Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 161.9 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.e.491.19 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.62650 | − | 0.595404i | 0.939059 | − | 0.343757i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | −0.595404 | − | 1.62650i | −0.243073 | − | 0.664015i | ||||
\(7\) | −0.581871 | − | 1.00783i | −0.219927 | − | 0.380924i | 0.734859 | − | 0.678220i | \(-0.237248\pi\) |
−0.954785 | + | 0.297296i | \(0.903915\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.29099 | − | 1.93685i | 0.763663 | − | 0.645615i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0.0889568 | − | 0.154078i | 0.0268215 | − | 0.0464562i | −0.852303 | − | 0.523048i | \(-0.824795\pi\) |
0.879125 | + | 0.476592i | \(0.158128\pi\) | |||||||
\(12\) | −1.62650 | + | 0.595404i | −0.469529 | + | 0.171878i | ||||
\(13\) | −4.88952 | − | 2.82297i | −1.35611 | − | 0.782950i | −0.367012 | − | 0.930216i | \(-0.619619\pi\) |
−0.989097 | + | 0.147266i | \(0.952953\pi\) | |||||||
\(14\) | −1.00783 | + | 0.581871i | −0.269354 | + | 0.155512i | ||||
\(15\) | 1.70629 | + | 0.297614i | 0.440562 | + | 0.0768436i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.93896 | − | 3.35837i | −0.470266 | − | 0.814524i | 0.529156 | − | 0.848525i | \(-0.322509\pi\) |
−0.999422 | + | 0.0340003i | \(0.989175\pi\) | |||||||
\(18\) | −1.93685 | − | 2.29099i | −0.456519 | − | 0.539991i | ||||
\(19\) | −2.57689 | − | 4.46331i | −0.591179 | − | 1.02395i | −0.994074 | − | 0.108706i | \(-0.965329\pi\) |
0.402895 | − | 0.915246i | \(-0.368004\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | −1.54648 | − | 1.29279i | −0.337469 | − | 0.282109i | ||||
\(22\) | −0.154078 | − | 0.0889568i | −0.0328495 | − | 0.0189656i | ||||
\(23\) | 5.70722 | 1.19004 | 0.595019 | − | 0.803712i | \(-0.297145\pi\) | ||||
0.595019 | + | 0.803712i | \(0.297145\pi\) | |||||||
\(24\) | 0.595404 | + | 1.62650i | 0.121536 | + | 0.332007i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −2.82297 | + | 4.88952i | −0.553629 | + | 0.958914i | ||||
\(27\) | 2.57308 | − | 4.51434i | 0.495190 | − | 0.868785i | ||||
\(28\) | 0.581871 | + | 1.00783i | 0.109963 | + | 0.190462i | ||||
\(29\) | 5.56575 | 1.03353 | 0.516767 | − | 0.856126i | \(-0.327135\pi\) | ||||
0.516767 | + | 0.856126i | \(0.327135\pi\) | |||||||
\(30\) | 0.297614 | − | 1.70629i | 0.0543366 | − | 0.311525i | ||||
\(31\) | 5.12730 | − | 2.17043i | 0.920891 | − | 0.389821i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.0529495 | − | 0.303572i | 0.00921733 | − | 0.0528451i | ||||
\(34\) | −3.35837 | + | 1.93896i | −0.575956 | + | 0.332528i | ||||
\(35\) | − | 1.16374i | − | 0.196708i | ||||||
\(36\) | −2.29099 | + | 1.93685i | −0.381831 | + | 0.322808i | ||||
\(37\) | 0.782503 | − | 0.451779i | 0.128643 | − | 0.0742719i | −0.434298 | − | 0.900769i | \(-0.643003\pi\) |
0.562940 | + | 0.826497i | \(0.309670\pi\) | |||||||
\(38\) | −4.46331 | + | 2.57689i | −0.724044 | + | 0.418027i | ||||
\(39\) | −9.63360 | − | 1.68031i | −1.54261 | − | 0.269065i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 2.48692 | + | 1.43582i | 0.388391 | + | 0.224238i | 0.681463 | − | 0.731853i | \(-0.261344\pi\) |
−0.293072 | + | 0.956091i | \(0.594677\pi\) | |||||||
\(42\) | −1.29279 | + | 1.54648i | −0.199481 | + | 0.238627i | ||||
\(43\) | 0.735867 | − | 0.424853i | 0.112219 | − | 0.0647895i | −0.442840 | − | 0.896601i | \(-0.646029\pi\) |
0.555059 | + | 0.831811i | \(0.312696\pi\) | |||||||
\(44\) | −0.0889568 | + | 0.154078i | −0.0134107 | + | 0.0232281i | ||||
\(45\) | 2.95248 | − | 0.531863i | 0.440129 | − | 0.0792855i | ||||
\(46\) | − | 5.70722i | − | 0.841484i | ||||||
\(47\) | − | 4.11079i | − | 0.599620i | −0.953999 | − | 0.299810i | \(-0.903077\pi\) | ||
0.953999 | − | 0.299810i | \(-0.0969233\pi\) | |||||||
\(48\) | 1.62650 | − | 0.595404i | 0.234765 | − | 0.0859391i | ||||
\(49\) | 2.82285 | − | 4.88932i | 0.403265 | − | 0.698475i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | −5.15329 | − | 4.30792i | −0.721605 | − | 0.603229i | ||||
\(52\) | 4.88952 | + | 2.82297i | 0.678055 | + | 0.391475i | ||||
\(53\) | −6.25104 | + | 10.8271i | −0.858646 | + | 1.48722i | 0.0145750 | + | 0.999894i | \(0.495360\pi\) |
−0.873221 | + | 0.487325i | \(0.837973\pi\) | |||||||
\(54\) | −4.51434 | − | 2.57308i | −0.614324 | − | 0.350152i | ||||
\(55\) | 0.154078 | − | 0.0889568i | 0.0207758 | − | 0.0119949i | ||||
\(56\) | 1.00783 | − | 0.581871i | 0.134677 | − | 0.0777558i | ||||
\(57\) | −6.84878 | − | 5.72526i | −0.907142 | − | 0.758330i | ||||
\(58\) | − | 5.56575i | − | 0.730819i | ||||||
\(59\) | −4.27376 | + | 2.46746i | −0.556396 | + | 0.321235i | −0.751698 | − | 0.659508i | \(-0.770765\pi\) |
0.195302 | + | 0.980743i | \(0.437431\pi\) | |||||||
\(60\) | −1.70629 | − | 0.297614i | −0.220281 | − | 0.0384218i | ||||
\(61\) | − | 0.00227491i | − | 0.000291272i | −1.00000 | 0.000145636i | \(-0.999954\pi\) | |||
1.00000 | 0.000145636i | \(-4.63574e-5\pi\) | ||||||||
\(62\) | −2.17043 | − | 5.12730i | −0.275645 | − | 0.651168i | ||||
\(63\) | −3.28507 | − | 1.18193i | −0.413880 | − | 0.148910i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.82297 | − | 4.88952i | −0.350146 | − | 0.606471i | ||||
\(66\) | −0.303572 | − | 0.0529495i | −0.0373671 | − | 0.00651764i | ||||
\(67\) | −3.20296 | + | 5.54769i | −0.391304 | + | 0.677758i | −0.992622 | − | 0.121252i | \(-0.961309\pi\) |
0.601318 | + | 0.799010i | \(0.294642\pi\) | |||||||
\(68\) | 1.93896 | + | 3.35837i | 0.235133 | + | 0.407262i | ||||
\(69\) | 9.28278 | − | 3.39810i | 1.11752 | − | 0.409083i | ||||
\(70\) | −1.16374 | −0.139094 | ||||||||
\(71\) | 10.9712 | + | 6.33424i | 1.30204 | + | 0.751736i | 0.980754 | − | 0.195245i | \(-0.0625502\pi\) |
0.321290 | + | 0.946981i | \(0.395884\pi\) | |||||||
\(72\) | 1.93685 | + | 2.29099i | 0.228259 | + | 0.269996i | ||||
\(73\) | 9.32062 | + | 5.38127i | 1.09090 | + | 0.629829i | 0.933815 | − | 0.357756i | \(-0.116458\pi\) |
0.157082 | + | 0.987586i | \(0.449791\pi\) | |||||||
\(74\) | −0.451779 | − | 0.782503i | −0.0525182 | − | 0.0909642i | ||||
\(75\) | 1.32888 | + | 1.11089i | 0.153446 | + | 0.128274i | ||||
\(76\) | 2.57689 | + | 4.46331i | 0.295590 | + | 0.511976i | ||||
\(77\) | −0.207046 | −0.0235950 | ||||||||
\(78\) | −1.68031 | + | 9.63360i | −0.190257 | + | 1.09079i | ||||
\(79\) | −2.52627 | + | 1.45854i | −0.284228 | + | 0.164099i | −0.635336 | − | 0.772236i | \(-0.719138\pi\) |
0.351108 | + | 0.936335i | \(0.385805\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | 1.49726 | − | 8.87458i | 0.166362 | − | 0.986065i | ||||
\(82\) | 1.43582 | − | 2.48692i | 0.158560 | − | 0.274634i | ||||
\(83\) | −7.95846 | + | 13.7845i | −0.873555 | + | 1.51304i | −0.0152607 | + | 0.999884i | \(0.504858\pi\) |
−0.858294 | + | 0.513158i | \(0.828476\pi\) | |||||||
\(84\) | 1.54648 | + | 1.29279i | 0.168735 | + | 0.141054i | ||||
\(85\) | − | 3.87791i | − | 0.420618i | ||||||
\(86\) | −0.424853 | − | 0.735867i | −0.0458131 | − | 0.0793506i | ||||
\(87\) | 9.05268 | − | 3.31387i | 0.970549 | − | 0.355284i | ||||
\(88\) | 0.154078 | + | 0.0889568i | 0.0164247 | + | 0.00948282i | ||||
\(89\) | −5.20790 | −0.552036 | −0.276018 | − | 0.961152i | \(-0.589015\pi\) | ||||
−0.276018 | + | 0.961152i | \(0.589015\pi\) | |||||||
\(90\) | −0.531863 | − | 2.95248i | −0.0560633 | − | 0.311218i | ||||
\(91\) | 6.57041i | 0.688766i | ||||||||
\(92\) | −5.70722 | −0.595019 | ||||||||
\(93\) | 7.04726 | − | 6.58302i | 0.730767 | − | 0.682627i | ||||
\(94\) | −4.11079 | −0.423995 | ||||||||
\(95\) | − | 5.15378i | − | 0.528767i | ||||||
\(96\) | −0.595404 | − | 1.62650i | −0.0607682 | − | 0.166004i | ||||
\(97\) | −13.7078 | −1.39181 | −0.695907 | − | 0.718132i | \(-0.744997\pi\) | ||||
−0.695907 | + | 0.718132i | \(0.744997\pi\) | |||||||
\(98\) | −4.88932 | − | 2.82285i | −0.493896 | − | 0.285151i | ||||
\(99\) | −0.0946257 | − | 0.525286i | −0.00951024 | − | 0.0527932i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | − | 2.34879i | − | 0.233713i | −0.993149 | − | 0.116856i | \(-0.962718\pi\) | ||
0.993149 | − | 0.116856i | \(-0.0372817\pi\) | |||||||
\(102\) | −4.30792 | + | 5.15329i | −0.426547 | + | 0.510252i | ||||
\(103\) | −8.49332 | + | 14.7109i | −0.836872 | + | 1.44950i | 0.0556251 | + | 0.998452i | \(0.482285\pi\) |
−0.892497 | + | 0.451053i | \(0.851048\pi\) | |||||||
\(104\) | 2.82297 | − | 4.88952i | 0.276815 | − | 0.479457i | ||||
\(105\) | −0.692897 | − | 1.89282i | −0.0676198 | − | 0.184721i | ||||
\(106\) | 10.8271 | + | 6.25104i | 1.05162 | + | 0.607154i | ||||
\(107\) | −4.00394 | + | 2.31167i | −0.387075 | + | 0.223478i | −0.680892 | − | 0.732384i | \(-0.738408\pi\) |
0.293817 | + | 0.955862i | \(0.405074\pi\) | |||||||
\(108\) | −2.57308 | + | 4.51434i | −0.247595 | + | 0.434392i | ||||
\(109\) | 18.3302 | 1.75571 | 0.877856 | − | 0.478925i | \(-0.158973\pi\) | ||||
0.877856 | + | 0.478925i | \(0.158973\pi\) | |||||||
\(110\) | −0.0889568 | − | 0.154078i | −0.00848170 | − | 0.0146907i | ||||
\(111\) | 1.00375 | − | 1.20072i | 0.0952716 | − | 0.113968i | ||||
\(112\) | −0.581871 | − | 1.00783i | −0.0549817 | − | 0.0952310i | ||||
\(113\) | 0.376805 | + | 0.217548i | 0.0354468 | + | 0.0204652i | 0.517619 | − | 0.855611i | \(-0.326819\pi\) |
−0.482172 | + | 0.876077i | \(0.660152\pi\) | |||||||
\(114\) | −5.72526 | + | 6.84878i | −0.536220 | + | 0.641447i | ||||
\(115\) | 4.94260 | + | 2.85361i | 0.460900 | + | 0.266101i | ||||
\(116\) | −5.56575 | −0.516767 | ||||||||
\(117\) | −16.6695 | + | 3.00287i | −1.54109 | + | 0.277615i | ||||
\(118\) | 2.46746 | + | 4.27376i | 0.227148 | + | 0.393431i | ||||
\(119\) | −2.25644 | + | 3.90828i | −0.206848 | + | 0.358271i | ||||
\(120\) | −0.297614 | + | 1.70629i | −0.0271683 | + | 0.155762i | ||||
\(121\) | 5.48417 | + | 9.49887i | 0.498561 | + | 0.863533i | ||||
\(122\) | −0.00227491 | −0.000205960 | ||||||||
\(123\) | 4.89986 | + | 0.854642i | 0.441806 | + | 0.0770604i | ||||
\(124\) | −5.12730 | + | 2.17043i | −0.460445 | + | 0.194911i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.18193 | + | 3.28507i | −0.105295 | + | 0.292657i | ||||
\(127\) | 10.9132 | − | 6.30073i | 0.968388 | − | 0.559099i | 0.0696438 | − | 0.997572i | \(-0.477814\pi\) |
0.898745 | + | 0.438473i | \(0.144480\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0.943927 | − | 1.12916i | 0.0831081 | − | 0.0994170i | ||||
\(130\) | −4.88952 | + | 2.82297i | −0.428839 | + | 0.247591i | ||||
\(131\) | −18.3335 | + | 10.5849i | −1.60181 | + | 0.924803i | −0.610679 | + | 0.791878i | \(0.709104\pi\) |
−0.991126 | + | 0.132925i | \(0.957563\pi\) | |||||||
\(132\) | −0.0529495 | + | 0.303572i | −0.00460867 | + | 0.0264226i | ||||
\(133\) | −2.99884 | + | 5.19414i | −0.260032 | + | 0.450389i | ||||
\(134\) | 5.54769 | + | 3.20296i | 0.479247 | + | 0.276693i | ||||
\(135\) | 4.48552 | − | 2.62299i | 0.386052 | − | 0.225751i | ||||
\(136\) | 3.35837 | − | 1.93896i | 0.287978 | − | 0.166264i | ||||
\(137\) | 6.42120 | − | 11.1218i | 0.548600 | − | 0.950203i | −0.449771 | − | 0.893144i | \(-0.648494\pi\) |
0.998371 | − | 0.0570592i | \(-0.0181724\pi\) | |||||||
\(138\) | −3.39810 | − | 9.28278i | −0.289266 | − | 0.790203i | ||||
\(139\) | 0.913499i | 0.0774820i | 0.999249 | + | 0.0387410i | \(0.0123347\pi\) | ||||
−0.999249 | + | 0.0387410i | \(0.987665\pi\) | |||||||
\(140\) | 1.16374i | 0.0983542i | ||||||||
\(141\) | −2.44758 | − | 6.68619i | −0.206123 | − | 0.563078i | ||||
\(142\) | 6.33424 | − | 10.9712i | 0.531557 | − | 0.920685i | ||||
\(143\) | −0.869912 | + | 0.502244i | −0.0727457 | + | 0.0419998i | ||||
\(144\) | 2.29099 | − | 1.93685i | 0.190916 | − | 0.161404i | ||||
\(145\) | 4.82008 | + | 2.78288i | 0.400286 | + | 0.231105i | ||||
\(146\) | 5.38127 | − | 9.32062i | 0.445357 | − | 0.771380i | ||||
\(147\) | 1.68024 | − | 9.63321i | 0.138584 | − | 0.794534i | ||||
\(148\) | −0.782503 | + | 0.451779i | −0.0643214 | + | 0.0371360i | ||||
\(149\) | 3.97105 | − | 2.29269i | 0.325321 | − | 0.187824i | −0.328441 | − | 0.944525i | \(-0.606523\pi\) |
0.653762 | + | 0.756700i | \(0.273190\pi\) | |||||||
\(150\) | 1.11089 | − | 1.32888i | 0.0907035 | − | 0.108503i | ||||
\(151\) | − | 18.0258i | − | 1.46692i | −0.679734 | − | 0.733458i | \(-0.737905\pi\) | ||
0.679734 | − | 0.733458i | \(-0.262095\pi\) | |||||||
\(152\) | 4.46331 | − | 2.57689i | 0.362022 | − | 0.209013i | ||||
\(153\) | −10.9468 | − | 3.93853i | −0.884994 | − | 0.318411i | ||||
\(154\) | 0.207046i | 0.0166842i | ||||||||
\(155\) | 5.52559 | + | 0.684001i | 0.443826 | + | 0.0549403i | ||||
\(156\) | 9.63360 | + | 1.68031i | 0.771305 | + | 0.134532i | ||||
\(157\) | −9.03549 | −0.721111 | −0.360555 | − | 0.932738i | \(-0.617413\pi\) | ||||
−0.360555 | + | 0.932738i | \(0.617413\pi\) | |||||||
\(158\) | 1.45854 | + | 2.52627i | 0.116036 | + | 0.200980i | ||||
\(159\) | −3.72079 | + | 21.3322i | −0.295078 | + | 1.69175i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −3.32087 | − | 5.75191i | −0.261721 | − | 0.453314i | ||||
\(162\) | −8.87458 | − | 1.49726i | −0.697253 | − | 0.117636i | ||||
\(163\) | 17.0876 | 1.33840 | 0.669201 | − | 0.743082i | \(-0.266637\pi\) | ||||
0.669201 | + | 0.743082i | \(0.266637\pi\) | |||||||
\(164\) | −2.48692 | − | 1.43582i | −0.194196 | − | 0.112119i | ||||
\(165\) | 0.197642 | − | 0.236426i | 0.0153864 | − | 0.0184058i | ||||
\(166\) | 13.7845 | + | 7.95846i | 1.06988 | + | 0.617697i | ||||
\(167\) | −4.44098 | − | 7.69200i | −0.343653 | − | 0.595225i | 0.641455 | − | 0.767161i | \(-0.278331\pi\) |
−0.985108 | + | 0.171936i | \(0.944998\pi\) | |||||||
\(168\) | 1.29279 | − | 1.54648i | 0.0997406 | − | 0.119313i | ||||
\(169\) | 9.43828 | + | 16.3476i | 0.726022 | + | 1.25751i | ||||
\(170\) | −3.87791 | −0.297422 | ||||||||
\(171\) | −14.5484 | − | 5.23434i | −1.11254 | − | 0.400280i | ||||
\(172\) | −0.735867 | + | 0.424853i | −0.0561093 | + | 0.0323947i | ||||
\(173\) | −2.18205 | − | 1.25981i | −0.165898 | − | 0.0957813i | 0.414752 | − | 0.909934i | \(-0.363868\pi\) |
−0.580650 | + | 0.814153i | \(0.697202\pi\) | |||||||
\(174\) | −3.31387 | − | 9.05268i | −0.251224 | − | 0.686282i | ||||
\(175\) | 0.581871 | − | 1.00783i | 0.0439853 | − | 0.0761848i | ||||
\(176\) | 0.0889568 | − | 0.154078i | 0.00670537 | − | 0.0116140i | ||||
\(177\) | −5.48213 | + | 6.55792i | −0.412062 | + | 0.492924i | ||||
\(178\) | 5.20790i | 0.390348i | ||||||||
\(179\) | 7.26572 | + | 12.5846i | 0.543065 | + | 0.940616i | 0.998726 | + | 0.0504628i | \(0.0160696\pi\) |
−0.455661 | + | 0.890153i | \(0.650597\pi\) | |||||||
\(180\) | −2.95248 | + | 0.531863i | −0.220065 | + | 0.0396428i | ||||
\(181\) | −3.27223 | − | 1.88922i | −0.243223 | − | 0.140425i | 0.373434 | − | 0.927657i | \(-0.378180\pi\) |
−0.616657 | + | 0.787232i | \(0.711513\pi\) | |||||||
\(182\) | 6.57041 | 0.487031 | ||||||||
\(183\) | −0.00135449 | − | 0.00370013i | −0.000100127 | − | 0.000273522i | ||||
\(184\) | 5.70722i | 0.420742i | ||||||||
\(185\) | 0.903557 | 0.0664308 | ||||||||
\(186\) | −6.58302 | − | 7.04726i | −0.482690 | − | 0.516730i | ||||
\(187\) | −0.689933 | −0.0504529 | ||||||||
\(188\) | 4.11079i | 0.299810i | ||||||||
\(189\) | −6.04689 | + | 0.0335334i | −0.439846 | + | 0.00243919i | ||||
\(190\) | −5.15378 | −0.373895 | ||||||||
\(191\) | 5.58732 | + | 3.22584i | 0.404284 | + | 0.233414i | 0.688331 | − | 0.725397i | \(-0.258344\pi\) |
−0.284047 | + | 0.958810i | \(0.591677\pi\) | |||||||
\(192\) | −1.62650 | + | 0.595404i | −0.117382 | + | 0.0429696i | ||||
\(193\) | −1.05136 | − | 1.82101i | −0.0756786 | − | 0.131079i | 0.825703 | − | 0.564106i | \(-0.190779\pi\) |
−0.901381 | + | 0.433027i | \(0.857446\pi\) | |||||||
\(194\) | 13.7078i | 0.984161i | ||||||||
\(195\) | −7.50279 | − | 6.27199i | −0.537286 | − | 0.449147i | ||||
\(196\) | −2.82285 | + | 4.88932i | −0.201632 | + | 0.349237i | ||||
\(197\) | 9.43359 | − | 16.3395i | 0.672115 | − | 1.16414i | −0.305188 | − | 0.952292i | \(-0.598719\pi\) |
0.977303 | − | 0.211846i | \(-0.0679474\pi\) | |||||||
\(198\) | −0.525286 | + | 0.0946257i | −0.0373304 | + | 0.00672476i | ||||
\(199\) | 16.6694 | + | 9.62408i | 1.18166 | + | 0.682233i | 0.956398 | − | 0.292065i | \(-0.0943425\pi\) |
0.225263 | + | 0.974298i | \(0.427676\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | −1.90649 | + | 10.9304i | −0.134473 | + | 0.770967i | ||||
\(202\) | −2.34879 | −0.165260 | ||||||||
\(203\) | −3.23855 | − | 5.60933i | −0.227302 | − | 0.393698i | ||||
\(204\) | 5.15329 | + | 4.30792i | 0.360803 | + | 0.301615i | ||||
\(205\) | 1.43582 | + | 2.48692i | 0.100282 | + | 0.173694i | ||||
\(206\) | 14.7109 | + | 8.49332i | 1.02495 | + | 0.591758i | ||||
\(207\) | 13.0752 | − | 11.0540i | 0.908788 | − | 0.768307i | ||||
\(208\) | −4.88952 | − | 2.82297i | −0.339027 | − | 0.195738i | ||||
\(209\) | −0.916927 | −0.0634252 | ||||||||
\(210\) | −1.89282 | + | 0.692897i | −0.130617 | + | 0.0478144i | ||||
\(211\) | 5.53532 | + | 9.58746i | 0.381067 | + | 0.660028i | 0.991215 | − | 0.132260i | \(-0.0422233\pi\) |
−0.610148 | + | 0.792288i | \(0.708890\pi\) | |||||||
\(212\) | 6.25104 | − | 10.8271i | 0.429323 | − | 0.743609i | ||||
\(213\) | 21.6161 | + | 3.77031i | 1.48111 | + | 0.258338i | ||||
\(214\) | 2.31167 | + | 4.00394i | 0.158023 | + | 0.273703i | ||||
\(215\) | 0.849706 | 0.0579495 | ||||||||
\(216\) | 4.51434 | + | 2.57308i | 0.307162 | + | 0.175076i | ||||
\(217\) | −5.17086 | − | 3.90454i | −0.351021 | − | 0.265057i | ||||
\(218\) | − | 18.3302i | − | 1.24148i | ||||||
\(219\) | 18.3640 | + | 3.20308i | 1.24092 | + | 0.216444i | ||||
\(220\) | −0.154078 | + | 0.0889568i | −0.0103879 | + | 0.00599746i | ||||
\(221\) | 21.8944i | 1.47278i | ||||||||
\(222\) | −1.20072 | − | 1.00375i | −0.0805872 | − | 0.0673672i | ||||
\(223\) | −3.79542 | + | 2.19128i | −0.254160 | + | 0.146739i | −0.621668 | − | 0.783281i | \(-0.713545\pi\) |
0.367508 | + | 0.930020i | \(0.380211\pi\) | |||||||
\(224\) | −1.00783 | + | 0.581871i | −0.0673385 | + | 0.0388779i | ||||
\(225\) | 2.82285 | + | 1.01563i | 0.188190 | + | 0.0677088i | ||||
\(226\) | 0.217548 | − | 0.376805i | 0.0144711 | − | 0.0250647i | ||||
\(227\) | −14.2337 | − | 8.21783i | −0.944724 | − | 0.545436i | −0.0532857 | − | 0.998579i | \(-0.516969\pi\) |
−0.891438 | + | 0.453143i | \(0.850303\pi\) | |||||||
\(228\) | 6.84878 | + | 5.72526i | 0.453571 | + | 0.379165i | ||||
\(229\) | 0.621599 | − | 0.358880i | 0.0410764 | − | 0.0237155i | −0.479321 | − | 0.877640i | \(-0.659117\pi\) |
0.520398 | + | 0.853924i | \(0.325784\pi\) | |||||||
\(230\) | 2.85361 | − | 4.94260i | 0.188162 | − | 0.325905i | ||||
\(231\) | −0.336759 | + | 0.123276i | −0.0221571 | + | 0.00811095i | ||||
\(232\) | 5.56575i | 0.365410i | ||||||||
\(233\) | − | 15.7057i | − | 1.02891i | −0.857517 | − | 0.514456i | \(-0.827994\pi\) | ||
0.857517 | − | 0.514456i | \(-0.172006\pi\) | |||||||
\(234\) | 3.00287 | + | 16.6695i | 0.196303 | + | 1.08972i | ||||
\(235\) | 2.05539 | − | 3.56005i | 0.134079 | − | 0.232232i | ||||
\(236\) | 4.27376 | − | 2.46746i | 0.278198 | − | 0.160618i | ||||
\(237\) | −3.24055 | + | 3.87647i | −0.210497 | + | 0.251804i | ||||
\(238\) | 3.90828 | + | 2.25644i | 0.253336 | + | 0.146264i | ||||
\(239\) | −2.90971 | + | 5.03976i | −0.188213 | + | 0.325995i | −0.944655 | − | 0.328067i | \(-0.893603\pi\) |
0.756441 | + | 0.654062i | \(0.226936\pi\) | |||||||
\(240\) | 1.70629 | + | 0.297614i | 0.110141 | + | 0.0192109i | ||||
\(241\) | 5.77410 | − | 3.33368i | 0.371942 | − | 0.214741i | −0.302364 | − | 0.953192i | \(-0.597776\pi\) |
0.674307 | + | 0.738451i | \(0.264443\pi\) | |||||||
\(242\) | 9.49887 | − | 5.48417i | 0.610610 | − | 0.352536i | ||||
\(243\) | −2.84868 | − | 15.3260i | −0.182743 | − | 0.983161i | ||||
\(244\) | 0.00227491i | 0.000145636i | ||||||||
\(245\) | 4.88932 | − | 2.82285i | 0.312367 | − | 0.180345i | ||||
\(246\) | 0.854642 | − | 4.89986i | 0.0544900 | − | 0.312404i | ||||
\(247\) | 29.0979i | 1.85146i | ||||||||
\(248\) | 2.17043 | + | 5.12730i | 0.137823 | + | 0.325584i | ||||
\(249\) | −4.73710 | + | 27.1589i | −0.300201 | + | 1.72113i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 4.15063 | + | 7.18911i | 0.261986 | + | 0.453773i | 0.966770 | − | 0.255650i | \(-0.0822893\pi\) |
−0.704784 | + | 0.709422i | \(0.748956\pi\) | |||||||
\(252\) | 3.28507 | + | 1.18193i | 0.206940 | + | 0.0744548i | ||||
\(253\) | 0.507696 | − | 0.879355i | 0.0319186 | − | 0.0552846i | ||||
\(254\) | −6.30073 | − | 10.9132i | −0.395343 | − | 0.684754i | ||||
\(255\) | −2.30892 | − | 6.30741i | −0.144590 | − | 0.394985i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.8110 | + | 12.0152i | 1.29815 | + | 0.749490i | 0.980085 | − | 0.198577i | \(-0.0636321\pi\) |
0.318070 | + | 0.948067i | \(0.396965\pi\) | |||||||
\(258\) | −1.12916 | − | 0.943927i | −0.0702984 | − | 0.0587663i | ||||
\(259\) | −0.910632 | − | 0.525754i | −0.0565839 | − | 0.0326688i | ||||
\(260\) | 2.82297 | + | 4.88952i | 0.175073 | + | 0.303235i | ||||
\(261\) | 12.7511 | − | 10.7800i | 0.789272 | − | 0.667266i | ||||
\(262\) | 10.5849 | + | 18.3335i | 0.653934 | + | 1.13265i | ||||
\(263\) | 13.3178 | 0.821209 | 0.410605 | − | 0.911813i | \(-0.365318\pi\) | ||||
0.410605 | + | 0.911813i | \(0.365318\pi\) | |||||||
\(264\) | 0.303572 | + | 0.0529495i | 0.0186836 | + | 0.00325882i | ||||
\(265\) | −10.8271 | + | 6.25104i | −0.665104 | + | 0.383998i | ||||
\(266\) | 5.19414 | + | 2.99884i | 0.318473 | + | 0.183870i | ||||
\(267\) | −8.47063 | + | 3.10080i | −0.518394 | + | 0.189766i | ||||
\(268\) | 3.20296 | − | 5.54769i | 0.195652 | − | 0.338879i | ||||
\(269\) | 0.769900 | − | 1.33351i | 0.0469416 | − | 0.0813052i | −0.841600 | − | 0.540101i | \(-0.818386\pi\) |
0.888542 | + | 0.458796i | \(0.151719\pi\) | |||||||
\(270\) | −2.62299 | − | 4.48552i | −0.159630 | − | 0.272980i | ||||
\(271\) | − | 8.84626i | − | 0.537372i | −0.963228 | − | 0.268686i | \(-0.913411\pi\) | ||
0.963228 | − | 0.268686i | \(-0.0865894\pi\) | |||||||
\(272\) | −1.93896 | − | 3.35837i | −0.117566 | − | 0.203631i | ||||
\(273\) | 3.91205 | + | 10.6868i | 0.236768 | + | 0.646792i | ||||
\(274\) | −11.1218 | − | 6.42120i | −0.671895 | − | 0.387919i | ||||
\(275\) | 0.177914 | 0.0107286 | ||||||||
\(276\) | −9.28278 | + | 3.39810i | −0.558758 | + | 0.204542i | ||||
\(277\) | − | 14.9715i | − | 0.899552i | −0.893141 | − | 0.449776i | \(-0.851504\pi\) | ||
0.893141 | − | 0.449776i | \(-0.148496\pi\) | |||||||
\(278\) | 0.913499 | 0.0547880 | ||||||||
\(279\) | 7.54280 | − | 14.9032i | 0.451575 | − | 0.892233i | ||||
\(280\) | 1.16374 | 0.0695469 | ||||||||
\(281\) | 7.32299i | 0.436853i | 0.975853 | + | 0.218426i | \(0.0700924\pi\) | ||||
−0.975853 | + | 0.218426i | \(0.929908\pi\) | |||||||
\(282\) | −6.68619 | + | 2.44758i | −0.398157 | + | 0.145751i | ||||
\(283\) | −14.6211 | −0.869133 | −0.434567 | − | 0.900640i | \(-0.643098\pi\) | ||||
−0.434567 | + | 0.900640i | \(0.643098\pi\) | |||||||
\(284\) | −10.9712 | − | 6.33424i | −0.651022 | − | 0.375868i | ||||
\(285\) | −3.06858 | − | 8.38261i | −0.181767 | − | 0.496543i | ||||
\(286\) | 0.502244 | + | 0.869912i | 0.0296983 | + | 0.0514390i | ||||
\(287\) | − | 3.34186i | − | 0.197263i | ||||||
\(288\) | −1.93685 | − | 2.29099i | −0.114130 | − | 0.134998i | ||||
\(289\) | 0.980903 | − | 1.69897i | 0.0577002 | − | 0.0999397i | ||||
\(290\) | 2.78288 | − | 4.82008i | 0.163416 | − | 0.283045i | ||||
\(291\) | −22.2957 | + | 8.16166i | −1.30700 | + | 0.478445i | ||||
\(292\) | −9.32062 | − | 5.38127i | −0.545448 | − | 0.314915i | ||||
\(293\) | 29.5457 | − | 17.0582i | 1.72608 | − | 0.996551i | 0.821545 | − | 0.570143i | \(-0.193112\pi\) |
0.904531 | − | 0.426408i | \(-0.140221\pi\) | |||||||
\(294\) | −9.63321 | − | 1.68024i | −0.561820 | − | 0.0979936i | ||||
\(295\) | −4.93491 | −0.287322 | ||||||||
\(296\) | 0.451779 | + | 0.782503i | 0.0262591 | + | 0.0454821i | ||||
\(297\) | −0.466666 | − | 0.798035i | −0.0270787 | − | 0.0463067i | ||||
\(298\) | −2.29269 | − | 3.97105i | −0.132812 | − | 0.230037i | ||||
\(299\) | −27.9056 | − | 16.1113i | −1.61382 | − | 0.931740i | ||||
\(300\) | −1.32888 | − | 1.11089i | −0.0767231 | − | 0.0641370i | ||||
\(301\) | −0.856359 | − | 0.494419i | −0.0493597 | − | 0.0284979i | ||||
\(302\) | −18.0258 | −1.03727 | ||||||||
\(303\) | −1.39848 | − | 3.82029i | −0.0803404 | − | 0.219470i | ||||
\(304\) | −2.57689 | − | 4.46331i | −0.147795 | − | 0.255988i | ||||
\(305\) | 0.00113745 | − | 0.00197013i | 6.51304e−5 | − | 0.000112809i | ||||
\(306\) | −3.93853 | + | 10.9468i | −0.225151 | + | 0.625785i | ||||
\(307\) | 8.94582 | + | 15.4946i | 0.510565 | + | 0.884324i | 0.999925 | + | 0.0122426i | \(0.00389705\pi\) |
−0.489360 | + | 0.872082i | \(0.662770\pi\) | |||||||
\(308\) | 0.207046 | 0.0117975 | ||||||||
\(309\) | −5.05546 | + | 28.9841i | −0.287595 | + | 1.64885i | ||||
\(310\) | 0.684001 | − | 5.52559i | 0.0388486 | − | 0.313832i | ||||
\(311\) | 14.8875i | 0.844194i | 0.906551 | + | 0.422097i | \(0.138706\pi\) | ||||
−0.906551 | + | 0.422097i | \(0.861294\pi\) | |||||||
\(312\) | 1.68031 | − | 9.63360i | 0.0951287 | − | 0.545395i | ||||
\(313\) | −6.65729 | + | 3.84359i | −0.376293 | + | 0.217253i | −0.676204 | − | 0.736714i | \(-0.736376\pi\) |
0.299911 | + | 0.953967i | \(0.403043\pi\) | |||||||
\(314\) | 9.03549i | 0.509902i | ||||||||
\(315\) | −2.25399 | − | 2.66612i | −0.126998 | − | 0.150219i | ||||
\(316\) | 2.52627 | − | 1.45854i | 0.142114 | − | 0.0820495i | ||||
\(317\) | 4.78141 | − | 2.76055i | 0.268551 | − | 0.155048i | −0.359678 | − | 0.933076i | \(-0.617114\pi\) |
0.628229 | + | 0.778029i | \(0.283780\pi\) | |||||||
\(318\) | 21.3322 | + | 3.72079i | 1.19625 | + | 0.208652i | ||||
\(319\) | 0.495111 | − | 0.857558i | 0.0277209 | − | 0.0480140i | ||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | −5.13601 | + | 6.14389i | −0.286664 | + | 0.342919i | ||||
\(322\) | −5.75191 | + | 3.32087i | −0.320542 | + | 0.185065i | ||||
\(323\) | −9.99295 | + | 17.3083i | −0.556023 | + | 0.963060i | ||||
\(324\) | −1.49726 | + | 8.87458i | −0.0831809 | + | 0.493032i | ||||
\(325\) | − | 5.64593i | − | 0.313180i | ||||||
\(326\) | − | 17.0876i | − | 0.946392i | ||||||
\(327\) | 29.8140 | − | 10.9139i | 1.64872 | − | 0.603537i | ||||
\(328\) | −1.43582 | + | 2.48692i | −0.0792800 | + | 0.137317i | ||||
\(329\) | −4.14298 | + | 2.39195i | −0.228410 | + | 0.131872i | ||||
\(330\) | −0.236426 | − | 0.197642i | −0.0130148 | − | 0.0108798i | ||||
\(331\) | −7.77002 | − | 4.48602i | −0.427079 | − | 0.246574i | 0.271022 | − | 0.962573i | \(-0.412638\pi\) |
−0.698101 | + | 0.715999i | \(0.745972\pi\) | |||||||
\(332\) | 7.95846 | − | 13.7845i | 0.436777 | − | 0.756521i | ||||
\(333\) | 0.917681 | − | 2.55061i | 0.0502886 | − | 0.139772i | ||||
\(334\) | −7.69200 | + | 4.44098i | −0.420888 | + | 0.243000i | ||||
\(335\) | −5.54769 | + | 3.20296i | −0.303102 | + | 0.174996i | ||||
\(336\) | −1.54648 | − | 1.29279i | −0.0843673 | − | 0.0705272i | ||||
\(337\) | − | 2.44574i | − | 0.133228i | −0.997779 | − | 0.0666141i | \(-0.978780\pi\) | ||
0.997779 | − | 0.0666141i | \(-0.0212196\pi\) | |||||||
\(338\) | 16.3476 | − | 9.43828i | 0.889191 | − | 0.513375i | ||||
\(339\) | 0.742401 | + | 0.129491i | 0.0403217 | + | 0.00703297i | ||||
\(340\) | 3.87791i | 0.210309i | ||||||||
\(341\) | 0.121693 | − | 0.983077i | 0.00659005 | − | 0.0532366i | ||||
\(342\) | −5.23434 | + | 14.5484i | −0.283041 | + | 0.786685i | ||||
\(343\) | −14.7163 | −0.794608 | ||||||||
\(344\) | 0.424853 | + | 0.735867i | 0.0229065 | + | 0.0396753i | ||||
\(345\) | 9.73818 | + | 1.69855i | 0.524286 | + | 0.0914468i | ||||
\(346\) | −1.25981 | + | 2.18205i | −0.0677276 | + | 0.117308i | ||||
\(347\) | −8.43977 | − | 14.6181i | −0.453071 | − | 0.784741i | 0.545504 | − | 0.838108i | \(-0.316338\pi\) |
−0.998575 | + | 0.0533666i | \(0.983005\pi\) | |||||||
\(348\) | −9.05268 | + | 3.31387i | −0.485275 | + | 0.177642i | ||||
\(349\) | 32.6846 | 1.74957 | 0.874783 | − | 0.484515i | \(-0.161004\pi\) | ||||
0.874783 | + | 0.484515i | \(0.161004\pi\) | |||||||
\(350\) | −1.00783 | − | 0.581871i | −0.0538708 | − | 0.0311023i | ||||
\(351\) | −25.3250 | + | 14.8092i | −1.35175 | + | 0.790458i | ||||
\(352\) | −0.154078 | − | 0.0889568i | −0.00821237 | − | 0.00474141i | ||||
\(353\) | 5.87229 | + | 10.1711i | 0.312551 | + | 0.541353i | 0.978914 | − | 0.204274i | \(-0.0654833\pi\) |
−0.666363 | + | 0.745627i | \(0.732150\pi\) | |||||||
\(354\) | 6.55792 | + | 5.48213i | 0.348550 | + | 0.291372i | ||||
\(355\) | 6.33424 | + | 10.9712i | 0.336186 | + | 0.582292i | ||||
\(356\) | 5.20790 | 0.276018 | ||||||||
\(357\) | −1.34310 | + | 7.70030i | −0.0710843 | + | 0.407543i | ||||
\(358\) | 12.5846 | − | 7.26572i | 0.665116 | − | 0.384005i | ||||
\(359\) | −9.22320 | − | 5.32502i | −0.486782 | − | 0.281044i | 0.236457 | − | 0.971642i | \(-0.424014\pi\) |
−0.723238 | + | 0.690598i | \(0.757347\pi\) | |||||||
\(360\) | 0.531863 | + | 2.95248i | 0.0280317 | + | 0.155609i | ||||
\(361\) | −3.78073 | + | 6.54841i | −0.198986 | + | 0.344653i | ||||
\(362\) | −1.88922 | + | 3.27223i | −0.0992953 | + | 0.171984i | ||||
\(363\) | 14.5757 | + | 12.1846i | 0.765024 | + | 0.639525i | ||||
\(364\) | − | 6.57041i | − | 0.344383i | ||||||
\(365\) | 5.38127 | + | 9.32062i | 0.281668 | + | 0.487864i | ||||
\(366\) | −0.00370013 | + | 0.00135449i | −0.000193409 | + | 7.08002e-5i | ||||
\(367\) | 25.0136 | + | 14.4416i | 1.30570 | + | 0.753847i | 0.981376 | − | 0.192099i | \(-0.0615294\pi\) |
0.324326 | + | 0.945946i | \(0.394863\pi\) | |||||||
\(368\) | 5.70722 | 0.297510 | ||||||||
\(369\) | 8.47847 | − | 1.52732i | 0.441371 | − | 0.0795093i | ||||
\(370\) | − | 0.903557i | − | 0.0469737i | ||||||
\(371\) | 14.5492 | 0.755356 | ||||||||
\(372\) | −7.04726 | + | 6.58302i | −0.365383 | + | 0.341314i | ||||
\(373\) | −15.4070 | −0.797744 | −0.398872 | − | 0.917007i | \(-0.630598\pi\) | ||||
−0.398872 | + | 0.917007i | \(0.630598\pi\) | |||||||
\(374\) | 0.689933i | 0.0356756i | ||||||||
\(375\) | 0.595404 | + | 1.62650i | 0.0307465 | + | 0.0839920i | ||||
\(376\) | 4.11079 | 0.211998 | ||||||||
\(377\) | −27.2139 | − | 15.7119i | −1.40159 | − | 0.809206i | ||||
\(378\) | 0.0335334 | + | 6.04689i | 0.00172477 | + | 0.311018i | ||||
\(379\) | −4.66494 | − | 8.07991i | −0.239622 | − | 0.415037i | 0.720984 | − | 0.692952i | \(-0.243690\pi\) |
−0.960606 | + | 0.277915i | \(0.910357\pi\) | |||||||
\(380\) | 5.15378i | 0.264383i | ||||||||
\(381\) | 13.9988 | − | 16.7459i | 0.717180 | − | 0.857917i | ||||
\(382\) | 3.22584 | − | 5.58732i | 0.165048 | − | 0.285872i | ||||
\(383\) | −11.7909 | + | 20.4225i | −0.602488 | + | 1.04354i | 0.389955 | + | 0.920834i | \(0.372491\pi\) |
−0.992443 | + | 0.122706i | \(0.960843\pi\) | |||||||
\(384\) | 0.595404 | + | 1.62650i | 0.0303841 | + | 0.0830019i | ||||
\(385\) | −0.179307 | − | 0.103523i | −0.00913831 | − | 0.00527601i | ||||
\(386\) | −1.82101 | + | 1.05136i | −0.0926870 | + | 0.0535129i | ||||
\(387\) | 0.862988 | − | 2.39859i | 0.0438681 | − | 0.121927i | ||||
\(388\) | 13.7078 | 0.695907 | ||||||||
\(389\) | 17.1562 | + | 29.7153i | 0.869852 | + | 1.50663i | 0.862148 | + | 0.506657i | \(0.169119\pi\) |
0.00770372 | + | 0.999970i | \(0.497548\pi\) | |||||||
\(390\) | −6.27199 | + | 7.50279i | −0.317595 | + | 0.379918i | ||||
\(391\) | −11.0660 | − | 19.1670i | −0.559634 | − | 0.969315i | ||||
\(392\) | 4.88932 | + | 2.82285i | 0.246948 | + | 0.142576i | ||||
\(393\) | −23.5171 | + | 28.1321i | −1.18628 | + | 1.41908i | ||||
\(394\) | −16.3395 | − | 9.43359i | −0.823170 | − | 0.475257i | ||||
\(395\) | −2.91709 | −0.146775 | ||||||||
\(396\) | 0.0946257 | + | 0.525286i | 0.00475512 | + | 0.0263966i | ||||
\(397\) | −13.0551 | − | 22.6122i | −0.655218 | − | 1.13487i | −0.981839 | − | 0.189716i | \(-0.939243\pi\) |
0.326621 | − | 0.945155i | \(-0.394090\pi\) | |||||||
\(398\) | 9.62408 | − | 16.6694i | 0.482411 | − | 0.835561i | ||||
\(399\) | −1.78499 | + | 10.2338i | −0.0893613 | + | 0.512329i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 1.81201 | 0.0904873 | 0.0452436 | − | 0.998976i | \(-0.485594\pi\) | ||||
0.0452436 | + | 0.998976i | \(0.485594\pi\) | |||||||
\(402\) | 10.9304 | + | 1.90649i | 0.545156 | + | 0.0950871i | ||||
\(403\) | −31.1971 | − | 3.86182i | −1.55404 | − | 0.192371i | ||||
\(404\) | 2.34879i | 0.116856i | ||||||||
\(405\) | 5.73395 | − | 6.93699i | 0.284922 | − | 0.344702i | ||||
\(406\) | −5.60933 | + | 3.23855i | −0.278387 | + | 0.160727i | ||||
\(407\) | − | 0.160755i | − | 0.00796833i | ||||||
\(408\) | 4.30792 | − | 5.15329i | 0.213274 | − | 0.255126i | ||||
\(409\) | −21.5022 | + | 12.4143i | −1.06322 | + | 0.613849i | −0.926320 | − | 0.376737i | \(-0.877046\pi\) |
−0.136897 | + | 0.990585i | \(0.543713\pi\) | |||||||
\(410\) | 2.48692 | − | 1.43582i | 0.122820 | − | 0.0709102i | ||||
\(411\) | 3.82208 | − | 21.9129i | 0.188529 | − | 1.08088i | ||||
\(412\) | 8.49332 | − | 14.7109i | 0.418436 | − | 0.724752i | ||||
\(413\) | 4.97356 | + | 2.87148i | 0.244733 | + | 0.141296i | ||||
\(414\) | −11.0540 | − | 13.0752i | −0.543275 | − | 0.642610i | ||||
\(415\) | −13.7845 | + | 7.95846i | −0.676653 | + | 0.390666i | ||||
\(416\) | −2.82297 | + | 4.88952i | −0.138407 | + | 0.239729i | ||||
\(417\) | 0.543901 | + | 1.48580i | 0.0266349 | + | 0.0727601i | ||||
\(418\) | 0.916927i | 0.0448484i | ||||||||
\(419\) | 16.9548i | 0.828295i | 0.910210 | + | 0.414148i | \(0.135920\pi\) | ||||
−0.910210 | + | 0.414148i | \(0.864080\pi\) | |||||||
\(420\) | 0.692897 | + | 1.89282i | 0.0338099 | + | 0.0923604i | ||||
\(421\) | 14.5265 | − | 25.1607i | 0.707980 | − | 1.22626i | −0.257625 | − | 0.966245i | \(-0.582940\pi\) |
0.965605 | − | 0.260013i | \(-0.0837267\pi\) | |||||||
\(422\) | 9.58746 | − | 5.53532i | 0.466710 | − | 0.269455i | ||||
\(423\) | −7.96196 | − | 9.41777i | −0.387124 | − | 0.457908i | ||||
\(424\) | −10.8271 | − | 6.25104i | −0.525811 | − | 0.303577i | ||||
\(425\) | 1.93896 | − | 3.35837i | 0.0940532 | − | 0.162905i | ||||
\(426\) | 3.77031 | − | 21.6161i | 0.182672 | − | 1.04730i | ||||
\(427\) | −0.00229272 | + | 0.00132370i | −0.000110953 | + | 6.40585e-5i | ||||
\(428\) | 4.00394 | − | 2.31167i | 0.193538 | − | 0.111739i | ||||
\(429\) | −1.11587 | + | 1.33485i | −0.0538748 | + | 0.0644471i | ||||
\(430\) | − | 0.849706i | − | 0.0409765i | ||||||
\(431\) | −18.8864 | + | 10.9041i | −0.909726 | + | 0.525231i | −0.880343 | − | 0.474337i | \(-0.842688\pi\) |
−0.0293833 | + | 0.999568i | \(0.509354\pi\) | |||||||
\(432\) | 2.57308 | − | 4.51434i | 0.123797 | − | 0.217196i | ||||
\(433\) | − | 22.8178i | − | 1.09655i | −0.836297 | − | 0.548277i | \(-0.815284\pi\) | ||
0.836297 | − | 0.548277i | \(-0.184716\pi\) | |||||||
\(434\) | −3.90454 | + | 5.17086i | −0.187424 | + | 0.248209i | ||||
\(435\) | 9.49679 | + | 1.65645i | 0.455336 | + | 0.0794205i | ||||
\(436\) | −18.3302 | −0.877856 | ||||||||
\(437\) | −14.7069 | − | 25.4731i | −0.703526 | − | 1.21854i | ||||
\(438\) | 3.20308 | − | 18.3640i | 0.153049 | − | 0.877466i | ||||
\(439\) | 11.9238 | − | 20.6527i | 0.569094 | − | 0.985699i | −0.427562 | − | 0.903986i | \(-0.640628\pi\) |
0.996656 | − | 0.0817131i | \(-0.0260391\pi\) | |||||||
\(440\) | 0.0889568 | + | 0.154078i | 0.00424085 | + | 0.00734536i | ||||
\(441\) | −3.00274 | − | 16.6688i | −0.142988 | − | 0.793753i | ||||
\(442\) | 21.8944 | 1.04141 | ||||||||
\(443\) | −18.1698 | − | 10.4904i | −0.863275 | − | 0.498412i | 0.00183237 | − | 0.999998i | \(-0.499417\pi\) |
−0.865108 | + | 0.501586i | \(0.832750\pi\) | |||||||
\(444\) | −1.00375 | + | 1.20072i | −0.0476358 | + | 0.0569838i | ||||
\(445\) | −4.51017 | − | 2.60395i | −0.213803 | − | 0.123439i | ||||
\(446\) | 2.19128 | + | 3.79542i | 0.103760 | + | 0.179718i | ||||
\(447\) | 5.09383 | − | 6.09343i | 0.240930 | − | 0.288209i | ||||
\(448\) | 0.581871 | + | 1.00783i | 0.0274908 | + | 0.0476155i | ||||
\(449\) | −30.8958 | −1.45806 | −0.729032 | − | 0.684479i | \(-0.760030\pi\) | ||||
−0.729032 | + | 0.684479i | \(0.760030\pi\) | |||||||
\(450\) | 1.01563 | − | 2.82285i | 0.0478773 | − | 0.133071i | ||||
\(451\) | 0.442456 | − | 0.255452i | 0.0208345 | − | 0.0120288i | ||||
\(452\) | −0.376805 | − | 0.217548i | −0.0177234 | − | 0.0102326i | ||||
\(453\) | −10.7326 | − | 29.3189i | −0.504262 | − | 1.37752i | ||||
\(454\) | −8.21783 | + | 14.2337i | −0.385682 | + | 0.668020i | ||||
\(455\) | −3.28521 | + | 5.69014i | −0.154013 | + | 0.266758i | ||||
\(456\) | 5.72526 | − | 6.84878i | 0.268110 | − | 0.320723i | ||||
\(457\) | − | 10.1581i | − | 0.475177i | −0.971366 | − | 0.237589i | \(-0.923643\pi\) | ||
0.971366 | − | 0.237589i | \(-0.0763570\pi\) | |||||||
\(458\) | −0.358880 | − | 0.621599i | −0.0167694 | − | 0.0290454i | ||||
\(459\) | −20.1499 | + | 0.111742i | −0.940517 | + | 0.00521569i | ||||
\(460\) | −4.94260 | − | 2.85361i | −0.230450 | − | 0.133050i | ||||
\(461\) | 19.8197 | 0.923095 | 0.461547 | − | 0.887116i | \(-0.347294\pi\) | ||||
0.461547 | + | 0.887116i | \(0.347294\pi\) | |||||||
\(462\) | 0.123276 | + | 0.336759i | 0.00573530 | + | 0.0156674i | ||||
\(463\) | − | 10.9325i | − | 0.508074i | −0.967194 | − | 0.254037i | \(-0.918241\pi\) | ||
0.967194 | − | 0.254037i | \(-0.0817586\pi\) | |||||||
\(464\) | 5.56575 | 0.258384 | ||||||||
\(465\) | 9.39461 | − | 2.17743i | 0.435665 | − | 0.100976i | ||||
\(466\) | −15.7057 | −0.727551 | ||||||||
\(467\) | 11.3377i | 0.524644i | 0.964980 | + | 0.262322i | \(0.0844883\pi\) | ||||
−0.964980 | + | 0.262322i | \(0.915512\pi\) | |||||||
\(468\) | 16.6695 | − | 3.00287i | 0.770547 | − | 0.138808i | ||||
\(469\) | 7.45483 | 0.344232 | ||||||||
\(470\) | −3.56005 | − | 2.05539i | −0.164213 | − | 0.0948083i | ||||
\(471\) | −14.6962 | + | 5.37977i | −0.677166 | + | 0.247887i | ||||
\(472\) | −2.46746 | − | 4.27376i | −0.113574 | − | 0.196716i | ||||
\(473\) | − | 0.151174i | − | 0.00695100i | ||||||
\(474\) | 3.87647 | + | 3.24055i | 0.178052 | + | 0.148844i | ||||
\(475\) | 2.57689 | − | 4.46331i | 0.118236 | − | 0.204790i | ||||
\(476\) | 2.25644 | − | 3.90828i | 0.103424 | − | 0.179136i | ||||
\(477\) | 6.64940 | + | 36.9121i | 0.304455 | + | 1.69009i | ||||
\(478\) | 5.03976 | + | 2.90971i | 0.230513 | + | 0.133087i | ||||
\(479\) | −35.3823 | + | 20.4280i | −1.61666 | + | 0.933377i | −0.628880 | + | 0.777502i | \(0.716486\pi\) |
−0.987777 | + | 0.155875i | \(0.950180\pi\) | |||||||
\(480\) | 0.297614 | − | 1.70629i | 0.0135842 | − | 0.0778811i | ||||
\(481\) | −5.10142 | −0.232605 | ||||||||
\(482\) | −3.33368 | − | 5.77410i | −0.151845 | − | 0.263003i | ||||
\(483\) | −8.82609 | − | 7.37821i | −0.401601 | − | 0.335720i | ||||
\(484\) | −5.48417 | − | 9.49887i | −0.249281 | − | 0.431767i | ||||
\(485\) | −11.8713 | − | 6.85389i | −0.539047 | − | 0.311219i | ||||
\(486\) | −15.3260 | + | 2.84868i | −0.695200 | + | 0.129219i | ||||
\(487\) | −31.5249 | − | 18.2009i | −1.42853 | − | 0.824761i | −0.431524 | − | 0.902102i | \(-0.642024\pi\) |
−0.997005 | + | 0.0773402i | \(0.975357\pi\) | |||||||
\(488\) | 0.00227491 | 0.000102980 | ||||||||
\(489\) | 27.7929 | − | 10.1740i | 1.25684 | − | 0.460084i | ||||
\(490\) | −2.82285 | − | 4.88932i | −0.127523 | − | 0.220877i | ||||
\(491\) | −16.2180 | + | 28.0904i | −0.731908 | + | 1.26770i | 0.224159 | + | 0.974553i | \(0.428037\pi\) |
−0.956067 | + | 0.293149i | \(0.905297\pi\) | |||||||
\(492\) | −4.89986 | − | 0.854642i | −0.220903 | − | 0.0385302i | ||||
\(493\) | −10.7917 | − | 18.6919i | −0.486036 | − | 0.841839i | ||||
\(494\) | 29.0979 | 1.30918 | ||||||||
\(495\) | 0.180695 | − | 0.502224i | 0.00812162 | − | 0.0225733i | ||||
\(496\) | 5.12730 | − | 2.17043i | 0.230223 | − | 0.0974553i | ||||
\(497\) | − | 14.7428i | − | 0.661307i | ||||||
\(498\) | 27.1589 | + | 4.73710i | 1.21702 | + | 0.212274i | ||||
\(499\) | 36.8738 | − | 21.2891i | 1.65070 | − | 0.953030i | 0.673911 | − | 0.738812i | \(-0.264613\pi\) |
0.976786 | − | 0.214218i | \(-0.0687203\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | −11.8031 | − | 9.86685i | −0.527323 | − | 0.440818i | ||||
\(502\) | 7.18911 | − | 4.15063i | 0.320866 | − | 0.185252i | ||||
\(503\) | −32.1602 | + | 18.5677i | −1.43395 | + | 0.827893i | −0.997419 | − | 0.0717951i | \(-0.977127\pi\) |
−0.436533 | + | 0.899688i | \(0.643794\pi\) | |||||||
\(504\) | 1.18193 | − | 3.28507i | 0.0526475 | − | 0.146329i | ||||
\(505\) | 1.17439 | − | 2.03411i | 0.0522598 | − | 0.0905166i | ||||
\(506\) | −0.879355 | − | 0.507696i | −0.0390921 | − | 0.0225698i | ||||
\(507\) | 25.0848 | + | 20.9697i | 1.11405 | + | 0.931298i | ||||
\(508\) | −10.9132 | + | 6.30073i | −0.484194 | + | 0.279550i | ||||
\(509\) | 7.91070 | − | 13.7017i | 0.350636 | − | 0.607319i | −0.635725 | − | 0.771915i | \(-0.719299\pi\) |
0.986361 | + | 0.164597i | \(0.0526322\pi\) | |||||||
\(510\) | −6.30741 | + | 2.30892i | −0.279297 | + | 0.102241i | ||||
\(511\) | − | 12.5248i | − | 0.554065i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −26.7794 | + | 0.148507i | −1.18234 | + | 0.00655673i | ||||
\(514\) | 12.0152 | − | 20.8110i | 0.529970 | − | 0.917934i | ||||
\(515\) | −14.7109 | + | 8.49332i | −0.648238 | + | 0.374261i | ||||
\(516\) | −0.943927 | + | 1.12916i | −0.0415540 | + | 0.0497085i | ||||
\(517\) | −0.633381 | − | 0.365682i | −0.0278560 | − | 0.0160827i | ||||
\(518\) | −0.525754 | + | 0.910632i | −0.0231003 | + | 0.0400109i | ||||
\(519\) | −4.29919 | − | 0.749872i | −0.188713 | − | 0.0329157i | ||||
\(520\) | 4.88952 | − | 2.82297i | 0.214420 | − | 0.123795i | ||||
\(521\) | 23.6227 | − | 13.6385i | 1.03493 | − | 0.597515i | 0.116535 | − | 0.993187i | \(-0.462821\pi\) |
0.918392 | + | 0.395671i | \(0.129488\pi\) | |||||||
\(522\) | −10.7800 | − | 12.7511i | −0.471828 | − | 0.558099i | ||||
\(523\) | 18.7630i | 0.820447i | 0.911985 | + | 0.410224i | \(0.134549\pi\) | ||||
−0.911985 | + | 0.410224i | \(0.865451\pi\) | |||||||
\(524\) | 18.3335 | − | 10.5849i | 0.800903 | − | 0.462401i | ||||
\(525\) | 0.346346 | − | 1.98568i | 0.0151158 | − | 0.0866623i | ||||
\(526\) | − | 13.3178i | − | 0.580683i | ||||||
\(527\) | −17.2307 | − | 13.0110i | −0.750582 | − | 0.566768i | ||||
\(528\) | 0.0529495 | − | 0.303572i | 0.00230433 | − | 0.0132113i | ||||
\(529\) | 9.57238 | 0.416191 | ||||||||
\(530\) | 6.25104 | + | 10.8271i | 0.271528 | + | 0.470300i | ||||
\(531\) | −5.01205 | + | 13.9305i | −0.217505 | + | 0.604533i | ||||
\(532\) | 2.99884 | − | 5.19414i | 0.130016 | − | 0.225194i | ||||
\(533\) | −8.10656 | − | 14.0410i | −0.351134 | − | 0.608182i | ||||
\(534\) | 3.10080 | + | 8.47063i | 0.134185 | + | 0.366560i | ||||
\(535\) | −4.62335 | −0.199885 | ||||||||
\(536\) | −5.54769 | − | 3.20296i | −0.239624 | − | 0.138347i | ||||
\(537\) | 19.3106 | + | 16.1428i | 0.833313 | + | 0.696612i | ||||
\(538\) | −1.33351 | − | 0.769900i | −0.0574915 | − | 0.0331927i | ||||
\(539\) | −0.502224 | − | 0.869877i | −0.0216323 | − | 0.0374682i | ||||
\(540\) | −4.48552 | + | 2.62299i | −0.193026 | + | 0.112876i | ||||
\(541\) | 9.14009 | + | 15.8311i | 0.392963 | + | 0.680632i | 0.992839 | − | 0.119461i | \(-0.0381167\pi\) |
−0.599876 | + | 0.800093i | \(0.704783\pi\) | |||||||
\(542\) | −8.84626 | −0.379979 | ||||||||
\(543\) | −6.44712 | − | 1.12452i | −0.276672 | − | 0.0482576i | ||||
\(544\) | −3.35837 | + | 1.93896i | −0.143989 | + | 0.0831320i | ||||
\(545\) | 15.8744 | + | 9.16508i | 0.679984 | + | 0.392589i | ||||
\(546\) | 10.6868 | − | 3.91205i | 0.457351 | − | 0.167420i | ||||
\(547\) | 4.88556 | − | 8.46204i | 0.208891 | − | 0.361811i | −0.742474 | − | 0.669875i | \(-0.766348\pi\) |
0.951366 | + | 0.308064i | \(0.0996811\pi\) | |||||||
\(548\) | −6.42120 | + | 11.1218i | −0.274300 | + | 0.475102i | ||||
\(549\) | −0.00440614 | − | 0.00521179i | −0.000188050 | − | 0.000222434i | ||||
\(550\) | − | 0.177914i | − | 0.00758626i | ||||||
\(551\) | −14.3423 | − | 24.8417i | −0.611004 | − | 1.05829i | ||||
\(552\) | 3.39810 | + | 9.28278i | 0.144633 | + | 0.395101i | ||||
\(553\) | 2.93993 | + | 1.69737i | 0.125019 | + | 0.0721795i | ||||
\(554\) | −14.9715 | −0.636080 | ||||||||
\(555\) | 1.46963 | − | 0.537981i | 0.0623825 | − | 0.0228360i | ||||
\(556\) | − | 0.913499i | − | 0.0387410i | ||||||
\(557\) | 23.4375 | 0.993081 | 0.496540 | − | 0.868014i | \(-0.334603\pi\) | ||||
0.496540 | + | 0.868014i | \(0.334603\pi\) | |||||||
\(558\) | −14.9032 | − | 7.54280i | −0.630904 | − | 0.319312i | ||||
\(559\) | −4.79738 | −0.202908 | ||||||||
\(560\) | − | 1.16374i | − | 0.0491771i | ||||||
\(561\) | −1.12217 | + | 0.410789i | −0.0473782 | + | 0.0173435i | ||||
\(562\) | 7.32299 | 0.308902 | ||||||||
\(563\) | −3.55872 | − | 2.05463i | −0.149982 | − | 0.0865923i | 0.423131 | − | 0.906069i | \(-0.360931\pi\) |
−0.573113 | + | 0.819476i | \(0.694264\pi\) | |||||||
\(564\) | 2.44758 | + | 6.68619i | 0.103062 | + | 0.281539i | ||||
\(565\) | 0.217548 | + | 0.376805i | 0.00915232 | + | 0.0158523i | ||||
\(566\) | 14.6211i | 0.614570i | ||||||||
\(567\) | −9.81528 | + | 3.65488i | −0.412203 | + | 0.153491i | ||||
\(568\) | −6.33424 | + | 10.9712i | −0.265779 | + | 0.460342i | ||||
\(569\) | 20.3967 | − | 35.3280i | 0.855072 | − | 1.48103i | −0.0215060 | − | 0.999769i | \(-0.506846\pi\) |
0.876578 | − | 0.481260i | \(-0.159821\pi\) | |||||||
\(570\) | −8.38261 | + | 3.06858i | −0.351109 | + | 0.128529i | ||||
\(571\) | −22.6637 | − | 13.0849i | −0.948445 | − | 0.547585i | −0.0558476 | − | 0.998439i | \(-0.517786\pi\) |
−0.892598 | + | 0.450854i | \(0.851119\pi\) | |||||||
\(572\) | 0.869912 | − | 0.502244i | 0.0363729 | − | 0.0209999i | ||||
\(573\) | 11.0084 | + | 1.92011i | 0.459884 | + | 0.0802137i | ||||
\(574\) | −3.34186 | −0.139486 | ||||||||
\(575\) | 2.85361 | + | 4.94260i | 0.119004 | + | 0.206121i | ||||
\(576\) | −2.29099 | + | 1.93685i | −0.0954579 | + | 0.0807019i | ||||
\(577\) | −10.2691 | − | 17.7866i | −0.427509 | − | 0.740467i | 0.569142 | − | 0.822239i | \(-0.307275\pi\) |
−0.996651 | + | 0.0817721i | \(0.973942\pi\) | |||||||
\(578\) | −1.69897 | − | 0.980903i | −0.0706680 | − | 0.0408002i | ||||
\(579\) | −2.79427 | − | 2.33589i | −0.116126 | − | 0.0970761i | ||||
\(580\) | −4.82008 | − | 2.78288i | −0.200143 | − | 0.115553i | ||||
\(581\) | 18.5232 | 0.768472 | ||||||||
\(582\) | 8.16166 | + | 22.2957i | 0.338312 | + | 0.924185i | ||||
\(583\) | 1.11214 | + | 1.92629i | 0.0460603 | + | 0.0797788i | ||||
\(584\) | −5.38127 | + | 9.32062i | −0.222678 | + | 0.385690i | ||||
\(585\) | −15.9376 | − | 5.73419i | −0.658940 | − | 0.237079i | ||||
\(586\) | −17.0582 | − | 29.5457i | −0.704668 | − | 1.22052i | ||||
\(587\) | −37.7684 | −1.55887 | −0.779433 | − | 0.626485i | \(-0.784493\pi\) | ||||
−0.779433 | + | 0.626485i | \(0.784493\pi\) | |||||||
\(588\) | −1.68024 | + | 9.63321i | −0.0692919 | + | 0.397267i | ||||
\(589\) | −22.8998 | − | 17.2917i | −0.943570 | − | 0.712494i | ||||
\(590\) | 4.93491i | 0.203167i | ||||||||
\(591\) | 5.61513 | − | 32.1929i | 0.230976 | − | 1.32424i | ||||
\(592\) | 0.782503 | − | 0.451779i | 0.0321607 | − | 0.0185680i | ||||
\(593\) | − | 37.0997i | − | 1.52350i | −0.647870 | − | 0.761751i | \(-0.724340\pi\) | ||
0.647870 | − | 0.761751i | \(-0.275660\pi\) | |||||||
\(594\) | −0.798035 | + | 0.466666i | −0.0327438 | + | 0.0191475i | ||||
\(595\) | −3.90828 | + | 2.25644i | −0.160224 | + | 0.0925052i | ||||
\(596\) | −3.97105 | + | 2.29269i | −0.162661 | + | 0.0939121i | ||||
\(597\) | 32.8429 | + | 5.72852i | 1.34417 | + | 0.234453i | ||||
\(598\) | −16.1113 | + | 27.9056i | −0.658840 | + | 1.14114i | ||||
\(599\) | 17.6250 | + | 10.1758i | 0.720139 | + | 0.415773i | 0.814804 | − | 0.579737i | \(-0.196845\pi\) |
−0.0946646 | + | 0.995509i | \(0.530178\pi\) | |||||||
\(600\) | −1.11089 | + | 1.32888i | −0.0453517 | + | 0.0542514i | ||||
\(601\) | −35.9489 | + | 20.7551i | −1.46639 | + | 0.846619i | −0.999293 | − | 0.0375894i | \(-0.988032\pi\) |
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(602\) | −0.494419 | + | 0.856359i | −0.0201510 | + | 0.0349026i | ||||
\(603\) | 3.40707 | + | 18.9133i | 0.138747 | + | 0.770210i | ||||
\(604\) | 18.0258i | 0.733458i | ||||||||
\(605\) | 10.9683i | 0.445927i | ||||||||
\(606\) | −3.82029 | + | 1.39848i | −0.155189 | + | 0.0568092i | ||||
\(607\) | −9.76384 | + | 16.9115i | −0.396302 | + | 0.686415i | −0.993266 | − | 0.115852i | \(-0.963040\pi\) |
0.596964 | + | 0.802268i | \(0.296373\pi\) | |||||||
\(608\) | −4.46331 | + | 2.57689i | −0.181011 | + | 0.104507i | ||||
\(609\) | −8.60731 | − | 7.19532i | −0.348786 | − | 0.291569i | ||||
\(610\) | −0.00197013 | − | 0.00113745i | −7.97681e−5 | − | 4.60541e-5i | ||||
\(611\) | −11.6046 | + | 20.0998i | −0.469473 | + | 0.813150i | ||||
\(612\) | 10.9468 | + | 3.93853i | 0.442497 | + | 0.159206i | ||||
\(613\) | −3.94704 | + | 2.27883i | −0.159420 | + | 0.0920409i | −0.577587 | − | 0.816329i | \(-0.696006\pi\) |
0.418168 | + | 0.908370i | \(0.362672\pi\) | |||||||
\(614\) | 15.4946 | − | 8.94582i | 0.625312 | − | 0.361024i | ||||
\(615\) | 3.81608 | + | 3.19007i | 0.153879 | + | 0.128636i | ||||
\(616\) | − | 0.207046i | − | 0.00834210i | ||||||
\(617\) | −17.5553 | + | 10.1355i | −0.706749 | + | 0.408042i | −0.809856 | − | 0.586628i | \(-0.800455\pi\) |
0.103107 | + | 0.994670i | \(0.467122\pi\) | |||||||
\(618\) | 28.9841 | + | 5.05546i | 1.16591 | + | 0.203361i | ||||
\(619\) | 13.7227i | 0.551561i | 0.961221 | + | 0.275781i | \(0.0889363\pi\) | ||||
−0.961221 | + | 0.275781i | \(0.911064\pi\) | |||||||
\(620\) | −5.52559 | − | 0.684001i | −0.221913 | − | 0.0274701i | ||||
\(621\) | 14.6851 | − | 25.7643i | 0.589295 | − | 1.03389i | ||||
\(622\) | 14.8875 | 0.596935 | ||||||||
\(623\) | 3.03032 | + | 5.24868i | 0.121407 | + | 0.210284i | ||||
\(624\) | −9.63360 | − | 1.68031i | −0.385653 | − | 0.0672662i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 3.84359 | + | 6.65729i | 0.153621 | + | 0.266079i | ||||
\(627\) | −1.49138 | + | 0.545942i | −0.0595600 | + | 0.0218028i | ||||
\(628\) | 9.03549 | 0.360555 | ||||||||
\(629\) | −3.03448 | − | 1.75196i | −0.120993 | − | 0.0698551i | ||||
\(630\) | −2.66612 | + | 2.25399i | −0.106221 | + | 0.0898011i | ||||
\(631\) | 9.02379 | + | 5.20989i | 0.359231 | + | 0.207402i | 0.668743 | − | 0.743493i | \(-0.266832\pi\) |
−0.309512 | + | 0.950895i | \(0.600166\pi\) | |||||||
\(632\) | −1.45854 | − | 2.52627i | −0.0580178 | − | 0.100490i | ||||
\(633\) | 14.7116 | + | 12.2982i | 0.584734 | + | 0.488811i | ||||
\(634\) | −2.76055 | − | 4.78141i | −0.109635 | − | 0.189894i | ||||
\(635\) | 12.6015 | 0.500074 | ||||||||
\(636\) | 3.72079 | − | 21.3322i | 0.147539 | − | 0.845875i | ||||
\(637\) | −27.6048 | + | 15.9376i | −1.09374 | + | 0.631472i | ||||
\(638\) | −0.857558 | − | 0.495111i | −0.0339510 | − | 0.0196016i | ||||
\(639\) | 37.4034 | − | 6.73790i | 1.47966 | − | 0.266547i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −10.4121 | + | 18.0343i | −0.411254 | + | 0.712313i | −0.995027 | − | 0.0996039i | \(-0.968242\pi\) |
0.583773 | + | 0.811917i | \(0.301576\pi\) | |||||||
\(642\) | 6.14389 | + | 5.13601i | 0.242480 | + | 0.202702i | ||||
\(643\) | − | 45.6261i | − | 1.79932i | −0.436595 | − | 0.899658i | \(-0.643816\pi\) | ||
0.436595 | − | 0.899658i | \(-0.356184\pi\) | |||||||
\(644\) | 3.32087 | + | 5.75191i | 0.130861 | + | 0.226657i | ||||
\(645\) | 1.38204 | − | 0.505918i | 0.0544179 | − | 0.0199205i | ||||
\(646\) | 17.3083 | + | 9.99295i | 0.680986 | + | 0.393167i | ||||
\(647\) | 29.3824 | 1.15514 | 0.577570 | − | 0.816341i | \(-0.304001\pi\) | ||||
0.577570 | + | 0.816341i | \(0.304001\pi\) | |||||||
\(648\) | 8.87458 | + | 1.49726i | 0.348627 | + | 0.0588178i | ||||
\(649\) | 0.877988i | 0.0344640i | ||||||||
\(650\) | −5.64593 | −0.221452 | ||||||||
\(651\) | −10.7352 | − | 3.27197i | −0.420744 | − | 0.128239i | ||||
\(652\) | −17.0876 | −0.669201 | ||||||||
\(653\) | 36.5284i | 1.42947i | 0.699397 | + | 0.714734i | \(0.253452\pi\) | ||||
−0.699397 | + | 0.714734i | \(0.746548\pi\) | |||||||
\(654\) | −10.9139 | − | 29.8140i | −0.426765 | − | 1.16582i | ||||
\(655\) | −21.1697 | −0.827169 | ||||||||
\(656\) | 2.48692 | + | 1.43582i | 0.0970978 | + | 0.0560595i | ||||
\(657\) | 31.7761 | − | 5.72420i | 1.23970 | − | 0.223322i | ||||
\(658\) | 2.39195 | + | 4.14298i | 0.0932479 | + | 0.161510i | ||||
\(659\) | − | 18.6641i | − | 0.727050i | −0.931584 | − | 0.363525i | \(-0.881573\pi\) | ||
0.931584 | − | 0.363525i | \(-0.118427\pi\) | |||||||
\(660\) | −0.197642 | + | 0.236426i | −0.00769319 | + | 0.00920289i | ||||
\(661\) | −16.6494 | + | 28.8377i | −0.647588 | + | 1.12166i | 0.336109 | + | 0.941823i | \(0.390889\pi\) |
−0.983697 | + | 0.179833i | \(0.942444\pi\) | |||||||
\(662\) | −4.48602 | + | 7.77002i | −0.174354 | + | 0.301990i | ||||
\(663\) | 13.0360 | + | 35.6112i | 0.506277 | + | 1.38303i | ||||
\(664\) | −13.7845 | − | 7.95846i | −0.534941 | − | 0.308848i | ||||
\(665\) | −5.19414 | + | 2.99884i | −0.201420 | + | 0.116290i | ||||
\(666\) | −2.55061 | − | 0.917681i | −0.0988340 | − | 0.0355594i | ||||
\(667\) | 31.7650 | 1.22995 | ||||||||
\(668\) | 4.44098 | + | 7.69200i | 0.171827 | + | 0.297613i | ||||
\(669\) | −4.86854 | + | 5.82392i | −0.188228 | + | 0.225166i | ||||
\(670\) | 3.20296 | + | 5.54769i | 0.123741 | + | 0.214326i | ||||
\(671\) | −0.000350512 | 0 | 0.000202368i | −1.35314e−5 | 0 | 7.81234e-6i | ||||
\(672\) | −1.29279 | + | 1.54648i | −0.0498703 | + | 0.0596567i | ||||
\(673\) | 28.5063 | + | 16.4581i | 1.09884 | + | 0.634414i | 0.935915 | − | 0.352225i | \(-0.114575\pi\) |
0.162922 | + | 0.986639i | \(0.447908\pi\) | |||||||
\(674\) | −2.44574 | −0.0942066 | ||||||||
\(675\) | 5.19607 | − | 0.0288151i | 0.199997 | − | 0.00110909i | ||||
\(676\) | −9.43828 | − | 16.3476i | −0.363011 | − | 0.628753i | ||||
\(677\) | −3.71782 | + | 6.43945i | −0.142887 | + | 0.247488i | −0.928583 | − | 0.371125i | \(-0.878972\pi\) |
0.785695 | + | 0.618614i | \(0.212305\pi\) | |||||||
\(678\) | 0.129491 | − | 0.742401i | 0.00497306 | − | 0.0285117i | ||||
\(679\) | 7.97616 | + | 13.8151i | 0.306097 | + | 0.530175i | ||||
\(680\) | 3.87791 | 0.148711 | ||||||||
\(681\) | −28.0440 | − | 4.89148i | −1.07465 | − | 0.187442i | ||||
\(682\) | −0.983077 | − | 0.121693i | −0.0376440 | − | 0.00465987i | ||||
\(683\) | 27.8306i | 1.06491i | 0.846459 | + | 0.532453i | \(0.178730\pi\) | ||||
−0.846459 | + | 0.532453i | \(0.821270\pi\) | |||||||
\(684\) | 14.5484 | + | 5.23434i | 0.556270 | + | 0.200140i | ||||
\(685\) | 11.1218 | − | 6.42120i | 0.424944 | − | 0.245341i | ||||
\(686\) | 14.7163i | 0.561872i | ||||||||
\(687\) | 0.797350 | − | 0.953820i | 0.0304208 | − | 0.0363905i | ||||
\(688\) | 0.735867 | − | 0.424853i | 0.0280547 | − | 0.0161974i | ||||
\(689\) | 61.1292 | − | 35.2929i | 2.32884 | − | 1.34455i | ||||
\(690\) | 1.69855 | − | 9.73818i | 0.0646626 | − | 0.370726i | ||||
\(691\) | −17.9160 | + | 31.0315i | −0.681558 | + | 1.18049i | 0.292947 | + | 0.956129i | \(0.405364\pi\) |
−0.974505 | + | 0.224365i | \(0.927969\pi\) | |||||||
\(692\) | 2.18205 | + | 1.25981i | 0.0829490 | + | 0.0478906i | ||||
\(693\) | −0.474339 | + | 0.401015i | −0.0180186 | + | 0.0152333i | ||||
\(694\) | −14.6181 | + | 8.43977i | −0.554896 | + | 0.320369i | ||||
\(695\) | −0.456749 | + | 0.791113i | −0.0173255 | + | 0.0300086i | ||||
\(696\) | 3.31387 | + | 9.05268i | 0.125612 | + | 0.343141i | ||||
\(697\) | − | 11.1360i | − | 0.421806i | ||||||
\(698\) | − | 32.6846i | − | 1.23713i | ||||||
\(699\) | −9.35121 | − | 25.5452i | −0.353695 | − | 0.966209i | ||||
\(700\) | −0.581871 | + | 1.00783i | −0.0219927 | + | 0.0380924i | ||||
\(701\) | −6.49145 | + | 3.74784i | −0.245179 | + | 0.141554i | −0.617555 | − | 0.786528i | \(-0.711877\pi\) |
0.372376 | + | 0.928082i | \(0.378543\pi\) | |||||||
\(702\) | 14.8092 | + | 25.3250i | 0.558938 | + | 0.955829i | ||||
\(703\) | −4.03285 | − | 2.32837i | −0.152102 | − | 0.0878160i | ||||
\(704\) | −0.0889568 | + | 0.154078i | −0.00335268 | + | 0.00580702i | ||||
\(705\) | 1.22343 | − | 7.01420i | 0.0460769 | − | 0.264170i | ||||
\(706\) | 10.1711 | − | 5.87229i | 0.382795 | − | 0.221007i | ||||
\(707\) | −2.36718 | + | 1.36669i | −0.0890269 | + | 0.0513997i | ||||
\(708\) | 5.48213 | − | 6.55792i | 0.206031 | − | 0.246462i | ||||
\(709\) | − | 1.59160i | − | 0.0597738i | −0.999553 | − | 0.0298869i | \(-0.990485\pi\) | ||
0.999553 | − | 0.0298869i | \(-0.00951471\pi\) | |||||||
\(710\) | 10.9712 | − | 6.33424i | 0.411743 | − | 0.237720i | ||||
\(711\) | −2.96269 | + | 8.23451i | −0.111109 | + | 0.308818i | ||||
\(712\) | − | 5.20790i | − | 0.195174i | ||||||
\(713\) | 29.2626 | − | 12.3871i | 1.09589 | − | 0.463902i | ||||
\(714\) | 7.70030 | + | 1.34310i | 0.288176 | + | 0.0502642i | ||||
\(715\) | −1.00449 | −0.0375657 | ||||||||
\(716\) | −7.26572 | − | 12.5846i | −0.271533 | − | 0.470308i | ||||
\(717\) | −1.73194 | + | 9.92961i | −0.0646804 | + | 0.370828i | ||||
\(718\) | −5.32502 | + | 9.22320i | −0.198728 | + | 0.344207i | ||||
\(719\) | −1.12193 | − | 1.94324i | −0.0418410 | − | 0.0724707i | 0.844347 | − | 0.535797i | \(-0.179989\pi\) |
−0.886188 | + | 0.463327i | \(0.846656\pi\) | |||||||
\(720\) | 2.95248 | − | 0.531863i | 0.110032 | − | 0.0198214i | ||||
\(721\) | 19.7681 | 0.736202 | ||||||||
\(722\) | 6.54841 | + | 3.78073i | 0.243707 | + | 0.140704i | ||||
\(723\) | 7.40667 | − | 8.86013i | 0.275457 | − | 0.329512i | ||||
\(724\) | 3.27223 | + | 1.88922i | 0.121611 | + | 0.0702124i | ||||
\(725\) | 2.78288 | + | 4.82008i | 0.103353 | + | 0.179013i | ||||
\(726\) | 12.1846 | − | 14.5757i | 0.452212 | − | 0.540953i | ||||
\(727\) | 16.3097 | + | 28.2493i | 0.604894 | + | 1.04771i | 0.992068 | + | 0.125701i | \(0.0401180\pi\) |
−0.387174 | + | 0.922007i | \(0.626549\pi\) | |||||||
\(728\) | −6.57041 | −0.243516 | ||||||||
\(729\) | −13.7585 | − | 23.2315i | −0.509574 | − | 0.860427i | ||||
\(730\) | 9.32062 | − | 5.38127i | 0.344972 | − | 0.199170i | ||||
\(731\) | −2.85363 | − | 1.64754i | −0.105545 | − | 0.0609365i | ||||
\(732\) | 0.00135449 | + | 0.00370013i | 5.00633e−5 | + | 0.000136761i | ||||
\(733\) | −4.82676 | + | 8.36019i | −0.178280 | + | 0.308791i | −0.941292 | − | 0.337594i | \(-0.890387\pi\) |
0.763011 | + | 0.646385i | \(0.223720\pi\) | |||||||
\(734\) | 14.4416 | − | 25.0136i | 0.533050 | − | 0.923270i | ||||
\(735\) | 6.27173 | − | 7.50248i | 0.231336 | − | 0.276733i | ||||
\(736\) | − | 5.70722i | − | 0.210371i | ||||||
\(737\) | 0.569850 | + | 0.987008i | 0.0209907 | + | 0.0363569i | ||||
\(738\) | −1.52732 | − | 8.47847i | −0.0562215 | − | 0.312097i | ||||
\(739\) | 20.5340 | + | 11.8553i | 0.755355 | + | 0.436105i | 0.827626 | − | 0.561281i | \(-0.189691\pi\) |
−0.0722704 | + | 0.997385i | \(0.523024\pi\) | |||||||
\(740\) | −0.903557 | −0.0332154 | ||||||||
\(741\) | 17.3250 | + | 47.3277i | 0.636450 | + | 1.73863i | ||||
\(742\) | − | 14.5492i | − | 0.534118i | ||||||
\(743\) | 33.9392 | 1.24511 | 0.622555 | − | 0.782576i | \(-0.286095\pi\) | ||||
0.622555 | + | 0.782576i | \(0.286095\pi\) | |||||||
\(744\) | 6.58302 | + | 7.04726i | 0.241345 | + | 0.258365i | ||||
\(745\) | 4.58537 | 0.167995 | ||||||||
\(746\) | 15.4070i | 0.564090i | ||||||||
\(747\) | 8.46563 | + | 46.9944i | 0.309741 | + | 1.71943i | ||||
\(748\) | 0.689933 | 0.0252264 | ||||||||
\(749\) | 4.65955 | + | 2.69019i | 0.170256 | + | 0.0982975i | ||||
\(750\) | 1.62650 | − | 0.595404i | 0.0593913 | − | 0.0217411i | ||||
\(751\) | −3.61672 | − | 6.26434i | −0.131976 | − | 0.228589i | 0.792462 | − | 0.609921i | \(-0.208799\pi\) |
−0.924438 | + | 0.381332i | \(0.875466\pi\) | |||||||
\(752\) | − | 4.11079i | − | 0.149905i | ||||||
\(753\) | 11.0314 | + | 9.22176i | 0.402007 | + | 0.336060i | ||||
\(754\) | −15.7119 | + | 27.2139i | −0.572195 | + | 0.991071i | ||||
\(755\) | 9.01289 | − | 15.6108i | 0.328013 | − | 0.568134i | ||||
\(756\) | 6.04689 | − | 0.0335334i | 0.219923 | − | 0.00121960i | ||||
\(757\) | −0.672009 | − | 0.387984i | −0.0244246 | − | 0.0141015i | 0.487738 | − | 0.872990i | \(-0.337822\pi\) |
−0.512163 | + | 0.858889i | \(0.671155\pi\) | |||||||
\(758\) | −8.07991 | + | 4.66494i | −0.293475 | + | 0.169438i | ||||
\(759\) | 0.302195 | − | 1.73255i | 0.0109690 | − | 0.0628877i | ||||
\(760\) | 5.15378 | 0.186947 | ||||||||
\(761\) | 3.20580 | + | 5.55261i | 0.116210 | + | 0.201282i | 0.918263 | − | 0.395971i | \(-0.129592\pi\) |
−0.802053 | + | 0.597253i | \(0.796259\pi\) | |||||||
\(762\) | −16.7459 | − | 13.9988i | −0.606639 | − | 0.507122i | ||||
\(763\) | −10.6658 | − | 18.4737i | −0.386128 | − | 0.668793i | ||||
\(764\) | −5.58732 | − | 3.22584i | −0.202142 | − | 0.116707i | ||||
\(765\) | −7.51092 | − | 8.88425i | −0.271558 | − | 0.321211i | ||||
\(766\) | 20.4225 | + | 11.7909i | 0.737895 | + | 0.426024i | ||||
\(767\) | 27.8622 | 1.00605 | ||||||||
\(768\) | 1.62650 | − | 0.595404i | 0.0586912 | − | 0.0214848i | ||||
\(769\) | 9.17949 | + | 15.8993i | 0.331021 | + | 0.573345i | 0.982712 | − | 0.185139i | \(-0.0592736\pi\) |
−0.651691 | + | 0.758484i | \(0.725940\pi\) | |||||||
\(770\) | −0.103523 | + | 0.179307i | −0.00373070 | + | 0.00646176i | ||||
\(771\) | 41.0030 | + | 7.15180i | 1.47669 | + | 0.257566i | ||||
\(772\) | 1.05136 | + | 1.82101i | 0.0378393 | + | 0.0655396i | ||||
\(773\) | −11.5363 | −0.414930 | −0.207465 | − | 0.978242i | \(-0.566521\pi\) | ||||
−0.207465 | + | 0.978242i | \(0.566521\pi\) | |||||||
\(774\) | −2.39859 | − | 0.862988i | −0.0862157 | − | 0.0310195i | ||||
\(775\) | 4.44330 | + | 3.35516i | 0.159608 | + | 0.120521i | ||||
\(776\) | − | 13.7078i | − | 0.492081i | ||||||
\(777\) | −1.79418 | − | 0.312943i | −0.0643657 | − | 0.0112268i | ||||
\(778\) | 29.7153 | − | 17.1562i | 1.06535 | − | 0.615078i | ||||
\(779\) | − | 14.7998i | − | 0.530259i | ||||||
\(780\) | 7.50279 | + | 6.27199i | 0.268643 | + | 0.224573i | ||||
\(781\) | 1.95193 | − | 1.12695i | 0.0698455 | − | 0.0403253i | ||||
\(782\) | −19.1670 | + | 11.0660i | −0.685409 | + | 0.395721i | ||||
\(783\) | 14.3211 | − | 25.1257i | 0.511796 | − | 0.897919i | ||||
\(784\) | 2.82285 | − | 4.88932i | 0.100816 | − | 0.174619i | ||||
\(785\) | −7.82497 | − | 4.51775i | −0.279285 | − | 0.161245i | ||||
\(786\) | 28.1321 | + | 23.5171i | 1.00344 | + | 0.838828i | ||||
\(787\) | −15.4169 | + | 8.90097i | −0.549554 | + | 0.317285i | −0.748942 | − | 0.662635i | \(-0.769438\pi\) |
0.199388 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(788\) | −9.43359 | + | 16.3395i | −0.336058 | + | 0.582069i | ||||
\(789\) | 21.6613 | − | 7.92946i | 0.771164 | − | 0.282296i | ||||
\(790\) | 2.91709i | 0.103785i | ||||||||
\(791\) | − | 0.506340i | − | 0.0180034i | ||||||
\(792\) | 0.525286 | − | 0.0946257i | 0.0186652 | − | 0.00336238i | ||||
\(793\) | −0.00642199 | + | 0.0111232i | −0.000228051 | + | 0.000394997i | ||||
\(794\) | −22.6122 | + | 13.0551i | −0.802475 | + | 0.463309i | ||||
\(795\) | −13.8884 | + | 16.6138i | −0.492570 | + | 0.589231i | ||||
\(796\) | −16.6694 | − | 9.62408i | −0.590831 | − | 0.341116i | ||||
\(797\) | −18.5843 | + | 32.1890i | −0.658291 | + | 1.14019i | 0.322767 | + | 0.946479i | \(0.395387\pi\) |
−0.981058 | + | 0.193715i | \(0.937946\pi\) | |||||||
\(798\) | 10.2338 | + | 1.78499i | 0.362272 | + | 0.0631880i | ||||
\(799\) | −13.8055 | + | 7.97063i | −0.488405 | + | 0.281981i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | −11.9312 | + | 10.0869i | −0.421569 | + | 0.356403i | ||||
\(802\) | − | 1.81201i | − | 0.0639842i | ||||||
\(803\) | 1.65827 | − | 0.957400i | 0.0585189 | − | 0.0337859i | ||||
\(804\) | 1.90649 | − | 10.9304i | 0.0672367 | − | 0.385484i | ||||
\(805\) | − | 6.64174i | − | 0.234090i | ||||||
\(806\) | −3.86182 | + | 31.1971i | −0.136027 | + | 1.09887i | ||||
\(807\) | 0.458266 | − | 2.62734i | 0.0161317 | − | 0.0924869i | ||||
\(808\) | 2.34879 | 0.0826300 | ||||||||
\(809\) | −6.71526 | − | 11.6312i | −0.236096 | − | 0.408930i | 0.723495 | − | 0.690330i | \(-0.242535\pi\) |
−0.959591 | + | 0.281400i | \(0.909201\pi\) | |||||||
\(810\) | −6.93699 | − | 5.73395i | −0.243741 | − | 0.201471i | ||||
\(811\) | −4.22401 | + | 7.31619i | −0.148325 | + | 0.256906i | −0.930608 | − | 0.366016i | \(-0.880721\pi\) |
0.782284 | + | 0.622922i | \(0.214055\pi\) | |||||||
\(812\) | 3.23855 | + | 5.60933i | 0.113651 | + | 0.196849i | ||||
\(813\) | −5.26710 | − | 14.3884i | −0.184725 | − | 0.504624i | ||||
\(814\) | −0.160755 | −0.00563446 | ||||||||
\(815\) | 14.7983 | + | 8.54378i | 0.518360 | + | 0.299276i | ||||
\(816\) | −5.15329 | − | 4.30792i | −0.180401 | − | 0.150807i | ||||
\(817\) | −3.79250 | − | 2.18960i | −0.132683 | − | 0.0766044i | ||||
\(818\) | 12.4143 | + | 21.5022i | 0.434056 | + | 0.751808i | ||||
\(819\) | 12.7259 | + | 15.0527i | 0.444678 | + | 0.525985i | ||||
\(820\) | −1.43582 | − | 2.48692i | −0.0501411 | − | 0.0868469i | ||||
\(821\) | 21.5718 | 0.752861 | 0.376431 | − | 0.926445i | \(-0.377151\pi\) | ||||
0.376431 | + | 0.926445i | \(0.377151\pi\) | |||||||
\(822\) | −21.9129 | − | 3.82208i | −0.764299 | − | 0.133310i | ||||
\(823\) | −23.2067 | + | 13.3984i | −0.808934 | + | 0.467038i | −0.846586 | − | 0.532253i | \(-0.821346\pi\) |
0.0376515 | + | 0.999291i | \(0.488012\pi\) | |||||||
\(824\) | −14.7109 | − | 8.49332i | −0.512477 | − | 0.295879i | ||||
\(825\) | 0.289376 | − | 0.105930i | 0.0100748 | − | 0.00368802i | ||||
\(826\) | 2.87148 | − | 4.97356i | 0.0999117 | − | 0.173052i | ||||
\(827\) | −8.45553 | + | 14.6454i | −0.294028 | + | 0.509271i | −0.974758 | − | 0.223263i | \(-0.928329\pi\) |
0.680731 | + | 0.732534i | \(0.261662\pi\) | |||||||
\(828\) | −13.0752 | + | 11.0540i | −0.454394 | + | 0.384153i | ||||
\(829\) | 6.47384i | 0.224846i | 0.993660 | + | 0.112423i | \(0.0358611\pi\) | ||||
−0.993660 | + | 0.112423i | \(0.964139\pi\) | |||||||
\(830\) | 7.95846 | + | 13.7845i | 0.276242 | + | 0.478466i | ||||
\(831\) | −8.91411 | − | 24.3512i | −0.309227 | − | 0.844732i | ||||
\(832\) | 4.88952 | + | 2.82297i | 0.169514 | + | 0.0978688i | ||||
\(833\) | −21.8935 | −0.758566 | ||||||||
\(834\) | 1.48580 | − | 0.543901i | 0.0514492 | − | 0.0188337i | ||||
\(835\) | − | 8.88196i | − | 0.307373i | ||||||
\(836\) | 0.916927 | 0.0317126 | ||||||||
\(837\) | 3.39490 | − | 28.7311i | 0.117345 | − | 0.993091i | ||||
\(838\) | 16.9548 | 0.585693 | ||||||||
\(839\) | − | 43.6645i | − | 1.50747i | −0.657180 | − | 0.753734i | \(-0.728251\pi\) | ||
0.657180 | − | 0.753734i | \(-0.271749\pi\) | |||||||
\(840\) | 1.89282 | − | 0.692897i | 0.0653086 | − | 0.0239072i | ||||
\(841\) | 1.97760 | 0.0681931 | ||||||||
\(842\) | −25.1607 | − | 14.5265i | −0.867095 | − | 0.500618i | ||||
\(843\) | 4.36013 | + | 11.9108i | 0.150171 | + | 0.410230i | ||||
\(844\) | −5.53532 | − | 9.58746i | −0.190534 | − | 0.330014i | ||||
\(845\) | 18.8766i | 0.649374i | ||||||||
\(846\) | −9.41777 | + | 7.96196i | −0.323790 | + | 0.273738i | ||||
\(847\) | 6.38216 | − | 11.0542i | 0.219294 | − | 0.379828i | ||||
\(848\) | −6.25104 | + | 10.8271i | −0.214661 | + | 0.371805i | ||||
\(849\) | −23.7812 | + | 8.70545i | −0.816167 | + | 0.298770i | ||||
\(850\) | −3.35837 | − | 1.93896i | −0.115191 | − | 0.0665056i | ||||
\(851\) | 4.46592 | − | 2.57840i | 0.153090 | − | 0.0883864i | ||||
\(852\) | −21.6161 | − | 3.77031i | −0.740555 | − | 0.129169i | ||||
\(853\) | 34.3980 | 1.17776 | 0.588882 | − | 0.808219i | \(-0.299568\pi\) | ||||
0.588882 | + | 0.808219i | \(0.299568\pi\) | |||||||
\(854\) | 0.00132370 | + | 0.00229272i | 4.52962e−5 | + | 7.84553e-5i | ||||
\(855\) | −9.98208 | − | 11.8073i | −0.341380 | − | 0.403800i | ||||
\(856\) | −2.31167 | − | 4.00394i | −0.0790114 | − | 0.136852i | ||||
\(857\) | −14.9622 | − | 8.63842i | −0.511098 | − | 0.295083i | 0.222187 | − | 0.975004i | \(-0.428681\pi\) |
−0.733285 | + | 0.679921i | \(0.762014\pi\) | |||||||
\(858\) | 1.33485 | + | 1.11587i | 0.0455710 | + | 0.0380952i | ||||
\(859\) | 4.18085 | + | 2.41382i | 0.142649 | + | 0.0823583i | 0.569626 | − | 0.821904i | \(-0.307088\pi\) |
−0.426977 | + | 0.904262i | \(0.640421\pi\) | |||||||
\(860\) | −0.849706 | −0.0289747 | ||||||||
\(861\) | −1.98975 | − | 5.43552i | −0.0678106 | − | 0.185242i | ||||
\(862\) | 10.9041 | + | 18.8864i | 0.371394 | + | 0.643274i | ||||
\(863\) | 8.63393 | − | 14.9544i | 0.293902 | − | 0.509054i | −0.680827 | − | 0.732445i | \(-0.738379\pi\) |
0.974729 | + | 0.223391i | \(0.0717126\pi\) | |||||||
\(864\) | −4.51434 | − | 2.57308i | −0.153581 | − | 0.0875380i | ||||
\(865\) | −1.25981 | − | 2.18205i | −0.0428347 | − | 0.0741919i | ||||
\(866\) | −22.8178 | −0.775380 | ||||||||
\(867\) | 0.583861 | − | 3.34741i | 0.0198290 | − | 0.113684i | ||||
\(868\) | 5.17086 | + | 3.90454i | 0.175510 | + | 0.132529i | ||||
\(869\) | 0.518990i | 0.0176055i | ||||||||
\(870\) | 1.65645 | − | 9.49679i | 0.0561588 | − | 0.321971i | ||||
\(871\) | 31.3219 | − | 18.0837i | 1.06130 | − | 0.612742i | ||||
\(872\) | 18.3302i | 0.620738i | ||||||||
\(873\) | −31.4044 | + | 26.5499i | −1.06288 | + | 0.898576i | ||||
\(874\) | −25.4731 | + | 14.7069i | −0.861640 | + | 0.497468i | ||||
\(875\) | 1.00783 | − | 0.581871i | 0.0340709 | − | 0.0196708i | ||||
\(876\) | −18.3640 | − | 3.20308i | −0.620462 | − | 0.108222i | ||||
\(877\) | −21.8659 | + | 37.8729i | −0.738359 | + | 1.27888i | 0.214874 | + | 0.976642i | \(0.431066\pi\) |
−0.953234 | + | 0.302234i | \(0.902268\pi\) | |||||||
\(878\) | −20.6527 | − | 11.9238i | −0.696994 | − | 0.402410i | ||||
\(879\) | 37.8994 | − | 45.3367i | 1.27832 | − | 1.52917i | ||||
\(880\) | 0.154078 | − | 0.0889568i | 0.00519396 | − | 0.00299873i | ||||
\(881\) | 18.1740 | − | 31.4783i | 0.612298 | − | 1.06053i | −0.378555 | − | 0.925579i | \(-0.623579\pi\) |
0.990852 | − | 0.134951i | \(-0.0430879\pi\) | |||||||
\(882\) | −16.6688 | + | 3.00274i | −0.561268 | + | 0.101108i | ||||
\(883\) | − | 51.2633i | − | 1.72515i | −0.505931 | − | 0.862574i | \(-0.668851\pi\) | ||
0.505931 | − | 0.862574i | \(-0.331149\pi\) | |||||||
\(884\) | − | 21.8944i | − | 0.736389i | ||||||
\(885\) | −8.02662 | + | 2.93827i | −0.269812 | + | 0.0987687i | ||||
\(886\) | −10.4904 | + | 18.1698i | −0.352431 | + | 0.610428i | ||||
\(887\) | −15.9684 | + | 9.21935i | −0.536166 | + | 0.309556i | −0.743524 | − | 0.668710i | \(-0.766847\pi\) |
0.207358 | + | 0.978265i | \(0.433514\pi\) | |||||||
\(888\) | 1.20072 | + | 1.00375i | 0.0402936 | + | 0.0336836i | ||||
\(889\) | −12.7001 | − | 7.33242i | −0.425949 | − | 0.245922i | ||||
\(890\) | −2.60395 | + | 4.51017i | −0.0872846 | + | 0.151181i | ||||
\(891\) | −1.23418 | − | 1.02015i | −0.0413467 | − | 0.0341762i | ||||
\(892\) | 3.79542 | − | 2.19128i | 0.127080 | − | 0.0733696i | ||||
\(893\) | −18.3477 | + | 10.5930i | −0.613982 | + | 0.354483i | ||||
\(894\) | −6.09343 | − | 5.09383i | −0.203795 | − | 0.170363i | ||||
\(895\) | 14.5314i | 0.485732i | ||||||||
\(896\) | 1.00783 | − | 0.581871i | 0.0336693 | − | 0.0194390i | ||||
\(897\) | −54.9811 | − | 9.58989i | −1.83577 | − | 0.320197i | ||||
\(898\) | 30.8958i | 1.03101i | ||||||||
\(899\) | 28.5373 | − | 12.0801i | 0.951772 | − | 0.402894i | ||||
\(900\) | −2.82285 | − | 1.01563i | −0.0940951 | − | 0.0338544i | ||||
\(901\) | 48.4819 | 1.61517 | ||||||||
\(902\) | −0.255452 | − | 0.442456i | −0.00850563 | − | 0.0147322i | ||||
\(903\) | −1.68725 | − | 0.294292i | −0.0561480 | − | 0.00979343i | ||||
\(904\) | −0.217548 | + | 0.376805i | −0.00723555 | + | 0.0125323i | ||||
\(905\) | −1.88922 | − | 3.27223i | −0.0627998 | − | 0.108773i | ||||
\(906\) | −29.3189 | + | 10.7326i | −0.974054 | + | 0.356567i | ||||
\(907\) | −4.08947 | −0.135789 | −0.0678943 | − | 0.997693i | \(-0.521628\pi\) | ||||
−0.0678943 | + | 0.997693i | \(0.521628\pi\) | |||||||
\(908\) | 14.2337 | + | 8.21783i | 0.472362 | + | 0.272718i | ||||
\(909\) | −4.54924 | − | 5.38104i | −0.150889 | − | 0.178478i | ||||
\(910\) | 5.69014 | + | 3.28521i | 0.188626 | + | 0.108904i | ||||
\(911\) | 27.6813 | + | 47.9455i | 0.917124 | + | 1.58851i | 0.803761 | + | 0.594952i | \(0.202829\pi\) |
0.113363 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(912\) | −6.84878 | − | 5.72526i | −0.226786 | − | 0.189582i | ||||
\(913\) | 1.41592 | + | 2.45244i | 0.0468601 | + | 0.0811640i | ||||
\(914\) | −10.1581 | −0.336001 | ||||||||
\(915\) | 0.000677044 | − | 0.00388165i | 2.23824e−5 | − | 0.000128323i | ||||
\(916\) | −0.621599 | + | 0.358880i | −0.0205382 | + | 0.0118577i | ||||
\(917\) | 21.3355 | + | 12.3180i | 0.704559 | + | 0.406778i | ||||
\(918\) | 0.111742 | + | 20.1499i | 0.00368805 | + | 0.665046i | ||||
\(919\) | 9.34101 | − | 16.1791i | 0.308132 | − | 0.533700i | −0.669822 | − | 0.742522i | \(-0.733630\pi\) |
0.977954 | + | 0.208822i | \(0.0669630\pi\) | |||||||
\(920\) | −2.85361 | + | 4.94260i | −0.0940808 | + | 0.162953i | ||||
\(921\) | 23.7759 | + | 19.8756i | 0.783443 | + | 0.654923i | ||||
\(922\) | − | 19.8197i | − | 0.652727i | ||||||
\(923\) | −35.7627 | − | 61.9428i | −1.17714 | − | 2.03887i | ||||
\(924\) | 0.336759 | − | 0.123276i | 0.0110786 | − | 0.00405547i | ||||
\(925\) | 0.782503 | + | 0.451779i | 0.0257286 | + | 0.0148544i | ||||
\(926\) | −10.9325 | −0.359263 | ||||||||
\(927\) | 9.03458 | + | 50.1527i | 0.296734 | + | 1.64723i | ||||
\(928\) | − | 5.56575i | − | 0.182705i | ||||||
\(929\) | 11.9745 | 0.392870 | 0.196435 | − | 0.980517i | \(-0.437063\pi\) | ||||
0.196435 | + | 0.980517i | \(0.437063\pi\) | |||||||
\(930\) | −2.17743 | − | 9.39461i | −0.0714008 | − | 0.308062i | ||||
\(931\) | −29.0967 | −0.953606 | ||||||||
\(932\) | 15.7057i | 0.514456i | ||||||||
\(933\) | 8.86409 | + | 24.2145i | 0.290197 | + | 0.792748i | ||||
\(934\) | 11.3377 | 0.370980 | ||||||||
\(935\) | −0.597499 | − | 0.344966i | −0.0195403 | − | 0.0112816i | ||||
\(936\) | −3.00287 | − | 16.6695i | −0.0981517 | − | 0.544859i | ||||
\(937\) | 4.88152 | + | 8.45503i | 0.159472 | + | 0.276214i | 0.934678 | − | 0.355494i | \(-0.115687\pi\) |
−0.775206 | + | 0.631708i | \(0.782354\pi\) | |||||||
\(938\) | − | 7.45483i | − | 0.243409i | ||||||
\(939\) | −8.53958 | + | 10.2154i | −0.278679 | + | 0.333366i | ||||
\(940\) | −2.05539 | + | 3.56005i | −0.0670396 | + | 0.116116i | ||||
\(941\) | 3.76669 | − | 6.52409i | 0.122790 | − | 0.212679i | −0.798077 | − | 0.602556i | \(-0.794149\pi\) |
0.920867 | + | 0.389877i | \(0.127482\pi\) | |||||||
\(942\) | 5.37977 | + | 14.6962i | 0.175282 | + | 0.478828i | ||||
\(943\) | 14.1934 | + | 8.19456i | 0.462200 | + | 0.266852i | ||||
\(944\) | −4.27376 | + | 2.46746i | −0.139099 | + | 0.0803089i | ||||
\(945\) | −5.25353 | − | 2.99440i | −0.170897 | − | 0.0974080i | ||||
\(946\) | −0.151174 | −0.00491510 | ||||||||
\(947\) | 17.9100 | + | 31.0211i | 0.581997 | + | 1.00805i | 0.995242 | + | 0.0974291i | \(0.0310619\pi\) |
−0.413245 | + | 0.910620i | \(0.635605\pi\) | |||||||
\(948\) | 3.24055 | − | 3.87647i | 0.105248 | − | 0.125902i | ||||
\(949\) | −30.3823 | − | 52.6236i | −0.986250 | − | 1.70824i | ||||
\(950\) | −4.46331 | − | 2.57689i | −0.144809 | − | 0.0836054i | ||||
\(951\) | 6.13331 | − | 7.33689i | 0.198886 | − | 0.237915i | ||||
\(952\) | −3.90828 | − | 2.25644i | −0.126668 | − | 0.0731318i | ||||
\(953\) | 8.04230 | 0.260516 | 0.130258 | − | 0.991480i | \(-0.458419\pi\) | ||||
0.130258 | + | 0.991480i | \(0.458419\pi\) | |||||||
\(954\) | 36.9121 | − | 6.64940i | 1.19507 | − | 0.215282i | ||||
\(955\) | 3.22584 | + | 5.58732i | 0.104386 | + | 0.180801i | ||||
\(956\) | 2.90971 | − | 5.03976i | 0.0941067 | − | 0.162998i | ||||
\(957\) | 0.294704 | − | 1.68961i | 0.00952643 | − | 0.0546172i | ||||
\(958\) | 20.4280 | + | 35.3823i | 0.659997 | + | 1.14315i | ||||
\(959\) | −14.9452 | −0.482607 | ||||||||
\(960\) | −1.70629 | − | 0.297614i | −0.0550703 | − | 0.00960545i | ||||
\(961\) | 21.5784 | − | 22.2569i | 0.696079 | − | 0.717965i | ||||
\(962\) | 5.10142i | 0.164476i | ||||||||
\(963\) | −4.69562 | + | 13.0510i | −0.151314 | + | 0.420563i | ||||
\(964\) | −5.77410 | + | 3.33368i | −0.185971 | + | 0.107370i | ||||
\(965\) | − | 2.10272i | − | 0.0676890i | ||||||
\(966\) | −7.37821 | + | 8.82609i | −0.237390 | + | 0.283975i | ||||
\(967\) | 0.283683 | − | 0.163784i | 0.00912262 | − | 0.00526695i | −0.495432 | − | 0.868647i | \(-0.664990\pi\) |
0.504554 | + | 0.863380i | \(0.331657\pi\) | |||||||
\(968\) | −9.49887 | + | 5.48417i | −0.305305 | + | 0.176268i | ||||
\(969\) | −5.94808 | + | 34.1017i | −0.191080 | + | 1.09551i | ||||
\(970\) | −6.85389 | + | 11.8713i | −0.220065 | + | 0.381164i | ||||
\(971\) | −9.78490 | − | 5.64932i | −0.314013 | − | 0.181295i | 0.334708 | − | 0.942322i | \(-0.391362\pi\) |
−0.648721 | + | 0.761027i | \(0.724696\pi\) | |||||||
\(972\) | 2.84868 | + | 15.3260i | 0.0913714 | + | 0.491580i | ||||
\(973\) | 0.920652 | − | 0.531539i | 0.0295147 | − | 0.0170403i | ||||
\(974\) | −18.2009 | + | 31.5249i | −0.583194 | + | 1.01012i | ||||
\(975\) | −3.36161 | − | 9.18310i | −0.107658 | − | 0.294094i | ||||
\(976\) | − | 0.00227491i | − | 7.28180e-5i | ||||||
\(977\) | 34.7208i | 1.11082i | 0.831578 | + | 0.555409i | \(0.187438\pi\) | ||||
−0.831578 | + | 0.555409i | \(0.812562\pi\) | |||||||
\(978\) | −10.1740 | − | 27.7929i | −0.325329 | − | 0.888718i | ||||
\(979\) | −0.463278 | + | 0.802421i | −0.0148064 | + | 0.0256455i | ||||
\(980\) | −4.88932 | + | 2.82285i | −0.156184 | + | 0.0901727i | ||||
\(981\) | 41.9942 | − | 35.5027i | 1.34077 | − | 1.13351i | ||||
\(982\) | 28.0904 | + | 16.2180i | 0.896400 | + | 0.517537i | ||||
\(983\) | 19.9164 | − | 34.4963i | 0.635235 | − | 1.10026i | −0.351230 | − | 0.936289i | \(-0.614236\pi\) |
0.986465 | − | 0.163971i | \(-0.0524302\pi\) | |||||||
\(984\) | −0.854642 | + | 4.89986i | −0.0272450 | + | 0.156202i | ||||
\(985\) | 16.3395 | − | 9.43359i | 0.520618 | − | 0.300579i | ||||
\(986\) | −18.6919 | + | 10.7917i | −0.595270 | + | 0.343679i | ||||
\(987\) | −5.31437 | + | 6.35724i | −0.169158 | + | 0.202353i | ||||
\(988\) | − | 29.0979i | − | 0.925728i | ||||||
\(989\) | 4.19976 | − | 2.42473i | 0.133544 | − | 0.0771019i | ||||
\(990\) | −0.502224 | − | 0.180695i | −0.0159617 | − | 0.00574285i | ||||
\(991\) | − | 5.61866i | − | 0.178483i | −0.996010 | − | 0.0892413i | \(-0.971556\pi\) | ||
0.996010 | − | 0.0892413i | \(-0.0284442\pi\) | |||||||
\(992\) | −2.17043 | − | 5.12730i | −0.0689113 | − | 0.162792i | ||||
\(993\) | −15.3089 | − | 2.67021i | −0.485814 | − | 0.0847364i | ||||
\(994\) | −14.7428 | −0.467615 | ||||||||
\(995\) | 9.62408 | + | 16.6694i | 0.305104 | + | 0.528455i | ||||
\(996\) | 4.73710 | − | 27.1589i | 0.150101 | − | 0.860563i | ||||
\(997\) | −4.87015 | + | 8.43535i | −0.154239 | + | 0.267150i | −0.932782 | − | 0.360442i | \(-0.882626\pi\) |
0.778542 | + | 0.627592i | \(0.215959\pi\) | |||||||
\(998\) | −21.2891 | − | 36.8738i | −0.673894 | − | 1.16722i | ||||
\(999\) | −0.0260361 | − | 4.69495i | −0.000823745 | − | 0.148542i |
(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 | 930.2.o.e.161.9 | ✓ | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.161.18 | yes | 40 | |
31.26 | odd | 6 | inner | 930.2.o.e.491.8 | yes | 40 | |
93.26 | even | 6 | inner | 930.2.o.e.491.19 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.9 | ✓ | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.161.18 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.8 | yes | 40 | 31.26 | odd | 6 | inner | |
930.2.o.e.491.19 | yes | 40 | 93.26 | even | 6 | inner |