Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(685,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.685");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.g (of order \(2\), degree \(1\), 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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + 48 x^{7} - 40 x^{6} + 32 x^{5} + 64 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 685.13 | ||
Root | \(0.340606 - 1.37258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.685 |
Dual form | 1368.2.g.b.685.14 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37258 | − | 0.340606i | 0.970564 | − | 0.240845i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.76798 | − | 0.935021i | 0.883988 | − | 0.467510i | ||||
\(5\) | − | 2.13486i | − | 0.954737i | −0.878703 | − | 0.477369i | \(-0.841591\pi\) | ||
0.878703 | − | 0.477369i | \(-0.158409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.29464 | 1.24526 | 0.622629 | − | 0.782517i | \(-0.286064\pi\) | ||||
0.622629 | + | 0.782517i | \(0.286064\pi\) | |||||||
\(8\) | 2.10822 | − | 1.88558i | 0.745369 | − | 0.666653i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.727145 | − | 2.93027i | −0.229944 | − | 0.926633i | ||||
\(11\) | 3.71210i | 1.11924i | 0.828749 | + | 0.559620i | \(0.189053\pi\) | ||||
−0.828749 | + | 0.559620i | \(0.810947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.32843i | 0.645792i | 0.946435 | + | 0.322896i | \(0.104656\pi\) | ||||
−0.946435 | + | 0.322896i | \(0.895344\pi\) | |||||||
\(14\) | 4.52218 | − | 1.12218i | 1.20860 | − | 0.299914i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.25147 | − | 3.30619i | 0.562868 | − | 0.826547i | ||||
\(17\) | 6.48822 | 1.57362 | 0.786812 | − | 0.617192i | \(-0.211730\pi\) | ||||
0.786812 | + | 0.617192i | \(0.211730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −1.99614 | − | 3.77437i | −0.446350 | − | 0.843976i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.26436 | + | 5.09517i | 0.269563 | + | 1.08629i | ||||
\(23\) | −7.32651 | −1.52768 | −0.763842 | − | 0.645404i | \(-0.776689\pi\) | ||||
−0.763842 | + | 0.645404i | \(0.776689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.442384 | 0.0884769 | ||||||||
\(26\) | 0.793079 | + | 3.19597i | 0.155536 | + | 0.626782i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.82485 | − | 3.08056i | 1.10079 | − | 0.582171i | ||||
\(29\) | 2.59857i | 0.482542i | 0.970458 | + | 0.241271i | \(0.0775643\pi\) | ||||
−0.970458 | + | 0.241271i | \(0.922436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.34204 | −0.241037 | −0.120518 | − | 0.992711i | \(-0.538456\pi\) | ||||
−0.120518 | + | 0.992711i | \(0.538456\pi\) | |||||||
\(32\) | 1.96423 | − | 5.30489i | 0.347230 | − | 0.937780i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.90563 | − | 2.20993i | 1.52730 | − | 0.378999i | ||||
\(35\) | − | 7.03360i | − | 1.18889i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.72986i | − | 0.613186i | −0.951841 | − | 0.306593i | \(-0.900811\pi\) | ||
0.951841 | − | 0.306593i | \(-0.0991890\pi\) | |||||||
\(38\) | −0.340606 | − | 1.37258i | −0.0552536 | − | 0.222663i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.02544 | − | 4.50075i | −0.636478 | − | 0.711631i | ||||
\(41\) | −6.52385 | −1.01885 | −0.509427 | − | 0.860514i | \(-0.670143\pi\) | ||||
−0.509427 | + | 0.860514i | \(0.670143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.97202i | − | 0.300729i | −0.988631 | − | 0.150365i | \(-0.951955\pi\) | ||
0.988631 | − | 0.150365i | \(-0.0480448\pi\) | |||||||
\(44\) | 3.47089 | + | 6.56290i | 0.523256 | + | 0.989394i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0563 | + | 2.49545i | −1.48271 | + | 0.367935i | ||||
\(47\) | −5.45991 | −0.796410 | −0.398205 | − | 0.917297i | \(-0.630367\pi\) | ||||
−0.398205 | + | 0.917297i | \(0.630367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.85468 | 0.550669 | ||||||||
\(50\) | 0.607210 | − | 0.150679i | 0.0858724 | − | 0.0213092i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.17714 | + | 4.11661i | 0.301914 | + | 0.570872i | ||||
\(53\) | − | 4.98640i | − | 0.684935i | −0.939530 | − | 0.342467i | \(-0.888737\pi\) | ||
0.939530 | − | 0.342467i | \(-0.111263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.92480 | 1.06858 | ||||||||
\(56\) | 6.94584 | − | 6.21231i | 0.928177 | − | 0.830155i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.885089 | + | 3.56676i | 0.116218 | + | 0.468338i | ||||
\(59\) | − | 9.67136i | − | 1.25910i | −0.776958 | − | 0.629552i | \(-0.783238\pi\) | ||
0.776958 | − | 0.629552i | \(-0.216762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15570i | 1.04423i | 0.852875 | + | 0.522115i | \(0.174857\pi\) | ||||
−0.852875 | + | 0.522115i | \(0.825143\pi\) | |||||||
\(62\) | −1.84206 | + | 0.457105i | −0.233941 | + | 0.0580525i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.889191 | − | 7.95043i | 0.111149 | − | 0.993804i | ||||
\(65\) | 4.97088 | 0.616561 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.524986i | − | 0.0641372i | −0.999486 | − | 0.0320686i | \(-0.989790\pi\) | ||
0.999486 | − | 0.0320686i | \(-0.0102095\pi\) | |||||||
\(68\) | 11.4710 | − | 6.06662i | 1.39106 | − | 0.735686i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.39569 | − | 9.65420i | −0.286339 | − | 1.15390i | ||||
\(71\) | −7.17489 | −0.851503 | −0.425751 | − | 0.904840i | \(-0.639990\pi\) | ||||
−0.425751 | + | 0.904840i | \(0.639990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.33130 | −0.741022 | −0.370511 | − | 0.928828i | \(-0.620817\pi\) | ||||
−0.370511 | + | 0.928828i | \(0.620817\pi\) | |||||||
\(74\) | −1.27041 | − | 5.11955i | −0.147683 | − | 0.595136i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.935021 | − | 1.76798i | −0.107254 | − | 0.202801i | ||||
\(77\) | 12.2300i | 1.39374i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.75644 | −0.985176 | −0.492588 | − | 0.870263i | \(-0.663949\pi\) | ||||
−0.492588 | + | 0.870263i | \(0.663949\pi\) | |||||||
\(80\) | −7.05824 | − | 4.80657i | −0.789135 | − | 0.537391i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.95453 | + | 2.22206i | −0.988862 | + | 0.245386i | ||||
\(83\) | 7.74008i | 0.849585i | 0.905291 | + | 0.424792i | \(0.139653\pi\) | ||||
−0.905291 | + | 0.424792i | \(0.860347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.8514i | − | 1.50240i | ||||||
\(86\) | −0.671680 | − | 2.70676i | −0.0724291 | − | 0.291877i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.99945 | + | 7.82592i | 0.746144 | + | 0.834246i | ||||
\(89\) | 1.04368 | 0.110630 | 0.0553148 | − | 0.998469i | \(-0.482384\pi\) | ||||
0.0553148 | + | 0.998469i | \(0.482384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.67136i | 0.804178i | ||||||||
\(92\) | −12.9531 | + | 6.85044i | −1.35045 | + | 0.714208i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.49419 | + | 1.85968i | −0.772966 | + | 0.191811i | ||||
\(95\) | −2.13486 | −0.219032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.117594 | −0.0119398 | −0.00596992 | − | 0.999982i | \(-0.501900\pi\) | ||||
−0.00596992 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(98\) | 5.29088 | − | 1.31293i | 0.534459 | − | 0.132626i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.782125 | − | 0.413639i | 0.0782125 | − | 0.0413639i | ||||
\(101\) | 10.6142i | 1.05615i | 0.849197 | + | 0.528077i | \(0.177087\pi\) | ||||
−0.849197 | + | 0.528077i | \(0.822913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4190 | 1.22368 | 0.611840 | − | 0.790982i | \(-0.290430\pi\) | ||||
0.611840 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(104\) | 4.39045 | + | 4.90885i | 0.430519 | + | 0.481353i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.69840 | − | 6.84425i | −0.164963 | − | 0.664773i | ||||
\(107\) | 16.5439i | 1.59936i | 0.600430 | + | 0.799678i | \(0.294996\pi\) | ||||
−0.600430 | + | 0.799678i | \(0.705004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.4437i | − | 1.67080i | −0.549641 | − | 0.835401i | \(-0.685235\pi\) | ||
0.549641 | − | 0.835401i | \(-0.314765\pi\) | |||||||
\(110\) | 10.8775 | − | 2.69924i | 1.03712 | − | 0.257362i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.41780 | − | 10.8927i | 0.700916 | − | 1.02926i | ||||
\(113\) | 14.3193 | 1.34705 | 0.673523 | − | 0.739166i | \(-0.264780\pi\) | ||||
0.673523 | + | 0.739166i | \(0.264780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6411i | 1.45854i | ||||||||
\(116\) | 2.42972 | + | 4.59421i | 0.225594 | + | 0.426561i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.29413 | − | 13.2748i | −0.303249 | − | 1.22204i | ||||
\(119\) | 21.3764 | 1.95957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.77968 | −0.252698 | ||||||||
\(122\) | 2.77788 | + | 11.1944i | 0.251498 | + | 1.01349i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.37269 | + | 1.25483i | −0.213073 | + | 0.112687i | ||||
\(125\) | − | 11.6187i | − | 1.03921i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.63985 | 0.234248 | 0.117124 | − | 0.993117i | \(-0.462632\pi\) | ||||
0.117124 | + | 0.993117i | \(0.462632\pi\) | |||||||
\(128\) | −1.48748 | − | 11.2155i | −0.131475 | − | 0.991319i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.82295 | − | 1.69311i | 0.598412 | − | 0.148496i | ||||
\(131\) | 15.3670i | 1.34263i | 0.741174 | + | 0.671313i | \(0.234269\pi\) | ||||
−0.741174 | + | 0.671313i | \(0.765731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.29464i | − | 0.285682i | ||||||
\(134\) | −0.178813 | − | 0.720587i | −0.0154471 | − | 0.0622492i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.6786 | − | 12.2340i | 1.17293 | − | 1.04906i | ||||
\(137\) | 4.91853 | 0.420218 | 0.210109 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210109 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.80377i | 0.831545i | 0.909469 | + | 0.415773i | \(0.136489\pi\) | ||||
−0.909469 | + | 0.415773i | \(0.863511\pi\) | |||||||
\(140\) | −6.57656 | − | 12.4352i | −0.555821 | − | 1.05097i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.84814 | + | 2.44381i | −0.826438 | + | 0.205080i | ||||
\(143\) | −8.64338 | −0.722796 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.54758 | 0.460701 | ||||||||
\(146\) | −8.69024 | + | 2.15648i | −0.719209 | + | 0.178471i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.48750 | − | 6.59431i | −0.286671 | − | 0.542049i | ||||
\(149\) | 0.724147i | 0.0593244i | 0.999560 | + | 0.0296622i | \(0.00944316\pi\) | ||||
−0.999560 | + | 0.0296622i | \(0.990557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7252 | −1.27970 | −0.639850 | − | 0.768500i | \(-0.721003\pi\) | ||||
−0.639850 | + | 0.768500i | \(0.721003\pi\) | |||||||
\(152\) | −1.88558 | − | 2.10822i | −0.152941 | − | 0.170999i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.16563 | + | 16.7868i | 0.335676 | + | 1.35272i | ||||
\(155\) | 2.86505i | 0.230127i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.141127i | 0.0112632i | 0.999984 | + | 0.00563160i | \(0.00179260\pi\) | ||||
−0.999984 | + | 0.00563160i | \(0.998207\pi\) | |||||||
\(158\) | −12.0189 | + | 2.98249i | −0.956176 | + | 0.237275i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.3252 | − | 4.19334i | −0.895334 | − | 0.331513i | ||||
\(161\) | −24.1383 | −1.90236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.41859i | 0.659395i | 0.944087 | + | 0.329697i | \(0.106947\pi\) | ||||
−0.944087 | + | 0.329697i | \(0.893053\pi\) | |||||||
\(164\) | −11.5340 | + | 6.09993i | −0.900654 | + | 0.476325i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.63632 | + | 10.6239i | 0.204618 | + | 0.824576i | ||||
\(167\) | −5.16538 | −0.399709 | −0.199854 | − | 0.979826i | \(-0.564047\pi\) | ||||
−0.199854 | + | 0.979826i | \(0.564047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.57839 | 0.582953 | ||||||||
\(170\) | −4.71788 | − | 19.0123i | −0.361845 | − | 1.45817i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.84388 | − | 3.48647i | −0.140594 | − | 0.265841i | ||||
\(173\) | 3.13988i | 0.238721i | 0.992851 | + | 0.119360i | \(0.0380844\pi\) | ||||
−0.992851 | + | 0.119360i | \(0.961916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.45750 | 0.110177 | ||||||||
\(176\) | 12.2729 | + | 8.35769i | 0.925104 | + | 0.629984i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.43254 | − | 0.355483i | 0.107373 | − | 0.0266446i | ||||
\(179\) | 18.1898i | 1.35957i | 0.733410 | + | 0.679786i | \(0.237927\pi\) | ||||
−0.733410 | + | 0.679786i | \(0.762073\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.0798i | − | 1.04654i | −0.852166 | − | 0.523271i | \(-0.824712\pi\) | ||
0.852166 | − | 0.523271i | \(-0.175288\pi\) | |||||||
\(182\) | 2.61291 | + | 10.5296i | 0.193682 | + | 0.780505i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.4459 | + | 13.8147i | −1.13869 | + | 1.01843i | ||||
\(185\) | −7.96273 | −0.585431 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.0849i | 1.76126i | ||||||||
\(188\) | −9.65299 | + | 5.10513i | −0.704016 | + | 0.372330i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.93027 | + | 0.727145i | −0.212584 | + | 0.0527527i | ||||
\(191\) | −4.87409 | −0.352677 | −0.176338 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176338 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.99845 | −0.719704 | −0.359852 | − | 0.933009i | \(-0.617173\pi\) | ||||
−0.359852 | + | 0.933009i | \(0.617173\pi\) | |||||||
\(194\) | −0.161407 | + | 0.0400531i | −0.0115884 | + | 0.00287565i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.81498 | − | 3.60421i | 0.486785 | − | 0.257444i | ||||
\(197\) | − | 19.2209i | − | 1.36943i | −0.728810 | − | 0.684716i | \(-0.759926\pi\) | ||
0.728810 | − | 0.684716i | \(-0.240074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7323 | −0.831683 | −0.415842 | − | 0.909437i | \(-0.636513\pi\) | ||||
−0.415842 | + | 0.909437i | \(0.636513\pi\) | |||||||
\(200\) | 0.932644 | − | 0.834150i | 0.0659479 | − | 0.0589833i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.61526 | + | 14.5689i | 0.254369 | + | 1.02506i | ||||
\(203\) | 8.56137i | 0.600890i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9275i | 0.972737i | ||||||||
\(206\) | 17.0461 | − | 4.22998i | 1.18766 | − | 0.294717i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.69824 | + | 5.24240i | 0.533777 | + | 0.363495i | ||||
\(209\) | 3.71210 | 0.256771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.399383i | 0.0274947i | 0.999906 | + | 0.0137473i | \(0.00437605\pi\) | ||||
−0.999906 | + | 0.0137473i | \(0.995624\pi\) | |||||||
\(212\) | −4.66239 | − | 8.81583i | −0.320214 | − | 0.605474i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.63494 | + | 22.7078i | 0.385196 | + | 1.55228i | ||||
\(215\) | −4.20997 | −0.287118 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.42153 | −0.300153 | ||||||||
\(218\) | −5.94142 | − | 23.9429i | −0.402404 | − | 1.62162i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.0109 | − | 7.40986i | 0.944611 | − | 0.499572i | ||||
\(221\) | 15.1074i | 1.01623i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.2548 | −1.28939 | −0.644697 | − | 0.764438i | \(-0.723017\pi\) | ||||
−0.644697 | + | 0.764438i | \(0.723017\pi\) | |||||||
\(224\) | 6.47143 | − | 17.4777i | 0.432391 | − | 1.16778i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.6545 | − | 4.87724i | 1.30739 | − | 0.324429i | ||||
\(227\) | − | 20.0414i | − | 1.33019i | −0.746758 | − | 0.665096i | \(-0.768391\pi\) | ||
0.746758 | − | 0.665096i | \(-0.231609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2013i | 1.20277i | 0.798958 | + | 0.601387i | \(0.205385\pi\) | ||||
−0.798958 | + | 0.601387i | \(0.794615\pi\) | |||||||
\(230\) | 5.32744 | + | 21.4687i | 0.351281 | + | 1.41560i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.89981 | + | 5.47836i | 0.321688 | + | 0.359672i | ||||
\(233\) | −14.2376 | −0.932739 | −0.466369 | − | 0.884590i | \(-0.654438\pi\) | ||||
−0.466369 | + | 0.884590i | \(0.654438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6561i | 0.760362i | ||||||||
\(236\) | −9.04293 | − | 17.0987i | −0.588645 | − | 1.11303i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 29.3409 | − | 7.28093i | 1.90189 | − | 0.471952i | ||||
\(239\) | −8.31368 | −0.537767 | −0.268884 | − | 0.963173i | \(-0.586655\pi\) | ||||
−0.268884 | + | 0.963173i | \(0.586655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1776 | −1.68625 | −0.843125 | − | 0.537718i | \(-0.819287\pi\) | ||||
−0.843125 | + | 0.537718i | \(0.819287\pi\) | |||||||
\(242\) | −3.81534 | + | 0.946775i | −0.245260 | + | 0.0608610i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.62575 | + | 14.4191i | 0.488189 | + | 0.923087i | ||||
\(245\) | − | 8.22920i | − | 0.525744i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.32843 | 0.148155 | ||||||||
\(248\) | −2.82931 | + | 2.53051i | −0.179661 | + | 0.160688i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.95740 | − | 15.9477i | −0.250288 | − | 1.00862i | ||||
\(251\) | 29.4740i | 1.86038i | 0.367075 | + | 0.930191i | \(0.380359\pi\) | ||||
−0.367075 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 27.1967i | − | 1.70984i | ||||||
\(254\) | 3.62341 | − | 0.899147i | 0.227353 | − | 0.0564175i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.86175 | − | 14.8876i | −0.366360 | − | 0.930473i | ||||
\(257\) | −1.28195 | −0.0799657 | −0.0399828 | − | 0.999200i | \(-0.512730\pi\) | ||||
−0.0399828 | + | 0.999200i | \(0.512730\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.2886i | − | 0.763575i | ||||||
\(260\) | 8.78838 | − | 4.64787i | 0.545032 | − | 0.288249i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.23411 | + | 21.0926i | 0.323364 | + | 1.30310i | ||||
\(263\) | 29.2736 | 1.80509 | 0.902544 | − | 0.430597i | \(-0.141697\pi\) | ||||
0.902544 | + | 0.430597i | \(0.141697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6453 | −0.653933 | ||||||||
\(266\) | −1.12218 | − | 4.52218i | −0.0688050 | − | 0.277272i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.490873 | − | 0.928161i | −0.0299848 | − | 0.0566965i | ||||
\(269\) | 14.1850i | 0.864875i | 0.901664 | + | 0.432437i | \(0.142346\pi\) | ||||
−0.901664 | + | 0.432437i | \(0.857654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.3185 | 1.59874 | 0.799369 | − | 0.600840i | \(-0.205167\pi\) | ||||
0.799369 | + | 0.600840i | \(0.205167\pi\) | |||||||
\(272\) | 14.6080 | − | 21.4513i | 0.885743 | − | 1.30067i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.75110 | − | 1.67528i | 0.407849 | − | 0.101207i | ||||
\(275\) | 1.64217i | 0.0990269i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.58863i | 0.215620i | 0.994172 | + | 0.107810i | \(0.0343838\pi\) | ||||
−0.994172 | + | 0.107810i | \(0.965616\pi\) | |||||||
\(278\) | 3.33922 | + | 13.4565i | 0.200273 | + | 0.807068i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.2624 | − | 14.8284i | −0.792580 | − | 0.886165i | ||||
\(281\) | 4.42597 | 0.264031 | 0.132016 | − | 0.991248i | \(-0.457855\pi\) | ||||
0.132016 | + | 0.991248i | \(0.457855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.493151i | 0.0293148i | 0.999893 | + | 0.0146574i | \(0.00466576\pi\) | ||||
−0.999893 | + | 0.0146574i | \(0.995334\pi\) | |||||||
\(284\) | −12.6850 | + | 6.70867i | −0.752718 | + | 0.398086i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.8638 | + | 2.94399i | −0.701519 | + | 0.174082i | ||||
\(287\) | −21.4938 | −1.26874 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.0970 | 1.47630 | ||||||||
\(290\) | 7.61452 | − | 1.88954i | 0.447140 | − | 0.110957i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1936 | + | 5.91989i | −0.655054 | + | 0.346436i | ||||
\(293\) | − | 12.7228i | − | 0.743275i | −0.928378 | − | 0.371637i | \(-0.878796\pi\) | ||
0.928378 | − | 0.371637i | \(-0.121204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.6470 | −1.20211 | ||||||||
\(296\) | −7.03295 | − | 7.86338i | −0.408782 | − | 0.457050i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.246649 | + | 0.993952i | 0.0142880 | + | 0.0575781i | ||||
\(299\) | − | 17.0593i | − | 0.986565i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.49709i | − | 0.374486i | ||||||
\(302\) | −21.5842 | + | 5.35610i | −1.24203 | + | 0.308209i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.30619 | − | 2.25147i | −0.189623 | − | 0.129131i | ||||
\(305\) | 17.4113 | 0.996966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.2166i | − | 0.583092i | −0.956557 | − | 0.291546i | \(-0.905830\pi\) | ||
0.956557 | − | 0.291546i | \(-0.0941697\pi\) | |||||||
\(308\) | 11.4354 | + | 21.6224i | 0.651590 | + | 1.23205i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.975855 | + | 3.93253i | 0.0554248 | + | 0.223353i | ||||
\(311\) | −0.184934 | −0.0104867 | −0.00524333 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524333 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0733 | −1.07809 | −0.539044 | − | 0.842278i | \(-0.681214\pi\) | ||||
−0.539044 | + | 0.842278i | \(0.681214\pi\) | |||||||
\(314\) | 0.0480689 | + | 0.193709i | 0.00271268 | + | 0.0109317i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.4812 | + | 8.18745i | −0.870883 | + | 0.460580i | ||||
\(317\) | − | 0.911635i | − | 0.0512025i | −0.999672 | − | 0.0256013i | \(-0.991850\pi\) | ||
0.999672 | − | 0.0256013i | \(-0.00815002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.64615 | −0.540081 | ||||||||
\(320\) | −16.9730 | − | 1.89830i | −0.948821 | − | 0.106118i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −33.1318 | + | 8.22164i | −1.84636 | + | 0.458174i | ||||
\(323\) | − | 6.48822i | − | 0.361014i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.03006i | 0.0571376i | ||||||||
\(326\) | 2.86742 | + | 11.5552i | 0.158812 | + | 0.639984i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.7537 | + | 12.3012i | −0.759422 | + | 0.679221i | ||||
\(329\) | −17.9885 | −0.991736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.45230i | 0.134791i | 0.997726 | + | 0.0673953i | \(0.0214689\pi\) | ||||
−0.997726 | + | 0.0673953i | \(0.978531\pi\) | |||||||
\(332\) | 7.23714 | + | 13.6843i | 0.397190 | + | 0.751022i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.08992 | + | 1.75936i | −0.387943 | + | 0.0962678i | ||||
\(335\) | −1.12077 | −0.0612342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.1467 | 1.91456 | 0.957282 | − | 0.289156i | \(-0.0933746\pi\) | ||||
0.957282 | + | 0.289156i | \(0.0933746\pi\) | |||||||
\(338\) | 10.4020 | − | 2.58125i | 0.565793 | − | 0.140401i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.9514 | − | 24.4890i | −0.702387 | − | 1.32810i | ||||
\(341\) | − | 4.98177i | − | 0.269778i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3627 | −0.559533 | ||||||||
\(344\) | −3.71839 | − | 4.15744i | −0.200482 | − | 0.224154i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.06946 | + | 4.30975i | 0.0574946 | + | 0.231694i | ||||
\(347\) | − | 5.30643i | − | 0.284864i | −0.989805 | − | 0.142432i | \(-0.954508\pi\) | ||
0.989805 | − | 0.142432i | \(-0.0454922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.8913i | − | 1.43946i | −0.694255 | − | 0.719729i | \(-0.744266\pi\) | ||
0.694255 | − | 0.719729i | \(-0.255734\pi\) | |||||||
\(350\) | 2.00054 | − | 0.496433i | 0.106933 | − | 0.0265355i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.6923 | + | 7.29140i | 1.04960 | + | 0.388633i | ||||
\(353\) | 3.21383 | 0.171055 | 0.0855275 | − | 0.996336i | \(-0.472742\pi\) | ||||
0.0855275 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3174i | 0.812961i | ||||||||
\(356\) | 1.84520 | − | 0.975861i | 0.0977952 | − | 0.0517205i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.19557 | + | 24.9671i | 0.327446 | + | 1.31955i | ||||
\(359\) | 15.6827 | 0.827699 | 0.413850 | − | 0.910345i | \(-0.364184\pi\) | ||||
0.413850 | + | 0.910345i | \(0.364184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −4.79566 | − | 19.3257i | −0.252054 | − | 1.01574i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.17289 | + | 13.5628i | 0.375961 | + | 0.710883i | ||||
\(365\) | 13.5164i | 0.707481i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3509 | 0.749111 | 0.374555 | − | 0.927205i | \(-0.377795\pi\) | ||||
0.374555 | + | 0.927205i | \(0.377795\pi\) | |||||||
\(368\) | −16.4954 | + | 24.2228i | −0.859884 | + | 1.26270i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.9295 | + | 2.71215i | −0.568198 | + | 0.140998i | ||||
\(371\) | − | 16.4284i | − | 0.852921i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.08701i | − | 0.470508i | −0.971934 | − | 0.235254i | \(-0.924408\pi\) | ||
0.971934 | − | 0.235254i | \(-0.0755921\pi\) | |||||||
\(374\) | 8.20347 | + | 33.0586i | 0.424191 | + | 1.70942i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.5107 | + | 10.2951i | −0.593619 | + | 0.530929i | ||||
\(377\) | −6.05060 | −0.311622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.2006i | − | 0.934900i | −0.884020 | − | 0.467450i | \(-0.845173\pi\) | ||
0.884020 | − | 0.467450i | \(-0.154827\pi\) | |||||||
\(380\) | −3.77437 | + | 1.99614i | −0.193621 | + | 0.102400i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.69010 | + | 1.66015i | −0.342295 | + | 0.0849404i | ||||
\(383\) | 22.4154 | 1.14537 | 0.572686 | − | 0.819775i | \(-0.305901\pi\) | ||||
0.572686 | + | 0.819775i | \(0.305901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.1094 | 1.33066 | ||||||||
\(386\) | −13.7237 | + | 3.40553i | −0.698518 | + | 0.173337i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.207903 | + | 0.109953i | −0.0105547 | + | 0.00558200i | ||||
\(389\) | − | 34.9213i | − | 1.77058i | −0.465038 | − | 0.885291i | \(-0.653959\pi\) | ||
0.465038 | − | 0.885291i | \(-0.346041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.5360 | −2.40400 | ||||||||
\(392\) | 8.12652 | − | 7.26831i | 0.410451 | − | 0.367105i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.54676 | − | 26.3823i | −0.329821 | − | 1.32912i | ||||
\(395\) | 18.6937i | 0.940584i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3443i | 1.57313i | 0.617510 | + | 0.786563i | \(0.288142\pi\) | ||||
−0.617510 | + | 0.786563i | \(0.711858\pi\) | |||||||
\(398\) | −16.1036 | + | 3.99610i | −0.807201 | + | 0.200307i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.996016 | − | 1.46261i | 0.0498008 | − | 0.0731303i | ||||
\(401\) | −1.64321 | −0.0820579 | −0.0410290 | − | 0.999158i | \(-0.513064\pi\) | ||||
−0.0410290 | + | 0.999158i | \(0.513064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.12484i | − | 0.155659i | ||||||
\(404\) | 9.92451 | + | 18.7657i | 0.493763 | + | 0.933627i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.91605 | + | 11.7512i | 0.144721 | + | 0.583202i | ||||
\(407\) | 13.8456 | 0.686302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.46645 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(410\) | 4.74378 | + | 19.1166i | 0.234279 | + | 0.944104i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.9565 | − | 11.6120i | 1.08172 | − | 0.572083i | ||||
\(413\) | − | 31.8637i | − | 1.56791i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.5240 | 0.811130 | ||||||||
\(416\) | 12.3521 | + | 4.57357i | 0.605611 | + | 0.224238i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.09517 | − | 1.26436i | 0.249213 | − | 0.0618420i | ||||
\(419\) | − | 4.25063i | − | 0.207657i | −0.994595 | − | 0.103828i | \(-0.966891\pi\) | ||
0.994595 | − | 0.103828i | \(-0.0331093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4900i | 1.53473i | 0.641212 | + | 0.767364i | \(0.278432\pi\) | ||||
−0.641212 | + | 0.767364i | \(0.721568\pi\) | |||||||
\(422\) | 0.136032 | + | 0.548187i | 0.00662195 | + | 0.0266853i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.40224 | − | 10.5124i | −0.456613 | − | 0.510529i | ||||
\(425\) | 2.87029 | 0.139229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8701i | 1.30034i | ||||||||
\(428\) | 15.4689 | + | 29.2491i | 0.747715 | + | 1.41381i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.77854 | + | 1.43394i | −0.278666 | + | 0.0691508i | ||||
\(431\) | 21.0564 | 1.01425 | 0.507125 | − | 0.861872i | \(-0.330708\pi\) | ||||
0.507125 | + | 0.861872i | \(0.330708\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.53125 | −0.361929 | −0.180964 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180964 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(434\) | −6.06892 | + | 1.50600i | −0.291318 | + | 0.0722903i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.3102 | − | 30.8400i | −0.781117 | − | 1.47697i | ||||
\(437\) | 7.32651i | 0.350475i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.823995 | 0.0393271 | 0.0196636 | − | 0.999807i | \(-0.493740\pi\) | ||||
0.0196636 | + | 0.999807i | \(0.493740\pi\) | |||||||
\(440\) | 16.7072 | − | 14.9428i | 0.796486 | − | 0.712372i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.14567 | + | 20.7362i | 0.244755 | + | 0.986319i | ||||
\(443\) | 8.58526i | 0.407898i | 0.978982 | + | 0.203949i | \(0.0653777\pi\) | ||||
−0.978982 | + | 0.203949i | \(0.934622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.22810i | − | 0.105622i | ||||||
\(446\) | −26.4288 | + | 6.55829i | −1.25144 | + | 0.310544i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.92957 | − | 26.1938i | 0.138409 | − | 1.23754i | ||||
\(449\) | −2.49451 | −0.117723 | −0.0588615 | − | 0.998266i | \(-0.518747\pi\) | ||||
−0.0588615 | + | 0.998266i | \(0.518747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 24.2172i | − | 1.14034i | ||||||
\(452\) | 25.3162 | − | 13.3888i | 1.19077 | − | 0.629759i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.82621 | − | 27.5085i | −0.320370 | − | 1.29104i | ||||
\(455\) | 16.3773 | 0.767778 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5004 | 0.678301 | 0.339150 | − | 0.940732i | \(-0.389860\pi\) | ||||
0.339150 | + | 0.940732i | \(0.389860\pi\) | |||||||
\(458\) | 6.19947 | + | 24.9828i | 0.289682 | + | 1.16737i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.6247 | + | 27.6530i | 0.681881 | + | 1.28933i | ||||
\(461\) | 23.1930i | 1.08020i | 0.841600 | + | 0.540102i | \(0.181614\pi\) | ||||
−0.841600 | + | 0.540102i | \(0.818386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0637 | 1.21128 | 0.605642 | − | 0.795737i | \(-0.292916\pi\) | ||||
0.605642 | + | 0.795737i | \(0.292916\pi\) | |||||||
\(464\) | 8.59136 | + | 5.85061i | 0.398844 | + | 0.271608i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.5424 | + | 4.84943i | −0.905282 | + | 0.224645i | ||||
\(467\) | − | 12.1953i | − | 0.564332i | −0.959366 | − | 0.282166i | \(-0.908947\pi\) | ||
0.959366 | − | 0.282166i | \(-0.0910529\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.72964i | − | 0.0798674i | ||||||
\(470\) | 3.97015 | + | 15.9990i | 0.183129 | + | 0.737980i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.2361 | − | 20.3894i | −0.839385 | − | 0.938497i | ||||
\(473\) | 7.32031 | 0.336588 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.442384i | − | 0.0202980i | ||||||
\(476\) | 37.7929 | − | 19.9874i | 1.73224 | − | 0.916120i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.4112 | + | 2.83169i | −0.521937 | + | 0.129518i | ||||
\(479\) | −18.1883 | −0.831045 | −0.415523 | − | 0.909583i | \(-0.636401\pi\) | ||||
−0.415523 | + | 0.909583i | \(0.636401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68475 | 0.395990 | ||||||||
\(482\) | −35.9310 | + | 8.91626i | −1.63661 | + | 0.406125i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.91440 | + | 2.59906i | −0.223382 | + | 0.118139i | ||||
\(485\) | 0.251046i | 0.0113994i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.13693 | −0.0968334 | −0.0484167 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484167 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(488\) | 15.3782 | + | 17.1940i | 0.696139 | + | 0.778337i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.80291 | − | 11.2953i | −0.126623 | − | 0.510268i | ||||
\(491\) | 2.32773i | 0.105049i | 0.998620 | + | 0.0525244i | \(0.0167267\pi\) | ||||
−0.998620 | + | 0.0525244i | \(0.983273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8601i | 0.759341i | ||||||||
\(494\) | 3.19597 | − | 0.793079i | 0.143794 | − | 0.0356823i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.02156 | + | 4.43702i | −0.135672 | + | 0.199228i | ||||
\(497\) | −23.6387 | −1.06034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9382i | 0.758260i | 0.925343 | + | 0.379130i | \(0.123777\pi\) | ||||
−0.925343 | + | 0.379130i | \(0.876223\pi\) | |||||||
\(500\) | −10.8637 | − | 20.5416i | −0.485841 | − | 0.918648i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0390 | + | 40.4555i | 0.448063 | + | 1.80562i | ||||
\(503\) | −8.22413 | −0.366696 | −0.183348 | − | 0.983048i | \(-0.558693\pi\) | ||||
−0.183348 | + | 0.983048i | \(0.558693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6598 | 1.00835 | ||||||||
\(506\) | −9.26337 | − | 37.3298i | −0.411807 | − | 1.65951i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.66718 | − | 2.46831i | 0.207073 | − | 0.109514i | ||||
\(509\) | − | 19.8145i | − | 0.878261i | −0.898423 | − | 0.439131i | \(-0.855287\pi\) | ||
0.898423 | − | 0.439131i | \(-0.144713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.8594 | −0.922764 | ||||||||
\(512\) | −13.1165 | − | 18.4379i | −0.579675 | − | 0.814848i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.75958 | + | 0.436639i | −0.0776118 | + | 0.0192593i | ||||
\(515\) | − | 26.5128i | − | 1.16829i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.2677i | − | 0.891374i | ||||||
\(518\) | −4.18556 | − | 16.8671i | −0.183903 | − | 0.741098i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.4797 | − | 9.37297i | 0.459565 | − | 0.411032i | ||||
\(521\) | 36.0978 | 1.58147 | 0.790737 | − | 0.612156i | \(-0.209698\pi\) | ||||
0.790737 | + | 0.612156i | \(0.209698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.19475i | 0.183424i | 0.995786 | + | 0.0917119i | \(0.0292339\pi\) | ||||
−0.995786 | + | 0.0917119i | \(0.970766\pi\) | |||||||
\(524\) | 14.3685 | + | 27.1686i | 0.627691 | + | 1.18686i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.1805 | − | 9.97077i | 1.75195 | − | 0.434746i | ||||
\(527\) | −8.70743 | −0.379301 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.6778 | 1.33382 | ||||||||
\(530\) | −14.6115 | + | 3.62584i | −0.634683 | + | 0.157496i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.08056 | − | 5.82485i | −0.133559 | − | 0.252539i | ||||
\(533\) | − | 15.1903i | − | 0.657967i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.3188 | 1.52696 | ||||||||
\(536\) | −0.989901 | − | 1.10679i | −0.0427572 | − | 0.0478059i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.83150 | + | 19.4701i | 0.208301 | + | 0.839416i | ||||
\(539\) | 14.3090i | 0.616331i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.12211i | − | 0.263210i | −0.991302 | − | 0.131605i | \(-0.957987\pi\) | ||
0.991302 | − | 0.131605i | \(-0.0420131\pi\) | |||||||
\(542\) | 36.1244 | − | 8.96426i | 1.55168 | − | 0.385048i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.7443 | − | 34.4193i | 0.546409 | − | 1.47571i | ||||
\(545\) | −37.2398 | −1.59518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.88879i | − | 0.209029i | −0.994523 | − | 0.104515i | \(-0.966671\pi\) | ||
0.994523 | − | 0.104515i | \(-0.0333289\pi\) | |||||||
\(548\) | 8.69584 | − | 4.59893i | 0.371468 | − | 0.196457i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.559335 | + | 2.25402i | 0.0238501 | + | 0.0961119i | ||||
\(551\) | 2.59857 | 0.110703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.8493 | −1.22680 | ||||||||
\(554\) | 1.22231 | + | 4.92570i | 0.0519310 | + | 0.209273i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.16673 | + | 17.3328i | 0.388756 | + | 0.735076i | ||||
\(557\) | − | 28.5987i | − | 1.21176i | −0.795554 | − | 0.605882i | \(-0.792820\pi\) | ||
0.795554 | − | 0.605882i | \(-0.207180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.59171 | 0.194209 | ||||||||
\(560\) | −23.2544 | − | 15.8359i | −0.982677 | − | 0.669191i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.07501 | − | 1.50751i | 0.256259 | − | 0.0635905i | ||||
\(563\) | − | 9.83345i | − | 0.414431i | −0.978295 | − | 0.207215i | \(-0.933560\pi\) | ||
0.978295 | − | 0.207215i | \(-0.0664401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 30.5697i | − | 1.28608i | ||||||
\(566\) | 0.167970 | + | 0.676891i | 0.00706032 | + | 0.0284519i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.1263 | + | 13.5288i | −0.634683 | + | 0.567656i | ||||
\(569\) | 10.3543 | 0.434075 | 0.217037 | − | 0.976163i | \(-0.430361\pi\) | ||||
0.217037 | + | 0.976163i | \(0.430361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 36.7988i | − | 1.53998i | −0.638055 | − | 0.769991i | \(-0.720261\pi\) | ||
0.638055 | − | 0.769991i | \(-0.279739\pi\) | |||||||
\(572\) | −15.2813 | + | 8.08174i | −0.638942 | + | 0.337915i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −29.5020 | + | 7.32090i | −1.23139 | + | 0.305569i | ||||
\(575\) | −3.24113 | −0.135165 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.22871 | −0.342566 | −0.171283 | − | 0.985222i | \(-0.554791\pi\) | ||||
−0.171283 | + | 0.985222i | \(0.554791\pi\) | |||||||
\(578\) | 34.4478 | − | 8.54820i | 1.43284 | − | 0.355558i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.80798 | − | 5.18710i | 0.407254 | − | 0.215383i | ||||
\(581\) | 25.5008i | 1.05795i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.5100 | 0.766606 | ||||||||
\(584\) | −13.3478 | + | 11.9382i | −0.552335 | + | 0.494004i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.33347 | − | 17.4631i | −0.179014 | − | 0.721395i | ||||
\(587\) | 7.18047i | 0.296370i | 0.988960 | + | 0.148185i | \(0.0473431\pi\) | ||||
−0.988960 | + | 0.148185i | \(0.952657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.34204i | 0.0552976i | ||||||||
\(590\) | −28.3397 | + | 7.03249i | −1.16673 | + | 0.289523i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.3316 | − | 8.39768i | −0.506827 | − | 0.345143i | ||||
\(593\) | 24.7687 | 1.01713 | 0.508564 | − | 0.861024i | \(-0.330177\pi\) | ||||
0.508564 | + | 0.861024i | \(0.330177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 45.6355i | − | 1.87087i | ||||||
\(596\) | 0.677092 | + | 1.28027i | 0.0277348 | + | 0.0524420i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.81050 | − | 23.4153i | −0.237609 | − | 0.957524i | ||||
\(599\) | −41.9307 | −1.71324 | −0.856621 | − | 0.515946i | \(-0.827440\pi\) | ||||
−0.856621 | + | 0.515946i | \(0.827440\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.10027 | 0.0856718 | 0.0428359 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428359 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(602\) | −2.21295 | − | 8.91780i | −0.0901930 | − | 0.363462i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.8018 | + | 14.7034i | −1.13124 | + | 0.598273i | ||||
\(605\) | 5.93422i | 0.241260i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2877 | −0.458152 | −0.229076 | − | 0.973409i | \(-0.573570\pi\) | ||||
−0.229076 | + | 0.973409i | \(0.573570\pi\) | |||||||
\(608\) | −5.30489 | − | 1.96423i | −0.215142 | − | 0.0796599i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.8984 | − | 5.93038i | 0.967619 | − | 0.240114i | ||||
\(611\) | − | 12.7130i | − | 0.514315i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 31.4983i | − | 1.27220i | −0.771605 | − | 0.636102i | \(-0.780546\pi\) | ||
0.771605 | − | 0.636102i | \(-0.219454\pi\) | |||||||
\(614\) | −3.47984 | − | 14.0231i | −0.140435 | − | 0.565928i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.0607 | + | 25.7836i | 0.929142 | + | 1.03885i | ||||
\(617\) | 11.4563 | 0.461214 | 0.230607 | − | 0.973047i | \(-0.425929\pi\) | ||||
0.230607 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.6816i | 1.51455i | 0.653095 | + | 0.757276i | \(0.273470\pi\) | ||||
−0.653095 | + | 0.757276i | \(0.726530\pi\) | |||||||
\(620\) | 2.67889 | + | 5.06534i | 0.107587 | + | 0.203429i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.253838 | + | 0.0629898i | −0.0101780 | + | 0.00252566i | ||||
\(623\) | 3.43855 | 0.137763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.5924 | −0.903695 | ||||||||
\(626\) | −26.1797 | + | 6.49649i | −1.04635 | + | 0.259652i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.131957 | + | 0.249510i | 0.00526566 | + | 0.00995653i | ||||
\(629\) | − | 24.2002i | − | 0.964925i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.99670 | 0.278534 | 0.139267 | − | 0.990255i | \(-0.455525\pi\) | ||||
0.139267 | + | 0.990255i | \(0.455525\pi\) | |||||||
\(632\) | −18.4605 | + | 16.5109i | −0.734319 | + | 0.656770i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.310508 | − | 1.25130i | −0.0123319 | − | 0.0496953i | ||||
\(635\) | − | 5.63569i | − | 0.223646i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.97538i | 0.355617i | ||||||||
\(638\) | −13.2402 | + | 3.28554i | −0.524183 | + | 0.130076i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.9435 | + | 3.17555i | −0.946450 | + | 0.125525i | ||||
\(641\) | 6.20749 | 0.245181 | 0.122591 | − | 0.992457i | \(-0.460880\pi\) | ||||
0.122591 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.4008i | 1.15945i | 0.814811 | + | 0.579726i | \(0.196841\pi\) | ||||
−0.814811 | + | 0.579726i | \(0.803159\pi\) | |||||||
\(644\) | −42.6758 | + | 22.5698i | −1.68166 | + | 0.889374i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.20993 | − | 8.90563i | −0.0869484 | − | 0.350387i | ||||
\(647\) | −5.62285 | −0.221057 | −0.110529 | − | 0.993873i | \(-0.535254\pi\) | ||||
−0.110529 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9011 | 1.40924 | ||||||||
\(650\) | 0.350846 | + | 1.41385i | 0.0137613 | + | 0.0554557i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.87156 | + | 14.8839i | 0.308274 | + | 0.582897i | ||||
\(653\) | 34.9447i | 1.36749i | 0.729721 | + | 0.683745i | \(0.239650\pi\) | ||||
−0.729721 | + | 0.683745i | \(0.760350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.8064 | 1.28185 | ||||||||
\(656\) | −14.6883 | + | 21.5691i | −0.573480 | + | 0.842130i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.6907 | + | 6.12698i | −0.962543 | + | 0.238855i | ||||
\(659\) | − | 37.8768i | − | 1.47547i | −0.675090 | − | 0.737736i | \(-0.735895\pi\) | ||
0.675090 | − | 0.737736i | \(-0.264105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.77264i | − | 0.263425i | −0.991288 | − | 0.131713i | \(-0.957952\pi\) | ||
0.991288 | − | 0.131713i | \(-0.0420476\pi\) | |||||||
\(662\) | 0.835268 | + | 3.36599i | 0.0324636 | + | 0.130823i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5945 | + | 16.3178i | 0.566378 | + | 0.633254i | ||||
\(665\) | −7.03360 | −0.272751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 19.0385i | − | 0.737172i | ||||||
\(668\) | −9.13226 | + | 4.82974i | −0.353338 | + | 0.186868i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.53835 | + | 0.381741i | −0.0594317 | + | 0.0147479i | ||||
\(671\) | −30.2748 | −1.16874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6355 | 0.949630 | 0.474815 | − | 0.880086i | \(-0.342515\pi\) | ||||
0.474815 | + | 0.880086i | \(0.342515\pi\) | |||||||
\(674\) | 48.2418 | − | 11.9712i | 1.85821 | − | 0.461113i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.3984 | − | 7.08596i | 0.515323 | − | 0.272537i | ||||
\(677\) | 28.2956i | 1.08749i | 0.839251 | + | 0.543744i | \(0.182994\pi\) | ||||
−0.839251 | + | 0.543744i | \(0.817006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.387430 | −0.0148682 | ||||||||
\(680\) | −26.1179 | − | 29.2019i | −1.00158 | − | 1.11984i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.69682 | − | 6.83790i | −0.0649746 | − | 0.261837i | ||||
\(683\) | − | 34.4333i | − | 1.31755i | −0.752339 | − | 0.658777i | \(-0.771074\pi\) | ||
0.752339 | − | 0.658777i | \(-0.228926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.5004i | − | 0.401198i | ||||||
\(686\) | −14.2237 | + | 3.52960i | −0.543063 | + | 0.134761i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.51985 | − | 4.43994i | −0.248567 | − | 0.169271i | ||||
\(689\) | 11.6105 | 0.442325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.19928i | 0.0836646i | 0.999125 | + | 0.0418323i | \(0.0133195\pi\) | ||||
−0.999125 | + | 0.0418323i | \(0.986680\pi\) | |||||||
\(692\) | 2.93585 | + | 5.55123i | 0.111604 | + | 0.211026i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.80740 | − | 7.28352i | −0.0686080 | − | 0.276479i | ||||
\(695\) | 20.9297 | 0.793907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.3282 | −1.60329 | ||||||||
\(698\) | −9.15934 | − | 36.9106i | −0.346686 | − | 1.39709i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.57682 | − | 1.36279i | 0.0973947 | − | 0.0515087i | ||||
\(701\) | − | 36.0608i | − | 1.36200i | −0.732285 | − | 0.680999i | \(-0.761546\pi\) | ||
0.732285 | − | 0.680999i | \(-0.238454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.72986 | −0.140675 | ||||||||
\(704\) | 29.5128 | + | 3.30076i | 1.11230 | + | 0.124402i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.41126 | − | 1.09465i | 0.166020 | − | 0.0411977i | ||||
\(707\) | 34.9701i | 1.31518i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.7299i | − | 0.402970i | −0.979492 | − | 0.201485i | \(-0.935423\pi\) | ||
0.979492 | − | 0.201485i | \(-0.0645768\pi\) | |||||||
\(710\) | 5.21719 | + | 21.0244i | 0.195798 | + | 0.789031i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.20030 | − | 1.96794i | 0.0824599 | − | 0.0737515i | ||||
\(713\) | 9.83244 | 0.368228 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.4524i | 0.690080i | ||||||||
\(716\) | 17.0079 | + | 32.1592i | 0.635614 | + | 1.20185i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.5258 | − | 5.34161i | 0.803335 | − | 0.199347i | ||||
\(719\) | −29.1037 | −1.08539 | −0.542693 | − | 0.839931i | \(-0.682595\pi\) | ||||
−0.542693 | + | 0.839931i | \(0.682595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.9162 | 1.52380 | ||||||||
\(722\) | −1.37258 | + | 0.340606i | −0.0510823 | + | 0.0126760i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.1649 | − | 24.8927i | −0.489269 | − | 0.925130i | ||||
\(725\) | 1.14957i | 0.0426938i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.5850 | −1.50521 | −0.752607 | − | 0.658470i | \(-0.771204\pi\) | ||||
−0.752607 | + | 0.658470i | \(0.771204\pi\) | |||||||
\(728\) | 14.4650 | + | 16.1729i | 0.536107 | + | 0.599409i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.60377 | + | 18.5524i | 0.170393 | + | 0.686656i | ||||
\(731\) | − | 12.7949i | − | 0.473235i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.6206i | 0.687766i | 0.939012 | + | 0.343883i | \(0.111742\pi\) | ||||
−0.939012 | + | 0.343883i | \(0.888258\pi\) | |||||||
\(734\) | 19.6978 | − | 4.88800i | 0.727059 | − | 0.180419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.3909 | + | 38.8663i | −0.530457 | + | 1.43263i | ||||
\(737\) | 1.94880 | 0.0717849 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.89939i | 0.290584i | 0.989389 | + | 0.145292i | \(0.0464121\pi\) | ||||
−0.989389 | + | 0.145292i | \(0.953588\pi\) | |||||||
\(740\) | −14.0779 | + | 7.44532i | −0.517514 | + | 0.273695i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.59562 | − | 22.5494i | −0.205422 | − | 0.827814i | ||||
\(743\) | 14.4064 | 0.528521 | 0.264261 | − | 0.964451i | \(-0.414872\pi\) | ||||
0.264261 | + | 0.964451i | \(0.414872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.54595 | 0.0566392 | ||||||||
\(746\) | −3.09509 | − | 12.4727i | −0.113319 | − | 0.456658i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.5199 | + | 42.5815i | 0.823409 | + | 1.55694i | ||||
\(749\) | 54.5061i | 1.99161i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0914 | 0.514204 | 0.257102 | − | 0.966384i | \(-0.417232\pi\) | ||||
0.257102 | + | 0.966384i | \(0.417232\pi\) | |||||||
\(752\) | −12.2928 | + | 18.0515i | −0.448273 | + | 0.658270i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.30496 | + | 2.06087i | −0.302449 | + | 0.0750525i | ||||
\(755\) | 33.5711i | 1.22178i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.2311i | 1.82568i | 0.408318 | + | 0.912840i | \(0.366116\pi\) | ||||
−0.408318 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(758\) | −6.19922 | − | 24.9818i | −0.225166 | − | 0.907380i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50075 | + | 4.02544i | −0.163259 | + | 0.146018i | ||||
\(761\) | −23.7483 | −0.860875 | −0.430437 | − | 0.902620i | \(-0.641641\pi\) | ||||
−0.430437 | + | 0.902620i | \(0.641641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 57.4707i | − | 2.08058i | ||||||
\(764\) | −8.61727 | + | 4.55738i | −0.311762 | + | 0.164880i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.7670 | − | 7.63481i | 1.11166 | − | 0.275857i | ||||
\(767\) | 22.5191 | 0.813119 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.4035 | −1.70942 | −0.854708 | − | 0.519109i | \(-0.826264\pi\) | ||||
−0.854708 | + | 0.519109i | \(0.826264\pi\) | |||||||
\(770\) | 35.8374 | − | 8.89302i | 1.29149 | − | 0.320482i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.6770 | + | 9.34876i | −0.636209 | + | 0.336469i | ||||
\(773\) | − | 11.8508i | − | 0.426242i | −0.977026 | − | 0.213121i | \(-0.931637\pi\) | ||
0.977026 | − | 0.213121i | \(-0.0683628\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.593696 | −0.0213262 | ||||||||
\(776\) | −0.247914 | + | 0.221732i | −0.00889958 | + | 0.00795972i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.8944 | − | 47.9325i | −0.426435 | − | 1.71846i | ||||
\(779\) | 6.52385i | 0.233741i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 26.6339i | − | 0.953036i | ||||||
\(782\) | −65.2472 | + | 16.1911i | −2.33324 | + | 0.578991i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.67871 | − | 12.7443i | 0.309954 | − | 0.455154i | ||||
\(785\) | 0.301287 | 0.0107534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3903i | 0.940713i | 0.882477 | + | 0.470356i | \(0.155875\pi\) | ||||
−0.882477 | + | 0.470356i | \(0.844125\pi\) | |||||||
\(788\) | −17.9719 | − | 33.9821i | −0.640224 | − | 1.21056i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.36720 | + | 25.6587i | 0.226535 | + | 0.912897i | ||||
\(791\) | 47.1770 | 1.67742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.9900 | −0.674356 | ||||||||
\(794\) | 10.6761 | + | 43.0227i | 0.378879 | + | 1.52682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.7425 | + | 10.9700i | −0.735197 | + | 0.388821i | ||||
\(797\) | − | 14.1893i | − | 0.502610i | −0.967908 | − | 0.251305i | \(-0.919140\pi\) | ||
0.967908 | − | 0.251305i | \(-0.0808597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.4251 | −1.25325 | ||||||||
\(800\) | 0.868943 | − | 2.34680i | 0.0307218 | − | 0.0829719i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.25544 | + | 0.559687i | −0.0796424 | + | 0.0197632i | ||||
\(803\) | − | 23.5024i | − | 0.829382i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.5317i | 1.81625i | ||||||||
\(806\) | −1.06434 | − | 4.28911i | −0.0374898 | − | 0.151077i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20.0139 | + | 22.3771i | 0.704087 | + | 0.787224i | ||||
\(809\) | 29.9998 | 1.05474 | 0.527368 | − | 0.849637i | \(-0.323179\pi\) | ||||
0.527368 | + | 0.849637i | \(0.323179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.8833i | − | 1.40049i | −0.713901 | − | 0.700246i | \(-0.753073\pi\) | ||
0.713901 | − | 0.700246i | \(-0.246927\pi\) | |||||||
\(812\) | 8.00506 | + | 15.1363i | 0.280922 | + | 0.531179i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.0043 | − | 4.71590i | 0.666100 | − | 0.165292i | ||||
\(815\) | 17.9725 | 0.629549 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.97202 | −0.0689921 | ||||||||
\(818\) | −3.38541 | + | 0.840089i | −0.118368 | + | 0.0293730i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.0225 | + | 24.6234i | 0.454765 | + | 0.859888i | ||||
\(821\) | − | 56.4395i | − | 1.96975i | −0.173256 | − | 0.984877i | \(-0.555429\pi\) | ||
0.173256 | − | 0.984877i | \(-0.444571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.7360 | −1.45482 | −0.727412 | − | 0.686201i | \(-0.759277\pi\) | ||||
−0.727412 | + | 0.686201i | \(0.759277\pi\) | |||||||
\(824\) | 26.1820 | − | 23.4170i | 0.912093 | − | 0.815769i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.8530 | − | 43.7356i | −0.377623 | − | 1.52176i | ||||
\(827\) | − | 17.4248i | − | 0.605921i | −0.953003 | − | 0.302960i | \(-0.902025\pi\) | ||
0.953003 | − | 0.302960i | \(-0.0979750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 52.2723i | − | 1.81549i | −0.419519 | − | 0.907747i | \(-0.637801\pi\) | ||
0.419519 | − | 0.907747i | \(-0.362199\pi\) | |||||||
\(830\) | 22.6805 | − | 5.62817i | 0.787253 | − | 0.195356i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.5121 | + | 2.07042i | 0.641790 | + | 0.0717790i | ||||
\(833\) | 25.0100 | 0.866547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0273i | 0.381617i | ||||||||
\(836\) | 6.56290 | − | 3.47089i | 0.226983 | − | 0.120043i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.44779 | − | 5.83434i | −0.0500130 | − | 0.201544i | ||||
\(839\) | −40.8429 | −1.41005 | −0.705027 | − | 0.709180i | \(-0.749065\pi\) | ||||
−0.705027 | + | 0.709180i | \(0.749065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2474 | 0.767153 | ||||||||
\(842\) | 10.7257 | + | 43.2226i | 0.369631 | + | 1.48955i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.373432 | + | 0.706100i | 0.0128541 | + | 0.0243050i | ||||
\(845\) | − | 16.1788i | − | 0.556567i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.15805 | −0.314674 | ||||||||
\(848\) | −16.4860 | − | 11.2267i | −0.566131 | − | 0.385528i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.93971 | − | 0.977638i | 0.135131 | − | 0.0335327i | ||||
\(851\) | 27.3269i | 0.936754i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.8153i | − | 1.46597i | −0.680245 | − | 0.732984i | \(-0.738127\pi\) | ||
0.680245 | − | 0.732984i | \(-0.261873\pi\) | |||||||
\(854\) | 9.15213 | + | 36.8815i | 0.313180 | + | 1.26206i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.1947 | + | 34.8781i | 1.06621 | + | 1.19211i | ||||
\(857\) | −23.2947 | −0.795732 | −0.397866 | − | 0.917444i | \(-0.630249\pi\) | ||||
−0.397866 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.5879i | 0.600091i | 0.953925 | + | 0.300045i | \(0.0970018\pi\) | ||||
−0.953925 | + | 0.300045i | \(0.902998\pi\) | |||||||
\(860\) | −7.44312 | + | 3.93641i | −0.253808 | + | 0.134230i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.9017 | − | 7.17193i | 0.984394 | − | 0.244277i | ||||
\(863\) | 11.8886 | 0.404692 | 0.202346 | − | 0.979314i | \(-0.435143\pi\) | ||||
0.202346 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.70319 | 0.227915 | ||||||||
\(866\) | −10.3373 | + | 2.56519i | −0.351275 | + | 0.0871687i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.81716 | + | 4.13422i | −0.265332 | + | 0.140325i | ||||
\(869\) | − | 32.5048i | − | 1.10265i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22239 | 0.0414193 | ||||||||
\(872\) | −32.8914 | − | 36.7751i | −1.11384 | − | 1.24536i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.49545 | + | 10.0563i | 0.0844100 | + | 0.340158i | ||||
\(875\) | − | 38.2795i | − | 1.29408i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6698i | 0.968111i | 0.875037 | + | 0.484056i | \(0.160837\pi\) | ||||
−0.875037 | + | 0.484056i | \(0.839163\pi\) | |||||||
\(878\) | 1.13100 | − | 0.280658i | 0.0381695 | − | 0.00947173i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.8425 | − | 26.2009i | 0.601469 | − | 0.883231i | ||||
\(881\) | 44.2297 | 1.49014 | 0.745069 | − | 0.666988i | \(-0.232417\pi\) | ||||
0.745069 | + | 0.666988i | \(0.232417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.5869i | − | 0.894719i | −0.894354 | − | 0.447359i | \(-0.852364\pi\) | ||
0.894354 | − | 0.447359i | \(-0.147636\pi\) | |||||||
\(884\) | 14.1257 | + | 26.7095i | 0.475100 | + | 0.898338i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.92419 | + | 11.7840i | 0.0982401 | + | 0.395891i | ||||
\(887\) | −16.4124 | −0.551074 | −0.275537 | − | 0.961290i | \(-0.588856\pi\) | ||||
−0.275537 | + | 0.961290i | \(0.588856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.69735 | 0.291700 | ||||||||
\(890\) | −0.758906 | − | 3.05826i | −0.0254386 | − | 0.102513i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.0420 | + | 18.0036i | −1.13981 | + | 0.602806i | ||||
\(893\) | 5.45991i | 0.182709i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.8327 | 1.29803 | ||||||||
\(896\) | −4.90070 | − | 36.9511i | −0.163721 | − | 1.23445i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.42392 | + | 0.849644i | −0.114258 | + | 0.0283530i | ||||
\(899\) | − | 3.48737i | − | 0.116310i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 32.3529i | − | 1.07783i | ||||||
\(902\) | −8.24851 | − | 33.2401i | −0.274645 | − | 1.10677i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30.1883 | − | 27.0002i | 1.00405 | − | 0.898012i | ||||
\(905\) | −30.0583 | −0.999172 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47.3380i | − | 1.57183i | −0.618333 | − | 0.785916i | \(-0.712192\pi\) | ||
0.618333 | − | 0.785916i | \(-0.287808\pi\) | |||||||
\(908\) | −18.7391 | − | 35.4326i | −0.621879 | − | 1.17587i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.4792 | − | 5.57820i | 0.745178 | − | 0.184915i | ||||
\(911\) | −5.30896 | −0.175894 | −0.0879469 | − | 0.996125i | \(-0.528031\pi\) | ||||
−0.0879469 | + | 0.996125i | \(0.528031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.7320 | −0.950889 | ||||||||
\(914\) | 19.9030 | − | 4.93893i | 0.658334 | − | 0.163365i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.0186 | + | 32.1794i | 0.562310 | + | 1.06324i | ||||
\(917\) | 50.6290i | 1.67192i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.2513 | 1.62465 | 0.812326 | − | 0.583204i | \(-0.198201\pi\) | ||||
0.812326 | + | 0.583204i | \(0.198201\pi\) | |||||||
\(920\) | 29.4924 | + | 32.9748i | 0.972337 | + | 1.08715i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.89966 | + | 31.8343i | 0.260162 | + | 1.04841i | ||||
\(923\) | − | 16.7063i | − | 0.549893i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.65003i | − | 0.0542528i | ||||||
\(926\) | 35.7747 | − | 8.87746i | 1.17563 | − | 0.291732i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.7851 | + | 5.10418i | 0.452519 | + | 0.167553i | ||||
\(929\) | 29.2990 | 0.961270 | 0.480635 | − | 0.876921i | \(-0.340406\pi\) | ||||
0.480635 | + | 0.876921i | \(0.340406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.85468i | − | 0.126332i | ||||||
\(932\) | −25.1718 | + | 13.3125i | −0.824529 | + | 0.436065i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.15380 | − | 16.7391i | −0.135916 | − | 0.547720i | ||||
\(935\) | 51.4179 | 1.68154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.35345 | −0.207558 | −0.103779 | − | 0.994600i | \(-0.533093\pi\) | ||||
−0.103779 | + | 0.994600i | \(0.533093\pi\) | |||||||
\(938\) | −0.589126 | − | 2.37408i | −0.0192357 | − | 0.0775164i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.8987 | + | 20.6077i | 0.355477 | + | 0.672151i | ||||
\(941\) | − | 2.07523i | − | 0.0676505i | −0.999428 | − | 0.0338253i | \(-0.989231\pi\) | ||
0.999428 | − | 0.0338253i | \(-0.0107690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.7970 | 1.55649 | ||||||||
\(944\) | −31.9753 | − | 21.7748i | −1.04071 | − | 0.708709i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0477 | − | 2.49334i | 0.326680 | − | 0.0810656i | ||||
\(947\) | − | 13.3618i | − | 0.434201i | −0.976149 | − | 0.217101i | \(-0.930340\pi\) | ||
0.976149 | − | 0.217101i | \(-0.0696600\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.7420i | − | 0.478546i | ||||||
\(950\) | −0.150679 | − | 0.607210i | −0.00488867 | − | 0.0197005i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 45.0661 | − | 40.3068i | 1.46060 | − | 1.30635i | ||||
\(953\) | 52.6796 | 1.70646 | 0.853231 | − | 0.521534i | \(-0.174640\pi\) | ||||
0.853231 | + | 0.521534i | \(0.174640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4055i | 0.336714i | ||||||||
\(956\) | −14.6984 | + | 7.77347i | −0.475380 | + | 0.251412i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.9650 | + | 6.19505i | −0.806582 | + | 0.200153i | ||||
\(959\) | 16.2048 | 0.523281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1989 | −0.941901 | ||||||||
\(962\) | 11.9205 | − | 2.95808i | 0.384334 | − | 0.0953722i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −46.2814 | + | 24.4766i | −1.49062 | + | 0.788339i | ||||
\(965\) | 21.3453i | 0.687128i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.17519 | −0.230739 | −0.115369 | − | 0.993323i | \(-0.536805\pi\) | ||||
−0.115369 | + | 0.993323i | \(0.536805\pi\) | |||||||
\(968\) | −5.86018 | + | 5.24130i | −0.188353 | + | 0.168462i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0855077 | + | 0.344582i | 0.00274549 | + | 0.0110638i | ||||
\(971\) | − | 14.6991i | − | 0.471718i | −0.971787 | − | 0.235859i | \(-0.924210\pi\) | ||
0.971787 | − | 0.235859i | \(-0.0757903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.3000i | 1.03549i | ||||||||
\(974\) | −2.93311 | + | 0.727851i | −0.0939830 | + | 0.0233218i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.9643 | + | 18.3623i | 0.863106 | + | 0.587764i | ||||
\(977\) | −19.5470 | −0.625365 | −0.312682 | − | 0.949858i | \(-0.601228\pi\) | ||||
−0.312682 | + | 0.949858i | \(0.601228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.87424i | 0.123821i | ||||||||
\(980\) | −7.69447 | − | 14.5490i | −0.245791 | − | 0.464751i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.792838 | + | 3.19500i | 0.0253005 | + | 0.101957i | ||||
\(983\) | −24.0339 | −0.766562 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.0339 | −1.30745 | ||||||||
\(986\) | 5.74265 | + | 23.1419i | 0.182883 | + | 0.736988i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.11661 | − | 2.17714i | 0.130967 | − | 0.0692639i | ||||
\(989\) | 14.4480i | 0.459419i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.5419 | 1.60552 | 0.802758 | − | 0.596305i | \(-0.203365\pi\) | ||||
0.802758 | + | 0.596305i | \(0.203365\pi\) | |||||||
\(992\) | −2.63606 | + | 7.11935i | −0.0836951 | + | 0.226039i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.4461 | + | 8.05149i | −1.02913 | + | 0.255378i | ||||
\(995\) | 25.0469i | 0.794039i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 21.9225i | − | 0.694293i | −0.937811 | − | 0.347147i | \(-0.887151\pi\) | ||
0.937811 | − | 0.347147i | \(-0.112849\pi\) | |||||||
\(998\) | 5.76927 | + | 23.2492i | 0.182623 | + | 0.735939i | ||||
\(999\) | 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 | 1368.2.g.b.685.13 | 16 | ||
3.2 | odd | 2 | 152.2.c.b.77.4 | yes | 16 | ||
4.3 | odd | 2 | 5472.2.g.b.2737.4 | 16 | |||
8.3 | odd | 2 | 5472.2.g.b.2737.13 | 16 | |||
8.5 | even | 2 | inner | 1368.2.g.b.685.14 | 16 | ||
12.11 | even | 2 | 608.2.c.b.305.2 | 16 | |||
24.5 | odd | 2 | 152.2.c.b.77.3 | ✓ | 16 | ||
24.11 | even | 2 | 608.2.c.b.305.15 | 16 | |||
48.5 | odd | 4 | 4864.2.a.bo.1.8 | 8 | |||
48.11 | even | 4 | 4864.2.a.bn.1.1 | 8 | |||
48.29 | odd | 4 | 4864.2.a.bq.1.1 | 8 | |||
48.35 | even | 4 | 4864.2.a.bp.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.3 | ✓ | 16 | 24.5 | odd | 2 | ||
152.2.c.b.77.4 | yes | 16 | 3.2 | odd | 2 | ||
608.2.c.b.305.2 | 16 | 12.11 | even | 2 | |||
608.2.c.b.305.15 | 16 | 24.11 | even | 2 | |||
1368.2.g.b.685.13 | 16 | 1.1 | even | 1 | trivial | ||
1368.2.g.b.685.14 | 16 | 8.5 | even | 2 | inner | ||
4864.2.a.bn.1.1 | 8 | 48.11 | even | 4 | |||
4864.2.a.bo.1.8 | 8 | 48.5 | odd | 4 | |||
4864.2.a.bp.1.8 | 8 | 48.35 | even | 4 | |||
4864.2.a.bq.1.1 | 8 | 48.29 | odd | 4 | |||
5472.2.g.b.2737.4 | 16 | 4.3 | odd | 2 | |||
5472.2.g.b.2737.13 | 16 | 8.3 | odd | 2 |