Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(827,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.827");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.h (of order \(2\), degree \(1\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 827.7 | ||
Character | \(\chi\) | \(=\) | 966.827 |
Dual form | 966.2.h.a.827.19 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.656415 | + | 1.60285i | 0.378981 | + | 0.925404i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.252332 | −0.112846 | −0.0564231 | − | 0.998407i | \(-0.517970\pi\) | ||||
−0.0564231 | + | 0.998407i | \(0.517970\pi\) | |||||||
\(6\) | 1.60285 | − | 0.656415i | 0.654360 | − | 0.267980i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.13824 | + | 2.10426i | −0.712747 | + | 0.701422i | ||||
\(10\) | 0.252332i | 0.0797944i | ||||||||
\(11\) | 5.50149 | 1.65876 | 0.829381 | − | 0.558684i | \(-0.188693\pi\) | ||||
0.829381 | + | 0.558684i | \(0.188693\pi\) | |||||||
\(12\) | −0.656415 | − | 1.60285i | −0.189491 | − | 0.462702i | ||||
\(13\) | −3.10049 | −0.859921 | −0.429961 | − | 0.902848i | \(-0.641473\pi\) | ||||
−0.429961 | + | 0.902848i | \(0.641473\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.165634 | − | 0.404450i | −0.0427666 | − | 0.104428i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.471124 | −0.114264 | −0.0571321 | − | 0.998367i | \(-0.518196\pi\) | ||||
−0.0571321 | + | 0.998367i | \(0.518196\pi\) | |||||||
\(18\) | 2.10426 | + | 2.13824i | 0.495980 | + | 0.503988i | ||||
\(19\) | 2.38906i | 0.548089i | 0.961717 | + | 0.274044i | \(0.0883615\pi\) | ||||
−0.961717 | + | 0.274044i | \(0.911638\pi\) | |||||||
\(20\) | 0.252332 | 0.0564231 | ||||||||
\(21\) | −1.60285 | + | 0.656415i | −0.349770 | + | 0.143241i | ||||
\(22\) | − | 5.50149i | − | 1.17292i | ||||||
\(23\) | 3.43621 | + | 3.34552i | 0.716499 | + | 0.697589i | ||||
\(24\) | −1.60285 | + | 0.656415i | −0.327180 | + | 0.133990i | ||||
\(25\) | −4.93633 | −0.987266 | ||||||||
\(26\) | 3.10049i | 0.608056i | ||||||||
\(27\) | −4.77639 | − | 2.04600i | −0.919216 | − | 0.393753i | ||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | 6.08436i | 1.12984i | 0.825147 | + | 0.564918i | \(0.191092\pi\) | ||||
−0.825147 | + | 0.564918i | \(0.808908\pi\) | |||||||
\(30\) | −0.404450 | + | 0.165634i | −0.0738421 | + | 0.0302406i | ||||
\(31\) | 1.40614 | 0.252550 | 0.126275 | − | 0.991995i | \(-0.459698\pi\) | ||||
0.126275 | + | 0.991995i | \(0.459698\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 3.61126 | + | 8.81805i | 0.628639 | + | 1.53503i | ||||
\(34\) | 0.471124i | 0.0807970i | ||||||||
\(35\) | − | 0.252332i | − | 0.0426519i | ||||||
\(36\) | 2.13824 | − | 2.10426i | 0.356373 | − | 0.350711i | ||||
\(37\) | 5.87175i | 0.965310i | 0.875811 | + | 0.482655i | \(0.160328\pi\) | ||||
−0.875811 | + | 0.482655i | \(0.839672\pi\) | |||||||
\(38\) | 2.38906 | 0.387557 | ||||||||
\(39\) | −2.03521 | − | 4.96961i | −0.325894 | − | 0.795775i | ||||
\(40\) | − | 0.252332i | − | 0.0398972i | ||||||
\(41\) | 4.64674i | 0.725699i | 0.931848 | + | 0.362850i | \(0.118196\pi\) | ||||
−0.931848 | + | 0.362850i | \(0.881804\pi\) | |||||||
\(42\) | 0.656415 | + | 1.60285i | 0.101287 | + | 0.247325i | ||||
\(43\) | 5.09258i | 0.776611i | 0.921531 | + | 0.388305i | \(0.126939\pi\) | ||||
−0.921531 | + | 0.388305i | \(0.873061\pi\) | |||||||
\(44\) | −5.50149 | −0.829381 | ||||||||
\(45\) | 0.539546 | − | 0.530973i | 0.0804308 | − | 0.0791528i | ||||
\(46\) | 3.34552 | − | 3.43621i | 0.493270 | − | 0.506641i | ||||
\(47\) | − | 4.02078i | − | 0.586492i | −0.956037 | − | 0.293246i | \(-0.905265\pi\) | ||
0.956037 | − | 0.293246i | \(-0.0947355\pi\) | |||||||
\(48\) | 0.656415 | + | 1.60285i | 0.0947453 | + | 0.231351i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.93633i | 0.698102i | ||||||||
\(51\) | −0.309252 | − | 0.755139i | −0.0433040 | − | 0.105741i | ||||
\(52\) | 3.10049 | 0.429961 | ||||||||
\(53\) | 1.95854 | 0.269026 | 0.134513 | − | 0.990912i | \(-0.457053\pi\) | ||||
0.134513 | + | 0.990912i | \(0.457053\pi\) | |||||||
\(54\) | −2.04600 | + | 4.77639i | −0.278426 | + | 0.649984i | ||||
\(55\) | −1.38820 | −0.187185 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.82930 | + | 1.56822i | −0.507204 | + | 0.207715i | ||||
\(58\) | 6.08436 | 0.798915 | ||||||||
\(59\) | − | 3.53472i | − | 0.460181i | −0.973169 | − | 0.230091i | \(-0.926098\pi\) | ||
0.973169 | − | 0.230091i | \(-0.0739023\pi\) | |||||||
\(60\) | 0.165634 | + | 0.404450i | 0.0213833 | + | 0.0522142i | ||||
\(61\) | − | 2.10168i | − | 0.269092i | −0.990907 | − | 0.134546i | \(-0.957042\pi\) | ||
0.990907 | − | 0.134546i | \(-0.0429577\pi\) | |||||||
\(62\) | − | 1.40614i | − | 0.178580i | ||||||
\(63\) | −2.10426 | − | 2.13824i | −0.265112 | − | 0.269393i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.782353 | 0.0970389 | ||||||||
\(66\) | 8.81805 | − | 3.61126i | 1.08543 | − | 0.444515i | ||||
\(67\) | − | 5.88882i | − | 0.719434i | −0.933061 | − | 0.359717i | \(-0.882873\pi\) | ||
0.933061 | − | 0.359717i | \(-0.117127\pi\) | |||||||
\(68\) | 0.471124 | 0.0571321 | ||||||||
\(69\) | −3.10678 | + | 7.70376i | −0.374012 | + | 0.927424i | ||||
\(70\) | −0.252332 | −0.0301594 | ||||||||
\(71\) | 15.2386i | 1.80849i | 0.427019 | + | 0.904243i | \(0.359564\pi\) | ||||
−0.427019 | + | 0.904243i | \(0.640436\pi\) | |||||||
\(72\) | −2.10426 | − | 2.13824i | −0.247990 | − | 0.251994i | ||||
\(73\) | −3.34062 | −0.390990 | −0.195495 | − | 0.980705i | \(-0.562631\pi\) | ||||
−0.195495 | + | 0.980705i | \(0.562631\pi\) | |||||||
\(74\) | 5.87175 | 0.682577 | ||||||||
\(75\) | −3.24028 | − | 7.91218i | −0.374155 | − | 0.913620i | ||||
\(76\) | − | 2.38906i | − | 0.274044i | ||||||
\(77\) | 5.50149i | 0.626953i | ||||||||
\(78\) | −4.96961 | + | 2.03521i | −0.562698 | + | 0.230442i | ||||
\(79\) | 13.9496i | 1.56945i | 0.619845 | + | 0.784725i | \(0.287196\pi\) | ||||
−0.619845 | + | 0.784725i | \(0.712804\pi\) | |||||||
\(80\) | −0.252332 | −0.0282116 | ||||||||
\(81\) | 0.144138 | − | 8.99885i | 0.0160154 | − | 0.999872i | ||||
\(82\) | 4.64674 | 0.513147 | ||||||||
\(83\) | 9.18343 | 1.00801 | 0.504006 | − | 0.863700i | \(-0.331859\pi\) | ||||
0.504006 | + | 0.863700i | \(0.331859\pi\) | |||||||
\(84\) | 1.60285 | − | 0.656415i | 0.174885 | − | 0.0716207i | ||||
\(85\) | 0.118880 | 0.0128943 | ||||||||
\(86\) | 5.09258 | 0.549147 | ||||||||
\(87\) | −9.75230 | + | 3.99386i | −1.04556 | + | 0.428187i | ||||
\(88\) | 5.50149i | 0.586461i | ||||||||
\(89\) | 12.9856 | 1.37647 | 0.688235 | − | 0.725488i | \(-0.258386\pi\) | ||||
0.688235 | + | 0.725488i | \(0.258386\pi\) | |||||||
\(90\) | −0.530973 | − | 0.539546i | −0.0559695 | − | 0.0568732i | ||||
\(91\) | − | 3.10049i | − | 0.325020i | ||||||
\(92\) | −3.43621 | − | 3.34552i | −0.358249 | − | 0.348794i | ||||
\(93\) | 0.923009 | + | 2.25382i | 0.0957116 | + | 0.233711i | ||||
\(94\) | −4.02078 | −0.414712 | ||||||||
\(95\) | − | 0.602837i | − | 0.0618498i | ||||||
\(96\) | 1.60285 | − | 0.656415i | 0.163590 | − | 0.0669950i | ||||
\(97\) | − | 17.8515i | − | 1.81254i | −0.422695 | − | 0.906272i | \(-0.638916\pi\) | ||
0.422695 | − | 0.906272i | \(-0.361084\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −11.7635 | + | 11.5766i | −1.18228 | + | 1.16349i | ||||
\(100\) | 4.93633 | 0.493633 | ||||||||
\(101\) | 0.803060i | 0.0799074i | 0.999202 | + | 0.0399537i | \(0.0127210\pi\) | ||||
−0.999202 | + | 0.0399537i | \(0.987279\pi\) | |||||||
\(102\) | −0.755139 | + | 0.309252i | −0.0747699 | + | 0.0306205i | ||||
\(103\) | − | 11.9640i | − | 1.17885i | −0.807823 | − | 0.589425i | \(-0.799354\pi\) | ||
0.807823 | − | 0.589425i | \(-0.200646\pi\) | |||||||
\(104\) | − | 3.10049i | − | 0.304028i | ||||||
\(105\) | 0.404450 | − | 0.165634i | 0.0394702 | − | 0.0161643i | ||||
\(106\) | − | 1.95854i | − | 0.190230i | ||||||
\(107\) | −11.6433 | −1.12560 | −0.562800 | − | 0.826593i | \(-0.690276\pi\) | ||||
−0.562800 | + | 0.826593i | \(0.690276\pi\) | |||||||
\(108\) | 4.77639 | + | 2.04600i | 0.459608 | + | 0.196877i | ||||
\(109\) | − | 1.11725i | − | 0.107013i | −0.998567 | − | 0.0535066i | \(-0.982960\pi\) | ||
0.998567 | − | 0.0535066i | \(-0.0170398\pi\) | |||||||
\(110\) | 1.38820i | 0.132360i | ||||||||
\(111\) | −9.41152 | + | 3.85430i | −0.893302 | + | 0.365834i | ||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −10.4257 | −0.980770 | −0.490385 | − | 0.871506i | \(-0.663144\pi\) | ||||
−0.490385 | + | 0.871506i | \(0.663144\pi\) | |||||||
\(114\) | 1.56822 | + | 3.82930i | 0.146877 | + | 0.358647i | ||||
\(115\) | −0.867065 | − | 0.844181i | −0.0808542 | − | 0.0787203i | ||||
\(116\) | − | 6.08436i | − | 0.564918i | ||||||
\(117\) | 6.62959 | − | 6.52425i | 0.612906 | − | 0.603167i | ||||
\(118\) | −3.53472 | −0.325397 | ||||||||
\(119\) | − | 0.471124i | − | 0.0431878i | ||||||
\(120\) | 0.404450 | − | 0.165634i | 0.0369210 | − | 0.0151203i | ||||
\(121\) | 19.2664 | 1.75149 | ||||||||
\(122\) | −2.10168 | −0.190277 | ||||||||
\(123\) | −7.44802 | + | 3.05019i | −0.671565 | + | 0.275026i | ||||
\(124\) | −1.40614 | −0.126275 | ||||||||
\(125\) | 2.50725 | 0.224256 | ||||||||
\(126\) | −2.13824 | + | 2.10426i | −0.190490 | + | 0.187463i | ||||
\(127\) | 0.430922 | 0.0382382 | 0.0191191 | − | 0.999817i | \(-0.493914\pi\) | ||||
0.0191191 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −8.16263 | + | 3.34284i | −0.718679 | + | 0.294321i | ||||
\(130\) | − | 0.782353i | − | 0.0686169i | ||||||
\(131\) | − | 11.1468i | − | 0.973904i | −0.873429 | − | 0.486952i | \(-0.838109\pi\) | ||
0.873429 | − | 0.486952i | \(-0.161891\pi\) | |||||||
\(132\) | −3.61126 | − | 8.81805i | −0.314320 | − | 0.767513i | ||||
\(133\) | −2.38906 | −0.207158 | ||||||||
\(134\) | −5.88882 | −0.508717 | ||||||||
\(135\) | 1.20524 | + | 0.516272i | 0.103730 | + | 0.0444336i | ||||
\(136\) | − | 0.471124i | − | 0.0403985i | ||||||
\(137\) | 13.0016 | 1.11080 | 0.555400 | − | 0.831583i | \(-0.312565\pi\) | ||||
0.555400 | + | 0.831583i | \(0.312565\pi\) | |||||||
\(138\) | 7.70376 | + | 3.10678i | 0.655788 | + | 0.264466i | ||||
\(139\) | 18.5932 | 1.57705 | 0.788526 | − | 0.615001i | \(-0.210844\pi\) | ||||
0.788526 | + | 0.615001i | \(0.210844\pi\) | |||||||
\(140\) | 0.252332i | 0.0213259i | ||||||||
\(141\) | 6.44470 | − | 2.63930i | 0.542742 | − | 0.222269i | ||||
\(142\) | 15.2386 | 1.27879 | ||||||||
\(143\) | −17.0573 | −1.42640 | ||||||||
\(144\) | −2.13824 | + | 2.10426i | −0.178187 | + | 0.175355i | ||||
\(145\) | − | 1.53528i | − | 0.127498i | ||||||
\(146\) | 3.34062i | 0.276472i | ||||||||
\(147\) | −0.656415 | − | 1.60285i | −0.0541402 | − | 0.132201i | ||||
\(148\) | − | 5.87175i | − | 0.482655i | ||||||
\(149\) | 11.4109 | 0.934821 | 0.467410 | − | 0.884040i | \(-0.345187\pi\) | ||||
0.467410 | + | 0.884040i | \(0.345187\pi\) | |||||||
\(150\) | −7.91218 | + | 3.24028i | −0.646027 | + | 0.264568i | ||||
\(151\) | 2.55551 | 0.207964 | 0.103982 | − | 0.994579i | \(-0.466841\pi\) | ||||
0.103982 | + | 0.994579i | \(0.466841\pi\) | |||||||
\(152\) | −2.38906 | −0.193779 | ||||||||
\(153\) | 1.00738 | − | 0.991369i | 0.0814415 | − | 0.0801474i | ||||
\(154\) | 5.50149 | 0.443323 | ||||||||
\(155\) | −0.354813 | −0.0284993 | ||||||||
\(156\) | 2.03521 | + | 4.96961i | 0.162947 | + | 0.397887i | ||||
\(157\) | − | 12.5401i | − | 1.00081i | −0.865792 | − | 0.500403i | \(-0.833185\pi\) | ||
0.865792 | − | 0.500403i | \(-0.166815\pi\) | |||||||
\(158\) | 13.9496 | 1.10977 | ||||||||
\(159\) | 1.28562 | + | 3.13924i | 0.101956 | + | 0.248958i | ||||
\(160\) | 0.252332i | 0.0199486i | ||||||||
\(161\) | −3.34552 | + | 3.43621i | −0.263664 | + | 0.270811i | ||||
\(162\) | −8.99885 | − | 0.144138i | −0.707016 | − | 0.0113246i | ||||
\(163\) | 8.16445 | 0.639489 | 0.319745 | − | 0.947504i | \(-0.396403\pi\) | ||||
0.319745 | + | 0.947504i | \(0.396403\pi\) | |||||||
\(164\) | − | 4.64674i | − | 0.362850i | ||||||
\(165\) | −0.911236 | − | 2.22508i | −0.0709396 | − | 0.173222i | ||||
\(166\) | − | 9.18343i | − | 0.712772i | ||||||
\(167\) | − | 18.6643i | − | 1.44429i | −0.691743 | − | 0.722144i | \(-0.743157\pi\) | ||
0.691743 | − | 0.722144i | \(-0.256843\pi\) | |||||||
\(168\) | −0.656415 | − | 1.60285i | −0.0506435 | − | 0.123662i | ||||
\(169\) | −3.38696 | −0.260535 | ||||||||
\(170\) | − | 0.118880i | − | 0.00911764i | ||||||
\(171\) | −5.02722 | − | 5.10839i | −0.384441 | − | 0.390648i | ||||
\(172\) | − | 5.09258i | − | 0.388305i | ||||||
\(173\) | 3.66045i | 0.278299i | 0.990271 | + | 0.139149i | \(0.0444368\pi\) | ||||
−0.990271 | + | 0.139149i | \(0.955563\pi\) | |||||||
\(174\) | 3.99386 | + | 9.75230i | 0.302774 | + | 0.739320i | ||||
\(175\) | − | 4.93633i | − | 0.373151i | ||||||
\(176\) | 5.50149 | 0.414690 | ||||||||
\(177\) | 5.66562 | − | 2.32024i | 0.425854 | − | 0.174400i | ||||
\(178\) | − | 12.9856i | − | 0.973312i | ||||||
\(179\) | − | 17.2447i | − | 1.28893i | −0.764633 | − | 0.644466i | \(-0.777080\pi\) | ||
0.764633 | − | 0.644466i | \(-0.222920\pi\) | |||||||
\(180\) | −0.539546 | + | 0.530973i | −0.0402154 | + | 0.0395764i | ||||
\(181\) | − | 5.76109i | − | 0.428219i | −0.976810 | − | 0.214109i | \(-0.931315\pi\) | ||
0.976810 | − | 0.214109i | \(-0.0686849\pi\) | |||||||
\(182\) | −3.10049 | −0.229824 | ||||||||
\(183\) | 3.36867 | − | 1.37957i | 0.249019 | − | 0.101981i | ||||
\(184\) | −3.34552 | + | 3.43621i | −0.246635 | + | 0.253321i | ||||
\(185\) | − | 1.48163i | − | 0.108932i | ||||||
\(186\) | 2.25382 | − | 0.923009i | 0.165258 | − | 0.0676783i | ||||
\(187\) | −2.59188 | −0.189537 | ||||||||
\(188\) | 4.02078i | 0.293246i | ||||||||
\(189\) | 2.04600 | − | 4.77639i | 0.148825 | − | 0.347431i | ||||
\(190\) | −0.602837 | −0.0437344 | ||||||||
\(191\) | −17.4889 | −1.26545 | −0.632725 | − | 0.774376i | \(-0.718064\pi\) | ||||
−0.632725 | + | 0.774376i | \(0.718064\pi\) | |||||||
\(192\) | −0.656415 | − | 1.60285i | −0.0473726 | − | 0.115676i | ||||
\(193\) | 20.4201 | 1.46987 | 0.734934 | − | 0.678139i | \(-0.237213\pi\) | ||||
0.734934 | + | 0.678139i | \(0.237213\pi\) | |||||||
\(194\) | −17.8515 | −1.28166 | ||||||||
\(195\) | 0.513548 | + | 1.25399i | 0.0367759 | + | 0.0898003i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 8.17726i | − | 0.582606i | −0.956631 | − | 0.291303i | \(-0.905911\pi\) | ||
0.956631 | − | 0.291303i | \(-0.0940887\pi\) | |||||||
\(198\) | 11.5766 | + | 11.7635i | 0.822713 | + | 0.835996i | ||||
\(199\) | − | 0.0625989i | − | 0.00443752i | −0.999998 | − | 0.00221876i | \(-0.999294\pi\) | ||
0.999998 | − | 0.00221876i | \(-0.000706253\pi\) | |||||||
\(200\) | − | 4.93633i | − | 0.349051i | ||||||
\(201\) | 9.43888 | − | 3.86551i | 0.665768 | − | 0.272652i | ||||
\(202\) | 0.803060 | 0.0565031 | ||||||||
\(203\) | −6.08436 | −0.427038 | ||||||||
\(204\) | 0.309252 | + | 0.755139i | 0.0216520 | + | 0.0528703i | ||||
\(205\) | − | 1.17252i | − | 0.0818925i | ||||||
\(206\) | −11.9640 | −0.833573 | ||||||||
\(207\) | −14.3873 | + | 0.0771712i | −0.999986 | + | 0.00536377i | ||||
\(208\) | −3.10049 | −0.214980 | ||||||||
\(209\) | 13.1434i | 0.909149i | ||||||||
\(210\) | −0.165634 | − | 0.404450i | −0.0114299 | − | 0.0279097i | ||||
\(211\) | 2.20409 | 0.151736 | 0.0758680 | − | 0.997118i | \(-0.475827\pi\) | ||||
0.0758680 | + | 0.997118i | \(0.475827\pi\) | |||||||
\(212\) | −1.95854 | −0.134513 | ||||||||
\(213\) | −24.4251 | + | 10.0028i | −1.67358 | + | 0.685382i | ||||
\(214\) | 11.6433i | 0.795920i | ||||||||
\(215\) | − | 1.28502i | − | 0.0876377i | ||||||
\(216\) | 2.04600 | − | 4.77639i | 0.139213 | − | 0.324992i | ||||
\(217\) | 1.40614i | 0.0954548i | ||||||||
\(218\) | −1.11725 | −0.0756698 | ||||||||
\(219\) | −2.19283 | − | 5.35451i | −0.148178 | − | 0.361824i | ||||
\(220\) | 1.38820 | 0.0935925 | ||||||||
\(221\) | 1.46071 | 0.0982583 | ||||||||
\(222\) | 3.85430 | + | 9.41152i | 0.258684 | + | 0.631660i | ||||
\(223\) | −25.4713 | −1.70569 | −0.852843 | − | 0.522168i | \(-0.825124\pi\) | ||||
−0.852843 | + | 0.522168i | \(0.825124\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 10.5551 | − | 10.3873i | 0.703670 | − | 0.692490i | ||||
\(226\) | 10.4257i | 0.693509i | ||||||||
\(227\) | 17.5961 | 1.16790 | 0.583949 | − | 0.811791i | \(-0.301507\pi\) | ||||
0.583949 | + | 0.811791i | \(0.301507\pi\) | |||||||
\(228\) | 3.82930 | − | 1.56822i | 0.253602 | − | 0.103858i | ||||
\(229\) | 8.59906i | 0.568242i | 0.958788 | + | 0.284121i | \(0.0917017\pi\) | ||||
−0.958788 | + | 0.284121i | \(0.908298\pi\) | |||||||
\(230\) | −0.844181 | + | 0.867065i | −0.0556636 | + | 0.0571726i | ||||
\(231\) | −8.81805 | + | 3.61126i | −0.580185 | + | 0.237603i | ||||
\(232\) | −6.08436 | −0.399458 | ||||||||
\(233\) | 2.93410i | 0.192219i | 0.995371 | + | 0.0961097i | \(0.0306400\pi\) | ||||
−0.995371 | + | 0.0961097i | \(0.969360\pi\) | |||||||
\(234\) | −6.52425 | − | 6.62959i | −0.426504 | − | 0.433390i | ||||
\(235\) | 1.01457i | 0.0661834i | ||||||||
\(236\) | 3.53472i | 0.230091i | ||||||||
\(237\) | −22.3590 | + | 9.15670i | −1.45238 | + | 0.594792i | ||||
\(238\) | −0.471124 | −0.0305384 | ||||||||
\(239\) | 1.13350i | 0.0733199i | 0.999328 | + | 0.0366599i | \(0.0116718\pi\) | ||||
−0.999328 | + | 0.0366599i | \(0.988328\pi\) | |||||||
\(240\) | −0.165634 | − | 0.404450i | −0.0106917 | − | 0.0261071i | ||||
\(241\) | − | 21.7858i | − | 1.40335i | −0.712499 | − | 0.701673i | \(-0.752437\pi\) | ||
0.712499 | − | 0.701673i | \(-0.247563\pi\) | |||||||
\(242\) | − | 19.2664i | − | 1.23849i | ||||||
\(243\) | 14.5184 | − | 5.67594i | 0.931355 | − | 0.364112i | ||||
\(244\) | 2.10168i | 0.134546i | ||||||||
\(245\) | 0.252332 | 0.0161209 | ||||||||
\(246\) | 3.05019 | + | 7.44802i | 0.194473 | + | 0.474868i | ||||
\(247\) | − | 7.40727i | − | 0.471313i | ||||||
\(248\) | 1.40614i | 0.0892898i | ||||||||
\(249\) | 6.02814 | + | 14.7196i | 0.382018 | + | 0.932819i | ||||
\(250\) | − | 2.50725i | − | 0.158573i | ||||||
\(251\) | −24.3418 | −1.53644 | −0.768220 | − | 0.640186i | \(-0.778857\pi\) | ||||
−0.768220 | + | 0.640186i | \(0.778857\pi\) | |||||||
\(252\) | 2.10426 | + | 2.13824i | 0.132556 | + | 0.134696i | ||||
\(253\) | 18.9043 | + | 18.4053i | 1.18850 | + | 1.15713i | ||||
\(254\) | − | 0.430922i | − | 0.0270385i | ||||||
\(255\) | 0.0780343 | + | 0.190546i | 0.00488670 | + | 0.0119324i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.49482i | 0.405135i | 0.979268 | + | 0.202568i | \(0.0649286\pi\) | ||||
−0.979268 | + | 0.202568i | \(0.935071\pi\) | |||||||
\(258\) | 3.34284 | + | 8.16263i | 0.208116 | + | 0.508183i | ||||
\(259\) | −5.87175 | −0.364853 | ||||||||
\(260\) | −0.782353 | −0.0485195 | ||||||||
\(261\) | −12.8031 | − | 13.0098i | −0.792492 | − | 0.805287i | ||||
\(262\) | −11.1468 | −0.688654 | ||||||||
\(263\) | 10.0922 | 0.622309 | 0.311155 | − | 0.950359i | \(-0.399284\pi\) | ||||
0.311155 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(264\) | −8.81805 | + | 3.61126i | −0.542713 | + | 0.222258i | ||||
\(265\) | −0.494203 | −0.0303586 | ||||||||
\(266\) | 2.38906i | 0.146483i | ||||||||
\(267\) | 8.52394 | + | 20.8139i | 0.521656 | + | 1.27379i | ||||
\(268\) | 5.88882i | 0.359717i | ||||||||
\(269\) | 15.0560i | 0.917983i | 0.888441 | + | 0.458991i | \(0.151789\pi\) | ||||
−0.888441 | + | 0.458991i | \(0.848211\pi\) | |||||||
\(270\) | 0.516272 | − | 1.20524i | 0.0314193 | − | 0.0733483i | ||||
\(271\) | −21.4792 | −1.30477 | −0.652386 | − | 0.757887i | \(-0.726232\pi\) | ||||
−0.652386 | + | 0.757887i | \(0.726232\pi\) | |||||||
\(272\) | −0.471124 | −0.0285661 | ||||||||
\(273\) | 4.96961 | − | 2.03521i | 0.300775 | − | 0.123176i | ||||
\(274\) | − | 13.0016i | − | 0.785454i | ||||||
\(275\) | −27.1572 | −1.63764 | ||||||||
\(276\) | 3.10678 | − | 7.70376i | 0.187006 | − | 0.463712i | ||||
\(277\) | 11.6898 | 0.702374 | 0.351187 | − | 0.936305i | \(-0.385778\pi\) | ||||
0.351187 | + | 0.936305i | \(0.385778\pi\) | |||||||
\(278\) | − | 18.5932i | − | 1.11514i | ||||||
\(279\) | −3.00666 | + | 2.95889i | −0.180004 | + | 0.177144i | ||||
\(280\) | 0.252332 | 0.0150797 | ||||||||
\(281\) | −17.4066 | −1.03839 | −0.519194 | − | 0.854656i | \(-0.673768\pi\) | ||||
−0.519194 | + | 0.854656i | \(0.673768\pi\) | |||||||
\(282\) | −2.63930 | − | 6.44470i | −0.157168 | − | 0.383777i | ||||
\(283\) | 20.2774i | 1.20537i | 0.797980 | + | 0.602683i | \(0.205902\pi\) | ||||
−0.797980 | + | 0.602683i | \(0.794098\pi\) | |||||||
\(284\) | − | 15.2386i | − | 0.904243i | ||||||
\(285\) | 0.966256 | − | 0.395711i | 0.0572361 | − | 0.0234399i | ||||
\(286\) | 17.0573i | 1.00862i | ||||||||
\(287\) | −4.64674 | −0.274289 | ||||||||
\(288\) | 2.10426 | + | 2.13824i | 0.123995 | + | 0.125997i | ||||
\(289\) | −16.7780 | −0.986944 | ||||||||
\(290\) | −1.53528 | −0.0901546 | ||||||||
\(291\) | 28.6132 | − | 11.7180i | 1.67734 | − | 0.686920i | ||||
\(292\) | 3.34062 | 0.195495 | ||||||||
\(293\) | 16.3179 | 0.953301 | 0.476650 | − | 0.879093i | \(-0.341851\pi\) | ||||
0.476650 | + | 0.879093i | \(0.341851\pi\) | |||||||
\(294\) | −1.60285 | + | 0.656415i | −0.0934800 | + | 0.0382829i | ||||
\(295\) | 0.891923i | 0.0519298i | ||||||||
\(296\) | −5.87175 | −0.341289 | ||||||||
\(297\) | −26.2772 | − | 11.2561i | −1.52476 | − | 0.653143i | ||||
\(298\) | − | 11.4109i | − | 0.661018i | ||||||
\(299\) | −10.6539 | − | 10.3727i | −0.616132 | − | 0.599871i | ||||
\(300\) | 3.24028 | + | 7.91218i | 0.187078 | + | 0.456810i | ||||
\(301\) | −5.09258 | −0.293531 | ||||||||
\(302\) | − | 2.55551i | − | 0.147053i | ||||||
\(303\) | −1.28718 | + | 0.527140i | −0.0739467 | + | 0.0302834i | ||||
\(304\) | 2.38906i | 0.137022i | ||||||||
\(305\) | 0.530321i | 0.0303661i | ||||||||
\(306\) | −0.991369 | − | 1.00738i | −0.0566728 | − | 0.0575878i | ||||
\(307\) | 15.9791 | 0.911973 | 0.455987 | − | 0.889987i | \(-0.349286\pi\) | ||||
0.455987 | + | 0.889987i | \(0.349286\pi\) | |||||||
\(308\) | − | 5.50149i | − | 0.313476i | ||||||
\(309\) | 19.1765 | − | 7.85336i | 1.09091 | − | 0.446762i | ||||
\(310\) | 0.354813i | 0.0201520i | ||||||||
\(311\) | 20.1658i | 1.14350i | 0.820428 | + | 0.571750i | \(0.193735\pi\) | ||||
−0.820428 | + | 0.571750i | \(0.806265\pi\) | |||||||
\(312\) | 4.96961 | − | 2.03521i | 0.281349 | − | 0.115221i | ||||
\(313\) | − | 0.269860i | − | 0.0152534i | −0.999971 | − | 0.00762669i | \(-0.997572\pi\) | ||
0.999971 | − | 0.00762669i | \(-0.00242767\pi\) | |||||||
\(314\) | −12.5401 | −0.707677 | ||||||||
\(315\) | 0.530973 | + | 0.539546i | 0.0299170 | + | 0.0304000i | ||||
\(316\) | − | 13.9496i | − | 0.784725i | ||||||
\(317\) | − | 8.37234i | − | 0.470237i | −0.971967 | − | 0.235119i | \(-0.924452\pi\) | ||
0.971967 | − | 0.235119i | \(-0.0755479\pi\) | |||||||
\(318\) | 3.13924 | − | 1.28562i | 0.176040 | − | 0.0720937i | ||||
\(319\) | 33.4730i | 1.87413i | ||||||||
\(320\) | 0.252332 | 0.0141058 | ||||||||
\(321\) | −7.64284 | − | 18.6624i | −0.426581 | − | 1.04164i | ||||
\(322\) | 3.43621 | + | 3.34552i | 0.191492 | + | 0.186438i | ||||
\(323\) | − | 1.12554i | − | 0.0626269i | ||||||
\(324\) | −0.144138 | + | 8.99885i | −0.00800768 | + | 0.499936i | ||||
\(325\) | 15.3050 | 0.848971 | ||||||||
\(326\) | − | 8.16445i | − | 0.452187i | ||||||
\(327\) | 1.79078 | − | 0.733380i | 0.0990305 | − | 0.0405560i | ||||
\(328\) | −4.64674 | −0.256573 | ||||||||
\(329\) | 4.02078 | 0.221673 | ||||||||
\(330\) | −2.22508 | + | 0.911236i | −0.122486 | + | 0.0501619i | ||||
\(331\) | −7.84024 | −0.430939 | −0.215469 | − | 0.976511i | \(-0.569128\pi\) | ||||
−0.215469 | + | 0.976511i | \(0.569128\pi\) | |||||||
\(332\) | −9.18343 | −0.504006 | ||||||||
\(333\) | −12.3557 | − | 12.5552i | −0.677089 | − | 0.688022i | ||||
\(334\) | −18.6643 | −1.02127 | ||||||||
\(335\) | 1.48594i | 0.0811855i | ||||||||
\(336\) | −1.60285 | + | 0.656415i | −0.0874425 | + | 0.0358104i | ||||
\(337\) | − | 25.3403i | − | 1.38037i | −0.723631 | − | 0.690187i | \(-0.757528\pi\) | ||
0.723631 | − | 0.690187i | \(-0.242472\pi\) | |||||||
\(338\) | 3.38696i | 0.184226i | ||||||||
\(339\) | −6.84360 | − | 16.7109i | −0.371693 | − | 0.907609i | ||||
\(340\) | −0.118880 | −0.00644715 | ||||||||
\(341\) | 7.73585 | 0.418920 | ||||||||
\(342\) | −5.10839 | + | 5.02722i | −0.276230 | + | 0.271841i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −5.09258 | −0.274573 | ||||||||
\(345\) | 0.783939 | − | 1.94391i | 0.0422059 | − | 0.104656i | ||||
\(346\) | 3.66045 | 0.196787 | ||||||||
\(347\) | − | 32.1330i | − | 1.72499i | −0.506065 | − | 0.862495i | \(-0.668900\pi\) | ||
0.506065 | − | 0.862495i | \(-0.331100\pi\) | |||||||
\(348\) | 9.75230 | − | 3.99386i | 0.522778 | − | 0.214093i | ||||
\(349\) | −22.8049 | −1.22072 | −0.610360 | − | 0.792124i | \(-0.708975\pi\) | ||||
−0.610360 | + | 0.792124i | \(0.708975\pi\) | |||||||
\(350\) | −4.93633 | −0.263858 | ||||||||
\(351\) | 14.8091 | + | 6.34361i | 0.790454 | + | 0.338597i | ||||
\(352\) | − | 5.50149i | − | 0.293230i | ||||||
\(353\) | − | 1.38461i | − | 0.0736952i | −0.999321 | − | 0.0368476i | \(-0.988268\pi\) | ||
0.999321 | − | 0.0368476i | \(-0.0117316\pi\) | |||||||
\(354\) | −2.32024 | − | 5.66562i | −0.123319 | − | 0.301124i | ||||
\(355\) | − | 3.84518i | − | 0.204081i | ||||||
\(356\) | −12.9856 | −0.688235 | ||||||||
\(357\) | 0.755139 | − | 0.309252i | 0.0399662 | − | 0.0163674i | ||||
\(358\) | −17.2447 | −0.911412 | ||||||||
\(359\) | 24.6312 | 1.29999 | 0.649994 | − | 0.759940i | \(-0.274771\pi\) | ||||
0.649994 | + | 0.759940i | \(0.274771\pi\) | |||||||
\(360\) | 0.530973 | + | 0.539546i | 0.0279847 | + | 0.0284366i | ||||
\(361\) | 13.2924 | 0.699599 | ||||||||
\(362\) | −5.76109 | −0.302796 | ||||||||
\(363\) | 12.6467 | + | 30.8811i | 0.663782 | + | 1.62084i | ||||
\(364\) | 3.10049i | 0.162510i | ||||||||
\(365\) | 0.842946 | 0.0441218 | ||||||||
\(366\) | −1.37957 | − | 3.36867i | −0.0721114 | − | 0.176083i | ||||
\(367\) | 28.4245i | 1.48375i | 0.670541 | + | 0.741873i | \(0.266062\pi\) | ||||
−0.670541 | + | 0.741873i | \(0.733938\pi\) | |||||||
\(368\) | 3.43621 | + | 3.34552i | 0.179125 | + | 0.174397i | ||||
\(369\) | −9.77798 | − | 9.93585i | −0.509021 | − | 0.517240i | ||||
\(370\) | −1.48163 | −0.0770263 | ||||||||
\(371\) | 1.95854i | 0.101682i | ||||||||
\(372\) | −0.923009 | − | 2.25382i | −0.0478558 | − | 0.116855i | ||||
\(373\) | − | 5.51022i | − | 0.285309i | −0.989773 | − | 0.142654i | \(-0.954436\pi\) | ||
0.989773 | − | 0.142654i | \(-0.0455637\pi\) | |||||||
\(374\) | 2.59188i | 0.134023i | ||||||||
\(375\) | 1.64580 | + | 4.01874i | 0.0849886 | + | 0.207527i | ||||
\(376\) | 4.02078 | 0.207356 | ||||||||
\(377\) | − | 18.8645i | − | 0.971571i | ||||||
\(378\) | −4.77639 | − | 2.04600i | −0.245671 | − | 0.105235i | ||||
\(379\) | − | 27.8007i | − | 1.42803i | −0.700131 | − | 0.714014i | \(-0.746875\pi\) | ||
0.700131 | − | 0.714014i | \(-0.253125\pi\) | |||||||
\(380\) | 0.602837i | 0.0309249i | ||||||||
\(381\) | 0.282864 | + | 0.690703i | 0.0144915 | + | 0.0353858i | ||||
\(382\) | 17.4889i | 0.894809i | ||||||||
\(383\) | 33.3811 | 1.70570 | 0.852848 | − | 0.522159i | \(-0.174873\pi\) | ||||
0.852848 | + | 0.522159i | \(0.174873\pi\) | |||||||
\(384\) | −1.60285 | + | 0.656415i | −0.0817950 | + | 0.0334975i | ||||
\(385\) | − | 1.38820i | − | 0.0707493i | ||||||
\(386\) | − | 20.4201i | − | 1.03935i | ||||||
\(387\) | −10.7161 | − | 10.8892i | −0.544732 | − | 0.553527i | ||||
\(388\) | 17.8515i | 0.906272i | ||||||||
\(389\) | −4.72149 | −0.239389 | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119694 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(390\) | 1.25399 | − | 0.513548i | 0.0634984 | − | 0.0260045i | ||||
\(391\) | −1.61888 | − | 1.57615i | −0.0818702 | − | 0.0797094i | ||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 17.8667 | − | 7.31695i | 0.901255 | − | 0.369091i | ||||
\(394\) | −8.17726 | −0.411964 | ||||||||
\(395\) | − | 3.51992i | − | 0.177107i | ||||||
\(396\) | 11.7635 | − | 11.5766i | 0.591138 | − | 0.581746i | ||||
\(397\) | 7.48413 | 0.375618 | 0.187809 | − | 0.982206i | \(-0.439861\pi\) | ||||
0.187809 | + | 0.982206i | \(0.439861\pi\) | |||||||
\(398\) | −0.0625989 | −0.00313780 | ||||||||
\(399\) | −1.56822 | − | 3.82930i | −0.0785090 | − | 0.191705i | ||||
\(400\) | −4.93633 | −0.246816 | ||||||||
\(401\) | 35.5877 | 1.77716 | 0.888582 | − | 0.458718i | \(-0.151691\pi\) | ||||
0.888582 | + | 0.458718i | \(0.151691\pi\) | |||||||
\(402\) | −3.86551 | − | 9.43888i | −0.192794 | − | 0.470769i | ||||
\(403\) | −4.35972 | −0.217173 | ||||||||
\(404\) | − | 0.803060i | − | 0.0399537i | ||||||
\(405\) | −0.0363707 | + | 2.27070i | −0.00180727 | + | 0.112832i | ||||
\(406\) | 6.08436i | 0.301962i | ||||||||
\(407\) | 32.3034i | 1.60122i | ||||||||
\(408\) | 0.755139 | − | 0.309252i | 0.0373850 | − | 0.0153103i | ||||
\(409\) | 31.9276 | 1.57872 | 0.789358 | − | 0.613933i | \(-0.210413\pi\) | ||||
0.789358 | + | 0.613933i | \(0.210413\pi\) | |||||||
\(410\) | −1.17252 | −0.0579067 | ||||||||
\(411\) | 8.53443 | + | 20.8396i | 0.420972 | + | 1.02794i | ||||
\(412\) | 11.9640i | 0.589425i | ||||||||
\(413\) | 3.53472 | 0.173932 | ||||||||
\(414\) | 0.0771712 | + | 14.3873i | 0.00379276 | + | 0.707097i | ||||
\(415\) | −2.31727 | −0.113750 | ||||||||
\(416\) | 3.10049i | 0.152014i | ||||||||
\(417\) | 12.2048 | + | 29.8020i | 0.597673 | + | 1.45941i | ||||
\(418\) | 13.1434 | 0.642865 | ||||||||
\(419\) | −17.3290 | −0.846576 | −0.423288 | − | 0.905995i | \(-0.639124\pi\) | ||||
−0.423288 | + | 0.905995i | \(0.639124\pi\) | |||||||
\(420\) | −0.404450 | + | 0.165634i | −0.0197351 | + | 0.00808213i | ||||
\(421\) | 25.2378i | 1.23001i | 0.788521 | + | 0.615007i | \(0.210847\pi\) | ||||
−0.788521 | + | 0.615007i | \(0.789153\pi\) | |||||||
\(422\) | − | 2.20409i | − | 0.107294i | ||||||
\(423\) | 8.46080 | + | 8.59740i | 0.411378 | + | 0.418020i | ||||
\(424\) | 1.95854i | 0.0951152i | ||||||||
\(425\) | 2.32562 | 0.112809 | ||||||||
\(426\) | 10.0028 | + | 24.4251i | 0.484638 | + | 1.18340i | ||||
\(427\) | 2.10168 | 0.101707 | ||||||||
\(428\) | 11.6433 | 0.562800 | ||||||||
\(429\) | −11.1967 | − | 27.3403i | −0.540580 | − | 1.32000i | ||||
\(430\) | −1.28502 | −0.0619692 | ||||||||
\(431\) | 26.1039 | 1.25738 | 0.628690 | − | 0.777656i | \(-0.283591\pi\) | ||||
0.628690 | + | 0.777656i | \(0.283591\pi\) | |||||||
\(432\) | −4.77639 | − | 2.04600i | −0.229804 | − | 0.0984383i | ||||
\(433\) | − | 2.34431i | − | 0.112660i | −0.998412 | − | 0.0563302i | \(-0.982060\pi\) | ||
0.998412 | − | 0.0563302i | \(-0.0179400\pi\) | |||||||
\(434\) | 1.40614 | 0.0674968 | ||||||||
\(435\) | 2.46082 | − | 1.00778i | 0.117987 | − | 0.0483193i | ||||
\(436\) | 1.11725i | 0.0535066i | ||||||||
\(437\) | −7.99265 | + | 8.20932i | −0.382340 | + | 0.392705i | ||||
\(438\) | −5.35451 | + | 2.19283i | −0.255848 | + | 0.104778i | ||||
\(439\) | −7.50867 | −0.358369 | −0.179185 | − | 0.983815i | \(-0.557346\pi\) | ||||
−0.179185 | + | 0.983815i | \(0.557346\pi\) | |||||||
\(440\) | − | 1.38820i | − | 0.0661799i | ||||||
\(441\) | 2.13824 | − | 2.10426i | 0.101821 | − | 0.100203i | ||||
\(442\) | − | 1.46071i | − | 0.0694791i | ||||||
\(443\) | 15.1702i | 0.720760i | 0.932806 | + | 0.360380i | \(0.117353\pi\) | ||||
−0.932806 | + | 0.360380i | \(0.882647\pi\) | |||||||
\(444\) | 9.41152 | − | 3.85430i | 0.446651 | − | 0.182917i | ||||
\(445\) | −3.27668 | −0.155330 | ||||||||
\(446\) | 25.4713i | 1.20610i | ||||||||
\(447\) | 7.49031 | + | 18.2900i | 0.354279 | + | 0.865087i | ||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 19.0138i | 0.897318i | 0.893703 | + | 0.448659i | \(0.148098\pi\) | ||||
−0.893703 | + | 0.448659i | \(0.851902\pi\) | |||||||
\(450\) | −10.3873 | − | 10.5551i | −0.489664 | − | 0.497570i | ||||
\(451\) | 25.5640i | 1.20376i | ||||||||
\(452\) | 10.4257 | 0.490385 | ||||||||
\(453\) | 1.67747 | + | 4.09609i | 0.0788146 | + | 0.192451i | ||||
\(454\) | − | 17.5961i | − | 0.825828i | ||||||
\(455\) | 0.782353i | 0.0366773i | ||||||||
\(456\) | −1.56822 | − | 3.82930i | −0.0734385 | − | 0.179324i | ||||
\(457\) | − | 3.65320i | − | 0.170890i | −0.996343 | − | 0.0854448i | \(-0.972769\pi\) | ||
0.996343 | − | 0.0854448i | \(-0.0272311\pi\) | |||||||
\(458\) | 8.59906 | 0.401808 | ||||||||
\(459\) | 2.25027 | + | 0.963920i | 0.105034 | + | 0.0449919i | ||||
\(460\) | 0.867065 | + | 0.844181i | 0.0404271 | + | 0.0393601i | ||||
\(461\) | 41.7766i | 1.94573i | 0.231374 | + | 0.972865i | \(0.425678\pi\) | ||||
−0.231374 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(462\) | 3.61126 | + | 8.81805i | 0.168011 | + | 0.410253i | ||||
\(463\) | −19.4404 | −0.903471 | −0.451735 | − | 0.892152i | \(-0.649195\pi\) | ||||
−0.451735 | + | 0.892152i | \(0.649195\pi\) | |||||||
\(464\) | 6.08436i | 0.282459i | ||||||||
\(465\) | −0.232905 | − | 0.568712i | −0.0108007 | − | 0.0263734i | ||||
\(466\) | 2.93410 | 0.135920 | ||||||||
\(467\) | 26.0964 | 1.20760 | 0.603798 | − | 0.797137i | \(-0.293653\pi\) | ||||
0.603798 | + | 0.797137i | \(0.293653\pi\) | |||||||
\(468\) | −6.62959 | + | 6.52425i | −0.306453 | + | 0.301584i | ||||
\(469\) | 5.88882 | 0.271921 | ||||||||
\(470\) | 1.01457 | 0.0467987 | ||||||||
\(471\) | 20.0998 | − | 8.23149i | 0.926151 | − | 0.379287i | ||||
\(472\) | 3.53472 | 0.162699 | ||||||||
\(473\) | 28.0168i | 1.28821i | ||||||||
\(474\) | 9.15670 | + | 22.3590i | 0.420581 | + | 1.02698i | ||||
\(475\) | − | 11.7932i | − | 0.541109i | ||||||
\(476\) | 0.471124i | 0.0215939i | ||||||||
\(477\) | −4.18783 | + | 4.12129i | −0.191748 | + | 0.188701i | ||||
\(478\) | 1.13350 | 0.0518450 | ||||||||
\(479\) | 24.4346 | 1.11645 | 0.558224 | − | 0.829690i | \(-0.311483\pi\) | ||||
0.558224 | + | 0.829690i | \(0.311483\pi\) | |||||||
\(480\) | −0.404450 | + | 0.165634i | −0.0184605 | + | 0.00756014i | ||||
\(481\) | − | 18.2053i | − | 0.830091i | ||||||
\(482\) | −21.7858 | −0.992316 | ||||||||
\(483\) | −7.70376 | − | 3.10678i | −0.350533 | − | 0.141363i | ||||
\(484\) | −19.2664 | −0.875745 | ||||||||
\(485\) | 4.50450i | 0.204539i | ||||||||
\(486\) | −5.67594 | − | 14.5184i | −0.257466 | − | 0.658568i | ||||
\(487\) | 12.0770 | 0.547261 | 0.273631 | − | 0.961835i | \(-0.411775\pi\) | ||||
0.273631 | + | 0.961835i | \(0.411775\pi\) | |||||||
\(488\) | 2.10168 | 0.0951385 | ||||||||
\(489\) | 5.35927 | + | 13.0864i | 0.242354 | + | 0.591786i | ||||
\(490\) | − | 0.252332i | − | 0.0113992i | ||||||
\(491\) | 7.93573i | 0.358134i | 0.983837 | + | 0.179067i | \(0.0573080\pi\) | ||||
−0.983837 | + | 0.179067i | \(0.942692\pi\) | |||||||
\(492\) | 7.44802 | − | 3.05019i | 0.335783 | − | 0.137513i | ||||
\(493\) | − | 2.86648i | − | 0.129100i | ||||||
\(494\) | −7.40727 | −0.333269 | ||||||||
\(495\) | 2.96831 | − | 2.92114i | 0.133416 | − | 0.131296i | ||||
\(496\) | 1.40614 | 0.0631374 | ||||||||
\(497\) | −15.2386 | −0.683543 | ||||||||
\(498\) | 14.7196 | − | 6.02814i | 0.659603 | − | 0.270127i | ||||
\(499\) | −23.7262 | −1.06213 | −0.531066 | − | 0.847330i | \(-0.678208\pi\) | ||||
−0.531066 | + | 0.847330i | \(0.678208\pi\) | |||||||
\(500\) | −2.50725 | −0.112128 | ||||||||
\(501\) | 29.9161 | − | 12.2515i | 1.33655 | − | 0.547358i | ||||
\(502\) | 24.3418i | 1.08643i | ||||||||
\(503\) | 5.27424 | 0.235167 | 0.117583 | − | 0.993063i | \(-0.462485\pi\) | ||||
0.117583 | + | 0.993063i | \(0.462485\pi\) | |||||||
\(504\) | 2.13824 | − | 2.10426i | 0.0952448 | − | 0.0937314i | ||||
\(505\) | − | 0.202638i | − | 0.00901725i | ||||||
\(506\) | 18.4053 | − | 18.9043i | 0.818217 | − | 0.840397i | ||||
\(507\) | −2.22325 | − | 5.42878i | −0.0987380 | − | 0.241100i | ||||
\(508\) | −0.430922 | −0.0191191 | ||||||||
\(509\) | − | 7.73592i | − | 0.342888i | −0.985194 | − | 0.171444i | \(-0.945157\pi\) | ||
0.985194 | − | 0.171444i | \(-0.0548433\pi\) | |||||||
\(510\) | 0.190546 | − | 0.0780343i | 0.00843751 | − | 0.00345542i | ||||
\(511\) | − | 3.34062i | − | 0.147780i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.88803 | − | 11.4111i | 0.215812 | − | 0.503812i | ||||
\(514\) | 6.49482 | 0.286474 | ||||||||
\(515\) | 3.01891i | 0.133029i | ||||||||
\(516\) | 8.16263 | − | 3.34284i | 0.359340 | − | 0.147160i | ||||
\(517\) | − | 22.1203i | − | 0.972850i | ||||||
\(518\) | 5.87175i | 0.257990i | ||||||||
\(519\) | −5.86714 | + | 2.40277i | −0.257539 | + | 0.105470i | ||||
\(520\) | 0.782353i | 0.0343084i | ||||||||
\(521\) | 32.8623 | 1.43972 | 0.719861 | − | 0.694118i | \(-0.244205\pi\) | ||||
0.719861 | + | 0.694118i | \(0.244205\pi\) | |||||||
\(522\) | −13.0098 | + | 12.8031i | −0.569424 | + | 0.560376i | ||||
\(523\) | − | 41.1952i | − | 1.80134i | −0.434501 | − | 0.900671i | \(-0.643075\pi\) | ||
0.434501 | − | 0.900671i | \(-0.356925\pi\) | |||||||
\(524\) | 11.1468i | 0.486952i | ||||||||
\(525\) | 7.91218 | − | 3.24028i | 0.345316 | − | 0.141417i | ||||
\(526\) | − | 10.0922i | − | 0.440039i | ||||||
\(527\) | −0.662465 | −0.0288574 | ||||||||
\(528\) | 3.61126 | + | 8.81805i | 0.157160 | + | 0.383756i | ||||
\(529\) | 0.615030 | + | 22.9918i | 0.0267404 | + | 0.999642i | ||||
\(530\) | 0.494203i | 0.0214668i | ||||||||
\(531\) | 7.43799 | + | 7.55808i | 0.322781 | + | 0.327993i | ||||
\(532\) | 2.38906 | 0.103579 | ||||||||
\(533\) | − | 14.4072i | − | 0.624044i | ||||||
\(534\) | 20.8139 | − | 8.52394i | 0.900707 | − | 0.368867i | ||||
\(535\) | 2.93798 | 0.127020 | ||||||||
\(536\) | 5.88882 | 0.254358 | ||||||||
\(537\) | 27.6407 | − | 11.3197i | 1.19278 | − | 0.488481i | ||||
\(538\) | 15.0560 | 0.649112 | ||||||||
\(539\) | −5.50149 | −0.236966 | ||||||||
\(540\) | −1.20524 | − | 0.516272i | −0.0518651 | − | 0.0222168i | ||||
\(541\) | 11.6640 | 0.501473 | 0.250736 | − | 0.968055i | \(-0.419327\pi\) | ||||
0.250736 | + | 0.968055i | \(0.419327\pi\) | |||||||
\(542\) | 21.4792i | 0.922612i | ||||||||
\(543\) | 9.23416 | − | 3.78167i | 0.396276 | − | 0.162287i | ||||
\(544\) | 0.471124i | 0.0201993i | ||||||||
\(545\) | 0.281918i | 0.0120760i | ||||||||
\(546\) | −2.03521 | − | 4.96961i | −0.0870988 | − | 0.212680i | ||||
\(547\) | −24.1526 | −1.03269 | −0.516346 | − | 0.856380i | \(-0.672708\pi\) | ||||
−0.516346 | + | 0.856380i | \(0.672708\pi\) | |||||||
\(548\) | −13.0016 | −0.555400 | ||||||||
\(549\) | 4.42249 | + | 4.49389i | 0.188747 | + | 0.191795i | ||||
\(550\) | 27.1572i | 1.15799i | ||||||||
\(551\) | −14.5359 | −0.619251 | ||||||||
\(552\) | −7.70376 | − | 3.10678i | −0.327894 | − | 0.132233i | ||||
\(553\) | −13.9496 | −0.593196 | ||||||||
\(554\) | − | 11.6898i | − | 0.496654i | ||||||
\(555\) | 2.37483 | − | 0.972564i | 0.100806 | − | 0.0412830i | ||||
\(556\) | −18.5932 | −0.788526 | ||||||||
\(557\) | −33.0696 | −1.40120 | −0.700602 | − | 0.713553i | \(-0.747085\pi\) | ||||
−0.700602 | + | 0.713553i | \(0.747085\pi\) | |||||||
\(558\) | 2.95889 | + | 3.00666i | 0.125260 | + | 0.127282i | ||||
\(559\) | − | 15.7895i | − | 0.667824i | ||||||
\(560\) | − | 0.252332i | − | 0.0106630i | ||||||
\(561\) | −1.70135 | − | 4.15439i | −0.0718310 | − | 0.175399i | ||||
\(562\) | 17.4066i | 0.734252i | ||||||||
\(563\) | −24.2673 | −1.02274 | −0.511371 | − | 0.859360i | \(-0.670862\pi\) | ||||
−0.511371 | + | 0.859360i | \(0.670862\pi\) | |||||||
\(564\) | −6.44470 | + | 2.63930i | −0.271371 | + | 0.111135i | ||||
\(565\) | 2.63074 | 0.110676 | ||||||||
\(566\) | 20.2774 | 0.852323 | ||||||||
\(567\) | 8.99885 | + | 0.144138i | 0.377916 | + | 0.00605324i | ||||
\(568\) | −15.2386 | −0.639396 | ||||||||
\(569\) | 44.1025 | 1.84887 | 0.924436 | − | 0.381338i | \(-0.124536\pi\) | ||||
0.924436 | + | 0.381338i | \(0.124536\pi\) | |||||||
\(570\) | −0.395711 | − | 0.966256i | −0.0165745 | − | 0.0404720i | ||||
\(571\) | − | 5.02125i | − | 0.210133i | −0.994465 | − | 0.105066i | \(-0.966494\pi\) | ||
0.994465 | − | 0.105066i | \(-0.0335055\pi\) | |||||||
\(572\) | 17.0573 | 0.713202 | ||||||||
\(573\) | −11.4800 | − | 28.0320i | −0.479582 | − | 1.17105i | ||||
\(574\) | 4.64674i | 0.193951i | ||||||||
\(575\) | −16.9622 | − | 16.5146i | −0.707374 | − | 0.688705i | ||||
\(576\) | 2.13824 | − | 2.10426i | 0.0890933 | − | 0.0876777i | ||||
\(577\) | −1.04410 | −0.0434663 | −0.0217331 | − | 0.999764i | \(-0.506918\pi\) | ||||
−0.0217331 | + | 0.999764i | \(0.506918\pi\) | |||||||
\(578\) | 16.7780i | 0.697875i | ||||||||
\(579\) | 13.4040 | + | 32.7302i | 0.557052 | + | 1.36022i | ||||
\(580\) | 1.53528i | 0.0637489i | ||||||||
\(581\) | 9.18343i | 0.380993i | ||||||||
\(582\) | −11.7180 | − | 28.6132i | −0.485726 | − | 1.18606i | ||||
\(583\) | 10.7749 | 0.446251 | ||||||||
\(584\) | − | 3.34062i | − | 0.138236i | ||||||
\(585\) | −1.67286 | + | 1.64628i | −0.0691642 | + | 0.0680652i | ||||
\(586\) | − | 16.3179i | − | 0.674085i | ||||||
\(587\) | 14.4825i | 0.597758i | 0.954291 | + | 0.298879i | \(0.0966127\pi\) | ||||
−0.954291 | + | 0.298879i | \(0.903387\pi\) | |||||||
\(588\) | 0.656415 | + | 1.60285i | 0.0270701 | + | 0.0661003i | ||||
\(589\) | 3.35935i | 0.138420i | ||||||||
\(590\) | 0.891923 | 0.0367199 | ||||||||
\(591\) | 13.1069 | − | 5.36767i | 0.539146 | − | 0.220797i | ||||
\(592\) | 5.87175i | 0.241328i | ||||||||
\(593\) | 3.58230i | 0.147107i | 0.997291 | + | 0.0735537i | \(0.0234340\pi\) | ||||
−0.997291 | + | 0.0735537i | \(0.976566\pi\) | |||||||
\(594\) | −11.2561 | + | 26.2772i | −0.461842 | + | 1.07817i | ||||
\(595\) | 0.118880i | 0.00487359i | ||||||||
\(596\) | −11.4109 | −0.467410 | ||||||||
\(597\) | 0.100336 | − | 0.0410908i | 0.00410650 | − | 0.00168174i | ||||
\(598\) | −10.3727 | + | 10.6539i | −0.424173 | + | 0.435671i | ||||
\(599\) | 7.95060i | 0.324853i | 0.986721 | + | 0.162426i | \(0.0519320\pi\) | ||||
−0.986721 | + | 0.162426i | \(0.948068\pi\) | |||||||
\(600\) | 7.91218 | − | 3.24028i | 0.323013 | − | 0.132284i | ||||
\(601\) | −23.9355 | −0.976350 | −0.488175 | − | 0.872746i | \(-0.662337\pi\) | ||||
−0.488175 | + | 0.872746i | \(0.662337\pi\) | |||||||
\(602\) | 5.09258i | 0.207558i | ||||||||
\(603\) | 12.3916 | + | 12.5917i | 0.504627 | + | 0.512774i | ||||
\(604\) | −2.55551 | −0.103982 | ||||||||
\(605\) | −4.86153 | −0.197649 | ||||||||
\(606\) | 0.527140 | + | 1.28718i | 0.0214136 | + | 0.0522882i | ||||
\(607\) | −36.7347 | −1.49102 | −0.745508 | − | 0.666497i | \(-0.767793\pi\) | ||||
−0.745508 | + | 0.666497i | \(0.767793\pi\) | |||||||
\(608\) | 2.38906 | 0.0968893 | ||||||||
\(609\) | −3.99386 | − | 9.75230i | −0.161839 | − | 0.395183i | ||||
\(610\) | 0.530321 | 0.0214721 | ||||||||
\(611\) | 12.4664i | 0.504337i | ||||||||
\(612\) | −1.00738 | + | 0.991369i | −0.0407207 | + | 0.0400737i | ||||
\(613\) | 4.62698i | 0.186882i | 0.995625 | + | 0.0934410i | \(0.0297866\pi\) | ||||
−0.995625 | + | 0.0934410i | \(0.970213\pi\) | |||||||
\(614\) | − | 15.9791i | − | 0.644862i | ||||||
\(615\) | 1.87937 | − | 0.769660i | 0.0757836 | − | 0.0310357i | ||||
\(616\) | −5.50149 | −0.221661 | ||||||||
\(617\) | 5.21923 | 0.210118 | 0.105059 | − | 0.994466i | \(-0.466497\pi\) | ||||
0.105059 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(618\) | −7.85336 | − | 19.1765i | −0.315908 | − | 0.771392i | ||||
\(619\) | 19.6131i | 0.788316i | 0.919043 | + | 0.394158i | \(0.128964\pi\) | ||||
−0.919043 | + | 0.394158i | \(0.871036\pi\) | |||||||
\(620\) | 0.354813 | 0.0142497 | ||||||||
\(621\) | −9.56772 | − | 23.0100i | −0.383939 | − | 0.923358i | ||||
\(622\) | 20.1658 | 0.808577 | ||||||||
\(623\) | 12.9856i | 0.520257i | ||||||||
\(624\) | −2.03521 | − | 4.96961i | −0.0814735 | − | 0.198944i | ||||
\(625\) | 24.0490 | 0.961959 | ||||||||
\(626\) | −0.269860 | −0.0107858 | ||||||||
\(627\) | −21.0669 | + | 8.62753i | −0.841330 | + | 0.344550i | ||||
\(628\) | 12.5401i | 0.500403i | ||||||||
\(629\) | − | 2.76632i | − | 0.110300i | ||||||
\(630\) | 0.539546 | − | 0.530973i | 0.0214960 | − | 0.0211545i | ||||
\(631\) | 23.2849i | 0.926958i | 0.886108 | + | 0.463479i | \(0.153399\pi\) | ||||
−0.886108 | + | 0.463479i | \(0.846601\pi\) | |||||||
\(632\) | −13.9496 | −0.554884 | ||||||||
\(633\) | 1.44680 | + | 3.53283i | 0.0575051 | + | 0.140417i | ||||
\(634\) | −8.37234 | −0.332508 | ||||||||
\(635\) | −0.108735 | −0.00431504 | ||||||||
\(636\) | −1.28562 | − | 3.13924i | −0.0509780 | − | 0.124479i | ||||
\(637\) | 3.10049 | 0.122846 | ||||||||
\(638\) | 33.4730 | 1.32521 | ||||||||
\(639\) | −32.0660 | − | 32.5837i | −1.26851 | − | 1.28899i | ||||
\(640\) | − | 0.252332i | − | 0.00997430i | ||||||
\(641\) | 19.5620 | 0.772653 | 0.386327 | − | 0.922362i | \(-0.373744\pi\) | ||||
0.386327 | + | 0.922362i | \(0.373744\pi\) | |||||||
\(642\) | −18.6624 | + | 7.64284i | −0.736548 | + | 0.301639i | ||||
\(643\) | 47.1630i | 1.85993i | 0.367651 | + | 0.929964i | \(0.380162\pi\) | ||||
−0.367651 | + | 0.929964i | \(0.619838\pi\) | |||||||
\(644\) | 3.34552 | − | 3.43621i | 0.131832 | − | 0.135406i | ||||
\(645\) | 2.05969 | − | 0.843506i | 0.0811003 | − | 0.0332130i | ||||
\(646\) | −1.12554 | −0.0442839 | ||||||||
\(647\) | − | 20.4000i | − | 0.802006i | −0.916077 | − | 0.401003i | \(-0.868662\pi\) | ||
0.916077 | − | 0.401003i | \(-0.131338\pi\) | |||||||
\(648\) | 8.99885 | + | 0.144138i | 0.353508 | + | 0.00566229i | ||||
\(649\) | − | 19.4462i | − | 0.763331i | ||||||
\(650\) | − | 15.3050i | − | 0.600313i | ||||||
\(651\) | −2.25382 | + | 0.923009i | −0.0883343 | + | 0.0361756i | ||||
\(652\) | −8.16445 | −0.319745 | ||||||||
\(653\) | 2.53918i | 0.0993660i | 0.998765 | + | 0.0496830i | \(0.0158211\pi\) | ||||
−0.998765 | + | 0.0496830i | \(0.984179\pi\) | |||||||
\(654\) | −0.733380 | − | 1.79078i | −0.0286774 | − | 0.0700251i | ||||
\(655\) | 2.81270i | 0.109901i | ||||||||
\(656\) | 4.64674i | 0.181425i | ||||||||
\(657\) | 7.14305 | − | 7.02955i | 0.278677 | − | 0.274249i | ||||
\(658\) | − | 4.02078i | − | 0.156747i | ||||||
\(659\) | −32.5218 | −1.26687 | −0.633435 | − | 0.773796i | \(-0.718356\pi\) | ||||
−0.633435 | + | 0.773796i | \(0.718356\pi\) | |||||||
\(660\) | 0.911236 | + | 2.22508i | 0.0354698 | + | 0.0866109i | ||||
\(661\) | 26.2380i | 1.02054i | 0.860014 | + | 0.510270i | \(0.170455\pi\) | ||||
−0.860014 | + | 0.510270i | \(0.829545\pi\) | |||||||
\(662\) | 7.84024i | 0.304720i | ||||||||
\(663\) | 0.958834 | + | 2.34130i | 0.0372380 | + | 0.0909286i | ||||
\(664\) | 9.18343i | 0.356386i | ||||||||
\(665\) | 0.602837 | 0.0233770 | ||||||||
\(666\) | −12.5552 | + | 12.3557i | −0.486505 | + | 0.478775i | ||||
\(667\) | −20.3553 | + | 20.9071i | −0.788161 | + | 0.809526i | ||||
\(668\) | 18.6643i | 0.722144i | ||||||||
\(669\) | −16.7197 | − | 40.8266i | −0.646423 | − | 1.57845i | ||||
\(670\) | 1.48594 | 0.0574068 | ||||||||
\(671\) | − | 11.5624i | − | 0.446360i | ||||||
\(672\) | 0.656415 | + | 1.60285i | 0.0253217 | + | 0.0618312i | ||||
\(673\) | 6.70202 | 0.258344 | 0.129172 | − | 0.991622i | \(-0.458768\pi\) | ||||
0.129172 | + | 0.991622i | \(0.458768\pi\) | |||||||
\(674\) | −25.3403 | −0.976071 | ||||||||
\(675\) | 23.5778 | + | 10.0997i | 0.907511 | + | 0.388739i | ||||
\(676\) | 3.38696 | 0.130268 | ||||||||
\(677\) | −12.0244 | −0.462137 | −0.231068 | − | 0.972938i | \(-0.574222\pi\) | ||||
−0.231068 | + | 0.972938i | \(0.574222\pi\) | |||||||
\(678\) | −16.7109 | + | 6.84360i | −0.641776 | + | 0.262827i | ||||
\(679\) | 17.8515 | 0.685077 | ||||||||
\(680\) | 0.118880i | 0.00455882i | ||||||||
\(681\) | 11.5504 | + | 28.2039i | 0.442611 | + | 1.08078i | ||||
\(682\) | − | 7.73585i | − | 0.296221i | ||||||
\(683\) | − | 30.3967i | − | 1.16310i | −0.813512 | − | 0.581548i | \(-0.802447\pi\) | ||
0.813512 | − | 0.581548i | \(-0.197553\pi\) | |||||||
\(684\) | 5.02722 | + | 5.10839i | 0.192221 | + | 0.195324i | ||||
\(685\) | −3.28072 | −0.125350 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −13.7830 | + | 5.64455i | −0.525854 | + | 0.215353i | ||||
\(688\) | 5.09258i | 0.194153i | ||||||||
\(689\) | −6.07244 | −0.231342 | ||||||||
\(690\) | −1.94391 | − | 0.783939i | −0.0740032 | − | 0.0298441i | ||||
\(691\) | −17.3792 | −0.661137 | −0.330568 | − | 0.943782i | \(-0.607240\pi\) | ||||
−0.330568 | + | 0.943782i | \(0.607240\pi\) | |||||||
\(692\) | − | 3.66045i | − | 0.139149i | ||||||
\(693\) | −11.5766 | − | 11.7635i | −0.439758 | − | 0.446859i | ||||
\(694\) | −32.1330 | −1.21975 | ||||||||
\(695\) | −4.69165 | −0.177965 | ||||||||
\(696\) | −3.99386 | − | 9.75230i | −0.151387 | − | 0.369660i | ||||
\(697\) | − | 2.18919i | − | 0.0829215i | ||||||
\(698\) | 22.8049i | 0.863180i | ||||||||
\(699\) | −4.70292 | + | 1.92599i | −0.177881 | + | 0.0728476i | ||||
\(700\) | 4.93633i | 0.186576i | ||||||||
\(701\) | 29.2013 | 1.10292 | 0.551459 | − | 0.834202i | \(-0.314071\pi\) | ||||
0.551459 | + | 0.834202i | \(0.314071\pi\) | |||||||
\(702\) | 6.34361 | − | 14.8091i | 0.239424 | − | 0.558935i | ||||
\(703\) | −14.0280 | −0.529076 | ||||||||
\(704\) | −5.50149 | −0.207345 | ||||||||
\(705\) | −1.62620 | + | 0.665980i | −0.0612464 | + | 0.0250823i | ||||
\(706\) | −1.38461 | −0.0521103 | ||||||||
\(707\) | −0.803060 | −0.0302022 | ||||||||
\(708\) | −5.66562 | + | 2.32024i | −0.212927 | + | 0.0872001i | ||||
\(709\) | 12.6452i | 0.474900i | 0.971400 | + | 0.237450i | \(0.0763117\pi\) | ||||
−0.971400 | + | 0.237450i | \(0.923688\pi\) | |||||||
\(710\) | −3.84518 | −0.144307 | ||||||||
\(711\) | −29.3536 | − | 29.8275i | −1.10085 | − | 1.11862i | ||||
\(712\) | 12.9856i | 0.486656i | ||||||||
\(713\) | 4.83178 | + | 4.70426i | 0.180952 | + | 0.176176i | ||||
\(714\) | −0.309252 | − | 0.755139i | −0.0115735 | − | 0.0282604i | ||||
\(715\) | 4.30411 | 0.160964 | ||||||||
\(716\) | 17.2447i | 0.644466i | ||||||||
\(717\) | −1.81682 | + | 0.744045i | −0.0678505 | + | 0.0277869i | ||||
\(718\) | − | 24.6312i | − | 0.919230i | ||||||
\(719\) | − | 29.1016i | − | 1.08531i | −0.839957 | − | 0.542654i | \(-0.817420\pi\) | ||
0.839957 | − | 0.542654i | \(-0.182580\pi\) | |||||||
\(720\) | 0.539546 | − | 0.530973i | 0.0201077 | − | 0.0197882i | ||||
\(721\) | 11.9640 | 0.445564 | ||||||||
\(722\) | − | 13.2924i | − | 0.494691i | ||||||
\(723\) | 34.9193 | − | 14.3005i | 1.29866 | − | 0.531842i | ||||
\(724\) | 5.76109i | 0.214109i | ||||||||
\(725\) | − | 30.0344i | − | 1.11545i | ||||||
\(726\) | 30.8811 | − | 12.6467i | 1.14610 | − | 0.469365i | ||||
\(727\) | 48.1236i | 1.78480i | 0.451240 | + | 0.892402i | \(0.350982\pi\) | ||||
−0.451240 | + | 0.892402i | \(0.649018\pi\) | |||||||
\(728\) | 3.10049 | 0.114912 | ||||||||
\(729\) | 18.6278 | + | 19.5450i | 0.689917 | + | 0.723889i | ||||
\(730\) | − | 0.842946i | − | 0.0311988i | ||||||
\(731\) | − | 2.39923i | − | 0.0887389i | ||||||
\(732\) | −3.36867 | + | 1.37957i | −0.124510 | + | 0.0509905i | ||||
\(733\) | − | 10.4367i | − | 0.385487i | −0.981249 | − | 0.192743i | \(-0.938261\pi\) | ||
0.981249 | − | 0.192743i | \(-0.0617385\pi\) | |||||||
\(734\) | 28.4245 | 1.04917 | ||||||||
\(735\) | 0.165634 | + | 0.404450i | 0.00610952 | + | 0.0149183i | ||||
\(736\) | 3.34552 | − | 3.43621i | 0.123317 | − | 0.126660i | ||||
\(737\) | − | 32.3973i | − | 1.19337i | ||||||
\(738\) | −9.93585 | + | 9.77798i | −0.365744 | + | 0.359932i | ||||
\(739\) | 0.383508 | 0.0141076 | 0.00705379 | − | 0.999975i | \(-0.497755\pi\) | ||||
0.00705379 | + | 0.999975i | \(0.497755\pi\) | |||||||
\(740\) | 1.48163i | 0.0544658i | ||||||||
\(741\) | 11.8727 | − | 4.86224i | 0.436155 | − | 0.178619i | ||||
\(742\) | 1.95854 | 0.0719003 | ||||||||
\(743\) | −4.50514 | −0.165278 | −0.0826389 | − | 0.996580i | \(-0.526335\pi\) | ||||
−0.0826389 | + | 0.996580i | \(0.526335\pi\) | |||||||
\(744\) | −2.25382 | + | 0.923009i | −0.0826292 | + | 0.0338392i | ||||
\(745\) | −2.87935 | −0.105491 | ||||||||
\(746\) | −5.51022 | −0.201744 | ||||||||
\(747\) | −19.6364 | + | 19.3244i | −0.718457 | + | 0.707042i | ||||
\(748\) | 2.59188 | 0.0947686 | ||||||||
\(749\) | − | 11.6433i | − | 0.425437i | ||||||
\(750\) | 4.01874 | − | 1.64580i | 0.146744 | − | 0.0600960i | ||||
\(751\) | − | 39.9527i | − | 1.45790i | −0.684569 | − | 0.728948i | \(-0.740010\pi\) | ||
0.684569 | − | 0.728948i | \(-0.259990\pi\) | |||||||
\(752\) | − | 4.02078i | − | 0.146623i | ||||||
\(753\) | −15.9783 | − | 39.0162i | −0.582282 | − | 1.42183i | ||||
\(754\) | −18.8645 | −0.687004 | ||||||||
\(755\) | −0.644837 | −0.0234680 | ||||||||
\(756\) | −2.04600 | + | 4.77639i | −0.0744124 | + | 0.173716i | ||||
\(757\) | 7.19221i | 0.261405i | 0.991422 | + | 0.130703i | \(0.0417233\pi\) | ||||
−0.991422 | + | 0.130703i | \(0.958277\pi\) | |||||||
\(758\) | −27.8007 | −1.00977 | ||||||||
\(759\) | −17.0919 | + | 42.3822i | −0.620397 | + | 1.53838i | ||||
\(760\) | 0.602837 | 0.0218672 | ||||||||
\(761\) | − | 2.47057i | − | 0.0895580i | −0.998997 | − | 0.0447790i | \(-0.985742\pi\) | ||
0.998997 | − | 0.0447790i | \(-0.0142584\pi\) | |||||||
\(762\) | 0.690703 | − | 0.282864i | 0.0250215 | − | 0.0102471i | ||||
\(763\) | 1.11725 | 0.0404472 | ||||||||
\(764\) | 17.4889 | 0.632725 | ||||||||
\(765\) | −0.254193 | + | 0.250154i | −0.00919037 | + | 0.00904434i | ||||
\(766\) | − | 33.3811i | − | 1.20611i | ||||||
\(767\) | 10.9594i | 0.395720i | ||||||||
\(768\) | 0.656415 | + | 1.60285i | 0.0236863 | + | 0.0578378i | ||||
\(769\) | − | 47.0485i | − | 1.69661i | −0.529505 | − | 0.848307i | \(-0.677622\pi\) | ||
0.529505 | − | 0.848307i | \(-0.322378\pi\) | |||||||
\(770\) | −1.38820 | −0.0500273 | ||||||||
\(771\) | −10.4102 | + | 4.26329i | −0.374914 | + | 0.153539i | ||||
\(772\) | −20.4201 | −0.734934 | ||||||||
\(773\) | −42.5654 | −1.53097 | −0.765486 | − | 0.643453i | \(-0.777501\pi\) | ||||
−0.765486 | + | 0.643453i | \(0.777501\pi\) | |||||||
\(774\) | −10.8892 | + | 10.7161i | −0.391403 | + | 0.385183i | ||||
\(775\) | −6.94116 | −0.249334 | ||||||||
\(776\) | 17.8515 | 0.640831 | ||||||||
\(777\) | −3.85430 | − | 9.41152i | −0.138272 | − | 0.337637i | ||||
\(778\) | 4.72149i | 0.169273i | ||||||||
\(779\) | −11.1014 | −0.397748 | ||||||||
\(780\) | −0.513548 | − | 1.25399i | −0.0183880 | − | 0.0449001i | ||||
\(781\) | 83.8348i | 2.99985i | ||||||||
\(782\) | −1.57615 | + | 1.61888i | −0.0563631 | + | 0.0578910i | ||||
\(783\) | 12.4486 | − | 29.0612i | 0.444877 | − | 1.03856i | ||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 3.16426i | 0.112937i | ||||||||
\(786\) | −7.31695 | − | 17.8667i | −0.260987 | − | 0.637283i | ||||
\(787\) | − | 42.2758i | − | 1.50697i | −0.657464 | − | 0.753486i | \(-0.728371\pi\) | ||
0.657464 | − | 0.753486i | \(-0.271629\pi\) | |||||||
\(788\) | 8.17726i | 0.291303i | ||||||||
\(789\) | 6.62464 | + | 16.1762i | 0.235843 | + | 0.575888i | ||||
\(790\) | −3.51992 | −0.125233 | ||||||||
\(791\) | − | 10.4257i | − | 0.370696i | ||||||
\(792\) | −11.5766 | − | 11.7635i | −0.411356 | − | 0.417998i | ||||
\(793\) | 6.51624i | 0.231398i | ||||||||
\(794\) | − | 7.48413i | − | 0.265602i | ||||||
\(795\) | −0.324402 | − | 0.792131i | −0.0115053 | − | 0.0280940i | ||||
\(796\) | 0.0625989i | 0.00221876i | ||||||||
\(797\) | −10.6019 | −0.375540 | −0.187770 | − | 0.982213i | \(-0.560126\pi\) | ||||
−0.187770 | + | 0.982213i | \(0.560126\pi\) | |||||||
\(798\) | −3.82930 | + | 1.56822i | −0.135556 | + | 0.0555143i | ||||
\(799\) | 1.89429i | 0.0670150i | ||||||||
\(800\) | 4.93633i | 0.174526i | ||||||||
\(801\) | −27.7663 | + | 27.3251i | −0.981075 | + | 0.965486i | ||||
\(802\) | − | 35.5877i | − | 1.25664i | ||||||
\(803\) | −18.3784 | −0.648560 | ||||||||
\(804\) | −9.43888 | + | 3.86551i | −0.332884 | + | 0.136326i | ||||
\(805\) | 0.844181 | − | 0.867065i | 0.0297535 | − | 0.0305600i | ||||
\(806\) | 4.35972i | 0.153564i | ||||||||
\(807\) | −24.1325 | + | 9.88300i | −0.849505 | + | 0.347898i | ||||
\(808\) | −0.803060 | −0.0282515 | ||||||||
\(809\) | 22.8185i | 0.802256i | 0.916022 | + | 0.401128i | \(0.131382\pi\) | ||||
−0.916022 | + | 0.401128i | \(0.868618\pi\) | |||||||
\(810\) | 2.27070 | + | 0.0363707i | 0.0797841 | + | 0.00127794i | ||||
\(811\) | −46.9286 | −1.64789 | −0.823943 | − | 0.566673i | \(-0.808230\pi\) | ||||
−0.823943 | + | 0.566673i | \(0.808230\pi\) | |||||||
\(812\) | 6.08436 | 0.213519 | ||||||||
\(813\) | −14.0993 | − | 34.4279i | −0.494484 | − | 1.20744i | ||||
\(814\) | 32.3034 | 1.13223 | ||||||||
\(815\) | −2.06015 | −0.0721640 | ||||||||
\(816\) | −0.309252 | − | 0.755139i | −0.0108260 | − | 0.0264352i | ||||
\(817\) | −12.1665 | −0.425652 | ||||||||
\(818\) | − | 31.9276i | − | 1.11632i | ||||||
\(819\) | 6.52425 | + | 6.62959i | 0.227976 | + | 0.231657i | ||||
\(820\) | 1.17252i | 0.0409462i | ||||||||
\(821\) | − | 45.8336i | − | 1.59960i | −0.600265 | − | 0.799801i | \(-0.704938\pi\) | ||
0.600265 | − | 0.799801i | \(-0.295062\pi\) | |||||||
\(822\) | 20.8396 | − | 8.53443i | 0.726863 | − | 0.297672i | ||||
\(823\) | 54.7532 | 1.90858 | 0.954288 | − | 0.298889i | \(-0.0966161\pi\) | ||||
0.954288 | + | 0.298889i | \(0.0966161\pi\) | |||||||
\(824\) | 11.9640 | 0.416787 | ||||||||
\(825\) | −17.8264 | − | 43.5288i | −0.620634 | − | 1.51548i | ||||
\(826\) | − | 3.53472i | − | 0.122989i | ||||||
\(827\) | −35.4582 | −1.23300 | −0.616502 | − | 0.787353i | \(-0.711451\pi\) | ||||
−0.616502 | + | 0.787353i | \(0.711451\pi\) | |||||||
\(828\) | 14.3873 | − | 0.0771712i | 0.499993 | − | 0.00268188i | ||||
\(829\) | −24.2004 | −0.840514 | −0.420257 | − | 0.907405i | \(-0.638060\pi\) | ||||
−0.420257 | + | 0.907405i | \(0.638060\pi\) | |||||||
\(830\) | 2.31727i | 0.0804337i | ||||||||
\(831\) | 7.67338 | + | 18.7370i | 0.266187 | + | 0.649980i | ||||
\(832\) | 3.10049 | 0.107490 | ||||||||
\(833\) | 0.471124 | 0.0163235 | ||||||||
\(834\) | 29.8020 | − | 12.2048i | 1.03196 | − | 0.422619i | ||||
\(835\) | 4.70960i | 0.162983i | ||||||||
\(836\) | − | 13.1434i | − | 0.454574i | ||||||
\(837\) | −6.71626 | − | 2.87696i | −0.232148 | − | 0.0994423i | ||||
\(838\) | 17.3290i | 0.598619i | ||||||||
\(839\) | 56.4665 | 1.94944 | 0.974720 | − | 0.223431i | \(-0.0717258\pi\) | ||||
0.974720 | + | 0.223431i | \(0.0717258\pi\) | |||||||
\(840\) | 0.165634 | + | 0.404450i | 0.00571493 | + | 0.0139548i | ||||
\(841\) | −8.01939 | −0.276531 | ||||||||
\(842\) | 25.2378 | 0.869752 | ||||||||
\(843\) | −11.4259 | − | 27.9001i | −0.393530 | − | 0.960930i | ||||
\(844\) | −2.20409 | −0.0758680 | ||||||||
\(845\) | 0.854638 | 0.0294004 | ||||||||
\(846\) | 8.59740 | − | 8.46080i | 0.295585 | − | 0.290888i | ||||
\(847\) | 19.2664i | 0.662001i | ||||||||
\(848\) | 1.95854 | 0.0672566 | ||||||||
\(849\) | −32.5016 | + | 13.3104i | −1.11545 | + | 0.456811i | ||||
\(850\) | − | 2.32562i | − | 0.0797681i | ||||||
\(851\) | −19.6440 | + | 20.1766i | −0.673389 | + | 0.691643i | ||||
\(852\) | 24.4251 | − | 10.0028i | 0.836790 | − | 0.342691i | ||||
\(853\) | −28.7879 | −0.985679 | −0.492840 | − | 0.870120i | \(-0.664041\pi\) | ||||
−0.492840 | + | 0.870120i | \(0.664041\pi\) | |||||||
\(854\) | − | 2.10168i | − | 0.0719180i | ||||||
\(855\) | 1.26853 | + | 1.28901i | 0.0433828 | + | 0.0440832i | ||||
\(856\) | − | 11.6433i | − | 0.397960i | ||||||
\(857\) | − | 10.2674i | − | 0.350728i | −0.984504 | − | 0.175364i | \(-0.943890\pi\) | ||
0.984504 | − | 0.175364i | \(-0.0561103\pi\) | |||||||
\(858\) | −27.3403 | + | 11.1967i | −0.933382 | + | 0.382248i | ||||
\(859\) | −47.6303 | −1.62512 | −0.812562 | − | 0.582875i | \(-0.801928\pi\) | ||||
−0.812562 | + | 0.582875i | \(0.801928\pi\) | |||||||
\(860\) | 1.28502i | 0.0438188i | ||||||||
\(861\) | −3.05019 | − | 7.44802i | −0.103950 | − | 0.253828i | ||||
\(862\) | − | 26.1039i | − | 0.889102i | ||||||
\(863\) | − | 6.69188i | − | 0.227794i | −0.993493 | − | 0.113897i | \(-0.963667\pi\) | ||
0.993493 | − | 0.113897i | \(-0.0363334\pi\) | |||||||
\(864\) | −2.04600 | + | 4.77639i | −0.0696064 | + | 0.162496i | ||||
\(865\) | − | 0.923648i | − | 0.0314050i | ||||||
\(866\) | −2.34431 | −0.0796630 | ||||||||
\(867\) | −11.0134 | − | 26.8926i | −0.374033 | − | 0.913322i | ||||
\(868\) | − | 1.40614i | − | 0.0477274i | ||||||
\(869\) | 76.7434i | 2.60334i | ||||||||
\(870\) | −1.00778 | − | 2.46082i | −0.0341669 | − | 0.0834295i | ||||
\(871\) | 18.2582i | 0.618657i | ||||||||
\(872\) | 1.11725 | 0.0378349 | ||||||||
\(873\) | 37.5643 | + | 38.1708i | 1.27136 | + | 1.29188i | ||||
\(874\) | 8.20932 | + | 7.99265i | 0.277684 | + | 0.270356i | ||||
\(875\) | 2.50725i | 0.0847606i | ||||||||
\(876\) | 2.19283 | + | 5.35451i | 0.0740890 | + | 0.180912i | ||||
\(877\) | 14.7866 | 0.499307 | 0.249653 | − | 0.968335i | \(-0.419683\pi\) | ||||
0.249653 | + | 0.968335i | \(0.419683\pi\) | |||||||
\(878\) | 7.50867i | 0.253405i | ||||||||
\(879\) | 10.7113 | + | 26.1551i | 0.361283 | + | 0.882189i | ||||
\(880\) | −1.38820 | −0.0467963 | ||||||||
\(881\) | −13.0104 | −0.438331 | −0.219165 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219165 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(882\) | −2.10426 | − | 2.13824i | −0.0708543 | − | 0.0719983i | ||||
\(883\) | 45.8305 | 1.54232 | 0.771160 | − | 0.636641i | \(-0.219677\pi\) | ||||
0.771160 | + | 0.636641i | \(0.219677\pi\) | |||||||
\(884\) | −1.46071 | −0.0491291 | ||||||||
\(885\) | −1.42962 | + | 0.585471i | −0.0480560 | + | 0.0196804i | ||||
\(886\) | 15.1702 | 0.509654 | ||||||||
\(887\) | − | 4.88742i | − | 0.164104i | −0.996628 | − | 0.0820518i | \(-0.973853\pi\) | ||
0.996628 | − | 0.0820518i | \(-0.0261473\pi\) | |||||||
\(888\) | −3.85430 | − | 9.41152i | −0.129342 | − | 0.315830i | ||||
\(889\) | 0.430922i | 0.0144527i | ||||||||
\(890\) | 3.27668i | 0.109835i | ||||||||
\(891\) | 0.792975 | − | 49.5071i | 0.0265657 | − | 1.65855i | ||||
\(892\) | 25.4713 | 0.852843 | ||||||||
\(893\) | 9.60591 | 0.321450 | ||||||||
\(894\) | 18.2900 | − | 7.49031i | 0.611709 | − | 0.250513i | ||||
\(895\) | 4.35140i | 0.145451i | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 9.63253 | − | 23.8854i | 0.321621 | − | 0.797512i | ||||
\(898\) | 19.0138 | 0.634500 | ||||||||
\(899\) | 8.55544i | 0.285340i | ||||||||
\(900\) | −10.5551 | + | 10.3873i | −0.351835 | + | 0.346245i | ||||
\(901\) | −0.922715 | −0.0307401 | ||||||||
\(902\) | 25.5640 | 0.851188 | ||||||||
\(903\) | −3.34284 | − | 8.16263i | −0.111243 | − | 0.271635i | ||||
\(904\) | − | 10.4257i | − | 0.346755i | ||||||
\(905\) | 1.45371i | 0.0483229i | ||||||||
\(906\) | 4.09609 | − | 1.67747i | 0.136084 | − | 0.0557303i | ||||
\(907\) | 2.27033i | 0.0753852i | 0.999289 | + | 0.0376926i | \(0.0120008\pi\) | ||||
−0.999289 | + | 0.0376926i | \(0.987999\pi\) | |||||||
\(908\) | −17.5961 | −0.583949 | ||||||||
\(909\) | −1.68985 | − | 1.71713i | −0.0560488 | − | 0.0569537i | ||||
\(910\) | 0.782353 | 0.0259347 | ||||||||
\(911\) | −9.42780 | −0.312357 | −0.156178 | − | 0.987729i | \(-0.549917\pi\) | ||||
−0.156178 | + | 0.987729i | \(0.549917\pi\) | |||||||
\(912\) | −3.82930 | + | 1.56822i | −0.126801 | + | 0.0519288i | ||||
\(913\) | 50.5225 | 1.67205 | ||||||||
\(914\) | −3.65320 | −0.120837 | ||||||||
\(915\) | −0.850023 | + | 0.348110i | −0.0281009 | + | 0.0115082i | ||||
\(916\) | − | 8.59906i | − | 0.284121i | ||||||
\(917\) | 11.1468 | 0.368101 | ||||||||
\(918\) | 0.963920 | − | 2.25027i | 0.0318141 | − | 0.0742699i | ||||
\(919\) | 12.6728i | 0.418038i | 0.977912 | + | 0.209019i | \(0.0670271\pi\) | ||||
−0.977912 | + | 0.209019i | \(0.932973\pi\) | |||||||
\(920\) | 0.844181 | − | 0.867065i | 0.0278318 | − | 0.0285863i | ||||
\(921\) | 10.4889 | + | 25.6120i | 0.345621 | + | 0.843944i | ||||
\(922\) | 41.7766 | 1.37584 | ||||||||
\(923\) | − | 47.2470i | − | 1.55516i | ||||||
\(924\) | 8.81805 | − | 3.61126i | 0.290093 | − | 0.118802i | ||||
\(925\) | − | 28.9849i | − | 0.953018i | ||||||
\(926\) | 19.4404i | 0.638850i | ||||||||
\(927\) | 25.1755 | + | 25.5820i | 0.826871 | + | 0.840222i | ||||
\(928\) | 6.08436 | 0.199729 | ||||||||
\(929\) | 57.5072i | 1.88675i | 0.331730 | + | 0.943375i | \(0.392368\pi\) | ||||
−0.331730 | + | 0.943375i | \(0.607632\pi\) | |||||||
\(930\) | −0.568712 | + | 0.232905i | −0.0186488 | + | 0.00763725i | ||||
\(931\) | − | 2.38906i | − | 0.0782984i | ||||||
\(932\) | − | 2.93410i | − | 0.0961097i | ||||||
\(933\) | −32.3228 | + | 13.2372i | −1.05820 | + | 0.433365i | ||||
\(934\) | − | 26.0964i | − | 0.853900i | ||||||
\(935\) | 0.654015 | 0.0213886 | ||||||||
\(936\) | 6.52425 | + | 6.62959i | 0.213252 | + | 0.216695i | ||||
\(937\) | 11.1132i | 0.363053i | 0.983386 | + | 0.181526i | \(0.0581038\pi\) | ||||
−0.983386 | + | 0.181526i | \(0.941896\pi\) | |||||||
\(938\) | − | 5.88882i | − | 0.192277i | ||||||
\(939\) | 0.432544 | − | 0.177140i | 0.0141155 | − | 0.00578074i | ||||
\(940\) | − | 1.01457i | − | 0.0330917i | ||||||
\(941\) | 27.8230 | 0.907003 | 0.453502 | − | 0.891255i | \(-0.350175\pi\) | ||||
0.453502 | + | 0.891255i | \(0.350175\pi\) | |||||||
\(942\) | −8.23149 | − | 20.0998i | −0.268196 | − | 0.654888i | ||||
\(943\) | −15.5458 | + | 15.9672i | −0.506239 | + | 0.519962i | ||||
\(944\) | − | 3.53472i | − | 0.115045i | ||||||
\(945\) | −0.516272 | + | 1.20524i | −0.0167943 | + | 0.0392063i | ||||
\(946\) | 28.0168 | 0.910904 | ||||||||
\(947\) | − | 21.5751i | − | 0.701096i | −0.936545 | − | 0.350548i | \(-0.885995\pi\) | ||
0.936545 | − | 0.350548i | \(-0.114005\pi\) | |||||||
\(948\) | 22.3590 | − | 9.15670i | 0.726188 | − | 0.297396i | ||||
\(949\) | 10.3576 | 0.336221 | ||||||||
\(950\) | −11.7932 | −0.382622 | ||||||||
\(951\) | 13.4196 | − | 5.49573i | 0.435160 | − | 0.178211i | ||||
\(952\) | 0.471124 | 0.0152692 | ||||||||
\(953\) | −0.898982 | −0.0291209 | −0.0145604 | − | 0.999894i | \(-0.504635\pi\) | ||||
−0.0145604 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(954\) | 4.12129 | + | 4.18783i | 0.133432 | + | 0.135586i | ||||
\(955\) | 4.41300 | 0.142801 | ||||||||
\(956\) | − | 1.13350i | − | 0.0366599i | ||||||
\(957\) | −53.6522 | + | 21.9722i | −1.73433 | + | 0.710260i | ||||
\(958\) | − | 24.4346i | − | 0.789448i | ||||||
\(959\) | 13.0016i | 0.419843i | ||||||||
\(960\) | 0.165634 | + | 0.404450i | 0.00534583 | + | 0.0130536i | ||||
\(961\) | −29.0228 | −0.936219 | ||||||||
\(962\) | −18.2053 | −0.586963 | ||||||||
\(963\) | 24.8962 | − | 24.5006i | 0.802268 | − | 0.789521i | ||||
\(964\) | 21.7858i | 0.701673i | ||||||||
\(965\) | −5.15263 | −0.165869 | ||||||||
\(966\) | −3.10678 | + | 7.70376i | −0.0999589 | + | 0.247864i | ||||
\(967\) | 24.7064 | 0.794504 | 0.397252 | − | 0.917710i | \(-0.369964\pi\) | ||||
0.397252 | + | 0.917710i | \(0.369964\pi\) | |||||||
\(968\) | 19.2664i | 0.619245i | ||||||||
\(969\) | 1.80408 | − | 0.738824i | 0.0579553 | − | 0.0237344i | ||||
\(970\) | 4.50450 | 0.144631 | ||||||||
\(971\) | −35.9227 | −1.15281 | −0.576407 | − | 0.817163i | \(-0.695546\pi\) | ||||
−0.576407 | + | 0.817163i | \(0.695546\pi\) | |||||||
\(972\) | −14.5184 | + | 5.67594i | −0.465678 | + | 0.182056i | ||||
\(973\) | 18.5932i | 0.596070i | ||||||||
\(974\) | − | 12.0770i | − | 0.386972i | ||||||
\(975\) | 10.0465 | + | 24.5316i | 0.321744 | + | 0.785641i | ||||
\(976\) | − | 2.10168i | − | 0.0672731i | ||||||
\(977\) | 8.43803 | 0.269956 | 0.134978 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134978 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(978\) | 13.0864 | − | 5.35927i | 0.418456 | − | 0.171370i | ||||
\(979\) | 71.4401 | 2.28324 | ||||||||
\(980\) | −0.252332 | −0.00806045 | ||||||||
\(981\) | 2.35099 | + | 2.38895i | 0.0750614 | + | 0.0762733i | ||||
\(982\) | 7.93573 | 0.253239 | ||||||||
\(983\) | −19.1227 | −0.609920 | −0.304960 | − | 0.952365i | \(-0.598643\pi\) | ||||
−0.304960 | + | 0.952365i | \(0.598643\pi\) | |||||||
\(984\) | −3.05019 | − | 7.44802i | −0.0972365 | − | 0.237434i | ||||
\(985\) | 2.06338i | 0.0657449i | ||||||||
\(986\) | −2.86648 | −0.0912874 | ||||||||
\(987\) | 2.63930 | + | 6.44470i | 0.0840099 | + | 0.205137i | ||||
\(988\) | 7.40727i | 0.235657i | ||||||||
\(989\) | −17.0373 | + | 17.4992i | −0.541755 | + | 0.556441i | ||||
\(990\) | −2.92114 | − | 2.96831i | −0.0928401 | − | 0.0943390i | ||||
\(991\) | −22.4016 | −0.711609 | −0.355805 | − | 0.934560i | \(-0.615793\pi\) | ||||
−0.355805 | + | 0.934560i | \(0.615793\pi\) | |||||||
\(992\) | − | 1.40614i | − | 0.0446449i | ||||||
\(993\) | −5.14645 | − | 12.5667i | −0.163318 | − | 0.398792i | ||||
\(994\) | 15.2386i | 0.483338i | ||||||||
\(995\) | 0.0157957i | 0.000500757i | ||||||||
\(996\) | −6.02814 | − | 14.7196i | −0.191009 | − | 0.466409i | ||||
\(997\) | −40.4484 | −1.28102 | −0.640508 | − | 0.767952i | \(-0.721276\pi\) | ||||
−0.640508 | + | 0.767952i | \(0.721276\pi\) | |||||||
\(998\) | 23.7262i | 0.751041i | ||||||||
\(999\) | 12.0136 | − | 28.0458i | 0.380094 | − | 0.887329i |
(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 | 966.2.h.a.827.7 | ✓ | 24 | |
3.2 | odd | 2 | 966.2.h.b.827.19 | yes | 24 | ||
23.22 | odd | 2 | 966.2.h.b.827.7 | yes | 24 | ||
69.68 | even | 2 | inner | 966.2.h.a.827.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.h.a.827.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
966.2.h.a.827.19 | yes | 24 | 69.68 | even | 2 | inner | |
966.2.h.b.827.7 | yes | 24 | 23.22 | odd | 2 | ||
966.2.h.b.827.19 | yes | 24 | 3.2 | odd | 2 |