Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(451,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, 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("1170.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.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: | \(9.34249703649\) |
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: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.2 | ||
Root | \(-0.780776 + 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.991 |
Dual form | 1170.2.i.o.451.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.280776 | − | 0.486319i | 0.106124 | − | 0.183811i | −0.808073 | − | 0.589082i | \(-0.799489\pi\) |
0.914197 | + | 0.405271i | \(0.132823\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 2.06155 | + | 3.57071i | 0.621582 | + | 1.07661i | 0.989191 | + | 0.146631i | \(0.0468429\pi\) |
−0.367610 | + | 0.929980i | \(0.619824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.84233 | − | 2.21837i | 0.788320 | − | 0.615265i | ||||
\(14\) | 0.561553 | 0.150081 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.56155 | + | 2.70469i | −0.378732 | + | 0.655983i | −0.990878 | − | 0.134761i | \(-0.956973\pi\) |
0.612146 | + | 0.790745i | \(0.290307\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.280776 | + | 0.486319i | −0.0644145 | + | 0.111569i | −0.896434 | − | 0.443177i | \(-0.853851\pi\) |
0.832020 | + | 0.554746i | \(0.187185\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.06155 | + | 3.57071i | −0.439525 | + | 0.761279i | ||||
\(23\) | 2.34233 | + | 4.05703i | 0.488409 | + | 0.845950i | 0.999911 | − | 0.0133324i | \(-0.00424395\pi\) |
−0.511502 | + | 0.859282i | \(0.670911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.34233 | + | 1.35234i | 0.655485 | + | 0.265217i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.280776 | + | 0.486319i | 0.0530618 | + | 0.0919057i | ||||
\(29\) | 1.21922 | + | 2.11176i | 0.226404 | + | 0.392143i | 0.956740 | − | 0.290945i | \(-0.0939697\pi\) |
−0.730336 | + | 0.683088i | \(0.760636\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | −0.280776 | + | 0.486319i | −0.0474599 | + | 0.0822029i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.06155 | + | 3.57071i | 0.338917 | + | 0.587022i | 0.984229 | − | 0.176897i | \(-0.0566060\pi\) |
−0.645312 | + | 0.763919i | \(0.723273\pi\) | |||||||
\(38\) | −0.561553 | −0.0910959 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.12311 | + | 10.6055i | 0.956268 | + | 1.65631i | 0.731438 | + | 0.681908i | \(0.238849\pi\) |
0.224830 | + | 0.974398i | \(0.427817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.219224 | + | 0.379706i | −0.0334313 | + | 0.0579047i | −0.882257 | − | 0.470768i | \(-0.843977\pi\) |
0.848826 | + | 0.528673i | \(0.177310\pi\) | |||||||
\(44\) | −4.12311 | −0.621582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34233 | + | 4.05703i | −0.345358 | + | 0.598177i | ||||
\(47\) | −7.00000 | −1.02105 | −0.510527 | − | 0.859861i | \(-0.670550\pi\) | ||||
−0.510527 | + | 0.859861i | \(0.670550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.34233 | + | 5.78908i | 0.477476 | + | 0.827012i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 3.57071i | 0.0693375 | + | 0.495169i | ||||
\(53\) | −8.56155 | −1.17602 | −0.588010 | − | 0.808854i | \(-0.700088\pi\) | ||||
−0.588010 | + | 0.808854i | \(0.700088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.06155 | − | 3.57071i | −0.277980 | − | 0.481475i | ||||
\(56\) | −0.280776 | + | 0.486319i | −0.0375203 | + | 0.0649871i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.21922 | + | 2.11176i | −0.160092 | + | 0.277287i | ||||
\(59\) | 3.21922 | − | 5.57586i | 0.419107 | − | 0.725915i | −0.576743 | − | 0.816926i | \(-0.695676\pi\) |
0.995850 | + | 0.0910109i | \(0.0290098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 5.19615i | −0.384111 | + | 0.665299i | −0.991645 | − | 0.128994i | \(-0.958825\pi\) |
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(62\) | −3.34233 | − | 5.78908i | −0.424476 | − | 0.735214i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.84233 | + | 2.21837i | −0.352548 | + | 0.275155i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.12311 | + | 1.94528i | 0.137209 | + | 0.237653i | 0.926439 | − | 0.376444i | \(-0.122853\pi\) |
−0.789230 | + | 0.614098i | \(0.789520\pi\) | |||||||
\(68\) | −1.56155 | − | 2.70469i | −0.189366 | − | 0.327992i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.561553 | −0.0671184 | ||||||||
\(71\) | −6.56155 | + | 11.3649i | −0.778713 | + | 1.34877i | 0.153971 | + | 0.988075i | \(0.450794\pi\) |
−0.932684 | + | 0.360695i | \(0.882539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 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 | 0 | ||||||||
\(76\) | −0.280776 | − | 0.486319i | −0.0322073 | − | 0.0557846i | ||||
\(77\) | 2.31534 | 0.263858 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 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 | 0 | ||||||||
\(82\) | −6.12311 | + | 10.6055i | −0.676184 | + | 1.17118i | ||||
\(83\) | 7.12311 | 0.781862 | 0.390931 | − | 0.920420i | \(-0.372153\pi\) | ||||
0.390931 | + | 0.920420i | \(0.372153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56155 | − | 2.70469i | 0.169374 | − | 0.293365i | ||||
\(86\) | −0.438447 | −0.0472790 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.06155 | − | 3.57071i | −0.219762 | − | 0.380639i | ||||
\(89\) | −9.40388 | − | 16.2880i | −0.996810 | − | 1.72652i | −0.567529 | − | 0.823354i | \(-0.692100\pi\) |
−0.429281 | − | 0.903171i | \(-0.641233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.280776 | − | 2.00514i | −0.0294334 | − | 0.210196i | ||||
\(92\) | −4.68466 | −0.488409 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.50000 | − | 6.06218i | −0.360997 | − | 0.625266i | ||||
\(95\) | 0.280776 | − | 0.486319i | 0.0288071 | − | 0.0498953i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.56155 | − | 6.16879i | 0.361621 | − | 0.626346i | −0.626607 | − | 0.779335i | \(-0.715557\pi\) |
0.988228 | + | 0.152990i | \(0.0488901\pi\) | |||||||
\(98\) | −3.34233 | + | 5.78908i | −0.337626 | + | 0.584786i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.43845 | − | 7.68762i | −0.441642 | − | 0.764946i | 0.556170 | − | 0.831069i | \(-0.312271\pi\) |
−0.997812 | + | 0.0661225i | \(0.978937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | 0 | ||||||||
\(106\) | −4.28078 | − | 7.41452i | −0.415786 | − | 0.720162i | ||||
\(107\) | 1.00000 | + | 1.73205i | 0.0966736 | + | 0.167444i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −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 | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.561553 | −0.0530618 | ||||||||
\(113\) | 4.34233 | − | 7.52113i | 0.408492 | − | 0.707529i | −0.586229 | − | 0.810145i | \(-0.699388\pi\) |
0.994721 | + | 0.102617i | \(0.0327215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.34233 | − | 4.05703i | −0.218423 | − | 0.378320i | ||||
\(116\) | −2.43845 | −0.226404 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.43845 | 0.592707 | ||||||||
\(119\) | 0.876894 | + | 1.51883i | 0.0803848 | + | 0.139231i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | + | 5.19615i | −0.272727 | + | 0.472377i | ||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.34233 | − | 5.78908i | 0.300150 | − | 0.519875i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.28078 | + | 7.41452i | 0.379857 | + | 0.657932i | 0.991041 | − | 0.133556i | \(-0.0426397\pi\) |
−0.611184 | + | 0.791489i | \(0.709306\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.34233 | − | 1.35234i | −0.293142 | − | 0.118608i | ||||
\(131\) | 2.12311 | 0.185497 | 0.0927483 | − | 0.995690i | \(-0.470435\pi\) | ||||
0.0927483 | + | 0.995690i | \(0.470435\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.157671 | + | 0.273094i | 0.0136718 | + | 0.0236802i | ||||
\(134\) | −1.12311 | + | 1.94528i | −0.0970215 | + | 0.168046i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.56155 | − | 2.70469i | 0.133902 | − | 0.231925i | ||||
\(137\) | 5.90388 | − | 10.2258i | 0.504403 | − | 0.873651i | −0.495584 | − | 0.868560i | \(-0.665046\pi\) |
0.999987 | − | 0.00509126i | \(-0.00162061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.28078 | + | 10.8786i | −0.532729 | + | 0.922713i | 0.466541 | + | 0.884500i | \(0.345500\pi\) |
−0.999270 | + | 0.0382133i | \(0.987833\pi\) | |||||||
\(140\) | −0.280776 | − | 0.486319i | −0.0237299 | − | 0.0411015i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1231 | −1.10127 | ||||||||
\(143\) | 13.7808 | + | 5.57586i | 1.15241 | + | 0.466277i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.21922 | − | 2.11176i | −0.101251 | − | 0.175372i | ||||
\(146\) | 4.68466 | + | 8.11407i | 0.387705 | + | 0.671525i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.12311 | −0.338917 | ||||||||
\(149\) | −1.09612 | + | 1.89853i | −0.0897975 | + | 0.155534i | −0.907425 | − | 0.420213i | \(-0.861955\pi\) |
0.817628 | + | 0.575747i | \(0.195289\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.15767 | + | 2.00514i | 0.0932878 | + | 0.161579i | ||||
\(155\) | 6.68466 | 0.536925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 2.63068 | 0.207327 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.21922 | − | 12.5041i | 0.565453 | − | 0.979394i | −0.431554 | − | 0.902087i | \(-0.642035\pi\) |
0.997007 | − | 0.0773067i | \(-0.0246321\pi\) | |||||||
\(164\) | −12.2462 | −0.956268 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.56155 | + | 6.16879i | 0.276430 | + | 0.478791i | ||||
\(167\) | 2.18466 | + | 3.78394i | 0.169054 | + | 0.292810i | 0.938087 | − | 0.346398i | \(-0.112595\pi\) |
−0.769034 | + | 0.639208i | \(0.779262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.15767 | − | 12.6107i | 0.242898 | − | 0.970052i | ||||
\(170\) | 3.12311 | 0.239531 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.219224 | − | 0.379706i | −0.0167156 | − | 0.0289523i | ||||
\(173\) | 10.0885 | − | 17.4739i | 0.767018 | − | 1.32851i | −0.172156 | − | 0.985070i | \(-0.555073\pi\) |
0.939173 | − | 0.343444i | \(-0.111593\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.280776 | − | 0.486319i | 0.0212247 | − | 0.0367623i | ||||
\(176\) | 2.06155 | − | 3.57071i | 0.155395 | − | 0.269153i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.40388 | − | 16.2880i | 0.704851 | − | 1.22084i | ||||
\(179\) | −6.34233 | − | 10.9852i | −0.474048 | − | 0.821075i | 0.525511 | − | 0.850787i | \(-0.323874\pi\) |
−0.999559 | + | 0.0297120i | \(0.990541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.34233 | − | 4.05703i | −0.172679 | − | 0.299088i | ||||
\(185\) | −2.06155 | − | 3.57071i | −0.151568 | − | 0.262524i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.8769 | −0.941652 | ||||||||
\(188\) | 3.50000 | − | 6.06218i | 0.255264 | − | 0.442130i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.561553 | 0.0407393 | ||||||||
\(191\) | 5.43845 | − | 9.41967i | 0.393512 | − | 0.681583i | −0.599398 | − | 0.800451i | \(-0.704593\pi\) |
0.992910 | + | 0.118868i | \(0.0379266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(194\) | 7.12311 | 0.511409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 6.40388 | + | 11.0918i | 0.456258 | + | 0.790262i | 0.998760 | − | 0.0497931i | \(-0.0158562\pi\) |
−0.542502 | + | 0.840055i | \(0.682523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.43845 | + | 2.49146i | −0.101969 | + | 0.176615i | −0.912496 | − | 0.409086i | \(-0.865848\pi\) |
0.810527 | + | 0.585701i | \(0.199181\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.43845 | − | 7.68762i | 0.312288 | − | 0.540899i | ||||
\(203\) | 1.36932 | 0.0961072 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.12311 | − | 10.6055i | −0.427656 | − | 0.740722i | ||||
\(206\) | 2.28078 | + | 3.95042i | 0.158909 | + | 0.275239i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.34233 | − | 1.35234i | −0.231749 | − | 0.0937682i | ||||
\(209\) | −2.31534 | −0.160156 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9654 | + | 18.9927i | 0.754892 | + | 1.30751i | 0.945428 | + | 0.325831i | \(0.105644\pi\) |
−0.190536 | + | 0.981680i | \(0.561023\pi\) | |||||||
\(212\) | 4.28078 | − | 7.41452i | 0.294005 | − | 0.509231i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.00000 | + | 1.73205i | −0.0683586 | + | 0.118401i | ||||
\(215\) | 0.219224 | − | 0.379706i | 0.0149509 | − | 0.0258958i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.87689 | + | 3.25088i | −0.127412 | + | 0.220684i | ||||
\(218\) | −1.87689 | − | 3.25088i | −0.127119 | − | 0.220177i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.12311 | 0.277980 | ||||||||
\(221\) | 1.56155 | + | 11.1517i | 0.105041 | + | 0.750146i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6501 | − | 23.6427i | −0.914078 | − | 1.58323i | −0.808246 | − | 0.588845i | \(-0.799583\pi\) |
−0.105832 | − | 0.994384i | \(-0.533751\pi\) | |||||||
\(224\) | −0.280776 | − | 0.486319i | −0.0187602 | − | 0.0324936i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.68466 | 0.577695 | ||||||||
\(227\) | −10.0000 | + | 17.3205i | −0.663723 | + | 1.14960i | 0.315906 | + | 0.948790i | \(0.397691\pi\) |
−0.979630 | + | 0.200812i | \(0.935642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.21922 | − | 2.11176i | −0.0800460 | − | 0.138644i | ||||
\(233\) | 5.31534 | 0.348220 | 0.174110 | − | 0.984726i | \(-0.444295\pi\) | ||||
0.174110 | + | 0.984726i | \(0.444295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | 3.21922 | + | 5.57586i | 0.209554 | + | 0.362957i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.876894 | + | 1.51883i | −0.0568406 | + | 0.0984508i | ||||
\(239\) | 11.3693 | 0.735420 | 0.367710 | − | 0.929941i | \(-0.380142\pi\) | ||||
0.367710 | + | 0.929941i | \(0.380142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0616 | − | 24.3553i | 0.905784 | − | 1.56886i | 0.0859232 | − | 0.996302i | \(-0.472616\pi\) |
0.819861 | − | 0.572563i | \(-0.194051\pi\) | |||||||
\(242\) | −6.00000 | −0.385695 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.00000 | − | 5.19615i | −0.192055 | − | 0.332650i | ||||
\(245\) | −3.34233 | − | 5.78908i | −0.213534 | − | 0.369851i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.280776 | + | 2.00514i | 0.0178654 | + | 0.127584i | ||||
\(248\) | 6.68466 | 0.424476 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | −4.06155 | + | 7.03482i | −0.256363 | + | 0.444034i | −0.965265 | − | 0.261273i | \(-0.915858\pi\) |
0.708902 | + | 0.705307i | \(0.249191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.65767 | + | 16.7276i | −0.607173 | + | 1.05165i | ||||
\(254\) | −4.28078 | + | 7.41452i | −0.268600 | + | 0.465229i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.78078 | − | 4.81645i | −0.173460 | − | 0.300442i | 0.766167 | − | 0.642641i | \(-0.222161\pi\) |
−0.939627 | + | 0.342200i | \(0.888828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.31534 | 0.143868 | ||||||||
\(260\) | −0.500000 | − | 3.57071i | −0.0310087 | − | 0.221446i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.06155 | + | 1.83866i | 0.0655830 | + | 0.113593i | ||||
\(263\) | −6.50000 | − | 11.2583i | −0.400807 | − | 0.694218i | 0.593016 | − | 0.805190i | \(-0.297937\pi\) |
−0.993824 | + | 0.110972i | \(0.964604\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.56155 | 0.525932 | ||||||||
\(266\) | −0.157671 | + | 0.273094i | −0.00966742 | + | 0.0167445i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.24621 | −0.137209 | ||||||||
\(269\) | 10.6847 | − | 18.5064i | 0.651455 | − | 1.12835i | −0.331315 | − | 0.943520i | \(-0.607492\pi\) |
0.982770 | − | 0.184833i | \(-0.0591745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.58854 | + | 11.4117i | 0.400225 | + | 0.693211i | 0.993753 | − | 0.111603i | \(-0.0355985\pi\) |
−0.593528 | + | 0.804814i | \(0.702265\pi\) | |||||||
\(272\) | 3.12311 | 0.189366 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8078 | 0.713333 | ||||||||
\(275\) | 2.06155 | + | 3.57071i | 0.124316 | + | 0.215322i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | −12.5616 | −0.753392 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.280776 | − | 0.486319i | 0.0167796 | − | 0.0290631i | ||||
\(281\) | −16.2462 | −0.969168 | −0.484584 | − | 0.874745i | \(-0.661029\pi\) | ||||
−0.484584 | + | 0.874745i | \(0.661029\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.78078 | − | 13.4767i | −0.462519 | − | 0.801107i | 0.536567 | − | 0.843858i | \(-0.319721\pi\) |
−0.999086 | + | 0.0427513i | \(0.986388\pi\) | |||||||
\(284\) | −6.56155 | − | 11.3649i | −0.389357 | − | 0.674385i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.06155 | + | 14.7224i | 0.121902 | + | 0.870556i | ||||
\(287\) | 6.87689 | 0.405930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.62311 | + | 6.27540i | 0.213124 | + | 0.369141i | ||||
\(290\) | 1.21922 | − | 2.11176i | 0.0715953 | − | 0.124007i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.68466 | + | 8.11407i | −0.274149 | + | 0.474840i | ||||
\(293\) | 1.96543 | − | 3.40423i | 0.114822 | − | 0.198877i | −0.802887 | − | 0.596132i | \(-0.796704\pi\) |
0.917709 | + | 0.397254i | \(0.130037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.21922 | + | 5.57586i | −0.187430 | + | 0.324639i | ||||
\(296\) | −2.06155 | − | 3.57071i | −0.119825 | − | 0.207544i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.19224 | −0.126993 | ||||||||
\(299\) | 15.6577 | + | 6.33527i | 0.905506 | + | 0.366378i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.123106 | + | 0.213225i | 0.00709569 | + | 0.0122901i | ||||
\(302\) | −7.68466 | − | 13.3102i | −0.442202 | − | 0.765917i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.561553 | 0.0322073 | ||||||||
\(305\) | 3.00000 | − | 5.19615i | 0.171780 | − | 0.297531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.34233 | + | 5.78908i | 0.189832 | + | 0.328798i | ||||
\(311\) | −30.7386 | −1.74303 | −0.871514 | − | 0.490371i | \(-0.836861\pi\) | ||||
−0.871514 | + | 0.490371i | \(0.836861\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | 0 | ||||||||
\(316\) | −5.78078 | + | 10.0126i | −0.325194 | + | 0.563253i | ||||
\(317\) | 24.8078 | 1.39334 | 0.696671 | − | 0.717390i | \(-0.254664\pi\) | ||||
0.696671 | + | 0.717390i | \(0.254664\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.02699 | + | 8.70700i | −0.281457 | + | 0.487498i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.31534 | + | 2.27824i | 0.0733011 | + | 0.126961i | ||||
\(323\) | −0.876894 | − | 1.51883i | −0.0487917 | − | 0.0845097i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.84233 | − | 2.21837i | 0.157664 | − | 0.123053i | ||||
\(326\) | 14.4384 | 0.799672 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.12311 | − | 10.6055i | −0.338092 | − | 0.585592i | ||||
\(329\) | −1.96543 | + | 3.40423i | −0.108358 | + | 0.187681i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3693 | + | 26.6204i | −0.844774 | + | 1.46319i | 0.0410432 | + | 0.999157i | \(0.486932\pi\) |
−0.885817 | + | 0.464034i | \(0.846401\pi\) | |||||||
\(332\) | −3.56155 | + | 6.16879i | −0.195466 | + | 0.338556i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.18466 | + | 3.78394i | −0.119539 | + | 0.207048i | ||||
\(335\) | −1.12311 | − | 1.94528i | −0.0613618 | − | 0.106282i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.56155 | + | 2.70469i | 0.0846871 | + | 0.146682i | ||||
\(341\) | −13.7808 | − | 23.8690i | −0.746271 | − | 1.29258i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0.219224 | − | 0.379706i | 0.0118197 | − | 0.0204724i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1771 | 1.08473 | ||||||||
\(347\) | 0.438447 | − | 0.759413i | 0.0235371 | − | 0.0407674i | −0.854017 | − | 0.520245i | \(-0.825841\pi\) |
0.877554 | + | 0.479478i | \(0.159174\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.24621 | − | 7.35465i | −0.227294 | − | 0.393686i | 0.729711 | − | 0.683756i | \(-0.239655\pi\) |
−0.957005 | + | 0.290070i | \(0.906321\pi\) | |||||||
\(350\) | 0.561553 | 0.0300163 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.12311 | 0.219762 | ||||||||
\(353\) | −12.9309 | − | 22.3969i | −0.688241 | − | 1.19207i | −0.972407 | − | 0.233293i | \(-0.925050\pi\) |
0.284166 | − | 0.958775i | \(-0.408283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.56155 | − | 11.3649i | 0.348251 | − | 0.603189i | ||||
\(356\) | 18.8078 | 0.996810 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.34233 | − | 10.9852i | 0.335203 | − | 0.580588i | ||||
\(359\) | −13.1231 | −0.692611 | −0.346306 | − | 0.938122i | \(-0.612564\pi\) | ||||
−0.346306 | + | 0.938122i | \(0.612564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.34233 | + | 16.1814i | 0.491702 | + | 0.851652i | ||||
\(362\) | 1.43845 | + | 2.49146i | 0.0756031 | + | 0.130948i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.87689 | + | 0.759413i | 0.0983760 | + | 0.0398040i | ||||
\(365\) | −9.36932 | −0.490412 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.24621 | − | 10.8188i | −0.326050 | − | 0.564734i | 0.655675 | − | 0.755044i | \(-0.272384\pi\) |
−0.981724 | + | 0.190309i | \(0.939051\pi\) | |||||||
\(368\) | 2.34233 | − | 4.05703i | 0.122102 | − | 0.211487i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.06155 | − | 3.57071i | 0.107175 | − | 0.185633i | ||||
\(371\) | −2.40388 | + | 4.16365i | −0.124803 | + | 0.216166i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9039 | − | 22.3502i | 0.668138 | − | 1.15725i | −0.310287 | − | 0.950643i | \(-0.600425\pi\) |
0.978424 | − | 0.206605i | \(-0.0662416\pi\) | |||||||
\(374\) | −6.43845 | − | 11.1517i | −0.332924 | − | 0.576642i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 8.15009 | + | 3.29762i | 0.419751 | + | 0.169836i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.84233 | + | 15.3154i | 0.454200 | + | 0.786697i | 0.998642 | − | 0.0521012i | \(-0.0165918\pi\) |
−0.544442 | + | 0.838799i | \(0.683259\pi\) | |||||||
\(380\) | 0.280776 | + | 0.486319i | 0.0144035 | + | 0.0249476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.8769 | 0.556510 | ||||||||
\(383\) | 0.0961180 | − | 0.166481i | 0.00491140 | − | 0.00850679i | −0.863559 | − | 0.504247i | \(-0.831770\pi\) |
0.868471 | + | 0.495741i | \(0.165103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31534 | −0.118001 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.56155 | + | 6.16879i | 0.180810 | + | 0.313173i | ||||
\(389\) | 18.0540 | 0.915373 | 0.457686 | − | 0.889114i | \(-0.348678\pi\) | ||||
0.457686 | + | 0.889114i | \(0.348678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6307 | −0.739905 | ||||||||
\(392\) | −3.34233 | − | 5.78908i | −0.168813 | − | 0.292393i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.40388 | + | 11.0918i | −0.322623 | + | 0.558799i | ||||
\(395\) | −11.5616 | −0.581725 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0616 | − | 17.4271i | 0.504975 | − | 0.874642i | −0.495009 | − | 0.868888i | \(-0.664835\pi\) |
0.999983 | − | 0.00575403i | \(-0.00183158\pi\) | |||||||
\(398\) | −2.87689 | −0.144206 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 0.157671 | + | 0.273094i | 0.00787370 | + | 0.0136377i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
−0.862062 | + | 0.506803i | \(0.830827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0000 | + | 14.8290i | −0.946457 | + | 0.738687i | ||||
\(404\) | 8.87689 | 0.441642 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.684658 | + | 1.18586i | 0.0339790 | + | 0.0588534i | ||||
\(407\) | −8.50000 | + | 14.7224i | −0.421329 | + | 0.729764i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.40388 | − | 16.2880i | 0.464992 | − | 0.805390i | −0.534209 | − | 0.845352i | \(-0.679391\pi\) |
0.999201 | + | 0.0399625i | \(0.0127239\pi\) | |||||||
\(410\) | 6.12311 | − | 10.6055i | 0.302399 | − | 0.523770i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.28078 | + | 3.95042i | −0.112366 | + | 0.194623i | ||||
\(413\) | −1.80776 | − | 3.13114i | −0.0889543 | − | 0.154073i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.12311 | −0.349660 | ||||||||
\(416\) | −0.500000 | − | 3.57071i | −0.0245145 | − | 0.175069i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.15767 | − | 2.00514i | −0.0566235 | − | 0.0980748i | ||||
\(419\) | 16.2462 | + | 28.1393i | 0.793679 | + | 1.37469i | 0.923674 | + | 0.383178i | \(0.125171\pi\) |
−0.129995 | + | 0.991515i | \(0.541496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.56155 | 0.415786 | ||||||||
\(425\) | −1.56155 | + | 2.70469i | −0.0757464 | + | 0.131197i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.68466 | + | 2.91791i | 0.0815263 | + | 0.141208i | ||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.438447 | 0.0211438 | ||||||||
\(431\) | −11.3693 | − | 19.6922i | −0.547641 | − | 0.948542i | −0.998436 | − | 0.0559140i | \(-0.982193\pi\) |
0.450795 | − | 0.892628i | \(-0.351141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.36932 | − | 16.2281i | 0.450261 | − | 0.779874i | −0.548141 | − | 0.836386i | \(-0.684664\pi\) |
0.998402 | + | 0.0565114i | \(0.0179977\pi\) | |||||||
\(434\) | −3.75379 | −0.180188 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.87689 | − | 3.25088i | 0.0898869 | − | 0.155689i | ||||
\(437\) | −2.63068 | −0.125843 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5616 | − | 21.7572i | −0.599530 | − | 1.03842i | −0.992890 | − | 0.119032i | \(-0.962021\pi\) |
0.393360 | − | 0.919384i | \(-0.371313\pi\) | |||||||
\(440\) | 2.06155 | + | 3.57071i | 0.0982807 | + | 0.170227i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.87689 | + | 6.92820i | −0.422231 | + | 0.329541i | ||||
\(443\) | 13.1231 | 0.623498 | 0.311749 | − | 0.950165i | \(-0.399085\pi\) | ||||
0.311749 | + | 0.950165i | \(0.399085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.40388 | + | 16.2880i | 0.445787 | + | 0.772125i | ||||
\(446\) | 13.6501 | − | 23.6427i | 0.646351 | − | 1.11951i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.280776 | − | 0.486319i | 0.0132654 | − | 0.0229764i | ||||
\(449\) | −10.0885 | + | 17.4739i | −0.476108 | + | 0.824643i | −0.999625 | − | 0.0273722i | \(-0.991286\pi\) |
0.523518 | + | 0.852015i | \(0.324619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.2462 | + | 43.7277i | −1.18880 | + | 2.05906i | ||||
\(452\) | 4.34233 | + | 7.52113i | 0.204246 | + | 0.353764i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0.280776 | + | 2.00514i | 0.0131630 | + | 0.0940026i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1231 | − | 17.5337i | −0.473539 | − | 0.820193i | 0.526002 | − | 0.850483i | \(-0.323690\pi\) |
−0.999541 | + | 0.0302897i | \(0.990357\pi\) | |||||||
\(458\) | −12.1231 | − | 20.9978i | −0.566476 | − | 0.981164i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.68466 | 0.218423 | ||||||||
\(461\) | −15.0270 | + | 26.0275i | −0.699877 | + | 1.21222i | 0.268632 | + | 0.963243i | \(0.413428\pi\) |
−0.968509 | + | 0.248979i | \(0.919905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.65767 | + | 4.60322i | 0.123114 | + | 0.213240i | ||||
\(467\) | 17.8617 | 0.826543 | 0.413271 | − | 0.910608i | \(-0.364386\pi\) | ||||
0.413271 | + | 0.910608i | \(0.364386\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.26137 | 0.0582445 | ||||||||
\(470\) | 3.50000 | + | 6.06218i | 0.161443 | + | 0.279627i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.21922 | + | 5.57586i | −0.148177 | + | 0.256650i | ||||
\(473\) | −1.80776 | −0.0831211 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.280776 | + | 0.486319i | −0.0128829 | + | 0.0223138i | ||||
\(476\) | −1.75379 | −0.0803848 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.68466 | + | 9.84612i | 0.260010 | + | 0.450351i | ||||
\(479\) | −19.1231 | − | 33.1222i | −0.873757 | − | 1.51339i | −0.858081 | − | 0.513514i | \(-0.828343\pi\) |
−0.0156760 | − | 0.999877i | \(-0.504990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7808 | + | 5.57586i | 0.628349 | + | 0.254237i | ||||
\(482\) | 28.1231 | 1.28097 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.00000 | − | 5.19615i | −0.136364 | − | 0.236189i | ||||
\(485\) | −3.56155 | + | 6.16879i | −0.161722 | + | 0.280110i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.52699 | + | 11.3051i | −0.295766 | + | 0.512282i | −0.975163 | − | 0.221489i | \(-0.928908\pi\) |
0.679397 | + | 0.733771i | \(0.262242\pi\) | |||||||
\(488\) | 3.00000 | − | 5.19615i | 0.135804 | − | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.34233 | − | 5.78908i | 0.150991 | − | 0.261524i | ||||
\(491\) | −8.71922 | − | 15.1021i | −0.393493 | − | 0.681550i | 0.599415 | − | 0.800439i | \(-0.295400\pi\) |
−0.992908 | + | 0.118889i | \(0.962067\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.61553 | −0.342986 | ||||||||
\(494\) | −1.59612 | + | 1.24573i | −0.0718127 | + | 0.0560481i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.34233 | + | 5.78908i | 0.150075 | + | 0.259938i | ||||
\(497\) | 3.68466 | + | 6.38202i | 0.165280 | + | 0.286273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.12311 | −0.362552 | ||||||||
\(503\) | −21.5270 | + | 37.2858i | −0.959841 | + | 1.66249i | −0.236962 | + | 0.971519i | \(0.576152\pi\) |
−0.722879 | + | 0.690974i | \(0.757182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.43845 | + | 7.68762i | 0.197508 | + | 0.342094i | ||||
\(506\) | −19.3153 | −0.858672 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.56155 | −0.379857 | ||||||||
\(509\) | 20.2732 | + | 35.1142i | 0.898594 | + | 1.55641i | 0.829293 | + | 0.558814i | \(0.188744\pi\) |
0.0693009 | + | 0.997596i | \(0.477923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.63068 | − | 4.55648i | 0.116375 | − | 0.201567i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.78078 | − | 4.81645i | 0.122655 | − | 0.212444i | ||||
\(515\) | −4.56155 | −0.201006 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4309 | − | 24.9950i | −0.634669 | − | 1.09928i | ||||
\(518\) | 1.15767 | + | 2.00514i | 0.0508651 | + | 0.0881010i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.84233 | − | 2.21837i | 0.124644 | − | 0.0972820i | ||||
\(521\) | 6.31534 | 0.276680 | 0.138340 | − | 0.990385i | \(-0.455823\pi\) | ||||
0.138340 | + | 0.990385i | \(0.455823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9039 | + | 25.8143i | 0.651701 | + | 1.12878i | 0.982710 | + | 0.185152i | \(0.0592777\pi\) |
−0.331009 | + | 0.943628i | \(0.607389\pi\) | |||||||
\(524\) | −1.06155 | + | 1.83866i | −0.0463741 | + | 0.0803224i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.50000 | − | 11.2583i | 0.283413 | − | 0.490887i | ||||
\(527\) | 10.4384 | − | 18.0799i | 0.454706 | − | 0.787574i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.526988 | − | 0.912769i | 0.0229125 | − | 0.0396856i | ||||
\(530\) | 4.28078 | + | 7.41452i | 0.185945 | + | 0.322066i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.315342 | −0.0136718 | ||||||||
\(533\) | 40.9309 | + | 16.5611i | 1.77291 | + | 0.717341i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00000 | − | 1.73205i | −0.0432338 | − | 0.0748831i | ||||
\(536\) | −1.12311 | − | 1.94528i | −0.0485108 | − | 0.0840231i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.3693 | 0.921297 | ||||||||
\(539\) | −13.7808 | + | 23.8690i | −0.593580 | + | 1.02811i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.56155 | + | 2.70469i | 0.0669510 | + | 0.115963i | ||||
\(545\) | 3.75379 | 0.160795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.06155 | + | 3.57071i | −0.0879049 | + | 0.152256i | ||||
\(551\) | −1.36932 | −0.0583349 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.24621 | − | 5.62260i | 0.138043 | − | 0.239097i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.28078 | − | 10.8786i | −0.266364 | − | 0.461356i | ||||
\(557\) | −4.28078 | − | 7.41452i | −0.181382 | − | 0.314163i | 0.760969 | − | 0.648788i | \(-0.224724\pi\) |
−0.942352 | + | 0.334625i | \(0.891390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.219224 | + | 1.56557i | 0.00927217 | + | 0.0662165i | ||||
\(560\) | 0.561553 | 0.0237299 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.12311 | − | 14.0696i | −0.342653 | − | 0.593492i | ||||
\(563\) | −16.4924 | + | 28.5657i | −0.695073 | + | 1.20390i | 0.275083 | + | 0.961420i | \(0.411295\pi\) |
−0.970156 | + | 0.242481i | \(0.922039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.34233 | + | 7.52113i | −0.182683 | + | 0.316417i | ||||
\(566\) | 7.78078 | − | 13.4767i | 0.327050 | − | 0.566468i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.56155 | − | 11.3649i | 0.275317 | − | 0.476862i | ||||
\(569\) | 13.0885 | + | 22.6700i | 0.548700 | + | 0.950377i | 0.998364 | + | 0.0571787i | \(0.0182105\pi\) |
−0.449664 | + | 0.893198i | \(0.648456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.43845 | + | 5.95557i | 0.143518 | + | 0.248580i | ||||
\(575\) | 2.34233 | + | 4.05703i | 0.0976819 | + | 0.169190i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −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 | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.6501 | − | 30.5709i | −0.730992 | − | 1.26612i | ||||
\(584\) | −9.36932 | −0.387705 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.93087 | 0.162383 | ||||||||
\(587\) | −20.1231 | − | 34.8542i | −0.830569 | − | 1.43859i | −0.897587 | − | 0.440837i | \(-0.854682\pi\) |
0.0670179 | − | 0.997752i | \(-0.478652\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.87689 | − | 3.25088i | 0.0773361 | − | 0.133950i | ||||
\(590\) | −6.43845 | −0.265067 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.06155 | − | 3.57071i | 0.0847293 | − | 0.146755i | ||||
\(593\) | −33.1771 | −1.36242 | −0.681210 | − | 0.732088i | \(-0.738546\pi\) | ||||
−0.681210 | + | 0.732088i | \(0.738546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.876894 | − | 1.51883i | −0.0359492 | − | 0.0622658i | ||||
\(596\) | −1.09612 | − | 1.89853i | −0.0448987 | − | 0.0777669i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.34233 | + | 16.7276i | 0.0957850 | + | 0.684041i | ||||
\(599\) | 14.0000 | 0.572024 | 0.286012 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286012 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9924 | − | 25.9676i | −0.611554 | − | 1.05924i | −0.990979 | − | 0.134020i | \(-0.957212\pi\) |
0.379425 | − | 0.925222i | \(-0.376122\pi\) | |||||||
\(602\) | −0.123106 | + | 0.213225i | −0.00501741 | + | 0.00869041i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.68466 | − | 13.3102i | 0.312684 | − | 0.541585i | ||||
\(605\) | 3.00000 | − | 5.19615i | 0.121967 | − | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.2116 | + | 28.0794i | −0.658010 | + | 1.13971i | 0.323120 | + | 0.946358i | \(0.395268\pi\) |
−0.981130 | + | 0.193349i | \(0.938065\pi\) | |||||||
\(608\) | 0.280776 | + | 0.486319i | 0.0113870 | + | 0.0197228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −19.8963 | + | 15.5286i | −0.804918 | + | 0.628219i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.93845 | − | 17.2139i | −0.401410 | − | 0.695263i | 0.592486 | − | 0.805581i | \(-0.298146\pi\) |
−0.993896 | + | 0.110318i | \(0.964813\pi\) | |||||||
\(614\) | 12.8078 | + | 22.1837i | 0.516879 | + | 0.895261i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.31534 | −0.0932878 | ||||||||
\(617\) | −14.6577 | + | 25.3878i | −0.590096 | + | 1.02208i | 0.404123 | + | 0.914704i | \(0.367577\pi\) |
−0.994219 | + | 0.107371i | \(0.965757\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −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 | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.3693 | − | 26.6204i | −0.616253 | − | 1.06738i | ||||
\(623\) | −10.5616 | −0.423140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 15.6847 | + | 27.1666i | 0.626885 | + | 1.08580i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.93845 | + | 12.0177i | −0.276874 | + | 0.479560i | ||||
\(629\) | −12.8769 | −0.513435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.87689 | − | 11.9111i | 0.273765 | − | 0.474175i | −0.696058 | − | 0.717986i | \(-0.745064\pi\) |
0.969823 | + | 0.243811i | \(0.0783977\pi\) | |||||||
\(632\) | −11.5616 | −0.459894 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.4039 | + | 21.4842i | 0.492621 | + | 0.853245i | ||||
\(635\) | −4.28078 | − | 7.41452i | −0.169877 | − | 0.294236i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3423 | + | 9.03996i | 0.885235 | + | 0.358176i | ||||
\(638\) | −10.0540 | −0.398041 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −5.71922 | + | 9.90599i | −0.225896 | + | 0.391263i | −0.956588 | − | 0.291444i | \(-0.905864\pi\) |
0.730692 | + | 0.682707i | \(0.239198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8769 | + | 18.8393i | −0.428943 | + | 0.742951i | −0.996780 | − | 0.0801904i | \(-0.974447\pi\) |
0.567837 | + | 0.823141i | \(0.307780\pi\) | |||||||
\(644\) | −1.31534 | + | 2.27824i | −0.0518317 | + | 0.0897752i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.876894 | − | 1.51883i | 0.0345009 | − | 0.0597574i | ||||
\(647\) | 17.5270 | + | 30.3576i | 0.689057 | + | 1.19348i | 0.972143 | + | 0.234387i | \(0.0753084\pi\) |
−0.283086 | + | 0.959094i | \(0.591358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.5464 | 1.04204 | ||||||||
\(650\) | 3.34233 | + | 1.35234i | 0.131097 | + | 0.0530433i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.21922 | + | 12.5041i | 0.282727 | + | 0.489697i | ||||
\(653\) | −22.2808 | − | 38.5914i | −0.871914 | − | 1.51020i | −0.860014 | − | 0.510270i | \(-0.829545\pi\) |
−0.0119002 | − | 0.999929i | \(-0.503788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.12311 | −0.0829566 | ||||||||
\(656\) | 6.12311 | − | 10.6055i | 0.239067 | − | 0.414076i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.93087 | −0.153241 | ||||||||
\(659\) | −3.02699 | + | 5.24290i | −0.117915 | + | 0.204234i | −0.918941 | − | 0.394395i | \(-0.870954\pi\) |
0.801026 | + | 0.598629i | \(0.204288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8078 | − | 25.6478i | −0.575955 | − | 0.997584i | −0.995937 | − | 0.0900513i | \(-0.971297\pi\) |
0.419982 | − | 0.907532i | \(-0.362036\pi\) | |||||||
\(662\) | −30.7386 | −1.19469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.12311 | −0.276430 | ||||||||
\(665\) | −0.157671 | − | 0.273094i | −0.00611421 | − | 0.0105901i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.71165 | + | 9.89286i | −0.221156 | + | 0.383053i | ||||
\(668\) | −4.36932 | −0.169054 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.12311 | − | 1.94528i | 0.0433894 | − | 0.0751526i | ||||
\(671\) | −24.7386 | −0.955024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8769 | − | 22.3034i | −0.496368 | − | 0.859734i | 0.503623 | − | 0.863923i | \(-0.332000\pi\) |
−0.999991 | + | 0.00418904i | \(0.998667\pi\) | |||||||
\(674\) | −3.00000 | − | 5.19615i | −0.115556 | − | 0.200148i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.34233 | + | 9.03996i | 0.359320 | + | 0.347691i | ||||
\(677\) | 37.1231 | 1.42676 | 0.713378 | − | 0.700779i | \(-0.247164\pi\) | ||||
0.713378 | + | 0.700779i | \(0.247164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | −1.56155 | + | 2.70469i | −0.0598828 | + | 0.103720i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.7808 | − | 23.8690i | 0.527693 | − | 0.913991i | ||||
\(683\) | 8.56155 | − | 14.8290i | 0.327599 | − | 0.567418i | −0.654436 | − | 0.756117i | \(-0.727094\pi\) |
0.982035 | + | 0.188700i | \(0.0604273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.90388 | + | 10.2258i | −0.225576 | + | 0.390709i | ||||
\(686\) | 3.84233 | + | 6.65511i | 0.146701 | + | 0.254093i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.438447 | 0.0167156 | ||||||||
\(689\) | −24.3348 | + | 18.9927i | −0.927080 | + | 0.723564i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2808 | + | 17.8068i | 0.391099 | + | 0.677404i | 0.992595 | − | 0.121472i | \(-0.0387616\pi\) |
−0.601496 | + | 0.798876i | \(0.705428\pi\) | |||||||
\(692\) | 10.0885 | + | 17.4739i | 0.383509 | + | 0.664257i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.876894 | 0.0332865 | ||||||||
\(695\) | 6.28078 | − | 10.8786i | 0.238243 | − | 0.412650i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.2462 | −1.44868 | ||||||||
\(698\) | 4.24621 | − | 7.35465i | 0.160721 | − | 0.278378i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.280776 | + | 0.486319i | 0.0106124 | + | 0.0183811i | ||||
\(701\) | 36.3002 | 1.37104 | 0.685520 | − | 0.728054i | \(-0.259575\pi\) | ||||
0.685520 | + | 0.728054i | \(0.259575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.31534 | −0.0873248 | ||||||||
\(704\) | 2.06155 | + | 3.57071i | 0.0776977 | + | 0.134576i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.9309 | − | 22.3969i | 0.486660 | − | 0.842919i | ||||
\(707\) | −4.98485 | −0.187474 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1231 | + | 29.6581i | −0.643072 | + | 1.11383i | 0.341672 | + | 0.939819i | \(0.389007\pi\) |
−0.984743 | + | 0.174013i | \(0.944326\pi\) | |||||||
\(710\) | 13.1231 | 0.492501 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.40388 | + | 16.2880i | 0.352425 | + | 0.610419i | ||||
\(713\) | −15.6577 | − | 27.1199i | −0.586384 | − | 1.01565i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.7808 | − | 5.57586i | −0.515372 | − | 0.208525i | ||||
\(716\) | 12.6847 | 0.474048 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.56155 | − | 11.3649i | −0.244875 | − | 0.424136i | ||||
\(719\) | 22.4924 | − | 38.9580i | 0.838826 | − | 1.45289i | −0.0520512 | − | 0.998644i | \(-0.516576\pi\) |
0.890877 | − | 0.454245i | \(-0.150091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28078 | − | 2.21837i | 0.0476986 | − | 0.0826164i | ||||
\(722\) | −9.34233 | + | 16.1814i | −0.347685 | + | 0.602209i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.43845 | + | 2.49146i | −0.0534595 | + | 0.0925945i | ||||
\(725\) | 1.21922 | + | 2.11176i | 0.0452808 | + | 0.0784287i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.68466 | − | 8.11407i | −0.173387 | − | 0.300315i | ||||
\(731\) | −0.684658 | − | 1.18586i | −0.0253230 | − | 0.0438607i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | −4.63068 | + | 8.02058i | −0.170573 | + | 0.295442i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.7732 | + | 23.8559i | 0.506655 | + | 0.877553i | 0.999970 | + | 0.00770202i | \(0.00245165\pi\) |
−0.493315 | + | 0.869851i | \(0.664215\pi\) | |||||||
\(740\) | 4.12311 | 0.151568 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.80776 | −0.176499 | ||||||||
\(743\) | 6.58854 | + | 11.4117i | 0.241710 | + | 0.418654i | 0.961202 | − | 0.275847i | \(-0.0889584\pi\) |
−0.719491 | + | 0.694501i | \(0.755625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.09612 | − | 1.89853i | 0.0401587 | − | 0.0695568i | ||||
\(746\) | 25.8078 | 0.944889 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.43845 | − | 11.1517i | 0.235413 | − | 0.407747i | ||||
\(749\) | 1.12311 | 0.0410374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9039 | + | 20.6181i | 0.434379 | + | 0.752366i | 0.997245 | − | 0.0741820i | \(-0.0236346\pi\) |
−0.562866 | + | 0.826548i | \(0.690301\pi\) | |||||||
\(752\) | 3.50000 | + | 6.06218i | 0.127632 | + | 0.221065i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.21922 | + | 8.70700i | 0.0444015 | + | 0.317090i | ||||
\(755\) | 15.3693 | 0.559347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.2116 | + | 24.6153i | 0.516531 | + | 0.894658i | 0.999816 | + | 0.0191948i | \(0.00611027\pi\) |
−0.483285 | + | 0.875463i | \(0.660556\pi\) | |||||||
\(758\) | −8.84233 | + | 15.3154i | −0.321168 | + | 0.556279i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.280776 | + | 0.486319i | −0.0101848 | + | 0.0176406i | ||||
\(761\) | −8.96543 | + | 15.5286i | −0.324997 | + | 0.562911i | −0.981512 | − | 0.191402i | \(-0.938697\pi\) |
0.656515 | + | 0.754313i | \(0.272030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.05398 | + | 1.82554i | −0.0381565 | + | 0.0660889i | ||||
\(764\) | 5.43845 | + | 9.41967i | 0.196756 | + | 0.340792i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.192236 | 0.00694577 | ||||||||
\(767\) | −3.21922 | − | 22.9899i | −0.116239 | − | 0.830116i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6577 | + | 28.8519i | 0.600691 | + | 1.04043i | 0.992717 | + | 0.120473i | \(0.0384411\pi\) |
−0.392026 | + | 0.919954i | \(0.628226\pi\) | |||||||
\(770\) | −1.15767 | − | 2.00514i | −0.0417196 | − | 0.0722604i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0885 | − | 20.9380i | 0.434795 | − | 0.753086i | −0.562484 | − | 0.826808i | \(-0.690154\pi\) |
0.997279 | + | 0.0737217i | \(0.0234876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.68466 | −0.240120 | ||||||||
\(776\) | −3.56155 | + | 6.16879i | −0.127852 | + | 0.221447i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.02699 | + | 15.6352i | 0.323633 | + | 0.560549i | ||||
\(779\) | −6.87689 | −0.246390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1080 | −1.93613 | ||||||||
\(782\) | −7.31534 | − | 12.6705i | −0.261596 | − | 0.453098i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.34233 | − | 5.78908i | 0.119369 | − | 0.206753i | ||||
\(785\) | −13.8769 | −0.495288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6577 | + | 27.1199i | −0.558136 | + | 0.966719i | 0.439516 | + | 0.898235i | \(0.355150\pi\) |
−0.997652 | + | 0.0684848i | \(0.978184\pi\) | |||||||
\(788\) | −12.8078 | −0.456258 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.78078 | − | 10.0126i | −0.205671 | − | 0.356232i | ||||
\(791\) | −2.43845 | − | 4.22351i | −0.0867012 | − | 0.150171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.00000 | + | 21.4243i | 0.106533 | + | 0.760799i | ||||
\(794\) | 20.1231 | 0.714142 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.43845 | − | 2.49146i | −0.0509844 | − | 0.0883076i | ||||
\(797\) | 6.56155 | − | 11.3649i | 0.232422 | − | 0.402567i | −0.726098 | − | 0.687591i | \(-0.758668\pi\) |
0.958520 | + | 0.285024i | \(0.0920016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9309 | − | 18.9328i | 0.386706 | − | 0.669795i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.157671 | + | 0.273094i | −0.00556755 | + | 0.00964328i | ||||
\(803\) | 19.3153 | + | 33.4552i | 0.681624 | + | 1.18061i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.63068 | −0.0927194 | ||||||||
\(806\) | −22.3423 | − | 9.03996i | −0.786975 | − | 0.318419i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.43845 | + | 7.68762i | 0.156144 | + | 0.270449i | ||||
\(809\) | −7.24621 | − | 12.5508i | −0.254763 | − | 0.441263i | 0.710068 | − | 0.704133i | \(-0.248664\pi\) |
−0.964831 | + | 0.262870i | \(0.915331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.0000 | −0.595850 | ||||||||
\(815\) | −7.21922 | + | 12.5041i | −0.252878 | + | 0.437998i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.123106 | − | 0.213225i | −0.00430692 | − | 0.00745981i | ||||
\(818\) | 18.8078 | 0.657598 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.2462 | 0.427656 | ||||||||
\(821\) | −4.21922 | − | 7.30791i | −0.147252 | − | 0.255048i | 0.782959 | − | 0.622073i | \(-0.213709\pi\) |
−0.930211 | + | 0.367026i | \(0.880376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.52699 | + | 4.37687i | −0.0880853 | + | 0.152568i | −0.906702 | − | 0.421772i | \(-0.861408\pi\) |
0.818616 | + | 0.574341i | \(0.194741\pi\) | |||||||
\(824\) | −4.56155 | −0.158909 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.80776 | − | 3.13114i | 0.0629002 | − | 0.108946i | ||||
\(827\) | 28.2462 | 0.982217 | 0.491109 | − | 0.871098i | \(-0.336592\pi\) | ||||
0.491109 | + | 0.871098i | \(0.336592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.19224 | − | 10.7253i | −0.215065 | − | 0.372504i | 0.738228 | − | 0.674552i | \(-0.235663\pi\) |
−0.953293 | + | 0.302048i | \(0.902330\pi\) | |||||||
\(830\) | −3.56155 | − | 6.16879i | −0.123623 | − | 0.214122i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.84233 | − | 2.21837i | 0.0985400 | − | 0.0769081i | ||||
\(833\) | −20.8769 | −0.723342 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.18466 | − | 3.78394i | −0.0756032 | − | 0.130949i | ||||
\(836\) | 1.15767 | − | 2.00514i | 0.0400389 | − | 0.0693494i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.2462 | + | 28.1393i | −0.561216 | + | 0.972055i | ||||
\(839\) | 18.3693 | − | 31.8166i | 0.634179 | − | 1.09843i | −0.352509 | − | 0.935808i | \(-0.614671\pi\) |
0.986688 | − | 0.162622i | \(-0.0519952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5270 | − | 19.9653i | 0.397482 | − | 0.688460i | ||||
\(842\) | −16.2462 | − | 28.1393i | −0.559881 | − | 0.969743i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.9309 | −0.754892 | ||||||||
\(845\) | −3.15767 | + | 12.6107i | −0.108627 | + | 0.433820i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.68466 | + | 2.91791i | 0.0578855 | + | 0.100261i | ||||
\(848\) | 4.28078 | + | 7.41452i | 0.147002 | + | 0.254616i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.12311 | −0.107122 | ||||||||
\(851\) | −9.65767 | + | 16.7276i | −0.331061 | + | 0.573414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 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 | 0 | ||||||||
\(856\) | −1.00000 | − | 1.73205i | −0.0341793 | − | 0.0592003i | ||||
\(857\) | 6.19224 | 0.211523 | 0.105761 | − | 0.994392i | \(-0.466272\pi\) | ||||
0.105761 | + | 0.994392i | \(0.466272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 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 | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.3693 | − | 19.6922i | 0.387240 | − | 0.670720i | ||||
\(863\) | −2.43845 | −0.0830057 | −0.0415029 | − | 0.999138i | \(-0.513215\pi\) | ||||
−0.0415029 | + | 0.999138i | \(0.513215\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0885 | + | 17.4739i | −0.343021 | + | 0.594129i | ||||
\(866\) | 18.7386 | 0.636765 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.87689 | − | 3.25088i | −0.0637059 | − | 0.110342i | ||||
\(869\) | 23.8348 | + | 41.2830i | 0.808539 | + | 1.40043i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.50758 | + | 3.03765i | 0.254385 | + | 0.102927i | ||||
\(872\) | 3.75379 | 0.127119 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.31534 | − | 2.27824i | −0.0444921 | − | 0.0770626i | ||||
\(875\) | −0.280776 | + | 0.486319i | −0.00949197 | + | 0.0164406i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.21922 | + | 7.30791i | −0.142473 | + | 0.246771i | −0.928427 | − | 0.371514i | \(-0.878839\pi\) |
0.785954 | + | 0.618285i | \(0.212172\pi\) | |||||||
\(878\) | 12.5616 | − | 21.7572i | 0.423932 | − | 0.734272i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.06155 | + | 3.57071i | −0.0694949 | + | 0.120369i | ||||
\(881\) | −12.2808 | − | 21.2709i | −0.413750 | − | 0.716636i | 0.581546 | − | 0.813513i | \(-0.302448\pi\) |
−0.995296 | + | 0.0968774i | \(0.969115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −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 | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.56155 | + | 11.3649i | 0.220440 | + | 0.381813i | ||||
\(887\) | −16.5540 | − | 28.6723i | −0.555828 | − | 0.962722i | −0.997839 | − | 0.0657126i | \(-0.979068\pi\) |
0.442010 | − | 0.897010i | \(-0.354265\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.80776 | 0.161247 | ||||||||
\(890\) | −9.40388 | + | 16.2880i | −0.315219 | + | 0.545975i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.3002 | 0.914078 | ||||||||
\(893\) | 1.96543 | − | 3.40423i | 0.0657708 | − | 0.113918i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.34233 | + | 10.9852i | 0.212001 | + | 0.367196i | ||||
\(896\) | 0.561553 | 0.0187602 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.1771 | −0.673318 | ||||||||
\(899\) | −8.15009 | − | 14.1164i | −0.271821 | − | 0.470807i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.3693 | − | 23.1563i | 0.445397 | − | 0.771449i | ||||
\(902\) | −50.4924 | −1.68121 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.34233 | + | 7.52113i | −0.144424 | + | 0.250149i | ||||
\(905\) | −2.87689 | −0.0956312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.9579 | + | 46.6924i | 0.895121 | + | 1.55039i | 0.833655 | + | 0.552286i | \(0.186244\pi\) |
0.0614661 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(908\) | −10.0000 | − | 17.3205i | −0.331862 | − | 0.574801i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.59612 | + | 1.24573i | −0.0529108 | + | 0.0412956i | ||||
\(911\) | 18.6307 | 0.617262 | 0.308631 | − | 0.951182i | \(-0.400129\pi\) | ||||
0.308631 | + | 0.951182i | \(0.400129\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6847 | + | 25.4346i | 0.485991 | + | 0.841762i | ||||
\(914\) | 10.1231 | − | 17.5337i | 0.334843 | − | 0.579964i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.1231 | − | 20.9978i | 0.400559 | − | 0.693788i | ||||
\(917\) | 0.596118 | − | 1.03251i | 0.0196855 | − | 0.0340964i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.31534 | + | 14.4026i | −0.274298 | + | 0.475098i | −0.969958 | − | 0.243274i | \(-0.921779\pi\) |
0.695660 | + | 0.718371i | \(0.255112\pi\) | |||||||
\(920\) | 2.34233 | + | 4.05703i | 0.0772243 | + | 0.133756i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.0540 | −0.989775 | ||||||||
\(923\) | 6.56155 | + | 46.8589i | 0.215976 | + | 1.54238i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.06155 | + | 3.57071i | 0.0677834 | + | 0.117404i | ||||
\(926\) | −3.80776 | − | 6.59524i | −0.125131 | − | 0.216733i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.43845 | 0.0800460 | ||||||||
\(929\) | −12.5616 | + | 21.7572i | −0.412131 | + | 0.713832i | −0.995123 | − | 0.0986462i | \(-0.968549\pi\) |
0.582991 | + | 0.812478i | \(0.301882\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.75379 | −0.123025 | ||||||||
\(932\) | −2.65767 | + | 4.60322i | −0.0870549 | + | 0.150784i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.93087 | + | 15.4687i | 0.292227 | + | 0.506152i | ||||
\(935\) | 12.8769 | 0.421119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.50000 | + | 6.06218i | −0.114157 | + | 0.197726i | ||||
\(941\) | 25.3693 | 0.827016 | 0.413508 | − | 0.910500i | \(-0.364303\pi\) | ||||
0.413508 | + | 0.910500i | \(0.364303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.6847 | + | 49.6833i | −0.934101 | + | 1.61791i | ||||
\(944\) | −6.43845 | −0.209554 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.903882 | − | 1.56557i | −0.0293877 | − | 0.0509011i | ||||
\(947\) | −21.9309 | − | 37.9854i | −0.712658 | − | 1.23436i | −0.963856 | − | 0.266423i | \(-0.914158\pi\) |
0.251199 | − | 0.967936i | \(-0.419175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.6307 | − | 20.7846i | 0.864469 | − | 0.674697i | ||||
\(950\) | −0.561553 | −0.0182192 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.876894 | − | 1.51883i | −0.0284203 | − | 0.0492254i | ||||
\(953\) | 25.5885 | − | 44.3207i | 0.828894 | − | 1.43569i | −0.0700123 | − | 0.997546i | \(-0.522304\pi\) |
0.898906 | − | 0.438141i | \(-0.144363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.43845 | + | 9.41967i | −0.175984 | + | 0.304813i | ||||
\(956\) | −5.68466 | + | 9.84612i | −0.183855 | + | 0.318446i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.1231 | − | 33.1222i | 0.617839 | − | 1.07013i | ||||
\(959\) | −3.31534 | − | 5.74234i | −0.107058 | − | 0.185430i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6847 | 0.441441 | ||||||||
\(962\) | 2.06155 | + | 14.7224i | 0.0664671 | + | 0.474670i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.0616 | + | 24.3553i | 0.452892 | + | 0.784432i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 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 | 0 | ||||||||
\(970\) | −7.12311 | −0.228709 | ||||||||
\(971\) | −2.15767 | + | 3.73720i | −0.0692430 | + | 0.119932i | −0.898568 | − | 0.438834i | \(-0.855392\pi\) |
0.829325 | + | 0.558766i | \(0.188725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.52699 | + | 6.10892i | 0.113070 | + | 0.195843i | ||||
\(974\) | −13.0540 | −0.418276 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −24.1501 | − | 41.8292i | −0.772630 | − | 1.33823i | −0.936117 | − | 0.351689i | \(-0.885608\pi\) |
0.163487 | − | 0.986545i | \(-0.447726\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.7732 | − | 67.1572i | 1.23920 | − | 2.14635i | ||||
\(980\) | 6.68466 | 0.213534 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.71922 | − | 15.1021i | 0.278242 | − | 0.481929i | ||||
\(983\) | −32.1231 | −1.02457 | −0.512284 | − | 0.858816i | \(-0.671200\pi\) | ||||
−0.512284 | + | 0.858816i | \(0.671200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.40388 | − | 11.0918i | −0.204045 | − | 0.353416i | ||||
\(986\) | −3.80776 | − | 6.59524i | −0.121264 | − | 0.210035i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.87689 | − | 0.759413i | −0.0597120 | − | 0.0241601i | ||||
\(989\) | −2.05398 | −0.0653126 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.7116 | − | 42.8018i | −0.784991 | − | 1.35964i | −0.929004 | − | 0.370069i | \(-0.879334\pi\) |
0.144013 | − | 0.989576i | \(-0.453999\pi\) | |||||||
\(992\) | −3.34233 | + | 5.78908i | −0.106119 | + | 0.183804i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.68466 | + | 6.38202i | −0.116870 | + | 0.202425i | ||||
\(995\) | 1.43845 | − | 2.49146i | 0.0456018 | − | 0.0789847i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7732 | − | 32.5161i | 0.594553 | − | 1.02980i | −0.399057 | − | 0.916926i | \(-0.630662\pi\) |
0.993610 | − | 0.112870i | \(-0.0360044\pi\) | |||||||
\(998\) | 2.00000 | + | 3.46410i | 0.0633089 | + | 0.109654i | ||||
\(999\) | 0 | 0 |
(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 | 1170.2.i.o.991.2 | 4 | ||
3.2 | odd | 2 | 390.2.i.g.211.2 | yes | 4 | ||
13.9 | even | 3 | inner | 1170.2.i.o.451.2 | 4 | ||
15.2 | even | 4 | 1950.2.z.n.1849.4 | 8 | |||
15.8 | even | 4 | 1950.2.z.n.1849.1 | 8 | |||
15.14 | odd | 2 | 1950.2.i.bi.601.1 | 4 | |||
39.2 | even | 12 | 5070.2.b.r.1351.1 | 4 | |||
39.11 | even | 12 | 5070.2.b.r.1351.4 | 4 | |||
39.23 | odd | 6 | 5070.2.a.bb.1.2 | 2 | |||
39.29 | odd | 6 | 5070.2.a.bi.1.1 | 2 | |||
39.35 | odd | 6 | 390.2.i.g.61.2 | ✓ | 4 | ||
195.74 | odd | 6 | 1950.2.i.bi.451.1 | 4 | |||
195.113 | even | 12 | 1950.2.z.n.1699.4 | 8 | |||
195.152 | even | 12 | 1950.2.z.n.1699.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.2 | ✓ | 4 | 39.35 | odd | 6 | ||
390.2.i.g.211.2 | yes | 4 | 3.2 | odd | 2 | ||
1170.2.i.o.451.2 | 4 | 13.9 | even | 3 | inner | ||
1170.2.i.o.991.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.i.bi.451.1 | 4 | 195.74 | odd | 6 | |||
1950.2.i.bi.601.1 | 4 | 15.14 | odd | 2 | |||
1950.2.z.n.1699.1 | 8 | 195.152 | even | 12 | |||
1950.2.z.n.1699.4 | 8 | 195.113 | even | 12 | |||
1950.2.z.n.1849.1 | 8 | 15.8 | even | 4 | |||
1950.2.z.n.1849.4 | 8 | 15.2 | even | 4 | |||
5070.2.a.bb.1.2 | 2 | 39.23 | odd | 6 | |||
5070.2.a.bi.1.1 | 2 | 39.29 | odd | 6 | |||
5070.2.b.r.1351.1 | 4 | 39.2 | even | 12 | |||
5070.2.b.r.1351.4 | 4 | 39.11 | even | 12 |