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: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.j.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||
\(5\) | −3.27492 | −1.46459 | −0.732294 | − | 0.680989i | \(-0.761550\pi\) | ||||
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | −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 | ||||
\(10\) | 1.63746 | + | 2.83616i | 0.517810 | + | 0.896873i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.63746 | + | 2.83616i | 0.422790 | + | 0.732294i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.27492 | − | 7.40437i | 0.980733 | − | 1.69868i | 0.321187 | − | 0.947016i | \(-0.395918\pi\) |
0.659546 | − | 0.751664i | \(-0.270749\pi\) | |||||||
\(20\) | 1.63746 | − | 2.83616i | 0.366147 | − | 0.634185i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 2.00000 | − | 3.46410i | 0.426401 | − | 0.738549i | ||||
\(23\) | −1.13746 | − | 1.97014i | −0.237177 | − | 0.410802i | 0.722726 | − | 0.691134i | \(-0.242889\pi\) |
−0.959903 | + | 0.280332i | \(0.909555\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 5.72508 | 1.14502 | ||||||||
\(26\) | −2.50000 | − | 2.59808i | −0.490290 | − | 0.509525i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −0.362541 | − | 0.627940i | −0.0673222 | − | 0.116606i | 0.830400 | − | 0.557168i | \(-0.188112\pi\) |
−0.897722 | + | 0.440563i | \(0.854779\pi\) | |||||||
\(30\) | 1.63746 | − | 2.83616i | 0.298958 | − | 0.517810i | ||||
\(31\) | 6.27492 | 1.12701 | 0.563504 | − | 0.826113i | \(-0.309453\pi\) | ||||
0.563504 | + | 0.826113i | \(0.309453\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 1.63746 | − | 2.83616i | 0.276781 | − | 0.479399i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 3.63746 | + | 6.30026i | 0.597995 | + | 1.03576i | 0.993117 | + | 0.117128i | \(0.0373689\pi\) |
−0.395122 | + | 0.918629i | \(0.629298\pi\) | |||||||
\(38\) | −8.54983 | −1.38697 | ||||||||
\(39\) | −2.50000 | − | 2.59808i | −0.400320 | − | 0.416025i | ||||
\(40\) | −3.27492 | −0.517810 | ||||||||
\(41\) | −0.362541 | − | 0.627940i | −0.0566195 | − | 0.0980678i | 0.836326 | − | 0.548232i | \(-0.184699\pi\) |
−0.892946 | + | 0.450164i | \(0.851366\pi\) | |||||||
\(42\) | −0.500000 | − | 0.866025i | −0.0771517 | − | 0.133631i | ||||
\(43\) | −5.41238 | + | 9.37451i | −0.825380 | + | 1.42960i | 0.0762493 | + | 0.997089i | \(0.475706\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 1.63746 | − | 2.83616i | 0.244098 | − | 0.422790i | ||||
\(46\) | −1.13746 | + | 1.97014i | −0.167709 | + | 0.290481i | ||||
\(47\) | 8.54983 | 1.24712 | 0.623561 | − | 0.781775i | \(-0.285685\pi\) | ||||
0.623561 | + | 0.781775i | \(0.285685\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −2.86254 | − | 4.95807i | −0.404824 | − | 0.701177i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | −1.00000 | + | 3.46410i | −0.138675 | + | 0.480384i | ||||
\(53\) | 11.5498 | 1.58649 | 0.793246 | − | 0.608901i | \(-0.208390\pi\) | ||||
0.793246 | + | 0.608901i | \(0.208390\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −6.54983 | − | 11.3446i | −0.883179 | − | 1.52971i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | −8.54983 | −1.13245 | ||||||||
\(58\) | −0.362541 | + | 0.627940i | −0.0476040 | + | 0.0824526i | ||||
\(59\) | −5.41238 | + | 9.37451i | −0.704631 | + | 1.22046i | 0.262193 | + | 0.965015i | \(0.415554\pi\) |
−0.966824 | + | 0.255442i | \(0.917779\pi\) | |||||||
\(60\) | −3.27492 | −0.422790 | ||||||||
\(61\) | 4.50000 | − | 7.79423i | 0.576166 | − | 0.997949i | −0.419748 | − | 0.907641i | \(-0.637882\pi\) |
0.995914 | − | 0.0903080i | \(-0.0287851\pi\) | |||||||
\(62\) | −3.13746 | − | 5.43424i | −0.398458 | − | 0.690149i | ||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.4622 | + | 2.83616i | −1.42171 | + | 0.351783i | ||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 5.13746 | + | 8.89834i | 0.627640 | + | 1.08711i | 0.988024 | + | 0.154301i | \(0.0493125\pi\) |
−0.360383 | + | 0.932804i | \(0.617354\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | −1.13746 | + | 1.97014i | −0.136934 | + | 0.237177i | ||||
\(70\) | −3.27492 | −0.391427 | ||||||||
\(71\) | 1.13746 | − | 1.97014i | 0.134992 | − | 0.233812i | −0.790603 | − | 0.612329i | \(-0.790233\pi\) |
0.925594 | + | 0.378517i | \(0.123566\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 13.2749 | 1.55371 | 0.776856 | − | 0.629679i | \(-0.216813\pi\) | ||||
0.776856 | + | 0.629679i | \(0.216813\pi\) | |||||||
\(74\) | 3.63746 | − | 6.30026i | 0.422846 | − | 0.732391i | ||||
\(75\) | −2.86254 | − | 4.95807i | −0.330538 | − | 0.572508i | ||||
\(76\) | 4.27492 | + | 7.40437i | 0.490367 | + | 0.849340i | ||||
\(77\) | −4.00000 | −0.455842 | ||||||||
\(78\) | −1.00000 | + | 3.46410i | −0.113228 | + | 0.392232i | ||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 1.63746 | + | 2.83616i | 0.183073 | + | 0.317092i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.362541 | + | 0.627940i | −0.0400360 | + | 0.0693444i | ||||
\(83\) | 10.8248 | 1.18817 | 0.594085 | − | 0.804402i | \(-0.297514\pi\) | ||||
0.594085 | + | 0.804402i | \(0.297514\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | 4.91238 | − | 8.50848i | 0.532822 | − | 0.922875i | ||||
\(86\) | 10.8248 | 1.16726 | ||||||||
\(87\) | −0.362541 | + | 0.627940i | −0.0388685 | + | 0.0673222i | ||||
\(88\) | 2.00000 | + | 3.46410i | 0.213201 | + | 0.369274i | ||||
\(89\) | −4.13746 | − | 7.16629i | −0.438570 | − | 0.759625i | 0.559010 | − | 0.829161i | \(-0.311181\pi\) |
−0.997579 | + | 0.0695360i | \(0.977848\pi\) | |||||||
\(90\) | −3.27492 | −0.345207 | ||||||||
\(91\) | −1.00000 | + | 3.46410i | −0.104828 | + | 0.363137i | ||||
\(92\) | 2.27492 | 0.237177 | ||||||||
\(93\) | −3.13746 | − | 5.43424i | −0.325339 | − | 0.563504i | ||||
\(94\) | −4.27492 | − | 7.40437i | −0.440924 | − | 0.763703i | ||||
\(95\) | −14.0000 | + | 24.2487i | −1.43637 | + | 2.48787i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.27492 | + | 12.6005i | −0.738656 | + | 1.27939i | 0.214445 | + | 0.976736i | \(0.431206\pi\) |
−0.953101 | + | 0.302653i | \(0.902128\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | −2.86254 | + | 4.95807i | −0.286254 | + | 0.495807i | ||||
\(101\) | −4.63746 | − | 8.03231i | −0.461444 | − | 0.799245i | 0.537589 | − | 0.843207i | \(-0.319335\pi\) |
−0.999033 | + | 0.0439620i | \(0.986002\pi\) | |||||||
\(102\) | −1.50000 | − | 2.59808i | −0.148522 | − | 0.257248i | ||||
\(103\) | −2.27492 | −0.224154 | −0.112077 | − | 0.993700i | \(-0.535750\pi\) | ||||
−0.112077 | + | 0.993700i | \(0.535750\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | −3.27492 | −0.319599 | ||||||||
\(106\) | −5.77492 | − | 10.0025i | −0.560910 | − | 0.971524i | ||||
\(107\) | 6.27492 | + | 10.8685i | 0.606619 | + | 1.05070i | 0.991793 | + | 0.127851i | \(0.0408080\pi\) |
−0.385174 | + | 0.922844i | \(0.625859\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 10.5498 | 1.01049 | 0.505245 | − | 0.862976i | \(-0.331402\pi\) | ||||
0.505245 | + | 0.862976i | \(0.331402\pi\) | |||||||
\(110\) | −6.54983 | + | 11.3446i | −0.624502 | + | 1.08167i | ||||
\(111\) | 3.63746 | − | 6.30026i | 0.345252 | − | 0.597995i | ||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 3.91238 | − | 6.77643i | 0.368045 | − | 0.637473i | −0.621215 | − | 0.783641i | \(-0.713360\pi\) |
0.989260 | + | 0.146167i | \(0.0466938\pi\) | |||||||
\(114\) | 4.27492 | + | 7.40437i | 0.400383 | + | 0.693483i | ||||
\(115\) | 3.72508 | + | 6.45203i | 0.347366 | + | 0.601655i | ||||
\(116\) | 0.725083 | 0.0673222 | ||||||||
\(117\) | −1.00000 | + | 3.46410i | −0.0924500 | + | 0.320256i | ||||
\(118\) | 10.8248 | 0.996499 | ||||||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | 1.63746 | + | 2.83616i | 0.149479 | + | 0.258905i | ||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −9.00000 | −0.814822 | ||||||||
\(123\) | −0.362541 | + | 0.627940i | −0.0326893 | + | 0.0566195i | ||||
\(124\) | −3.13746 | + | 5.43424i | −0.281752 | + | 0.488009i | ||||
\(125\) | −2.37459 | −0.212389 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | −4.00000 | − | 6.92820i | −0.354943 | − | 0.614779i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.8248 | 0.953066 | ||||||||
\(130\) | 8.18729 | + | 8.50848i | 0.718073 | + | 0.746243i | ||||
\(131\) | −10.2749 | −0.897724 | −0.448862 | − | 0.893601i | \(-0.648170\pi\) | ||||
−0.448862 | + | 0.893601i | \(0.648170\pi\) | |||||||
\(132\) | 2.00000 | + | 3.46410i | 0.174078 | + | 0.301511i | ||||
\(133\) | 4.27492 | + | 7.40437i | 0.370682 | + | 0.642041i | ||||
\(134\) | 5.13746 | − | 8.89834i | 0.443809 | − | 0.768699i | ||||
\(135\) | −3.27492 | −0.281860 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | −0.0876242 | + | 0.151770i | −0.00748624 | + | 0.0129665i | −0.869744 | − | 0.493503i | \(-0.835716\pi\) |
0.862258 | + | 0.506469i | \(0.169050\pi\) | |||||||
\(138\) | 2.27492 | 0.193654 | ||||||||
\(139\) | −10.5498 | + | 18.2728i | −0.894825 | + | 1.54988i | −0.0608046 | + | 0.998150i | \(0.519367\pi\) |
−0.834021 | + | 0.551733i | \(0.813967\pi\) | |||||||
\(140\) | 1.63746 | + | 2.83616i | 0.138391 | + | 0.239699i | ||||
\(141\) | −4.27492 | − | 7.40437i | −0.360013 | − | 0.623561i | ||||
\(142\) | −2.27492 | −0.190907 | ||||||||
\(143\) | 10.0000 | + | 10.3923i | 0.836242 | + | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.18729 | + | 2.05645i | 0.0985993 | + | 0.170779i | ||||
\(146\) | −6.63746 | − | 11.4964i | −0.549320 | − | 0.951450i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | −7.27492 | −0.597995 | ||||||||
\(149\) | 0.500000 | − | 0.866025i | 0.0409616 | − | 0.0709476i | −0.844818 | − | 0.535054i | \(-0.820291\pi\) |
0.885779 | + | 0.464107i | \(0.153625\pi\) | |||||||
\(150\) | −2.86254 | + | 4.95807i | −0.233726 | + | 0.404824i | ||||
\(151\) | −17.0997 | −1.39155 | −0.695776 | − | 0.718259i | \(-0.744939\pi\) | ||||
−0.695776 | + | 0.718259i | \(0.744939\pi\) | |||||||
\(152\) | 4.27492 | − | 7.40437i | 0.346742 | − | 0.600574i | ||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | 2.00000 | + | 3.46410i | 0.161165 | + | 0.279145i | ||||
\(155\) | −20.5498 | −1.65060 | ||||||||
\(156\) | 3.50000 | − | 0.866025i | 0.280224 | − | 0.0693375i | ||||
\(157\) | −11.2749 | −0.899836 | −0.449918 | − | 0.893070i | \(-0.648547\pi\) | ||||
−0.449918 | + | 0.893070i | \(0.648547\pi\) | |||||||
\(158\) | 4.00000 | + | 6.92820i | 0.318223 | + | 0.551178i | ||||
\(159\) | −5.77492 | − | 10.0025i | −0.457981 | − | 0.793246i | ||||
\(160\) | 1.63746 | − | 2.83616i | 0.129452 | − | 0.224218i | ||||
\(161\) | 2.27492 | 0.179289 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 2.86254 | − | 4.95807i | 0.224212 | − | 0.388346i | −0.731871 | − | 0.681443i | \(-0.761353\pi\) |
0.956083 | + | 0.293097i | \(0.0946860\pi\) | |||||||
\(164\) | 0.725083 | 0.0566195 | ||||||||
\(165\) | −6.54983 | + | 11.3446i | −0.509904 | + | 0.883179i | ||||
\(166\) | −5.41238 | − | 9.37451i | −0.420082 | − | 0.727603i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −9.82475 | −0.753524 | ||||||||
\(171\) | 4.27492 | + | 7.40437i | 0.326911 | + | 0.566227i | ||||
\(172\) | −5.41238 | − | 9.37451i | −0.412690 | − | 0.714800i | ||||
\(173\) | −5.27492 | + | 9.13642i | −0.401045 | + | 0.694630i | −0.993852 | − | 0.110715i | \(-0.964686\pi\) |
0.592808 | + | 0.805344i | \(0.298019\pi\) | |||||||
\(174\) | 0.725083 | 0.0549684 | ||||||||
\(175\) | −2.86254 | + | 4.95807i | −0.216388 | + | 0.374795i | ||||
\(176\) | 2.00000 | − | 3.46410i | 0.150756 | − | 0.261116i | ||||
\(177\) | 10.8248 | 0.813638 | ||||||||
\(178\) | −4.13746 | + | 7.16629i | −0.310116 | + | 0.537136i | ||||
\(179\) | −8.27492 | − | 14.3326i | −0.618496 | − | 1.07127i | −0.989760 | − | 0.142740i | \(-0.954409\pi\) |
0.371264 | − | 0.928527i | \(-0.378925\pi\) | |||||||
\(180\) | 1.63746 | + | 2.83616i | 0.122049 | + | 0.211395i | ||||
\(181\) | 5.82475 | 0.432950 | 0.216475 | − | 0.976288i | \(-0.430544\pi\) | ||||
0.216475 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(182\) | 3.50000 | − | 0.866025i | 0.259437 | − | 0.0641941i | ||||
\(183\) | −9.00000 | −0.665299 | ||||||||
\(184\) | −1.13746 | − | 1.97014i | −0.0838546 | − | 0.145240i | ||||
\(185\) | −11.9124 | − | 20.6328i | −0.875815 | − | 1.51696i | ||||
\(186\) | −3.13746 | + | 5.43424i | −0.230050 | + | 0.398458i | ||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | −4.27492 | + | 7.40437i | −0.311780 | + | 0.540019i | ||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | 28.0000 | 2.03133 | ||||||||
\(191\) | −7.13746 | + | 12.3624i | −0.516448 | + | 0.894515i | 0.483369 | + | 0.875417i | \(0.339413\pi\) |
−0.999818 | + | 0.0190983i | \(0.993920\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 1.08762 | + | 1.88382i | 0.0782889 | + | 0.135600i | 0.902512 | − | 0.430665i | \(-0.141721\pi\) |
−0.824223 | + | 0.566266i | \(0.808388\pi\) | |||||||
\(194\) | 14.5498 | 1.04462 | ||||||||
\(195\) | 8.18729 | + | 8.50848i | 0.586304 | + | 0.609305i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.412376 | − | 0.714256i | −0.0293806 | − | 0.0508886i | 0.850961 | − | 0.525228i | \(-0.176020\pi\) |
−0.880342 | + | 0.474340i | \(0.842687\pi\) | |||||||
\(198\) | 2.00000 | + | 3.46410i | 0.142134 | + | 0.246183i | ||||
\(199\) | 5.41238 | − | 9.37451i | 0.383673 | − | 0.664541i | −0.607911 | − | 0.794005i | \(-0.707992\pi\) |
0.991584 | + | 0.129464i | \(0.0413256\pi\) | |||||||
\(200\) | 5.72508 | 0.404824 | ||||||||
\(201\) | 5.13746 | − | 8.89834i | 0.362368 | − | 0.627640i | ||||
\(202\) | −4.63746 | + | 8.03231i | −0.326290 | + | 0.565152i | ||||
\(203\) | 0.725083 | 0.0508908 | ||||||||
\(204\) | −1.50000 | + | 2.59808i | −0.105021 | + | 0.181902i | ||||
\(205\) | 1.18729 | + | 2.05645i | 0.0829241 | + | 0.143629i | ||||
\(206\) | 1.13746 | + | 1.97014i | 0.0792505 | + | 0.137266i | ||||
\(207\) | 2.27492 | 0.158118 | ||||||||
\(208\) | −2.50000 | − | 2.59808i | −0.173344 | − | 0.180144i | ||||
\(209\) | 34.1993 | 2.36562 | ||||||||
\(210\) | 1.63746 | + | 2.83616i | 0.112995 | + | 0.195714i | ||||
\(211\) | 4.54983 | + | 7.88054i | 0.313224 | + | 0.542519i | 0.979058 | − | 0.203580i | \(-0.0652578\pi\) |
−0.665835 | + | 0.746099i | \(0.731924\pi\) | |||||||
\(212\) | −5.77492 | + | 10.0025i | −0.396623 | + | 0.686971i | ||||
\(213\) | −2.27492 | −0.155875 | ||||||||
\(214\) | 6.27492 | − | 10.8685i | 0.428945 | − | 0.742954i | ||||
\(215\) | 17.7251 | − | 30.7007i | 1.20884 | − | 2.09377i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.13746 | + | 5.43424i | −0.212985 | + | 0.368900i | ||||
\(218\) | −5.27492 | − | 9.13642i | −0.357262 | − | 0.618797i | ||||
\(219\) | −6.63746 | − | 11.4964i | −0.448518 | − | 0.776856i | ||||
\(220\) | 13.0997 | 0.883179 | ||||||||
\(221\) | −3.00000 | + | 10.3923i | −0.201802 | + | 0.699062i | ||||
\(222\) | −7.27492 | −0.488260 | ||||||||
\(223\) | −9.13746 | − | 15.8265i | −0.611889 | − | 1.05982i | −0.990922 | − | 0.134440i | \(-0.957076\pi\) |
0.379032 | − | 0.925383i | \(-0.376257\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | −2.86254 | + | 4.95807i | −0.190836 | + | 0.330538i | ||||
\(226\) | −7.82475 | −0.520495 | ||||||||
\(227\) | −4.54983 | + | 7.88054i | −0.301983 | + | 0.523050i | −0.976585 | − | 0.215132i | \(-0.930982\pi\) |
0.674602 | + | 0.738182i | \(0.264315\pi\) | |||||||
\(228\) | 4.27492 | − | 7.40437i | 0.283113 | − | 0.490367i | ||||
\(229\) | 20.2749 | 1.33980 | 0.669902 | − | 0.742449i | \(-0.266336\pi\) | ||||
0.669902 | + | 0.742449i | \(0.266336\pi\) | |||||||
\(230\) | 3.72508 | − | 6.45203i | 0.245625 | − | 0.425434i | ||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | −0.362541 | − | 0.627940i | −0.0238020 | − | 0.0412263i | ||||
\(233\) | 22.5498 | 1.47729 | 0.738644 | − | 0.674095i | \(-0.235466\pi\) | ||||
0.738644 | + | 0.674095i | \(0.235466\pi\) | |||||||
\(234\) | 3.50000 | − | 0.866025i | 0.228802 | − | 0.0566139i | ||||
\(235\) | −28.0000 | −1.82652 | ||||||||
\(236\) | −5.41238 | − | 9.37451i | −0.352316 | − | 0.610229i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | −1.50000 | + | 2.59808i | −0.0972306 | + | 0.168408i | ||||
\(239\) | 2.27492 | 0.147152 | 0.0735761 | − | 0.997290i | \(-0.476559\pi\) | ||||
0.0735761 | + | 0.997290i | \(0.476559\pi\) | |||||||
\(240\) | 1.63746 | − | 2.83616i | 0.105697 | − | 0.183073i | ||||
\(241\) | 11.6375 | − | 20.1567i | 0.749635 | − | 1.29841i | −0.198363 | − | 0.980129i | \(-0.563563\pi\) |
0.947998 | − | 0.318277i | \(-0.103104\pi\) | |||||||
\(242\) | 5.00000 | 0.321412 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 4.50000 | + | 7.79423i | 0.288083 | + | 0.498974i | ||||
\(245\) | 1.63746 | + | 2.83616i | 0.104613 | + | 0.181196i | ||||
\(246\) | 0.725083 | 0.0462296 | ||||||||
\(247\) | 8.54983 | − | 29.6175i | 0.544013 | − | 1.88452i | ||||
\(248\) | 6.27492 | 0.398458 | ||||||||
\(249\) | −5.41238 | − | 9.37451i | −0.342995 | − | 0.594085i | ||||
\(250\) | 1.18729 | + | 2.05645i | 0.0750910 | + | 0.130061i | ||||
\(251\) | −2.86254 | + | 4.95807i | −0.180682 | + | 0.312950i | −0.942113 | − | 0.335296i | \(-0.891164\pi\) |
0.761431 | + | 0.648246i | \(0.224497\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 4.54983 | − | 7.88054i | 0.286046 | − | 0.495446i | ||||
\(254\) | −4.00000 | + | 6.92820i | −0.250982 | + | 0.434714i | ||||
\(255\) | −9.82475 | −0.615250 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | −5.41238 | − | 9.37451i | −0.336960 | − | 0.583631i | ||||
\(259\) | −7.27492 | −0.452041 | ||||||||
\(260\) | 3.27492 | − | 11.3446i | 0.203102 | − | 0.703565i | ||||
\(261\) | 0.725083 | 0.0448815 | ||||||||
\(262\) | 5.13746 | + | 8.89834i | 0.317393 | + | 0.549741i | ||||
\(263\) | 4.54983 | + | 7.88054i | 0.280555 | + | 0.485935i | 0.971522 | − | 0.236951i | \(-0.0761482\pi\) |
−0.690967 | + | 0.722887i | \(0.742815\pi\) | |||||||
\(264\) | 2.00000 | − | 3.46410i | 0.123091 | − | 0.213201i | ||||
\(265\) | −37.8248 | −2.32356 | ||||||||
\(266\) | 4.27492 | − | 7.40437i | 0.262112 | − | 0.453991i | ||||
\(267\) | −4.13746 | + | 7.16629i | −0.253208 | + | 0.438570i | ||||
\(268\) | −10.2749 | −0.627640 | ||||||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 1.63746 | + | 2.83616i | 0.0996526 | + | 0.172603i | ||||
\(271\) | −8.86254 | − | 15.3504i | −0.538361 | − | 0.932469i | −0.998993 | − | 0.0448772i | \(-0.985710\pi\) |
0.460631 | − | 0.887591i | \(-0.347623\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 3.50000 | − | 0.866025i | 0.211830 | − | 0.0524142i | ||||
\(274\) | 0.175248 | 0.0105871 | ||||||||
\(275\) | 11.4502 | + | 19.8323i | 0.690471 | + | 1.19593i | ||||
\(276\) | −1.13746 | − | 1.97014i | −0.0684670 | − | 0.118588i | ||||
\(277\) | 3.91238 | − | 6.77643i | 0.235072 | − | 0.407156i | −0.724222 | − | 0.689567i | \(-0.757801\pi\) |
0.959294 | + | 0.282411i | \(0.0911341\pi\) | |||||||
\(278\) | 21.0997 | 1.26547 | ||||||||
\(279\) | −3.13746 | + | 5.43424i | −0.187835 | + | 0.325339i | ||||
\(280\) | 1.63746 | − | 2.83616i | 0.0978569 | − | 0.169493i | ||||
\(281\) | 1.82475 | 0.108856 | 0.0544278 | − | 0.998518i | \(-0.482667\pi\) | ||||
0.0544278 | + | 0.998518i | \(0.482667\pi\) | |||||||
\(282\) | −4.27492 | + | 7.40437i | −0.254568 | + | 0.440924i | ||||
\(283\) | 12.2749 | + | 21.2608i | 0.729668 | + | 1.26382i | 0.957024 | + | 0.290010i | \(0.0936588\pi\) |
−0.227355 | + | 0.973812i | \(0.573008\pi\) | |||||||
\(284\) | 1.13746 | + | 1.97014i | 0.0674958 | + | 0.116906i | ||||
\(285\) | 28.0000 | 1.65858 | ||||||||
\(286\) | 4.00000 | − | 13.8564i | 0.236525 | − | 0.819346i | ||||
\(287\) | 0.725083 | 0.0428003 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 1.18729 | − | 2.05645i | 0.0697202 | − | 0.120759i | ||||
\(291\) | 14.5498 | 0.852926 | ||||||||
\(292\) | −6.63746 | + | 11.4964i | −0.388428 | + | 0.672777i | ||||
\(293\) | 5.36254 | − | 9.28819i | 0.313283 | − | 0.542622i | −0.665788 | − | 0.746141i | \(-0.731904\pi\) |
0.979071 | + | 0.203519i | \(0.0652378\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 17.7251 | − | 30.7007i | 1.03199 | − | 1.78747i | ||||
\(296\) | 3.63746 | + | 6.30026i | 0.211423 | + | 0.366195i | ||||
\(297\) | 2.00000 | + | 3.46410i | 0.116052 | + | 0.201008i | ||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −5.68729 | − | 5.91041i | −0.328905 | − | 0.341808i | ||||
\(300\) | 5.72508 | 0.330538 | ||||||||
\(301\) | −5.41238 | − | 9.37451i | −0.311964 | − | 0.540338i | ||||
\(302\) | 8.54983 | + | 14.8087i | 0.491988 | + | 0.852148i | ||||
\(303\) | −4.63746 | + | 8.03231i | −0.266415 | + | 0.461444i | ||||
\(304\) | −8.54983 | −0.490367 | ||||||||
\(305\) | −14.7371 | + | 25.5255i | −0.843845 | + | 1.46158i | ||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | −16.5498 | −0.944549 | −0.472274 | − | 0.881452i | \(-0.656567\pi\) | ||||
−0.472274 | + | 0.881452i | \(0.656567\pi\) | |||||||
\(308\) | 2.00000 | − | 3.46410i | 0.113961 | − | 0.197386i | ||||
\(309\) | 1.13746 | + | 1.97014i | 0.0647078 | + | 0.112077i | ||||
\(310\) | 10.2749 | + | 17.7967i | 0.583576 | + | 1.01078i | ||||
\(311\) | 12.5498 | 0.711636 | 0.355818 | − | 0.934555i | \(-0.384202\pi\) | ||||
0.355818 | + | 0.934555i | \(0.384202\pi\) | |||||||
\(312\) | −2.50000 | − | 2.59808i | −0.141535 | − | 0.147087i | ||||
\(313\) | −27.6495 | −1.56284 | −0.781421 | − | 0.624004i | \(-0.785505\pi\) | ||||
−0.781421 | + | 0.624004i | \(0.785505\pi\) | |||||||
\(314\) | 5.63746 | + | 9.76436i | 0.318140 | + | 0.551035i | ||||
\(315\) | 1.63746 | + | 2.83616i | 0.0922603 | + | 0.159800i | ||||
\(316\) | 4.00000 | − | 6.92820i | 0.225018 | − | 0.389742i | ||||
\(317\) | 7.54983 | 0.424041 | 0.212020 | − | 0.977265i | \(-0.431996\pi\) | ||||
0.212020 | + | 0.977265i | \(0.431996\pi\) | |||||||
\(318\) | −5.77492 | + | 10.0025i | −0.323841 | + | 0.560910i | ||||
\(319\) | 1.45017 | − | 2.51176i | 0.0811937 | − | 0.140632i | ||||
\(320\) | −3.27492 | −0.183073 | ||||||||
\(321\) | 6.27492 | − | 10.8685i | 0.350232 | − | 0.606619i | ||||
\(322\) | −1.13746 | − | 1.97014i | −0.0633881 | − | 0.109791i | ||||
\(323\) | 12.8248 | + | 22.2131i | 0.713588 | + | 1.23597i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 20.0378 | − | 4.95807i | 1.11150 | − | 0.275024i | ||||
\(326\) | −5.72508 | −0.317083 | ||||||||
\(327\) | −5.27492 | − | 9.13642i | −0.291704 | − | 0.505245i | ||||
\(328\) | −0.362541 | − | 0.627940i | −0.0200180 | − | 0.0346722i | ||||
\(329\) | −4.27492 | + | 7.40437i | −0.235684 | + | 0.408216i | ||||
\(330\) | 13.0997 | 0.721113 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | −5.41238 | + | 9.37451i | −0.297043 | + | 0.514493i | ||||
\(333\) | −7.27492 | −0.398663 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.8248 | − | 29.1413i | −0.919234 | − | 1.59216i | ||||
\(336\) | −0.500000 | − | 0.866025i | −0.0272772 | − | 0.0472456i | ||||
\(337\) | −7.27492 | −0.396290 | −0.198145 | − | 0.980173i | \(-0.563492\pi\) | ||||
−0.198145 | + | 0.980173i | \(0.563492\pi\) | |||||||
\(338\) | −11.0000 | − | 6.92820i | −0.598321 | − | 0.376845i | ||||
\(339\) | −7.82475 | −0.424982 | ||||||||
\(340\) | 4.91238 | + | 8.50848i | 0.266411 | + | 0.461437i | ||||
\(341\) | 12.5498 | + | 21.7370i | 0.679612 | + | 1.17712i | ||||
\(342\) | 4.27492 | − | 7.40437i | 0.231161 | − | 0.400383i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.41238 | + | 9.37451i | −0.291816 | + | 0.505440i | ||||
\(345\) | 3.72508 | − | 6.45203i | 0.200552 | − | 0.347366i | ||||
\(346\) | 10.5498 | 0.567163 | ||||||||
\(347\) | −7.72508 | + | 13.3802i | −0.414704 | + | 0.718289i | −0.995397 | − | 0.0958338i | \(-0.969448\pi\) |
0.580693 | + | 0.814122i | \(0.302782\pi\) | |||||||
\(348\) | −0.362541 | − | 0.627940i | −0.0194343 | − | 0.0336611i | ||||
\(349\) | −8.96221 | − | 15.5230i | −0.479736 | − | 0.830927i | 0.519994 | − | 0.854170i | \(-0.325934\pi\) |
−0.999730 | + | 0.0232427i | \(0.992601\pi\) | |||||||
\(350\) | 5.72508 | 0.306019 | ||||||||
\(351\) | 3.50000 | − | 0.866025i | 0.186816 | − | 0.0462250i | ||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | 2.22508 | + | 3.85396i | 0.118429 | + | 0.205125i | 0.919145 | − | 0.393919i | \(-0.128881\pi\) |
−0.800716 | + | 0.599044i | \(0.795547\pi\) | |||||||
\(354\) | −5.41238 | − | 9.37451i | −0.287665 | − | 0.498250i | ||||
\(355\) | −3.72508 | + | 6.45203i | −0.197707 | + | 0.342438i | ||||
\(356\) | 8.27492 | 0.438570 | ||||||||
\(357\) | −1.50000 | + | 2.59808i | −0.0793884 | + | 0.137505i | ||||
\(358\) | −8.27492 | + | 14.3326i | −0.437343 | + | 0.757500i | ||||
\(359\) | 29.0997 | 1.53582 | 0.767911 | − | 0.640557i | \(-0.221296\pi\) | ||||
0.767911 | + | 0.640557i | \(0.221296\pi\) | |||||||
\(360\) | 1.63746 | − | 2.83616i | 0.0863016 | − | 0.149479i | ||||
\(361\) | −27.0498 | − | 46.8517i | −1.42368 | − | 2.46588i | ||||
\(362\) | −2.91238 | − | 5.04438i | −0.153071 | − | 0.265127i | ||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | −2.50000 | − | 2.59808i | −0.131036 | − | 0.136176i | ||||
\(365\) | −43.4743 | −2.27555 | ||||||||
\(366\) | 4.50000 | + | 7.79423i | 0.235219 | + | 0.407411i | ||||
\(367\) | −2.86254 | − | 4.95807i | −0.149423 | − | 0.258809i | 0.781591 | − | 0.623791i | \(-0.214408\pi\) |
−0.931015 | + | 0.364982i | \(0.881075\pi\) | |||||||
\(368\) | −1.13746 | + | 1.97014i | −0.0592941 | + | 0.102700i | ||||
\(369\) | 0.725083 | 0.0377463 | ||||||||
\(370\) | −11.9124 | + | 20.6328i | −0.619295 | + | 1.07265i | ||||
\(371\) | −5.77492 | + | 10.0025i | −0.299819 | + | 0.519301i | ||||
\(372\) | 6.27492 | 0.325339 | ||||||||
\(373\) | −2.08762 | + | 3.61587i | −0.108093 | + | 0.187223i | −0.914998 | − | 0.403459i | \(-0.867808\pi\) |
0.806905 | + | 0.590682i | \(0.201141\pi\) | |||||||
\(374\) | 6.00000 | + | 10.3923i | 0.310253 | + | 0.537373i | ||||
\(375\) | 1.18729 | + | 2.05645i | 0.0613115 | + | 0.106195i | ||||
\(376\) | 8.54983 | 0.440924 | ||||||||
\(377\) | −1.81271 | − | 1.88382i | −0.0933592 | − | 0.0970217i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 10.0000 | + | 17.3205i | 0.513665 | + | 0.889695i | 0.999874 | + | 0.0158521i | \(0.00504609\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(380\) | −14.0000 | − | 24.2487i | −0.718185 | − | 1.24393i | ||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | 14.2749 | 0.730368 | ||||||||
\(383\) | 19.0997 | − | 33.0816i | 0.975947 | − | 1.69039i | 0.299175 | − | 0.954198i | \(-0.403288\pi\) |
0.676772 | − | 0.736192i | \(-0.263378\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 13.0997 | 0.667621 | ||||||||
\(386\) | 1.08762 | − | 1.88382i | 0.0553586 | − | 0.0958839i | ||||
\(387\) | −5.41238 | − | 9.37451i | −0.275127 | − | 0.476533i | ||||
\(388\) | −7.27492 | − | 12.6005i | −0.369328 | − | 0.639695i | ||||
\(389\) | 20.6495 | 1.04697 | 0.523486 | − | 0.852034i | \(-0.324631\pi\) | ||||
0.523486 | + | 0.852034i | \(0.324631\pi\) | |||||||
\(390\) | 3.27492 | − | 11.3446i | 0.165832 | − | 0.574458i | ||||
\(391\) | 6.82475 | 0.345143 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | 5.13746 | + | 8.89834i | 0.259151 | + | 0.448862i | ||||
\(394\) | −0.412376 | + | 0.714256i | −0.0207752 | + | 0.0359837i | ||||
\(395\) | 26.1993 | 1.31823 | ||||||||
\(396\) | 2.00000 | − | 3.46410i | 0.100504 | − | 0.174078i | ||||
\(397\) | −7.86254 | + | 13.6183i | −0.394610 | + | 0.683484i | −0.993051 | − | 0.117682i | \(-0.962454\pi\) |
0.598442 | + | 0.801166i | \(0.295787\pi\) | |||||||
\(398\) | −10.8248 | −0.542596 | ||||||||
\(399\) | 4.27492 | − | 7.40437i | 0.214014 | − | 0.370682i | ||||
\(400\) | −2.86254 | − | 4.95807i | −0.143127 | − | 0.247903i | ||||
\(401\) | −2.63746 | − | 4.56821i | −0.131708 | − | 0.228126i | 0.792627 | − | 0.609707i | \(-0.208713\pi\) |
−0.924335 | + | 0.381581i | \(0.875380\pi\) | |||||||
\(402\) | −10.2749 | −0.512466 | ||||||||
\(403\) | 21.9622 | − | 5.43424i | 1.09402 | − | 0.270699i | ||||
\(404\) | 9.27492 | 0.461444 | ||||||||
\(405\) | 1.63746 | + | 2.83616i | 0.0813660 | + | 0.140930i | ||||
\(406\) | −0.362541 | − | 0.627940i | −0.0179926 | − | 0.0311641i | ||||
\(407\) | −14.5498 | + | 25.2011i | −0.721209 | + | 1.24917i | ||||
\(408\) | 3.00000 | 0.148522 | ||||||||
\(409\) | −11.4622 | + | 19.8531i | −0.566770 | + | 0.981674i | 0.430113 | + | 0.902775i | \(0.358474\pi\) |
−0.996883 | + | 0.0788990i | \(0.974860\pi\) | |||||||
\(410\) | 1.18729 | − | 2.05645i | 0.0586362 | − | 0.101561i | ||||
\(411\) | 0.175248 | 0.00864436 | ||||||||
\(412\) | 1.13746 | − | 1.97014i | 0.0560386 | − | 0.0970616i | ||||
\(413\) | −5.41238 | − | 9.37451i | −0.266326 | − | 0.461289i | ||||
\(414\) | −1.13746 | − | 1.97014i | −0.0559030 | − | 0.0968269i | ||||
\(415\) | −35.4502 | −1.74018 | ||||||||
\(416\) | −1.00000 | + | 3.46410i | −0.0490290 | + | 0.169842i | ||||
\(417\) | 21.0997 | 1.03326 | ||||||||
\(418\) | −17.0997 | − | 29.6175i | −0.836372 | − | 1.44864i | ||||
\(419\) | −7.68729 | − | 13.3148i | −0.375549 | − | 0.650470i | 0.614860 | − | 0.788636i | \(-0.289212\pi\) |
−0.990409 | + | 0.138166i | \(0.955879\pi\) | |||||||
\(420\) | 1.63746 | − | 2.83616i | 0.0798998 | − | 0.138391i | ||||
\(421\) | 0.725083 | 0.0353384 | 0.0176692 | − | 0.999844i | \(-0.494375\pi\) | ||||
0.0176692 | + | 0.999844i | \(0.494375\pi\) | |||||||
\(422\) | 4.54983 | − | 7.88054i | 0.221482 | − | 0.383619i | ||||
\(423\) | −4.27492 | + | 7.40437i | −0.207854 | + | 0.360013i | ||||
\(424\) | 11.5498 | 0.560910 | ||||||||
\(425\) | −8.58762 | + | 14.8742i | −0.416561 | + | 0.721505i | ||||
\(426\) | 1.13746 | + | 1.97014i | 0.0551100 | + | 0.0954534i | ||||
\(427\) | 4.50000 | + | 7.79423i | 0.217770 | + | 0.377189i | ||||
\(428\) | −12.5498 | −0.606619 | ||||||||
\(429\) | 4.00000 | − | 13.8564i | 0.193122 | − | 0.668994i | ||||
\(430\) | −35.4502 | −1.70956 | ||||||||
\(431\) | 2.86254 | + | 4.95807i | 0.137884 | + | 0.238822i | 0.926695 | − | 0.375813i | \(-0.122637\pi\) |
−0.788812 | + | 0.614635i | \(0.789303\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 1.36254 | − | 2.35999i | 0.0654796 | − | 0.113414i | −0.831427 | − | 0.555634i | \(-0.812476\pi\) |
0.896907 | + | 0.442220i | \(0.145809\pi\) | |||||||
\(434\) | 6.27492 | 0.301206 | ||||||||
\(435\) | 1.18729 | − | 2.05645i | 0.0569263 | − | 0.0985993i | ||||
\(436\) | −5.27492 | + | 9.13642i | −0.252623 | + | 0.437555i | ||||
\(437\) | −19.4502 | −0.930428 | ||||||||
\(438\) | −6.63746 | + | 11.4964i | −0.317150 | + | 0.549320i | ||||
\(439\) | 8.54983 | + | 14.8087i | 0.408061 | + | 0.706783i | 0.994672 | − | 0.103086i | \(-0.0328716\pi\) |
−0.586611 | + | 0.809869i | \(0.699538\pi\) | |||||||
\(440\) | −6.54983 | − | 11.3446i | −0.312251 | − | 0.540835i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 10.5000 | − | 2.59808i | 0.499434 | − | 0.123578i | ||||
\(443\) | 19.4502 | 0.924105 | 0.462053 | − | 0.886853i | \(-0.347113\pi\) | ||||
0.462053 | + | 0.886853i | \(0.347113\pi\) | |||||||
\(444\) | 3.63746 | + | 6.30026i | 0.172626 | + | 0.298997i | ||||
\(445\) | 13.5498 | + | 23.4690i | 0.642324 | + | 1.11254i | ||||
\(446\) | −9.13746 | + | 15.8265i | −0.432671 | + | 0.749409i | ||||
\(447\) | −1.00000 | −0.0472984 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −5.54983 | + | 9.61260i | −0.261913 | + | 0.453646i | −0.966750 | − | 0.255723i | \(-0.917687\pi\) |
0.704837 | + | 0.709369i | \(0.251020\pi\) | |||||||
\(450\) | 5.72508 | 0.269883 | ||||||||
\(451\) | 1.45017 | − | 2.51176i | 0.0682856 | − | 0.118274i | ||||
\(452\) | 3.91238 | + | 6.77643i | 0.184023 | + | 0.318737i | ||||
\(453\) | 8.54983 | + | 14.8087i | 0.401706 | + | 0.695776i | ||||
\(454\) | 9.09967 | 0.427069 | ||||||||
\(455\) | 3.27492 | − | 11.3446i | 0.153530 | − | 0.531845i | ||||
\(456\) | −8.54983 | −0.400383 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | −10.1375 | − | 17.5586i | −0.473692 | − | 0.820459i | ||||
\(459\) | −1.50000 | + | 2.59808i | −0.0700140 | + | 0.121268i | ||||
\(460\) | −7.45017 | −0.347366 | ||||||||
\(461\) | −9.18729 | + | 15.9129i | −0.427895 | + | 0.741136i | −0.996686 | − | 0.0813464i | \(-0.974078\pi\) |
0.568791 | + | 0.822482i | \(0.307411\pi\) | |||||||
\(462\) | 2.00000 | − | 3.46410i | 0.0930484 | − | 0.161165i | ||||
\(463\) | 4.54983 | 0.211449 | 0.105724 | − | 0.994395i | \(-0.466284\pi\) | ||||
0.105724 | + | 0.994395i | \(0.466284\pi\) | |||||||
\(464\) | −0.362541 | + | 0.627940i | −0.0168306 | + | 0.0291514i | ||||
\(465\) | 10.2749 | + | 17.7967i | 0.476488 | + | 0.825301i | ||||
\(466\) | −11.2749 | − | 19.5287i | −0.522300 | − | 0.904651i | ||||
\(467\) | −30.8248 | −1.42640 | −0.713200 | − | 0.700961i | \(-0.752755\pi\) | ||||
−0.713200 | + | 0.700961i | \(0.752755\pi\) | |||||||
\(468\) | −2.50000 | − | 2.59808i | −0.115563 | − | 0.120096i | ||||
\(469\) | −10.2749 | −0.474452 | ||||||||
\(470\) | 14.0000 | + | 24.2487i | 0.645772 | + | 1.11851i | ||||
\(471\) | 5.63746 | + | 9.76436i | 0.259760 | + | 0.449918i | ||||
\(472\) | −5.41238 | + | 9.37451i | −0.249125 | + | 0.431497i | ||||
\(473\) | −43.2990 | −1.99089 | ||||||||
\(474\) | 4.00000 | − | 6.92820i | 0.183726 | − | 0.318223i | ||||
\(475\) | 24.4743 | − | 42.3907i | 1.12296 | − | 1.94502i | ||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | −5.77492 | + | 10.0025i | −0.264415 | + | 0.457981i | ||||
\(478\) | −1.13746 | − | 1.97014i | −0.0520261 | − | 0.0901119i | ||||
\(479\) | −10.0000 | − | 17.3205i | −0.456912 | − | 0.791394i | 0.541884 | − | 0.840453i | \(-0.317711\pi\) |
−0.998796 | + | 0.0490589i | \(0.984378\pi\) | |||||||
\(480\) | −3.27492 | −0.149479 | ||||||||
\(481\) | 18.1873 | + | 18.9008i | 0.829269 | + | 0.861802i | ||||
\(482\) | −23.2749 | −1.06014 | ||||||||
\(483\) | −1.13746 | − | 1.97014i | −0.0517562 | − | 0.0896443i | ||||
\(484\) | −2.50000 | − | 4.33013i | −0.113636 | − | 0.196824i | ||||
\(485\) | 23.8248 | − | 41.2657i | 1.08183 | − | 1.87378i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −14.5498 | + | 25.2011i | −0.659316 | + | 1.14197i | 0.321477 | + | 0.946917i | \(0.395821\pi\) |
−0.980793 | + | 0.195051i | \(0.937513\pi\) | |||||||
\(488\) | 4.50000 | − | 7.79423i | 0.203705 | − | 0.352828i | ||||
\(489\) | −5.72508 | −0.258897 | ||||||||
\(490\) | 1.63746 | − | 2.83616i | 0.0739728 | − | 0.128125i | ||||
\(491\) | 2.54983 | + | 4.41644i | 0.115072 | + | 0.199311i | 0.917809 | − | 0.397023i | \(-0.129957\pi\) |
−0.802736 | + | 0.596334i | \(0.796623\pi\) | |||||||
\(492\) | −0.362541 | − | 0.627940i | −0.0163446 | − | 0.0283097i | ||||
\(493\) | 2.17525 | 0.0979683 | ||||||||
\(494\) | −29.9244 | + | 7.40437i | −1.34636 | + | 0.333139i | ||||
\(495\) | 13.0997 | 0.588786 | ||||||||
\(496\) | −3.13746 | − | 5.43424i | −0.140876 | − | 0.244004i | ||||
\(497\) | 1.13746 | + | 1.97014i | 0.0510220 | + | 0.0883727i | ||||
\(498\) | −5.41238 | + | 9.37451i | −0.242534 | + | 0.420082i | ||||
\(499\) | −9.17525 | −0.410741 | −0.205370 | − | 0.978684i | \(-0.565840\pi\) | ||||
−0.205370 | + | 0.978684i | \(0.565840\pi\) | |||||||
\(500\) | 1.18729 | − | 2.05645i | 0.0530974 | − | 0.0919673i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.72508 | 0.255523 | ||||||||
\(503\) | −4.54983 | + | 7.88054i | −0.202867 | + | 0.351376i | −0.949451 | − | 0.313915i | \(-0.898359\pi\) |
0.746584 | + | 0.665291i | \(0.231693\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | 15.1873 | + | 26.3052i | 0.675826 | + | 1.17056i | ||||
\(506\) | −9.09967 | −0.404530 | ||||||||
\(507\) | −11.0000 | − | 6.92820i | −0.488527 | − | 0.307692i | ||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | 17.9124 | + | 31.0251i | 0.793952 | + | 1.37517i | 0.923502 | + | 0.383593i | \(0.125313\pi\) |
−0.129550 | + | 0.991573i | \(0.541353\pi\) | |||||||
\(510\) | 4.91238 | + | 8.50848i | 0.217524 | + | 0.376762i | ||||
\(511\) | −6.63746 | + | 11.4964i | −0.293624 | + | 0.508571i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.27492 | − | 7.40437i | 0.188742 | − | 0.326911i | ||||
\(514\) | −7.50000 | + | 12.9904i | −0.330811 | + | 0.572981i | ||||
\(515\) | 7.45017 | 0.328294 | ||||||||
\(516\) | −5.41238 | + | 9.37451i | −0.238267 | + | 0.412690i | ||||
\(517\) | 17.0997 | + | 29.6175i | 0.752043 | + | 1.30258i | ||||
\(518\) | 3.63746 | + | 6.30026i | 0.159821 | + | 0.276818i | ||||
\(519\) | 10.5498 | 0.463086 | ||||||||
\(520\) | −11.4622 | + | 2.83616i | −0.502651 | + | 0.124374i | ||||
\(521\) | 1.82475 | 0.0799438 | 0.0399719 | − | 0.999201i | \(-0.487273\pi\) | ||||
0.0399719 | + | 0.999201i | \(0.487273\pi\) | |||||||
\(522\) | −0.362541 | − | 0.627940i | −0.0158680 | − | 0.0274842i | ||||
\(523\) | −17.0997 | − | 29.6175i | −0.747716 | − | 1.29508i | −0.948915 | − | 0.315532i | \(-0.897817\pi\) |
0.201199 | − | 0.979550i | \(-0.435516\pi\) | |||||||
\(524\) | 5.13746 | − | 8.89834i | 0.224431 | − | 0.388726i | ||||
\(525\) | 5.72508 | 0.249863 | ||||||||
\(526\) | 4.54983 | − | 7.88054i | 0.198382 | − | 0.343608i | ||||
\(527\) | −9.41238 | + | 16.3027i | −0.410010 | + | 0.710157i | ||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | 8.91238 | − | 15.4367i | 0.387495 | − | 0.671160i | ||||
\(530\) | 18.9124 | + | 32.7572i | 0.821501 | + | 1.42288i | ||||
\(531\) | −5.41238 | − | 9.37451i | −0.234877 | − | 0.406819i | ||||
\(532\) | −8.54983 | −0.370682 | ||||||||
\(533\) | −1.81271 | − | 1.88382i | −0.0785171 | − | 0.0815973i | ||||
\(534\) | 8.27492 | 0.358091 | ||||||||
\(535\) | −20.5498 | − | 35.5934i | −0.888447 | − | 1.53884i | ||||
\(536\) | 5.13746 | + | 8.89834i | 0.221904 | + | 0.384350i | ||||
\(537\) | −8.27492 | + | 14.3326i | −0.357089 | + | 0.618496i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 2.00000 | − | 3.46410i | 0.0861461 | − | 0.149209i | ||||
\(540\) | 1.63746 | − | 2.83616i | 0.0704650 | − | 0.122049i | ||||
\(541\) | −12.3746 | −0.532025 | −0.266013 | − | 0.963970i | \(-0.585706\pi\) | ||||
−0.266013 | + | 0.963970i | \(0.585706\pi\) | |||||||
\(542\) | −8.86254 | + | 15.3504i | −0.380679 | + | 0.659355i | ||||
\(543\) | −2.91238 | − | 5.04438i | −0.124982 | − | 0.216475i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | −34.5498 | −1.47995 | ||||||||
\(546\) | −2.50000 | − | 2.59808i | −0.106990 | − | 0.111187i | ||||
\(547\) | 33.0997 | 1.41524 | 0.707620 | − | 0.706593i | \(-0.249769\pi\) | ||||
0.707620 | + | 0.706593i | \(0.249769\pi\) | |||||||
\(548\) | −0.0876242 | − | 0.151770i | −0.00374312 | − | 0.00648327i | ||||
\(549\) | 4.50000 | + | 7.79423i | 0.192055 | + | 0.332650i | ||||
\(550\) | 11.4502 | − | 19.8323i | 0.488237 | − | 0.845651i | ||||
\(551\) | −6.19934 | −0.264101 | ||||||||
\(552\) | −1.13746 | + | 1.97014i | −0.0484135 | + | 0.0838546i | ||||
\(553\) | 4.00000 | − | 6.92820i | 0.170097 | − | 0.294617i | ||||
\(554\) | −7.82475 | −0.332442 | ||||||||
\(555\) | −11.9124 | + | 20.6328i | −0.505652 | + | 0.875815i | ||||
\(556\) | −10.5498 | − | 18.2728i | −0.447413 | − | 0.774941i | ||||
\(557\) | −12.5997 | − | 21.8233i | −0.533865 | − | 0.924681i | −0.999217 | − | 0.0395559i | \(-0.987406\pi\) |
0.465352 | − | 0.885126i | \(-0.345928\pi\) | |||||||
\(558\) | 6.27492 | 0.265638 | ||||||||
\(559\) | −10.8248 | + | 37.4980i | −0.457838 | + | 1.58600i | ||||
\(560\) | −3.27492 | −0.138391 | ||||||||
\(561\) | 6.00000 | + | 10.3923i | 0.253320 | + | 0.438763i | ||||
\(562\) | −0.912376 | − | 1.58028i | −0.0384863 | − | 0.0666601i | ||||
\(563\) | −12.0000 | + | 20.7846i | −0.505740 | + | 0.875967i | 0.494238 | + | 0.869326i | \(0.335447\pi\) |
−0.999978 | + | 0.00664037i | \(0.997886\pi\) | |||||||
\(564\) | 8.54983 | 0.360013 | ||||||||
\(565\) | −12.8127 | + | 22.1923i | −0.539035 | + | 0.933635i | ||||
\(566\) | 12.2749 | − | 21.2608i | 0.515953 | − | 0.893657i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 1.13746 | − | 1.97014i | 0.0477267 | − | 0.0826651i | ||||
\(569\) | −17.5498 | − | 30.3972i | −0.735727 | − | 1.27432i | −0.954403 | − | 0.298520i | \(-0.903507\pi\) |
0.218676 | − | 0.975797i | \(-0.429826\pi\) | |||||||
\(570\) | −14.0000 | − | 24.2487i | −0.586395 | − | 1.01567i | ||||
\(571\) | −22.2749 | −0.932176 | −0.466088 | − | 0.884738i | \(-0.654337\pi\) | ||||
−0.466088 | + | 0.884738i | \(0.654337\pi\) | |||||||
\(572\) | −14.0000 | + | 3.46410i | −0.585369 | + | 0.144841i | ||||
\(573\) | 14.2749 | 0.596343 | ||||||||
\(574\) | −0.362541 | − | 0.627940i | −0.0151322 | − | 0.0262097i | ||||
\(575\) | −6.51204 | − | 11.2792i | −0.271571 | − | 0.470375i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −28.3746 | −1.18125 | −0.590625 | − | 0.806946i | \(-0.701119\pi\) | ||||
−0.590625 | + | 0.806946i | \(0.701119\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 1.08762 | − | 1.88382i | 0.0452001 | − | 0.0782889i | ||||
\(580\) | −2.37459 | −0.0985993 | ||||||||
\(581\) | −5.41238 | + | 9.37451i | −0.224543 | + | 0.388920i | ||||
\(582\) | −7.27492 | − | 12.6005i | −0.301555 | − | 0.522309i | ||||
\(583\) | 23.0997 | + | 40.0098i | 0.956691 | + | 1.65704i | ||||
\(584\) | 13.2749 | 0.549320 | ||||||||
\(585\) | 3.27492 | − | 11.3446i | 0.135401 | − | 0.469043i | ||||
\(586\) | −10.7251 | −0.443049 | ||||||||
\(587\) | 21.9622 | + | 38.0397i | 0.906477 | + | 1.57006i | 0.818922 | + | 0.573905i | \(0.194572\pi\) |
0.0875558 | + | 0.996160i | \(0.472094\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | 26.8248 | − | 46.4618i | 1.10529 | − | 1.91443i | ||||
\(590\) | −35.4502 | −1.45946 | ||||||||
\(591\) | −0.412376 | + | 0.714256i | −0.0169629 | + | 0.0293806i | ||||
\(592\) | 3.63746 | − | 6.30026i | 0.149499 | − | 0.258939i | ||||
\(593\) | 19.5498 | 0.802815 | 0.401408 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401408 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(594\) | 2.00000 | − | 3.46410i | 0.0820610 | − | 0.142134i | ||||
\(595\) | 4.91238 | + | 8.50848i | 0.201388 | + | 0.348814i | ||||
\(596\) | 0.500000 | + | 0.866025i | 0.0204808 | + | 0.0354738i | ||||
\(597\) | −10.8248 | −0.443028 | ||||||||
\(598\) | −2.27492 | + | 7.88054i | −0.0930283 | + | 0.322259i | ||||
\(599\) | −18.2749 | −0.746693 | −0.373346 | − | 0.927692i | \(-0.621790\pi\) | ||||
−0.373346 | + | 0.927692i | \(0.621790\pi\) | |||||||
\(600\) | −2.86254 | − | 4.95807i | −0.116863 | − | 0.202412i | ||||
\(601\) | 7.63746 | + | 13.2285i | 0.311538 | + | 0.539600i | 0.978696 | − | 0.205317i | \(-0.0658224\pi\) |
−0.667157 | + | 0.744917i | \(0.732489\pi\) | |||||||
\(602\) | −5.41238 | + | 9.37451i | −0.220592 | + | 0.382077i | ||||
\(603\) | −10.2749 | −0.418427 | ||||||||
\(604\) | 8.54983 | − | 14.8087i | 0.347888 | − | 0.602559i | ||||
\(605\) | 8.18729 | − | 14.1808i | 0.332861 | − | 0.576532i | ||||
\(606\) | 9.27492 | 0.376768 | ||||||||
\(607\) | −11.1375 | + | 19.2906i | −0.452055 | + | 0.782983i | −0.998514 | − | 0.0545034i | \(-0.982642\pi\) |
0.546458 | + | 0.837486i | \(0.315976\pi\) | |||||||
\(608\) | 4.27492 | + | 7.40437i | 0.173371 | + | 0.300287i | ||||
\(609\) | −0.362541 | − | 0.627940i | −0.0146909 | − | 0.0254454i | ||||
\(610\) | 29.4743 | 1.19338 | ||||||||
\(611\) | 29.9244 | − | 7.40437i | 1.21061 | − | 0.299549i | ||||
\(612\) | 3.00000 | 0.121268 | ||||||||
\(613\) | 4.18729 | + | 7.25260i | 0.169123 | + | 0.292930i | 0.938112 | − | 0.346332i | \(-0.112573\pi\) |
−0.768989 | + | 0.639262i | \(0.779240\pi\) | |||||||
\(614\) | 8.27492 | + | 14.3326i | 0.333948 | + | 0.578416i | ||||
\(615\) | 1.18729 | − | 2.05645i | 0.0478763 | − | 0.0829241i | ||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 6.46221 | − | 11.1929i | 0.260159 | − | 0.450608i | −0.706125 | − | 0.708087i | \(-0.749558\pi\) |
0.966284 | + | 0.257479i | \(0.0828918\pi\) | |||||||
\(618\) | 1.13746 | − | 1.97014i | 0.0457553 | − | 0.0792505i | ||||
\(619\) | 29.6495 | 1.19171 | 0.595857 | − | 0.803090i | \(-0.296812\pi\) | ||||
0.595857 | + | 0.803090i | \(0.296812\pi\) | |||||||
\(620\) | 10.2749 | − | 17.7967i | 0.412651 | − | 0.714732i | ||||
\(621\) | −1.13746 | − | 1.97014i | −0.0456446 | − | 0.0790588i | ||||
\(622\) | −6.27492 | − | 10.8685i | −0.251601 | − | 0.435786i | ||||
\(623\) | 8.27492 | 0.331528 | ||||||||
\(624\) | −1.00000 | + | 3.46410i | −0.0400320 | + | 0.138675i | ||||
\(625\) | −20.8488 | −0.833954 | ||||||||
\(626\) | 13.8248 | + | 23.9452i | 0.552548 | + | 0.957042i | ||||
\(627\) | −17.0997 | − | 29.6175i | −0.682895 | − | 1.18281i | ||||
\(628\) | 5.63746 | − | 9.76436i | 0.224959 | − | 0.389641i | ||||
\(629\) | −21.8248 | −0.870210 | ||||||||
\(630\) | 1.63746 | − | 2.83616i | 0.0652379 | − | 0.112995i | ||||
\(631\) | −0.549834 | + | 0.952341i | −0.0218886 | + | 0.0379121i | −0.876762 | − | 0.480924i | \(-0.840301\pi\) |
0.854874 | + | 0.518836i | \(0.173635\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | 4.54983 | − | 7.88054i | 0.180840 | − | 0.313224i | ||||
\(634\) | −3.77492 | − | 6.53835i | −0.149921 | − | 0.259671i | ||||
\(635\) | 13.0997 | + | 22.6893i | 0.519845 | + | 0.900397i | ||||
\(636\) | 11.5498 | 0.457981 | ||||||||
\(637\) | −2.50000 | − | 2.59808i | −0.0990536 | − | 0.102940i | ||||
\(638\) | −2.90033 | −0.114825 | ||||||||
\(639\) | 1.13746 | + | 1.97014i | 0.0449972 | + | 0.0779374i | ||||
\(640\) | 1.63746 | + | 2.83616i | 0.0647262 | + | 0.112109i | ||||
\(641\) | 1.91238 | − | 3.31233i | 0.0755343 | − | 0.130829i | −0.825784 | − | 0.563986i | \(-0.809267\pi\) |
0.901318 | + | 0.433157i | \(0.142600\pi\) | |||||||
\(642\) | −12.5498 | −0.495302 | ||||||||
\(643\) | −21.3746 | + | 37.0219i | −0.842931 | + | 1.46000i | 0.0444742 | + | 0.999011i | \(0.485839\pi\) |
−0.887406 | + | 0.460989i | \(0.847495\pi\) | |||||||
\(644\) | −1.13746 | + | 1.97014i | −0.0448221 | + | 0.0776342i | ||||
\(645\) | −35.4502 | −1.39585 | ||||||||
\(646\) | 12.8248 | − | 22.2131i | 0.504583 | − | 0.873964i | ||||
\(647\) | −12.2749 | − | 21.2608i | −0.482577 | − | 0.835848i | 0.517223 | − | 0.855851i | \(-0.326966\pi\) |
−0.999800 | + | 0.0200031i | \(0.993632\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −43.2990 | −1.69963 | ||||||||
\(650\) | −14.3127 | − | 14.8742i | −0.561391 | − | 0.583414i | ||||
\(651\) | 6.27492 | 0.245933 | ||||||||
\(652\) | 2.86254 | + | 4.95807i | 0.112106 | + | 0.194173i | ||||
\(653\) | 17.2371 | + | 29.8556i | 0.674541 | + | 1.16834i | 0.976603 | + | 0.215051i | \(0.0689917\pi\) |
−0.302062 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(654\) | −5.27492 | + | 9.13642i | −0.206266 | + | 0.357262i | ||||
\(655\) | 33.6495 | 1.31479 | ||||||||
\(656\) | −0.362541 | + | 0.627940i | −0.0141549 | + | 0.0245169i | ||||
\(657\) | −6.63746 | + | 11.4964i | −0.258952 | + | 0.448518i | ||||
\(658\) | 8.54983 | 0.333307 | ||||||||
\(659\) | 14.2749 | − | 24.7249i | 0.556072 | − | 0.963145i | −0.441747 | − | 0.897139i | \(-0.645641\pi\) |
0.997819 | − | 0.0660052i | \(-0.0210254\pi\) | |||||||
\(660\) | −6.54983 | − | 11.3446i | −0.254952 | − | 0.441590i | ||||
\(661\) | −20.0498 | − | 34.7273i | −0.779848 | − | 1.35074i | −0.932029 | − | 0.362384i | \(-0.881963\pi\) |
0.152181 | − | 0.988353i | \(-0.451370\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 10.5000 | − | 2.59808i | 0.407786 | − | 0.100901i | ||||
\(664\) | 10.8248 | 0.420082 | ||||||||
\(665\) | −14.0000 | − | 24.2487i | −0.542897 | − | 0.940325i | ||||
\(666\) | 3.63746 | + | 6.30026i | 0.140949 | + | 0.244130i | ||||
\(667\) | −0.824752 | + | 1.42851i | −0.0319345 | + | 0.0553122i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.13746 | + | 15.8265i | −0.353275 | + | 0.611889i | ||||
\(670\) | −16.8248 | + | 29.1413i | −0.649997 | + | 1.12583i | ||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | −0.500000 | + | 0.866025i | −0.0192879 | + | 0.0334077i | ||||
\(673\) | −6.04983 | − | 10.4786i | −0.233204 | − | 0.403921i | 0.725545 | − | 0.688174i | \(-0.241588\pi\) |
−0.958749 | + | 0.284253i | \(0.908254\pi\) | |||||||
\(674\) | 3.63746 | + | 6.30026i | 0.140110 | + | 0.242677i | ||||
\(675\) | 5.72508 | 0.220359 | ||||||||
\(676\) | −0.500000 | + | 12.9904i | −0.0192308 | + | 0.499630i | ||||
\(677\) | 11.6495 | 0.447727 | 0.223863 | − | 0.974621i | \(-0.428133\pi\) | ||||
0.223863 | + | 0.974621i | \(0.428133\pi\) | |||||||
\(678\) | 3.91238 | + | 6.77643i | 0.150254 | + | 0.260247i | ||||
\(679\) | −7.27492 | − | 12.6005i | −0.279186 | − | 0.483564i | ||||
\(680\) | 4.91238 | − | 8.50848i | 0.188381 | − | 0.326285i | ||||
\(681\) | 9.09967 | 0.348700 | ||||||||
\(682\) | 12.5498 | − | 21.7370i | 0.480558 | − | 0.832351i | ||||
\(683\) | 24.8248 | − | 42.9977i | 0.949893 | − | 1.64526i | 0.204248 | − | 0.978919i | \(-0.434525\pi\) |
0.745645 | − | 0.666343i | \(-0.232141\pi\) | |||||||
\(684\) | −8.54983 | −0.326911 | ||||||||
\(685\) | 0.286962 | − | 0.497033i | 0.0109643 | − | 0.0189906i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −10.1375 | − | 17.5586i | −0.386768 | − | 0.669902i | ||||
\(688\) | 10.8248 | 0.412690 | ||||||||
\(689\) | 40.4244 | − | 10.0025i | 1.54005 | − | 0.381063i | ||||
\(690\) | −7.45017 | −0.283623 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | −5.27492 | − | 9.13642i | −0.200522 | − | 0.347315i | ||||
\(693\) | 2.00000 | − | 3.46410i | 0.0759737 | − | 0.131590i | ||||
\(694\) | 15.4502 | 0.586480 | ||||||||
\(695\) | 34.5498 | − | 59.8421i | 1.31055 | − | 2.26994i | ||||
\(696\) | −0.362541 | + | 0.627940i | −0.0137421 | + | 0.0238020i | ||||
\(697\) | 2.17525 | 0.0823934 | ||||||||
\(698\) | −8.96221 | + | 15.5230i | −0.339225 | + | 0.587554i | ||||
\(699\) | −11.2749 | − | 19.5287i | −0.426457 | − | 0.738644i | ||||
\(700\) | −2.86254 | − | 4.95807i | −0.108194 | − | 0.187397i | ||||
\(701\) | −37.9244 | −1.43239 | −0.716193 | − | 0.697902i | \(-0.754117\pi\) | ||||
−0.716193 | + | 0.697902i | \(0.754117\pi\) | |||||||
\(702\) | −2.50000 | − | 2.59808i | −0.0943564 | − | 0.0980581i | ||||
\(703\) | 62.1993 | 2.34589 | ||||||||
\(704\) | 2.00000 | + | 3.46410i | 0.0753778 | + | 0.130558i | ||||
\(705\) | 14.0000 | + | 24.2487i | 0.527271 | + | 0.913259i | ||||
\(706\) | 2.22508 | − | 3.85396i | 0.0837421 | − | 0.145046i | ||||
\(707\) | 9.27492 | 0.348819 | ||||||||
\(708\) | −5.41238 | + | 9.37451i | −0.203410 | + | 0.352316i | ||||
\(709\) | 4.81271 | − | 8.33585i | 0.180745 | − | 0.313060i | −0.761389 | − | 0.648295i | \(-0.775482\pi\) |
0.942134 | + | 0.335235i | \(0.108816\pi\) | |||||||
\(710\) | 7.45017 | 0.279600 | ||||||||
\(711\) | 4.00000 | − | 6.92820i | 0.150012 | − | 0.259828i | ||||
\(712\) | −4.13746 | − | 7.16629i | −0.155058 | − | 0.268568i | ||||
\(713\) | −7.13746 | − | 12.3624i | −0.267300 | − | 0.462977i | ||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | −32.7492 | − | 34.0339i | −1.22475 | − | 1.27280i | ||||
\(716\) | 16.5498 | 0.618496 | ||||||||
\(717\) | −1.13746 | − | 1.97014i | −0.0424792 | − | 0.0735761i | ||||
\(718\) | −14.5498 | − | 25.2011i | −0.542995 | − | 0.940495i | ||||
\(719\) | 4.00000 | − | 6.92820i | 0.149175 | − | 0.258378i | −0.781748 | − | 0.623595i | \(-0.785672\pi\) |
0.930923 | + | 0.365216i | \(0.119005\pi\) | |||||||
\(720\) | −3.27492 | −0.122049 | ||||||||
\(721\) | 1.13746 | − | 1.97014i | 0.0423612 | − | 0.0733717i | ||||
\(722\) | −27.0498 | + | 46.8517i | −1.00669 | + | 1.74364i | ||||
\(723\) | −23.2749 | −0.865603 | ||||||||
\(724\) | −2.91238 | + | 5.04438i | −0.108238 | + | 0.187473i | ||||
\(725\) | −2.07558 | − | 3.59501i | −0.0770851 | − | 0.133515i | ||||
\(726\) | −2.50000 | − | 4.33013i | −0.0927837 | − | 0.160706i | ||||
\(727\) | −2.82475 | −0.104764 | −0.0523821 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523821 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(728\) | −1.00000 | + | 3.46410i | −0.0370625 | + | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.7371 | + | 37.6498i | 0.804527 | + | 1.39348i | ||||
\(731\) | −16.2371 | − | 28.1235i | −0.600552 | − | 1.04019i | ||||
\(732\) | 4.50000 | − | 7.79423i | 0.166325 | − | 0.288083i | ||||
\(733\) | 12.6495 | 0.467220 | 0.233610 | − | 0.972330i | \(-0.424946\pi\) | ||||
0.233610 | + | 0.972330i | \(0.424946\pi\) | |||||||
\(734\) | −2.86254 | + | 4.95807i | −0.105658 | + | 0.183006i | ||||
\(735\) | 1.63746 | − | 2.83616i | 0.0603986 | − | 0.104613i | ||||
\(736\) | 2.27492 | 0.0838546 | ||||||||
\(737\) | −20.5498 | + | 35.5934i | −0.756963 | + | 1.31110i | ||||
\(738\) | −0.362541 | − | 0.627940i | −0.0133453 | − | 0.0231148i | ||||
\(739\) | 20.8625 | + | 36.1350i | 0.767441 | + | 1.32925i | 0.938946 | + | 0.344064i | \(0.111804\pi\) |
−0.171505 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(740\) | 23.8248 | 0.875815 | ||||||||
\(741\) | −29.9244 | + | 7.40437i | −1.09930 | + | 0.272006i | ||||
\(742\) | 11.5498 | 0.424008 | ||||||||
\(743\) | 13.4124 | + | 23.2309i | 0.492052 | + | 0.852260i | 0.999958 | − | 0.00915297i | \(-0.00291352\pi\) |
−0.507906 | + | 0.861413i | \(0.669580\pi\) | |||||||
\(744\) | −3.13746 | − | 5.43424i | −0.115025 | − | 0.199229i | ||||
\(745\) | −1.63746 | + | 2.83616i | −0.0599918 | + | 0.103909i | ||||
\(746\) | 4.17525 | 0.152867 | ||||||||
\(747\) | −5.41238 | + | 9.37451i | −0.198028 | + | 0.342995i | ||||
\(748\) | 6.00000 | − | 10.3923i | 0.219382 | − | 0.379980i | ||||
\(749\) | −12.5498 | −0.458561 | ||||||||
\(750\) | 1.18729 | − | 2.05645i | 0.0433538 | − | 0.0750910i | ||||
\(751\) | 1.72508 | + | 2.98793i | 0.0629492 | + | 0.109031i | 0.895782 | − | 0.444493i | \(-0.146616\pi\) |
−0.832833 | + | 0.553524i | \(0.813283\pi\) | |||||||
\(752\) | −4.27492 | − | 7.40437i | −0.155890 | − | 0.270010i | ||||
\(753\) | 5.72508 | 0.208634 | ||||||||
\(754\) | −0.725083 | + | 2.51176i | −0.0264060 | + | 0.0914729i | ||||
\(755\) | 56.0000 | 2.03805 | ||||||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | 13.0000 | + | 22.5167i | 0.472493 | + | 0.818382i | 0.999505 | − | 0.0314762i | \(-0.0100208\pi\) |
−0.527011 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | −9.09967 | −0.330297 | ||||||||
\(760\) | −14.0000 | + | 24.2487i | −0.507833 | + | 0.879593i | ||||
\(761\) | 20.0997 | − | 34.8136i | 0.728612 | − | 1.26199i | −0.228857 | − | 0.973460i | \(-0.573499\pi\) |
0.957470 | − | 0.288534i | \(-0.0931677\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | −5.27492 | + | 9.13642i | −0.190965 | + | 0.330761i | ||||
\(764\) | −7.13746 | − | 12.3624i | −0.258224 | − | 0.447257i | ||||
\(765\) | 4.91238 | + | 8.50848i | 0.177607 | + | 0.307625i | ||||
\(766\) | −38.1993 | −1.38020 | ||||||||
\(767\) | −10.8248 | + | 37.4980i | −0.390859 | + | 1.35398i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 1.82475 | + | 3.16056i | 0.0658022 | + | 0.113973i | 0.897050 | − | 0.441930i | \(-0.145706\pi\) |
−0.831247 | + | 0.555903i | \(0.812373\pi\) | |||||||
\(770\) | −6.54983 | − | 11.3446i | −0.236040 | − | 0.408833i | ||||
\(771\) | −7.50000 | + | 12.9904i | −0.270106 | + | 0.467837i | ||||
\(772\) | −2.17525 | −0.0782889 | ||||||||
\(773\) | 25.5498 | − | 44.2536i | 0.918964 | − | 1.59169i | 0.117971 | − | 0.993017i | \(-0.462361\pi\) |
0.800992 | − | 0.598675i | \(-0.204306\pi\) | |||||||
\(774\) | −5.41238 | + | 9.37451i | −0.194544 | + | 0.336960i | ||||
\(775\) | 35.9244 | 1.29044 | ||||||||
\(776\) | −7.27492 | + | 12.6005i | −0.261154 | + | 0.452333i | ||||
\(777\) | 3.63746 | + | 6.30026i | 0.130493 | + | 0.226021i | ||||
\(778\) | −10.3248 | − | 17.8830i | −0.370160 | − | 0.641136i | ||||
\(779\) | −6.19934 | −0.222114 | ||||||||
\(780\) | −11.4622 | + | 2.83616i | −0.410413 | + | 0.101551i | ||||
\(781\) | 9.09967 | 0.325612 | ||||||||
\(782\) | −3.41238 | − | 5.91041i | −0.122026 | − | 0.211356i | ||||
\(783\) | −0.362541 | − | 0.627940i | −0.0129562 | − | 0.0224407i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | 36.9244 | 1.31789 | ||||||||
\(786\) | 5.13746 | − | 8.89834i | 0.183247 | − | 0.317393i | ||||
\(787\) | 4.54983 | − | 7.88054i | 0.162184 | − | 0.280911i | −0.773468 | − | 0.633836i | \(-0.781479\pi\) |
0.935652 | + | 0.352925i | \(0.114813\pi\) | |||||||
\(788\) | 0.824752 | 0.0293806 | ||||||||
\(789\) | 4.54983 | − | 7.88054i | 0.161978 | − | 0.280555i | ||||
\(790\) | −13.0997 | − | 22.6893i | −0.466065 | − | 0.807249i | ||||
\(791\) | 3.91238 | + | 6.77643i | 0.139108 | + | 0.240942i | ||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 9.00000 | − | 31.1769i | 0.319599 | − | 1.10712i | ||||
\(794\) | 15.7251 | 0.558062 | ||||||||
\(795\) | 18.9124 | + | 32.7572i | 0.670753 | + | 1.16178i | ||||
\(796\) | 5.41238 | + | 9.37451i | 0.191837 | + | 0.332271i | ||||
\(797\) | −0.725083 | + | 1.25588i | −0.0256837 | + | 0.0444856i | −0.878582 | − | 0.477592i | \(-0.841510\pi\) |
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(798\) | −8.54983 | −0.302661 | ||||||||
\(799\) | −12.8248 | + | 22.2131i | −0.453707 | + | 0.785844i | ||||
\(800\) | −2.86254 | + | 4.95807i | −0.101206 | + | 0.175294i | ||||
\(801\) | 8.27492 | 0.292380 | ||||||||
\(802\) | −2.63746 | + | 4.56821i | −0.0931319 | + | 0.161309i | ||||
\(803\) | 26.5498 | + | 45.9857i | 0.936923 | + | 1.62280i | ||||
\(804\) | 5.13746 | + | 8.89834i | 0.181184 | + | 0.313820i | ||||
\(805\) | −7.45017 | −0.262584 | ||||||||
\(806\) | −15.6873 | − | 16.3027i | −0.552561 | − | 0.574239i | ||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | −4.63746 | − | 8.03231i | −0.163145 | − | 0.282576i | ||||
\(809\) | −8.63746 | − | 14.9605i | −0.303677 | − | 0.525984i | 0.673289 | − | 0.739379i | \(-0.264881\pi\) |
−0.976966 | + | 0.213396i | \(0.931548\pi\) | |||||||
\(810\) | 1.63746 | − | 2.83616i | 0.0575344 | − | 0.0996526i | ||||
\(811\) | −25.0997 | −0.881369 | −0.440684 | − | 0.897662i | \(-0.645264\pi\) | ||||
−0.440684 | + | 0.897662i | \(0.645264\pi\) | |||||||
\(812\) | −0.362541 | + | 0.627940i | −0.0127227 | + | 0.0220364i | ||||
\(813\) | −8.86254 | + | 15.3504i | −0.310823 | + | 0.538361i | ||||
\(814\) | 29.0997 | 1.01994 | ||||||||
\(815\) | −9.37459 | + | 16.2373i | −0.328377 | + | 0.568766i | ||||
\(816\) | −1.50000 | − | 2.59808i | −0.0525105 | − | 0.0909509i | ||||
\(817\) | 46.2749 | + | 80.1505i | 1.61895 | + | 2.80411i | ||||
\(818\) | 22.9244 | 0.801534 | ||||||||
\(819\) | −2.50000 | − | 2.59808i | −0.0873571 | − | 0.0907841i | ||||
\(820\) | −2.37459 | −0.0829241 | ||||||||
\(821\) | −3.86254 | − | 6.69012i | −0.134804 | − | 0.233487i | 0.790719 | − | 0.612180i | \(-0.209707\pi\) |
−0.925522 | + | 0.378693i | \(0.876374\pi\) | |||||||
\(822\) | −0.0876242 | − | 0.151770i | −0.00305624 | − | 0.00529357i | ||||
\(823\) | 18.5498 | − | 32.1293i | 0.646607 | − | 1.11996i | −0.337321 | − | 0.941390i | \(-0.609521\pi\) |
0.983928 | − | 0.178566i | \(-0.0571458\pi\) | |||||||
\(824\) | −2.27492 | −0.0792505 | ||||||||
\(825\) | 11.4502 | − | 19.8323i | 0.398644 | − | 0.690471i | ||||
\(826\) | −5.41238 | + | 9.37451i | −0.188321 | + | 0.326181i | ||||
\(827\) | −25.0997 | −0.872801 | −0.436401 | − | 0.899753i | \(-0.643747\pi\) | ||||
−0.436401 | + | 0.899753i | \(0.643747\pi\) | |||||||
\(828\) | −1.13746 | + | 1.97014i | −0.0395294 | + | 0.0684670i | ||||
\(829\) | 11.0876 | + | 19.2043i | 0.385089 | + | 0.666994i | 0.991782 | − | 0.127943i | \(-0.0408374\pi\) |
−0.606692 | + | 0.794937i | \(0.707504\pi\) | |||||||
\(830\) | 17.7251 | + | 30.7007i | 0.615247 | + | 1.06564i | ||||
\(831\) | −7.82475 | −0.271438 | ||||||||
\(832\) | 3.50000 | − | 0.866025i | 0.121341 | − | 0.0300240i | ||||
\(833\) | 3.00000 | 0.103944 | ||||||||
\(834\) | −10.5498 | − | 18.2728i | −0.365311 | − | 0.632737i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.0997 | + | 29.6175i | −0.591404 | + | 1.02434i | ||||
\(837\) | 6.27492 | 0.216893 | ||||||||
\(838\) | −7.68729 | + | 13.3148i | −0.265553 | + | 0.459952i | ||||
\(839\) | −27.3746 | + | 47.4142i | −0.945076 | + | 1.63692i | −0.189476 | + | 0.981885i | \(0.560679\pi\) |
−0.755600 | + | 0.655034i | \(0.772654\pi\) | |||||||
\(840\) | −3.27492 | −0.112995 | ||||||||
\(841\) | 14.2371 | − | 24.6594i | 0.490935 | − | 0.850325i | ||||
\(842\) | −0.362541 | − | 0.627940i | −0.0124940 | − | 0.0216402i | ||||
\(843\) | −0.912376 | − | 1.58028i | −0.0314239 | − | 0.0544278i | ||||
\(844\) | −9.09967 | −0.313224 | ||||||||
\(845\) | −37.6615 | + | 19.8531i | −1.29560 | + | 0.682968i | ||||
\(846\) | 8.54983 | 0.293949 | ||||||||
\(847\) | −2.50000 | − | 4.33013i | −0.0859010 | − | 0.148785i | ||||
\(848\) | −5.77492 | − | 10.0025i | −0.198311 | − | 0.343486i | ||||
\(849\) | 12.2749 | − | 21.2608i | 0.421274 | − | 0.729668i | ||||
\(850\) | 17.1752 | 0.589106 | ||||||||
\(851\) | 8.27492 | − | 14.3326i | 0.283661 | − | 0.491314i | ||||
\(852\) | 1.13746 | − | 1.97014i | 0.0389687 | − | 0.0674958i | ||||
\(853\) | −29.5498 | −1.01177 | −0.505884 | − | 0.862602i | \(-0.668833\pi\) | ||||
−0.505884 | + | 0.862602i | \(0.668833\pi\) | |||||||
\(854\) | 4.50000 | − | 7.79423i | 0.153987 | − | 0.266713i | ||||
\(855\) | −14.0000 | − | 24.2487i | −0.478790 | − | 0.829288i | ||||
\(856\) | 6.27492 | + | 10.8685i | 0.214472 | + | 0.371477i | ||||
\(857\) | −14.1752 | −0.484217 | −0.242109 | − | 0.970249i | \(-0.577839\pi\) | ||||
−0.242109 | + | 0.970249i | \(0.577839\pi\) | |||||||
\(858\) | −14.0000 | + | 3.46410i | −0.477952 | + | 0.118262i | ||||
\(859\) | 17.6495 | 0.602193 | 0.301097 | − | 0.953594i | \(-0.402647\pi\) | ||||
0.301097 | + | 0.953594i | \(0.402647\pi\) | |||||||
\(860\) | 17.7251 | + | 30.7007i | 0.604420 | + | 1.04689i | ||||
\(861\) | −0.362541 | − | 0.627940i | −0.0123554 | − | 0.0214001i | ||||
\(862\) | 2.86254 | − | 4.95807i | 0.0974985 | − | 0.168872i | ||||
\(863\) | −55.2990 | −1.88240 | −0.941200 | − | 0.337850i | \(-0.890300\pi\) | ||||
−0.941200 | + | 0.337850i | \(0.890300\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 17.2749 | − | 29.9210i | 0.587365 | − | 1.01735i | ||||
\(866\) | −2.72508 | −0.0926021 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | −3.13746 | − | 5.43424i | −0.106492 | − | 0.184450i | ||||
\(869\) | −16.0000 | − | 27.7128i | −0.542763 | − | 0.940093i | ||||
\(870\) | −2.37459 | −0.0805060 | ||||||||
\(871\) | 25.6873 | + | 26.6950i | 0.870381 | + | 0.904526i | ||||
\(872\) | 10.5498 | 0.357262 | ||||||||
\(873\) | −7.27492 | − | 12.6005i | −0.246219 | − | 0.426463i | ||||
\(874\) | 9.72508 | + | 16.8443i | 0.328956 | + | 0.569768i | ||||
\(875\) | 1.18729 | − | 2.05645i | 0.0401378 | − | 0.0695208i | ||||
\(876\) | 13.2749 | 0.448518 | ||||||||
\(877\) | 5.63746 | − | 9.76436i | 0.190363 | − | 0.329719i | −0.755007 | − | 0.655716i | \(-0.772367\pi\) |
0.945371 | + | 0.325997i | \(0.105700\pi\) | |||||||
\(878\) | 8.54983 | − | 14.8087i | 0.288543 | − | 0.499771i | ||||
\(879\) | −10.7251 | −0.361748 | ||||||||
\(880\) | −6.54983 | + | 11.3446i | −0.220795 | + | 0.382428i | ||||
\(881\) | 6.77492 | + | 11.7345i | 0.228253 | + | 0.395345i | 0.957290 | − | 0.289128i | \(-0.0933654\pi\) |
−0.729038 | + | 0.684474i | \(0.760032\pi\) | |||||||
\(882\) | −0.500000 | − | 0.866025i | −0.0168359 | − | 0.0291606i | ||||
\(883\) | −25.0241 | −0.842128 | −0.421064 | − | 0.907031i | \(-0.638343\pi\) | ||||
−0.421064 | + | 0.907031i | \(0.638343\pi\) | |||||||
\(884\) | −7.50000 | − | 7.79423i | −0.252252 | − | 0.262148i | ||||
\(885\) | −35.4502 | −1.19164 | ||||||||
\(886\) | −9.72508 | − | 16.8443i | −0.326721 | − | 0.565897i | ||||
\(887\) | −15.7251 | − | 27.2366i | −0.527997 | − | 0.914517i | −0.999467 | − | 0.0326352i | \(-0.989610\pi\) |
0.471471 | − | 0.881882i | \(-0.343723\pi\) | |||||||
\(888\) | 3.63746 | − | 6.30026i | 0.122065 | − | 0.211423i | ||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 13.5498 | − | 23.4690i | 0.454191 | − | 0.786683i | ||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | 18.2749 | 0.611889 | ||||||||
\(893\) | 36.5498 | − | 63.3062i | 1.22309 | − | 2.11846i | ||||
\(894\) | 0.500000 | + | 0.866025i | 0.0167225 | + | 0.0289642i | ||||
\(895\) | 27.0997 | + | 46.9380i | 0.905842 | + | 1.56896i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −2.27492 | + | 7.88054i | −0.0759573 | + | 0.263124i | ||||
\(898\) | 11.0997 | 0.370401 | ||||||||
\(899\) | −2.27492 | − | 3.94027i | −0.0758727 | − | 0.131415i | ||||
\(900\) | −2.86254 | − | 4.95807i | −0.0954180 | − | 0.165269i | ||||
\(901\) | −17.3248 | + | 30.0074i | −0.577171 | + | 0.999690i | ||||
\(902\) | −2.90033 | −0.0965705 | ||||||||
\(903\) | −5.41238 | + | 9.37451i | −0.180113 | + | 0.311964i | ||||
\(904\) | 3.91238 | − | 6.77643i | 0.130124 | − | 0.225381i | ||||
\(905\) | −19.0756 | −0.634094 | ||||||||
\(906\) | 8.54983 | − | 14.8087i | 0.284049 | − | 0.491988i | ||||
\(907\) | 8.58762 | + | 14.8742i | 0.285147 | + | 0.493890i | 0.972645 | − | 0.232297i | \(-0.0746241\pi\) |
−0.687498 | + | 0.726187i | \(0.741291\pi\) | |||||||
\(908\) | −4.54983 | − | 7.88054i | −0.150992 | − | 0.261525i | ||||
\(909\) | 9.27492 | 0.307630 | ||||||||
\(910\) | −11.4622 | + | 2.83616i | −0.379969 | + | 0.0940178i | ||||
\(911\) | 5.09967 | 0.168960 | 0.0844798 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844798 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(912\) | 4.27492 | + | 7.40437i | 0.141557 | + | 0.245183i | ||||
\(913\) | 21.6495 | + | 37.4980i | 0.716494 | + | 1.24100i | ||||
\(914\) | 8.50000 | − | 14.7224i | 0.281155 | − | 0.486975i | ||||
\(915\) | 29.4743 | 0.974389 | ||||||||
\(916\) | −10.1375 | + | 17.5586i | −0.334951 | + | 0.580152i | ||||
\(917\) | 5.13746 | − | 8.89834i | 0.169654 | − | 0.293849i | ||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | 2.82475 | − | 4.89261i | 0.0931800 | − | 0.161392i | −0.815668 | − | 0.578521i | \(-0.803630\pi\) |
0.908848 | + | 0.417128i | \(0.136963\pi\) | |||||||
\(920\) | 3.72508 | + | 6.45203i | 0.122812 | + | 0.212717i | ||||
\(921\) | 8.27492 | + | 14.3326i | 0.272668 | + | 0.472274i | ||||
\(922\) | 18.3746 | 0.605135 | ||||||||
\(923\) | 2.27492 | − | 7.88054i | 0.0748798 | − | 0.259391i | ||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | 20.8248 | + | 36.0695i | 0.684714 | + | 1.18596i | ||||
\(926\) | −2.27492 | − | 3.94027i | −0.0747584 | − | 0.129485i | ||||
\(927\) | 1.13746 | − | 1.97014i | 0.0373590 | − | 0.0647078i | ||||
\(928\) | 0.725083 | 0.0238020 | ||||||||
\(929\) | −19.2251 | + | 33.2988i | −0.630755 | + | 1.09250i | 0.356643 | + | 0.934241i | \(0.383921\pi\) |
−0.987398 | + | 0.158258i | \(0.949412\pi\) | |||||||
\(930\) | 10.2749 | − | 17.7967i | 0.336928 | − | 0.583576i | ||||
\(931\) | −8.54983 | −0.280210 | ||||||||
\(932\) | −11.2749 | + | 19.5287i | −0.369322 | + | 0.639685i | ||||
\(933\) | −6.27492 | − | 10.8685i | −0.205432 | − | 0.355818i | ||||
\(934\) | 15.4124 | + | 26.6950i | 0.504308 | + | 0.873488i | ||||
\(935\) | 39.2990 | 1.28521 | ||||||||
\(936\) | −1.00000 | + | 3.46410i | −0.0326860 | + | 0.113228i | ||||
\(937\) | 41.8248 | 1.36636 | 0.683178 | − | 0.730252i | \(-0.260598\pi\) | ||||
0.683178 | + | 0.730252i | \(0.260598\pi\) | |||||||
\(938\) | 5.13746 | + | 8.89834i | 0.167744 | + | 0.290541i | ||||
\(939\) | 13.8248 | + | 23.9452i | 0.451154 | + | 0.781421i | ||||
\(940\) | 14.0000 | − | 24.2487i | 0.456630 | − | 0.790906i | ||||
\(941\) | −7.64950 | −0.249367 | −0.124683 | − | 0.992197i | \(-0.539791\pi\) | ||||
−0.124683 | + | 0.992197i | \(0.539791\pi\) | |||||||
\(942\) | 5.63746 | − | 9.76436i | 0.183678 | − | 0.318140i | ||||
\(943\) | −0.824752 | + | 1.42851i | −0.0268576 | + | 0.0465187i | ||||
\(944\) | 10.8248 | 0.352316 | ||||||||
\(945\) | 1.63746 | − | 2.83616i | 0.0532665 | − | 0.0922603i | ||||
\(946\) | 21.6495 | + | 37.4980i | 0.703886 | + | 1.21917i | ||||
\(947\) | −10.5498 | − | 18.2728i | −0.342824 | − | 0.593788i | 0.642132 | − | 0.766594i | \(-0.278050\pi\) |
−0.984956 | + | 0.172806i | \(0.944717\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 46.4622 | − | 11.4964i | 1.50823 | − | 0.373189i | ||||
\(950\) | −48.9485 | −1.58810 | ||||||||
\(951\) | −3.77492 | − | 6.53835i | −0.122410 | − | 0.212020i | ||||
\(952\) | −1.50000 | − | 2.59808i | −0.0486153 | − | 0.0842041i | ||||
\(953\) | −9.54983 | + | 16.5408i | −0.309349 | + | 0.535809i | −0.978220 | − | 0.207570i | \(-0.933445\pi\) |
0.668871 | + | 0.743379i | \(0.266778\pi\) | |||||||
\(954\) | 11.5498 | 0.373940 | ||||||||
\(955\) | 23.3746 | − | 40.4860i | 0.756384 | − | 1.31010i | ||||
\(956\) | −1.13746 | + | 1.97014i | −0.0367880 | + | 0.0637188i | ||||
\(957\) | −2.90033 | −0.0937544 | ||||||||
\(958\) | −10.0000 | + | 17.3205i | −0.323085 | + | 0.559600i | ||||
\(959\) | −0.0876242 | − | 0.151770i | −0.00282953 | − | 0.00490089i | ||||
\(960\) | 1.63746 | + | 2.83616i | 0.0528487 | + | 0.0915367i | ||||
\(961\) | 8.37459 | 0.270148 | ||||||||
\(962\) | 7.27492 | − | 25.2011i | 0.234553 | − | 0.812515i | ||||
\(963\) | −12.5498 | −0.404413 | ||||||||
\(964\) | 11.6375 | + | 20.1567i | 0.374817 | + | 0.649203i | ||||
\(965\) | −3.56188 | − | 6.16936i | −0.114661 | − | 0.198599i | ||||
\(966\) | −1.13746 | + | 1.97014i | −0.0365971 | + | 0.0633881i | ||||
\(967\) | −3.45017 | −0.110950 | −0.0554749 | − | 0.998460i | \(-0.517667\pi\) | ||||
−0.0554749 | + | 0.998460i | \(0.517667\pi\) | |||||||
\(968\) | −2.50000 | + | 4.33013i | −0.0803530 | + | 0.139176i | ||||
\(969\) | 12.8248 | − | 22.2131i | 0.411990 | − | 0.713588i | ||||
\(970\) | −47.6495 | −1.52993 | ||||||||
\(971\) | 24.7870 | − | 42.9323i | 0.795451 | − | 1.37776i | −0.127101 | − | 0.991890i | \(-0.540567\pi\) |
0.922552 | − | 0.385873i | \(-0.126100\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −10.5498 | − | 18.2728i | −0.338212 | − | 0.585801i | ||||
\(974\) | 29.0997 | 0.932414 | ||||||||
\(975\) | −14.3127 | − | 14.8742i | −0.458373 | − | 0.476356i | ||||
\(976\) | −9.00000 | −0.288083 | ||||||||
\(977\) | −31.1873 | − | 54.0180i | −0.997770 | − | 1.72819i | −0.556690 | − | 0.830720i | \(-0.687929\pi\) |
−0.441080 | − | 0.897468i | \(-0.645404\pi\) | |||||||
\(978\) | 2.86254 | + | 4.95807i | 0.0915340 | + | 0.158542i | ||||
\(979\) | 16.5498 | − | 28.6652i | 0.528935 | − | 0.916142i | ||||
\(980\) | −3.27492 | −0.104613 | ||||||||
\(981\) | −5.27492 | + | 9.13642i | −0.168415 | + | 0.291704i | ||||
\(982\) | 2.54983 | − | 4.41644i | 0.0813685 | − | 0.140934i | ||||
\(983\) | −51.8488 | −1.65372 | −0.826861 | − | 0.562407i | \(-0.809875\pi\) | ||||
−0.826861 | + | 0.562407i | \(0.809875\pi\) | |||||||
\(984\) | −0.362541 | + | 0.627940i | −0.0115574 | + | 0.0200180i | ||||
\(985\) | 1.35050 | + | 2.33913i | 0.0430304 | + | 0.0745308i | ||||
\(986\) | −1.08762 | − | 1.88382i | −0.0346370 | − | 0.0599931i | ||||
\(987\) | 8.54983 | 0.272144 | ||||||||
\(988\) | 21.3746 | + | 22.2131i | 0.680016 | + | 0.706694i | ||||
\(989\) | 24.6254 | 0.783043 | ||||||||
\(990\) | −6.54983 | − | 11.3446i | −0.208167 | − | 0.360557i | ||||
\(991\) | −19.3746 | − | 33.5578i | −0.615454 | − | 1.06600i | −0.990305 | − | 0.138912i | \(-0.955639\pi\) |
0.374851 | − | 0.927085i | \(-0.377694\pi\) | |||||||
\(992\) | −3.13746 | + | 5.43424i | −0.0996144 | + | 0.172537i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 1.13746 | − | 1.97014i | 0.0360780 | − | 0.0624889i | ||||
\(995\) | −17.7251 | + | 30.7007i | −0.561923 | + | 0.973279i | ||||
\(996\) | 10.8248 | 0.342995 | ||||||||
\(997\) | 17.0498 | − | 29.5312i | 0.539974 | − | 0.935262i | −0.458931 | − | 0.888472i | \(-0.651768\pi\) |
0.998905 | − | 0.0467900i | \(-0.0148991\pi\) | |||||||
\(998\) | 4.58762 | + | 7.94600i | 0.145219 | + | 0.251526i | ||||
\(999\) | 3.63746 | + | 6.30026i | 0.115084 | + | 0.199332i |
(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.j.211.1 | ✓ | 4 | |
3.2 | odd | 2 | 1638.2.r.x.757.2 | 4 | |||
13.3 | even | 3 | 7098.2.a.ca.1.1 | 2 | |||
13.9 | even | 3 | inner | 546.2.l.j.295.1 | yes | 4 | |
13.10 | even | 6 | 7098.2.a.bm.1.2 | 2 | |||
39.35 | odd | 6 | 1638.2.r.x.1387.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.j.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.l.j.295.1 | yes | 4 | 13.9 | even | 3 | inner | |
1638.2.r.x.757.2 | 4 | 3.2 | odd | 2 | |||
1638.2.r.x.1387.2 | 4 | 39.35 | odd | 6 | |||
7098.2.a.bm.1.2 | 2 | 13.10 | even | 6 | |||
7098.2.a.ca.1.1 | 2 | 13.3 | even | 3 |