Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(451,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("975.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.i (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: | \(7.78541419707\) |
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: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 451.3 | ||
Root | \(0.500000 + 0.385124i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.451 |
Dual form | 975.2.i.l.601.3 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30084 | − | 2.25312i | 0.919832 | − | 1.59320i | 0.120165 | − | 0.992754i | \(-0.461658\pi\) |
0.799668 | − | 0.600443i | \(-0.205009\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −2.38437 | − | 4.12985i | −1.19218 | − | 2.06492i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.30084 | + | 2.25312i | 0.531066 | + | 0.919832i | ||||
\(7\) | 1.80084 | + | 3.11915i | 0.680653 | + | 1.17893i | 0.974782 | + | 0.223160i | \(0.0716373\pi\) |
−0.294128 | + | 0.955766i | \(0.595029\pi\) | |||||||
\(8\) | −7.20336 | −2.54677 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.60168 | − | 4.50624i | 0.784436 | − | 1.35868i | −0.144900 | − | 0.989446i | \(-0.546286\pi\) |
0.929336 | − | 0.369236i | \(-0.120381\pi\) | |||||||
\(12\) | 4.76873 | 1.37662 | ||||||||
\(13\) | −3.01815 | − | 1.97250i | −0.837085 | − | 0.547073i | ||||
\(14\) | 9.37041 | 2.50435 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.60168 | + | 7.97034i | −1.15042 | + | 1.99259i | ||||
\(17\) | −1.46789 | − | 2.54247i | −0.356017 | − | 0.616639i | 0.631275 | − | 0.775559i | \(-0.282532\pi\) |
−0.987291 | + | 0.158920i | \(0.949199\pi\) | |||||||
\(18\) | −2.60168 | −0.613222 | ||||||||
\(19\) | −3.38437 | − | 5.86190i | −0.776427 | − | 1.34481i | −0.933989 | − | 0.357302i | \(-0.883697\pi\) |
0.157562 | − | 0.987509i | \(-0.449637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.60168 | −0.785951 | ||||||||
\(22\) | −6.76873 | − | 11.7238i | −1.44310 | − | 2.49952i | ||||
\(23\) | 2.76873 | − | 4.79559i | 0.577321 | − | 0.999949i | −0.418464 | − | 0.908233i | \(-0.637431\pi\) |
0.995785 | − | 0.0917160i | \(-0.0292352\pi\) | |||||||
\(24\) | 3.60168 | − | 6.23829i | 0.735190 | − | 1.27339i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.37041 | + | 4.23435i | −1.64157 | + | 0.830424i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 8.58773 | − | 14.8744i | 1.62293 | − | 2.81099i | ||||
\(29\) | −0.916472 | + | 1.58738i | −0.170185 | + | 0.294768i | −0.938484 | − | 0.345322i | \(-0.887770\pi\) |
0.768300 | + | 0.640090i | \(0.221103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.10284 | 0.736893 | 0.368446 | − | 0.929649i | \(-0.379890\pi\) | ||||
0.368446 | + | 0.929649i | \(0.379890\pi\) | |||||||
\(32\) | 4.76873 | + | 8.25969i | 0.843001 | + | 1.46012i | ||||
\(33\) | 2.60168 | + | 4.50624i | 0.452894 | + | 0.784436i | ||||
\(34\) | −7.63798 | −1.30990 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.38437 | + | 4.12985i | −0.397395 | + | 0.688308i | ||||
\(37\) | −1.76873 | + | 3.06354i | −0.290778 | + | 0.503642i | −0.973994 | − | 0.226574i | \(-0.927247\pi\) |
0.683216 | + | 0.730217i | \(0.260581\pi\) | |||||||
\(38\) | −17.6101 | −2.85673 | ||||||||
\(39\) | 3.21731 | − | 1.62755i | 0.515182 | − | 0.260616i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68521 | − | 4.65091i | 0.419359 | − | 0.726351i | −0.576516 | − | 0.817086i | \(-0.695588\pi\) |
0.995875 | + | 0.0907349i | \(0.0289216\pi\) | |||||||
\(42\) | −4.68521 | + | 8.11502i | −0.722943 | + | 1.25217i | ||||
\(43\) | 1.58353 | + | 2.74275i | 0.241486 | + | 0.418265i | 0.961138 | − | 0.276069i | \(-0.0890320\pi\) |
−0.719652 | + | 0.694335i | \(0.755699\pi\) | |||||||
\(44\) | −24.8134 | −3.74077 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.20336 | − | 12.4766i | −1.06208 | − | 1.83957i | ||||
\(47\) | −3.80504 | −0.555022 | −0.277511 | − | 0.960722i | \(-0.589509\pi\) | ||||
−0.277511 | + | 0.960722i | \(0.589509\pi\) | |||||||
\(48\) | −4.60168 | − | 7.97034i | −0.664195 | − | 1.15042i | ||||
\(49\) | −2.98605 | + | 5.17198i | −0.426578 | + | 0.738855i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.93579 | 0.411093 | ||||||||
\(52\) | −0.949743 | + | 17.1677i | −0.131706 | + | 2.38073i | ||||
\(53\) | 5.20336 | 0.714736 | 0.357368 | − | 0.933964i | \(-0.383674\pi\) | ||||
0.357368 | + | 0.933964i | \(0.383674\pi\) | |||||||
\(54\) | 1.30084 | − | 2.25312i | 0.177022 | − | 0.306611i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.9721 | − | 22.4683i | −1.73347 | − | 3.00246i | ||||
\(57\) | 6.76873 | 0.896541 | ||||||||
\(58\) | 2.38437 | + | 4.12985i | 0.313083 | + | 0.542275i | ||||
\(59\) | 3.68521 | + | 6.38297i | 0.479773 | + | 0.830991i | 0.999731 | − | 0.0232007i | \(-0.00738566\pi\) |
−0.519958 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.71731 | + | 2.97447i | 0.219879 | + | 0.380842i | 0.954771 | − | 0.297343i | \(-0.0961003\pi\) |
−0.734892 | + | 0.678185i | \(0.762767\pi\) | |||||||
\(62\) | 5.33714 | − | 9.24420i | 0.677818 | − | 1.17401i | ||||
\(63\) | 1.80084 | − | 3.11915i | 0.226884 | − | 0.392975i | ||||
\(64\) | 6.40672 | 0.800840 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.5375 | 1.66635 | ||||||||
\(67\) | 1.75058 | − | 3.03210i | 0.213868 | − | 0.370430i | −0.739054 | − | 0.673646i | \(-0.764727\pi\) |
0.952922 | + | 0.303216i | \(0.0980605\pi\) | |||||||
\(68\) | −7.00000 | + | 12.1244i | −0.848875 | + | 1.47029i | ||||
\(69\) | 2.76873 | + | 4.79559i | 0.333316 | + | 0.577321i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.85226 | + | 8.40436i | 0.575858 | + | 0.997415i | 0.995948 | + | 0.0899322i | \(0.0286650\pi\) |
−0.420090 | + | 0.907482i | \(0.638002\pi\) | |||||||
\(72\) | 3.60168 | + | 6.23829i | 0.424462 | + | 0.735190i | ||||
\(73\) | 0.805037 | 0.0942225 | 0.0471113 | − | 0.998890i | \(-0.484998\pi\) | ||||
0.0471113 | + | 0.998890i | \(0.484998\pi\) | |||||||
\(74\) | 4.60168 | + | 7.97034i | 0.534934 | + | 0.926533i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.1391 | + | 27.9538i | −1.85129 | + | 3.20652i | ||||
\(77\) | 18.7408 | 2.13572 | ||||||||
\(78\) | 0.518152 | − | 9.36617i | 0.0586691 | − | 1.06051i | ||||
\(79\) | −4.10284 | −0.461606 | −0.230803 | − | 0.973000i | \(-0.574135\pi\) | ||||
−0.230803 | + | 0.973000i | \(0.574135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.98605 | − | 12.1002i | −0.771480 | − | 1.33624i | ||||
\(83\) | 11.5375 | 1.26640 | 0.633201 | − | 0.773988i | \(-0.281741\pi\) | ||||
0.633201 | + | 0.773988i | \(0.281741\pi\) | |||||||
\(84\) | 8.58773 | + | 14.8744i | 0.936998 | + | 1.62293i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.23966 | 0.888506 | ||||||||
\(87\) | −0.916472 | − | 1.58738i | −0.0982562 | − | 0.170185i | ||||
\(88\) | −18.7408 | + | 32.4601i | −1.99778 | + | 3.46025i | ||||
\(89\) | −4.91647 | + | 8.51558i | −0.521145 | + | 0.902650i | 0.478553 | + | 0.878059i | \(0.341162\pi\) |
−0.999698 | + | 0.0245908i | \(0.992172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.717312 | − | 12.9662i | 0.0751947 | − | 1.35923i | ||||
\(92\) | −26.4067 | −2.75309 | ||||||||
\(93\) | −2.05142 | + | 3.55317i | −0.212723 | + | 0.368446i | ||||
\(94\) | −4.94974 | + | 8.57321i | −0.510527 | + | 0.884259i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.53747 | −0.973414 | ||||||||
\(97\) | −2.78689 | − | 4.82703i | −0.282965 | − | 0.490110i | 0.689148 | − | 0.724620i | \(-0.257985\pi\) |
−0.972114 | + | 0.234510i | \(0.924651\pi\) | |||||||
\(98\) | 7.76873 | + | 13.4558i | 0.784761 | + | 1.35925i | ||||
\(99\) | −5.20336 | −0.522957 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.20336 | + | 2.08428i | −0.119739 | + | 0.207393i | −0.919664 | − | 0.392706i | \(-0.871539\pi\) |
0.799925 | + | 0.600099i | \(0.204872\pi\) | |||||||
\(102\) | 3.81899 | − | 6.61469i | 0.378136 | − | 0.654952i | ||||
\(103\) | −18.4430 | −1.81724 | −0.908622 | − | 0.417619i | \(-0.862865\pi\) | ||||
−0.908622 | + | 0.417619i | \(0.862865\pi\) | |||||||
\(104\) | 21.7408 | + | 14.2086i | 2.13186 | + | 1.39327i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.76873 | − | 11.7238i | 0.657438 | − | 1.13872i | ||||
\(107\) | 5.46789 | − | 9.47067i | 0.528601 | − | 0.915564i | −0.470842 | − | 0.882217i | \(-0.656050\pi\) |
0.999444 | − | 0.0333471i | \(-0.0106167\pi\) | |||||||
\(108\) | −2.38437 | − | 4.12985i | −0.229436 | − | 0.397395i | ||||
\(109\) | 13.8692 | 1.32843 | 0.664217 | − | 0.747540i | \(-0.268765\pi\) | ||||
0.664217 | + | 0.747540i | \(0.268765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.76873 | − | 3.06354i | −0.167881 | − | 0.290778i | ||||
\(112\) | −33.1475 | −3.13215 | ||||||||
\(113\) | −5.60168 | − | 9.70239i | −0.526962 | − | 0.912724i | −0.999506 | − | 0.0314176i | \(-0.989998\pi\) |
0.472545 | − | 0.881307i | \(-0.343336\pi\) | |||||||
\(114\) | 8.80504 | − | 15.2508i | 0.824667 | − | 1.42837i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.74083 | 0.811565 | ||||||||
\(117\) | −0.199160 | + | 3.60005i | −0.0184124 | + | 0.332824i | ||||
\(118\) | 19.1755 | 1.76524 | ||||||||
\(119\) | 5.28689 | − | 9.15715i | 0.484648 | − | 0.839435i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.03747 | − | 13.9213i | −0.730679 | − | 1.26557i | ||||
\(122\) | 8.93579 | 0.809008 | ||||||||
\(123\) | 2.68521 | + | 4.65091i | 0.242117 | + | 0.419359i | ||||
\(124\) | −9.78269 | − | 16.9441i | −0.878511 | − | 1.52163i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.68521 | − | 8.11502i | −0.417391 | − | 0.722943i | ||||
\(127\) | −1.59748 | + | 2.76692i | −0.141754 | + | 0.245524i | −0.928157 | − | 0.372189i | \(-0.878607\pi\) |
0.786403 | + | 0.617713i | \(0.211941\pi\) | |||||||
\(128\) | −1.20336 | + | 2.08428i | −0.106363 | + | 0.184226i | ||||
\(129\) | −3.16706 | −0.278844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.57377 | −0.399612 | −0.199806 | − | 0.979835i | \(-0.564031\pi\) | ||||
−0.199806 | + | 0.979835i | \(0.564031\pi\) | |||||||
\(132\) | 12.4067 | − | 21.4891i | 1.07987 | − | 1.87038i | ||||
\(133\) | 12.1894 | − | 21.1127i | 1.05696 | − | 1.83070i | ||||
\(134\) | −4.55445 | − | 7.88855i | −0.393445 | − | 0.681467i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.5738 | + | 18.3143i | 0.906693 | + | 1.57044i | ||||
\(137\) | 5.33714 | + | 9.24420i | 0.455983 | + | 0.789785i | 0.998744 | − | 0.0501015i | \(-0.0159545\pi\) |
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(138\) | 14.4067 | 1.22638 | ||||||||
\(139\) | 8.07377 | + | 13.9842i | 0.684808 | + | 1.18612i | 0.973497 | + | 0.228700i | \(0.0734474\pi\) |
−0.288689 | + | 0.957423i | \(0.593219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.90252 | − | 3.29526i | 0.160221 | − | 0.277511i | ||||
\(142\) | 25.2481 | 2.11877 | ||||||||
\(143\) | −16.7408 | + | 8.46870i | −1.39994 | + | 0.708188i | ||||
\(144\) | 9.20336 | 0.766947 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.04722 | − | 1.81385i | 0.0866689 | − | 0.150115i | ||||
\(147\) | −2.98605 | − | 5.17198i | −0.246285 | − | 0.426578i | ||||
\(148\) | 16.8692 | 1.38664 | ||||||||
\(149\) | 4.83294 | + | 8.37091i | 0.395930 | + | 0.685771i | 0.993219 | − | 0.116255i | \(-0.0370889\pi\) |
−0.597289 | + | 0.802026i | \(0.703756\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7129 | −1.52284 | −0.761418 | − | 0.648261i | \(-0.775496\pi\) | ||||
−0.761418 | + | 0.648261i | \(0.775496\pi\) | |||||||
\(152\) | 24.3788 | + | 42.2253i | 1.97738 | + | 3.42493i | ||||
\(153\) | −1.46789 | + | 2.54247i | −0.118672 | + | 0.205546i | ||||
\(154\) | 24.3788 | − | 42.2253i | 1.96450 | − | 3.40261i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.3928 | − | 9.40633i | −1.15234 | − | 0.753109i | ||||
\(157\) | 10.3704 | 0.827649 | 0.413825 | − | 0.910357i | \(-0.364193\pi\) | ||||
0.413825 | + | 0.910357i | \(0.364193\pi\) | |||||||
\(158\) | −5.33714 | + | 9.24420i | −0.424600 | + | 0.735429i | ||||
\(159\) | −2.60168 | + | 4.50624i | −0.206327 | + | 0.357368i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.9442 | 1.57182 | ||||||||
\(162\) | 1.30084 | + | 2.25312i | 0.102204 | + | 0.177022i | ||||
\(163\) | −5.73663 | − | 9.93613i | −0.449327 | − | 0.778258i | 0.549015 | − | 0.835813i | \(-0.315003\pi\) |
−0.998342 | + | 0.0575546i | \(0.981670\pi\) | |||||||
\(164\) | −25.6101 | −1.99981 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0084 | − | 25.9953i | 1.16488 | − | 2.01763i | ||||
\(167\) | −1.56538 | + | 2.71131i | −0.121132 | + | 0.209808i | −0.920215 | − | 0.391414i | \(-0.871986\pi\) |
0.799082 | + | 0.601222i | \(0.205319\pi\) | |||||||
\(168\) | 25.9442 | 2.00164 | ||||||||
\(169\) | 5.21848 | + | 11.9066i | 0.401421 | + | 0.915893i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.38437 | + | 5.86190i | −0.258809 | + | 0.448270i | ||||
\(172\) | 7.55142 | − | 13.0794i | 0.575791 | − | 0.997298i | ||||
\(173\) | 4.13378 | + | 7.15992i | 0.314286 | + | 0.544359i | 0.979285 | − | 0.202485i | \(-0.0649016\pi\) |
−0.665000 | + | 0.746844i | \(0.731568\pi\) | |||||||
\(174\) | −4.76873 | −0.361517 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.9442 | + | 41.4725i | 1.80486 | + | 3.12611i | ||||
\(177\) | −7.37041 | −0.553994 | ||||||||
\(178\) | 12.7911 | + | 22.1548i | 0.958732 | + | 1.66057i | ||||
\(179\) | 9.22268 | − | 15.9741i | 0.689335 | − | 1.19396i | −0.282718 | − | 0.959203i | \(-0.591236\pi\) |
0.972053 | − | 0.234760i | \(-0.0754306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1028 | 1.56856 | 0.784281 | − | 0.620406i | \(-0.213032\pi\) | ||||
0.784281 | + | 0.620406i | \(0.213032\pi\) | |||||||
\(182\) | −28.2813 | − | 18.4832i | −2.09635 | − | 1.37006i | ||||
\(183\) | −3.43462 | −0.253895 | ||||||||
\(184\) | −19.9442 | + | 34.5443i | −1.47030 | + | 2.54664i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.33714 | + | 9.24420i | 0.391338 | + | 0.677818i | ||||
\(187\) | −15.2760 | −1.11709 | ||||||||
\(188\) | 9.07261 | + | 15.7142i | 0.661688 | + | 1.14608i | ||||
\(189\) | 1.80084 | + | 3.11915i | 0.130992 | + | 0.226884i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.35110 | + | 7.53632i | 0.314834 | + | 0.545309i | 0.979402 | − | 0.201919i | \(-0.0647177\pi\) |
−0.664568 | + | 0.747228i | \(0.731384\pi\) | |||||||
\(192\) | −3.20336 | + | 5.54838i | −0.231182 | + | 0.400420i | ||||
\(193\) | 9.63378 | − | 16.6862i | 0.693455 | − | 1.20110i | −0.277244 | − | 0.960800i | \(-0.589421\pi\) |
0.970699 | − | 0.240300i | \(-0.0772457\pi\) | |||||||
\(194\) | −14.5012 | −1.04112 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.4793 | 2.03424 | ||||||||
\(197\) | −7.57377 | + | 13.1182i | −0.539609 | + | 0.934630i | 0.459316 | + | 0.888273i | \(0.348095\pi\) |
−0.998925 | + | 0.0463571i | \(0.985239\pi\) | |||||||
\(198\) | −6.76873 | + | 11.7238i | −0.481033 | + | 0.833174i | ||||
\(199\) | 2.26873 | + | 3.92956i | 0.160826 | + | 0.278559i | 0.935165 | − | 0.354212i | \(-0.115251\pi\) |
−0.774339 | + | 0.632771i | \(0.781917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.75058 | + | 3.03210i | 0.123477 | + | 0.213868i | ||||
\(202\) | 3.13075 | + | 5.42262i | 0.220279 | + | 0.381534i | ||||
\(203\) | −6.60168 | −0.463347 | ||||||||
\(204\) | −7.00000 | − | 12.1244i | −0.490098 | − | 0.848875i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.9914 | + | 41.5543i | −1.67156 | + | 2.89523i | ||||
\(207\) | −5.53747 | −0.384881 | ||||||||
\(208\) | 29.6101 | − | 14.9789i | 2.05309 | − | 1.03860i | ||||
\(209\) | −35.2201 | −2.43623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0738 | − | 19.1803i | 0.762350 | − | 1.32043i | −0.179286 | − | 0.983797i | \(-0.557379\pi\) |
0.941636 | − | 0.336632i | \(-0.109288\pi\) | |||||||
\(212\) | −12.4067 | − | 21.4891i | −0.852097 | − | 1.47587i | ||||
\(213\) | −9.70452 | −0.664943 | ||||||||
\(214\) | −14.2257 | − | 24.6396i | −0.972449 | − | 1.68433i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.20336 | −0.490126 | ||||||||
\(217\) | 7.38856 | + | 12.7974i | 0.501568 | + | 0.868742i | ||||
\(218\) | 18.0417 | − | 31.2491i | 1.22194 | − | 2.11645i | ||||
\(219\) | −0.402519 | + | 0.697183i | −0.0271997 | + | 0.0471113i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.584693 | + | 10.5690i | −0.0393307 | + | 0.710946i | ||||
\(222\) | −9.20336 | −0.617689 | ||||||||
\(223\) | −3.80504 | + | 6.59052i | −0.254804 | + | 0.441334i | −0.964842 | − | 0.262829i | \(-0.915344\pi\) |
0.710038 | + | 0.704163i | \(0.248678\pi\) | |||||||
\(224\) | −17.1755 | + | 29.7488i | −1.14758 | + | 1.98767i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.1475 | −1.93887 | ||||||||
\(227\) | 11.6713 | + | 20.2152i | 0.774648 | + | 1.34173i | 0.934992 | + | 0.354669i | \(0.115406\pi\) |
−0.160344 | + | 0.987061i | \(0.551260\pi\) | |||||||
\(228\) | −16.1391 | − | 27.9538i | −1.06884 | − | 1.85129i | ||||
\(229\) | 0.824549 | 0.0544877 | 0.0272439 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272439 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.37041 | + | 16.2300i | −0.616528 | + | 1.06786i | ||||
\(232\) | 6.60168 | − | 11.4344i | 0.433421 | − | 0.750708i | ||||
\(233\) | 13.4044 | 0.878150 | 0.439075 | − | 0.898450i | \(-0.355306\pi\) | ||||
0.439075 | + | 0.898450i | \(0.355306\pi\) | |||||||
\(234\) | 7.85226 | + | 5.13182i | 0.513318 | + | 0.335477i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 17.5738 | − | 30.4387i | 1.14396 | − | 1.98139i | ||||
\(237\) | 2.05142 | − | 3.55317i | 0.133254 | − | 0.230803i | ||||
\(238\) | −13.7548 | − | 23.8240i | −0.891590 | − | 1.54428i | ||||
\(239\) | 12.7966 | 0.827746 | 0.413873 | − | 0.910335i | \(-0.364176\pi\) | ||||
0.413873 | + | 0.910335i | \(0.364176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.38437 | − | 11.0580i | −0.411253 | − | 0.712312i | 0.583774 | − | 0.811916i | \(-0.301575\pi\) |
−0.995027 | + | 0.0996048i | \(0.968242\pi\) | |||||||
\(242\) | −41.8218 | −2.68841 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 8.18940 | − | 14.1845i | 0.524273 | − | 0.908067i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.9721 | 0.890828 | ||||||||
\(247\) | −1.34806 | + | 24.3678i | −0.0857753 | + | 1.55048i | ||||
\(248\) | −29.5543 | −1.87670 | ||||||||
\(249\) | −5.76873 | + | 9.99174i | −0.365579 | + | 0.633201i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.20336 | + | 7.28043i | 0.265314 | + | 0.459537i | 0.967646 | − | 0.252313i | \(-0.0811912\pi\) |
−0.702332 | + | 0.711849i | \(0.747858\pi\) | |||||||
\(252\) | −17.1755 | −1.08195 | ||||||||
\(253\) | −14.4067 | − | 24.9532i | −0.905743 | − | 1.56879i | ||||
\(254\) | 4.15613 | + | 7.19863i | 0.260779 | + | 0.451683i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.53747 | + | 16.5194i | 0.596092 | + | 1.03246i | ||||
\(257\) | 3.06957 | − | 5.31666i | 0.191475 | − | 0.331644i | −0.754264 | − | 0.656571i | \(-0.772006\pi\) |
0.945739 | + | 0.324927i | \(0.105340\pi\) | |||||||
\(258\) | −4.11983 | + | 7.13576i | −0.256489 | + | 0.444253i | ||||
\(259\) | −12.7408 | −0.791676 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83294 | 0.113456 | ||||||||
\(262\) | −5.94974 | + | 10.3053i | −0.367576 | + | 0.636661i | ||||
\(263\) | −2.36505 | + | 4.09639i | −0.145835 | + | 0.252594i | −0.929684 | − | 0.368357i | \(-0.879920\pi\) |
0.783849 | + | 0.620951i | \(0.213254\pi\) | |||||||
\(264\) | −18.7408 | − | 32.4601i | −1.15342 | − | 1.99778i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −31.7129 | − | 54.9284i | −1.94444 | − | 3.36788i | ||||
\(267\) | −4.91647 | − | 8.51558i | −0.300883 | − | 0.521145i | ||||
\(268\) | −16.6961 | −1.01988 | ||||||||
\(269\) | 2.72151 | + | 4.71379i | 0.165933 | + | 0.287405i | 0.936986 | − | 0.349366i | \(-0.113603\pi\) |
−0.771053 | + | 0.636771i | \(0.780270\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7397 | + | 22.0657i | −0.773879 | + | 1.34040i | 0.161543 | + | 0.986866i | \(0.448353\pi\) |
−0.935422 | + | 0.353533i | \(0.884980\pi\) | |||||||
\(272\) | 27.0191 | 1.63827 | ||||||||
\(273\) | 10.8704 | + | 7.10432i | 0.657907 | + | 0.429973i | ||||
\(274\) | 27.7711 | 1.67771 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.2034 | − | 22.8689i | 0.794749 | − | 1.37655i | ||||
\(277\) | −11.4067 | − | 19.7570i | −0.685363 | − | 1.18708i | −0.973323 | − | 0.229441i | \(-0.926310\pi\) |
0.287959 | − | 0.957643i | \(-0.407023\pi\) | |||||||
\(278\) | 42.0107 | 2.51964 | ||||||||
\(279\) | −2.05142 | − | 3.55317i | −0.122815 | − | 0.212723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.16706 | −0.129276 | −0.0646378 | − | 0.997909i | \(-0.520589\pi\) | ||||
−0.0646378 | + | 0.997909i | \(0.520589\pi\) | |||||||
\(282\) | −4.94974 | − | 8.57321i | −0.294753 | − | 0.510527i | ||||
\(283\) | −14.8734 | + | 25.7616i | −0.884135 | + | 1.53137i | −0.0374322 | + | 0.999299i | \(0.511918\pi\) |
−0.846702 | + | 0.532067i | \(0.821416\pi\) | |||||||
\(284\) | 23.1391 | − | 40.0782i | 1.37306 | − | 2.37820i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.69613 | + | 48.7355i | −0.159425 | + | 2.88179i | ||||
\(287\) | 19.3425 | 1.14175 | ||||||||
\(288\) | 4.76873 | − | 8.25969i | 0.281000 | − | 0.486707i | ||||
\(289\) | 4.19057 | − | 7.25828i | 0.246504 | − | 0.426958i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.57377 | 0.326740 | ||||||||
\(292\) | −1.91950 | − | 3.32468i | −0.112331 | − | 0.194562i | ||||
\(293\) | 16.5428 | + | 28.6530i | 0.966443 | + | 1.67393i | 0.705688 | + | 0.708522i | \(0.250638\pi\) |
0.260754 | + | 0.965405i | \(0.416029\pi\) | |||||||
\(294\) | −15.5375 | −0.906164 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.7408 | − | 22.0678i | 0.740546 | − | 1.28266i | ||||
\(297\) | 2.60168 | − | 4.50624i | 0.150965 | − | 0.261479i | ||||
\(298\) | 25.1475 | 1.45676 | ||||||||
\(299\) | −17.8158 | + | 9.01248i | −1.03031 | + | 0.521205i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.70336 | + | 9.87851i | −0.328736 | + | 0.569388i | ||||
\(302\) | −24.3425 | + | 42.1625i | −1.40075 | + | 2.42618i | ||||
\(303\) | −1.20336 | − | 2.08428i | −0.0691311 | − | 0.119739i | ||||
\(304\) | 62.2951 | 3.57287 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.81899 | + | 6.61469i | 0.218317 | + | 0.378136i | ||||
\(307\) | 14.3704 | 0.820163 | 0.410081 | − | 0.912049i | \(-0.365500\pi\) | ||||
0.410081 | + | 0.912049i | \(0.365500\pi\) | |||||||
\(308\) | −44.6850 | − | 77.3967i | −2.54616 | − | 4.41009i | ||||
\(309\) | 9.22151 | − | 15.9721i | 0.524593 | − | 0.908622i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.70685 | −0.493720 | −0.246860 | − | 0.969051i | \(-0.579399\pi\) | ||||
−0.246860 | + | 0.969051i | \(0.579399\pi\) | |||||||
\(312\) | −23.1755 | + | 11.7238i | −1.31205 | + | 0.663729i | ||||
\(313\) | 8.16472 | 0.461497 | 0.230749 | − | 0.973013i | \(-0.425882\pi\) | ||||
0.230749 | + | 0.973013i | \(0.425882\pi\) | |||||||
\(314\) | 13.4902 | − | 23.3658i | 0.761299 | − | 1.31861i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.78269 | + | 16.9441i | 0.550319 | + | 0.953181i | ||||
\(317\) | −13.4090 | −0.753127 | −0.376564 | − | 0.926391i | \(-0.622894\pi\) | ||||
−0.376564 | + | 0.926391i | \(0.622894\pi\) | |||||||
\(318\) | 6.76873 | + | 11.7238i | 0.379572 | + | 0.657438i | ||||
\(319\) | 4.76873 | + | 8.25969i | 0.266998 | + | 0.462454i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.46789 | + | 9.47067i | 0.305188 | + | 0.528601i | ||||
\(322\) | 25.9442 | − | 44.9366i | 1.44581 | − | 2.50422i | ||||
\(323\) | −9.93579 | + | 17.2093i | −0.552842 | + | 0.957551i | ||||
\(324\) | 4.76873 | 0.264930 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.8497 | −1.65322 | ||||||||
\(327\) | −6.93462 | + | 12.0111i | −0.383486 | + | 0.664217i | ||||
\(328\) | −19.3425 | + | 33.5022i | −1.06801 | + | 1.84985i | ||||
\(329\) | −6.85226 | − | 11.8685i | −0.377777 | − | 0.654330i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7397 | − | 18.6016i | −0.590305 | − | 1.02244i | −0.994191 | − | 0.107629i | \(-0.965674\pi\) |
0.403886 | − | 0.914809i | \(-0.367659\pi\) | |||||||
\(332\) | −27.5096 | − | 47.6480i | −1.50978 | − | 2.61502i | ||||
\(333\) | 3.53747 | 0.193852 | ||||||||
\(334\) | 4.07261 | + | 7.05396i | 0.222843 | + | 0.385976i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.5738 | − | 28.7066i | 0.904173 | − | 1.56607i | ||||
\(337\) | 7.44535 | 0.405574 | 0.202787 | − | 0.979223i | \(-0.435000\pi\) | ||||
0.202787 | + | 0.979223i | \(0.435000\pi\) | |||||||
\(338\) | 33.6154 | + | 3.73074i | 1.82844 | + | 0.202925i | ||||
\(339\) | 11.2034 | 0.608483 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.6743 | − | 18.4884i | 0.578045 | − | 1.00120i | ||||
\(342\) | 8.80504 | + | 15.2508i | 0.476122 | + | 0.824667i | ||||
\(343\) | 3.70219 | 0.199900 | ||||||||
\(344\) | −11.4067 | − | 19.7570i | −0.615009 | − | 1.06523i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.5096 | 1.15636 | ||||||||
\(347\) | −12.4733 | − | 21.6043i | −0.669600 | − | 1.15978i | −0.978016 | − | 0.208529i | \(-0.933132\pi\) |
0.308417 | − | 0.951251i | \(-0.400201\pi\) | |||||||
\(348\) | −4.37041 | + | 7.56978i | −0.234279 | + | 0.405783i | ||||
\(349\) | −1.05142 | + | 1.82112i | −0.0562813 | + | 0.0974822i | −0.892793 | − | 0.450466i | \(-0.851258\pi\) |
0.836512 | + | 0.547949i | \(0.184591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.01815 | − | 1.97250i | −0.161097 | − | 0.105284i | ||||
\(352\) | 49.6269 | 2.64512 | ||||||||
\(353\) | 9.26990 | − | 16.0559i | 0.493387 | − | 0.854571i | −0.506584 | − | 0.862191i | \(-0.669092\pi\) |
0.999971 | + | 0.00761929i | \(0.00242532\pi\) | |||||||
\(354\) | −9.58773 | + | 16.6064i | −0.509582 | + | 0.882622i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 46.8907 | 2.48520 | ||||||||
\(357\) | 5.28689 | + | 9.15715i | 0.279812 | + | 0.484648i | ||||
\(358\) | −23.9944 | − | 41.5596i | −1.26815 | − | 2.19649i | ||||
\(359\) | −4.75801 | −0.251118 | −0.125559 | − | 0.992086i | \(-0.540072\pi\) | ||||
−0.125559 | + | 0.992086i | \(0.540072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4079 | + | 23.2231i | −0.705678 | + | 1.22227i | ||||
\(362\) | 27.4514 | − | 47.5472i | 1.44281 | − | 2.49903i | ||||
\(363\) | 16.0749 | 0.843715 | ||||||||
\(364\) | −55.2588 | + | 27.9538i | −2.89635 | + | 1.46518i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.46789 | + | 7.73862i | −0.233541 | + | 0.404504i | ||||
\(367\) | −5.12100 | + | 8.86983i | −0.267314 | + | 0.463001i | −0.968167 | − | 0.250304i | \(-0.919469\pi\) |
0.700853 | + | 0.713305i | \(0.252803\pi\) | |||||||
\(368\) | 25.4817 | + | 44.1355i | 1.32832 | + | 2.30072i | ||||
\(369\) | −5.37041 | −0.279573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.37041 | + | 16.2300i | 0.486488 | + | 0.842621i | ||||
\(372\) | 19.5654 | 1.01442 | ||||||||
\(373\) | −11.6701 | − | 20.2132i | −0.604254 | − | 1.04660i | −0.992169 | − | 0.124904i | \(-0.960138\pi\) |
0.387915 | − | 0.921695i | \(-0.373196\pi\) | |||||||
\(374\) | −19.8716 | + | 34.4186i | −1.02753 | + | 1.77974i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.4090 | 1.41351 | ||||||||
\(377\) | 5.89716 | − | 2.98320i | 0.303719 | − | 0.153643i | ||||
\(378\) | 9.37041 | 0.481962 | ||||||||
\(379\) | 17.8286 | − | 30.8800i | 0.915791 | − | 1.58620i | 0.110052 | − | 0.993926i | \(-0.464898\pi\) |
0.805739 | − | 0.592271i | \(-0.201769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.59748 | − | 2.76692i | −0.0818414 | − | 0.141754i | ||||
\(382\) | 22.6403 | 1.15838 | ||||||||
\(383\) | −15.3092 | − | 26.5164i | −0.782265 | − | 1.35492i | −0.930619 | − | 0.365989i | \(-0.880731\pi\) |
0.148354 | − | 0.988934i | \(-0.452603\pi\) | |||||||
\(384\) | −1.20336 | − | 2.08428i | −0.0614086 | − | 0.106363i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.0640 | − | 43.4121i | −1.27572 | − | 2.20962i | ||||
\(387\) | 1.58353 | − | 2.74275i | 0.0804952 | − | 0.139422i | ||||
\(388\) | −13.2899 | + | 23.0188i | −0.674693 | + | 1.16860i | ||||
\(389\) | 25.0191 | 1.26852 | 0.634260 | − | 0.773120i | \(-0.281305\pi\) | ||||
0.634260 | + | 0.773120i | \(0.281305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2568 | −0.822144 | ||||||||
\(392\) | 21.5096 | − | 37.2557i | 1.08640 | − | 1.88169i | ||||
\(393\) | 2.28689 | − | 3.96100i | 0.115358 | − | 0.199806i | ||||
\(394\) | 19.7045 | + | 34.1292i | 0.992700 | + | 1.71941i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.4067 | + | 21.4891i | 0.623461 | + | 1.07987i | ||||
\(397\) | 5.41647 | + | 9.38161i | 0.271845 | + | 0.470849i | 0.969334 | − | 0.245746i | \(-0.0790329\pi\) |
−0.697489 | + | 0.716595i | \(0.745700\pi\) | |||||||
\(398\) | 11.8050 | 0.591733 | ||||||||
\(399\) | 12.1894 | + | 21.1127i | 0.610233 | + | 1.05696i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2397 | − | 21.1997i | 0.611220 | − | 1.05866i | −0.379816 | − | 0.925062i | \(-0.624013\pi\) |
0.991035 | − | 0.133601i | \(-0.0426541\pi\) | |||||||
\(402\) | 9.10891 | 0.454311 | ||||||||
\(403\) | −12.3830 | − | 8.09287i | −0.616842 | − | 0.403134i | ||||
\(404\) | 11.4770 | 0.571002 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.58773 | + | 14.8744i | −0.426202 | + | 0.738203i | ||||
\(407\) | 9.20336 | + | 15.9407i | 0.456194 | + | 0.790150i | ||||
\(408\) | −21.1475 | −1.04696 | ||||||||
\(409\) | −13.3553 | − | 23.1320i | −0.660377 | − | 1.14381i | −0.980517 | − | 0.196436i | \(-0.937063\pi\) |
0.320140 | − | 0.947370i | \(-0.396270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6743 | −0.526524 | ||||||||
\(412\) | 43.9749 | + | 76.1668i | 2.16649 | + | 3.75247i | ||||
\(413\) | −13.2729 | + | 22.9894i | −0.653118 | + | 1.13123i | ||||
\(414\) | −7.20336 | + | 12.4766i | −0.354026 | + | 0.613191i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.89949 | − | 34.3353i | 0.0931300 | − | 1.68343i | ||||
\(417\) | −16.1475 | −0.790749 | ||||||||
\(418\) | −45.8158 | + | 79.3552i | −2.24092 | + | 3.88139i | ||||
\(419\) | −7.51815 | + | 13.0218i | −0.367286 | + | 0.636158i | −0.989140 | − | 0.146975i | \(-0.953046\pi\) |
0.621854 | + | 0.783133i | \(0.286380\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.90182 | −0.287637 | −0.143818 | − | 0.989604i | \(-0.545938\pi\) | ||||
−0.143818 | + | 0.989604i | \(0.545938\pi\) | |||||||
\(422\) | −28.8104 | − | 49.9011i | −1.40247 | − | 2.42915i | ||||
\(423\) | 1.90252 | + | 3.29526i | 0.0925036 | + | 0.160221i | ||||
\(424\) | −37.4817 | −1.82027 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.6240 | + | 21.8655i | −0.611636 | + | 1.05938i | ||||
\(427\) | −6.18521 | + | 10.7131i | −0.299323 | + | 0.518443i | ||||
\(428\) | −52.1499 | −2.52076 | ||||||||
\(429\) | 1.03630 | − | 18.7323i | 0.0500332 | − | 0.904406i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.6743 | + | 34.0769i | −0.947677 | + | 1.64142i | −0.197376 | + | 0.980328i | \(0.563242\pi\) |
−0.750301 | + | 0.661097i | \(0.770091\pi\) | |||||||
\(432\) | −4.60168 | + | 7.97034i | −0.221398 | + | 0.383473i | ||||
\(433\) | 6.20756 | + | 10.7518i | 0.298316 | + | 0.516699i | 0.975751 | − | 0.218884i | \(-0.0702417\pi\) |
−0.677435 | + | 0.735583i | \(0.736908\pi\) | |||||||
\(434\) | 38.4454 | 1.84544 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −33.0694 | − | 57.2778i | −1.58374 | − | 2.74311i | ||||
\(437\) | −37.4817 | −1.79299 | ||||||||
\(438\) | 1.04722 | + | 1.81385i | 0.0500383 | + | 0.0866689i | ||||
\(439\) | −15.9207 | + | 27.5754i | −0.759852 | + | 1.31610i | 0.183074 | + | 0.983099i | \(0.441395\pi\) |
−0.942926 | + | 0.333003i | \(0.891938\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.97209 | 0.284385 | ||||||||
\(442\) | 23.0526 | + | 15.0659i | 1.09650 | + | 0.716613i | ||||
\(443\) | 1.06421 | 0.0505622 | 0.0252811 | − | 0.999680i | \(-0.491952\pi\) | ||||
0.0252811 | + | 0.999680i | \(0.491952\pi\) | |||||||
\(444\) | −8.43462 | + | 14.6092i | −0.400290 | + | 0.693322i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.89949 | + | 17.1464i | 0.468754 | + | 0.811906i | ||||
\(447\) | −9.66589 | −0.457181 | ||||||||
\(448\) | 11.5375 | + | 19.9835i | 0.545094 | + | 0.944131i | ||||
\(449\) | −7.70219 | − | 13.3406i | −0.363489 | − | 0.629581i | 0.625044 | − | 0.780590i | \(-0.285081\pi\) |
−0.988532 | + | 0.151009i | \(0.951748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.9721 | − | 24.2004i | −0.657920 | − | 1.13955i | ||||
\(452\) | −26.7129 | + | 46.2681i | −1.25647 | + | 2.17627i | ||||
\(453\) | 9.35646 | − | 16.2059i | 0.439605 | − | 0.761418i | ||||
\(454\) | 60.7297 | 2.85019 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.7576 | −2.28328 | ||||||||
\(457\) | −4.78689 | + | 8.29113i | −0.223921 | + | 0.387843i | −0.955995 | − | 0.293382i | \(-0.905219\pi\) |
0.732074 | + | 0.681225i | \(0.238552\pi\) | |||||||
\(458\) | 1.07261 | − | 1.85781i | 0.0501196 | − | 0.0868097i | ||||
\(459\) | −1.46789 | − | 2.54247i | −0.0685155 | − | 0.118672i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.18637 | − | 14.1792i | −0.381277 | − | 0.660392i | 0.609968 | − | 0.792426i | \(-0.291182\pi\) |
−0.991245 | + | 0.132034i | \(0.957849\pi\) | |||||||
\(462\) | 24.3788 | + | 42.2253i | 1.13420 | + | 1.96450i | ||||
\(463\) | 24.6487 | 1.14552 | 0.572761 | − | 0.819722i | \(-0.305872\pi\) | ||||
0.572761 | + | 0.819722i | \(0.305872\pi\) | |||||||
\(464\) | −8.43462 | − | 14.6092i | −0.391568 | − | 0.678215i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.4370 | − | 30.2017i | 0.807751 | − | 1.39907i | ||||
\(467\) | 20.3402 | 0.941231 | 0.470616 | − | 0.882338i | \(-0.344032\pi\) | ||||
0.470616 | + | 0.882338i | \(0.344032\pi\) | |||||||
\(468\) | 15.3425 | − | 7.76133i | 0.709208 | − | 0.358768i | ||||
\(469\) | 12.6101 | 0.582279 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.18521 | + | 8.98104i | −0.238922 | + | 0.413825i | ||||
\(472\) | −26.5459 | − | 45.9788i | −1.22187 | − | 2.11635i | ||||
\(473\) | 16.4793 | 0.757720 | ||||||||
\(474\) | −5.33714 | − | 9.24420i | −0.245143 | − | 0.424600i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −50.4235 | −2.31116 | ||||||||
\(477\) | −2.60168 | − | 4.50624i | −0.119123 | − | 0.206327i | ||||
\(478\) | 16.6464 | − | 28.8324i | 0.761388 | − | 1.31876i | ||||
\(479\) | 0.0811965 | − | 0.140637i | 0.00370996 | − | 0.00642585i | −0.864164 | − | 0.503209i | \(-0.832152\pi\) |
0.867874 | + | 0.496784i | \(0.165486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3811 | − | 5.75739i | 0.518935 | − | 0.262514i | ||||
\(482\) | −33.2201 | −1.51314 | ||||||||
\(483\) | −9.97209 | + | 17.2722i | −0.453746 | + | 0.785911i | ||||
\(484\) | −38.3286 | + | 66.3870i | −1.74221 | + | 3.01759i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.60168 | −0.118015 | ||||||||
\(487\) | 1.28152 | + | 2.21966i | 0.0580713 | + | 0.100582i | 0.893600 | − | 0.448865i | \(-0.148172\pi\) |
−0.835528 | + | 0.549447i | \(0.814838\pi\) | |||||||
\(488\) | −12.3704 | − | 21.4262i | −0.559982 | − | 0.969918i | ||||
\(489\) | 11.4733 | 0.518839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2203 | + | 24.6304i | −0.641755 | + | 1.11155i | 0.343286 | + | 0.939231i | \(0.388460\pi\) |
−0.985041 | + | 0.172321i | \(0.944873\pi\) | |||||||
\(492\) | 12.8050 | − | 22.1790i | 0.577296 | − | 0.999905i | ||||
\(493\) | 5.38114 | 0.242354 | ||||||||
\(494\) | 53.1499 | + | 34.7359i | 2.39133 | + | 1.56284i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.8800 | + | 32.7011i | −0.847736 | + | 1.46832i | ||||
\(497\) | −17.4763 | + | 30.2698i | −0.783919 | + | 1.35779i | ||||
\(498\) | 15.0084 | + | 25.9953i | 0.672542 | + | 1.16488i | ||||
\(499\) | −27.8605 | −1.24721 | −0.623603 | − | 0.781741i | \(-0.714332\pi\) | ||||
−0.623603 | + | 0.781741i | \(0.714332\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.56538 | − | 2.71131i | −0.0699358 | − | 0.121132i | ||||
\(502\) | 21.8716 | 0.976176 | ||||||||
\(503\) | 15.7129 | + | 27.2156i | 0.700604 | + | 1.21348i | 0.968255 | + | 0.249966i | \(0.0804196\pi\) |
−0.267650 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(504\) | −12.9721 | + | 22.4683i | −0.577823 | + | 1.00082i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −74.9633 | −3.33253 | ||||||||
\(507\) | −12.9207 | − | 1.43397i | −0.573827 | − | 0.0636850i | ||||
\(508\) | 15.2359 | 0.675985 | ||||||||
\(509\) | −8.11124 | + | 14.0491i | −0.359524 | + | 0.622715i | −0.987881 | − | 0.155211i | \(-0.950394\pi\) |
0.628357 | + | 0.777925i | \(0.283728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.44974 | + | 2.51103i | 0.0641329 | + | 0.111081i | ||||
\(512\) | 44.8134 | 1.98049 | ||||||||
\(513\) | −3.38437 | − | 5.86190i | −0.149423 | − | 0.258809i | ||||
\(514\) | −7.98605 | − | 13.8322i | −0.352249 | − | 0.610114i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.55142 | + | 13.0794i | 0.332433 | + | 0.575791i | ||||
\(517\) | −9.89949 | + | 17.1464i | −0.435379 | + | 0.754098i | ||||
\(518\) | −16.5738 | + | 28.7066i | −0.728210 | + | 1.26130i | ||||
\(519\) | −8.26757 | −0.362906 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0386 | −0.877909 | −0.438954 | − | 0.898509i | \(-0.644651\pi\) | ||||
−0.438954 | + | 0.898509i | \(0.644651\pi\) | |||||||
\(522\) | 2.38437 | − | 4.12985i | 0.104361 | − | 0.180758i | ||||
\(523\) | −6.62959 | + | 11.4828i | −0.289892 | + | 0.502107i | −0.973784 | − | 0.227476i | \(-0.926953\pi\) |
0.683892 | + | 0.729583i | \(0.260286\pi\) | |||||||
\(524\) | 10.9056 | + | 18.8890i | 0.476411 | + | 0.825168i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.15310 | + | 10.6575i | 0.268288 | + | 0.464688i | ||||
\(527\) | −6.02254 | − | 10.4314i | −0.262346 | − | 0.454397i | ||||
\(528\) | −47.8884 | −2.08407 | ||||||||
\(529\) | −3.83178 | − | 6.63684i | −0.166599 | − | 0.288558i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.68521 | − | 6.38297i | 0.159924 | − | 0.276997i | ||||
\(532\) | −116.256 | −5.04034 | ||||||||
\(533\) | −17.2783 | + | 8.74059i | −0.748406 | + | 0.378597i | ||||
\(534\) | −25.5822 | −1.10705 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.6101 | + | 21.8413i | −0.544672 | + | 0.943400i | ||||
\(537\) | 9.22268 | + | 15.9741i | 0.397988 | + | 0.689335i | ||||
\(538\) | 14.1610 | 0.610524 | ||||||||
\(539\) | 15.5375 | + | 26.9117i | 0.669246 | + | 1.15917i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.6850 | 1.53422 | 0.767109 | − | 0.641516i | \(-0.221694\pi\) | ||||
0.767109 | + | 0.641516i | \(0.221694\pi\) | |||||||
\(542\) | 33.1445 | + | 57.4080i | 1.42368 | + | 2.46588i | ||||
\(543\) | −10.5514 | + | 18.2756i | −0.452805 | + | 0.784281i | ||||
\(544\) | 14.0000 | − | 24.2487i | 0.600245 | − | 1.03965i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.1475 | − | 15.2508i | 1.29020 | − | 0.652673i | ||||
\(547\) | 0.627256 | 0.0268195 | 0.0134098 | − | 0.999910i | \(-0.495731\pi\) | ||||
0.0134098 | + | 0.999910i | \(0.495731\pi\) | |||||||
\(548\) | 25.4514 | − | 44.0831i | 1.08723 | − | 1.88314i | ||||
\(549\) | 1.71731 | − | 2.97447i | 0.0732931 | − | 0.126947i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4067 | 0.528544 | ||||||||
\(552\) | −19.9442 | − | 34.5443i | −0.848881 | − | 1.47030i | ||||
\(553\) | −7.38856 | − | 12.7974i | −0.314194 | − | 0.544200i | ||||
\(554\) | −59.3532 | −2.52168 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.5017 | − | 66.6869i | 1.63283 | − | 2.82815i | ||||
\(557\) | 4.60401 | − | 7.97438i | 0.195078 | − | 0.337885i | −0.751848 | − | 0.659337i | \(-0.770837\pi\) |
0.946926 | + | 0.321451i | \(0.104171\pi\) | |||||||
\(558\) | −10.6743 | −0.451879 | ||||||||
\(559\) | 0.630752 | − | 11.4015i | 0.0266780 | − | 0.482234i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.63798 | − | 13.2294i | 0.322476 | − | 0.558545i | ||||
\(562\) | −2.81899 | + | 4.88264i | −0.118912 | + | 0.205962i | ||||
\(563\) | 1.33411 | + | 2.31075i | 0.0562260 | + | 0.0973864i | 0.892768 | − | 0.450516i | \(-0.148760\pi\) |
−0.836542 | + | 0.547902i | \(0.815427\pi\) | |||||||
\(564\) | −18.1452 | −0.764051 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.6959 | + | 67.0233i | 1.62651 | + | 2.81720i | ||||
\(567\) | −3.60168 | −0.151256 | ||||||||
\(568\) | −34.9526 | − | 60.5396i | −1.46658 | − | 2.54019i | ||||
\(569\) | 13.0919 | − | 22.6759i | 0.548842 | − | 0.950622i | −0.449512 | − | 0.893274i | \(-0.648402\pi\) |
0.998354 | − | 0.0573480i | \(-0.0182645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2481 | −0.805506 | −0.402753 | − | 0.915309i | \(-0.631947\pi\) | ||||
−0.402753 | + | 0.915309i | \(0.631947\pi\) | |||||||
\(572\) | 74.8907 | + | 48.9445i | 3.13134 | + | 2.04647i | ||||
\(573\) | −8.70219 | −0.363539 | ||||||||
\(574\) | 25.1615 | − | 43.5810i | 1.05022 | − | 1.81904i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.20336 | − | 5.54838i | −0.133473 | − | 0.231182i | ||||
\(577\) | −23.8716 | −0.993787 | −0.496893 | − | 0.867812i | \(-0.665526\pi\) | ||||
−0.496893 | + | 0.867812i | \(0.665526\pi\) | |||||||
\(578\) | −10.9025 | − | 18.8837i | −0.453485 | − | 0.785459i | ||||
\(579\) | 9.63378 | + | 16.6862i | 0.400366 | + | 0.693455i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7771 | + | 35.9870i | 0.861981 | + | 1.49299i | ||||
\(582\) | 7.25058 | − | 12.5584i | 0.300546 | − | 0.520562i | ||||
\(583\) | 13.5375 | − | 23.4476i | 0.560665 | − | 0.971100i | ||||
\(584\) | −5.79897 | −0.239963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 86.0783 | 3.55586 | ||||||||
\(587\) | 14.4377 | − | 25.0068i | 0.595906 | − | 1.03214i | −0.397513 | − | 0.917597i | \(-0.630126\pi\) |
0.993418 | − | 0.114542i | \(-0.0365402\pi\) | |||||||
\(588\) | −14.2397 | + | 24.6638i | −0.587234 | + | 1.01712i | ||||
\(589\) | −13.8855 | − | 24.0504i | −0.572143 | − | 0.990981i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.57377 | − | 13.1182i | −0.311543 | − | 0.539609i | ||||
\(592\) | −16.2783 | − | 28.1948i | −0.669034 | − | 1.15880i | ||||
\(593\) | 8.74083 | 0.358943 | 0.179471 | − | 0.983763i | \(-0.442561\pi\) | ||||
0.179471 | + | 0.983763i | \(0.442561\pi\) | |||||||
\(594\) | −6.76873 | − | 11.7238i | −0.277725 | − | 0.481033i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.0470 | − | 39.9186i | 0.944043 | − | 1.63513i | ||||
\(597\) | −4.53747 | −0.185706 | ||||||||
\(598\) | −2.86925 | + | 51.8649i | −0.117332 | + | 2.12091i | ||||
\(599\) | 21.5929 | 0.882262 | 0.441131 | − | 0.897443i | \(-0.354577\pi\) | ||||
0.441131 | + | 0.897443i | \(0.354577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1252 | + | 26.1976i | −0.616970 | + | 1.06862i | 0.373066 | + | 0.927805i | \(0.378306\pi\) |
−0.990036 | + | 0.140818i | \(0.955027\pi\) | |||||||
\(602\) | 14.8383 | + | 25.7007i | 0.604764 | + | 1.04748i | ||||
\(603\) | −3.50117 | −0.142578 | ||||||||
\(604\) | 44.6185 | + | 77.2815i | 1.81550 | + | 3.14454i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.26150 | −0.254356 | ||||||||
\(607\) | −11.2536 | − | 19.4918i | −0.456770 | − | 0.791149i | 0.542018 | − | 0.840367i | \(-0.317660\pi\) |
−0.998788 | + | 0.0492178i | \(0.984327\pi\) | |||||||
\(608\) | 32.2783 | − | 55.9076i | 1.30906 | − | 2.26735i | ||||
\(609\) | 3.30084 | − | 5.71722i | 0.133757 | − | 0.231674i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4842 | + | 7.50544i | 0.464600 | + | 0.303638i | ||||
\(612\) | 14.0000 | 0.565916 | ||||||||
\(613\) | 9.38856 | − | 16.2615i | 0.379201 | − | 0.656795i | −0.611746 | − | 0.791055i | \(-0.709532\pi\) |
0.990946 | + | 0.134260i | \(0.0428657\pi\) | |||||||
\(614\) | 18.6936 | − | 32.3783i | 0.754412 | − | 1.30668i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −134.997 | −5.43918 | ||||||||
\(617\) | −1.80504 | − | 3.12642i | −0.0726681 | − | 0.125865i | 0.827402 | − | 0.561610i | \(-0.189818\pi\) |
−0.900070 | + | 0.435746i | \(0.856485\pi\) | |||||||
\(618\) | −23.9914 | − | 41.5543i | −0.965076 | − | 1.67156i | ||||
\(619\) | 2.87158 | 0.115419 | 0.0577093 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577093 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.76873 | − | 4.79559i | 0.111105 | − | 0.192440i | ||||
\(622\) | −11.3262 | + | 19.6176i | −0.454140 | + | 0.786594i | ||||
\(623\) | −35.4151 | −1.41888 | ||||||||
\(624\) | −1.83294 | + | 33.1325i | −0.0733765 | + | 1.32636i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.6210 | − | 18.3961i | 0.424500 | − | 0.735256i | ||||
\(627\) | 17.6101 | − | 30.5015i | 0.703279 | − | 1.21811i | ||||
\(628\) | −24.7269 | − | 42.8282i | −0.986710 | − | 1.70903i | ||||
\(629\) | 10.3853 | 0.414088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.49444 | − | 14.7128i | −0.338158 | − | 0.585708i | 0.645928 | − | 0.763398i | \(-0.276471\pi\) |
−0.984086 | + | 0.177691i | \(0.943137\pi\) | |||||||
\(632\) | 29.5543 | 1.17561 | ||||||||
\(633\) | 11.0738 | + | 19.1803i | 0.440143 | + | 0.762350i | ||||
\(634\) | −17.4430 | + | 30.2122i | −0.692751 | + | 1.19988i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 24.8134 | 0.983917 | ||||||||
\(637\) | 19.2141 | − | 9.71985i | 0.761290 | − | 0.385115i | ||||
\(638\) | 24.8134 | 0.982373 | ||||||||
\(639\) | 4.85226 | − | 8.40436i | 0.191953 | − | 0.332472i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.30620 | + | 14.3868i | 0.328075 | + | 0.568243i | 0.982130 | − | 0.188204i | \(-0.0602667\pi\) |
−0.654055 | + | 0.756447i | \(0.726933\pi\) | |||||||
\(642\) | 28.4514 | 1.12289 | ||||||||
\(643\) | 22.6701 | + | 39.2657i | 0.894021 | + | 1.54849i | 0.835012 | + | 0.550232i | \(0.185461\pi\) |
0.0590094 | + | 0.998257i | \(0.481206\pi\) | |||||||
\(644\) | −47.5543 | − | 82.3664i | −1.87390 | − | 3.24569i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.8497 | + | 44.7731i | 1.01704 | + | 1.76157i | ||||
\(647\) | 2.43462 | − | 4.21689i | 0.0957149 | − | 0.165783i | −0.814192 | − | 0.580596i | \(-0.802820\pi\) |
0.909907 | + | 0.414813i | \(0.136153\pi\) | |||||||
\(648\) | 3.60168 | − | 6.23829i | 0.141487 | − | 0.245063i | ||||
\(649\) | 38.3509 | 1.50540 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7771 | −0.579161 | ||||||||
\(652\) | −27.3565 | + | 47.3828i | −1.07136 | + | 1.85565i | ||||
\(653\) | 9.63495 | − | 16.6882i | 0.377045 | − | 0.653061i | −0.613586 | − | 0.789628i | \(-0.710274\pi\) |
0.990631 | + | 0.136567i | \(0.0436070\pi\) | |||||||
\(654\) | 18.0417 | + | 31.2491i | 0.705485 | + | 1.22194i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 24.7129 | + | 42.8040i | 0.964877 | + | 1.67122i | ||||
\(657\) | −0.402519 | − | 0.697183i | −0.0157038 | − | 0.0271997i | ||||
\(658\) | −35.6548 | −1.38997 | ||||||||
\(659\) | −0.167055 | − | 0.289348i | −0.00650755 | − | 0.0112714i | 0.862753 | − | 0.505625i | \(-0.168738\pi\) |
−0.869261 | + | 0.494354i | \(0.835405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.83411 | − | 11.8370i | 0.265816 | − | 0.460407i | −0.701961 | − | 0.712215i | \(-0.747692\pi\) |
0.967777 | + | 0.251808i | \(0.0810253\pi\) | |||||||
\(662\) | −55.8823 | −2.17193 | ||||||||
\(663\) | −8.86066 | − | 5.79085i | −0.344119 | − | 0.224898i | ||||
\(664\) | −83.1085 | −3.22524 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.60168 | − | 7.97034i | 0.178311 | − | 0.308844i | ||||
\(667\) | 5.07494 | + | 8.79005i | 0.196502 | + | 0.340352i | ||||
\(668\) | 14.9297 | 0.577648 | ||||||||
\(669\) | −3.80504 | − | 6.59052i | −0.147111 | − | 0.254804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8716 | 0.689925 | ||||||||
\(672\) | −17.1755 | − | 29.7488i | −0.662557 | − | 1.14758i | ||||
\(673\) | −10.9400 | + | 18.9486i | −0.421706 | + | 0.730415i | −0.996106 | − | 0.0881587i | \(-0.971902\pi\) |
0.574401 | + | 0.818574i | \(0.305235\pi\) | |||||||
\(674\) | 9.68521 | − | 16.7753i | 0.373060 | − | 0.646159i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 36.7297 | − | 49.9412i | 1.41268 | − | 1.92082i | ||||
\(677\) | 17.0749 | 0.656243 | 0.328122 | − | 0.944636i | \(-0.393584\pi\) | ||||
0.328122 | + | 0.944636i | \(0.393584\pi\) | |||||||
\(678\) | 14.5738 | − | 25.2425i | 0.559702 | − | 0.969433i | ||||
\(679\) | 10.0375 | − | 17.3854i | 0.385203 | − | 0.667191i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.3425 | −0.894487 | ||||||||
\(682\) | −27.7711 | − | 48.1009i | −1.06341 | − | 1.84188i | ||||
\(683\) | −13.3651 | − | 23.1489i | −0.511399 | − | 0.885770i | −0.999913 | − | 0.0132133i | \(-0.995794\pi\) |
0.488513 | − | 0.872556i | \(-0.337539\pi\) | |||||||
\(684\) | 32.2783 | 1.23419 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.81596 | − | 8.34149i | 0.183874 | − | 0.318479i | ||||
\(687\) | −0.412275 | + | 0.714081i | −0.0157293 | + | 0.0272439i | ||||
\(688\) | −29.1475 | −1.11124 | ||||||||
\(689\) | −15.7045 | − | 10.2636i | −0.598295 | − | 0.391013i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.3576 | + | 42.1886i | −0.926608 | + | 1.60493i | −0.137653 | + | 0.990481i | \(0.543956\pi\) |
−0.788955 | + | 0.614451i | \(0.789378\pi\) | |||||||
\(692\) | 19.7129 | − | 34.1438i | 0.749373 | − | 1.29795i | ||||
\(693\) | −9.37041 | − | 16.2300i | −0.355953 | − | 0.616528i | ||||
\(694\) | −64.9028 | −2.46368 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.60168 | + | 11.4344i | 0.250236 | + | 0.433421i | ||||
\(697\) | −15.7664 | −0.597195 | ||||||||
\(698\) | 2.73546 | + | 4.73796i | 0.103539 | + | 0.179334i | ||||
\(699\) | −6.70219 | + | 11.6085i | −0.253500 | + | 0.439075i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9419 | 0.866502 | 0.433251 | − | 0.901273i | \(-0.357366\pi\) | ||||
0.433251 | + | 0.901273i | \(0.357366\pi\) | |||||||
\(702\) | −8.37041 | + | 4.23435i | −0.315921 | + | 0.159815i | ||||
\(703\) | 23.9442 | 0.903072 | ||||||||
\(704\) | 16.6682 | − | 28.8702i | 0.628207 | − | 1.08809i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.1173 | − | 41.7724i | −0.907667 | − | 1.57212i | ||||
\(707\) | −8.66822 | −0.326002 | ||||||||
\(708\) | 17.5738 | + | 30.4387i | 0.660463 | + | 1.14396i | ||||
\(709\) | 3.57261 | + | 6.18794i | 0.134172 | + | 0.232393i | 0.925281 | − | 0.379283i | \(-0.123829\pi\) |
−0.791109 | + | 0.611675i | \(0.790496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.05142 | + | 3.55317i | 0.0769343 | + | 0.133254i | ||||
\(712\) | 35.4151 | − | 61.3408i | 1.32724 | − | 2.29884i | ||||
\(713\) | 11.3597 | − | 19.6756i | 0.425424 | − | 0.736855i | ||||
\(714\) | 27.5096 | 1.02952 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −87.9610 | −3.28726 | ||||||||
\(717\) | −6.39832 | + | 11.0822i | −0.238950 | + | 0.413873i | ||||
\(718\) | −6.18940 | + | 10.7204i | −0.230987 | + | 0.400080i | ||||
\(719\) | −20.9891 | − | 36.3542i | −0.782761 | − | 1.35578i | −0.930328 | − | 0.366729i | \(-0.880478\pi\) |
0.147567 | − | 0.989052i | \(-0.452856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.2129 | − | 57.5265i | −1.23691 | − | 2.14240i | ||||
\(722\) | 34.8830 | + | 60.4191i | 1.29821 | + | 2.24857i | ||||
\(723\) | 12.7687 | 0.474874 | ||||||||
\(724\) | −50.3169 | − | 87.1515i | −1.87001 | − | 3.23896i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.9109 | − | 36.2188i | 0.776077 | − | 1.34420i | ||||
\(727\) | 11.4965 | 0.426382 | 0.213191 | − | 0.977011i | \(-0.431614\pi\) | ||||
0.213191 | + | 0.977011i | \(0.431614\pi\) | |||||||
\(728\) | −5.16706 | + | 93.4003i | −0.191504 | + | 3.46164i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.64890 | − | 8.05214i | 0.171946 | − | 0.297819i | ||||
\(732\) | 8.18940 | + | 14.1845i | 0.302689 | + | 0.524273i | ||||
\(733\) | −46.1136 | −1.70324 | −0.851622 | − | 0.524157i | \(-0.824381\pi\) | ||||
−0.851622 | + | 0.524157i | \(0.824381\pi\) | |||||||
\(734\) | 13.3232 | + | 23.0764i | 0.491768 | + | 0.851767i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 52.8134 | 1.94673 | ||||||||
\(737\) | −9.10891 | − | 15.7771i | −0.335531 | − | 0.581157i | ||||
\(738\) | −6.98605 | + | 12.1002i | −0.257160 | + | 0.445414i | ||||
\(739\) | 5.80504 | − | 10.0546i | 0.213542 | − | 0.369865i | −0.739279 | − | 0.673400i | \(-0.764833\pi\) |
0.952820 | + | 0.303534i | \(0.0981667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.4291 | − | 13.3513i | −0.750480 | − | 0.490474i | ||||
\(742\) | 48.7576 | 1.78995 | ||||||||
\(743\) | 6.70756 | − | 11.6178i | 0.246076 | − | 0.426217i | −0.716357 | − | 0.697734i | \(-0.754192\pi\) |
0.962434 | + | 0.271517i | \(0.0875253\pi\) | |||||||
\(744\) | 14.7771 | − | 25.5947i | 0.541756 | − | 0.938349i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −60.7236 | −2.22325 | ||||||||
\(747\) | −5.76873 | − | 9.99174i | −0.211067 | − | 0.365579i | ||||
\(748\) | 36.4235 | + | 63.0874i | 1.33178 | + | 2.30670i | ||||
\(749\) | 39.3872 | 1.43918 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0866 | + | 38.2550i | −0.805950 | + | 1.39595i | 0.109698 | + | 0.993965i | \(0.465012\pi\) |
−0.915648 | + | 0.401981i | \(0.868322\pi\) | |||||||
\(752\) | 17.5096 | − | 30.3274i | 0.638508 | − | 1.10593i | ||||
\(753\) | −8.40672 | −0.306358 | ||||||||
\(754\) | 0.949743 | − | 17.1677i | 0.0345876 | − | 0.625210i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.58773 | − | 14.8744i | 0.312333 | − | 0.540976i | ||||
\(757\) | 3.98605 | − | 6.90403i | 0.144875 | − | 0.250931i | −0.784451 | − | 0.620191i | \(-0.787055\pi\) |
0.929326 | + | 0.369259i | \(0.120389\pi\) | |||||||
\(758\) | −46.3842 | − | 80.3397i | −1.68475 | − | 2.91807i | ||||
\(759\) | 28.8134 | 1.04586 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.83294 | − | 11.8350i | −0.247694 | − | 0.429019i | 0.715192 | − | 0.698928i | \(-0.246339\pi\) |
−0.962886 | + | 0.269910i | \(0.913006\pi\) | |||||||
\(762\) | −8.31227 | −0.301122 | ||||||||
\(763\) | 24.9763 | + | 43.2602i | 0.904202 | + | 1.56612i | ||||
\(764\) | 20.7492 | − | 35.9387i | 0.750681 | − | 1.30022i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −79.6594 | −2.87821 | ||||||||
\(767\) | 1.46789 | − | 26.5338i | 0.0530026 | − | 0.958081i | ||||
\(768\) | −19.0749 | −0.688308 | ||||||||
\(769\) | −8.24522 | + | 14.2811i | −0.297330 | + | 0.514991i | −0.975524 | − | 0.219892i | \(-0.929430\pi\) |
0.678194 | + | 0.734883i | \(0.262763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.06957 | + | 5.31666i | 0.110548 | + | 0.191475i | ||||
\(772\) | −91.8819 | −3.30690 | ||||||||
\(773\) | −22.8521 | − | 39.5809i | −0.821932 | − | 1.42363i | −0.904242 | − | 0.427021i | \(-0.859563\pi\) |
0.0823101 | − | 0.996607i | \(-0.473770\pi\) | |||||||
\(774\) | −4.11983 | − | 7.13576i | −0.148084 | − | 0.256489i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.0749 | + | 34.7708i | 0.720648 | + | 1.24820i | ||||
\(777\) | 6.37041 | − | 11.0339i | 0.228537 | − | 0.395838i | ||||
\(778\) | 32.5459 | − | 56.3711i | 1.16683 | − | 2.02100i | ||||
\(779\) | −36.3509 | −1.30241 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.4961 | 1.80689 | ||||||||
\(782\) | −21.1475 | + | 36.6286i | −0.756235 | + | 1.30984i | ||||
\(783\) | −0.916472 | + | 1.58738i | −0.0327521 | + | 0.0567282i | ||||
\(784\) | −27.4817 | − | 47.5996i | −0.981488 | − | 1.69999i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.94974 | − | 10.3053i | −0.212220 | − | 0.367576i | ||||
\(787\) | −24.4109 | − | 42.2809i | −0.870155 | − | 1.50715i | −0.861836 | − | 0.507187i | \(-0.830685\pi\) |
−0.00831938 | − | 0.999965i | \(-0.502648\pi\) | |||||||
\(788\) | 72.2346 | 2.57325 | ||||||||
\(789\) | −2.36505 | − | 4.09639i | −0.0841980 | − | 0.145835i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.1755 | − | 34.9449i | 0.717356 | − | 1.24250i | ||||
\(792\) | 37.4817 | 1.33185 | ||||||||
\(793\) | 0.684041 | − | 12.3648i | 0.0242910 | − | 0.439087i | ||||
\(794\) | 28.1838 | 1.00021 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.8190 | − | 18.7390i | 0.383469 | − | 0.664188i | ||||
\(797\) | 6.87461 | + | 11.9072i | 0.243511 | + | 0.421774i | 0.961712 | − | 0.274062i | \(-0.0883674\pi\) |
−0.718201 | + | 0.695836i | \(0.755034\pi\) | |||||||
\(798\) | 63.4258 | 2.24525 | ||||||||
\(799\) | 5.58539 | + | 9.67419i | 0.197597 | + | 0.342248i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.83294 | 0.347430 | ||||||||
\(802\) | −31.8437 | − | 55.1549i | −1.12444 | − | 1.94759i | ||||
\(803\) | 2.09445 | − | 3.62769i | 0.0739115 | − | 0.128018i | ||||
\(804\) | 8.34806 | − | 14.4593i | 0.294414 | − | 0.509939i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.3425 | + | 17.3729i | −1.20966 | + | 0.611934i | ||||
\(807\) | −5.44302 | −0.191603 | ||||||||
\(808\) | 8.66822 | − | 15.0138i | 0.304947 | − | 0.528184i | ||||
\(809\) | −10.1671 | + | 17.6099i | −0.357455 | + | 0.619130i | −0.987535 | − | 0.157400i | \(-0.949689\pi\) |
0.630080 | + | 0.776530i | \(0.283022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.4817 | 0.789438 | 0.394719 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394719 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(812\) | 15.7408 | + | 27.2639i | 0.552395 | + | 0.956776i | ||||
\(813\) | −12.7397 | − | 22.0657i | −0.446799 | − | 0.773879i | ||||
\(814\) | 47.8884 | 1.67849 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.5096 | + | 23.3992i | −0.472929 | + | 0.819137i | ||||
\(817\) | 10.7185 | − | 18.5649i | 0.374992 | − | 0.649505i | ||||
\(818\) | −69.4924 | −2.42974 | ||||||||
\(819\) | −11.5877 | + | 5.86190i | −0.404908 | + | 0.204831i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3039 | − | 28.2391i | 0.569009 | − | 0.985553i | −0.427655 | − | 0.903942i | \(-0.640660\pi\) |
0.996664 | − | 0.0816107i | \(-0.0260064\pi\) | |||||||
\(822\) | −13.8855 | + | 24.0504i | −0.484314 | + | 0.838856i | ||||
\(823\) | 16.7408 | + | 28.9960i | 0.583549 | + | 1.01074i | 0.995055 | + | 0.0993287i | \(0.0316695\pi\) |
−0.411506 | + | 0.911407i | \(0.634997\pi\) | |||||||
\(824\) | 132.852 | 4.62811 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.5319 | + | 59.8110i | 1.20152 | + | 2.08109i | ||||
\(827\) | 51.0298 | 1.77448 | 0.887241 | − | 0.461306i | \(-0.152619\pi\) | ||||
0.887241 | + | 0.461306i | \(0.152619\pi\) | |||||||
\(828\) | 13.2034 | + | 22.8689i | 0.458848 | + | 0.794749i | ||||
\(829\) | −10.5973 | + | 18.3550i | −0.368059 | + | 0.637497i | −0.989262 | − | 0.146153i | \(-0.953311\pi\) |
0.621203 | + | 0.783650i | \(0.286644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.8134 | 0.791389 | ||||||||
\(832\) | −19.3364 | − | 12.6373i | −0.670370 | − | 0.438118i | ||||
\(833\) | 17.5328 | 0.607476 | ||||||||
\(834\) | −21.0054 | + | 36.3824i | −0.727356 | + | 1.25982i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 83.9778 | + | 145.454i | 2.90443 | + | 5.03062i | ||||
\(837\) | 4.10284 | 0.141815 | ||||||||
\(838\) | 19.5598 | + | 33.8786i | 0.675683 | + | 1.17032i | ||||
\(839\) | −26.9419 | − | 46.6647i | −0.930136 | − | 1.61104i | −0.783086 | − | 0.621914i | \(-0.786355\pi\) |
−0.147051 | − | 0.989129i | \(-0.546978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8202 | + | 22.2052i | 0.442074 | + | 0.765695i | ||||
\(842\) | −7.67732 | + | 13.2975i | −0.264578 | + | 0.458262i | ||||
\(843\) | 1.08353 | − | 1.87672i | 0.0373187 | − | 0.0646378i | ||||
\(844\) | −105.616 | −3.63544 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.89949 | 0.340351 | ||||||||
\(847\) | 28.9484 | − | 50.1401i | 0.994678 | − | 1.72283i | ||||
\(848\) | −23.9442 | + | 41.4725i | −0.822247 | + | 1.42417i | ||||
\(849\) | −14.8734 | − | 25.7616i | −0.510455 | − | 0.884135i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.79431 | + | 16.9642i | 0.335745 | + | 0.581527i | ||||
\(852\) | 23.1391 | + | 40.0782i | 0.792734 | + | 1.37306i | ||||
\(853\) | 4.06421 | 0.139156 | 0.0695780 | − | 0.997577i | \(-0.477835\pi\) | ||||
0.0695780 | + | 0.997577i | \(0.477835\pi\) | |||||||
\(854\) | 16.0919 | + | 27.8720i | 0.550654 | + | 0.953761i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.3872 | + | 68.2206i | −1.34623 | + | 2.33173i | ||||
\(857\) | 39.2141 | 1.33953 | 0.669764 | − | 0.742574i | \(-0.266395\pi\) | ||||
0.669764 | + | 0.742574i | \(0.266395\pi\) | |||||||
\(858\) | −40.8581 | − | 26.7027i | −1.39487 | − | 0.911614i | ||||
\(859\) | −5.64031 | −0.192445 | −0.0962225 | − | 0.995360i | \(-0.530676\pi\) | ||||
−0.0962225 | + | 0.995360i | \(0.530676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.67125 | + | 16.7511i | −0.329595 | + | 0.570876i | ||||
\(862\) | 51.1862 | + | 88.6571i | 1.74341 | + | 3.01967i | ||||
\(863\) | 9.66589 | 0.329031 | 0.164515 | − | 0.986375i | \(-0.447394\pi\) | ||||
0.164515 | + | 0.986375i | \(0.447394\pi\) | |||||||
\(864\) | 4.76873 | + | 8.25969i | 0.162236 | + | 0.281000i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.3001 | 1.09760 | ||||||||
\(867\) | 4.19057 | + | 7.25828i | 0.142319 | + | 0.246504i | ||||
\(868\) | 35.2341 | − | 61.0273i | 1.19592 | − | 2.07140i | ||||
\(869\) | −10.6743 | + | 18.4884i | −0.362100 | + | 0.627176i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2643 | + | 5.69831i | −0.381678 | + | 0.193080i | ||||
\(872\) | −99.9052 | −3.38322 | ||||||||
\(873\) | −2.78689 | + | 4.82703i | −0.0943218 | + | 0.163370i | ||||
\(874\) | −48.7576 | + | 84.4507i | −1.64925 | + | 2.85659i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.83901 | 0.129708 | ||||||||
\(877\) | 7.93579 | + | 13.7452i | 0.267973 | + | 0.464142i | 0.968338 | − | 0.249642i | \(-0.0803130\pi\) |
−0.700366 | + | 0.713784i | \(0.746980\pi\) | |||||||
\(878\) | 41.4205 | + | 71.7424i | 1.39787 | + | 2.42119i | ||||
\(879\) | −33.0857 | −1.11595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.6017 | − | 25.2909i | 0.491943 | − | 0.852070i | −0.508014 | − | 0.861349i | \(-0.669620\pi\) |
0.999957 | + | 0.00927849i | \(0.00295348\pi\) | |||||||
\(882\) | 7.76873 | − | 13.4558i | 0.261587 | − | 0.453082i | ||||
\(883\) | −30.4598 | −1.02505 | −0.512527 | − | 0.858671i | \(-0.671291\pi\) | ||||
−0.512527 | + | 0.858671i | \(0.671291\pi\) | |||||||
\(884\) | 45.0424 | − | 22.7856i | 1.51494 | − | 0.766364i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.38437 | − | 2.39779i | 0.0465087 | − | 0.0805555i | ||||
\(887\) | 5.79967 | − | 10.0453i | 0.194734 | − | 0.337289i | −0.752079 | − | 0.659073i | \(-0.770949\pi\) |
0.946813 | + | 0.321783i | \(0.104282\pi\) | |||||||
\(888\) | 12.7408 | + | 22.0678i | 0.427554 | + | 0.740546i | ||||
\(889\) | −11.5072 | −0.385940 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.60168 | + | 4.50624i | 0.0871595 | + | 0.150965i | ||||
\(892\) | 36.2904 | 1.21509 | ||||||||
\(893\) | 12.8776 | + | 22.3047i | 0.430934 | + | 0.746399i | ||||
\(894\) | −12.5738 | + | 21.7784i | −0.420530 | + | 0.728379i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.66822 | −0.289585 | ||||||||
\(897\) | 1.10284 | − | 19.9351i | 0.0368229 | − | 0.665615i | ||||
\(898\) | −40.0773 | −1.33740 | ||||||||
\(899\) | −3.76014 | + | 6.51276i | −0.125408 | + | 0.217213i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.63798 | − | 13.2294i | −0.254458 | − | 0.440734i | ||||
\(902\) | −72.7018 | −2.42071 | ||||||||
\(903\) | −5.70336 | − | 9.87851i | −0.189796 | − | 0.328736i | ||||
\(904\) | 40.3509 | + | 69.8898i | 1.34205 | + | 2.32450i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −24.3425 | − | 42.1625i | −0.808726 | − | 1.40075i | ||||
\(907\) | 21.4593 | − | 37.1686i | 0.712545 | − | 1.23416i | −0.251354 | − | 0.967895i | \(-0.580876\pi\) |
0.963899 | − | 0.266268i | \(-0.0857907\pi\) | |||||||
\(908\) | 55.6571 | − | 96.4009i | 1.84705 | − | 3.19918i | ||||
\(909\) | 2.40672 | 0.0798257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0726 | 1.39393 | 0.696964 | − | 0.717106i | \(-0.254534\pi\) | ||||
0.696964 | + | 0.717106i | \(0.254534\pi\) | |||||||
\(912\) | −31.1475 | + | 53.9491i | −1.03140 | + | 1.78643i | ||||
\(913\) | 30.0168 | − | 51.9906i | 0.993411 | − | 1.72064i | ||||
\(914\) | 12.4539 | + | 21.5709i | 0.411940 | + | 0.713501i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.96603 | − | 3.40526i | −0.0649594 | − | 0.112513i | ||||
\(917\) | −8.23663 | − | 14.2663i | −0.271997 | − | 0.471113i | ||||
\(918\) | −7.63798 | −0.252091 | ||||||||
\(919\) | −19.5575 | − | 33.8746i | −0.645142 | − | 1.11742i | −0.984269 | − | 0.176678i | \(-0.943465\pi\) |
0.339127 | − | 0.940741i | \(-0.389868\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.18521 | + | 12.4451i | −0.236761 | + | 0.410081i | ||||
\(922\) | −42.5966 | −1.40285 | ||||||||
\(923\) | 1.93276 | − | 34.9367i | 0.0636175 | − | 1.14996i | ||||
\(924\) | 89.3700 | 2.94006 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.0640 | − | 55.5365i | 1.05369 | − | 1.82504i | ||||
\(927\) | 9.22151 | + | 15.9721i | 0.302874 | + | 0.524593i | ||||
\(928\) | −17.4817 | −0.573863 | ||||||||
\(929\) | −5.23127 | − | 9.06082i | −0.171632 | − | 0.297276i | 0.767358 | − | 0.641218i | \(-0.221571\pi\) |
−0.938991 | + | 0.343943i | \(0.888237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.4235 | 1.32483 | ||||||||
\(932\) | −31.9610 | − | 55.3580i | −1.04692 | − | 1.81331i | ||||
\(933\) | 4.35343 | − | 7.54036i | 0.142525 | − | 0.246860i | ||||
\(934\) | 26.4593 | − | 45.8289i | 0.865775 | − | 1.49957i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.43462 | − | 25.9324i | 0.0468922 | − | 0.847628i | ||||
\(937\) | −39.6269 | −1.29455 | −0.647277 | − | 0.762255i | \(-0.724092\pi\) | ||||
−0.647277 | + | 0.762255i | \(0.724092\pi\) | |||||||
\(938\) | 16.4037 | − | 28.4120i | 0.535599 | − | 0.927685i | ||||
\(939\) | −4.08236 | + | 7.07086i | −0.133223 | + | 0.230749i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3146 | 0.499242 | 0.249621 | − | 0.968344i | \(-0.419694\pi\) | ||||
0.249621 | + | 0.968344i | \(0.419694\pi\) | |||||||
\(942\) | 13.4902 | + | 23.3658i | 0.439536 | + | 0.761299i | ||||
\(943\) | −14.8692 | − | 25.7543i | −0.484209 | − | 0.838675i | ||||
\(944\) | −67.8326 | −2.20776 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.4370 | − | 37.1299i | 0.696976 | − | 1.20720i | ||||
\(947\) | −16.6433 | + | 28.8271i | −0.540836 | + | 0.936756i | 0.458020 | + | 0.888942i | \(0.348559\pi\) |
−0.998856 | + | 0.0478138i | \(0.984775\pi\) | |||||||
\(948\) | −19.5654 | −0.635454 | ||||||||
\(949\) | −2.42972 | − | 1.58794i | −0.0788722 | − | 0.0515466i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.70452 | − | 11.6126i | 0.217409 | − | 0.376564i | ||||
\(952\) | −38.0833 | + | 65.9623i | −1.23429 | + | 2.13785i | ||||
\(953\) | 11.7045 | + | 20.2728i | 0.379147 | + | 0.656701i | 0.990938 | − | 0.134318i | \(-0.0428842\pi\) |
−0.611792 | + | 0.791019i | \(0.709551\pi\) | |||||||
\(954\) | −13.5375 | −0.438292 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −30.5119 | − | 52.8481i | −0.986825 | − | 1.70923i | ||||
\(957\) | −9.53747 | −0.308303 | ||||||||
\(958\) | −0.211247 | − | 0.365891i | −0.00682509 | − | 0.0118214i | ||||
\(959\) | −19.2227 | + | 33.2947i | −0.620733 | + | 1.07514i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1667 | −0.456989 | ||||||||
\(962\) | 1.83294 | − | 33.1325i | 0.0590965 | − | 1.06824i | ||||
\(963\) | −10.9358 | −0.352401 | ||||||||
\(964\) | −30.4454 | + | 52.7329i | −0.980579 | + | 1.69841i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 25.9442 | + | 44.9366i | 0.834740 | + | 1.44581i | ||||
\(967\) | −27.8669 | −0.896140 | −0.448070 | − | 0.893999i | \(-0.647888\pi\) | ||||
−0.448070 | + | 0.893999i | \(0.647888\pi\) | |||||||
\(968\) | 57.8968 | + | 100.280i | 1.86087 | + | 3.22313i | ||||
\(969\) | −9.93579 | − | 17.2093i | −0.319184 | − | 0.552842i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.25917 | + | 3.91300i | 0.0725003 | + | 0.125574i | 0.899997 | − | 0.435897i | \(-0.143569\pi\) |
−0.827496 | + | 0.561471i | \(0.810236\pi\) | |||||||
\(972\) | −2.38437 | + | 4.12985i | −0.0764786 | + | 0.132465i | ||||
\(973\) | −29.0791 | + | 50.3665i | −0.932234 | + | 1.61468i | ||||
\(974\) | 6.66822 | 0.213664 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.6101 | −1.01181 | ||||||||
\(977\) | −21.2420 | + | 36.7922i | −0.679592 | + | 1.17709i | 0.295512 | + | 0.955339i | \(0.404510\pi\) |
−0.975104 | + | 0.221748i | \(0.928824\pi\) | |||||||
\(978\) | 14.9249 | − | 25.8506i | 0.477245 | − | 0.826612i | ||||
\(979\) | 25.5822 | + | 44.3096i | 0.817610 | + | 1.41614i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.93462 | − | 12.0111i | −0.221406 | − | 0.383486i | ||||
\(982\) | 36.9968 | + | 64.0803i | 1.18061 | + | 2.04488i | ||||
\(983\) | −9.87158 | −0.314854 | −0.157427 | − | 0.987531i | \(-0.550320\pi\) | ||||
−0.157427 | + | 0.987531i | \(0.550320\pi\) | |||||||
\(984\) | −19.3425 | − | 33.5022i | −0.616617 | − | 1.06801i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.00000 | − | 12.1244i | 0.222925 | − | 0.386118i | ||||
\(987\) | 13.7045 | 0.436220 | ||||||||
\(988\) | 103.849 | − | 52.5344i | 3.30389 | − | 1.67134i | ||||
\(989\) | 17.5375 | 0.557659 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5598 | + | 18.2901i | −0.335444 | + | 0.581005i | −0.983570 | − | 0.180527i | \(-0.942220\pi\) |
0.648126 | + | 0.761533i | \(0.275553\pi\) | |||||||
\(992\) | 19.5654 | + | 33.8882i | 0.621201 | + | 1.07595i | ||||
\(993\) | 21.4793 | 0.681626 | ||||||||
\(994\) | 45.4677 | + | 78.7524i | 1.44215 | + | 2.49787i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 55.0191 | 1.74335 | ||||||||
\(997\) | 8.54167 | + | 14.7946i | 0.270517 | + | 0.468550i | 0.968994 | − | 0.247083i | \(-0.0794719\pi\) |
−0.698477 | + | 0.715632i | \(0.746139\pi\) | |||||||
\(998\) | −36.2420 | + | 62.7730i | −1.14722 | + | 1.98704i | ||||
\(999\) | −1.76873 | + | 3.06354i | −0.0559603 | + | 0.0969260i |
(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 | 975.2.i.l.451.3 | 6 | ||
5.2 | odd | 4 | 975.2.bb.k.724.6 | 12 | |||
5.3 | odd | 4 | 975.2.bb.k.724.1 | 12 | |||
5.4 | even | 2 | 195.2.i.d.61.1 | yes | 6 | ||
13.3 | even | 3 | inner | 975.2.i.l.601.3 | 6 | ||
15.14 | odd | 2 | 585.2.j.f.451.3 | 6 | |||
65.3 | odd | 12 | 975.2.bb.k.874.6 | 12 | |||
65.4 | even | 6 | 2535.2.a.ba.1.1 | 3 | |||
65.9 | even | 6 | 2535.2.a.bb.1.3 | 3 | |||
65.29 | even | 6 | 195.2.i.d.16.1 | ✓ | 6 | ||
65.42 | odd | 12 | 975.2.bb.k.874.1 | 12 | |||
195.29 | odd | 6 | 585.2.j.f.406.3 | 6 | |||
195.74 | odd | 6 | 7605.2.a.bv.1.1 | 3 | |||
195.134 | odd | 6 | 7605.2.a.bw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.1 | ✓ | 6 | 65.29 | even | 6 | ||
195.2.i.d.61.1 | yes | 6 | 5.4 | even | 2 | ||
585.2.j.f.406.3 | 6 | 195.29 | odd | 6 | |||
585.2.j.f.451.3 | 6 | 15.14 | odd | 2 | |||
975.2.i.l.451.3 | 6 | 1.1 | even | 1 | trivial | ||
975.2.i.l.601.3 | 6 | 13.3 | even | 3 | inner | ||
975.2.bb.k.724.1 | 12 | 5.3 | odd | 4 | |||
975.2.bb.k.724.6 | 12 | 5.2 | odd | 4 | |||
975.2.bb.k.874.1 | 12 | 65.42 | odd | 12 | |||
975.2.bb.k.874.6 | 12 | 65.3 | odd | 12 | |||
2535.2.a.ba.1.1 | 3 | 65.4 | even | 6 | |||
2535.2.a.bb.1.3 | 3 | 65.9 | even | 6 | |||
7605.2.a.bv.1.1 | 3 | 195.74 | odd | 6 | |||
7605.2.a.bw.1.3 | 3 | 195.134 | odd | 6 |