Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(201,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.4 | ||
Root | \(-0.664633 + 1.15118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.201 |
Dual form | 950.2.e.o.501.4 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.664633 | − | 1.15118i | 0.383726 | − | 0.664633i | −0.607866 | − | 0.794040i | \(-0.707974\pi\) |
0.991592 | + | 0.129407i | \(0.0413074\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.664633 | − | 1.15118i | −0.271335 | − | 0.469966i | ||||
\(7\) | 2.32927 | 0.880379 | 0.440190 | − | 0.897905i | \(-0.354911\pi\) | ||||
0.440190 | + | 0.897905i | \(0.354911\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.616527 | + | 1.06786i | 0.205509 | + | 0.355952i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.39380 | 1.92780 | 0.963901 | − | 0.266260i | \(-0.0857880\pi\) | ||||
0.963901 | + | 0.266260i | \(0.0857880\pi\) | |||||||
\(12\) | −1.32927 | −0.383726 | ||||||||
\(13\) | 0.429320 | + | 0.743604i | 0.119072 | + | 0.206239i | 0.919400 | − | 0.393324i | \(-0.128675\pi\) |
−0.800328 | + | 0.599562i | \(0.795341\pi\) | |||||||
\(14\) | 1.16463 | − | 2.01720i | 0.311261 | − | 0.539120i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.34506 | + | 4.06176i | −0.568760 | + | 0.985122i | 0.427929 | + | 0.903813i | \(0.359243\pi\) |
−0.996689 | + | 0.0813093i | \(0.974090\pi\) | |||||||
\(18\) | 1.23305 | 0.290634 | ||||||||
\(19\) | 3.75178 | − | 2.21903i | 0.860718 | − | 0.509081i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.54811 | − | 2.68140i | 0.337824 | − | 0.585129i | ||||
\(22\) | 3.19690 | − | 5.53719i | 0.681581 | − | 1.18053i | ||||
\(23\) | −1.73531 | − | 3.00565i | −0.361838 | − | 0.626721i | 0.626426 | − | 0.779481i | \(-0.284517\pi\) |
−0.988263 | + | 0.152760i | \(0.951184\pi\) | |||||||
\(24\) | −0.664633 | + | 1.15118i | −0.135668 | + | 0.234983i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.858640 | 0.168393 | ||||||||
\(27\) | 5.62685 | 1.08289 | ||||||||
\(28\) | −1.16463 | − | 2.01720i | −0.220095 | − | 0.381216i | ||||
\(29\) | 2.21048 | + | 3.82866i | 0.410476 | + | 0.710965i | 0.994942 | − | 0.100453i | \(-0.0320293\pi\) |
−0.584466 | + | 0.811418i | \(0.698696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.25244 | −1.48218 | −0.741091 | − | 0.671405i | \(-0.765691\pi\) | ||||
−0.741091 | + | 0.671405i | \(0.765691\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 4.24953 | − | 7.36040i | 0.739748 | − | 1.28128i | ||||
\(34\) | 2.34506 | + | 4.06176i | 0.402174 | + | 0.696586i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.616527 | − | 1.06786i | 0.102754 | − | 0.177976i | ||||
\(37\) | −9.76821 | −1.60588 | −0.802942 | − | 0.596057i | \(-0.796733\pi\) | ||||
−0.802942 | + | 0.596057i | \(0.796733\pi\) | |||||||
\(38\) | −0.0458469 | − | 4.35866i | −0.00743735 | − | 0.707068i | ||||
\(39\) | 1.14136 | 0.182764 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.84506 | + | 3.19574i | −0.288150 | + | 0.499090i | −0.973368 | − | 0.229248i | \(-0.926373\pi\) |
0.685218 | + | 0.728338i | \(0.259707\pi\) | |||||||
\(42\) | −1.54811 | − | 2.68140i | −0.238878 | − | 0.413749i | ||||
\(43\) | 3.56232 | − | 6.17012i | 0.543249 | − | 0.940934i | −0.455466 | − | 0.890253i | \(-0.650527\pi\) |
0.998715 | − | 0.0506811i | \(-0.0161392\pi\) | |||||||
\(44\) | −3.19690 | − | 5.53719i | −0.481951 | − | 0.834763i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.47063 | −0.511716 | ||||||||
\(47\) | −3.59684 | − | 6.22992i | −0.524654 | − | 0.908727i | −0.999588 | − | 0.0287055i | \(-0.990862\pi\) |
0.474934 | − | 0.880021i | \(-0.342472\pi\) | |||||||
\(48\) | 0.664633 | + | 1.15118i | 0.0959315 | + | 0.166158i | ||||
\(49\) | −1.57452 | −0.224932 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.11721 | + | 5.39916i | 0.436496 | + | 0.756033i | ||||
\(52\) | 0.429320 | − | 0.743604i | 0.0595360 | − | 0.103119i | ||||
\(53\) | −3.10295 | − | 5.37446i | −0.426222 | − | 0.738239i | 0.570311 | − | 0.821429i | \(-0.306823\pi\) |
−0.996534 | + | 0.0831897i | \(0.973489\pi\) | |||||||
\(54\) | 2.81343 | − | 4.87300i | 0.382859 | − | 0.663131i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.32927 | −0.311261 | ||||||||
\(57\) | −0.0609427 | − | 5.79381i | −0.00807206 | − | 0.767409i | ||||
\(58\) | 4.42096 | 0.580500 | ||||||||
\(59\) | 3.09395 | − | 5.35888i | 0.402798 | − | 0.697667i | −0.591264 | − | 0.806478i | \(-0.701371\pi\) |
0.994062 | + | 0.108811i | \(0.0347043\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.01037 | + | 6.94616i | 0.513475 | + | 0.889365i | 0.999878 | + | 0.0156304i | \(0.00497553\pi\) |
−0.486403 | + | 0.873735i | \(0.661691\pi\) | |||||||
\(62\) | −4.12622 | + | 7.14682i | −0.524030 | + | 0.907647i | ||||
\(63\) | 1.43605 | + | 2.48732i | 0.180926 | + | 0.313373i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.24953 | − | 7.36040i | −0.523081 | − | 0.906002i | ||||
\(67\) | −2.45257 | − | 4.24798i | −0.299629 | − | 0.518973i | 0.676422 | − | 0.736515i | \(-0.263530\pi\) |
−0.976051 | + | 0.217541i | \(0.930196\pi\) | |||||||
\(68\) | 4.69012 | 0.568760 | ||||||||
\(69\) | −4.61338 | −0.555386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.10005 | + | 1.90535i | −0.130552 | + | 0.226124i | −0.923890 | − | 0.382659i | \(-0.875008\pi\) |
0.793337 | + | 0.608782i | \(0.208342\pi\) | |||||||
\(72\) | −0.616527 | − | 1.06786i | −0.0726584 | − | 0.125848i | ||||
\(73\) | −2.32859 | + | 4.03323i | −0.272540 | + | 0.472054i | −0.969512 | − | 0.245045i | \(-0.921197\pi\) |
0.696971 | + | 0.717099i | \(0.254531\pi\) | |||||||
\(74\) | −4.88411 | + | 8.45952i | −0.567766 | + | 0.983399i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.79763 | − | 2.13962i | −0.435618 | − | 0.245432i | ||||
\(77\) | 14.8928 | 1.69720 | ||||||||
\(78\) | 0.570680 | − | 0.988447i | 0.0646168 | − | 0.111920i | ||||
\(79\) | −5.79153 | + | 10.0312i | −0.651598 | + | 1.12860i | 0.331137 | + | 0.943583i | \(0.392568\pi\) |
−0.982735 | + | 0.185018i | \(0.940766\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.89021 | − | 3.27394i | 0.210023 | − | 0.363771i | ||||
\(82\) | 1.84506 | + | 3.19574i | 0.203753 | + | 0.352910i | ||||
\(83\) | −6.07809 | −0.667157 | −0.333579 | − | 0.942722i | \(-0.608256\pi\) | ||||
−0.333579 | + | 0.942722i | \(0.608256\pi\) | |||||||
\(84\) | −3.09621 | −0.337824 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.56232 | − | 6.17012i | −0.384135 | − | 0.665341i | ||||
\(87\) | 5.87663 | 0.630041 | ||||||||
\(88\) | −6.39380 | −0.681581 | ||||||||
\(89\) | −5.64947 | − | 9.78517i | −0.598843 | − | 1.03723i | −0.992992 | − | 0.118180i | \(-0.962294\pi\) |
0.394149 | − | 0.919046i | \(-0.371039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | + | 1.73205i | 0.104828 | + | 0.181568i | ||||
\(92\) | −1.73531 | + | 3.00565i | −0.180919 | + | 0.313361i | ||||
\(93\) | −5.48484 | + | 9.50002i | −0.568751 | + | 0.985106i | ||||
\(94\) | −7.19369 | −0.741972 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.32927 | 0.135668 | ||||||||
\(97\) | −5.67500 | + | 9.82939i | −0.576209 | + | 0.998024i | 0.419700 | + | 0.907663i | \(0.362135\pi\) |
−0.995909 | + | 0.0903607i | \(0.971198\pi\) | |||||||
\(98\) | −0.787262 | + | 1.36358i | −0.0795254 | + | 0.137742i | ||||
\(99\) | 3.94195 | + | 6.82766i | 0.396181 | + | 0.686205i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.11042 | − | 1.92331i | −0.110491 | − | 0.191377i | 0.805477 | − | 0.592627i | \(-0.201909\pi\) |
−0.915968 | + | 0.401250i | \(0.868576\pi\) | |||||||
\(102\) | 6.23441 | 0.617299 | ||||||||
\(103\) | 3.26464 | 0.321675 | 0.160837 | − | 0.986981i | \(-0.448581\pi\) | ||||
0.160837 | + | 0.986981i | \(0.448581\pi\) | |||||||
\(104\) | −0.429320 | − | 0.743604i | −0.0420983 | − | 0.0729164i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.20589 | −0.602770 | ||||||||
\(107\) | 10.0000 | 0.966736 | 0.483368 | − | 0.875417i | \(-0.339413\pi\) | ||||
0.483368 | + | 0.875417i | \(0.339413\pi\) | |||||||
\(108\) | −2.81343 | − | 4.87300i | −0.270722 | − | 0.468904i | ||||
\(109\) | 1.51717 | − | 2.62782i | 0.145319 | − | 0.251699i | −0.784173 | − | 0.620542i | \(-0.786913\pi\) |
0.929492 | + | 0.368843i | \(0.120246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.49227 | + | 11.2449i | −0.616219 | + | 1.06732i | ||||
\(112\) | −1.16463 | + | 2.01720i | −0.110047 | + | 0.190608i | ||||
\(113\) | 4.97420 | 0.467933 | 0.233966 | − | 0.972245i | \(-0.424829\pi\) | ||||
0.233966 | + | 0.972245i | \(0.424829\pi\) | |||||||
\(114\) | −5.04806 | − | 2.84413i | −0.472794 | − | 0.266377i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.21048 | − | 3.82866i | 0.205238 | − | 0.355482i | ||||
\(117\) | −0.529375 | + | 0.916904i | −0.0489407 | + | 0.0847678i | ||||
\(118\) | −3.09395 | − | 5.35888i | −0.284821 | − | 0.493325i | ||||
\(119\) | −5.46226 | + | 9.46092i | −0.500725 | + | 0.867281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.8806 | 2.71642 | ||||||||
\(122\) | 8.02074 | 0.726164 | ||||||||
\(123\) | 2.45257 | + | 4.24798i | 0.221141 | + | 0.383028i | ||||
\(124\) | 4.12622 | + | 7.14682i | 0.370545 | + | 0.641803i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.87211 | 0.255868 | ||||||||
\(127\) | −7.14949 | − | 12.3833i | −0.634415 | − | 1.09884i | −0.986639 | − | 0.162923i | \(-0.947908\pi\) |
0.352224 | − | 0.935916i | \(-0.385426\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.73527 | − | 8.20172i | −0.416917 | − | 0.722121i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.18947 | + | 2.06022i | −0.103924 | + | 0.180002i | −0.913298 | − | 0.407292i | \(-0.866473\pi\) |
0.809374 | + | 0.587294i | \(0.199807\pi\) | |||||||
\(132\) | −8.49905 | −0.739748 | ||||||||
\(133\) | 8.73890 | − | 5.16872i | 0.757759 | − | 0.448185i | ||||
\(134\) | −4.90515 | −0.423740 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.34506 | − | 4.06176i | 0.201087 | − | 0.348293i | ||||
\(137\) | −4.54585 | − | 7.87364i | −0.388378 | − | 0.672690i | 0.603854 | − | 0.797095i | \(-0.293631\pi\) |
−0.992232 | + | 0.124405i | \(0.960298\pi\) | |||||||
\(138\) | −2.30669 | + | 3.99531i | −0.196359 | + | 0.340103i | ||||
\(139\) | 10.5329 | + | 18.2435i | 0.893389 | + | 1.54739i | 0.835786 | + | 0.549055i | \(0.185012\pi\) |
0.0576028 | + | 0.998340i | \(0.481654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.56232 | −0.805293 | ||||||||
\(142\) | 1.10005 | + | 1.90535i | 0.0923145 | + | 0.159893i | ||||
\(143\) | 2.74498 | + | 4.75445i | 0.229547 | + | 0.397587i | ||||
\(144\) | −1.23305 | −0.102754 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.32859 | + | 4.03323i | 0.192715 | + | 0.333793i | ||||
\(147\) | −1.04648 | + | 1.81256i | −0.0863122 | + | 0.149497i | ||||
\(148\) | 4.88411 | + | 8.45952i | 0.401471 | + | 0.695368i | ||||
\(149\) | 3.17889 | − | 5.50600i | 0.260425 | − | 0.451069i | −0.705930 | − | 0.708282i | \(-0.749471\pi\) |
0.966355 | + | 0.257212i | \(0.0828040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.05559 | −0.248660 | −0.124330 | − | 0.992241i | \(-0.539678\pi\) | ||||
−0.124330 | + | 0.992241i | \(0.539678\pi\) | |||||||
\(152\) | −3.75178 | + | 2.21903i | −0.304310 | + | 0.179987i | ||||
\(153\) | −5.78317 | −0.467541 | ||||||||
\(154\) | 7.44642 | − | 12.8976i | 0.600050 | − | 1.03932i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.570680 | − | 0.988447i | −0.0456910 | − | 0.0791391i | ||||
\(157\) | −4.07136 | + | 7.05180i | −0.324930 | + | 0.562795i | −0.981498 | − | 0.191472i | \(-0.938674\pi\) |
0.656568 | + | 0.754267i | \(0.272007\pi\) | |||||||
\(158\) | 5.79153 | + | 10.0312i | 0.460749 | + | 0.798041i | ||||
\(159\) | −8.24928 | −0.654210 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.04200 | − | 7.00096i | −0.318554 | − | 0.551753i | ||||
\(162\) | −1.89021 | − | 3.27394i | −0.148509 | − | 0.257225i | ||||
\(163\) | −13.4100 | −1.05035 | −0.525177 | − | 0.850993i | \(-0.676001\pi\) | ||||
−0.525177 | + | 0.850993i | \(0.676001\pi\) | |||||||
\(164\) | 3.69012 | 0.288150 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.03905 | + | 5.26378i | −0.235876 | + | 0.408549i | ||||
\(167\) | 6.49232 | + | 11.2450i | 0.502391 | + | 0.870166i | 0.999996 | + | 0.00276265i | \(0.000879380\pi\) |
−0.497606 | + | 0.867403i | \(0.665787\pi\) | |||||||
\(168\) | −1.54811 | + | 2.68140i | −0.119439 | + | 0.206874i | ||||
\(169\) | 6.13137 | − | 10.6198i | 0.471644 | − | 0.816911i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.68269 | + | 2.63827i | 0.358094 | + | 0.201754i | ||||
\(172\) | −7.12464 | −0.543249 | ||||||||
\(173\) | −1.05780 | + | 1.83216i | −0.0804228 | + | 0.139296i | −0.903432 | − | 0.428732i | \(-0.858960\pi\) |
0.823009 | + | 0.568029i | \(0.192294\pi\) | |||||||
\(174\) | 2.93831 | − | 5.08931i | 0.222753 | − | 0.385819i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.19690 | + | 5.53719i | −0.240975 | + | 0.417381i | ||||
\(177\) | −4.11268 | − | 7.12338i | −0.309128 | − | 0.535426i | ||||
\(178\) | −11.2989 | −0.846892 | ||||||||
\(179\) | −9.87938 | −0.738420 | −0.369210 | − | 0.929346i | \(-0.620372\pi\) | ||||
−0.369210 | + | 0.929346i | \(0.620372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.53974 | − | 13.0592i | −0.560425 | − | 0.970684i | −0.997459 | − | 0.0712395i | \(-0.977305\pi\) |
0.437034 | − | 0.899445i | \(-0.356029\pi\) | |||||||
\(182\) | 2.00000 | 0.148250 | ||||||||
\(183\) | 10.6617 | 0.788135 | ||||||||
\(184\) | 1.73531 | + | 3.00565i | 0.127929 | + | 0.221579i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.48484 | + | 9.50002i | 0.402168 | + | 0.696575i | ||||
\(187\) | −14.9938 | + | 25.9701i | −1.09646 | + | 1.89912i | ||||
\(188\) | −3.59684 | + | 6.22992i | −0.262327 | + | 0.454363i | ||||
\(189\) | 13.1064 | 0.953352 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.84192 | 0.639779 | 0.319889 | − | 0.947455i | \(-0.396354\pi\) | ||||
0.319889 | + | 0.947455i | \(0.396354\pi\) | |||||||
\(192\) | 0.664633 | − | 1.15118i | 0.0479657 | − | 0.0830791i | ||||
\(193\) | −9.34642 | + | 16.1885i | −0.672770 | + | 1.16527i | 0.304346 | + | 0.952562i | \(0.401562\pi\) |
−0.977115 | + | 0.212710i | \(0.931771\pi\) | |||||||
\(194\) | 5.67500 | + | 9.82939i | 0.407441 | + | 0.705709i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.787262 | + | 1.36358i | 0.0562330 | + | 0.0973984i | ||||
\(197\) | 16.3169 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(198\) | 7.88390 | 0.560284 | ||||||||
\(199\) | 1.57452 | + | 2.72715i | 0.111615 | + | 0.193323i | 0.916422 | − | 0.400214i | \(-0.131064\pi\) |
−0.804807 | + | 0.593537i | \(0.797731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.52024 | −0.459902 | ||||||||
\(202\) | −2.22085 | −0.156258 | ||||||||
\(203\) | 5.14879 | + | 8.91797i | 0.361374 | + | 0.625919i | ||||
\(204\) | 3.11721 | − | 5.39916i | 0.218248 | − | 0.378017i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.63232 | − | 2.82726i | 0.113729 | − | 0.196985i | ||||
\(207\) | 2.13973 | − | 3.70613i | 0.148722 | − | 0.257594i | ||||
\(208\) | −0.858640 | −0.0595360 | ||||||||
\(209\) | 23.9882 | − | 14.1881i | 1.65930 | − | 0.981408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.95415 | − | 6.84879i | 0.272215 | − | 0.471490i | −0.697214 | − | 0.716863i | \(-0.745577\pi\) |
0.969429 | + | 0.245373i | \(0.0789104\pi\) | |||||||
\(212\) | −3.10295 | + | 5.37446i | −0.213111 | + | 0.369119i | ||||
\(213\) | 1.46226 | + | 2.53272i | 0.100193 | + | 0.173539i | ||||
\(214\) | 5.00000 | − | 8.66025i | 0.341793 | − | 0.592003i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.62685 | −0.382859 | ||||||||
\(217\) | −19.2221 | −1.30488 | ||||||||
\(218\) | −1.51717 | − | 2.62782i | −0.102756 | − | 0.177978i | ||||
\(219\) | 3.09531 | + | 5.36123i | 0.209162 | + | 0.362279i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.02712 | −0.270894 | ||||||||
\(222\) | 6.49227 | + | 11.2449i | 0.435733 | + | 0.754711i | ||||
\(223\) | 4.16463 | − | 7.21336i | 0.278884 | − | 0.483042i | −0.692223 | − | 0.721683i | \(-0.743369\pi\) |
0.971108 | + | 0.238641i | \(0.0767020\pi\) | |||||||
\(224\) | 1.16463 | + | 2.01720i | 0.0778153 | + | 0.134780i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.48710 | − | 4.30778i | 0.165439 | − | 0.286549i | ||||
\(227\) | 11.3680 | 0.754523 | 0.377261 | − | 0.926107i | \(-0.376866\pi\) | ||||
0.377261 | + | 0.926107i | \(0.376866\pi\) | |||||||
\(228\) | −4.98712 | + | 2.94968i | −0.330280 | + | 0.195348i | ||||
\(229\) | −2.25560 | −0.149054 | −0.0745270 | − | 0.997219i | \(-0.523745\pi\) | ||||
−0.0745270 | + | 0.997219i | \(0.523745\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.89827 | − | 17.1443i | 0.651259 | − | 1.12801i | ||||
\(232\) | −2.21048 | − | 3.82866i | −0.145125 | − | 0.251364i | ||||
\(233\) | −7.96900 | + | 13.8027i | −0.522067 | + | 0.904246i | 0.477604 | + | 0.878575i | \(0.341505\pi\) |
−0.999670 | + | 0.0256705i | \(0.991828\pi\) | |||||||
\(234\) | 0.529375 | + | 0.916904i | 0.0346063 | + | 0.0599399i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.18791 | −0.402798 | ||||||||
\(237\) | 7.69848 | + | 13.3342i | 0.500070 | + | 0.866147i | ||||
\(238\) | 5.46226 | + | 9.46092i | 0.354066 | + | 0.613260i | ||||
\(239\) | 6.63412 | 0.429126 | 0.214563 | − | 0.976710i | \(-0.431167\pi\) | ||||
0.214563 | + | 0.976710i | \(0.431167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0397 | + | 19.1213i | 0.711130 | + | 1.23171i | 0.964433 | + | 0.264326i | \(0.0851494\pi\) |
−0.253304 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(242\) | 14.9403 | − | 25.8774i | 0.960400 | − | 1.66346i | ||||
\(243\) | 5.92769 | + | 10.2671i | 0.380261 | + | 0.658632i | ||||
\(244\) | 4.01037 | − | 6.94616i | 0.256738 | − | 0.444683i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.90515 | 0.312741 | ||||||||
\(247\) | 3.26080 | + | 1.83717i | 0.207480 | + | 0.116896i | ||||
\(248\) | 8.25244 | 0.524030 | ||||||||
\(249\) | −4.03970 | + | 6.99696i | −0.256006 | + | 0.443415i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.72558 | − | 8.18494i | −0.298276 | − | 0.516629i | 0.677466 | − | 0.735554i | \(-0.263078\pi\) |
−0.975742 | + | 0.218926i | \(0.929745\pi\) | |||||||
\(252\) | 1.43605 | − | 2.48732i | 0.0904630 | − | 0.156686i | ||||
\(253\) | −11.0952 | − | 19.2175i | −0.697552 | − | 1.20819i | ||||
\(254\) | −14.2990 | −0.897198 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.3945 | − | 23.1999i | −0.835524 | − | 1.44717i | −0.893603 | − | 0.448859i | \(-0.851831\pi\) |
0.0580783 | − | 0.998312i | \(-0.481503\pi\) | |||||||
\(258\) | −9.47053 | −0.589610 | ||||||||
\(259\) | −22.7528 | −1.41379 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.72564 | + | 4.72095i | −0.168713 | + | 0.292219i | ||||
\(262\) | 1.18947 | + | 2.06022i | 0.0734854 | + | 0.127281i | ||||
\(263\) | 7.19364 | − | 12.4598i | 0.443579 | − | 0.768301i | −0.554373 | − | 0.832268i | \(-0.687042\pi\) |
0.997952 | + | 0.0639670i | \(0.0203752\pi\) | |||||||
\(264\) | −4.24953 | + | 7.36040i | −0.261540 | + | 0.453001i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.106790 | − | 10.1525i | −0.00654769 | − | 0.622488i | ||||
\(267\) | −15.0193 | −0.919166 | ||||||||
\(268\) | −2.45257 | + | 4.24798i | −0.149815 | + | 0.259487i | ||||
\(269\) | −6.44486 | + | 11.1628i | −0.392950 | + | 0.680609i | −0.992837 | − | 0.119475i | \(-0.961879\pi\) |
0.599887 | + | 0.800085i | \(0.295212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0907 | + | 17.4776i | −0.612966 | + | 1.06169i | 0.377772 | + | 0.925899i | \(0.376690\pi\) |
−0.990738 | + | 0.135790i | \(0.956643\pi\) | |||||||
\(272\) | −2.34506 | − | 4.06176i | −0.142190 | − | 0.246280i | ||||
\(273\) | 2.65853 | 0.160902 | ||||||||
\(274\) | −9.09169 | −0.549249 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.30669 | + | 3.99531i | 0.138846 | + | 0.240489i | ||||
\(277\) | −7.40098 | −0.444682 | −0.222341 | − | 0.974969i | \(-0.571370\pi\) | ||||
−0.222341 | + | 0.974969i | \(0.571370\pi\) | |||||||
\(278\) | 21.0658 | 1.26344 | ||||||||
\(279\) | −5.08785 | − | 8.81242i | −0.304602 | − | 0.527586i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.36083 | − | 2.35703i | −0.0811805 | − | 0.140609i | 0.822577 | − | 0.568654i | \(-0.192536\pi\) |
−0.903757 | + | 0.428045i | \(0.859202\pi\) | |||||||
\(282\) | −4.78116 | + | 8.28121i | −0.284714 | + | 0.493139i | ||||
\(283\) | −10.2721 | + | 17.7918i | −0.610613 | + | 1.05761i | 0.380524 | + | 0.924771i | \(0.375744\pi\) |
−0.991137 | + | 0.132842i | \(0.957590\pi\) | |||||||
\(284\) | 2.20011 | 0.130552 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.48997 | 0.324629 | ||||||||
\(287\) | −4.29763 | + | 7.44372i | −0.253681 | + | 0.439389i | ||||
\(288\) | −0.616527 | + | 1.06786i | −0.0363292 | + | 0.0629240i | ||||
\(289\) | −2.49860 | − | 4.32771i | −0.146977 | − | 0.254571i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.54358 | + | 13.0659i | 0.442213 | + | 0.765935i | ||||
\(292\) | 4.65717 | 0.272540 | ||||||||
\(293\) | −26.7315 | −1.56167 | −0.780836 | − | 0.624736i | \(-0.785206\pi\) | ||||
−0.780836 | + | 0.624736i | \(0.785206\pi\) | |||||||
\(294\) | 1.04648 | + | 1.81256i | 0.0610319 | + | 0.105710i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.76821 | 0.567766 | ||||||||
\(297\) | 35.9769 | 2.08759 | ||||||||
\(298\) | −3.17889 | − | 5.50600i | −0.184148 | − | 0.318954i | ||||
\(299\) | 1.49001 | − | 2.58077i | 0.0861694 | − | 0.149250i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.29759 | − | 14.3718i | 0.478265 | − | 0.828379i | ||||
\(302\) | −1.52779 | + | 2.64622i | −0.0879147 | + | 0.152273i | ||||
\(303\) | −2.95210 | −0.169594 | ||||||||
\(304\) | 0.0458469 | + | 4.35866i | 0.00262950 | + | 0.249986i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.89158 | + | 5.00837i | −0.165301 | + | 0.286310i | ||||
\(307\) | −6.38026 | + | 11.0509i | −0.364141 | + | 0.630710i | −0.988638 | − | 0.150317i | \(-0.951971\pi\) |
0.624497 | + | 0.781027i | \(0.285304\pi\) | |||||||
\(308\) | −7.44642 | − | 12.8976i | −0.424299 | − | 0.734908i | ||||
\(309\) | 2.16979 | − | 3.75818i | 0.123435 | − | 0.213795i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.96646 | −0.395031 | −0.197516 | − | 0.980300i | \(-0.563287\pi\) | ||||
−0.197516 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(312\) | −1.14136 | −0.0646168 | ||||||||
\(313\) | 13.0846 | + | 22.6632i | 0.739585 | + | 1.28100i | 0.952682 | + | 0.303968i | \(0.0983115\pi\) |
−0.213097 | + | 0.977031i | \(0.568355\pi\) | |||||||
\(314\) | 4.07136 | + | 7.05180i | 0.229760 | + | 0.397956i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.5831 | 0.651598 | ||||||||
\(317\) | 4.37870 | + | 7.58413i | 0.245932 | + | 0.425967i | 0.962393 | − | 0.271660i | \(-0.0875725\pi\) |
−0.716461 | + | 0.697627i | \(0.754239\pi\) | |||||||
\(318\) | −4.12464 | + | 7.14408i | −0.231298 | + | 0.400620i | ||||
\(319\) | 14.1334 | + | 24.4797i | 0.791316 | + | 1.37060i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.64633 | − | 11.5118i | 0.370962 | − | 0.642525i | ||||
\(322\) | −8.08401 | −0.450504 | ||||||||
\(323\) | 0.215028 | + | 20.4426i | 0.0119645 | + | 1.13746i | ||||
\(324\) | −3.78042 | −0.210023 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.70501 | + | 11.6134i | −0.371356 | + | 0.643208i | ||||
\(327\) | −2.01672 | − | 3.49306i | −0.111525 | − | 0.193167i | ||||
\(328\) | 1.84506 | − | 3.19574i | 0.101876 | − | 0.176455i | ||||
\(329\) | −8.37800 | − | 14.5111i | −0.461894 | − | 0.800024i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.34738 | −0.513779 | −0.256889 | − | 0.966441i | \(-0.582698\pi\) | ||||
−0.256889 | + | 0.966441i | \(0.582698\pi\) | |||||||
\(332\) | 3.03905 | + | 5.26378i | 0.166789 | + | 0.288888i | ||||
\(333\) | −6.02237 | − | 10.4310i | −0.330024 | − | 0.571618i | ||||
\(334\) | 12.9846 | 0.710488 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.54811 | + | 2.68140i | 0.0844561 | + | 0.146282i | ||||
\(337\) | 4.87376 | − | 8.44159i | 0.265490 | − | 0.459843i | −0.702202 | − | 0.711978i | \(-0.747799\pi\) |
0.967692 | + | 0.252135i | \(0.0811328\pi\) | |||||||
\(338\) | −6.13137 | − | 10.6198i | −0.333502 | − | 0.577643i | ||||
\(339\) | 3.30601 | − | 5.72618i | 0.179558 | − | 0.311003i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52.7644 | −2.85735 | ||||||||
\(342\) | 4.62615 | − | 2.73619i | 0.250154 | − | 0.147956i | ||||
\(343\) | −19.9723 | −1.07840 | ||||||||
\(344\) | −3.56232 | + | 6.17012i | −0.192067 | + | 0.332670i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.05780 | + | 1.83216i | 0.0568675 | + | 0.0984975i | ||||
\(347\) | 7.38162 | − | 12.7853i | 0.396266 | − | 0.686353i | −0.596996 | − | 0.802244i | \(-0.703639\pi\) |
0.993262 | + | 0.115891i | \(0.0369724\pi\) | |||||||
\(348\) | −2.93831 | − | 5.08931i | −0.157510 | − | 0.272816i | ||||
\(349\) | 14.8315 | 0.793913 | 0.396956 | − | 0.917837i | \(-0.370066\pi\) | ||||
0.396956 | + | 0.917837i | \(0.370066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.41572 | + | 4.18415i | 0.128942 | + | 0.223333i | ||||
\(352\) | 3.19690 | + | 5.53719i | 0.170395 | + | 0.295133i | ||||
\(353\) | 26.8115 | 1.42703 | 0.713516 | − | 0.700639i | \(-0.247102\pi\) | ||||
0.713516 | + | 0.700639i | \(0.247102\pi\) | |||||||
\(354\) | −8.22537 | −0.437173 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.64947 | + | 9.78517i | −0.299421 | + | 0.518613i | ||||
\(357\) | 7.26080 | + | 12.5761i | 0.384282 | + | 0.665596i | ||||
\(358\) | −4.93969 | + | 8.55579i | −0.261071 | + | 0.452188i | ||||
\(359\) | −0.197846 | + | 0.342680i | −0.0104419 | + | 0.0180859i | −0.871199 | − | 0.490930i | \(-0.836657\pi\) |
0.860757 | + | 0.509016i | \(0.169990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.15178 | − | 16.6507i | 0.481673 | − | 0.876351i | ||||
\(362\) | −15.0795 | −0.792560 | ||||||||
\(363\) | 19.8597 | − | 34.3979i | 1.04236 | − | 1.80542i | ||||
\(364\) | 1.00000 | − | 1.73205i | 0.0524142 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.33085 | − | 9.23330i | 0.278648 | − | 0.482632i | ||||
\(367\) | −3.49227 | − | 6.04879i | −0.182295 | − | 0.315744i | 0.760367 | − | 0.649494i | \(-0.225019\pi\) |
−0.942662 | + | 0.333750i | \(0.891686\pi\) | |||||||
\(368\) | 3.47063 | 0.180919 | ||||||||
\(369\) | −4.55011 | −0.236870 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.22758 | − | 12.5185i | −0.375237 | − | 0.649930i | ||||
\(372\) | 10.9697 | 0.568751 | ||||||||
\(373\) | 2.52621 | 0.130802 | 0.0654012 | − | 0.997859i | \(-0.479167\pi\) | ||||
0.0654012 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(374\) | 14.9938 | + | 25.9701i | 0.775313 | + | 1.34288i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.59684 | + | 6.22992i | 0.185493 | + | 0.321283i | ||||
\(377\) | −1.89801 | + | 3.28744i | −0.0977523 | + | 0.169312i | ||||
\(378\) | 6.55321 | − | 11.3505i | 0.337061 | − | 0.583807i | ||||
\(379\) | −29.3075 | −1.50543 | −0.752713 | − | 0.658349i | \(-0.771255\pi\) | ||||
−0.752713 | + | 0.658349i | \(0.771255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.0071 | −0.973765 | ||||||||
\(382\) | 4.42096 | − | 7.65733i | 0.226196 | − | 0.391783i | ||||
\(383\) | −3.11717 | + | 5.39911i | −0.159280 | + | 0.275881i | −0.934609 | − | 0.355676i | \(-0.884251\pi\) |
0.775329 | + | 0.631557i | \(0.217584\pi\) | |||||||
\(384\) | −0.664633 | − | 1.15118i | −0.0339169 | − | 0.0587458i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.34642 | + | 16.1885i | 0.475720 | + | 0.823971i | ||||
\(387\) | 8.78506 | 0.446570 | ||||||||
\(388\) | 11.3500 | 0.576209 | ||||||||
\(389\) | −13.2183 | − | 22.8947i | −0.670193 | − | 1.16081i | −0.977849 | − | 0.209311i | \(-0.932878\pi\) |
0.307656 | − | 0.951498i | \(-0.400455\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.2776 | 0.823196 | ||||||||
\(392\) | 1.57452 | 0.0795254 | ||||||||
\(393\) | 1.58112 | + | 2.73857i | 0.0797567 | + | 0.138143i | ||||
\(394\) | 8.15847 | − | 14.1309i | 0.411018 | − | 0.711903i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.94195 | − | 6.82766i | 0.198090 | − | 0.343103i | ||||
\(397\) | 4.36575 | − | 7.56171i | 0.219111 | − | 0.379511i | −0.735426 | − | 0.677606i | \(-0.763018\pi\) |
0.954536 | + | 0.298094i | \(0.0963510\pi\) | |||||||
\(398\) | 3.14905 | 0.157847 | ||||||||
\(399\) | −0.141952 | − | 13.4953i | −0.00710648 | − | 0.675611i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.58356 | − | 2.74281i | 0.0790794 | − | 0.136969i | −0.823774 | − | 0.566919i | \(-0.808135\pi\) |
0.902853 | + | 0.429949i | \(0.141469\pi\) | |||||||
\(402\) | −3.26012 | + | 5.64669i | −0.162600 | + | 0.281631i | ||||
\(403\) | −3.54294 | − | 6.13654i | −0.176486 | − | 0.305683i | ||||
\(404\) | −1.11042 | + | 1.92331i | −0.0552457 | + | 0.0956884i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.2976 | 0.511061 | ||||||||
\(407\) | −62.4560 | −3.09583 | ||||||||
\(408\) | −3.11721 | − | 5.39916i | −0.154325 | − | 0.267298i | ||||
\(409\) | −8.54431 | − | 14.7992i | −0.422489 | − | 0.731773i | 0.573693 | − | 0.819070i | \(-0.305510\pi\) |
−0.996182 | + | 0.0872978i | \(0.972177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0853 | −0.596123 | ||||||||
\(412\) | −1.63232 | − | 2.82726i | −0.0804187 | − | 0.139289i | ||||
\(413\) | 7.20664 | − | 12.4823i | 0.354615 | − | 0.614212i | ||||
\(414\) | −2.13973 | − | 3.70613i | −0.105162 | − | 0.182146i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.429320 | + | 0.743604i | −0.0210491 | + | 0.0364582i | ||||
\(417\) | 28.0020 | 1.37127 | ||||||||
\(418\) | −0.293136 | − | 27.8684i | −0.0143378 | − | 1.36309i | ||||
\(419\) | 7.80296 | 0.381200 | 0.190600 | − | 0.981668i | \(-0.438957\pi\) | ||||
0.190600 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9845 | + | 29.4180i | −0.827773 | + | 1.43374i | 0.0720091 | + | 0.997404i | \(0.477059\pi\) |
−0.899782 | + | 0.436340i | \(0.856274\pi\) | |||||||
\(422\) | −3.95415 | − | 6.84879i | −0.192485 | − | 0.333394i | ||||
\(423\) | 4.43510 | − | 7.68182i | 0.215642 | − | 0.373503i | ||||
\(424\) | 3.10295 | + | 5.37446i | 0.150692 | + | 0.261007i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.92453 | 0.141694 | ||||||||
\(427\) | 9.34122 | + | 16.1795i | 0.452053 | + | 0.782979i | ||||
\(428\) | −5.00000 | − | 8.66025i | −0.241684 | − | 0.418609i | ||||
\(429\) | 7.29763 | 0.352333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.07565 | − | 15.7195i | −0.437158 | − | 0.757181i | 0.560311 | − | 0.828283i | \(-0.310682\pi\) |
−0.997469 | + | 0.0711019i | \(0.977348\pi\) | |||||||
\(432\) | −2.81343 | + | 4.87300i | −0.135361 | + | 0.234452i | ||||
\(433\) | 0.157154 | + | 0.272199i | 0.00755234 | + | 0.0130810i | 0.869777 | − | 0.493445i | \(-0.164263\pi\) |
−0.862225 | + | 0.506526i | \(0.830929\pi\) | |||||||
\(434\) | −9.61106 | + | 16.6468i | −0.461346 | + | 0.799074i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.03434 | −0.145319 | ||||||||
\(437\) | −13.1802 | − | 7.42583i | −0.630492 | − | 0.355226i | ||||
\(438\) | 6.19062 | 0.295799 | ||||||||
\(439\) | −4.33220 | + | 7.50359i | −0.206765 | + | 0.358127i | −0.950694 | − | 0.310132i | \(-0.899627\pi\) |
0.743929 | + | 0.668259i | \(0.232960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.970736 | − | 1.68136i | −0.0462255 | − | 0.0800650i | ||||
\(442\) | −2.01356 | + | 3.48759i | −0.0957753 | + | 0.165888i | ||||
\(443\) | −1.94419 | − | 3.36744i | −0.0923714 | − | 0.159992i | 0.816137 | − | 0.577858i | \(-0.196111\pi\) |
−0.908509 | + | 0.417866i | \(0.862778\pi\) | |||||||
\(444\) | 12.9845 | 0.616219 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.16463 | − | 7.21336i | −0.197201 | − | 0.341562i | ||||
\(447\) | −4.22559 | − | 7.31894i | −0.199864 | − | 0.346174i | ||||
\(448\) | 2.32927 | 0.110047 | ||||||||
\(449\) | 32.9375 | 1.55442 | 0.777208 | − | 0.629243i | \(-0.216635\pi\) | ||||
0.777208 | + | 0.629243i | \(0.216635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7969 | + | 20.4329i | −0.555496 | + | 0.962147i | ||||
\(452\) | −2.48710 | − | 4.30778i | −0.116983 | − | 0.202621i | ||||
\(453\) | −2.03084 | + | 3.51752i | −0.0954174 | + | 0.165268i | ||||
\(454\) | 5.68402 | − | 9.84500i | 0.266764 | − | 0.462049i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0609427 | + | 5.79381i | 0.00285390 | + | 0.271320i | ||||
\(457\) | −1.22533 | −0.0573184 | −0.0286592 | − | 0.999589i | \(-0.509124\pi\) | ||||
−0.0286592 | + | 0.999589i | \(0.509124\pi\) | |||||||
\(458\) | −1.12780 | + | 1.95341i | −0.0526986 | + | 0.0912766i | ||||
\(459\) | −13.1953 | + | 22.8549i | −0.615904 | + | 1.06678i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5927 | − | 33.9356i | 0.912524 | − | 1.58054i | 0.102038 | − | 0.994781i | \(-0.467464\pi\) |
0.810486 | − | 0.585758i | \(-0.199203\pi\) | |||||||
\(462\) | −9.89827 | − | 17.1443i | −0.460509 | − | 0.797626i | ||||
\(463\) | 32.5754 | 1.51391 | 0.756953 | − | 0.653469i | \(-0.226687\pi\) | ||||
0.756953 | + | 0.653469i | \(0.226687\pi\) | |||||||
\(464\) | −4.42096 | −0.205238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.96900 | + | 13.8027i | 0.369157 | + | 0.639398i | ||||
\(467\) | 16.9079 | 0.782406 | 0.391203 | − | 0.920304i | \(-0.372059\pi\) | ||||
0.391203 | + | 0.920304i | \(0.372059\pi\) | |||||||
\(468\) | 1.05875 | 0.0489407 | ||||||||
\(469\) | −5.71269 | − | 9.89467i | −0.263788 | − | 0.456894i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.41192 | + | 9.37371i | 0.249368 | + | 0.431918i | ||||
\(472\) | −3.09395 | + | 5.35888i | −0.142411 | + | 0.246663i | ||||
\(473\) | 22.7767 | − | 39.4505i | 1.04728 | − | 1.81394i | ||||
\(474\) | 15.3970 | 0.707206 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.9245 | 0.500725 | ||||||||
\(477\) | 3.82610 | − | 6.62700i | 0.175185 | − | 0.303429i | ||||
\(478\) | 3.31706 | − | 5.74532i | 0.151719 | − | 0.262785i | ||||
\(479\) | −1.82570 | − | 3.16220i | −0.0834181 | − | 0.144484i | 0.821298 | − | 0.570500i | \(-0.193250\pi\) |
−0.904716 | + | 0.426015i | \(0.859917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.19369 | − | 7.26368i | −0.191216 | − | 0.331195i | ||||
\(482\) | 22.0794 | 1.00569 | ||||||||
\(483\) | −10.7458 | −0.488950 | ||||||||
\(484\) | −14.9403 | − | 25.8774i | −0.679106 | − | 1.17625i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.8554 | 0.537771 | ||||||||
\(487\) | 13.7416 | 0.622691 | 0.311346 | − | 0.950297i | \(-0.399220\pi\) | ||||
0.311346 | + | 0.950297i | \(0.399220\pi\) | |||||||
\(488\) | −4.01037 | − | 6.94616i | −0.181541 | − | 0.314438i | ||||
\(489\) | −8.91274 | + | 15.4373i | −0.403048 | + | 0.698099i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3839 | − | 30.1098i | 0.784525 | − | 1.35884i | −0.144758 | − | 0.989467i | \(-0.546240\pi\) |
0.929283 | − | 0.369369i | \(-0.120426\pi\) | |||||||
\(492\) | 2.45257 | − | 4.24798i | 0.110571 | − | 0.191514i | ||||
\(493\) | −20.7348 | −0.933849 | ||||||||
\(494\) | 3.22143 | − | 1.90535i | 0.144939 | − | 0.0857258i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.12622 | − | 7.14682i | 0.185273 | − | 0.320902i | ||||
\(497\) | −2.56232 | + | 4.43807i | −0.114936 | + | 0.199075i | ||||
\(498\) | 4.03970 | + | 6.99696i | 0.181023 | + | 0.313541i | ||||
\(499\) | −8.31410 | + | 14.4005i | −0.372190 | + | 0.644653i | −0.989902 | − | 0.141752i | \(-0.954726\pi\) |
0.617712 | + | 0.786405i | \(0.288060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.2600 | 0.771121 | ||||||||
\(502\) | −9.45115 | −0.421825 | ||||||||
\(503\) | 2.37970 | + | 4.12176i | 0.106106 | + | 0.183780i | 0.914189 | − | 0.405287i | \(-0.132829\pi\) |
−0.808084 | + | 0.589068i | \(0.799495\pi\) | |||||||
\(504\) | −1.43605 | − | 2.48732i | −0.0639670 | − | 0.110794i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1905 | −0.986487 | ||||||||
\(507\) | −8.15022 | − | 14.1166i | −0.361964 | − | 0.626940i | ||||
\(508\) | −7.14949 | + | 12.3833i | −0.317207 | + | 0.549419i | ||||
\(509\) | 1.41576 | + | 2.45217i | 0.0627524 | + | 0.108690i | 0.895695 | − | 0.444669i | \(-0.146679\pi\) |
−0.832942 | + | 0.553360i | \(0.813345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.42390 | + | 9.39446i | −0.239939 | + | 0.415587i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.1107 | − | 12.4862i | 0.932062 | − | 0.551278i | ||||
\(514\) | −26.7890 | −1.18161 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.73527 | + | 8.20172i | −0.208459 | + | 0.361061i | ||||
\(517\) | −22.9975 | − | 39.8328i | −1.01143 | − | 1.75185i | ||||
\(518\) | −11.3764 | + | 19.7045i | −0.499849 | + | 0.865764i | ||||
\(519\) | 1.40609 | + | 2.43542i | 0.0617206 | + | 0.106903i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.92317 | 0.215688 | 0.107844 | − | 0.994168i | \(-0.465605\pi\) | ||||
0.107844 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(522\) | 2.72564 | + | 4.72095i | 0.119298 | + | 0.206630i | ||||
\(523\) | −14.4447 | − | 25.0190i | −0.631624 | − | 1.09400i | −0.987220 | − | 0.159365i | \(-0.949055\pi\) |
0.355596 | − | 0.934640i | \(-0.384278\pi\) | |||||||
\(524\) | 2.37893 | 0.103924 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.19364 | − | 12.4598i | −0.313658 | − | 0.543271i | ||||
\(527\) | 19.3525 | − | 33.5194i | 0.843006 | − | 1.46013i | ||||
\(528\) | 4.24953 | + | 7.36040i | 0.184937 | + | 0.320320i | ||||
\(529\) | 5.47738 | − | 9.48710i | 0.238147 | − | 0.412483i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.63002 | 0.331115 | ||||||||
\(532\) | −8.84569 | − | 4.98375i | −0.383509 | − | 0.216073i | ||||
\(533\) | −3.16848 | −0.137242 | ||||||||
\(534\) | −7.50965 | + | 13.0071i | −0.324974 | + | 0.562872i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.45257 | + | 4.24798i | 0.105935 | + | 0.183485i | ||||
\(537\) | −6.56616 | + | 11.3729i | −0.283351 | + | 0.490778i | ||||
\(538\) | 6.44486 | + | 11.1628i | 0.277858 | + | 0.481264i | ||||
\(539\) | −10.0672 | −0.433624 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.30730 | − | 3.99637i | −0.0991987 | − | 0.171817i | 0.812154 | − | 0.583442i | \(-0.198295\pi\) |
−0.911353 | + | 0.411625i | \(0.864961\pi\) | |||||||
\(542\) | 10.0907 | + | 17.4776i | 0.433433 | + | 0.750727i | ||||
\(543\) | −20.0446 | −0.860198 | ||||||||
\(544\) | −4.69012 | −0.201087 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.32927 | − | 2.30235i | 0.0568873 | − | 0.0985317i | ||||
\(547\) | 12.1562 | + | 21.0552i | 0.519763 | + | 0.900255i | 0.999736 | + | 0.0229724i | \(0.00731297\pi\) |
−0.479973 | + | 0.877283i | \(0.659354\pi\) | |||||||
\(548\) | −4.54585 | + | 7.87364i | −0.194189 | + | 0.336345i | ||||
\(549\) | −4.94500 | + | 8.56500i | −0.211048 | + | 0.365545i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7892 | + | 9.45919i | 0.715243 | + | 0.402975i | ||||
\(552\) | 4.61338 | 0.196359 | ||||||||
\(553\) | −13.4900 | + | 23.3654i | −0.573654 | + | 0.993597i | ||||
\(554\) | −3.70049 | + | 6.40943i | −0.157219 | + | 0.272311i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.5329 | − | 18.2435i | 0.446694 | − | 0.773697i | ||||
\(557\) | 12.2154 | + | 21.1577i | 0.517582 | + | 0.896479i | 0.999791 | + | 0.0204227i | \(0.00650119\pi\) |
−0.482209 | + | 0.876056i | \(0.660165\pi\) | |||||||
\(558\) | −10.1757 | −0.430772 | ||||||||
\(559\) | 6.11750 | 0.258743 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.9308 | + | 34.5211i | 0.841478 | + | 1.45748i | ||||
\(562\) | −2.72167 | −0.114807 | ||||||||
\(563\) | 19.7981 | 0.834390 | 0.417195 | − | 0.908817i | \(-0.363013\pi\) | ||||
0.417195 | + | 0.908817i | \(0.363013\pi\) | |||||||
\(564\) | 4.78116 | + | 8.28121i | 0.201323 | + | 0.348702i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.2721 | + | 17.7918i | 0.431769 | + | 0.747845i | ||||
\(567\) | 4.40280 | − | 7.62587i | 0.184900 | − | 0.320256i | ||||
\(568\) | 1.10005 | − | 1.90535i | 0.0461573 | − | 0.0799467i | ||||
\(569\) | −39.9935 | −1.67662 | −0.838308 | − | 0.545197i | \(-0.816455\pi\) | ||||
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.3255 | −1.26908 | −0.634542 | − | 0.772889i | \(-0.718811\pi\) | ||||
−0.634542 | + | 0.772889i | \(0.718811\pi\) | |||||||
\(572\) | 2.74498 | − | 4.75445i | 0.114774 | − | 0.198794i | ||||
\(573\) | 5.87663 | − | 10.1786i | 0.245500 | − | 0.425218i | ||||
\(574\) | 4.29763 | + | 7.44372i | 0.179380 | + | 0.310695i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.616527 | + | 1.06786i | 0.0256886 | + | 0.0444940i | ||||
\(577\) | −31.8330 | −1.32523 | −0.662613 | − | 0.748962i | \(-0.730552\pi\) | ||||
−0.662613 | + | 0.748962i | \(0.730552\pi\) | |||||||
\(578\) | −4.99721 | −0.207856 | ||||||||
\(579\) | 12.4239 | + | 21.5188i | 0.516318 | + | 0.894289i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.1575 | −0.587352 | ||||||||
\(582\) | 15.0872 | 0.625383 | ||||||||
\(583\) | −19.8396 | − | 34.3632i | −0.821673 | − | 1.42318i | ||||
\(584\) | 2.32859 | − | 4.03323i | 0.0963576 | − | 0.166896i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.3658 | + | 23.1502i | −0.552134 | + | 0.956324i | ||||
\(587\) | 0.530771 | − | 0.919322i | 0.0219073 | − | 0.0379445i | −0.854864 | − | 0.518852i | \(-0.826359\pi\) |
0.876771 | + | 0.480908i | \(0.159693\pi\) | |||||||
\(588\) | 2.09296 | 0.0863122 | ||||||||
\(589\) | −30.9614 | + | 18.3124i | −1.27574 | + | 0.754551i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.8448 | − | 18.7837i | 0.446094 | − | 0.772657i | ||||
\(592\) | 4.88411 | − | 8.45952i | 0.200736 | − | 0.347684i | ||||
\(593\) | −18.7747 | − | 32.5188i | −0.770985 | − | 1.33539i | −0.937024 | − | 0.349266i | \(-0.886431\pi\) |
0.166039 | − | 0.986119i | \(-0.446902\pi\) | |||||||
\(594\) | 17.9885 | − | 31.1570i | 0.738076 | − | 1.27839i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.35778 | −0.260425 | ||||||||
\(597\) | 4.18592 | 0.171318 | ||||||||
\(598\) | −1.49001 | − | 2.58077i | −0.0609310 | − | 0.105536i | ||||
\(599\) | 5.02165 | + | 8.69775i | 0.205179 | + | 0.355380i | 0.950190 | − | 0.311672i | \(-0.100889\pi\) |
−0.745011 | + | 0.667052i | \(0.767556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.56630 | 0.308636 | 0.154318 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154318 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(602\) | −8.29759 | − | 14.3718i | −0.338184 | − | 0.585753i | ||||
\(603\) | 3.02415 | − | 5.23799i | 0.123153 | − | 0.213307i | ||||
\(604\) | 1.52779 | + | 2.64622i | 0.0621651 | + | 0.107673i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.47605 | + | 2.55659i | −0.0599604 | + | 0.103854i | ||||
\(607\) | −30.8174 | −1.25084 | −0.625420 | − | 0.780288i | \(-0.715072\pi\) | ||||
−0.625420 | + | 0.780288i | \(0.715072\pi\) | |||||||
\(608\) | 3.79763 | + | 2.13962i | 0.154014 | + | 0.0867732i | ||||
\(609\) | 13.6882 | 0.554675 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.08839 | − | 5.34925i | 0.124943 | − | 0.216408i | ||||
\(612\) | 2.89158 | + | 5.00837i | 0.116885 | + | 0.202451i | ||||
\(613\) | 9.36510 | − | 16.2208i | 0.378253 | − | 0.655153i | −0.612555 | − | 0.790428i | \(-0.709858\pi\) |
0.990808 | + | 0.135275i | \(0.0431916\pi\) | |||||||
\(614\) | 6.38026 | + | 11.0509i | 0.257486 | + | 0.445980i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.8928 | −0.600050 | ||||||||
\(617\) | 23.1741 | + | 40.1386i | 0.932952 | + | 1.61592i | 0.778245 | + | 0.627960i | \(0.216110\pi\) |
0.154707 | + | 0.987960i | \(0.450557\pi\) | |||||||
\(618\) | −2.16979 | − | 3.75818i | −0.0872816 | − | 0.151176i | ||||
\(619\) | 11.5591 | 0.464600 | 0.232300 | − | 0.972644i | \(-0.425375\pi\) | ||||
0.232300 | + | 0.972644i | \(0.425375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.76435 | − | 16.9123i | −0.391830 | − | 0.678669i | ||||
\(622\) | −3.48323 | + | 6.03313i | −0.139665 | + | 0.241906i | ||||
\(623\) | −13.1591 | − | 22.7923i | −0.527209 | − | 0.913153i | ||||
\(624\) | −0.570680 | + | 0.988447i | −0.0228455 | + | 0.0395695i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.1692 | 1.04593 | ||||||||
\(627\) | −0.389655 | − | 37.0445i | −0.0155613 | − | 1.47941i | ||||
\(628\) | 8.14272 | 0.324930 | ||||||||
\(629\) | 22.9070 | − | 39.6761i | 0.913363 | − | 1.58199i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.4567 | − | 38.8962i | −0.893989 | − | 1.54843i | −0.835051 | − | 0.550173i | \(-0.814562\pi\) |
−0.0589383 | − | 0.998262i | \(-0.518772\pi\) | |||||||
\(632\) | 5.79153 | − | 10.0312i | 0.230375 | − | 0.399021i | ||||
\(633\) | −5.25612 | − | 9.10386i | −0.208912 | − | 0.361846i | ||||
\(634\) | 8.75740 | 0.347801 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.12464 | + | 7.14408i | 0.163553 | + | 0.283281i | ||||
\(637\) | −0.675974 | − | 1.17082i | −0.0267831 | − | 0.0463897i | ||||
\(638\) | 28.2667 | 1.11909 | ||||||||
\(639\) | −2.71285 | −0.107319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3522 | − | 30.0549i | 0.685371 | − | 1.18710i | −0.287949 | − | 0.957646i | \(-0.592973\pi\) |
0.973320 | − | 0.229451i | \(-0.0736932\pi\) | |||||||
\(642\) | −6.64633 | − | 11.5118i | −0.262310 | − | 0.454333i | ||||
\(643\) | −18.7485 | + | 32.4734i | −0.739369 | + | 1.28062i | 0.213411 | + | 0.976963i | \(0.431543\pi\) |
−0.952780 | + | 0.303662i | \(0.901791\pi\) | |||||||
\(644\) | −4.04200 | + | 7.00096i | −0.159277 | + | 0.275876i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8113 | + | 10.0351i | 0.700778 | + | 0.394825i | ||||
\(647\) | 22.6592 | 0.890823 | 0.445412 | − | 0.895326i | \(-0.353057\pi\) | ||||
0.445412 | + | 0.895326i | \(0.353057\pi\) | |||||||
\(648\) | −1.89021 | + | 3.27394i | −0.0742544 | + | 0.128612i | ||||
\(649\) | 19.7821 | − | 34.2636i | 0.776516 | − | 1.34496i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7756 | + | 22.1281i | −0.500717 | + | 0.867267i | ||||
\(652\) | 6.70501 | + | 11.6134i | 0.262588 | + | 0.454817i | ||||
\(653\) | 17.7667 | 0.695266 | 0.347633 | − | 0.937631i | \(-0.386986\pi\) | ||||
0.347633 | + | 0.937631i | \(0.386986\pi\) | |||||||
\(654\) | −4.03344 | −0.157720 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.84506 | − | 3.19574i | −0.0720375 | − | 0.124773i | ||||
\(657\) | −5.74255 | −0.224038 | ||||||||
\(658\) | −16.7560 | −0.653217 | ||||||||
\(659\) | −0.991869 | − | 1.71797i | −0.0386377 | − | 0.0669225i | 0.846060 | − | 0.533088i | \(-0.178969\pi\) |
−0.884698 | + | 0.466165i | \(0.845635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.1253 | − | 22.7337i | −0.510515 | − | 0.884237i | −0.999926 | − | 0.0121841i | \(-0.996122\pi\) |
0.489411 | − | 0.872053i | \(-0.337212\pi\) | |||||||
\(662\) | −4.67369 | + | 8.09507i | −0.181648 | + | 0.314624i | ||||
\(663\) | −2.67656 | + | 4.63593i | −0.103949 | + | 0.180045i | ||||
\(664\) | 6.07809 | 0.235876 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0447 | −0.466724 | ||||||||
\(667\) | 7.67175 | − | 13.2879i | 0.297051 | − | 0.514508i | ||||
\(668\) | 6.49232 | − | 11.2450i | 0.251195 | − | 0.435083i | ||||
\(669\) | −5.53590 | − | 9.58846i | −0.214030 | − | 0.370711i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.6415 | + | 44.4124i | 0.989879 | + | 1.71452i | ||||
\(672\) | 3.09621 | 0.119439 | ||||||||
\(673\) | 16.0432 | 0.618418 | 0.309209 | − | 0.950994i | \(-0.399936\pi\) | ||||
0.309209 | + | 0.950994i | \(0.399936\pi\) | |||||||
\(674\) | −4.87376 | − | 8.44159i | −0.187730 | − | 0.325158i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2627 | −0.471644 | ||||||||
\(677\) | 48.5483 | 1.86586 | 0.932931 | − | 0.360056i | \(-0.117243\pi\) | ||||
0.932931 | + | 0.360056i | \(0.117243\pi\) | |||||||
\(678\) | −3.30601 | − | 5.72618i | −0.126967 | − | 0.219913i | ||||
\(679\) | −13.2186 | + | 22.8953i | −0.507283 | + | 0.878640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.55556 | − | 13.0866i | 0.289530 | − | 0.501480i | ||||
\(682\) | −26.3822 | + | 45.6953i | −1.01023 | + | 1.74976i | ||||
\(683\) | 13.3802 | 0.511981 | 0.255990 | − | 0.966679i | \(-0.417598\pi\) | ||||
0.255990 | + | 0.966679i | \(0.417598\pi\) | |||||||
\(684\) | −0.0565317 | − | 5.37446i | −0.00216155 | − | 0.205498i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.98617 | + | 17.2966i | −0.381274 | + | 0.660385i | ||||
\(687\) | −1.49914 | + | 2.59659i | −0.0571959 | + | 0.0990662i | ||||
\(688\) | 3.56232 | + | 6.17012i | 0.135812 | + | 0.235234i | ||||
\(689\) | 2.66431 | − | 4.61473i | 0.101502 | − | 0.175807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8354 | −0.982825 | −0.491413 | − | 0.870927i | \(-0.663519\pi\) | ||||
−0.491413 | + | 0.870927i | \(0.663519\pi\) | |||||||
\(692\) | 2.11559 | 0.0804228 | ||||||||
\(693\) | 9.18184 | + | 15.9034i | 0.348789 | + | 0.604121i | ||||
\(694\) | −7.38162 | − | 12.7853i | −0.280202 | − | 0.485325i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.87663 | −0.222753 | ||||||||
\(697\) | −8.65354 | − | 14.9884i | −0.327776 | − | 0.567725i | ||||
\(698\) | 7.41576 | − | 12.8445i | 0.280691 | − | 0.486170i | ||||
\(699\) | 10.5929 | + | 18.3475i | 0.400661 | + | 0.693965i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.6167 | + | 42.6373i | −0.929758 | + | 1.61039i | −0.146034 | + | 0.989280i | \(0.546651\pi\) |
−0.783724 | + | 0.621109i | \(0.786682\pi\) | |||||||
\(702\) | 4.83144 | 0.182351 | ||||||||
\(703\) | −36.6482 | + | 21.6760i | −1.38221 | + | 0.817525i | ||||
\(704\) | 6.39380 | 0.240975 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.4058 | − | 23.2194i | 0.504532 | − | 0.873875i | ||||
\(707\) | −2.58647 | − | 4.47990i | −0.0972744 | − | 0.168484i | ||||
\(708\) | −4.11268 | + | 7.12338i | −0.154564 | + | 0.267713i | ||||
\(709\) | −5.44796 | − | 9.43614i | −0.204602 | − | 0.354382i | 0.745404 | − | 0.666613i | \(-0.232257\pi\) |
−0.950006 | + | 0.312232i | \(0.898923\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.2825 | −0.535637 | ||||||||
\(712\) | 5.64947 | + | 9.78517i | 0.211723 | + | 0.366715i | ||||
\(713\) | 14.3206 | + | 24.8039i | 0.536309 | + | 0.928915i | ||||
\(714\) | 14.5216 | 0.543457 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.93969 | + | 8.55579i | 0.184605 | + | 0.319745i | ||||
\(717\) | 4.40925 | − | 7.63705i | 0.164667 | − | 0.285211i | ||||
\(718\) | 0.197846 | + | 0.342680i | 0.00738355 | + | 0.0127887i | ||||
\(719\) | 16.9141 | − | 29.2961i | 0.630789 | − | 1.09256i | −0.356602 | − | 0.934257i | \(-0.616065\pi\) |
0.987391 | − | 0.158302i | \(-0.0506020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.60422 | 0.283196 | ||||||||
\(722\) | −9.84402 | − | 16.2510i | −0.366356 | − | 0.604800i | ||||
\(723\) | 29.3494 | 1.09152 | ||||||||
\(724\) | −7.53974 | + | 13.0592i | −0.280212 | + | 0.485342i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −19.8597 | − | 34.3979i | −0.737061 | − | 1.27663i | ||||
\(727\) | −25.4674 | + | 44.1108i | −0.944533 | + | 1.63598i | −0.187848 | + | 0.982198i | \(0.560151\pi\) |
−0.756684 | + | 0.653780i | \(0.773182\pi\) | |||||||
\(728\) | −1.00000 | − | 1.73205i | −0.0370625 | − | 0.0641941i | ||||
\(729\) | 27.1002 | 1.00371 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.7077 | + | 28.9386i | 0.617957 | + | 1.07033i | ||||
\(732\) | −5.33085 | − | 9.23330i | −0.197034 | − | 0.341272i | ||||
\(733\) | 30.8270 | 1.13862 | 0.569310 | − | 0.822123i | \(-0.307210\pi\) | ||||
0.569310 | + | 0.822123i | \(0.307210\pi\) | |||||||
\(734\) | −6.98454 | −0.257804 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.73531 | − | 3.00565i | 0.0639645 | − | 0.110790i | ||||
\(737\) | −15.6813 | − | 27.1607i | −0.577626 | − | 1.00048i | ||||
\(738\) | −2.27506 | + | 3.94052i | −0.0837460 | + | 0.145052i | ||||
\(739\) | 18.8645 | − | 32.6742i | 0.693941 | − | 1.20194i | −0.276596 | − | 0.960986i | \(-0.589206\pi\) |
0.970536 | − | 0.240954i | \(-0.0774604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.28214 | − | 2.53272i | 0.157308 | − | 0.0930417i | ||||
\(742\) | −14.4552 | −0.530666 | ||||||||
\(743\) | −16.3990 | + | 28.4038i | −0.601619 | + | 1.04204i | 0.390957 | + | 0.920409i | \(0.372144\pi\) |
−0.992576 | + | 0.121626i | \(0.961189\pi\) | |||||||
\(744\) | 5.48484 | − | 9.50002i | 0.201084 | − | 0.348288i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.26311 | − | 2.18777i | 0.0462456 | − | 0.0800998i | ||||
\(747\) | −3.74731 | − | 6.49053i | −0.137107 | − | 0.237476i | ||||
\(748\) | 29.9877 | 1.09646 | ||||||||
\(749\) | 23.2927 | 0.851095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.19685 | − | 3.80505i | −0.0801641 | − | 0.138848i | 0.823156 | − | 0.567815i | \(-0.192211\pi\) |
−0.903320 | + | 0.428967i | \(0.858878\pi\) | |||||||
\(752\) | 7.19369 | 0.262327 | ||||||||
\(753\) | −12.5631 | −0.457824 | ||||||||
\(754\) | 1.89801 | + | 3.28744i | 0.0691213 | + | 0.119722i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.55321 | − | 11.3505i | −0.238338 | − | 0.412814i | ||||
\(757\) | −25.4884 | + | 44.1472i | −0.926391 | + | 1.60456i | −0.137082 | + | 0.990560i | \(0.543773\pi\) |
−0.789309 | + | 0.613997i | \(0.789561\pi\) | |||||||
\(758\) | −14.6538 | + | 25.3811i | −0.532248 | + | 0.921881i | ||||
\(759\) | −29.4970 | −1.07067 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5364 | 0.381945 | 0.190973 | − | 0.981595i | \(-0.438836\pi\) | ||||
0.190973 | + | 0.981595i | \(0.438836\pi\) | |||||||
\(762\) | −9.50357 | + | 16.4607i | −0.344278 | + | 0.596307i | ||||
\(763\) | 3.53389 | − | 6.12088i | 0.127935 | − | 0.221591i | ||||
\(764\) | −4.42096 | − | 7.65733i | −0.159945 | − | 0.277032i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.11717 | + | 5.39911i | 0.112628 | + | 0.195078i | ||||
\(767\) | 5.31318 | 0.191848 | ||||||||
\(768\) | −1.32927 | −0.0479657 | ||||||||
\(769\) | 22.2243 | + | 38.4936i | 0.801429 | + | 1.38812i | 0.918676 | + | 0.395013i | \(0.129260\pi\) |
−0.117246 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.6096 | −1.28245 | ||||||||
\(772\) | 18.6928 | 0.672770 | ||||||||
\(773\) | 23.1902 | + | 40.1667i | 0.834095 | + | 1.44469i | 0.894766 | + | 0.446536i | \(0.147343\pi\) |
−0.0606710 | + | 0.998158i | \(0.519324\pi\) | |||||||
\(774\) | 4.39253 | − | 7.60809i | 0.157886 | − | 0.273467i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.67500 | − | 9.82939i | 0.203721 | − | 0.352855i | ||||
\(777\) | −15.1222 | + | 26.1925i | −0.542507 | + | 0.939649i | ||||
\(778\) | −26.4365 | −0.947796 | ||||||||
\(779\) | 0.169181 | + | 16.0840i | 0.00606152 | + | 0.576268i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.03353 | + | 12.1824i | −0.251679 | + | 0.435921i | ||||
\(782\) | 8.13882 | − | 14.0969i | 0.291044 | − | 0.504102i | ||||
\(783\) | 12.4380 | + | 21.5433i | 0.444499 | + | 0.769895i | ||||
\(784\) | 0.787262 | − | 1.36358i | 0.0281165 | − | 0.0486992i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.16223 | 0.112793 | ||||||||
\(787\) | 13.6958 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(788\) | −8.15847 | − | 14.1309i | −0.290633 | − | 0.503392i | ||||
\(789\) | −9.56226 | − | 16.5623i | −0.340425 | − | 0.589634i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5862 | 0.411959 | ||||||||
\(792\) | −3.94195 | − | 6.82766i | −0.140071 | − | 0.242610i | ||||
\(793\) | −3.44346 | + | 5.96425i | −0.122281 | + | 0.211797i | ||||
\(794\) | −4.36575 | − | 7.56171i | −0.154935 | − | 0.268355i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.57452 | − | 2.72715i | 0.0558075 | − | 0.0966614i | ||||
\(797\) | −30.5751 | −1.08303 | −0.541513 | − | 0.840692i | \(-0.682148\pi\) | ||||
−0.541513 | + | 0.840692i | \(0.682148\pi\) | |||||||
\(798\) | −11.7583 | − | 6.62473i | −0.416238 | − | 0.234513i | ||||
\(799\) | 33.7392 | 1.19361 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.96610 | − | 12.0656i | 0.246135 | − | 0.426319i | ||||
\(802\) | −1.58356 | − | 2.74281i | −0.0559175 | − | 0.0968520i | ||||
\(803\) | −14.8885 | + | 25.7877i | −0.525404 | + | 0.910027i | ||||
\(804\) | 3.26012 | + | 5.64669i | 0.114976 | + | 0.199144i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.08587 | −0.249589 | ||||||||
\(807\) | 8.56693 | + | 14.8384i | 0.301570 | + | 0.522335i | ||||
\(808\) | 1.11042 | + | 1.92331i | 0.0390646 | + | 0.0676619i | ||||
\(809\) | −27.5436 | −0.968381 | −0.484191 | − | 0.874963i | \(-0.660886\pi\) | ||||
−0.484191 | + | 0.874963i | \(0.660886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.07845 | + | 15.7243i | 0.318787 | + | 0.552156i | 0.980235 | − | 0.197835i | \(-0.0633911\pi\) |
−0.661448 | + | 0.749991i | \(0.730058\pi\) | |||||||
\(812\) | 5.14879 | − | 8.91797i | 0.180687 | − | 0.312959i | ||||
\(813\) | 13.4132 | + | 23.2324i | 0.470422 | + | 0.814795i | ||||
\(814\) | −31.2280 | + | 54.0885i | −1.09454 | + | 1.89580i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.23441 | −0.218248 | ||||||||
\(817\) | −0.326643 | − | 31.0539i | −0.0114278 | − | 1.08644i | ||||
\(818\) | −17.0886 | −0.597490 | ||||||||
\(819\) | −1.23305 | + | 2.13571i | −0.0430864 | + | 0.0746278i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.2072 | + | 21.1436i | 0.426036 | + | 0.737916i | 0.996517 | − | 0.0833952i | \(-0.0265764\pi\) |
−0.570481 | + | 0.821311i | \(0.693243\pi\) | |||||||
\(822\) | −6.04264 | + | 10.4662i | −0.210761 | + | 0.365049i | ||||
\(823\) | 5.62916 | + | 9.74999i | 0.196220 | + | 0.339863i | 0.947300 | − | 0.320348i | \(-0.103800\pi\) |
−0.751080 | + | 0.660212i | \(0.770467\pi\) | |||||||
\(824\) | −3.26464 | −0.113729 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.20664 | − | 12.4823i | −0.250751 | − | 0.434313i | ||||
\(827\) | 27.1179 | + | 46.9696i | 0.942983 | + | 1.63329i | 0.759740 | + | 0.650227i | \(0.225326\pi\) |
0.183243 | + | 0.983068i | \(0.441340\pi\) | |||||||
\(828\) | −4.27947 | −0.148722 | ||||||||
\(829\) | 1.30919 | 0.0454701 | 0.0227350 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227350 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.91893 | + | 8.51984i | −0.170636 | + | 0.295550i | ||||
\(832\) | 0.429320 | + | 0.743604i | 0.0148840 | + | 0.0257798i | ||||
\(833\) | 3.69235 | − | 6.39534i | 0.127932 | − | 0.221585i | ||||
\(834\) | 14.0010 | − | 24.2505i | 0.484816 | − | 0.839725i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.2813 | − | 13.6803i | −0.839786 | − | 0.473144i | ||||
\(837\) | −46.4352 | −1.60504 | ||||||||
\(838\) | 3.90148 | − | 6.75756i | 0.134774 | − | 0.233436i | ||||
\(839\) | 14.7642 | − | 25.5723i | 0.509716 | − | 0.882854i | −0.490220 | − | 0.871598i | \(-0.663084\pi\) |
0.999937 | − | 0.0112559i | \(-0.00358294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.72756 | − | 8.18837i | 0.163019 | − | 0.282358i | ||||
\(842\) | 16.9845 | + | 29.4180i | 0.585324 | + | 1.01381i | ||||
\(843\) | −3.61782 | −0.124604 | ||||||||
\(844\) | −7.90831 | −0.272215 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.43510 | − | 7.68182i | −0.152482 | − | 0.264107i | ||||
\(847\) | 69.5999 | 2.39148 | ||||||||
\(848\) | 6.20589 | 0.213111 | ||||||||
\(849\) | 13.6543 | + | 23.6500i | 0.468616 | + | 0.811667i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.9509 | + | 29.3598i | 0.581069 | + | 1.00644i | ||||
\(852\) | 1.46226 | − | 2.53272i | 0.0500964 | − | 0.0867694i | ||||
\(853\) | −4.20847 | + | 7.28928i | −0.144095 | + | 0.249580i | −0.929035 | − | 0.369992i | \(-0.879361\pi\) |
0.784940 | + | 0.619572i | \(0.212694\pi\) | |||||||
\(854\) | 18.6824 | 0.639300 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | −6.82088 | + | 11.8141i | −0.232997 | + | 0.403562i | −0.958689 | − | 0.284458i | \(-0.908187\pi\) |
0.725692 | + | 0.688020i | \(0.241520\pi\) | |||||||
\(858\) | 3.64881 | − | 6.31993i | 0.124568 | − | 0.215759i | ||||
\(859\) | 7.70524 | + | 13.3459i | 0.262899 | + | 0.455355i | 0.967011 | − | 0.254734i | \(-0.0819879\pi\) |
−0.704112 | + | 0.710089i | \(0.748655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.71269 | + | 9.89467i | 0.194688 | + | 0.337210i | ||||
\(862\) | −18.1513 | −0.618235 | ||||||||
\(863\) | −45.4425 | −1.54688 | −0.773440 | − | 0.633869i | \(-0.781466\pi\) | ||||
−0.773440 | + | 0.633869i | \(0.781466\pi\) | |||||||
\(864\) | 2.81343 | + | 4.87300i | 0.0957147 | + | 0.165783i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.314308 | 0.0106806 | ||||||||
\(867\) | −6.64261 | −0.225595 | ||||||||
\(868\) | 9.61106 | + | 16.6468i | 0.326221 | + | 0.565031i | ||||
\(869\) | −37.0299 | + | 64.1376i | −1.25615 | + | 2.17572i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.10588 | − | 3.64749i | 0.0713549 | − | 0.123590i | ||||
\(872\) | −1.51717 | + | 2.62782i | −0.0513779 | + | 0.0889891i | ||||
\(873\) | −13.9952 | −0.473665 | ||||||||
\(874\) | −13.0210 | + | 7.70143i | −0.440443 | + | 0.260505i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.09531 | − | 5.36123i | 0.104581 | − | 0.181139i | ||||
\(877\) | 18.7041 | − | 32.3964i | 0.631591 | − | 1.09395i | −0.355635 | − | 0.934625i | \(-0.615735\pi\) |
0.987226 | − | 0.159323i | \(-0.0509312\pi\) | |||||||
\(878\) | 4.33220 | + | 7.50359i | 0.146205 | + | 0.253234i | ||||
\(879\) | −17.7666 | + | 30.7727i | −0.599254 | + | 1.03794i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.04062 | 0.102441 | 0.0512206 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512206 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(882\) | −1.94147 | −0.0653728 | ||||||||
\(883\) | 4.07515 | + | 7.05837i | 0.137140 | + | 0.237533i | 0.926413 | − | 0.376509i | \(-0.122876\pi\) |
−0.789273 | + | 0.614042i | \(0.789542\pi\) | |||||||
\(884\) | 2.01356 | + | 3.48759i | 0.0677234 | + | 0.117300i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.88838 | −0.130633 | ||||||||
\(887\) | −23.0769 | − | 39.9704i | −0.774847 | − | 1.34207i | −0.934881 | − | 0.354963i | \(-0.884494\pi\) |
0.160034 | − | 0.987112i | \(-0.448840\pi\) | |||||||
\(888\) | 6.49227 | − | 11.2449i | 0.217866 | − | 0.377356i | ||||
\(889\) | −16.6531 | − | 28.8439i | −0.558526 | − | 0.967395i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.0856 | − | 20.9329i | 0.404883 | − | 0.701278i | ||||
\(892\) | −8.32927 | −0.278884 | ||||||||
\(893\) | −27.3190 | − | 15.3918i | −0.914195 | − | 0.515067i | ||||
\(894\) | −8.45118 | −0.282650 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.16463 | − | 2.01720i | 0.0389076 | − | 0.0673900i | ||||
\(897\) | −1.98062 | − | 3.43053i | −0.0661309 | − | 0.114542i | ||||
\(898\) | 16.4687 | − | 28.5247i | 0.549569 | − | 0.951882i | ||||
\(899\) | −18.2418 | − | 31.5958i | −0.608400 | − | 1.05378i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.1064 | 0.969674 | ||||||||
\(902\) | 11.7969 | + | 20.4329i | 0.392795 | + | 0.680341i | ||||
\(903\) | −11.0297 | − | 19.1040i | −0.367045 | − | 0.635741i | ||||
\(904\) | −4.97420 | −0.165439 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.03084 | + | 3.51752i | 0.0674703 | + | 0.116862i | ||||
\(907\) | 15.6360 | − | 27.0823i | 0.519184 | − | 0.899252i | −0.480568 | − | 0.876958i | \(-0.659569\pi\) |
0.999751 | − | 0.0222948i | \(-0.00709723\pi\) | |||||||
\(908\) | −5.68402 | − | 9.84500i | −0.188631 | − | 0.326718i | ||||
\(909\) | 1.36921 | − | 2.37155i | 0.0454140 | − | 0.0786593i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3430 | 1.33662 | 0.668312 | − | 0.743881i | \(-0.267017\pi\) | ||||
0.668312 | + | 0.743881i | \(0.267017\pi\) | |||||||
\(912\) | 5.04806 | + | 2.84413i | 0.167158 | + | 0.0941785i | ||||
\(913\) | −38.8621 | −1.28615 | ||||||||
\(914\) | −0.612664 | + | 1.06116i | −0.0202651 | + | 0.0351002i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.12780 | + | 1.95341i | 0.0372635 | + | 0.0645423i | ||||
\(917\) | −2.77058 | + | 4.79879i | −0.0914927 | + | 0.158470i | ||||
\(918\) | 13.1953 | + | 22.8549i | 0.435510 | + | 0.754325i | ||||
\(919\) | 33.5859 | 1.10790 | 0.553948 | − | 0.832552i | \(-0.313121\pi\) | ||||
0.553948 | + | 0.832552i | \(0.313121\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.48106 | + | 14.6896i | 0.279460 | + | 0.484040i | ||||
\(922\) | −19.5927 | − | 33.9356i | −0.645252 | − | 1.11761i | ||||
\(923\) | −1.88910 | −0.0621805 | ||||||||
\(924\) | −19.7965 | −0.651259 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.2877 | − | 28.2111i | 0.535247 | − | 0.927075i | ||||
\(927\) | 2.01274 | + | 3.48617i | 0.0661070 | + | 0.114501i | ||||
\(928\) | −2.21048 | + | 3.82866i | −0.0725625 | + | 0.125682i | ||||
\(929\) | −4.06819 | + | 7.04632i | −0.133473 | + | 0.231182i | −0.925013 | − | 0.379935i | \(-0.875946\pi\) |
0.791540 | + | 0.611117i | \(0.209280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.90727 | + | 3.49392i | −0.193603 | + | 0.114509i | ||||
\(932\) | 15.9380 | 0.522067 | ||||||||
\(933\) | −4.63013 | + | 8.01963i | −0.151584 | + | 0.262551i | ||||
\(934\) | 8.45397 | − | 14.6427i | 0.276622 | − | 0.479124i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.529375 | − | 0.916904i | 0.0173032 | − | 0.0299699i | ||||
\(937\) | 7.30278 | + | 12.6488i | 0.238571 | + | 0.413218i | 0.960305 | − | 0.278953i | \(-0.0899875\pi\) |
−0.721733 | + | 0.692171i | \(0.756654\pi\) | |||||||
\(938\) | −11.4254 | −0.373052 | ||||||||
\(939\) | 34.7858 | 1.13519 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.92629 | + | 17.1928i | 0.323588 | + | 0.560471i | 0.981226 | − | 0.192864i | \(-0.0617775\pi\) |
−0.657638 | + | 0.753334i | \(0.728444\pi\) | |||||||
\(942\) | 10.8238 | 0.352659 | ||||||||
\(943\) | 12.8070 | 0.417054 | ||||||||
\(944\) | 3.09395 | + | 5.35888i | 0.100700 | + | 0.174417i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7767 | − | 39.4505i | −0.740536 | − | 1.28265i | ||||
\(947\) | −10.9218 | + | 18.9171i | −0.354911 | + | 0.614724i | −0.987103 | − | 0.160088i | \(-0.948822\pi\) |
0.632191 | + | 0.774812i | \(0.282156\pi\) | |||||||
\(948\) | 7.69848 | − | 13.3342i | 0.250035 | − | 0.433073i | ||||
\(949\) | −3.99883 | −0.129808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6409 | 0.377482 | ||||||||
\(952\) | 5.46226 | − | 9.46092i | 0.177033 | − | 0.306630i | ||||
\(953\) | 2.75267 | − | 4.76776i | 0.0891676 | − | 0.154443i | −0.817992 | − | 0.575230i | \(-0.804913\pi\) |
0.907160 | + | 0.420787i | \(0.138246\pi\) | |||||||
\(954\) | −3.82610 | − | 6.62700i | −0.123875 | − | 0.214557i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.31706 | − | 5.74532i | −0.107281 | − | 0.185817i | ||||
\(957\) | 37.5740 | 1.21459 | ||||||||
\(958\) | −3.65139 | −0.117971 | ||||||||
\(959\) | −10.5885 | − | 18.3398i | −0.341920 | − | 0.592223i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.1027 | 1.19686 | ||||||||
\(962\) | −8.38738 | −0.270420 | ||||||||
\(963\) | 6.16527 | + | 10.6786i | 0.198673 | + | 0.344112i | ||||
\(964\) | 11.0397 | − | 19.1213i | 0.355565 | − | 0.615856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.37289 | + | 9.30613i | −0.172870 | + | 0.299420i | ||||
\(967\) | −28.3693 | + | 49.1371i | −0.912295 | + | 1.58014i | −0.101481 | + | 0.994837i | \(0.532358\pi\) |
−0.810814 | + | 0.585304i | \(0.800975\pi\) | |||||||
\(968\) | −29.8806 | −0.960400 | ||||||||
\(969\) | 23.6760 | + | 13.3393i | 0.760583 | + | 0.428520i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.20815 | − | 12.4849i | 0.231321 | − | 0.400659i | −0.726876 | − | 0.686768i | \(-0.759029\pi\) |
0.958197 | + | 0.286109i | \(0.0923620\pi\) | |||||||
\(972\) | 5.92769 | − | 10.2671i | 0.190131 | − | 0.329316i | ||||
\(973\) | 24.5339 | + | 42.4940i | 0.786521 | + | 1.36229i | ||||
\(974\) | 6.87080 | − | 11.9006i | 0.220155 | − | 0.381319i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.02074 | −0.256738 | ||||||||
\(977\) | 31.9776 | 1.02305 | 0.511527 | − | 0.859267i | \(-0.329080\pi\) | ||||
0.511527 | + | 0.859267i | \(0.329080\pi\) | |||||||
\(978\) | 8.91274 | + | 15.4373i | 0.284998 | + | 0.493631i | ||||
\(979\) | −36.1216 | − | 62.5644i | −1.15445 | − | 1.99957i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.74151 | 0.119457 | ||||||||
\(982\) | −17.3839 | − | 30.1098i | −0.554743 | − | 0.960842i | ||||
\(983\) | −7.61623 | + | 13.1917i | −0.242920 | + | 0.420750i | −0.961545 | − | 0.274648i | \(-0.911439\pi\) |
0.718625 | + | 0.695398i | \(0.244772\pi\) | |||||||
\(984\) | −2.45257 | − | 4.24798i | −0.0781852 | − | 0.135421i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.3674 | + | 17.9569i | −0.330166 | + | 0.571864i | ||||
\(987\) | −22.2732 | −0.708963 | ||||||||
\(988\) | −0.0393660 | − | 3.74252i | −0.00125240 | − | 0.119065i | ||||
\(989\) | −24.7270 | −0.786271 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.16214 | − | 14.1372i | 0.259279 | − | 0.449084i | −0.706770 | − | 0.707443i | \(-0.749848\pi\) |
0.966049 | + | 0.258359i | \(0.0831818\pi\) | |||||||
\(992\) | −4.12622 | − | 7.14682i | −0.131008 | − | 0.226912i | ||||
\(993\) | −6.21258 | + | 10.7605i | −0.197150 | + | 0.341474i | ||||
\(994\) | 2.56232 | + | 4.43807i | 0.0812718 | + | 0.140767i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.07940 | 0.256006 | ||||||||
\(997\) | 11.1218 | + | 19.2635i | 0.352230 | + | 0.610081i | 0.986640 | − | 0.162916i | \(-0.0520901\pi\) |
−0.634410 | + | 0.772997i | \(0.718757\pi\) | |||||||
\(998\) | 8.31410 | + | 14.4005i | 0.263178 | + | 0.455838i | ||||
\(999\) | −54.9643 | −1.73899 |
(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 | 950.2.e.o.201.4 | 10 | ||
5.2 | odd | 4 | 190.2.i.a.49.7 | yes | 20 | ||
5.3 | odd | 4 | 190.2.i.a.49.4 | ✓ | 20 | ||
5.4 | even | 2 | 950.2.e.n.201.2 | 10 | |||
15.2 | even | 4 | 1710.2.t.d.1189.1 | 20 | |||
15.8 | even | 4 | 1710.2.t.d.1189.9 | 20 | |||
19.7 | even | 3 | inner | 950.2.e.o.501.4 | 10 | ||
95.7 | odd | 12 | 190.2.i.a.159.4 | yes | 20 | ||
95.64 | even | 6 | 950.2.e.n.501.2 | 10 | |||
95.83 | odd | 12 | 190.2.i.a.159.7 | yes | 20 | ||
285.83 | even | 12 | 1710.2.t.d.919.1 | 20 | |||
285.197 | even | 12 | 1710.2.t.d.919.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.i.a.49.4 | ✓ | 20 | 5.3 | odd | 4 | ||
190.2.i.a.49.7 | yes | 20 | 5.2 | odd | 4 | ||
190.2.i.a.159.4 | yes | 20 | 95.7 | odd | 12 | ||
190.2.i.a.159.7 | yes | 20 | 95.83 | odd | 12 | ||
950.2.e.n.201.2 | 10 | 5.4 | even | 2 | |||
950.2.e.n.501.2 | 10 | 95.64 | even | 6 | |||
950.2.e.o.201.4 | 10 | 1.1 | even | 1 | trivial | ||
950.2.e.o.501.4 | 10 | 19.7 | even | 3 | inner | ||
1710.2.t.d.919.1 | 20 | 285.83 | even | 12 | |||
1710.2.t.d.919.9 | 20 | 285.197 | even | 12 | |||
1710.2.t.d.1189.1 | 20 | 15.2 | even | 4 | |||
1710.2.t.d.1189.9 | 20 | 15.8 | even | 4 |