Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,2,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14186074890\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1714608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) |
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 | 100.3 | ||
Root | \(0.500000 + 2.23871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 143.100 |
Dual form | 143.2.e.a.133.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | 1.13090 | − | 1.95878i | 0.652926 | − | 1.13090i | −0.329483 | − | 0.944161i | \(-0.606875\pi\) |
0.982409 | − | 0.186740i | \(-0.0597921\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 2.11575 | 0.946192 | 0.473096 | − | 0.881011i | \(-0.343136\pi\) | ||||
0.473096 | + | 0.881011i | \(0.343136\pi\) | |||||||
\(6\) | 1.13090 | + | 1.95878i | 0.461688 | + | 0.799668i | ||||
\(7\) | −1.68878 | − | 2.92505i | −0.638297 | − | 1.10556i | −0.985806 | − | 0.167887i | \(-0.946306\pi\) |
0.347509 | − | 0.937677i | \(-0.387028\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | −1.05787 | − | 1.83229i | −0.352625 | − | 0.610764i | ||||
\(10\) | −1.05787 | + | 1.83229i | −0.334529 | + | 0.579422i | ||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 2.26180 | 0.652926 | ||||||||
\(13\) | 2.63090 | + | 2.46543i | 0.729681 | + | 0.683788i | ||||
\(14\) | 3.37755 | 0.902689 | ||||||||
\(15\) | 2.39270 | − | 4.14428i | 0.617793 | − | 1.07005i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 1.07303 | + | 1.85854i | 0.260247 | + | 0.450761i | 0.966308 | − | 0.257390i | \(-0.0828626\pi\) |
−0.706060 | + | 0.708152i | \(0.749529\pi\) | |||||||
\(18\) | 2.11575 | 0.498687 | ||||||||
\(19\) | −1.57303 | − | 2.72456i | −0.360877 | − | 0.625057i | 0.627228 | − | 0.778835i | \(-0.284189\pi\) |
−0.988105 | + | 0.153778i | \(0.950856\pi\) | |||||||
\(20\) | 1.05787 | + | 1.83229i | 0.236548 | + | 0.409713i | ||||
\(21\) | −7.63935 | −1.66704 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | −2.26180 | + | 3.91756i | −0.471618 | + | 0.816867i | −0.999473 | − | 0.0324679i | \(-0.989663\pi\) |
0.527854 | + | 0.849335i | \(0.322997\pi\) | |||||||
\(24\) | −3.39270 | + | 5.87633i | −0.692533 | + | 1.19950i | ||||
\(25\) | −0.523604 | −0.104721 | ||||||||
\(26\) | −3.45058 | + | 1.04571i | −0.676714 | + | 0.205081i | ||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | 1.68878 | − | 2.92505i | 0.319149 | − | 0.552782i | ||||
\(29\) | −1.74665 | + | 3.02529i | −0.324345 | + | 0.561782i | −0.981380 | − | 0.192079i | \(-0.938477\pi\) |
0.657035 | + | 0.753860i | \(0.271810\pi\) | |||||||
\(30\) | 2.39270 | + | 4.14428i | 0.436846 | + | 0.756639i | ||||
\(31\) | −9.27871 | −1.66651 | −0.833253 | − | 0.552893i | \(-0.813524\pi\) | ||||
−0.833253 | + | 0.552893i | \(0.813524\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | 1.13090 | + | 1.95878i | 0.196865 | + | 0.340980i | ||||
\(34\) | −2.14605 | −0.368045 | ||||||||
\(35\) | −3.57303 | − | 6.18866i | −0.603952 | − | 1.04608i | ||||
\(36\) | 1.05787 | − | 1.83229i | 0.176312 | − | 0.305382i | ||||
\(37\) | 4.58148 | − | 7.93535i | 0.753191 | − | 1.30456i | −0.193078 | − | 0.981183i | \(-0.561847\pi\) |
0.946269 | − | 0.323381i | \(-0.104820\pi\) | |||||||
\(38\) | 3.14605 | 0.510357 | ||||||||
\(39\) | 7.80453 | − | 2.36519i | 1.24972 | − | 0.378734i | ||||
\(40\) | −6.34725 | −1.00359 | ||||||||
\(41\) | −5.00845 | + | 8.67489i | −0.782189 | + | 1.35479i | 0.148475 | + | 0.988916i | \(0.452563\pi\) |
−0.930664 | + | 0.365875i | \(0.880770\pi\) | |||||||
\(42\) | 3.81968 | − | 6.61587i | 0.589389 | − | 1.02085i | ||||
\(43\) | −1.26180 | − | 2.18551i | −0.192423 | − | 0.333286i | 0.753630 | − | 0.657299i | \(-0.228301\pi\) |
−0.946053 | + | 0.324013i | \(0.894968\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −2.23820 | − | 3.87667i | −0.333651 | − | 0.577900i | ||||
\(46\) | −2.26180 | − | 3.91756i | −0.333485 | − | 0.577612i | ||||
\(47\) | −1.96970 | −0.287310 | −0.143655 | − | 0.989628i | \(-0.545886\pi\) | ||||
−0.143655 | + | 0.989628i | \(0.545886\pi\) | |||||||
\(48\) | −1.13090 | − | 1.95878i | −0.163232 | − | 0.282725i | ||||
\(49\) | −2.20393 | + | 3.81731i | −0.314847 | + | 0.545331i | ||||
\(50\) | 0.261802 | − | 0.453455i | 0.0370244 | − | 0.0641282i | ||||
\(51\) | 4.85395 | 0.679689 | ||||||||
\(52\) | −0.819677 | + | 3.51114i | −0.113669 | + | 0.486908i | ||||
\(53\) | 7.75510 | 1.06525 | 0.532623 | − | 0.846353i | \(-0.321206\pi\) | ||||
0.532623 | + | 0.846353i | \(0.321206\pi\) | |||||||
\(54\) | −1.00000 | + | 1.73205i | −0.136083 | + | 0.235702i | ||||
\(55\) | −1.05787 | + | 1.83229i | −0.142644 | + | 0.247066i | ||||
\(56\) | 5.06633 | + | 8.77514i | 0.677016 | + | 1.17263i | ||||
\(57\) | −7.11575 | −0.942504 | ||||||||
\(58\) | −1.74665 | − | 3.02529i | −0.229346 | − | 0.397240i | ||||
\(59\) | 3.01515 | + | 5.22240i | 0.392539 | + | 0.679898i | 0.992784 | − | 0.119919i | \(-0.0382634\pi\) |
−0.600244 | + | 0.799817i | \(0.704930\pi\) | |||||||
\(60\) | 4.78541 | 0.617793 | ||||||||
\(61\) | −4.89270 | − | 8.47441i | −0.626446 | − | 1.08504i | −0.988259 | − | 0.152786i | \(-0.951175\pi\) |
0.361813 | − | 0.932251i | \(-0.382158\pi\) | |||||||
\(62\) | 4.63935 | − | 8.03560i | 0.589199 | − | 1.02052i | ||||
\(63\) | −3.57303 | + | 6.18866i | −0.450159 | + | 0.779698i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 5.56633 | + | 5.21624i | 0.690418 | + | 0.646995i | ||||
\(66\) | −2.26180 | −0.278409 | ||||||||
\(67\) | −2.01515 | + | 3.49035i | −0.246190 | + | 0.426414i | −0.962466 | − | 0.271404i | \(-0.912512\pi\) |
0.716276 | + | 0.697818i | \(0.245845\pi\) | |||||||
\(68\) | −1.07303 | + | 1.85854i | −0.130124 | + | 0.225381i | ||||
\(69\) | 5.11575 | + | 8.86074i | 0.615864 | + | 1.06671i | ||||
\(70\) | 7.14605 | 0.854117 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | 3.17362 | + | 5.49688i | 0.374015 | + | 0.647813i | ||||
\(73\) | 10.8405 | 1.26879 | 0.634395 | − | 0.773009i | \(-0.281249\pi\) | ||||
0.634395 | + | 0.773009i | \(0.281249\pi\) | |||||||
\(74\) | 4.58148 | + | 7.93535i | 0.532586 | + | 0.922466i | ||||
\(75\) | −0.592145 | + | 1.02563i | −0.0683750 | + | 0.118429i | ||||
\(76\) | 1.57303 | − | 2.72456i | 0.180439 | − | 0.312529i | ||||
\(77\) | 3.37755 | 0.384908 | ||||||||
\(78\) | −1.85395 | + | 7.94151i | −0.209918 | + | 0.899199i | ||||
\(79\) | 1.66966 | 0.187851 | 0.0939256 | − | 0.995579i | \(-0.470058\pi\) | ||||
0.0939256 | + | 0.995579i | \(0.470058\pi\) | |||||||
\(80\) | 1.05787 | − | 1.83229i | 0.118274 | − | 0.204857i | ||||
\(81\) | 5.43543 | − | 9.41443i | 0.603936 | − | 1.04605i | ||||
\(82\) | −5.00845 | − | 8.67489i | −0.553091 | − | 0.957982i | ||||
\(83\) | 5.66966 | 0.622326 | 0.311163 | − | 0.950357i | \(-0.399282\pi\) | ||||
0.311163 | + | 0.950357i | \(0.399282\pi\) | |||||||
\(84\) | −3.81968 | − | 6.61587i | −0.416761 | − | 0.721851i | ||||
\(85\) | 2.27026 | + | 3.93220i | 0.246244 | + | 0.426507i | ||||
\(86\) | 2.52360 | 0.272127 | ||||||||
\(87\) | 3.95058 | + | 6.84260i | 0.423546 | + | 0.733604i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −4.67362 | + | 8.09495i | −0.495403 | + | 0.858063i | −0.999986 | − | 0.00529986i | \(-0.998313\pi\) |
0.504583 | + | 0.863363i | \(0.331646\pi\) | |||||||
\(90\) | 4.47640 | 0.471854 | ||||||||
\(91\) | 2.76850 | − | 11.8591i | 0.290218 | − | 1.24317i | ||||
\(92\) | −4.52360 | −0.471618 | ||||||||
\(93\) | −10.4933 | + | 18.1749i | −1.08810 | + | 1.88465i | ||||
\(94\) | 0.984848 | − | 1.70581i | 0.101579 | − | 0.175941i | ||||
\(95\) | −3.32813 | − | 5.76449i | −0.341459 | − | 0.591424i | ||||
\(96\) | −11.3090 | −1.15422 | ||||||||
\(97\) | −5.81968 | − | 10.0800i | −0.590899 | − | 1.02347i | −0.994112 | − | 0.108360i | \(-0.965440\pi\) |
0.403213 | − | 0.915106i | \(-0.367893\pi\) | |||||||
\(98\) | −2.20393 | − | 3.81731i | −0.222630 | − | 0.385607i | ||||
\(99\) | 2.11575 | 0.212641 | ||||||||
\(100\) | −0.261802 | − | 0.453455i | −0.0261802 | − | 0.0453455i | ||||
\(101\) | −0.450578 | + | 0.780424i | −0.0448342 | + | 0.0776551i | −0.887572 | − | 0.460670i | \(-0.847609\pi\) |
0.842737 | + | 0.538325i | \(0.180943\pi\) | |||||||
\(102\) | −2.42697 | + | 4.20364i | −0.240306 | + | 0.416223i | ||||
\(103\) | 13.0472 | 1.28558 | 0.642790 | − | 0.766043i | \(-0.277777\pi\) | ||||
0.642790 | + | 0.766043i | \(0.277777\pi\) | |||||||
\(104\) | −7.89270 | − | 7.39630i | −0.773943 | − | 0.725267i | ||||
\(105\) | −16.1630 | −1.57734 | ||||||||
\(106\) | −3.87755 | + | 6.71612i | −0.376621 | + | 0.652327i | ||||
\(107\) | 6.80453 | − | 11.7858i | 0.657818 | − | 1.13937i | −0.323361 | − | 0.946276i | \(-0.604813\pi\) |
0.981179 | − | 0.193099i | \(-0.0618539\pi\) | |||||||
\(108\) | 1.00000 | + | 1.73205i | 0.0962250 | + | 0.166667i | ||||
\(109\) | 18.6866 | 1.78985 | 0.894924 | − | 0.446218i | \(-0.147230\pi\) | ||||
0.894924 | + | 0.446218i | \(0.147230\pi\) | |||||||
\(110\) | −1.05787 | − | 1.83229i | −0.100864 | − | 0.174702i | ||||
\(111\) | −10.3624 | − | 17.9482i | −0.983555 | − | 1.70357i | ||||
\(112\) | −3.37755 | −0.319149 | ||||||||
\(113\) | −6.31968 | − | 10.9460i | −0.594505 | − | 1.02971i | −0.993616 | − | 0.112811i | \(-0.964015\pi\) |
0.399111 | − | 0.916902i | \(-0.369319\pi\) | |||||||
\(114\) | 3.55787 | − | 6.16242i | 0.333225 | − | 0.577163i | ||||
\(115\) | −4.78541 | + | 8.28857i | −0.446241 | + | 0.772913i | ||||
\(116\) | −3.49330 | −0.324345 | ||||||||
\(117\) | 1.73423 | − | 7.42870i | 0.160330 | − | 0.686784i | ||||
\(118\) | −6.03030 | −0.555134 | ||||||||
\(119\) | 3.62420 | − | 6.27730i | 0.332230 | − | 0.575439i | ||||
\(120\) | −7.17811 | + | 12.4329i | −0.655269 | + | 1.13496i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 9.78541 | 0.885929 | ||||||||
\(123\) | 11.3281 | + | 19.6209i | 1.02142 | + | 1.76916i | ||||
\(124\) | −4.63935 | − | 8.03560i | −0.416626 | − | 0.721618i | ||||
\(125\) | −11.6866 | −1.04528 | ||||||||
\(126\) | −3.57303 | − | 6.18866i | −0.318310 | − | 0.551330i | ||||
\(127\) | −5.75510 | + | 9.96813i | −0.510683 | + | 0.884529i | 0.489241 | + | 0.872149i | \(0.337274\pi\) |
−0.999923 | + | 0.0123797i | \(0.996059\pi\) | |||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | −5.70789 | −0.502552 | ||||||||
\(130\) | −7.30056 | + | 2.21246i | −0.640301 | + | 0.194046i | ||||
\(131\) | 13.6091 | 1.18903 | 0.594514 | − | 0.804085i | \(-0.297344\pi\) | ||||
0.594514 | + | 0.804085i | \(0.297344\pi\) | |||||||
\(132\) | −1.13090 | + | 1.95878i | −0.0984323 | + | 0.170490i | ||||
\(133\) | −5.31298 | + | 9.20235i | −0.460694 | + | 0.797945i | ||||
\(134\) | −2.01515 | − | 3.49035i | −0.174083 | − | 0.301520i | ||||
\(135\) | 4.23150 | 0.364189 | ||||||||
\(136\) | −3.21908 | − | 5.57561i | −0.276034 | − | 0.478105i | ||||
\(137\) | 7.55118 | + | 13.0790i | 0.645140 | + | 1.11742i | 0.984269 | + | 0.176676i | \(0.0565345\pi\) |
−0.339129 | + | 0.940740i | \(0.610132\pi\) | |||||||
\(138\) | −10.2315 | −0.870963 | ||||||||
\(139\) | 7.63935 | + | 13.2317i | 0.647962 | + | 1.12230i | 0.983609 | + | 0.180315i | \(0.0577116\pi\) |
−0.335647 | + | 0.941988i | \(0.608955\pi\) | |||||||
\(140\) | 3.57303 | − | 6.18866i | 0.301976 | − | 0.523038i | ||||
\(141\) | −2.22753 | + | 3.85820i | −0.187592 | + | 0.324919i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −3.45058 | + | 1.04571i | −0.288552 | + | 0.0874467i | ||||
\(144\) | −2.11575 | −0.176312 | ||||||||
\(145\) | −3.69547 | + | 6.40075i | −0.306892 | + | 0.531553i | ||||
\(146\) | −5.42027 | + | 9.38819i | −0.448585 | + | 0.776972i | ||||
\(147\) | 4.98485 | + | 8.63401i | 0.411143 | + | 0.712121i | ||||
\(148\) | 9.16296 | 0.753191 | ||||||||
\(149\) | −2.18878 | − | 3.79107i | −0.179312 | − | 0.310577i | 0.762333 | − | 0.647184i | \(-0.224054\pi\) |
−0.941645 | + | 0.336608i | \(0.890720\pi\) | |||||||
\(150\) | −0.592145 | − | 1.02563i | −0.0483484 | − | 0.0837419i | ||||
\(151\) | 2.29211 | 0.186529 | 0.0932645 | − | 0.995641i | \(-0.470270\pi\) | ||||
0.0932645 | + | 0.995641i | \(0.470270\pi\) | |||||||
\(152\) | 4.71908 | + | 8.17369i | 0.382768 | + | 0.662973i | ||||
\(153\) | 2.27026 | − | 3.93220i | 0.183539 | − | 0.317899i | ||||
\(154\) | −1.68878 | + | 2.92505i | −0.136085 | + | 0.235707i | ||||
\(155\) | −19.6314 | −1.57683 | ||||||||
\(156\) | 5.95058 | + | 5.57632i | 0.476428 | + | 0.446463i | ||||
\(157\) | −24.0472 | −1.91918 | −0.959588 | − | 0.281408i | \(-0.909198\pi\) | ||||
−0.959588 | + | 0.281408i | \(0.909198\pi\) | |||||||
\(158\) | −0.834829 | + | 1.44597i | −0.0664154 | + | 0.115035i | ||||
\(159\) | 8.77026 | − | 15.1905i | 0.695526 | − | 1.20469i | ||||
\(160\) | −5.28937 | − | 9.16146i | −0.418162 | − | 0.724277i | ||||
\(161\) | 15.2787 | 1.20413 | ||||||||
\(162\) | 5.43543 | + | 9.41443i | 0.427047 | + | 0.739668i | ||||
\(163\) | 3.27695 | + | 5.67585i | 0.256671 | + | 0.444567i | 0.965348 | − | 0.260966i | \(-0.0840410\pi\) |
−0.708677 | + | 0.705533i | \(0.750708\pi\) | |||||||
\(164\) | −10.0169 | −0.782189 | ||||||||
\(165\) | 2.39270 | + | 4.14428i | 0.186272 | + | 0.322632i | ||||
\(166\) | −2.83483 | + | 4.91007i | −0.220025 | + | 0.381095i | ||||
\(167\) | 9.16296 | − | 15.8707i | 0.709051 | − | 1.22811i | −0.256159 | − | 0.966635i | \(-0.582457\pi\) |
0.965210 | − | 0.261478i | \(-0.0842098\pi\) | |||||||
\(168\) | 22.9181 | 1.76817 | ||||||||
\(169\) | 0.843281 | + | 12.9726i | 0.0648678 | + | 0.997894i | ||||
\(170\) | −4.54051 | −0.348241 | ||||||||
\(171\) | −3.32813 | + | 5.76449i | −0.254508 | + | 0.440822i | ||||
\(172\) | 1.26180 | − | 2.18551i | 0.0962115 | − | 0.166643i | ||||
\(173\) | −7.34328 | − | 12.7189i | −0.558299 | − | 0.967003i | −0.997639 | − | 0.0686816i | \(-0.978121\pi\) |
0.439339 | − | 0.898321i | \(-0.355213\pi\) | |||||||
\(174\) | −7.90116 | −0.598985 | ||||||||
\(175\) | 0.884251 | + | 1.53157i | 0.0668431 | + | 0.115776i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 13.6394 | 1.02520 | ||||||||
\(178\) | −4.67362 | − | 8.09495i | −0.350303 | − | 0.606742i | ||||
\(179\) | 3.24665 | − | 5.62336i | 0.242666 | − | 0.420310i | −0.718807 | − | 0.695210i | \(-0.755311\pi\) |
0.961473 | + | 0.274900i | \(0.0886447\pi\) | |||||||
\(180\) | 2.23820 | − | 3.87667i | 0.166825 | − | 0.288950i | ||||
\(181\) | −17.1630 | −1.27571 | −0.637856 | − | 0.770155i | \(-0.720179\pi\) | ||||
−0.637856 | + | 0.770155i | \(0.720179\pi\) | |||||||
\(182\) | 8.88600 | + | 8.32713i | 0.658674 | + | 0.617248i | ||||
\(183\) | −22.1327 | −1.63609 | ||||||||
\(184\) | 6.78541 | − | 11.7527i | 0.500227 | − | 0.866418i | ||||
\(185\) | 9.69326 | − | 16.7892i | 0.712663 | − | 1.23437i | ||||
\(186\) | −10.4933 | − | 18.1749i | −0.769406 | − | 1.33265i | ||||
\(187\) | −2.14605 | −0.156935 | ||||||||
\(188\) | −0.984848 | − | 1.70581i | −0.0718274 | − | 0.124409i | ||||
\(189\) | −3.37755 | − | 5.85009i | −0.245681 | − | 0.425532i | ||||
\(190\) | 6.65626 | 0.482896 | ||||||||
\(191\) | −8.98485 | − | 15.5622i | −0.650121 | − | 1.12604i | −0.983093 | − | 0.183106i | \(-0.941385\pi\) |
0.332972 | − | 0.942937i | \(-0.391948\pi\) | |||||||
\(192\) | 7.91631 | − | 13.7114i | 0.571310 | − | 0.989538i | ||||
\(193\) | 1.48485 | − | 2.57183i | 0.106882 | − | 0.185125i | −0.807624 | − | 0.589698i | \(-0.799247\pi\) |
0.914505 | + | 0.404574i | \(0.132580\pi\) | |||||||
\(194\) | 11.6394 | 0.835657 | ||||||||
\(195\) | 16.5124 | − | 5.00415i | 1.18248 | − | 0.358355i | ||||
\(196\) | −4.40786 | −0.314847 | ||||||||
\(197\) | −6.11575 | + | 10.5928i | −0.435729 | + | 0.754705i | −0.997355 | − | 0.0726865i | \(-0.976843\pi\) |
0.561626 | + | 0.827391i | \(0.310176\pi\) | |||||||
\(198\) | −1.05787 | + | 1.83229i | −0.0751799 | + | 0.130215i | ||||
\(199\) | 0.100598 | + | 0.174240i | 0.00713118 | + | 0.0123516i | 0.869569 | − | 0.493812i | \(-0.164397\pi\) |
−0.862438 | + | 0.506163i | \(0.831063\pi\) | |||||||
\(200\) | 1.57081 | 0.111073 | ||||||||
\(201\) | 4.55787 | + | 7.89447i | 0.321488 | + | 0.556833i | ||||
\(202\) | −0.450578 | − | 0.780424i | −0.0317026 | − | 0.0549104i | ||||
\(203\) | 11.7988 | 0.828114 | ||||||||
\(204\) | 2.42697 | + | 4.20364i | 0.169922 | + | 0.294314i | ||||
\(205\) | −10.5966 | + | 18.3539i | −0.740101 | + | 1.28189i | ||||
\(206\) | −6.52360 | + | 11.2992i | −0.454521 | + | 0.787254i | ||||
\(207\) | 9.57081 | 0.665218 | ||||||||
\(208\) | 3.45058 | − | 1.04571i | 0.239255 | − | 0.0725070i | ||||
\(209\) | 3.14605 | 0.217617 | ||||||||
\(210\) | 8.08148 | − | 13.9975i | 0.557675 | − | 0.965922i | ||||
\(211\) | −5.83483 | + | 10.1062i | −0.401686 | + | 0.695741i | −0.993930 | − | 0.110018i | \(-0.964909\pi\) |
0.592243 | + | 0.805759i | \(0.298242\pi\) | |||||||
\(212\) | 3.87755 | + | 6.71612i | 0.266311 | + | 0.461265i | ||||
\(213\) | −13.5708 | −0.929857 | ||||||||
\(214\) | 6.80453 | + | 11.7858i | 0.465148 | + | 0.805660i | ||||
\(215\) | −2.66966 | − | 4.62398i | −0.182069 | − | 0.315353i | ||||
\(216\) | −6.00000 | −0.408248 | ||||||||
\(217\) | 15.6697 | + | 27.1406i | 1.06373 | + | 1.84243i | ||||
\(218\) | −9.34328 | + | 16.1830i | −0.632807 | + | 1.09605i | ||||
\(219\) | 12.2596 | − | 21.2342i | 0.828426 | − | 1.43488i | ||||
\(220\) | −2.11575 | −0.142644 | ||||||||
\(221\) | −1.75907 | + | 7.53510i | −0.118328 | + | 0.506866i | ||||
\(222\) | 20.7248 | 1.39096 | ||||||||
\(223\) | 3.75335 | − | 6.50099i | 0.251343 | − | 0.435339i | −0.712553 | − | 0.701618i | \(-0.752461\pi\) |
0.963896 | + | 0.266280i | \(0.0857945\pi\) | |||||||
\(224\) | −8.44388 | + | 14.6252i | −0.564180 | + | 0.977189i | ||||
\(225\) | 0.553908 | + | 0.959397i | 0.0369272 | + | 0.0639598i | ||||
\(226\) | 12.6394 | 0.840757 | ||||||||
\(227\) | 1.73820 | + | 3.01065i | 0.115368 | + | 0.199824i | 0.917927 | − | 0.396750i | \(-0.129862\pi\) |
−0.802559 | + | 0.596573i | \(0.796529\pi\) | |||||||
\(228\) | −3.55787 | − | 6.16242i | −0.235626 | − | 0.408116i | ||||
\(229\) | 13.4079 | 0.886016 | 0.443008 | − | 0.896518i | \(-0.353911\pi\) | ||||
0.443008 | + | 0.896518i | \(0.353911\pi\) | |||||||
\(230\) | −4.78541 | − | 8.28857i | −0.315540 | − | 0.546532i | ||||
\(231\) | 3.81968 | − | 6.61587i | 0.251316 | − | 0.435293i | ||||
\(232\) | 5.23995 | − | 9.07586i | 0.344020 | − | 0.595860i | ||||
\(233\) | 0.292106 | 0.0191365 | 0.00956824 | − | 0.999954i | \(-0.496954\pi\) | ||||
0.00956824 | + | 0.999954i | \(0.496954\pi\) | |||||||
\(234\) | 5.56633 | + | 5.21624i | 0.363882 | + | 0.340996i | ||||
\(235\) | −4.16738 | −0.271850 | ||||||||
\(236\) | −3.01515 | + | 5.22240i | −0.196270 | + | 0.339949i | ||||
\(237\) | 1.88822 | − | 3.27049i | 0.122653 | − | 0.212441i | ||||
\(238\) | 3.62420 | + | 6.27730i | 0.234922 | + | 0.406897i | ||||
\(239\) | −21.8023 | −1.41027 | −0.705137 | − | 0.709071i | \(-0.749115\pi\) | ||||
−0.705137 | + | 0.709071i | \(0.749115\pi\) | |||||||
\(240\) | −2.39270 | − | 4.14428i | −0.154448 | − | 0.267512i | ||||
\(241\) | 1.27422 | + | 2.20702i | 0.0820798 | + | 0.142166i | 0.904143 | − | 0.427230i | \(-0.140510\pi\) |
−0.822063 | + | 0.569396i | \(0.807177\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −9.29386 | − | 16.0974i | −0.596201 | − | 1.03265i | ||||
\(244\) | 4.89270 | − | 8.47441i | 0.313223 | − | 0.542519i | ||||
\(245\) | −4.66296 | + | 8.07648i | −0.297905 | + | 0.515987i | ||||
\(246\) | −22.6563 | −1.44451 | ||||||||
\(247\) | 2.57875 | − | 11.0462i | 0.164082 | − | 0.702856i | ||||
\(248\) | 27.8361 | 1.76760 | ||||||||
\(249\) | 6.41182 | − | 11.1056i | 0.406333 | − | 0.703789i | ||||
\(250\) | 5.84328 | − | 10.1209i | 0.369562 | − | 0.640099i | ||||
\(251\) | 13.4096 | + | 23.2261i | 0.846407 | + | 1.46602i | 0.884394 | + | 0.466742i | \(0.154572\pi\) |
−0.0379867 | + | 0.999278i | \(0.512094\pi\) | |||||||
\(252\) | −7.14605 | −0.450159 | ||||||||
\(253\) | −2.26180 | − | 3.91756i | −0.142198 | − | 0.246295i | ||||
\(254\) | −5.75510 | − | 9.96813i | −0.361107 | − | 0.625456i | ||||
\(255\) | 10.2697 | 0.643116 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −1.53427 | + | 2.65743i | −0.0957051 | + | 0.165766i | −0.909903 | − | 0.414822i | \(-0.863844\pi\) |
0.814198 | + | 0.580588i | \(0.197177\pi\) | |||||||
\(258\) | 2.85395 | − | 4.94318i | 0.177679 | − | 0.307749i | ||||
\(259\) | −30.9484 | −1.92304 | ||||||||
\(260\) | −1.73423 | + | 7.42870i | −0.107552 | + | 0.460708i | ||||
\(261\) | 7.39095 | 0.457488 | ||||||||
\(262\) | −6.80453 | + | 11.7858i | −0.420385 | + | 0.728128i | ||||
\(263\) | −1.14605 | + | 1.98502i | −0.0706686 | + | 0.122402i | −0.899195 | − | 0.437549i | \(-0.855847\pi\) |
0.828526 | + | 0.559951i | \(0.189180\pi\) | |||||||
\(264\) | −3.39270 | − | 5.87633i | −0.208806 | − | 0.361663i | ||||
\(265\) | 16.4079 | 1.00793 | ||||||||
\(266\) | −5.31298 | − | 9.20235i | −0.325760 | − | 0.564232i | ||||
\(267\) | 10.5708 | + | 18.3092i | 0.646923 | + | 1.12050i | ||||
\(268\) | −4.03030 | −0.246190 | ||||||||
\(269\) | −5.62245 | − | 9.73837i | −0.342807 | − | 0.593759i | 0.642146 | − | 0.766582i | \(-0.278044\pi\) |
−0.984953 | + | 0.172824i | \(0.944711\pi\) | |||||||
\(270\) | −2.11575 | + | 3.66459i | −0.128760 | + | 0.223020i | ||||
\(271\) | 2.14605 | − | 3.71707i | 0.130363 | − | 0.225796i | −0.793453 | − | 0.608631i | \(-0.791719\pi\) |
0.923817 | + | 0.382835i | \(0.125052\pi\) | |||||||
\(272\) | 2.14605 | 0.130124 | ||||||||
\(273\) | −20.0984 | − | 18.8343i | −1.21641 | − | 1.13990i | ||||
\(274\) | −15.1024 | −0.912366 | ||||||||
\(275\) | 0.261802 | − | 0.453455i | 0.0157873 | − | 0.0273444i | ||||
\(276\) | −5.11575 | + | 8.86074i | −0.307932 | + | 0.533354i | ||||
\(277\) | 2.41631 | + | 4.18517i | 0.145182 | + | 0.251462i | 0.929441 | − | 0.368971i | \(-0.120290\pi\) |
−0.784259 | + | 0.620434i | \(0.786957\pi\) | |||||||
\(278\) | −15.2787 | −0.916356 | ||||||||
\(279\) | 9.81571 | + | 17.0013i | 0.587651 | + | 1.01784i | ||||
\(280\) | 10.7191 | + | 18.5660i | 0.640588 | + | 1.10953i | ||||
\(281\) | 3.78541 | 0.225818 | 0.112909 | − | 0.993605i | \(-0.463983\pi\) | ||||
0.112909 | + | 0.993605i | \(0.463983\pi\) | |||||||
\(282\) | −2.22753 | − | 3.85820i | −0.132648 | − | 0.229752i | ||||
\(283\) | 6.21238 | − | 10.7602i | 0.369288 | − | 0.639625i | −0.620167 | − | 0.784470i | \(-0.712935\pi\) |
0.989454 | + | 0.144845i | \(0.0462684\pi\) | |||||||
\(284\) | 3.00000 | − | 5.19615i | 0.178017 | − | 0.308335i | ||||
\(285\) | −15.0551 | −0.891790 | ||||||||
\(286\) | 0.819677 | − | 3.51114i | 0.0484685 | − | 0.207618i | ||||
\(287\) | 33.8326 | 1.99708 | ||||||||
\(288\) | −5.28937 | + | 9.16146i | −0.311679 | + | 0.539844i | ||||
\(289\) | 6.19723 | − | 10.7339i | 0.364543 | − | 0.631407i | ||||
\(290\) | −3.69547 | − | 6.40075i | −0.217006 | − | 0.375865i | ||||
\(291\) | −26.3259 | −1.54325 | ||||||||
\(292\) | 5.42027 | + | 9.38819i | 0.317198 | + | 0.549402i | ||||
\(293\) | −8.45058 | − | 14.6368i | −0.493688 | − | 0.855093i | 0.506286 | − | 0.862366i | \(-0.331018\pi\) |
−0.999974 | + | 0.00727315i | \(0.997685\pi\) | |||||||
\(294\) | −9.96970 | −0.581445 | ||||||||
\(295\) | 6.37931 | + | 11.0493i | 0.371418 | + | 0.643314i | ||||
\(296\) | −13.7444 | + | 23.8061i | −0.798879 | + | 1.38370i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 4.37755 | 0.253585 | ||||||||
\(299\) | −15.6091 | + | 4.73038i | −0.902695 | + | 0.273565i | ||||
\(300\) | −1.18429 | −0.0683750 | ||||||||
\(301\) | −4.26180 | + | 7.38166i | −0.245646 | + | 0.425472i | ||||
\(302\) | −1.14605 | + | 1.98502i | −0.0659479 | + | 0.114225i | ||||
\(303\) | 1.01912 | + | 1.76516i | 0.0585468 | + | 0.101406i | ||||
\(304\) | −3.14605 | −0.180439 | ||||||||
\(305\) | −10.3517 | − | 17.9297i | −0.592739 | − | 1.02665i | ||||
\(306\) | 2.27026 | + | 3.93220i | 0.129782 | + | 0.224789i | ||||
\(307\) | −8.42476 | −0.480826 | −0.240413 | − | 0.970671i | \(-0.577283\pi\) | ||||
−0.240413 | + | 0.970671i | \(0.577283\pi\) | |||||||
\(308\) | 1.68878 | + | 2.92505i | 0.0962269 | + | 0.166670i | ||||
\(309\) | 14.7551 | − | 25.5566i | 0.839388 | − | 1.45386i | ||||
\(310\) | 9.81571 | − | 17.0013i | 0.557495 | − | 0.965609i | ||||
\(311\) | −28.5877 | −1.62106 | −0.810530 | − | 0.585697i | \(-0.800821\pi\) | ||||
−0.810530 | + | 0.585697i | \(0.800821\pi\) | |||||||
\(312\) | −23.4136 | + | 7.09557i | −1.32553 | + | 0.401708i | ||||
\(313\) | 22.3945 | 1.26581 | 0.632905 | − | 0.774230i | \(-0.281862\pi\) | ||||
0.632905 | + | 0.774230i | \(0.281862\pi\) | |||||||
\(314\) | 12.0236 | − | 20.8255i | 0.678531 | − | 1.17525i | ||||
\(315\) | −7.55963 | + | 13.0937i | −0.425937 | + | 0.737744i | ||||
\(316\) | 0.834829 | + | 1.44597i | 0.0469628 | + | 0.0813419i | ||||
\(317\) | −26.2708 | −1.47551 | −0.737757 | − | 0.675067i | \(-0.764115\pi\) | ||||
−0.737757 | + | 0.675067i | \(0.764115\pi\) | |||||||
\(318\) | 8.77026 | + | 15.1905i | 0.491811 | + | 0.851842i | ||||
\(319\) | −1.74665 | − | 3.02529i | −0.0977937 | − | 0.169384i | ||||
\(320\) | 14.8102 | 0.827918 | ||||||||
\(321\) | −15.3905 | − | 26.6571i | −0.859013 | − | 1.48785i | ||||
\(322\) | −7.63935 | + | 13.2317i | −0.425725 | + | 0.737377i | ||||
\(323\) | 3.37580 | − | 5.84705i | 0.187834 | − | 0.325339i | ||||
\(324\) | 10.8709 | 0.603936 | ||||||||
\(325\) | −1.37755 | − | 1.29091i | −0.0764128 | − | 0.0716069i | ||||
\(326\) | −6.55391 | −0.362987 | ||||||||
\(327\) | 21.1327 | − | 36.6028i | 1.16864 | − | 2.02414i | ||||
\(328\) | 15.0254 | − | 26.0247i | 0.829637 | − | 1.43697i | ||||
\(329\) | 3.32638 | + | 5.76145i | 0.183389 | + | 0.317639i | ||||
\(330\) | −4.78541 | −0.263428 | ||||||||
\(331\) | 4.14605 | + | 7.18117i | 0.227888 | + | 0.394713i | 0.957182 | − | 0.289487i | \(-0.0934848\pi\) |
−0.729294 | + | 0.684200i | \(0.760151\pi\) | |||||||
\(332\) | 2.83483 | + | 4.91007i | 0.155581 | + | 0.269475i | ||||
\(333\) | −19.3865 | −1.06237 | ||||||||
\(334\) | 9.16296 | + | 15.8707i | 0.501375 | + | 0.868407i | ||||
\(335\) | −4.26356 | + | 7.38470i | −0.232943 | + | 0.403469i | ||||
\(336\) | −3.81968 | + | 6.61587i | −0.208380 | + | 0.360926i | ||||
\(337\) | −0.0516349 | −0.00281273 | −0.00140637 | − | 0.999999i | \(-0.500448\pi\) | ||||
−0.00140637 | + | 0.999999i | \(0.500448\pi\) | |||||||
\(338\) | −11.6563 | − | 5.75601i | −0.634017 | − | 0.313086i | ||||
\(339\) | −28.5877 | −1.55267 | ||||||||
\(340\) | −2.27026 | + | 3.93220i | −0.123122 | + | 0.213253i | ||||
\(341\) | 4.63935 | − | 8.03560i | 0.251235 | − | 0.435152i | ||||
\(342\) | −3.32813 | − | 5.76449i | −0.179965 | − | 0.311708i | ||||
\(343\) | −8.75510 | −0.472731 | ||||||||
\(344\) | 3.78541 | + | 6.55652i | 0.204095 | + | 0.353504i | ||||
\(345\) | 10.8236 | + | 18.7471i | 0.582725 | + | 1.00931i | ||||
\(346\) | 14.6866 | 0.789555 | ||||||||
\(347\) | 4.31122 | + | 7.46726i | 0.231439 | + | 0.400863i | 0.958232 | − | 0.285993i | \(-0.0923234\pi\) |
−0.726793 | + | 0.686856i | \(0.758990\pi\) | |||||||
\(348\) | −3.95058 | + | 6.84260i | −0.211773 | + | 0.366802i | ||||
\(349\) | −15.0000 | + | 25.9808i | −0.802932 | + | 1.39072i | 0.114747 | + | 0.993395i | \(0.463394\pi\) |
−0.917679 | + | 0.397324i | \(0.869939\pi\) | |||||||
\(350\) | −1.76850 | −0.0945304 | ||||||||
\(351\) | 5.26180 | + | 4.93087i | 0.280854 | + | 0.263190i | ||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | 0.238198 | − | 0.412571i | 0.0126780 | − | 0.0219589i | −0.859617 | − | 0.510939i | \(-0.829298\pi\) |
0.872295 | + | 0.488980i | \(0.162631\pi\) | |||||||
\(354\) | −6.81968 | + | 11.8120i | −0.362462 | + | 0.627802i | ||||
\(355\) | −6.34725 | − | 10.9938i | −0.336877 | − | 0.583488i | ||||
\(356\) | −9.34725 | −0.495403 | ||||||||
\(357\) | −8.19723 | − | 14.1980i | −0.433843 | − | 0.751439i | ||||
\(358\) | 3.24665 | + | 5.62336i | 0.171591 | + | 0.297204i | ||||
\(359\) | −10.2315 | −0.539998 | −0.269999 | − | 0.962861i | \(-0.587023\pi\) | ||||
−0.269999 | + | 0.962861i | \(0.587023\pi\) | |||||||
\(360\) | 6.71459 | + | 11.6300i | 0.353890 | + | 0.612956i | ||||
\(361\) | 4.55118 | − | 7.88287i | 0.239536 | − | 0.414888i | ||||
\(362\) | 8.58148 | − | 14.8636i | 0.451033 | − | 0.781211i | ||||
\(363\) | −2.26180 | −0.118714 | ||||||||
\(364\) | 11.6545 | − | 3.53194i | 0.610862 | − | 0.185124i | ||||
\(365\) | 22.9359 | 1.20052 | ||||||||
\(366\) | 11.0663 | − | 19.1674i | 0.578446 | − | 1.00190i | ||||
\(367\) | −10.6697 | + | 18.4804i | −0.556952 | + | 0.964668i | 0.440797 | + | 0.897607i | \(0.354696\pi\) |
−0.997749 | + | 0.0670617i | \(0.978638\pi\) | |||||||
\(368\) | 2.26180 | + | 3.91756i | 0.117905 | + | 0.204217i | ||||
\(369\) | 21.1933 | 1.10328 | ||||||||
\(370\) | 9.69326 | + | 16.7892i | 0.503929 | + | 0.872830i | ||||
\(371\) | −13.0966 | − | 22.6840i | −0.679943 | − | 1.17770i | ||||
\(372\) | −20.9866 | −1.08810 | ||||||||
\(373\) | −10.6135 | − | 18.3832i | −0.549548 | − | 0.951845i | −0.998305 | − | 0.0581916i | \(-0.981467\pi\) |
0.448757 | − | 0.893654i | \(-0.351867\pi\) | |||||||
\(374\) | 1.07303 | − | 1.85854i | 0.0554849 | − | 0.0961026i | ||||
\(375\) | −13.2163 | + | 22.8914i | −0.682489 | + | 1.18211i | ||||
\(376\) | 5.90909 | 0.304738 | ||||||||
\(377\) | −12.0539 | + | 3.65298i | −0.620808 | + | 0.188138i | ||||
\(378\) | 6.75510 | 0.347445 | ||||||||
\(379\) | 0.523604 | − | 0.906910i | 0.0268958 | − | 0.0465848i | −0.852264 | − | 0.523112i | \(-0.824771\pi\) |
0.879160 | + | 0.476527i | \(0.158104\pi\) | |||||||
\(380\) | 3.32813 | − | 5.76449i | 0.170729 | − | 0.295712i | ||||
\(381\) | 13.0169 | + | 22.5459i | 0.666876 | + | 1.15506i | ||||
\(382\) | 17.9697 | 0.919410 | ||||||||
\(383\) | 14.4933 | + | 25.1031i | 0.740573 | + | 1.28271i | 0.952235 | + | 0.305367i | \(0.0987792\pi\) |
−0.211662 | + | 0.977343i | \(0.567887\pi\) | |||||||
\(384\) | −3.39270 | − | 5.87633i | −0.173133 | − | 0.299875i | ||||
\(385\) | 7.14605 | 0.364197 | ||||||||
\(386\) | 1.48485 | + | 2.57183i | 0.0755768 | + | 0.130903i | ||||
\(387\) | −2.66966 | + | 4.62398i | −0.135706 | + | 0.235050i | ||||
\(388\) | 5.81968 | − | 10.0800i | 0.295449 | − | 0.511733i | ||||
\(389\) | 15.5653 | 0.789195 | 0.394597 | − | 0.918854i | \(-0.370884\pi\) | ||||
0.394597 | + | 0.918854i | \(0.370884\pi\) | |||||||
\(390\) | −3.92249 | + | 16.8023i | −0.198623 | + | 0.850815i | ||||
\(391\) | −9.70789 | −0.490949 | ||||||||
\(392\) | 6.61178 | − | 11.4519i | 0.333945 | − | 0.578410i | ||||
\(393\) | 15.3905 | − | 26.6571i | 0.776348 | − | 1.34467i | ||||
\(394\) | −6.11575 | − | 10.5928i | −0.308107 | − | 0.533657i | ||||
\(395\) | 3.53258 | 0.177743 | ||||||||
\(396\) | 1.05787 | + | 1.83229i | 0.0531602 | + | 0.0920762i | ||||
\(397\) | −9.48933 | − | 16.4360i | −0.476256 | − | 0.824900i | 0.523374 | − | 0.852103i | \(-0.324673\pi\) |
−0.999630 | + | 0.0272035i | \(0.991340\pi\) | |||||||
\(398\) | −0.201195 | −0.0100850 | ||||||||
\(399\) | 12.0169 | + | 20.8139i | 0.601598 | + | 1.04200i | ||||
\(400\) | −0.261802 | + | 0.453455i | −0.0130901 | + | 0.0226727i | ||||
\(401\) | 4.76180 | − | 8.24768i | 0.237793 | − | 0.411870i | −0.722288 | − | 0.691593i | \(-0.756909\pi\) |
0.960081 | + | 0.279723i | \(0.0902427\pi\) | |||||||
\(402\) | −9.11575 | −0.454652 | ||||||||
\(403\) | −24.4114 | − | 22.8760i | −1.21602 | − | 1.13954i | ||||
\(404\) | −0.901156 | −0.0448342 | ||||||||
\(405\) | 11.5000 | − | 19.9186i | 0.571440 | − | 0.989762i | ||||
\(406\) | −5.89940 | + | 10.2181i | −0.292782 | + | 0.507114i | ||||
\(407\) | 4.58148 | + | 7.93535i | 0.227095 | + | 0.393341i | ||||
\(408\) | −14.5618 | −0.720919 | ||||||||
\(409\) | −4.95728 | − | 8.58626i | −0.245122 | − | 0.424563i | 0.717044 | − | 0.697028i | \(-0.245495\pi\) |
−0.962166 | + | 0.272465i | \(0.912161\pi\) | |||||||
\(410\) | −10.5966 | − | 18.3539i | −0.523330 | − | 0.906435i | ||||
\(411\) | 34.1585 | 1.68492 | ||||||||
\(412\) | 6.52360 | + | 11.2992i | 0.321395 | + | 0.556672i | ||||
\(413\) | 10.1838 | − | 17.6389i | 0.501114 | − | 0.867954i | ||||
\(414\) | −4.78541 | + | 8.28857i | −0.235190 | + | 0.407361i | ||||
\(415\) | 11.9956 | 0.588840 | ||||||||
\(416\) | 4.09838 | − | 17.5557i | 0.200940 | − | 0.860740i | ||||
\(417\) | 34.5574 | 1.69228 | ||||||||
\(418\) | −1.57303 | + | 2.72456i | −0.0769392 | + | 0.133263i | ||||
\(419\) | −3.50670 | + | 6.07378i | −0.171313 | + | 0.296724i | −0.938879 | − | 0.344246i | \(-0.888134\pi\) |
0.767566 | + | 0.640970i | \(0.221468\pi\) | |||||||
\(420\) | −8.08148 | − | 13.9975i | −0.394336 | − | 0.683010i | ||||
\(421\) | 33.9787 | 1.65602 | 0.828009 | − | 0.560714i | \(-0.189473\pi\) | ||||
0.828009 | + | 0.560714i | \(0.189473\pi\) | |||||||
\(422\) | −5.83483 | − | 10.1062i | −0.284035 | − | 0.491963i | ||||
\(423\) | 2.08369 | + | 3.60906i | 0.101313 | + | 0.175479i | ||||
\(424\) | −23.2653 | −1.12986 | ||||||||
\(425\) | −0.561841 | − | 0.973138i | −0.0272533 | − | 0.0472041i | ||||
\(426\) | 6.78541 | − | 11.7527i | 0.328754 | − | 0.569419i | ||||
\(427\) | −16.5254 | + | 28.6228i | −0.799718 | + | 1.38515i | ||||
\(428\) | 13.6091 | 0.657818 | ||||||||
\(429\) | −1.85395 | + | 7.94151i | −0.0895094 | + | 0.383420i | ||||
\(430\) | 5.33931 | 0.257485 | ||||||||
\(431\) | −3.93367 | + | 6.81332i | −0.189478 | + | 0.328186i | −0.945076 | − | 0.326849i | \(-0.894013\pi\) |
0.755598 | + | 0.655036i | \(0.227346\pi\) | |||||||
\(432\) | 1.00000 | − | 1.73205i | 0.0481125 | − | 0.0833333i | ||||
\(433\) | 6.82638 | + | 11.8236i | 0.328055 | + | 0.568207i | 0.982126 | − | 0.188226i | \(-0.0602736\pi\) |
−0.654071 | + | 0.756433i | \(0.726940\pi\) | |||||||
\(434\) | −31.3393 | −1.50434 | ||||||||
\(435\) | 8.35843 | + | 14.4772i | 0.400756 | + | 0.694130i | ||||
\(436\) | 9.34328 | + | 16.1830i | 0.447462 | + | 0.775027i | ||||
\(437\) | 14.2315 | 0.680785 | ||||||||
\(438\) | 12.2596 | + | 21.2342i | 0.585786 | + | 1.01461i | ||||
\(439\) | 4.16517 | − | 7.21429i | 0.198793 | − | 0.344319i | −0.749344 | − | 0.662180i | \(-0.769631\pi\) |
0.948137 | + | 0.317861i | \(0.102965\pi\) | |||||||
\(440\) | 3.17362 | − | 5.49688i | 0.151297 | − | 0.262053i | ||||
\(441\) | 9.32592 | 0.444091 | ||||||||
\(442\) | −5.64605 | − | 5.29095i | −0.268555 | − | 0.251665i | ||||
\(443\) | −25.2484 | −1.19959 | −0.599794 | − | 0.800154i | \(-0.704751\pi\) | ||||
−0.599794 | + | 0.800154i | \(0.704751\pi\) | |||||||
\(444\) | 10.3624 | − | 17.9482i | 0.491778 | − | 0.851784i | ||||
\(445\) | −9.88822 | + | 17.1269i | −0.468746 | + | 0.811893i | ||||
\(446\) | 3.75335 | + | 6.50099i | 0.177726 | + | 0.307831i | ||||
\(447\) | −9.90116 | −0.468309 | ||||||||
\(448\) | −11.8214 | − | 20.4753i | −0.558510 | − | 0.967368i | ||||
\(449\) | 18.6354 | + | 32.2774i | 0.879458 | + | 1.52327i | 0.851936 | + | 0.523645i | \(0.175428\pi\) |
0.0275219 | + | 0.999621i | \(0.491238\pi\) | |||||||
\(450\) | −1.10782 | −0.0522229 | ||||||||
\(451\) | −5.00845 | − | 8.67489i | −0.235839 | − | 0.408485i | ||||
\(452\) | 6.31968 | − | 10.9460i | 0.297253 | − | 0.514857i | ||||
\(453\) | 2.59214 | − | 4.48973i | 0.121790 | − | 0.210946i | ||||
\(454\) | −3.47640 | −0.163155 | ||||||||
\(455\) | 5.85745 | − | 25.0908i | 0.274602 | − | 1.17628i | ||||
\(456\) | 21.3472 | 0.999676 | ||||||||
\(457\) | 1.54546 | − | 2.67681i | 0.0722933 | − | 0.125216i | −0.827613 | − | 0.561300i | \(-0.810302\pi\) |
0.899906 | + | 0.436084i | \(0.143635\pi\) | |||||||
\(458\) | −6.70393 | + | 11.6115i | −0.313254 | + | 0.542572i | ||||
\(459\) | 2.14605 | + | 3.71707i | 0.100169 | + | 0.173498i | ||||
\(460\) | −9.57081 | −0.446241 | ||||||||
\(461\) | 11.2400 | + | 19.4682i | 0.523497 | + | 0.906723i | 0.999626 | + | 0.0273476i | \(0.00870611\pi\) |
−0.476129 | + | 0.879375i | \(0.657961\pi\) | |||||||
\(462\) | 3.81968 | + | 6.61587i | 0.177707 | + | 0.307798i | ||||
\(463\) | −29.0507 | −1.35010 | −0.675051 | − | 0.737771i | \(-0.735878\pi\) | ||||
−0.675051 | + | 0.737771i | \(0.735878\pi\) | |||||||
\(464\) | 1.74665 | + | 3.02529i | 0.0810862 | + | 0.140445i | ||||
\(465\) | −22.2012 | + | 38.4536i | −1.02956 | + | 1.78324i | ||||
\(466\) | −0.146053 | + | 0.252971i | −0.00676577 | + | 0.0117187i | ||||
\(467\) | −7.47990 | −0.346129 | −0.173064 | − | 0.984911i | \(-0.555367\pi\) | ||||
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(468\) | 7.30056 | − | 2.21246i | 0.337468 | − | 0.102271i | ||||
\(469\) | 13.6126 | 0.628570 | ||||||||
\(470\) | 2.08369 | − | 3.60906i | 0.0961136 | − | 0.166474i | ||||
\(471\) | −27.1950 | + | 47.1031i | −1.25308 | + | 2.17040i | ||||
\(472\) | −9.04546 | − | 15.6672i | −0.416351 | − | 0.721141i | ||||
\(473\) | 2.52360 | 0.116035 | ||||||||
\(474\) | 1.88822 | + | 3.27049i | 0.0867287 | + | 0.150219i | ||||
\(475\) | 0.823644 | + | 1.42659i | 0.0377914 | + | 0.0654566i | ||||
\(476\) | 7.24840 | 0.332230 | ||||||||
\(477\) | −8.20393 | − | 14.2096i | −0.375632 | − | 0.650614i | ||||
\(478\) | 10.9012 | − | 18.8814i | 0.498607 | − | 0.863613i | ||||
\(479\) | −4.31122 | + | 7.46726i | −0.196985 | + | 0.341188i | −0.947549 | − | 0.319609i | \(-0.896448\pi\) |
0.750565 | + | 0.660797i | \(0.229782\pi\) | |||||||
\(480\) | −23.9270 | −1.09211 | ||||||||
\(481\) | 31.6175 | − | 9.58180i | 1.44163 | − | 0.436893i | ||||
\(482\) | −2.54844 | −0.116078 | ||||||||
\(483\) | 17.2787 | − | 29.9276i | 0.786208 | − | 1.36175i | ||||
\(484\) | 0.500000 | − | 0.866025i | 0.0227273 | − | 0.0393648i | ||||
\(485\) | −12.3130 | − | 21.3267i | −0.559104 | − | 0.968396i | ||||
\(486\) | 18.5877 | 0.843156 | ||||||||
\(487\) | −4.04546 | − | 7.00693i | −0.183317 | − | 0.317514i | 0.759691 | − | 0.650284i | \(-0.225350\pi\) |
−0.943008 | + | 0.332770i | \(0.892017\pi\) | |||||||
\(488\) | 14.6781 | + | 25.4232i | 0.664447 | + | 1.15086i | ||||
\(489\) | 14.8236 | 0.670348 | ||||||||
\(490\) | −4.66296 | − | 8.07648i | −0.210651 | − | 0.364858i | ||||
\(491\) | −2.31122 | + | 4.00316i | −0.104304 | + | 0.180660i | −0.913454 | − | 0.406943i | \(-0.866595\pi\) |
0.809150 | + | 0.587603i | \(0.199928\pi\) | |||||||
\(492\) | −11.3281 | + | 19.6209i | −0.510712 | + | 0.884578i | ||||
\(493\) | −7.49681 | −0.337639 | ||||||||
\(494\) | 8.27695 | + | 7.75638i | 0.372398 | + | 0.348976i | ||||
\(495\) | 4.47640 | 0.201199 | ||||||||
\(496\) | −4.63935 | + | 8.03560i | −0.208313 | + | 0.360809i | ||||
\(497\) | −10.1327 | + | 17.5503i | −0.454512 | + | 0.787237i | ||||
\(498\) | 6.41182 | + | 11.1056i | 0.287321 | + | 0.497654i | ||||
\(499\) | 39.5137 | 1.76888 | 0.884438 | − | 0.466657i | \(-0.154542\pi\) | ||||
0.884438 | + | 0.466657i | \(0.154542\pi\) | |||||||
\(500\) | −5.84328 | − | 10.1209i | −0.261319 | − | 0.452619i | ||||
\(501\) | −20.7248 | − | 35.8964i | −0.925916 | − | 1.60373i | ||||
\(502\) | −26.8192 | −1.19700 | ||||||||
\(503\) | 18.8517 | + | 32.6522i | 0.840557 | + | 1.45589i | 0.889424 | + | 0.457083i | \(0.151106\pi\) |
−0.0488670 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(504\) | 10.7191 | − | 18.5660i | 0.477466 | − | 0.826995i | ||||
\(505\) | −0.953310 | + | 1.65118i | −0.0424218 | + | 0.0734766i | ||||
\(506\) | 4.52360 | 0.201099 | ||||||||
\(507\) | 26.3642 | + | 13.0189i | 1.17087 | + | 0.578192i | ||||
\(508\) | −11.5102 | −0.510683 | ||||||||
\(509\) | 3.86065 | − | 6.68684i | 0.171120 | − | 0.296389i | −0.767692 | − | 0.640819i | \(-0.778595\pi\) |
0.938812 | + | 0.344431i | \(0.111928\pi\) | |||||||
\(510\) | −5.13487 | + | 8.89385i | −0.227376 | + | 0.393826i | ||||
\(511\) | −18.3073 | − | 31.7091i | −0.809865 | − | 1.40273i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | −3.14605 | − | 5.44912i | −0.138902 | − | 0.240585i | ||||
\(514\) | −1.53427 | − | 2.65743i | −0.0676738 | − | 0.117214i | ||||
\(515\) | 27.6046 | 1.21641 | ||||||||
\(516\) | −2.85395 | − | 4.94318i | −0.125638 | − | 0.217611i | ||||
\(517\) | 0.984848 | − | 1.70581i | 0.0433136 | − | 0.0750213i | ||||
\(518\) | 15.4742 | − | 26.8021i | 0.679897 | − | 1.17762i | ||||
\(519\) | −33.2181 | −1.45811 | ||||||||
\(520\) | −16.6990 | − | 15.6487i | −0.732299 | − | 0.686242i | ||||
\(521\) | 5.48979 | 0.240512 | 0.120256 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120256 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(522\) | −3.69547 | + | 6.40075i | −0.161747 | + | 0.280153i | ||||
\(523\) | −20.6068 | + | 35.6921i | −0.901074 | + | 1.56071i | −0.0749720 | + | 0.997186i | \(0.523887\pi\) |
−0.826102 | + | 0.563520i | \(0.809447\pi\) | |||||||
\(524\) | 6.80453 | + | 11.7858i | 0.297257 | + | 0.514864i | ||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −1.14605 | − | 1.98502i | −0.0499703 | − | 0.0865511i | ||||
\(527\) | −9.95630 | − | 17.2448i | −0.433703 | − | 0.751196i | ||||
\(528\) | 2.26180 | 0.0984323 | ||||||||
\(529\) | 1.26850 | + | 2.19711i | 0.0551522 | + | 0.0955265i | ||||
\(530\) | −8.20393 | + | 14.2096i | −0.356356 | + | 0.617226i | ||||
\(531\) | 6.37931 | − | 11.0493i | 0.276838 | − | 0.479498i | ||||
\(532\) | −10.6260 | −0.460694 | ||||||||
\(533\) | −34.5641 | + | 10.4748i | −1.49714 | + | 0.453713i | ||||
\(534\) | −21.1416 | −0.914888 | ||||||||
\(535\) | 14.3967 | − | 24.9358i | 0.622422 | − | 1.07807i | ||||
\(536\) | 6.04546 | − | 10.4710i | 0.261124 | − | 0.452280i | ||||
\(537\) | −7.34328 | − | 12.7189i | −0.316886 | − | 0.548863i | ||||
\(538\) | 11.2449 | 0.484802 | ||||||||
\(539\) | −2.20393 | − | 3.81731i | −0.0949299 | − | 0.164423i | ||||
\(540\) | 2.11575 | + | 3.66459i | 0.0910474 | + | 0.157699i | ||||
\(541\) | 31.2539 | 1.34371 | 0.671854 | − | 0.740683i | \(-0.265498\pi\) | ||||
0.671854 | + | 0.740683i | \(0.265498\pi\) | |||||||
\(542\) | 2.14605 | + | 3.71707i | 0.0921809 | + | 0.159662i | ||||
\(543\) | −19.4096 | + | 33.6184i | −0.832946 | + | 1.44270i | ||||
\(544\) | 5.36513 | − | 9.29268i | 0.230028 | − | 0.398420i | ||||
\(545\) | 39.5361 | 1.69354 | ||||||||
\(546\) | 26.3602 | − | 7.98855i | 1.12811 | − | 0.341879i | ||||
\(547\) | 2.40239 | 0.102719 | 0.0513594 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513594 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(548\) | −7.55118 | + | 13.0790i | −0.322570 | + | 0.558708i | ||||
\(549\) | −10.3517 | + | 17.9297i | −0.441801 | + | 0.765222i | ||||
\(550\) | 0.261802 | + | 0.453455i | 0.0111633 | + | 0.0193354i | ||||
\(551\) | 10.9901 | 0.468194 | ||||||||
\(552\) | −15.3472 | − | 26.5822i | −0.653222 | − | 1.13141i | ||||
\(553\) | −2.81968 | − | 4.88382i | −0.119905 | − | 0.207681i | ||||
\(554\) | −4.83262 | −0.205318 | ||||||||
\(555\) | −21.9242 | − | 37.9739i | −0.930632 | − | 1.61190i | ||||
\(556\) | −7.63935 | + | 13.2317i | −0.323981 | + | 0.561151i | ||||
\(557\) | −1.22305 | + | 2.11838i | −0.0518221 | + | 0.0897586i | −0.890773 | − | 0.454449i | \(-0.849836\pi\) |
0.838951 | + | 0.544207i | \(0.183170\pi\) | |||||||
\(558\) | −19.6314 | −0.831064 | ||||||||
\(559\) | 2.06854 | − | 8.86074i | 0.0874899 | − | 0.374769i | ||||
\(560\) | −7.14605 | −0.301976 | ||||||||
\(561\) | −2.42697 | + | 4.20364i | −0.102467 | + | 0.177478i | ||||
\(562\) | −1.89270 | + | 3.27826i | −0.0798389 | + | 0.138285i | ||||
\(563\) | −19.2293 | − | 33.3061i | −0.810418 | − | 1.40368i | −0.912572 | − | 0.408916i | \(-0.865907\pi\) |
0.102154 | − | 0.994769i | \(-0.467426\pi\) | |||||||
\(564\) | −4.45506 | −0.187592 | ||||||||
\(565\) | −13.3709 | − | 23.1590i | −0.562516 | − | 0.974306i | ||||
\(566\) | 6.21238 | + | 10.7602i | 0.261126 | + | 0.452283i | ||||
\(567\) | −36.7169 | −1.54196 | ||||||||
\(568\) | 9.00000 | + | 15.5885i | 0.377632 | + | 0.654077i | ||||
\(569\) | −19.6260 | + | 33.9932i | −0.822763 | + | 1.42507i | 0.0808542 | + | 0.996726i | \(0.474235\pi\) |
−0.903617 | + | 0.428341i | \(0.859098\pi\) | |||||||
\(570\) | 7.52757 | − | 13.0381i | 0.315295 | − | 0.546107i | ||||
\(571\) | −39.3349 | −1.64611 | −0.823057 | − | 0.567959i | \(-0.807733\pi\) | ||||
−0.823057 | + | 0.567959i | \(0.807733\pi\) | |||||||
\(572\) | −2.63090 | − | 2.46543i | −0.110004 | − | 0.103085i | ||||
\(573\) | −40.6439 | −1.69792 | ||||||||
\(574\) | −16.9163 | + | 29.2999i | −0.706073 | + | 1.22295i | ||||
\(575\) | 1.18429 | − | 2.05125i | 0.0493883 | − | 0.0855430i | ||||
\(576\) | −7.40512 | − | 12.8260i | −0.308547 | − | 0.534419i | ||||
\(577\) | −24.0890 | −1.00284 | −0.501418 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501418 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(578\) | 6.19723 | + | 10.7339i | 0.257771 | + | 0.446472i | ||||
\(579\) | −3.35843 | − | 5.81698i | −0.139572 | − | 0.241745i | ||||
\(580\) | −7.39095 | −0.306892 | ||||||||
\(581\) | −9.57478 | − | 16.5840i | −0.397229 | − | 0.688020i | ||||
\(582\) | 13.1630 | − | 22.7989i | 0.545622 | − | 0.945045i | ||||
\(583\) | −3.87755 | + | 6.71612i | −0.160592 | + | 0.278153i | ||||
\(584\) | −32.5216 | −1.34576 | ||||||||
\(585\) | 3.66920 | − | 15.7173i | 0.151703 | − | 0.649829i | ||||
\(586\) | 16.9012 | 0.698180 | ||||||||
\(587\) | −12.2333 | + | 21.1886i | −0.504920 | + | 0.874548i | 0.495063 | + | 0.868857i | \(0.335145\pi\) |
−0.999984 | + | 0.00569090i | \(0.998189\pi\) | |||||||
\(588\) | −4.98485 | + | 8.63401i | −0.205572 | + | 0.356061i | ||||
\(589\) | 14.5957 | + | 25.2804i | 0.601403 | + | 1.04166i | ||||
\(590\) | −12.7586 | −0.525264 | ||||||||
\(591\) | 13.8326 | + | 23.9588i | 0.568998 | + | 0.985533i | ||||
\(592\) | −4.58148 | − | 7.93535i | −0.188298 | − | 0.326141i | ||||
\(593\) | 33.6215 | 1.38067 | 0.690335 | − | 0.723490i | \(-0.257463\pi\) | ||||
0.690335 | + | 0.723490i | \(0.257463\pi\) | |||||||
\(594\) | −1.00000 | − | 1.73205i | −0.0410305 | − | 0.0710669i | ||||
\(595\) | 7.66790 | − | 13.2812i | 0.314353 | − | 0.544476i | ||||
\(596\) | 2.18878 | − | 3.79107i | 0.0896558 | − | 0.155288i | ||||
\(597\) | 0.455064 | 0.0186245 | ||||||||
\(598\) | 3.70789 | − | 15.8830i | 0.151627 | − | 0.649505i | ||||
\(599\) | 3.01340 | 0.123124 | 0.0615621 | − | 0.998103i | \(-0.480392\pi\) | ||||
0.0615621 | + | 0.998103i | \(0.480392\pi\) | |||||||
\(600\) | 1.77643 | − | 3.07688i | 0.0725226 | − | 0.125613i | ||||
\(601\) | 9.28716 | − | 16.0858i | 0.378831 | − | 0.656155i | −0.612061 | − | 0.790810i | \(-0.709659\pi\) |
0.990892 | + | 0.134655i | \(0.0429928\pi\) | |||||||
\(602\) | −4.26180 | − | 7.38166i | −0.173698 | − | 0.300854i | ||||
\(603\) | 8.52711 | 0.347251 | ||||||||
\(604\) | 1.14605 | + | 1.98502i | 0.0466322 | + | 0.0807694i | ||||
\(605\) | −1.05787 | − | 1.83229i | −0.0430087 | − | 0.0744933i | ||||
\(606\) | −2.03824 | −0.0827977 | ||||||||
\(607\) | 9.60684 | + | 16.6395i | 0.389930 | + | 0.675378i | 0.992440 | − | 0.122733i | \(-0.0391660\pi\) |
−0.602510 | + | 0.798111i | \(0.705833\pi\) | |||||||
\(608\) | −7.86513 | + | 13.6228i | −0.318973 | + | 0.552478i | ||||
\(609\) | 13.3433 | − | 23.1112i | 0.540697 | − | 0.936515i | ||||
\(610\) | 20.7035 | 0.838259 | ||||||||
\(611\) | −5.18208 | − | 4.85615i | −0.209644 | − | 0.196459i | ||||
\(612\) | 4.54051 | 0.183539 | ||||||||
\(613\) | −9.46748 | + | 16.3982i | −0.382388 | + | 0.662316i | −0.991403 | − | 0.130843i | \(-0.958232\pi\) |
0.609015 | + | 0.793159i | \(0.291565\pi\) | |||||||
\(614\) | 4.21238 | − | 7.29606i | 0.169998 | − | 0.294445i | ||||
\(615\) | 23.9675 | + | 41.5129i | 0.966462 | + | 1.67396i | ||||
\(616\) | −10.1327 | −0.408256 | ||||||||
\(617\) | 0.860646 | + | 1.49068i | 0.0346483 | + | 0.0600126i | 0.882830 | − | 0.469693i | \(-0.155636\pi\) |
−0.848181 | + | 0.529706i | \(0.822302\pi\) | |||||||
\(618\) | 14.7551 | + | 25.5566i | 0.593537 | + | 1.02804i | ||||
\(619\) | 16.3562 | 0.657412 | 0.328706 | − | 0.944432i | \(-0.393387\pi\) | ||||
0.328706 | + | 0.944432i | \(0.393387\pi\) | |||||||
\(620\) | −9.81571 | − | 17.0013i | −0.394208 | − | 0.682789i | ||||
\(621\) | −4.52360 | + | 7.83511i | −0.181526 | + | 0.314412i | ||||
\(622\) | 14.2939 | − | 24.7577i | 0.573132 | − | 0.992693i | ||||
\(623\) | 31.5708 | 1.26486 | ||||||||
\(624\) | 1.85395 | − | 7.94151i | 0.0742173 | − | 0.317915i | ||||
\(625\) | −22.1078 | −0.884313 | ||||||||
\(626\) | −11.1972 | + | 19.3942i | −0.447531 | + | 0.775147i | ||||
\(627\) | 3.55787 | − | 6.16242i | 0.142088 | − | 0.246103i | ||||
\(628\) | −12.0236 | − | 20.8255i | −0.479794 | − | 0.831028i | ||||
\(629\) | 19.6642 | 0.784063 | ||||||||
\(630\) | −7.55963 | − | 13.0937i | −0.301183 | − | 0.521664i | ||||
\(631\) | 10.5388 | + | 18.2537i | 0.419541 | + | 0.726667i | 0.995893 | − | 0.0905347i | \(-0.0288576\pi\) |
−0.576352 | + | 0.817202i | \(0.695524\pi\) | |||||||
\(632\) | −5.00897 | −0.199246 | ||||||||
\(633\) | 13.1972 | + | 22.8583i | 0.524543 | + | 0.908535i | ||||
\(634\) | 13.1354 | − | 22.7512i | 0.521673 | − | 0.903564i | ||||
\(635\) | −12.1764 | + | 21.0901i | −0.483204 | + | 0.836934i | ||||
\(636\) | 17.5405 | 0.695526 | ||||||||
\(637\) | −15.2096 | + | 4.60934i | −0.602628 | + | 0.182629i | ||||
\(638\) | 3.49330 | 0.138301 | ||||||||
\(639\) | −6.34725 | + | 10.9938i | −0.251093 | + | 0.434906i | ||||
\(640\) | 3.17362 | − | 5.49688i | 0.125449 | − | 0.217283i | ||||
\(641\) | 2.26850 | + | 3.92916i | 0.0896004 | + | 0.155192i | 0.907342 | − | 0.420393i | \(-0.138108\pi\) |
−0.817742 | + | 0.575585i | \(0.804774\pi\) | |||||||
\(642\) | 30.7810 | 1.21483 | ||||||||
\(643\) | 0.491547 | + | 0.851385i | 0.0193847 | + | 0.0335753i | 0.875555 | − | 0.483118i | \(-0.160496\pi\) |
−0.856170 | + | 0.516694i | \(0.827163\pi\) | |||||||
\(644\) | 7.63935 | + | 13.2317i | 0.301033 | + | 0.521404i | ||||
\(645\) | −12.0765 | −0.475511 | ||||||||
\(646\) | 3.37580 | + | 5.84705i | 0.132819 | + | 0.230049i | ||||
\(647\) | 23.3428 | − | 40.4310i | 0.917701 | − | 1.58950i | 0.114803 | − | 0.993388i | \(-0.463376\pi\) |
0.802898 | − | 0.596117i | \(-0.203290\pi\) | |||||||
\(648\) | −16.3063 | + | 28.2433i | −0.640571 | + | 1.10950i | ||||
\(649\) | −6.03030 | −0.236710 | ||||||||
\(650\) | 1.80674 | − | 0.547539i | 0.0708661 | − | 0.0214762i | ||||
\(651\) | 70.8833 | 2.77814 | ||||||||
\(652\) | −3.27695 | + | 5.67585i | −0.128335 | + | 0.222283i | ||||
\(653\) | 12.9354 | − | 22.4048i | 0.506202 | − | 0.876768i | −0.493772 | − | 0.869591i | \(-0.664382\pi\) |
0.999974 | − | 0.00717672i | \(-0.00228444\pi\) | |||||||
\(654\) | 21.1327 | + | 36.6028i | 0.826352 | + | 1.43128i | ||||
\(655\) | 28.7933 | 1.12505 | ||||||||
\(656\) | 5.00845 | + | 8.67489i | 0.195547 | + | 0.338698i | ||||
\(657\) | −11.4679 | − | 19.8631i | −0.447407 | − | 0.774932i | ||||
\(658\) | −6.65275 | −0.259351 | ||||||||
\(659\) | −8.74938 | − | 15.1544i | −0.340828 | − | 0.590331i | 0.643759 | − | 0.765228i | \(-0.277374\pi\) |
−0.984587 | + | 0.174898i | \(0.944041\pi\) | |||||||
\(660\) | −2.39270 | + | 4.14428i | −0.0931359 | + | 0.161316i | ||||
\(661\) | −10.8264 | + | 18.7518i | −0.421097 | + | 0.729362i | −0.996047 | − | 0.0888269i | \(-0.971688\pi\) |
0.574950 | + | 0.818189i | \(0.305022\pi\) | |||||||
\(662\) | −8.29211 | −0.322282 | ||||||||
\(663\) | 12.7703 | + | 11.9671i | 0.495956 | + | 0.464763i | ||||
\(664\) | −17.0090 | −0.660076 | ||||||||
\(665\) | −11.2409 | + | 19.4699i | −0.435905 | + | 0.755009i | ||||
\(666\) | 9.69326 | − | 16.7892i | 0.375606 | − | 0.650569i | ||||
\(667\) | −7.90116 | − | 13.6852i | −0.305934 | − | 0.529893i | ||||
\(668\) | 18.3259 | 0.709051 | ||||||||
\(669\) | −8.48933 | − | 14.7040i | −0.328217 | − | 0.568488i | ||||
\(670\) | −4.26356 | − | 7.38470i | −0.164716 | − | 0.285296i | ||||
\(671\) | 9.78541 | 0.377761 | ||||||||
\(672\) | 19.0984 | + | 33.0794i | 0.736736 | + | 1.27606i | ||||
\(673\) | 11.9399 | − | 20.6805i | 0.460250 | − | 0.797176i | −0.538723 | − | 0.842483i | \(-0.681093\pi\) |
0.998973 | + | 0.0453067i | \(0.0144265\pi\) | |||||||
\(674\) | 0.0258174 | − | 0.0447171i | 0.000994451 | − | 0.00172244i | ||||
\(675\) | −1.04721 | −0.0403071 | ||||||||
\(676\) | −10.8130 | + | 7.21661i | −0.415884 | + | 0.277562i | ||||
\(677\) | −12.6945 | −0.487889 | −0.243945 | − | 0.969789i | \(-0.578441\pi\) | ||||
−0.243945 | + | 0.969789i | \(0.578441\pi\) | |||||||
\(678\) | 14.2939 | − | 24.7577i | 0.548952 | − | 0.950813i | ||||
\(679\) | −19.6563 | + | 34.0456i | −0.754338 | + | 1.30655i | ||||
\(680\) | −6.81077 | − | 11.7966i | −0.261181 | − | 0.452379i | ||||
\(681\) | 7.86292 | 0.301308 | ||||||||
\(682\) | 4.63935 | + | 8.03560i | 0.177650 | + | 0.307699i | ||||
\(683\) | 18.9350 | + | 32.7963i | 0.724526 | + | 1.25492i | 0.959169 | + | 0.282835i | \(0.0912748\pi\) |
−0.234642 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(684\) | −6.65626 | −0.254508 | ||||||||
\(685\) | 15.9764 | + | 27.6719i | 0.610427 | + | 1.05729i | ||||
\(686\) | 4.37755 | − | 7.58214i | 0.167136 | − | 0.289488i | ||||
\(687\) | 15.1630 | − | 26.2630i | 0.578503 | − | 1.00200i | ||||
\(688\) | −2.52360 | −0.0962115 | ||||||||
\(689\) | 20.4029 | + | 19.1197i | 0.777289 | + | 0.728402i | ||||
\(690\) | −21.6473 | −0.824098 | ||||||||
\(691\) | −12.8709 | + | 22.2930i | −0.489630 | + | 0.848065i | −0.999929 | − | 0.0119328i | \(-0.996202\pi\) |
0.510298 | + | 0.859997i | \(0.329535\pi\) | |||||||
\(692\) | 7.34328 | − | 12.7189i | 0.279150 | − | 0.483501i | ||||
\(693\) | −3.57303 | − | 6.18866i | −0.135728 | − | 0.235088i | ||||
\(694\) | −8.62245 | −0.327304 | ||||||||
\(695\) | 16.1630 | + | 27.9951i | 0.613096 | + | 1.06191i | ||||
\(696\) | −11.8517 | − | 20.5278i | −0.449239 | − | 0.778104i | ||||
\(697\) | −21.4968 | −0.814250 | ||||||||
\(698\) | −15.0000 | − | 25.9808i | −0.567758 | − | 0.983386i | ||||
\(699\) | 0.330343 | − | 0.572170i | 0.0124947 | − | 0.0216415i | ||||
\(700\) | −0.884251 | + | 1.53157i | −0.0334215 | + | 0.0578878i | ||||
\(701\) | −33.5023 | −1.26536 | −0.632682 | − | 0.774412i | \(-0.718046\pi\) | ||||
−0.632682 | + | 0.774412i | \(0.718046\pi\) | |||||||
\(702\) | −6.90116 | + | 2.09142i | −0.260467 | + | 0.0789356i | ||||
\(703\) | −28.8272 | −1.08724 | ||||||||
\(704\) | −3.50000 | + | 6.06218i | −0.131911 | + | 0.228477i | ||||
\(705\) | −4.71290 | + | 8.16298i | −0.177498 | + | 0.307436i | ||||
\(706\) | 0.238198 | + | 0.412571i | 0.00896469 | + | 0.0155273i | ||||
\(707\) | 3.04370 | 0.114470 | ||||||||
\(708\) | 6.81968 | + | 11.8120i | 0.256299 | + | 0.443923i | ||||
\(709\) | 15.4618 | + | 26.7806i | 0.580679 | + | 1.00577i | 0.995399 | + | 0.0958161i | \(0.0305461\pi\) |
−0.414720 | + | 0.909949i | \(0.636121\pi\) | |||||||
\(710\) | 12.6945 | 0.476416 | ||||||||
\(711\) | −1.76629 | − | 3.05930i | −0.0662410 | − | 0.114733i | ||||
\(712\) | 14.0209 | − | 24.2849i | 0.525454 | − | 0.910114i | ||||
\(713\) | 20.9866 | − | 36.3499i | 0.785954 | − | 1.36131i | ||||
\(714\) | 16.3945 | 0.613547 | ||||||||
\(715\) | −7.30056 | + | 2.21246i | −0.273025 | + | 0.0827414i | ||||
\(716\) | 6.49330 | 0.242666 | ||||||||
\(717\) | −24.6563 | + | 42.7059i | −0.920805 | + | 1.59488i | ||||
\(718\) | 5.11575 | − | 8.86074i | 0.190918 | − | 0.330680i | ||||
\(719\) | −4.60905 | − | 7.98311i | −0.171889 | − | 0.297720i | 0.767192 | − | 0.641418i | \(-0.221654\pi\) |
−0.939080 | + | 0.343698i | \(0.888320\pi\) | |||||||
\(720\) | −4.47640 | −0.166825 | ||||||||
\(721\) | −22.0338 | − | 38.1637i | −0.820582 | − | 1.42129i | ||||
\(722\) | 4.55118 | + | 7.88287i | 0.169377 | + | 0.293370i | ||||
\(723\) | 5.76408 | 0.214368 | ||||||||
\(724\) | −8.58148 | − | 14.8636i | −0.318928 | − | 0.552400i | ||||
\(725\) | 0.914554 | − | 1.58405i | 0.0339657 | − | 0.0588303i | ||||
\(726\) | 1.13090 | − | 1.95878i | 0.0419717 | − | 0.0726971i | ||||
\(727\) | 33.5102 | 1.24282 | 0.621412 | − | 0.783484i | \(-0.286559\pi\) | ||||
0.621412 | + | 0.783484i | \(0.286559\pi\) | |||||||
\(728\) | −8.30550 | + | 35.5772i | −0.307822 | + | 1.31858i | ||||
\(729\) | −9.42919 | −0.349229 | ||||||||
\(730\) | −11.4679 | + | 19.8631i | −0.424448 | + | 0.735165i | ||||
\(731\) | 2.70789 | − | 4.69021i | 0.100155 | − | 0.173474i | ||||
\(732\) | −11.0663 | − | 19.1674i | −0.409023 | − | 0.708449i | ||||
\(733\) | −1.29561 | −0.0478546 | −0.0239273 | − | 0.999714i | \(-0.507617\pi\) | ||||
−0.0239273 | + | 0.999714i | \(0.507617\pi\) | |||||||
\(734\) | −10.6697 | − | 18.4804i | −0.393824 | − | 0.682124i | ||||
\(735\) | 10.5467 | + | 18.2674i | 0.389021 | + | 0.673803i | ||||
\(736\) | 22.6180 | 0.833711 | ||||||||
\(737\) | −2.01515 | − | 3.49035i | −0.0742291 | − | 0.128569i | ||||
\(738\) | −10.5966 | + | 18.3539i | −0.390067 | + | 0.675617i | ||||
\(739\) | −14.4248 | + | 24.9844i | −0.530623 | + | 0.919067i | 0.468738 | + | 0.883337i | \(0.344709\pi\) |
−0.999361 | + | 0.0357295i | \(0.988625\pi\) | |||||||
\(740\) | 19.3865 | 0.712663 | ||||||||
\(741\) | −18.7208 | − | 17.5434i | −0.687727 | − | 0.644473i | ||||
\(742\) | 26.1933 | 0.961585 | ||||||||
\(743\) | 15.8686 | − | 27.4853i | 0.582164 | − | 1.00834i | −0.413059 | − | 0.910704i | \(-0.635540\pi\) |
0.995222 | − | 0.0976330i | \(-0.0311271\pi\) | |||||||
\(744\) | 31.4799 | − | 54.5248i | 1.15411 | − | 1.99898i | ||||
\(745\) | −4.63090 | − | 8.02096i | −0.169663 | − | 0.293865i | ||||
\(746\) | 21.2271 | 0.777178 | ||||||||
\(747\) | −5.99779 | − | 10.3885i | −0.219448 | − | 0.380094i | ||||
\(748\) | −1.07303 | − | 1.85854i | −0.0392337 | − | 0.0679548i | ||||
\(749\) | −45.9653 | −1.67953 | ||||||||
\(750\) | −13.2163 | − | 22.8914i | −0.482593 | − | 0.835875i | ||||
\(751\) | 18.0641 | − | 31.2880i | 0.659169 | − | 1.14171i | −0.321662 | − | 0.946854i | \(-0.604242\pi\) |
0.980831 | − | 0.194860i | \(-0.0624251\pi\) | |||||||
\(752\) | −0.984848 | + | 1.70581i | −0.0359137 | + | 0.0622044i | ||||
\(753\) | 60.6598 | 2.21056 | ||||||||
\(754\) | 2.86338 | − | 12.2655i | 0.104278 | − | 0.446682i | ||||
\(755\) | 4.84952 | 0.176492 | ||||||||
\(756\) | 3.37755 | − | 5.85009i | 0.122840 | − | 0.212766i | ||||
\(757\) | 11.0263 | − | 19.0982i | 0.400759 | − | 0.694135i | −0.593059 | − | 0.805159i | \(-0.702080\pi\) |
0.993818 | + | 0.111024i | \(0.0354131\pi\) | |||||||
\(758\) | 0.523604 | + | 0.906910i | 0.0190182 | + | 0.0329404i | ||||
\(759\) | −10.2315 | −0.371380 | ||||||||
\(760\) | 9.98439 | + | 17.2935i | 0.362172 | + | 0.627300i | ||||
\(761\) | −20.0810 | − | 34.7813i | −0.727936 | − | 1.26082i | −0.957754 | − | 0.287589i | \(-0.907146\pi\) |
0.229817 | − | 0.973234i | \(-0.426187\pi\) | |||||||
\(762\) | −26.0338 | −0.943105 | ||||||||
\(763\) | −31.5574 | − | 54.6590i | −1.14246 | − | 1.97879i | ||||
\(764\) | 8.98485 | − | 15.5622i | 0.325060 | − | 0.563021i | ||||
\(765\) | 4.80329 | − | 8.31954i | 0.173663 | − | 0.300794i | ||||
\(766\) | −28.9866 | −1.04733 | ||||||||
\(767\) | −4.94290 | + | 21.1733i | −0.178478 | + | 0.764522i | ||||
\(768\) | 38.4506 | 1.38747 | ||||||||
\(769\) | 12.4799 | − | 21.6158i | 0.450037 | − | 0.779487i | −0.548351 | − | 0.836248i | \(-0.684744\pi\) |
0.998388 | + | 0.0567617i | \(0.0180775\pi\) | |||||||
\(770\) | −3.57303 | + | 6.18866i | −0.128763 | + | 0.223024i | ||||
\(771\) | 3.47022 | + | 6.01059i | 0.124977 | + | 0.216466i | ||||
\(772\) | 2.96970 | 0.106882 | ||||||||
\(773\) | −2.73423 | − | 4.73583i | −0.0983435 | − | 0.170336i | 0.812656 | − | 0.582744i | \(-0.198021\pi\) |
−0.910999 | + | 0.412408i | \(0.864688\pi\) | |||||||
\(774\) | −2.66966 | − | 4.62398i | −0.0959589 | − | 0.166206i | ||||
\(775\) | 4.85837 | 0.174518 | ||||||||
\(776\) | 17.4590 | + | 30.2399i | 0.626743 | + | 1.08555i | ||||
\(777\) | −34.9995 | + | 60.6210i | −1.25560 | + | 2.17477i | ||||
\(778\) | −7.78267 | + | 13.4800i | −0.279022 | + | 0.483281i | ||||
\(779\) | 31.5137 | 1.12910 | ||||||||
\(780\) | 12.5899 | + | 11.7981i | 0.450792 | + | 0.422440i | ||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 4.85395 | − | 8.40728i | 0.173577 | − | 0.300644i | ||||
\(783\) | −3.49330 | + | 6.05057i | −0.124840 | + | 0.216230i | ||||
\(784\) | 2.20393 | + | 3.81731i | 0.0787117 | + | 0.136333i | ||||
\(785\) | −50.8779 | −1.81591 | ||||||||
\(786\) | 15.3905 | + | 26.6571i | 0.548961 | + | 0.950828i | ||||
\(787\) | −18.7742 | − | 32.5179i | −0.669229 | − | 1.15914i | −0.978120 | − | 0.208041i | \(-0.933291\pi\) |
0.308891 | − | 0.951097i | \(-0.400042\pi\) | |||||||
\(788\) | −12.2315 | −0.435729 | ||||||||
\(789\) | 2.59214 | + | 4.48973i | 0.0922828 | + | 0.159839i | ||||
\(790\) | −1.76629 | + | 3.05930i | −0.0628417 | + | 0.108845i | ||||
\(791\) | −21.3450 | + | 36.9707i | −0.758942 | + | 1.31453i | ||||
\(792\) | −6.34725 | −0.225540 | ||||||||
\(793\) | 8.02087 | − | 34.3580i | 0.284830 | − | 1.22009i | ||||
\(794\) | 18.9787 | 0.673528 | ||||||||
\(795\) | 18.5557 | − | 32.1393i | 0.658102 | − | 1.13987i | ||||
\(796\) | −0.100598 | + | 0.174240i | −0.00356559 | + | 0.00617578i | ||||
\(797\) | −3.88028 | − | 6.72085i | −0.137447 | − | 0.238065i | 0.789083 | − | 0.614287i | \(-0.210556\pi\) |
−0.926529 | + | 0.376222i | \(0.877223\pi\) | |||||||
\(798\) | −24.0338 | −0.850788 | ||||||||
\(799\) | −2.11354 | − | 3.66075i | −0.0747715 | − | 0.129508i | ||||
\(800\) | 1.30901 | + | 2.26727i | 0.0462805 | + | 0.0801602i | ||||
\(801\) | 19.7764 | 0.698766 | ||||||||
\(802\) | 4.76180 | + | 8.24768i | 0.168145 | + | 0.291236i | ||||
\(803\) | −5.42027 | + | 9.38819i | −0.191277 | + | 0.331302i | ||||
\(804\) | −4.55787 | + | 7.89447i | −0.160744 | + | 0.278417i | ||||
\(805\) | 32.3259 | 1.13934 | ||||||||
\(806\) | 32.0169 | − | 9.70284i | 1.12775 | − | 0.341768i | ||||
\(807\) | −25.4337 | −0.895310 | ||||||||
\(808\) | 1.35173 | − | 2.34127i | 0.0475538 | − | 0.0823657i | ||||
\(809\) | 3.40337 | − | 5.89481i | 0.119656 | − | 0.207250i | −0.799975 | − | 0.600033i | \(-0.795154\pi\) |
0.919631 | + | 0.392782i | \(0.128487\pi\) | |||||||
\(810\) | 11.5000 | + | 19.9186i | 0.404069 | + | 0.699868i | ||||
\(811\) | −37.0810 | −1.30209 | −0.651045 | − | 0.759039i | \(-0.725669\pi\) | ||||
−0.651045 | + | 0.759039i | \(0.725669\pi\) | |||||||
\(812\) | 5.89940 | + | 10.2181i | 0.207028 | + | 0.358584i | ||||
\(813\) | −4.85395 | − | 8.40728i | −0.170235 | − | 0.294856i | ||||
\(814\) | −9.16296 | −0.321162 | ||||||||
\(815\) | 6.93321 | + | 12.0087i | 0.242860 | + | 0.420646i | ||||
\(816\) | 2.42697 | − | 4.20364i | 0.0849611 | − | 0.147157i | ||||
\(817\) | −3.96970 | + | 6.87572i | −0.138882 | + | 0.240551i | ||||
\(818\) | 9.91455 | 0.346654 | ||||||||
\(819\) | −24.6580 | + | 7.47270i | −0.861621 | + | 0.261117i | ||||
\(820\) | −21.1933 | −0.740101 | ||||||||
\(821\) | 0.0854459 | − | 0.147997i | 0.00298208 | − | 0.00516512i | −0.864531 | − | 0.502580i | \(-0.832384\pi\) |
0.867513 | + | 0.497415i | \(0.165717\pi\) | |||||||
\(822\) | −17.0793 | + | 29.5822i | −0.595708 | + | 1.03180i | ||||
\(823\) | −7.46300 | − | 12.9263i | −0.260144 | − | 0.450582i | 0.706136 | − | 0.708076i | \(-0.250437\pi\) |
−0.966280 | + | 0.257494i | \(0.917103\pi\) | |||||||
\(824\) | −39.1416 | −1.36356 | ||||||||
\(825\) | −0.592145 | − | 1.02563i | −0.0206158 | − | 0.0357077i | ||||
\(826\) | 10.1838 | + | 17.6389i | 0.354341 | + | 0.613736i | ||||
\(827\) | 10.0114 | 0.348132 | 0.174066 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174066 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(828\) | 4.78541 | + | 8.28857i | 0.166304 | + | 0.288048i | ||||
\(829\) | 1.79607 | − | 3.11089i | 0.0623802 | − | 0.108046i | −0.833149 | − | 0.553049i | \(-0.813464\pi\) |
0.895529 | + | 0.445003i | \(0.146798\pi\) | |||||||
\(830\) | −5.99779 | + | 10.3885i | −0.208186 | + | 0.360589i | ||||
\(831\) | 10.9304 | 0.379172 | ||||||||
\(832\) | 18.4163 | + | 17.2580i | 0.638471 | + | 0.598315i | ||||
\(833\) | −9.45949 | −0.327752 | ||||||||
\(834\) | −17.2787 | + | 29.9276i | −0.598313 | + | 1.03631i | ||||
\(835\) | 19.3865 | − | 33.5784i | 0.670898 | − | 1.16203i | ||||
\(836\) | 1.57303 | + | 2.72456i | 0.0544043 | + | 0.0942309i | ||||
\(837\) | −18.5574 | −0.641438 | ||||||||
\(838\) | −3.50670 | − | 6.07378i | −0.121137 | − | 0.209815i | ||||
\(839\) | 13.6108 | + | 23.5746i | 0.469897 | + | 0.813886i | 0.999408 | − | 0.0344177i | \(-0.0109577\pi\) |
−0.529510 | + | 0.848303i | \(0.677624\pi\) | |||||||
\(840\) | 48.4889 | 1.67303 | ||||||||
\(841\) | 8.39842 | + | 14.5465i | 0.289601 | + | 0.501603i | ||||
\(842\) | −16.9893 | + | 29.4264i | −0.585491 | + | 1.01410i | ||||
\(843\) | 4.28092 | − | 7.41477i | 0.147443 | − | 0.255378i | ||||
\(844\) | −11.6697 | −0.401686 | ||||||||
\(845\) | 1.78417 | + | 27.4468i | 0.0613774 | + | 0.944199i | ||||
\(846\) | −4.16738 | −0.143278 | ||||||||
\(847\) | −1.68878 | + | 2.92505i | −0.0580270 | + | 0.100506i | ||||
\(848\) | 3.87755 | − | 6.71612i | 0.133156 | − | 0.230632i | ||||
\(849\) | −14.0512 | − | 24.3374i | −0.482235 | − | 0.835256i | ||||
\(850\) | 1.12368 | 0.0385420 | ||||||||
\(851\) | 20.7248 | + | 35.8964i | 0.710437 | + | 1.23051i | ||||
\(852\) | −6.78541 | − | 11.7527i | −0.232464 | − | 0.402640i | ||||
\(853\) | 26.7114 | 0.914581 | 0.457290 | − | 0.889317i | \(-0.348820\pi\) | ||||
0.457290 | + | 0.889317i | \(0.348820\pi\) | |||||||
\(854\) | −16.5254 | − | 28.6228i | −0.565486 | − | 0.979451i | ||||
\(855\) | −7.04149 | + | 12.1962i | −0.240814 | + | 0.417102i | ||||
\(856\) | −20.4136 | + | 35.3574i | −0.697722 | + | 1.20849i | ||||
\(857\) | −26.6955 | −0.911902 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(858\) | −5.95058 | − | 5.57632i | −0.203149 | − | 0.190372i | ||||
\(859\) | −21.3855 | −0.729663 | −0.364832 | − | 0.931073i | \(-0.618873\pi\) | ||||
−0.364832 | + | 0.931073i | \(0.618873\pi\) | |||||||
\(860\) | 2.66966 | − | 4.62398i | 0.0910346 | − | 0.157676i | ||||
\(861\) | 38.2613 | − | 66.2706i | 1.30394 | − | 2.25850i | ||||
\(862\) | −3.93367 | − | 6.81332i | −0.133981 | − | 0.232063i | ||||
\(863\) | 0.694496 | 0.0236409 | 0.0118205 | − | 0.999930i | \(-0.496237\pi\) | ||||
0.0118205 | + | 0.999930i | \(0.496237\pi\) | |||||||
\(864\) | −5.00000 | − | 8.66025i | −0.170103 | − | 0.294628i | ||||
\(865\) | −15.5365 | − | 26.9101i | −0.528258 | − | 0.914970i | ||||
\(866\) | −13.6528 | −0.463939 | ||||||||
\(867\) | −14.0169 | − | 24.2780i | −0.476039 | − | 0.824524i | ||||
\(868\) | −15.6697 | + | 27.1406i | −0.531863 | + | 0.921213i | ||||
\(869\) | −0.834829 | + | 1.44597i | −0.0283196 | + | 0.0490510i | ||||
\(870\) | −16.7169 | −0.566755 | ||||||||
\(871\) | −13.9069 | + | 4.21453i | −0.471217 | + | 0.142804i | ||||
\(872\) | −56.0597 | −1.89842 | ||||||||
\(873\) | −12.3130 | + | 21.3267i | −0.416731 | + | 0.721800i | ||||
\(874\) | −7.11575 | + | 12.3248i | −0.240694 | + | 0.416894i | ||||
\(875\) | 19.7360 | + | 34.1837i | 0.667198 | + | 1.15562i | ||||
\(876\) | 24.5192 | 0.828426 | ||||||||
\(877\) | 8.63044 | + | 14.9484i | 0.291429 | + | 0.504770i | 0.974148 | − | 0.225911i | \(-0.0725359\pi\) |
−0.682719 | + | 0.730681i | \(0.739203\pi\) | |||||||
\(878\) | 4.16517 | + | 7.21429i | 0.140568 | + | 0.243470i | ||||
\(879\) | −38.2271 | −1.28937 | ||||||||
\(880\) | 1.05787 | + | 1.83229i | 0.0356609 | + | 0.0617666i | ||||
\(881\) | −13.8945 | + | 24.0659i | −0.468116 | + | 0.810801i | −0.999336 | − | 0.0364330i | \(-0.988400\pi\) |
0.531220 | + | 0.847234i | \(0.321734\pi\) | |||||||
\(882\) | −4.66296 | + | 8.07648i | −0.157010 | + | 0.271949i | ||||
\(883\) | 13.1505 | 0.442549 | 0.221274 | − | 0.975212i | \(-0.428978\pi\) | ||||
0.221274 | + | 0.975212i | \(0.428978\pi\) | |||||||
\(884\) | −7.40512 | + | 2.24415i | −0.249061 | + | 0.0754790i | ||||
\(885\) | 28.8575 | 0.970033 | ||||||||
\(886\) | 12.6242 | − | 21.8658i | 0.424118 | − | 0.734595i | ||||
\(887\) | 26.5102 | − | 45.9170i | 0.890126 | − | 1.54174i | 0.0504018 | − | 0.998729i | \(-0.483950\pi\) |
0.839724 | − | 0.543014i | \(-0.182717\pi\) | |||||||
\(888\) | 31.0872 | + | 53.8446i | 1.04322 | + | 1.80691i | ||||
\(889\) | 38.8763 | 1.30387 | ||||||||
\(890\) | −9.88822 | − | 17.1269i | −0.331454 | − | 0.574095i | ||||
\(891\) | 5.43543 | + | 9.41443i | 0.182094 | + | 0.315395i | ||||
\(892\) | 7.50670 | 0.251343 | ||||||||
\(893\) | 3.09838 | + | 5.36656i | 0.103683 | + | 0.179585i | ||||
\(894\) | 4.95058 | − | 8.57465i | 0.165572 | − | 0.286779i | ||||
\(895\) | 6.86910 | − | 11.8976i | 0.229609 | − | 0.397694i | ||||
\(896\) | −10.1327 | −0.338508 | ||||||||
\(897\) | −8.38652 | + | 35.9243i | −0.280018 | + | 1.19948i | ||||
\(898\) | −37.2708 | −1.24374 | ||||||||
\(899\) | 16.2067 | − | 28.0708i | 0.540522 | − | 0.936212i | ||||
\(900\) | −0.553908 | + | 0.959397i | −0.0184636 | + | 0.0319799i | ||||
\(901\) | 8.32143 | + | 14.4131i | 0.277227 | + | 0.480171i | ||||
\(902\) | 10.0169 | 0.333526 | ||||||||
\(903\) | 9.63935 | + | 16.6959i | 0.320778 | + | 0.555603i | ||||
\(904\) | 18.9590 | + | 32.8380i | 0.630568 | + | 1.09218i | ||||
\(905\) | −36.3125 | −1.20707 | ||||||||
\(906\) | 2.59214 | + | 4.48973i | 0.0861182 | + | 0.149161i | ||||
\(907\) | 27.4096 | − | 47.4748i | 0.910121 | − | 1.57638i | 0.0962296 | − | 0.995359i | \(-0.469322\pi\) |
0.813892 | − | 0.581017i | \(-0.197345\pi\) | |||||||
\(908\) | −1.73820 | + | 3.01065i | −0.0576841 | + | 0.0999118i | ||||
\(909\) | 1.90662 | 0.0632386 | ||||||||
\(910\) | 18.8006 | + | 17.6181i | 0.623232 | + | 0.584035i | ||||
\(911\) | −25.4799 | −0.844187 | −0.422093 | − | 0.906552i | \(-0.638705\pi\) | ||||
−0.422093 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(912\) | −3.55787 | + | 6.16242i | −0.117813 | + | 0.204058i | ||||
\(913\) | −2.83483 | + | 4.91007i | −0.0938191 | + | 0.162500i | ||||
\(914\) | 1.54546 | + | 2.67681i | 0.0511191 | + | 0.0885409i | ||||
\(915\) | −46.8272 | −1.54806 | ||||||||
\(916\) | 6.70393 | + | 11.6115i | 0.221504 | + | 0.383656i | ||||
\(917\) | −22.9826 | − | 39.8071i | −0.758953 | − | 1.31455i | ||||
\(918\) | −4.29211 | −0.141661 | ||||||||
\(919\) | 7.10782 | + | 12.3111i | 0.234465 | + | 0.406106i | 0.959117 | − | 0.283009i | \(-0.0913328\pi\) |
−0.724652 | + | 0.689115i | \(0.757999\pi\) | |||||||
\(920\) | 14.3562 | − | 24.8657i | 0.473311 | − | 0.819798i | ||||
\(921\) | −9.52757 | + | 16.5022i | −0.313944 | + | 0.543767i | ||||
\(922\) | −22.4799 | −0.740336 | ||||||||
\(923\) | 4.91806 | − | 21.0669i | 0.161880 | − | 0.693424i | ||||
\(924\) | 7.63935 | 0.251316 | ||||||||
\(925\) | −2.39888 | + | 4.15499i | −0.0788748 | + | 0.136615i | ||||
\(926\) | 14.5254 | − | 25.1587i | 0.477333 | − | 0.826765i | ||||
\(927\) | −13.8023 | − | 23.9063i | −0.453327 | − | 0.785186i | ||||
\(928\) | 17.4665 | 0.573366 | ||||||||
\(929\) | 2.30231 | + | 3.98772i | 0.0755364 | + | 0.130833i | 0.901319 | − | 0.433155i | \(-0.142600\pi\) |
−0.825783 | + | 0.563988i | \(0.809266\pi\) | |||||||
\(930\) | −22.2012 | − | 38.4536i | −0.728006 | − | 1.26094i | ||||
\(931\) | 13.8673 | 0.454484 | ||||||||
\(932\) | 0.146053 | + | 0.252971i | 0.00478412 | + | 0.00828634i | ||||
\(933\) | −32.3299 | + | 55.9970i | −1.05843 | + | 1.83326i | ||||
\(934\) | 3.73995 | − | 6.47779i | 0.122375 | − | 0.211960i | ||||
\(935\) | −4.54051 | −0.148491 | ||||||||
\(936\) | −5.20269 | + | 22.2861i | −0.170055 | + | 0.728444i | ||||
\(937\) | −54.9002 | −1.79351 | −0.896756 | − | 0.442525i | \(-0.854083\pi\) | ||||
−0.896756 | + | 0.442525i | \(0.854083\pi\) | |||||||
\(938\) | −6.80628 | + | 11.7888i | −0.222233 | + | 0.384919i | ||||
\(939\) | 25.3259 | − | 43.8658i | 0.826480 | − | 1.43151i | ||||
\(940\) | −2.08369 | − | 3.60906i | −0.0679625 | − | 0.117715i | ||||
\(941\) | −0.292106 | −0.00952237 | −0.00476119 | − | 0.999989i | \(-0.501516\pi\) | ||||
−0.00476119 | + | 0.999989i | \(0.501516\pi\) | |||||||
\(942\) | −27.1950 | − | 47.1031i | −0.886061 | − | 1.53470i | ||||
\(943\) | −22.6563 | − | 39.2418i | −0.737789 | − | 1.27789i | ||||
\(944\) | 6.03030 | 0.196270 | ||||||||
\(945\) | −7.14605 | − | 12.3773i | −0.232461 | − | 0.402634i | ||||
\(946\) | −1.26180 | + | 2.18551i | −0.0410247 | + | 0.0710569i | ||||
\(947\) | 2.23150 | − | 3.86507i | 0.0725140 | − | 0.125598i | −0.827489 | − | 0.561483i | \(-0.810231\pi\) |
0.900002 | + | 0.435885i | \(0.143564\pi\) | |||||||
\(948\) | 3.77643 | 0.122653 | ||||||||
\(949\) | 28.5204 | + | 26.7266i | 0.925812 | + | 0.867584i | ||||
\(950\) | −1.64729 | −0.0534451 | ||||||||
\(951\) | −29.7096 | + | 51.4586i | −0.963401 | + | 1.66866i | ||||
\(952\) | −10.8726 | + | 18.8319i | −0.352383 | + | 0.610346i | ||||
\(953\) | 20.2405 | + | 35.0575i | 0.655653 | + | 1.13562i | 0.981730 | + | 0.190281i | \(0.0609400\pi\) |
−0.326076 | + | 0.945343i | \(0.605727\pi\) | |||||||
\(954\) | 16.4079 | 0.531224 | ||||||||
\(955\) | −19.0097 | − | 32.9257i | −0.615139 | − | 1.06545i | ||||
\(956\) | −10.9012 | − | 18.8814i | −0.352569 | − | 0.610667i | ||||
\(957\) | −7.90116 | −0.255408 | ||||||||
\(958\) | −4.31122 | − | 7.46726i | −0.139289 | − | 0.241256i | ||||
\(959\) | 25.5045 | − | 44.1751i | 0.823583 | − | 1.42649i | ||||
\(960\) | 16.7489 | − | 29.0100i | 0.540569 | − | 0.936293i | ||||
\(961\) | 55.0944 | 1.77724 | ||||||||
\(962\) | −7.51067 | + | 32.1725i | −0.242154 | + | 1.03728i | ||||
\(963\) | −28.7933 | −0.927852 | ||||||||
\(964\) | −1.27422 | + | 2.20702i | −0.0410399 | + | 0.0710832i | ||||
\(965\) | 3.14157 | − | 5.44135i | 0.101131 | − | 0.175163i | ||||
\(966\) | 17.2787 | + | 29.9276i | 0.555933 | + | 0.962905i | ||||
\(967\) | −1.00897 | −0.0324464 | −0.0162232 | − | 0.999868i | \(-0.505164\pi\) | ||||
−0.0162232 | + | 0.999868i | \(0.505164\pi\) | |||||||
\(968\) | 1.50000 | + | 2.59808i | 0.0482118 | + | 0.0835053i | ||||
\(969\) | −7.63539 | − | 13.2249i | −0.245284 | − | 0.424844i | ||||
\(970\) | 24.6260 | 0.790692 | ||||||||
\(971\) | −12.9332 | − | 22.4010i | −0.415047 | − | 0.718882i | 0.580387 | − | 0.814341i | \(-0.302901\pi\) |
−0.995433 | + | 0.0954592i | \(0.969568\pi\) | |||||||
\(972\) | 9.29386 | − | 16.0974i | 0.298101 | − | 0.516326i | ||||
\(973\) | 25.8023 | − | 44.6909i | 0.827184 | − | 1.43272i | ||||
\(974\) | 8.09091 | 0.259249 | ||||||||
\(975\) | −4.08648 | + | 1.23842i | −0.130872 | + | 0.0396613i | ||||
\(976\) | −9.78541 | −0.313223 | ||||||||
\(977\) | 21.6838 | − | 37.5575i | 0.693727 | − | 1.20157i | −0.276881 | − | 0.960904i | \(-0.589301\pi\) |
0.970608 | − | 0.240666i | \(-0.0773660\pi\) | |||||||
\(978\) | −7.41182 | + | 12.8377i | −0.237004 | + | 0.410503i | ||||
\(979\) | −4.67362 | − | 8.09495i | −0.149370 | − | 0.258716i | ||||
\(980\) | −9.32592 | −0.297905 | ||||||||
\(981\) | −19.7680 | − | 34.2393i | −0.631145 | − | 1.09318i | ||||
\(982\) | −2.31122 | − | 4.00316i | −0.0737541 | − | 0.127746i | ||||
\(983\) | −17.0472 | −0.543722 | −0.271861 | − | 0.962337i | \(-0.587639\pi\) | ||||
−0.271861 | + | 0.962337i | \(0.587639\pi\) | |||||||
\(984\) | −33.9844 | − | 58.8627i | −1.08338 | − | 1.87647i | ||||
\(985\) | −12.9394 | + | 22.4117i | −0.412283 | + | 0.714096i | ||||
\(986\) | 3.74840 | − | 6.49243i | 0.119374 | − | 0.206761i | ||||
\(987\) | 15.0472 | 0.478958 | ||||||||
\(988\) | 10.8557 | − | 3.28986i | 0.345366 | − | 0.104664i | ||||
\(989\) | 11.4158 | 0.363001 | ||||||||
\(990\) | −2.23820 | + | 3.87667i | −0.0711346 | + | 0.123209i | ||||
\(991\) | 20.0490 | − | 34.7258i | 0.636876 | − | 1.10310i | −0.349238 | − | 0.937034i | \(-0.613560\pi\) |
0.986114 | − | 0.166068i | \(-0.0531071\pi\) | |||||||
\(992\) | 23.1968 | + | 40.1780i | 0.736498 | + | 1.27565i | ||||
\(993\) | 18.7551 | 0.595175 | ||||||||
\(994\) | −10.1327 | − | 17.5503i | −0.321388 | − | 0.556661i | ||||
\(995\) | 0.212839 | + | 0.368649i | 0.00674746 | + | 0.0116870i | ||||
\(996\) | 12.8236 | 0.406333 | ||||||||
\(997\) | 27.0214 | + | 46.8024i | 0.855776 | + | 1.48225i | 0.875923 | + | 0.482451i | \(0.160253\pi\) |
−0.0201471 | + | 0.999797i | \(0.506413\pi\) | |||||||
\(998\) | −19.7569 | + | 34.2199i | −0.625392 | + | 1.08321i | ||||
\(999\) | 9.16296 | − | 15.8707i | 0.289903 | − | 0.502127i |
(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 | 143.2.e.a.100.3 | ✓ | 6 | |
13.3 | even | 3 | inner | 143.2.e.a.133.3 | yes | 6 | |
13.4 | even | 6 | 1859.2.a.e.1.1 | 3 | |||
13.9 | even | 3 | 1859.2.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.a.100.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
143.2.e.a.133.3 | yes | 6 | 13.3 | even | 3 | inner | |
1859.2.a.e.1.1 | 3 | 13.4 | even | 6 | |||
1859.2.a.h.1.1 | 3 | 13.9 | even | 3 |