Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(589,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.c (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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.4 | ||
Root | \(0.621372 - 1.27039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.589 |
Dual form | 1176.2.c.c.589.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.621372 | + | 1.27039i | −0.439377 | + | 0.898303i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.22779 | − | 1.57877i | −0.613897 | − | 0.789387i | ||||
\(5\) | − | 3.69833i | − | 1.65394i | −0.562243 | − | 0.826972i | \(-0.690062\pi\) | ||
0.562243 | − | 0.826972i | \(-0.309938\pi\) | |||||||
\(6\) | −1.27039 | − | 0.621372i | −0.518635 | − | 0.253674i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.76858 | − | 0.578773i | 0.978840 | − | 0.204627i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.69833 | + | 2.29804i | 1.48574 | + | 0.726704i | ||||
\(11\) | 3.21284i | 0.968708i | 0.874872 | + | 0.484354i | \(0.160945\pi\) | ||||
−0.874872 | + | 0.484354i | \(0.839055\pi\) | |||||||
\(12\) | 1.57877 | − | 1.22779i | 0.455753 | − | 0.354433i | ||||
\(13\) | − | 5.08157i | − | 1.40937i | −0.709518 | − | 0.704687i | \(-0.751088\pi\) | ||
0.709518 | − | 0.704687i | \(-0.248912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.69833 | 0.954905 | ||||||||
\(16\) | −0.985049 | + | 3.87681i | −0.246262 | + | 0.969203i | ||||
\(17\) | −0.616762 | −0.149587 | −0.0747933 | − | 0.997199i | \(-0.523830\pi\) | ||||
−0.0747933 | + | 0.997199i | \(0.523830\pi\) | |||||||
\(18\) | 0.621372 | − | 1.27039i | 0.146459 | − | 0.299434i | ||||
\(19\) | 4.48549i | 1.02904i | 0.857478 | + | 0.514521i | \(0.172030\pi\) | ||||
−0.857478 | + | 0.514521i | \(0.827970\pi\) | |||||||
\(20\) | −5.83882 | + | 4.54078i | −1.30560 | + | 1.01535i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.08157 | − | 1.99637i | −0.870193 | − | 0.425628i | ||||
\(23\) | 1.38324 | 0.288425 | 0.144213 | − | 0.989547i | \(-0.453935\pi\) | ||||
0.144213 | + | 0.989547i | \(0.453935\pi\) | |||||||
\(24\) | 0.578773 | + | 2.76858i | 0.118142 | + | 0.565134i | ||||
\(25\) | −8.67765 | −1.73553 | ||||||||
\(26\) | 6.45559 | + | 3.15755i | 1.26604 | + | 0.619246i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.67765i | − | 1.05431i | −0.849768 | − | 0.527156i | \(-0.823258\pi\) | ||
0.849768 | − | 0.527156i | \(-0.176742\pi\) | |||||||
\(30\) | −2.29804 | + | 4.69833i | −0.419563 | + | 0.857794i | ||||
\(31\) | −6.91117 | −1.24128 | −0.620642 | − | 0.784094i | \(-0.713128\pi\) | ||||
−0.620642 | + | 0.784094i | \(0.713128\pi\) | |||||||
\(32\) | −4.31299 | − | 3.66034i | −0.762436 | − | 0.647063i | ||||
\(33\) | −3.21284 | −0.559284 | ||||||||
\(34\) | 0.383238 | − | 0.783529i | 0.0657249 | − | 0.134374i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.22779 | + | 1.57877i | 0.204632 | + | 0.263129i | ||||
\(37\) | − | 6.91117i | − | 1.13619i | −0.822963 | − | 0.568095i | \(-0.807681\pi\) | ||
0.822963 | − | 0.568095i | \(-0.192319\pi\) | |||||||
\(38\) | −5.69833 | − | 2.78716i | −0.924391 | − | 0.452137i | ||||
\(39\) | 5.08157 | 0.813702 | ||||||||
\(40\) | −2.14049 | − | 10.2391i | −0.338442 | − | 1.61895i | ||||
\(41\) | 0.616762 | 0.0963220 | 0.0481610 | − | 0.998840i | \(-0.484664\pi\) | ||||
0.0481610 | + | 0.998840i | \(0.484664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.99274i | − | 1.21888i | −0.792832 | − | 0.609441i | \(-0.791394\pi\) | ||
0.792832 | − | 0.609441i | \(-0.208606\pi\) | |||||||
\(44\) | 5.07235 | − | 3.94470i | 0.764685 | − | 0.594687i | ||||
\(45\) | 3.69833i | 0.551315i | ||||||||
\(46\) | −0.859506 | + | 1.75726i | −0.126727 | + | 0.259093i | ||||
\(47\) | −4.97098 | −0.725092 | −0.362546 | − | 0.931966i | \(-0.618092\pi\) | ||||
−0.362546 | + | 0.931966i | \(0.618092\pi\) | |||||||
\(48\) | −3.87681 | − | 0.985049i | −0.559570 | − | 0.142180i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.39205 | − | 11.0240i | 0.762551 | − | 1.55903i | ||||
\(51\) | − | 0.616762i | − | 0.0863639i | ||||||
\(52\) | −8.02264 | + | 6.23912i | −1.11254 | + | 0.865210i | ||||
\(53\) | 4.48549i | 0.616129i | 0.951365 | + | 0.308065i | \(0.0996813\pi\) | ||||
−0.951365 | + | 0.308065i | \(0.900319\pi\) | |||||||
\(54\) | 1.27039 | + | 0.621372i | 0.172878 | + | 0.0845581i | ||||
\(55\) | 11.8822 | 1.60219 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.48549 | −0.594118 | ||||||||
\(58\) | 7.21284 | + | 3.52793i | 0.947092 | + | 0.463240i | ||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | −4.54078 | − | 5.83882i | −0.586213 | − | 0.753789i | ||||
\(61\) | − | 12.4782i | − | 1.59767i | −0.601548 | − | 0.798837i | \(-0.705449\pi\) | ||
0.601548 | − | 0.798837i | \(-0.294551\pi\) | |||||||
\(62\) | 4.29441 | − | 8.77990i | 0.545391 | − | 1.11505i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.33004 | − | 3.20476i | 0.916255 | − | 0.400595i | ||||
\(65\) | −18.7933 | −2.33102 | ||||||||
\(66\) | 1.99637 | − | 4.08157i | 0.245736 | − | 0.502406i | ||||
\(67\) | − | 9.56706i | − | 1.16880i | −0.811465 | − | 0.584401i | \(-0.801329\pi\) | ||
0.811465 | − | 0.584401i | \(-0.198671\pi\) | |||||||
\(68\) | 0.757255 | + | 0.973726i | 0.0918307 | + | 0.118082i | ||||
\(69\) | 1.38324i | 0.166522i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.2056 | −1.80457 | −0.902285 | − | 0.431139i | \(-0.858112\pi\) | ||||
−0.902285 | + | 0.431139i | \(0.858112\pi\) | |||||||
\(72\) | −2.76858 | + | 0.578773i | −0.326280 | + | 0.0682091i | ||||
\(73\) | −15.5598 | −1.82114 | −0.910568 | − | 0.413358i | \(-0.864356\pi\) | ||||
−0.910568 | + | 0.413358i | \(0.864356\pi\) | |||||||
\(74\) | 8.77990 | + | 4.29441i | 1.02064 | + | 0.499215i | ||||
\(75\) | − | 8.67765i | − | 1.00201i | ||||||
\(76\) | 7.08157 | − | 5.50725i | 0.812312 | − | 0.631725i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.15755 | + | 6.45559i | −0.357522 | + | 0.730951i | ||||
\(79\) | −5.23352 | −0.588817 | −0.294409 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294409 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(80\) | 14.3377 | + | 3.64304i | 1.60301 | + | 0.407304i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.383238 | + | 0.783529i | −0.0423216 | + | 0.0865263i | ||||
\(83\) | 10.4257i | 1.14437i | 0.820125 | + | 0.572184i | \(0.193904\pi\) | ||||
−0.820125 | + | 0.572184i | \(0.806096\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28099i | 0.247408i | ||||||||
\(86\) | 10.1539 | + | 4.96647i | 1.09492 | + | 0.535548i | ||||
\(87\) | 5.67765 | 0.608708 | ||||||||
\(88\) | 1.85951 | + | 8.89500i | 0.198224 | + | 0.948210i | ||||
\(89\) | 14.1766 | 1.50271 | 0.751356 | − | 0.659897i | \(-0.229400\pi\) | ||||
0.751356 | + | 0.659897i | \(0.229400\pi\) | |||||||
\(90\) | −4.69833 | − | 2.29804i | −0.495248 | − | 0.242235i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.69833 | − | 2.18382i | −0.177063 | − | 0.227679i | ||||
\(93\) | − | 6.91117i | − | 0.716655i | ||||||
\(94\) | 3.08883 | − | 6.31509i | 0.318588 | − | 0.651352i | ||||
\(95\) | 16.5888 | 1.70198 | ||||||||
\(96\) | 3.66034 | − | 4.31299i | 0.373582 | − | 0.440193i | ||||
\(97\) | −9.73746 | −0.988689 | −0.494344 | − | 0.869266i | \(-0.664592\pi\) | ||||
−0.494344 | + | 0.869266i | \(0.664592\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.21284i | − | 0.322903i | ||||||
\(100\) | 10.6544 | + | 13.7000i | 1.06544 | + | 1.37000i | ||||
\(101\) | 5.27265i | 0.524648i | 0.964980 | + | 0.262324i | \(0.0844889\pi\) | ||||
−0.964980 | + | 0.262324i | \(0.915511\pi\) | |||||||
\(102\) | 0.783529 | + | 0.383238i | 0.0775809 | + | 0.0379463i | ||||
\(103\) | −1.94019 | −0.191173 | −0.0955865 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955865 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(104\) | −2.94108 | − | 14.0687i | −0.288396 | − | 1.37955i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.69833 | − | 2.78716i | −0.553471 | − | 0.270713i | ||||
\(107\) | 4.78716i | 0.462792i | 0.972860 | + | 0.231396i | \(0.0743293\pi\) | ||||
−0.972860 | + | 0.231396i | \(0.925671\pi\) | |||||||
\(108\) | −1.57877 | + | 1.22779i | −0.151918 | + | 0.118144i | ||||
\(109\) | 0.970978i | 0.0930028i | 0.998918 | + | 0.0465014i | \(0.0148072\pi\) | ||||
−0.998918 | + | 0.0465014i | \(0.985193\pi\) | |||||||
\(110\) | −7.38324 | + | 15.0950i | −0.703964 | + | 1.43925i | ||||
\(111\) | 6.91117 | 0.655979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5598 | 1.46374 | 0.731871 | − | 0.681443i | \(-0.238647\pi\) | ||||
0.731871 | + | 0.681443i | \(0.238647\pi\) | |||||||
\(114\) | 2.78716 | − | 5.69833i | 0.261041 | − | 0.533698i | ||||
\(115\) | − | 5.11567i | − | 0.477039i | ||||||
\(116\) | −8.96372 | + | 6.97098i | −0.832260 | + | 0.647239i | ||||
\(117\) | 5.08157i | 0.469791i | ||||||||
\(118\) | 5.08157 | + | 2.48549i | 0.467796 | + | 0.228808i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.2391 | − | 2.14049i | 0.934699 | − | 0.195399i | ||||
\(121\) | 0.677649 | 0.0616045 | ||||||||
\(122\) | 15.8522 | + | 7.75363i | 1.43520 | + | 0.701980i | ||||
\(123\) | 0.616762i | 0.0556115i | ||||||||
\(124\) | 8.48549 | + | 10.9112i | 0.762019 | + | 0.979852i | ||||
\(125\) | 13.6012i | 1.21652i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.73746 | −0.331646 | −0.165823 | − | 0.986156i | \(-0.553028\pi\) | ||||
−0.165823 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(128\) | −0.483388 | + | 11.3034i | −0.0427259 | + | 0.999087i | ||||
\(129\) | 7.99274 | 0.703722 | ||||||||
\(130\) | 11.6776 | − | 23.8749i | 1.02420 | − | 2.09397i | ||||
\(131\) | − | 3.39666i | − | 0.296768i | −0.988930 | − | 0.148384i | \(-0.952593\pi\) | ||
0.988930 | − | 0.148384i | \(-0.0474071\pi\) | |||||||
\(132\) | 3.94470 | + | 5.07235i | 0.343342 | + | 0.441491i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.1539 | + | 5.94470i | 1.04994 | + | 0.513544i | ||||
\(135\) | −3.69833 | −0.318302 | ||||||||
\(136\) | −1.70755 | + | 0.356965i | −0.146421 | + | 0.0306095i | ||||
\(137\) | 13.0559 | 1.11544 | 0.557719 | − | 0.830030i | \(-0.311677\pi\) | ||||
0.557719 | + | 0.830030i | \(0.311677\pi\) | |||||||
\(138\) | −1.75726 | − | 0.859506i | −0.149588 | − | 0.0731660i | ||||
\(139\) | − | 2.80784i | − | 0.238158i | −0.992885 | − | 0.119079i | \(-0.962006\pi\) | ||
0.992885 | − | 0.119079i | \(-0.0379942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.97098i | − | 0.418632i | ||||||
\(142\) | 9.44833 | − | 19.3171i | 0.792886 | − | 1.62105i | ||||
\(143\) | 16.3263 | 1.36527 | ||||||||
\(144\) | 0.985049 | − | 3.87681i | 0.0820874 | − | 0.323068i | ||||
\(145\) | −20.9978 | −1.74377 | ||||||||
\(146\) | 9.66843 | − | 19.7670i | 0.800165 | − | 1.63593i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9112 | + | 8.48549i | −0.896893 | + | 0.697503i | ||||
\(149\) | 12.4855i | 1.02285i | 0.859328 | + | 0.511426i | \(0.170882\pi\) | ||||
−0.859328 | + | 0.511426i | \(0.829118\pi\) | |||||||
\(150\) | 11.0240 | + | 5.39205i | 0.900107 | + | 0.440259i | ||||
\(151\) | 8.97098 | 0.730048 | 0.365024 | − | 0.930998i | \(-0.381061\pi\) | ||||
0.365024 | + | 0.930998i | \(0.381061\pi\) | |||||||
\(152\) | 2.59608 | + | 12.4184i | 0.210570 | + | 1.00727i | ||||
\(153\) | 0.616762 | 0.0498622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.5598i | 2.05301i | ||||||||
\(156\) | −6.23912 | − | 8.02264i | −0.499529 | − | 0.642326i | ||||
\(157\) | − | 15.1665i | − | 1.21042i | −0.796068 | − | 0.605208i | \(-0.793090\pi\) | ||
0.796068 | − | 0.605208i | \(-0.206910\pi\) | |||||||
\(158\) | 3.25197 | − | 6.64863i | 0.258713 | − | 0.528936i | ||||
\(159\) | −4.48549 | −0.355722 | ||||||||
\(160\) | −13.5372 | + | 15.9509i | −1.07021 | + | 1.26103i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.621372 | + | 1.27039i | −0.0488196 | + | 0.0998114i | ||||
\(163\) | − | 13.2263i | − | 1.03596i | −0.855392 | − | 0.517980i | \(-0.826684\pi\) | ||
0.855392 | − | 0.517980i | \(-0.173316\pi\) | |||||||
\(164\) | −0.757255 | − | 0.973726i | −0.0591317 | − | 0.0760353i | ||||
\(165\) | 11.8822i | 0.925024i | ||||||||
\(166\) | −13.2447 | − | 6.47823i | −1.02799 | − | 0.502808i | ||||
\(167\) | −3.05587 | −0.236470 | −0.118235 | − | 0.992986i | \(-0.537724\pi\) | ||||
−0.118235 | + | 0.992986i | \(0.537724\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8223 | −0.986334 | ||||||||
\(170\) | −2.89775 | − | 1.41734i | −0.222247 | − | 0.108705i | ||||
\(171\) | − | 4.48549i | − | 0.343014i | ||||||
\(172\) | −12.6187 | + | 9.81343i | −0.962169 | + | 0.748267i | ||||
\(173\) | 13.8615i | 1.05387i | 0.849906 | + | 0.526934i | \(0.176658\pi\) | ||||
−0.849906 | + | 0.526934i | \(0.823342\pi\) | |||||||
\(174\) | −3.52793 | + | 7.21284i | −0.267452 | + | 0.546804i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.4556 | − | 3.16480i | −0.938875 | − | 0.238556i | ||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −8.80892 | + | 18.0098i | −0.660257 | + | 1.34989i | ||||
\(179\) | − | 18.3883i | − | 1.37441i | −0.726465 | − | 0.687204i | \(-0.758838\pi\) | ||
0.726465 | − | 0.687204i | \(-0.241162\pi\) | |||||||
\(180\) | 5.83882 | − | 4.54078i | 0.435200 | − | 0.338450i | ||||
\(181\) | 6.05255i | 0.449882i | 0.974372 | + | 0.224941i | \(0.0722190\pi\) | ||||
−0.974372 | + | 0.224941i | \(0.927781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4782 | 0.922417 | ||||||||
\(184\) | 3.82960 | − | 0.800581i | 0.282322 | − | 0.0590196i | ||||
\(185\) | −25.5598 | −1.87919 | ||||||||
\(186\) | 8.77990 | + | 4.29441i | 0.643773 | + | 0.314881i | ||||
\(187\) | − | 1.98156i | − | 0.144906i | ||||||
\(188\) | 6.10333 | + | 7.84805i | 0.445131 | + | 0.572378i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.3078 | + | 21.0743i | −0.747809 | + | 1.52889i | ||||
\(191\) | −15.2056 | −1.10024 | −0.550119 | − | 0.835086i | \(-0.685418\pi\) | ||||
−0.550119 | + | 0.835086i | \(0.685418\pi\) | |||||||
\(192\) | 3.20476 | + | 7.33004i | 0.231283 | + | 0.529000i | ||||
\(193\) | −19.4419 | −1.39946 | −0.699731 | − | 0.714406i | \(-0.746697\pi\) | ||||
−0.699731 | + | 0.714406i | \(0.746697\pi\) | |||||||
\(194\) | 6.05058 | − | 12.3704i | 0.434407 | − | 0.888142i | ||||
\(195\) | − | 18.7933i | − | 1.34582i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.2520i | − | 1.08666i | −0.839520 | − | 0.543329i | \(-0.817164\pi\) | ||
0.839520 | − | 0.543329i | \(-0.182836\pi\) | |||||||
\(198\) | 4.08157 | + | 1.99637i | 0.290064 | + | 0.141876i | ||||
\(199\) | 3.02902 | 0.214722 | 0.107361 | − | 0.994220i | \(-0.465760\pi\) | ||||
0.107361 | + | 0.994220i | \(0.465760\pi\) | |||||||
\(200\) | −24.0247 | + | 5.02239i | −1.69881 | + | 0.355137i | ||||
\(201\) | 9.56706 | 0.674808 | ||||||||
\(202\) | −6.69833 | − | 3.27628i | −0.471293 | − | 0.230518i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.973726 | + | 0.757255i | −0.0681745 | + | 0.0530185i | ||||
\(205\) | − | 2.28099i | − | 0.159311i | ||||||
\(206\) | 1.20558 | − | 2.46481i | 0.0839969 | − | 0.171731i | ||||
\(207\) | −1.38324 | −0.0961417 | ||||||||
\(208\) | 19.7003 | + | 5.00559i | 1.36597 | + | 0.347075i | ||||
\(209\) | −14.4112 | −0.996841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.963719i | 0.0663452i | 0.999450 | + | 0.0331726i | \(0.0105611\pi\) | ||||
−0.999450 | + | 0.0331726i | \(0.989439\pi\) | |||||||
\(212\) | 7.08157 | − | 5.50725i | 0.486364 | − | 0.378240i | ||||
\(213\) | − | 15.2056i | − | 1.04187i | ||||||
\(214\) | −6.08157 | − | 2.97461i | −0.415728 | − | 0.203340i | ||||
\(215\) | −29.5598 | −2.01596 | ||||||||
\(216\) | −0.578773 | − | 2.76858i | −0.0393805 | − | 0.188378i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.23352 | − | 0.603339i | −0.0835447 | − | 0.0408633i | ||||
\(219\) | − | 15.5598i | − | 1.05143i | ||||||
\(220\) | −14.5888 | − | 18.7592i | −0.983578 | − | 1.26475i | ||||
\(221\) | 3.13412i | 0.210823i | ||||||||
\(222\) | −4.29441 | + | 8.77990i | −0.288222 | + | 0.589268i | ||||
\(223\) | 22.1486 | 1.48318 | 0.741591 | − | 0.670853i | \(-0.234072\pi\) | ||||
0.741591 | + | 0.670853i | \(0.234072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.67765 | 0.578510 | ||||||||
\(226\) | −9.66843 | + | 19.7670i | −0.643134 | + | 1.31488i | ||||
\(227\) | − | 0.929615i | − | 0.0617007i | −0.999524 | − | 0.0308504i | \(-0.990178\pi\) | ||
0.999524 | − | 0.0308504i | \(-0.00982153\pi\) | |||||||
\(228\) | 5.50725 | + | 7.08157i | 0.364727 | + | 0.468988i | ||||
\(229\) | − | 1.42236i | − | 0.0939924i | −0.998895 | − | 0.0469962i | \(-0.985035\pi\) | ||
0.998895 | − | 0.0469962i | \(-0.0149649\pi\) | |||||||
\(230\) | 6.49891 | + | 3.17874i | 0.428526 | + | 0.209600i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.28607 | − | 15.7190i | −0.215741 | − | 1.03200i | ||||
\(233\) | 10.9710 | 0.718733 | 0.359366 | − | 0.933197i | \(-0.382993\pi\) | ||||
0.359366 | + | 0.933197i | \(0.382993\pi\) | |||||||
\(234\) | −6.45559 | − | 3.15755i | −0.422015 | − | 0.206415i | ||||
\(235\) | 18.3843i | 1.19926i | ||||||||
\(236\) | −6.31509 | + | 4.91117i | −0.411077 | + | 0.319690i | ||||
\(237\) | − | 5.23352i | − | 0.339954i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.82126 | −0.311862 | −0.155931 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155931 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(240\) | −3.64304 | + | 14.3377i | −0.235157 | + | 0.925497i | ||||
\(241\) | 0.204501 | 0.0131731 | 0.00658654 | − | 0.999978i | \(-0.497903\pi\) | ||||
0.00658654 | + | 0.999978i | \(0.497903\pi\) | |||||||
\(242\) | −0.421072 | + | 0.860880i | −0.0270676 | + | 0.0553395i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −19.7003 | + | 15.3207i | −1.26118 | + | 0.980806i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.783529 | − | 0.383238i | −0.0499560 | − | 0.0244344i | ||||
\(247\) | 22.7933 | 1.45030 | ||||||||
\(248\) | −19.1341 | + | 4.00000i | −1.21502 | + | 0.254000i | ||||
\(249\) | −10.4257 | −0.660701 | ||||||||
\(250\) | −17.2788 | − | 8.45138i | −1.09281 | − | 0.534513i | ||||
\(251\) | − | 3.10727i | − | 0.196129i | −0.995180 | − | 0.0980646i | \(-0.968735\pi\) | ||
0.995180 | − | 0.0980646i | \(-0.0312652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.44413i | 0.279400i | ||||||||
\(254\) | 2.32235 | − | 4.74803i | 0.145717 | − | 0.297918i | ||||
\(255\) | −2.28099 | −0.142841 | ||||||||
\(256\) | −14.0594 | − | 7.63770i | −0.878710 | − | 0.477356i | ||||
\(257\) | 14.1497 | 0.882635 | 0.441318 | − | 0.897351i | \(-0.354511\pi\) | ||||
0.441318 | + | 0.897351i | \(0.354511\pi\) | |||||||
\(258\) | −4.96647 | + | 10.1539i | −0.309199 | + | 0.632155i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 23.0743 | + | 29.6704i | 1.43101 | + | 1.84008i | ||||
\(261\) | 5.67765i | 0.351438i | ||||||||
\(262\) | 4.31509 | + | 2.11059i | 0.266587 | + | 0.130393i | ||||
\(263\) | 2.94304 | 0.181475 | 0.0907377 | − | 0.995875i | \(-0.471077\pi\) | ||||
0.0907377 | + | 0.995875i | \(0.471077\pi\) | |||||||
\(264\) | −8.89500 | + | 1.85951i | −0.547449 | + | 0.114445i | ||||
\(265\) | 16.5888 | 1.01904 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.1766i | 0.867591i | ||||||||
\(268\) | −15.1042 | + | 11.7464i | −0.922637 | + | 0.717524i | ||||
\(269\) | − | 0.642463i | − | 0.0391717i | −0.999808 | − | 0.0195858i | \(-0.993765\pi\) | ||
0.999808 | − | 0.0195858i | \(-0.00623476\pi\) | |||||||
\(270\) | 2.29804 | − | 4.69833i | 0.139854 | − | 0.285931i | ||||
\(271\) | 0.526852 | 0.0320040 | 0.0160020 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160020 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(272\) | 0.607540 | − | 2.39107i | 0.0368375 | − | 0.144980i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.11255 | + | 16.5861i | −0.490097 | + | 1.00200i | ||||
\(275\) | − | 27.8799i | − | 1.68122i | ||||||
\(276\) | 2.18382 | − | 1.69833i | 0.131450 | − | 0.102227i | ||||
\(277\) | 21.7190i | 1.30497i | 0.757802 | + | 0.652484i | \(0.226273\pi\) | ||||
−0.757802 | + | 0.652484i | \(0.773727\pi\) | |||||||
\(278\) | 3.56706 | + | 1.74471i | 0.213938 | + | 0.104641i | ||||
\(279\) | 6.91117 | 0.413761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.79332 | −0.285946 | −0.142973 | − | 0.989727i | \(-0.545666\pi\) | ||||
−0.142973 | + | 0.989727i | \(0.545666\pi\) | |||||||
\(282\) | 6.31509 | + | 3.08883i | 0.376058 | + | 0.183937i | ||||
\(283\) | − | 22.6486i | − | 1.34632i | −0.739496 | − | 0.673161i | \(-0.764936\pi\) | ||
0.739496 | − | 0.673161i | \(-0.235064\pi\) | |||||||
\(284\) | 18.6693 | + | 24.0062i | 1.10782 | + | 1.42450i | ||||
\(285\) | 16.5888i | 0.982637i | ||||||||
\(286\) | −10.1447 | + | 20.7408i | −0.599868 | + | 1.22643i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.31299 | + | 3.66034i | 0.254145 | + | 0.215688i | ||||
\(289\) | −16.6196 | −0.977624 | ||||||||
\(290\) | 13.0475 | − | 26.6755i | 0.766174 | − | 1.56644i | ||||
\(291\) | − | 9.73746i | − | 0.570820i | ||||||
\(292\) | 19.1042 | + | 24.5654i | 1.11799 | + | 1.43758i | ||||
\(293\) | 24.3285i | 1.42129i | 0.703552 | + | 0.710644i | \(0.251596\pi\) | ||||
−0.703552 | + | 0.710644i | \(0.748404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.7933 | −0.861301 | ||||||||
\(296\) | −4.00000 | − | 19.1341i | −0.232495 | − | 1.11215i | ||||
\(297\) | 3.21284 | 0.186428 | ||||||||
\(298\) | −15.8615 | − | 7.75814i | −0.918830 | − | 0.449417i | ||||
\(299\) | − | 7.02902i | − | 0.406499i | ||||||
\(300\) | −13.7000 | + | 10.6544i | −0.790972 | + | 0.615130i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.57432 | + | 11.3967i | −0.320766 | + | 0.655804i | ||||
\(303\) | −5.27265 | −0.302906 | ||||||||
\(304\) | −17.3894 | − | 4.41842i | −0.997351 | − | 0.253414i | ||||
\(305\) | −46.1486 | −2.64246 | ||||||||
\(306\) | −0.383238 | + | 0.783529i | −0.0219083 | + | 0.0447914i | ||||
\(307\) | 3.51451i | 0.200584i | 0.994958 | + | 0.100292i | \(0.0319777\pi\) | ||||
−0.994958 | + | 0.100292i | \(0.968022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.94019i | − | 0.110374i | ||||||
\(310\) | −32.4710 | − | 15.8822i | −1.84423 | − | 0.902046i | ||||
\(311\) | 4.97098 | 0.281878 | 0.140939 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140939 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(312\) | 14.0687 | − | 2.94108i | 0.796484 | − | 0.166506i | ||||
\(313\) | 25.6447 | 1.44952 | 0.724762 | − | 0.689000i | \(-0.241950\pi\) | ||||
0.724762 | + | 0.689000i | \(0.241950\pi\) | |||||||
\(314\) | 19.2674 | + | 9.42402i | 1.08732 | + | 0.531828i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.42568 | + | 8.26254i | 0.361473 | + | 0.464804i | ||||
\(317\) | − | 3.51451i | − | 0.197395i | −0.995118 | − | 0.0986973i | \(-0.968532\pi\) | ||
0.995118 | − | 0.0986973i | \(-0.0314676\pi\) | |||||||
\(318\) | 2.78716 | − | 5.69833i | 0.156296 | − | 0.319547i | ||||
\(319\) | 18.2414 | 1.02132 | ||||||||
\(320\) | −11.8522 | − | 27.1089i | −0.662561 | − | 1.51543i | ||||
\(321\) | −4.78716 | −0.267193 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.76648i | − | 0.153931i | ||||||
\(324\) | −1.22779 | − | 1.57877i | −0.0682107 | − | 0.0877096i | ||||
\(325\) | 44.0961i | 2.44601i | ||||||||
\(326\) | 16.8025 | + | 8.21843i | 0.930607 | + | 0.455177i | ||||
\(327\) | −0.970978 | −0.0536952 | ||||||||
\(328\) | 1.70755 | − | 0.356965i | 0.0942838 | − | 0.0197101i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −15.0950 | − | 7.38324i | −0.830952 | − | 0.406434i | ||||
\(331\) | 25.1849i | 1.38429i | 0.721760 | + | 0.692144i | \(0.243334\pi\) | ||||
−0.721760 | + | 0.692144i | \(0.756666\pi\) | |||||||
\(332\) | 16.4598 | − | 12.8006i | 0.903348 | − | 0.702523i | ||||
\(333\) | 6.91117i | 0.378730i | ||||||||
\(334\) | 1.89883 | − | 3.88215i | 0.103899 | − | 0.212422i | ||||
\(335\) | −35.3821 | −1.93313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7643 | 1.18558 | 0.592788 | − | 0.805358i | \(-0.298027\pi\) | ||||
0.592788 | + | 0.805358i | \(0.298027\pi\) | |||||||
\(338\) | 7.96745 | − | 16.2894i | 0.433372 | − | 0.886027i | ||||
\(339\) | 15.5598i | 0.845092i | ||||||||
\(340\) | 3.60116 | − | 2.80058i | 0.195300 | − | 0.151883i | ||||
\(341\) | − | 22.2045i | − | 1.20244i | ||||||
\(342\) | 5.69833 | + | 2.78716i | 0.308130 | + | 0.150712i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.62598 | − | 22.1285i | −0.249416 | − | 1.19309i | ||||
\(345\) | 5.11567 | 0.275419 | ||||||||
\(346\) | −17.6095 | − | 8.61313i | −0.946693 | − | 0.463045i | ||||
\(347\) | − | 31.9068i | − | 1.71284i | −0.516276 | − | 0.856422i | \(-0.672682\pi\) | ||
0.516276 | − | 0.856422i | \(-0.327318\pi\) | |||||||
\(348\) | −6.97098 | − | 8.96372i | −0.373684 | − | 0.480506i | ||||
\(349\) | 1.04021i | 0.0556810i | 0.999612 | + | 0.0278405i | \(0.00886305\pi\) | ||||
−0.999612 | + | 0.0278405i | \(0.991137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.08157 | −0.271234 | ||||||||
\(352\) | 11.7601 | − | 13.8570i | 0.626815 | − | 0.738578i | ||||
\(353\) | 13.8503 | 0.737176 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(354\) | −2.48549 | + | 5.08157i | −0.132102 | + | 0.270082i | ||||
\(355\) | 56.2353i | 2.98466i | ||||||||
\(356\) | −17.4059 | − | 22.3816i | −0.922510 | − | 1.18622i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.3604 | + | 11.4260i | 1.23463 | + | 0.603882i | ||||
\(359\) | 0.412260 | 0.0217583 | 0.0108791 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108791 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(360\) | 2.14049 | + | 10.2391i | 0.112814 | + | 0.539649i | ||||
\(361\) | −1.11961 | −0.0589269 | ||||||||
\(362\) | −7.68911 | − | 3.76088i | −0.404131 | − | 0.197668i | ||||
\(363\) | 0.677649i | 0.0355674i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 57.5453i | 3.01206i | ||||||||
\(366\) | −7.75363 | + | 15.8522i | −0.405289 | + | 0.828610i | ||||
\(367\) | −4.97098 | −0.259483 | −0.129741 | − | 0.991548i | \(-0.541415\pi\) | ||||
−0.129741 | + | 0.991548i | \(0.541415\pi\) | |||||||
\(368\) | −1.36256 | + | 5.36256i | −0.0710282 | + | 0.279543i | ||||
\(369\) | −0.616762 | −0.0321073 | ||||||||
\(370\) | 15.8822 | − | 32.4710i | 0.825674 | − | 1.68809i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.9112 | + | 8.48549i | −0.565718 | + | 0.439952i | ||||
\(373\) | − | 2.16314i | − | 0.112003i | −0.998431 | − | 0.0560015i | \(-0.982165\pi\) | ||
0.998431 | − | 0.0560015i | \(-0.0178352\pi\) | |||||||
\(374\) | 2.51735 | + | 1.23128i | 0.130169 | + | 0.0636682i | ||||
\(375\) | −13.6012 | −0.702361 | ||||||||
\(376\) | −13.7625 | + | 2.87707i | −0.709749 | + | 0.148373i | ||||
\(377\) | −28.8514 | −1.48592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.7570i | − | 1.22032i | −0.792279 | − | 0.610159i | \(-0.791106\pi\) | ||
0.792279 | − | 0.610159i | \(-0.208894\pi\) | |||||||
\(380\) | −20.3676 | − | 26.1900i | −1.04484 | − | 1.34352i | ||||
\(381\) | − | 3.73746i | − | 0.191476i | ||||||
\(382\) | 9.44833 | − | 19.3171i | 0.483418 | − | 0.988347i | ||||
\(383\) | 37.5598 | 1.91922 | 0.959608 | − | 0.281340i | \(-0.0907790\pi\) | ||||
0.959608 | + | 0.281340i | \(0.0907790\pi\) | |||||||
\(384\) | −11.3034 | − | 0.483388i | −0.576823 | − | 0.0246678i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0807 | − | 24.6989i | 0.614891 | − | 1.25714i | ||||
\(387\) | 7.99274i | 0.406294i | ||||||||
\(388\) | 11.9556 | + | 15.3732i | 0.606953 | + | 0.780458i | ||||
\(389\) | 0.826283i | 0.0418942i | 0.999781 | + | 0.0209471i | \(0.00666816\pi\) | ||||
−0.999781 | + | 0.0209471i | \(0.993332\pi\) | |||||||
\(390\) | 23.8749 | + | 11.6776i | 1.20895 | + | 0.591321i | ||||
\(391\) | −0.853128 | −0.0431446 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.39666 | 0.171339 | ||||||||
\(394\) | 19.3760 | + | 9.47715i | 0.976148 | + | 0.477452i | ||||
\(395\) | 19.3553i | 0.973871i | ||||||||
\(396\) | −5.07235 | + | 3.94470i | −0.254895 | + | 0.198229i | ||||
\(397\) | − | 8.81902i | − | 0.442614i | −0.975204 | − | 0.221307i | \(-0.928968\pi\) | ||
0.975204 | − | 0.221307i | \(-0.0710323\pi\) | |||||||
\(398\) | −1.88215 | + | 3.84805i | −0.0943437 | + | 0.192885i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.54791 | − | 33.6416i | 0.427395 | − | 1.68208i | ||||
\(401\) | −8.64687 | −0.431804 | −0.215902 | − | 0.976415i | \(-0.569269\pi\) | ||||
−0.215902 | + | 0.976415i | \(0.569269\pi\) | |||||||
\(402\) | −5.94470 | + | 12.1539i | −0.296495 | + | 0.606182i | ||||
\(403\) | 35.1196i | 1.74943i | ||||||||
\(404\) | 8.32431 | − | 6.47372i | 0.414150 | − | 0.322080i | ||||
\(405\) | − | 3.69833i | − | 0.183772i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.2045 | 1.10064 | ||||||||
\(408\) | −0.356965 | − | 1.70755i | −0.0176724 | − | 0.0845364i | ||||
\(409\) | 18.7084 | 0.925072 | 0.462536 | − | 0.886600i | \(-0.346940\pi\) | ||||
0.462536 | + | 0.886600i | \(0.346940\pi\) | |||||||
\(410\) | 2.89775 | + | 1.41734i | 0.143110 | + | 0.0699976i | ||||
\(411\) | 13.0559i | 0.643998i | ||||||||
\(412\) | 2.38216 | + | 3.06313i | 0.117360 | + | 0.150909i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.859506 | − | 1.75726i | 0.0422424 | − | 0.0863644i | ||||
\(415\) | 38.5576 | 1.89272 | ||||||||
\(416\) | −18.6003 | + | 21.9168i | −0.911954 | + | 1.07456i | ||||
\(417\) | 2.80784 | 0.137501 | ||||||||
\(418\) | 8.95470 | − | 18.3078i | 0.437989 | − | 0.895465i | ||||
\(419\) | 12.9710i | 0.633674i | 0.948480 | + | 0.316837i | \(0.102621\pi\) | ||||
−0.948480 | + | 0.316837i | \(0.897379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.54136i | 0.172595i | 0.996269 | + | 0.0862976i | \(0.0275036\pi\) | ||||
−0.996269 | + | 0.0862976i | \(0.972496\pi\) | |||||||
\(422\) | −1.22430 | − | 0.598828i | −0.0595981 | − | 0.0291505i | ||||
\(423\) | 4.97098 | 0.241697 | ||||||||
\(424\) | 2.59608 | + | 12.4184i | 0.126077 | + | 0.603092i | ||||
\(425\) | 5.35204 | 0.259612 | ||||||||
\(426\) | 19.3171 | + | 9.44833i | 0.935914 | + | 0.457773i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.55784 | − | 5.87764i | 0.365322 | − | 0.284106i | ||||
\(429\) | 16.3263i | 0.788240i | ||||||||
\(430\) | 18.3676 | − | 37.5525i | 0.885766 | − | 1.81094i | ||||
\(431\) | 14.6168 | 0.704065 | 0.352032 | − | 0.935988i | \(-0.385491\pi\) | ||||
0.352032 | + | 0.935988i | \(0.385491\pi\) | |||||||
\(432\) | 3.87681 | + | 0.985049i | 0.186523 | + | 0.0473932i | ||||
\(433\) | 2.97098 | 0.142776 | 0.0713880 | − | 0.997449i | \(-0.477257\pi\) | ||||
0.0713880 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 20.9978i | − | 1.00677i | ||||||
\(436\) | 1.53295 | − | 1.19216i | 0.0734152 | − | 0.0570941i | ||||
\(437\) | 6.20450i | 0.296802i | ||||||||
\(438\) | 19.7670 | + | 9.66843i | 0.944506 | + | 0.461975i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 32.8967 | − | 6.87707i | 1.56829 | − | 0.327851i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.98156 | − | 1.94745i | −0.189383 | − | 0.0926309i | ||||
\(443\) | 27.1983i | 1.29223i | 0.763239 | + | 0.646116i | \(0.223608\pi\) | ||||
−0.763239 | + | 0.646116i | \(0.776392\pi\) | |||||||
\(444\) | −8.48549 | − | 10.9112i | −0.402703 | − | 0.517821i | ||||
\(445\) | − | 52.4296i | − | 2.48540i | ||||||
\(446\) | −13.7625 | + | 28.1374i | −0.651675 | + | 1.33235i | ||||
\(447\) | −12.4855 | −0.590543 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5598 | −1.48940 | −0.744700 | − | 0.667400i | \(-0.767407\pi\) | ||||
−0.744700 | + | 0.667400i | \(0.767407\pi\) | |||||||
\(450\) | −5.39205 | + | 11.0240i | −0.254184 | + | 0.519677i | ||||
\(451\) | 1.98156i | 0.0933079i | ||||||||
\(452\) | −19.1042 | − | 24.5654i | −0.898587 | − | 1.15546i | ||||
\(453\) | 8.97098i | 0.421493i | ||||||||
\(454\) | 1.18098 | + | 0.577637i | 0.0554259 | + | 0.0271099i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.4184 | + | 2.59608i | −0.581546 | + | 0.121573i | ||||
\(457\) | 28.1117 | 1.31501 | 0.657506 | − | 0.753450i | \(-0.271612\pi\) | ||||
0.657506 | + | 0.753450i | \(0.271612\pi\) | |||||||
\(458\) | 1.80696 | + | 0.883817i | 0.0844336 | + | 0.0412981i | ||||
\(459\) | 0.616762i | 0.0287880i | ||||||||
\(460\) | −8.07649 | + | 6.28099i | −0.376568 | + | 0.292853i | ||||
\(461\) | − | 5.19440i | − | 0.241927i | −0.992657 | − | 0.120964i | \(-0.961402\pi\) | ||
0.992657 | − | 0.120964i | \(-0.0385984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7665 | −0.500361 | −0.250180 | − | 0.968199i | \(-0.580490\pi\) | ||||
−0.250180 | + | 0.968199i | \(0.580490\pi\) | |||||||
\(464\) | 22.0112 | + | 5.59276i | 1.02184 | + | 0.259637i | ||||
\(465\) | −25.5598 | −1.18531 | ||||||||
\(466\) | −6.81706 | + | 13.9374i | −0.315794 | + | 0.645640i | ||||
\(467\) | − | 30.7520i | − | 1.42303i | −0.702670 | − | 0.711515i | \(-0.748009\pi\) | ||
0.702670 | − | 0.711515i | \(-0.251991\pi\) | |||||||
\(468\) | 8.02264 | − | 6.23912i | 0.370847 | − | 0.288403i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −23.3553 | − | 11.4235i | −1.07730 | − | 0.526927i | ||||
\(471\) | 15.1665 | 0.698834 | ||||||||
\(472\) | −2.31509 | − | 11.0743i | −0.106561 | − | 0.509736i | ||||
\(473\) | 25.6794 | 1.18074 | ||||||||
\(474\) | 6.64863 | + | 3.25197i | 0.305382 | + | 0.149368i | ||||
\(475\) | − | 38.9235i | − | 1.78593i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.48549i | − | 0.205376i | ||||||
\(478\) | 2.99580 | − | 6.12489i | 0.137025 | − | 0.280146i | ||||
\(479\) | −16.3263 | −0.745967 | −0.372983 | − | 0.927838i | \(-0.621665\pi\) | ||||
−0.372983 | + | 0.927838i | \(0.621665\pi\) | |||||||
\(480\) | −15.9509 | − | 13.5372i | −0.728054 | − | 0.617884i | ||||
\(481\) | −35.1196 | −1.60132 | ||||||||
\(482\) | −0.127071 | + | 0.259797i | −0.00578794 | + | 0.0118334i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.832013 | − | 1.06985i | −0.0378188 | − | 0.0486297i | ||||
\(485\) | 36.0123i | 1.63524i | ||||||||
\(486\) | −1.27039 | − | 0.621372i | −0.0576262 | − | 0.0281860i | ||||
\(487\) | 14.7933 | 0.670349 | 0.335175 | − | 0.942156i | \(-0.391205\pi\) | ||||
0.335175 | + | 0.942156i | \(0.391205\pi\) | |||||||
\(488\) | −7.22206 | − | 34.5469i | −0.326927 | − | 1.56387i | ||||
\(489\) | 13.2263 | 0.598112 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0475i | 0.633956i | 0.948433 | + | 0.316978i | \(0.102668\pi\) | ||||
−0.948433 | + | 0.316978i | \(0.897332\pi\) | |||||||
\(492\) | 0.973726 | − | 0.757255i | 0.0438990 | − | 0.0341397i | ||||
\(493\) | 3.50176i | 0.157711i | ||||||||
\(494\) | −14.1631 | + | 28.9565i | −0.637230 | + | 1.30281i | ||||
\(495\) | −11.8822 | −0.534063 | ||||||||
\(496\) | 6.80784 | − | 26.7933i | 0.305681 | − | 1.20306i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.47823 | − | 13.2447i | 0.290296 | − | 0.593510i | ||||
\(499\) | 34.1414i | 1.52838i | 0.644993 | + | 0.764189i | \(0.276860\pi\) | ||||
−0.644993 | + | 0.764189i | \(0.723140\pi\) | |||||||
\(500\) | 21.4731 | − | 16.6994i | 0.960308 | − | 0.746820i | ||||
\(501\) | − | 3.05587i | − | 0.136526i | ||||||
\(502\) | 3.94745 | + | 1.93077i | 0.176183 | + | 0.0861746i | ||||
\(503\) | 27.3821 | 1.22091 | 0.610455 | − | 0.792051i | \(-0.290987\pi\) | ||||
0.610455 | + | 0.792051i | \(0.290987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5000 | 0.867738 | ||||||||
\(506\) | −5.64578 | − | 2.76146i | −0.250986 | − | 0.122762i | ||||
\(507\) | − | 12.8223i | − | 0.569460i | ||||||
\(508\) | 4.58882 | + | 5.90059i | 0.203596 | + | 0.261796i | ||||
\(509\) | − | 2.49165i | − | 0.110441i | −0.998474 | − | 0.0552203i | \(-0.982414\pi\) | ||
0.998474 | − | 0.0552203i | \(-0.0175861\pi\) | |||||||
\(510\) | 1.41734 | − | 2.89775i | 0.0627610 | − | 0.128315i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.4390 | − | 13.1150i | 0.814895 | − | 0.579609i | ||||
\(513\) | 4.48549 | 0.198039 | ||||||||
\(514\) | −8.79224 | + | 17.9757i | −0.387809 | + | 0.792874i | ||||
\(515\) | 7.17548i | 0.316189i | ||||||||
\(516\) | −9.81343 | − | 12.6187i | −0.432012 | − | 0.555508i | ||||
\(517\) | − | 15.9710i | − | 0.702402i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.8615 | −0.608451 | ||||||||
\(520\) | −52.0308 | + | 10.8771i | −2.28170 | + | 0.476991i | ||||
\(521\) | 3.00108 | 0.131480 | 0.0657399 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657399 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(522\) | −7.21284 | − | 3.52793i | −0.315697 | − | 0.154413i | ||||
\(523\) | 16.8514i | 0.736859i | 0.929656 | + | 0.368429i | \(0.120104\pi\) | ||||
−0.929656 | + | 0.368429i | \(0.879896\pi\) | |||||||
\(524\) | −5.36256 | + | 4.17040i | −0.234264 | + | 0.182185i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.82872 | + | 3.73881i | −0.0797361 | + | 0.163020i | ||||
\(527\) | 4.26254 | 0.185679 | ||||||||
\(528\) | 3.16480 | − | 12.4556i | 0.137730 | − | 0.542060i | ||||
\(529\) | −21.0867 | −0.916811 | ||||||||
\(530\) | −10.3078 | + | 21.0743i | −0.447744 | + | 0.915410i | ||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.13412i | − | 0.135754i | ||||||
\(534\) | −18.0098 | − | 8.80892i | −0.779360 | − | 0.381199i | ||||
\(535\) | 17.7045 | 0.765432 | ||||||||
\(536\) | −5.53716 | − | 26.4871i | −0.239169 | − | 1.14407i | ||||
\(537\) | 18.3883 | 0.793515 | ||||||||
\(538\) | 0.816180 | + | 0.399209i | 0.0351880 | + | 0.0172111i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.54078 | + | 5.83882i | 0.195404 | + | 0.251263i | ||||
\(541\) | − | 24.6319i | − | 1.05901i | −0.848307 | − | 0.529505i | \(-0.822378\pi\) | ||
0.848307 | − | 0.529505i | \(-0.177622\pi\) | |||||||
\(542\) | −0.327371 | + | 0.669309i | −0.0140618 | + | 0.0287493i | ||||
\(543\) | −6.05255 | −0.259740 | ||||||||
\(544\) | 2.66009 | + | 2.25756i | 0.114050 | + | 0.0967920i | ||||
\(545\) | 3.59100 | 0.153821 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.8564i | 1.10554i | 0.833333 | + | 0.552771i | \(0.186430\pi\) | ||||
−0.833333 | + | 0.552771i | \(0.813570\pi\) | |||||||
\(548\) | −16.0299 | − | 20.6123i | −0.684764 | − | 0.880512i | ||||
\(549\) | 12.4782i | 0.532558i | ||||||||
\(550\) | 35.4184 | + | 17.3238i | 1.51025 | + | 0.738689i | ||||
\(551\) | 25.4670 | 1.08493 | ||||||||
\(552\) | 0.800581 | + | 3.82960i | 0.0340750 | + | 0.162999i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.5917 | − | 13.4956i | −1.17226 | − | 0.573373i | ||||
\(555\) | − | 25.5598i | − | 1.08495i | ||||||
\(556\) | −4.43294 | + | 3.44745i | −0.187999 | + | 0.146204i | ||||
\(557\) | − | 27.2788i | − | 1.15584i | −0.816093 | − | 0.577920i | \(-0.803864\pi\) | ||
0.816093 | − | 0.577920i | \(-0.196136\pi\) | |||||||
\(558\) | −4.29441 | + | 8.77990i | −0.181797 | + | 0.371683i | ||||
\(559\) | −40.6157 | −1.71786 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.98156 | 0.0836614 | ||||||||
\(562\) | 2.97844 | − | 6.08940i | 0.125638 | − | 0.256866i | ||||
\(563\) | 13.1776i | 0.555371i | 0.960672 | + | 0.277686i | \(0.0895674\pi\) | ||||
−0.960672 | + | 0.277686i | \(0.910433\pi\) | |||||||
\(564\) | −7.84805 | + | 6.10333i | −0.330462 | + | 0.256997i | ||||
\(565\) | − | 57.5453i | − | 2.42095i | ||||||
\(566\) | 28.7726 | + | 14.0732i | 1.20940 | + | 0.591542i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −42.0978 | + | 8.80058i | −1.76639 | + | 0.369264i | ||||
\(569\) | 17.4380 | 0.731040 | 0.365520 | − | 0.930803i | \(-0.380891\pi\) | ||||
0.365520 | + | 0.930803i | \(0.380891\pi\) | |||||||
\(570\) | −21.0743 | − | 10.3078i | −0.882706 | − | 0.431748i | ||||
\(571\) | 4.71569i | 0.197346i | 0.995120 | + | 0.0986728i | \(0.0314597\pi\) | ||||
−0.995120 | + | 0.0986728i | \(0.968540\pi\) | |||||||
\(572\) | −20.0453 | − | 25.7755i | −0.838136 | − | 1.07773i | ||||
\(573\) | − | 15.2056i | − | 0.635222i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0033 | −0.500570 | ||||||||
\(576\) | −7.33004 | + | 3.20476i | −0.305418 | + | 0.133532i | ||||
\(577\) | 11.8223 | 0.492171 | 0.246085 | − | 0.969248i | \(-0.420856\pi\) | ||||
0.246085 | + | 0.969248i | \(0.420856\pi\) | |||||||
\(578\) | 10.3270 | − | 21.1134i | 0.429545 | − | 0.878202i | ||||
\(579\) | − | 19.4419i | − | 0.807980i | ||||||
\(580\) | 25.7810 | + | 33.1508i | 1.07050 | + | 1.37651i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.3704 | + | 6.05058i | 0.512769 | + | 0.250805i | ||||
\(583\) | −14.4112 | −0.596849 | ||||||||
\(584\) | −43.0785 | + | 9.00559i | −1.78260 | + | 0.372654i | ||||
\(585\) | 18.7933 | 0.777008 | ||||||||
\(586\) | −30.9068 | − | 15.1171i | −1.27675 | − | 0.624480i | ||||
\(587\) | − | 13.7810i | − | 0.568802i | −0.958705 | − | 0.284401i | \(-0.908205\pi\) | ||
0.958705 | − | 0.284401i | \(-0.0917947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 31.0000i | − | 1.27733i | ||||||
\(590\) | 9.19216 | − | 18.7933i | 0.378435 | − | 0.773709i | ||||
\(591\) | 15.2520 | 0.627382 | ||||||||
\(592\) | 26.7933 | + | 6.80784i | 1.10120 | + | 0.279800i | ||||
\(593\) | −36.8872 | −1.51477 | −0.757387 | − | 0.652966i | \(-0.773524\pi\) | ||||
−0.757387 | + | 0.652966i | \(0.773524\pi\) | |||||||
\(594\) | −1.99637 | + | 4.08157i | −0.0819121 | + | 0.167469i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.7118 | − | 15.3296i | 0.807425 | − | 0.627925i | ||||
\(597\) | 3.02902i | 0.123970i | ||||||||
\(598\) | 8.92962 | + | 4.36764i | 0.365159 | + | 0.178606i | ||||
\(599\) | −35.0895 | −1.43372 | −0.716859 | − | 0.697218i | \(-0.754421\pi\) | ||||
−0.716859 | + | 0.697218i | \(0.754421\pi\) | |||||||
\(600\) | −5.02239 | − | 24.0247i | −0.205038 | − | 0.980806i | ||||
\(601\) | −18.3263 | −0.747544 | −0.373772 | − | 0.927521i | \(-0.621936\pi\) | ||||
−0.373772 | + | 0.927521i | \(0.621936\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.56706i | 0.389601i | ||||||||
\(604\) | −11.0145 | − | 14.1631i | −0.448174 | − | 0.576290i | ||||
\(605\) | − | 2.50617i | − | 0.101890i | ||||||
\(606\) | 3.27628 | − | 6.69833i | 0.133090 | − | 0.272101i | ||||
\(607\) | 12.4459 | 0.505163 | 0.252582 | − | 0.967576i | \(-0.418720\pi\) | ||||
0.252582 | + | 0.967576i | \(0.418720\pi\) | |||||||
\(608\) | 16.4184 | − | 19.3459i | 0.665855 | − | 0.784579i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.6755 | − | 58.6269i | 1.16104 | − | 2.37373i | ||||
\(611\) | 25.2604i | 1.02193i | ||||||||
\(612\) | −0.757255 | − | 0.973726i | −0.0306102 | − | 0.0393606i | ||||
\(613\) | − | 14.2682i | − | 0.576288i | −0.957587 | − | 0.288144i | \(-0.906962\pi\) | ||
0.957587 | − | 0.288144i | \(-0.0930383\pi\) | |||||||
\(614\) | −4.46481 | − | 2.18382i | −0.180185 | − | 0.0881318i | ||||
\(615\) | 2.28099 | 0.0919783 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.94413 | 0.118526 | 0.0592632 | − | 0.998242i | \(-0.481125\pi\) | ||||
0.0592632 | + | 0.998242i | \(0.481125\pi\) | |||||||
\(618\) | 2.46481 | + | 1.20558i | 0.0991491 | + | 0.0484957i | ||||
\(619\) | 13.2604i | 0.532979i | 0.963838 | + | 0.266490i | \(0.0858638\pi\) | ||||
−0.963838 | + | 0.266490i | \(0.914136\pi\) | |||||||
\(620\) | 40.3531 | − | 31.3821i | 1.62062 | − | 1.26034i | ||||
\(621\) | − | 1.38324i | − | 0.0555074i | ||||||
\(622\) | −3.08883 | + | 6.31509i | −0.123851 | + | 0.253212i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.00559 | + | 19.7003i | −0.200384 | + | 0.788643i | ||||
\(625\) | 6.91335 | 0.276534 | ||||||||
\(626\) | −15.9349 | + | 32.5788i | −0.636887 | + | 1.30211i | ||||
\(627\) | − | 14.4112i | − | 0.575527i | ||||||
\(628\) | −23.9444 | + | 18.6213i | −0.955485 | + | 0.743070i | ||||
\(629\) | 4.26254i | 0.169959i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.2335 | 1.44243 | 0.721217 | − | 0.692710i | \(-0.243583\pi\) | ||||
0.721217 | + | 0.692710i | \(0.243583\pi\) | |||||||
\(632\) | −14.4894 | + | 3.02902i | −0.576358 | + | 0.120488i | ||||
\(633\) | −0.963719 | −0.0383044 | ||||||||
\(634\) | 4.46481 | + | 2.18382i | 0.177320 | + | 0.0867306i | ||||
\(635\) | 13.8223i | 0.548523i | ||||||||
\(636\) | 5.50725 | + | 7.08157i | 0.218377 | + | 0.280802i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.3347 | + | 23.1737i | −0.448745 | + | 0.917456i | ||||
\(639\) | 15.2056 | 0.601524 | ||||||||
\(640\) | 41.8036 | + | 1.78773i | 1.65243 | + | 0.0706662i | ||||
\(641\) | 25.9441 | 1.02473 | 0.512366 | − | 0.858767i | \(-0.328769\pi\) | ||||
0.512366 | + | 0.858767i | \(0.328769\pi\) | |||||||
\(642\) | 2.97461 | − | 6.08157i | 0.117398 | − | 0.240020i | ||||
\(643\) | 27.2643i | 1.07520i | 0.843200 | + | 0.537599i | \(0.180669\pi\) | ||||
−0.843200 | + | 0.537599i | \(0.819331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 29.5598i | − | 1.16392i | ||||||
\(646\) | 3.51451 | + | 1.71901i | 0.138277 | + | 0.0676336i | ||||
\(647\) | 7.41118 | 0.291364 | 0.145682 | − | 0.989332i | \(-0.453462\pi\) | ||||
0.145682 | + | 0.989332i | \(0.453462\pi\) | |||||||
\(648\) | 2.76858 | − | 0.578773i | 0.108760 | − | 0.0227364i | ||||
\(649\) | 12.8514 | 0.504460 | ||||||||
\(650\) | −56.0193 | − | 27.4001i | −2.19726 | − | 1.07472i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.8813 | + | 16.2391i | −0.817774 | + | 0.635973i | ||||
\(653\) | 17.7045i | 0.692830i | 0.938081 | + | 0.346415i | \(0.112601\pi\) | ||||
−0.938081 | + | 0.346415i | \(0.887399\pi\) | |||||||
\(654\) | 0.603339 | − | 1.23352i | 0.0235924 | − | 0.0482346i | ||||
\(655\) | −12.5620 | −0.490837 | ||||||||
\(656\) | −0.607540 | + | 2.39107i | −0.0237205 | + | 0.0933556i | ||||
\(657\) | 15.5598 | 0.607046 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 39.2252i | − | 1.52800i | −0.645219 | − | 0.763998i | \(-0.723234\pi\) | ||
0.645219 | − | 0.763998i | \(-0.276766\pi\) | |||||||
\(660\) | 18.7592 | − | 14.5888i | 0.730202 | − | 0.567869i | ||||
\(661\) | 8.35862i | 0.325113i | 0.986699 | + | 0.162556i | \(0.0519739\pi\) | ||||
−0.986699 | + | 0.162556i | \(0.948026\pi\) | |||||||
\(662\) | −31.9947 | − | 15.6492i | −1.24351 | − | 0.608223i | ||||
\(663\) | −3.13412 | −0.121719 | ||||||||
\(664\) | 6.03410 | + | 28.8643i | 0.234169 | + | 1.12015i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.77990 | − | 4.29441i | −0.340214 | − | 0.166405i | ||||
\(667\) | − | 7.85354i | − | 0.304090i | ||||||
\(668\) | 3.75197 | + | 4.82452i | 0.145168 | + | 0.186666i | ||||
\(669\) | 22.1486i | 0.856315i | ||||||||
\(670\) | 21.9855 | − | 44.9492i | 0.849373 | − | 1.73654i | ||||
\(671\) | 40.0906 | 1.54768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9090 | 1.46128 | 0.730642 | − | 0.682761i | \(-0.239221\pi\) | ||||
0.730642 | + | 0.682761i | \(0.239221\pi\) | |||||||
\(674\) | −13.5237 | + | 27.6492i | −0.520915 | + | 1.06501i | ||||
\(675\) | 8.67765i | 0.334003i | ||||||||
\(676\) | 15.7432 | + | 20.2436i | 0.605507 | + | 0.778599i | ||||
\(677\) | 41.5844i | 1.59822i | 0.601186 | + | 0.799109i | \(0.294695\pi\) | ||||
−0.601186 | + | 0.799109i | \(0.705305\pi\) | |||||||
\(678\) | −19.7670 | − | 9.66843i | −0.759149 | − | 0.371314i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.32017 | + | 6.31509i | 0.0506264 | + | 0.242173i | ||||
\(681\) | 0.929615 | 0.0356229 | ||||||||
\(682\) | 28.2084 | + | 13.7973i | 1.08016 | + | 0.528324i | ||||
\(683\) | 1.49559i | 0.0572272i | 0.999591 | + | 0.0286136i | \(0.00910924\pi\) | ||||
−0.999591 | + | 0.0286136i | \(0.990891\pi\) | |||||||
\(684\) | −7.08157 | + | 5.50725i | −0.270771 | + | 0.210575i | ||||
\(685\) | − | 48.2849i | − | 1.84487i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.42236 | 0.0542665 | ||||||||
\(688\) | 30.9864 | + | 7.87324i | 1.18134 | + | 0.300164i | ||||
\(689\) | 22.7933 | 0.868356 | ||||||||
\(690\) | −3.17874 | + | 6.49891i | −0.121012 | + | 0.247409i | ||||
\(691\) | 19.9028i | 0.757137i | 0.925573 | + | 0.378568i | \(0.123583\pi\) | ||||
−0.925573 | + | 0.378568i | \(0.876417\pi\) | |||||||
\(692\) | 21.8841 | − | 17.0190i | 0.831909 | − | 0.646966i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.5341 | + | 19.8260i | 1.53865 | + | 0.752584i | ||||
\(695\) | −10.3843 | −0.393900 | ||||||||
\(696\) | 15.7190 | − | 3.28607i | 0.595828 | − | 0.124558i | ||||
\(697\) | −0.380395 | −0.0144085 | ||||||||
\(698\) | −1.32147 | − | 0.646355i | −0.0500184 | − | 0.0244649i | ||||
\(699\) | 10.9710i | 0.414961i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.5347i | − | 1.68205i | −0.540994 | − | 0.841026i | \(-0.681952\pi\) | ||
0.540994 | − | 0.841026i | \(-0.318048\pi\) | |||||||
\(702\) | 3.15755 | − | 6.45559i | 0.119174 | − | 0.243650i | ||||
\(703\) | 31.0000 | 1.16919 | ||||||||
\(704\) | 10.2964 | + | 23.5503i | 0.388059 | + | 0.887584i | ||||
\(705\) | −18.3843 | −0.692394 | ||||||||
\(706\) | −8.60618 | + | 17.5953i | −0.323898 | + | 0.662208i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.91117 | − | 6.31509i | −0.184573 | − | 0.237336i | ||||
\(709\) | − | 35.3553i | − | 1.32780i | −0.747823 | − | 0.663898i | \(-0.768901\pi\) | ||
0.747823 | − | 0.663898i | \(-0.231099\pi\) | |||||||
\(710\) | −71.4409 | − | 34.9430i | −2.68113 | − | 1.31139i | ||||
\(711\) | 5.23352 | 0.196272 | ||||||||
\(712\) | 39.2489 | − | 8.20501i | 1.47092 | − | 0.307496i | ||||
\(713\) | −9.55980 | −0.358017 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 60.3800i | − | 2.25808i | ||||||
\(716\) | −29.0310 | + | 22.5771i | −1.08494 | + | 0.843744i | ||||
\(717\) | − | 4.82126i | − | 0.180053i | ||||||
\(718\) | −0.256167 | + | 0.523732i | −0.00956007 | + | 0.0195455i | ||||
\(719\) | −11.0928 | −0.413690 | −0.206845 | − | 0.978374i | \(-0.566320\pi\) | ||||
−0.206845 | + | 0.978374i | \(0.566320\pi\) | |||||||
\(720\) | −14.3377 | − | 3.64304i | −0.534336 | − | 0.135768i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.695696 | − | 1.42235i | 0.0258911 | − | 0.0529342i | ||||
\(723\) | 0.204501i | 0.00760548i | ||||||||
\(724\) | 9.55560 | − | 7.43128i | 0.355131 | − | 0.276181i | ||||
\(725\) | 49.2686i | 1.82979i | ||||||||
\(726\) | −0.860880 | − | 0.421072i | −0.0319503 | − | 0.0156275i | ||||
\(727\) | 38.1135 | 1.41355 | 0.706776 | − | 0.707438i | \(-0.250149\pi\) | ||||
0.706776 | + | 0.707438i | \(0.250149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −73.1051 | − | 35.7570i | −2.70574 | − | 1.32343i | ||||
\(731\) | 4.92962i | 0.182328i | ||||||||
\(732\) | −15.3207 | − | 19.7003i | −0.566269 | − | 0.728144i | ||||
\(733\) | 27.9576i | 1.03264i | 0.856396 | + | 0.516319i | \(0.172698\pi\) | ||||
−0.856396 | + | 0.516319i | \(0.827302\pi\) | |||||||
\(734\) | 3.08883 | − | 6.31509i | 0.114011 | − | 0.233094i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.96590 | − | 5.06313i | −0.219906 | − | 0.186629i | ||||
\(737\) | 30.7374 | 1.13223 | ||||||||
\(738\) | 0.383238 | − | 0.783529i | 0.0141072 | − | 0.0288421i | ||||
\(739\) | 1.56706i | 0.0576452i | 0.999585 | + | 0.0288226i | \(0.00917578\pi\) | ||||
−0.999585 | + | 0.0288226i | \(0.990824\pi\) | |||||||
\(740\) | 31.3821 | + | 40.3531i | 1.15363 | + | 1.48341i | ||||
\(741\) | 22.7933i | 0.837334i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.0569 | 1.61629 | 0.808146 | − | 0.588982i | \(-0.200471\pi\) | ||||
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(744\) | −4.00000 | − | 19.1341i | −0.146647 | − | 0.701491i | ||||
\(745\) | 46.1755 | 1.69174 | ||||||||
\(746\) | 2.74803 | + | 1.34411i | 0.100613 | + | 0.0492115i | ||||
\(747\) | − | 10.4257i | − | 0.381456i | ||||||
\(748\) | −3.12843 | + | 2.43294i | −0.114387 | + | 0.0889572i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.45138 | − | 17.2788i | 0.308601 | − | 0.630933i | ||||
\(751\) | −53.5039 | −1.95239 | −0.976193 | − | 0.216904i | \(-0.930404\pi\) | ||||
−0.976193 | + | 0.216904i | \(0.930404\pi\) | |||||||
\(752\) | 4.89665 | − | 19.2716i | 0.178563 | − | 0.702761i | ||||
\(753\) | 3.10727 | 0.113235 | ||||||||
\(754\) | 17.9274 | − | 36.6526i | 0.652879 | − | 1.33481i | ||||
\(755\) | − | 33.1776i | − | 1.20746i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.1486i | 1.24115i | 0.784146 | + | 0.620576i | \(0.213101\pi\) | ||||
−0.784146 | + | 0.620576i | \(0.786899\pi\) | |||||||
\(758\) | 30.1808 | + | 14.7620i | 1.09621 | + | 0.536179i | ||||
\(759\) | −4.44413 | −0.161312 | ||||||||
\(760\) | 45.9274 | − | 9.60116i | 1.66596 | − | 0.348271i | ||||
\(761\) | 8.23460 | 0.298504 | 0.149252 | − | 0.988799i | \(-0.452313\pi\) | ||||
0.149252 | + | 0.988799i | \(0.452313\pi\) | |||||||
\(762\) | 4.74803 | + | 2.32235i | 0.172003 | + | 0.0841299i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.6693 | + | 24.0062i | 0.675432 | + | 0.868513i | ||||
\(765\) | − | 2.28099i | − | 0.0824693i | ||||||
\(766\) | −23.3386 | + | 47.7157i | −0.843259 | + | 1.72404i | ||||
\(767\) | −20.3263 | −0.733939 | ||||||||
\(768\) | 7.63770 | − | 14.0594i | 0.275602 | − | 0.507323i | ||||
\(769\) | −17.4380 | −0.628831 | −0.314416 | − | 0.949285i | \(-0.601809\pi\) | ||||
−0.314416 | + | 0.949285i | \(0.601809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1497i | 0.509590i | ||||||||
\(772\) | 23.8707 | + | 30.6944i | 0.859125 | + | 1.10472i | ||||
\(773\) | − | 13.8470i | − | 0.498040i | −0.968498 | − | 0.249020i | \(-0.919891\pi\) | ||
0.968498 | − | 0.249020i | \(-0.0801085\pi\) | |||||||
\(774\) | −10.1539 | − | 4.96647i | −0.364975 | − | 0.178516i | ||||
\(775\) | 59.9727 | 2.15428 | ||||||||
\(776\) | −26.9589 | + | 5.63578i | −0.967768 | + | 0.202313i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.04970 | − | 0.513429i | −0.0376337 | − | 0.0184073i | ||||
\(779\) | 2.76648i | 0.0991193i | ||||||||
\(780\) | −29.6704 | + | 23.0743i | −1.06237 | + | 0.826193i | ||||
\(781\) | − | 48.8531i | − | 1.74810i | ||||||
\(782\) | 0.530110 | − | 1.08381i | 0.0189567 | − | 0.0387569i | ||||
\(783\) | −5.67765 | −0.202903 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.0906 | −2.00196 | ||||||||
\(786\) | −2.11059 | + | 4.31509i | −0.0752823 | + | 0.153914i | ||||
\(787\) | − | 48.8368i | − | 1.74085i | −0.492305 | − | 0.870423i | \(-0.663845\pi\) | ||
0.492305 | − | 0.870423i | \(-0.336155\pi\) | |||||||
\(788\) | −24.0794 | + | 18.7263i | −0.857793 | + | 0.667095i | ||||
\(789\) | 2.94304i | 0.104775i | ||||||||
\(790\) | −24.5888 | − | 12.0268i | −0.874831 | − | 0.427896i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.85951 | − | 8.89500i | −0.0660747 | − | 0.316070i | ||||
\(793\) | −63.4090 | −2.25172 | ||||||||
\(794\) | 11.2036 | + | 5.47990i | 0.397602 | + | 0.194474i | ||||
\(795\) | 16.5888i | 0.588345i | ||||||||
\(796\) | −3.71901 | − | 4.78214i | −0.131817 | − | 0.169498i | ||||
\(797\) | − | 44.7330i | − | 1.58453i | −0.610180 | − | 0.792263i | \(-0.708903\pi\) | ||
0.610180 | − | 0.792263i | \(-0.291097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.06591 | 0.108464 | ||||||||
\(800\) | 37.4266 | + | 31.7632i | 1.32323 | + | 1.12300i | ||||
\(801\) | −14.1766 | −0.500904 | ||||||||
\(802\) | 5.37292 | − | 10.9849i | 0.189724 | − | 0.387891i | ||||
\(803\) | − | 49.9912i | − | 1.76415i | ||||||
\(804\) | −11.7464 | − | 15.1042i | −0.414262 | − | 0.532685i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.6157 | − | 21.8223i | −1.57152 | − | 0.768659i | ||||
\(807\) | 0.642463 | 0.0226158 | ||||||||
\(808\) | 3.05167 | + | 14.5977i | 0.107357 | + | 0.513546i | ||||
\(809\) | 7.79550 | 0.274075 | 0.137038 | − | 0.990566i | \(-0.456242\pi\) | ||||
0.137038 | + | 0.990566i | \(0.456242\pi\) | |||||||
\(810\) | 4.69833 | + | 2.29804i | 0.165083 | + | 0.0807449i | ||||
\(811\) | 9.53295i | 0.334747i | 0.985894 | + | 0.167374i | \(0.0535286\pi\) | ||||
−0.985894 | + | 0.167374i | \(0.946471\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.526852i | 0.0184775i | ||||||||
\(814\) | −13.7973 | + | 28.2084i | −0.483594 | + | 0.988705i | ||||
\(815\) | −48.9151 | −1.71342 | ||||||||
\(816\) | 2.39107 | + | 0.607540i | 0.0837042 | + | 0.0212682i | ||||
\(817\) | 35.8514 | 1.25428 | ||||||||
\(818\) | −11.6249 | + | 23.7670i | −0.406455 | + | 0.830995i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.60116 | + | 2.80058i | −0.125758 | + | 0.0978005i | ||||
\(821\) | − | 12.2498i | − | 0.427521i | −0.976886 | − | 0.213760i | \(-0.931429\pi\) | ||
0.976886 | − | 0.213760i | \(-0.0685711\pi\) | |||||||
\(822\) | −16.5861 | − | 8.11255i | −0.578506 | − | 0.282958i | ||||
\(823\) | −49.7665 | −1.73475 | −0.867375 | − | 0.497655i | \(-0.834194\pi\) | ||||
−0.867375 | + | 0.497655i | \(0.834194\pi\) | |||||||
\(824\) | −5.37158 | + | 1.12293i | −0.187128 | + | 0.0391192i | ||||
\(825\) | 27.8799 | 0.970654 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.1403i | 0.456932i | 0.973552 | + | 0.228466i | \(0.0733710\pi\) | ||||
−0.973552 | + | 0.228466i | \(0.926629\pi\) | |||||||
\(828\) | 1.69833 | + | 2.18382i | 0.0590211 | + | 0.0758930i | ||||
\(829\) | 0.961957i | 0.0334102i | 0.999860 | + | 0.0167051i | \(0.00531764\pi\) | ||||
−0.999860 | + | 0.0167051i | \(0.994682\pi\) | |||||||
\(830\) | −23.9586 | + | 48.9833i | −0.831616 | + | 1.70024i | ||||
\(831\) | −21.7190 | −0.753424 | ||||||||
\(832\) | −16.2852 | − | 37.2481i | −0.564587 | − | 1.29135i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.74471 | + | 3.56706i | −0.0604145 | + | 0.123517i | ||||
\(835\) | 11.3016i | 0.391108i | ||||||||
\(836\) | 17.6939 | + | 22.7520i | 0.611957 | + | 0.786893i | ||||
\(837\) | 6.91117i | 0.238885i | ||||||||
\(838\) | −16.4782 | − | 8.05981i | −0.569231 | − | 0.278421i | ||||
\(839\) | −51.4727 | −1.77704 | −0.888518 | − | 0.458842i | \(-0.848264\pi\) | ||||
−0.888518 | + | 0.458842i | \(0.848264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.23570 | −0.111576 | ||||||||
\(842\) | −4.49891 | − | 2.20050i | −0.155043 | − | 0.0758343i | ||||
\(843\) | − | 4.79332i | − | 0.165091i | ||||||
\(844\) | 1.52149 | − | 1.18325i | 0.0523720 | − | 0.0407291i | ||||
\(845\) | 47.4213i | 1.63134i | ||||||||
\(846\) | −3.08883 | + | 6.31509i | −0.106196 | + | 0.217117i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −17.3894 | − | 4.41842i | −0.597155 | − | 0.151729i | ||||
\(849\) | 22.6486 | 0.777299 | ||||||||
\(850\) | −3.32561 | + | 6.79919i | −0.114067 | + | 0.233210i | ||||
\(851\) | − | 9.55980i | − | 0.327706i | ||||||
\(852\) | −24.0062 | + | 18.6693i | −0.822438 | + | 0.639600i | ||||
\(853\) | 3.72843i | 0.127659i | 0.997961 | + | 0.0638296i | \(0.0203314\pi\) | ||||
−0.997961 | + | 0.0638296i | \(0.979669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.5888 | −0.567326 | ||||||||
\(856\) | 2.77068 | + | 13.2536i | 0.0946998 | + | 0.452999i | ||||
\(857\) | 0.473828 | 0.0161857 | 0.00809283 | − | 0.999967i | \(-0.497424\pi\) | ||||
0.00809283 | + | 0.999967i | \(0.497424\pi\) | |||||||
\(858\) | −20.7408 | − | 10.1447i | −0.708078 | − | 0.346334i | ||||
\(859\) | − | 41.3078i | − | 1.40940i | −0.709503 | − | 0.704702i | \(-0.751081\pi\) | ||
0.709503 | − | 0.704702i | \(-0.248919\pi\) | |||||||
\(860\) | 36.2933 | + | 46.6682i | 1.23759 | + | 1.59137i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.08245 | + | 18.5690i | −0.309349 | + | 0.632463i | ||||
\(863\) | 29.9162 | 1.01836 | 0.509179 | − | 0.860660i | \(-0.329949\pi\) | ||||
0.509179 | + | 0.860660i | \(0.329949\pi\) | |||||||
\(864\) | −3.66034 | + | 4.31299i | −0.124527 | + | 0.146731i | ||||
\(865\) | 51.2643 | 1.74304 | ||||||||
\(866\) | −1.84608 | + | 3.77431i | −0.0627325 | + | 0.128256i | ||||
\(867\) | − | 16.6196i | − | 0.564431i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.8145i | − | 0.570392i | ||||||
\(870\) | 26.6755 | + | 13.0475i | 0.904383 | + | 0.442350i | ||||
\(871\) | −48.6157 | −1.64728 | ||||||||
\(872\) | 0.561976 | + | 2.68823i | 0.0190309 | + | 0.0910349i | ||||
\(873\) | 9.73746 | 0.329563 | ||||||||
\(874\) | −7.88215 | − | 3.85530i | −0.266618 | − | 0.130408i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.5654 | + | 19.1042i | −0.829988 | + | 0.645472i | ||||
\(877\) | 18.4670i | 0.623588i | 0.950150 | + | 0.311794i | \(0.100930\pi\) | ||||
−0.950150 | + | 0.311794i | \(0.899070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.3285 | −0.820580 | ||||||||
\(880\) | −11.7045 | + | 46.0649i | −0.394558 | + | 1.55285i | ||||
\(881\) | 50.5297 | 1.70239 | 0.851194 | − | 0.524851i | \(-0.175879\pi\) | ||||
0.851194 | + | 0.524851i | \(0.175879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8688i | 1.81283i | 0.422390 | + | 0.906414i | \(0.361191\pi\) | ||||
−0.422390 | + | 0.906414i | \(0.638809\pi\) | |||||||
\(884\) | 4.94806 | − | 3.84805i | 0.166421 | − | 0.129424i | ||||
\(885\) | − | 14.7933i | − | 0.497272i | ||||||
\(886\) | −34.5525 | − | 16.9003i | −1.16082 | − | 0.567776i | ||||
\(887\) | −36.9978 | −1.24227 | −0.621133 | − | 0.783705i | \(-0.713327\pi\) | ||||
−0.621133 | + | 0.783705i | \(0.713327\pi\) | |||||||
\(888\) | 19.1341 | − | 4.00000i | 0.642099 | − | 0.134231i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 66.6062 | + | 32.5783i | 2.23264 | + | 1.09203i | ||||
\(891\) | 3.21284i | 0.107634i | ||||||||
\(892\) | −27.1939 | − | 34.9676i | −0.910520 | − | 1.17080i | ||||
\(893\) | − | 22.2973i | − | 0.746150i | ||||||
\(894\) | 7.75814 | − | 15.8615i | 0.259471 | − | 0.530487i | ||||
\(895\) | −68.0061 | −2.27319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.02902 | 0.234692 | ||||||||
\(898\) | 19.6104 | − | 40.0933i | 0.654407 | − | 1.33793i | ||||
\(899\) | 39.2392i | 1.30870i | ||||||||
\(900\) | −10.6544 | − | 13.7000i | −0.355145 | − | 0.456668i | ||||
\(901\) | − | 2.76648i | − | 0.0921647i | ||||||
\(902\) | −2.51735 | − | 1.23128i | −0.0838187 | − | 0.0409973i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43.0785 | − | 9.00559i | 1.43277 | − | 0.299522i | ||||
\(905\) | 22.3843 | 0.744080 | ||||||||
\(906\) | −11.3967 | − | 5.57432i | −0.378629 | − | 0.185194i | ||||
\(907\) | − | 53.5112i | − | 1.77681i | −0.459061 | − | 0.888405i | \(-0.651814\pi\) | ||
0.459061 | − | 0.888405i | \(-0.348186\pi\) | |||||||
\(908\) | −1.46765 | + | 1.14137i | −0.0487057 | + | 0.0378779i | ||||
\(909\) | − | 5.27265i | − | 0.174883i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.0860 | −0.367295 | −0.183647 | − | 0.982992i | \(-0.558790\pi\) | ||||
−0.183647 | + | 0.982992i | \(0.558790\pi\) | |||||||
\(912\) | 4.41842 | − | 17.3894i | 0.146309 | − | 0.575821i | ||||
\(913\) | −33.4961 | −1.10856 | ||||||||
\(914\) | −17.4679 | + | 35.7129i | −0.577785 | + | 1.18128i | ||||
\(915\) | − | 46.1486i | − | 1.52563i | ||||||
\(916\) | −2.24559 | + | 1.74637i | −0.0741963 | + | 0.0577016i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.783529 | − | 0.383238i | −0.0258603 | − | 0.0126488i | ||||
\(919\) | 47.5286 | 1.56782 | 0.783912 | − | 0.620872i | \(-0.213221\pi\) | ||||
0.783912 | + | 0.620872i | \(0.213221\pi\) | |||||||
\(920\) | −2.96081 | − | 14.1631i | −0.0976151 | − | 0.466945i | ||||
\(921\) | −3.51451 | −0.115807 | ||||||||
\(922\) | 6.59892 | + | 3.22766i | 0.217324 | + | 0.106297i | ||||
\(923\) | 77.2682i | 2.54331i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.9727i | 1.97189i | ||||||||
\(926\) | 6.68999 | − | 13.6776i | 0.219847 | − | 0.449475i | ||||
\(927\) | 1.94019 | 0.0637243 | ||||||||
\(928\) | −20.7821 | + | 24.4877i | −0.682207 | + | 0.803847i | ||||
\(929\) | 33.2425 | 1.09065 | 0.545325 | − | 0.838225i | \(-0.316406\pi\) | ||||
0.545325 | + | 0.838225i | \(0.316406\pi\) | |||||||
\(930\) | 15.8822 | − | 32.4710i | 0.520796 | − | 1.06477i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −13.4701 | − | 17.3207i | −0.441227 | − | 0.567358i | ||||
\(933\) | 4.97098i | 0.162743i | ||||||||
\(934\) | 39.0671 | + | 19.1084i | 1.27831 | + | 0.625246i | ||||
\(935\) | −7.32845 | −0.239666 | ||||||||
\(936\) | 2.94108 | + | 14.0687i | 0.0961320 | + | 0.459850i | ||||
\(937\) | 14.8514 | 0.485173 | 0.242586 | − | 0.970130i | \(-0.422004\pi\) | ||||
0.242586 | + | 0.970130i | \(0.422004\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.6447i | 0.836883i | ||||||||
\(940\) | 29.0247 | − | 22.5721i | 0.946680 | − | 0.736222i | ||||
\(941\) | − | 53.6258i | − | 1.74815i | −0.485791 | − | 0.874075i | \(-0.661468\pi\) | ||
0.485791 | − | 0.874075i | \(-0.338532\pi\) | |||||||
\(942\) | −9.42402 | + | 19.2674i | −0.307051 | + | 0.627764i | ||||
\(943\) | 0.853128 | 0.0277817 | ||||||||
\(944\) | 15.5073 | + | 3.94019i | 0.504718 | + | 0.128242i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.9565 | + | 32.6229i | −0.518790 | + | 1.06066i | ||||
\(947\) | − | 24.1324i | − | 0.784198i | −0.919923 | − | 0.392099i | \(-0.871749\pi\) | ||
0.919923 | − | 0.392099i | \(-0.128251\pi\) | |||||||
\(948\) | −8.26254 | + | 6.42568i | −0.268355 | + | 0.208696i | ||||
\(949\) | 79.0682i | 2.56666i | ||||||||
\(950\) | 49.4481 | + | 24.1860i | 1.60431 | + | 0.784697i | ||||
\(951\) | 3.51451 | 0.113966 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.347434 | 0.0112545 | 0.00562725 | − | 0.999984i | \(-0.498209\pi\) | ||||
0.00562725 | + | 0.999984i | \(0.498209\pi\) | |||||||
\(954\) | 5.69833 | + | 2.78716i | 0.184490 | + | 0.0902376i | ||||
\(955\) | 56.2353i | 1.81973i | ||||||||
\(956\) | 5.91951 | + | 7.61168i | 0.191451 | + | 0.246179i | ||||
\(957\) | 18.2414i | 0.589660i | ||||||||
\(958\) | 10.1447 | − | 20.7408i | 0.327760 | − | 0.670104i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 27.1089 | − | 11.8522i | 0.874937 | − | 0.382530i | ||||
\(961\) | 16.7643 | 0.540784 | ||||||||
\(962\) | 21.8223 | − | 44.6157i | 0.703581 | − | 1.43847i | ||||
\(963\) | − | 4.78716i | − | 0.154264i | ||||||
\(964\) | −0.251085 | − | 0.322861i | −0.00808690 | − | 0.0103986i | ||||
\(965\) | 71.9028i | 2.31463i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.14646 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(968\) | 1.87612 | − | 0.392205i | 0.0603009 | − | 0.0126059i | ||||
\(969\) | 2.76648 | 0.0888720 | ||||||||
\(970\) | −45.7498 | − | 22.3771i | −1.46894 | − | 0.718484i | ||||
\(971\) | 3.02902i | 0.0972059i | 0.998818 | + | 0.0486030i | \(0.0154769\pi\) | ||||
−0.998818 | + | 0.0486030i | \(0.984523\pi\) | |||||||
\(972\) | 1.57877 | − | 1.22779i | 0.0506392 | − | 0.0393815i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.19216 | + | 18.7933i | −0.294536 | + | 0.602177i | ||||
\(975\) | −44.0961 | −1.41220 | ||||||||
\(976\) | 48.3758 | + | 12.2917i | 1.54847 | + | 0.393447i | ||||
\(977\) | 18.7353 | 0.599395 | 0.299697 | − | 0.954034i | \(-0.403114\pi\) | ||||
0.299697 | + | 0.954034i | \(0.403114\pi\) | |||||||
\(978\) | −8.21843 | + | 16.8025i | −0.262797 | + | 0.537286i | ||||
\(979\) | 45.5470i | 1.45569i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.970978i | − | 0.0310009i | ||||||
\(982\) | −17.8459 | − | 8.72874i | −0.569485 | − | 0.278545i | ||||
\(983\) | −18.2313 | −0.581490 | −0.290745 | − | 0.956801i | \(-0.593903\pi\) | ||||
−0.290745 | + | 0.956801i | \(0.593903\pi\) | |||||||
\(984\) | 0.356965 | + | 1.70755i | 0.0113796 | + | 0.0544348i | ||||
\(985\) | −56.4068 | −1.79727 | ||||||||
\(986\) | −4.44860 | − | 2.17589i | −0.141672 | − | 0.0692946i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.9855 | − | 35.9855i | −0.890337 | − | 1.14485i | ||||
\(989\) | − | 11.0559i | − | 0.351556i | ||||||
\(990\) | 7.38324 | − | 15.0950i | 0.234655 | − | 0.479750i | ||||
\(991\) | −21.2973 | −0.676530 | −0.338265 | − | 0.941051i | \(-0.609840\pi\) | ||||
−0.338265 | + | 0.941051i | \(0.609840\pi\) | |||||||
\(992\) | 29.8078 | + | 25.2973i | 0.946399 | + | 0.803189i | ||||
\(993\) | −25.1849 | −0.799219 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11.2023i | − | 0.355138i | ||||||
\(996\) | 12.8006 | + | 16.4598i | 0.405602 | + | 0.521548i | ||||
\(997\) | − | 24.7900i | − | 0.785107i | −0.919729 | − | 0.392553i | \(-0.871592\pi\) | ||
0.919729 | − | 0.392553i | \(-0.128408\pi\) | |||||||
\(998\) | −43.3729 | − | 21.2145i | −1.37295 | − | 0.671533i | ||||
\(999\) | −6.91117 | −0.218660 |
(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 | 1176.2.c.c.589.4 | 8 | ||
4.3 | odd | 2 | 4704.2.c.c.2353.1 | 8 | |||
7.6 | odd | 2 | 168.2.c.b.85.4 | yes | 8 | ||
8.3 | odd | 2 | 4704.2.c.c.2353.8 | 8 | |||
8.5 | even | 2 | inner | 1176.2.c.c.589.3 | 8 | ||
21.20 | even | 2 | 504.2.c.f.253.5 | 8 | |||
28.27 | even | 2 | 672.2.c.b.337.8 | 8 | |||
56.13 | odd | 2 | 168.2.c.b.85.3 | ✓ | 8 | ||
56.27 | even | 2 | 672.2.c.b.337.1 | 8 | |||
84.83 | odd | 2 | 2016.2.c.e.1009.2 | 8 | |||
112.13 | odd | 4 | 5376.2.a.bp.1.4 | 4 | |||
112.27 | even | 4 | 5376.2.a.bq.1.1 | 4 | |||
112.69 | odd | 4 | 5376.2.a.bm.1.1 | 4 | |||
112.83 | even | 4 | 5376.2.a.bl.1.4 | 4 | |||
168.83 | odd | 2 | 2016.2.c.e.1009.7 | 8 | |||
168.125 | even | 2 | 504.2.c.f.253.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.3 | ✓ | 8 | 56.13 | odd | 2 | ||
168.2.c.b.85.4 | yes | 8 | 7.6 | odd | 2 | ||
504.2.c.f.253.5 | 8 | 21.20 | even | 2 | |||
504.2.c.f.253.6 | 8 | 168.125 | even | 2 | |||
672.2.c.b.337.1 | 8 | 56.27 | even | 2 | |||
672.2.c.b.337.8 | 8 | 28.27 | even | 2 | |||
1176.2.c.c.589.3 | 8 | 8.5 | even | 2 | inner | ||
1176.2.c.c.589.4 | 8 | 1.1 | even | 1 | trivial | ||
2016.2.c.e.1009.2 | 8 | 84.83 | odd | 2 | |||
2016.2.c.e.1009.7 | 8 | 168.83 | odd | 2 | |||
4704.2.c.c.2353.1 | 8 | 4.3 | odd | 2 | |||
4704.2.c.c.2353.8 | 8 | 8.3 | odd | 2 | |||
5376.2.a.bl.1.4 | 4 | 112.83 | even | 4 | |||
5376.2.a.bm.1.1 | 4 | 112.69 | odd | 4 | |||
5376.2.a.bp.1.4 | 4 | 112.13 | odd | 4 | |||
5376.2.a.bq.1.1 | 4 | 112.27 | even | 4 |