Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 221.3 | ||
Character | \(\chi\) | \(=\) | 570.221 |
Dual form | 570.2.s.b.521.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.33656 | + | 1.10164i | −0.771662 | + | 0.636032i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | −1.62233 | − | 0.606673i | −0.662313 | − | 0.247673i | ||||
\(7\) | −1.76552 | −0.667305 | −0.333652 | − | 0.942696i | \(-0.608281\pi\) | ||||
−0.333652 | + | 0.942696i | \(0.608281\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.572776 | − | 2.94481i | 0.190925 | − | 0.981605i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | − | 3.02678i | − | 0.912607i | −0.889824 | − | 0.456304i | \(-0.849173\pi\) | ||
0.889824 | − | 0.456304i | \(-0.150827\pi\) | |||||||
\(12\) | −0.285770 | − | 1.70831i | −0.0824946 | − | 0.493148i | ||||
\(13\) | −3.25407 | − | 1.87874i | −0.902518 | − | 0.521069i | −0.0245016 | − | 0.999700i | \(-0.507800\pi\) |
−0.878016 | + | 0.478631i | \(0.841133\pi\) | |||||||
\(14\) | −0.882761 | − | 1.52899i | −0.235928 | − | 0.408639i | ||||
\(15\) | 0.606673 | − | 1.62233i | 0.156642 | − | 0.418883i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.76712 | + | 1.59760i | −0.671126 | + | 0.387475i | −0.796503 | − | 0.604634i | \(-0.793319\pi\) |
0.125377 | + | 0.992109i | \(0.459986\pi\) | |||||||
\(18\) | 2.83667 | − | 0.976368i | 0.668610 | − | 0.230132i | ||||
\(19\) | 4.29047 | − | 0.769325i | 0.984301 | − | 0.176495i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | 2.35972 | − | 1.94497i | 0.514934 | − | 0.424427i | ||||
\(22\) | 2.62126 | − | 1.51339i | 0.558855 | − | 0.322655i | ||||
\(23\) | 0.844837 | + | 0.487767i | 0.176161 | + | 0.101706i | 0.585488 | − | 0.810681i | \(-0.300903\pi\) |
−0.409327 | + | 0.912388i | \(0.634236\pi\) | |||||||
\(24\) | 1.33656 | − | 1.10164i | 0.272824 | − | 0.224871i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | − | 3.75748i | − | 0.736903i | ||||||
\(27\) | 2.47858 | + | 4.56691i | 0.477002 | + | 0.878902i | ||||
\(28\) | 0.882761 | − | 1.52899i | 0.166826 | − | 0.288951i | ||||
\(29\) | −3.19725 | + | 5.53779i | −0.593714 | + | 1.02834i | 0.400014 | + | 0.916509i | \(0.369005\pi\) |
−0.993727 | + | 0.111833i | \(0.964328\pi\) | |||||||
\(30\) | 1.70831 | − | 0.285770i | 0.311894 | − | 0.0521741i | ||||
\(31\) | − | 7.64334i | − | 1.37278i | −0.727232 | − | 0.686392i | \(-0.759194\pi\) | ||
0.727232 | − | 0.686392i | \(-0.240806\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 3.33442 | + | 4.04546i | 0.580448 | + | 0.704224i | ||||
\(34\) | −2.76712 | − | 1.59760i | −0.474558 | − | 0.273986i | ||||
\(35\) | 1.52899 | − | 0.882761i | 0.258446 | − | 0.149214i | ||||
\(36\) | 2.26390 | + | 1.96845i | 0.377316 | + | 0.328074i | ||||
\(37\) | − | 8.22349i | − | 1.35193i | −0.736932 | − | 0.675966i | \(-0.763726\pi\) | ||
0.736932 | − | 0.675966i | \(-0.236274\pi\) | |||||||
\(38\) | 2.81149 | + | 3.33099i | 0.456084 | + | 0.540359i | ||||
\(39\) | 6.41896 | − | 1.07377i | 1.02786 | − | 0.171941i | ||||
\(40\) | 0.866025 | − | 0.500000i | 0.136931 | − | 0.0790569i | ||||
\(41\) | 0.0664620 | + | 0.115116i | 0.0103796 | + | 0.0179780i | 0.871169 | − | 0.490984i | \(-0.163363\pi\) |
−0.860789 | + | 0.508962i | \(0.830029\pi\) | |||||||
\(42\) | 2.86426 | + | 1.07109i | 0.441964 | + | 0.165274i | ||||
\(43\) | −4.92098 | − | 8.52339i | −0.750443 | − | 1.29981i | −0.947608 | − | 0.319435i | \(-0.896507\pi\) |
0.197165 | − | 0.980370i | \(-0.436826\pi\) | |||||||
\(44\) | 2.62126 | + | 1.51339i | 0.395170 | + | 0.228152i | ||||
\(45\) | 0.976368 | + | 2.83667i | 0.145548 | + | 0.422866i | ||||
\(46\) | 0.975534i | 0.143835i | ||||||||
\(47\) | −7.38774 | − | 4.26531i | −1.07761 | − | 0.622160i | −0.147361 | − | 0.989083i | \(-0.547078\pi\) |
−0.930251 | + | 0.366923i | \(0.880411\pi\) | |||||||
\(48\) | 1.62233 | + | 0.606673i | 0.234163 | + | 0.0875657i | ||||
\(49\) | −3.88293 | −0.554705 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.93844 | − | 5.18366i | 0.271436 | − | 0.725857i | ||||
\(52\) | 3.25407 | − | 1.87874i | 0.451259 | − | 0.260534i | ||||
\(53\) | −5.92218 | + | 10.2575i | −0.813474 | + | 1.40898i | 0.0969441 | + | 0.995290i | \(0.469093\pi\) |
−0.910418 | + | 0.413689i | \(0.864240\pi\) | |||||||
\(54\) | −2.71577 | + | 4.42997i | −0.369569 | + | 0.602842i | ||||
\(55\) | 1.51339 | + | 2.62126i | 0.204065 | + | 0.353451i | ||||
\(56\) | 1.76552 | 0.235928 | ||||||||
\(57\) | −4.88694 | + | 5.75480i | −0.647292 | + | 0.762242i | ||||
\(58\) | −6.39449 | −0.839638 | ||||||||
\(59\) | 3.82758 | + | 6.62956i | 0.498308 | + | 0.863095i | 0.999998 | − | 0.00195269i | \(-0.000621562\pi\) |
−0.501690 | + | 0.865047i | \(0.667288\pi\) | |||||||
\(60\) | 1.10164 | + | 1.33656i | 0.142221 | + | 0.172549i | ||||
\(61\) | −1.00006 | + | 1.73216i | −0.128045 | + | 0.221780i | −0.922919 | − | 0.384994i | \(-0.874204\pi\) |
0.794874 | + | 0.606774i | \(0.207537\pi\) | |||||||
\(62\) | 6.61932 | − | 3.82167i | 0.840655 | − | 0.485352i | ||||
\(63\) | −1.01125 | + | 5.19913i | −0.127405 | + | 0.655029i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.75748 | 0.466058 | ||||||||
\(66\) | −1.83626 | + | 4.91042i | −0.226028 | + | 0.604431i | ||||
\(67\) | 0.649931 | + | 0.375238i | 0.0794017 | + | 0.0458426i | 0.539175 | − | 0.842194i | \(-0.318736\pi\) |
−0.459773 | + | 0.888036i | \(0.652069\pi\) | |||||||
\(68\) | − | 3.19520i | − | 0.387475i | ||||||
\(69\) | −1.66652 | + | 0.278778i | −0.200625 | + | 0.0335609i | ||||
\(70\) | 1.52899 | + | 0.882761i | 0.182749 | + | 0.105510i | ||||
\(71\) | −8.14418 | − | 14.1061i | −0.966536 | − | 1.67409i | −0.705430 | − | 0.708779i | \(-0.749246\pi\) |
−0.261106 | − | 0.965310i | \(-0.584087\pi\) | |||||||
\(72\) | −0.572776 | + | 2.94481i | −0.0675023 | + | 0.347050i | ||||
\(73\) | 0.477929 | + | 0.827798i | 0.0559374 | + | 0.0968864i | 0.892638 | − | 0.450774i | \(-0.148852\pi\) |
−0.836701 | + | 0.547660i | \(0.815519\pi\) | |||||||
\(74\) | 7.12175 | − | 4.11174i | 0.827886 | − | 0.477980i | ||||
\(75\) | 0.285770 | + | 1.70831i | 0.0329978 | + | 0.197259i | ||||
\(76\) | −1.47898 | + | 4.10032i | −0.169651 | + | 0.470339i | ||||
\(77\) | 5.34384i | 0.608987i | ||||||||
\(78\) | 4.13939 | + | 5.02209i | 0.468694 | + | 0.568640i | ||||
\(79\) | 2.26576 | − | 1.30814i | 0.254918 | − | 0.147177i | −0.367096 | − | 0.930183i | \(-0.619648\pi\) |
0.622014 | + | 0.783006i | \(0.286315\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −8.34386 | − | 3.37344i | −0.927095 | − | 0.374826i | ||||
\(82\) | −0.0664620 | + | 0.115116i | −0.00733950 | + | 0.0127124i | ||||
\(83\) | 4.67129i | 0.512741i | 0.966579 | + | 0.256370i | \(0.0825267\pi\) | ||||
−0.966579 | + | 0.256370i | \(0.917473\pi\) | |||||||
\(84\) | 0.504532 | + | 3.01607i | 0.0550490 | + | 0.329080i | ||||
\(85\) | 1.59760 | − | 2.76712i | 0.173284 | − | 0.300137i | ||||
\(86\) | 4.92098 | − | 8.52339i | 0.530643 | − | 0.919101i | ||||
\(87\) | −1.82735 | − | 10.9238i | −0.195913 | − | 1.17115i | ||||
\(88\) | 3.02678i | 0.322655i | ||||||||
\(89\) | −4.36131 | + | 7.55401i | −0.462298 | + | 0.800724i | −0.999075 | − | 0.0430003i | \(-0.986308\pi\) |
0.536777 | + | 0.843724i | \(0.319642\pi\) | |||||||
\(90\) | −1.96845 | + | 2.26390i | −0.207492 | + | 0.238636i | ||||
\(91\) | 5.74514 | + | 3.31696i | 0.602254 | + | 0.347712i | ||||
\(92\) | −0.844837 | + | 0.487767i | −0.0880803 | + | 0.0508532i | ||||
\(93\) | 8.42021 | + | 10.2158i | 0.873135 | + | 1.05933i | ||||
\(94\) | − | 8.53062i | − | 0.879867i | ||||||
\(95\) | −3.33099 | + | 2.81149i | −0.341753 | + | 0.288453i | ||||
\(96\) | 0.285770 | + | 1.70831i | 0.0291662 | + | 0.174354i | ||||
\(97\) | −12.4237 | + | 7.17285i | −1.26144 | + | 0.728292i | −0.973353 | − | 0.229312i | \(-0.926352\pi\) |
−0.288087 | + | 0.957604i | \(0.593019\pi\) | |||||||
\(98\) | −1.94147 | − | 3.36272i | −0.196118 | − | 0.339686i | ||||
\(99\) | −8.91329 | − | 1.73366i | −0.895819 | − | 0.174240i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −13.7972 | − | 7.96584i | −1.37288 | − | 0.792630i | −0.381587 | − | 0.924333i | \(-0.624622\pi\) |
−0.991289 | + | 0.131703i | \(0.957956\pi\) | |||||||
\(102\) | 5.45840 | − | 0.913090i | 0.540462 | − | 0.0904094i | ||||
\(103\) | 6.24459i | 0.615298i | 0.951500 | + | 0.307649i | \(0.0995422\pi\) | ||||
−0.951500 | + | 0.307649i | \(0.900458\pi\) | |||||||
\(104\) | 3.25407 | + | 1.87874i | 0.319088 | + | 0.184226i | ||||
\(105\) | −1.07109 | + | 2.86426i | −0.104528 | + | 0.279523i | ||||
\(106\) | −11.8444 | −1.15043 | ||||||||
\(107\) | 2.50860 | 0.242516 | 0.121258 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121258 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(108\) | −5.19435 | − | 0.136943i | −0.499826 | − | 0.0131773i | ||||
\(109\) | −0.194529 | + | 0.112311i | −0.0186325 | + | 0.0107575i | −0.509287 | − | 0.860597i | \(-0.670091\pi\) |
0.490655 | + | 0.871354i | \(0.336758\pi\) | |||||||
\(110\) | −1.51339 | + | 2.62126i | −0.144296 | + | 0.249928i | ||||
\(111\) | 9.05933 | + | 10.9912i | 0.859873 | + | 1.04324i | ||||
\(112\) | 0.882761 | + | 1.52899i | 0.0834131 | + | 0.144476i | ||||
\(113\) | 12.6900 | 1.19377 | 0.596887 | − | 0.802326i | \(-0.296404\pi\) | ||||
0.596887 | + | 0.802326i | \(0.296404\pi\) | |||||||
\(114\) | −7.42728 | − | 1.35482i | −0.695628 | − | 0.126890i | ||||
\(115\) | −0.975534 | −0.0909690 | ||||||||
\(116\) | −3.19725 | − | 5.53779i | −0.296857 | − | 0.514171i | ||||
\(117\) | −7.39640 | + | 8.50654i | −0.683797 | + | 0.786430i | ||||
\(118\) | −3.82758 | + | 6.62956i | −0.352357 | + | 0.610300i | ||||
\(119\) | 4.88542 | − | 2.82060i | 0.447845 | − | 0.258564i | ||||
\(120\) | −0.606673 | + | 1.62233i | −0.0553814 | + | 0.148098i | ||||
\(121\) | 1.83863 | 0.167148 | ||||||||
\(122\) | −2.00013 | −0.181083 | ||||||||
\(123\) | −0.215646 | − | 0.0806415i | −0.0194442 | − | 0.00727120i | ||||
\(124\) | 6.61932 | + | 3.82167i | 0.594433 | + | 0.343196i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −5.00821 | + | 1.72380i | −0.446166 | + | 0.153568i | ||||
\(127\) | 3.90891 | + | 2.25681i | 0.346860 | + | 0.200260i | 0.663301 | − | 0.748352i | \(-0.269155\pi\) |
−0.316442 | + | 0.948612i | \(0.602488\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 15.9669 | + | 5.97086i | 1.40581 | + | 0.525705i | ||||
\(130\) | 1.87874 | + | 3.25407i | 0.164776 | + | 0.285401i | ||||
\(131\) | −3.84003 | + | 2.21704i | −0.335505 | + | 0.193704i | −0.658282 | − | 0.752771i | \(-0.728717\pi\) |
0.322778 | + | 0.946475i | \(0.395383\pi\) | |||||||
\(132\) | −5.17068 | + | 0.864960i | −0.450050 | + | 0.0752851i | ||||
\(133\) | −7.57492 | + | 1.35826i | −0.656829 | + | 0.117776i | ||||
\(134\) | 0.750475i | 0.0648312i | ||||||||
\(135\) | −4.42997 | − | 2.71577i | −0.381271 | − | 0.233736i | ||||
\(136\) | 2.76712 | − | 1.59760i | 0.237279 | − | 0.136993i | ||||
\(137\) | −12.7182 | − | 7.34284i | −1.08659 | − | 0.627341i | −0.153921 | − | 0.988083i | \(-0.549190\pi\) |
−0.932666 | + | 0.360742i | \(0.882524\pi\) | |||||||
\(138\) | −1.07469 | − | 1.30386i | −0.0914835 | − | 0.110992i | ||||
\(139\) | −9.42690 | + | 16.3279i | −0.799579 | + | 1.38491i | 0.120311 | + | 0.992736i | \(0.461611\pi\) |
−0.919890 | + | 0.392176i | \(0.871722\pi\) | |||||||
\(140\) | 1.76552i | 0.149214i | ||||||||
\(141\) | 14.5730 | − | 2.43779i | 1.22727 | − | 0.205299i | ||||
\(142\) | 8.14418 | − | 14.1061i | 0.683444 | − | 1.18376i | ||||
\(143\) | −5.68653 | + | 9.84935i | −0.475531 | + | 0.823644i | ||||
\(144\) | −2.83667 | + | 0.976368i | −0.236389 | + | 0.0813640i | ||||
\(145\) | − | 6.39449i | − | 0.531033i | ||||||
\(146\) | −0.477929 | + | 0.827798i | −0.0395537 | + | 0.0685090i | ||||
\(147\) | 5.18976 | − | 4.27760i | 0.428045 | − | 0.352810i | ||||
\(148\) | 7.12175 | + | 4.11174i | 0.585404 | + | 0.337983i | ||||
\(149\) | 2.37618 | − | 1.37189i | 0.194664 | − | 0.112390i | −0.399500 | − | 0.916733i | \(-0.630816\pi\) |
0.594164 | + | 0.804344i | \(0.297483\pi\) | |||||||
\(150\) | −1.33656 | + | 1.10164i | −0.109130 | + | 0.0899486i | ||||
\(151\) | − | 22.7604i | − | 1.85221i | −0.377263 | − | 0.926106i | \(-0.623135\pi\) | ||
0.377263 | − | 0.926106i | \(-0.376865\pi\) | |||||||
\(152\) | −4.29047 | + | 0.769325i | −0.348003 | + | 0.0624005i | ||||
\(153\) | 3.11969 | + | 9.06373i | 0.252212 | + | 0.732759i | ||||
\(154\) | −4.62790 | + | 2.67192i | −0.372927 | + | 0.215309i | ||||
\(155\) | 3.82167 | + | 6.61932i | 0.306964 | + | 0.531677i | ||||
\(156\) | −2.27956 | + | 6.09587i | −0.182511 | + | 0.488060i | ||||
\(157\) | 4.01105 | + | 6.94734i | 0.320117 | + | 0.554458i | 0.980512 | − | 0.196460i | \(-0.0629446\pi\) |
−0.660395 | + | 0.750918i | \(0.729611\pi\) | |||||||
\(158\) | 2.26576 | + | 1.30814i | 0.180254 | + | 0.104070i | ||||
\(159\) | −3.38476 | − | 20.2339i | −0.268429 | − | 1.60465i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −1.49158 | − | 0.861163i | −0.117553 | − | 0.0678692i | ||||
\(162\) | −1.25044 | − | 8.91271i | −0.0982442 | − | 0.700249i | ||||
\(163\) | −3.70552 | −0.290239 | −0.145119 | − | 0.989414i | \(-0.546357\pi\) | ||||
−0.145119 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(164\) | −0.132924 | −0.0103796 | ||||||||
\(165\) | −4.91042 | − | 1.83626i | −0.382276 | − | 0.142953i | ||||
\(166\) | −4.04546 | + | 2.33564i | −0.313988 | + | 0.181281i | ||||
\(167\) | 0.0687715 | − | 0.119116i | 0.00532170 | − | 0.00921746i | −0.863352 | − | 0.504602i | \(-0.831639\pi\) |
0.868674 | + | 0.495384i | \(0.164973\pi\) | |||||||
\(168\) | −2.35972 | + | 1.94497i | −0.182057 | + | 0.150058i | ||||
\(169\) | 0.559332 | + | 0.968791i | 0.0430255 | + | 0.0745224i | ||||
\(170\) | 3.19520 | 0.245061 | ||||||||
\(171\) | 0.191961 | − | 13.0753i | 0.0146796 | − | 0.999892i | ||||
\(172\) | 9.84197 | 0.750443 | ||||||||
\(173\) | 1.62087 | + | 2.80743i | 0.123232 | + | 0.213445i | 0.921041 | − | 0.389467i | \(-0.127341\pi\) |
−0.797808 | + | 0.602911i | \(0.794007\pi\) | |||||||
\(174\) | 8.54661 | − | 7.04443i | 0.647917 | − | 0.534037i | ||||
\(175\) | −0.882761 | + | 1.52899i | −0.0667305 | + | 0.115581i | ||||
\(176\) | −2.62126 | + | 1.51339i | −0.197585 | + | 0.114076i | ||||
\(177\) | −12.4192 | − | 4.64418i | −0.933482 | − | 0.349078i | ||||
\(178\) | −8.72262 | −0.653788 | ||||||||
\(179\) | 18.0338 | 1.34791 | 0.673954 | − | 0.738773i | \(-0.264594\pi\) | ||||
0.673954 | + | 0.738773i | \(0.264594\pi\) | |||||||
\(180\) | −2.94481 | − | 0.572776i | −0.219493 | − | 0.0426922i | ||||
\(181\) | 9.17503 | + | 5.29721i | 0.681974 | + | 0.393738i | 0.800599 | − | 0.599201i | \(-0.204515\pi\) |
−0.118624 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(182\) | 6.63392i | 0.491739i | ||||||||
\(183\) | −0.571575 | − | 3.41684i | −0.0422521 | − | 0.252580i | ||||
\(184\) | −0.844837 | − | 0.487767i | −0.0622822 | − | 0.0359586i | ||||
\(185\) | 4.11174 | + | 7.12175i | 0.302301 | + | 0.523601i | ||||
\(186\) | −4.63701 | + | 12.4000i | −0.340002 | + | 0.909212i | ||||
\(187\) | 4.83557 | + | 8.37546i | 0.353612 | + | 0.612474i | ||||
\(188\) | 7.38774 | − | 4.26531i | 0.538806 | − | 0.311080i | ||||
\(189\) | −4.37598 | − | 8.06298i | −0.318306 | − | 0.586495i | ||||
\(190\) | −4.10032 | − | 1.47898i | −0.297468 | − | 0.107297i | ||||
\(191\) | 5.83776i | 0.422406i | 0.977442 | + | 0.211203i | \(0.0677380\pi\) | ||||
−0.977442 | + | 0.211203i | \(0.932262\pi\) | |||||||
\(192\) | −1.33656 | + | 1.10164i | −0.0964578 | + | 0.0795041i | ||||
\(193\) | 12.2299 | − | 7.06095i | 0.880329 | − | 0.508258i | 0.00956246 | − | 0.999954i | \(-0.496956\pi\) |
0.870767 | + | 0.491696i | \(0.163623\pi\) | |||||||
\(194\) | −12.4237 | − | 7.17285i | −0.891973 | − | 0.514981i | ||||
\(195\) | −5.02209 | + | 4.13939i | −0.359640 | + | 0.296428i | ||||
\(196\) | 1.94147 | − | 3.36272i | 0.138676 | − | 0.240194i | ||||
\(197\) | − | 0.287064i | − | 0.0204525i | −0.999948 | − | 0.0102262i | \(-0.996745\pi\) | ||
0.999948 | − | 0.0102262i | \(-0.00325517\pi\) | |||||||
\(198\) | −2.95525 | − | 8.58597i | −0.210020 | − | 0.610178i | ||||
\(199\) | 9.44058 | − | 16.3516i | 0.669225 | − | 1.15913i | −0.308896 | − | 0.951096i | \(-0.599960\pi\) |
0.978121 | − | 0.208036i | \(-0.0667071\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −1.28205 | + | 0.214463i | −0.0904287 | + | 0.0151271i | ||||
\(202\) | − | 15.9317i | − | 1.12095i | ||||||
\(203\) | 5.64481 | − | 9.77709i | 0.396188 | − | 0.686217i | ||||
\(204\) | 3.51996 | + | 4.27057i | 0.246446 | + | 0.299000i | ||||
\(205\) | −0.115116 | − | 0.0664620i | −0.00804002 | − | 0.00464191i | ||||
\(206\) | −5.40798 | + | 3.12230i | −0.376791 | + | 0.217541i | ||||
\(207\) | 1.92028 | − | 2.20851i | 0.133469 | − | 0.153502i | ||||
\(208\) | 3.75748i | 0.260534i | ||||||||
\(209\) | −2.32857 | − | 12.9863i | −0.161071 | − | 0.898281i | ||||
\(210\) | −3.01607 | + | 0.504532i | −0.208128 | + | 0.0348160i | ||||
\(211\) | −16.5023 | + | 9.52758i | −1.13606 | + | 0.655906i | −0.945453 | − | 0.325760i | \(-0.894380\pi\) |
−0.190610 | + | 0.981666i | \(0.561047\pi\) | |||||||
\(212\) | −5.92218 | − | 10.2575i | −0.406737 | − | 0.704489i | ||||
\(213\) | 26.4251 | + | 9.88171i | 1.81061 | + | 0.677083i | ||||
\(214\) | 1.25430 | + | 2.17252i | 0.0857423 | + | 0.148510i | ||||
\(215\) | 8.52339 | + | 4.92098i | 0.581291 | + | 0.335608i | ||||
\(216\) | −2.47858 | − | 4.56691i | −0.168646 | − | 0.310739i | ||||
\(217\) | 13.4945i | 0.916065i | ||||||||
\(218\) | −0.194529 | − | 0.112311i | −0.0131751 | − | 0.00760667i | ||||
\(219\) | −1.55072 | − | 0.579894i | −0.104788 | − | 0.0391856i | ||||
\(220\) | −3.02678 | −0.204065 | ||||||||
\(221\) | 12.0059 | 0.807604 | ||||||||
\(222\) | −4.98897 | + | 13.3412i | −0.334838 | + | 0.895402i | ||||
\(223\) | −1.45190 | + | 0.838252i | −0.0972261 | + | 0.0561335i | −0.547825 | − | 0.836593i | \(-0.684544\pi\) |
0.450599 | + | 0.892727i | \(0.351211\pi\) | |||||||
\(224\) | −0.882761 | + | 1.52899i | −0.0589820 | + | 0.102160i | ||||
\(225\) | −2.26390 | − | 1.96845i | −0.150926 | − | 0.131230i | ||||
\(226\) | 6.34499 | + | 10.9898i | 0.422063 | + | 0.731034i | ||||
\(227\) | 11.2504 | 0.746714 | 0.373357 | − | 0.927688i | \(-0.378207\pi\) | ||||
0.373357 | + | 0.927688i | \(0.378207\pi\) | |||||||
\(228\) | −2.54033 | − | 7.10962i | −0.168238 | − | 0.470846i | ||||
\(229\) | −22.6516 | −1.49686 | −0.748431 | − | 0.663213i | \(-0.769192\pi\) | ||||
−0.748431 | + | 0.663213i | \(0.769192\pi\) | |||||||
\(230\) | −0.487767 | − | 0.844837i | −0.0321624 | − | 0.0557069i | ||||
\(231\) | −5.88699 | − | 7.14235i | −0.387335 | − | 0.469932i | ||||
\(232\) | 3.19725 | − | 5.53779i | 0.209909 | − | 0.363574i | ||||
\(233\) | −9.24441 | + | 5.33726i | −0.605622 | + | 0.349656i | −0.771250 | − | 0.636532i | \(-0.780368\pi\) |
0.165628 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(234\) | −11.0651 | − | 2.15220i | −0.723347 | − | 0.140693i | ||||
\(235\) | 8.53062 | 0.556477 | ||||||||
\(236\) | −7.65515 | −0.498308 | ||||||||
\(237\) | −1.58722 | + | 4.24445i | −0.103101 | + | 0.275707i | ||||
\(238\) | 4.88542 | + | 2.82060i | 0.316674 | + | 0.182832i | ||||
\(239\) | − | 21.9874i | − | 1.42225i | −0.703066 | − | 0.711124i | \(-0.748186\pi\) | ||
0.703066 | − | 0.711124i | \(-0.251814\pi\) | |||||||
\(240\) | −1.70831 | + | 0.285770i | −0.110271 | + | 0.0184463i | ||||
\(241\) | 1.68423 | + | 0.972389i | 0.108491 | + | 0.0626371i | 0.553263 | − | 0.833006i | \(-0.313382\pi\) |
−0.444773 | + | 0.895643i | \(0.646716\pi\) | |||||||
\(242\) | 0.919316 | + | 1.59230i | 0.0590958 | + | 0.102357i | ||||
\(243\) | 14.8684 | − | 4.68313i | 0.953806 | − | 0.300423i | ||||
\(244\) | −1.00006 | − | 1.73216i | −0.0640225 | − | 0.110890i | ||||
\(245\) | 3.36272 | − | 1.94147i | 0.214836 | − | 0.124036i | ||||
\(246\) | −0.0379857 | − | 0.227076i | −0.00242188 | − | 0.0144778i | ||||
\(247\) | −15.4069 | − | 5.55724i | −0.980316 | − | 0.353599i | ||||
\(248\) | 7.64334i | 0.485352i | ||||||||
\(249\) | −5.14608 | − | 6.24345i | −0.326120 | − | 0.395663i | ||||
\(250\) | −0.866025 | + | 0.500000i | −0.0547723 | + | 0.0316228i | ||||
\(251\) | 23.4450 | + | 13.5360i | 1.47983 | + | 0.854383i | 0.999739 | − | 0.0228337i | \(-0.00726884\pi\) |
0.480095 | + | 0.877216i | \(0.340602\pi\) | |||||||
\(252\) | −3.99696 | − | 3.47533i | −0.251785 | − | 0.218925i | ||||
\(253\) | 1.47636 | − | 2.55713i | 0.0928180 | − | 0.160765i | ||||
\(254\) | 4.51362i | 0.283210i | ||||||||
\(255\) | 0.913090 | + | 5.45840i | 0.0571799 | + | 0.341818i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 12.4732 | − | 21.6042i | 0.778057 | − | 1.34764i | −0.155002 | − | 0.987914i | \(-0.549539\pi\) |
0.933060 | − | 0.359721i | \(-0.117128\pi\) | |||||||
\(258\) | 2.81253 | + | 16.8132i | 0.175101 | + | 1.04674i | ||||
\(259\) | 14.5187i | 0.902151i | ||||||||
\(260\) | −1.87874 | + | 3.25407i | −0.116515 | + | 0.201809i | ||||
\(261\) | 14.4765 | + | 12.5872i | 0.896070 | + | 0.779128i | ||||
\(262\) | −3.84003 | − | 2.21704i | −0.237238 | − | 0.136969i | ||||
\(263\) | 1.88439 | − | 1.08795i | 0.116196 | − | 0.0670860i | −0.440775 | − | 0.897617i | \(-0.645296\pi\) |
0.556972 | + | 0.830531i | \(0.311963\pi\) | |||||||
\(264\) | −3.33442 | − | 4.04546i | −0.205219 | − | 0.248981i | ||||
\(265\) | − | 11.8444i | − | 0.727593i | ||||||
\(266\) | −4.96375 | − | 5.88094i | −0.304347 | − | 0.360584i | ||||
\(267\) | −2.49266 | − | 14.9010i | −0.152548 | − | 0.911925i | ||||
\(268\) | −0.649931 | + | 0.375238i | −0.0397008 | + | 0.0229213i | ||||
\(269\) | 16.1461 | + | 27.9659i | 0.984447 | + | 1.70511i | 0.644368 | + | 0.764715i | \(0.277120\pi\) |
0.340079 | + | 0.940397i | \(0.389546\pi\) | |||||||
\(270\) | 0.136943 | − | 5.19435i | 0.00833409 | − | 0.316118i | ||||
\(271\) | 1.71811 | + | 2.97585i | 0.104368 | + | 0.180770i | 0.913480 | − | 0.406884i | \(-0.133385\pi\) |
−0.809112 | + | 0.587654i | \(0.800052\pi\) | |||||||
\(272\) | 2.76712 | + | 1.59760i | 0.167781 | + | 0.0968687i | ||||
\(273\) | −11.3328 | + | 1.89577i | −0.685893 | + | 0.114737i | ||||
\(274\) | − | 14.6857i | − | 0.887194i | ||||||
\(275\) | −2.62126 | − | 1.51339i | −0.158068 | − | 0.0912607i | ||||
\(276\) | 0.591830 | − | 1.58264i | 0.0356240 | − | 0.0952635i | ||||
\(277\) | 10.6992 | 0.642854 | 0.321427 | − | 0.946934i | \(-0.395838\pi\) | ||||
0.321427 | + | 0.946934i | \(0.395838\pi\) | |||||||
\(278\) | −18.8538 | −1.13078 | ||||||||
\(279\) | −22.5082 | − | 4.37792i | −1.34753 | − | 0.262099i | ||||
\(280\) | −1.52899 | + | 0.882761i | −0.0913744 | + | 0.0527551i | ||||
\(281\) | −5.77482 | + | 10.0023i | −0.344497 | + | 0.596687i | −0.985262 | − | 0.171050i | \(-0.945284\pi\) |
0.640765 | + | 0.767737i | \(0.278617\pi\) | |||||||
\(282\) | 9.39768 | + | 11.4017i | 0.559624 | + | 0.678960i | ||||
\(283\) | −1.20364 | − | 2.08476i | −0.0715488 | − | 0.123926i | 0.828031 | − | 0.560682i | \(-0.189461\pi\) |
−0.899580 | + | 0.436755i | \(0.856128\pi\) | |||||||
\(284\) | 16.2884 | 0.966536 | ||||||||
\(285\) | 1.35482 | − | 7.42728i | 0.0802524 | − | 0.439954i | ||||
\(286\) | −11.3731 | −0.672503 | ||||||||
\(287\) | −0.117340 | − | 0.203239i | −0.00692637 | − | 0.0119968i | ||||
\(288\) | −2.26390 | − | 1.96845i | −0.133401 | − | 0.115992i | ||||
\(289\) | −3.39535 | + | 5.88093i | −0.199727 | + | 0.345937i | ||||
\(290\) | 5.53779 | − | 3.19725i | 0.325190 | − | 0.187749i | ||||
\(291\) | 8.70315 | − | 23.2734i | 0.510188 | − | 1.36431i | ||||
\(292\) | −0.955858 | −0.0559374 | ||||||||
\(293\) | −12.2680 | −0.716707 | −0.358353 | − | 0.933586i | \(-0.616662\pi\) | ||||
−0.358353 | + | 0.933586i | \(0.616662\pi\) | |||||||
\(294\) | 6.29939 | + | 2.35567i | 0.367388 | + | 0.137385i | ||||
\(295\) | −6.62956 | − | 3.82758i | −0.385988 | − | 0.222850i | ||||
\(296\) | 8.22349i | 0.477980i | ||||||||
\(297\) | 13.8230 | − | 7.50210i | 0.802092 | − | 0.435316i | ||||
\(298\) | 2.37618 | + | 1.37189i | 0.137649 | + | 0.0794714i | ||||
\(299\) | −1.83277 | − | 3.17446i | −0.105992 | − | 0.183584i | ||||
\(300\) | −1.62233 | − | 0.606673i | −0.0936651 | − | 0.0350263i | ||||
\(301\) | 8.68810 | + | 15.0482i | 0.500774 | + | 0.867366i | ||||
\(302\) | 19.7111 | − | 11.3802i | 1.13424 | − | 0.654856i | ||||
\(303\) | 27.2163 | − | 4.55279i | 1.56354 | − | 0.261551i | ||||
\(304\) | −2.81149 | − | 3.33099i | −0.161250 | − | 0.191046i | ||||
\(305\) | − | 2.00013i | − | 0.114527i | ||||||
\(306\) | −6.28957 | + | 7.23359i | −0.359551 | + | 0.413517i | ||||
\(307\) | 18.5689 | − | 10.7208i | 1.05978 | − | 0.611866i | 0.134410 | − | 0.990926i | \(-0.457086\pi\) |
0.925372 | + | 0.379060i | \(0.123753\pi\) | |||||||
\(308\) | −4.62790 | − | 2.67192i | −0.263699 | − | 0.152247i | ||||
\(309\) | −6.87930 | − | 8.34626i | −0.391349 | − | 0.474802i | ||||
\(310\) | −3.82167 | + | 6.61932i | −0.217056 | + | 0.375952i | ||||
\(311\) | − | 2.40119i | − | 0.136159i | −0.997680 | − | 0.0680795i | \(-0.978313\pi\) | ||
0.997680 | − | 0.0680795i | \(-0.0216872\pi\) | |||||||
\(312\) | −6.41896 | + | 1.07377i | −0.363402 | + | 0.0607905i | ||||
\(313\) | 3.85122 | − | 6.67052i | 0.217684 | − | 0.377040i | −0.736415 | − | 0.676530i | \(-0.763483\pi\) |
0.954100 | + | 0.299490i | \(0.0968164\pi\) | |||||||
\(314\) | −4.01105 | + | 6.94734i | −0.226357 | + | 0.392061i | ||||
\(315\) | −1.72380 | − | 5.00821i | −0.0971251 | − | 0.282180i | ||||
\(316\) | 2.61627i | 0.147177i | ||||||||
\(317\) | −10.1993 | + | 17.6656i | −0.572848 | + | 0.992201i | 0.423424 | + | 0.905932i | \(0.360828\pi\) |
−0.996272 | + | 0.0862698i | \(0.972505\pi\) | |||||||
\(318\) | 15.8307 | − | 13.0482i | 0.887741 | − | 0.731709i | ||||
\(319\) | 16.7616 | + | 9.67734i | 0.938472 | + | 0.541827i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −3.35290 | + | 2.76358i | −0.187140 | + | 0.154248i | ||||
\(322\) | − | 1.72233i | − | 0.0959815i | ||||||
\(323\) | −10.6432 | + | 8.98327i | −0.592203 | + | 0.499842i | ||||
\(324\) | 7.09341 | − | 5.53927i | 0.394078 | − | 0.307737i | ||||
\(325\) | −3.25407 | + | 1.87874i | −0.180504 | + | 0.104214i | ||||
\(326\) | −1.85276 | − | 3.20908i | −0.102615 | − | 0.177734i | ||||
\(327\) | 0.136272 | − | 0.364411i | 0.00753588 | − | 0.0201520i | ||||
\(328\) | −0.0664620 | − | 0.115116i | −0.00366975 | − | 0.00635620i | ||||
\(329\) | 13.0432 | + | 7.53050i | 0.719096 | + | 0.415170i | ||||
\(330\) | −0.864960 | − | 5.17068i | −0.0476145 | − | 0.284637i | ||||
\(331\) | − | 25.4526i | − | 1.39900i | −0.714631 | − | 0.699502i | \(-0.753405\pi\) | ||
0.714631 | − | 0.699502i | \(-0.246595\pi\) | |||||||
\(332\) | −4.04546 | − | 2.33564i | −0.222023 | − | 0.128185i | ||||
\(333\) | −24.2166 | − | 4.71022i | −1.32706 | − | 0.258118i | ||||
\(334\) | 0.137543 | 0.00752602 | ||||||||
\(335\) | −0.750475 | −0.0410029 | ||||||||
\(336\) | −2.86426 | − | 1.07109i | −0.156258 | − | 0.0584330i | ||||
\(337\) | 14.8031 | − | 8.54657i | 0.806376 | − | 0.465561i | −0.0393200 | − | 0.999227i | \(-0.512519\pi\) |
0.845696 | + | 0.533665i | \(0.179186\pi\) | |||||||
\(338\) | −0.559332 | + | 0.968791i | −0.0304236 | + | 0.0526953i | ||||
\(339\) | −16.9609 | + | 13.9798i | −0.921190 | + | 0.759279i | ||||
\(340\) | 1.59760 | + | 2.76712i | 0.0866420 | + | 0.150068i | ||||
\(341\) | −23.1347 | −1.25281 | ||||||||
\(342\) | 11.4195 | − | 6.37140i | 0.617496 | − | 0.344526i | ||||
\(343\) | 19.2141 | 1.03746 | ||||||||
\(344\) | 4.92098 | + | 8.52339i | 0.265322 | + | 0.459551i | ||||
\(345\) | 1.30386 | − | 1.07469i | 0.0701973 | − | 0.0578592i | ||||
\(346\) | −1.62087 | + | 2.80743i | −0.0871384 | + | 0.150928i | ||||
\(347\) | −0.366418 | + | 0.211552i | −0.0196703 | + | 0.0113567i | −0.509803 | − | 0.860291i | \(-0.670282\pi\) |
0.490133 | + | 0.871648i | \(0.336948\pi\) | |||||||
\(348\) | 10.3740 | + | 3.87937i | 0.556103 | + | 0.207956i | ||||
\(349\) | −29.6588 | −1.58760 | −0.793799 | − | 0.608180i | \(-0.791900\pi\) | ||||
−0.793799 | + | 0.608180i | \(0.791900\pi\) | |||||||
\(350\) | −1.76552 | −0.0943711 | ||||||||
\(351\) | 0.514561 | − | 19.5177i | 0.0274652 | − | 1.04178i | ||||
\(352\) | −2.62126 | − | 1.51339i | −0.139714 | − | 0.0806638i | ||||
\(353\) | − | 29.5091i | − | 1.57061i | −0.619110 | − | 0.785304i | \(-0.712506\pi\) | ||
0.619110 | − | 0.785304i | \(-0.287494\pi\) | |||||||
\(354\) | −2.18761 | − | 13.0774i | −0.116270 | − | 0.695056i | ||||
\(355\) | 14.1061 | + | 8.14418i | 0.748676 | + | 0.432248i | ||||
\(356\) | −4.36131 | − | 7.55401i | −0.231149 | − | 0.400362i | ||||
\(357\) | −3.42236 | + | 9.15186i | −0.181130 | + | 0.484368i | ||||
\(358\) | 9.01690 | + | 15.6177i | 0.476558 | + | 0.825422i | ||||
\(359\) | −23.2838 | + | 13.4429i | −1.22887 | + | 0.709490i | −0.966794 | − | 0.255557i | \(-0.917741\pi\) |
−0.262079 | + | 0.965047i | \(0.584408\pi\) | |||||||
\(360\) | −0.976368 | − | 2.83667i | −0.0514591 | − | 0.149506i | ||||
\(361\) | 17.8163 | − | 6.60153i | 0.937699 | − | 0.347449i | ||||
\(362\) | 10.5944i | 0.556830i | ||||||||
\(363\) | −2.45744 | + | 2.02551i | −0.128982 | + | 0.106312i | ||||
\(364\) | −5.74514 | + | 3.31696i | −0.301127 | + | 0.173856i | ||||
\(365\) | −0.827798 | − | 0.477929i | −0.0433289 | − | 0.0250160i | ||||
\(366\) | 2.67328 | − | 2.20342i | 0.139735 | − | 0.115175i | ||||
\(367\) | −4.10312 | + | 7.10681i | −0.214181 | + | 0.370973i | −0.953019 | − | 0.302911i | \(-0.902042\pi\) |
0.738838 | + | 0.673883i | \(0.235375\pi\) | |||||||
\(368\) | − | 0.975534i | − | 0.0508532i | ||||||
\(369\) | 0.377062 | − | 0.129783i | 0.0196291 | − | 0.00675622i | ||||
\(370\) | −4.11174 | + | 7.12175i | −0.213759 | + | 0.370242i | ||||
\(371\) | 10.4557 | − | 18.1099i | 0.542835 | − | 0.940218i | ||||
\(372\) | −13.0572 | + | 2.18423i | −0.676985 | + | 0.113247i | ||||
\(373\) | − | 6.85659i | − | 0.355021i | −0.984119 | − | 0.177510i | \(-0.943196\pi\) | ||
0.984119 | − | 0.177510i | \(-0.0568043\pi\) | |||||||
\(374\) | −4.83557 | + | 8.37546i | −0.250042 | + | 0.433085i | ||||
\(375\) | −1.10164 | − | 1.33656i | −0.0568885 | − | 0.0690196i | ||||
\(376\) | 7.38774 | + | 4.26531i | 0.380993 | + | 0.219967i | ||||
\(377\) | 20.8081 | − | 12.0136i | 1.07167 | − | 0.618731i | ||||
\(378\) | 4.79475 | − | 7.82120i | 0.246615 | − | 0.402279i | ||||
\(379\) | − | 4.08608i | − | 0.209888i | −0.994478 | − | 0.104944i | \(-0.966534\pi\) | ||
0.994478 | − | 0.104944i | \(-0.0334663\pi\) | |||||||
\(380\) | −0.769325 | − | 4.29047i | −0.0394655 | − | 0.220097i | ||||
\(381\) | −7.71068 | + | 1.28986i | −0.395030 | + | 0.0660813i | ||||
\(382\) | −5.05565 | + | 2.91888i | −0.258670 | + | 0.149343i | ||||
\(383\) | −15.1709 | − | 26.2767i | −0.775196 | − | 1.34268i | −0.934684 | − | 0.355479i | \(-0.884318\pi\) |
0.159489 | − | 0.987200i | \(-0.449015\pi\) | |||||||
\(384\) | −1.62233 | − | 0.606673i | −0.0827891 | − | 0.0309592i | ||||
\(385\) | −2.67192 | − | 4.62790i | −0.136174 | − | 0.235860i | ||||
\(386\) | 12.2299 | + | 7.06095i | 0.622487 | + | 0.359393i | ||||
\(387\) | −27.9184 | + | 9.60938i | −1.41917 | + | 0.488472i | ||||
\(388\) | − | 14.3457i | − | 0.728292i | ||||||
\(389\) | 0.212061 | + | 0.122434i | 0.0107519 | + | 0.00620763i | 0.505366 | − | 0.862905i | \(-0.331357\pi\) |
−0.494614 | + | 0.869113i | \(0.664691\pi\) | |||||||
\(390\) | −6.09587 | − | 2.27956i | −0.308676 | − | 0.115430i | ||||
\(391\) | −3.11702 | −0.157635 | ||||||||
\(392\) | 3.88293 | 0.196118 | ||||||||
\(393\) | 2.69004 | − | 7.19353i | 0.135694 | − | 0.362866i | ||||
\(394\) | 0.248605 | − | 0.143532i | 0.0125245 | − | 0.00723103i | ||||
\(395\) | −1.30814 | + | 2.26576i | −0.0658195 | + | 0.114003i | ||||
\(396\) | 5.95804 | − | 6.85230i | 0.299403 | − | 0.344341i | ||||
\(397\) | 15.2157 | + | 26.3543i | 0.763652 | + | 1.32268i | 0.940957 | + | 0.338527i | \(0.109929\pi\) |
−0.177305 | + | 0.984156i | \(0.556738\pi\) | |||||||
\(398\) | 18.8812 | 0.946427 | ||||||||
\(399\) | 8.62801 | − | 10.1602i | 0.431941 | − | 0.508648i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −4.69167 | − | 8.12622i | −0.234291 | − | 0.405804i | 0.724775 | − | 0.688985i | \(-0.241944\pi\) |
−0.959066 | + | 0.283181i | \(0.908610\pi\) | |||||||
\(402\) | −0.826754 | − | 1.00305i | −0.0412347 | − | 0.0500278i | ||||
\(403\) | −14.3598 | + | 24.8720i | −0.715315 | + | 1.23896i | ||||
\(404\) | 13.7972 | − | 7.96584i | 0.686438 | − | 0.396315i | ||||
\(405\) | 8.91271 | − | 1.25044i | 0.442876 | − | 0.0621351i | ||||
\(406\) | 11.2896 | 0.560294 | ||||||||
\(407\) | −24.8906 | −1.23378 | ||||||||
\(408\) | −1.93844 | + | 5.18366i | −0.0959671 | + | 0.256629i | ||||
\(409\) | −2.29099 | − | 1.32271i | −0.113282 | − | 0.0654036i | 0.442288 | − | 0.896873i | \(-0.354167\pi\) |
−0.555571 | + | 0.831469i | \(0.687500\pi\) | |||||||
\(410\) | − | 0.132924i | − | 0.00656465i | ||||||
\(411\) | 25.0878 | − | 4.19672i | 1.23749 | − | 0.207009i | ||||
\(412\) | −5.40798 | − | 3.12230i | −0.266432 | − | 0.153824i | ||||
\(413\) | −6.75767 | − | 11.7046i | −0.332523 | − | 0.575947i | ||||
\(414\) | 2.87276 | + | 0.558762i | 0.141189 | + | 0.0274617i | ||||
\(415\) | −2.33564 | − | 4.04546i | −0.114652 | − | 0.198584i | ||||
\(416\) | −3.25407 | + | 1.87874i | −0.159544 | + | 0.0921128i | ||||
\(417\) | −5.38784 | − | 32.2082i | −0.263844 | − | 1.57724i | ||||
\(418\) | 10.0822 | − | 8.50975i | 0.493135 | − | 0.416225i | ||||
\(419\) | 17.5775i | 0.858719i | 0.903134 | + | 0.429359i | \(0.141261\pi\) | ||||
−0.903134 | + | 0.429359i | \(0.858739\pi\) | |||||||
\(420\) | −1.94497 | − | 2.35972i | −0.0949049 | − | 0.115143i | ||||
\(421\) | 17.0375 | − | 9.83661i | 0.830357 | − | 0.479407i | −0.0236179 | − | 0.999721i | \(-0.507519\pi\) |
0.853975 | + | 0.520314i | \(0.174185\pi\) | |||||||
\(422\) | −16.5023 | − | 9.52758i | −0.803317 | − | 0.463796i | ||||
\(423\) | −16.7921 | + | 19.3124i | −0.816458 | + | 0.939003i | ||||
\(424\) | 5.92218 | − | 10.2575i | 0.287607 | − | 0.498149i | ||||
\(425\) | 3.19520i | 0.154990i | ||||||||
\(426\) | 4.65472 | + | 27.8256i | 0.225522 | + | 1.34816i | ||||
\(427\) | 1.76563 | − | 3.05817i | 0.0854450 | − | 0.147995i | ||||
\(428\) | −1.25430 | + | 2.17252i | −0.0606290 | + | 0.105012i | ||||
\(429\) | −3.25007 | − | 19.4287i | −0.156915 | − | 0.938028i | ||||
\(430\) | 9.84197i | 0.474622i | ||||||||
\(431\) | 4.39080 | − | 7.60508i | 0.211497 | − | 0.366324i | −0.740686 | − | 0.671851i | \(-0.765499\pi\) |
0.952183 | + | 0.305527i | \(0.0988327\pi\) | |||||||
\(432\) | 2.71577 | − | 4.42997i | 0.130663 | − | 0.213137i | ||||
\(433\) | 22.6952 | + | 13.1031i | 1.09066 | + | 0.629693i | 0.933752 | − | 0.357920i | \(-0.116514\pi\) |
0.156908 | + | 0.987613i | \(0.449847\pi\) | |||||||
\(434\) | −11.6866 | + | 6.74724i | −0.560973 | + | 0.323878i | ||||
\(435\) | 7.04443 | + | 8.54661i | 0.337755 | + | 0.409779i | ||||
\(436\) | − | 0.224622i | − | 0.0107575i | ||||||
\(437\) | 4.00000 | + | 1.44280i | 0.191346 | + | 0.0690183i | ||||
\(438\) | −0.273155 | − | 1.63291i | −0.0130519 | − | 0.0780233i | ||||
\(439\) | −23.3862 | + | 13.5020i | −1.11616 | + | 0.644417i | −0.940419 | − | 0.340018i | \(-0.889567\pi\) |
−0.175745 | + | 0.984436i | \(0.556233\pi\) | |||||||
\(440\) | −1.51339 | − | 2.62126i | −0.0721479 | − | 0.124964i | ||||
\(441\) | −2.22405 | + | 11.4345i | −0.105907 | + | 0.544501i | ||||
\(442\) | 6.00295 | + | 10.3974i | 0.285531 | + | 0.494554i | ||||
\(443\) | −12.9795 | − | 7.49371i | −0.616674 | − | 0.356037i | 0.158899 | − | 0.987295i | \(-0.449206\pi\) |
−0.775573 | + | 0.631258i | \(0.782539\pi\) | |||||||
\(444\) | −14.0483 | + | 2.35002i | −0.666703 | + | 0.111527i | ||||
\(445\) | − | 8.72262i | − | 0.413492i | ||||||
\(446\) | −1.45190 | − | 0.838252i | −0.0687492 | − | 0.0396924i | ||||
\(447\) | −1.66458 | + | 4.45131i | −0.0787318 | + | 0.210540i | ||||
\(448\) | −1.76552 | −0.0834131 | ||||||||
\(449\) | 1.07127 | 0.0505565 | 0.0252782 | − | 0.999680i | \(-0.491953\pi\) | ||||
0.0252782 | + | 0.999680i | \(0.491953\pi\) | |||||||
\(450\) | 0.572776 | − | 2.94481i | 0.0270009 | − | 0.138820i | ||||
\(451\) | 0.348429 | − | 0.201166i | 0.0164069 | − | 0.00947252i | ||||
\(452\) | −6.34499 | + | 10.9898i | −0.298443 | + | 0.516919i | ||||
\(453\) | 25.0737 | + | 30.4206i | 1.17807 | + | 1.42928i | ||||
\(454\) | 5.62519 | + | 9.74312i | 0.264003 | + | 0.457267i | ||||
\(455\) | −6.63392 | −0.311003 | ||||||||
\(456\) | 4.88694 | − | 5.75480i | 0.228852 | − | 0.269493i | ||||
\(457\) | −7.60858 | −0.355914 | −0.177957 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177957 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(458\) | −11.3258 | − | 19.6169i | −0.529220 | − | 0.916637i | ||||
\(459\) | −14.1546 | − | 8.67742i | −0.660681 | − | 0.405027i | ||||
\(460\) | 0.487767 | − | 0.844837i | 0.0227422 | − | 0.0393907i | ||||
\(461\) | −2.94051 | + | 1.69770i | −0.136953 | + | 0.0790699i | −0.566911 | − | 0.823779i | \(-0.691862\pi\) |
0.429958 | + | 0.902849i | \(0.358528\pi\) | |||||||
\(462\) | 3.24196 | − | 8.66946i | 0.150830 | − | 0.403340i | ||||
\(463\) | −14.1271 | −0.656543 | −0.328271 | − | 0.944583i | \(-0.606466\pi\) | ||||
−0.328271 | + | 0.944583i | \(0.606466\pi\) | |||||||
\(464\) | 6.39449 | 0.296857 | ||||||||
\(465\) | −12.4000 | − | 4.63701i | −0.575036 | − | 0.215036i | ||||
\(466\) | −9.24441 | − | 5.33726i | −0.428239 | − | 0.247244i | ||||
\(467\) | 11.4238i | 0.528631i | 0.964436 | + | 0.264315i | \(0.0851460\pi\) | ||||
−0.964436 | + | 0.264315i | \(0.914854\pi\) | |||||||
\(468\) | −3.66869 | − | 10.6587i | −0.169585 | − | 0.492700i | ||||
\(469\) | −1.14747 | − | 0.662490i | −0.0529851 | − | 0.0305910i | ||||
\(470\) | 4.26531 | + | 7.38774i | 0.196744 | + | 0.340771i | ||||
\(471\) | −13.0145 | − | 4.86679i | −0.599675 | − | 0.224250i | ||||
\(472\) | −3.82758 | − | 6.62956i | −0.176178 | − | 0.305150i | ||||
\(473\) | −25.7984 | + | 14.8947i | −1.18621 | + | 0.684860i | ||||
\(474\) | −4.46941 | + | 0.747651i | −0.205287 | + | 0.0343407i | ||||
\(475\) | 1.47898 | − | 4.10032i | 0.0678603 | − | 0.188136i | ||||
\(476\) | 5.64119i | 0.258564i | ||||||||
\(477\) | 26.8144 | + | 23.3150i | 1.22775 | + | 1.06752i | ||||
\(478\) | 19.0417 | − | 10.9937i | 0.870946 | − | 0.502841i | ||||
\(479\) | 31.4439 | + | 18.1542i | 1.43671 | + | 0.829485i | 0.997620 | − | 0.0689574i | \(-0.0219673\pi\) |
0.439091 | + | 0.898443i | \(0.355301\pi\) | |||||||
\(480\) | −1.10164 | − | 1.33656i | −0.0502828 | − | 0.0610053i | ||||
\(481\) | −15.4498 | + | 26.7598i | −0.704450 | + | 1.22014i | ||||
\(482\) | 1.94478i | 0.0885822i | ||||||||
\(483\) | 2.94227 | − | 0.492188i | 0.133878 | − | 0.0223954i | ||||
\(484\) | −0.919316 | + | 1.59230i | −0.0417871 | + | 0.0723773i | ||||
\(485\) | 7.17285 | − | 12.4237i | 0.325702 | − | 0.564133i | ||||
\(486\) | 11.4899 | + | 10.5348i | 0.521192 | + | 0.477869i | ||||
\(487\) | − | 9.01284i | − | 0.408411i | −0.978928 | − | 0.204205i | \(-0.934539\pi\) | ||
0.978928 | − | 0.204205i | \(-0.0654610\pi\) | |||||||
\(488\) | 1.00006 | − | 1.73216i | 0.0452707 | − | 0.0784112i | ||||
\(489\) | 4.95265 | − | 4.08215i | 0.223966 | − | 0.184601i | ||||
\(490\) | 3.36272 | + | 1.94147i | 0.151912 | + | 0.0877065i | ||||
\(491\) | −19.3513 | + | 11.1725i | −0.873313 | + | 0.504208i | −0.868448 | − | 0.495780i | \(-0.834882\pi\) |
−0.00486554 | + | 0.999988i | \(0.501549\pi\) | |||||||
\(492\) | 0.177661 | − | 0.146435i | 0.00800957 | − | 0.00660178i | ||||
\(493\) | − | 20.4317i | − | 0.920196i | ||||||
\(494\) | −2.89072 | − | 16.1214i | −0.130060 | − | 0.725334i | ||||
\(495\) | 8.58597 | − | 2.95525i | 0.385911 | − | 0.132828i | ||||
\(496\) | −6.61932 | + | 3.82167i | −0.297216 | + | 0.171598i | ||||
\(497\) | 14.3787 | + | 24.9047i | 0.644974 | + | 1.11713i | ||||
\(498\) | 2.83395 | − | 7.57836i | 0.126992 | − | 0.339595i | ||||
\(499\) | 19.8988 | + | 34.4658i | 0.890795 | + | 1.54290i | 0.838925 | + | 0.544248i | \(0.183185\pi\) |
0.0518700 | + | 0.998654i | \(0.483482\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | 0.0393056 | + | 0.234967i | 0.00175605 | + | 0.0104975i | ||||
\(502\) | 27.0719i | 1.20828i | ||||||||
\(503\) | −29.8559 | − | 17.2373i | −1.33121 | − | 0.768575i | −0.345726 | − | 0.938336i | \(-0.612367\pi\) |
−0.985485 | + | 0.169761i | \(0.945701\pi\) | |||||||
\(504\) | 1.01125 | − | 5.19913i | 0.0450446 | − | 0.231588i | ||||
\(505\) | 15.9317 | 0.708950 | ||||||||
\(506\) | 2.95272 | 0.131264 | ||||||||
\(507\) | −1.81484 | − | 0.678663i | −0.0805999 | − | 0.0301405i | ||||
\(508\) | −3.90891 | + | 2.25681i | −0.173430 | + | 0.100130i | ||||
\(509\) | 18.5767 | − | 32.1758i | 0.823398 | − | 1.42617i | −0.0797396 | − | 0.996816i | \(-0.525409\pi\) |
0.903138 | − | 0.429351i | \(-0.141258\pi\) | |||||||
\(510\) | −4.27057 | + | 3.51996i | −0.189104 | + | 0.155866i | ||||
\(511\) | −0.843794 | − | 1.46149i | −0.0373273 | − | 0.0646527i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.1477 | + | 17.6874i | 0.624636 | + | 0.780916i | ||||
\(514\) | 24.9464 | 1.10034 | ||||||||
\(515\) | −3.12230 | − | 5.40798i | −0.137585 | − | 0.238304i | ||||
\(516\) | −13.1544 | + | 10.8423i | −0.579088 | + | 0.477306i | ||||
\(517\) | −12.9101 | + | 22.3610i | −0.567787 | + | 0.983437i | ||||
\(518\) | −12.5736 | + | 7.25937i | −0.552452 | + | 0.318959i | ||||
\(519\) | −5.25916 | − | 1.96667i | −0.230851 | − | 0.0863274i | ||||
\(520\) | −3.75748 | −0.164776 | ||||||||
\(521\) | 18.7548 | 0.821664 | 0.410832 | − | 0.911711i | \(-0.365238\pi\) | ||||
0.410832 | + | 0.911711i | \(0.365238\pi\) | |||||||
\(522\) | −3.66261 | + | 18.8306i | −0.160308 | + | 0.824192i | ||||
\(523\) | −11.5841 | − | 6.68808i | −0.506537 | − | 0.292449i | 0.224872 | − | 0.974388i | \(-0.427804\pi\) |
−0.731409 | + | 0.681939i | \(0.761137\pi\) | |||||||
\(524\) | − | 4.43408i | − | 0.193704i | ||||||
\(525\) | −0.504532 | − | 3.01607i | −0.0220196 | − | 0.131632i | ||||
\(526\) | 1.88439 | + | 1.08795i | 0.0821633 | + | 0.0474370i | ||||
\(527\) | 12.2110 | + | 21.1500i | 0.531919 | + | 0.921310i | ||||
\(528\) | 1.83626 | − | 4.91042i | 0.0799131 | − | 0.213699i | ||||
\(529\) | −11.0242 | − | 19.0944i | −0.479312 | − | 0.830192i | ||||
\(530\) | 10.2575 | − | 5.92218i | 0.445558 | − | 0.257243i | ||||
\(531\) | 21.7152 | − | 7.47425i | 0.942357 | − | 0.324355i | ||||
\(532\) | 2.61117 | − | 7.23920i | 0.113209 | − | 0.313859i | ||||
\(533\) | − | 0.499460i | − | 0.0216340i | ||||||
\(534\) | 11.6583 | − | 9.60920i | 0.504504 | − | 0.415831i | ||||
\(535\) | −2.17252 | + | 1.25430i | −0.0939260 | + | 0.0542282i | ||||
\(536\) | −0.649931 | − | 0.375238i | −0.0280727 | − | 0.0162078i | ||||
\(537\) | −24.1032 | + | 19.8668i | −1.04013 | + | 0.857314i | ||||
\(538\) | −16.1461 | + | 27.9659i | −0.696109 | + | 1.20570i | ||||
\(539\) | 11.7528i | 0.506227i | ||||||||
\(540\) | 4.56691 | − | 2.47858i | 0.196528 | − | 0.106661i | ||||
\(541\) | −12.9791 | + | 22.4805i | −0.558017 | + | 0.966513i | 0.439645 | + | 0.898171i | \(0.355104\pi\) |
−0.997662 | + | 0.0683416i | \(0.978229\pi\) | |||||||
\(542\) | −1.71811 | + | 2.97585i | −0.0737990 | + | 0.127824i | ||||
\(543\) | −18.0986 | + | 3.02756i | −0.776684 | + | 0.129925i | ||||
\(544\) | 3.19520i | 0.136993i | ||||||||
\(545\) | 0.112311 | − | 0.194529i | 0.00481088 | − | 0.00833269i | ||||
\(546\) | −7.30819 | − | 8.86661i | −0.312762 | − | 0.379456i | ||||
\(547\) | −21.9902 | − | 12.6960i | −0.940232 | − | 0.542843i | −0.0501992 | − | 0.998739i | \(-0.515986\pi\) |
−0.890033 | + | 0.455896i | \(0.849319\pi\) | |||||||
\(548\) | 12.7182 | − | 7.34284i | 0.543293 | − | 0.313671i | ||||
\(549\) | 4.52808 | + | 3.93714i | 0.193254 | + | 0.168033i | ||||
\(550\) | − | 3.02678i | − | 0.129062i | ||||||
\(551\) | −9.45733 | + | 26.2194i | −0.402896 | + | 1.11699i | ||||
\(552\) | 1.66652 | − | 0.278778i | 0.0709317 | − | 0.0118656i | ||||
\(553\) | −4.00025 | + | 2.30954i | −0.170108 | + | 0.0982118i | ||||
\(554\) | 5.34961 | + | 9.26579i | 0.227283 | + | 0.393666i | ||||
\(555\) | −13.3412 | − | 4.98897i | −0.566302 | − | 0.211770i | ||||
\(556\) | −9.42690 | − | 16.3279i | −0.399790 | − | 0.692456i | ||||
\(557\) | −29.9344 | − | 17.2826i | −1.26836 | − | 0.732288i | −0.293683 | − | 0.955903i | \(-0.594881\pi\) |
−0.974678 | + | 0.223615i | \(0.928214\pi\) | |||||||
\(558\) | −7.46271 | − | 21.6816i | −0.315922 | − | 0.917857i | ||||
\(559\) | 36.9810i | 1.56413i | ||||||||
\(560\) | −1.52899 | − | 0.882761i | −0.0646115 | − | 0.0373035i | ||||
\(561\) | −15.6898 | − | 5.86722i | −0.662423 | − | 0.247714i | ||||
\(562\) | −11.5496 | −0.487193 | ||||||||
\(563\) | 37.7990 | 1.59304 | 0.796520 | − | 0.604612i | \(-0.206672\pi\) | ||||
0.796520 | + | 0.604612i | \(0.206672\pi\) | |||||||
\(564\) | −5.17530 | + | 13.8395i | −0.217919 | + | 0.582747i | ||||
\(565\) | −10.9898 | + | 6.34499i | −0.462346 | + | 0.266936i | ||||
\(566\) | 1.20364 | − | 2.08476i | 0.0505926 | − | 0.0876290i | ||||
\(567\) | 14.7313 | + | 5.95588i | 0.618655 | + | 0.250123i | ||||
\(568\) | 8.14418 | + | 14.1061i | 0.341722 | + | 0.591880i | ||||
\(569\) | −36.6704 | −1.53730 | −0.768652 | − | 0.639667i | \(-0.779072\pi\) | ||||
−0.768652 | + | 0.639667i | \(0.779072\pi\) | |||||||
\(570\) | 7.10962 | − | 2.54033i | 0.297789 | − | 0.106403i | ||||
\(571\) | 29.7545 | 1.24519 | 0.622593 | − | 0.782546i | \(-0.286079\pi\) | ||||
0.622593 | + | 0.782546i | \(0.286079\pi\) | |||||||
\(572\) | −5.68653 | − | 9.84935i | −0.237766 | − | 0.411822i | ||||
\(573\) | −6.43111 | − | 7.80251i | −0.268664 | − | 0.325954i | ||||
\(574\) | 0.117340 | − | 0.203239i | 0.00489768 | − | 0.00848304i | ||||
\(575\) | 0.844837 | − | 0.487767i | 0.0352321 | − | 0.0203413i | ||||
\(576\) | 0.572776 | − | 2.94481i | 0.0238657 | − | 0.122701i | ||||
\(577\) | −16.0955 | −0.670064 | −0.335032 | − | 0.942207i | \(-0.608747\pi\) | ||||
−0.335032 | + | 0.942207i | \(0.608747\pi\) | |||||||
\(578\) | −6.79071 | −0.282456 | ||||||||
\(579\) | −8.56738 | + | 22.9104i | −0.356048 | + | 0.952122i | ||||
\(580\) | 5.53779 | + | 3.19725i | 0.229944 | + | 0.132758i | ||||
\(581\) | − | 8.24726i | − | 0.342154i | ||||||
\(582\) | 24.5070 | − | 4.09956i | 1.01585 | − | 0.169932i | ||||
\(583\) | 31.0472 | + | 17.9251i | 1.28584 | + | 0.742382i | ||||
\(584\) | −0.477929 | − | 0.827798i | −0.0197769 | − | 0.0342545i | ||||
\(585\) | 2.15220 | − | 11.0651i | 0.0889823 | − | 0.457485i | ||||
\(586\) | −6.13402 | − | 10.6244i | −0.253394 | − | 0.438891i | ||||
\(587\) | −11.3554 | + | 6.55606i | −0.468688 | + | 0.270597i | −0.715691 | − | 0.698418i | \(-0.753888\pi\) |
0.247002 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(588\) | 1.10962 | + | 6.63327i | 0.0457601 | + | 0.273551i | ||||
\(589\) | −5.88021 | − | 32.7935i | −0.242290 | − | 1.35123i | ||||
\(590\) | − | 7.65515i | − | 0.315158i | ||||||
\(591\) | 0.316241 | + | 0.383678i | 0.0130084 | + | 0.0157824i | ||||
\(592\) | −7.12175 | + | 4.11174i | −0.292702 | + | 0.168992i | ||||
\(593\) | −21.2078 | − | 12.2443i | −0.870900 | − | 0.502814i | −0.00325292 | − | 0.999995i | \(-0.501035\pi\) |
−0.867647 | + | 0.497180i | \(0.834369\pi\) | |||||||
\(594\) | 13.4085 | + | 8.22003i | 0.550158 | + | 0.337272i | ||||
\(595\) | −2.82060 | + | 4.88542i | −0.115633 | + | 0.200283i | ||||
\(596\) | 2.74378i | 0.112390i | ||||||||
\(597\) | 5.39566 | + | 32.2549i | 0.220830 | + | 1.32011i | ||||
\(598\) | 1.83277 | − | 3.17446i | 0.0749477 | − | 0.129813i | ||||
\(599\) | −6.98997 | + | 12.1070i | −0.285603 | + | 0.494678i | −0.972755 | − | 0.231835i | \(-0.925527\pi\) |
0.687153 | + | 0.726513i | \(0.258860\pi\) | |||||||
\(600\) | −0.285770 | − | 1.70831i | −0.0116665 | − | 0.0697416i | ||||
\(601\) | 41.6645i | 1.69953i | 0.527161 | + | 0.849766i | \(0.323257\pi\) | ||||
−0.527161 | + | 0.849766i | \(0.676743\pi\) | |||||||
\(602\) | −8.68810 | + | 15.0482i | −0.354101 | + | 0.613320i | ||||
\(603\) | 1.47727 | − | 1.69900i | 0.0601591 | − | 0.0691885i | ||||
\(604\) | 19.7111 | + | 11.3802i | 0.802032 | + | 0.463053i | ||||
\(605\) | −1.59230 | + | 0.919316i | −0.0647362 | + | 0.0373755i | ||||
\(606\) | 17.5510 | + | 21.2936i | 0.712960 | + | 0.864994i | ||||
\(607\) | 31.5810i | 1.28183i | 0.767610 | + | 0.640917i | \(0.221446\pi\) | ||||
−0.767610 | + | 0.640917i | \(0.778554\pi\) | |||||||
\(608\) | 1.47898 | − | 4.10032i | 0.0599806 | − | 0.166290i | ||||
\(609\) | 3.22623 | + | 19.2862i | 0.130733 | + | 0.781516i | ||||
\(610\) | 1.73216 | − | 1.00006i | 0.0701331 | − | 0.0404914i | ||||
\(611\) | 16.0268 | + | 27.7593i | 0.648376 | + | 1.12302i | ||||
\(612\) | −9.40926 | − | 1.83013i | −0.380347 | − | 0.0739787i | ||||
\(613\) | 0.700918 | + | 1.21403i | 0.0283098 | + | 0.0490340i | 0.879833 | − | 0.475283i | \(-0.157654\pi\) |
−0.851523 | + | 0.524317i | \(0.824321\pi\) | |||||||
\(614\) | 18.5689 | + | 10.7208i | 0.749379 | + | 0.432654i | ||||
\(615\) | 0.227076 | − | 0.0379857i | 0.00915659 | − | 0.00153173i | ||||
\(616\) | − | 5.34384i | − | 0.215309i | ||||||
\(617\) | −9.13701 | − | 5.27526i | −0.367842 | − | 0.212374i | 0.304673 | − | 0.952457i | \(-0.401453\pi\) |
−0.672515 | + | 0.740083i | \(0.734786\pi\) | |||||||
\(618\) | 3.78843 | − | 10.1308i | 0.152393 | − | 0.407520i | ||||
\(619\) | −4.98387 | −0.200318 | −0.100159 | − | 0.994971i | \(-0.531935\pi\) | ||||
−0.100159 | + | 0.994971i | \(0.531935\pi\) | |||||||
\(620\) | −7.64334 | −0.306964 | ||||||||
\(621\) | −0.133593 | + | 5.06726i | −0.00536088 | + | 0.203342i | ||||
\(622\) | 2.07949 | − | 1.20060i | 0.0833801 | − | 0.0481395i | ||||
\(623\) | 7.69999 | − | 13.3368i | 0.308494 | − | 0.534327i | ||||
\(624\) | −4.13939 | − | 5.02209i | −0.165708 | − | 0.201045i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7.70245 | 0.307852 | ||||||||
\(627\) | 17.4185 | + | 14.7917i | 0.695628 | + | 0.590723i | ||||
\(628\) | −8.02210 | −0.320117 | ||||||||
\(629\) | 13.1378 | + | 22.7554i | 0.523840 | + | 0.907317i | ||||
\(630\) | 3.47533 | − | 3.99696i | 0.138461 | − | 0.159243i | ||||
\(631\) | −4.99217 | + | 8.64668i | −0.198735 | + | 0.344219i | −0.948119 | − | 0.317917i | \(-0.897017\pi\) |
0.749384 | + | 0.662136i | \(0.230350\pi\) | |||||||
\(632\) | −2.26576 | + | 1.30814i | −0.0901270 | + | 0.0520349i | ||||
\(633\) | 11.5603 | − | 30.9137i | 0.459479 | − | 1.22871i | ||||
\(634\) | −20.3985 | −0.810129 | ||||||||
\(635\) | −4.51362 | −0.179118 | ||||||||
\(636\) | 19.2154 | + | 7.18566i | 0.761942 | + | 0.284930i | ||||
\(637\) | 12.6353 | + | 7.29502i | 0.500631 | + | 0.289039i | ||||
\(638\) | 19.3547i | 0.766259i | ||||||||
\(639\) | −46.2047 | + | 15.9034i | −1.82783 | + | 0.629130i | ||||
\(640\) | −0.866025 | − | 0.500000i | −0.0342327 | − | 0.0197642i | ||||
\(641\) | −11.0764 | − | 19.1848i | −0.437490 | − | 0.757755i | 0.560005 | − | 0.828489i | \(-0.310799\pi\) |
−0.997495 | + | 0.0707341i | \(0.977466\pi\) | |||||||
\(642\) | −4.06978 | − | 1.52190i | −0.160621 | − | 0.0600647i | ||||
\(643\) | −24.4476 | − | 42.3446i | −0.964121 | − | 1.66991i | −0.711958 | − | 0.702222i | \(-0.752191\pi\) |
−0.252163 | − | 0.967685i | \(-0.581142\pi\) | |||||||
\(644\) | 1.49158 | − | 0.861163i | 0.0587764 | − | 0.0339346i | ||||
\(645\) | −16.8132 | + | 2.81253i | −0.662018 | + | 0.110743i | ||||
\(646\) | −13.1013 | − | 4.72564i | −0.515465 | − | 0.185928i | ||||
\(647\) | 2.69718i | 0.106037i | 0.998594 | + | 0.0530185i | \(0.0168842\pi\) | ||||
−0.998594 | + | 0.0530185i | \(0.983116\pi\) | |||||||
\(648\) | 8.34386 | + | 3.37344i | 0.327778 | + | 0.132521i | ||||
\(649\) | 20.0662 | − | 11.5852i | 0.787666 | − | 0.454759i | ||||
\(650\) | −3.25407 | − | 1.87874i | −0.127635 | − | 0.0736903i | ||||
\(651\) | −14.8661 | − | 18.0362i | −0.582647 | − | 0.706893i | ||||
\(652\) | 1.85276 | − | 3.20908i | 0.0725597 | − | 0.125677i | ||||
\(653\) | − | 0.588679i | − | 0.0230368i | −0.999934 | − | 0.0115184i | \(-0.996334\pi\) | ||
0.999934 | − | 0.0115184i | \(-0.00366650\pi\) | |||||||
\(654\) | 0.383725 | − | 0.0641902i | 0.0150049 | − | 0.00251004i | ||||
\(655\) | 2.21704 | − | 3.84003i | 0.0866269 | − | 0.150042i | ||||
\(656\) | 0.0664620 | − | 0.115116i | 0.00259491 | − | 0.00449451i | ||||
\(657\) | 2.71146 | − | 0.933270i | 0.105784 | − | 0.0364103i | ||||
\(658\) | 15.0610i | 0.587139i | ||||||||
\(659\) | 11.1918 | − | 19.3847i | 0.435970 | − | 0.755121i | −0.561405 | − | 0.827541i | \(-0.689739\pi\) |
0.997374 | + | 0.0724200i | \(0.0230722\pi\) | |||||||
\(660\) | 4.04546 | − | 3.33442i | 0.157469 | − | 0.129792i | ||||
\(661\) | 12.9940 | + | 7.50211i | 0.505409 | + | 0.291798i | 0.730945 | − | 0.682437i | \(-0.239080\pi\) |
−0.225535 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(662\) | 22.0426 | − | 12.7263i | 0.856711 | − | 0.494622i | ||||
\(663\) | −16.0466 | + | 13.2262i | −0.623198 | + | 0.513662i | ||||
\(664\) | − | 4.67129i | − | 0.181281i | ||||||
\(665\) | 5.88094 | − | 4.96375i | 0.228053 | − | 0.192486i | ||||
\(666\) | −8.02915 | − | 23.3273i | −0.311123 | − | 0.903916i | ||||
\(667\) | −5.40230 | + | 3.11902i | −0.209178 | + | 0.120769i | ||||
\(668\) | 0.0687715 | + | 0.119116i | 0.00266085 | + | 0.00460873i | ||||
\(669\) | 1.01709 | − | 2.71984i | 0.0393230 | − | 0.105155i | ||||
\(670\) | −0.375238 | − | 0.649931i | −0.0144967 | − | 0.0251090i | ||||
\(671\) | 5.24286 | + | 3.02697i | 0.202398 | + | 0.116855i | ||||
\(672\) | −0.504532 | − | 3.01607i | −0.0194628 | − | 0.116347i | ||||
\(673\) | 13.1927i | 0.508543i | 0.967133 | + | 0.254271i | \(0.0818356\pi\) | ||||
−0.967133 | + | 0.254271i | \(0.918164\pi\) | |||||||
\(674\) | 14.8031 | + | 8.54657i | 0.570194 | + | 0.329202i | ||||
\(675\) | 5.19435 | + | 0.136943i | 0.199931 | + | 0.00527094i | ||||
\(676\) | −1.11866 | −0.0430255 | ||||||||
\(677\) | 15.1704 | 0.583047 | 0.291523 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291523 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(678\) | −20.5873 | − | 7.69867i | −0.790651 | − | 0.295666i | ||||
\(679\) | 21.9344 | − | 12.6638i | 0.841764 | − | 0.485993i | ||||
\(680\) | −1.59760 | + | 2.76712i | −0.0612651 | + | 0.106114i | ||||
\(681\) | −15.0368 | + | 12.3939i | −0.576211 | + | 0.474934i | ||||
\(682\) | −11.5673 | − | 20.0352i | −0.442936 | − | 0.767188i | ||||
\(683\) | 26.8136 | 1.02599 | 0.512997 | − | 0.858390i | \(-0.328535\pi\) | ||||
0.512997 | + | 0.858390i | \(0.328535\pi\) | |||||||
\(684\) | 11.2276 | + | 6.70389i | 0.429296 | + | 0.256330i | ||||
\(685\) | 14.6857 | 0.561111 | ||||||||
\(686\) | 9.60703 | + | 16.6399i | 0.366798 | + | 0.635313i | ||||
\(687\) | 30.2752 | − | 24.9539i | 1.15507 | − | 0.952052i | ||||
\(688\) | −4.92098 | + | 8.52339i | −0.187611 | + | 0.324951i | ||||
\(689\) | 38.5424 | − | 22.2525i | 1.46835 | − | 0.847752i | ||||
\(690\) | 1.58264 | + | 0.591830i | 0.0602499 | + | 0.0225306i | ||||
\(691\) | −18.3997 | −0.699959 | −0.349980 | − | 0.936757i | \(-0.613811\pi\) | ||||
−0.349980 | + | 0.936757i | \(0.613811\pi\) | |||||||
\(692\) | −3.24174 | −0.123232 | ||||||||
\(693\) | 15.7366 | + | 3.06082i | 0.597784 | + | 0.116271i | ||||
\(694\) | −0.366418 | − | 0.211552i | −0.0139090 | − | 0.00803039i | ||||
\(695\) | − | 18.8538i | − | 0.715166i | ||||||
\(696\) | 1.82735 | + | 10.9238i | 0.0692656 | + | 0.414065i | ||||
\(697\) | −0.367817 | − | 0.212359i | −0.0139321 | − | 0.00804368i | ||||
\(698\) | −14.8294 | − | 25.6853i | −0.561301 | − | 0.972201i | ||||
\(699\) | 6.47595 | − | 17.3176i | 0.244943 | − | 0.655011i | ||||
\(700\) | −0.882761 | − | 1.52899i | −0.0333652 | − | 0.0577903i | ||||
\(701\) | −4.07681 | + | 2.35374i | −0.153979 | + | 0.0888997i | −0.575010 | − | 0.818147i | \(-0.695002\pi\) |
0.421031 | + | 0.907046i | \(0.361668\pi\) | |||||||
\(702\) | 17.1601 | − | 9.31321i | 0.647665 | − | 0.351504i | ||||
\(703\) | −6.32653 | − | 35.2826i | −0.238610 | − | 1.33071i | ||||
\(704\) | − | 3.02678i | − | 0.114076i | ||||||
\(705\) | −11.4017 | + | 9.39768i | −0.429412 | + | 0.353937i | ||||
\(706\) | 25.5556 | − | 14.7545i | 0.961798 | − | 0.555294i | ||||
\(707\) | 24.3593 | + | 14.0639i | 0.916127 | + | 0.528926i | ||||
\(708\) | 10.2316 | − | 8.43323i | 0.384525 | − | 0.316940i | ||||
\(709\) | 15.3247 | − | 26.5431i | 0.575531 | − | 0.996849i | −0.420453 | − | 0.907314i | \(-0.638129\pi\) |
0.995984 | − | 0.0895342i | \(-0.0285378\pi\) | |||||||
\(710\) | 16.2884i | 0.611291i | ||||||||
\(711\) | −2.55444 | − | 7.42150i | −0.0957992 | − | 0.278328i | ||||
\(712\) | 4.36131 | − | 7.55401i | 0.163447 | − | 0.283099i | ||||
\(713\) | 3.72817 | − | 6.45737i | 0.139621 | − | 0.241830i | ||||
\(714\) | −9.63693 | + | 1.61208i | −0.360653 | + | 0.0603306i | ||||
\(715\) | − | 11.3731i | − | 0.425328i | ||||||
\(716\) | −9.01690 | + | 15.6177i | −0.336977 | + | 0.583662i | ||||
\(717\) | 24.2222 | + | 29.3875i | 0.904596 | + | 1.09750i | ||||
\(718\) | −23.2838 | − | 13.4429i | −0.868944 | − | 0.501685i | ||||
\(719\) | −20.3745 | + | 11.7632i | −0.759841 | + | 0.438694i | −0.829239 | − | 0.558895i | \(-0.811226\pi\) |
0.0693979 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(720\) | 1.96845 | − | 2.26390i | 0.0733596 | − | 0.0843704i | ||||
\(721\) | − | 11.0250i | − | 0.410591i | ||||||
\(722\) | 14.6252 | + | 12.1286i | 0.544295 | + | 0.451379i | ||||
\(723\) | −3.32229 | + | 0.555758i | −0.123557 | + | 0.0206689i | ||||
\(724\) | −9.17503 | + | 5.29721i | −0.340987 | + | 0.196869i | ||||
\(725\) | 3.19725 | + | 5.53779i | 0.118743 | + | 0.205668i | ||||
\(726\) | −2.98286 | − | 1.11545i | −0.110704 | − | 0.0413982i | ||||
\(727\) | 0.310241 | + | 0.537354i | 0.0115062 | + | 0.0199293i | 0.871721 | − | 0.490002i | \(-0.163004\pi\) |
−0.860215 | + | 0.509932i | \(0.829671\pi\) | |||||||
\(728\) | −5.74514 | − | 3.31696i | −0.212929 | − | 0.122935i | ||||
\(729\) | −14.7133 | + | 22.6389i | −0.544937 | + | 0.838477i | ||||
\(730\) | − | 0.955858i | − | 0.0353779i | ||||||
\(731\) | 27.2339 | + | 15.7235i | 1.00728 | + | 0.581555i | ||||
\(732\) | 3.24486 | + | 1.21342i | 0.119933 | + | 0.0448494i | ||||
\(733\) | −46.1349 | −1.70403 | −0.852016 | − | 0.523515i | \(-0.824620\pi\) | ||||
−0.852016 | + | 0.523515i | \(0.824620\pi\) | |||||||
\(734\) | −8.20624 | −0.302898 | ||||||||
\(735\) | −2.35567 | + | 6.29939i | −0.0868902 | + | 0.232356i | ||||
\(736\) | 0.844837 | − | 0.487767i | 0.0311411 | − | 0.0179793i | ||||
\(737\) | 1.13576 | − | 1.96719i | 0.0418363 | − | 0.0724625i | ||||
\(738\) | 0.300926 | + | 0.261654i | 0.0110772 | + | 0.00963161i | ||||
\(739\) | 10.7620 | + | 18.6403i | 0.395886 | + | 0.685694i | 0.993214 | − | 0.116303i | \(-0.0371044\pi\) |
−0.597328 | + | 0.801997i | \(0.703771\pi\) | |||||||
\(740\) | −8.22349 | −0.302301 | ||||||||
\(741\) | 26.7143 | − | 9.54526i | 0.981373 | − | 0.350654i | ||||
\(742\) | 20.9115 | 0.767685 | ||||||||
\(743\) | −16.8709 | − | 29.2213i | −0.618935 | − | 1.07203i | −0.989680 | − | 0.143292i | \(-0.954231\pi\) |
0.370746 | − | 0.928734i | \(-0.379102\pi\) | |||||||
\(744\) | −8.42021 | − | 10.2158i | −0.308700 | − | 0.374528i | ||||
\(745\) | −1.37189 | + | 2.37618i | −0.0502622 | + | 0.0870566i | ||||
\(746\) | 5.93798 | − | 3.42829i | 0.217405 | − | 0.125519i | ||||
\(747\) | 13.7561 | + | 2.67560i | 0.503309 | + | 0.0978952i | ||||
\(748\) | −9.67115 | −0.353612 | ||||||||
\(749\) | −4.42900 | −0.161832 | ||||||||
\(750\) | 0.606673 | − | 1.62233i | 0.0221526 | − | 0.0592390i | ||||
\(751\) | −37.8615 | − | 21.8593i | −1.38158 | − | 0.797658i | −0.389237 | − | 0.921137i | \(-0.627261\pi\) |
−0.992347 | + | 0.123479i | \(0.960595\pi\) | |||||||
\(752\) | 8.53062i | 0.311080i | ||||||||
\(753\) | −46.2474 | + | 7.73634i | −1.68535 | + | 0.281928i | ||||
\(754\) | 20.8081 | + | 12.0136i | 0.757788 | + | 0.437509i | ||||
\(755\) | 11.3802 | + | 19.7111i | 0.414167 | + | 0.717359i | ||||
\(756\) | 9.17073 | + | 0.241776i | 0.333536 | + | 0.00879331i | ||||
\(757\) | −9.68232 | − | 16.7703i | −0.351910 | − | 0.609526i | 0.634674 | − | 0.772780i | \(-0.281134\pi\) |
−0.986584 | + | 0.163254i | \(0.947801\pi\) | |||||||
\(758\) | 3.53865 | − | 2.04304i | 0.128529 | − | 0.0742065i | ||||
\(759\) | 0.843798 | + | 5.04417i | 0.0306279 | + | 0.183092i | ||||
\(760\) | 3.33099 | − | 2.81149i | 0.120828 | − | 0.101983i | ||||
\(761\) | 36.1398i | 1.31007i | 0.755600 | + | 0.655033i | \(0.227345\pi\) | ||||
−0.755600 | + | 0.655033i | \(0.772655\pi\) | |||||||
\(762\) | −4.97239 | − | 6.03272i | −0.180131 | − | 0.218542i | ||||
\(763\) | 0.343445 | − | 0.198288i | 0.0124335 | − | 0.00717850i | ||||
\(764\) | −5.05565 | − | 2.91888i | −0.182907 | − | 0.105601i | ||||
\(765\) | −7.23359 | − | 6.28957i | −0.261531 | − | 0.227400i | ||||
\(766\) | 15.1709 | − | 26.2767i | 0.548146 | − | 0.949417i | ||||
\(767\) | − | 28.7641i | − | 1.03861i | ||||||
\(768\) | −0.285770 | − | 1.70831i | −0.0103118 | − | 0.0616435i | ||||
\(769\) | 20.4227 | − | 35.3732i | 0.736462 | − | 1.27559i | −0.217617 | − | 0.976034i | \(-0.569828\pi\) |
0.954079 | − | 0.299555i | \(-0.0968382\pi\) | |||||||
\(770\) | 2.67192 | − | 4.62790i | 0.0962893 | − | 0.166778i | ||||
\(771\) | 7.12893 | + | 42.6163i | 0.256742 | + | 1.53479i | ||||
\(772\) | 14.1219i | 0.508258i | ||||||||
\(773\) | 26.9826 | − | 46.7352i | 0.970495 | − | 1.68095i | 0.276432 | − | 0.961034i | \(-0.410848\pi\) |
0.694064 | − | 0.719914i | \(-0.255819\pi\) | |||||||
\(774\) | −22.2812 | − | 19.3734i | −0.800881 | − | 0.696362i | ||||
\(775\) | −6.61932 | − | 3.82167i | −0.237773 | − | 0.137278i | ||||
\(776\) | 12.4237 | − | 7.17285i | 0.445986 | − | 0.257490i | ||||
\(777\) | −15.9944 | − | 19.4052i | −0.573797 | − | 0.696156i | ||||
\(778\) | 0.244867i | 0.00877891i | ||||||||
\(779\) | 0.373715 | + | 0.442769i | 0.0133897 | + | 0.0158639i | ||||
\(780\) | −1.07377 | − | 6.41896i | −0.0384473 | − | 0.229836i | ||||
\(781\) | −42.6961 | + | 24.6506i | −1.52779 | + | 0.882068i | ||||
\(782\) | −1.55851 | − | 2.69942i | −0.0557323 | − | 0.0965311i | ||||
\(783\) | −33.2152 | − | 0.875681i | −1.18701 | − | 0.0312943i | ||||
\(784\) | 1.94147 | + | 3.36272i | 0.0693381 | + | 0.120097i | ||||
\(785\) | −6.94734 | − | 4.01105i | −0.247961 | − | 0.143161i | ||||
\(786\) | 7.57480 | − | 1.26713i | 0.270184 | − | 0.0451969i | ||||
\(787\) | − | 25.3024i | − | 0.901933i | −0.892541 | − | 0.450967i | \(-0.851079\pi\) | ||
0.892541 | − | 0.450967i | \(-0.148921\pi\) | |||||||
\(788\) | 0.248605 | + | 0.143532i | 0.00885617 | + | 0.00511311i | ||||
\(789\) | −1.32006 | + | 3.53003i | −0.0469955 | + | 0.125672i | ||||
\(790\) | −2.61627 | −0.0930828 | ||||||||
\(791\) | −22.4044 | −0.796610 | ||||||||
\(792\) | 8.91329 | + | 1.73366i | 0.316720 | + | 0.0616031i | ||||
\(793\) | 6.50856 | − | 3.75772i | 0.231126 | − | 0.133440i | ||||
\(794\) | −15.2157 | + | 26.3543i | −0.539983 | + | 0.935278i | ||||
\(795\) | 13.0482 | + | 15.8307i | 0.462773 | + | 0.561456i | ||||
\(796\) | 9.44058 | + | 16.3516i | 0.334612 | + | 0.579566i | ||||
\(797\) | −50.5277 | −1.78978 | −0.894891 | − | 0.446284i | \(-0.852747\pi\) | ||||
−0.894891 | + | 0.446284i | \(0.852747\pi\) | |||||||
\(798\) | 13.1130 | + | 2.39196i | 0.464196 | + | 0.0846744i | ||||
\(799\) | 27.2570 | 0.964285 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 19.7471 | + | 17.1700i | 0.697730 | + | 0.606672i | ||||
\(802\) | 4.69167 | − | 8.12622i | 0.165669 | − | 0.286947i | ||||
\(803\) | 2.50556 | − | 1.44658i | 0.0884192 | − | 0.0510489i | ||||
\(804\) | 0.455293 | − | 1.21752i | 0.0160570 | − | 0.0429385i | ||||
\(805\) | 1.72233 | 0.0607040 | ||||||||
\(806\) | −28.7197 | −1.01161 | ||||||||
\(807\) | −52.3886 | − | 19.5908i | −1.84417 | − | 0.689631i | ||||
\(808\) | 13.7972 | + | 7.96584i | 0.485385 | + | 0.280237i | ||||
\(809\) | − | 27.9215i | − | 0.981667i | −0.871253 | − | 0.490833i | \(-0.836692\pi\) | ||
0.871253 | − | 0.490833i | \(-0.163308\pi\) | |||||||
\(810\) | 5.53927 | + | 7.09341i | 0.194630 | + | 0.249237i | ||||
\(811\) | 35.5579 | + | 20.5294i | 1.24861 | + | 0.720883i | 0.970831 | − | 0.239763i | \(-0.0770697\pi\) |
0.277775 | + | 0.960646i | \(0.410403\pi\) | |||||||
\(812\) | 5.64481 | + | 9.77709i | 0.198094 | + | 0.343109i | ||||
\(813\) | −5.57466 | − | 2.08466i | −0.195512 | − | 0.0731121i | ||||
\(814\) | −12.4453 | − | 21.5559i | −0.436208 | − | 0.755535i | ||||
\(815\) | 3.20908 | − | 1.85276i | 0.112409 | − | 0.0648994i | ||||
\(816\) | −5.45840 | + | 0.913090i | −0.191082 | + | 0.0319646i | ||||
\(817\) | −27.6706 | − | 32.7835i | −0.968071 | − | 1.14695i | ||||
\(818\) | − | 2.64541i | − | 0.0924947i | ||||||
\(819\) | 13.0585 | − | 15.0185i | 0.456301 | − | 0.524789i | ||||
\(820\) | 0.115116 | − | 0.0664620i | 0.00402001 | − | 0.00232096i | ||||
\(821\) | 7.15533 | + | 4.13113i | 0.249723 | + | 0.144178i | 0.619637 | − | 0.784888i | \(-0.287280\pi\) |
−0.369915 | + | 0.929066i | \(0.620613\pi\) | |||||||
\(822\) | 16.1783 | + | 19.6283i | 0.564284 | + | 0.684614i | ||||
\(823\) | 20.6142 | − | 35.7048i | 0.718566 | − | 1.24459i | −0.243003 | − | 0.970026i | \(-0.578132\pi\) |
0.961568 | − | 0.274566i | \(-0.0885343\pi\) | |||||||
\(824\) | − | 6.24459i | − | 0.217541i | ||||||
\(825\) | 5.17068 | − | 0.864960i | 0.180020 | − | 0.0301141i | ||||
\(826\) | 6.75767 | − | 11.7046i | 0.235129 | − | 0.407256i | ||||
\(827\) | 1.41094 | − | 2.44382i | 0.0490632 | − | 0.0849800i | −0.840451 | − | 0.541888i | \(-0.817710\pi\) |
0.889514 | + | 0.456908i | \(0.151043\pi\) | |||||||
\(828\) | 0.952480 | + | 2.76727i | 0.0331010 | + | 0.0961692i | ||||
\(829\) | − | 44.2077i | − | 1.53540i | −0.640811 | − | 0.767699i | \(-0.721402\pi\) | ||
0.640811 | − | 0.767699i | \(-0.278598\pi\) | |||||||
\(830\) | 2.33564 | − | 4.04546i | 0.0810714 | − | 0.140420i | ||||
\(831\) | −14.3001 | + | 11.7867i | −0.496066 | + | 0.408876i | ||||
\(832\) | −3.25407 | − | 1.87874i | −0.112815 | − | 0.0651336i | ||||
\(833\) | 10.7445 | − | 6.20337i | 0.372277 | − | 0.214934i | ||||
\(834\) | 25.1992 | − | 20.7701i | 0.872577 | − | 0.719210i | ||||
\(835\) | 0.137543i | 0.00475987i | ||||||||
\(836\) | 12.4107 | + | 4.47654i | 0.429235 | + | 0.154824i | ||||
\(837\) | 34.9064 | − | 18.9446i | 1.20654 | − | 0.654821i | ||||
\(838\) | −15.2226 | + | 8.78877i | −0.525856 | + | 0.303603i | ||||
\(839\) | 6.60690 | + | 11.4435i | 0.228096 | + | 0.395073i | 0.957244 | − | 0.289283i | \(-0.0934168\pi\) |
−0.729148 | + | 0.684356i | \(0.760083\pi\) | |||||||
\(840\) | 1.07109 | − | 2.86426i | 0.0369563 | − | 0.0988262i | ||||
\(841\) | −5.94475 | − | 10.2966i | −0.204991 | − | 0.355056i | ||||
\(842\) | 17.0375 | + | 9.83661i | 0.587151 | + | 0.338992i | ||||
\(843\) | −3.30054 | − | 19.7304i | −0.113677 | − | 0.679552i | ||||
\(844\) | − | 19.0552i | − | 0.655906i | ||||||
\(845\) | −0.968791 | − | 0.559332i | −0.0333274 | − | 0.0192416i | ||||
\(846\) | −25.1211 | − | 4.88614i | −0.863681 | − | 0.167989i | ||||
\(847\) | −3.24614 | −0.111539 | ||||||||
\(848\) | 11.8444 | 0.406737 | ||||||||
\(849\) | 3.90539 | + | 1.46043i | 0.134033 | + | 0.0501218i | ||||
\(850\) | −2.76712 | + | 1.59760i | −0.0949115 | + | 0.0547972i | ||||
\(851\) | 4.01114 | − | 6.94751i | 0.137500 | − | 0.238157i | ||||
\(852\) | −21.7703 | + | 17.9439i | −0.745839 | + | 0.614748i | ||||
\(853\) | 1.06604 | + | 1.84644i | 0.0365006 | + | 0.0632208i | 0.883699 | − | 0.468056i | \(-0.155046\pi\) |
−0.847198 | + | 0.531277i | \(0.821712\pi\) | |||||||
\(854\) | 3.53127 | 0.120837 | ||||||||
\(855\) | 6.37140 | + | 11.4195i | 0.217897 | + | 0.390539i | ||||
\(856\) | −2.50860 | −0.0857423 | ||||||||
\(857\) | −25.1218 | − | 43.5123i | −0.858145 | − | 1.48635i | −0.873696 | − | 0.486472i | \(-0.838283\pi\) |
0.0155507 | − | 0.999879i | \(-0.495050\pi\) | |||||||
\(858\) | 15.2007 | − | 12.5290i | 0.518945 | − | 0.427734i | ||||
\(859\) | 1.48228 | − | 2.56738i | 0.0505746 | − | 0.0875978i | −0.839630 | − | 0.543159i | \(-0.817228\pi\) |
0.890204 | + | 0.455561i | \(0.150561\pi\) | |||||||
\(860\) | −8.52339 | + | 4.92098i | −0.290645 | + | 0.167804i | ||||
\(861\) | 0.380729 | + | 0.142374i | 0.0129752 | + | 0.00485210i | ||||
\(862\) | 8.78159 | 0.299102 | ||||||||
\(863\) | −0.298281 | −0.0101536 | −0.00507680 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507680 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(864\) | 5.19435 | + | 0.136943i | 0.176715 | + | 0.00465890i | ||||
\(865\) | −2.80743 | − | 1.62087i | −0.0954553 | − | 0.0551112i | ||||
\(866\) | 26.2061i | 0.890520i | ||||||||
\(867\) | −1.94058 | − | 11.6007i | −0.0659055 | − | 0.393979i | ||||
\(868\) | −11.6866 | − | 6.74724i | −0.396668 | − | 0.229016i | ||||
\(869\) | −3.95943 | − | 6.85794i | −0.134315 | − | 0.232640i | ||||
\(870\) | −3.87937 | + | 10.3740i | −0.131523 | + | 0.351710i | ||||
\(871\) | −1.40995 | − | 2.44210i | −0.0477743 | − | 0.0827475i | ||||
\(872\) | 0.194529 | − | 0.112311i | 0.00658757 | − | 0.00380334i | ||||
\(873\) | 14.0067 | + | 40.6940i | 0.474054 | + | 1.37728i | ||||
\(874\) | 0.750502 | + | 4.18550i | 0.0253861 | + | 0.141577i | ||||
\(875\) | − | 1.76552i | − | 0.0596855i | ||||||
\(876\) | 1.27756 | − | 1.05301i | 0.0431648 | − | 0.0355780i | ||||
\(877\) | 31.2808 | − | 18.0600i | 1.05628 | − | 0.609843i | 0.131878 | − | 0.991266i | \(-0.457899\pi\) |
0.924401 | + | 0.381423i | \(0.124566\pi\) | |||||||
\(878\) | −23.3862 | − | 13.5020i | −0.789247 | − | 0.455672i | ||||
\(879\) | 16.3970 | − | 13.5150i | 0.553055 | − | 0.455849i | ||||
\(880\) | 1.51339 | − | 2.62126i | 0.0510163 | − | 0.0883628i | ||||
\(881\) | − | 24.2198i | − | 0.815986i | −0.912985 | − | 0.407993i | \(-0.866229\pi\) | ||
0.912985 | − | 0.407993i | \(-0.133771\pi\) | |||||||
\(882\) | −11.0146 | + | 3.79117i | −0.370881 | + | 0.127655i | ||||
\(883\) | 18.5924 | − | 32.2029i | 0.625683 | − | 1.08371i | −0.362726 | − | 0.931896i | \(-0.618154\pi\) |
0.988408 | − | 0.151818i | \(-0.0485128\pi\) | |||||||
\(884\) | −6.00295 | + | 10.3974i | −0.201901 | + | 0.349703i | ||||
\(885\) | 13.0774 | − | 2.18761i | 0.439592 | − | 0.0735357i | ||||
\(886\) | − | 14.9874i | − | 0.503512i | ||||||
\(887\) | 8.18050 | − | 14.1690i | 0.274674 | − | 0.475750i | −0.695379 | − | 0.718644i | \(-0.744763\pi\) |
0.970053 | + | 0.242894i | \(0.0780966\pi\) | |||||||
\(888\) | −9.05933 | − | 10.9912i | −0.304011 | − | 0.368839i | ||||
\(889\) | −6.90127 | − | 3.98445i | −0.231461 | − | 0.133634i | ||||
\(890\) | 7.55401 | − | 4.36131i | 0.253211 | − | 0.146192i | ||||
\(891\) | −10.2106 | + | 25.2550i | −0.342069 | + | 0.846073i | ||||
\(892\) | − | 1.67650i | − | 0.0561335i | ||||||
\(893\) | −34.9783 | − | 12.6166i | −1.17050 | − | 0.422199i | ||||
\(894\) | −4.68724 | + | 0.784089i | −0.156765 | + | 0.0262239i | ||||
\(895\) | −15.6177 | + | 9.01690i | −0.522043 | + | 0.301402i | ||||
\(896\) | −0.882761 | − | 1.52899i | −0.0294910 | − | 0.0510799i | ||||
\(897\) | 5.94672 | + | 2.22379i | 0.198555 | + | 0.0742502i | ||||
\(898\) | 0.535636 | + | 0.927749i | 0.0178744 | + | 0.0309594i | ||||
\(899\) | 42.3272 | + | 24.4376i | 1.41169 | + | 0.815040i | ||||
\(900\) | 2.83667 | − | 0.976368i | 0.0945557 | − | 0.0325456i | ||||
\(901\) | − | 37.8451i | − | 1.26080i | ||||||
\(902\) | 0.348429 | + | 0.201166i | 0.0116014 | + | 0.00669808i | ||||
\(903\) | −28.1899 | − | 10.5417i | −0.938101 | − | 0.350805i | ||||
\(904\) | −12.6900 | −0.422063 | ||||||||
\(905\) | −10.5944 | −0.352170 | ||||||||
\(906\) | −13.8081 | + | 36.9248i | −0.458744 | + | 1.22674i | ||||
\(907\) | −37.5272 | + | 21.6663i | −1.24607 | + | 0.719418i | −0.970323 | − | 0.241812i | \(-0.922258\pi\) |
−0.275746 | + | 0.961230i | \(0.588925\pi\) | |||||||
\(908\) | −5.62519 | + | 9.74312i | −0.186679 | + | 0.323337i | ||||
\(909\) | −31.3606 | + | 36.0676i | −1.04017 | + | 1.19629i | ||||
\(910\) | −3.31696 | − | 5.74514i | −0.109956 | − | 0.190450i | ||||
\(911\) | 35.9636 | 1.19153 | 0.595764 | − | 0.803159i | \(-0.296849\pi\) | ||||
0.595764 | + | 0.803159i | \(0.296849\pi\) | |||||||
\(912\) | 7.42728 | + | 1.35482i | 0.245942 | + | 0.0448624i | ||||
\(913\) | 14.1389 | 0.467931 | ||||||||
\(914\) | −3.80429 | − | 6.58922i | −0.125835 | − | 0.217952i | ||||
\(915\) | 2.20342 | + | 2.67328i | 0.0728428 | + | 0.0883761i | ||||
\(916\) | 11.3258 | − | 19.6169i | 0.374215 | − | 0.648160i | ||||
\(917\) | 6.77965 | − | 3.91423i | 0.223884 | − | 0.129259i | ||||
\(918\) | 0.437560 | − | 16.5970i | 0.0144416 | − | 0.547782i | ||||
\(919\) | 39.6618 | 1.30832 | 0.654161 | − | 0.756355i | \(-0.273022\pi\) | ||||
0.654161 | + | 0.756355i | \(0.273022\pi\) | |||||||
\(920\) | 0.975534 | 0.0321624 | ||||||||
\(921\) | −13.0080 | + | 34.7852i | −0.428628 | + | 1.14621i | ||||
\(922\) | −2.94051 | − | 1.69770i | −0.0968405 | − | 0.0559109i | ||||
\(923\) | 61.2032i | 2.01453i | ||||||||
\(924\) | 9.12895 | − | 1.52711i | 0.300320 | − | 0.0502381i | ||||
\(925\) | −7.12175 | − | 4.11174i | −0.234162 | − | 0.135193i | ||||
\(926\) | −7.06356 | − | 12.2344i | −0.232123 | − | 0.402049i | ||||
\(927\) | 18.3892 | + | 3.57675i | 0.603979 | + | 0.117476i | ||||
\(928\) | 3.19725 | + | 5.53779i | 0.104955 | + | 0.181787i | ||||
\(929\) | −8.50595 | + | 4.91091i | −0.279071 | + | 0.161122i | −0.633003 | − | 0.774150i | \(-0.718178\pi\) |
0.353932 | + | 0.935271i | \(0.384845\pi\) | |||||||
\(930\) | −2.18423 | − | 13.0572i | −0.0716238 | − | 0.428163i | ||||
\(931\) | −16.6596 | + | 2.98724i | −0.545997 | + | 0.0979027i | ||||
\(932\) | − | 10.6745i | − | 0.349656i | ||||||
\(933\) | 2.64525 | + | 3.20933i | 0.0866016 | + | 0.105069i | ||||
\(934\) | −9.89331 | + | 5.71190i | −0.323719 | + | 0.186899i | ||||
\(935\) | −8.37546 | − | 4.83557i | −0.273907 | − | 0.158140i | ||||
\(936\) | 7.39640 | − | 8.50654i | 0.241759 | − | 0.278045i | ||||
\(937\) | −14.1222 | + | 24.4603i | −0.461351 | + | 0.799084i | −0.999029 | − | 0.0440667i | \(-0.985969\pi\) |
0.537677 | + | 0.843151i | \(0.319302\pi\) | |||||||
\(938\) | − | 1.32498i | − | 0.0432622i | ||||||
\(939\) | 2.20113 | + | 13.1582i | 0.0718310 | + | 0.429402i | ||||
\(940\) | −4.26531 | + | 7.38774i | −0.139119 | + | 0.240961i | ||||
\(941\) | −10.4415 | + | 18.0853i | −0.340385 | + | 0.589563i | −0.984504 | − | 0.175361i | \(-0.943891\pi\) |
0.644119 | + | 0.764925i | \(0.277224\pi\) | |||||||
\(942\) | −2.29247 | − | 13.7043i | −0.0746928 | − | 0.446509i | ||||
\(943\) | 0.129672i | 0.00422270i | ||||||||
\(944\) | 3.82758 | − | 6.62956i | 0.124577 | − | 0.215774i | ||||
\(945\) | 7.82120 | + | 4.79475i | 0.254424 | + | 0.155973i | ||||
\(946\) | −25.7984 | − | 14.8947i | −0.838778 | − | 0.484269i | ||||
\(947\) | 51.7967 | − | 29.9048i | 1.68317 | − | 0.971777i | 0.723632 | − | 0.690186i | \(-0.242471\pi\) |
0.959534 | − | 0.281591i | \(-0.0908622\pi\) | |||||||
\(948\) | −2.88219 | − | 3.49680i | −0.0936092 | − | 0.113571i | ||||
\(949\) | − | 3.59162i | − | 0.116589i | ||||||
\(950\) | 4.29047 | − | 0.769325i | 0.139201 | − | 0.0249602i | ||||
\(951\) | −5.82928 | − | 34.8471i | −0.189027 | − | 1.12999i | ||||
\(952\) | −4.88542 | + | 2.82060i | −0.158337 | + | 0.0914160i | ||||
\(953\) | −2.55708 | − | 4.42900i | −0.0828321 | − | 0.143469i | 0.821633 | − | 0.570016i | \(-0.193063\pi\) |
−0.904465 | + | 0.426547i | \(0.859730\pi\) | |||||||
\(954\) | −6.78417 | + | 34.8794i | −0.219646 | + | 1.12926i | ||||
\(955\) | −2.91888 | − | 5.05565i | −0.0944528 | − | 0.163597i | ||||
\(956\) | 19.0417 | + | 10.9937i | 0.615852 | + | 0.355562i | ||||
\(957\) | −33.0639 | + | 5.53098i | −1.06880 | + | 0.178791i | ||||
\(958\) | 36.3083i | 1.17307i | ||||||||
\(959\) | 22.4542 | + | 12.9639i | 0.725084 | + | 0.418628i | ||||
\(960\) | 0.606673 | − | 1.62233i | 0.0195803 | − | 0.0523604i | ||||
\(961\) | −27.4206 | −0.884535 | ||||||||
\(962\) | −30.8996 | −0.996243 | ||||||||
\(963\) | 1.43687 | − | 7.38737i | 0.0463024 | − | 0.238055i | ||||
\(964\) | −1.68423 | + | 0.972389i | −0.0542453 | + | 0.0313185i | ||||
\(965\) | −7.06095 | + | 12.2299i | −0.227300 | + | 0.393695i | ||||
\(966\) | 1.89738 | + | 2.30199i | 0.0610473 | + | 0.0740653i | ||||
\(967\) | −14.7197 | − | 25.4953i | −0.473354 | − | 0.819873i | 0.526181 | − | 0.850373i | \(-0.323623\pi\) |
−0.999535 | + | 0.0304996i | \(0.990290\pi\) | |||||||
\(968\) | −1.83863 | −0.0590958 | ||||||||
\(969\) | 4.32891 | − | 23.7316i | 0.139065 | − | 0.762370i | ||||
\(970\) | 14.3457 | 0.460613 | ||||||||
\(971\) | −9.07896 | − | 15.7252i | −0.291358 | − | 0.504646i | 0.682773 | − | 0.730630i | \(-0.260774\pi\) |
−0.974131 | + | 0.225984i | \(0.927440\pi\) | |||||||
\(972\) | −3.37847 | + | 15.2179i | −0.108364 | + | 0.488116i | ||||
\(973\) | 16.6434 | − | 28.8272i | 0.533563 | − | 0.924158i | ||||
\(974\) | 7.80535 | − | 4.50642i | 0.250099 | − | 0.144395i | ||||
\(975\) | 2.27956 | − | 6.09587i | 0.0730044 | − | 0.195224i | ||||
\(976\) | 2.00013 | 0.0640225 | ||||||||
\(977\) | 37.0070 | 1.18396 | 0.591980 | − | 0.805953i | \(-0.298346\pi\) | ||||
0.591980 | + | 0.805953i | \(0.298346\pi\) | |||||||
\(978\) | 6.01157 | + | 2.24804i | 0.192229 | + | 0.0718844i | ||||
\(979\) | 22.8643 | + | 13.2007i | 0.730746 | + | 0.421897i | ||||
\(980\) | 3.88293i | 0.124036i | ||||||||
\(981\) | 0.219314 | + | 0.637180i | 0.00700216 | + | 0.0203436i | ||||
\(982\) | −19.3513 | − | 11.1725i | −0.617526 | − | 0.356529i | ||||
\(983\) | −4.26025 | − | 7.37898i | −0.135881 | − | 0.235353i | 0.790053 | − | 0.613039i | \(-0.210053\pi\) |
−0.925934 | + | 0.377686i | \(0.876720\pi\) | |||||||
\(984\) | 0.215646 | + | 0.0806415i | 0.00687456 | + | 0.00257076i | ||||
\(985\) | 0.143532 | + | 0.248605i | 0.00457331 | + | 0.00792120i | ||||
\(986\) | 17.6943 | − | 10.2158i | 0.563503 | − | 0.325338i | ||||
\(987\) | −25.7289 | + | 4.30398i | −0.818961 | + | 0.136997i | ||||
\(988\) | 12.5161 | − | 10.5641i | 0.398192 | − | 0.336089i | ||||
\(989\) | − | 9.60117i | − | 0.305299i | ||||||
\(990\) | 6.85230 | + | 5.95804i | 0.217780 | + | 0.189359i | ||||
\(991\) | −7.55231 | + | 4.36033i | −0.239907 | + | 0.138510i | −0.615134 | − | 0.788423i | \(-0.710898\pi\) |
0.375227 | + | 0.926933i | \(0.377565\pi\) | |||||||
\(992\) | −6.61932 | − | 3.82167i | −0.210164 | − | 0.121338i | ||||
\(993\) | 28.0397 | + | 34.0189i | 0.889812 | + | 1.07956i | ||||
\(994\) | −14.3787 | + | 24.9047i | −0.456065 | + | 0.789929i | ||||
\(995\) | 18.8812i | 0.598573i | ||||||||
\(996\) | 7.98003 | − | 1.33491i | 0.252857 | − | 0.0422983i | ||||
\(997\) | 4.82494 | − | 8.35704i | 0.152807 | − | 0.264670i | −0.779451 | − | 0.626463i | \(-0.784502\pi\) |
0.932258 | + | 0.361793i | \(0.117835\pi\) | |||||||
\(998\) | −19.8988 | + | 34.4658i | −0.629887 | + | 1.09100i | ||||
\(999\) | 37.5559 | − | 20.3825i | 1.18822 | − | 0.644875i |
(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 | 570.2.s.b.221.3 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.a.221.1 | ✓ | 24 | ||
19.8 | odd | 6 | 570.2.s.a.521.1 | yes | 24 | ||
57.8 | even | 6 | inner | 570.2.s.b.521.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.1 | ✓ | 24 | 3.2 | odd | 2 | ||
570.2.s.a.521.1 | yes | 24 | 19.8 | odd | 6 | ||
570.2.s.b.221.3 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.521.3 | yes | 24 | 57.8 | even | 6 | inner |