Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(61,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, 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("390.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.2 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.61 |
Dual form | 390.2.i.g.211.2 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.280776 | + | 0.486319i | 0.106124 | + | 0.183811i | 0.914197 | − | 0.405271i | \(-0.132823\pi\) |
−0.808073 | + | 0.589082i | \(0.799489\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | −2.06155 | + | 3.57071i | −0.621582 | + | 1.07661i | 0.367610 | + | 0.929980i | \(0.380176\pi\) |
−0.989191 | + | 0.146631i | \(0.953157\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.84233 | + | 2.21837i | 0.788320 | + | 0.615265i | ||||
\(14\) | −0.561553 | −0.150081 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.56155 | + | 2.70469i | 0.378732 | + | 0.655983i | 0.990878 | − | 0.134761i | \(-0.0430268\pi\) |
−0.612146 | + | 0.790745i | \(0.709693\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.280776 | − | 0.486319i | −0.0644145 | − | 0.111569i | 0.832020 | − | 0.554746i | \(-0.187185\pi\) |
−0.896434 | + | 0.443177i | \(0.853851\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −0.561553 | −0.122541 | ||||||||
\(22\) | −2.06155 | − | 3.57071i | −0.439525 | − | 0.761279i | ||||
\(23\) | −2.34233 | + | 4.05703i | −0.488409 | + | 0.845950i | −0.999911 | − | 0.0133324i | \(-0.995756\pi\) |
0.511502 | + | 0.859282i | \(0.329089\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.34233 | + | 1.35234i | −0.655485 | + | 0.265217i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.280776 | − | 0.486319i | 0.0530618 | − | 0.0919057i | ||||
\(29\) | −1.21922 | + | 2.11176i | −0.226404 | + | 0.392143i | −0.956740 | − | 0.290945i | \(-0.906030\pi\) |
0.730336 | + | 0.683088i | \(0.239364\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | −6.68466 | −1.20060 | −0.600300 | − | 0.799775i | \(-0.704952\pi\) | ||||
−0.600300 | + | 0.799775i | \(0.704952\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −2.06155 | − | 3.57071i | −0.358870 | − | 0.621582i | ||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | 0.280776 | + | 0.486319i | 0.0474599 | + | 0.0822029i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 2.06155 | − | 3.57071i | 0.338917 | − | 0.587022i | −0.645312 | − | 0.763919i | \(-0.723273\pi\) |
0.984229 | + | 0.176897i | \(0.0566060\pi\) | |||||||
\(38\) | 0.561553 | 0.0910959 | ||||||||
\(39\) | −3.34233 | + | 1.35234i | −0.535201 | + | 0.216548i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −6.12311 | + | 10.6055i | −0.956268 | + | 1.65631i | −0.224830 | + | 0.974398i | \(0.572183\pi\) |
−0.731438 | + | 0.681908i | \(0.761151\pi\) | |||||||
\(42\) | 0.280776 | − | 0.486319i | 0.0433247 | − | 0.0750407i | ||||
\(43\) | −0.219224 | − | 0.379706i | −0.0334313 | − | 0.0579047i | 0.848826 | − | 0.528673i | \(-0.177310\pi\) |
−0.882257 | + | 0.470768i | \(0.843977\pi\) | |||||||
\(44\) | 4.12311 | 0.621582 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | −2.34233 | − | 4.05703i | −0.345358 | − | 0.598177i | ||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 3.34233 | − | 5.78908i | 0.477476 | − | 0.827012i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | −3.12311 | −0.437322 | ||||||||
\(52\) | 0.500000 | − | 3.57071i | 0.0693375 | − | 0.495169i | ||||
\(53\) | 8.56155 | 1.17602 | 0.588010 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588010 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −2.06155 | + | 3.57071i | −0.277980 | + | 0.481475i | ||||
\(56\) | 0.280776 | + | 0.486319i | 0.0375203 | + | 0.0649871i | ||||
\(57\) | 0.561553 | 0.0743795 | ||||||||
\(58\) | −1.21922 | − | 2.11176i | −0.160092 | − | 0.277287i | ||||
\(59\) | −3.21922 | − | 5.57586i | −0.419107 | − | 0.725915i | 0.576743 | − | 0.816926i | \(-0.304324\pi\) |
−0.995850 | + | 0.0910109i | \(0.970990\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 3.34233 | − | 5.78908i | 0.424476 | − | 0.735214i | ||||
\(63\) | 0.280776 | − | 0.486319i | 0.0353745 | − | 0.0612704i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.84233 | + | 2.21837i | 0.352548 | + | 0.275155i | ||||
\(66\) | 4.12311 | 0.507519 | ||||||||
\(67\) | 1.12311 | − | 1.94528i | 0.137209 | − | 0.237653i | −0.789230 | − | 0.614098i | \(-0.789520\pi\) |
0.926439 | + | 0.376444i | \(0.122853\pi\) | |||||||
\(68\) | 1.56155 | − | 2.70469i | 0.189366 | − | 0.327992i | ||||
\(69\) | −2.34233 | − | 4.05703i | −0.281983 | − | 0.488409i | ||||
\(70\) | −0.561553 | −0.0671184 | ||||||||
\(71\) | 6.56155 | + | 11.3649i | 0.778713 | + | 1.34877i | 0.932684 | + | 0.360695i | \(0.117461\pi\) |
−0.153971 | + | 0.988075i | \(0.549206\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 9.36932 | 1.09660 | 0.548298 | − | 0.836283i | \(-0.315276\pi\) | ||||
0.548298 | + | 0.836283i | \(0.315276\pi\) | |||||||
\(74\) | 2.06155 | + | 3.57071i | 0.239651 | + | 0.415087i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | −0.280776 | + | 0.486319i | −0.0322073 | + | 0.0557846i | ||||
\(77\) | −2.31534 | −0.263858 | ||||||||
\(78\) | 0.500000 | − | 3.57071i | 0.0566139 | − | 0.404304i | ||||
\(79\) | 11.5616 | 1.30078 | 0.650388 | − | 0.759602i | \(-0.274606\pi\) | ||||
0.650388 | + | 0.759602i | \(0.274606\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6.12311 | − | 10.6055i | −0.676184 | − | 1.17118i | ||||
\(83\) | −7.12311 | −0.781862 | −0.390931 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390931 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(84\) | 0.280776 | + | 0.486319i | 0.0306352 | + | 0.0530618i | ||||
\(85\) | 1.56155 | + | 2.70469i | 0.169374 | + | 0.293365i | ||||
\(86\) | 0.438447 | 0.0472790 | ||||||||
\(87\) | −1.21922 | − | 2.11176i | −0.130714 | − | 0.226404i | ||||
\(88\) | −2.06155 | + | 3.57071i | −0.219762 | + | 0.380639i | ||||
\(89\) | 9.40388 | − | 16.2880i | 0.996810 | − | 1.72652i | 0.429281 | − | 0.903171i | \(-0.358767\pi\) |
0.567529 | − | 0.823354i | \(-0.307900\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −0.280776 | + | 2.00514i | −0.0294334 | + | 0.210196i | ||||
\(92\) | 4.68466 | 0.488409 | ||||||||
\(93\) | 3.34233 | − | 5.78908i | 0.346583 | − | 0.600300i | ||||
\(94\) | −3.50000 | + | 6.06218i | −0.360997 | + | 0.625266i | ||||
\(95\) | −0.280776 | − | 0.486319i | −0.0288071 | − | 0.0498953i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.56155 | + | 6.16879i | 0.361621 | + | 0.626346i | 0.988228 | − | 0.152990i | \(-0.0488901\pi\) |
−0.626607 | + | 0.779335i | \(0.715557\pi\) | |||||||
\(98\) | 3.34233 | + | 5.78908i | 0.337626 | + | 0.584786i | ||||
\(99\) | 4.12311 | 0.414388 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.43845 | − | 7.68762i | 0.441642 | − | 0.764946i | −0.556170 | − | 0.831069i | \(-0.687729\pi\) |
0.997812 | + | 0.0661225i | \(0.0210628\pi\) | |||||||
\(102\) | 1.56155 | − | 2.70469i | 0.154617 | − | 0.267804i | ||||
\(103\) | 4.56155 | 0.449463 | 0.224732 | − | 0.974421i | \(-0.427849\pi\) | ||||
0.224732 | + | 0.974421i | \(0.427849\pi\) | |||||||
\(104\) | 2.84233 | + | 2.21837i | 0.278713 | + | 0.217529i | ||||
\(105\) | −0.561553 | −0.0548019 | ||||||||
\(106\) | −4.28078 | + | 7.41452i | −0.415786 | + | 0.720162i | ||||
\(107\) | −1.00000 | + | 1.73205i | −0.0966736 | + | 0.167444i | −0.910306 | − | 0.413936i | \(-0.864154\pi\) |
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −3.75379 | −0.359548 | −0.179774 | − | 0.983708i | \(-0.557537\pi\) | ||||
−0.179774 | + | 0.983708i | \(0.557537\pi\) | |||||||
\(110\) | −2.06155 | − | 3.57071i | −0.196561 | − | 0.340454i | ||||
\(111\) | 2.06155 | + | 3.57071i | 0.195674 | + | 0.338917i | ||||
\(112\) | −0.561553 | −0.0530618 | ||||||||
\(113\) | −4.34233 | − | 7.52113i | −0.408492 | − | 0.707529i | 0.586229 | − | 0.810145i | \(-0.300612\pi\) |
−0.994721 | + | 0.102617i | \(0.967279\pi\) | |||||||
\(114\) | −0.280776 | + | 0.486319i | −0.0262971 | + | 0.0455479i | ||||
\(115\) | −2.34233 | + | 4.05703i | −0.218423 | + | 0.378320i | ||||
\(116\) | 2.43845 | 0.226404 | ||||||||
\(117\) | 0.500000 | − | 3.57071i | 0.0462250 | − | 0.330113i | ||||
\(118\) | 6.43845 | 0.592707 | ||||||||
\(119\) | −0.876894 | + | 1.51883i | −0.0803848 | + | 0.139231i | ||||
\(120\) | −0.500000 | + | 0.866025i | −0.0456435 | + | 0.0790569i | ||||
\(121\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | ||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | −6.12311 | − | 10.6055i | −0.552102 | − | 0.956268i | ||||
\(124\) | 3.34233 | + | 5.78908i | 0.300150 | + | 0.519875i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.280776 | + | 0.486319i | 0.0250136 | + | 0.0433247i | ||||
\(127\) | 4.28078 | − | 7.41452i | 0.379857 | − | 0.657932i | −0.611184 | − | 0.791489i | \(-0.709306\pi\) |
0.991041 | + | 0.133556i | \(0.0426397\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.438447 | 0.0386031 | ||||||||
\(130\) | −3.34233 | + | 1.35234i | −0.293142 | + | 0.118608i | ||||
\(131\) | −2.12311 | −0.185497 | −0.0927483 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927483 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(132\) | −2.06155 | + | 3.57071i | −0.179435 | + | 0.310791i | ||||
\(133\) | 0.157671 | − | 0.273094i | 0.0136718 | − | 0.0236802i | ||||
\(134\) | 1.12311 | + | 1.94528i | 0.0970215 | + | 0.168046i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 1.56155 | + | 2.70469i | 0.133902 | + | 0.231925i | ||||
\(137\) | −5.90388 | − | 10.2258i | −0.504403 | − | 0.873651i | −0.999987 | − | 0.00509126i | \(-0.998379\pi\) |
0.495584 | − | 0.868560i | \(-0.334954\pi\) | |||||||
\(138\) | 4.68466 | 0.398785 | ||||||||
\(139\) | −6.28078 | − | 10.8786i | −0.532729 | − | 0.922713i | −0.999270 | − | 0.0382133i | \(-0.987833\pi\) |
0.466541 | − | 0.884500i | \(-0.345500\pi\) | |||||||
\(140\) | 0.280776 | − | 0.486319i | 0.0237299 | − | 0.0411015i | ||||
\(141\) | −3.50000 | + | 6.06218i | −0.294753 | + | 0.510527i | ||||
\(142\) | −13.1231 | −1.10127 | ||||||||
\(143\) | −13.7808 | + | 5.57586i | −1.15241 | + | 0.466277i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.21922 | + | 2.11176i | −0.101251 | + | 0.175372i | ||||
\(146\) | −4.68466 | + | 8.11407i | −0.387705 | + | 0.671525i | ||||
\(147\) | 3.34233 | + | 5.78908i | 0.275671 | + | 0.477476i | ||||
\(148\) | −4.12311 | −0.338917 | ||||||||
\(149\) | 1.09612 | + | 1.89853i | 0.0897975 | + | 0.155534i | 0.907425 | − | 0.420213i | \(-0.138045\pi\) |
−0.817628 | + | 0.575747i | \(0.804711\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −15.3693 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715051\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715051\pi\) | |||||||
\(152\) | −0.280776 | − | 0.486319i | −0.0227740 | − | 0.0394457i | ||||
\(153\) | 1.56155 | − | 2.70469i | 0.126244 | − | 0.218661i | ||||
\(154\) | 1.15767 | − | 2.00514i | 0.0932878 | − | 0.161579i | ||||
\(155\) | −6.68466 | −0.536925 | ||||||||
\(156\) | 2.84233 | + | 2.21837i | 0.227568 | + | 0.177612i | ||||
\(157\) | 13.8769 | 1.10750 | 0.553748 | − | 0.832684i | \(-0.313197\pi\) | ||||
0.553748 | + | 0.832684i | \(0.313197\pi\) | |||||||
\(158\) | −5.78078 | + | 10.0126i | −0.459894 | + | 0.796560i | ||||
\(159\) | −4.28078 | + | 7.41452i | −0.339488 | + | 0.588010i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −2.63068 | −0.207327 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 7.21922 | + | 12.5041i | 0.565453 | + | 0.979394i | 0.997007 | + | 0.0773067i | \(0.0246321\pi\) |
−0.431554 | + | 0.902087i | \(0.642035\pi\) | |||||||
\(164\) | 12.2462 | 0.956268 | ||||||||
\(165\) | −2.06155 | − | 3.57071i | −0.160492 | − | 0.277980i | ||||
\(166\) | 3.56155 | − | 6.16879i | 0.276430 | − | 0.478791i | ||||
\(167\) | −2.18466 | + | 3.78394i | −0.169054 | + | 0.292810i | −0.938087 | − | 0.346398i | \(-0.887405\pi\) |
0.769034 | + | 0.639208i | \(0.220738\pi\) | |||||||
\(168\) | −0.561553 | −0.0433247 | ||||||||
\(169\) | 3.15767 | + | 12.6107i | 0.242898 | + | 0.970052i | ||||
\(170\) | −3.12311 | −0.239531 | ||||||||
\(171\) | −0.280776 | + | 0.486319i | −0.0214715 | + | 0.0371897i | ||||
\(172\) | −0.219224 | + | 0.379706i | −0.0167156 | + | 0.0289523i | ||||
\(173\) | −10.0885 | − | 17.4739i | −0.767018 | − | 1.32851i | −0.939173 | − | 0.343444i | \(-0.888407\pi\) |
0.172156 | − | 0.985070i | \(-0.444927\pi\) | |||||||
\(174\) | 2.43845 | 0.184858 | ||||||||
\(175\) | 0.280776 | + | 0.486319i | 0.0212247 | + | 0.0367623i | ||||
\(176\) | −2.06155 | − | 3.57071i | −0.155395 | − | 0.269153i | ||||
\(177\) | 6.43845 | 0.483943 | ||||||||
\(178\) | 9.40388 | + | 16.2880i | 0.704851 | + | 1.22084i | ||||
\(179\) | 6.34233 | − | 10.9852i | 0.474048 | − | 0.821075i | −0.525511 | − | 0.850787i | \(-0.676126\pi\) |
0.999559 | + | 0.0297120i | \(0.00945900\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 2.87689 | 0.213838 | 0.106919 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106919 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(182\) | −1.59612 | − | 1.24573i | −0.118312 | − | 0.0923398i | ||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | −2.34233 | + | 4.05703i | −0.172679 | + | 0.299088i | ||||
\(185\) | 2.06155 | − | 3.57071i | 0.151568 | − | 0.262524i | ||||
\(186\) | 3.34233 | + | 5.78908i | 0.245071 | + | 0.424476i | ||||
\(187\) | −12.8769 | −0.941652 | ||||||||
\(188\) | −3.50000 | − | 6.06218i | −0.255264 | − | 0.442130i | ||||
\(189\) | 0.280776 | + | 0.486319i | 0.0204235 | + | 0.0353745i | ||||
\(190\) | 0.561553 | 0.0407393 | ||||||||
\(191\) | −5.43845 | − | 9.41967i | −0.393512 | − | 0.681583i | 0.599398 | − | 0.800451i | \(-0.295407\pi\) |
−0.992910 | + | 0.118868i | \(0.962073\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(194\) | −7.12311 | −0.511409 | ||||||||
\(195\) | −3.34233 | + | 1.35234i | −0.239349 | + | 0.0968434i | ||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | −6.40388 | + | 11.0918i | −0.456258 | + | 0.790262i | −0.998760 | − | 0.0497931i | \(-0.984144\pi\) |
0.542502 | + | 0.840055i | \(0.317477\pi\) | |||||||
\(198\) | −2.06155 | + | 3.57071i | −0.146508 | + | 0.253760i | ||||
\(199\) | −1.43845 | − | 2.49146i | −0.101969 | − | 0.176615i | 0.810527 | − | 0.585701i | \(-0.199181\pi\) |
−0.912496 | + | 0.409086i | \(0.865848\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 1.12311 | + | 1.94528i | 0.0792178 | + | 0.137209i | ||||
\(202\) | 4.43845 | + | 7.68762i | 0.312288 | + | 0.540899i | ||||
\(203\) | −1.36932 | −0.0961072 | ||||||||
\(204\) | 1.56155 | + | 2.70469i | 0.109331 | + | 0.189366i | ||||
\(205\) | −6.12311 | + | 10.6055i | −0.427656 | + | 0.740722i | ||||
\(206\) | −2.28078 | + | 3.95042i | −0.158909 | + | 0.275239i | ||||
\(207\) | 4.68466 | 0.325606 | ||||||||
\(208\) | −3.34233 | + | 1.35234i | −0.231749 | + | 0.0937682i | ||||
\(209\) | 2.31534 | 0.160156 | ||||||||
\(210\) | 0.280776 | − | 0.486319i | 0.0193754 | − | 0.0335592i | ||||
\(211\) | 10.9654 | − | 18.9927i | 0.754892 | − | 1.30751i | −0.190536 | − | 0.981680i | \(-0.561023\pi\) |
0.945428 | − | 0.325831i | \(-0.105644\pi\) | |||||||
\(212\) | −4.28078 | − | 7.41452i | −0.294005 | − | 0.509231i | ||||
\(213\) | −13.1231 | −0.899180 | ||||||||
\(214\) | −1.00000 | − | 1.73205i | −0.0683586 | − | 0.118401i | ||||
\(215\) | −0.219224 | − | 0.379706i | −0.0149509 | − | 0.0258958i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.87689 | − | 3.25088i | −0.127412 | − | 0.220684i | ||||
\(218\) | 1.87689 | − | 3.25088i | 0.127119 | − | 0.220177i | ||||
\(219\) | −4.68466 | + | 8.11407i | −0.316560 | + | 0.548298i | ||||
\(220\) | 4.12311 | 0.277980 | ||||||||
\(221\) | −1.56155 | + | 11.1517i | −0.105041 | + | 0.750146i | ||||
\(222\) | −4.12311 | −0.276725 | ||||||||
\(223\) | −13.6501 | + | 23.6427i | −0.914078 | + | 1.58323i | −0.105832 | + | 0.994384i | \(0.533751\pi\) |
−0.808246 | + | 0.588845i | \(0.799583\pi\) | |||||||
\(224\) | 0.280776 | − | 0.486319i | 0.0187602 | − | 0.0324936i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 8.68466 | 0.577695 | ||||||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | −0.280776 | − | 0.486319i | −0.0185949 | − | 0.0322073i | ||||
\(229\) | −24.2462 | −1.60223 | −0.801117 | − | 0.598507i | \(-0.795761\pi\) | ||||
−0.801117 | + | 0.598507i | \(0.795761\pi\) | |||||||
\(230\) | −2.34233 | − | 4.05703i | −0.154449 | − | 0.267513i | ||||
\(231\) | 1.15767 | − | 2.00514i | 0.0761691 | − | 0.131929i | ||||
\(232\) | −1.21922 | + | 2.11176i | −0.0800460 | + | 0.138644i | ||||
\(233\) | −5.31534 | −0.348220 | −0.174110 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174110 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(234\) | 2.84233 | + | 2.21837i | 0.185809 | + | 0.145019i | ||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | −3.21922 | + | 5.57586i | −0.209554 | + | 0.362957i | ||||
\(237\) | −5.78078 | + | 10.0126i | −0.375502 | + | 0.650388i | ||||
\(238\) | −0.876894 | − | 1.51883i | −0.0568406 | − | 0.0984508i | ||||
\(239\) | −11.3693 | −0.735420 | −0.367710 | − | 0.929941i | \(-0.619858\pi\) | ||||
−0.367710 | + | 0.929941i | \(0.619858\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | 14.0616 | + | 24.3553i | 0.905784 | + | 1.56886i | 0.819861 | + | 0.572563i | \(0.194051\pi\) |
0.0859232 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(242\) | 6.00000 | 0.385695 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.00000 | + | 5.19615i | −0.192055 | + | 0.332650i | ||||
\(245\) | 3.34233 | − | 5.78908i | 0.213534 | − | 0.369851i | ||||
\(246\) | 12.2462 | 0.780790 | ||||||||
\(247\) | 0.280776 | − | 2.00514i | 0.0178654 | − | 0.127584i | ||||
\(248\) | −6.68466 | −0.424476 | ||||||||
\(249\) | 3.56155 | − | 6.16879i | 0.225704 | − | 0.390931i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 4.06155 | + | 7.03482i | 0.256363 | + | 0.444034i | 0.965265 | − | 0.261273i | \(-0.0841424\pi\) |
−0.708902 | + | 0.705307i | \(0.750809\pi\) | |||||||
\(252\) | −0.561553 | −0.0353745 | ||||||||
\(253\) | −9.65767 | − | 16.7276i | −0.607173 | − | 1.05165i | ||||
\(254\) | 4.28078 | + | 7.41452i | 0.268600 | + | 0.465229i | ||||
\(255\) | −3.12311 | −0.195576 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.78078 | − | 4.81645i | 0.173460 | − | 0.300442i | −0.766167 | − | 0.642641i | \(-0.777839\pi\) |
0.939627 | + | 0.342200i | \(0.111172\pi\) | |||||||
\(258\) | −0.219224 | + | 0.379706i | −0.0136483 | + | 0.0236395i | ||||
\(259\) | 2.31534 | 0.143868 | ||||||||
\(260\) | 0.500000 | − | 3.57071i | 0.0310087 | − | 0.221446i | ||||
\(261\) | 2.43845 | 0.150936 | ||||||||
\(262\) | 1.06155 | − | 1.83866i | 0.0655830 | − | 0.113593i | ||||
\(263\) | 6.50000 | − | 11.2583i | 0.400807 | − | 0.694218i | −0.593016 | − | 0.805190i | \(-0.702063\pi\) |
0.993824 | + | 0.110972i | \(0.0353964\pi\) | |||||||
\(264\) | −2.06155 | − | 3.57071i | −0.126880 | − | 0.219762i | ||||
\(265\) | 8.56155 | 0.525932 | ||||||||
\(266\) | 0.157671 | + | 0.273094i | 0.00966742 | + | 0.0167445i | ||||
\(267\) | 9.40388 | + | 16.2880i | 0.575508 | + | 0.996810i | ||||
\(268\) | −2.24621 | −0.137209 | ||||||||
\(269\) | −10.6847 | − | 18.5064i | −0.651455 | − | 1.12835i | −0.982770 | − | 0.184833i | \(-0.940826\pi\) |
0.331315 | − | 0.943520i | \(-0.392508\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | 6.58854 | − | 11.4117i | 0.400225 | − | 0.693211i | −0.593528 | − | 0.804814i | \(-0.702265\pi\) |
0.993753 | + | 0.111603i | \(0.0355985\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | −1.59612 | − | 1.24573i | −0.0966015 | − | 0.0753951i | ||||
\(274\) | 11.8078 | 0.713333 | ||||||||
\(275\) | −2.06155 | + | 3.57071i | −0.124316 | + | 0.215322i | ||||
\(276\) | −2.34233 | + | 4.05703i | −0.140992 | + | 0.244205i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 12.5616 | 0.753392 | ||||||||
\(279\) | 3.34233 | + | 5.78908i | 0.200100 | + | 0.346583i | ||||
\(280\) | 0.280776 | + | 0.486319i | 0.0167796 | + | 0.0290631i | ||||
\(281\) | 16.2462 | 0.969168 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(282\) | −3.50000 | − | 6.06218i | −0.208422 | − | 0.360997i | ||||
\(283\) | −7.78078 | + | 13.4767i | −0.462519 | + | 0.801107i | −0.999086 | − | 0.0427513i | \(-0.986388\pi\) |
0.536567 | + | 0.843858i | \(0.319721\pi\) | |||||||
\(284\) | 6.56155 | − | 11.3649i | 0.389357 | − | 0.674385i | ||||
\(285\) | 0.561553 | 0.0332635 | ||||||||
\(286\) | 2.06155 | − | 14.7224i | 0.121902 | − | 0.870556i | ||||
\(287\) | −6.87689 | −0.405930 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 3.62311 | − | 6.27540i | 0.213124 | − | 0.369141i | ||||
\(290\) | −1.21922 | − | 2.11176i | −0.0715953 | − | 0.124007i | ||||
\(291\) | −7.12311 | −0.417564 | ||||||||
\(292\) | −4.68466 | − | 8.11407i | −0.274149 | − | 0.474840i | ||||
\(293\) | −1.96543 | − | 3.40423i | −0.114822 | − | 0.198877i | 0.802887 | − | 0.596132i | \(-0.203296\pi\) |
−0.917709 | + | 0.397254i | \(0.869963\pi\) | |||||||
\(294\) | −6.68466 | −0.389857 | ||||||||
\(295\) | −3.21922 | − | 5.57586i | −0.187430 | − | 0.324639i | ||||
\(296\) | 2.06155 | − | 3.57071i | 0.119825 | − | 0.207544i | ||||
\(297\) | −2.06155 | + | 3.57071i | −0.119623 | + | 0.207194i | ||||
\(298\) | −2.19224 | −0.126993 | ||||||||
\(299\) | −15.6577 | + | 6.33527i | −0.905506 | + | 0.366378i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0.123106 | − | 0.213225i | 0.00709569 | − | 0.0122901i | ||||
\(302\) | 7.68466 | − | 13.3102i | 0.442202 | − | 0.765917i | ||||
\(303\) | 4.43845 | + | 7.68762i | 0.254982 | + | 0.441642i | ||||
\(304\) | 0.561553 | 0.0322073 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | 1.56155 | + | 2.70469i | 0.0892680 | + | 0.154617i | ||||
\(307\) | 25.6155 | 1.46196 | 0.730978 | − | 0.682401i | \(-0.239064\pi\) | ||||
0.730978 | + | 0.682401i | \(0.239064\pi\) | |||||||
\(308\) | 1.15767 | + | 2.00514i | 0.0659644 | + | 0.114254i | ||||
\(309\) | −2.28078 | + | 3.95042i | −0.129749 | + | 0.224732i | ||||
\(310\) | 3.34233 | − | 5.78908i | 0.189832 | − | 0.328798i | ||||
\(311\) | 30.7386 | 1.74303 | 0.871514 | − | 0.490371i | \(-0.163139\pi\) | ||||
0.871514 | + | 0.490371i | \(0.163139\pi\) | |||||||
\(312\) | −3.34233 | + | 1.35234i | −0.189222 | + | 0.0765614i | ||||
\(313\) | 31.3693 | 1.77310 | 0.886549 | − | 0.462634i | \(-0.153096\pi\) | ||||
0.886549 | + | 0.462634i | \(0.153096\pi\) | |||||||
\(314\) | −6.93845 | + | 12.0177i | −0.391559 | + | 0.678200i | ||||
\(315\) | 0.280776 | − | 0.486319i | 0.0158200 | − | 0.0274010i | ||||
\(316\) | −5.78078 | − | 10.0126i | −0.325194 | − | 0.563253i | ||||
\(317\) | −24.8078 | −1.39334 | −0.696671 | − | 0.717390i | \(-0.745336\pi\) | ||||
−0.696671 | + | 0.717390i | \(0.745336\pi\) | |||||||
\(318\) | −4.28078 | − | 7.41452i | −0.240054 | − | 0.415786i | ||||
\(319\) | −5.02699 | − | 8.70700i | −0.281457 | − | 0.487498i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.00000 | − | 1.73205i | −0.0558146 | − | 0.0966736i | ||||
\(322\) | 1.31534 | − | 2.27824i | 0.0733011 | − | 0.126961i | ||||
\(323\) | 0.876894 | − | 1.51883i | 0.0487917 | − | 0.0845097i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.84233 | + | 2.21837i | 0.157664 | + | 0.123053i | ||||
\(326\) | −14.4384 | −0.799672 | ||||||||
\(327\) | 1.87689 | − | 3.25088i | 0.103792 | − | 0.179774i | ||||
\(328\) | −6.12311 | + | 10.6055i | −0.338092 | + | 0.585592i | ||||
\(329\) | 1.96543 | + | 3.40423i | 0.108358 | + | 0.187681i | ||||
\(330\) | 4.12311 | 0.226969 | ||||||||
\(331\) | −15.3693 | − | 26.6204i | −0.844774 | − | 1.46319i | −0.885817 | − | 0.464034i | \(-0.846401\pi\) |
0.0410432 | − | 0.999157i | \(-0.486932\pi\) | |||||||
\(332\) | 3.56155 | + | 6.16879i | 0.195466 | + | 0.338556i | ||||
\(333\) | −4.12311 | −0.225945 | ||||||||
\(334\) | −2.18466 | − | 3.78394i | −0.119539 | − | 0.207048i | ||||
\(335\) | 1.12311 | − | 1.94528i | 0.0613618 | − | 0.106282i | ||||
\(336\) | 0.280776 | − | 0.486319i | 0.0153176 | − | 0.0265309i | ||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | −12.5000 | − | 3.57071i | −0.679910 | − | 0.194221i | ||||
\(339\) | 8.68466 | 0.471686 | ||||||||
\(340\) | 1.56155 | − | 2.70469i | 0.0846871 | − | 0.146682i | ||||
\(341\) | 13.7808 | − | 23.8690i | 0.746271 | − | 1.29258i | ||||
\(342\) | −0.280776 | − | 0.486319i | −0.0151826 | − | 0.0262971i | ||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | −0.219224 | − | 0.379706i | −0.0118197 | − | 0.0204724i | ||||
\(345\) | −2.34233 | − | 4.05703i | −0.126107 | − | 0.218423i | ||||
\(346\) | 20.1771 | 1.08473 | ||||||||
\(347\) | −0.438447 | − | 0.759413i | −0.0235371 | − | 0.0407674i | 0.854017 | − | 0.520245i | \(-0.174159\pi\) |
−0.877554 | + | 0.479478i | \(0.840826\pi\) | |||||||
\(348\) | −1.21922 | + | 2.11176i | −0.0653572 | + | 0.113202i | ||||
\(349\) | −4.24621 | + | 7.35465i | −0.227294 | + | 0.393686i | −0.957005 | − | 0.290070i | \(-0.906321\pi\) |
0.729711 | + | 0.683756i | \(0.239655\pi\) | |||||||
\(350\) | −0.561553 | −0.0300163 | ||||||||
\(351\) | 2.84233 | + | 2.21837i | 0.151712 | + | 0.118408i | ||||
\(352\) | 4.12311 | 0.219762 | ||||||||
\(353\) | 12.9309 | − | 22.3969i | 0.688241 | − | 1.19207i | −0.284166 | − | 0.958775i | \(-0.591717\pi\) |
0.972407 | − | 0.233293i | \(-0.0749501\pi\) | |||||||
\(354\) | −3.21922 | + | 5.57586i | −0.171100 | + | 0.296354i | ||||
\(355\) | 6.56155 | + | 11.3649i | 0.348251 | + | 0.603189i | ||||
\(356\) | −18.8078 | −0.996810 | ||||||||
\(357\) | −0.876894 | − | 1.51883i | −0.0464102 | − | 0.0803848i | ||||
\(358\) | 6.34233 | + | 10.9852i | 0.335203 | + | 0.580588i | ||||
\(359\) | 13.1231 | 0.692611 | 0.346306 | − | 0.938122i | \(-0.387436\pi\) | ||||
0.346306 | + | 0.938122i | \(0.387436\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 9.34233 | − | 16.1814i | 0.491702 | − | 0.851652i | ||||
\(362\) | −1.43845 | + | 2.49146i | −0.0756031 | + | 0.130948i | ||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 1.87689 | − | 0.759413i | 0.0983760 | − | 0.0398040i | ||||
\(365\) | 9.36932 | 0.490412 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −6.24621 | + | 10.8188i | −0.326050 | + | 0.564734i | −0.981724 | − | 0.190309i | \(-0.939051\pi\) |
0.655675 | + | 0.755044i | \(0.272384\pi\) | |||||||
\(368\) | −2.34233 | − | 4.05703i | −0.122102 | − | 0.211487i | ||||
\(369\) | 12.2462 | 0.637512 | ||||||||
\(370\) | 2.06155 | + | 3.57071i | 0.107175 | + | 0.185633i | ||||
\(371\) | 2.40388 | + | 4.16365i | 0.124803 | + | 0.216166i | ||||
\(372\) | −6.68466 | −0.346583 | ||||||||
\(373\) | 12.9039 | + | 22.3502i | 0.668138 | + | 1.15725i | 0.978424 | + | 0.206605i | \(0.0662416\pi\) |
−0.310287 | + | 0.950643i | \(0.600425\pi\) | |||||||
\(374\) | 6.43845 | − | 11.1517i | 0.332924 | − | 0.576642i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | −8.15009 | + | 3.29762i | −0.419751 | + | 0.169836i | ||||
\(378\) | −0.561553 | −0.0288832 | ||||||||
\(379\) | 8.84233 | − | 15.3154i | 0.454200 | − | 0.786697i | −0.544442 | − | 0.838799i | \(-0.683259\pi\) |
0.998642 | + | 0.0521012i | \(0.0165918\pi\) | |||||||
\(380\) | −0.280776 | + | 0.486319i | −0.0144035 | + | 0.0249476i | ||||
\(381\) | 4.28078 | + | 7.41452i | 0.219311 | + | 0.379857i | ||||
\(382\) | 10.8769 | 0.556510 | ||||||||
\(383\) | −0.0961180 | − | 0.166481i | −0.00491140 | − | 0.00850679i | 0.863559 | − | 0.504247i | \(-0.168230\pi\) |
−0.868471 | + | 0.495741i | \(0.834897\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −2.31534 | −0.118001 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.219224 | + | 0.379706i | −0.0111438 | + | 0.0193016i | ||||
\(388\) | 3.56155 | − | 6.16879i | 0.180810 | − | 0.313173i | ||||
\(389\) | −18.0540 | −0.915373 | −0.457686 | − | 0.889114i | \(-0.651322\pi\) | ||||
−0.457686 | + | 0.889114i | \(0.651322\pi\) | |||||||
\(390\) | 0.500000 | − | 3.57071i | 0.0253185 | − | 0.180810i | ||||
\(391\) | −14.6307 | −0.739905 | ||||||||
\(392\) | 3.34233 | − | 5.78908i | 0.168813 | − | 0.292393i | ||||
\(393\) | 1.06155 | − | 1.83866i | 0.0535483 | − | 0.0927483i | ||||
\(394\) | −6.40388 | − | 11.0918i | −0.322623 | − | 0.558799i | ||||
\(395\) | 11.5616 | 0.581725 | ||||||||
\(396\) | −2.06155 | − | 3.57071i | −0.103597 | − | 0.179435i | ||||
\(397\) | 10.0616 | + | 17.4271i | 0.504975 | + | 0.874642i | 0.999983 | + | 0.00575403i | \(0.00183158\pi\) |
−0.495009 | + | 0.868888i | \(0.664835\pi\) | |||||||
\(398\) | 2.87689 | 0.144206 | ||||||||
\(399\) | 0.157671 | + | 0.273094i | 0.00789341 | + | 0.0136718i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −0.157671 | + | 0.273094i | −0.00787370 | + | 0.0136377i | −0.869935 | − | 0.493166i | \(-0.835840\pi\) |
0.862062 | + | 0.506803i | \(0.169173\pi\) | |||||||
\(402\) | −2.24621 | −0.112031 | ||||||||
\(403\) | −19.0000 | − | 14.8290i | −0.946457 | − | 0.738687i | ||||
\(404\) | −8.87689 | −0.441642 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 0.684658 | − | 1.18586i | 0.0339790 | − | 0.0588534i | ||||
\(407\) | 8.50000 | + | 14.7224i | 0.421329 | + | 0.729764i | ||||
\(408\) | −3.12311 | −0.154617 | ||||||||
\(409\) | 9.40388 | + | 16.2880i | 0.464992 | + | 0.805390i | 0.999201 | − | 0.0399625i | \(-0.0127239\pi\) |
−0.534209 | + | 0.845352i | \(0.679391\pi\) | |||||||
\(410\) | −6.12311 | − | 10.6055i | −0.302399 | − | 0.523770i | ||||
\(411\) | 11.8078 | 0.582434 | ||||||||
\(412\) | −2.28078 | − | 3.95042i | −0.112366 | − | 0.194623i | ||||
\(413\) | 1.80776 | − | 3.13114i | 0.0889543 | − | 0.154073i | ||||
\(414\) | −2.34233 | + | 4.05703i | −0.115119 | + | 0.199392i | ||||
\(415\) | −7.12311 | −0.349660 | ||||||||
\(416\) | 0.500000 | − | 3.57071i | 0.0245145 | − | 0.175069i | ||||
\(417\) | 12.5616 | 0.615142 | ||||||||
\(418\) | −1.15767 | + | 2.00514i | −0.0566235 | + | 0.0980748i | ||||
\(419\) | −16.2462 | + | 28.1393i | −0.793679 | + | 1.37469i | 0.129995 | + | 0.991515i | \(0.458504\pi\) |
−0.923674 | + | 0.383178i | \(0.874829\pi\) | |||||||
\(420\) | 0.280776 | + | 0.486319i | 0.0137005 | + | 0.0237299i | ||||
\(421\) | −32.4924 | −1.58358 | −0.791792 | − | 0.610791i | \(-0.790852\pi\) | ||||
−0.791792 | + | 0.610791i | \(0.790852\pi\) | |||||||
\(422\) | 10.9654 | + | 18.9927i | 0.533789 | + | 0.924550i | ||||
\(423\) | −3.50000 | − | 6.06218i | −0.170176 | − | 0.294753i | ||||
\(424\) | 8.56155 | 0.415786 | ||||||||
\(425\) | 1.56155 | + | 2.70469i | 0.0757464 | + | 0.131197i | ||||
\(426\) | 6.56155 | − | 11.3649i | 0.317908 | − | 0.550633i | ||||
\(427\) | 1.68466 | − | 2.91791i | 0.0815263 | − | 0.141208i | ||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 2.06155 | − | 14.7224i | 0.0995327 | − | 0.710806i | ||||
\(430\) | 0.438447 | 0.0211438 | ||||||||
\(431\) | 11.3693 | − | 19.6922i | 0.547641 | − | 0.948542i | −0.450795 | − | 0.892628i | \(-0.648859\pi\) |
0.998436 | − | 0.0559140i | \(-0.0178073\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 9.36932 | + | 16.2281i | 0.450261 | + | 0.779874i | 0.998402 | − | 0.0565114i | \(-0.0179977\pi\) |
−0.548141 | + | 0.836386i | \(0.684664\pi\) | |||||||
\(434\) | 3.75379 | 0.180188 | ||||||||
\(435\) | −1.21922 | − | 2.11176i | −0.0584573 | − | 0.101251i | ||||
\(436\) | 1.87689 | + | 3.25088i | 0.0898869 | + | 0.155689i | ||||
\(437\) | 2.63068 | 0.125843 | ||||||||
\(438\) | −4.68466 | − | 8.11407i | −0.223842 | − | 0.387705i | ||||
\(439\) | −12.5616 | + | 21.7572i | −0.599530 | + | 1.03842i | 0.393360 | + | 0.919384i | \(0.371313\pi\) |
−0.992890 | + | 0.119032i | \(0.962021\pi\) | |||||||
\(440\) | −2.06155 | + | 3.57071i | −0.0982807 | + | 0.170227i | ||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | −8.87689 | − | 6.92820i | −0.422231 | − | 0.329541i | ||||
\(443\) | −13.1231 | −0.623498 | −0.311749 | − | 0.950165i | \(-0.600915\pi\) | ||||
−0.311749 | + | 0.950165i | \(0.600915\pi\) | |||||||
\(444\) | 2.06155 | − | 3.57071i | 0.0978370 | − | 0.169459i | ||||
\(445\) | 9.40388 | − | 16.2880i | 0.445787 | − | 0.772125i | ||||
\(446\) | −13.6501 | − | 23.6427i | −0.646351 | − | 1.11951i | ||||
\(447\) | −2.19224 | −0.103689 | ||||||||
\(448\) | 0.280776 | + | 0.486319i | 0.0132654 | + | 0.0229764i | ||||
\(449\) | 10.0885 | + | 17.4739i | 0.476108 | + | 0.824643i | 0.999625 | − | 0.0273722i | \(-0.00871392\pi\) |
−0.523518 | + | 0.852015i | \(0.675381\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −25.2462 | − | 43.7277i | −1.18880 | − | 2.05906i | ||||
\(452\) | −4.34233 | + | 7.52113i | −0.204246 | + | 0.353764i | ||||
\(453\) | 7.68466 | − | 13.3102i | 0.361057 | − | 0.625369i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | −0.280776 | + | 2.00514i | −0.0131630 | + | 0.0940026i | ||||
\(456\) | 0.561553 | 0.0262971 | ||||||||
\(457\) | −10.1231 | + | 17.5337i | −0.473539 | + | 0.820193i | −0.999541 | − | 0.0302897i | \(-0.990357\pi\) |
0.526002 | + | 0.850483i | \(0.323690\pi\) | |||||||
\(458\) | 12.1231 | − | 20.9978i | 0.566476 | − | 0.981164i | ||||
\(459\) | 1.56155 | + | 2.70469i | 0.0728870 | + | 0.126244i | ||||
\(460\) | 4.68466 | 0.218423 | ||||||||
\(461\) | 15.0270 | + | 26.0275i | 0.699877 | + | 1.21222i | 0.968509 | + | 0.248979i | \(0.0800950\pi\) |
−0.268632 | + | 0.963243i | \(0.586572\pi\) | |||||||
\(462\) | 1.15767 | + | 2.00514i | 0.0538597 | + | 0.0932878i | ||||
\(463\) | −7.61553 | −0.353924 | −0.176962 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176962 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(464\) | −1.21922 | − | 2.11176i | −0.0566010 | − | 0.0980359i | ||||
\(465\) | 3.34233 | − | 5.78908i | 0.154997 | − | 0.268462i | ||||
\(466\) | 2.65767 | − | 4.60322i | 0.123114 | − | 0.213240i | ||||
\(467\) | −17.8617 | −0.826543 | −0.413271 | − | 0.910608i | \(-0.635614\pi\) | ||||
−0.413271 | + | 0.910608i | \(0.635614\pi\) | |||||||
\(468\) | −3.34233 | + | 1.35234i | −0.154499 | + | 0.0625121i | ||||
\(469\) | 1.26137 | 0.0582445 | ||||||||
\(470\) | −3.50000 | + | 6.06218i | −0.161443 | + | 0.279627i | ||||
\(471\) | −6.93845 | + | 12.0177i | −0.319707 | + | 0.553748i | ||||
\(472\) | −3.21922 | − | 5.57586i | −0.148177 | − | 0.256650i | ||||
\(473\) | 1.80776 | 0.0831211 | ||||||||
\(474\) | −5.78078 | − | 10.0126i | −0.265520 | − | 0.459894i | ||||
\(475\) | −0.280776 | − | 0.486319i | −0.0128829 | − | 0.0223138i | ||||
\(476\) | 1.75379 | 0.0803848 | ||||||||
\(477\) | −4.28078 | − | 7.41452i | −0.196003 | − | 0.339488i | ||||
\(478\) | 5.68466 | − | 9.84612i | 0.260010 | − | 0.450351i | ||||
\(479\) | 19.1231 | − | 33.1222i | 0.873757 | − | 1.51339i | 0.0156760 | − | 0.999877i | \(-0.495010\pi\) |
0.858081 | − | 0.513514i | \(-0.171657\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 13.7808 | − | 5.57586i | 0.628349 | − | 0.254237i | ||||
\(482\) | −28.1231 | −1.28097 | ||||||||
\(483\) | 1.31534 | − | 2.27824i | 0.0598501 | − | 0.103663i | ||||
\(484\) | −3.00000 | + | 5.19615i | −0.136364 | + | 0.236189i | ||||
\(485\) | 3.56155 | + | 6.16879i | 0.161722 | + | 0.280110i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.52699 | − | 11.3051i | −0.295766 | − | 0.512282i | 0.679397 | − | 0.733771i | \(-0.262242\pi\) |
−0.975163 | + | 0.221489i | \(0.928908\pi\) | |||||||
\(488\) | −3.00000 | − | 5.19615i | −0.135804 | − | 0.235219i | ||||
\(489\) | −14.4384 | −0.652929 | ||||||||
\(490\) | 3.34233 | + | 5.78908i | 0.150991 | + | 0.261524i | ||||
\(491\) | 8.71922 | − | 15.1021i | 0.393493 | − | 0.681550i | −0.599415 | − | 0.800439i | \(-0.704600\pi\) |
0.992908 | + | 0.118889i | \(0.0379332\pi\) | |||||||
\(492\) | −6.12311 | + | 10.6055i | −0.276051 | + | 0.478134i | ||||
\(493\) | −7.61553 | −0.342986 | ||||||||
\(494\) | 1.59612 | + | 1.24573i | 0.0718127 | + | 0.0560481i | ||||
\(495\) | 4.12311 | 0.185320 | ||||||||
\(496\) | 3.34233 | − | 5.78908i | 0.150075 | − | 0.259938i | ||||
\(497\) | −3.68466 | + | 6.38202i | −0.165280 | + | 0.286273i | ||||
\(498\) | 3.56155 | + | 6.16879i | 0.159597 | + | 0.276430i | ||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −2.18466 | − | 3.78394i | −0.0976033 | − | 0.169054i | ||||
\(502\) | −8.12311 | −0.362552 | ||||||||
\(503\) | 21.5270 | + | 37.2858i | 0.959841 | + | 1.66249i | 0.722879 | + | 0.690974i | \(0.242818\pi\) |
0.236962 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(504\) | 0.280776 | − | 0.486319i | 0.0125068 | − | 0.0216624i | ||||
\(505\) | 4.43845 | − | 7.68762i | 0.197508 | − | 0.342094i | ||||
\(506\) | 19.3153 | 0.858672 | ||||||||
\(507\) | −12.5000 | − | 3.57071i | −0.555144 | − | 0.158581i | ||||
\(508\) | −8.56155 | −0.379857 | ||||||||
\(509\) | −20.2732 | + | 35.1142i | −0.898594 | + | 1.55641i | −0.0693009 | + | 0.997596i | \(0.522077\pi\) |
−0.829293 | + | 0.558814i | \(0.811256\pi\) | |||||||
\(510\) | 1.56155 | − | 2.70469i | 0.0691467 | − | 0.119766i | ||||
\(511\) | 2.63068 | + | 4.55648i | 0.116375 | + | 0.201567i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.280776 | − | 0.486319i | −0.0123966 | − | 0.0214715i | ||||
\(514\) | 2.78078 | + | 4.81645i | 0.122655 | + | 0.212444i | ||||
\(515\) | 4.56155 | 0.201006 | ||||||||
\(516\) | −0.219224 | − | 0.379706i | −0.00965078 | − | 0.0167156i | ||||
\(517\) | −14.4309 | + | 24.9950i | −0.634669 | + | 1.09928i | ||||
\(518\) | −1.15767 | + | 2.00514i | −0.0508651 | + | 0.0881010i | ||||
\(519\) | 20.1771 | 0.885676 | ||||||||
\(520\) | 2.84233 | + | 2.21837i | 0.124644 | + | 0.0972820i | ||||
\(521\) | −6.31534 | −0.276680 | −0.138340 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138340 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(522\) | −1.21922 | + | 2.11176i | −0.0533640 | + | 0.0924291i | ||||
\(523\) | 14.9039 | − | 25.8143i | 0.651701 | − | 1.12878i | −0.331009 | − | 0.943628i | \(-0.607389\pi\) |
0.982710 | − | 0.185152i | \(-0.0592777\pi\) | |||||||
\(524\) | 1.06155 | + | 1.83866i | 0.0463741 | + | 0.0803224i | ||||
\(525\) | −0.561553 | −0.0245082 | ||||||||
\(526\) | 6.50000 | + | 11.2583i | 0.283413 | + | 0.490887i | ||||
\(527\) | −10.4384 | − | 18.0799i | −0.454706 | − | 0.787574i | ||||
\(528\) | 4.12311 | 0.179435 | ||||||||
\(529\) | 0.526988 | + | 0.912769i | 0.0229125 | + | 0.0396856i | ||||
\(530\) | −4.28078 | + | 7.41452i | −0.185945 | + | 0.322066i | ||||
\(531\) | −3.21922 | + | 5.57586i | −0.139702 | + | 0.241972i | ||||
\(532\) | −0.315342 | −0.0136718 | ||||||||
\(533\) | −40.9309 | + | 16.5611i | −1.77291 | + | 0.717341i | ||||
\(534\) | −18.8078 | −0.813892 | ||||||||
\(535\) | −1.00000 | + | 1.73205i | −0.0432338 | + | 0.0748831i | ||||
\(536\) | 1.12311 | − | 1.94528i | 0.0485108 | − | 0.0840231i | ||||
\(537\) | 6.34233 | + | 10.9852i | 0.273692 | + | 0.474048i | ||||
\(538\) | 21.3693 | 0.921297 | ||||||||
\(539\) | 13.7808 | + | 23.8690i | 0.593580 | + | 1.02811i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −27.3693 | −1.17670 | −0.588349 | − | 0.808607i | \(-0.700222\pi\) | ||||
−0.588349 | + | 0.808607i | \(0.700222\pi\) | |||||||
\(542\) | 6.58854 | + | 11.4117i | 0.283002 | + | 0.490174i | ||||
\(543\) | −1.43845 | + | 2.49146i | −0.0617297 | + | 0.106919i | ||||
\(544\) | 1.56155 | − | 2.70469i | 0.0669510 | − | 0.115963i | ||||
\(545\) | −3.75379 | −0.160795 | ||||||||
\(546\) | 1.87689 | − | 0.759413i | 0.0803237 | − | 0.0324999i | ||||
\(547\) | −5.61553 | −0.240103 | −0.120051 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120051 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(548\) | −5.90388 | + | 10.2258i | −0.252201 | + | 0.436826i | ||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | −2.06155 | − | 3.57071i | −0.0879049 | − | 0.152256i | ||||
\(551\) | 1.36932 | 0.0583349 | ||||||||
\(552\) | −2.34233 | − | 4.05703i | −0.0996962 | − | 0.172679i | ||||
\(553\) | 3.24621 | + | 5.62260i | 0.138043 | + | 0.239097i | ||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | 2.06155 | + | 3.57071i | 0.0875080 | + | 0.151568i | ||||
\(556\) | −6.28078 | + | 10.8786i | −0.266364 | + | 0.461356i | ||||
\(557\) | 4.28078 | − | 7.41452i | 0.181382 | − | 0.314163i | −0.760969 | − | 0.648788i | \(-0.775276\pi\) |
0.942352 | + | 0.334625i | \(0.108610\pi\) | |||||||
\(558\) | −6.68466 | −0.282984 | ||||||||
\(559\) | 0.219224 | − | 1.56557i | 0.00927217 | − | 0.0662165i | ||||
\(560\) | −0.561553 | −0.0237299 | ||||||||
\(561\) | 6.43845 | − | 11.1517i | 0.271831 | − | 0.470826i | ||||
\(562\) | −8.12311 | + | 14.0696i | −0.342653 | + | 0.593492i | ||||
\(563\) | 16.4924 | + | 28.5657i | 0.695073 | + | 1.20390i | 0.970156 | + | 0.242481i | \(0.0779612\pi\) |
−0.275083 | + | 0.961420i | \(0.588705\pi\) | |||||||
\(564\) | 7.00000 | 0.294753 | ||||||||
\(565\) | −4.34233 | − | 7.52113i | −0.182683 | − | 0.316417i | ||||
\(566\) | −7.78078 | − | 13.4767i | −0.327050 | − | 0.566468i | ||||
\(567\) | −0.561553 | −0.0235830 | ||||||||
\(568\) | 6.56155 | + | 11.3649i | 0.275317 | + | 0.476862i | ||||
\(569\) | −13.0885 | + | 22.6700i | −0.548700 | + | 0.950377i | 0.449664 | + | 0.893198i | \(0.351544\pi\) |
−0.998364 | + | 0.0571787i | \(0.981790\pi\) | |||||||
\(570\) | −0.280776 | + | 0.486319i | −0.0117604 | + | 0.0203697i | ||||
\(571\) | 23.6847 | 0.991172 | 0.495586 | − | 0.868559i | \(-0.334953\pi\) | ||||
0.495586 | + | 0.868559i | \(0.334953\pi\) | |||||||
\(572\) | 11.7192 | + | 9.14657i | 0.490005 | + | 0.382437i | ||||
\(573\) | 10.8769 | 0.454389 | ||||||||
\(574\) | 3.43845 | − | 5.95557i | 0.143518 | − | 0.248580i | ||||
\(575\) | −2.34233 | + | 4.05703i | −0.0976819 | + | 0.169190i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −40.7386 | −1.69597 | −0.847986 | − | 0.530019i | \(-0.822185\pi\) | ||||
−0.847986 | + | 0.530019i | \(0.822185\pi\) | |||||||
\(578\) | 3.62311 | + | 6.27540i | 0.150701 | + | 0.261022i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.43845 | 0.101251 | ||||||||
\(581\) | −2.00000 | − | 3.46410i | −0.0829740 | − | 0.143715i | ||||
\(582\) | 3.56155 | − | 6.16879i | 0.147631 | − | 0.255705i | ||||
\(583\) | −17.6501 | + | 30.5709i | −0.730992 | + | 1.26612i | ||||
\(584\) | 9.36932 | 0.387705 | ||||||||
\(585\) | 0.500000 | − | 3.57071i | 0.0206725 | − | 0.147631i | ||||
\(586\) | 3.93087 | 0.162383 | ||||||||
\(587\) | 20.1231 | − | 34.8542i | 0.830569 | − | 1.43859i | −0.0670179 | − | 0.997752i | \(-0.521348\pi\) |
0.897587 | − | 0.440837i | \(-0.145318\pi\) | |||||||
\(588\) | 3.34233 | − | 5.78908i | 0.137835 | − | 0.238738i | ||||
\(589\) | 1.87689 | + | 3.25088i | 0.0773361 | + | 0.133950i | ||||
\(590\) | 6.43845 | 0.265067 | ||||||||
\(591\) | −6.40388 | − | 11.0918i | −0.263421 | − | 0.456258i | ||||
\(592\) | 2.06155 | + | 3.57071i | 0.0847293 | + | 0.146755i | ||||
\(593\) | 33.1771 | 1.36242 | 0.681210 | − | 0.732088i | \(-0.261454\pi\) | ||||
0.681210 | + | 0.732088i | \(0.261454\pi\) | |||||||
\(594\) | −2.06155 | − | 3.57071i | −0.0845865 | − | 0.146508i | ||||
\(595\) | −0.876894 | + | 1.51883i | −0.0359492 | + | 0.0622658i | ||||
\(596\) | 1.09612 | − | 1.89853i | 0.0448987 | − | 0.0777669i | ||||
\(597\) | 2.87689 | 0.117743 | ||||||||
\(598\) | 2.34233 | − | 16.7276i | 0.0957850 | − | 0.684041i | ||||
\(599\) | −14.0000 | −0.572024 | −0.286012 | − | 0.958226i | \(-0.592330\pi\) | ||||
−0.286012 | + | 0.958226i | \(0.592330\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −14.9924 | + | 25.9676i | −0.611554 | + | 1.05924i | 0.379425 | + | 0.925222i | \(0.376122\pi\) |
−0.990979 | + | 0.134020i | \(0.957212\pi\) | |||||||
\(602\) | 0.123106 | + | 0.213225i | 0.00501741 | + | 0.00869041i | ||||
\(603\) | −2.24621 | −0.0914728 | ||||||||
\(604\) | 7.68466 | + | 13.3102i | 0.312684 | + | 0.541585i | ||||
\(605\) | −3.00000 | − | 5.19615i | −0.121967 | − | 0.211254i | ||||
\(606\) | −8.87689 | −0.360599 | ||||||||
\(607\) | −16.2116 | − | 28.0794i | −0.658010 | − | 1.13971i | −0.981130 | − | 0.193349i | \(-0.938065\pi\) |
0.323120 | − | 0.946358i | \(-0.395268\pi\) | |||||||
\(608\) | −0.280776 | + | 0.486319i | −0.0113870 | + | 0.0197228i | ||||
\(609\) | 0.684658 | − | 1.18586i | 0.0277438 | − | 0.0480536i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 19.8963 | + | 15.5286i | 0.804918 | + | 0.628219i | ||||
\(612\) | −3.12311 | −0.126244 | ||||||||
\(613\) | −9.93845 | + | 17.2139i | −0.401410 | + | 0.695263i | −0.993896 | − | 0.110318i | \(-0.964813\pi\) |
0.592486 | + | 0.805581i | \(0.298146\pi\) | |||||||
\(614\) | −12.8078 | + | 22.1837i | −0.516879 | + | 0.895261i | ||||
\(615\) | −6.12311 | − | 10.6055i | −0.246907 | − | 0.427656i | ||||
\(616\) | −2.31534 | −0.0932878 | ||||||||
\(617\) | 14.6577 | + | 25.3878i | 0.590096 | + | 1.02208i | 0.994219 | + | 0.107371i | \(0.0342433\pi\) |
−0.404123 | + | 0.914704i | \(0.632423\pi\) | |||||||
\(618\) | −2.28078 | − | 3.95042i | −0.0917463 | − | 0.158909i | ||||
\(619\) | −20.5616 | −0.826439 | −0.413219 | − | 0.910632i | \(-0.635596\pi\) | ||||
−0.413219 | + | 0.910632i | \(0.635596\pi\) | |||||||
\(620\) | 3.34233 | + | 5.78908i | 0.134231 | + | 0.232495i | ||||
\(621\) | −2.34233 | + | 4.05703i | −0.0939944 | + | 0.162803i | ||||
\(622\) | −15.3693 | + | 26.6204i | −0.616253 | + | 1.06738i | ||||
\(623\) | 10.5616 | 0.423140 | ||||||||
\(624\) | 0.500000 | − | 3.57071i | 0.0200160 | − | 0.142943i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.6847 | + | 27.1666i | −0.626885 | + | 1.08580i | ||||
\(627\) | −1.15767 | + | 2.00514i | −0.0462329 | + | 0.0800778i | ||||
\(628\) | −6.93845 | − | 12.0177i | −0.276874 | − | 0.479560i | ||||
\(629\) | 12.8769 | 0.513435 | ||||||||
\(630\) | 0.280776 | + | 0.486319i | 0.0111864 | + | 0.0193754i | ||||
\(631\) | 6.87689 | + | 11.9111i | 0.273765 | + | 0.474175i | 0.969823 | − | 0.243811i | \(-0.0783977\pi\) |
−0.696058 | + | 0.717986i | \(0.745064\pi\) | |||||||
\(632\) | 11.5616 | 0.459894 | ||||||||
\(633\) | 10.9654 | + | 18.9927i | 0.435837 | + | 0.754892i | ||||
\(634\) | 12.4039 | − | 21.4842i | 0.492621 | − | 0.853245i | ||||
\(635\) | 4.28078 | − | 7.41452i | 0.169877 | − | 0.294236i | ||||
\(636\) | 8.56155 | 0.339488 | ||||||||
\(637\) | 22.3423 | − | 9.03996i | 0.885235 | − | 0.358176i | ||||
\(638\) | 10.0540 | 0.398041 | ||||||||
\(639\) | 6.56155 | − | 11.3649i | 0.259571 | − | 0.449590i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 5.71922 | + | 9.90599i | 0.225896 | + | 0.391263i | 0.956588 | − | 0.291444i | \(-0.0941358\pi\) |
−0.730692 | + | 0.682707i | \(0.760802\pi\) | |||||||
\(642\) | 2.00000 | 0.0789337 | ||||||||
\(643\) | −10.8769 | − | 18.8393i | −0.428943 | − | 0.742951i | 0.567837 | − | 0.823141i | \(-0.307780\pi\) |
−0.996780 | + | 0.0801904i | \(0.974447\pi\) | |||||||
\(644\) | 1.31534 | + | 2.27824i | 0.0518317 | + | 0.0897752i | ||||
\(645\) | 0.438447 | 0.0172638 | ||||||||
\(646\) | 0.876894 | + | 1.51883i | 0.0345009 | + | 0.0597574i | ||||
\(647\) | −17.5270 | + | 30.3576i | −0.689057 | + | 1.19348i | 0.283086 | + | 0.959094i | \(0.408642\pi\) |
−0.972143 | + | 0.234387i | \(0.924692\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 26.5464 | 1.04204 | ||||||||
\(650\) | −3.34233 | + | 1.35234i | −0.131097 | + | 0.0530433i | ||||
\(651\) | 3.75379 | 0.147123 | ||||||||
\(652\) | 7.21922 | − | 12.5041i | 0.282727 | − | 0.489697i | ||||
\(653\) | 22.2808 | − | 38.5914i | 0.871914 | − | 1.51020i | 0.0119002 | − | 0.999929i | \(-0.496212\pi\) |
0.860014 | − | 0.510270i | \(-0.170455\pi\) | |||||||
\(654\) | 1.87689 | + | 3.25088i | 0.0733924 | + | 0.127119i | ||||
\(655\) | −2.12311 | −0.0829566 | ||||||||
\(656\) | −6.12311 | − | 10.6055i | −0.239067 | − | 0.414076i | ||||
\(657\) | −4.68466 | − | 8.11407i | −0.182766 | − | 0.316560i | ||||
\(658\) | −3.93087 | −0.153241 | ||||||||
\(659\) | 3.02699 | + | 5.24290i | 0.117915 | + | 0.204234i | 0.918941 | − | 0.394395i | \(-0.129046\pi\) |
−0.801026 | + | 0.598629i | \(0.795712\pi\) | |||||||
\(660\) | −2.06155 | + | 3.57071i | −0.0802458 | + | 0.138990i | ||||
\(661\) | −14.8078 | + | 25.6478i | −0.575955 | + | 0.997584i | 0.419982 | + | 0.907532i | \(0.362036\pi\) |
−0.995937 | + | 0.0900513i | \(0.971297\pi\) | |||||||
\(662\) | 30.7386 | 1.19469 | ||||||||
\(663\) | −8.87689 | − | 6.92820i | −0.344750 | − | 0.269069i | ||||
\(664\) | −7.12311 | −0.276430 | ||||||||
\(665\) | 0.157671 | − | 0.273094i | 0.00611421 | − | 0.0105901i | ||||
\(666\) | 2.06155 | − | 3.57071i | 0.0798835 | − | 0.138362i | ||||
\(667\) | −5.71165 | − | 9.89286i | −0.221156 | − | 0.383053i | ||||
\(668\) | 4.36932 | 0.169054 | ||||||||
\(669\) | −13.6501 | − | 23.6427i | −0.527743 | − | 0.914078i | ||||
\(670\) | 1.12311 | + | 1.94528i | 0.0433894 | + | 0.0751526i | ||||
\(671\) | 24.7386 | 0.955024 | ||||||||
\(672\) | 0.280776 | + | 0.486319i | 0.0108312 | + | 0.0187602i | ||||
\(673\) | −12.8769 | + | 22.3034i | −0.496368 | + | 0.859734i | −0.999991 | − | 0.00418904i | \(-0.998667\pi\) |
0.503623 | + | 0.863923i | \(0.332000\pi\) | |||||||
\(674\) | 3.00000 | − | 5.19615i | 0.115556 | − | 0.200148i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.34233 | − | 9.03996i | 0.359320 | − | 0.347691i | ||||
\(677\) | −37.1231 | −1.42676 | −0.713378 | − | 0.700779i | \(-0.752836\pi\) | ||||
−0.713378 | + | 0.700779i | \(0.752836\pi\) | |||||||
\(678\) | −4.34233 | + | 7.52113i | −0.166766 | + | 0.288847i | ||||
\(679\) | −2.00000 | + | 3.46410i | −0.0767530 | + | 0.132940i | ||||
\(680\) | 1.56155 | + | 2.70469i | 0.0598828 | + | 0.103720i | ||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 13.7808 | + | 23.8690i | 0.527693 | + | 0.913991i | ||||
\(683\) | −8.56155 | − | 14.8290i | −0.327599 | − | 0.567418i | 0.654436 | − | 0.756117i | \(-0.272906\pi\) |
−0.982035 | + | 0.188700i | \(0.939573\pi\) | |||||||
\(684\) | 0.561553 | 0.0214715 | ||||||||
\(685\) | −5.90388 | − | 10.2258i | −0.225576 | − | 0.390709i | ||||
\(686\) | −3.84233 | + | 6.65511i | −0.146701 | + | 0.254093i | ||||
\(687\) | 12.1231 | − | 20.9978i | 0.462525 | − | 0.801117i | ||||
\(688\) | 0.438447 | 0.0167156 | ||||||||
\(689\) | 24.3348 | + | 18.9927i | 0.927080 | + | 0.723564i | ||||
\(690\) | 4.68466 | 0.178342 | ||||||||
\(691\) | 10.2808 | − | 17.8068i | 0.391099 | − | 0.677404i | −0.601496 | − | 0.798876i | \(-0.705428\pi\) |
0.992595 | + | 0.121472i | \(0.0387616\pi\) | |||||||
\(692\) | −10.0885 | + | 17.4739i | −0.383509 | + | 0.664257i | ||||
\(693\) | 1.15767 | + | 2.00514i | 0.0439763 | + | 0.0761691i | ||||
\(694\) | 0.876894 | 0.0332865 | ||||||||
\(695\) | −6.28078 | − | 10.8786i | −0.238243 | − | 0.412650i | ||||
\(696\) | −1.21922 | − | 2.11176i | −0.0462146 | − | 0.0800460i | ||||
\(697\) | −38.2462 | −1.44868 | ||||||||
\(698\) | −4.24621 | − | 7.35465i | −0.160721 | − | 0.278378i | ||||
\(699\) | 2.65767 | − | 4.60322i | 0.100522 | − | 0.174110i | ||||
\(700\) | 0.280776 | − | 0.486319i | 0.0106124 | − | 0.0183811i | ||||
\(701\) | −36.3002 | −1.37104 | −0.685520 | − | 0.728054i | \(-0.740425\pi\) | ||||
−0.685520 | + | 0.728054i | \(0.740425\pi\) | |||||||
\(702\) | −3.34233 | + | 1.35234i | −0.126148 | + | 0.0510410i | ||||
\(703\) | −2.31534 | −0.0873248 | ||||||||
\(704\) | −2.06155 | + | 3.57071i | −0.0776977 | + | 0.134576i | ||||
\(705\) | −3.50000 | + | 6.06218i | −0.131818 | + | 0.228315i | ||||
\(706\) | 12.9309 | + | 22.3969i | 0.486660 | + | 0.842919i | ||||
\(707\) | 4.98485 | 0.187474 | ||||||||
\(708\) | −3.21922 | − | 5.57586i | −0.120986 | − | 0.209554i | ||||
\(709\) | −17.1231 | − | 29.6581i | −0.643072 | − | 1.11383i | −0.984743 | − | 0.174013i | \(-0.944326\pi\) |
0.341672 | − | 0.939819i | \(-0.389007\pi\) | |||||||
\(710\) | −13.1231 | −0.492501 | ||||||||
\(711\) | −5.78078 | − | 10.0126i | −0.216796 | − | 0.375502i | ||||
\(712\) | 9.40388 | − | 16.2880i | 0.352425 | − | 0.610419i | ||||
\(713\) | 15.6577 | − | 27.1199i | 0.586384 | − | 1.01565i | ||||
\(714\) | 1.75379 | 0.0656339 | ||||||||
\(715\) | −13.7808 | + | 5.57586i | −0.515372 | + | 0.208525i | ||||
\(716\) | −12.6847 | −0.474048 | ||||||||
\(717\) | 5.68466 | − | 9.84612i | 0.212297 | − | 0.367710i | ||||
\(718\) | −6.56155 | + | 11.3649i | −0.244875 | + | 0.424136i | ||||
\(719\) | −22.4924 | − | 38.9580i | −0.838826 | − | 1.45289i | −0.890877 | − | 0.454245i | \(-0.849909\pi\) |
0.0520512 | − | 0.998644i | \(-0.483424\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 1.28078 | + | 2.21837i | 0.0476986 | + | 0.0826164i | ||||
\(722\) | 9.34233 | + | 16.1814i | 0.347685 | + | 0.602209i | ||||
\(723\) | −28.1231 | −1.04591 | ||||||||
\(724\) | −1.43845 | − | 2.49146i | −0.0534595 | − | 0.0925945i | ||||
\(725\) | −1.21922 | + | 2.11176i | −0.0452808 | + | 0.0784287i | ||||
\(726\) | −3.00000 | + | 5.19615i | −0.111340 | + | 0.192847i | ||||
\(727\) | 38.4233 | 1.42504 | 0.712521 | − | 0.701651i | \(-0.247554\pi\) | ||||
0.712521 | + | 0.701651i | \(0.247554\pi\) | |||||||
\(728\) | −0.280776 | + | 2.00514i | −0.0104063 | + | 0.0743156i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.68466 | + | 8.11407i | −0.173387 | + | 0.300315i | ||||
\(731\) | 0.684658 | − | 1.18586i | 0.0253230 | − | 0.0438607i | ||||
\(732\) | −3.00000 | − | 5.19615i | −0.110883 | − | 0.192055i | ||||
\(733\) | 20.0691 | 0.741270 | 0.370635 | − | 0.928779i | \(-0.379140\pi\) | ||||
0.370635 | + | 0.928779i | \(0.379140\pi\) | |||||||
\(734\) | −6.24621 | − | 10.8188i | −0.230552 | − | 0.399328i | ||||
\(735\) | 3.34233 | + | 5.78908i | 0.123284 | + | 0.213534i | ||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | 4.63068 | + | 8.02058i | 0.170573 | + | 0.295442i | ||||
\(738\) | −6.12311 | + | 10.6055i | −0.225395 | + | 0.390395i | ||||
\(739\) | 13.7732 | − | 23.8559i | 0.506655 | − | 0.877553i | −0.493315 | − | 0.869851i | \(-0.664215\pi\) |
0.999970 | − | 0.00770202i | \(-0.00245165\pi\) | |||||||
\(740\) | −4.12311 | −0.151568 | ||||||||
\(741\) | 1.59612 | + | 1.24573i | 0.0586349 | + | 0.0457631i | ||||
\(742\) | −4.80776 | −0.176499 | ||||||||
\(743\) | −6.58854 | + | 11.4117i | −0.241710 | + | 0.418654i | −0.961202 | − | 0.275847i | \(-0.911042\pi\) |
0.719491 | + | 0.694501i | \(0.244375\pi\) | |||||||
\(744\) | 3.34233 | − | 5.78908i | 0.122536 | − | 0.212238i | ||||
\(745\) | 1.09612 | + | 1.89853i | 0.0401587 | + | 0.0695568i | ||||
\(746\) | −25.8078 | −0.944889 | ||||||||
\(747\) | 3.56155 | + | 6.16879i | 0.130310 | + | 0.225704i | ||||
\(748\) | 6.43845 | + | 11.1517i | 0.235413 | + | 0.407747i | ||||
\(749\) | −1.12311 | −0.0410374 | ||||||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | 11.9039 | − | 20.6181i | 0.434379 | − | 0.752366i | −0.562866 | − | 0.826548i | \(-0.690301\pi\) |
0.997245 | + | 0.0741820i | \(0.0236346\pi\) | |||||||
\(752\) | −3.50000 | + | 6.06218i | −0.127632 | + | 0.221065i | ||||
\(753\) | −8.12311 | −0.296022 | ||||||||
\(754\) | 1.21922 | − | 8.70700i | 0.0444015 | − | 0.317090i | ||||
\(755\) | −15.3693 | −0.559347 | ||||||||
\(756\) | 0.280776 | − | 0.486319i | 0.0102117 | − | 0.0176873i | ||||
\(757\) | 14.2116 | − | 24.6153i | 0.516531 | − | 0.894658i | −0.483285 | − | 0.875463i | \(-0.660556\pi\) |
0.999816 | − | 0.0191948i | \(-0.00611027\pi\) | |||||||
\(758\) | 8.84233 | + | 15.3154i | 0.321168 | + | 0.556279i | ||||
\(759\) | 19.3153 | 0.701102 | ||||||||
\(760\) | −0.280776 | − | 0.486319i | −0.0101848 | − | 0.0176406i | ||||
\(761\) | 8.96543 | + | 15.5286i | 0.324997 | + | 0.562911i | 0.981512 | − | 0.191402i | \(-0.0613035\pi\) |
−0.656515 | + | 0.754313i | \(0.727970\pi\) | |||||||
\(762\) | −8.56155 | −0.310152 | ||||||||
\(763\) | −1.05398 | − | 1.82554i | −0.0381565 | − | 0.0660889i | ||||
\(764\) | −5.43845 | + | 9.41967i | −0.196756 | + | 0.340792i | ||||
\(765\) | 1.56155 | − | 2.70469i | 0.0564581 | − | 0.0977882i | ||||
\(766\) | 0.192236 | 0.00694577 | ||||||||
\(767\) | 3.21922 | − | 22.9899i | 0.116239 | − | 0.830116i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 16.6577 | − | 28.8519i | 0.600691 | − | 1.04043i | −0.392026 | − | 0.919954i | \(-0.628226\pi\) |
0.992717 | − | 0.120473i | \(-0.0384411\pi\) | |||||||
\(770\) | 1.15767 | − | 2.00514i | 0.0417196 | − | 0.0722604i | ||||
\(771\) | 2.78078 | + | 4.81645i | 0.100147 | + | 0.173460i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.0885 | − | 20.9380i | −0.434795 | − | 0.753086i | 0.562484 | − | 0.826808i | \(-0.309846\pi\) |
−0.997279 | + | 0.0737217i | \(0.976512\pi\) | |||||||
\(774\) | −0.219224 | − | 0.379706i | −0.00787983 | − | 0.0136483i | ||||
\(775\) | −6.68466 | −0.240120 | ||||||||
\(776\) | 3.56155 | + | 6.16879i | 0.127852 | + | 0.221447i | ||||
\(777\) | −1.15767 | + | 2.00514i | −0.0415312 | + | 0.0719342i | ||||
\(778\) | 9.02699 | − | 15.6352i | 0.323633 | − | 0.560549i | ||||
\(779\) | 6.87689 | 0.246390 | ||||||||
\(780\) | 2.84233 | + | 2.21837i | 0.101772 | + | 0.0794304i | ||||
\(781\) | −54.1080 | −1.93613 | ||||||||
\(782\) | 7.31534 | − | 12.6705i | 0.261596 | − | 0.453098i | ||||
\(783\) | −1.21922 | + | 2.11176i | −0.0435715 | + | 0.0754680i | ||||
\(784\) | 3.34233 | + | 5.78908i | 0.119369 | + | 0.206753i | ||||
\(785\) | 13.8769 | 0.495288 | ||||||||
\(786\) | 1.06155 | + | 1.83866i | 0.0378643 | + | 0.0655830i | ||||
\(787\) | −15.6577 | − | 27.1199i | −0.558136 | − | 0.966719i | −0.997652 | − | 0.0684848i | \(-0.978184\pi\) |
0.439516 | − | 0.898235i | \(-0.355150\pi\) | |||||||
\(788\) | 12.8078 | 0.456258 | ||||||||
\(789\) | 6.50000 | + | 11.2583i | 0.231406 | + | 0.400807i | ||||
\(790\) | −5.78078 | + | 10.0126i | −0.205671 | + | 0.356232i | ||||
\(791\) | 2.43845 | − | 4.22351i | 0.0867012 | − | 0.150171i | ||||
\(792\) | 4.12311 | 0.146508 | ||||||||
\(793\) | 3.00000 | − | 21.4243i | 0.106533 | − | 0.760799i | ||||
\(794\) | −20.1231 | −0.714142 | ||||||||
\(795\) | −4.28078 | + | 7.41452i | −0.151823 | + | 0.262966i | ||||
\(796\) | −1.43845 | + | 2.49146i | −0.0509844 | + | 0.0883076i | ||||
\(797\) | −6.56155 | − | 11.3649i | −0.232422 | − | 0.402567i | 0.726098 | − | 0.687591i | \(-0.241332\pi\) |
−0.958520 | + | 0.285024i | \(0.907998\pi\) | |||||||
\(798\) | −0.315342 | −0.0111630 | ||||||||
\(799\) | 10.9309 | + | 18.9328i | 0.386706 | + | 0.669795i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −18.8078 | −0.664540 | ||||||||
\(802\) | −0.157671 | − | 0.273094i | −0.00556755 | − | 0.00964328i | ||||
\(803\) | −19.3153 | + | 33.4552i | −0.681624 | + | 1.18061i | ||||
\(804\) | 1.12311 | − | 1.94528i | 0.0396089 | − | 0.0686046i | ||||
\(805\) | −2.63068 | −0.0927194 | ||||||||
\(806\) | 22.3423 | − | 9.03996i | 0.786975 | − | 0.318419i | ||||
\(807\) | 21.3693 | 0.752236 | ||||||||
\(808\) | 4.43845 | − | 7.68762i | 0.156144 | − | 0.270449i | ||||
\(809\) | 7.24621 | − | 12.5508i | 0.254763 | − | 0.441263i | −0.710068 | − | 0.704133i | \(-0.751336\pi\) |
0.964831 | + | 0.262870i | \(0.0846691\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 47.5464 | 1.66958 | 0.834790 | − | 0.550569i | \(-0.185589\pi\) | ||||
0.834790 | + | 0.550569i | \(0.185589\pi\) | |||||||
\(812\) | 0.684658 | + | 1.18586i | 0.0240268 | + | 0.0416156i | ||||
\(813\) | 6.58854 | + | 11.4117i | 0.231070 | + | 0.400225i | ||||
\(814\) | −17.0000 | −0.595850 | ||||||||
\(815\) | 7.21922 | + | 12.5041i | 0.252878 | + | 0.437998i | ||||
\(816\) | 1.56155 | − | 2.70469i | 0.0546653 | − | 0.0946830i | ||||
\(817\) | −0.123106 | + | 0.213225i | −0.00430692 | + | 0.00745981i | ||||
\(818\) | −18.8078 | −0.657598 | ||||||||
\(819\) | 1.87689 | − | 0.759413i | 0.0655840 | − | 0.0265360i | ||||
\(820\) | 12.2462 | 0.427656 | ||||||||
\(821\) | 4.21922 | − | 7.30791i | 0.147252 | − | 0.255048i | −0.782959 | − | 0.622073i | \(-0.786291\pi\) |
0.930211 | + | 0.367026i | \(0.119624\pi\) | |||||||
\(822\) | −5.90388 | + | 10.2258i | −0.205922 | + | 0.356667i | ||||
\(823\) | −2.52699 | − | 4.37687i | −0.0880853 | − | 0.152568i | 0.818616 | − | 0.574341i | \(-0.194741\pi\) |
−0.906702 | + | 0.421772i | \(0.861408\pi\) | |||||||
\(824\) | 4.56155 | 0.158909 | ||||||||
\(825\) | −2.06155 | − | 3.57071i | −0.0717741 | − | 0.124316i | ||||
\(826\) | 1.80776 | + | 3.13114i | 0.0629002 | + | 0.108946i | ||||
\(827\) | −28.2462 | −0.982217 | −0.491109 | − | 0.871098i | \(-0.663408\pi\) | ||||
−0.491109 | + | 0.871098i | \(0.663408\pi\) | |||||||
\(828\) | −2.34233 | − | 4.05703i | −0.0814016 | − | 0.140992i | ||||
\(829\) | −6.19224 | + | 10.7253i | −0.215065 | + | 0.372504i | −0.953293 | − | 0.302048i | \(-0.902330\pi\) |
0.738228 | + | 0.674552i | \(0.235663\pi\) | |||||||
\(830\) | 3.56155 | − | 6.16879i | 0.123623 | − | 0.214122i | ||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | 2.84233 | + | 2.21837i | 0.0985400 | + | 0.0769081i | ||||
\(833\) | 20.8769 | 0.723342 | ||||||||
\(834\) | −6.28078 | + | 10.8786i | −0.217486 | + | 0.376696i | ||||
\(835\) | −2.18466 | + | 3.78394i | −0.0756032 | + | 0.130949i | ||||
\(836\) | −1.15767 | − | 2.00514i | −0.0400389 | − | 0.0693494i | ||||
\(837\) | −6.68466 | −0.231056 | ||||||||
\(838\) | −16.2462 | − | 28.1393i | −0.561216 | − | 0.972055i | ||||
\(839\) | −18.3693 | − | 31.8166i | −0.634179 | − | 1.09843i | −0.986688 | − | 0.162622i | \(-0.948005\pi\) |
0.352509 | − | 0.935808i | \(-0.385329\pi\) | |||||||
\(840\) | −0.561553 | −0.0193754 | ||||||||
\(841\) | 11.5270 | + | 19.9653i | 0.397482 | + | 0.688460i | ||||
\(842\) | 16.2462 | − | 28.1393i | 0.559881 | − | 0.969743i | ||||
\(843\) | −8.12311 | + | 14.0696i | −0.279775 | + | 0.484584i | ||||
\(844\) | −21.9309 | −0.754892 | ||||||||
\(845\) | 3.15767 | + | 12.6107i | 0.108627 | + | 0.433820i | ||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | 1.68466 | − | 2.91791i | 0.0578855 | − | 0.100261i | ||||
\(848\) | −4.28078 | + | 7.41452i | −0.147002 | + | 0.254616i | ||||
\(849\) | −7.78078 | − | 13.4767i | −0.267036 | − | 0.462519i | ||||
\(850\) | −3.12311 | −0.107122 | ||||||||
\(851\) | 9.65767 | + | 16.7276i | 0.331061 | + | 0.573414i | ||||
\(852\) | 6.56155 | + | 11.3649i | 0.224795 | + | 0.389357i | ||||
\(853\) | 2.30019 | 0.0787569 | 0.0393784 | − | 0.999224i | \(-0.487462\pi\) | ||||
0.0393784 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(854\) | 1.68466 | + | 2.91791i | 0.0576478 | + | 0.0998490i | ||||
\(855\) | −0.280776 | + | 0.486319i | −0.00960235 | + | 0.0166318i | ||||
\(856\) | −1.00000 | + | 1.73205i | −0.0341793 | + | 0.0592003i | ||||
\(857\) | −6.19224 | −0.211523 | −0.105761 | − | 0.994392i | \(-0.533728\pi\) | ||||
−0.105761 | + | 0.994392i | \(0.533728\pi\) | |||||||
\(858\) | 11.7192 | + | 9.14657i | 0.400088 | + | 0.312259i | ||||
\(859\) | 39.7926 | 1.35771 | 0.678853 | − | 0.734274i | \(-0.262477\pi\) | ||||
0.678853 | + | 0.734274i | \(0.262477\pi\) | |||||||
\(860\) | −0.219224 | + | 0.379706i | −0.00747546 | + | 0.0129479i | ||||
\(861\) | 3.43845 | − | 5.95557i | 0.117182 | − | 0.202965i | ||||
\(862\) | 11.3693 | + | 19.6922i | 0.387240 | + | 0.670720i | ||||
\(863\) | 2.43845 | 0.0830057 | 0.0415029 | − | 0.999138i | \(-0.486785\pi\) | ||||
0.0415029 | + | 0.999138i | \(0.486785\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −10.0885 | − | 17.4739i | −0.343021 | − | 0.594129i | ||||
\(866\) | −18.7386 | −0.636765 | ||||||||
\(867\) | 3.62311 | + | 6.27540i | 0.123047 | + | 0.213124i | ||||
\(868\) | −1.87689 | + | 3.25088i | −0.0637059 | + | 0.110342i | ||||
\(869\) | −23.8348 | + | 41.2830i | −0.808539 | + | 1.40043i | ||||
\(870\) | 2.43845 | 0.0826711 | ||||||||
\(871\) | 7.50758 | − | 3.03765i | 0.254385 | − | 0.102927i | ||||
\(872\) | −3.75379 | −0.127119 | ||||||||
\(873\) | 3.56155 | − | 6.16879i | 0.120540 | − | 0.208782i | ||||
\(874\) | −1.31534 | + | 2.27824i | −0.0444921 | + | 0.0770626i | ||||
\(875\) | 0.280776 | + | 0.486319i | 0.00949197 | + | 0.0164406i | ||||
\(876\) | 9.36932 | 0.316560 | ||||||||
\(877\) | −4.21922 | − | 7.30791i | −0.142473 | − | 0.246771i | 0.785954 | − | 0.618285i | \(-0.212172\pi\) |
−0.928427 | + | 0.371514i | \(0.878839\pi\) | |||||||
\(878\) | −12.5616 | − | 21.7572i | −0.423932 | − | 0.734272i | ||||
\(879\) | 3.93087 | 0.132585 | ||||||||
\(880\) | −2.06155 | − | 3.57071i | −0.0694949 | − | 0.120369i | ||||
\(881\) | 12.2808 | − | 21.2709i | 0.413750 | − | 0.716636i | −0.581546 | − | 0.813513i | \(-0.697552\pi\) |
0.995296 | + | 0.0968774i | \(0.0308855\pi\) | |||||||
\(882\) | 3.34233 | − | 5.78908i | 0.112542 | − | 0.194929i | ||||
\(883\) | −19.1771 | −0.645360 | −0.322680 | − | 0.946508i | \(-0.604584\pi\) | ||||
−0.322680 | + | 0.946508i | \(0.604584\pi\) | |||||||
\(884\) | 10.4384 | − | 4.22351i | 0.351083 | − | 0.142052i | ||||
\(885\) | 6.43845 | 0.216426 | ||||||||
\(886\) | 6.56155 | − | 11.3649i | 0.220440 | − | 0.381813i | ||||
\(887\) | 16.5540 | − | 28.6723i | 0.555828 | − | 0.962722i | −0.442010 | − | 0.897010i | \(-0.645735\pi\) |
0.997839 | − | 0.0657126i | \(-0.0209321\pi\) | |||||||
\(888\) | 2.06155 | + | 3.57071i | 0.0691812 | + | 0.119825i | ||||
\(889\) | 4.80776 | 0.161247 | ||||||||
\(890\) | 9.40388 | + | 16.2880i | 0.315219 | + | 0.545975i | ||||
\(891\) | −2.06155 | − | 3.57071i | −0.0690646 | − | 0.119623i | ||||
\(892\) | 27.3002 | 0.914078 | ||||||||
\(893\) | −1.96543 | − | 3.40423i | −0.0657708 | − | 0.113918i | ||||
\(894\) | 1.09612 | − | 1.89853i | 0.0366597 | − | 0.0634964i | ||||
\(895\) | 6.34233 | − | 10.9852i | 0.212001 | − | 0.367196i | ||||
\(896\) | −0.561553 | −0.0187602 | ||||||||
\(897\) | 2.34233 | − | 16.7276i | 0.0782081 | − | 0.558518i | ||||
\(898\) | −20.1771 | −0.673318 | ||||||||
\(899\) | 8.15009 | − | 14.1164i | 0.271821 | − | 0.470807i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | 13.3693 | + | 23.1563i | 0.445397 | + | 0.771449i | ||||
\(902\) | 50.4924 | 1.68121 | ||||||||
\(903\) | 0.123106 | + | 0.213225i | 0.00409670 | + | 0.00709569i | ||||
\(904\) | −4.34233 | − | 7.52113i | −0.144424 | − | 0.250149i | ||||
\(905\) | 2.87689 | 0.0956312 | ||||||||
\(906\) | 7.68466 | + | 13.3102i | 0.255306 | + | 0.442202i | ||||
\(907\) | 26.9579 | − | 46.6924i | 0.895121 | − | 1.55039i | 0.0614661 | − | 0.998109i | \(-0.480422\pi\) |
0.833655 | − | 0.552286i | \(-0.186244\pi\) | |||||||
\(908\) | 10.0000 | − | 17.3205i | 0.331862 | − | 0.574801i | ||||
\(909\) | −8.87689 | −0.294428 | ||||||||
\(910\) | −1.59612 | − | 1.24573i | −0.0529108 | − | 0.0412956i | ||||
\(911\) | −18.6307 | −0.617262 | −0.308631 | − | 0.951182i | \(-0.599871\pi\) | ||||
−0.308631 | + | 0.951182i | \(0.599871\pi\) | |||||||
\(912\) | −0.280776 | + | 0.486319i | −0.00929744 | + | 0.0161036i | ||||
\(913\) | 14.6847 | − | 25.4346i | 0.485991 | − | 0.841762i | ||||
\(914\) | −10.1231 | − | 17.5337i | −0.334843 | − | 0.579964i | ||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 12.1231 | + | 20.9978i | 0.400559 | + | 0.693788i | ||||
\(917\) | −0.596118 | − | 1.03251i | −0.0196855 | − | 0.0340964i | ||||
\(918\) | −3.12311 | −0.103078 | ||||||||
\(919\) | −8.31534 | − | 14.4026i | −0.274298 | − | 0.475098i | 0.695660 | − | 0.718371i | \(-0.255112\pi\) |
−0.969958 | + | 0.243274i | \(0.921779\pi\) | |||||||
\(920\) | −2.34233 | + | 4.05703i | −0.0772243 | + | 0.133756i | ||||
\(921\) | −12.8078 | + | 22.1837i | −0.422030 | + | 0.730978i | ||||
\(922\) | −30.0540 | −0.989775 | ||||||||
\(923\) | −6.56155 | + | 46.8589i | −0.215976 | + | 1.54238i | ||||
\(924\) | −2.31534 | −0.0761691 | ||||||||
\(925\) | 2.06155 | − | 3.57071i | 0.0677834 | − | 0.117404i | ||||
\(926\) | 3.80776 | − | 6.59524i | 0.125131 | − | 0.216733i | ||||
\(927\) | −2.28078 | − | 3.95042i | −0.0749105 | − | 0.129749i | ||||
\(928\) | 2.43845 | 0.0800460 | ||||||||
\(929\) | 12.5616 | + | 21.7572i | 0.412131 | + | 0.713832i | 0.995123 | − | 0.0986462i | \(-0.0314512\pi\) |
−0.582991 | + | 0.812478i | \(0.698118\pi\) | |||||||
\(930\) | 3.34233 | + | 5.78908i | 0.109599 | + | 0.189832i | ||||
\(931\) | −3.75379 | −0.123025 | ||||||||
\(932\) | 2.65767 | + | 4.60322i | 0.0870549 | + | 0.150784i | ||||
\(933\) | −15.3693 | + | 26.6204i | −0.503169 | + | 0.871514i | ||||
\(934\) | 8.93087 | − | 15.4687i | 0.292227 | − | 0.506152i | ||||
\(935\) | −12.8769 | −0.421119 | ||||||||
\(936\) | 0.500000 | − | 3.57071i | 0.0163430 | − | 0.116712i | ||||
\(937\) | 53.2311 | 1.73898 | 0.869491 | − | 0.493948i | \(-0.164447\pi\) | ||||
0.869491 | + | 0.493948i | \(0.164447\pi\) | |||||||
\(938\) | −0.630683 | + | 1.09238i | −0.0205925 | + | 0.0356673i | ||||
\(939\) | −15.6847 | + | 27.1666i | −0.511849 | + | 0.886549i | ||||
\(940\) | −3.50000 | − | 6.06218i | −0.114157 | − | 0.197726i | ||||
\(941\) | −25.3693 | −0.827016 | −0.413508 | − | 0.910500i | \(-0.635697\pi\) | ||||
−0.413508 | + | 0.910500i | \(0.635697\pi\) | |||||||
\(942\) | −6.93845 | − | 12.0177i | −0.226067 | − | 0.391559i | ||||
\(943\) | −28.6847 | − | 49.6833i | −0.934101 | − | 1.61791i | ||||
\(944\) | 6.43845 | 0.209554 | ||||||||
\(945\) | 0.280776 | + | 0.486319i | 0.00913366 | + | 0.0158200i | ||||
\(946\) | −0.903882 | + | 1.56557i | −0.0293877 | + | 0.0509011i | ||||
\(947\) | 21.9309 | − | 37.9854i | 0.712658 | − | 1.23436i | −0.251199 | − | 0.967936i | \(-0.580825\pi\) |
0.963856 | − | 0.266423i | \(-0.0858419\pi\) | |||||||
\(948\) | 11.5616 | 0.375502 | ||||||||
\(949\) | 26.6307 | + | 20.7846i | 0.864469 | + | 0.674697i | ||||
\(950\) | 0.561553 | 0.0182192 | ||||||||
\(951\) | 12.4039 | − | 21.4842i | 0.402223 | − | 0.696671i | ||||
\(952\) | −0.876894 | + | 1.51883i | −0.0284203 | + | 0.0492254i | ||||
\(953\) | −25.5885 | − | 44.3207i | −0.828894 | − | 1.43569i | −0.898906 | − | 0.438141i | \(-0.855637\pi\) |
0.0700123 | − | 0.997546i | \(-0.477696\pi\) | |||||||
\(954\) | 8.56155 | 0.277191 | ||||||||
\(955\) | −5.43845 | − | 9.41967i | −0.175984 | − | 0.304813i | ||||
\(956\) | 5.68466 | + | 9.84612i | 0.183855 | + | 0.318446i | ||||
\(957\) | 10.0540 | 0.324999 | ||||||||
\(958\) | 19.1231 | + | 33.1222i | 0.617839 | + | 1.07013i | ||||
\(959\) | 3.31534 | − | 5.74234i | 0.107058 | − | 0.185430i | ||||
\(960\) | −0.500000 | + | 0.866025i | −0.0161374 | + | 0.0279508i | ||||
\(961\) | 13.6847 | 0.441441 | ||||||||
\(962\) | −2.06155 | + | 14.7224i | −0.0664671 | + | 0.474670i | ||||
\(963\) | 2.00000 | 0.0644491 | ||||||||
\(964\) | 14.0616 | − | 24.3553i | 0.452892 | − | 0.784432i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.31534 | + | 2.27824i | 0.0423204 | + | 0.0733011i | ||||
\(967\) | 15.6847 | 0.504385 | 0.252192 | − | 0.967677i | \(-0.418848\pi\) | ||||
0.252192 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(968\) | −3.00000 | − | 5.19615i | −0.0964237 | − | 0.167011i | ||||
\(969\) | 0.876894 | + | 1.51883i | 0.0281699 | + | 0.0487917i | ||||
\(970\) | −7.12311 | −0.228709 | ||||||||
\(971\) | 2.15767 | + | 3.73720i | 0.0692430 | + | 0.119932i | 0.898568 | − | 0.438834i | \(-0.144608\pi\) |
−0.829325 | + | 0.558766i | \(0.811275\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 3.52699 | − | 6.10892i | 0.113070 | − | 0.195843i | ||||
\(974\) | 13.0540 | 0.418276 | ||||||||
\(975\) | −3.34233 | + | 1.35234i | −0.107040 | + | 0.0433097i | ||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 24.1501 | − | 41.8292i | 0.772630 | − | 1.33823i | −0.163487 | − | 0.986545i | \(-0.552274\pi\) |
0.936117 | − | 0.351689i | \(-0.114392\pi\) | |||||||
\(978\) | 7.21922 | − | 12.5041i | 0.230845 | − | 0.399836i | ||||
\(979\) | 38.7732 | + | 67.1572i | 1.23920 | + | 2.14635i | ||||
\(980\) | −6.68466 | −0.213534 | ||||||||
\(981\) | 1.87689 | + | 3.25088i | 0.0599246 | + | 0.103792i | ||||
\(982\) | 8.71922 | + | 15.1021i | 0.278242 | + | 0.481929i | ||||
\(983\) | 32.1231 | 1.02457 | 0.512284 | − | 0.858816i | \(-0.328800\pi\) | ||||
0.512284 | + | 0.858816i | \(0.328800\pi\) | |||||||
\(984\) | −6.12311 | − | 10.6055i | −0.195197 | − | 0.338092i | ||||
\(985\) | −6.40388 | + | 11.0918i | −0.204045 | + | 0.353416i | ||||
\(986\) | 3.80776 | − | 6.59524i | 0.121264 | − | 0.210035i | ||||
\(987\) | −3.93087 | −0.125121 | ||||||||
\(988\) | −1.87689 | + | 0.759413i | −0.0597120 | + | 0.0241601i | ||||
\(989\) | 2.05398 | 0.0653126 | ||||||||
\(990\) | −2.06155 | + | 3.57071i | −0.0655204 | + | 0.113485i | ||||
\(991\) | −24.7116 | + | 42.8018i | −0.784991 | + | 1.35964i | 0.144013 | + | 0.989576i | \(0.453999\pi\) |
−0.929004 | + | 0.370069i | \(0.879334\pi\) | |||||||
\(992\) | 3.34233 | + | 5.78908i | 0.106119 | + | 0.183804i | ||||
\(993\) | 30.7386 | 0.975461 | ||||||||
\(994\) | −3.68466 | − | 6.38202i | −0.116870 | − | 0.202425i | ||||
\(995\) | −1.43845 | − | 2.49146i | −0.0456018 | − | 0.0789847i | ||||
\(996\) | −7.12311 | −0.225704 | ||||||||
\(997\) | 18.7732 | + | 32.5161i | 0.594553 | + | 1.02980i | 0.993610 | + | 0.112870i | \(0.0360044\pi\) |
−0.399057 | + | 0.916926i | \(0.630662\pi\) | |||||||
\(998\) | −2.00000 | + | 3.46410i | −0.0633089 | + | 0.109654i | ||||
\(999\) | 2.06155 | − | 3.57071i | 0.0652246 | − | 0.112972i |
(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 | 390.2.i.g.61.2 | ✓ | 4 | |
3.2 | odd | 2 | 1170.2.i.o.451.2 | 4 | |||
5.2 | odd | 4 | 1950.2.z.n.1699.1 | 8 | |||
5.3 | odd | 4 | 1950.2.z.n.1699.4 | 8 | |||
5.4 | even | 2 | 1950.2.i.bi.451.1 | 4 | |||
13.3 | even | 3 | inner | 390.2.i.g.211.2 | yes | 4 | |
13.4 | even | 6 | 5070.2.a.bb.1.2 | 2 | |||
13.6 | odd | 12 | 5070.2.b.r.1351.1 | 4 | |||
13.7 | odd | 12 | 5070.2.b.r.1351.4 | 4 | |||
13.9 | even | 3 | 5070.2.a.bi.1.1 | 2 | |||
39.29 | odd | 6 | 1170.2.i.o.991.2 | 4 | |||
65.3 | odd | 12 | 1950.2.z.n.1849.1 | 8 | |||
65.29 | even | 6 | 1950.2.i.bi.601.1 | 4 | |||
65.42 | odd | 12 | 1950.2.z.n.1849.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
390.2.i.g.211.2 | yes | 4 | 13.3 | even | 3 | inner | |
1170.2.i.o.451.2 | 4 | 3.2 | odd | 2 | |||
1170.2.i.o.991.2 | 4 | 39.29 | odd | 6 | |||
1950.2.i.bi.451.1 | 4 | 5.4 | even | 2 | |||
1950.2.i.bi.601.1 | 4 | 65.29 | even | 6 | |||
1950.2.z.n.1699.1 | 8 | 5.2 | odd | 4 | |||
1950.2.z.n.1699.4 | 8 | 5.3 | odd | 4 | |||
1950.2.z.n.1849.1 | 8 | 65.3 | odd | 12 | |||
1950.2.z.n.1849.4 | 8 | 65.42 | odd | 12 | |||
5070.2.a.bb.1.2 | 2 | 13.4 | even | 6 | |||
5070.2.a.bi.1.1 | 2 | 13.9 | even | 3 | |||
5070.2.b.r.1351.1 | 4 | 13.6 | odd | 12 | |||
5070.2.b.r.1351.4 | 4 | 13.7 | odd | 12 |