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 | 491.8 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.e.161.18 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||
\(3\) | 1.32888 | + | 1.11089i | 0.767231 | + | 0.641370i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | 1.11089 | − | 1.32888i | 0.453517 | − | 0.542514i | ||||
\(7\) | −0.581871 | + | 1.00783i | −0.219927 | + | 0.380924i | −0.954785 | − | 0.297296i | \(-0.903915\pi\) |
0.734859 | + | 0.678220i | \(0.237248\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.531863 | + | 2.95248i | 0.177288 | + | 0.984159i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −0.0889568 | − | 0.154078i | −0.0268215 | − | 0.0464562i | 0.852303 | − | 0.523048i | \(-0.175205\pi\) |
−0.879125 | + | 0.476592i | \(0.841872\pi\) | |||||||
\(12\) | −1.32888 | − | 1.11089i | −0.383616 | − | 0.320685i | ||||
\(13\) | −4.88952 | + | 2.82297i | −1.35611 | + | 0.782950i | −0.989097 | − | 0.147266i | \(-0.952953\pi\) |
−0.367012 | + | 0.930216i | \(0.619619\pi\) | |||||||
\(14\) | 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 | \(-0.677491\pi\) |
0.999422 | + | 0.0340003i | \(0.0108247\pi\) | |||||||
\(18\) | 2.95248 | − | 0.531863i | 0.695906 | − | 0.125361i | ||||
\(19\) | −2.57689 | + | 4.46331i | −0.591179 | + | 1.02395i | 0.402895 | + | 0.915246i | \(0.368004\pi\) |
−0.994074 | + | 0.108706i | \(0.965329\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | −1.89282 | + | 0.692897i | −0.413048 | + | 0.151202i | ||||
\(22\) | −0.154078 | + | 0.0889568i | −0.0328495 | + | 0.0189656i | ||||
\(23\) | −5.70722 | −1.19004 | −0.595019 | − | 0.803712i | \(-0.702855\pi\) | ||||
−0.595019 | + | 0.803712i | \(0.702855\pi\) | |||||||
\(24\) | −1.11089 | + | 1.32888i | −0.226759 | + | 0.271257i | ||||
\(25\) | 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 | \(-0.672865\pi\) | ||||
−0.516767 | + | 0.856126i | \(0.672865\pi\) | |||||||
\(30\) | −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 | ||||||
\(36\) | −0.531863 | − | 2.95248i | −0.0886439 | − | 0.492080i | ||||
\(37\) | 0.782503 | + | 0.451779i | 0.128643 | + | 0.0742719i | 0.562940 | − | 0.826497i | \(-0.309670\pi\) |
−0.434298 | + | 0.900769i | \(0.643003\pi\) | |||||||
\(38\) | 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 | \(-0.738656\pi\) |
0.293072 | + | 0.956091i | \(0.405323\pi\) | |||||||
\(42\) | 0.692897 | + | 1.89282i | 0.106916 | + | 0.292069i | ||||
\(43\) | 0.735867 | + | 0.424853i | 0.112219 | + | 0.0647895i | 0.555059 | − | 0.831811i | \(-0.312696\pi\) |
−0.442840 | + | 0.896601i | \(0.646029\pi\) | |||||||
\(44\) | 0.0889568 | + | 0.154078i | 0.0134107 | + | 0.0232281i | ||||
\(45\) | −1.93685 | − | 2.29099i | −0.288728 | − | 0.341520i | ||||
\(46\) | 5.70722i | 0.841484i | ||||||||
\(47\) | − | 4.11079i | − | 0.599620i | −0.953999 | − | 0.299810i | \(-0.903077\pi\) | ||
0.953999 | − | 0.299810i | \(-0.0969233\pi\) | |||||||
\(48\) | 1.32888 | + | 1.11089i | 0.191808 | + | 0.160343i | ||||
\(49\) | 2.82285 | + | 4.88932i | 0.403265 | + | 0.698475i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 6.30741 | − | 2.30892i | 0.883214 | − | 0.323314i | ||||
\(52\) | 4.88952 | − | 2.82297i | 0.678055 | − | 0.391475i | ||||
\(53\) | 6.25104 | + | 10.8271i | 0.858646 | + | 1.48722i | 0.873221 | + | 0.487325i | \(0.162027\pi\) |
−0.0145750 | + | 0.999894i | \(0.504640\pi\) | |||||||
\(54\) | 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 | ||||
\(57\) | −8.38261 | + | 3.06858i | −1.11030 | + | 0.406443i | ||||
\(58\) | 5.56575i | 0.730819i | ||||||||
\(59\) | 4.27376 | + | 2.46746i | 0.556396 | + | 0.321235i | 0.751698 | − | 0.659508i | \(-0.229235\pi\) |
−0.195302 | + | 0.980743i | \(0.562569\pi\) | |||||||
\(60\) | 1.70629 | + | 0.297614i | 0.220281 | + | 0.0384218i | ||||
\(61\) | 0.00227491i | 0.000291272i | 1.00000 | 0.000145636i | \(4.63574e-5\pi\) | |||||
−1.00000 | 0.000145636i | \(0.999954\pi\) | ||||||||
\(62\) | 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 | 0.601318 | − | 0.799010i | \(-0.294642\pi\) |
−0.992622 | + | 0.121252i | \(0.961309\pi\) | |||||||
\(68\) | −1.93896 | + | 3.35837i | −0.235133 | + | 0.407262i | ||||
\(69\) | −7.58423 | − | 6.34007i | −0.913034 | − | 0.763255i | ||||
\(70\) | −1.16374 | −0.139094 | ||||||||
\(71\) | −10.9712 | + | 6.33424i | −1.30204 | + | 0.751736i | −0.980754 | − | 0.195245i | \(-0.937450\pi\) |
−0.321290 | + | 0.946981i | \(0.604116\pi\) | |||||||
\(72\) | −2.95248 | + | 0.531863i | −0.347953 | + | 0.0626807i | ||||
\(73\) | 9.32062 | − | 5.38127i | 1.09090 | − | 0.629829i | 0.157082 | − | 0.987586i | \(-0.449791\pi\) |
0.933815 | + | 0.357756i | \(0.116458\pi\) | |||||||
\(74\) | 0.451779 | − | 0.782503i | 0.0525182 | − | 0.0909642i | ||||
\(75\) | 1.62650 | − | 0.595404i | 0.187812 | − | 0.0687513i | ||||
\(76\) | 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 | 0.351108 | − | 0.936335i | \(-0.385805\pi\) |
−0.635336 | + | 0.772236i | \(0.719138\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | −8.43424 | + | 3.14063i | −0.937138 | + | 0.348959i | ||||
\(82\) | 1.43582 | + | 2.48692i | 0.158560 | + | 0.274634i | ||||
\(83\) | 7.95846 | + | 13.7845i | 0.873555 | + | 1.51304i | 0.858294 | + | 0.513158i | \(0.171524\pi\) |
0.0152607 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(84\) | 1.89282 | − | 0.692897i | 0.206524 | − | 0.0756012i | ||||
\(85\) | 3.87791i | 0.420618i | ||||||||
\(86\) | 0.424853 | − | 0.735867i | 0.0458131 | − | 0.0793506i | ||||
\(87\) | −7.39624 | − | 6.18292i | −0.792960 | − | 0.662878i | ||||
\(88\) | 0.154078 | − | 0.0889568i | 0.0164247 | − | 0.00948282i | ||||
\(89\) | 5.20790 | 0.552036 | 0.276018 | − | 0.961152i | \(-0.410985\pi\) | ||||
0.276018 | + | 0.961152i | \(0.410985\pi\) | |||||||
\(90\) | −2.29099 | + | 1.93685i | −0.241491 | + | 0.204161i | ||||
\(91\) | − | 6.57041i | − | 0.688766i | ||||||
\(92\) | 5.70722 | 0.595019 | ||||||||
\(93\) | 4.40248 | + | 8.58010i | 0.456516 | + | 0.889715i | ||||
\(94\) | −4.11079 | −0.423995 | ||||||||
\(95\) | − | 5.15378i | − | 0.528767i | ||||||
\(96\) | 1.11089 | − | 1.32888i | 0.113379 | − | 0.135629i | ||||
\(97\) | −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 | ||||
\(99\) | 0.407598 | − | 0.344591i | 0.0409651 | − | 0.0346327i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | − | 2.34879i | − | 0.233713i | −0.993149 | − | 0.116856i | \(-0.962718\pi\) | ||
0.993149 | − | 0.116856i | \(-0.0372817\pi\) | |||||||
\(102\) | −2.30892 | − | 6.30741i | −0.228617 | − | 0.624527i | ||||
\(103\) | −8.49332 | − | 14.7109i | −0.836872 | − | 1.44950i | −0.892497 | − | 0.451053i | \(-0.851048\pi\) |
0.0556251 | − | 0.998452i | \(-0.482285\pi\) | |||||||
\(104\) | −2.82297 | − | 4.88952i | −0.276815 | − | 0.479457i | ||||
\(105\) | 1.29279 | − | 1.54648i | 0.126163 | − | 0.150921i | ||||
\(106\) | 10.8271 | − | 6.25104i | 1.05162 | − | 0.607154i | ||||
\(107\) | 4.00394 | + | 2.31167i | 0.387075 | + | 0.223478i | 0.680892 | − | 0.732384i | \(-0.261592\pi\) |
−0.293817 | + | 0.955862i | \(0.594926\pi\) | |||||||
\(108\) | 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 | ||||
\(111\) | 0.537981 | + | 1.46963i | 0.0510629 | + | 0.139491i | ||||
\(112\) | −0.581871 | + | 1.00783i | −0.0549817 | + | 0.0952310i | ||||
\(113\) | −0.376805 | + | 0.217548i | −0.0354468 | + | 0.0204652i | −0.517619 | − | 0.855611i | \(-0.673181\pi\) |
0.482172 | + | 0.876077i | \(0.339848\pi\) | |||||||
\(114\) | 3.06858 | + | 8.38261i | 0.287399 | + | 0.785104i | ||||
\(115\) | 4.94260 | − | 2.85361i | 0.460900 | − | 0.266101i | ||||
\(116\) | 5.56575 | 0.516767 | ||||||||
\(117\) | −10.9353 | − | 12.9348i | −1.01097 | − | 1.19582i | ||||
\(118\) | 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 | 0.898745 | − | 0.438473i | \(-0.144480\pi\) |
0.0696438 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0.505918 | + | 1.38204i | 0.0445436 | + | 0.121682i | ||||
\(130\) | −4.88952 | − | 2.82297i | −0.428839 | − | 0.247591i | ||||
\(131\) | 18.3335 | + | 10.5849i | 1.60181 | + | 0.924803i | 0.991126 | + | 0.132925i | \(0.0424369\pi\) |
0.610679 | + | 0.791878i | \(0.290896\pi\) | |||||||
\(132\) | −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 | ||||
\(135\) | −0.0288151 | − | 5.19607i | −0.00248001 | − | 0.447207i | ||||
\(136\) | 3.35837 | + | 1.93896i | 0.287978 | + | 0.166264i | ||||
\(137\) | −6.42120 | − | 11.1218i | −0.548600 | − | 0.950203i | −0.998371 | − | 0.0570592i | \(-0.981828\pi\) |
0.449771 | − | 0.893144i | \(-0.351506\pi\) | |||||||
\(138\) | −6.34007 | + | 7.58423i | −0.539703 | + | 0.645613i | ||||
\(139\) | − | 0.913499i | − | 0.0774820i | −0.999249 | − | 0.0387410i | \(-0.987665\pi\) | ||
0.999249 | − | 0.0387410i | \(-0.0123347\pi\) | |||||||
\(140\) | 1.16374i | 0.0983542i | ||||||||
\(141\) | 4.56662 | − | 5.46276i | 0.384579 | − | 0.460047i | ||||
\(142\) | 6.33424 | + | 10.9712i | 0.531557 | + | 0.920685i | ||||
\(143\) | 0.869912 | + | 0.502244i | 0.0727457 | + | 0.0419998i | ||||
\(144\) | 0.531863 | + | 2.95248i | 0.0443220 | + | 0.246040i | ||||
\(145\) | 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 | \(-0.393477\pi\) |
−0.653762 | + | 0.756700i | \(0.726810\pi\) | |||||||
\(150\) | −0.595404 | − | 1.62650i | −0.0486145 | − | 0.132803i | ||||
\(151\) | 18.0258i | 1.46692i | 0.679734 | + | 0.733458i | \(0.262095\pi\) | ||||
−0.679734 | + | 0.733458i | \(0.737905\pi\) | |||||||
\(152\) | −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 | ||||
\(162\) | 3.14063 | + | 8.43424i | 0.246751 | + | 0.662657i | ||||
\(163\) | 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 | ||||
\(165\) | 0.105930 | + | 0.289376i | 0.00824667 | + | 0.0225279i | ||||
\(166\) | 13.7845 | − | 7.95846i | 1.06988 | − | 0.617697i | ||||
\(167\) | 4.44098 | − | 7.69200i | 0.343653 | − | 0.595225i | −0.641455 | − | 0.767161i | \(-0.721669\pi\) |
0.985108 | + | 0.171936i | \(0.0550021\pi\) | |||||||
\(168\) | −0.692897 | − | 1.89282i | −0.0534581 | − | 0.146035i | ||||
\(169\) | 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 | \(-0.636132\pi\) |
0.580650 | + | 0.814153i | \(0.302798\pi\) | |||||||
\(174\) | −6.18292 | + | 7.39624i | −0.468726 | + | 0.560707i | ||||
\(175\) | 0.581871 | + | 1.00783i | 0.0439853 | + | 0.0761848i | ||||
\(176\) | −0.0889568 | − | 0.154078i | −0.00670537 | − | 0.0116140i | ||||
\(177\) | 2.93827 | + | 8.02662i | 0.220854 | + | 0.603318i | ||||
\(178\) | − | 5.20790i | − | 0.390348i | ||||||
\(179\) | −7.26572 | + | 12.5846i | −0.543065 | + | 0.940616i | 0.455661 | + | 0.890153i | \(0.349403\pi\) |
−0.998726 | + | 0.0504628i | \(0.983930\pi\) | |||||||
\(180\) | 1.93685 | + | 2.29099i | 0.144364 | + | 0.170760i | ||||
\(181\) | −3.27223 | + | 1.88922i | −0.243223 | + | 0.140425i | −0.616657 | − | 0.787232i | \(-0.711513\pi\) |
0.373434 | + | 0.927657i | \(0.378180\pi\) | |||||||
\(182\) | −6.57041 | −0.487031 | ||||||||
\(183\) | −0.00252716 | + | 0.00302309i | −0.000186813 | + | 0.000223473i | ||||
\(184\) | − | 5.70722i | − | 0.420742i | ||||||
\(185\) | −0.903557 | −0.0664308 | ||||||||
\(186\) | 8.58010 | − | 4.40248i | 0.629124 | − | 0.322806i | ||||
\(187\) | −0.689933 | −0.0504529 | ||||||||
\(188\) | 4.11079i | 0.299810i | ||||||||
\(189\) | −3.05249 | − | 5.21999i | −0.222036 | − | 0.379699i | ||||
\(190\) | −5.15378 | −0.373895 | ||||||||
\(191\) | −5.58732 | + | 3.22584i | −0.404284 | + | 0.233414i | −0.688331 | − | 0.725397i | \(-0.741656\pi\) |
0.284047 | + | 0.958810i | \(0.408323\pi\) | |||||||
\(192\) | −1.32888 | − | 1.11089i | −0.0959039 | − | 0.0801713i | ||||
\(193\) | −1.05136 | + | 1.82101i | −0.0756786 | + | 0.131079i | −0.901381 | − | 0.433027i | \(-0.857446\pi\) |
0.825703 | + | 0.564106i | \(0.190779\pi\) | |||||||
\(194\) | 13.7078i | 0.984161i | ||||||||
\(195\) | 9.18310 | − | 3.36161i | 0.657615 | − | 0.240730i | ||||
\(196\) | −2.82285 | − | 4.88932i | −0.201632 | − | 0.349237i | ||||
\(197\) | −9.43359 | − | 16.3395i | −0.672115 | − | 1.16414i | −0.977303 | − | 0.211846i | \(-0.932053\pi\) |
0.305188 | − | 0.952292i | \(-0.401281\pi\) | |||||||
\(198\) | −0.344591 | − | 0.407598i | −0.0244890 | − | 0.0289667i | ||||
\(199\) | 16.6694 | − | 9.62408i | 1.18166 | − | 0.682233i | 0.225263 | − | 0.974298i | \(-0.427676\pi\) |
0.956398 | + | 0.292065i | \(0.0943425\pi\) | |||||||
\(200\) | 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 | ||||
\(204\) | −6.30741 | + | 2.30892i | −0.441607 | + | 0.161657i | ||||
\(205\) | 1.43582 | − | 2.48692i | 0.100282 | − | 0.173694i | ||||
\(206\) | −14.7109 | + | 8.49332i | −1.02495 | + | 0.591758i | ||||
\(207\) | −3.03546 | − | 16.8504i | −0.210979 | − | 1.17119i | ||||
\(208\) | −4.88952 | + | 2.82297i | −0.339027 | + | 0.195738i | ||||
\(209\) | 0.916927 | 0.0634252 | ||||||||
\(210\) | −1.54648 | − | 1.29279i | −0.106717 | − | 0.0892107i | ||||
\(211\) | 5.53532 | − | 9.58746i | 0.381067 | − | 0.660028i | −0.610148 | − | 0.792288i | \(-0.708890\pi\) |
0.991215 | + | 0.132260i | \(0.0422233\pi\) | |||||||
\(212\) | −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 | ||||||||
\(222\) | 1.46963 | − | 0.537981i | 0.0986353 | − | 0.0361069i | ||||
\(223\) | −3.79542 | − | 2.19128i | −0.254160 | − | 0.146739i | 0.367508 | − | 0.930020i | \(-0.380211\pi\) |
−0.621668 | + | 0.783281i | \(0.713545\pi\) | |||||||
\(224\) | 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 | \(-0.483031\pi\) |
0.891438 | + | 0.453143i | \(0.149697\pi\) | |||||||
\(228\) | 8.38261 | − | 3.06858i | 0.555152 | − | 0.203222i | ||||
\(229\) | 0.621599 | + | 0.358880i | 0.0410764 | + | 0.0237155i | 0.520398 | − | 0.853924i | \(-0.325784\pi\) |
−0.479321 | + | 0.877640i | \(0.659117\pi\) | |||||||
\(230\) | −2.85361 | − | 4.94260i | −0.188162 | − | 0.325905i | ||||
\(231\) | 0.275139 | + | 0.230004i | 0.0181028 | + | 0.0151332i | ||||
\(232\) | − | 5.56575i | − | 0.365410i | ||||||
\(233\) | − | 15.7057i | − | 1.02891i | −0.857517 | − | 0.514456i | \(-0.827994\pi\) | ||
0.857517 | − | 0.514456i | \(-0.172006\pi\) | |||||||
\(234\) | −12.9348 | + | 10.9353i | −0.845572 | + | 0.714863i | ||||
\(235\) | 2.05539 | + | 3.56005i | 0.134079 | + | 0.232232i | ||||
\(236\) | −4.27376 | − | 2.46746i | −0.278198 | − | 0.160618i | ||||
\(237\) | −1.73685 | − | 4.74464i | −0.112820 | − | 0.308197i | ||||
\(238\) | 3.90828 | − | 2.25644i | 0.253336 | − | 0.146264i | ||||
\(239\) | 2.90971 | + | 5.03976i | 0.188213 | + | 0.325995i | 0.944655 | − | 0.328067i | \(-0.106397\pi\) |
−0.756441 | + | 0.654062i | \(0.773064\pi\) | |||||||
\(240\) | −1.70629 | − | 0.297614i | −0.110141 | − | 0.0192109i | ||||
\(241\) | 5.77410 | + | 3.33368i | 0.371942 | + | 0.214741i | 0.674307 | − | 0.738451i | \(-0.264443\pi\) |
−0.302364 | + | 0.953192i | \(0.597776\pi\) | |||||||
\(242\) | −9.49887 | − | 5.48417i | −0.610610 | − | 0.352536i | ||||
\(243\) | −14.6970 | − | 5.19595i | −0.942814 | − | 0.333321i | ||||
\(244\) | − | 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 | \(-0.917711\pi\) |
0.704784 | + | 0.709422i | \(0.251044\pi\) | |||||||
\(252\) | 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 | ||||
\(255\) | −4.30792 | + | 5.15329i | −0.269772 | + | 0.322712i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.8110 | + | 12.0152i | −1.29815 | + | 0.749490i | −0.980085 | − | 0.198577i | \(-0.936368\pi\) |
−0.318070 | + | 0.948067i | \(0.603035\pi\) | |||||||
\(258\) | 1.38204 | − | 0.505918i | 0.0860423 | − | 0.0314971i | ||||
\(259\) | −0.910632 | + | 0.525754i | −0.0565839 | + | 0.0326688i | ||||
\(260\) | −2.82297 | + | 4.88952i | −0.175073 | + | 0.303235i | ||||
\(261\) | −2.96022 | − | 16.4328i | −0.183233 | − | 1.01716i | ||||
\(262\) | 10.5849 | − | 18.3335i | 0.653934 | − | 1.13265i | ||||
\(263\) | −13.3178 | −0.821209 | −0.410605 | − | 0.911813i | \(-0.634682\pi\) | ||||
−0.410605 | + | 0.911813i | \(0.634682\pi\) | |||||||
\(264\) | 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 | ||||
\(267\) | 6.92069 | + | 5.78538i | 0.423539 | + | 0.354060i | ||||
\(268\) | 3.20296 | + | 5.54769i | 0.195652 | + | 0.338879i | ||||
\(269\) | −0.769900 | − | 1.33351i | −0.0469416 | − | 0.0813052i | 0.841600 | − | 0.540101i | \(-0.181614\pi\) |
−0.888542 | + | 0.458796i | \(0.848281\pi\) | |||||||
\(270\) | −5.19607 | + | 0.0288151i | −0.316223 | + | 0.00175363i | ||||
\(271\) | 8.84626i | 0.537372i | 0.963228 | + | 0.268686i | \(0.0865894\pi\) | ||||
−0.963228 | + | 0.268686i | \(0.913411\pi\) | |||||||
\(272\) | 1.93896 | − | 3.35837i | 0.117566 | − | 0.203631i | ||||
\(273\) | 7.29898 | − | 8.73131i | 0.441754 | − | 0.528443i | ||||
\(274\) | −11.1218 | + | 6.42120i | −0.671895 | + | 0.387919i | ||||
\(275\) | −0.177914 | −0.0107286 | ||||||||
\(276\) | 7.58423 | + | 6.34007i | 0.456517 | + | 0.381628i | ||||
\(277\) | 14.9715i | 0.899552i | 0.893141 | + | 0.449776i | \(0.148496\pi\) | ||||
−0.893141 | + | 0.449776i | \(0.851504\pi\) | |||||||
\(278\) | −0.913499 | −0.0547880 | ||||||||
\(279\) | −3.68113 | + | 16.2926i | −0.220383 | + | 0.975413i | ||||
\(280\) | 1.16374 | 0.0695469 | ||||||||
\(281\) | 7.32299i | 0.436853i | 0.975853 | + | 0.218426i | \(0.0700924\pi\) | ||||
−0.975853 | + | 0.218426i | \(0.929908\pi\) | |||||||
\(282\) | −5.46276 | − | 4.56662i | −0.325303 | − | 0.271938i | ||||
\(283\) | −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 | ||||
\(285\) | 5.72526 | − | 6.84878i | 0.339135 | − | 0.405686i | ||||
\(286\) | 0.502244 | − | 0.869912i | 0.0296983 | − | 0.0514390i | ||||
\(287\) | − | 3.34186i | − | 0.197263i | ||||||
\(288\) | 2.95248 | − | 0.531863i | 0.173976 | − | 0.0313404i | ||||
\(289\) | 0.980903 | + | 1.69897i | 0.0577002 | + | 0.0999397i | ||||
\(290\) | −2.78288 | − | 4.82008i | −0.163416 | − | 0.283045i | ||||
\(291\) | −18.2160 | − | 15.2278i | −1.06784 | − | 0.892668i | ||||
\(292\) | −9.32062 | + | 5.38127i | −0.545448 | + | 0.314915i | ||||
\(293\) | −29.5457 | − | 17.0582i | −1.72608 | − | 0.996551i | −0.904531 | − | 0.426408i | \(-0.859779\pi\) |
−0.821545 | − | 0.570143i | \(-0.806888\pi\) | |||||||
\(294\) | 9.63321 | + | 1.68024i | 0.561820 | + | 0.0979936i | ||||
\(295\) | −4.93491 | −0.287322 | ||||||||
\(296\) | −0.451779 | + | 0.782503i | −0.0262591 | + | 0.0454821i | ||||
\(297\) | 0.924452 | − | 0.00512660i | 0.0536421 | − | 0.000297475i | ||||
\(298\) | −2.29269 | + | 3.97105i | −0.132812 | + | 0.230037i | ||||
\(299\) | 27.9056 | − | 16.1113i | 1.61382 | − | 0.931740i | ||||
\(300\) | −1.62650 | + | 0.595404i | −0.0939059 | + | 0.0343757i | ||||
\(301\) | −0.856359 | + | 0.494419i | −0.0493597 | + | 0.0284979i | ||||
\(302\) | 18.0258 | 1.03727 | ||||||||
\(303\) | 2.60923 | − | 3.12126i | 0.149897 | − | 0.179312i | ||||
\(304\) | −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 | −0.489360 | − | 0.872082i | \(-0.662770\pi\) |
0.999925 | − | 0.0122426i | \(-0.00389705\pi\) | |||||||
\(308\) | −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 | 0.299911 | − | 0.953967i | \(-0.403043\pi\) |
−0.676204 | + | 0.736714i | \(0.736376\pi\) | |||||||
\(314\) | 9.03549i | 0.509902i | ||||||||
\(315\) | 3.43592 | − | 0.618952i | 0.193592 | − | 0.0348740i | ||||
\(316\) | 2.52627 | + | 1.45854i | 0.142114 | + | 0.0820495i | ||||
\(317\) | −4.78141 | − | 2.76055i | −0.268551 | − | 0.155048i | 0.359678 | − | 0.933076i | \(-0.382886\pi\) |
−0.628229 | + | 0.778029i | \(0.716220\pi\) | |||||||
\(318\) | 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 | ||||
\(321\) | 2.75276 | + | 7.51986i | 0.153644 | + | 0.419718i | ||||
\(322\) | −5.75191 | − | 3.32087i | −0.320542 | − | 0.185065i | ||||
\(323\) | 9.99295 | + | 17.3083i | 0.556023 | + | 0.963060i | ||||
\(324\) | 8.43424 | − | 3.14063i | 0.468569 | − | 0.174479i | ||||
\(325\) | 5.64593i | 0.313180i | ||||||||
\(326\) | − | 17.0876i | − | 0.946392i | ||||||
\(327\) | 24.3587 | + | 20.3627i | 1.34704 | + | 1.12606i | ||||
\(328\) | −1.43582 | − | 2.48692i | −0.0792800 | − | 0.137317i | ||||
\(329\) | 4.14298 | + | 2.39195i | 0.228410 | + | 0.131872i | ||||
\(330\) | 0.289376 | − | 0.105930i | 0.0159296 | − | 0.00583128i | ||||
\(331\) | −7.77002 | + | 4.48602i | −0.427079 | + | 0.246574i | −0.698101 | − | 0.715999i | \(-0.745972\pi\) |
0.271022 | + | 0.962573i | \(0.412638\pi\) | |||||||
\(332\) | −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 | ||||
\(336\) | −1.89282 | + | 0.692897i | −0.103262 | + | 0.0378006i | ||||
\(337\) | 2.44574i | 0.133228i | 0.997779 | + | 0.0666141i | \(0.0212196\pi\) | ||||
−0.997779 | + | 0.0666141i | \(0.978780\pi\) | |||||||
\(338\) | −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 | \(-0.683662\pi\) |
0.998575 | + | 0.0533666i | \(0.0169952\pi\) | |||||||
\(348\) | 7.39624 | + | 6.18292i | 0.396480 | + | 0.331439i | ||||
\(349\) | 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 | ||||
\(351\) | −0.162688 | − | 29.3367i | −0.00868365 | − | 1.56588i | ||||
\(352\) | −0.154078 | + | 0.0889568i | −0.00821237 | + | 0.00474141i | ||||
\(353\) | −5.87229 | + | 10.1711i | −0.312551 | + | 0.541353i | −0.978914 | − | 0.204274i | \(-0.934517\pi\) |
0.666363 | + | 0.745627i | \(0.267850\pi\) | |||||||
\(354\) | 8.02662 | − | 2.93827i | 0.426610 | − | 0.156167i | ||||
\(355\) | 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 | \(-0.575986\pi\) |
0.723238 | + | 0.690598i | \(0.242653\pi\) | |||||||
\(360\) | 2.29099 | − | 1.93685i | 0.120746 | − | 0.102081i | ||||
\(361\) | −3.78073 | − | 6.54841i | −0.198986 | − | 0.344653i | ||||
\(362\) | 1.88922 | + | 3.27223i | 0.0992953 | + | 0.171984i | ||||
\(363\) | 17.8400 | − | 6.53060i | 0.936357 | − | 0.342767i | ||||
\(364\) | 6.57041i | 0.344383i | ||||||||
\(365\) | −5.38127 | + | 9.32062i | −0.281668 | + | 0.487864i | ||||
\(366\) | 0.00302309 | + | 0.00252716i | 0.000158019 | + | 0.000132097i | ||||
\(367\) | 25.0136 | − | 14.4416i | 1.30570 | − | 0.753847i | 0.324326 | − | 0.945946i | \(-0.394863\pi\) |
0.981376 | + | 0.192099i | \(0.0615294\pi\) | |||||||
\(368\) | −5.70722 | −0.297510 | ||||||||
\(369\) | −5.56193 | − | 6.57891i | −0.289543 | − | 0.342484i | ||||
\(370\) | 0.903557i | 0.0469737i | ||||||||
\(371\) | −14.5492 | −0.755356 | ||||||||
\(372\) | −4.40248 | − | 8.58010i | −0.228258 | − | 0.444858i | ||||
\(373\) | −15.4070 | −0.797744 | −0.398872 | − | 0.917007i | \(-0.630598\pi\) | ||||
−0.398872 | + | 0.917007i | \(0.630598\pi\) | |||||||
\(374\) | 0.689933i | 0.0356756i | ||||||||
\(375\) | −1.11089 | + | 1.32888i | −0.0573659 | + | 0.0686233i | ||||
\(376\) | 4.11079 | 0.211998 | ||||||||
\(377\) | 27.2139 | − | 15.7119i | 1.40159 | − | 0.809206i | ||||
\(378\) | −5.21999 | + | 3.05249i | −0.268487 | + | 0.157003i | ||||
\(379\) | −4.66494 | + | 8.07991i | −0.239622 | + | 0.415037i | −0.960606 | − | 0.277915i | \(-0.910357\pi\) |
0.720984 | + | 0.692952i | \(0.243690\pi\) | |||||||
\(380\) | 5.15378i | 0.264383i | ||||||||
\(381\) | 7.50296 | + | 20.4962i | 0.384388 | + | 1.05005i | ||||
\(382\) | 3.22584 | + | 5.58732i | 0.165048 | + | 0.285872i | ||||
\(383\) | 11.7909 | + | 20.4225i | 0.602488 | + | 1.04354i | 0.992443 | + | 0.122706i | \(0.0391574\pi\) |
−0.389955 | + | 0.920834i | \(0.627509\pi\) | |||||||
\(384\) | −1.11089 | + | 1.32888i | −0.0566897 | + | 0.0678143i | ||||
\(385\) | −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 | −0.00770372 | + | 0.999970i | \(0.502452\pi\) |
−0.862148 | + | 0.506657i | \(0.830881\pi\) | |||||||
\(390\) | −3.36161 | − | 9.18310i | −0.170222 | − | 0.465004i | ||||
\(391\) | −11.0660 | + | 19.1670i | −0.559634 | + | 0.969315i | ||||
\(392\) | −4.88932 | + | 2.82285i | −0.246948 | + | 0.142576i | ||||
\(393\) | 12.6045 | + | 34.4325i | 0.635814 | + | 1.73689i | ||||
\(394\) | −16.3395 | + | 9.43359i | −0.823170 | + | 0.475257i | ||||
\(395\) | 2.91709 | 0.146775 | ||||||||
\(396\) | −0.407598 | + | 0.344591i | −0.0204826 | + | 0.0173164i | ||||
\(397\) | −13.0551 | + | 22.6122i | −0.655218 | + | 1.13487i | 0.326621 | + | 0.945155i | \(0.394090\pi\) |
−0.981839 | + | 0.189716i | \(0.939243\pi\) | |||||||
\(398\) | −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 | \(-0.514406\pi\) | ||||
−0.0452436 | + | 0.998976i | \(0.514406\pi\) | |||||||
\(402\) | −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 | ||||||
\(408\) | 2.30892 | + | 6.30741i | 0.114309 | + | 0.312263i | ||||
\(409\) | −21.5022 | − | 12.4143i | −1.06322 | − | 0.613849i | −0.136897 | − | 0.990585i | \(-0.543713\pi\) |
−0.926320 | + | 0.376737i | \(0.877046\pi\) | |||||||
\(410\) | −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 | ||||
\(414\) | −16.8504 | + | 3.03546i | −0.828154 | + | 0.149185i | ||||
\(415\) | −13.7845 | − | 7.95846i | −0.676653 | − | 0.390666i | ||||
\(416\) | 2.82297 | + | 4.88952i | 0.138407 | + | 0.239729i | ||||
\(417\) | 1.01479 | − | 1.21393i | 0.0496946 | − | 0.0594466i | ||||
\(418\) | − | 0.916927i | − | 0.0448484i | ||||||
\(419\) | 16.9548i | 0.828295i | 0.910210 | + | 0.414148i | \(0.135920\pi\) | ||||
−0.910210 | + | 0.414148i | \(0.864080\pi\) | |||||||
\(420\) | −1.29279 | + | 1.54648i | −0.0630815 | + | 0.0754604i | ||||
\(421\) | 14.5265 | + | 25.1607i | 0.707980 | + | 1.22626i | 0.965605 | + | 0.260013i | \(0.0837267\pi\) |
−0.257625 | + | 0.966245i | \(0.582940\pi\) | |||||||
\(422\) | −9.58746 | − | 5.53532i | −0.466710 | − | 0.269455i | ||||
\(423\) | 12.1370 | − | 2.18638i | 0.590121 | − | 0.106305i | ||||
\(424\) | −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 | ||||
\(429\) | 0.598076 | + | 1.63380i | 0.0288754 | + | 0.0788805i | ||||
\(430\) | 0.849706i | 0.0409765i | ||||||||
\(431\) | 18.8864 | + | 10.9041i | 0.909726 | + | 0.525231i | 0.880343 | − | 0.474337i | \(-0.157312\pi\) |
0.0293833 | + | 0.999568i | \(0.490646\pi\) | |||||||
\(432\) | −2.57308 | + | 4.51434i | −0.123797 | + | 0.217196i | ||||
\(433\) | 22.8178i | 1.09655i | 0.836297 | + | 0.548277i | \(0.184716\pi\) | ||||
−0.836297 | + | 0.548277i | \(0.815284\pi\) | |||||||
\(434\) | 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 | 0.996656 | + | 0.0817131i | \(0.0260391\pi\) |
−0.427562 | + | 0.903986i | \(0.640628\pi\) | |||||||
\(440\) | −0.0889568 | + | 0.154078i | −0.00424085 | + | 0.00734536i | ||||
\(441\) | −12.9342 | + | 10.9349i | −0.615916 | + | 0.520708i | ||||
\(442\) | 21.8944 | 1.04141 | ||||||||
\(443\) | 18.1698 | − | 10.4904i | 0.863275 | − | 0.498412i | −0.00183237 | − | 0.999998i | \(-0.500583\pi\) |
0.865108 | + | 0.501586i | \(0.167250\pi\) | |||||||
\(444\) | −0.537981 | − | 1.46963i | −0.0255315 | − | 0.0697457i | ||||
\(445\) | −4.51017 | + | 2.60395i | −0.213803 | + | 0.123439i | ||||
\(446\) | −2.19128 | + | 3.79542i | −0.103760 | + | 0.179718i | ||||
\(447\) | −2.73015 | − | 7.45810i | −0.129132 | − | 0.352756i | ||||
\(448\) | 0.581871 | − | 1.00783i | 0.0274908 | − | 0.0476155i | ||||
\(449\) | 30.8958 | 1.45806 | 0.729032 | − | 0.684479i | \(-0.239970\pi\) | ||||
0.729032 | + | 0.684479i | \(0.239970\pi\) | |||||||
\(450\) | 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 | ||||
\(453\) | −20.0246 | + | 23.9542i | −0.940837 | + | 1.12546i | ||||
\(454\) | −8.21783 | − | 14.2337i | −0.385682 | − | 0.668020i | ||||
\(455\) | 3.28521 | + | 5.69014i | 0.154013 | + | 0.266758i | ||||
\(456\) | −3.06858 | − | 8.38261i | −0.143699 | − | 0.392552i | ||||
\(457\) | 10.1581i | 0.475177i | 0.971366 | + | 0.237589i | \(0.0763570\pi\) | ||||
−0.971366 | + | 0.237589i | \(0.923643\pi\) | |||||||
\(458\) | 0.358880 | − | 0.621599i | 0.0167694 | − | 0.0290454i | ||||
\(459\) | 10.1717 | + | 17.3945i | 0.474775 | + | 0.811904i | ||||
\(460\) | −4.94260 | + | 2.85361i | −0.230450 | + | 0.133050i | ||||
\(461\) | −19.8197 | −0.923095 | −0.461547 | − | 0.887116i | \(-0.652706\pi\) | ||||
−0.461547 | + | 0.887116i | \(0.652706\pi\) | |||||||
\(462\) | 0.230004 | − | 0.275139i | 0.0107008 | − | 0.0128006i | ||||
\(463\) | 10.9325i | 0.508074i | 0.967194 | + | 0.254037i | \(0.0817586\pi\) | ||||
−0.967194 | + | 0.254037i | \(0.918241\pi\) | |||||||
\(464\) | −5.56575 | −0.258384 | ||||||||
\(465\) | −8.10271 | − | 5.22934i | −0.375754 | − | 0.242505i | ||||
\(466\) | −15.7057 | −0.727551 | ||||||||
\(467\) | 11.3377i | 0.524644i | 0.964980 | + | 0.262322i | \(0.0844883\pi\) | ||||
−0.964980 | + | 0.262322i | \(0.915512\pi\) | |||||||
\(468\) | 10.9353 | + | 12.9348i | 0.505485 | + | 0.597910i | ||||
\(469\) | 7.45483 | 0.344232 | ||||||||
\(470\) | 3.56005 | − | 2.05539i | 0.164213 | − | 0.0948083i | ||||
\(471\) | −12.0071 | − | 10.0374i | −0.553259 | − | 0.462499i | ||||
\(472\) | −2.46746 | + | 4.27376i | −0.113574 | + | 0.196716i | ||||
\(473\) | − | 0.151174i | − | 0.00695100i | ||||||
\(474\) | −4.74464 | + | 1.73685i | −0.217928 | + | 0.0797760i | ||||
\(475\) | 2.57689 | + | 4.46331i | 0.118236 | + | 0.204790i | ||||
\(476\) | −2.25644 | − | 3.90828i | −0.103424 | − | 0.179136i | ||||
\(477\) | −28.6421 | + | 24.2146i | −1.31143 | + | 1.10871i | ||||
\(478\) | 5.03976 | − | 2.90971i | 0.230513 | − | 0.133087i | ||||
\(479\) | 35.3823 | + | 20.4280i | 1.61666 | + | 0.933377i | 0.987777 | + | 0.155875i | \(0.0498198\pi\) |
0.628880 | + | 0.777502i | \(0.283514\pi\) | |||||||
\(480\) | −0.297614 | + | 1.70629i | −0.0135842 | + | 0.0778811i | ||||
\(481\) | −5.10142 | −0.232605 | ||||||||
\(482\) | 3.33368 | − | 5.77410i | 0.151845 | − | 0.263003i | ||||
\(483\) | 10.8028 | − | 3.95452i | 0.491543 | − | 0.179937i | ||||
\(484\) | −5.48417 | + | 9.49887i | −0.249281 | + | 0.431767i | ||||
\(485\) | 11.8713 | − | 6.85389i | 0.539047 | − | 0.311219i | ||||
\(486\) | −5.19595 | + | 14.6970i | −0.235693 | + | 0.666670i | ||||
\(487\) | −31.5249 | + | 18.2009i | −1.42853 | + | 0.824761i | −0.997005 | − | 0.0773402i | \(-0.975357\pi\) |
−0.431524 | + | 0.902102i | \(0.642024\pi\) | |||||||
\(488\) | −0.00227491 | −0.000102980 | ||||||||
\(489\) | 22.7074 | + | 18.9823i | 1.02686 | + | 0.858411i | ||||
\(490\) | −2.82285 | + | 4.88932i | −0.127523 | + | 0.220877i | ||||
\(491\) | 16.2180 | + | 28.0904i | 0.731908 | + | 1.26770i | 0.956067 | + | 0.293149i | \(0.0947032\pi\) |
−0.224159 | + | 0.974553i | \(0.571963\pi\) | |||||||
\(492\) | 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 | 0.976786 | + | 0.214218i | \(0.0687203\pi\) |
0.673911 | + | 0.738812i | \(0.264613\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 14.4465 | − | 5.28835i | 0.645421 | − | 0.236266i | ||||
\(502\) | 7.18911 | + | 4.15063i | 0.320866 | + | 0.185252i | ||||
\(503\) | 32.1602 | + | 18.5677i | 1.43395 | + | 0.827893i | 0.997419 | − | 0.0717951i | \(-0.0228728\pi\) |
0.436533 | + | 0.899688i | \(0.356206\pi\) | |||||||
\(504\) | 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 | ||||
\(507\) | 30.7027 | − | 11.2392i | 1.36355 | − | 0.499150i | ||||
\(508\) | −10.9132 | − | 6.30073i | −0.484194 | − | 0.279550i | ||||
\(509\) | −7.91070 | − | 13.7017i | −0.350636 | − | 0.607319i | 0.635725 | − | 0.771915i | \(-0.280701\pi\) |
−0.986361 | + | 0.164597i | \(0.947368\pi\) | |||||||
\(510\) | 5.15329 | + | 4.30792i | 0.228192 | + | 0.190758i | ||||
\(511\) | 12.5248i | 0.554065i | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −13.5183 | − | 23.1174i | −0.596848 | − | 1.02066i | ||||
\(514\) | 12.0152 | + | 20.8110i | 0.529970 | + | 0.917934i | ||||
\(515\) | 14.7109 | + | 8.49332i | 0.648238 | + | 0.374261i | ||||
\(516\) | −0.505918 | − | 1.38204i | −0.0222718 | − | 0.0608411i | ||||
\(517\) | −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 | \(-0.537179\pi\) |
−0.918392 | + | 0.395671i | \(0.870512\pi\) | |||||||
\(522\) | −16.4328 | + | 2.96022i | −0.719242 | + | 0.129565i | ||||
\(523\) | − | 18.7630i | − | 0.820447i | −0.911985 | − | 0.410224i | \(-0.865451\pi\) | ||
0.911985 | − | 0.410224i | \(-0.134549\pi\) | |||||||
\(524\) | −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 | ||||
\(534\) | 5.78538 | − | 6.92069i | 0.250358 | − | 0.299488i | ||||
\(535\) | −4.62335 | −0.199885 | ||||||||
\(536\) | 5.54769 | − | 3.20296i | 0.239624 | − | 0.138347i | ||||
\(537\) | −23.6353 | + | 8.65207i | −1.01994 | + | 0.373364i | ||||
\(538\) | −1.33351 | + | 0.769900i | −0.0574915 | + | 0.0331927i | ||||
\(539\) | 0.502224 | − | 0.869877i | 0.0216323 | − | 0.0374682i | ||||
\(540\) | 0.0288151 | + | 5.19607i | 0.00124000 | + | 0.223603i | ||||
\(541\) | 9.14009 | − | 15.8311i | 0.392963 | − | 0.680632i | −0.599876 | − | 0.800093i | \(-0.704783\pi\) |
0.992839 | + | 0.119461i | \(0.0381167\pi\) | |||||||
\(542\) | 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 | ||||
\(546\) | −8.73131 | − | 7.29898i | −0.373666 | − | 0.312368i | ||||
\(547\) | 4.88556 | + | 8.46204i | 0.208891 | + | 0.361811i | 0.951366 | − | 0.308064i | \(-0.0996811\pi\) |
−0.742474 | + | 0.669875i | \(0.766348\pi\) | |||||||
\(548\) | 6.42120 | + | 11.1218i | 0.274300 | + | 0.475102i | ||||
\(549\) | −0.00671661 | + | 0.00120994i | −0.000286658 | + | 5.16390e-5i | ||||
\(550\) | 0.177914i | 0.00758626i | ||||||||
\(551\) | 14.3423 | − | 24.8417i | 0.611004 | − | 1.05829i | ||||
\(552\) | 6.34007 | − | 7.58423i | 0.269851 | − | 0.322806i | ||||
\(553\) | 2.93993 | − | 1.69737i | 0.125019 | − | 0.0721795i | ||||
\(554\) | 14.9715 | 0.636080 | ||||||||
\(555\) | −1.20072 | − | 1.00375i | −0.0509678 | − | 0.0426068i | ||||
\(556\) | 0.913499i | 0.0387410i | ||||||||
\(557\) | −23.4375 | −0.993081 | −0.496540 | − | 0.868014i | \(-0.665397\pi\) | ||||
−0.496540 | + | 0.868014i | \(0.665397\pi\) | |||||||
\(558\) | 16.2926 | + | 3.68113i | 0.689721 | + | 0.155835i | ||||
\(559\) | −4.79738 | −0.202908 | ||||||||
\(560\) | − | 1.16374i | − | 0.0491771i | ||||||
\(561\) | −0.916841 | − | 0.766437i | −0.0387090 | − | 0.0323590i | ||||
\(562\) | 7.32299 | 0.308902 | ||||||||
\(563\) | 3.55872 | − | 2.05463i | 0.149982 | − | 0.0865923i | −0.423131 | − | 0.906069i | \(-0.639069\pi\) |
0.573113 | + | 0.819476i | \(0.305736\pi\) | |||||||
\(564\) | −4.56662 | + | 5.46276i | −0.192289 | + | 0.230024i | ||||
\(565\) | 0.217548 | − | 0.376805i | 0.00915232 | − | 0.0158523i | ||||
\(566\) | 14.6211i | 0.614570i | ||||||||
\(567\) | 1.74242 | − | 10.3277i | 0.0731748 | − | 0.433724i | ||||
\(568\) | −6.33424 | − | 10.9712i | −0.265779 | − | 0.460342i | ||||
\(569\) | −20.3967 | − | 35.3280i | −0.855072 | − | 1.48103i | −0.876578 | − | 0.481260i | \(-0.840179\pi\) |
0.0215060 | − | 0.999769i | \(-0.493154\pi\) | |||||||
\(570\) | −6.84878 | − | 5.72526i | −0.286864 | − | 0.239805i | ||||
\(571\) | −22.6637 | + | 13.0849i | −0.948445 | + | 0.547585i | −0.892598 | − | 0.450854i | \(-0.851119\pi\) |
−0.0558476 | + | 0.998439i | \(0.517786\pi\) | |||||||
\(572\) | −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 | ||||
\(576\) | −0.531863 | − | 2.95248i | −0.0221610 | − | 0.123020i | ||||
\(577\) | −10.2691 | + | 17.7866i | −0.427509 | + | 0.740467i | −0.996651 | − | 0.0817721i | \(-0.973942\pi\) |
0.569142 | + | 0.822239i | \(0.307275\pi\) | |||||||
\(578\) | 1.69897 | − | 0.980903i | 0.0706680 | − | 0.0408002i | ||||
\(579\) | −3.42007 | + | 1.25197i | −0.142133 | + | 0.0520301i | ||||
\(580\) | −4.82008 | + | 2.78288i | −0.200143 | + | 0.115553i | ||||
\(581\) | −18.5232 | −0.768472 | ||||||||
\(582\) | −15.2278 | + | 18.2160i | −0.631212 | + | 0.755079i | ||||
\(583\) | 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 | \(-0.215507\pi\) | ||||
0.779433 | + | 0.626485i | \(0.215507\pi\) | |||||||
\(588\) | 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 | \(-0.275660\pi\) | |||||||
\(594\) | −0.00512660 | − | 0.924452i | −0.000210347 | − | 0.0379307i | ||||
\(595\) | −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 | \(-0.803155\pi\) |
0.0946646 | + | 0.995509i | \(0.469822\pi\) | |||||||
\(600\) | 0.595404 | + | 1.62650i | 0.0243073 | + | 0.0664015i | ||||
\(601\) | −35.9489 | − | 20.7551i | −1.46639 | − | 0.846619i | −0.467093 | − | 0.884208i | \(-0.654699\pi\) |
−0.999293 | + | 0.0375894i | \(0.988032\pi\) | |||||||
\(602\) | 0.494419 | + | 0.856359i | 0.0201510 | + | 0.0349026i | ||||
\(603\) | 14.6759 | − | 12.4073i | 0.597648 | − | 0.505263i | ||||
\(604\) | − | 18.0258i | − | 0.733458i | ||||||
\(605\) | 10.9683i | 0.445927i | ||||||||
\(606\) | −3.12126 | − | 2.60923i | −0.126793 | − | 0.105993i | ||||
\(607\) | −9.76384 | − | 16.9115i | −0.396302 | − | 0.686415i | 0.596964 | − | 0.802268i | \(-0.296373\pi\) |
−0.993266 | + | 0.115852i | \(0.963040\pi\) | |||||||
\(608\) | 4.46331 | + | 2.57689i | 0.181011 | + | 0.104507i | ||||
\(609\) | 10.5350 | − | 3.85649i | 0.426899 | − | 0.156273i | ||||
\(610\) | −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 | 0.418168 | − | 0.908370i | \(-0.362672\pi\) |
−0.577587 | + | 0.816329i | \(0.696006\pi\) | |||||||
\(614\) | −15.4946 | − | 8.94582i | −0.625312 | − | 0.361024i | ||||
\(615\) | 4.67072 | − | 1.70979i | 0.188342 | − | 0.0689453i | ||||
\(616\) | 0.207046i | 0.00834210i | ||||||||
\(617\) | 17.5553 | + | 10.1355i | 0.706749 | + | 0.408042i | 0.809856 | − | 0.586628i | \(-0.199545\pi\) |
−0.103107 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(618\) | −28.9841 | − | 5.05546i | −1.16591 | − | 0.203361i | ||||
\(619\) | − | 13.7227i | − | 0.551561i | −0.961221 | − | 0.275781i | \(-0.911064\pi\) | ||
0.961221 | − | 0.275781i | \(-0.0889363\pi\) | |||||||
\(620\) | 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 | ||||
\(627\) | 1.21849 | + | 1.01860i | 0.0486618 | + | 0.0406790i | ||||
\(628\) | 9.03549 | 0.360555 | ||||||||
\(629\) | 3.03448 | − | 1.75196i | 0.120993 | − | 0.0698551i | ||||
\(630\) | −0.618952 | − | 3.43592i | −0.0246596 | − | 0.136890i | ||||
\(631\) | 9.02379 | − | 5.20989i | 0.359231 | − | 0.207402i | −0.309512 | − | 0.950895i | \(-0.600166\pi\) |
0.668743 | + | 0.743493i | \(0.266832\pi\) | |||||||
\(632\) | 1.45854 | − | 2.52627i | 0.0580178 | − | 0.100490i | ||||
\(633\) | 18.0064 | − | 6.59151i | 0.715689 | − | 0.261989i | ||||
\(634\) | −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 | ||||
\(639\) | −24.5369 | − | 29.0233i | −0.970664 | − | 1.14815i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 10.4121 | + | 18.0343i | 0.411254 | + | 0.712313i | 0.995027 | − | 0.0996039i | \(-0.0317576\pi\) |
−0.583773 | + | 0.811917i | \(0.698424\pi\) | |||||||
\(642\) | 7.51986 | − | 2.75276i | 0.296785 | − | 0.108643i | ||||
\(643\) | 45.6261i | 1.79932i | 0.436595 | + | 0.899658i | \(0.356184\pi\) | ||||
−0.436595 | + | 0.899658i | \(0.643816\pi\) | |||||||
\(644\) | −3.32087 | + | 5.75191i | −0.130861 | + | 0.226657i | ||||
\(645\) | −1.12916 | − | 0.943927i | −0.0444606 | − | 0.0371671i | ||||
\(646\) | 17.3083 | − | 9.99295i | 0.680986 | − | 0.393167i | ||||
\(647\) | −29.3824 | −1.15514 | −0.577570 | − | 0.816341i | \(-0.695999\pi\) | ||||
−0.577570 | + | 0.816341i | \(0.695999\pi\) | |||||||
\(648\) | −3.14063 | − | 8.43424i | −0.123376 | − | 0.331328i | ||||
\(649\) | − | 0.877988i | − | 0.0344640i | ||||||
\(650\) | 5.64593 | 0.221452 | ||||||||
\(651\) | −11.2090 | − | 0.555557i | −0.439314 | − | 0.0217740i | ||||
\(652\) | −17.0876 | −0.669201 | ||||||||
\(653\) | 36.5284i | 1.42947i | 0.699397 | + | 0.714734i | \(0.253452\pi\) | ||||
−0.699397 | + | 0.714734i | \(0.746548\pi\) | |||||||
\(654\) | 20.3627 | − | 24.3587i | 0.796246 | − | 0.952499i | ||||
\(655\) | −21.1697 | −0.827169 | ||||||||
\(656\) | −2.48692 | + | 1.43582i | −0.0970978 | + | 0.0560595i | ||||
\(657\) | 20.8454 | + | 24.6568i | 0.813255 | + | 0.961955i | ||||
\(658\) | 2.39195 | − | 4.14298i | 0.0932479 | − | 0.161510i | ||||
\(659\) | − | 18.6641i | − | 0.727050i | −0.931584 | − | 0.363525i | \(-0.881573\pi\) | ||
0.931584 | − | 0.363525i | \(-0.118427\pi\) | |||||||
\(660\) | −0.105930 | − | 0.289376i | −0.00412334 | − | 0.0112639i | ||||
\(661\) | −16.6494 | − | 28.8377i | −0.647588 | − | 1.12166i | −0.983697 | − | 0.179833i | \(-0.942444\pi\) |
0.336109 | − | 0.941823i | \(-0.390889\pi\) | |||||||
\(662\) | 4.48602 | + | 7.77002i | 0.174354 | + | 0.301990i | ||||
\(663\) | −24.3222 | + | 29.0951i | −0.944597 | + | 1.12996i | ||||
\(664\) | −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 | ||||
\(669\) | −2.60940 | − | 7.12824i | −0.100885 | − | 0.275594i | ||||
\(670\) | 3.20296 | − | 5.54769i | 0.123741 | − | 0.214326i | ||||
\(671\) | 0.000350512 | 0 | 0.000202368i | 1.35314e−5 | 0 | 7.81234e-6i | ||||
\(672\) | 0.692897 | + | 1.89282i | 0.0267291 | + | 0.0730173i | ||||
\(673\) | 28.5063 | − | 16.4581i | 1.09884 | − | 0.634414i | 0.162922 | − | 0.986639i | \(-0.447908\pi\) |
0.935915 | + | 0.352225i | \(0.114575\pi\) | |||||||
\(674\) | 2.44574 | 0.0942066 | ||||||||
\(675\) | 2.62299 | + | 4.48552i | 0.100959 | + | 0.172648i | ||||
\(676\) | −9.43828 | + | 16.3476i | −0.363011 | + | 0.628753i | ||||
\(677\) | 3.71782 | + | 6.43945i | 0.142887 | + | 0.247488i | 0.928583 | − | 0.371125i | \(-0.121028\pi\) |
−0.785695 | + | 0.618614i | \(0.787695\pi\) | |||||||
\(678\) | −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 | ||||||||
\(687\) | 0.427357 | + | 1.16744i | 0.0163047 | + | 0.0445405i | ||||
\(688\) | 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 | −0.974505 | − | 0.224365i | \(-0.927969\pi\) |
0.292947 | − | 0.956129i | \(-0.405364\pi\) | |||||||
\(692\) | −2.18205 | + | 1.25981i | −0.0829490 | + | 0.0478906i | ||||
\(693\) | 0.110120 | + | 0.611297i | 0.00418311 | + | 0.0232213i | ||||
\(694\) | −14.6181 | − | 8.43977i | −0.554896 | − | 0.320369i | ||||
\(695\) | 0.456749 | + | 0.791113i | 0.0173255 | + | 0.0300086i | ||||
\(696\) | 6.18292 | − | 7.39624i | 0.234363 | − | 0.280354i | ||||
\(697\) | 11.1360i | 0.421806i | ||||||||
\(698\) | − | 32.6846i | − | 1.23713i | ||||||
\(699\) | 17.4472 | − | 20.8710i | 0.659914 | − | 0.789414i | ||||
\(700\) | −0.581871 | − | 1.00783i | −0.0219927 | − | 0.0380924i | ||||
\(701\) | 6.49145 | + | 3.74784i | 0.245179 | + | 0.141554i | 0.617555 | − | 0.786528i | \(-0.288123\pi\) |
−0.372376 | + | 0.928082i | \(0.621457\pi\) | |||||||
\(702\) | −29.3367 | + | 0.162688i | −1.10724 | + | 0.00614027i | ||||
\(703\) | −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 | ||||
\(708\) | −2.93827 | − | 8.02662i | −0.110427 | − | 0.301659i | ||||
\(709\) | 1.59160i | 0.0597738i | 0.999553 | + | 0.0298869i | \(0.00951471\pi\) | ||||
−0.999553 | + | 0.0298869i | \(0.990485\pi\) | |||||||
\(710\) | −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 | \(-0.820011\pi\) |
0.886188 | + | 0.463327i | \(0.153344\pi\) | |||||||
\(720\) | −1.93685 | − | 2.29099i | −0.0721820 | − | 0.0853801i | ||||
\(721\) | 19.7681 | 0.736202 | ||||||||
\(722\) | −6.54841 | + | 3.78073i | −0.243707 | + | 0.140704i | ||||
\(723\) | 3.96977 | + | 10.8444i | 0.147637 | + | 0.403309i | ||||
\(724\) | 3.27223 | − | 1.88922i | 0.121611 | − | 0.0702124i | ||||
\(725\) | −2.78288 | + | 4.82008i | −0.103353 | + | 0.179013i | ||||
\(726\) | −6.53060 | − | 17.8400i | −0.242373 | − | 0.662104i | ||||
\(727\) | 16.3097 | − | 28.2493i | 0.604894 | − | 1.04771i | −0.387174 | − | 0.922007i | \(-0.626549\pi\) |
0.992068 | − | 0.125701i | \(-0.0401180\pi\) | |||||||
\(728\) | 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 | ||||
\(732\) | 0.00252716 | − | 0.00302309i | 9.34066e−5 | − | 0.000111736i | ||||
\(733\) | −4.82676 | − | 8.36019i | −0.178280 | − | 0.308791i | 0.763011 | − | 0.646385i | \(-0.223720\pi\) |
−0.941292 | + | 0.337594i | \(0.890387\pi\) | |||||||
\(734\) | −14.4416 | − | 25.0136i | −0.533050 | − | 0.923270i | ||||
\(735\) | −3.36147 | − | 9.18272i | −0.123990 | − | 0.338710i | ||||
\(736\) | 5.70722i | 0.210371i | ||||||||
\(737\) | −0.569850 | + | 0.987008i | −0.0209907 | + | 0.0363569i | ||||
\(738\) | −6.57891 | + | 5.56193i | −0.242173 | + | 0.204738i | ||||
\(739\) | 20.5340 | − | 11.8553i | 0.755355 | − | 0.436105i | −0.0722704 | − | 0.997385i | \(-0.523024\pi\) |
0.827626 | + | 0.561281i | \(0.189691\pi\) | |||||||
\(740\) | 0.903557 | 0.0332154 | ||||||||
\(741\) | 32.3245 | − | 38.6677i | 1.18747 | − | 1.42049i | ||||
\(742\) | 14.5492i | 0.534118i | ||||||||
\(743\) | −33.9392 | −1.24511 | −0.622555 | − | 0.782576i | \(-0.713905\pi\) | ||||
−0.622555 | + | 0.782576i | \(0.713905\pi\) | |||||||
\(744\) | −8.58010 | + | 4.40248i | −0.314562 | + | 0.161403i | ||||
\(745\) | 4.58537 | 0.167995 | ||||||||
\(746\) | 15.4070i | 0.564090i | ||||||||
\(747\) | −36.4655 | + | 30.8286i | −1.33420 | + | 1.12796i | ||||
\(748\) | 0.689933 | 0.0252264 | ||||||||
\(749\) | −4.65955 | + | 2.69019i | −0.170256 | + | 0.0982975i | ||||
\(750\) | 1.32888 | + | 1.11089i | 0.0485240 | + | 0.0405638i | ||||
\(751\) | −3.61672 | + | 6.26434i | −0.131976 | + | 0.228589i | −0.924438 | − | 0.381332i | \(-0.875466\pi\) |
0.792462 | + | 0.609921i | \(0.208799\pi\) | |||||||
\(752\) | − | 4.11079i | − | 0.149905i | ||||||
\(753\) | −13.5020 | + | 4.94261i | −0.492040 | + | 0.180119i | ||||
\(754\) | −15.7119 | − | 27.2139i | −0.572195 | − | 0.991071i | ||||
\(755\) | −9.01289 | − | 15.6108i | −0.328013 | − | 0.568134i | ||||
\(756\) | 3.05249 | + | 5.21999i | 0.111018 | + | 0.189849i | ||||
\(757\) | −0.672009 | + | 0.387984i | −0.0244246 | + | 0.0141015i | −0.512163 | − | 0.858889i | \(-0.671155\pi\) |
0.487738 | + | 0.872990i | \(0.337822\pi\) | |||||||
\(758\) | 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 | \(-0.870408\pi\) |
0.802053 | + | 0.597253i | \(0.203741\pi\) | |||||||
\(762\) | 20.4962 | − | 7.50296i | 0.742500 | − | 0.271803i | ||||
\(763\) | −10.6658 | + | 18.4737i | −0.386128 | + | 0.668793i | ||||
\(764\) | 5.58732 | − | 3.22584i | 0.202142 | − | 0.116707i | ||||
\(765\) | −11.4494 | + | 2.06252i | −0.413955 | + | 0.0745705i | ||||
\(766\) | 20.4225 | − | 11.7909i | 0.737895 | − | 0.426024i | ||||
\(767\) | −27.8622 | −1.00605 | ||||||||
\(768\) | 1.32888 | + | 1.11089i | 0.0479520 | + | 0.0400857i | ||||
\(769\) | 9.17949 | − | 15.8993i | 0.331021 | − | 0.573345i | −0.651691 | − | 0.758484i | \(-0.725940\pi\) |
0.982712 | + | 0.185139i | \(0.0592736\pi\) | |||||||
\(770\) | 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 | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978242i | \(0.433479\pi\) | |||||||
\(774\) | 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 | ||||||
\(780\) | −9.18310 | + | 3.36161i | −0.328808 | + | 0.120365i | ||||
\(781\) | 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 | ||||
\(786\) | 34.4325 | − | 12.6045i | 1.22817 | − | 0.449588i | ||||
\(787\) | −15.4169 | − | 8.90097i | −0.549554 | − | 0.317285i | 0.199388 | − | 0.979921i | \(-0.436105\pi\) |
−0.748942 | + | 0.662635i | \(0.769438\pi\) | |||||||
\(788\) | 9.43359 | + | 16.3395i | 0.336058 | + | 0.582069i | ||||
\(789\) | −17.6978 | − | 14.7945i | −0.630058 | − | 0.526699i | ||||
\(790\) | − | 2.91709i | − | 0.103785i | ||||||
\(791\) | − | 0.506340i | − | 0.0180034i | ||||||
\(792\) | 0.344591 | + | 0.407598i | 0.0122445 | + | 0.0144834i | ||||
\(793\) | −0.00642199 | − | 0.0111232i | −0.000228051 | − | 0.000394997i | ||||
\(794\) | 22.6122 | + | 13.0551i | 0.802475 | + | 0.463309i | ||||
\(795\) | −7.44378 | − | 20.3346i | −0.264004 | − | 0.721194i | ||||
\(796\) | −16.6694 | + | 9.62408i | −0.590831 | + | 0.341116i | ||||
\(797\) | 18.5843 | + | 32.1890i | 0.658291 | + | 1.14019i | 0.981058 | + | 0.193715i | \(0.0620537\pi\) |
−0.322767 | + | 0.946479i | \(0.604613\pi\) | |||||||
\(798\) | −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 | ||||
\(801\) | 2.76989 | + | 15.3762i | 0.0978693 | + | 0.543291i | ||||
\(802\) | 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 | \(-0.757465\pi\) |
0.959591 | + | 0.281400i | \(0.0907987\pi\) | |||||||
\(810\) | −6.93699 | − | 5.73395i | −0.243741 | − | 0.201471i | ||||
\(811\) | −4.22401 | − | 7.31619i | −0.148325 | − | 0.256906i | 0.782284 | − | 0.622922i | \(-0.214055\pi\) |
−0.930608 | + | 0.366016i | \(0.880721\pi\) | |||||||
\(812\) | −3.23855 | + | 5.60933i | −0.113651 | + | 0.196849i | ||||
\(813\) | −9.82719 | + | 11.7556i | −0.344654 | + | 0.412289i | ||||
\(814\) | −0.160755 | −0.00563446 | ||||||||
\(815\) | −14.7983 | + | 8.54378i | −0.518360 | + | 0.299276i | ||||
\(816\) | 6.30741 | − | 2.30892i | 0.220804 | − | 0.0808285i | ||||
\(817\) | −3.79250 | + | 2.18960i | −0.132683 | + | 0.0766044i | ||||
\(818\) | −12.4143 | + | 21.5022i | −0.434056 | + | 0.751808i | ||||
\(819\) | 19.3990 | − | 3.49456i | 0.677856 | − | 0.122110i | ||||
\(820\) | −1.43582 | + | 2.48692i | −0.0501411 | + | 0.0868469i | ||||
\(821\) | −21.5718 | −0.752861 | −0.376431 | − | 0.926445i | \(-0.622849\pi\) | ||||
−0.376431 | + | 0.926445i | \(0.622849\pi\) | |||||||
\(822\) | −21.9129 | − | 3.82208i | −0.764299 | − | 0.133310i | ||||
\(823\) | −23.2067 | − | 13.3984i | −0.808934 | − | 0.467038i | 0.0376515 | − | 0.999291i | \(-0.488012\pi\) |
−0.846586 | + | 0.532253i | \(0.821346\pi\) | |||||||
\(824\) | 14.7109 | − | 8.49332i | 0.512477 | − | 0.295879i | ||||
\(825\) | −0.236426 | − | 0.197642i | −0.00823131 | − | 0.00688100i | ||||
\(826\) | 2.87148 | + | 4.97356i | 0.0999117 | + | 0.173052i | ||||
\(827\) | 8.45553 | + | 14.6454i | 0.294028 | + | 0.509271i | 0.974758 | − | 0.223263i | \(-0.0716709\pi\) |
−0.680731 | + | 0.732534i | \(0.738338\pi\) | |||||||
\(828\) | 3.03546 | + | 16.8504i | 0.105490 | + | 0.585593i | ||||
\(829\) | − | 6.47384i | − | 0.224846i | −0.993660 | − | 0.112423i | \(-0.964139\pi\) | ||
0.993660 | − | 0.112423i | \(-0.0358611\pi\) | |||||||
\(830\) | −7.95846 | + | 13.7845i | −0.276242 | + | 0.478466i | ||||
\(831\) | −16.6317 | + | 19.8954i | −0.576946 | + | 0.690165i | ||||
\(832\) | 4.88952 | − | 2.82297i | 0.169514 | − | 0.0978688i | ||||
\(833\) | 21.8935 | 0.758566 | ||||||||
\(834\) | −1.21393 | − | 1.01479i | −0.0420351 | − | 0.0351394i | ||||
\(835\) | 8.88196i | 0.307373i | ||||||||
\(836\) | −0.916927 | −0.0317126 | ||||||||
\(837\) | −22.9910 | + | 17.5617i | −0.794686 | + | 0.607020i | ||||
\(838\) | 16.9548 | 0.585693 | ||||||||
\(839\) | − | 43.6645i | − | 1.50747i | −0.657180 | − | 0.753734i | \(-0.728251\pi\) | ||
0.657180 | − | 0.753734i | \(-0.271749\pi\) | |||||||
\(840\) | 1.54648 | + | 1.29279i | 0.0533586 | + | 0.0446053i | ||||
\(841\) | 1.97760 | 0.0681931 | ||||||||
\(842\) | 25.1607 | − | 14.5265i | 0.867095 | − | 0.500618i | ||||
\(843\) | −8.13501 | + | 9.73140i | −0.280184 | + | 0.335167i | ||||
\(844\) | −5.53532 | + | 9.58746i | −0.190534 | + | 0.330014i | ||||
\(845\) | 18.8766i | 0.649374i | ||||||||
\(846\) | −2.18638 | − | 12.1370i | −0.0751692 | − | 0.417279i | ||||
\(847\) | 6.38216 | + | 11.0542i | 0.219294 | + | 0.379828i | ||||
\(848\) | 6.25104 | + | 10.8271i | 0.214661 | + | 0.371805i | ||||
\(849\) | −19.4297 | − | 16.2424i | −0.666826 | − | 0.557436i | ||||
\(850\) | −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 | ||||
\(855\) | 15.2164 | − | 2.74111i | 0.520391 | − | 0.0937439i | ||||
\(856\) | −2.31167 | + | 4.00394i | −0.0790114 | + | 0.136852i | ||||
\(857\) | 14.9622 | − | 8.63842i | 0.511098 | − | 0.295083i | −0.222187 | − | 0.975004i | \(-0.571319\pi\) |
0.733285 | + | 0.679921i | \(0.237986\pi\) | |||||||
\(858\) | 1.63380 | − | 0.598076i | 0.0557769 | − | 0.0204180i | ||||
\(859\) | 4.18085 | − | 2.41382i | 0.142649 | − | 0.0823583i | −0.426977 | − | 0.904262i | \(-0.640421\pi\) |
0.569626 | + | 0.821904i | \(0.307088\pi\) | |||||||
\(860\) | 0.849706 | 0.0289747 | ||||||||
\(861\) | 3.71242 | − | 4.44094i | 0.126519 | − | 0.151347i | ||||
\(862\) | 10.9041 | − | 18.8864i | 0.371394 | − | 0.643274i | ||||
\(863\) | −8.63393 | − | 14.9544i | −0.293902 | − | 0.509054i | 0.680827 | − | 0.732445i | \(-0.261621\pi\) |
−0.974729 | + | 0.223391i | \(0.928287\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −7.29067 | − | 40.4719i | −0.246752 | − | 1.36977i | ||||
\(874\) | −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 | −0.953234 | − | 0.302234i | \(-0.902268\pi\) |
0.214874 | − | 0.976642i | \(-0.431066\pi\) | |||||||
\(878\) | 20.6527 | − | 11.9238i | 0.696994 | − | 0.402410i | ||||
\(879\) | −20.3130 | − | 55.4902i | −0.685142 | − | 1.87164i | ||||
\(880\) | 0.154078 | + | 0.0889568i | 0.00519396 | + | 0.00299873i | ||||
\(881\) | −18.1740 | − | 31.4783i | −0.612298 | − | 1.06053i | −0.990852 | − | 0.134951i | \(-0.956912\pi\) |
0.378555 | − | 0.925579i | \(-0.376421\pi\) | |||||||
\(882\) | 10.9349 | + | 12.9342i | 0.368196 | + | 0.435519i | ||||
\(883\) | 51.2633i | 1.72515i | 0.505931 | + | 0.862574i | \(0.331149\pi\) | ||||
−0.505931 | + | 0.862574i | \(0.668851\pi\) | |||||||
\(884\) | − | 21.8944i | − | 0.736389i | ||||||
\(885\) | −6.55792 | − | 5.48213i | −0.220442 | − | 0.184280i | ||||
\(886\) | −10.4904 | − | 18.1698i | −0.352431 | − | 0.610428i | ||||
\(887\) | 15.9684 | + | 9.21935i | 0.536166 | + | 0.309556i | 0.743524 | − | 0.668710i | \(-0.233153\pi\) |
−0.207358 | + | 0.978265i | \(0.566486\pi\) | |||||||
\(888\) | −1.46963 | + | 0.537981i | −0.0493177 | + | 0.0180535i | ||||
\(889\) | −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 | ||||
\(894\) | −7.45810 | + | 2.73015i | −0.249436 | + | 0.0913099i | ||||
\(895\) | − | 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 | ||||
\(906\) | 23.9542 | + | 20.0246i | 0.795823 | + | 0.665272i | ||||
\(907\) | −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 | ||||
\(909\) | 6.93474 | − | 1.24923i | 0.230011 | − | 0.0414345i | ||||
\(910\) | 5.69014 | − | 3.28521i | 0.188626 | − | 0.108904i | ||||
\(911\) | −27.6813 | + | 47.9455i | −0.917124 | + | 1.58851i | −0.113363 | + | 0.993554i | \(0.536162\pi\) |
−0.803761 | + | 0.594952i | \(0.797171\pi\) | |||||||
\(912\) | −8.38261 | + | 3.06858i | −0.277576 | + | 0.101611i | ||||
\(913\) | 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 | ||||
\(918\) | 17.3945 | − | 10.1717i | 0.574103 | − | 0.335717i | ||||
\(919\) | 9.34101 | + | 16.1791i | 0.308132 | + | 0.533700i | 0.977954 | − | 0.208822i | \(-0.0669630\pi\) |
−0.669822 | + | 0.742522i | \(0.733630\pi\) | |||||||
\(920\) | 2.85361 | + | 4.94260i | 0.0940808 | + | 0.162953i | ||||
\(921\) | 29.1007 | − | 10.6528i | 0.958901 | − | 0.351020i | ||||
\(922\) | 19.8197i | 0.652727i | ||||||||
\(923\) | 35.7627 | − | 61.9428i | 1.17714 | − | 2.03887i | ||||
\(924\) | −0.275139 | − | 0.230004i | −0.00905142 | − | 0.00756658i | ||||
\(925\) | 0.782503 | − | 0.451779i | 0.0257286 | − | 0.0148544i | ||||
\(926\) | 10.9325 | 0.359263 | ||||||||
\(927\) | 38.9162 | − | 32.9005i | 1.27818 | − | 1.08059i | ||||
\(928\) | 5.56575i | 0.182705i | ||||||||
\(929\) | −11.9745 | −0.392870 | −0.196435 | − | 0.980517i | \(-0.562937\pi\) | ||||
−0.196435 | + | 0.980517i | \(0.562937\pi\) | |||||||
\(930\) | −5.22934 | + | 8.10271i | −0.171477 | + | 0.265698i | ||||
\(931\) | −29.0967 | −0.953606 | ||||||||
\(932\) | 15.7057i | 0.514456i | ||||||||
\(933\) | −16.5383 | + | 19.7838i | −0.541441 | + | 0.647692i | ||||
\(934\) | 11.3377 | 0.370980 | ||||||||
\(935\) | 0.597499 | − | 0.344966i | 0.0195403 | − | 0.0112816i | ||||
\(936\) | 12.9348 | − | 10.9353i | 0.422786 | − | 0.357432i | ||||
\(937\) | 4.88152 | − | 8.45503i | 0.159472 | − | 0.276214i | −0.775206 | − | 0.631708i | \(-0.782354\pi\) |
0.934678 | + | 0.355494i | \(0.115687\pi\) | |||||||
\(938\) | − | 7.45483i | − | 0.243409i | ||||||
\(939\) | −4.57698 | − | 12.5032i | −0.149364 | − | 0.408026i | ||||
\(940\) | −2.05539 | − | 3.56005i | −0.0670396 | − | 0.116116i | ||||
\(941\) | −3.76669 | − | 6.52409i | −0.122790 | − | 0.212679i | 0.798077 | − | 0.602556i | \(-0.205851\pi\) |
−0.920867 | + | 0.389877i | \(0.872518\pi\) | |||||||
\(942\) | −10.0374 | + | 12.0071i | −0.327036 | + | 0.391213i | ||||
\(943\) | 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 | 0.413245 | + | 0.910620i | \(0.364395\pi\) |
−0.995242 | + | 0.0974291i | \(0.968938\pi\) | |||||||
\(948\) | 1.73685 | + | 4.74464i | 0.0564101 | + | 0.154099i | ||||
\(949\) | −30.3823 | + | 52.6236i | −0.986250 | + | 1.70824i | ||||
\(950\) | 4.46331 | − | 2.57689i | 0.144809 | − | 0.0836054i | ||||
\(951\) | −3.28728 | − | 8.98005i | −0.106597 | − | 0.291198i | ||||
\(952\) | −3.90828 | + | 2.25644i | −0.126668 | + | 0.0731318i | ||||
\(953\) | −8.04230 | −0.260516 | −0.130258 | − | 0.991480i | \(-0.541581\pi\) | ||||
−0.130258 | + | 0.991480i | \(0.541581\pi\) | |||||||
\(954\) | 24.2146 | + | 28.6421i | 0.783976 | + | 0.927322i | ||||
\(955\) | 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 | ||||||
\(966\) | −3.95452 | − | 10.8028i | −0.127234 | − | 0.347573i | ||||
\(967\) | 0.283683 | + | 0.163784i | 0.00912262 | + | 0.00526695i | 0.504554 | − | 0.863380i | \(-0.331657\pi\) |
−0.495432 | + | 0.868647i | \(0.664990\pi\) | |||||||
\(968\) | 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 | \(-0.608638\pi\) |
0.648721 | + | 0.761027i | \(0.275304\pi\) | |||||||
\(972\) | 14.6970 | + | 5.19595i | 0.471407 | + | 0.166660i | ||||
\(973\) | 0.920652 | + | 0.531539i | 0.0295147 | + | 0.0170403i | ||||
\(974\) | 18.2009 | + | 31.5249i | 0.583194 | + | 1.01012i | ||||
\(975\) | −6.27199 | + | 7.50279i | −0.200864 | + | 0.240282i | ||||
\(976\) | 0.00227491i | 7.28180e-5i | ||||||||
\(977\) | 34.7208i | 1.11082i | 0.831578 | + | 0.555409i | \(0.187438\pi\) | ||||
−0.831578 | + | 0.555409i | \(0.812562\pi\) | |||||||
\(978\) | 18.9823 | − | 22.7074i | 0.606988 | − | 0.726102i | ||||
\(979\) | −0.463278 | − | 0.802421i | −0.0148064 | − | 0.0256455i | ||||
\(980\) | 4.88932 | + | 2.82285i | 0.156184 | + | 0.0901727i | ||||
\(981\) | 9.74915 | + | 54.1194i | 0.311266 | + | 1.72790i | ||||
\(982\) | 28.0904 | − | 16.2180i | 0.896400 | − | 0.517537i | ||||
\(983\) | −19.9164 | − | 34.4963i | −0.635235 | − | 1.10026i | −0.986465 | − | 0.163971i | \(-0.947570\pi\) |
0.351230 | − | 0.936289i | \(-0.385764\pi\) | |||||||
\(984\) | 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 | ||||
\(987\) | 2.84835 | + | 7.78100i | 0.0906640 | + | 0.247672i | ||||
\(988\) | 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 | \(0.0284442\pi\) | ||||
−0.996010 | + | 0.0892413i | \(0.971556\pi\) | |||||||
\(992\) | 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 | 0.778542 | − | 0.627592i | \(-0.215959\pi\) |
−0.932782 | + | 0.360442i | \(0.882626\pi\) | |||||||
\(998\) | 21.2891 | − | 36.8738i | 0.673894 | − | 1.16722i | ||||
\(999\) | −4.05293 | + | 2.37002i | −0.128229 | + | 0.0749842i |
(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.491.8 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.491.19 | yes | 40 | |
31.6 | odd | 6 | inner | 930.2.o.e.161.9 | ✓ | 40 | |
93.68 | even | 6 | inner | 930.2.o.e.161.18 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.9 | ✓ | 40 | 31.6 | odd | 6 | inner | |
930.2.o.e.161.18 | yes | 40 | 93.68 | even | 6 | inner | |
930.2.o.e.491.8 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.491.19 | yes | 40 | 3.2 | odd | 2 | inner |