Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-43})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} - 11x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.1 | ||
Root | \(-2.58945 + 2.07237i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.295 |
Dual form | 546.2.l.k.211.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | −3.08945 | + | 5.35109i | −0.931505 | + | 1.61341i | −0.150756 | + | 0.988571i | \(0.548171\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.50000 | − | 3.27872i | −0.416025 | − | 0.909353i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.00000 | + | 1.73205i | −0.258199 | + | 0.447214i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.08945 | + | 7.08314i | 0.938185 | + | 1.62498i | 0.768853 | + | 0.639425i | \(0.220828\pi\) |
0.169332 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −3.08945 | − | 5.35109i | −0.658674 | − | 1.14086i | ||||
\(23\) | −1.58945 | + | 2.75302i | −0.331424 | + | 0.574043i | −0.982791 | − | 0.184719i | \(-0.940862\pi\) |
0.651367 | + | 0.758763i | \(0.274196\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.58945 | + | 0.340322i | 0.703950 | + | 0.0667425i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | −4.08945 | + | 7.08314i | −0.759393 | + | 1.31531i | 0.183768 | + | 0.982970i | \(0.441170\pi\) |
−0.943161 | + | 0.332337i | \(0.892163\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | −7.17891 | −1.28937 | −0.644685 | − | 0.764448i | \(-0.723011\pi\) | ||||
−0.644685 | + | 0.764448i | \(0.723011\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 3.08945 | + | 5.35109i | 0.537805 | + | 0.931505i | ||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −1.00000 | − | 1.73205i | −0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | −8.17891 | −1.32679 | ||||||||
\(39\) | −3.58945 | − | 0.340322i | −0.574773 | − | 0.0544951i | ||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −2.08945 | + | 3.61904i | −0.326318 | + | 0.565199i | −0.981778 | − | 0.190030i | \(-0.939141\pi\) |
0.655460 | + | 0.755230i | \(0.272475\pi\) | |||||||
\(42\) | −0.500000 | + | 0.866025i | −0.0771517 | + | 0.133631i | ||||
\(43\) | −0.410546 | − | 0.711086i | −0.0626077 | − | 0.108440i | 0.833023 | − | 0.553239i | \(-0.186608\pi\) |
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(44\) | 6.17891 | 0.931505 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | −1.58945 | − | 2.75302i | −0.234352 | − | 0.405910i | ||||
\(47\) | 4.17891 | 0.609556 | 0.304778 | − | 0.952423i | \(-0.401418\pi\) | ||||
0.304778 | + | 0.952423i | \(0.401418\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −2.08945 | + | 2.93840i | −0.289755 | + | 0.407482i | ||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 6.17891 | − | 10.7022i | 0.833164 | − | 1.44308i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 8.17891 | 1.08332 | ||||||||
\(58\) | −4.08945 | − | 7.08314i | −0.536972 | − | 0.930062i | ||||
\(59\) | 0.410546 | + | 0.711086i | 0.0534485 | + | 0.0925755i | 0.891512 | − | 0.452998i | \(-0.149645\pi\) |
−0.838063 | + | 0.545573i | \(0.816312\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 1.50000 | + | 2.59808i | 0.192055 | + | 0.332650i | 0.945931 | − | 0.324367i | \(-0.105151\pi\) |
−0.753876 | + | 0.657017i | \(0.771818\pi\) | |||||||
\(62\) | 3.58945 | − | 6.21712i | 0.455861 | − | 0.789575i | ||||
\(63\) | 0.500000 | − | 0.866025i | 0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | + | 6.55744i | 0.372104 | + | 0.813350i | ||||
\(66\) | −6.17891 | −0.760571 | ||||||||
\(67\) | 7.58945 | − | 13.1453i | 0.927199 | − | 1.60596i | 0.139214 | − | 0.990262i | \(-0.455542\pi\) |
0.787985 | − | 0.615694i | \(-0.211124\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | 1.58945 | + | 2.75302i | 0.191348 | + | 0.331424i | ||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | −4.58945 | − | 7.94917i | −0.544668 | − | 0.943393i | −0.998628 | − | 0.0523705i | \(-0.983322\pi\) |
0.453960 | − | 0.891022i | \(-0.350011\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 4.08945 | − | 7.08314i | 0.469093 | − | 0.812492i | ||||
\(77\) | −6.17891 | −0.704152 | ||||||||
\(78\) | 2.08945 | − | 2.93840i | 0.236584 | − | 0.332708i | ||||
\(79\) | 1.82109 | 0.204889 | 0.102444 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102444 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.08945 | − | 3.61904i | −0.230742 | − | 0.399656i | ||||
\(83\) | −5.17891 | −0.568459 | −0.284230 | − | 0.958756i | \(-0.591738\pi\) | ||||
−0.284230 | + | 0.958756i | \(0.591738\pi\) | |||||||
\(84\) | −0.500000 | − | 0.866025i | −0.0545545 | − | 0.0944911i | ||||
\(85\) | 5.00000 | + | 8.66025i | 0.542326 | + | 0.939336i | ||||
\(86\) | 0.821092 | 0.0885406 | ||||||||
\(87\) | 4.08945 | + | 7.08314i | 0.438436 | + | 0.759393i | ||||
\(88\) | −3.08945 | + | 5.35109i | −0.329337 | + | 0.570428i | ||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 2.08945 | − | 2.93840i | 0.219034 | − | 0.308028i | ||||
\(92\) | 3.17891 | 0.331424 | ||||||||
\(93\) | −3.58945 | + | 6.21712i | −0.372209 | + | 0.644685i | ||||
\(94\) | −2.08945 | + | 3.61904i | −0.215511 | + | 0.373276i | ||||
\(95\) | −8.17891 | − | 14.1663i | −0.839138 | − | 1.45343i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.17891 | − | 10.7022i | −0.627373 | − | 1.08664i | −0.988077 | − | 0.153962i | \(-0.950797\pi\) |
0.360704 | − | 0.932680i | \(-0.382537\pi\) | |||||||
\(98\) | −0.500000 | − | 0.866025i | −0.0505076 | − | 0.0874818i | ||||
\(99\) | 6.17891 | 0.621004 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 8.17891 | − | 14.1663i | 0.813832 | − | 1.40960i | −0.0963319 | − | 0.995349i | \(-0.530711\pi\) |
0.910164 | − | 0.414249i | \(-0.135956\pi\) | |||||||
\(102\) | 2.50000 | − | 4.33013i | 0.247537 | − | 0.428746i | ||||
\(103\) | 3.17891 | 0.313227 | 0.156614 | − | 0.987660i | \(-0.449942\pi\) | ||||
0.156614 | + | 0.987660i | \(0.449942\pi\) | |||||||
\(104\) | −1.50000 | − | 3.27872i | −0.147087 | − | 0.321505i | ||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −3.91055 | + | 6.77326i | −0.378047 | + | 0.654796i | −0.990778 | − | 0.135495i | \(-0.956737\pi\) |
0.612731 | + | 0.790291i | \(0.290071\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 6.17891 | + | 10.7022i | 0.589136 | + | 1.02041i | ||||
\(111\) | 1.00000 | + | 1.73205i | 0.0949158 | + | 0.164399i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.17891 | + | 3.77398i | 0.204974 | + | 0.355026i | 0.950125 | − | 0.311871i | \(-0.100956\pi\) |
−0.745150 | + | 0.666897i | \(0.767622\pi\) | |||||||
\(114\) | −4.08945 | + | 7.08314i | −0.383012 | + | 0.663397i | ||||
\(115\) | 3.17891 | − | 5.50603i | 0.296435 | − | 0.513440i | ||||
\(116\) | 8.17891 | 0.759393 | ||||||||
\(117\) | −2.08945 | + | 2.93840i | −0.193170 | + | 0.271655i | ||||
\(118\) | −0.821092 | −0.0755876 | ||||||||
\(119\) | 2.50000 | − | 4.33013i | 0.229175 | − | 0.396942i | ||||
\(120\) | −1.00000 | + | 1.73205i | −0.0912871 | + | 0.158114i | ||||
\(121\) | −13.5895 | − | 23.5376i | −1.23540 | − | 2.13978i | ||||
\(122\) | −3.00000 | −0.271607 | ||||||||
\(123\) | 2.08945 | + | 3.61904i | 0.188400 | + | 0.326318i | ||||
\(124\) | 3.58945 | + | 6.21712i | 0.322343 | + | 0.558314i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0.500000 | + | 0.866025i | 0.0445435 | + | 0.0771517i | ||||
\(127\) | −6.00000 | + | 10.3923i | −0.532414 | + | 0.922168i | 0.466870 | + | 0.884326i | \(0.345382\pi\) |
−0.999284 | + | 0.0378419i | \(0.987952\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.821092 | −0.0722931 | ||||||||
\(130\) | −7.17891 | − | 0.680643i | −0.629632 | − | 0.0596963i | ||||
\(131\) | 19.5367 | 1.70693 | 0.853466 | − | 0.521149i | \(-0.174496\pi\) | ||||
0.853466 | + | 0.521149i | \(0.174496\pi\) | |||||||
\(132\) | 3.08945 | − | 5.35109i | 0.268902 | − | 0.465753i | ||||
\(133\) | −4.08945 | + | 7.08314i | −0.354601 | + | 0.614186i | ||||
\(134\) | 7.58945 | + | 13.1453i | 0.655629 | + | 1.13558i | ||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | 8.17891 | + | 14.1663i | 0.698771 | + | 1.21031i | 0.968893 | + | 0.247481i | \(0.0796028\pi\) |
−0.270121 | + | 0.962826i | \(0.587064\pi\) | |||||||
\(138\) | −3.17891 | −0.270607 | ||||||||
\(139\) | 9.08945 | + | 15.7434i | 0.770957 | + | 1.33534i | 0.937039 | + | 0.349225i | \(0.113555\pi\) |
−0.166081 | + | 0.986112i | \(0.553111\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | 2.08945 | − | 3.61904i | 0.175964 | − | 0.304778i | ||||
\(142\) | 9.17891 | 0.770277 | ||||||||
\(143\) | 22.1789 | + | 2.10282i | 1.85469 | + | 0.175846i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.17891 | − | 14.1663i | 0.679221 | − | 1.17645i | ||||
\(146\) | −2.00000 | + | 3.46410i | −0.165521 | + | 0.286691i | ||||
\(147\) | 0.500000 | + | 0.866025i | 0.0412393 | + | 0.0714286i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −2.41055 | − | 4.17519i | −0.197480 | − | 0.342045i | 0.750231 | − | 0.661176i | \(-0.229942\pi\) |
−0.947711 | + | 0.319131i | \(0.896609\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −14.5367 | −1.18298 | −0.591491 | − | 0.806312i | \(-0.701460\pi\) | ||||
−0.591491 | + | 0.806312i | \(0.701460\pi\) | |||||||
\(152\) | 4.08945 | + | 7.08314i | 0.331699 | + | 0.574519i | ||||
\(153\) | −2.50000 | + | 4.33013i | −0.202113 | + | 0.350070i | ||||
\(154\) | 3.08945 | − | 5.35109i | 0.248955 | − | 0.431203i | ||||
\(155\) | 14.3578 | 1.15325 | ||||||||
\(156\) | 1.50000 | + | 3.27872i | 0.120096 | + | 0.262508i | ||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −0.910546 | + | 1.57711i | −0.0724391 | + | 0.125468i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 1.00000 | + | 1.73205i | 0.0790569 | + | 0.136931i | ||||
\(161\) | −3.17891 | −0.250533 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 4.41055 | + | 7.63929i | 0.345461 | + | 0.598355i | 0.985437 | − | 0.170039i | \(-0.0543894\pi\) |
−0.639977 | + | 0.768394i | \(0.721056\pi\) | |||||||
\(164\) | 4.17891 | 0.326318 | ||||||||
\(165\) | −6.17891 | − | 10.7022i | −0.481027 | − | 0.833164i | ||||
\(166\) | 2.58945 | − | 4.48507i | 0.200981 | − | 0.348109i | ||||
\(167\) | 4.00000 | − | 6.92820i | 0.309529 | − | 0.536120i | −0.668730 | − | 0.743505i | \(-0.733162\pi\) |
0.978259 | + | 0.207385i | \(0.0664952\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −8.50000 | + | 9.83616i | −0.653846 | + | 0.756628i | ||||
\(170\) | −10.0000 | −0.766965 | ||||||||
\(171\) | 4.08945 | − | 7.08314i | 0.312728 | − | 0.541661i | ||||
\(172\) | −0.410546 | + | 0.711086i | −0.0313038 | + | 0.0542198i | ||||
\(173\) | −2.00000 | − | 3.46410i | −0.152057 | − | 0.263371i | 0.779926 | − | 0.625871i | \(-0.215256\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | −8.17891 | −0.620041 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | −3.08945 | − | 5.35109i | −0.232876 | − | 0.403354i | ||||
\(177\) | 0.821092 | 0.0617170 | ||||||||
\(178\) | −4.50000 | − | 7.79423i | −0.337289 | − | 0.584202i | ||||
\(179\) | 7.17891 | − | 12.4342i | 0.536577 | − | 0.929378i | −0.462508 | − | 0.886615i | \(-0.653051\pi\) |
0.999085 | − | 0.0427634i | \(-0.0136162\pi\) | |||||||
\(180\) | 1.00000 | − | 1.73205i | 0.0745356 | − | 0.129099i | ||||
\(181\) | 7.82109 | 0.581337 | 0.290669 | − | 0.956824i | \(-0.406122\pi\) | ||||
0.290669 | + | 0.956824i | \(0.406122\pi\) | |||||||
\(182\) | 1.50000 | + | 3.27872i | 0.111187 | + | 0.243035i | ||||
\(183\) | 3.00000 | 0.221766 | ||||||||
\(184\) | −1.58945 | + | 2.75302i | −0.117176 | + | 0.202955i | ||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | −3.58945 | − | 6.21712i | −0.263192 | − | 0.455861i | ||||
\(187\) | 30.8945 | 2.25923 | ||||||||
\(188\) | −2.08945 | − | 3.61904i | −0.152389 | − | 0.263946i | ||||
\(189\) | −0.500000 | − | 0.866025i | −0.0363696 | − | 0.0629941i | ||||
\(190\) | 16.3578 | 1.18672 | ||||||||
\(191\) | −13.7684 | − | 23.8475i | −0.996244 | − | 1.72554i | −0.573114 | − | 0.819476i | \(-0.694265\pi\) |
−0.423130 | − | 0.906069i | \(-0.639069\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −10.2684 | + | 17.7853i | −0.739133 | + | 1.28022i | 0.213753 | + | 0.976888i | \(0.431431\pi\) |
−0.952886 | + | 0.303328i | \(0.901902\pi\) | |||||||
\(194\) | 12.3578 | 0.887240 | ||||||||
\(195\) | 7.17891 | + | 0.680643i | 0.514092 | + | 0.0487419i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −8.50000 | + | 14.7224i | −0.605600 | + | 1.04893i | 0.386356 | + | 0.922350i | \(0.373733\pi\) |
−0.991956 | + | 0.126580i | \(0.959600\pi\) | |||||||
\(198\) | −3.08945 | + | 5.35109i | −0.219558 | + | 0.380286i | ||||
\(199\) | −6.41055 | − | 11.1034i | −0.454432 | − | 0.787099i | 0.544224 | − | 0.838940i | \(-0.316824\pi\) |
−0.998655 | + | 0.0518416i | \(0.983491\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −7.58945 | − | 13.1453i | −0.535319 | − | 0.927199i | ||||
\(202\) | 8.17891 | + | 14.1663i | 0.575466 | + | 0.996736i | ||||
\(203\) | −8.17891 | −0.574047 | ||||||||
\(204\) | 2.50000 | + | 4.33013i | 0.175035 | + | 0.303170i | ||||
\(205\) | 4.17891 | − | 7.23808i | 0.291868 | − | 0.505530i | ||||
\(206\) | −1.58945 | + | 2.75302i | −0.110743 | + | 0.191812i | ||||
\(207\) | 3.17891 | 0.220949 | ||||||||
\(208\) | 3.58945 | + | 0.340322i | 0.248884 | + | 0.0235971i | ||||
\(209\) | −50.5367 | −3.49570 | ||||||||
\(210\) | 1.00000 | − | 1.73205i | 0.0690066 | − | 0.119523i | ||||
\(211\) | −8.17891 | + | 14.1663i | −0.563059 | + | 0.975247i | 0.434168 | + | 0.900832i | \(0.357042\pi\) |
−0.997227 | + | 0.0744154i | \(0.976291\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | −9.17891 | −0.628928 | ||||||||
\(214\) | −3.91055 | − | 6.77326i | −0.267319 | − | 0.463011i | ||||
\(215\) | 0.821092 | + | 1.42217i | 0.0559980 | + | 0.0969914i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.58945 | − | 6.21712i | −0.243668 | − | 0.422045i | ||||
\(218\) | −2.00000 | + | 3.46410i | −0.135457 | + | 0.234619i | ||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | −12.3578 | −0.833164 | ||||||||
\(221\) | −10.4473 | + | 14.6920i | −0.702759 | + | 0.988290i | ||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | −4.58945 | + | 7.94917i | −0.307333 | + | 0.532316i | −0.977778 | − | 0.209643i | \(-0.932770\pi\) |
0.670445 | + | 0.741959i | \(0.266103\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | −4.35782 | −0.289878 | ||||||||
\(227\) | −4.17891 | − | 7.23808i | −0.277364 | − | 0.480408i | 0.693365 | − | 0.720587i | \(-0.256127\pi\) |
−0.970729 | + | 0.240178i | \(0.922794\pi\) | |||||||
\(228\) | −4.08945 | − | 7.08314i | −0.270831 | − | 0.469093i | ||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | 3.17891 | + | 5.50603i | 0.209611 | + | 0.363057i | ||||
\(231\) | −3.08945 | + | 5.35109i | −0.203271 | + | 0.352076i | ||||
\(232\) | −4.08945 | + | 7.08314i | −0.268486 | + | 0.465031i | ||||
\(233\) | −0.357817 | −0.0234414 | −0.0117207 | − | 0.999931i | \(-0.503731\pi\) | ||||
−0.0117207 | + | 0.999931i | \(0.503731\pi\) | |||||||
\(234\) | −1.50000 | − | 3.27872i | −0.0980581 | − | 0.214337i | ||||
\(235\) | −8.35782 | −0.545204 | ||||||||
\(236\) | 0.410546 | − | 0.711086i | 0.0267243 | − | 0.0462878i | ||||
\(237\) | 0.910546 | − | 1.57711i | 0.0591463 | − | 0.102444i | ||||
\(238\) | 2.50000 | + | 4.33013i | 0.162051 | + | 0.280680i | ||||
\(239\) | −1.17891 | −0.0762572 | −0.0381286 | − | 0.999273i | \(-0.512140\pi\) | ||||
−0.0381286 | + | 0.999273i | \(0.512140\pi\) | |||||||
\(240\) | −1.00000 | − | 1.73205i | −0.0645497 | − | 0.111803i | ||||
\(241\) | 9.17891 | + | 15.8983i | 0.591265 | + | 1.02410i | 0.994062 | + | 0.108812i | \(0.0347048\pi\) |
−0.402797 | + | 0.915289i | \(0.631962\pi\) | |||||||
\(242\) | 27.1789 | 1.74713 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.50000 | − | 2.59808i | 0.0960277 | − | 0.166325i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | −4.17891 | −0.266437 | ||||||||
\(247\) | 17.0895 | − | 24.0329i | 1.08738 | − | 1.52918i | ||||
\(248\) | −7.17891 | −0.455861 | ||||||||
\(249\) | −2.58945 | + | 4.48507i | −0.164100 | + | 0.284230i | ||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | −5.41055 | − | 9.37134i | −0.341511 | − | 0.591514i | 0.643203 | − | 0.765696i | \(-0.277605\pi\) |
−0.984713 | + | 0.174182i | \(0.944272\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −9.82109 | − | 17.0106i | −0.617447 | − | 1.06945i | ||||
\(254\) | −6.00000 | − | 10.3923i | −0.376473 | − | 0.652071i | ||||
\(255\) | 10.0000 | 0.626224 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −12.8578 | + | 22.2704i | −0.802049 | + | 1.38919i | 0.116217 | + | 0.993224i | \(0.462923\pi\) |
−0.918266 | + | 0.395965i | \(0.870410\pi\) | |||||||
\(258\) | 0.410546 | − | 0.711086i | 0.0255595 | − | 0.0442703i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 4.17891 | − | 5.87680i | 0.259165 | − | 0.364463i | ||||
\(261\) | 8.17891 | 0.506262 | ||||||||
\(262\) | −9.76836 | + | 16.9193i | −0.603491 | + | 1.04528i | ||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 3.08945 | + | 5.35109i | 0.190143 | + | 0.329337i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −4.08945 | − | 7.08314i | −0.250741 | − | 0.434295i | ||||
\(267\) | 4.50000 | + | 7.79423i | 0.275396 | + | 0.476999i | ||||
\(268\) | −15.1789 | −0.927199 | ||||||||
\(269\) | −9.17891 | − | 15.8983i | −0.559648 | − | 0.969339i | −0.997526 | − | 0.0703041i | \(-0.977603\pi\) |
0.437878 | − | 0.899035i | \(-0.355730\pi\) | |||||||
\(270\) | −1.00000 | + | 1.73205i | −0.0608581 | + | 0.105409i | ||||
\(271\) | −15.5895 | + | 27.0017i | −0.946992 | + | 1.64024i | −0.195279 | + | 0.980748i | \(0.562561\pi\) |
−0.751713 | + | 0.659490i | \(0.770772\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | −1.50000 | − | 3.27872i | −0.0907841 | − | 0.198437i | ||||
\(274\) | −16.3578 | −0.988212 | ||||||||
\(275\) | 3.08945 | − | 5.35109i | 0.186301 | − | 0.322683i | ||||
\(276\) | 1.58945 | − | 2.75302i | 0.0956739 | − | 0.165712i | ||||
\(277\) | −14.1789 | − | 24.5586i | −0.851928 | − | 1.47558i | −0.879466 | − | 0.475962i | \(-0.842100\pi\) |
0.0275379 | − | 0.999621i | \(-0.491233\pi\) | |||||||
\(278\) | −18.1789 | −1.09030 | ||||||||
\(279\) | 3.58945 | + | 6.21712i | 0.214895 | + | 0.372209i | ||||
\(280\) | −1.00000 | − | 1.73205i | −0.0597614 | − | 0.103510i | ||||
\(281\) | 5.64218 | 0.336584 | 0.168292 | − | 0.985737i | \(-0.446175\pi\) | ||||
0.168292 | + | 0.985737i | \(0.446175\pi\) | |||||||
\(282\) | 2.08945 | + | 3.61904i | 0.124425 | + | 0.215511i | ||||
\(283\) | −15.1789 | + | 26.2906i | −0.902292 | + | 1.56282i | −0.0777814 | + | 0.996970i | \(0.524784\pi\) |
−0.824511 | + | 0.565846i | \(0.808550\pi\) | |||||||
\(284\) | −4.58945 | + | 7.94917i | −0.272334 | + | 0.471696i | ||||
\(285\) | −16.3578 | −0.968953 | ||||||||
\(286\) | −12.9105 | + | 18.1561i | −0.763417 | + | 1.07359i | ||||
\(287\) | −4.17891 | −0.246673 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 8.17891 | + | 14.1663i | 0.480282 | + | 0.831873i | ||||
\(291\) | −12.3578 | −0.724428 | ||||||||
\(292\) | −2.00000 | − | 3.46410i | −0.117041 | − | 0.202721i | ||||
\(293\) | −6.00000 | − | 10.3923i | −0.350524 | − | 0.607125i | 0.635818 | − | 0.771839i | \(-0.280663\pi\) |
−0.986341 | + | 0.164714i | \(0.947330\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −0.821092 | − | 1.42217i | −0.0478058 | − | 0.0828021i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 3.08945 | − | 5.35109i | 0.179268 | − | 0.310502i | ||||
\(298\) | 4.82109 | 0.279278 | ||||||||
\(299\) | 11.4105 | + | 1.08185i | 0.659889 | + | 0.0625651i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0.410546 | − | 0.711086i | 0.0236635 | − | 0.0409863i | ||||
\(302\) | 7.26836 | − | 12.5892i | 0.418247 | − | 0.724426i | ||||
\(303\) | −8.17891 | − | 14.1663i | −0.469866 | − | 0.813832i | ||||
\(304\) | −8.17891 | −0.469093 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | −2.50000 | − | 4.33013i | −0.142915 | − | 0.247537i | ||||
\(307\) | 24.8945 | 1.42081 | 0.710403 | − | 0.703795i | \(-0.248513\pi\) | ||||
0.710403 | + | 0.703795i | \(0.248513\pi\) | |||||||
\(308\) | 3.08945 | + | 5.35109i | 0.176038 | + | 0.304907i | ||||
\(309\) | 1.58945 | − | 2.75302i | 0.0904209 | − | 0.156614i | ||||
\(310\) | −7.17891 | + | 12.4342i | −0.407735 | + | 0.706217i | ||||
\(311\) | −8.53673 | −0.484073 | −0.242037 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242037 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(312\) | −3.58945 | − | 0.340322i | −0.203213 | − | 0.0192669i | ||||
\(313\) | 4.00000 | 0.226093 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(314\) | −1.00000 | + | 1.73205i | −0.0564333 | + | 0.0977453i | ||||
\(315\) | −1.00000 | + | 1.73205i | −0.0563436 | + | 0.0975900i | ||||
\(316\) | −0.910546 | − | 1.57711i | −0.0512222 | − | 0.0887195i | ||||
\(317\) | 7.17891 | 0.403208 | 0.201604 | − | 0.979467i | \(-0.435385\pi\) | ||||
0.201604 | + | 0.979467i | \(0.435385\pi\) | |||||||
\(318\) | −1.50000 | − | 2.59808i | −0.0841158 | − | 0.145693i | ||||
\(319\) | −25.2684 | − | 43.7661i | −1.41476 | − | 2.45043i | ||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 3.91055 | + | 6.77326i | 0.218265 | + | 0.378047i | ||||
\(322\) | 1.58945 | − | 2.75302i | 0.0885768 | − | 0.153420i | ||||
\(323\) | 20.4473 | − | 35.4157i | 1.13772 | − | 1.97058i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.50000 | + | 3.27872i | 0.0832050 | + | 0.181871i | ||||
\(326\) | −8.82109 | −0.488555 | ||||||||
\(327\) | 2.00000 | − | 3.46410i | 0.110600 | − | 0.191565i | ||||
\(328\) | −2.08945 | + | 3.61904i | −0.115371 | + | 0.199828i | ||||
\(329\) | 2.08945 | + | 3.61904i | 0.115195 | + | 0.199524i | ||||
\(330\) | 12.3578 | 0.680275 | ||||||||
\(331\) | 12.1789 | + | 21.0945i | 0.669413 | + | 1.15946i | 0.978068 | + | 0.208284i | \(0.0667878\pi\) |
−0.308655 | + | 0.951174i | \(0.599879\pi\) | |||||||
\(332\) | 2.58945 | + | 4.48507i | 0.142115 | + | 0.246150i | ||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 4.00000 | + | 6.92820i | 0.218870 | + | 0.379094i | ||||
\(335\) | −15.1789 | + | 26.2906i | −0.829312 | + | 1.43641i | ||||
\(336\) | −0.500000 | + | 0.866025i | −0.0272772 | + | 0.0472456i | ||||
\(337\) | −0.536725 | −0.0292373 | −0.0146186 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146186 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(338\) | −4.26836 | − | 12.2793i | −0.232168 | − | 0.667906i | ||||
\(339\) | 4.35782 | 0.236684 | ||||||||
\(340\) | 5.00000 | − | 8.66025i | 0.271163 | − | 0.469668i | ||||
\(341\) | 22.1789 | − | 38.4150i | 1.20106 | − | 2.08029i | ||||
\(342\) | 4.08945 | + | 7.08314i | 0.221132 | + | 0.383012i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −0.410546 | − | 0.711086i | −0.0221351 | − | 0.0383392i | ||||
\(345\) | −3.17891 | − | 5.50603i | −0.171147 | − | 0.296435i | ||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 3.91055 | + | 6.77326i | 0.209929 | + | 0.363608i | 0.951692 | − | 0.307054i | \(-0.0993433\pi\) |
−0.741763 | + | 0.670662i | \(0.766010\pi\) | |||||||
\(348\) | 4.08945 | − | 7.08314i | 0.219218 | − | 0.379696i | ||||
\(349\) | 1.58945 | − | 2.75302i | 0.0850815 | − | 0.147366i | −0.820344 | − | 0.571870i | \(-0.806218\pi\) |
0.905426 | + | 0.424504i | \(0.139552\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 1.50000 | + | 3.27872i | 0.0800641 | + | 0.175005i | ||||
\(352\) | 6.17891 | 0.329337 | ||||||||
\(353\) | 3.58945 | − | 6.21712i | 0.191047 | − | 0.330904i | −0.754550 | − | 0.656242i | \(-0.772145\pi\) |
0.945598 | + | 0.325339i | \(0.105478\pi\) | |||||||
\(354\) | −0.410546 | + | 0.711086i | −0.0218203 | + | 0.0377938i | ||||
\(355\) | 9.17891 | + | 15.8983i | 0.487166 | + | 0.843796i | ||||
\(356\) | 9.00000 | 0.476999 | ||||||||
\(357\) | −2.50000 | − | 4.33013i | −0.132314 | − | 0.229175i | ||||
\(358\) | 7.17891 | + | 12.4342i | 0.379417 | + | 0.657170i | ||||
\(359\) | 12.3578 | 0.652221 | 0.326110 | − | 0.945332i | \(-0.394262\pi\) | ||||
0.326110 | + | 0.945332i | \(0.394262\pi\) | |||||||
\(360\) | 1.00000 | + | 1.73205i | 0.0527046 | + | 0.0912871i | ||||
\(361\) | −23.9473 | + | 41.4779i | −1.26038 | + | 2.18305i | ||||
\(362\) | −3.91055 | + | 6.77326i | −0.205534 | + | 0.355995i | ||||
\(363\) | −27.1789 | −1.42652 | ||||||||
\(364\) | −3.58945 | − | 0.340322i | −0.188139 | − | 0.0178377i | ||||
\(365\) | −8.00000 | −0.418739 | ||||||||
\(366\) | −1.50000 | + | 2.59808i | −0.0784063 | + | 0.135804i | ||||
\(367\) | −1.58945 | + | 2.75302i | −0.0829688 | + | 0.143706i | −0.904524 | − | 0.426423i | \(-0.859774\pi\) |
0.821555 | + | 0.570129i | \(0.193107\pi\) | |||||||
\(368\) | −1.58945 | − | 2.75302i | −0.0828560 | − | 0.143511i | ||||
\(369\) | 4.17891 | 0.217545 | ||||||||
\(370\) | 2.00000 | + | 3.46410i | 0.103975 | + | 0.180090i | ||||
\(371\) | −1.50000 | − | 2.59808i | −0.0778761 | − | 0.134885i | ||||
\(372\) | 7.17891 | 0.372209 | ||||||||
\(373\) | 10.0000 | + | 17.3205i | 0.517780 | + | 0.896822i | 0.999787 | + | 0.0206542i | \(0.00657489\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(374\) | −15.4473 | + | 26.7555i | −0.798759 | + | 1.38349i | ||||
\(375\) | 6.00000 | − | 10.3923i | 0.309839 | − | 0.536656i | ||||
\(376\) | 4.17891 | 0.215511 | ||||||||
\(377\) | 29.3578 | + | 2.78346i | 1.51200 | + | 0.143355i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −10.3578 | + | 17.9403i | −0.532045 | + | 0.921530i | 0.467255 | + | 0.884123i | \(0.345243\pi\) |
−0.999300 | + | 0.0374068i | \(0.988090\pi\) | |||||||
\(380\) | −8.17891 | + | 14.1663i | −0.419569 | + | 0.726715i | ||||
\(381\) | 6.00000 | + | 10.3923i | 0.307389 | + | 0.532414i | ||||
\(382\) | 27.5367 | 1.40890 | ||||||||
\(383\) | −4.91055 | − | 8.50531i | −0.250917 | − | 0.434601i | 0.712861 | − | 0.701305i | \(-0.247399\pi\) |
−0.963779 | + | 0.266704i | \(0.914066\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 12.3578 | 0.629813 | ||||||||
\(386\) | −10.2684 | − | 17.7853i | −0.522646 | − | 0.905249i | ||||
\(387\) | −0.410546 | + | 0.711086i | −0.0208692 | + | 0.0361465i | ||||
\(388\) | −6.17891 | + | 10.7022i | −0.313687 | + | 0.543321i | ||||
\(389\) | −0.821092 | −0.0416310 | −0.0208155 | − | 0.999783i | \(-0.506626\pi\) | ||||
−0.0208155 | + | 0.999783i | \(0.506626\pi\) | |||||||
\(390\) | −4.17891 | + | 5.87680i | −0.211607 | + | 0.297583i | ||||
\(391\) | 15.8945 | 0.803822 | ||||||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | 9.76836 | − | 16.9193i | 0.492749 | − | 0.853466i | ||||
\(394\) | −8.50000 | − | 14.7224i | −0.428224 | − | 0.741705i | ||||
\(395\) | −3.64218 | −0.183258 | ||||||||
\(396\) | −3.08945 | − | 5.35109i | −0.155251 | − | 0.268902i | ||||
\(397\) | −1.50000 | − | 2.59808i | −0.0752828 | − | 0.130394i | 0.825926 | − | 0.563778i | \(-0.190653\pi\) |
−0.901209 | + | 0.433384i | \(0.857319\pi\) | |||||||
\(398\) | 12.8211 | 0.642663 | ||||||||
\(399\) | 4.08945 | + | 7.08314i | 0.204729 | + | 0.354601i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −16.1789 | + | 28.0227i | −0.807936 | + | 1.39939i | 0.106355 | + | 0.994328i | \(0.466082\pi\) |
−0.914291 | + | 0.405058i | \(0.867251\pi\) | |||||||
\(402\) | 15.1789 | 0.757055 | ||||||||
\(403\) | 10.7684 | + | 23.5376i | 0.536410 | + | 1.17249i | ||||
\(404\) | −16.3578 | −0.813832 | ||||||||
\(405\) | 1.00000 | − | 1.73205i | 0.0496904 | − | 0.0860663i | ||||
\(406\) | 4.08945 | − | 7.08314i | 0.202956 | − | 0.351530i | ||||
\(407\) | −6.17891 | − | 10.7022i | −0.306277 | − | 0.530488i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 6.82109 | + | 11.8145i | 0.337281 | + | 0.584188i | 0.983920 | − | 0.178608i | \(-0.0571593\pi\) |
−0.646639 | + | 0.762796i | \(0.723826\pi\) | |||||||
\(410\) | 4.17891 | + | 7.23808i | 0.206382 | + | 0.357463i | ||||
\(411\) | 16.3578 | 0.806872 | ||||||||
\(412\) | −1.58945 | − | 2.75302i | −0.0783068 | − | 0.135631i | ||||
\(413\) | −0.410546 | + | 0.711086i | −0.0202016 | + | 0.0349903i | ||||
\(414\) | −1.58945 | + | 2.75302i | −0.0781174 | + | 0.135303i | ||||
\(415\) | 10.3578 | 0.508445 | ||||||||
\(416\) | −2.08945 | + | 2.93840i | −0.102444 | + | 0.144067i | ||||
\(417\) | 18.1789 | 0.890225 | ||||||||
\(418\) | 25.2684 | − | 43.7661i | 1.23592 | − | 2.14067i | ||||
\(419\) | −14.9473 | + | 25.8894i | −0.730222 | + | 1.26478i | 0.226566 | + | 0.973996i | \(0.427250\pi\) |
−0.956788 | + | 0.290786i | \(0.906083\pi\) | |||||||
\(420\) | 1.00000 | + | 1.73205i | 0.0487950 | + | 0.0845154i | ||||
\(421\) | −34.7156 | −1.69194 | −0.845968 | − | 0.533233i | \(-0.820977\pi\) | ||||
−0.845968 | + | 0.533233i | \(0.820977\pi\) | |||||||
\(422\) | −8.17891 | − | 14.1663i | −0.398143 | − | 0.689604i | ||||
\(423\) | −2.08945 | − | 3.61904i | −0.101593 | − | 0.175964i | ||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 2.50000 | + | 4.33013i | 0.121268 | + | 0.210042i | ||||
\(426\) | 4.58945 | − | 7.94917i | 0.222360 | − | 0.385138i | ||||
\(427\) | −1.50000 | + | 2.59808i | −0.0725901 | + | 0.125730i | ||||
\(428\) | 7.82109 | 0.378047 | ||||||||
\(429\) | 12.9105 | − | 18.1561i | 0.623327 | − | 0.876584i | ||||
\(430\) | −1.64218 | −0.0791931 | ||||||||
\(431\) | 0.589454 | − | 1.02096i | 0.0283930 | − | 0.0491781i | −0.851480 | − | 0.524387i | \(-0.824294\pi\) |
0.879873 | + | 0.475209i | \(0.157628\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −5.82109 | − | 10.0824i | −0.279744 | − | 0.484530i | 0.691577 | − | 0.722303i | \(-0.256916\pi\) |
−0.971321 | + | 0.237772i | \(0.923583\pi\) | |||||||
\(434\) | 7.17891 | 0.344599 | ||||||||
\(435\) | −8.17891 | − | 14.1663i | −0.392149 | − | 0.679221i | ||||
\(436\) | −2.00000 | − | 3.46410i | −0.0957826 | − | 0.165900i | ||||
\(437\) | −26.0000 | −1.24375 | ||||||||
\(438\) | 2.00000 | + | 3.46410i | 0.0955637 | + | 0.165521i | ||||
\(439\) | 2.35782 | − | 4.08386i | 0.112532 | − | 0.194912i | −0.804258 | − | 0.594280i | \(-0.797437\pi\) |
0.916791 | + | 0.399368i | \(0.130770\pi\) | |||||||
\(440\) | 6.17891 | − | 10.7022i | 0.294568 | − | 0.510207i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.50000 | − | 16.3936i | −0.356739 | − | 0.779764i | ||||
\(443\) | −8.17891 | −0.388592 | −0.194296 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194296 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(444\) | 1.00000 | − | 1.73205i | 0.0474579 | − | 0.0821995i | ||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | −4.58945 | − | 7.94917i | −0.217317 | − | 0.376404i | ||||
\(447\) | −4.82109 | −0.228030 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | 7.00000 | + | 12.1244i | 0.330350 | + | 0.572184i | 0.982581 | − | 0.185837i | \(-0.0594997\pi\) |
−0.652230 | + | 0.758021i | \(0.726166\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −12.9105 | − | 22.3617i | −0.607934 | − | 1.05297i | ||||
\(452\) | 2.17891 | − | 3.77398i | 0.102487 | − | 0.177513i | ||||
\(453\) | −7.26836 | + | 12.5892i | −0.341497 | + | 0.591491i | ||||
\(454\) | 8.35782 | 0.392252 | ||||||||
\(455\) | −4.17891 | + | 5.87680i | −0.195910 | + | 0.275508i | ||||
\(456\) | 8.17891 | 0.383012 | ||||||||
\(457\) | 15.9473 | − | 27.6215i | 0.745982 | − | 1.29208i | −0.203753 | − | 0.979022i | \(-0.565314\pi\) |
0.949735 | − | 0.313056i | \(-0.101353\pi\) | |||||||
\(458\) | −0.500000 | + | 0.866025i | −0.0233635 | + | 0.0404667i | ||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | −6.35782 | −0.296435 | ||||||||
\(461\) | 12.3578 | + | 21.4044i | 0.575561 | + | 0.996901i | 0.995980 | + | 0.0895709i | \(0.0285496\pi\) |
−0.420420 | + | 0.907330i | \(0.638117\pi\) | |||||||
\(462\) | −3.08945 | − | 5.35109i | −0.143734 | − | 0.248955i | ||||
\(463\) | −28.8945 | −1.34284 | −0.671422 | − | 0.741076i | \(-0.734316\pi\) | ||||
−0.671422 | + | 0.741076i | \(0.734316\pi\) | |||||||
\(464\) | −4.08945 | − | 7.08314i | −0.189848 | − | 0.328827i | ||||
\(465\) | 7.17891 | − | 12.4342i | 0.332914 | − | 0.576624i | ||||
\(466\) | 0.178908 | − | 0.309878i | 0.00828777 | − | 0.0143548i | ||||
\(467\) | 33.8945 | 1.56845 | 0.784226 | − | 0.620475i | \(-0.213060\pi\) | ||||
0.784226 | + | 0.620475i | \(0.213060\pi\) | |||||||
\(468\) | 3.58945 | + | 0.340322i | 0.165923 | + | 0.0157314i | ||||
\(469\) | 15.1789 | 0.700897 | ||||||||
\(470\) | 4.17891 | − | 7.23808i | 0.192759 | − | 0.333868i | ||||
\(471\) | 1.00000 | − | 1.73205i | 0.0460776 | − | 0.0798087i | ||||
\(472\) | 0.410546 | + | 0.711086i | 0.0188969 | + | 0.0327304i | ||||
\(473\) | 5.07345 | 0.233277 | ||||||||
\(474\) | 0.910546 | + | 1.57711i | 0.0418228 | + | 0.0724391i | ||||
\(475\) | −4.08945 | − | 7.08314i | −0.187637 | − | 0.324997i | ||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | 1.50000 | + | 2.59808i | 0.0686803 | + | 0.118958i | ||||
\(478\) | 0.589454 | − | 1.02096i | 0.0269610 | − | 0.0466978i | ||||
\(479\) | 14.9105 | − | 25.8258i | 0.681280 | − | 1.18001i | −0.293310 | − | 0.956017i | \(-0.594757\pi\) |
0.974590 | − | 0.223995i | \(-0.0719098\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | 7.17891 | + | 0.680643i | 0.327330 | + | 0.0310347i | ||||
\(482\) | −18.3578 | −0.836176 | ||||||||
\(483\) | −1.58945 | + | 2.75302i | −0.0723227 | + | 0.125267i | ||||
\(484\) | −13.5895 | + | 23.5376i | −0.617702 | + | 1.06989i | ||||
\(485\) | 12.3578 | + | 21.4044i | 0.561140 | + | 0.971922i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 19.0895 | + | 33.0639i | 0.865026 | + | 1.49827i | 0.867022 | + | 0.498271i | \(0.166031\pi\) |
−0.00199588 | + | 0.999998i | \(0.500635\pi\) | |||||||
\(488\) | 1.50000 | + | 2.59808i | 0.0679018 | + | 0.117609i | ||||
\(489\) | 8.82109 | 0.398904 | ||||||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 2.08945 | − | 3.61904i | 0.0941999 | − | 0.163159i | ||||
\(493\) | 40.8945 | 1.84180 | ||||||||
\(494\) | 12.2684 | + | 26.8163i | 0.551980 | + | 1.20652i | ||||
\(495\) | −12.3578 | −0.555443 | ||||||||
\(496\) | 3.58945 | − | 6.21712i | 0.161171 | − | 0.279157i | ||||
\(497\) | 4.58945 | − | 7.94917i | 0.205865 | − | 0.356569i | ||||
\(498\) | −2.58945 | − | 4.48507i | −0.116036 | − | 0.200981i | ||||
\(499\) | −3.17891 | −0.142307 | −0.0711537 | − | 0.997465i | \(-0.522668\pi\) | ||||
−0.0711537 | + | 0.997465i | \(0.522668\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | −4.00000 | − | 6.92820i | −0.178707 | − | 0.309529i | ||||
\(502\) | 10.8211 | 0.482969 | ||||||||
\(503\) | 12.0000 | + | 20.7846i | 0.535054 | + | 0.926740i | 0.999161 | + | 0.0409609i | \(0.0130419\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(504\) | 0.500000 | − | 0.866025i | 0.0222718 | − | 0.0385758i | ||||
\(505\) | −16.3578 | + | 28.3326i | −0.727913 | + | 1.26078i | ||||
\(506\) | 19.6422 | 0.873202 | ||||||||
\(507\) | 4.26836 | + | 12.2793i | 0.189565 | + | 0.545343i | ||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | −14.3578 | + | 24.8685i | −0.636399 | + | 1.10228i | 0.349818 | + | 0.936818i | \(0.386243\pi\) |
−0.986217 | + | 0.165458i | \(0.947090\pi\) | |||||||
\(510\) | −5.00000 | + | 8.66025i | −0.221404 | + | 0.383482i | ||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.08945 | − | 7.08314i | −0.180554 | − | 0.312728i | ||||
\(514\) | −12.8578 | − | 22.2704i | −0.567134 | − | 0.982305i | ||||
\(515\) | −6.35782 | −0.280159 | ||||||||
\(516\) | 0.410546 | + | 0.711086i | 0.0180733 | + | 0.0313038i | ||||
\(517\) | −12.9105 | + | 22.3617i | −0.567805 | + | 0.983467i | ||||
\(518\) | 1.00000 | − | 1.73205i | 0.0439375 | − | 0.0761019i | ||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 3.00000 | + | 6.55744i | 0.131559 | + | 0.287563i | ||||
\(521\) | −4.17891 | −0.183081 | −0.0915406 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915406 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(522\) | −4.08945 | + | 7.08314i | −0.178991 | + | 0.310021i | ||||
\(523\) | 11.2684 | − | 19.5174i | 0.492731 | − | 0.853435i | −0.507234 | − | 0.861808i | \(-0.669332\pi\) |
0.999965 | + | 0.00837317i | \(0.00266530\pi\) | |||||||
\(524\) | −9.76836 | − | 16.9193i | −0.426733 | − | 0.739123i | ||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 6.00000 | + | 10.3923i | 0.261612 | + | 0.453126i | ||||
\(527\) | 17.9473 | + | 31.0856i | 0.781795 | + | 1.35411i | ||||
\(528\) | −6.17891 | −0.268902 | ||||||||
\(529\) | 6.44727 | + | 11.1670i | 0.280316 | + | 0.485522i | ||||
\(530\) | −3.00000 | + | 5.19615i | −0.130312 | + | 0.225706i | ||||
\(531\) | 0.410546 | − | 0.711086i | 0.0178162 | − | 0.0308585i | ||||
\(532\) | 8.17891 | 0.354601 | ||||||||
\(533\) | 15.0000 | + | 1.42217i | 0.649722 | + | 0.0616011i | ||||
\(534\) | −9.00000 | −0.389468 | ||||||||
\(535\) | 7.82109 | − | 13.5465i | 0.338135 | − | 0.585667i | ||||
\(536\) | 7.58945 | − | 13.1453i | 0.327814 | − | 0.567791i | ||||
\(537\) | −7.17891 | − | 12.4342i | −0.309793 | − | 0.536577i | ||||
\(538\) | 18.3578 | 0.791462 | ||||||||
\(539\) | −3.08945 | − | 5.35109i | −0.133072 | − | 0.230488i | ||||
\(540\) | −1.00000 | − | 1.73205i | −0.0430331 | − | 0.0745356i | ||||
\(541\) | 2.35782 | 0.101370 | 0.0506852 | − | 0.998715i | \(-0.483859\pi\) | ||||
0.0506852 | + | 0.998715i | \(0.483859\pi\) | |||||||
\(542\) | −15.5895 | − | 27.0017i | −0.669624 | − | 1.15982i | ||||
\(543\) | 3.91055 | − | 6.77326i | 0.167818 | − | 0.290669i | ||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 3.58945 | + | 0.340322i | 0.153614 | + | 0.0145644i | ||||
\(547\) | 36.0000 | 1.53925 | 0.769624 | − | 0.638497i | \(-0.220443\pi\) | ||||
0.769624 | + | 0.638497i | \(0.220443\pi\) | |||||||
\(548\) | 8.17891 | − | 14.1663i | 0.349386 | − | 0.605154i | ||||
\(549\) | 1.50000 | − | 2.59808i | 0.0640184 | − | 0.110883i | ||||
\(550\) | 3.08945 | + | 5.35109i | 0.131735 | + | 0.228171i | ||||
\(551\) | −66.8945 | −2.84980 | ||||||||
\(552\) | 1.58945 | + | 2.75302i | 0.0676517 | + | 0.117176i | ||||
\(553\) | 0.910546 | + | 1.57711i | 0.0387203 | + | 0.0670656i | ||||
\(554\) | 28.3578 | 1.20481 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | 9.08945 | − | 15.7434i | 0.385479 | − | 0.667669i | ||||
\(557\) | 10.8578 | − | 18.8063i | 0.460060 | − | 0.796848i | −0.538903 | − | 0.842368i | \(-0.681161\pi\) |
0.998963 | + | 0.0455198i | \(0.0144944\pi\) | |||||||
\(558\) | −7.17891 | −0.303907 | ||||||||
\(559\) | −1.71563 | + | 2.41269i | −0.0725636 | + | 0.102046i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 15.4473 | − | 26.7555i | 0.652184 | − | 1.12962i | ||||
\(562\) | −2.82109 | + | 4.88627i | −0.119001 | + | 0.206115i | ||||
\(563\) | −2.17891 | − | 3.77398i | −0.0918300 | − | 0.159054i | 0.816451 | − | 0.577414i | \(-0.195938\pi\) |
−0.908281 | + | 0.418360i | \(0.862605\pi\) | |||||||
\(564\) | −4.17891 | −0.175964 | ||||||||
\(565\) | −4.35782 | − | 7.54796i | −0.183335 | − | 0.317545i | ||||
\(566\) | −15.1789 | − | 26.2906i | −0.638017 | − | 1.10508i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −4.58945 | − | 7.94917i | −0.192569 | − | 0.333540i | ||||
\(569\) | 13.1789 | − | 22.8265i | 0.552489 | − | 0.956938i | −0.445606 | − | 0.895229i | \(-0.647012\pi\) |
0.998094 | − | 0.0617089i | \(-0.0196550\pi\) | |||||||
\(570\) | 8.17891 | − | 14.1663i | 0.342577 | − | 0.593360i | ||||
\(571\) | −22.8211 | −0.955033 | −0.477516 | − | 0.878623i | \(-0.658463\pi\) | ||||
−0.477516 | + | 0.878623i | \(0.658463\pi\) | |||||||
\(572\) | −9.26836 | − | 20.2589i | −0.387530 | − | 0.847067i | ||||
\(573\) | −27.5367 | −1.15036 | ||||||||
\(574\) | 2.08945 | − | 3.61904i | 0.0872121 | − | 0.151056i | ||||
\(575\) | 1.58945 | − | 2.75302i | 0.0662848 | − | 0.114809i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −5.64218 | −0.234887 | −0.117444 | − | 0.993080i | \(-0.537470\pi\) | ||||
−0.117444 | + | 0.993080i | \(0.537470\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 10.2684 | + | 17.7853i | 0.426739 | + | 0.739133i | ||||
\(580\) | −16.3578 | −0.679221 | ||||||||
\(581\) | −2.58945 | − | 4.48507i | −0.107429 | − | 0.186072i | ||||
\(582\) | 6.17891 | − | 10.7022i | 0.256124 | − | 0.443620i | ||||
\(583\) | 9.26836 | − | 16.0533i | 0.383856 | − | 0.664859i | ||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 4.17891 | − | 5.87680i | 0.172777 | − | 0.242976i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 5.58945 | − | 9.68122i | 0.230701 | − | 0.399587i | −0.727313 | − | 0.686306i | \(-0.759231\pi\) |
0.958015 | + | 0.286719i | \(0.0925646\pi\) | |||||||
\(588\) | 0.500000 | − | 0.866025i | 0.0206197 | − | 0.0357143i | ||||
\(589\) | −29.3578 | − | 50.8492i | −1.20967 | − | 2.09521i | ||||
\(590\) | 1.64218 | 0.0676076 | ||||||||
\(591\) | 8.50000 | + | 14.7224i | 0.349643 | + | 0.605600i | ||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | 3.08945 | + | 5.35109i | 0.126762 | + | 0.219558i | ||||
\(595\) | −5.00000 | + | 8.66025i | −0.204980 | + | 0.355036i | ||||
\(596\) | −2.41055 | + | 4.17519i | −0.0987398 | + | 0.171022i | ||||
\(597\) | −12.8211 | −0.524732 | ||||||||
\(598\) | −6.64218 | + | 9.34090i | −0.271619 | + | 0.381978i | ||||
\(599\) | 28.8211 | 1.17760 | 0.588799 | − | 0.808280i | \(-0.299601\pi\) | ||||
0.588799 | + | 0.808280i | \(0.299601\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 11.0000 | − | 19.0526i | 0.448699 | − | 0.777170i | −0.549602 | − | 0.835426i | \(-0.685221\pi\) |
0.998302 | + | 0.0582563i | \(0.0185541\pi\) | |||||||
\(602\) | 0.410546 | + | 0.711086i | 0.0167326 | + | 0.0289817i | ||||
\(603\) | −15.1789 | −0.618133 | ||||||||
\(604\) | 7.26836 | + | 12.5892i | 0.295745 | + | 0.512246i | ||||
\(605\) | 27.1789 | + | 47.0753i | 1.10498 | + | 1.91388i | ||||
\(606\) | 16.3578 | 0.664491 | ||||||||
\(607\) | −16.7684 | − | 29.0437i | −0.680607 | − | 1.17885i | −0.974796 | − | 0.223098i | \(-0.928383\pi\) |
0.294189 | − | 0.955747i | \(-0.404950\pi\) | |||||||
\(608\) | 4.08945 | − | 7.08314i | 0.165849 | − | 0.287259i | ||||
\(609\) | −4.08945 | + | 7.08314i | −0.165713 | + | 0.287023i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −6.26836 | − | 13.7015i | −0.253591 | − | 0.554302i | ||||
\(612\) | 5.00000 | 0.202113 | ||||||||
\(613\) | −19.1789 | + | 33.2188i | −0.774629 | + | 1.34170i | 0.160374 | + | 0.987056i | \(0.448730\pi\) |
−0.935003 | + | 0.354640i | \(0.884603\pi\) | |||||||
\(614\) | −12.4473 | + | 21.5593i | −0.502331 | + | 0.870063i | ||||
\(615\) | −4.17891 | − | 7.23808i | −0.168510 | − | 0.291868i | ||||
\(616\) | −6.17891 | −0.248955 | ||||||||
\(617\) | −16.0000 | − | 27.7128i | −0.644136 | − | 1.11568i | −0.984500 | − | 0.175382i | \(-0.943884\pi\) |
0.340365 | − | 0.940294i | \(-0.389449\pi\) | |||||||
\(618\) | 1.58945 | + | 2.75302i | 0.0639372 | + | 0.110743i | ||||
\(619\) | −8.53673 | −0.343120 | −0.171560 | − | 0.985174i | \(-0.554881\pi\) | ||||
−0.171560 | + | 0.985174i | \(0.554881\pi\) | |||||||
\(620\) | −7.17891 | − | 12.4342i | −0.288312 | − | 0.499371i | ||||
\(621\) | 1.58945 | − | 2.75302i | 0.0637826 | − | 0.110475i | ||||
\(622\) | 4.26836 | − | 7.39302i | 0.171146 | − | 0.296433i | ||||
\(623\) | −9.00000 | −0.360577 | ||||||||
\(624\) | 2.08945 | − | 2.93840i | 0.0836451 | − | 0.117630i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −2.00000 | + | 3.46410i | −0.0799361 | + | 0.138453i | ||||
\(627\) | −25.2684 | + | 43.7661i | −1.00912 | + | 1.74785i | ||||
\(628\) | −1.00000 | − | 1.73205i | −0.0399043 | − | 0.0691164i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | −1.00000 | − | 1.73205i | −0.0398410 | − | 0.0690066i | ||||
\(631\) | 15.4473 | + | 26.7555i | 0.614946 | + | 1.06512i | 0.990394 | + | 0.138274i | \(0.0441556\pi\) |
−0.375448 | + | 0.926844i | \(0.622511\pi\) | |||||||
\(632\) | 1.82109 | 0.0724391 | ||||||||
\(633\) | 8.17891 | + | 14.1663i | 0.325082 | + | 0.563059i | ||||
\(634\) | −3.58945 | + | 6.21712i | −0.142555 | + | 0.246913i | ||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 3.58945 | + | 0.340322i | 0.142219 | + | 0.0134840i | ||||
\(638\) | 50.5367 | 2.00077 | ||||||||
\(639\) | −4.58945 | + | 7.94917i | −0.181556 | + | 0.314464i | ||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 20.5367 | + | 35.5707i | 0.811152 | + | 1.40496i | 0.912058 | + | 0.410060i | \(0.134492\pi\) |
−0.100907 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(642\) | −7.82109 | −0.308674 | ||||||||
\(643\) | 10.0895 | + | 17.4754i | 0.397889 | + | 0.689164i | 0.993465 | − | 0.114135i | \(-0.0364095\pi\) |
−0.595576 | + | 0.803299i | \(0.703076\pi\) | |||||||
\(644\) | 1.58945 | + | 2.75302i | 0.0626333 | + | 0.108484i | ||||
\(645\) | 1.64218 | 0.0646609 | ||||||||
\(646\) | 20.4473 | + | 35.4157i | 0.804487 | + | 1.39341i | ||||
\(647\) | 4.44727 | − | 7.70290i | 0.174840 | − | 0.302832i | −0.765266 | − | 0.643715i | \(-0.777392\pi\) |
0.940106 | + | 0.340882i | \(0.110726\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −5.07345 | −0.199150 | ||||||||
\(650\) | −3.58945 | − | 0.340322i | −0.140790 | − | 0.0133485i | ||||
\(651\) | −7.17891 | −0.281364 | ||||||||
\(652\) | 4.41055 | − | 7.63929i | 0.172730 | − | 0.299178i | ||||
\(653\) | −10.5000 | + | 18.1865i | −0.410897 | + | 0.711694i | −0.994988 | − | 0.0999939i | \(-0.968118\pi\) |
0.584091 | + | 0.811688i | \(0.301451\pi\) | |||||||
\(654\) | 2.00000 | + | 3.46410i | 0.0782062 | + | 0.135457i | ||||
\(655\) | −39.0735 | −1.52673 | ||||||||
\(656\) | −2.08945 | − | 3.61904i | −0.0815795 | − | 0.141300i | ||||
\(657\) | −2.00000 | − | 3.46410i | −0.0780274 | − | 0.135147i | ||||
\(658\) | −4.17891 | −0.162911 | ||||||||
\(659\) | 8.26836 | + | 14.3212i | 0.322090 | + | 0.557876i | 0.980919 | − | 0.194417i | \(-0.0622814\pi\) |
−0.658829 | + | 0.752292i | \(0.728948\pi\) | |||||||
\(660\) | −6.17891 | + | 10.7022i | −0.240514 | + | 0.416582i | ||||
\(661\) | 8.76836 | − | 15.1872i | 0.341050 | − | 0.590716i | −0.643578 | − | 0.765380i | \(-0.722551\pi\) |
0.984628 | + | 0.174665i | \(0.0558842\pi\) | |||||||
\(662\) | −24.3578 | −0.946693 | ||||||||
\(663\) | 7.50000 | + | 16.3936i | 0.291276 | + | 0.636675i | ||||
\(664\) | −5.17891 | −0.200981 | ||||||||
\(665\) | 8.17891 | − | 14.1663i | 0.317164 | − | 0.549345i | ||||
\(666\) | −1.00000 | + | 1.73205i | −0.0387492 | + | 0.0671156i | ||||
\(667\) | −13.0000 | − | 22.5167i | −0.503362 | − | 0.871849i | ||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | 4.58945 | + | 7.94917i | 0.177439 | + | 0.307333i | ||||
\(670\) | −15.1789 | − | 26.2906i | −0.586412 | − | 1.01570i | ||||
\(671\) | −18.5367 | −0.715602 | ||||||||
\(672\) | −0.500000 | − | 0.866025i | −0.0192879 | − | 0.0334077i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | 0.268363 | − | 0.464818i | 0.0103369 | − | 0.0179041i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 12.7684 | + | 2.44314i | 0.491091 | + | 0.0939668i | ||||
\(677\) | 12.0000 | 0.461197 | 0.230599 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230599 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(678\) | −2.17891 | + | 3.77398i | −0.0836805 | + | 0.144939i | ||||
\(679\) | 6.17891 | − | 10.7022i | 0.237125 | − | 0.410712i | ||||
\(680\) | 5.00000 | + | 8.66025i | 0.191741 | + | 0.332106i | ||||
\(681\) | −8.35782 | −0.320272 | ||||||||
\(682\) | 22.1789 | + | 38.4150i | 0.849274 | + | 1.47099i | ||||
\(683\) | 7.17891 | + | 12.4342i | 0.274693 | + | 0.475783i | 0.970058 | − | 0.242875i | \(-0.0780903\pi\) |
−0.695364 | + | 0.718657i | \(0.744757\pi\) | |||||||
\(684\) | −8.17891 | −0.312728 | ||||||||
\(685\) | −16.3578 | − | 28.3326i | −0.625000 | − | 1.08253i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0.500000 | − | 0.866025i | 0.0190762 | − | 0.0330409i | ||||
\(688\) | 0.821092 | 0.0313038 | ||||||||
\(689\) | 4.50000 | + | 9.83616i | 0.171436 | + | 0.374728i | ||||
\(690\) | 6.35782 | 0.242038 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | −2.00000 | + | 3.46410i | −0.0760286 | + | 0.131685i | ||||
\(693\) | 3.08945 | + | 5.35109i | 0.117359 | + | 0.203271i | ||||
\(694\) | −7.82109 | −0.296885 | ||||||||
\(695\) | −18.1789 | − | 31.4868i | −0.689565 | − | 1.19436i | ||||
\(696\) | 4.08945 | + | 7.08314i | 0.155010 | + | 0.268486i | ||||
\(697\) | 20.8945 | 0.791437 | ||||||||
\(698\) | 1.58945 | + | 2.75302i | 0.0601617 | + | 0.104203i | ||||
\(699\) | −0.178908 | + | 0.309878i | −0.00676694 | + | 0.0117207i | ||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | 23.7156 | 0.895727 | 0.447864 | − | 0.894102i | \(-0.352185\pi\) | ||||
0.447864 | + | 0.894102i | \(0.352185\pi\) | |||||||
\(702\) | −3.58945 | − | 0.340322i | −0.135475 | − | 0.0128446i | ||||
\(703\) | −16.3578 | −0.616947 | ||||||||
\(704\) | −3.08945 | + | 5.35109i | −0.116438 | + | 0.201677i | ||||
\(705\) | −4.17891 | + | 7.23808i | −0.157387 | + | 0.272602i | ||||
\(706\) | 3.58945 | + | 6.21712i | 0.135091 | + | 0.233984i | ||||
\(707\) | 16.3578 | 0.615199 | ||||||||
\(708\) | −0.410546 | − | 0.711086i | −0.0154293 | − | 0.0267243i | ||||
\(709\) | 8.00000 | + | 13.8564i | 0.300446 | + | 0.520388i | 0.976237 | − | 0.216705i | \(-0.0695310\pi\) |
−0.675791 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(710\) | −18.3578 | −0.688957 | ||||||||
\(711\) | −0.910546 | − | 1.57711i | −0.0341481 | − | 0.0591463i | ||||
\(712\) | −4.50000 | + | 7.79423i | −0.168645 | + | 0.292101i | ||||
\(713\) | 11.4105 | − | 19.7636i | 0.427328 | − | 0.740154i | ||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | −44.3578 | − | 4.20563i | −1.65889 | − | 0.157282i | ||||
\(716\) | −14.3578 | −0.536577 | ||||||||
\(717\) | −0.589454 | + | 1.02096i | −0.0220136 | + | 0.0381286i | ||||
\(718\) | −6.17891 | + | 10.7022i | −0.230595 | + | 0.399402i | ||||
\(719\) | 12.9105 | + | 22.3617i | 0.481482 | + | 0.833951i | 0.999774 | − | 0.0212522i | \(-0.00676530\pi\) |
−0.518292 | + | 0.855204i | \(0.673432\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 1.58945 | + | 2.75302i | 0.0591944 | + | 0.102528i | ||||
\(722\) | −23.9473 | − | 41.4779i | −0.891225 | − | 1.54365i | ||||
\(723\) | 18.3578 | 0.682735 | ||||||||
\(724\) | −3.91055 | − | 6.77326i | −0.145334 | − | 0.251726i | ||||
\(725\) | 4.08945 | − | 7.08314i | 0.151879 | − | 0.263061i | ||||
\(726\) | 13.5895 | − | 23.5376i | 0.504352 | − | 0.873563i | ||||
\(727\) | 0.463275 | 0.0171819 | 0.00859096 | − | 0.999963i | \(-0.497265\pi\) | ||||
0.00859096 | + | 0.999963i | \(0.497265\pi\) | |||||||
\(728\) | 2.08945 | − | 2.93840i | 0.0774403 | − | 0.108904i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.00000 | − | 6.92820i | 0.148047 | − | 0.256424i | ||||
\(731\) | −2.05273 | + | 3.55543i | −0.0759229 | + | 0.131502i | ||||
\(732\) | −1.50000 | − | 2.59808i | −0.0554416 | − | 0.0960277i | ||||
\(733\) | −25.7156 | −0.949829 | −0.474914 | − | 0.880032i | \(-0.657521\pi\) | ||||
−0.474914 | + | 0.880032i | \(0.657521\pi\) | |||||||
\(734\) | −1.58945 | − | 2.75302i | −0.0586678 | − | 0.101616i | ||||
\(735\) | −1.00000 | − | 1.73205i | −0.0368856 | − | 0.0638877i | ||||
\(736\) | 3.17891 | 0.117176 | ||||||||
\(737\) | 46.8945 | + | 81.2237i | 1.72738 | + | 2.99191i | ||||
\(738\) | −2.08945 | + | 3.61904i | −0.0769139 | + | 0.133219i | ||||
\(739\) | 2.41055 | − | 4.17519i | 0.0886734 | − | 0.153587i | −0.818277 | − | 0.574824i | \(-0.805071\pi\) |
0.906951 | + | 0.421237i | \(0.138404\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | −12.2684 | − | 26.8163i | −0.450690 | − | 0.985123i | ||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | −21.5895 | + | 37.3940i | −0.792040 | + | 1.37185i | 0.132661 | + | 0.991161i | \(0.457648\pi\) |
−0.924702 | + | 0.380693i | \(0.875686\pi\) | |||||||
\(744\) | −3.58945 | + | 6.21712i | −0.131596 | + | 0.227931i | ||||
\(745\) | 4.82109 | + | 8.35038i | 0.176631 | + | 0.305934i | ||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | 2.58945 | + | 4.48507i | 0.0947432 | + | 0.164100i | ||||
\(748\) | −15.4473 | − | 26.7555i | −0.564808 | − | 0.978276i | ||||
\(749\) | −7.82109 | −0.285776 | ||||||||
\(750\) | 6.00000 | + | 10.3923i | 0.219089 | + | 0.379473i | ||||
\(751\) | −10.4473 | + | 18.0952i | −0.381226 | + | 0.660303i | −0.991238 | − | 0.132089i | \(-0.957831\pi\) |
0.610012 | + | 0.792393i | \(0.291165\pi\) | |||||||
\(752\) | −2.08945 | + | 3.61904i | −0.0761946 | + | 0.131973i | ||||
\(753\) | −10.8211 | −0.394343 | ||||||||
\(754\) | −17.0895 | + | 24.0329i | −0.622361 | + | 0.875226i | ||||
\(755\) | 29.0735 | 1.05809 | ||||||||
\(756\) | −0.500000 | + | 0.866025i | −0.0181848 | + | 0.0314970i | ||||
\(757\) | −1.17891 | + | 2.04193i | −0.0428482 | + | 0.0742152i | −0.886654 | − | 0.462433i | \(-0.846977\pi\) |
0.843806 | + | 0.536648i | \(0.180310\pi\) | |||||||
\(758\) | −10.3578 | − | 17.9403i | −0.376213 | − | 0.651620i | ||||
\(759\) | −19.6422 | −0.712966 | ||||||||
\(760\) | −8.17891 | − | 14.1663i | −0.296680 | − | 0.513865i | ||||
\(761\) | −23.7156 | − | 41.0767i | −0.859691 | − | 1.48903i | −0.872224 | − | 0.489107i | \(-0.837323\pi\) |
0.0125327 | − | 0.999921i | \(-0.496011\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | 2.00000 | + | 3.46410i | 0.0724049 | + | 0.125409i | ||||
\(764\) | −13.7684 | + | 23.8475i | −0.498122 | + | 0.862772i | ||||
\(765\) | 5.00000 | − | 8.66025i | 0.180775 | − | 0.313112i | ||||
\(766\) | 9.82109 | 0.354850 | ||||||||
\(767\) | 1.71563 | − | 2.41269i | 0.0619479 | − | 0.0871173i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 2.17891 | − | 3.77398i | 0.0785734 | − | 0.136093i | −0.824061 | − | 0.566501i | \(-0.808297\pi\) |
0.902635 | + | 0.430408i | \(0.141630\pi\) | |||||||
\(770\) | −6.17891 | + | 10.7022i | −0.222672 | + | 0.385680i | ||||
\(771\) | 12.8578 | + | 22.2704i | 0.463063 | + | 0.802049i | ||||
\(772\) | 20.5367 | 0.739133 | ||||||||
\(773\) | 15.3578 | + | 26.6005i | 0.552382 | + | 0.956754i | 0.998102 | + | 0.0615816i | \(0.0196144\pi\) |
−0.445720 | + | 0.895173i | \(0.647052\pi\) | |||||||
\(774\) | −0.410546 | − | 0.711086i | −0.0147568 | − | 0.0255595i | ||||
\(775\) | 7.17891 | 0.257874 | ||||||||
\(776\) | −6.17891 | − | 10.7022i | −0.221810 | − | 0.384186i | ||||
\(777\) | −1.00000 | + | 1.73205i | −0.0358748 | + | 0.0621370i | ||||
\(778\) | 0.410546 | − | 0.711086i | 0.0147188 | − | 0.0254937i | ||||
\(779\) | −34.1789 | −1.22459 | ||||||||
\(780\) | −3.00000 | − | 6.55744i | −0.107417 | − | 0.234794i | ||||
\(781\) | 56.7156 | 2.02944 | ||||||||
\(782\) | −7.94727 | + | 13.7651i | −0.284194 | + | 0.492238i | ||||
\(783\) | 4.08945 | − | 7.08314i | 0.146145 | − | 0.253131i | ||||
\(784\) | −0.500000 | − | 0.866025i | −0.0178571 | − | 0.0309295i | ||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 9.76836 | + | 16.9193i | 0.348426 | + | 0.603491i | ||||
\(787\) | 11.0895 | + | 19.2075i | 0.395296 | + | 0.684673i | 0.993139 | − | 0.116940i | \(-0.0373086\pi\) |
−0.597843 | + | 0.801614i | \(0.703975\pi\) | |||||||
\(788\) | 17.0000 | 0.605600 | ||||||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | 1.82109 | − | 3.15422i | 0.0647915 | − | 0.112222i | ||||
\(791\) | −2.17891 | + | 3.77398i | −0.0774731 | + | 0.134187i | ||||
\(792\) | 6.17891 | 0.219558 | ||||||||
\(793\) | 6.26836 | − | 8.81519i | 0.222596 | − | 0.313037i | ||||
\(794\) | 3.00000 | 0.106466 | ||||||||
\(795\) | 3.00000 | − | 5.19615i | 0.106399 | − | 0.184289i | ||||
\(796\) | −6.41055 | + | 11.1034i | −0.227216 | + | 0.393549i | ||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | −8.17891 | −0.289530 | ||||||||
\(799\) | −10.4473 | − | 18.0952i | −0.369598 | − | 0.640162i | ||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | −16.1789 | − | 28.0227i | −0.571297 | − | 0.989516i | ||||
\(803\) | −12.3578 | + | 21.4044i | −0.436098 | + | 0.755344i | ||||
\(804\) | −7.58945 | + | 13.1453i | −0.267659 | + | 0.463600i | ||||
\(805\) | 6.35782 | 0.224084 | ||||||||
\(806\) | −25.7684 | − | 2.44314i | −0.907652 | − | 0.0860558i | ||||
\(807\) | −18.3578 | −0.646226 | ||||||||
\(808\) | 8.17891 | − | 14.1663i | 0.287733 | − | 0.498368i | ||||
\(809\) | 10.0000 | − | 17.3205i | 0.351581 | − | 0.608957i | −0.634945 | − | 0.772557i | \(-0.718977\pi\) |
0.986527 | + | 0.163600i | \(0.0523108\pi\) | |||||||
\(810\) | 1.00000 | + | 1.73205i | 0.0351364 | + | 0.0608581i | ||||
\(811\) | 32.7156 | 1.14880 | 0.574401 | − | 0.818574i | \(-0.305235\pi\) | ||||
0.574401 | + | 0.818574i | \(0.305235\pi\) | |||||||
\(812\) | 4.08945 | + | 7.08314i | 0.143512 | + | 0.248570i | ||||
\(813\) | 15.5895 | + | 27.0017i | 0.546746 | + | 0.946992i | ||||
\(814\) | 12.3578 | 0.433141 | ||||||||
\(815\) | −8.82109 | − | 15.2786i | −0.308989 | − | 0.535185i | ||||
\(816\) | 2.50000 | − | 4.33013i | 0.0875175 | − | 0.151585i | ||||
\(817\) | 3.35782 | − | 5.81591i | 0.117475 | − | 0.203473i | ||||
\(818\) | −13.6422 | −0.476988 | ||||||||
\(819\) | −3.58945 | − | 0.340322i | −0.125426 | − | 0.0118918i | ||||
\(820\) | −8.35782 | −0.291868 | ||||||||
\(821\) | −22.8578 | + | 39.5909i | −0.797743 | + | 1.38173i | 0.123339 | + | 0.992365i | \(0.460640\pi\) |
−0.921083 | + | 0.389367i | \(0.872694\pi\) | |||||||
\(822\) | −8.17891 | + | 14.1663i | −0.285272 | + | 0.494106i | ||||
\(823\) | 6.35782 | + | 11.0121i | 0.221620 | + | 0.383856i | 0.955300 | − | 0.295638i | \(-0.0955324\pi\) |
−0.733680 | + | 0.679495i | \(0.762199\pi\) | |||||||
\(824\) | 3.17891 | 0.110743 | ||||||||
\(825\) | −3.08945 | − | 5.35109i | −0.107561 | − | 0.186301i | ||||
\(826\) | −0.410546 | − | 0.711086i | −0.0142847 | − | 0.0247419i | ||||
\(827\) | 4.71563 | 0.163979 | 0.0819893 | − | 0.996633i | \(-0.473873\pi\) | ||||
0.0819893 | + | 0.996633i | \(0.473873\pi\) | |||||||
\(828\) | −1.58945 | − | 2.75302i | −0.0552374 | − | 0.0956739i | ||||
\(829\) | −4.08945 | + | 7.08314i | −0.142033 | + | 0.246008i | −0.928262 | − | 0.371927i | \(-0.878697\pi\) |
0.786229 | + | 0.617935i | \(0.212030\pi\) | |||||||
\(830\) | −5.17891 | + | 8.97013i | −0.179763 | + | 0.311358i | ||||
\(831\) | −28.3578 | −0.983722 | ||||||||
\(832\) | −1.50000 | − | 3.27872i | −0.0520031 | − | 0.113669i | ||||
\(833\) | 5.00000 | 0.173240 | ||||||||
\(834\) | −9.08945 | + | 15.7434i | −0.314742 | + | 0.545149i | ||||
\(835\) | −8.00000 | + | 13.8564i | −0.276851 | + | 0.479521i | ||||
\(836\) | 25.2684 | + | 43.7661i | 0.873925 | + | 1.51368i | ||||
\(837\) | 7.17891 | 0.248139 | ||||||||
\(838\) | −14.9473 | − | 25.8894i | −0.516345 | − | 0.894336i | ||||
\(839\) | −17.1789 | − | 29.7547i | −0.593082 | − | 1.02725i | −0.993815 | − | 0.111053i | \(-0.964578\pi\) |
0.400733 | − | 0.916195i | \(-0.368756\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | −18.9473 | − | 32.8176i | −0.653354 | − | 1.13164i | ||||
\(842\) | 17.3578 | − | 30.0646i | 0.598190 | − | 1.03610i | ||||
\(843\) | 2.82109 | − | 4.88627i | 0.0971636 | − | 0.168292i | ||||
\(844\) | 16.3578 | 0.563059 | ||||||||
\(845\) | 17.0000 | − | 19.6723i | 0.584818 | − | 0.676748i | ||||
\(846\) | 4.17891 | 0.143674 | ||||||||
\(847\) | 13.5895 | − | 23.5376i | 0.466939 | − | 0.808762i | ||||
\(848\) | 1.50000 | − | 2.59808i | 0.0515102 | − | 0.0892183i | ||||
\(849\) | 15.1789 | + | 26.2906i | 0.520939 | + | 0.902292i | ||||
\(850\) | −5.00000 | −0.171499 | ||||||||
\(851\) | −3.17891 | − | 5.50603i | −0.108972 | − | 0.188744i | ||||
\(852\) | 4.58945 | + | 7.94917i | 0.157232 | + | 0.272334i | ||||
\(853\) | −17.7156 | −0.606572 | −0.303286 | − | 0.952900i | \(-0.598084\pi\) | ||||
−0.303286 | + | 0.952900i | \(0.598084\pi\) | |||||||
\(854\) | −1.50000 | − | 2.59808i | −0.0513289 | − | 0.0889043i | ||||
\(855\) | −8.17891 | + | 14.1663i | −0.279713 | + | 0.484477i | ||||
\(856\) | −3.91055 | + | 6.77326i | −0.133660 | + | 0.231505i | ||||
\(857\) | 34.7156 | 1.18586 | 0.592932 | − | 0.805253i | \(-0.297970\pi\) | ||||
0.592932 | + | 0.805253i | \(0.297970\pi\) | |||||||
\(858\) | 9.26836 | + | 20.2589i | 0.316417 | + | 0.691628i | ||||
\(859\) | −36.8945 | −1.25883 | −0.629413 | − | 0.777071i | \(-0.716705\pi\) | ||||
−0.629413 | + | 0.777071i | \(0.716705\pi\) | |||||||
\(860\) | 0.821092 | − | 1.42217i | 0.0279990 | − | 0.0484957i | ||||
\(861\) | −2.08945 | + | 3.61904i | −0.0712084 | + | 0.123337i | ||||
\(862\) | 0.589454 | + | 1.02096i | 0.0200769 | + | 0.0347742i | ||||
\(863\) | 36.3578 | 1.23763 | 0.618817 | − | 0.785535i | \(-0.287612\pi\) | ||||
0.618817 | + | 0.785535i | \(0.287612\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.00000 | + | 6.92820i | 0.136004 | + | 0.235566i | ||||
\(866\) | 11.6422 | 0.395617 | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | −3.58945 | + | 6.21712i | −0.121834 | + | 0.211023i | ||||
\(869\) | −5.62618 | + | 9.74483i | −0.190855 | + | 0.330571i | ||||
\(870\) | 16.3578 | 0.554582 | ||||||||
\(871\) | −54.4840 | − | 5.16571i | −1.84612 | − | 0.175033i | ||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | −6.17891 | + | 10.7022i | −0.209124 | + | 0.362214i | ||||
\(874\) | 13.0000 | − | 22.5167i | 0.439732 | − | 0.761637i | ||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 8.82109 | + | 15.2786i | 0.297867 | + | 0.515921i | 0.975648 | − | 0.219343i | \(-0.0703914\pi\) |
−0.677781 | + | 0.735264i | \(0.737058\pi\) | |||||||
\(878\) | 2.35782 | + | 4.08386i | 0.0795725 | + | 0.137824i | ||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | 6.17891 | + | 10.7022i | 0.208291 | + | 0.360771i | ||||
\(881\) | −22.7684 | + | 39.4360i | −0.767086 | + | 1.32863i | 0.172051 | + | 0.985088i | \(0.444961\pi\) |
−0.939137 | + | 0.343543i | \(0.888373\pi\) | |||||||
\(882\) | −0.500000 | + | 0.866025i | −0.0168359 | + | 0.0291606i | ||||
\(883\) | −37.5367 | −1.26321 | −0.631606 | − | 0.775290i | \(-0.717604\pi\) | ||||
−0.631606 | + | 0.775290i | \(0.717604\pi\) | |||||||
\(884\) | 17.9473 | + | 1.70161i | 0.603632 | + | 0.0572313i | ||||
\(885\) | −1.64218 | −0.0552014 | ||||||||
\(886\) | 4.08945 | − | 7.08314i | 0.137388 | − | 0.237963i | ||||
\(887\) | 5.73164 | − | 9.92749i | 0.192450 | − | 0.333332i | −0.753612 | − | 0.657320i | \(-0.771690\pi\) |
0.946061 | + | 0.323987i | \(0.105023\pi\) | |||||||
\(888\) | 1.00000 | + | 1.73205i | 0.0335578 | + | 0.0581238i | ||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 9.00000 | + | 15.5885i | 0.301681 | + | 0.522526i | ||||
\(891\) | −3.08945 | − | 5.35109i | −0.103501 | − | 0.179268i | ||||
\(892\) | 9.17891 | 0.307333 | ||||||||
\(893\) | 17.0895 | + | 29.5998i | 0.571877 | + | 0.990520i | ||||
\(894\) | 2.41055 | − | 4.17519i | 0.0806207 | − | 0.139639i | ||||
\(895\) | −14.3578 | + | 24.8685i | −0.479929 | + | 0.831261i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 6.64218 | − | 9.34090i | 0.221776 | − | 0.311883i | ||||
\(898\) | −14.0000 | −0.467186 | ||||||||
\(899\) | 29.3578 | − | 50.8492i | 0.979138 | − | 1.69592i | ||||
\(900\) | 0.500000 | − | 0.866025i | 0.0166667 | − | 0.0288675i | ||||
\(901\) | 7.50000 | + | 12.9904i | 0.249861 | + | 0.432772i | ||||
\(902\) | 25.8211 | 0.859748 | ||||||||
\(903\) | −0.410546 | − | 0.711086i | −0.0136621 | − | 0.0236635i | ||||
\(904\) | 2.17891 | + | 3.77398i | 0.0724694 | + | 0.125521i | ||||
\(905\) | −15.6422 | −0.519964 | ||||||||
\(906\) | −7.26836 | − | 12.5892i | −0.241475 | − | 0.418247i | ||||
\(907\) | 26.3051 | − | 45.5617i | 0.873446 | − | 1.51285i | 0.0150372 | − | 0.999887i | \(-0.495213\pi\) |
0.858409 | − | 0.512966i | \(-0.171453\pi\) | |||||||
\(908\) | −4.17891 | + | 7.23808i | −0.138682 | + | 0.240204i | ||||
\(909\) | −16.3578 | −0.542555 | ||||||||
\(910\) | −3.00000 | − | 6.55744i | −0.0994490 | − | 0.217377i | ||||
\(911\) | −16.7156 | −0.553814 | −0.276907 | − | 0.960897i | \(-0.589309\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(912\) | −4.08945 | + | 7.08314i | −0.135415 | + | 0.234546i | ||||
\(913\) | 16.0000 | − | 27.7128i | 0.529523 | − | 0.917160i | ||||
\(914\) | 15.9473 | + | 27.6215i | 0.527489 | + | 0.913637i | ||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −0.500000 | − | 0.866025i | −0.0165205 | − | 0.0286143i | ||||
\(917\) | 9.76836 | + | 16.9193i | 0.322580 | + | 0.558725i | ||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | −10.6262 | − | 18.4051i | −0.350525 | − | 0.607128i | 0.635816 | − | 0.771840i | \(-0.280664\pi\) |
−0.986342 | + | 0.164713i | \(0.947330\pi\) | |||||||
\(920\) | 3.17891 | − | 5.50603i | 0.104806 | − | 0.181528i | ||||
\(921\) | 12.4473 | − | 21.5593i | 0.410152 | − | 0.710403i | ||||
\(922\) | −24.7156 | −0.813966 | ||||||||
\(923\) | −19.1789 | + | 26.9713i | −0.631281 | + | 0.887771i | ||||
\(924\) | 6.17891 | 0.203271 | ||||||||
\(925\) | 1.00000 | − | 1.73205i | 0.0328798 | − | 0.0569495i | ||||
\(926\) | 14.4473 | − | 25.0234i | 0.474767 | − | 0.822320i | ||||
\(927\) | −1.58945 | − | 2.75302i | −0.0522045 | − | 0.0904209i | ||||
\(928\) | 8.17891 | 0.268486 | ||||||||
\(929\) | −19.5000 | − | 33.7750i | −0.639774 | − | 1.10812i | −0.985482 | − | 0.169779i | \(-0.945695\pi\) |
0.345708 | − | 0.938342i | \(-0.387639\pi\) | |||||||
\(930\) | 7.17891 | + | 12.4342i | 0.235406 | + | 0.407735i | ||||
\(931\) | −8.17891 | −0.268053 | ||||||||
\(932\) | 0.178908 | + | 0.309878i | 0.00586034 | + | 0.0101504i | ||||
\(933\) | −4.26836 | + | 7.39302i | −0.139740 | + | 0.242037i | ||||
\(934\) | −16.9473 | + | 29.3535i | −0.554532 | + | 0.960477i | ||||
\(935\) | −61.7891 | −2.02072 | ||||||||
\(936\) | −2.08945 | + | 2.93840i | −0.0682959 | + | 0.0960445i | ||||
\(937\) | −47.0735 | −1.53782 | −0.768911 | − | 0.639355i | \(-0.779201\pi\) | ||||
−0.768911 | + | 0.639355i | \(0.779201\pi\) | |||||||
\(938\) | −7.58945 | + | 13.1453i | −0.247804 | + | 0.429210i | ||||
\(939\) | 2.00000 | − | 3.46410i | 0.0652675 | − | 0.113047i | ||||
\(940\) | 4.17891 | + | 7.23808i | 0.136301 | + | 0.236080i | ||||
\(941\) | −20.0000 | −0.651981 | −0.325991 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(942\) | 1.00000 | + | 1.73205i | 0.0325818 | + | 0.0564333i | ||||
\(943\) | −6.64218 | − | 11.5046i | −0.216299 | − | 0.374641i | ||||
\(944\) | −0.821092 | −0.0267243 | ||||||||
\(945\) | 1.00000 | + | 1.73205i | 0.0325300 | + | 0.0563436i | ||||
\(946\) | −2.53673 | + | 4.39374i | −0.0824760 | + | 0.142853i | ||||
\(947\) | −19.6262 | + | 33.9935i | −0.637765 | + | 1.10464i | 0.348157 | + | 0.937436i | \(0.386808\pi\) |
−0.985922 | + | 0.167205i | \(0.946526\pi\) | |||||||
\(948\) | −1.82109 | −0.0591463 | ||||||||
\(949\) | −6.00000 | − | 13.1149i | −0.194768 | − | 0.425727i | ||||
\(950\) | 8.17891 | 0.265359 | ||||||||
\(951\) | 3.58945 | − | 6.21712i | 0.116396 | − | 0.201604i | ||||
\(952\) | 2.50000 | − | 4.33013i | 0.0810255 | − | 0.140340i | ||||
\(953\) | −21.3578 | − | 36.9928i | −0.691848 | − | 1.19832i | −0.971232 | − | 0.238136i | \(-0.923464\pi\) |
0.279384 | − | 0.960179i | \(-0.409870\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | 27.5367 | + | 47.6950i | 0.891067 | + | 1.54337i | ||||
\(956\) | 0.589454 | + | 1.02096i | 0.0190643 | + | 0.0330204i | ||||
\(957\) | −50.5367 | −1.63362 | ||||||||
\(958\) | 14.9105 | + | 25.8258i | 0.481738 | + | 0.834394i | ||||
\(959\) | −8.17891 | + | 14.1663i | −0.264111 | + | 0.457453i | ||||
\(960\) | −1.00000 | + | 1.73205i | −0.0322749 | + | 0.0559017i | ||||
\(961\) | 20.5367 | 0.662475 | ||||||||
\(962\) | −4.17891 | + | 5.87680i | −0.134733 | + | 0.189475i | ||||
\(963\) | 7.82109 | 0.252031 | ||||||||
\(964\) | 9.17891 | − | 15.8983i | 0.295633 | − | 0.512051i | ||||
\(965\) | 20.5367 | − | 35.5707i | 0.661101 | − | 1.14506i | ||||
\(966\) | −1.58945 | − | 2.75302i | −0.0511398 | − | 0.0885768i | ||||
\(967\) | 34.3578 | 1.10487 | 0.552436 | − | 0.833555i | \(-0.313698\pi\) | ||||
0.552436 | + | 0.833555i | \(0.313698\pi\) | |||||||
\(968\) | −13.5895 | − | 23.5376i | −0.436782 | − | 0.756528i | ||||
\(969\) | −20.4473 | − | 35.4157i | −0.656861 | − | 1.13772i | ||||
\(970\) | −24.7156 | −0.793571 | ||||||||
\(971\) | 8.41055 | + | 14.5675i | 0.269907 | + | 0.467493i | 0.968838 | − | 0.247697i | \(-0.0796736\pi\) |
−0.698930 | + | 0.715190i | \(0.746340\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −9.08945 | + | 15.7434i | −0.291395 | + | 0.504710i | ||||
\(974\) | −38.1789 | −1.22333 | ||||||||
\(975\) | 3.58945 | + | 0.340322i | 0.114955 | + | 0.0108990i | ||||
\(976\) | −3.00000 | −0.0960277 | ||||||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | −4.41055 | + | 7.63929i | −0.141034 | + | 0.244278i | ||||
\(979\) | −27.8051 | − | 48.1598i | −0.888654 | − | 1.53919i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −2.00000 | − | 3.46410i | −0.0638551 | − | 0.110600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.0735 | 1.75657 | 0.878285 | − | 0.478137i | \(-0.158688\pi\) | ||||
0.878285 | + | 0.478137i | \(0.158688\pi\) | |||||||
\(984\) | 2.08945 | + | 3.61904i | 0.0666094 | + | 0.115371i | ||||
\(985\) | 17.0000 | − | 29.4449i | 0.541665 | − | 0.938191i | ||||
\(986\) | −20.4473 | + | 35.4157i | −0.651174 | + | 1.12787i | ||||
\(987\) | 4.17891 | 0.133016 | ||||||||
\(988\) | −29.3578 | − | 2.78346i | −0.933997 | − | 0.0885536i | ||||
\(989\) | 2.61018 | 0.0829987 | ||||||||
\(990\) | 6.17891 | − | 10.7022i | 0.196379 | − | 0.340138i | ||||
\(991\) | 7.73164 | − | 13.3916i | 0.245604 | − | 0.425398i | −0.716698 | − | 0.697384i | \(-0.754347\pi\) |
0.962301 | + | 0.271986i | \(0.0876805\pi\) | |||||||
\(992\) | 3.58945 | + | 6.21712i | 0.113965 | + | 0.197394i | ||||
\(993\) | 24.3578 | 0.772972 | ||||||||
\(994\) | 4.58945 | + | 7.94917i | 0.145569 | + | 0.252132i | ||||
\(995\) | 12.8211 | + | 22.2068i | 0.406456 | + | 0.704002i | ||||
\(996\) | 5.17891 | 0.164100 | ||||||||
\(997\) | −28.8578 | − | 49.9832i | −0.913936 | − | 1.58298i | −0.808451 | − | 0.588563i | \(-0.799694\pi\) |
−0.105485 | − | 0.994421i | \(-0.533639\pi\) | |||||||
\(998\) | 1.58945 | − | 2.75302i | 0.0503133 | − | 0.0871452i | ||||
\(999\) | 1.00000 | − | 1.73205i | 0.0316386 | − | 0.0547997i |
(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 | 546.2.l.k.295.1 | yes | 4 | |
3.2 | odd | 2 | 1638.2.r.ba.1387.2 | 4 | |||
13.3 | even | 3 | inner | 546.2.l.k.211.1 | ✓ | 4 | |
13.4 | even | 6 | 7098.2.a.bk.1.1 | 2 | |||
13.9 | even | 3 | 7098.2.a.br.1.2 | 2 | |||
39.29 | odd | 6 | 1638.2.r.ba.757.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.k.211.1 | ✓ | 4 | 13.3 | even | 3 | inner | |
546.2.l.k.295.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.r.ba.757.2 | 4 | 39.29 | odd | 6 | |||
1638.2.r.ba.1387.2 | 4 | 3.2 | odd | 2 | |||
7098.2.a.bk.1.1 | 2 | 13.4 | even | 6 | |||
7098.2.a.br.1.2 | 2 | 13.9 | even | 3 |