Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(11,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.e (of order \(3\), 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: | \(0.558952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 51.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.51 |
Dual form | 70.2.e.b.11.1 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −0.500000 | − | 2.59808i | −0.133631 | − | 0.694365i | ||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.00000 | − | 1.73205i | −1.09109 | − | 0.377964i | ||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 1.00000 | + | 1.73205i | 0.204124 | + | 0.353553i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.50000 | + | 4.33013i | −0.490290 | + | 0.849208i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 2.50000 | + | 0.866025i | 0.472456 | + | 0.163663i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0.500000 | + | 2.59808i | 0.0845154 | + | 0.439155i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.50000 | + | 9.52628i | −0.904194 | + | 1.56611i | −0.0821995 | + | 0.996616i | \(0.526194\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | 5.00000 | + | 8.66025i | 0.800641 | + | 1.38675i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 4.00000 | − | 3.46410i | 0.617213 | − | 0.534522i | ||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −1.50000 | − | 2.59808i | −0.221163 | − | 0.383065i | ||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 6.00000 | − | 10.3923i | 0.840168 | − | 1.45521i | ||||
\(52\) | −2.50000 | − | 4.33013i | −0.346688 | − | 0.600481i | ||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | −2.00000 | + | 3.46410i | −0.272166 | + | 0.471405i | ||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −1.00000 | − | 1.73205i | −0.129099 | − | 0.223607i | ||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | −0.500000 | − | 2.59808i | −0.0629941 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | − | 4.33013i | 0.310087 | − | 0.537086i | ||||
\(66\) | 3.00000 | + | 5.19615i | 0.369274 | + | 0.639602i | ||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | −3.00000 | + | 5.19615i | −0.363803 | + | 0.630126i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | −2.50000 | − | 0.866025i | −0.298807 | − | 0.103510i | ||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | −5.50000 | − | 9.52628i | −0.639362 | − | 1.10741i | ||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 7.50000 | + | 2.59808i | 0.854704 | + | 0.296078i | ||||
\(78\) | −10.0000 | −1.13228 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 1.00000 | + | 5.19615i | 0.109109 | + | 0.566947i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −10.0000 | + | 8.66025i | −1.04828 | + | 0.907841i | ||||
\(92\) | 3.00000 | 0.312772 | ||||||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | −0.500000 | − | 0.866025i | −0.0512989 | − | 0.0888523i | ||||
\(96\) | 1.00000 | − | 1.73205i | 0.102062 | − | 0.176777i | ||||
\(97\) | 14.0000 | 1.42148 | 0.710742 | − | 0.703452i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 5.50000 | + | 4.33013i | 0.555584 | + | 0.437409i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 6.00000 | + | 10.3923i | 0.594089 | + | 1.02899i | ||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | −4.00000 | + | 3.46410i | −0.390360 | + | 0.338062i | ||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 6.00000 | − | 10.3923i | 0.580042 | − | 1.00466i | −0.415432 | − | 0.909624i | \(-0.636370\pi\) |
0.995474 | − | 0.0950377i | \(-0.0302972\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 1.50000 | − | 2.59808i | 0.143019 | − | 0.247717i | ||||
\(111\) | −22.0000 | −2.08815 | ||||||||
\(112\) | −0.500000 | − | 2.59808i | −0.0472456 | − | 0.245495i | ||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 1.50000 | + | 2.59808i | 0.139876 | + | 0.242272i | ||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | −2.50000 | + | 4.33013i | −0.231125 | + | 0.400320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0000 | + | 5.19615i | 1.37505 | + | 0.476331i | ||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 2.00000 | + | 3.46410i | 0.181071 | + | 0.313625i | ||||
\(123\) | 3.00000 | + | 5.19615i | 0.270501 | + | 0.468521i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.50000 | + | 0.866025i | 0.222718 | + | 0.0771517i | ||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −10.0000 | − | 17.3205i | −0.880451 | − | 1.52499i | ||||
\(130\) | 2.50000 | + | 4.33013i | 0.219265 | + | 0.379777i | ||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | 0.500000 | + | 2.59808i | 0.0433555 | + | 0.225282i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 2.00000 | − | 3.46410i | 0.172133 | − | 0.298142i | ||||
\(136\) | −3.00000 | − | 5.19615i | −0.257248 | − | 0.445566i | ||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | 3.00000 | − | 5.19615i | 0.255377 | − | 0.442326i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 2.00000 | − | 1.73205i | 0.169031 | − | 0.146385i | ||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | −6.00000 | + | 10.3923i | −0.503509 | + | 0.872103i | ||||
\(143\) | −7.50000 | − | 12.9904i | −0.627182 | − | 1.08631i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −3.00000 | + | 5.19615i | −0.249136 | + | 0.431517i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 13.0000 | − | 5.19615i | 1.07222 | − | 0.428571i | ||||
\(148\) | 11.0000 | 0.904194 | ||||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 1.00000 | + | 1.73205i | 0.0816497 | + | 0.141421i | ||||
\(151\) | −7.00000 | − | 12.1244i | −0.569652 | − | 0.986666i | −0.996600 | − | 0.0823900i | \(-0.973745\pi\) |
0.426948 | − | 0.904276i | \(-0.359589\pi\) | |||||||
\(152\) | 0.500000 | − | 0.866025i | 0.0405554 | − | 0.0702439i | ||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | −6.00000 | + | 5.19615i | −0.483494 | + | 0.418718i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 5.00000 | − | 8.66025i | 0.400320 | − | 0.693375i | ||||
\(157\) | −2.50000 | − | 4.33013i | −0.199522 | − | 0.345582i | 0.748852 | − | 0.662738i | \(-0.230606\pi\) |
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(158\) | 5.00000 | + | 8.66025i | 0.397779 | + | 0.688973i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −1.50000 | − | 7.79423i | −0.118217 | − | 0.614271i | ||||
\(162\) | −11.0000 | −0.864242 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | −3.00000 | − | 5.19615i | −0.233550 | − | 0.404520i | ||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | 9.00000 | 0.696441 | 0.348220 | − | 0.937413i | \(-0.386786\pi\) | ||||
0.348220 | + | 0.937413i | \(0.386786\pi\) | |||||||
\(168\) | −5.00000 | − | 1.73205i | −0.385758 | − | 0.133631i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 3.00000 | − | 5.19615i | 0.230089 | − | 0.398527i | ||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | −1.50000 | + | 2.59808i | −0.114043 | + | 0.197528i | −0.917397 | − | 0.397974i | \(-0.869713\pi\) |
0.803354 | + | 0.595502i | \(0.203047\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 2.50000 | + | 0.866025i | 0.188982 | + | 0.0654654i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | 1.50000 | + | 2.59808i | 0.112115 | + | 0.194189i | 0.916623 | − | 0.399753i | \(-0.130904\pi\) |
−0.804508 | + | 0.593942i | \(0.797571\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −2.50000 | − | 12.9904i | −0.185312 | − | 0.962911i | ||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 5.50000 | + | 9.52628i | 0.404368 | + | 0.700386i | ||||
\(186\) | −4.00000 | − | 6.92820i | −0.293294 | − | 0.508001i | ||||
\(187\) | −9.00000 | + | 15.5885i | −0.658145 | + | 1.13994i | ||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | −8.00000 | + | 6.92820i | −0.581914 | + | 0.503953i | ||||
\(190\) | 1.00000 | 0.0725476 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | −7.00000 | + | 12.1244i | −0.502571 | + | 0.870478i | ||||
\(195\) | 10.0000 | 0.716115 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | −1.50000 | + | 2.59808i | −0.106600 | + | 0.184637i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −4.00000 | + | 6.92820i | −0.282138 | + | 0.488678i | ||||
\(202\) | −12.0000 | −0.844317 | ||||||||
\(203\) | 12.0000 | − | 10.3923i | 0.842235 | − | 0.729397i | ||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 1.50000 | − | 2.59808i | 0.104765 | − | 0.181458i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | −1.50000 | − | 2.59808i | −0.104257 | − | 0.180579i | ||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | −1.00000 | − | 5.19615i | −0.0690066 | − | 0.358569i | ||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 12.0000 | + | 20.7846i | 0.822226 | + | 1.42414i | ||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | −10.0000 | − | 3.46410i | −0.678844 | − | 0.235159i | ||||
\(218\) | −4.00000 | −0.270914 | ||||||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | −15.0000 | − | 25.9808i | −1.00901 | − | 1.74766i | ||||
\(222\) | 11.0000 | − | 19.0526i | 0.738272 | − | 1.27872i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 2.50000 | + | 0.866025i | 0.167038 | + | 0.0578638i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.00000 | + | 10.3923i | −0.399114 | + | 0.691286i | ||||
\(227\) | 12.0000 | + | 20.7846i | 0.796468 | + | 1.37952i | 0.921903 | + | 0.387421i | \(0.126634\pi\) |
−0.125435 | + | 0.992102i | \(0.540033\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −0.0662266 | − | 0.114708i | ||||
\(229\) | 14.0000 | − | 24.2487i | 0.925146 | − | 1.60240i | 0.133820 | − | 0.991006i | \(-0.457276\pi\) |
0.791326 | − | 0.611394i | \(-0.209391\pi\) | |||||||
\(230\) | −3.00000 | −0.197814 | ||||||||
\(231\) | 3.00000 | + | 15.5885i | 0.197386 | + | 1.02565i | ||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | −2.50000 | − | 4.33013i | −0.163430 | − | 0.283069i | ||||
\(235\) | 1.50000 | + | 2.59808i | 0.0978492 | + | 0.169480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.0000 | 1.29914 | ||||||||
\(238\) | −12.0000 | + | 10.3923i | −0.777844 | + | 0.673633i | ||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | −1.00000 | + | 1.73205i | −0.0645497 | + | 0.111803i | ||||
\(241\) | 12.5000 | + | 21.6506i | 0.805196 | + | 1.39464i | 0.916159 | + | 0.400815i | \(0.131273\pi\) |
−0.110963 | + | 0.993825i | \(0.535394\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −5.50000 | − | 4.33013i | −0.351382 | − | 0.276642i | ||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 2.50000 | − | 4.33013i | 0.159071 | − | 0.275519i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | −12.0000 | − | 20.7846i | −0.760469 | − | 1.31717i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | −2.00000 | + | 1.73205i | −0.125988 | + | 0.109109i | ||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 9.50000 | − | 16.4545i | 0.596083 | − | 1.03245i | ||||
\(255\) | −6.00000 | − | 10.3923i | −0.375735 | − | 0.650791i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | 20.0000 | 1.24515 | ||||||||
\(259\) | −5.50000 | − | 28.5788i | −0.341753 | − | 1.77580i | ||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | −1.50000 | − | 2.59808i | −0.0926703 | − | 0.160510i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 3.00000 | − | 5.19615i | 0.184637 | − | 0.319801i | ||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | −2.50000 | − | 0.866025i | −0.153285 | − | 0.0530994i | ||||
\(267\) | −12.0000 | −0.734388 | ||||||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | 6.00000 | + | 10.3923i | 0.365826 | + | 0.633630i | 0.988908 | − | 0.148527i | \(-0.0474530\pi\) |
−0.623082 | + | 0.782157i | \(0.714120\pi\) | |||||||
\(270\) | 2.00000 | + | 3.46410i | 0.121716 | + | 0.210819i | ||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | −25.0000 | − | 8.66025i | −1.51307 | − | 0.524142i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −1.50000 | + | 2.59808i | −0.0904534 | + | 0.156670i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0.500000 | + | 2.59808i | 0.0298807 | + | 0.155265i | ||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | −13.0000 | − | 22.5167i | −0.772770 | − | 1.33848i | −0.936039 | − | 0.351895i | \(-0.885537\pi\) |
0.163270 | − | 0.986581i | \(-0.447796\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | 1.00000 | − | 1.73205i | 0.0592349 | − | 0.102598i | ||||
\(286\) | 15.0000 | 0.886969 | ||||||||
\(287\) | −6.00000 | + | 5.19615i | −0.354169 | + | 0.306719i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | −3.00000 | − | 5.19615i | −0.176166 | − | 0.305129i | ||||
\(291\) | 14.0000 | + | 24.2487i | 0.820695 | + | 1.42148i | ||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −27.0000 | −1.57736 | −0.788678 | − | 0.614806i | \(-0.789234\pi\) | ||||
−0.788678 | + | 0.614806i | \(0.789234\pi\) | |||||||
\(294\) | −2.00000 | + | 13.8564i | −0.116642 | + | 0.808122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.50000 | + | 9.52628i | −0.319681 | + | 0.553704i | ||||
\(297\) | −6.00000 | − | 10.3923i | −0.348155 | − | 0.603023i | ||||
\(298\) | −9.00000 | − | 15.5885i | −0.521356 | − | 0.903015i | ||||
\(299\) | −7.50000 | + | 12.9904i | −0.433736 | + | 0.751253i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 20.0000 | − | 17.3205i | 1.15278 | − | 0.998337i | ||||
\(302\) | 14.0000 | 0.805609 | ||||||||
\(303\) | −12.0000 | + | 20.7846i | −0.689382 | + | 1.19404i | ||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | −2.00000 | − | 3.46410i | −0.114520 | − | 0.198354i | ||||
\(306\) | −3.00000 | + | 5.19615i | −0.171499 | + | 0.297044i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | −1.50000 | − | 7.79423i | −0.0854704 | − | 0.444117i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −2.00000 | + | 3.46410i | −0.113592 | + | 0.196748i | ||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | 5.00000 | + | 8.66025i | 0.283069 | + | 0.490290i | ||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | 5.00000 | 0.282166 | ||||||||
\(315\) | −2.50000 | − | 0.866025i | −0.140859 | − | 0.0487950i | ||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 3.00000 | + | 5.19615i | 0.168232 | + | 0.291386i | ||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 7.50000 | + | 2.59808i | 0.417959 | + | 0.144785i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | −2.50000 | − | 4.33013i | −0.138675 | − | 0.240192i | ||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −4.00000 | + | 6.92820i | −0.221201 | + | 0.383131i | ||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | −1.50000 | − | 7.79423i | −0.0826977 | − | 0.429710i | ||||
\(330\) | 6.00000 | 0.330289 | ||||||||
\(331\) | 3.50000 | − | 6.06218i | 0.192377 | − | 0.333207i | −0.753660 | − | 0.657264i | \(-0.771714\pi\) |
0.946038 | + | 0.324057i | \(0.105047\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | −5.50000 | − | 9.52628i | −0.301398 | − | 0.522037i | ||||
\(334\) | −4.50000 | + | 7.79423i | −0.246229 | + | 0.426481i | ||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 4.00000 | − | 3.46410i | 0.218218 | − | 0.188982i | ||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −6.00000 | + | 10.3923i | −0.326357 | + | 0.565267i | ||||
\(339\) | 12.0000 | + | 20.7846i | 0.651751 | + | 1.12887i | ||||
\(340\) | 3.00000 | + | 5.19615i | 0.162698 | + | 0.281801i | ||||
\(341\) | 6.00000 | − | 10.3923i | 0.324918 | − | 0.562775i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | −3.00000 | + | 5.19615i | −0.161515 | + | 0.279751i | ||||
\(346\) | −1.50000 | − | 2.59808i | −0.0806405 | − | 0.139673i | ||||
\(347\) | −12.0000 | − | 20.7846i | −0.644194 | − | 1.11578i | −0.984487 | − | 0.175457i | \(-0.943860\pi\) |
0.340293 | − | 0.940319i | \(-0.389474\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | −2.00000 | + | 1.73205i | −0.106904 | + | 0.0925820i | ||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | −6.00000 | − | 10.3923i | −0.319348 | − | 0.553127i | 0.661004 | − | 0.750382i | \(-0.270130\pi\) |
−0.980352 | + | 0.197256i | \(0.936797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 10.3923i | 0.318447 | − | 0.551566i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 6.00000 | + | 31.1769i | 0.317554 | + | 1.65006i | ||||
\(358\) | −3.00000 | −0.158555 | ||||||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −1.00000 | + | 1.73205i | −0.0525588 | + | 0.0910346i | ||||
\(363\) | 4.00000 | 0.209946 | ||||||||
\(364\) | 12.5000 | + | 4.33013i | 0.655178 | + | 0.226960i | ||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | −4.00000 | + | 6.92820i | −0.209083 | + | 0.362143i | ||||
\(367\) | 0.500000 | + | 0.866025i | 0.0260998 | + | 0.0452062i | 0.878780 | − | 0.477227i | \(-0.158358\pi\) |
−0.852680 | + | 0.522433i | \(0.825025\pi\) | |||||||
\(368\) | −1.50000 | − | 2.59808i | −0.0781929 | − | 0.135434i | ||||
\(369\) | −1.50000 | + | 2.59808i | −0.0780869 | + | 0.135250i | ||||
\(370\) | −11.0000 | −0.571863 | ||||||||
\(371\) | 7.50000 | + | 2.59808i | 0.389381 | + | 0.134885i | ||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | 17.0000 | − | 29.4449i | 0.880227 | − | 1.52460i | 0.0291379 | − | 0.999575i | \(-0.490724\pi\) |
0.851089 | − | 0.525022i | \(-0.175943\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | −1.00000 | − | 1.73205i | −0.0516398 | − | 0.0894427i | ||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | −30.0000 | −1.54508 | ||||||||
\(378\) | −2.00000 | − | 10.3923i | −0.102869 | − | 0.534522i | ||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | −0.500000 | + | 0.866025i | −0.0256495 | + | 0.0444262i | ||||
\(381\) | −19.0000 | − | 32.9090i | −0.973399 | − | 1.68598i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | −7.50000 | + | 12.9904i | −0.383232 | + | 0.663777i | −0.991522 | − | 0.129937i | \(-0.958522\pi\) |
0.608290 | + | 0.793715i | \(0.291856\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 6.00000 | − | 5.19615i | 0.305788 | − | 0.264820i | ||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | −7.00000 | − | 12.1244i | −0.355371 | − | 0.615521i | ||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | −5.00000 | + | 8.66025i | −0.253185 | + | 0.438529i | ||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | −6.00000 | −0.302660 | ||||||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | −5.00000 | − | 8.66025i | −0.251577 | − | 0.435745i | ||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −4.00000 | + | 3.46410i | −0.200250 | + | 0.173422i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −10.5000 | + | 18.1865i | −0.524345 | + | 0.908192i | 0.475253 | + | 0.879849i | \(0.342356\pi\) |
−0.999598 | + | 0.0283431i | \(0.990977\pi\) | |||||||
\(402\) | −4.00000 | − | 6.92820i | −0.199502 | − | 0.345547i | ||||
\(403\) | 10.0000 | + | 17.3205i | 0.498135 | + | 0.862796i | ||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | 11.0000 | 0.546594 | ||||||||
\(406\) | 3.00000 | + | 15.5885i | 0.148888 | + | 0.773642i | ||||
\(407\) | 33.0000 | 1.63575 | ||||||||
\(408\) | 6.00000 | − | 10.3923i | 0.297044 | − | 0.514496i | ||||
\(409\) | 11.0000 | + | 19.0526i | 0.543915 | + | 0.942088i | 0.998674 | + | 0.0514740i | \(0.0163919\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | 1.50000 | + | 2.59808i | 0.0740797 | + | 0.128310i | ||||
\(411\) | 12.0000 | − | 20.7846i | 0.591916 | − | 1.02523i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.00000 | 0.147442 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | −2.50000 | − | 4.33013i | −0.122573 | − | 0.212302i | ||||
\(417\) | −4.00000 | − | 6.92820i | −0.195881 | − | 0.339276i | ||||
\(418\) | 1.50000 | − | 2.59808i | 0.0733674 | − | 0.127076i | ||||
\(419\) | 15.0000 | 0.732798 | 0.366399 | − | 0.930458i | \(-0.380591\pi\) | ||||
0.366399 | + | 0.930458i | \(0.380591\pi\) | |||||||
\(420\) | 5.00000 | + | 1.73205i | 0.243975 | + | 0.0845154i | ||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0.500000 | − | 0.866025i | 0.0243396 | − | 0.0421575i | ||||
\(423\) | −1.50000 | − | 2.59808i | −0.0729325 | − | 0.126323i | ||||
\(424\) | −1.50000 | − | 2.59808i | −0.0728464 | − | 0.126174i | ||||
\(425\) | −3.00000 | + | 5.19615i | −0.145521 | + | 0.252050i | ||||
\(426\) | −24.0000 | −1.16280 | ||||||||
\(427\) | 2.00000 | + | 10.3923i | 0.0967868 | + | 0.502919i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 15.0000 | − | 25.9808i | 0.724207 | − | 1.25436i | ||||
\(430\) | −5.00000 | − | 8.66025i | −0.241121 | − | 0.417635i | ||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | 8.00000 | − | 6.92820i | 0.384012 | − | 0.332564i | ||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | 2.00000 | − | 3.46410i | 0.0957826 | − | 0.165900i | ||||
\(437\) | 1.50000 | + | 2.59808i | 0.0717547 | + | 0.124283i | ||||
\(438\) | −4.00000 | − | 6.92820i | −0.191127 | − | 0.331042i | ||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 11.0000 | + | 19.0526i | 0.522037 | + | 0.904194i | ||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | −4.00000 | + | 6.92820i | −0.189405 | + | 0.328060i | ||||
\(447\) | −36.0000 | −1.70274 | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | −3.00000 | −0.141579 | −0.0707894 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707894 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | 14.0000 | − | 24.2487i | 0.657777 | − | 1.13930i | ||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 2.50000 | + | 12.9904i | 0.117202 | + | 0.608998i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 14.0000 | + | 24.2487i | 0.654177 | + | 1.13307i | ||||
\(459\) | −12.0000 | − | 20.7846i | −0.560112 | − | 0.970143i | ||||
\(460\) | 1.50000 | − | 2.59808i | 0.0699379 | − | 0.121136i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | −15.0000 | − | 5.19615i | −0.697863 | − | 0.241747i | ||||
\(463\) | −19.0000 | −0.883005 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | 9.00000 | − | 15.5885i | 0.416470 | − | 0.721348i | −0.579111 | − | 0.815249i | \(-0.696600\pi\) |
0.995582 | + | 0.0939008i | \(0.0299336\pi\) | |||||||
\(468\) | 5.00000 | 0.231125 | ||||||||
\(469\) | −10.0000 | − | 3.46410i | −0.461757 | − | 0.159957i | ||||
\(470\) | −3.00000 | −0.138380 | ||||||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0000 | + | 25.9808i | 0.689701 | + | 1.19460i | ||||
\(474\) | −10.0000 | + | 17.3205i | −0.459315 | + | 0.795557i | ||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −3.00000 | − | 15.5885i | −0.137505 | − | 0.714496i | ||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | −3.00000 | + | 5.19615i | −0.137217 | + | 0.237666i | ||||
\(479\) | −12.0000 | − | 20.7846i | −0.548294 | − | 0.949673i | −0.998392 | − | 0.0566937i | \(-0.981944\pi\) |
0.450098 | − | 0.892979i | \(-0.351389\pi\) | |||||||
\(480\) | −1.00000 | − | 1.73205i | −0.0456435 | − | 0.0790569i | ||||
\(481\) | −27.5000 | + | 47.6314i | −1.25389 | + | 2.17180i | ||||
\(482\) | −25.0000 | −1.13872 | ||||||||
\(483\) | 12.0000 | − | 10.3923i | 0.546019 | − | 0.472866i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 7.00000 | − | 12.1244i | 0.317854 | − | 0.550539i | ||||
\(486\) | −5.00000 | − | 8.66025i | −0.226805 | − | 0.392837i | ||||
\(487\) | 8.00000 | + | 13.8564i | 0.362515 | + | 0.627894i | 0.988374 | − | 0.152042i | \(-0.0485850\pi\) |
−0.625859 | + | 0.779936i | \(0.715252\pi\) | |||||||
\(488\) | 2.00000 | − | 3.46410i | 0.0905357 | − | 0.156813i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 6.50000 | − | 2.59808i | 0.293640 | − | 0.117369i | ||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 3.00000 | − | 5.19615i | 0.135250 | − | 0.234261i | ||||
\(493\) | 18.0000 | + | 31.1769i | 0.810679 | + | 1.40414i | ||||
\(494\) | 2.50000 | + | 4.33013i | 0.112480 | + | 0.194822i | ||||
\(495\) | 1.50000 | − | 2.59808i | 0.0674200 | − | 0.116775i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −24.0000 | + | 20.7846i | −1.07655 | + | 0.932317i | ||||
\(498\) | 24.0000 | 1.07547 | ||||||||
\(499\) | 14.0000 | − | 24.2487i | 0.626726 | − | 1.08552i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.988204 | − | 0.153141i | \(-0.0489388\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 9.00000 | + | 15.5885i | 0.402090 | + | 0.696441i | ||||
\(502\) | 7.50000 | − | 12.9904i | 0.334741 | − | 0.579789i | ||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | −0.500000 | − | 2.59808i | −0.0222718 | − | 0.115728i | ||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | −4.50000 | + | 7.79423i | −0.200049 | + | 0.346496i | ||||
\(507\) | 12.0000 | + | 20.7846i | 0.532939 | + | 0.923077i | ||||
\(508\) | 9.50000 | + | 16.4545i | 0.421494 | + | 0.730050i | ||||
\(509\) | −3.00000 | + | 5.19615i | −0.132973 | + | 0.230315i | −0.924821 | − | 0.380402i | \(-0.875786\pi\) |
0.791849 | + | 0.610718i | \(0.209119\pi\) | |||||||
\(510\) | 12.0000 | 0.531369 | ||||||||
\(511\) | −10.0000 | − | 3.46410i | −0.442374 | − | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.00000 | − | 3.46410i | 0.0883022 | − | 0.152944i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | −10.0000 | + | 17.3205i | −0.440225 | + | 0.762493i | ||||
\(517\) | 9.00000 | 0.395820 | ||||||||
\(518\) | 27.5000 | + | 9.52628i | 1.20828 | + | 0.418561i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 2.50000 | − | 4.33013i | 0.109632 | − | 0.189889i | ||||
\(521\) | −16.5000 | − | 28.5788i | −0.722878 | − | 1.25206i | −0.959841 | − | 0.280543i | \(-0.909485\pi\) |
0.236963 | − | 0.971519i | \(-0.423848\pi\) | |||||||
\(522\) | 3.00000 | + | 5.19615i | 0.131306 | + | 0.227429i | ||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 1.00000 | + | 5.19615i | 0.0436436 | + | 0.226779i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 3.00000 | + | 5.19615i | 0.130558 | + | 0.226134i | ||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 1.50000 | − | 2.59808i | 0.0651558 | − | 0.112853i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | − | 1.73205i | 0.0867110 | − | 0.0750939i | ||||
\(533\) | 15.0000 | 0.649722 | ||||||||
\(534\) | 6.00000 | − | 10.3923i | 0.259645 | − | 0.449719i | ||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 2.00000 | + | 3.46410i | 0.0863868 | + | 0.149626i | ||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | −19.5000 | + | 7.79423i | −0.839924 | + | 0.335721i | ||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 8.00000 | + | 13.8564i | 0.343629 | + | 0.595184i | ||||
\(543\) | 2.00000 | + | 3.46410i | 0.0858282 | + | 0.148659i | ||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | 20.0000 | − | 17.3205i | 0.855921 | − | 0.741249i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | −1.50000 | − | 2.59808i | −0.0639602 | − | 0.110782i | ||||
\(551\) | −3.00000 | + | 5.19615i | −0.127804 | + | 0.221364i | ||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 5.00000 | + | 25.9808i | 0.212622 | + | 1.10481i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −11.0000 | + | 19.0526i | −0.466924 | + | 0.808736i | ||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 13.5000 | + | 23.3827i | 0.572013 | + | 0.990756i | 0.996359 | + | 0.0852559i | \(0.0271708\pi\) |
−0.424346 | + | 0.905500i | \(0.639496\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | −50.0000 | −2.11477 | ||||||||
\(560\) | −2.50000 | − | 0.866025i | −0.105644 | − | 0.0365963i | ||||
\(561\) | −36.0000 | −1.51992 | ||||||||
\(562\) | 1.50000 | − | 2.59808i | 0.0632737 | − | 0.109593i | ||||
\(563\) | 9.00000 | + | 15.5885i | 0.379305 | + | 0.656975i | 0.990961 | − | 0.134148i | \(-0.0428299\pi\) |
−0.611656 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(564\) | 3.00000 | + | 5.19615i | 0.126323 | + | 0.218797i | ||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | 26.0000 | 1.09286 | ||||||||
\(567\) | −27.5000 | − | 9.52628i | −1.15489 | − | 0.400066i | ||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | 1.50000 | − | 2.59808i | 0.0628833 | − | 0.108917i | −0.832870 | − | 0.553469i | \(-0.813304\pi\) |
0.895753 | + | 0.444552i | \(0.146637\pi\) | |||||||
\(570\) | 1.00000 | + | 1.73205i | 0.0418854 | + | 0.0725476i | ||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | −7.50000 | + | 12.9904i | −0.313591 | + | 0.543155i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | −1.50000 | − | 7.79423i | −0.0626088 | − | 0.325325i | ||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.0000 | − | 17.3205i | −0.416305 | − | 0.721062i | 0.579259 | − | 0.815144i | \(-0.303342\pi\) |
−0.995565 | + | 0.0940813i | \(0.970009\pi\) | |||||||
\(578\) | −9.50000 | − | 16.4545i | −0.395148 | − | 0.684416i | ||||
\(579\) | −4.00000 | + | 6.92820i | −0.166234 | + | 0.287926i | ||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 24.0000 | − | 20.7846i | 0.995688 | − | 0.862291i | ||||
\(582\) | −28.0000 | −1.16064 | ||||||||
\(583\) | −4.50000 | + | 7.79423i | −0.186371 | + | 0.322804i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | 2.50000 | + | 4.33013i | 0.103362 | + | 0.179029i | ||||
\(586\) | 13.5000 | − | 23.3827i | 0.557680 | − | 0.965930i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −11.0000 | − | 8.66025i | −0.453632 | − | 0.357143i | ||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | −5.50000 | − | 9.52628i | −0.226049 | − | 0.391528i | ||||
\(593\) | 18.0000 | − | 31.1769i | 0.739171 | − | 1.28028i | −0.213697 | − | 0.976900i | \(-0.568551\pi\) |
0.952869 | − | 0.303383i | \(-0.0981160\pi\) | |||||||
\(594\) | 12.0000 | 0.492366 | ||||||||
\(595\) | 12.0000 | − | 10.3923i | 0.491952 | − | 0.426043i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | −4.00000 | + | 6.92820i | −0.163709 | + | 0.283552i | ||||
\(598\) | −7.50000 | − | 12.9904i | −0.306698 | − | 0.531216i | ||||
\(599\) | −21.0000 | − | 36.3731i | −0.858037 | − | 1.48616i | −0.873799 | − | 0.486287i | \(-0.838351\pi\) |
0.0157622 | − | 0.999876i | \(-0.494983\pi\) | |||||||
\(600\) | 1.00000 | − | 1.73205i | 0.0408248 | − | 0.0707107i | ||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 5.00000 | + | 25.9808i | 0.203785 | + | 1.05890i | ||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −7.00000 | + | 12.1244i | −0.284826 | + | 0.493333i | ||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | −12.0000 | − | 20.7846i | −0.487467 | − | 0.844317i | ||||
\(607\) | 9.50000 | − | 16.4545i | 0.385593 | − | 0.667867i | −0.606258 | − | 0.795268i | \(-0.707330\pi\) |
0.991851 | + | 0.127401i | \(0.0406635\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 30.0000 | + | 10.3923i | 1.21566 | + | 0.421117i | ||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | −7.50000 | + | 12.9904i | −0.303418 | + | 0.525535i | ||||
\(612\) | −3.00000 | − | 5.19615i | −0.121268 | − | 0.210042i | ||||
\(613\) | −23.5000 | − | 40.7032i | −0.949156 | − | 1.64399i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
−0.201948 | − | 0.979396i | \(-0.564727\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | 7.50000 | + | 2.59808i | 0.302184 | + | 0.104679i | ||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −4.00000 | + | 6.92820i | −0.160904 | + | 0.278693i | ||||
\(619\) | 0.500000 | + | 0.866025i | 0.0200967 | + | 0.0348085i | 0.875899 | − | 0.482495i | \(-0.160269\pi\) |
−0.855802 | + | 0.517303i | \(0.826936\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | −6.00000 | + | 10.3923i | −0.240772 | + | 0.417029i | ||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | −3.00000 | − | 15.5885i | −0.120192 | − | 0.624538i | ||||
\(624\) | −10.0000 | −0.400320 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.00000 | − | 6.92820i | −0.159872 | − | 0.276907i | ||||
\(627\) | −3.00000 | − | 5.19615i | −0.119808 | − | 0.207514i | ||||
\(628\) | −2.50000 | + | 4.33013i | −0.0997609 | + | 0.172791i | ||||
\(629\) | 66.0000 | 2.63159 | ||||||||
\(630\) | 2.00000 | − | 1.73205i | 0.0796819 | − | 0.0690066i | ||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 5.00000 | − | 8.66025i | 0.198889 | − | 0.344486i | ||||
\(633\) | −1.00000 | − | 1.73205i | −0.0397464 | − | 0.0688428i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −9.50000 | + | 16.4545i | −0.376996 | + | 0.652976i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 5.00000 | − | 34.6410i | 0.198107 | − | 1.37253i | ||||
\(638\) | −18.0000 | −0.712627 | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 22.5000 | + | 38.9711i | 0.888697 | + | 1.53927i | 0.841417 | + | 0.540386i | \(0.181722\pi\) |
0.0472793 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(642\) | −12.0000 | + | 20.7846i | −0.473602 | + | 0.820303i | ||||
\(643\) | 38.0000 | 1.49857 | 0.749287 | − | 0.662246i | \(-0.230396\pi\) | ||||
0.749287 | + | 0.662246i | \(0.230396\pi\) | |||||||
\(644\) | −6.00000 | + | 5.19615i | −0.236433 | + | 0.204757i | ||||
\(645\) | −20.0000 | −0.787499 | ||||||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | 10.5000 | + | 18.1865i | 0.412798 | + | 0.714986i | 0.995194 | − | 0.0979182i | \(-0.0312184\pi\) |
−0.582397 | + | 0.812905i | \(0.697885\pi\) | |||||||
\(648\) | 5.50000 | + | 9.52628i | 0.216060 | + | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.00000 | 0.196116 | ||||||||
\(651\) | −4.00000 | − | 20.7846i | −0.156772 | − | 0.814613i | ||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −10.5000 | + | 18.1865i | −0.410897 | + | 0.711694i | −0.994988 | − | 0.0999939i | \(-0.968118\pi\) |
0.584091 | + | 0.811688i | \(0.301451\pi\) | |||||||
\(654\) | −4.00000 | − | 6.92820i | −0.156412 | − | 0.270914i | ||||
\(655\) | 1.50000 | + | 2.59808i | 0.0586098 | + | 0.101515i | ||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 7.50000 | + | 2.59808i | 0.292380 | + | 0.101284i | ||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | −3.00000 | + | 5.19615i | −0.116775 | + | 0.202260i | ||||
\(661\) | −22.0000 | − | 38.1051i | −0.855701 | − | 1.48212i | −0.875993 | − | 0.482323i | \(-0.839793\pi\) |
0.0202925 | − | 0.999794i | \(-0.493540\pi\) | |||||||
\(662\) | 3.50000 | + | 6.06218i | 0.136031 | + | 0.235613i | ||||
\(663\) | 30.0000 | − | 51.9615i | 1.16510 | − | 2.01802i | ||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 2.50000 | + | 0.866025i | 0.0969458 | + | 0.0335830i | ||||
\(666\) | 11.0000 | 0.426241 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | −4.50000 | − | 7.79423i | −0.174110 | − | 0.301568i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 1.00000 | + | 5.19615i | 0.0385758 | + | 0.200446i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −7.00000 | + | 12.1244i | −0.269630 | + | 0.467013i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | 1.50000 | − | 2.59808i | 0.0576497 | − | 0.0998522i | −0.835760 | − | 0.549095i | \(-0.814973\pi\) |
0.893410 | + | 0.449242i | \(0.148306\pi\) | |||||||
\(678\) | −24.0000 | −0.921714 | ||||||||
\(679\) | −28.0000 | + | 24.2487i | −1.07454 | + | 0.930580i | ||||
\(680\) | −6.00000 | −0.230089 | ||||||||
\(681\) | −24.0000 | + | 41.5692i | −0.919682 | + | 1.59294i | ||||
\(682\) | 6.00000 | + | 10.3923i | 0.229752 | + | 0.397942i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 56.0000 | 2.13653 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | −7.50000 | − | 12.9904i | −0.285727 | − | 0.494894i | ||||
\(690\) | −3.00000 | − | 5.19615i | −0.114208 | − | 0.197814i | ||||
\(691\) | −16.0000 | + | 27.7128i | −0.608669 | + | 1.05425i | 0.382791 | + | 0.923835i | \(0.374963\pi\) |
−0.991460 | + | 0.130410i | \(0.958371\pi\) | |||||||
\(692\) | 3.00000 | 0.114043 | ||||||||
\(693\) | −6.00000 | + | 5.19615i | −0.227921 | + | 0.197386i | ||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | −2.00000 | + | 3.46410i | −0.0758643 | + | 0.131401i | ||||
\(696\) | −6.00000 | − | 10.3923i | −0.227429 | − | 0.393919i | ||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 5.00000 | − | 8.66025i | 0.189253 | − | 0.327795i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | −0.500000 | − | 2.59808i | −0.0188982 | − | 0.0981981i | ||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | −10.0000 | + | 17.3205i | −0.377426 | + | 0.653720i | ||||
\(703\) | 5.50000 | + | 9.52628i | 0.207436 | + | 0.359290i | ||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | −3.00000 | + | 5.19615i | −0.112987 | + | 0.195698i | ||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | −30.0000 | − | 10.3923i | −1.12827 | − | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | + | 12.1244i | −0.262891 | + | 0.455340i | −0.967009 | − | 0.254743i | \(-0.918009\pi\) |
0.704118 | + | 0.710083i | \(0.251342\pi\) | |||||||
\(710\) | 6.00000 | + | 10.3923i | 0.225176 | + | 0.390016i | ||||
\(711\) | 5.00000 | + | 8.66025i | 0.187515 | + | 0.324785i | ||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | −30.0000 | − | 10.3923i | −1.12272 | − | 0.388922i | ||||
\(715\) | −15.0000 | −0.560968 | ||||||||
\(716\) | 1.50000 | − | 2.59808i | 0.0560576 | − | 0.0970947i | ||||
\(717\) | 6.00000 | + | 10.3923i | 0.224074 | + | 0.388108i | ||||
\(718\) | −3.00000 | − | 5.19615i | −0.111959 | − | 0.193919i | ||||
\(719\) | 18.0000 | − | 31.1769i | 0.671287 | − | 1.16270i | −0.306253 | − | 0.951950i | \(-0.599075\pi\) |
0.977539 | − | 0.210752i | \(-0.0675914\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 2.00000 | + | 10.3923i | 0.0744839 | + | 0.387030i | ||||
\(722\) | −18.0000 | −0.669891 | ||||||||
\(723\) | −25.0000 | + | 43.3013i | −0.929760 | + | 1.61039i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | −2.00000 | + | 3.46410i | −0.0742270 | + | 0.128565i | ||||
\(727\) | 29.0000 | 1.07555 | 0.537775 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537775 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(728\) | −10.0000 | + | 8.66025i | −0.370625 | + | 0.320970i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.00000 | + | 3.46410i | −0.0740233 | + | 0.128212i | ||||
\(731\) | 30.0000 | + | 51.9615i | 1.10959 | + | 1.92187i | ||||
\(732\) | −4.00000 | − | 6.92820i | −0.147844 | − | 0.256074i | ||||
\(733\) | −23.5000 | + | 40.7032i | −0.867992 | + | 1.50341i | −0.00394730 | + | 0.999992i | \(0.501256\pi\) |
−0.864045 | + | 0.503415i | \(0.832077\pi\) | |||||||
\(734\) | −1.00000 | −0.0369107 | ||||||||
\(735\) | 2.00000 | − | 13.8564i | 0.0737711 | − | 0.511101i | ||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 6.00000 | − | 10.3923i | 0.221013 | − | 0.382805i | ||||
\(738\) | −1.50000 | − | 2.59808i | −0.0552158 | − | 0.0956365i | ||||
\(739\) | 18.5000 | + | 32.0429i | 0.680534 | + | 1.17872i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 5.50000 | − | 9.52628i | 0.202184 | − | 0.350193i | ||||
\(741\) | 10.0000 | 0.367359 | ||||||||
\(742\) | −6.00000 | + | 5.19615i | −0.220267 | + | 0.190757i | ||||
\(743\) | 9.00000 | 0.330178 | 0.165089 | − | 0.986279i | \(-0.447209\pi\) | ||||
0.165089 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(744\) | −4.00000 | + | 6.92820i | −0.146647 | + | 0.254000i | ||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | 17.0000 | + | 29.4449i | 0.622414 | + | 1.07805i | ||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | 6.00000 | + | 31.1769i | 0.219235 | + | 1.13918i | ||||
\(750\) | 2.00000 | 0.0730297 | ||||||||
\(751\) | −13.0000 | + | 22.5167i | −0.474377 | + | 0.821645i | −0.999570 | − | 0.0293387i | \(-0.990660\pi\) |
0.525193 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | −15.0000 | − | 25.9808i | −0.546630 | − | 0.946792i | ||||
\(754\) | 15.0000 | − | 25.9808i | 0.546268 | − | 0.946164i | ||||
\(755\) | −14.0000 | −0.509512 | ||||||||
\(756\) | 10.0000 | + | 3.46410i | 0.363696 | + | 0.125988i | ||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 12.5000 | − | 21.6506i | 0.454020 | − | 0.786386i | ||||
\(759\) | 9.00000 | + | 15.5885i | 0.326679 | + | 0.565825i | ||||
\(760\) | −0.500000 | − | 0.866025i | −0.0181369 | − | 0.0314140i | ||||
\(761\) | 25.5000 | − | 44.1673i | 0.924374 | − | 1.60106i | 0.131810 | − | 0.991275i | \(-0.457921\pi\) |
0.792564 | − | 0.609788i | \(-0.208745\pi\) | |||||||
\(762\) | 38.0000 | 1.37659 | ||||||||
\(763\) | −10.0000 | − | 3.46410i | −0.362024 | − | 0.125409i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 3.00000 | − | 5.19615i | 0.108465 | − | 0.187867i | ||||
\(766\) | −7.50000 | − | 12.9904i | −0.270986 | − | 0.469362i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | − | 1.73205i | 0.0360844 | − | 0.0625000i | ||||
\(769\) | −49.0000 | −1.76699 | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||||
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 1.50000 | + | 7.79423i | 0.0540562 | + | 0.280885i | ||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | −19.5000 | − | 33.7750i | −0.701366 | − | 1.21480i | −0.967987 | − | 0.251000i | \(-0.919240\pi\) |
0.266621 | − | 0.963802i | \(-0.414093\pi\) | |||||||
\(774\) | 5.00000 | + | 8.66025i | 0.179721 | + | 0.311286i | ||||
\(775\) | 2.00000 | − | 3.46410i | 0.0718421 | − | 0.124434i | ||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 44.0000 | − | 38.1051i | 1.57849 | − | 1.36701i | ||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | 1.50000 | − | 2.59808i | 0.0537431 | − | 0.0930857i | ||||
\(780\) | −5.00000 | − | 8.66025i | −0.179029 | − | 0.310087i | ||||
\(781\) | −18.0000 | − | 31.1769i | −0.644091 | − | 1.11560i | ||||
\(782\) | −9.00000 | + | 15.5885i | −0.321839 | + | 0.557442i | ||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | −5.00000 | −0.178458 | ||||||||
\(786\) | 3.00000 | − | 5.19615i | 0.107006 | − | 0.185341i | ||||
\(787\) | 17.0000 | + | 29.4449i | 0.605985 | + | 1.04960i | 0.991895 | + | 0.127060i | \(0.0405540\pi\) |
−0.385911 | + | 0.922536i | \(0.626113\pi\) | |||||||
\(788\) | 1.50000 | + | 2.59808i | 0.0534353 | + | 0.0925526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.0000 | 0.355784 | ||||||||
\(791\) | −24.0000 | + | 20.7846i | −0.853342 | + | 0.739016i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | 10.0000 | − | 17.3205i | 0.355110 | − | 0.615069i | ||||
\(794\) | −1.00000 | − | 1.73205i | −0.0354887 | − | 0.0614682i | ||||
\(795\) | −3.00000 | − | 5.19615i | −0.106399 | − | 0.184289i | ||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | −1.00000 | − | 5.19615i | −0.0353996 | − | 0.183942i | ||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | −10.5000 | − | 18.1865i | −0.370768 | − | 0.642189i | ||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −7.50000 | − | 2.59808i | −0.264340 | − | 0.0915702i | ||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | −12.0000 | + | 20.7846i | −0.422420 | + | 0.731653i | ||||
\(808\) | 6.00000 | + | 10.3923i | 0.211079 | + | 0.365600i | ||||
\(809\) | −19.5000 | − | 33.7750i | −0.685583 | − | 1.18747i | −0.973253 | − | 0.229736i | \(-0.926214\pi\) |
0.287670 | − | 0.957730i | \(-0.407120\pi\) | |||||||
\(810\) | −5.50000 | + | 9.52628i | −0.193250 | + | 0.334719i | ||||
\(811\) | 47.0000 | 1.65039 | 0.825197 | − | 0.564846i | \(-0.191064\pi\) | ||||
0.825197 | + | 0.564846i | \(0.191064\pi\) | |||||||
\(812\) | −15.0000 | − | 5.19615i | −0.526397 | − | 0.182349i | ||||
\(813\) | 32.0000 | 1.12229 | ||||||||
\(814\) | −16.5000 | + | 28.5788i | −0.578325 | + | 1.00169i | ||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 6.00000 | + | 10.3923i | 0.210042 | + | 0.363803i | ||||
\(817\) | −5.00000 | + | 8.66025i | −0.174928 | + | 0.302984i | ||||
\(818\) | −22.0000 | −0.769212 | ||||||||
\(819\) | −2.50000 | − | 12.9904i | −0.0873571 | − | 0.453921i | ||||
\(820\) | −3.00000 | −0.104765 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 12.0000 | + | 20.7846i | 0.418548 | + | 0.724947i | ||||
\(823\) | −22.0000 | − | 38.1051i | −0.766872 | − | 1.32826i | −0.939251 | − | 0.343230i | \(-0.888479\pi\) |
0.172379 | − | 0.985031i | \(-0.444854\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.0000 | −1.87776 | −0.938882 | − | 0.344239i | \(-0.888137\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(828\) | −1.50000 | + | 2.59808i | −0.0521286 | + | 0.0902894i | ||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | −6.00000 | − | 10.3923i | −0.208263 | − | 0.360722i | ||||
\(831\) | 2.00000 | − | 3.46410i | 0.0693792 | − | 0.120168i | ||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | −39.0000 | + | 15.5885i | −1.35127 | + | 0.540108i | ||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | 4.50000 | − | 7.79423i | 0.155729 | − | 0.269730i | ||||
\(836\) | 1.50000 | + | 2.59808i | 0.0518786 | + | 0.0898563i | ||||
\(837\) | 8.00000 | + | 13.8564i | 0.276520 | + | 0.478947i | ||||
\(838\) | −7.50000 | + | 12.9904i | −0.259083 | + | 0.448745i | ||||
\(839\) | −6.00000 | −0.207143 | −0.103572 | − | 0.994622i | \(-0.533027\pi\) | ||||
−0.103572 | + | 0.994622i | \(0.533027\pi\) | |||||||
\(840\) | −4.00000 | + | 3.46410i | −0.138013 | + | 0.119523i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 17.0000 | − | 29.4449i | 0.585859 | − | 1.01474i | ||||
\(843\) | −3.00000 | − | 5.19615i | −0.103325 | − | 0.178965i | ||||
\(844\) | 0.500000 | + | 0.866025i | 0.0172107 | + | 0.0298098i | ||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 1.00000 | + | 5.19615i | 0.0343604 | + | 0.178542i | ||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | 26.0000 | − | 45.0333i | 0.892318 | − | 1.54554i | ||||
\(850\) | −3.00000 | − | 5.19615i | −0.102899 | − | 0.178227i | ||||
\(851\) | −16.5000 | − | 28.5788i | −0.565613 | − | 0.979670i | ||||
\(852\) | 12.0000 | − | 20.7846i | 0.411113 | − | 0.712069i | ||||
\(853\) | −1.00000 | −0.0342393 | −0.0171197 | − | 0.999853i | \(-0.505450\pi\) | ||||
−0.0171197 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(854\) | −10.0000 | − | 3.46410i | −0.342193 | − | 0.118539i | ||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 15.0000 | + | 25.9808i | 0.512092 | + | 0.886969i | ||||
\(859\) | −16.0000 | + | 27.7128i | −0.545913 | + | 0.945549i | 0.452636 | + | 0.891695i | \(0.350484\pi\) |
−0.998549 | + | 0.0538535i | \(0.982850\pi\) | |||||||
\(860\) | 10.0000 | 0.340997 | ||||||||
\(861\) | −15.0000 | − | 5.19615i | −0.511199 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.5000 | + | 33.7750i | −0.663788 | + | 1.14971i | 0.315825 | + | 0.948818i | \(0.397719\pi\) |
−0.979612 | + | 0.200897i | \(0.935615\pi\) | |||||||
\(864\) | −2.00000 | − | 3.46410i | −0.0680414 | − | 0.117851i | ||||
\(865\) | 1.50000 | + | 2.59808i | 0.0510015 | + | 0.0883372i | ||||
\(866\) | 8.00000 | − | 13.8564i | 0.271851 | − | 0.470860i | ||||
\(867\) | −38.0000 | −1.29055 | ||||||||
\(868\) | 2.00000 | + | 10.3923i | 0.0678844 | + | 0.352738i | ||||
\(869\) | −30.0000 | −1.01768 | ||||||||
\(870\) | 6.00000 | − | 10.3923i | 0.203419 | − | 0.352332i | ||||
\(871\) | 10.0000 | + | 17.3205i | 0.338837 | + | 0.586883i | ||||
\(872\) | 2.00000 | + | 3.46410i | 0.0677285 | + | 0.117309i | ||||
\(873\) | −7.00000 | + | 12.1244i | −0.236914 | + | 0.410347i | ||||
\(874\) | −3.00000 | −0.101477 | ||||||||
\(875\) | 2.00000 | − | 1.73205i | 0.0676123 | − | 0.0585540i | ||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 3.50000 | − | 6.06218i | 0.118187 | − | 0.204705i | −0.800862 | − | 0.598848i | \(-0.795625\pi\) |
0.919049 | + | 0.394143i | \(0.128959\pi\) | |||||||
\(878\) | 5.00000 | + | 8.66025i | 0.168742 | + | 0.292269i | ||||
\(879\) | −27.0000 | − | 46.7654i | −0.910687 | − | 1.57736i | ||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | −6.50000 | + | 2.59808i | −0.218866 | + | 0.0874818i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | −15.0000 | + | 25.9808i | −0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | + | 20.7846i | 0.403148 | + | 0.698273i | ||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | −22.0000 | −0.738272 | ||||||||
\(889\) | 38.0000 | − | 32.9090i | 1.27448 | − | 1.10373i | ||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 16.5000 | − | 28.5788i | 0.552771 | − | 0.957427i | ||||
\(892\) | −4.00000 | − | 6.92820i | −0.133930 | − | 0.231973i | ||||
\(893\) | 1.50000 | + | 2.59808i | 0.0501956 | + | 0.0869413i | ||||
\(894\) | 18.0000 | − | 31.1769i | 0.602010 | − | 1.04271i | ||||
\(895\) | 3.00000 | 0.100279 | ||||||||
\(896\) | −0.500000 | − | 2.59808i | −0.0167038 | − | 0.0867956i | ||||
\(897\) | −30.0000 | −1.00167 | ||||||||
\(898\) | 1.50000 | − | 2.59808i | 0.0500556 | − | 0.0866989i | ||||
\(899\) | −12.0000 | − | 20.7846i | −0.400222 | − | 0.693206i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −9.00000 | + | 15.5885i | −0.299833 | + | 0.519327i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 50.0000 | + | 17.3205i | 1.66390 | + | 0.576390i | ||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | 1.00000 | − | 1.73205i | 0.0332411 | − | 0.0575753i | ||||
\(906\) | 14.0000 | + | 24.2487i | 0.465119 | + | 0.805609i | ||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 12.0000 | − | 20.7846i | 0.398234 | − | 0.689761i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | −12.5000 | − | 4.33013i | −0.414371 | − | 0.143542i | ||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | −1.00000 | + | 1.73205i | −0.0331133 | + | 0.0573539i | ||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 11.0000 | + | 19.0526i | 0.363848 | + | 0.630203i | ||||
\(915\) | 4.00000 | − | 6.92820i | 0.132236 | − | 0.229039i | ||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | −1.50000 | − | 7.79423i | −0.0495344 | − | 0.257388i | ||||
\(918\) | 24.0000 | 0.792118 | ||||||||
\(919\) | −19.0000 | + | 32.9090i | −0.626752 | + | 1.08557i | 0.361447 | + | 0.932393i | \(0.382283\pi\) |
−0.988199 | + | 0.153174i | \(0.951051\pi\) | |||||||
\(920\) | 1.50000 | + | 2.59808i | 0.0494535 | + | 0.0856560i | ||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | −3.00000 | + | 5.19615i | −0.0987997 | + | 0.171126i | ||||
\(923\) | 60.0000 | 1.97492 | ||||||||
\(924\) | 12.0000 | − | 10.3923i | 0.394771 | − | 0.341882i | ||||
\(925\) | 11.0000 | 0.361678 | ||||||||
\(926\) | 9.50000 | − | 16.4545i | 0.312189 | − | 0.540728i | ||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | 3.00000 | + | 5.19615i | 0.0984798 | + | 0.170572i | ||||
\(929\) | −16.5000 | + | 28.5788i | −0.541347 | + | 0.937641i | 0.457480 | + | 0.889220i | \(0.348752\pi\) |
−0.998827 | + | 0.0484211i | \(0.984581\pi\) | |||||||
\(930\) | −8.00000 | −0.262330 | ||||||||
\(931\) | −5.50000 | − | 4.33013i | −0.180255 | − | 0.141914i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 12.0000 | − | 20.7846i | 0.392862 | − | 0.680458i | ||||
\(934\) | 9.00000 | + | 15.5885i | 0.294489 | + | 0.510070i | ||||
\(935\) | 9.00000 | + | 15.5885i | 0.294331 | + | 0.509797i | ||||
\(936\) | −2.50000 | + | 4.33013i | −0.0817151 | + | 0.141535i | ||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 8.00000 | − | 6.92820i | 0.261209 | − | 0.226214i | ||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | 1.50000 | − | 2.59808i | 0.0489246 | − | 0.0847399i | ||||
\(941\) | −12.0000 | − | 20.7846i | −0.391189 | − | 0.677559i | 0.601418 | − | 0.798935i | \(-0.294603\pi\) |
−0.992607 | + | 0.121376i | \(0.961269\pi\) | |||||||
\(942\) | 5.00000 | + | 8.66025i | 0.162909 | + | 0.282166i | ||||
\(943\) | −4.50000 | + | 7.79423i | −0.146540 | + | 0.253815i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | + | 10.3923i | 0.0650600 | + | 0.338062i | ||||
\(946\) | −30.0000 | −0.975384 | ||||||||
\(947\) | −15.0000 | + | 25.9808i | −0.487435 | + | 0.844261i | −0.999896 | − | 0.0144491i | \(-0.995401\pi\) |
0.512461 | + | 0.858710i | \(0.328734\pi\) | |||||||
\(948\) | −10.0000 | − | 17.3205i | −0.324785 | − | 0.562544i | ||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | 0.500000 | − | 0.866025i | 0.0162221 | − | 0.0280976i | ||||
\(951\) | −36.0000 | −1.16738 | ||||||||
\(952\) | 15.0000 | + | 5.19615i | 0.486153 | + | 0.168408i | ||||
\(953\) | −12.0000 | −0.388718 | −0.194359 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194359 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(954\) | −1.50000 | + | 2.59808i | −0.0485643 | + | 0.0841158i | ||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | −18.0000 | + | 31.1769i | −0.581857 | + | 1.00781i | ||||
\(958\) | 24.0000 | 0.775405 | ||||||||
\(959\) | 30.0000 | + | 10.3923i | 0.968751 | + | 0.335585i | ||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −27.5000 | − | 47.6314i | −0.886636 | − | 1.53570i | ||||
\(963\) | 6.00000 | + | 10.3923i | 0.193347 | + | 0.334887i | ||||
\(964\) | 12.5000 | − | 21.6506i | 0.402598 | − | 0.697320i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 3.00000 | + | 15.5885i | 0.0965234 | + | 0.501550i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | −6.00000 | − | 10.3923i | −0.192748 | − | 0.333849i | ||||
\(970\) | 7.00000 | + | 12.1244i | 0.224756 | + | 0.389290i | ||||
\(971\) | −13.5000 | + | 23.3827i | −0.433236 | + | 0.750386i | −0.997150 | − | 0.0754473i | \(-0.975962\pi\) |
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | 8.00000 | − | 6.92820i | 0.256468 | − | 0.222108i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 5.00000 | − | 8.66025i | 0.160128 | − | 0.277350i | ||||
\(976\) | 2.00000 | + | 3.46410i | 0.0640184 | + | 0.110883i | ||||
\(977\) | 15.0000 | + | 25.9808i | 0.479893 | + | 0.831198i | 0.999734 | − | 0.0230645i | \(-0.00734232\pi\) |
−0.519841 | + | 0.854263i | \(0.674009\pi\) | |||||||
\(978\) | −4.00000 | + | 6.92820i | −0.127906 | + | 0.221540i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | −1.00000 | + | 6.92820i | −0.0319438 | + | 0.221313i | ||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | −28.5000 | − | 49.3634i | −0.909009 | − | 1.57445i | −0.815444 | − | 0.578836i | \(-0.803507\pi\) |
−0.0935651 | − | 0.995613i | \(-0.529826\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | −1.50000 | + | 2.59808i | −0.0477940 | + | 0.0827816i | ||||
\(986\) | −36.0000 | −1.14647 | ||||||||
\(987\) | 12.0000 | − | 10.3923i | 0.381964 | − | 0.330791i | ||||
\(988\) | −5.00000 | −0.159071 | ||||||||
\(989\) | 15.0000 | − | 25.9808i | 0.476972 | − | 0.826140i | ||||
\(990\) | 1.50000 | + | 2.59808i | 0.0476731 | + | 0.0825723i | ||||
\(991\) | −10.0000 | − | 17.3205i | −0.317660 | − | 0.550204i | 0.662339 | − | 0.749204i | \(-0.269564\pi\) |
−0.979999 | + | 0.199000i | \(0.936231\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 14.0000 | 0.444277 | ||||||||
\(994\) | −6.00000 | − | 31.1769i | −0.190308 | − | 0.988872i | ||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | −12.0000 | + | 20.7846i | −0.380235 | + | 0.658586i | ||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | 14.0000 | + | 24.2487i | 0.443162 | + | 0.767580i | ||||
\(999\) | −22.0000 | + | 38.1051i | −0.696049 | + | 1.20559i |
(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 | 70.2.e.b.51.1 | yes | 2 | |
3.2 | odd | 2 | 630.2.k.e.541.1 | 2 | |||
4.3 | odd | 2 | 560.2.q.d.401.1 | 2 | |||
5.2 | odd | 4 | 350.2.j.a.149.1 | 4 | |||
5.3 | odd | 4 | 350.2.j.a.149.2 | 4 | |||
5.4 | even | 2 | 350.2.e.h.51.1 | 2 | |||
7.2 | even | 3 | 490.2.a.g.1.1 | 1 | |||
7.3 | odd | 6 | 490.2.e.a.361.1 | 2 | |||
7.4 | even | 3 | inner | 70.2.e.b.11.1 | ✓ | 2 | |
7.5 | odd | 6 | 490.2.a.j.1.1 | 1 | |||
7.6 | odd | 2 | 490.2.e.a.471.1 | 2 | |||
21.2 | odd | 6 | 4410.2.a.m.1.1 | 1 | |||
21.5 | even | 6 | 4410.2.a.c.1.1 | 1 | |||
21.11 | odd | 6 | 630.2.k.e.361.1 | 2 | |||
28.11 | odd | 6 | 560.2.q.d.81.1 | 2 | |||
28.19 | even | 6 | 3920.2.a.g.1.1 | 1 | |||
28.23 | odd | 6 | 3920.2.a.be.1.1 | 1 | |||
35.2 | odd | 12 | 2450.2.c.f.99.2 | 2 | |||
35.4 | even | 6 | 350.2.e.h.151.1 | 2 | |||
35.9 | even | 6 | 2450.2.a.p.1.1 | 1 | |||
35.12 | even | 12 | 2450.2.c.p.99.2 | 2 | |||
35.18 | odd | 12 | 350.2.j.a.249.1 | 4 | |||
35.19 | odd | 6 | 2450.2.a.f.1.1 | 1 | |||
35.23 | odd | 12 | 2450.2.c.f.99.1 | 2 | |||
35.32 | odd | 12 | 350.2.j.a.249.2 | 4 | |||
35.33 | even | 12 | 2450.2.c.p.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.b.11.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
70.2.e.b.51.1 | yes | 2 | 1.1 | even | 1 | trivial | |
350.2.e.h.51.1 | 2 | 5.4 | even | 2 | |||
350.2.e.h.151.1 | 2 | 35.4 | even | 6 | |||
350.2.j.a.149.1 | 4 | 5.2 | odd | 4 | |||
350.2.j.a.149.2 | 4 | 5.3 | odd | 4 | |||
350.2.j.a.249.1 | 4 | 35.18 | odd | 12 | |||
350.2.j.a.249.2 | 4 | 35.32 | odd | 12 | |||
490.2.a.g.1.1 | 1 | 7.2 | even | 3 | |||
490.2.a.j.1.1 | 1 | 7.5 | odd | 6 | |||
490.2.e.a.361.1 | 2 | 7.3 | odd | 6 | |||
490.2.e.a.471.1 | 2 | 7.6 | odd | 2 | |||
560.2.q.d.81.1 | 2 | 28.11 | odd | 6 | |||
560.2.q.d.401.1 | 2 | 4.3 | odd | 2 | |||
630.2.k.e.361.1 | 2 | 21.11 | odd | 6 | |||
630.2.k.e.541.1 | 2 | 3.2 | odd | 2 | |||
2450.2.a.f.1.1 | 1 | 35.19 | odd | 6 | |||
2450.2.a.p.1.1 | 1 | 35.9 | even | 6 | |||
2450.2.c.f.99.1 | 2 | 35.23 | odd | 12 | |||
2450.2.c.f.99.2 | 2 | 35.2 | odd | 12 | |||
2450.2.c.p.99.1 | 2 | 35.33 | even | 12 | |||
2450.2.c.p.99.2 | 2 | 35.12 | even | 12 | |||
3920.2.a.g.1.1 | 1 | 28.19 | even | 6 | |||
3920.2.a.be.1.1 | 1 | 28.23 | odd | 6 | |||
4410.2.a.c.1.1 | 1 | 21.5 | even | 6 | |||
4410.2.a.m.1.1 | 1 | 21.2 | odd | 6 |