Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, 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("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.3118758597603.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 133.3 | ||
Root | \(-1.80582 + 0.194943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.133 |
Dual form | 429.2.i.d.100.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.149489 | + | 0.258923i | 0.105705 | + | 0.183086i | 0.914026 | − | 0.405656i | \(-0.132957\pi\) |
−0.808321 | + | 0.588742i | \(0.799624\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.955306 | − | 1.65464i | 0.477653 | − | 0.827319i | ||||
\(5\) | −3.44245 | −1.53951 | −0.769755 | − | 0.638340i | \(-0.779621\pi\) | ||||
−0.769755 | + | 0.638340i | \(0.779621\pi\) | |||||||
\(6\) | −0.149489 | + | 0.258923i | −0.0610286 | + | 0.105705i | ||||
\(7\) | −2.46991 | + | 4.27802i | −0.933540 | + | 1.61694i | −0.156322 | + | 0.987706i | \(0.549964\pi\) |
−0.777217 | + | 0.629232i | \(0.783369\pi\) | |||||||
\(8\) | 1.16919 | 0.413370 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.514608 | − | 0.891327i | −0.162733 | − | 0.281862i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 1.91061 | 0.551546 | ||||||||
\(13\) | 1.73845 | + | 3.15876i | 0.482159 | + | 0.876084i | ||||
\(14\) | −1.47690 | −0.394718 | ||||||||
\(15\) | −1.72122 | − | 2.98125i | −0.444418 | − | 0.769755i | ||||
\(16\) | −1.73583 | − | 3.00655i | −0.433958 | − | 0.751637i | ||||
\(17\) | −2.78859 | + | 4.82998i | −0.676333 | + | 1.17144i | 0.299745 | + | 0.954019i | \(0.403098\pi\) |
−0.976077 | + | 0.217423i | \(0.930235\pi\) | |||||||
\(18\) | −0.298978 | −0.0704698 | ||||||||
\(19\) | −2.61940 | + | 4.53694i | −0.600932 | + | 1.04085i | 0.391748 | + | 0.920073i | \(0.371871\pi\) |
−0.992680 | + | 0.120773i | \(0.961463\pi\) | |||||||
\(20\) | −3.28859 | + | 5.69601i | −0.735351 | + | 1.27367i | ||||
\(21\) | −4.93983 | −1.07796 | ||||||||
\(22\) | 0.149489 | − | 0.258923i | 0.0318712 | − | 0.0552025i | ||||
\(23\) | −1.56999 | − | 2.71929i | −0.327365 | − | 0.567012i | 0.654623 | − | 0.755955i | \(-0.272827\pi\) |
−0.981988 | + | 0.188943i | \(0.939494\pi\) | |||||||
\(24\) | 0.584594 | + | 1.01255i | 0.119330 | + | 0.206685i | ||||
\(25\) | 6.85044 | 1.37009 | ||||||||
\(26\) | −0.557996 | + | 0.922325i | −0.109432 | + | 0.180883i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.71905 | + | 8.17363i | 0.891816 | + | 1.54467i | ||||
\(29\) | −1.54252 | − | 2.67172i | −0.286438 | − | 0.496126i | 0.686519 | − | 0.727112i | \(-0.259138\pi\) |
−0.972957 | + | 0.230986i | \(0.925805\pi\) | |||||||
\(30\) | 0.514608 | − | 0.891327i | 0.0939541 | − | 0.162733i | ||||
\(31\) | 8.42691 | 1.51352 | 0.756759 | − | 0.653694i | \(-0.226782\pi\) | ||||
0.756759 | + | 0.653694i | \(0.226782\pi\) | |||||||
\(32\) | 1.68816 | − | 2.92398i | 0.298428 | − | 0.516892i | ||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | −1.66745 | −0.285966 | ||||||||
\(35\) | 8.50255 | − | 14.7268i | 1.43719 | − | 2.48929i | ||||
\(36\) | 0.955306 | + | 1.65464i | 0.159218 | + | 0.275773i | ||||
\(37\) | 0.853486 | + | 1.47828i | 0.140312 | + | 0.243028i | 0.927614 | − | 0.373540i | \(-0.121856\pi\) |
−0.787302 | + | 0.616568i | \(0.788523\pi\) | |||||||
\(38\) | −1.56629 | −0.254085 | ||||||||
\(39\) | −1.86634 | + | 3.08492i | −0.298854 | + | 0.493983i | ||||
\(40\) | −4.02486 | −0.636387 | ||||||||
\(41\) | −0.234083 | − | 0.405443i | −0.0365576 | − | 0.0633196i | 0.847168 | − | 0.531326i | \(-0.178306\pi\) |
−0.883725 | + | 0.468006i | \(0.844973\pi\) | |||||||
\(42\) | −0.738450 | − | 1.27903i | −0.113945 | − | 0.197359i | ||||
\(43\) | −3.77835 | + | 6.54429i | −0.576193 | + | 0.997995i | 0.419718 | + | 0.907655i | \(0.362129\pi\) |
−0.995911 | + | 0.0903409i | \(0.971204\pi\) | |||||||
\(44\) | −1.91061 | −0.288036 | ||||||||
\(45\) | 1.72122 | − | 2.98125i | 0.256585 | − | 0.444418i | ||||
\(46\) | 0.469391 | − | 0.813009i | 0.0692080 | − | 0.119872i | ||||
\(47\) | −2.55670 | −0.372933 | −0.186466 | − | 0.982461i | \(-0.559704\pi\) | ||||
−0.186466 | + | 0.982461i | \(0.559704\pi\) | |||||||
\(48\) | 1.73583 | − | 3.00655i | 0.250546 | − | 0.433958i | ||||
\(49\) | −8.70095 | − | 15.0705i | −1.24299 | − | 2.15293i | ||||
\(50\) | 1.02407 | + | 1.77373i | 0.144825 | + | 0.250844i | ||||
\(51\) | −5.57718 | −0.780962 | ||||||||
\(52\) | 6.88737 | + | 0.141080i | 0.955106 | + | 0.0195643i | ||||
\(53\) | 6.18142 | 0.849083 | 0.424542 | − | 0.905408i | \(-0.360435\pi\) | ||||
0.424542 | + | 0.905408i | \(0.360435\pi\) | |||||||
\(54\) | −0.149489 | − | 0.258923i | −0.0203429 | − | 0.0352349i | ||||
\(55\) | 1.72122 | + | 2.98125i | 0.232090 | + | 0.401991i | ||||
\(56\) | −2.88779 | + | 5.00180i | −0.385897 | + | 0.668394i | ||||
\(57\) | −5.23881 | −0.693897 | ||||||||
\(58\) | 0.461179 | − | 0.798786i | 0.0605558 | − | 0.104886i | ||||
\(59\) | −5.17313 | + | 8.96012i | −0.673484 | + | 1.16651i | 0.303426 | + | 0.952855i | \(0.401870\pi\) |
−0.976910 | + | 0.213653i | \(0.931464\pi\) | |||||||
\(60\) | −6.57718 | −0.849110 | ||||||||
\(61\) | 6.79593 | − | 11.7709i | 0.870130 | − | 1.50711i | 0.00826842 | − | 0.999966i | \(-0.497368\pi\) |
0.861862 | − | 0.507144i | \(-0.169299\pi\) | |||||||
\(62\) | 1.25973 | + | 2.18192i | 0.159986 | + | 0.277104i | ||||
\(63\) | −2.46991 | − | 4.27802i | −0.311180 | − | 0.538979i | ||||
\(64\) | −5.93388 | −0.741735 | ||||||||
\(65\) | −5.98452 | − | 10.8739i | −0.742289 | − | 1.34874i | ||||
\(66\) | 0.298978 | 0.0368017 | ||||||||
\(67\) | 0.847892 | + | 1.46859i | 0.103587 | + | 0.179417i | 0.913160 | − | 0.407602i | \(-0.133635\pi\) |
−0.809573 | + | 0.587019i | \(0.800301\pi\) | |||||||
\(68\) | 5.32791 | + | 9.22822i | 0.646105 | + | 1.11909i | ||||
\(69\) | 1.56999 | − | 2.71929i | 0.189004 | − | 0.327365i | ||||
\(70\) | 5.08415 | 0.607672 | ||||||||
\(71\) | 3.42399 | − | 5.93053i | 0.406353 | − | 0.703825i | −0.588125 | − | 0.808770i | \(-0.700134\pi\) |
0.994478 | + | 0.104946i | \(0.0334669\pi\) | |||||||
\(72\) | −0.584594 | + | 1.01255i | −0.0688950 | + | 0.119330i | ||||
\(73\) | 1.86177 | 0.217904 | 0.108952 | − | 0.994047i | \(-0.465251\pi\) | ||||
0.108952 | + | 0.994047i | \(0.465251\pi\) | |||||||
\(74\) | −0.255174 | + | 0.441973i | −0.0296633 | + | 0.0513784i | ||||
\(75\) | 3.42522 | + | 5.93266i | 0.395510 | + | 0.685044i | ||||
\(76\) | 5.00466 | + | 8.66833i | 0.574074 | + | 0.994326i | ||||
\(77\) | 4.93983 | 0.562946 | ||||||||
\(78\) | −1.07775 | − | 0.0220766i | −0.122032 | − | 0.00249968i | ||||
\(79\) | 2.12106 | 0.238637 | 0.119319 | − | 0.992856i | \(-0.461929\pi\) | ||||
0.119319 | + | 0.992856i | \(0.461929\pi\) | |||||||
\(80\) | 5.97551 | + | 10.3499i | 0.668082 | + | 1.15715i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.0699856 | − | 0.121219i | 0.00772861 | − | 0.0133864i | ||||
\(83\) | −3.77309 | −0.414151 | −0.207075 | − | 0.978325i | \(-0.566395\pi\) | ||||
−0.207075 | + | 0.978325i | \(0.566395\pi\) | |||||||
\(84\) | −4.71905 | + | 8.17363i | −0.514890 | + | 0.891816i | ||||
\(85\) | 9.59957 | − | 16.6269i | 1.04122 | − | 1.80345i | ||||
\(86\) | −2.25929 | −0.243625 | ||||||||
\(87\) | 1.54252 | − | 2.67172i | 0.165375 | − | 0.286438i | ||||
\(88\) | −0.584594 | − | 1.01255i | −0.0623179 | − | 0.107938i | ||||
\(89\) | 1.55066 | + | 2.68583i | 0.164370 | + | 0.284697i | 0.936431 | − | 0.350851i | \(-0.114108\pi\) |
−0.772061 | + | 0.635548i | \(0.780774\pi\) | |||||||
\(90\) | 1.02922 | 0.108489 | ||||||||
\(91\) | −17.8071 | − | 0.364758i | −1.86669 | − | 0.0382370i | ||||
\(92\) | −5.99927 | −0.625467 | ||||||||
\(93\) | 4.21345 | + | 7.29792i | 0.436915 | + | 0.756759i | ||||
\(94\) | −0.382199 | − | 0.661987i | −0.0394208 | − | 0.0682788i | ||||
\(95\) | 9.01716 | − | 15.6182i | 0.925141 | − | 1.60239i | ||||
\(96\) | 3.37633 | 0.344595 | ||||||||
\(97\) | −4.65494 | + | 8.06258i | −0.472637 | + | 0.818631i | −0.999510 | − | 0.0313129i | \(-0.990031\pi\) |
0.526873 | + | 0.849944i | \(0.323365\pi\) | |||||||
\(98\) | 2.60139 | − | 4.50575i | 0.262780 | − | 0.455149i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 6.54427 | − | 11.3350i | 0.654427 | − | 1.13350i | ||||
\(101\) | 5.64129 | + | 9.77101i | 0.561330 | + | 0.972251i | 0.997381 | + | 0.0723296i | \(0.0230433\pi\) |
−0.436051 | + | 0.899922i | \(0.643623\pi\) | |||||||
\(102\) | −0.833727 | − | 1.44406i | −0.0825513 | − | 0.142983i | ||||
\(103\) | 11.0969 | 1.09341 | 0.546707 | − | 0.837324i | \(-0.315881\pi\) | ||||
0.546707 | + | 0.837324i | \(0.315881\pi\) | |||||||
\(104\) | 2.03257 | + | 3.69319i | 0.199310 | + | 0.362147i | ||||
\(105\) | 17.0051 | 1.65953 | ||||||||
\(106\) | 0.924054 | + | 1.60051i | 0.0897521 | + | 0.155455i | ||||
\(107\) | 9.02609 | + | 15.6336i | 0.872585 | + | 1.51136i | 0.859313 | + | 0.511450i | \(0.170891\pi\) |
0.0132720 | + | 0.999912i | \(0.495775\pi\) | |||||||
\(108\) | −0.955306 | + | 1.65464i | −0.0919244 | + | 0.159218i | ||||
\(109\) | −4.86248 | −0.465741 | −0.232871 | − | 0.972508i | \(-0.574812\pi\) | ||||
−0.232871 | + | 0.972508i | \(0.574812\pi\) | |||||||
\(110\) | −0.514608 | + | 0.891327i | −0.0490660 | + | 0.0849847i | ||||
\(111\) | −0.853486 | + | 1.47828i | −0.0810093 | + | 0.140312i | ||||
\(112\) | 17.1494 | 1.62047 | ||||||||
\(113\) | 7.25333 | − | 12.5631i | 0.682336 | − | 1.18184i | −0.291930 | − | 0.956440i | \(-0.594297\pi\) |
0.974266 | − | 0.225401i | \(-0.0723693\pi\) | |||||||
\(114\) | −0.783144 | − | 1.35645i | −0.0733482 | − | 0.127043i | ||||
\(115\) | 5.40459 | + | 9.36103i | 0.503981 | + | 0.872920i | ||||
\(116\) | −5.89431 | −0.547273 | ||||||||
\(117\) | −3.60480 | − | 0.0738401i | −0.333263 | − | 0.00682652i | ||||
\(118\) | −3.09330 | −0.284762 | ||||||||
\(119\) | −13.7752 | − | 23.8593i | −1.26277 | − | 2.18718i | ||||
\(120\) | −2.01243 | − | 3.48564i | −0.183709 | − | 0.318194i | ||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 4.06367 | 0.367907 | ||||||||
\(123\) | 0.234083 | − | 0.405443i | 0.0211065 | − | 0.0365576i | ||||
\(124\) | 8.05028 | − | 13.9435i | 0.722936 | − | 1.25216i | ||||
\(125\) | −6.37004 | −0.569754 | ||||||||
\(126\) | 0.738450 | − | 1.27903i | 0.0657864 | − | 0.113945i | ||||
\(127\) | 1.02449 | + | 1.77447i | 0.0909090 | + | 0.157459i | 0.907894 | − | 0.419200i | \(-0.137689\pi\) |
−0.816985 | + | 0.576659i | \(0.804356\pi\) | |||||||
\(128\) | −4.26338 | − | 7.38438i | −0.376833 | − | 0.652693i | ||||
\(129\) | −7.55670 | −0.665330 | ||||||||
\(130\) | 1.92087 | − | 3.17505i | 0.168472 | − | 0.278471i | ||||
\(131\) | −4.31366 | −0.376886 | −0.188443 | − | 0.982084i | \(-0.560344\pi\) | ||||
−0.188443 | + | 0.982084i | \(0.560344\pi\) | |||||||
\(132\) | −0.955306 | − | 1.65464i | −0.0831487 | − | 0.144018i | ||||
\(133\) | −12.9394 | − | 22.4117i | −1.12199 | − | 1.94334i | ||||
\(134\) | −0.253501 | + | 0.439077i | −0.0218992 | + | 0.0379305i | ||||
\(135\) | 3.44245 | 0.296279 | ||||||||
\(136\) | −3.26038 | + | 5.64715i | −0.279576 | + | 0.484239i | ||||
\(137\) | −8.98619 | + | 15.5645i | −0.767742 | + | 1.32977i | 0.171042 | + | 0.985264i | \(0.445286\pi\) |
−0.938785 | + | 0.344505i | \(0.888047\pi\) | |||||||
\(138\) | 0.938782 | 0.0799145 | ||||||||
\(139\) | −2.62799 | + | 4.55181i | −0.222903 | + | 0.386080i | −0.955688 | − | 0.294380i | \(-0.904887\pi\) |
0.732785 | + | 0.680460i | \(0.238220\pi\) | |||||||
\(140\) | −16.2451 | − | 28.1373i | −1.37296 | − | 2.37803i | ||||
\(141\) | −1.27835 | − | 2.21417i | −0.107656 | − | 0.186466i | ||||
\(142\) | 2.04740 | 0.171814 | ||||||||
\(143\) | 1.86634 | − | 3.08492i | 0.156072 | − | 0.257974i | ||||
\(144\) | 3.47166 | 0.289305 | ||||||||
\(145\) | 5.31004 | + | 9.19725i | 0.440975 | + | 0.763790i | ||||
\(146\) | 0.278314 | + | 0.482054i | 0.0230334 | + | 0.0398951i | ||||
\(147\) | 8.70095 | − | 15.0705i | 0.717642 | − | 1.24299i | ||||
\(148\) | 3.26136 | 0.268082 | ||||||||
\(149\) | −1.89740 | + | 3.28639i | −0.155441 | + | 0.269231i | −0.933219 | − | 0.359307i | \(-0.883013\pi\) |
0.777779 | + | 0.628538i | \(0.216346\pi\) | |||||||
\(150\) | −1.02407 | + | 1.77373i | −0.0836146 | + | 0.144825i | ||||
\(151\) | 6.43966 | 0.524052 | 0.262026 | − | 0.965061i | \(-0.415609\pi\) | ||||
0.262026 | + | 0.965061i | \(0.415609\pi\) | |||||||
\(152\) | −3.06257 | + | 5.30453i | −0.248407 | + | 0.430254i | ||||
\(153\) | −2.78859 | − | 4.82998i | −0.225444 | − | 0.390481i | ||||
\(154\) | 0.738450 | + | 1.27903i | 0.0595060 | + | 0.103067i | ||||
\(155\) | −29.0092 | −2.33007 | ||||||||
\(156\) | 3.32150 | + | 6.03517i | 0.265933 | + | 0.483201i | ||||
\(157\) | 15.7673 | 1.25837 | 0.629185 | − | 0.777255i | \(-0.283389\pi\) | ||||
0.629185 | + | 0.777255i | \(0.283389\pi\) | |||||||
\(158\) | 0.317075 | + | 0.549189i | 0.0252251 | + | 0.0436912i | ||||
\(159\) | 3.09071 | + | 5.35327i | 0.245109 | + | 0.424542i | ||||
\(160\) | −5.81141 | + | 10.0657i | −0.459432 | + | 0.795760i | ||||
\(161\) | 15.5109 | 1.22243 | ||||||||
\(162\) | 0.149489 | − | 0.258923i | 0.0117450 | − | 0.0203429i | ||||
\(163\) | −1.84629 | + | 3.19787i | −0.144613 | + | 0.250476i | −0.929228 | − | 0.369506i | \(-0.879527\pi\) |
0.784616 | + | 0.619982i | \(0.212860\pi\) | |||||||
\(164\) | −0.894482 | −0.0698473 | ||||||||
\(165\) | −1.72122 | + | 2.98125i | −0.133997 | + | 0.232090i | ||||
\(166\) | −0.564036 | − | 0.976939i | −0.0437777 | − | 0.0758252i | ||||
\(167\) | 3.45670 | + | 5.98718i | 0.267487 | + | 0.463302i | 0.968212 | − | 0.250130i | \(-0.0804733\pi\) |
−0.700725 | + | 0.713432i | \(0.747140\pi\) | |||||||
\(168\) | −5.77558 | −0.445596 | ||||||||
\(169\) | −6.95558 | + | 10.9827i | −0.535045 | + | 0.844824i | ||||
\(170\) | 5.74012 | 0.440247 | ||||||||
\(171\) | −2.61940 | − | 4.53694i | −0.200311 | − | 0.346948i | ||||
\(172\) | 7.21896 | + | 12.5036i | 0.550441 | + | 0.953391i | ||||
\(173\) | −3.56569 | + | 6.17596i | −0.271095 | + | 0.469550i | −0.969142 | − | 0.246501i | \(-0.920719\pi\) |
0.698048 | + | 0.716051i | \(0.254052\pi\) | |||||||
\(174\) | 0.922358 | 0.0699238 | ||||||||
\(175\) | −16.9200 | + | 29.3063i | −1.27903 | + | 2.21535i | ||||
\(176\) | −1.73583 | + | 3.00655i | −0.130843 | + | 0.226627i | ||||
\(177\) | −10.3463 | −0.777672 | ||||||||
\(178\) | −0.463614 | + | 0.803003i | −0.0347494 | + | 0.0601877i | ||||
\(179\) | 12.7023 | + | 22.0010i | 0.949412 | + | 1.64443i | 0.746666 | + | 0.665199i | \(0.231653\pi\) |
0.202747 | + | 0.979231i | \(0.435013\pi\) | |||||||
\(180\) | −3.28859 | − | 5.69601i | −0.245117 | − | 0.424555i | ||||
\(181\) | −15.0513 | −1.11875 | −0.559377 | − | 0.828913i | \(-0.688960\pi\) | ||||
−0.559377 | + | 0.828913i | \(0.688960\pi\) | |||||||
\(182\) | −2.56752 | − | 4.66518i | −0.190317 | − | 0.345806i | ||||
\(183\) | 13.5919 | 1.00474 | ||||||||
\(184\) | −1.83561 | − | 3.17936i | −0.135323 | − | 0.234386i | ||||
\(185\) | −2.93808 | − | 5.08890i | −0.216012 | − | 0.374144i | ||||
\(186\) | −1.25973 | + | 2.18192i | −0.0923679 | + | 0.159986i | ||||
\(187\) | 5.57718 | 0.407844 | ||||||||
\(188\) | −2.44243 | + | 4.23041i | −0.178133 | + | 0.308535i | ||||
\(189\) | 2.46991 | − | 4.27802i | 0.179660 | − | 0.311180i | ||||
\(190\) | 5.39186 | 0.391167 | ||||||||
\(191\) | −7.26456 | + | 12.5826i | −0.525645 | + | 0.910444i | 0.473909 | + | 0.880574i | \(0.342843\pi\) |
−0.999554 | + | 0.0298701i | \(0.990491\pi\) | |||||||
\(192\) | −2.96694 | − | 5.13889i | −0.214120 | − | 0.370867i | ||||
\(193\) | −7.83163 | − | 13.5648i | −0.563733 | − | 0.976414i | −0.997166 | − | 0.0752288i | \(-0.976031\pi\) |
0.433433 | − | 0.901186i | \(-0.357302\pi\) | |||||||
\(194\) | −2.78345 | −0.199840 | ||||||||
\(195\) | 6.42479 | − | 10.6197i | 0.460089 | − | 0.760492i | ||||
\(196\) | −33.2483 | −2.37488 | ||||||||
\(197\) | −5.04479 | − | 8.73783i | −0.359426 | − | 0.622545i | 0.628439 | − | 0.777859i | \(-0.283694\pi\) |
−0.987865 | + | 0.155314i | \(0.950361\pi\) | |||||||
\(198\) | 0.149489 | + | 0.258923i | 0.0106237 | + | 0.0184008i | ||||
\(199\) | −1.02274 | + | 1.77144i | −0.0725004 | + | 0.125574i | −0.899997 | − | 0.435897i | \(-0.856431\pi\) |
0.827496 | + | 0.561471i | \(0.189765\pi\) | |||||||
\(200\) | 8.00945 | 0.566353 | ||||||||
\(201\) | −0.847892 | + | 1.46859i | −0.0598057 | + | 0.103587i | ||||
\(202\) | −1.68662 | + | 2.92132i | −0.118670 | + | 0.205543i | ||||
\(203\) | 15.2396 | 1.06961 | ||||||||
\(204\) | −5.32791 | + | 9.22822i | −0.373029 | + | 0.646105i | ||||
\(205\) | 0.805817 | + | 1.39572i | 0.0562807 | + | 0.0974810i | ||||
\(206\) | 1.65887 | + | 2.87325i | 0.115579 | + | 0.200189i | ||||
\(207\) | 3.13997 | 0.218243 | ||||||||
\(208\) | 6.47932 | − | 10.7098i | 0.449260 | − | 0.742592i | ||||
\(209\) | 5.23881 | 0.362376 | ||||||||
\(210\) | 2.54208 | + | 4.40300i | 0.175420 | + | 0.303836i | ||||
\(211\) | 1.52745 | + | 2.64562i | 0.105154 | + | 0.182132i | 0.913801 | − | 0.406162i | \(-0.133133\pi\) |
−0.808647 | + | 0.588294i | \(0.799800\pi\) | |||||||
\(212\) | 5.90515 | − | 10.2280i | 0.405567 | − | 0.702463i | ||||
\(213\) | 6.84799 | 0.469216 | ||||||||
\(214\) | −2.69860 | + | 4.67412i | −0.184473 | + | 0.319516i | ||||
\(215\) | 13.0068 | − | 22.5284i | 0.887054 | − | 1.53642i | ||||
\(216\) | −1.16919 | −0.0795531 | ||||||||
\(217\) | −20.8137 | + | 36.0505i | −1.41293 | + | 2.44726i | ||||
\(218\) | −0.726888 | − | 1.25901i | −0.0492310 | − | 0.0852707i | ||||
\(219\) | 0.930884 | + | 1.61234i | 0.0629033 | + | 0.108952i | ||||
\(220\) | 6.57718 | 0.443433 | ||||||||
\(221\) | −20.1046 | − | 0.411820i | −1.35238 | − | 0.0277020i | ||||
\(222\) | −0.510347 | −0.0342522 | ||||||||
\(223\) | −7.14860 | − | 12.3817i | −0.478706 | − | 0.829142i | 0.520996 | − | 0.853559i | \(-0.325561\pi\) |
−0.999702 | + | 0.0244165i | \(0.992227\pi\) | |||||||
\(224\) | 8.33923 | + | 14.4440i | 0.557188 | + | 0.965079i | ||||
\(225\) | −3.42522 | + | 5.93266i | −0.228348 | + | 0.395510i | ||||
\(226\) | 4.33718 | 0.288505 | ||||||||
\(227\) | 13.6085 | − | 23.5706i | 0.903229 | − | 1.56444i | 0.0799521 | − | 0.996799i | \(-0.474523\pi\) |
0.823277 | − | 0.567640i | \(-0.192143\pi\) | |||||||
\(228\) | −5.00466 | + | 8.66833i | −0.331442 | + | 0.574074i | ||||
\(229\) | −5.42720 | −0.358640 | −0.179320 | − | 0.983791i | \(-0.557390\pi\) | ||||
−0.179320 | + | 0.983791i | \(0.557390\pi\) | |||||||
\(230\) | −1.61585 | + | 2.79874i | −0.106546 | + | 0.184544i | ||||
\(231\) | 2.46991 | + | 4.27802i | 0.162508 | + | 0.281473i | ||||
\(232\) | −1.80349 | − | 3.12374i | −0.118405 | − | 0.205084i | ||||
\(233\) | −22.5644 | −1.47824 | −0.739122 | − | 0.673572i | \(-0.764759\pi\) | ||||
−0.739122 | + | 0.673572i | \(0.764759\pi\) | |||||||
\(234\) | −0.519758 | − | 0.944401i | −0.0339777 | − | 0.0617374i | ||||
\(235\) | 8.80130 | 0.574134 | ||||||||
\(236\) | 9.88384 | + | 17.1193i | 0.643383 | + | 1.11437i | ||||
\(237\) | 1.06053 | + | 1.83689i | 0.0688887 | + | 0.119319i | ||||
\(238\) | 4.11847 | − | 7.13340i | 0.266961 | − | 0.462390i | ||||
\(239\) | 13.6503 | 0.882964 | 0.441482 | − | 0.897270i | \(-0.354453\pi\) | ||||
0.441482 | + | 0.897270i | \(0.354453\pi\) | |||||||
\(240\) | −5.97551 | + | 10.3499i | −0.385717 | + | 0.668082i | ||||
\(241\) | 4.44842 | − | 7.70488i | 0.286548 | − | 0.496315i | −0.686436 | − | 0.727191i | \(-0.740826\pi\) |
0.972983 | + | 0.230875i | \(0.0741590\pi\) | |||||||
\(242\) | −0.298978 | −0.0192190 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −12.9844 | − | 22.4896i | −0.831240 | − | 1.43975i | ||||
\(245\) | 29.9526 | + | 51.8794i | 1.91360 | + | 3.31445i | ||||
\(246\) | 0.139971 | 0.00892423 | ||||||||
\(247\) | −18.8848 | − | 0.386834i | −1.20161 | − | 0.0246137i | ||||
\(248\) | 9.85263 | 0.625643 | ||||||||
\(249\) | −1.88655 | − | 3.26759i | −0.119555 | − | 0.207075i | ||||
\(250\) | −0.952251 | − | 1.64935i | −0.0602257 | − | 0.104314i | ||||
\(251\) | −3.45655 | + | 5.98692i | −0.218176 | + | 0.377891i | −0.954250 | − | 0.299009i | \(-0.903344\pi\) |
0.736075 | + | 0.676900i | \(0.236677\pi\) | |||||||
\(252\) | −9.43810 | −0.594544 | ||||||||
\(253\) | −1.56999 | + | 2.71929i | −0.0987041 | + | 0.170961i | ||||
\(254\) | −0.306301 | + | 0.530528i | −0.0192190 | + | 0.0332883i | ||||
\(255\) | 19.1991 | 1.20230 | ||||||||
\(256\) | −4.65922 | + | 8.07001i | −0.291201 | + | 0.504376i | ||||
\(257\) | −5.05624 | − | 8.75766i | −0.315399 | − | 0.546288i | 0.664123 | − | 0.747623i | \(-0.268805\pi\) |
−0.979522 | + | 0.201336i | \(0.935472\pi\) | |||||||
\(258\) | −1.12964 | − | 1.95660i | −0.0703285 | − | 0.121813i | ||||
\(259\) | −8.43215 | −0.523948 | ||||||||
\(260\) | −23.7094 | − | 0.485660i | −1.47039 | − | 0.0301193i | ||||
\(261\) | 3.08504 | 0.190959 | ||||||||
\(262\) | −0.644845 | − | 1.11690i | −0.0398387 | − | 0.0690026i | ||||
\(263\) | 12.7328 | + | 22.0538i | 0.785137 | + | 1.35990i | 0.928917 | + | 0.370288i | \(0.120741\pi\) |
−0.143780 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(264\) | 0.584594 | − | 1.01255i | 0.0359792 | − | 0.0623179i | ||||
\(265\) | −21.2792 | −1.30717 | ||||||||
\(266\) | 3.86860 | − | 6.70061i | 0.237199 | − | 0.410841i | ||||
\(267\) | −1.55066 | + | 2.68583i | −0.0948990 | + | 0.164370i | ||||
\(268\) | 3.23999 | 0.197914 | ||||||||
\(269\) | 5.10232 | − | 8.83748i | 0.311094 | − | 0.538831i | −0.667505 | − | 0.744605i | \(-0.732638\pi\) |
0.978600 | + | 0.205774i | \(0.0659712\pi\) | |||||||
\(270\) | 0.514608 | + | 0.891327i | 0.0313180 | + | 0.0542444i | ||||
\(271\) | −8.77271 | − | 15.1948i | −0.532904 | − | 0.923017i | −0.999262 | − | 0.0384204i | \(-0.987767\pi\) |
0.466358 | − | 0.884596i | \(-0.345566\pi\) | |||||||
\(272\) | 19.3621 | 1.17400 | ||||||||
\(273\) | −8.58764 | − | 15.6038i | −0.519748 | − | 0.944382i | ||||
\(274\) | −5.37335 | −0.324616 | ||||||||
\(275\) | −3.42522 | − | 5.93266i | −0.206549 | − | 0.357753i | ||||
\(276\) | −2.99963 | − | 5.19552i | −0.180557 | − | 0.312733i | ||||
\(277\) | −7.45100 | + | 12.9055i | −0.447687 | + | 0.775417i | −0.998235 | − | 0.0593867i | \(-0.981085\pi\) |
0.550548 | + | 0.834804i | \(0.314419\pi\) | |||||||
\(278\) | −1.57142 | −0.0942477 | ||||||||
\(279\) | −4.21345 | + | 7.29792i | −0.252253 | + | 0.436915i | ||||
\(280\) | 9.94107 | − | 17.2184i | 0.594093 | − | 1.02900i | ||||
\(281\) | 21.3906 | 1.27605 | 0.638027 | − | 0.770014i | \(-0.279751\pi\) | ||||
0.638027 | + | 0.770014i | \(0.279751\pi\) | |||||||
\(282\) | 0.382199 | − | 0.661987i | 0.0227596 | − | 0.0394208i | ||||
\(283\) | 1.34148 | + | 2.32351i | 0.0797427 | + | 0.138118i | 0.903139 | − | 0.429349i | \(-0.141257\pi\) |
−0.823396 | + | 0.567467i | \(0.807923\pi\) | |||||||
\(284\) | −6.54192 | − | 11.3309i | −0.388192 | − | 0.672368i | ||||
\(285\) | 18.0343 | 1.06826 | ||||||||
\(286\) | 1.07775 | + | 0.0220766i | 0.0637290 | + | 0.00130542i | ||||
\(287\) | 2.31266 | 0.136512 | ||||||||
\(288\) | 1.68816 | + | 2.92398i | 0.0994759 | + | 0.172297i | ||||
\(289\) | −7.05247 | − | 12.2152i | −0.414851 | − | 0.718544i | ||||
\(290\) | −1.58758 | + | 2.74978i | −0.0932262 | + | 0.161472i | ||||
\(291\) | −9.30987 | −0.545754 | ||||||||
\(292\) | 1.77856 | − | 3.08055i | 0.104082 | − | 0.180276i | ||||
\(293\) | −9.39040 | + | 16.2647i | −0.548593 | + | 0.950191i | 0.449778 | + | 0.893140i | \(0.351503\pi\) |
−0.998371 | + | 0.0570508i | \(0.981830\pi\) | |||||||
\(294\) | 5.20279 | 0.303433 | ||||||||
\(295\) | 17.8082 | − | 30.8447i | 1.03683 | − | 1.79585i | ||||
\(296\) | 0.997885 | + | 1.72839i | 0.0580009 | + | 0.100460i | ||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | −1.13456 | −0.0657233 | ||||||||
\(299\) | 5.86027 | − | 9.68657i | 0.338908 | − | 0.560189i | ||||
\(300\) | 13.0885 | 0.755667 | ||||||||
\(301\) | −18.6644 | − | 32.3277i | −1.07580 | − | 1.86334i | ||||
\(302\) | 0.962659 | + | 1.66737i | 0.0553948 | + | 0.0959466i | ||||
\(303\) | −5.64129 | + | 9.77101i | −0.324084 | + | 0.561330i | ||||
\(304\) | 18.1874 | 1.04312 | ||||||||
\(305\) | −23.3946 | + | 40.5207i | −1.33957 | + | 2.32021i | ||||
\(306\) | 0.833727 | − | 1.44406i | 0.0476610 | − | 0.0825513i | ||||
\(307\) | −13.9915 | −0.798535 | −0.399267 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399267 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(308\) | 4.71905 | − | 8.17363i | 0.268893 | − | 0.465736i | ||||
\(309\) | 5.54847 | + | 9.61023i | 0.315641 | + | 0.546707i | ||||
\(310\) | −4.33655 | − | 7.51113i | −0.246300 | − | 0.426604i | ||||
\(311\) | 7.25887 | 0.411613 | 0.205806 | − | 0.978593i | \(-0.434018\pi\) | ||||
0.205806 | + | 0.978593i | \(0.434018\pi\) | |||||||
\(312\) | −2.18211 | + | 3.60685i | −0.123537 | + | 0.204198i | ||||
\(313\) | −5.75599 | −0.325348 | −0.162674 | − | 0.986680i | \(-0.552012\pi\) | ||||
−0.162674 | + | 0.986680i | \(0.552012\pi\) | |||||||
\(314\) | 2.35704 | + | 4.08252i | 0.133016 | + | 0.230390i | ||||
\(315\) | 8.50255 | + | 14.7268i | 0.479064 | + | 0.829764i | ||||
\(316\) | 2.02626 | − | 3.50958i | 0.113986 | − | 0.197429i | ||||
\(317\) | −23.1631 | −1.30097 | −0.650484 | − | 0.759520i | \(-0.725434\pi\) | ||||
−0.650484 | + | 0.759520i | \(0.725434\pi\) | |||||||
\(318\) | −0.924054 | + | 1.60051i | −0.0518184 | + | 0.0897521i | ||||
\(319\) | −1.54252 | + | 2.67172i | −0.0863644 | + | 0.149588i | ||||
\(320\) | 20.4271 | 1.14191 | ||||||||
\(321\) | −9.02609 | + | 15.6336i | −0.503787 | + | 0.872585i | ||||
\(322\) | 2.31871 | + | 4.01613i | 0.129217 | + | 0.223810i | ||||
\(323\) | −14.6089 | − | 25.3033i | −0.812860 | − | 1.40791i | ||||
\(324\) | −1.91061 | −0.106145 | ||||||||
\(325\) | 11.9091 | + | 21.6389i | 0.660601 | + | 1.20031i | ||||
\(326\) | −1.10400 | −0.0611449 | ||||||||
\(327\) | −2.43124 | − | 4.21103i | −0.134448 | − | 0.232871i | ||||
\(328\) | −0.273686 | − | 0.474039i | −0.0151118 | − | 0.0261744i | ||||
\(329\) | 6.31483 | − | 10.9376i | 0.348148 | − | 0.603010i | ||||
\(330\) | −1.02922 | −0.0566565 | ||||||||
\(331\) | −4.02848 | + | 6.97754i | −0.221426 | + | 0.383520i | −0.955241 | − | 0.295829i | \(-0.904404\pi\) |
0.733816 | + | 0.679349i | \(0.237738\pi\) | |||||||
\(332\) | −3.60446 | + | 6.24311i | −0.197820 | + | 0.342635i | ||||
\(333\) | −1.70697 | −0.0935415 | ||||||||
\(334\) | −1.03348 | + | 1.79003i | −0.0565493 | + | 0.0979463i | ||||
\(335\) | −2.91882 | − | 5.05555i | −0.159472 | − | 0.276214i | ||||
\(336\) | 8.57471 | + | 14.8518i | 0.467789 | + | 0.810234i | ||||
\(337\) | −11.3146 | −0.616344 | −0.308172 | − | 0.951331i | \(-0.599717\pi\) | ||||
−0.308172 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(338\) | −3.88345 | − | 0.159163i | −0.211232 | − | 0.00865733i | ||||
\(339\) | 14.5067 | 0.787894 | ||||||||
\(340\) | −18.3411 | − | 31.7677i | −0.994684 | − | 1.72284i | ||||
\(341\) | −4.21345 | − | 7.29792i | −0.228171 | − | 0.395204i | ||||
\(342\) | 0.783144 | − | 1.35645i | 0.0423476 | − | 0.0733482i | ||||
\(343\) | 51.3836 | 2.77445 | ||||||||
\(344\) | −4.41760 | + | 7.65150i | −0.238181 | + | 0.412541i | ||||
\(345\) | −5.40459 | + | 9.36103i | −0.290973 | + | 0.503981i | ||||
\(346\) | −2.13213 | −0.114624 | ||||||||
\(347\) | 9.89556 | − | 17.1396i | 0.531222 | − | 0.920103i | −0.468114 | − | 0.883668i | \(-0.655067\pi\) |
0.999336 | − | 0.0364349i | \(-0.0116002\pi\) | |||||||
\(348\) | −2.94715 | − | 5.10462i | −0.157984 | − | 0.273636i | ||||
\(349\) | −4.05073 | − | 7.01607i | −0.216831 | − | 0.375562i | 0.737007 | − | 0.675885i | \(-0.236239\pi\) |
−0.953837 | + | 0.300324i | \(0.902905\pi\) | |||||||
\(350\) | −10.1174 | −0.540799 | ||||||||
\(351\) | −1.73845 | − | 3.15876i | −0.0927916 | − | 0.168602i | ||||
\(352\) | −3.37633 | −0.179959 | ||||||||
\(353\) | 0.436757 | + | 0.756486i | 0.0232462 | + | 0.0402637i | 0.877415 | − | 0.479733i | \(-0.159266\pi\) |
−0.854168 | + | 0.519997i | \(0.825933\pi\) | |||||||
\(354\) | −1.54665 | − | 2.67888i | −0.0822036 | − | 0.142381i | ||||
\(355\) | −11.7869 | + | 20.4155i | −0.625585 | + | 1.08354i | ||||
\(356\) | 5.92543 | 0.314047 | ||||||||
\(357\) | 13.7752 | − | 23.8593i | 0.729059 | − | 1.26277i | ||||
\(358\) | −3.79770 | + | 6.57781i | −0.200715 | + | 0.347648i | ||||
\(359\) | 13.0320 | 0.687803 | 0.343901 | − | 0.939006i | \(-0.388251\pi\) | ||||
0.343901 | + | 0.939006i | \(0.388251\pi\) | |||||||
\(360\) | 2.01243 | − | 3.48564i | 0.106065 | − | 0.183709i | ||||
\(361\) | −4.22255 | − | 7.31366i | −0.222239 | − | 0.384930i | ||||
\(362\) | −2.25000 | − | 3.89712i | −0.118258 | − | 0.204828i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −17.6147 | + | 29.1158i | −0.923263 | + | 1.52608i | ||||
\(365\) | −6.40904 | −0.335464 | ||||||||
\(366\) | 2.03183 | + | 3.51924i | 0.106206 | + | 0.183954i | ||||
\(367\) | 11.3721 | + | 19.6971i | 0.593620 | + | 1.02818i | 0.993740 | + | 0.111718i | \(0.0356352\pi\) |
−0.400120 | + | 0.916463i | \(0.631031\pi\) | |||||||
\(368\) | −5.45046 | + | 9.44047i | −0.284125 | + | 0.492119i | ||||
\(369\) | 0.468165 | 0.0243717 | ||||||||
\(370\) | 0.878421 | − | 1.52147i | 0.0456669 | − | 0.0790975i | ||||
\(371\) | −15.2676 | + | 26.4442i | −0.792653 | + | 1.37292i | ||||
\(372\) | 16.1006 | 0.834775 | ||||||||
\(373\) | 5.69078 | − | 9.85672i | 0.294657 | − | 0.510362i | −0.680248 | − | 0.732982i | \(-0.738128\pi\) |
0.974905 | + | 0.222621i | \(0.0714611\pi\) | |||||||
\(374\) | 0.833727 | + | 1.44406i | 0.0431110 | + | 0.0746705i | ||||
\(375\) | −3.18502 | − | 5.51662i | −0.164474 | − | 0.284877i | ||||
\(376\) | −2.98926 | −0.154159 | ||||||||
\(377\) | 5.75774 | − | 9.51710i | 0.296539 | − | 0.490156i | ||||
\(378\) | 1.47690 | 0.0759636 | ||||||||
\(379\) | 2.40197 | + | 4.16034i | 0.123381 | + | 0.213702i | 0.921099 | − | 0.389329i | \(-0.127293\pi\) |
−0.797718 | + | 0.603031i | \(0.793960\pi\) | |||||||
\(380\) | −17.2283 | − | 29.8403i | −0.883793 | − | 1.53077i | ||||
\(381\) | −1.02449 | + | 1.77447i | −0.0524863 | + | 0.0909090i | ||||
\(382\) | −4.34389 | −0.222253 | ||||||||
\(383\) | 5.70145 | − | 9.87519i | 0.291330 | − | 0.504599i | −0.682794 | − | 0.730611i | \(-0.739235\pi\) |
0.974125 | + | 0.226012i | \(0.0725688\pi\) | |||||||
\(384\) | 4.26338 | − | 7.38438i | 0.217564 | − | 0.376833i | ||||
\(385\) | −17.0051 | −0.866660 | ||||||||
\(386\) | 2.34149 | − | 4.05557i | 0.119178 | − | 0.206423i | ||||
\(387\) | −3.77835 | − | 6.54429i | −0.192064 | − | 0.332665i | ||||
\(388\) | 8.89378 | + | 15.4045i | 0.451513 | + | 0.782044i | ||||
\(389\) | 35.5503 | 1.80247 | 0.901236 | − | 0.433329i | \(-0.142661\pi\) | ||||
0.901236 | + | 0.433329i | \(0.142661\pi\) | |||||||
\(390\) | 3.71011 | + | 0.0759974i | 0.187869 | + | 0.00384828i | ||||
\(391\) | 17.5122 | 0.885629 | ||||||||
\(392\) | −10.1730 | − | 17.6202i | −0.513816 | − | 0.889956i | ||||
\(393\) | −2.15683 | − | 3.73574i | −0.108798 | − | 0.188443i | ||||
\(394\) | 1.50828 | − | 2.61242i | 0.0759861 | − | 0.131612i | ||||
\(395\) | −7.30162 | −0.367384 | ||||||||
\(396\) | 0.955306 | − | 1.65464i | 0.0480059 | − | 0.0831487i | ||||
\(397\) | −10.8198 | + | 18.7405i | −0.543031 | + | 0.940557i | 0.455697 | + | 0.890135i | \(0.349390\pi\) |
−0.998728 | + | 0.0504221i | \(0.983943\pi\) | |||||||
\(398\) | −0.611556 | −0.0306545 | ||||||||
\(399\) | 12.9394 | − | 22.4117i | 0.647780 | − | 1.12199i | ||||
\(400\) | −11.8912 | − | 20.5962i | −0.594560 | − | 1.02981i | ||||
\(401\) | −17.0399 | − | 29.5140i | −0.850933 | − | 1.47386i | −0.880367 | − | 0.474293i | \(-0.842704\pi\) |
0.0294339 | − | 0.999567i | \(-0.490630\pi\) | |||||||
\(402\) | −0.507002 | −0.0252870 | ||||||||
\(403\) | 14.6498 | + | 26.6186i | 0.729757 | + | 1.32597i | ||||
\(404\) | 21.5566 | 1.07248 | ||||||||
\(405\) | 1.72122 | + | 2.98125i | 0.0855283 | + | 0.148139i | ||||
\(406\) | 2.27815 | + | 3.94586i | 0.113062 | + | 0.195830i | ||||
\(407\) | 0.853486 | − | 1.47828i | 0.0423057 | − | 0.0732757i | ||||
\(408\) | −6.52077 | −0.322826 | ||||||||
\(409\) | 7.23235 | − | 12.5268i | 0.357617 | − | 0.619410i | −0.629945 | − | 0.776639i | \(-0.716923\pi\) |
0.987562 | + | 0.157229i | \(0.0502561\pi\) | |||||||
\(410\) | −0.240922 | + | 0.417288i | −0.0118983 | + | 0.0206084i | ||||
\(411\) | −17.9724 | −0.886512 | ||||||||
\(412\) | 10.6010 | − | 18.3614i | 0.522272 | − | 0.904602i | ||||
\(413\) | −25.5544 | − | 44.2615i | −1.25745 | − | 2.17796i | ||||
\(414\) | 0.469391 | + | 0.813009i | 0.0230693 | + | 0.0399572i | ||||
\(415\) | 12.9887 | 0.637589 | ||||||||
\(416\) | 12.1710 | + | 0.249308i | 0.596730 | + | 0.0122233i | ||||
\(417\) | −5.25598 | −0.257387 | ||||||||
\(418\) | 0.783144 | + | 1.35645i | 0.0383048 | + | 0.0663459i | ||||
\(419\) | 8.58999 | + | 14.8783i | 0.419648 | + | 0.726852i | 0.995904 | − | 0.0904172i | \(-0.0288200\pi\) |
−0.576256 | + | 0.817270i | \(0.695487\pi\) | |||||||
\(420\) | 16.2451 | − | 28.1373i | 0.792678 | − | 1.37296i | ||||
\(421\) | 7.73984 | 0.377217 | 0.188608 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188608 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(422\) | −0.456673 | + | 0.790981i | −0.0222305 | + | 0.0385044i | ||||
\(423\) | 1.27835 | − | 2.21417i | 0.0621555 | − | 0.107656i | ||||
\(424\) | 7.22724 | 0.350986 | ||||||||
\(425\) | −19.1031 | + | 33.0875i | −0.926635 | + | 1.60498i | ||||
\(426\) | 1.02370 | + | 1.77310i | 0.0495984 | + | 0.0859069i | ||||
\(427\) | 33.5707 | + | 58.1462i | 1.62460 | + | 2.81389i | ||||
\(428\) | 34.4907 | 1.66717 | ||||||||
\(429\) | 3.60480 | + | 0.0738401i | 0.174041 | + | 0.00356503i | ||||
\(430\) | 7.77748 | 0.375063 | ||||||||
\(431\) | 0.534896 | + | 0.926468i | 0.0257651 | + | 0.0446264i | 0.878620 | − | 0.477521i | \(-0.158464\pi\) |
−0.852855 | + | 0.522147i | \(0.825131\pi\) | |||||||
\(432\) | 1.73583 | + | 3.00655i | 0.0835152 | + | 0.144653i | ||||
\(433\) | 16.2563 | − | 28.1568i | 0.781229 | − | 1.35313i | −0.149997 | − | 0.988686i | \(-0.547927\pi\) |
0.931226 | − | 0.364442i | \(-0.118740\pi\) | |||||||
\(434\) | −12.4457 | −0.597413 | ||||||||
\(435\) | −5.31004 | + | 9.19725i | −0.254597 | + | 0.440975i | ||||
\(436\) | −4.64516 | + | 8.04565i | −0.222463 | + | 0.385317i | ||||
\(437\) | 16.4497 | 0.786896 | ||||||||
\(438\) | −0.278314 | + | 0.482054i | −0.0132984 | + | 0.0230334i | ||||
\(439\) | 0.885747 | + | 1.53416i | 0.0422744 | + | 0.0732214i | 0.886388 | − | 0.462942i | \(-0.153206\pi\) |
−0.844114 | + | 0.536164i | \(0.819873\pi\) | |||||||
\(440\) | 2.01243 | + | 3.48564i | 0.0959390 | + | 0.166171i | ||||
\(441\) | 17.4019 | 0.828662 | ||||||||
\(442\) | −2.89879 | − | 5.26710i | −0.137881 | − | 0.250530i | ||||
\(443\) | 24.8844 | 1.18230 | 0.591148 | − | 0.806563i | \(-0.298675\pi\) | ||||
0.591148 | + | 0.806563i | \(0.298675\pi\) | |||||||
\(444\) | 1.63068 | + | 2.82442i | 0.0773887 | + | 0.134041i | ||||
\(445\) | −5.33808 | − | 9.24582i | −0.253049 | − | 0.438294i | ||||
\(446\) | 2.13727 | − | 3.70187i | 0.101203 | − | 0.175289i | ||||
\(447\) | −3.79479 | −0.179488 | ||||||||
\(448\) | 14.6562 | − | 25.3852i | 0.692439 | − | 1.19934i | ||||
\(449\) | 17.3470 | − | 30.0459i | 0.818655 | − | 1.41795i | −0.0880185 | − | 0.996119i | \(-0.528053\pi\) |
0.906673 | − | 0.421833i | \(-0.138613\pi\) | |||||||
\(450\) | −2.04813 | −0.0965498 | ||||||||
\(451\) | −0.234083 | + | 0.405443i | −0.0110225 | + | 0.0190916i | ||||
\(452\) | −13.8583 | − | 24.0033i | −0.651840 | − | 1.12902i | ||||
\(453\) | 3.21983 | + | 5.57691i | 0.151281 | + | 0.262026i | ||||
\(454\) | 8.13730 | 0.381902 | ||||||||
\(455\) | 61.2999 | + | 1.25566i | 2.87378 | + | 0.0588662i | ||||
\(456\) | −6.12515 | −0.286836 | ||||||||
\(457\) | 8.25684 | + | 14.3013i | 0.386239 | + | 0.668985i | 0.991940 | − | 0.126707i | \(-0.0404408\pi\) |
−0.605701 | + | 0.795692i | \(0.707107\pi\) | |||||||
\(458\) | −0.811307 | − | 1.40523i | −0.0379099 | − | 0.0656619i | ||||
\(459\) | 2.78859 | − | 4.82998i | 0.130160 | − | 0.225444i | ||||
\(460\) | 20.6522 | 0.962912 | ||||||||
\(461\) | −18.8636 | + | 32.6727i | −0.878565 | + | 1.52172i | −0.0256501 | + | 0.999671i | \(0.508166\pi\) |
−0.852915 | + | 0.522049i | \(0.825168\pi\) | |||||||
\(462\) | −0.738450 | + | 1.27903i | −0.0343558 | + | 0.0595060i | ||||
\(463\) | −2.63547 | −0.122481 | −0.0612404 | − | 0.998123i | \(-0.519506\pi\) | ||||
−0.0612404 | + | 0.998123i | \(0.519506\pi\) | |||||||
\(464\) | −5.35510 | + | 9.27531i | −0.248604 | + | 0.430596i | ||||
\(465\) | −14.5046 | − | 25.1227i | −0.672634 | − | 1.16504i | ||||
\(466\) | −3.37313 | − | 5.84243i | −0.156257 | − | 0.270646i | ||||
\(467\) | −34.6374 | −1.60283 | −0.801415 | − | 0.598109i | \(-0.795919\pi\) | ||||
−0.801415 | + | 0.598109i | \(0.795919\pi\) | |||||||
\(468\) | −3.56586 | + | 5.89409i | −0.164832 | + | 0.272455i | ||||
\(469\) | −8.37688 | −0.386809 | ||||||||
\(470\) | 1.31570 | + | 2.27886i | 0.0606886 | + | 0.105116i | ||||
\(471\) | 7.88367 | + | 13.6549i | 0.363260 | + | 0.629185i | ||||
\(472\) | −6.04836 | + | 10.4761i | −0.278398 | + | 0.482200i | ||||
\(473\) | 7.55670 | 0.347457 | ||||||||
\(474\) | −0.317075 | + | 0.549189i | −0.0145637 | + | 0.0252251i | ||||
\(475\) | −17.9441 | + | 31.0800i | −0.823330 | + | 1.42605i | ||||
\(476\) | −52.6380 | −2.41266 | ||||||||
\(477\) | −3.09071 | + | 5.35327i | −0.141514 | + | 0.245109i | ||||
\(478\) | 2.04057 | + | 3.53437i | 0.0933335 | + | 0.161658i | ||||
\(479\) | 7.85316 | + | 13.6021i | 0.358820 | + | 0.621494i | 0.987764 | − | 0.155956i | \(-0.0498459\pi\) |
−0.628944 | + | 0.777450i | \(0.716513\pi\) | |||||||
\(480\) | −11.6228 | −0.530507 | ||||||||
\(481\) | −3.18580 | + | 5.26588i | −0.145260 | + | 0.240103i | ||||
\(482\) | 2.65996 | 0.121158 | ||||||||
\(483\) | 7.75546 | + | 13.4328i | 0.352886 | + | 0.611216i | ||||
\(484\) | 0.955306 | + | 1.65464i | 0.0434230 | + | 0.0752108i | ||||
\(485\) | 16.0244 | − | 27.7550i | 0.727629 | − | 1.26029i | ||||
\(486\) | 0.298978 | 0.0135619 | ||||||||
\(487\) | 21.4208 | − | 37.1019i | 0.970669 | − | 1.68125i | 0.277123 | − | 0.960834i | \(-0.410619\pi\) |
0.693546 | − | 0.720413i | \(-0.256048\pi\) | |||||||
\(488\) | 7.94572 | − | 13.7624i | 0.359686 | − | 0.622994i | ||||
\(489\) | −3.69258 | −0.166984 | ||||||||
\(490\) | −8.95516 | + | 15.5108i | −0.404553 | + | 0.700706i | ||||
\(491\) | −0.226781 | − | 0.392796i | −0.0102345 | − | 0.0177266i | 0.860863 | − | 0.508837i | \(-0.169924\pi\) |
−0.871097 | + | 0.491110i | \(0.836591\pi\) | |||||||
\(492\) | −0.447241 | − | 0.774644i | −0.0201632 | − | 0.0349237i | ||||
\(493\) | 17.2058 | 0.774911 | ||||||||
\(494\) | −2.72291 | − | 4.94753i | −0.122510 | − | 0.222600i | ||||
\(495\) | −3.44245 | −0.154726 | ||||||||
\(496\) | −14.6277 | − | 25.3359i | −0.656803 | − | 1.13762i | ||||
\(497\) | 16.9139 | + | 29.2958i | 0.758694 | + | 1.31410i | ||||
\(498\) | 0.564036 | − | 0.976939i | 0.0252751 | − | 0.0437777i | ||||
\(499\) | 28.9465 | 1.29582 | 0.647911 | − | 0.761716i | \(-0.275643\pi\) | ||||
0.647911 | + | 0.761716i | \(0.275643\pi\) | |||||||
\(500\) | −6.08534 | + | 10.5401i | −0.272145 | + | 0.471368i | ||||
\(501\) | −3.45670 | + | 5.98718i | −0.154434 | + | 0.267487i | ||||
\(502\) | −2.06687 | −0.0922488 | ||||||||
\(503\) | 4.91649 | − | 8.51560i | 0.219215 | − | 0.379692i | −0.735353 | − | 0.677684i | \(-0.762984\pi\) |
0.954568 | + | 0.297992i | \(0.0963170\pi\) | |||||||
\(504\) | −2.88779 | − | 5.00180i | −0.128632 | − | 0.222798i | ||||
\(505\) | −19.4199 | − | 33.6362i | −0.864172 | − | 1.49679i | ||||
\(506\) | −0.938782 | −0.0417340 | ||||||||
\(507\) | −12.9891 | − | 0.532357i | −0.576866 | − | 0.0236428i | ||||
\(508\) | 3.91482 | 0.173692 | ||||||||
\(509\) | 7.27107 | + | 12.5939i | 0.322284 | + | 0.558213i | 0.980959 | − | 0.194215i | \(-0.0622159\pi\) |
−0.658675 | + | 0.752428i | \(0.728883\pi\) | |||||||
\(510\) | 2.87006 | + | 4.97109i | 0.127088 | + | 0.220124i | ||||
\(511\) | −4.59841 | + | 7.96468i | −0.203422 | + | 0.352337i | ||||
\(512\) | −19.8395 | −0.876791 | ||||||||
\(513\) | 2.61940 | − | 4.53694i | 0.115649 | − | 0.200311i | ||||
\(514\) | 1.51170 | − | 2.61835i | 0.0666784 | − | 0.115490i | ||||
\(515\) | −38.2006 | −1.68332 | ||||||||
\(516\) | −7.21896 | + | 12.5036i | −0.317797 | + | 0.550441i | ||||
\(517\) | 1.27835 | + | 2.21417i | 0.0562218 | + | 0.0973789i | ||||
\(518\) | −1.26051 | − | 2.18327i | −0.0553838 | − | 0.0959275i | ||||
\(519\) | −7.13139 | −0.313033 | ||||||||
\(520\) | −6.99703 | − | 12.7136i | −0.306840 | − | 0.557528i | ||||
\(521\) | 10.8892 | 0.477066 | 0.238533 | − | 0.971134i | \(-0.423333\pi\) | ||||
0.238533 | + | 0.971134i | \(0.423333\pi\) | |||||||
\(522\) | 0.461179 | + | 0.798786i | 0.0201853 | + | 0.0349619i | ||||
\(523\) | −7.18124 | − | 12.4383i | −0.314014 | − | 0.543888i | 0.665214 | − | 0.746653i | \(-0.268341\pi\) |
−0.979227 | + | 0.202765i | \(0.935007\pi\) | |||||||
\(524\) | −4.12087 | + | 7.13755i | −0.180021 | + | 0.311805i | ||||
\(525\) | −33.8400 | −1.47690 | ||||||||
\(526\) | −3.80682 | + | 6.59361i | −0.165985 | + | 0.287495i | ||||
\(527\) | −23.4992 | + | 40.7018i | −1.02364 | + | 1.77300i | ||||
\(528\) | −3.47166 | −0.151085 | ||||||||
\(529\) | 6.57029 | − | 11.3801i | 0.285665 | − | 0.494786i | ||||
\(530\) | −3.18101 | − | 5.50967i | −0.138174 | − | 0.239325i | ||||
\(531\) | −5.17313 | − | 8.96012i | −0.224495 | − | 0.388836i | ||||
\(532\) | −49.4444 | −2.14368 | ||||||||
\(533\) | 0.873758 | − | 1.44425i | 0.0378467 | − | 0.0625576i | ||||
\(534\) | −0.927228 | −0.0401251 | ||||||||
\(535\) | −31.0718 | − | 53.8180i | −1.34335 | − | 2.32676i | ||||
\(536\) | 0.991345 | + | 1.71706i | 0.0428196 | + | 0.0741657i | ||||
\(537\) | −12.7023 | + | 22.0010i | −0.548144 | + | 0.949412i | ||||
\(538\) | 3.05097 | 0.131536 | ||||||||
\(539\) | −8.70095 | + | 15.0705i | −0.374777 | + | 0.649132i | ||||
\(540\) | 3.28859 | − | 5.69601i | 0.141518 | − | 0.245117i | ||||
\(541\) | 1.24396 | 0.0534821 | 0.0267411 | − | 0.999642i | \(-0.491487\pi\) | ||||
0.0267411 | + | 0.999642i | \(0.491487\pi\) | |||||||
\(542\) | 2.62285 | − | 4.54290i | 0.112661 | − | 0.195134i | ||||
\(543\) | −7.52565 | − | 13.0348i | −0.322956 | − | 0.559377i | ||||
\(544\) | 9.41519 | + | 16.3076i | 0.403673 | + | 0.699182i | ||||
\(545\) | 16.7388 | 0.717013 | ||||||||
\(546\) | 2.75641 | − | 4.55613i | 0.117963 | − | 0.194984i | ||||
\(547\) | −24.0562 | −1.02857 | −0.514285 | − | 0.857620i | \(-0.671942\pi\) | ||||
−0.514285 | + | 0.857620i | \(0.671942\pi\) | |||||||
\(548\) | 17.1691 | + | 29.7378i | 0.733429 | + | 1.27034i | ||||
\(549\) | 6.79593 | + | 11.7709i | 0.290043 | + | 0.502370i | ||||
\(550\) | 1.02407 | − | 1.77373i | 0.0436663 | − | 0.0756323i | ||||
\(551\) | 16.1619 | 0.688520 | ||||||||
\(552\) | 1.83561 | − | 3.17936i | 0.0781286 | − | 0.135323i | ||||
\(553\) | −5.23883 | + | 9.07391i | −0.222778 | + | 0.385862i | ||||
\(554\) | −4.45537 | −0.189291 | ||||||||
\(555\) | 2.93808 | − | 5.08890i | 0.124715 | − | 0.216012i | ||||
\(556\) | 5.02107 | + | 8.69675i | 0.212941 | + | 0.368824i | ||||
\(557\) | −16.7249 | − | 28.9683i | −0.708655 | − | 1.22743i | −0.965356 | − | 0.260936i | \(-0.915969\pi\) |
0.256701 | − | 0.966491i | \(-0.417364\pi\) | |||||||
\(558\) | −2.51946 | −0.106657 | ||||||||
\(559\) | −27.2404 | − | 0.557988i | −1.15214 | − | 0.0236004i | ||||
\(560\) | −59.0360 | −2.49472 | ||||||||
\(561\) | 2.78859 | + | 4.82998i | 0.117734 | + | 0.203922i | ||||
\(562\) | 3.19766 | + | 5.53850i | 0.134885 | + | 0.233628i | ||||
\(563\) | 1.91284 | − | 3.31314i | 0.0806167 | − | 0.139632i | −0.822898 | − | 0.568189i | \(-0.807644\pi\) |
0.903515 | + | 0.428556i | \(0.140978\pi\) | |||||||
\(564\) | −4.88486 | −0.205690 | ||||||||
\(565\) | −24.9692 | + | 43.2480i | −1.05046 | + | 1.81946i | ||||
\(566\) | −0.401073 | + | 0.694679i | −0.0168584 | + | 0.0291995i | ||||
\(567\) | 4.93983 | 0.207453 | ||||||||
\(568\) | 4.00329 | − | 6.93390i | 0.167974 | − | 0.290940i | ||||
\(569\) | −1.11738 | − | 1.93537i | −0.0468432 | − | 0.0811347i | 0.841653 | − | 0.540019i | \(-0.181583\pi\) |
−0.888496 | + | 0.458884i | \(0.848249\pi\) | |||||||
\(570\) | 2.69593 | + | 4.66949i | 0.112920 | + | 0.195583i | ||||
\(571\) | 29.8859 | 1.25068 | 0.625342 | − | 0.780351i | \(-0.284959\pi\) | ||||
0.625342 | + | 0.780351i | \(0.284959\pi\) | |||||||
\(572\) | −3.32150 | − | 6.03517i | −0.138879 | − | 0.252343i | ||||
\(573\) | −14.5291 | −0.606963 | ||||||||
\(574\) | 0.345717 | + | 0.598799i | 0.0144299 | + | 0.0249934i | ||||
\(575\) | −10.7551 | − | 18.6284i | −0.448518 | − | 0.776857i | ||||
\(576\) | 2.96694 | − | 5.13889i | 0.123622 | − | 0.214120i | ||||
\(577\) | 25.5675 | 1.06439 | 0.532195 | − | 0.846622i | \(-0.321367\pi\) | ||||
0.532195 | + | 0.846622i | \(0.321367\pi\) | |||||||
\(578\) | 2.10853 | − | 3.65209i | 0.0877035 | − | 0.151907i | ||||
\(579\) | 7.83163 | − | 13.5648i | 0.325471 | − | 0.563733i | ||||
\(580\) | 20.2908 | 0.842531 | ||||||||
\(581\) | 9.31922 | − | 16.1414i | 0.386626 | − | 0.669656i | ||||
\(582\) | −1.39172 | − | 2.41054i | −0.0576888 | − | 0.0999199i | ||||
\(583\) | −3.09071 | − | 5.35327i | −0.128004 | − | 0.221710i | ||||
\(584\) | 2.17676 | 0.0900748 | ||||||||
\(585\) | 12.4093 | + | 0.254191i | 0.513062 | + | 0.0105095i | ||||
\(586\) | −5.61505 | −0.231955 | ||||||||
\(587\) | 15.8340 | + | 27.4253i | 0.653539 | + | 1.13196i | 0.982258 | + | 0.187535i | \(0.0600497\pi\) |
−0.328719 | + | 0.944428i | \(0.606617\pi\) | |||||||
\(588\) | −16.6241 | − | 28.7939i | −0.685568 | − | 1.18744i | ||||
\(589\) | −22.0735 | + | 38.2324i | −0.909522 | + | 1.57534i | ||||
\(590\) | 10.6485 | 0.438393 | ||||||||
\(591\) | 5.04479 | − | 8.73783i | 0.207515 | − | 0.359426i | ||||
\(592\) | 2.96301 | − | 5.13209i | 0.121779 | − | 0.210928i | ||||
\(593\) | 10.3336 | 0.424349 | 0.212175 | − | 0.977232i | \(-0.431945\pi\) | ||||
0.212175 | + | 0.977232i | \(0.431945\pi\) | |||||||
\(594\) | −0.149489 | + | 0.258923i | −0.00613361 | + | 0.0106237i | ||||
\(595\) | 47.4202 | + | 82.1343i | 1.94404 | + | 3.36718i | ||||
\(596\) | 3.62519 | + | 6.27901i | 0.148494 | + | 0.257198i | ||||
\(597\) | −2.04549 | −0.0837162 | ||||||||
\(598\) | 3.38412 | + | 0.0693198i | 0.138387 | + | 0.00283470i | ||||
\(599\) | 14.5906 | 0.596157 | 0.298079 | − | 0.954541i | \(-0.403654\pi\) | ||||
0.298079 | + | 0.954541i | \(0.403654\pi\) | |||||||
\(600\) | 4.00472 | + | 6.93638i | 0.163492 | + | 0.283177i | ||||
\(601\) | 10.1755 | + | 17.6246i | 0.415069 | + | 0.718920i | 0.995436 | − | 0.0954348i | \(-0.0304241\pi\) |
−0.580367 | + | 0.814355i | \(0.697091\pi\) | |||||||
\(602\) | 5.58025 | − | 9.66527i | 0.227434 | − | 0.393927i | ||||
\(603\) | −1.69578 | −0.0690577 | ||||||||
\(604\) | 6.15185 | − | 10.6553i | 0.250315 | − | 0.433559i | ||||
\(605\) | 1.72122 | − | 2.98125i | 0.0699777 | − | 0.121205i | ||||
\(606\) | −3.37325 | −0.137029 | ||||||||
\(607\) | 9.30102 | − | 16.1098i | 0.377517 | − | 0.653878i | −0.613183 | − | 0.789941i | \(-0.710111\pi\) |
0.990700 | + | 0.136062i | \(0.0434447\pi\) | |||||||
\(608\) | 8.84396 | + | 15.3182i | 0.358670 | + | 0.621234i | ||||
\(609\) | 7.61978 | + | 13.1978i | 0.308769 | + | 0.534803i | ||||
\(610\) | −13.9890 | −0.566397 | ||||||||
\(611\) | −4.44469 | − | 8.07601i | −0.179813 | − | 0.326720i | ||||
\(612\) | −10.6558 | −0.430736 | ||||||||
\(613\) | −11.6788 | − | 20.2282i | −0.471701 | − | 0.817010i | 0.527775 | − | 0.849384i | \(-0.323026\pi\) |
−0.999476 | + | 0.0323745i | \(0.989693\pi\) | |||||||
\(614\) | −2.09157 | − | 3.62270i | −0.0844089 | − | 0.146200i | ||||
\(615\) | −0.805817 | + | 1.39572i | −0.0324937 | + | 0.0562807i | ||||
\(616\) | 5.77558 | 0.232705 | ||||||||
\(617\) | 4.75083 | − | 8.22868i | 0.191261 | − | 0.331274i | −0.754407 | − | 0.656407i | \(-0.772076\pi\) |
0.945668 | + | 0.325132i | \(0.105409\pi\) | |||||||
\(618\) | −1.65887 | + | 2.87325i | −0.0667295 | + | 0.115579i | ||||
\(619\) | −45.3682 | −1.82350 | −0.911750 | − | 0.410745i | \(-0.865269\pi\) | ||||
−0.911750 | + | 0.410745i | \(0.865269\pi\) | |||||||
\(620\) | −27.7127 | + | 47.9997i | −1.11297 | + | 1.92772i | ||||
\(621\) | 1.56999 | + | 2.71929i | 0.0630014 | + | 0.109122i | ||||
\(622\) | 1.08512 | + | 1.87949i | 0.0435094 | + | 0.0753605i | ||||
\(623\) | −15.3200 | −0.613784 | ||||||||
\(624\) | 12.5146 | + | 0.256348i | 0.500986 | + | 0.0102621i | ||||
\(625\) | −12.3237 | −0.492947 | ||||||||
\(626\) | −0.860457 | − | 1.49036i | −0.0343908 | − | 0.0595666i | ||||
\(627\) | 2.61940 | + | 4.53694i | 0.104609 | + | 0.181188i | ||||
\(628\) | 15.0626 | − | 26.0892i | 0.601064 | − | 1.04107i | ||||
\(629\) | −9.52009 | −0.379591 | ||||||||
\(630\) | −2.54208 | + | 4.40300i | −0.101279 | + | 0.175420i | ||||
\(631\) | 7.16599 | − | 12.4119i | 0.285274 | − | 0.494109i | −0.687402 | − | 0.726277i | \(-0.741249\pi\) |
0.972676 | + | 0.232169i | \(0.0745822\pi\) | |||||||
\(632\) | 2.47991 | 0.0986456 | ||||||||
\(633\) | −1.52745 | + | 2.64562i | −0.0607106 | + | 0.105154i | ||||
\(634\) | −3.46263 | − | 5.99744i | −0.137518 | − | 0.238189i | ||||
\(635\) | −3.52676 | − | 6.10853i | −0.139955 | − | 0.242410i | ||||
\(636\) | 11.8103 | 0.468309 | ||||||||
\(637\) | 32.4780 | − | 53.6835i | 1.28682 | − | 2.12702i | ||||
\(638\) | −0.922358 | −0.0365165 | ||||||||
\(639\) | 3.42399 | + | 5.93053i | 0.135451 | + | 0.234608i | ||||
\(640\) | 14.6764 | + | 25.4203i | 0.580137 | + | 1.00483i | ||||
\(641\) | −12.4043 | + | 21.4848i | −0.489939 | + | 0.848599i | −0.999933 | − | 0.0115791i | \(-0.996314\pi\) |
0.509994 | + | 0.860178i | \(0.329648\pi\) | |||||||
\(642\) | −5.39721 | −0.213011 | ||||||||
\(643\) | −4.79370 | + | 8.30293i | −0.189045 | + | 0.327435i | −0.944932 | − | 0.327266i | \(-0.893873\pi\) |
0.755887 | + | 0.654702i | \(0.227206\pi\) | |||||||
\(644\) | 14.8177 | − | 25.6650i | 0.583898 | − | 1.01134i | ||||
\(645\) | 26.0135 | 1.02428 | ||||||||
\(646\) | 4.36774 | − | 7.56514i | 0.171846 | − | 0.297646i | ||||
\(647\) | 9.81662 | + | 17.0029i | 0.385931 | + | 0.668452i | 0.991898 | − | 0.127038i | \(-0.0405469\pi\) |
−0.605967 | + | 0.795490i | \(0.707214\pi\) | |||||||
\(648\) | −0.584594 | − | 1.01255i | −0.0229650 | − | 0.0397766i | ||||
\(649\) | 10.3463 | 0.406126 | ||||||||
\(650\) | −3.82252 | + | 6.31833i | −0.149932 | + | 0.247825i | ||||
\(651\) | −41.6275 | −1.63151 | ||||||||
\(652\) | 3.52755 | + | 6.10989i | 0.138149 | + | 0.239282i | ||||
\(653\) | −13.2856 | − | 23.0113i | −0.519906 | − | 0.900503i | −0.999732 | − | 0.0231400i | \(-0.992634\pi\) |
0.479826 | − | 0.877363i | \(-0.340700\pi\) | |||||||
\(654\) | 0.726888 | − | 1.25901i | 0.0284236 | − | 0.0492310i | ||||
\(655\) | 14.8496 | 0.580220 | ||||||||
\(656\) | −0.812656 | + | 1.40756i | −0.0317289 | + | 0.0549560i | ||||
\(657\) | −0.930884 | + | 1.61234i | −0.0363173 | + | 0.0629033i | ||||
\(658\) | 3.77599 | 0.147203 | ||||||||
\(659\) | 13.9721 | − | 24.2004i | 0.544277 | − | 0.942715i | −0.454375 | − | 0.890810i | \(-0.650137\pi\) |
0.998652 | − | 0.0519049i | \(-0.0165293\pi\) | |||||||
\(660\) | 3.28859 | + | 5.69601i | 0.128008 | + | 0.221717i | ||||
\(661\) | −0.541856 | − | 0.938522i | −0.0210758 | − | 0.0365043i | 0.855295 | − | 0.518141i | \(-0.173376\pi\) |
−0.876371 | + | 0.481637i | \(0.840042\pi\) | |||||||
\(662\) | −2.40886 | −0.0936229 | ||||||||
\(663\) | −9.69565 | − | 17.6170i | −0.376548 | − | 0.684188i | ||||
\(664\) | −4.41145 | −0.171198 | ||||||||
\(665\) | 44.5432 | + | 77.1511i | 1.72731 | + | 2.99179i | ||||
\(666\) | −0.255174 | − | 0.441973i | −0.00988777 | − | 0.0171261i | ||||
\(667\) | −4.84346 | + | 8.38912i | −0.187540 | + | 0.324828i | ||||
\(668\) | 13.2088 | 0.511065 | ||||||||
\(669\) | 7.14860 | − | 12.3817i | 0.276381 | − | 0.478706i | ||||
\(670\) | 0.872664 | − | 1.51150i | 0.0337140 | − | 0.0583943i | ||||
\(671\) | −13.5919 | −0.524708 | ||||||||
\(672\) | −8.33923 | + | 14.4440i | −0.321693 | + | 0.557188i | ||||
\(673\) | 21.5347 | + | 37.2992i | 0.830101 | + | 1.43778i | 0.897957 | + | 0.440082i | \(0.145051\pi\) |
−0.0678562 | + | 0.997695i | \(0.521616\pi\) | |||||||
\(674\) | −1.69140 | − | 2.92960i | −0.0651504 | − | 0.112844i | ||||
\(675\) | −6.85044 | −0.263674 | ||||||||
\(676\) | 11.5277 | + | 22.0008i | 0.443373 | + | 0.846185i | ||||
\(677\) | −27.2704 | −1.04808 | −0.524042 | − | 0.851692i | \(-0.675577\pi\) | ||||
−0.524042 | + | 0.851692i | \(0.675577\pi\) | |||||||
\(678\) | 2.16859 | + | 3.75610i | 0.0832841 | + | 0.144252i | ||||
\(679\) | −22.9946 | − | 39.8278i | −0.882451 | − | 1.52845i | ||||
\(680\) | 11.2237 | − | 19.4400i | 0.430409 | − | 0.745491i | ||||
\(681\) | 27.2170 | 1.04296 | ||||||||
\(682\) | 1.25973 | − | 2.18192i | 0.0482376 | − | 0.0835499i | ||||
\(683\) | −10.1262 | + | 17.5391i | −0.387468 | + | 0.671115i | −0.992108 | − | 0.125384i | \(-0.959984\pi\) |
0.604640 | + | 0.796499i | \(0.293317\pi\) | |||||||
\(684\) | −10.0093 | −0.382716 | ||||||||
\(685\) | 30.9345 | − | 53.5801i | 1.18195 | − | 2.04719i | ||||
\(686\) | 7.68129 | + | 13.3044i | 0.293273 | + | 0.507964i | ||||
\(687\) | −2.71360 | − | 4.70010i | −0.103530 | − | 0.179320i | ||||
\(688\) | 26.2343 | 1.00017 | ||||||||
\(689\) | 10.7461 | + | 19.5256i | 0.409393 | + | 0.743868i | ||||
\(690\) | −3.23171 | −0.123029 | ||||||||
\(691\) | 24.8315 | + | 43.0094i | 0.944634 | + | 1.63615i | 0.756482 | + | 0.654015i | \(0.226917\pi\) |
0.188153 | + | 0.982140i | \(0.439750\pi\) | |||||||
\(692\) | 6.81266 | + | 11.7999i | 0.258978 | + | 0.448564i | ||||
\(693\) | −2.46991 | + | 4.27802i | −0.0938243 | + | 0.162508i | ||||
\(694\) | 5.91711 | 0.224610 | ||||||||
\(695\) | 9.04672 | − | 15.6694i | 0.343162 | − | 0.594373i | ||||
\(696\) | 1.80349 | − | 3.12374i | 0.0683612 | − | 0.118405i | ||||
\(697\) | 2.61104 | 0.0989003 | ||||||||
\(698\) | 1.21108 | − | 2.09765i | 0.0458400 | − | 0.0793973i | ||||
\(699\) | −11.2822 | − | 19.5413i | −0.426732 | − | 0.739122i | ||||
\(700\) | 32.3276 | + | 55.9930i | 1.22187 | + | 2.11634i | ||||
\(701\) | −49.8338 | −1.88219 | −0.941097 | − | 0.338135i | \(-0.890204\pi\) | ||||
−0.941097 | + | 0.338135i | \(0.890204\pi\) | |||||||
\(702\) | 0.557996 | − | 0.922325i | 0.0210602 | − | 0.0348109i | ||||
\(703\) | −8.94249 | −0.337273 | ||||||||
\(704\) | 2.96694 | + | 5.13889i | 0.111821 | + | 0.193679i | ||||
\(705\) | 4.40065 | + | 7.62215i | 0.165738 | + | 0.287067i | ||||
\(706\) | −0.130581 | + | 0.226173i | −0.00491448 | + | 0.00851212i | ||||
\(707\) | −55.7340 | −2.09609 | ||||||||
\(708\) | −9.88384 | + | 17.1193i | −0.371457 | + | 0.643383i | ||||
\(709\) | −12.5828 | + | 21.7941i | −0.472558 | + | 0.818495i | −0.999507 | − | 0.0314023i | \(-0.990003\pi\) |
0.526949 | + | 0.849897i | \(0.323336\pi\) | |||||||
\(710\) | −7.04806 | −0.264509 | ||||||||
\(711\) | −1.06053 | + | 1.83689i | −0.0397729 | + | 0.0688887i | ||||
\(712\) | 1.81302 | + | 3.14023i | 0.0679456 | + | 0.117685i | ||||
\(713\) | −13.2301 | − | 22.9152i | −0.495472 | − | 0.858183i | ||||
\(714\) | 8.23694 | 0.308260 | ||||||||
\(715\) | −6.42479 | + | 10.6197i | −0.240274 | + | 0.397154i | ||||
\(716\) | 48.5382 | 1.81396 | ||||||||
\(717\) | 6.82515 | + | 11.8215i | 0.254890 | + | 0.441482i | ||||
\(718\) | 1.94814 | + | 3.37428i | 0.0727040 | + | 0.125927i | ||||
\(719\) | 6.02908 | − | 10.4427i | 0.224847 | − | 0.389446i | −0.731427 | − | 0.681920i | \(-0.761145\pi\) |
0.956273 | + | 0.292474i | \(0.0944786\pi\) | |||||||
\(720\) | −11.9510 | −0.445388 | ||||||||
\(721\) | −27.4085 | + | 47.4729i | −1.02075 | + | 1.76798i | ||||
\(722\) | 1.26245 | − | 2.18662i | 0.0469835 | − | 0.0813777i | ||||
\(723\) | 8.89683 | 0.330877 | ||||||||
\(724\) | −14.3786 | + | 24.9045i | −0.534376 | + | 0.925567i | ||||
\(725\) | −10.5669 | − | 18.3025i | −0.392446 | − | 0.679736i | ||||
\(726\) | −0.149489 | − | 0.258923i | −0.00554806 | − | 0.00960952i | ||||
\(727\) | −12.6614 | −0.469587 | −0.234793 | − | 0.972045i | \(-0.575441\pi\) | ||||
−0.234793 | + | 0.972045i | \(0.575441\pi\) | |||||||
\(728\) | −20.8198 | − | 0.426470i | −0.771633 | − | 0.0158060i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.958081 | − | 1.65945i | −0.0354602 | − | 0.0614188i | ||||
\(731\) | −21.0725 | − | 36.4987i | −0.779396 | − | 1.34995i | ||||
\(732\) | 12.9844 | − | 22.4896i | 0.479917 | − | 0.831240i | ||||
\(733\) | 5.66939 | 0.209404 | 0.104702 | − | 0.994504i | \(-0.466611\pi\) | ||||
0.104702 | + | 0.994504i | \(0.466611\pi\) | |||||||
\(734\) | −3.40002 | + | 5.88900i | −0.125497 | + | 0.217367i | ||||
\(735\) | −29.9526 | + | 51.8794i | −1.10482 | + | 1.91360i | ||||
\(736\) | −10.6016 | −0.390779 | ||||||||
\(737\) | 0.847892 | − | 1.46859i | 0.0312325 | − | 0.0540963i | ||||
\(738\) | 0.0699856 | + | 0.121219i | 0.00257620 | + | 0.00446212i | ||||
\(739\) | −21.8199 | − | 37.7933i | −0.802660 | − | 1.39025i | −0.917860 | − | 0.396905i | \(-0.870084\pi\) |
0.115200 | − | 0.993342i | \(-0.463249\pi\) | |||||||
\(740\) | −11.2271 | −0.412715 | ||||||||
\(741\) | −9.10740 | − | 16.5482i | −0.334569 | − | 0.607912i | ||||
\(742\) | −9.12934 | −0.335149 | ||||||||
\(743\) | −5.00136 | − | 8.66260i | −0.183482 | − | 0.317800i | 0.759582 | − | 0.650412i | \(-0.225404\pi\) |
−0.943064 | + | 0.332611i | \(0.892070\pi\) | |||||||
\(744\) | 4.92632 | + | 8.53263i | 0.180608 | + | 0.312821i | ||||
\(745\) | 6.53169 | − | 11.3132i | 0.239303 | − | 0.414484i | ||||
\(746\) | 3.40284 | 0.124587 | ||||||||
\(747\) | 1.88655 | − | 3.26759i | 0.0690251 | − | 0.119555i | ||||
\(748\) | 5.32791 | − | 9.22822i | 0.194808 | − | 0.337417i | ||||
\(749\) | −89.1747 | −3.25837 | ||||||||
\(750\) | 0.952251 | − | 1.64935i | 0.0347713 | − | 0.0602257i | ||||
\(751\) | 10.8252 | + | 18.7498i | 0.395017 | + | 0.684189i | 0.993103 | − | 0.117243i | \(-0.0374055\pi\) |
−0.598087 | + | 0.801431i | \(0.704072\pi\) | |||||||
\(752\) | 4.43800 | + | 7.68684i | 0.161837 | + | 0.280310i | ||||
\(753\) | −6.91310 | −0.251927 | ||||||||
\(754\) | 3.32491 | + | 0.0681071i | 0.121086 | + | 0.00248031i | ||||
\(755\) | −22.1682 | −0.806783 | ||||||||
\(756\) | −4.71905 | − | 8.17363i | −0.171630 | − | 0.297272i | ||||
\(757\) | −12.4573 | − | 21.5767i | −0.452769 | − | 0.784218i | 0.545788 | − | 0.837923i | \(-0.316230\pi\) |
−0.998557 | + | 0.0537048i | \(0.982897\pi\) | |||||||
\(758\) | −0.718137 | + | 1.24385i | −0.0260839 | + | 0.0451787i | ||||
\(759\) | −3.13997 | −0.113974 | ||||||||
\(760\) | 10.5427 | − | 18.2606i | 0.382426 | − | 0.662380i | ||||
\(761\) | 4.46193 | − | 7.72828i | 0.161745 | − | 0.280150i | −0.773750 | − | 0.633491i | \(-0.781621\pi\) |
0.935494 | + | 0.353341i | \(0.114955\pi\) | |||||||
\(762\) | −0.612602 | −0.0221922 | ||||||||
\(763\) | 12.0099 | − | 20.8018i | 0.434788 | − | 0.753075i | ||||
\(764\) | 13.8798 | + | 24.0404i | 0.502152 | + | 0.869753i | ||||
\(765\) | 9.59957 | + | 16.6269i | 0.347073 | + | 0.601149i | ||||
\(766\) | 3.40921 | 0.123180 | ||||||||
\(767\) | −37.2961 | − | 0.763969i | −1.34669 | − | 0.0275853i | ||||
\(768\) | −9.31845 | −0.336250 | ||||||||
\(769\) | 3.20555 | + | 5.55217i | 0.115595 | + | 0.200216i | 0.918017 | − | 0.396540i | \(-0.129789\pi\) |
−0.802422 | + | 0.596756i | \(0.796456\pi\) | |||||||
\(770\) | −2.54208 | − | 4.40300i | −0.0916100 | − | 0.158673i | ||||
\(771\) | 5.05624 | − | 8.75766i | 0.182096 | − | 0.315399i | ||||
\(772\) | −29.9264 | −1.07708 | ||||||||
\(773\) | −4.59372 | + | 7.95656i | −0.165225 | + | 0.286177i | −0.936735 | − | 0.350039i | \(-0.886168\pi\) |
0.771510 | + | 0.636217i | \(0.219502\pi\) | |||||||
\(774\) | 1.12964 | − | 1.95660i | 0.0406042 | − | 0.0703285i | ||||
\(775\) | 57.7280 | 2.07365 | ||||||||
\(776\) | −5.44249 | + | 9.42667i | −0.195374 | + | 0.338398i | ||||
\(777\) | −4.21607 | − | 7.30245i | −0.151251 | − | 0.261974i | ||||
\(778\) | 5.31438 | + | 9.20477i | 0.190530 | + | 0.330007i | ||||
\(779\) | 2.45263 | 0.0878745 | ||||||||
\(780\) | −11.4341 | − | 20.7758i | −0.409406 | − | 0.743892i | ||||
\(781\) | −6.84799 | −0.245040 | ||||||||
\(782\) | 2.61788 | + | 4.53430i | 0.0936152 | + | 0.162146i | ||||
\(783\) | 1.54252 | + | 2.67172i | 0.0551251 | + | 0.0954795i | ||||
\(784\) | −30.2068 | + | 52.3197i | −1.07881 | + | 1.86856i | ||||
\(785\) | −54.2782 | −1.93727 | ||||||||
\(786\) | 0.644845 | − | 1.11690i | 0.0230009 | − | 0.0398387i | ||||
\(787\) | 16.2306 | − | 28.1122i | 0.578558 | − | 1.00209i | −0.417087 | − | 0.908867i | \(-0.636949\pi\) |
0.995645 | − | 0.0932254i | \(-0.0297177\pi\) | |||||||
\(788\) | −19.2773 | −0.686724 | ||||||||
\(789\) | −12.7328 | + | 22.0538i | −0.453299 | + | 0.785137i | ||||
\(790\) | −1.09151 | − | 1.89055i | −0.0388343 | − | 0.0672629i | ||||
\(791\) | 35.8302 | + | 62.0598i | 1.27398 | + | 2.20659i | ||||
\(792\) | 1.16919 | 0.0415453 | ||||||||
\(793\) | 48.9959 | + | 1.00363i | 1.73990 | + | 0.0356398i | ||||
\(794\) | −6.46977 | −0.229604 | ||||||||
\(795\) | −10.6396 | − | 18.4283i | −0.377348 | − | 0.653586i | ||||
\(796\) | 1.95407 | + | 3.38454i | 0.0692600 | + | 0.119962i | ||||
\(797\) | −1.82915 | + | 3.16818i | −0.0647918 | + | 0.112223i | −0.896602 | − | 0.442838i | \(-0.853972\pi\) |
0.831810 | + | 0.555061i | \(0.187305\pi\) | |||||||
\(798\) | 7.73719 | 0.273894 | ||||||||
\(799\) | 7.12959 | − | 12.3488i | 0.252227 | − | 0.436869i | ||||
\(800\) | 11.5647 | − | 20.0306i | 0.408872 | − | 0.708188i | ||||
\(801\) | −3.10133 | −0.109580 | ||||||||
\(802\) | 5.09456 | − | 8.82404i | 0.179895 | − | 0.311588i | ||||
\(803\) | −0.930884 | − | 1.61234i | −0.0328502 | − | 0.0568982i | ||||
\(804\) | 1.61999 | + | 2.80591i | 0.0571328 | + | 0.0989568i | ||||
\(805\) | −53.3955 | −1.88194 | ||||||||
\(806\) | −4.70218 | + | 7.77235i | −0.165627 | + | 0.273769i | ||||
\(807\) | 10.2046 | 0.359221 | ||||||||
\(808\) | 6.59573 | + | 11.4241i | 0.232037 | + | 0.401900i | ||||
\(809\) | −4.55094 | − | 7.88246i | −0.160003 | − | 0.277132i | 0.774867 | − | 0.632125i | \(-0.217817\pi\) |
−0.934869 | + | 0.354992i | \(0.884484\pi\) | |||||||
\(810\) | −0.514608 | + | 0.891327i | −0.0180815 | + | 0.0313180i | ||||
\(811\) | 6.73229 | 0.236403 | 0.118201 | − | 0.992990i | \(-0.462287\pi\) | ||||
0.118201 | + | 0.992990i | \(0.462287\pi\) | |||||||
\(812\) | 14.5584 | − | 25.2159i | 0.510901 | − | 0.884906i | ||||
\(813\) | 8.77271 | − | 15.1948i | 0.307672 | − | 0.532904i | ||||
\(814\) | 0.510347 | 0.0178877 | ||||||||
\(815\) | 6.35576 | − | 11.0085i | 0.222632 | − | 0.385611i | ||||
\(816\) | 9.68105 | + | 16.7681i | 0.338904 | + | 0.587000i | ||||
\(817\) | −19.7940 | − | 34.2843i | −0.692506 | − | 1.19946i | ||||
\(818\) | 4.32463 | 0.151207 | ||||||||
\(819\) | 9.21942 | − | 15.2390i | 0.322153 | − | 0.532494i | ||||
\(820\) | 3.07921 | 0.107531 | ||||||||
\(821\) | 8.79034 | + | 15.2253i | 0.306785 | + | 0.531367i | 0.977657 | − | 0.210206i | \(-0.0674134\pi\) |
−0.670872 | + | 0.741573i | \(0.734080\pi\) | |||||||
\(822\) | −2.68667 | − | 4.65346i | −0.0937085 | − | 0.162308i | ||||
\(823\) | −12.1191 | + | 20.9908i | −0.422444 | + | 0.731695i | −0.996178 | − | 0.0873469i | \(-0.972161\pi\) |
0.573734 | + | 0.819042i | \(0.305494\pi\) | |||||||
\(824\) | 12.9744 | 0.451984 | ||||||||
\(825\) | 3.42522 | − | 5.93266i | 0.119251 | − | 0.206549i | ||||
\(826\) | 7.64019 | − | 13.2332i | 0.265836 | − | 0.460442i | ||||
\(827\) | −8.63617 | −0.300309 | −0.150154 | − | 0.988663i | \(-0.547977\pi\) | ||||
−0.150154 | + | 0.988663i | \(0.547977\pi\) | |||||||
\(828\) | 2.99963 | − | 5.19552i | 0.104244 | − | 0.180557i | ||||
\(829\) | −4.78638 | − | 8.29025i | −0.166238 | − | 0.287932i | 0.770856 | − | 0.637009i | \(-0.219829\pi\) |
−0.937094 | + | 0.349077i | \(0.886495\pi\) | |||||||
\(830\) | 1.94166 | + | 3.36306i | 0.0673961 | + | 0.116734i | ||||
\(831\) | −14.9020 | −0.516945 | ||||||||
\(832\) | −10.3158 | − | 18.7437i | −0.357634 | − | 0.649822i | ||||
\(833\) | 97.0536 | 3.36271 | ||||||||
\(834\) | −0.785712 | − | 1.36089i | −0.0272070 | − | 0.0471239i | ||||
\(835\) | −11.8995 | − | 20.6105i | −0.411799 | − | 0.713257i | ||||
\(836\) | 5.00466 | − | 8.66833i | 0.173090 | − | 0.299801i | ||||
\(837\) | −8.42691 | −0.291277 | ||||||||
\(838\) | −2.56822 | + | 4.44828i | −0.0887176 | + | 0.153663i | ||||
\(839\) | 18.9960 | − | 32.9020i | 0.655814 | − | 1.13590i | −0.325875 | − | 0.945413i | \(-0.605659\pi\) |
0.981689 | − | 0.190490i | \(-0.0610077\pi\) | |||||||
\(840\) | 19.8821 | 0.685999 | ||||||||
\(841\) | 9.74127 | − | 16.8724i | 0.335906 | − | 0.581806i | ||||
\(842\) | 1.15702 | + | 2.00402i | 0.0398736 | + | 0.0690631i | ||||
\(843\) | 10.6953 | + | 18.5248i | 0.368365 | + | 0.638027i | ||||
\(844\) | 5.83672 | 0.200908 | ||||||||
\(845\) | 23.9442 | − | 37.8074i | 0.823706 | − | 1.30061i | ||||
\(846\) | 0.764397 | 0.0262805 | ||||||||
\(847\) | −2.46991 | − | 4.27802i | −0.0848673 | − | 0.146994i | ||||
\(848\) | −10.7299 | − | 18.5847i | −0.368466 | − | 0.638202i | ||||
\(849\) | −1.34148 | + | 2.32351i | −0.0460395 | + | 0.0797427i | ||||
\(850\) | −11.4228 | −0.391799 | ||||||||
\(851\) | 2.67992 | − | 4.64176i | 0.0918665 | − | 0.159117i | ||||
\(852\) | 6.54192 | − | 11.3309i | 0.224123 | − | 0.388192i | ||||
\(853\) | 2.75690 | 0.0943945 | 0.0471972 | − | 0.998886i | \(-0.484971\pi\) | ||||
0.0471972 | + | 0.998886i | \(0.484971\pi\) | |||||||
\(854\) | −10.0369 | + | 17.3844i | −0.343456 | + | 0.594883i | ||||
\(855\) | 9.01716 | + | 15.6182i | 0.308380 | + | 0.534130i | ||||
\(856\) | 10.5532 | + | 18.2787i | 0.360701 | + | 0.624752i | ||||
\(857\) | 31.7546 | 1.08472 | 0.542359 | − | 0.840147i | \(-0.317531\pi\) | ||||
0.542359 | + | 0.840147i | \(0.317531\pi\) | |||||||
\(858\) | 0.519758 | + | 0.944401i | 0.0177443 | + | 0.0322413i | ||||
\(859\) | 37.6069 | 1.28313 | 0.641566 | − | 0.767068i | \(-0.278285\pi\) | ||||
0.641566 | + | 0.767068i | \(0.278285\pi\) | |||||||
\(860\) | −24.8509 | − | 43.0430i | −0.847408 | − | 1.46775i | ||||
\(861\) | 1.15633 | + | 2.00282i | 0.0394076 | + | 0.0682559i | ||||
\(862\) | −0.159922 | + | 0.276994i | −0.00544697 | + | 0.00943444i | ||||
\(863\) | 33.6440 | 1.14525 | 0.572627 | − | 0.819816i | \(-0.305924\pi\) | ||||
0.572627 | + | 0.819816i | \(0.305924\pi\) | |||||||
\(864\) | −1.68816 | + | 2.92398i | −0.0574325 | + | 0.0994759i | ||||
\(865\) | 12.2747 | − | 21.2604i | 0.417353 | − | 0.722876i | ||||
\(866\) | 9.72056 | 0.330318 | ||||||||
\(867\) | 7.05247 | − | 12.2152i | 0.239515 | − | 0.414851i | ||||
\(868\) | 39.7670 | + | 68.8784i | 1.34978 | + | 2.33789i | ||||
\(869\) | −1.06053 | − | 1.83689i | −0.0359759 | − | 0.0623122i | ||||
\(870\) | −3.17517 | −0.107648 | ||||||||
\(871\) | −3.16492 | + | 5.23137i | −0.107239 | + | 0.177258i | ||||
\(872\) | −5.68515 | −0.192523 | ||||||||
\(873\) | −4.65494 | − | 8.06258i | −0.157546 | − | 0.272877i | ||||
\(874\) | 2.45905 | + | 4.25920i | 0.0831786 | + | 0.144070i | ||||
\(875\) | 15.7335 | − | 27.2511i | 0.531888 | − | 0.921257i | ||||
\(876\) | 3.55712 | 0.120184 | ||||||||
\(877\) | 19.5396 | − | 33.8435i | 0.659804 | − | 1.14281i | −0.320862 | − | 0.947126i | \(-0.603972\pi\) |
0.980666 | − | 0.195689i | \(-0.0626942\pi\) | |||||||
\(878\) | −0.264819 | + | 0.458680i | −0.00893721 | + | 0.0154797i | ||||
\(879\) | −18.7808 | −0.633461 | ||||||||
\(880\) | 5.97551 | − | 10.3499i | 0.201434 | − | 0.348894i | ||||
\(881\) | −3.92975 | − | 6.80652i | −0.132396 | − | 0.229317i | 0.792203 | − | 0.610257i | \(-0.208934\pi\) |
−0.924600 | + | 0.380940i | \(0.875601\pi\) | |||||||
\(882\) | 2.60139 | + | 4.50575i | 0.0875935 | + | 0.151716i | ||||
\(883\) | 6.36927 | 0.214343 | 0.107171 | − | 0.994241i | \(-0.465821\pi\) | ||||
0.107171 | + | 0.994241i | \(0.465821\pi\) | |||||||
\(884\) | −19.8875 | + | 32.8724i | −0.668887 | + | 1.10562i | ||||
\(885\) | 35.6164 | 1.19723 | ||||||||
\(886\) | 3.71995 | + | 6.44314i | 0.124974 | + | 0.216462i | ||||
\(887\) | 1.37929 | + | 2.38900i | 0.0463120 | + | 0.0802148i | 0.888252 | − | 0.459356i | \(-0.151920\pi\) |
−0.841940 | + | 0.539571i | \(0.818586\pi\) | |||||||
\(888\) | −0.997885 | + | 1.72839i | −0.0334868 | + | 0.0580009i | ||||
\(889\) | −10.1216 | −0.339469 | ||||||||
\(890\) | 1.59597 | − | 2.76430i | 0.0534969 | − | 0.0926594i | ||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | −27.3164 | −0.914621 | ||||||||
\(893\) | 6.69703 | − | 11.5996i | 0.224107 | − | 0.388166i | ||||
\(894\) | −0.567280 | − | 0.982558i | −0.0189727 | − | 0.0328616i | ||||
\(895\) | −43.7269 | − | 75.7372i | −1.46163 | − | 2.53162i | ||||
\(896\) | 42.1207 | 1.40715 | ||||||||
\(897\) | 11.3190 | + | 0.231856i | 0.377929 | + | 0.00774144i | ||||
\(898\) | 10.3727 | 0.346143 | ||||||||
\(899\) | −12.9987 | − | 22.5143i | −0.433530 | − | 0.750895i | ||||
\(900\) | 6.54427 | + | 11.3350i | 0.218142 | + | 0.377833i | ||||
\(901\) | −17.2374 | + | 29.8561i | −0.574263 | + | 0.994652i | ||||
\(902\) | −0.139971 | −0.00466053 | ||||||||
\(903\) | 18.6644 | − | 32.3277i | 0.621112 | − | 1.07580i | ||||
\(904\) | 8.48051 | − | 14.6887i | 0.282057 | − | 0.488538i | ||||
\(905\) | 51.8133 | 1.72233 | ||||||||
\(906\) | −0.962659 | + | 1.66737i | −0.0319822 | + | 0.0553948i | ||||
\(907\) | −23.5142 | − | 40.7278i | −0.780777 | − | 1.35235i | −0.931490 | − | 0.363768i | \(-0.881490\pi\) |
0.150713 | − | 0.988578i | \(-0.451843\pi\) | |||||||
\(908\) | −26.0006 | − | 45.0344i | −0.862860 | − | 1.49452i | ||||
\(909\) | −11.2826 | −0.374220 | ||||||||
\(910\) | 8.83854 | + | 16.0596i | 0.292995 | + | 0.532372i | ||||
\(911\) | −21.5111 | −0.712693 | −0.356346 | − | 0.934354i | \(-0.615978\pi\) | ||||
−0.356346 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(912\) | 9.09368 | + | 15.7507i | 0.301122 | + | 0.521559i | ||||
\(913\) | 1.88655 | + | 3.26759i | 0.0624356 | + | 0.108142i | ||||
\(914\) | −2.46861 | + | 4.27577i | −0.0816545 | + | 0.141430i | ||||
\(915\) | −46.7893 | −1.54681 | ||||||||
\(916\) | −5.18464 | + | 8.98006i | −0.171305 | + | 0.296710i | ||||
\(917\) | 10.6544 | − | 18.4539i | 0.351838 | − | 0.609402i | ||||
\(918\) | 1.66745 | 0.0550342 | ||||||||
\(919\) | −10.2867 | + | 17.8171i | −0.339328 | + | 0.587733i | −0.984306 | − | 0.176467i | \(-0.943533\pi\) |
0.644979 | + | 0.764201i | \(0.276866\pi\) | |||||||
\(920\) | 6.31898 | + | 10.9448i | 0.208331 | + | 0.360839i | ||||
\(921\) | −6.99573 | − | 12.1170i | −0.230517 | − | 0.399267i | ||||
\(922\) | −11.2796 | −0.371474 | ||||||||
\(923\) | 24.6856 | + | 0.505656i | 0.812536 | + | 0.0166439i | ||||
\(924\) | 9.43810 | 0.310491 | ||||||||
\(925\) | 5.84675 | + | 10.1269i | 0.192240 | + | 0.332970i | ||||
\(926\) | −0.393974 | − | 0.682383i | −0.0129468 | − | 0.0224245i | ||||
\(927\) | −5.54847 | + | 9.61023i | −0.182236 | + | 0.315641i | ||||
\(928\) | −10.4161 | −0.341925 | ||||||||
\(929\) | −8.79355 | + | 15.2309i | −0.288507 | + | 0.499709i | −0.973454 | − | 0.228885i | \(-0.926492\pi\) |
0.684947 | + | 0.728593i | \(0.259825\pi\) | |||||||
\(930\) | 4.33655 | − | 7.51113i | 0.142201 | − | 0.246300i | ||||
\(931\) | 91.1652 | 2.98782 | ||||||||
\(932\) | −21.5559 | + | 37.3359i | −0.706087 | + | 1.22298i | ||||
\(933\) | 3.62943 | + | 6.28637i | 0.118822 | + | 0.205806i | ||||
\(934\) | −5.17792 | − | 8.96842i | −0.169427 | − | 0.293456i | ||||
\(935\) | −19.1991 | −0.627879 | ||||||||
\(936\) | −4.21468 | − | 0.0863329i | −0.137761 | − | 0.00282188i | ||||
\(937\) | −26.7279 | −0.873161 | −0.436580 | − | 0.899665i | \(-0.643811\pi\) | ||||
−0.436580 | + | 0.899665i | \(0.643811\pi\) | |||||||
\(938\) | −1.25225 | − | 2.16896i | −0.0408875 | − | 0.0708192i | ||||
\(939\) | −2.87799 | − | 4.98483i | −0.0939198 | − | 0.162674i | ||||
\(940\) | 8.40794 | − | 14.5630i | 0.274237 | − | 0.474992i | ||||
\(941\) | −48.0352 | −1.56590 | −0.782952 | − | 0.622082i | \(-0.786287\pi\) | ||||
−0.782952 | + | 0.622082i | \(0.786287\pi\) | |||||||
\(942\) | −2.35704 | + | 4.08252i | −0.0767966 | + | 0.133016i | ||||
\(943\) | −0.735013 | + | 1.27308i | −0.0239353 | + | 0.0414572i | ||||
\(944\) | 35.9187 | 1.16905 | ||||||||
\(945\) | −8.50255 | + | 14.7268i | −0.276588 | + | 0.479064i | ||||
\(946\) | 1.12964 | + | 1.95660i | 0.0367279 | + | 0.0636146i | ||||
\(947\) | 26.8330 | + | 46.4761i | 0.871955 | + | 1.51027i | 0.859971 | + | 0.510343i | \(0.170481\pi\) |
0.0119844 | + | 0.999928i | \(0.496185\pi\) | |||||||
\(948\) | 4.05252 | 0.131620 | ||||||||
\(949\) | 3.23659 | + | 5.88089i | 0.105064 | + | 0.190902i | ||||
\(950\) | −10.7298 | −0.348119 | ||||||||
\(951\) | −11.5815 | − | 20.0598i | −0.375557 | − | 0.650484i | ||||
\(952\) | −16.1057 | − | 27.8960i | −0.521990 | − | 0.904113i | ||||
\(953\) | 3.11176 | − | 5.38974i | 0.100800 | − | 0.174591i | −0.811215 | − | 0.584749i | \(-0.801193\pi\) |
0.912014 | + | 0.410158i | \(0.134526\pi\) | |||||||
\(954\) | −1.84811 | −0.0598347 | ||||||||
\(955\) | 25.0079 | − | 43.3149i | 0.809235 | − | 1.40164i | ||||
\(956\) | 13.0402 | − | 22.5863i | 0.421751 | − | 0.730493i | ||||
\(957\) | −3.08504 | −0.0997251 | ||||||||
\(958\) | −2.34792 | + | 4.06672i | −0.0758579 | + | 0.131390i | ||||
\(959\) | −44.3902 | − | 76.8862i | −1.43344 | − | 2.48278i | ||||
\(960\) | 10.2135 | + | 17.6904i | 0.329640 | + | 0.570954i | ||||
\(961\) | 40.0128 | 1.29074 | ||||||||
\(962\) | −1.83970 | − | 0.0376841i | −0.0593142 | − | 0.00121498i | ||||
\(963\) | −18.0522 | −0.581723 | ||||||||
\(964\) | −8.49920 | − | 14.7210i | −0.273741 | − | 0.474133i | ||||
\(965\) | 26.9600 | + | 46.6960i | 0.867872 | + | 1.50320i | ||||
\(966\) | −2.31871 | + | 4.01613i | −0.0746033 | + | 0.129217i | ||||
\(967\) | 22.8853 | 0.735943 | 0.367971 | − | 0.929837i | \(-0.380052\pi\) | ||||
0.367971 | + | 0.929837i | \(0.380052\pi\) | |||||||
\(968\) | −0.584594 | + | 1.01255i | −0.0187896 | + | 0.0325445i | ||||
\(969\) | 14.6089 | − | 25.3033i | 0.469305 | − | 0.812860i | ||||
\(970\) | 9.58187 | 0.307655 | ||||||||
\(971\) | −12.8177 | + | 22.2009i | −0.411339 | + | 0.712460i | −0.995036 | − | 0.0995114i | \(-0.968272\pi\) |
0.583698 | + | 0.811971i | \(0.301605\pi\) | |||||||
\(972\) | −0.955306 | − | 1.65464i | −0.0306415 | − | 0.0530726i | ||||
\(973\) | −12.9818 | − | 22.4852i | −0.416178 | − | 0.720842i | ||||
\(974\) | 12.8087 | 0.410417 | ||||||||
\(975\) | −12.7853 | + | 21.1331i | −0.409457 | + | 0.676800i | ||||
\(976\) | −47.1864 | −1.51040 | ||||||||
\(977\) | −1.64436 | − | 2.84811i | −0.0526077 | − | 0.0911192i | 0.838522 | − | 0.544867i | \(-0.183420\pi\) |
−0.891130 | + | 0.453748i | \(0.850087\pi\) | |||||||
\(978\) | −0.552000 | − | 0.956093i | −0.0176510 | − | 0.0305725i | ||||
\(979\) | 1.55066 | − | 2.68583i | 0.0495594 | − | 0.0858394i | ||||
\(980\) | 114.455 | 3.65615 | ||||||||
\(981\) | 2.43124 | − | 4.21103i | 0.0776235 | − | 0.134448i | ||||
\(982\) | 0.0678026 | − | 0.117437i | 0.00216367 | − | 0.00374758i | ||||
\(983\) | −35.2780 | −1.12519 | −0.562596 | − | 0.826732i | \(-0.690197\pi\) | ||||
−0.562596 | + | 0.826732i | \(0.690197\pi\) | |||||||
\(984\) | 0.273686 | − | 0.474039i | 0.00872480 | − | 0.0151118i | ||||
\(985\) | 17.3664 | + | 30.0795i | 0.553340 | + | 0.958413i | ||||
\(986\) | 2.57208 | + | 4.45497i | 0.0819117 | + | 0.141875i | ||||
\(987\) | 12.6297 | 0.402006 | ||||||||
\(988\) | −18.6809 | + | 30.8780i | −0.594317 | + | 0.982360i | ||||
\(989\) | 23.7278 | 0.754501 | ||||||||
\(990\) | −0.514608 | − | 0.891327i | −0.0163553 | − | 0.0283282i | ||||
\(991\) | −12.2850 | − | 21.2782i | −0.390245 | − | 0.675925i | 0.602236 | − | 0.798318i | \(-0.294277\pi\) |
−0.992482 | + | 0.122393i | \(0.960943\pi\) | |||||||
\(992\) | 14.2260 | − | 24.6401i | 0.451676 | − | 0.782325i | ||||
\(993\) | −8.05697 | −0.255680 | ||||||||
\(994\) | −5.05690 | + | 8.75880i | −0.160395 | + | 0.277812i | ||||
\(995\) | 3.52074 | − | 6.09810i | 0.111615 | − | 0.193323i | ||||
\(996\) | −7.20892 | −0.228423 | ||||||||
\(997\) | −21.7925 | + | 37.7457i | −0.690175 | + | 1.19542i | 0.281605 | + | 0.959530i | \(0.409133\pi\) |
−0.971780 | + | 0.235888i | \(0.924200\pi\) | |||||||
\(998\) | 4.32718 | + | 7.49490i | 0.136975 | + | 0.237247i | ||||
\(999\) | −0.853486 | − | 1.47828i | −0.0270031 | − | 0.0467707i |
(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 | 429.2.i.d.133.3 | yes | 10 | |
13.3 | even | 3 | 5577.2.a.r.1.3 | 5 | |||
13.9 | even | 3 | inner | 429.2.i.d.100.3 | ✓ | 10 | |
13.10 | even | 6 | 5577.2.a.s.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.d.100.3 | ✓ | 10 | 13.9 | even | 3 | inner | |
429.2.i.d.133.3 | yes | 10 | 1.1 | even | 1 | trivial | |
5577.2.a.r.1.3 | 5 | 13.3 | even | 3 | |||
5577.2.a.s.1.3 | 5 | 13.10 | even | 6 |