | 16.11 | odd | 4 | ||
112.2.w.c.93.7 | yes | 48 | 28.23 | odd | 6 | ||
112.2.w.c.109.3 | yes | 48 | 4.3 | odd | 2 | ||
448.2.ba.c.81.3 | 48 | 1.1 | even | 1 | trivial | ||
448.2.ba.c.177.3 | 48 | 112.37 | even | 12 | inner | ||
448.2.ba.c.305.10 | 48 | 16.5 | even | 4 | inner | ||
448.2.ba.c.401.10 | 48 | 7.2 | even | 3 | inner | ||
784.2.m.j.197.10 | 24 | 112.11 | odd | 12 | |||
784.2.m.j.589.10 | 24 | 28.11 | odd | 6 | |||
784.2.m.k.197.10 | 24 | 112.59 | even | 12 | |||
784.2.m.k.589.10 | 24 | 28.3 | even | 6 | |||
784.2.x.o.165.7 | 48 | 112.27 | even | 4 | |||
784.2.x.o.373.3 | 48 | 112.75 | even | 12 | |||
784.2.x.o.557.3 | 48 | 28.27 | even | 2 | |||
784.2.x.o.765.7 | 48 | 28.19 | even | 6 | |||
896.2.ba.e.289.3 | 48 | 56.37 | even | 6 | |||
896.2.ba.e.417.10 | 48 | 8.5 | even | 2 | |||
896.2.ba.e.737.10 | 48 | 112.93 | even | 12 | |||
896.2.ba.e.865.3 | 48 | 16.13 | even | 4 | |||
896.2.ba.f.289.10 | 48 | 56.51 | odd | 6 | |||
896.2.ba.f.417.3 | 48 | 8.3 | odd | 2 | |||
896.2.ba.f.737.3 | 48 | 112.51 | odd | 12 | |||
896.2.ba.f.865.10 | 48 | 16.3 | odd | 4 |