Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(76,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.76");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.9 | ||
Root | \(0.378061 - 0.654821i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.76 |
Dual form | 105.3.h.a.76.10 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.91758 | 1.45879 | 0.729394 | − | 0.684094i | \(-0.239802\pi\) | ||||
0.729394 | + | 0.684094i | \(0.239802\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 4.51225 | 1.12806 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | − | 5.05339i | − | 0.842231i | ||||||
\(7\) | 6.13981 | + | 3.36195i | 0.877116 | + | 0.480279i | ||||
\(8\) | 1.49451 | 0.186814 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | − | 6.52390i | − | 0.652390i | ||||||
\(11\) | −2.58757 | −0.235233 | −0.117617 | − | 0.993059i | \(-0.537525\pi\) | ||||
−0.117617 | + | 0.993059i | \(0.537525\pi\) | |||||||
\(12\) | − | 7.81544i | − | 0.651286i | ||||||
\(13\) | − | 0.0498225i | − | 0.00383250i | −0.999998 | − | 0.00191625i | \(-0.999390\pi\) | ||
0.999998 | − | 0.00191625i | \(-0.000609962\pi\) | |||||||
\(14\) | 17.9134 | + | 9.80876i | 1.27953 | + | 0.700625i | ||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | −13.6886 | −0.855539 | ||||||||
\(17\) | 14.2114i | 0.835965i | 0.908455 | + | 0.417982i | \(0.137263\pi\) | ||||
−0.908455 | + | 0.417982i | \(0.862737\pi\) | |||||||
\(18\) | −8.75273 | −0.486263 | ||||||||
\(19\) | 14.9314i | 0.785864i | 0.919567 | + | 0.392932i | \(0.128539\pi\) | ||||
−0.919567 | + | 0.392932i | \(0.871461\pi\) | |||||||
\(20\) | − | 10.0897i | − | 0.504484i | ||||||
\(21\) | 5.82308 | − | 10.6345i | 0.277289 | − | 0.506403i | ||||
\(22\) | −7.54942 | −0.343156 | ||||||||
\(23\) | −22.2765 | −0.968545 | −0.484273 | − | 0.874917i | \(-0.660916\pi\) | ||||
−0.484273 | + | 0.874917i | \(0.660916\pi\) | |||||||
\(24\) | − | 2.58857i | − | 0.107857i | ||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 0.145361i | − | 0.00559081i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 27.7043 | + | 15.1700i | 0.989440 | + | 0.541784i | ||||
\(29\) | 17.4169 | 0.600583 | 0.300291 | − | 0.953848i | \(-0.402916\pi\) | ||||
0.300291 | + | 0.953848i | \(0.402916\pi\) | |||||||
\(30\) | −11.2997 | −0.376657 | ||||||||
\(31\) | − | 6.36515i | − | 0.205327i | −0.994716 | − | 0.102664i | \(-0.967263\pi\) | ||
0.994716 | − | 0.102664i | \(-0.0327365\pi\) | |||||||
\(32\) | −45.9156 | −1.43486 | ||||||||
\(33\) | 4.48180i | 0.135812i | ||||||||
\(34\) | 41.4628i | 1.21950i | ||||||||
\(35\) | 7.51756 | − | 13.7290i | 0.214787 | − | 0.392258i | ||||
\(36\) | −13.5367 | −0.376020 | ||||||||
\(37\) | −7.14160 | −0.193016 | −0.0965081 | − | 0.995332i | \(-0.530767\pi\) | ||||
−0.0965081 | + | 0.995332i | \(0.530767\pi\) | |||||||
\(38\) | 43.5635i | 1.14641i | ||||||||
\(39\) | −0.0862951 | −0.00221270 | ||||||||
\(40\) | − | 3.34183i | − | 0.0835459i | ||||||
\(41\) | − | 74.5035i | − | 1.81716i | −0.417713 | − | 0.908579i | \(-0.637168\pi\) | ||
0.417713 | − | 0.908579i | \(-0.362832\pi\) | |||||||
\(42\) | 16.9893 | − | 31.0268i | 0.404506 | − | 0.738734i | ||||
\(43\) | 79.2782 | 1.84368 | 0.921840 | − | 0.387570i | \(-0.126686\pi\) | ||||
0.921840 | + | 0.387570i | \(0.126686\pi\) | |||||||
\(44\) | −11.6757 | −0.265358 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | −64.9935 | −1.41290 | ||||||||
\(47\) | − | 81.3603i | − | 1.73107i | −0.500848 | − | 0.865535i | \(-0.666978\pi\) | ||
0.500848 | − | 0.865535i | \(-0.333022\pi\) | |||||||
\(48\) | 23.7094i | 0.493946i | ||||||||
\(49\) | 26.3945 | + | 41.2835i | 0.538664 | + | 0.842521i | ||||
\(50\) | −14.5879 | −0.291758 | ||||||||
\(51\) | 24.6149 | 0.482644 | ||||||||
\(52\) | − | 0.224811i | − | 0.00432330i | ||||||
\(53\) | −67.1978 | −1.26788 | −0.633942 | − | 0.773381i | \(-0.718564\pi\) | ||||
−0.633942 | + | 0.773381i | \(0.718564\pi\) | |||||||
\(54\) | 15.1602i | 0.280744i | ||||||||
\(55\) | 5.78598i | 0.105200i | ||||||||
\(56\) | 9.17603 | + | 5.02449i | 0.163858 | + | 0.0897230i | ||||
\(57\) | 25.8620 | 0.453719 | ||||||||
\(58\) | 50.8151 | 0.876122 | ||||||||
\(59\) | − | 4.33175i | − | 0.0734195i | −0.999326 | − | 0.0367097i | \(-0.988312\pi\) | ||
0.999326 | − | 0.0367097i | \(-0.0116877\pi\) | |||||||
\(60\) | −17.4759 | −0.291264 | ||||||||
\(61\) | 109.670i | 1.79787i | 0.438082 | + | 0.898935i | \(0.355658\pi\) | ||||
−0.438082 | + | 0.898935i | \(0.644342\pi\) | |||||||
\(62\) | − | 18.5708i | − | 0.299529i | ||||||
\(63\) | −18.4194 | − | 10.0859i | −0.292372 | − | 0.160093i | ||||
\(64\) | −79.2079 | −1.23762 | ||||||||
\(65\) | −0.111407 | −0.00171395 | ||||||||
\(66\) | 13.0760i | 0.198121i | ||||||||
\(67\) | −49.1800 | −0.734030 | −0.367015 | − | 0.930215i | \(-0.619620\pi\) | ||||
−0.367015 | + | 0.930215i | \(0.619620\pi\) | |||||||
\(68\) | 64.1253i | 0.943020i | ||||||||
\(69\) | 38.5841i | 0.559190i | ||||||||
\(70\) | 21.9330 | − | 40.0555i | 0.313329 | − | 0.572221i | ||||
\(71\) | 97.3864 | 1.37164 | 0.685819 | − | 0.727772i | \(-0.259444\pi\) | ||||
0.685819 | + | 0.727772i | \(0.259444\pi\) | |||||||
\(72\) | −4.48354 | −0.0622714 | ||||||||
\(73\) | − | 116.398i | − | 1.59450i | −0.603651 | − | 0.797249i | \(-0.706288\pi\) | ||
0.603651 | − | 0.797249i | \(-0.293712\pi\) | |||||||
\(74\) | −20.8362 | −0.281570 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 67.3742i | 0.886503i | ||||||||
\(77\) | −15.8872 | − | 8.69929i | −0.206327 | − | 0.112978i | ||||
\(78\) | −0.251773 | −0.00322785 | ||||||||
\(79\) | 98.8343 | 1.25107 | 0.625534 | − | 0.780197i | \(-0.284881\pi\) | ||||
0.625534 | + | 0.780197i | \(0.284881\pi\) | |||||||
\(80\) | 30.6087i | 0.382609i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 217.370i | − | 2.65085i | ||||||
\(83\) | − | 112.111i | − | 1.35073i | −0.737484 | − | 0.675365i | \(-0.763986\pi\) | ||
0.737484 | − | 0.675365i | \(-0.236014\pi\) | |||||||
\(84\) | 26.2752 | − | 47.9853i | 0.312799 | − | 0.571254i | ||||
\(85\) | 31.7777 | 0.373855 | ||||||||
\(86\) | 231.300 | 2.68954 | ||||||||
\(87\) | − | 30.1669i | − | 0.346747i | ||||||
\(88\) | −3.86716 | −0.0439450 | ||||||||
\(89\) | 77.7603i | 0.873711i | 0.899532 | + | 0.436855i | \(0.143908\pi\) | ||||
−0.899532 | + | 0.436855i | \(0.856092\pi\) | |||||||
\(90\) | 19.5717i | 0.217463i | ||||||||
\(91\) | 0.167501 | − | 0.305901i | 0.00184067 | − | 0.00336155i | ||||
\(92\) | −100.517 | −1.09258 | ||||||||
\(93\) | −11.0248 | −0.118546 | ||||||||
\(94\) | − | 237.375i | − | 2.52526i | ||||||
\(95\) | 33.3877 | 0.351449 | ||||||||
\(96\) | 79.5282i | 0.828419i | ||||||||
\(97\) | 109.997i | 1.13399i | 0.823723 | + | 0.566993i | \(0.191893\pi\) | ||||
−0.823723 | + | 0.566993i | \(0.808107\pi\) | |||||||
\(98\) | 77.0080 | + | 120.448i | 0.785796 | + | 1.22906i | ||||
\(99\) | 7.76270 | 0.0784111 | ||||||||
\(100\) | −22.5612 | −0.225612 | ||||||||
\(101\) | 96.7400i | 0.957822i | 0.877864 | + | 0.478911i | \(0.158968\pi\) | ||||
−0.877864 | + | 0.478911i | \(0.841032\pi\) | |||||||
\(102\) | 71.8157 | 0.704076 | ||||||||
\(103\) | − | 106.961i | − | 1.03846i | −0.854635 | − | 0.519230i | \(-0.826219\pi\) | ||
0.854635 | − | 0.519230i | \(-0.173781\pi\) | |||||||
\(104\) | − | 0.0744604i | − | 0.000715966i | ||||||
\(105\) | −23.7794 | − | 13.0208i | −0.226470 | − | 0.124008i | ||||
\(106\) | −196.055 | −1.84957 | ||||||||
\(107\) | 33.0838 | 0.309195 | 0.154597 | − | 0.987978i | \(-0.450592\pi\) | ||||
0.154597 | + | 0.987978i | \(0.450592\pi\) | |||||||
\(108\) | 23.4463i | 0.217095i | ||||||||
\(109\) | −49.8791 | −0.457607 | −0.228803 | − | 0.973473i | \(-0.573481\pi\) | ||||
−0.228803 | + | 0.973473i | \(0.573481\pi\) | |||||||
\(110\) | 16.8810i | 0.153464i | ||||||||
\(111\) | 12.3696i | 0.111438i | ||||||||
\(112\) | −84.0455 | − | 46.0205i | −0.750407 | − | 0.410898i | ||||
\(113\) | −111.225 | −0.984291 | −0.492146 | − | 0.870513i | \(-0.663787\pi\) | ||||
−0.492146 | + | 0.870513i | \(0.663787\pi\) | |||||||
\(114\) | 75.4543 | 0.661880 | ||||||||
\(115\) | 49.8118i | 0.433146i | ||||||||
\(116\) | 78.5893 | 0.677494 | ||||||||
\(117\) | 0.149468i | 0.00127750i | ||||||||
\(118\) | − | 12.6382i | − | 0.107103i | ||||||
\(119\) | −47.7781 | + | 87.2553i | −0.401497 | + | 0.733238i | ||||
\(120\) | −5.78823 | −0.0482352 | ||||||||
\(121\) | −114.304 | −0.944665 | ||||||||
\(122\) | 319.971i | 2.62271i | ||||||||
\(123\) | −129.044 | −1.04914 | ||||||||
\(124\) | − | 28.7211i | − | 0.231622i | ||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −53.7401 | − | 29.4263i | −0.426508 | − | 0.233542i | ||||
\(127\) | −69.4347 | −0.546730 | −0.273365 | − | 0.961910i | \(-0.588137\pi\) | ||||
−0.273365 | + | 0.961910i | \(0.588137\pi\) | |||||||
\(128\) | −47.4323 | −0.370565 | ||||||||
\(129\) | − | 137.314i | − | 1.06445i | ||||||
\(130\) | −0.325037 | −0.00250028 | ||||||||
\(131\) | 39.7493i | 0.303430i | 0.988424 | + | 0.151715i | \(0.0484796\pi\) | ||||
−0.988424 | + | 0.151715i | \(0.951520\pi\) | |||||||
\(132\) | 20.2230i | 0.153204i | ||||||||
\(133\) | −50.1988 | + | 91.6761i | −0.377434 | + | 0.689294i | ||||
\(134\) | −143.486 | −1.07079 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 21.2391i | 0.156170i | ||||||||
\(137\) | −89.9621 | −0.656657 | −0.328329 | − | 0.944564i | \(-0.606485\pi\) | ||||
−0.328329 | + | 0.944564i | \(0.606485\pi\) | |||||||
\(138\) | 112.572i | 0.815739i | ||||||||
\(139\) | 126.585i | 0.910684i | 0.890317 | + | 0.455342i | \(0.150483\pi\) | ||||
−0.890317 | + | 0.455342i | \(0.849517\pi\) | |||||||
\(140\) | 33.9211 | − | 61.9488i | 0.242293 | − | 0.442491i | ||||
\(141\) | −140.920 | −0.999434 | ||||||||
\(142\) | 284.132 | 2.00093 | ||||||||
\(143\) | 0.128919i | 0.000901533i | ||||||||
\(144\) | 41.0659 | 0.285180 | ||||||||
\(145\) | − | 38.9454i | − | 0.268589i | ||||||
\(146\) | − | 339.601i | − | 2.32603i | ||||||
\(147\) | 71.5052 | − | 45.7166i | 0.486430 | − | 0.310998i | ||||
\(148\) | −32.2247 | −0.217734 | ||||||||
\(149\) | −91.3583 | −0.613143 | −0.306571 | − | 0.951848i | \(-0.599182\pi\) | ||||
−0.306571 | + | 0.951848i | \(0.599182\pi\) | |||||||
\(150\) | 25.2669i | 0.168446i | ||||||||
\(151\) | 21.2035 | 0.140421 | 0.0702104 | − | 0.997532i | \(-0.477633\pi\) | ||||
0.0702104 | + | 0.997532i | \(0.477633\pi\) | |||||||
\(152\) | 22.3152i | 0.146811i | ||||||||
\(153\) | − | 42.6342i | − | 0.278655i | ||||||
\(154\) | −46.3520 | − | 25.3808i | −0.300987 | − | 0.164811i | ||||
\(155\) | −14.2329 | −0.0918252 | ||||||||
\(156\) | −0.389385 | −0.00249606 | ||||||||
\(157\) | 268.749i | 1.71178i | 0.517159 | + | 0.855890i | \(0.326990\pi\) | ||||
−0.517159 | + | 0.855890i | \(0.673010\pi\) | |||||||
\(158\) | 288.357 | 1.82504 | ||||||||
\(159\) | 116.390i | 0.732013i | ||||||||
\(160\) | 102.671i | 0.641691i | ||||||||
\(161\) | −136.774 | − | 74.8927i | −0.849526 | − | 0.465172i | ||||
\(162\) | 26.2582 | 0.162088 | ||||||||
\(163\) | −51.5630 | −0.316338 | −0.158169 | − | 0.987412i | \(-0.550559\pi\) | ||||
−0.158169 | + | 0.987412i | \(0.550559\pi\) | |||||||
\(164\) | − | 336.178i | − | 2.04987i | ||||||
\(165\) | 10.0216 | 0.0607370 | ||||||||
\(166\) | − | 327.091i | − | 1.97043i | ||||||
\(167\) | 91.2114i | 0.546176i | 0.961989 | + | 0.273088i | \(0.0880450\pi\) | ||||
−0.961989 | + | 0.273088i | \(0.911955\pi\) | |||||||
\(168\) | 8.70267 | − | 15.8933i | 0.0518016 | − | 0.0946033i | ||||
\(169\) | 168.998 | 0.999985 | ||||||||
\(170\) | 92.7137 | 0.545375 | ||||||||
\(171\) | − | 44.7943i | − | 0.261955i | ||||||
\(172\) | 357.723 | 2.07978 | ||||||||
\(173\) | − | 120.543i | − | 0.696780i | −0.937350 | − | 0.348390i | \(-0.886729\pi\) | ||
0.937350 | − | 0.348390i | \(-0.113271\pi\) | |||||||
\(174\) | − | 88.0143i | − | 0.505830i | ||||||
\(175\) | −30.6990 | − | 16.8098i | −0.175423 | − | 0.0960559i | ||||
\(176\) | 35.4202 | 0.201251 | ||||||||
\(177\) | −7.50281 | −0.0423888 | ||||||||
\(178\) | 226.871i | 1.27456i | ||||||||
\(179\) | −51.2128 | −0.286105 | −0.143053 | − | 0.989715i | \(-0.545692\pi\) | ||||
−0.143053 | + | 0.989715i | \(0.545692\pi\) | |||||||
\(180\) | 30.2691i | 0.168161i | ||||||||
\(181\) | − | 54.0291i | − | 0.298503i | −0.988799 | − | 0.149252i | \(-0.952314\pi\) | ||
0.988799 | − | 0.149252i | \(-0.0476864\pi\) | |||||||
\(182\) | 0.488697 | − | 0.892489i | 0.00268515 | − | 0.00490378i | ||||
\(183\) | 189.954 | 1.03800 | ||||||||
\(184\) | −33.2926 | −0.180938 | ||||||||
\(185\) | 15.9691i | 0.0863195i | ||||||||
\(186\) | −32.1656 | −0.172933 | ||||||||
\(187\) | − | 36.7730i | − | 0.196647i | ||||||
\(188\) | − | 367.118i | − | 1.95275i | ||||||
\(189\) | −17.4692 | + | 31.9034i | −0.0924298 | + | 0.168801i | ||||
\(190\) | 97.4110 | 0.512690 | ||||||||
\(191\) | 43.9113 | 0.229902 | 0.114951 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114951 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(192\) | 137.192i | 0.714542i | ||||||||
\(193\) | −46.6855 | −0.241894 | −0.120947 | − | 0.992659i | \(-0.538593\pi\) | ||||
−0.120947 | + | 0.992659i | \(0.538593\pi\) | |||||||
\(194\) | 320.923i | 1.65424i | ||||||||
\(195\) | 0.192962i | 0.000989548i | ||||||||
\(196\) | 119.099 | + | 186.281i | 0.607646 | + | 0.950415i | ||||
\(197\) | 274.811 | 1.39498 | 0.697490 | − | 0.716595i | \(-0.254300\pi\) | ||||
0.697490 | + | 0.716595i | \(0.254300\pi\) | |||||||
\(198\) | 22.6483 | 0.114385 | ||||||||
\(199\) | − | 270.380i | − | 1.35870i | −0.733816 | − | 0.679348i | \(-0.762263\pi\) | ||
0.733816 | − | 0.679348i | \(-0.237737\pi\) | |||||||
\(200\) | −7.47257 | −0.0373628 | ||||||||
\(201\) | 85.1822i | 0.423792i | ||||||||
\(202\) | 282.246i | 1.39726i | ||||||||
\(203\) | 106.936 | + | 58.5548i | 0.526780 | + | 0.288447i | ||||
\(204\) | 111.068 | 0.544453 | ||||||||
\(205\) | −166.595 | −0.812658 | ||||||||
\(206\) | − | 312.068i | − | 1.51489i | ||||||
\(207\) | 66.8296 | 0.322848 | ||||||||
\(208\) | 0.682002i | 0.00327885i | ||||||||
\(209\) | − | 38.6361i | − | 0.184862i | ||||||
\(210\) | −69.3781 | − | 37.9892i | −0.330372 | − | 0.180901i | ||||
\(211\) | 385.058 | 1.82492 | 0.912460 | − | 0.409166i | \(-0.134180\pi\) | ||||
0.912460 | + | 0.409166i | \(0.134180\pi\) | |||||||
\(212\) | −303.213 | −1.43025 | ||||||||
\(213\) | − | 168.678i | − | 0.791916i | ||||||
\(214\) | 96.5246 | 0.451050 | ||||||||
\(215\) | − | 177.272i | − | 0.824519i | ||||||
\(216\) | 7.76572i | 0.0359524i | ||||||||
\(217\) | 21.3993 | − | 39.0808i | 0.0986144 | − | 0.180096i | ||||
\(218\) | −145.526 | −0.667551 | ||||||||
\(219\) | −201.608 | −0.920584 | ||||||||
\(220\) | 26.1078i | 0.118672i | ||||||||
\(221\) | 0.708048 | 0.00320384 | ||||||||
\(222\) | 36.0893i | 0.162564i | ||||||||
\(223\) | − | 141.356i | − | 0.633883i | −0.948445 | − | 0.316941i | \(-0.897344\pi\) | ||
0.948445 | − | 0.316941i | \(-0.102656\pi\) | |||||||
\(224\) | −281.913 | − | 154.366i | −1.25854 | − | 0.689135i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −324.507 | −1.43587 | ||||||||
\(227\) | 298.664i | 1.31570i | 0.753149 | + | 0.657850i | \(0.228534\pi\) | ||||
−0.753149 | + | 0.657850i | \(0.771466\pi\) | |||||||
\(228\) | 116.696 | 0.511823 | ||||||||
\(229\) | − | 2.37781i | − | 0.0103835i | −0.999987 | − | 0.00519173i | \(-0.998347\pi\) | ||
0.999987 | − | 0.00519173i | \(-0.00165259\pi\) | |||||||
\(230\) | 145.330i | 0.631869i | ||||||||
\(231\) | −15.0676 | + | 27.5174i | −0.0652277 | + | 0.119123i | ||||
\(232\) | 26.0298 | 0.112197 | ||||||||
\(233\) | −368.120 | −1.57991 | −0.789956 | − | 0.613163i | \(-0.789897\pi\) | ||||
−0.789956 | + | 0.613163i | \(0.789897\pi\) | |||||||
\(234\) | 0.436083i | 0.00186360i | ||||||||
\(235\) | −181.927 | −0.774158 | ||||||||
\(236\) | − | 19.5459i | − | 0.0828217i | ||||||
\(237\) | − | 171.186i | − | 0.722304i | ||||||
\(238\) | −139.396 | + | 254.574i | −0.585698 | + | 1.06964i | ||||
\(239\) | 420.588 | 1.75978 | 0.879892 | − | 0.475174i | \(-0.157615\pi\) | ||||
0.879892 | + | 0.475174i | \(0.157615\pi\) | |||||||
\(240\) | 53.0158 | 0.220899 | ||||||||
\(241\) | 143.604i | 0.595868i | 0.954586 | + | 0.297934i | \(0.0962976\pi\) | ||||
−0.954586 | + | 0.297934i | \(0.903702\pi\) | |||||||
\(242\) | −333.492 | −1.37807 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 494.858i | 2.02811i | ||||||||
\(245\) | 92.3128 | − | 59.0199i | 0.376787 | − | 0.240898i | ||||
\(246\) | −376.495 | −1.53047 | ||||||||
\(247\) | 0.743921 | 0.00301183 | ||||||||
\(248\) | − | 9.51280i | − | 0.0383581i | ||||||
\(249\) | −194.181 | −0.779844 | ||||||||
\(250\) | 32.6195i | 0.130478i | ||||||||
\(251\) | 298.338i | 1.18860i | 0.804245 | + | 0.594298i | \(0.202570\pi\) | ||||
−0.804245 | + | 0.594298i | \(0.797430\pi\) | |||||||
\(252\) | −83.1130 | − | 45.5099i | −0.329813 | − | 0.180595i | ||||
\(253\) | 57.6420 | 0.227834 | ||||||||
\(254\) | −202.581 | −0.797563 | ||||||||
\(255\) | − | 55.0405i | − | 0.215845i | ||||||
\(256\) | 178.444 | 0.697047 | ||||||||
\(257\) | 189.432i | 0.737089i | 0.929610 | + | 0.368545i | \(0.120144\pi\) | ||||
−0.929610 | + | 0.368545i | \(0.879856\pi\) | |||||||
\(258\) | − | 400.624i | − | 1.55281i | ||||||
\(259\) | −43.8481 | − | 24.0097i | −0.169298 | − | 0.0927017i | ||||
\(260\) | −0.502694 | −0.00193344 | ||||||||
\(261\) | −52.2507 | −0.200194 | ||||||||
\(262\) | 115.972i | 0.442640i | ||||||||
\(263\) | 233.105 | 0.886332 | 0.443166 | − | 0.896440i | \(-0.353855\pi\) | ||||
0.443166 | + | 0.896440i | \(0.353855\pi\) | |||||||
\(264\) | 6.69811i | 0.0253716i | ||||||||
\(265\) | 150.259i | 0.567015i | ||||||||
\(266\) | −146.459 | + | 267.472i | −0.550596 | + | 1.00553i | ||||
\(267\) | 134.685 | 0.504437 | ||||||||
\(268\) | −221.912 | −0.828030 | ||||||||
\(269\) | − | 261.173i | − | 0.970903i | −0.874264 | − | 0.485451i | \(-0.838655\pi\) | ||
0.874264 | − | 0.485451i | \(-0.161345\pi\) | |||||||
\(270\) | 33.8992 | 0.125552 | ||||||||
\(271\) | − | 172.256i | − | 0.635632i | −0.948152 | − | 0.317816i | \(-0.897050\pi\) | ||
0.948152 | − | 0.317816i | \(-0.102950\pi\) | |||||||
\(272\) | − | 194.535i | − | 0.715200i | ||||||
\(273\) | −0.529836 | − | 0.290120i | −0.00194079 | − | 0.00106271i | ||||
\(274\) | −262.471 | −0.957924 | ||||||||
\(275\) | 12.9378 | 0.0470467 | ||||||||
\(276\) | 174.101i | 0.630800i | ||||||||
\(277\) | 225.774 | 0.815070 | 0.407535 | − | 0.913190i | \(-0.366388\pi\) | ||||
0.407535 | + | 0.913190i | \(0.366388\pi\) | |||||||
\(278\) | 369.322i | 1.32849i | ||||||||
\(279\) | 19.0954i | 0.0684424i | ||||||||
\(280\) | 11.2351 | − | 20.5182i | 0.0401253 | − | 0.0732794i | ||||
\(281\) | 156.116 | 0.555573 | 0.277787 | − | 0.960643i | \(-0.410399\pi\) | ||||
0.277787 | + | 0.960643i | \(0.410399\pi\) | |||||||
\(282\) | −411.145 | −1.45796 | ||||||||
\(283\) | − | 94.6516i | − | 0.334458i | −0.985918 | − | 0.167229i | \(-0.946518\pi\) | ||
0.985918 | − | 0.167229i | \(-0.0534819\pi\) | |||||||
\(284\) | 439.431 | 1.54729 | ||||||||
\(285\) | − | 57.8291i | − | 0.202909i | ||||||
\(286\) | 0.376131i | 0.00131514i | ||||||||
\(287\) | 250.477 | − | 457.437i | 0.872744 | − | 1.59386i | ||||
\(288\) | 137.747 | 0.478288 | ||||||||
\(289\) | 87.0361 | 0.301163 | ||||||||
\(290\) | − | 113.626i | − | 0.391814i | ||||||
\(291\) | 190.520 | 0.654707 | ||||||||
\(292\) | − | 525.218i | − | 1.79869i | ||||||
\(293\) | 323.853i | 1.10530i | 0.833413 | + | 0.552650i | \(0.186383\pi\) | ||||
−0.833413 | + | 0.552650i | \(0.813617\pi\) | |||||||
\(294\) | 208.622 | − | 133.382i | 0.709598 | − | 0.453679i | ||||
\(295\) | −9.68609 | −0.0328342 | ||||||||
\(296\) | −10.6732 | −0.0360582 | ||||||||
\(297\) | − | 13.4454i | − | 0.0452707i | ||||||
\(298\) | −266.545 | −0.894445 | ||||||||
\(299\) | 1.10987i | 0.00371195i | ||||||||
\(300\) | 39.0772i | 0.130257i | ||||||||
\(301\) | 486.753 | + | 266.530i | 1.61712 | + | 0.885481i | ||||
\(302\) | 61.8629 | 0.204844 | ||||||||
\(303\) | 167.559 | 0.552999 | ||||||||
\(304\) | − | 204.391i | − | 0.672338i | ||||||
\(305\) | 245.230 | 0.804032 | ||||||||
\(306\) | − | 124.388i | − | 0.406498i | ||||||
\(307\) | − | 542.844i | − | 1.76822i | −0.467276 | − | 0.884112i | \(-0.654765\pi\) | ||
0.467276 | − | 0.884112i | \(-0.345235\pi\) | |||||||
\(308\) | −71.6868 | − | 39.2533i | −0.232749 | − | 0.127446i | ||||
\(309\) | −185.263 | −0.599555 | ||||||||
\(310\) | −41.5256 | −0.133953 | ||||||||
\(311\) | 405.345i | 1.30336i | 0.758494 | + | 0.651680i | \(0.225935\pi\) | ||||
−0.758494 | + | 0.651680i | \(0.774065\pi\) | |||||||
\(312\) | −0.128969 | −0.000413363 | ||||||||
\(313\) | − | 44.1040i | − | 0.140907i | −0.997515 | − | 0.0704536i | \(-0.977555\pi\) | ||
0.997515 | − | 0.0704536i | \(-0.0224447\pi\) | |||||||
\(314\) | 784.096i | 2.49712i | ||||||||
\(315\) | −22.5527 | + | 41.1871i | −0.0715958 | + | 0.130753i | ||||
\(316\) | 445.965 | 1.41128 | ||||||||
\(317\) | −244.609 | −0.771636 | −0.385818 | − | 0.922575i | \(-0.626081\pi\) | ||||
−0.385818 | + | 0.922575i | \(0.626081\pi\) | |||||||
\(318\) | 339.577i | 1.06785i | ||||||||
\(319\) | −45.0674 | −0.141277 | ||||||||
\(320\) | 177.114i | 0.553482i | ||||||||
\(321\) | − | 57.3029i | − | 0.178514i | ||||||
\(322\) | −399.047 | − | 218.505i | −1.23928 | − | 0.678587i | ||||
\(323\) | −212.196 | −0.656955 | ||||||||
\(324\) | 40.6102 | 0.125340 | ||||||||
\(325\) | 0.249113i | 0.000766500i | ||||||||
\(326\) | −150.439 | −0.461470 | ||||||||
\(327\) | 86.3932i | 0.264199i | ||||||||
\(328\) | − | 111.347i | − | 0.339471i | ||||||
\(329\) | 273.530 | − | 499.537i | 0.831397 | − | 1.51835i | ||||
\(330\) | 29.2388 | 0.0886024 | ||||||||
\(331\) | −516.884 | −1.56158 | −0.780792 | − | 0.624791i | \(-0.785184\pi\) | ||||
−0.780792 | + | 0.624791i | \(0.785184\pi\) | |||||||
\(332\) | − | 505.871i | − | 1.52371i | ||||||
\(333\) | 21.4248 | 0.0643388 | ||||||||
\(334\) | 266.116i | 0.796755i | ||||||||
\(335\) | 109.970i | 0.328268i | ||||||||
\(336\) | −79.7099 | + | 145.571i | −0.237232 | + | 0.433247i | ||||
\(337\) | −643.730 | −1.91018 | −0.955089 | − | 0.296320i | \(-0.904240\pi\) | ||||
−0.955089 | + | 0.296320i | \(0.904240\pi\) | |||||||
\(338\) | 493.063 | 1.45877 | ||||||||
\(339\) | 192.647i | 0.568281i | ||||||||
\(340\) | 143.389 | 0.421731 | ||||||||
\(341\) | 16.4702i | 0.0482998i | ||||||||
\(342\) | − | 130.691i | − | 0.382136i | ||||||
\(343\) | 23.2640 | + | 342.210i | 0.0678249 | + | 0.997697i | ||||
\(344\) | 118.482 | 0.344426 | ||||||||
\(345\) | 86.2766 | 0.250077 | ||||||||
\(346\) | − | 351.693i | − | 1.01645i | ||||||
\(347\) | −256.423 | −0.738971 | −0.369485 | − | 0.929237i | \(-0.620466\pi\) | ||||
−0.369485 | + | 0.929237i | \(0.620466\pi\) | |||||||
\(348\) | − | 136.121i | − | 0.391151i | ||||||
\(349\) | − | 410.197i | − | 1.17535i | −0.809097 | − | 0.587675i | \(-0.800043\pi\) | ||
0.809097 | − | 0.587675i | \(-0.199957\pi\) | |||||||
\(350\) | −89.5668 | − | 49.0438i | −0.255905 | − | 0.140125i | ||||
\(351\) | 0.258885 | 0.000737565 | ||||||||
\(352\) | 118.810 | 0.337528 | ||||||||
\(353\) | 258.233i | 0.731537i | 0.930706 | + | 0.365769i | \(0.119194\pi\) | ||||
−0.930706 | + | 0.365769i | \(0.880806\pi\) | |||||||
\(354\) | −21.8900 | −0.0618362 | ||||||||
\(355\) | − | 217.763i | − | 0.613416i | ||||||
\(356\) | 350.873i | 0.985599i | ||||||||
\(357\) | 151.131 | + | 82.7541i | 0.423335 | + | 0.231804i | ||||
\(358\) | −149.417 | −0.417366 | ||||||||
\(359\) | −152.789 | −0.425597 | −0.212798 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212798 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(360\) | 10.0255i | 0.0278486i | ||||||||
\(361\) | 138.053 | 0.382417 | ||||||||
\(362\) | − | 157.634i | − | 0.435453i | ||||||
\(363\) | 197.981i | 0.545403i | ||||||||
\(364\) | 0.755806 | − | 1.38030i | 0.00207639 | − | 0.00379203i | ||||
\(365\) | −260.275 | −0.713081 | ||||||||
\(366\) | 554.206 | 1.51422 | ||||||||
\(367\) | − | 393.499i | − | 1.07220i | −0.844153 | − | 0.536102i | \(-0.819896\pi\) | ||
0.844153 | − | 0.536102i | \(-0.180104\pi\) | |||||||
\(368\) | 304.935 | 0.828628 | ||||||||
\(369\) | 223.510i | 0.605719i | ||||||||
\(370\) | 46.5911i | 0.125922i | ||||||||
\(371\) | −412.582 | − | 225.916i | −1.11208 | − | 0.608938i | ||||
\(372\) | −49.7464 | −0.133727 | ||||||||
\(373\) | 324.962 | 0.871212 | 0.435606 | − | 0.900137i | \(-0.356534\pi\) | ||||
0.435606 | + | 0.900137i | \(0.356534\pi\) | |||||||
\(374\) | − | 107.288i | − | 0.286866i | ||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | − | 121.594i | − | 0.323389i | ||||||
\(377\) | − | 0.867754i | − | 0.00230173i | ||||||
\(378\) | −50.9678 | + | 93.0805i | −0.134835 | + | 0.246245i | ||||
\(379\) | −146.945 | −0.387718 | −0.193859 | − | 0.981029i | \(-0.562100\pi\) | ||||
−0.193859 | + | 0.981029i | \(0.562100\pi\) | |||||||
\(380\) | 150.653 | 0.396456 | ||||||||
\(381\) | 120.264i | 0.315655i | ||||||||
\(382\) | 128.115 | 0.335379 | ||||||||
\(383\) | − | 356.582i | − | 0.931025i | −0.885041 | − | 0.465512i | \(-0.845870\pi\) | ||
0.885041 | − | 0.465512i | \(-0.154130\pi\) | |||||||
\(384\) | 82.1551i | 0.213946i | ||||||||
\(385\) | −19.4522 | + | 35.5248i | −0.0505252 | + | 0.0922722i | ||||
\(386\) | −136.208 | −0.352872 | ||||||||
\(387\) | −237.835 | −0.614560 | ||||||||
\(388\) | 496.332i | 1.27921i | ||||||||
\(389\) | 99.7568 | 0.256444 | 0.128222 | − | 0.991745i | \(-0.459073\pi\) | ||||
0.128222 | + | 0.991745i | \(0.459073\pi\) | |||||||
\(390\) | 0.562981i | 0.00144354i | ||||||||
\(391\) | − | 316.581i | − | 0.809670i | ||||||
\(392\) | 39.4470 | + | 61.6988i | 0.100630 | + | 0.157395i | ||||
\(393\) | 68.8478 | 0.175185 | ||||||||
\(394\) | 801.782 | 2.03498 | ||||||||
\(395\) | − | 221.000i | − | 0.559494i | ||||||
\(396\) | 35.0272 | 0.0884526 | ||||||||
\(397\) | 646.374i | 1.62815i | 0.580763 | + | 0.814073i | \(0.302754\pi\) | ||||
−0.580763 | + | 0.814073i | \(0.697246\pi\) | |||||||
\(398\) | − | 788.855i | − | 1.98205i | ||||||
\(399\) | 158.788 | + | 86.9468i | 0.397964 | + | 0.217912i | ||||
\(400\) | 68.4431 | 0.171108 | ||||||||
\(401\) | 219.319 | 0.546931 | 0.273465 | − | 0.961882i | \(-0.411830\pi\) | ||||
0.273465 | + | 0.961882i | \(0.411830\pi\) | |||||||
\(402\) | 248.526i | 0.618223i | ||||||||
\(403\) | −0.317128 | −0.000786917 | ||||||||
\(404\) | 436.515i | 1.08048i | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | 311.995 | + | 170.838i | 0.768461 | + | 0.420783i | ||||
\(407\) | 18.4794 | 0.0454039 | ||||||||
\(408\) | 36.7873 | 0.0901649 | ||||||||
\(409\) | 98.2083i | 0.240118i | 0.992767 | + | 0.120059i | \(0.0383084\pi\) | ||||
−0.992767 | + | 0.120059i | \(0.961692\pi\) | |||||||
\(410\) | −486.053 | −1.18550 | ||||||||
\(411\) | 155.819i | 0.379121i | ||||||||
\(412\) | − | 482.636i | − | 1.17145i | ||||||
\(413\) | 14.5631 | − | 26.5961i | 0.0352619 | − | 0.0643974i | ||||
\(414\) | 194.980 | 0.470967 | ||||||||
\(415\) | −250.687 | −0.604065 | ||||||||
\(416\) | 2.28763i | 0.00549912i | ||||||||
\(417\) | 219.252 | 0.525784 | ||||||||
\(418\) | − | 112.724i | − | 0.269674i | ||||||
\(419\) | 397.174i | 0.947909i | 0.880549 | + | 0.473955i | \(0.157174\pi\) | ||||
−0.880549 | + | 0.473955i | \(0.842826\pi\) | |||||||
\(420\) | −107.298 | − | 58.7530i | −0.255472 | − | 0.139888i | ||||
\(421\) | −149.418 | −0.354911 | −0.177456 | − | 0.984129i | \(-0.556787\pi\) | ||||
−0.177456 | + | 0.984129i | \(0.556787\pi\) | |||||||
\(422\) | 1123.44 | 2.66217 | ||||||||
\(423\) | 244.081i | 0.577024i | ||||||||
\(424\) | −100.428 | −0.236859 | ||||||||
\(425\) | − | 71.0570i | − | 0.167193i | ||||||
\(426\) | − | 492.131i | − | 1.15524i | ||||||
\(427\) | −368.706 | + | 673.354i | −0.863480 | + | 1.57694i | ||||
\(428\) | 149.282 | 0.348791 | ||||||||
\(429\) | 0.223295 | 0.000520500 | ||||||||
\(430\) | − | 517.203i | − | 1.20280i | ||||||
\(431\) | −241.112 | −0.559425 | −0.279713 | − | 0.960084i | \(-0.590239\pi\) | ||||
−0.279713 | + | 0.960084i | \(0.590239\pi\) | |||||||
\(432\) | − | 71.1282i | − | 0.164649i | ||||||
\(433\) | − | 391.184i | − | 0.903426i | −0.892163 | − | 0.451713i | \(-0.850813\pi\) | ||
0.892163 | − | 0.451713i | \(-0.149187\pi\) | |||||||
\(434\) | 62.4342 | − | 114.021i | 0.143858 | − | 0.262721i | ||||
\(435\) | −67.4553 | −0.155070 | ||||||||
\(436\) | −225.067 | −0.516208 | ||||||||
\(437\) | − | 332.620i | − | 0.761145i | ||||||
\(438\) | −588.206 | −1.34294 | ||||||||
\(439\) | 111.468i | 0.253914i | 0.991908 | + | 0.126957i | \(0.0405210\pi\) | ||||
−0.991908 | + | 0.126957i | \(0.959479\pi\) | |||||||
\(440\) | 8.64722i | 0.0196528i | ||||||||
\(441\) | −79.1836 | − | 123.851i | −0.179555 | − | 0.280840i | ||||
\(442\) | 2.06578 | 0.00467372 | ||||||||
\(443\) | −25.3173 | −0.0571497 | −0.0285748 | − | 0.999592i | \(-0.509097\pi\) | ||||
−0.0285748 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(444\) | 55.8148i | 0.125709i | ||||||||
\(445\) | 173.877 | 0.390735 | ||||||||
\(446\) | − | 412.416i | − | 0.924700i | ||||||
\(447\) | 158.237i | 0.353998i | ||||||||
\(448\) | −486.321 | − | 266.293i | −1.08554 | − | 0.594405i | ||||
\(449\) | −486.460 | −1.08343 | −0.541715 | − | 0.840562i | \(-0.682225\pi\) | ||||
−0.541715 | + | 0.840562i | \(0.682225\pi\) | |||||||
\(450\) | 43.7636 | 0.0972525 | ||||||||
\(451\) | 192.783i | 0.427456i | ||||||||
\(452\) | −501.874 | −1.11034 | ||||||||
\(453\) | − | 36.7256i | − | 0.0810720i | ||||||
\(454\) | 871.375i | 1.91933i | ||||||||
\(455\) | −0.684015 | − | 0.374544i | −0.00150333 | − | 0.000823173i | ||||
\(456\) | 38.6511 | 0.0847612 | ||||||||
\(457\) | 352.023 | 0.770292 | 0.385146 | − | 0.922856i | \(-0.374151\pi\) | ||||
0.385146 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(458\) | − | 6.93745i | − | 0.0151473i | ||||||
\(459\) | −73.8446 | −0.160881 | ||||||||
\(460\) | 224.763i | 0.488616i | ||||||||
\(461\) | − | 213.924i | − | 0.464043i | −0.972711 | − | 0.232021i | \(-0.925466\pi\) | ||
0.972711 | − | 0.232021i | \(-0.0745339\pi\) | |||||||
\(462\) | −43.9609 | + | 80.2841i | −0.0951534 | + | 0.173775i | ||||
\(463\) | 144.676 | 0.312474 | 0.156237 | − | 0.987720i | \(-0.450064\pi\) | ||||
0.156237 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(464\) | −238.413 | −0.513822 | ||||||||
\(465\) | 24.6521i | 0.0530153i | ||||||||
\(466\) | −1074.02 | −2.30476 | ||||||||
\(467\) | 97.9108i | 0.209659i | 0.994490 | + | 0.104830i | \(0.0334297\pi\) | ||||
−0.994490 | + | 0.104830i | \(0.966570\pi\) | |||||||
\(468\) | 0.674434i | 0.00144110i | ||||||||
\(469\) | −301.956 | − | 165.341i | −0.643829 | − | 0.352539i | ||||
\(470\) | −530.786 | −1.12933 | ||||||||
\(471\) | 465.487 | 0.988296 | ||||||||
\(472\) | − | 6.47386i | − | 0.0137158i | ||||||
\(473\) | −205.138 | −0.433695 | ||||||||
\(474\) | − | 499.448i | − | 1.05369i | ||||||
\(475\) | − | 74.6571i | − | 0.157173i | ||||||
\(476\) | −215.586 | + | 393.717i | −0.452913 | + | 0.827137i | ||||
\(477\) | 201.594 | 0.422628 | ||||||||
\(478\) | 1227.10 | 2.56715 | ||||||||
\(479\) | 322.314i | 0.672890i | 0.941703 | + | 0.336445i | \(0.109225\pi\) | ||||
−0.941703 | + | 0.336445i | \(0.890775\pi\) | |||||||
\(480\) | 177.831 | 0.370480 | ||||||||
\(481\) | 0.355813i | 0.000739735i | ||||||||
\(482\) | 418.976i | 0.869245i | ||||||||
\(483\) | −129.718 | + | 236.899i | −0.268567 | + | 0.490474i | ||||
\(484\) | −515.770 | −1.06564 | ||||||||
\(485\) | 245.960 | 0.507134 | ||||||||
\(486\) | − | 45.4805i | − | 0.0935813i | ||||||
\(487\) | −349.967 | −0.718617 | −0.359309 | − | 0.933219i | \(-0.616987\pi\) | ||||
−0.359309 | + | 0.933219i | \(0.616987\pi\) | |||||||
\(488\) | 163.903i | 0.335868i | ||||||||
\(489\) | 89.3098i | 0.182638i | ||||||||
\(490\) | 269.329 | − | 172.195i | 0.549652 | − | 0.351419i | ||||
\(491\) | −487.352 | −0.992571 | −0.496286 | − | 0.868159i | \(-0.665303\pi\) | ||||
−0.496286 | + | 0.868159i | \(0.665303\pi\) | |||||||
\(492\) | −582.277 | −1.18349 | ||||||||
\(493\) | 247.518i | 0.502066i | ||||||||
\(494\) | 2.17045 | 0.00439361 | ||||||||
\(495\) | − | 17.3579i | − | 0.0350665i | ||||||
\(496\) | 87.1301i | 0.175666i | ||||||||
\(497\) | 597.934 | + | 327.409i | 1.20309 | + | 0.658770i | ||||
\(498\) | −566.538 | −1.13763 | ||||||||
\(499\) | −15.0073 | −0.0300748 | −0.0150374 | − | 0.999887i | \(-0.504787\pi\) | ||||
−0.0150374 | + | 0.999887i | \(0.504787\pi\) | |||||||
\(500\) | 50.4484i | 0.100897i | ||||||||
\(501\) | 157.983 | 0.315335 | ||||||||
\(502\) | 870.423i | 1.73391i | ||||||||
\(503\) | 868.775i | 1.72719i | 0.504189 | + | 0.863594i | \(0.331792\pi\) | ||||
−0.504189 | + | 0.863594i | \(0.668208\pi\) | |||||||
\(504\) | −27.5281 | − | 15.0735i | −0.0546192 | − | 0.0299077i | ||||
\(505\) | 216.317 | 0.428351 | ||||||||
\(506\) | 168.175 | 0.332362 | ||||||||
\(507\) | − | 292.712i | − | 0.577342i | ||||||
\(508\) | −313.307 | −0.616745 | ||||||||
\(509\) | − | 620.297i | − | 1.21866i | −0.792917 | − | 0.609330i | \(-0.791439\pi\) | ||
0.792917 | − | 0.609330i | \(-0.208561\pi\) | |||||||
\(510\) | − | 160.585i | − | 0.314872i | ||||||
\(511\) | 391.326 | − | 714.664i | 0.765804 | − | 1.39856i | ||||
\(512\) | 710.353 | 1.38741 | ||||||||
\(513\) | −77.5859 | −0.151240 | ||||||||
\(514\) | 552.682i | 1.07526i | ||||||||
\(515\) | −239.173 | −0.464413 | ||||||||
\(516\) | − | 619.594i | − | 1.20076i | ||||||
\(517\) | 210.525i | 0.407206i | ||||||||
\(518\) | −127.930 | − | 70.0502i | −0.246969 | − | 0.135232i | ||||
\(519\) | −208.786 | −0.402286 | ||||||||
\(520\) | −0.166499 | −0.000320190 | ||||||||
\(521\) | 73.0697i | 0.140249i | 0.997538 | + | 0.0701245i | \(0.0223396\pi\) | ||||
−0.997538 | + | 0.0701245i | \(0.977660\pi\) | |||||||
\(522\) | −152.445 | −0.292041 | ||||||||
\(523\) | − | 600.742i | − | 1.14865i | −0.818629 | − | 0.574323i | \(-0.805265\pi\) | ||
0.818629 | − | 0.574323i | \(-0.194735\pi\) | |||||||
\(524\) | 179.359i | 0.342287i | ||||||||
\(525\) | −29.1154 | + | 53.1723i | −0.0554579 | + | 0.101281i | ||||
\(526\) | 680.102 | 1.29297 | ||||||||
\(527\) | 90.4576 | 0.171646 | ||||||||
\(528\) | − | 61.3497i | − | 0.116193i | ||||||
\(529\) | −32.7560 | −0.0619206 | ||||||||
\(530\) | 438.392i | 0.827154i | ||||||||
\(531\) | 12.9952i | 0.0244732i | ||||||||
\(532\) | −226.509 | + | 413.665i | −0.425769 | + | 0.777566i | ||||
\(533\) | −3.71195 | −0.00696426 | ||||||||
\(534\) | 392.953 | 0.735867 | ||||||||
\(535\) | − | 73.9777i | − | 0.138276i | ||||||
\(536\) | −73.5002 | −0.137127 | ||||||||
\(537\) | 88.7032i | 0.165183i | ||||||||
\(538\) | − | 761.991i | − | 1.41634i | ||||||
\(539\) | −68.2976 | − | 106.824i | −0.126712 | − | 0.198189i | ||||
\(540\) | 52.4276 | 0.0970881 | ||||||||
\(541\) | −628.263 | −1.16130 | −0.580650 | − | 0.814153i | \(-0.697202\pi\) | ||||
−0.580650 | + | 0.814153i | \(0.697202\pi\) | |||||||
\(542\) | − | 502.571i | − | 0.927253i | ||||||
\(543\) | −93.5811 | −0.172341 | ||||||||
\(544\) | − | 652.526i | − | 1.19950i | ||||||
\(545\) | 111.533i | 0.204648i | ||||||||
\(546\) | −1.54584 | − | 0.846448i | −0.00283120 | − | 0.00155027i | ||||
\(547\) | −616.326 | −1.12674 | −0.563370 | − | 0.826205i | \(-0.690495\pi\) | ||||
−0.563370 | + | 0.826205i | \(0.690495\pi\) | |||||||
\(548\) | −405.931 | −0.740750 | ||||||||
\(549\) | − | 329.010i | − | 0.599290i | ||||||
\(550\) | 37.7471 | 0.0686311 | ||||||||
\(551\) | 260.059i | 0.471976i | ||||||||
\(552\) | 57.6645i | 0.104465i | ||||||||
\(553\) | 606.824 | + | 332.277i | 1.09733 | + | 0.600862i | ||||
\(554\) | 658.714 | 1.18901 | ||||||||
\(555\) | 27.6593 | 0.0498366 | ||||||||
\(556\) | 571.183i | 1.02731i | ||||||||
\(557\) | 444.374 | 0.797799 | 0.398900 | − | 0.916995i | \(-0.369392\pi\) | ||||
0.398900 | + | 0.916995i | \(0.369392\pi\) | |||||||
\(558\) | 55.7124i | 0.0998430i | ||||||||
\(559\) | − | 3.94984i | − | 0.00706591i | ||||||
\(560\) | −102.905 | + | 187.932i | −0.183759 | + | 0.335592i | ||||
\(561\) | −63.6926 | −0.113534 | ||||||||
\(562\) | 455.480 | 0.810464 | ||||||||
\(563\) | 490.184i | 0.870665i | 0.900270 | + | 0.435332i | \(0.143369\pi\) | ||||
−0.900270 | + | 0.435332i | \(0.856631\pi\) | |||||||
\(564\) | −635.867 | −1.12742 | ||||||||
\(565\) | 248.706i | 0.440188i | ||||||||
\(566\) | − | 276.153i | − | 0.487903i | ||||||
\(567\) | 55.2583 | + | 30.2576i | 0.0974573 | + | 0.0533644i | ||||
\(568\) | 145.545 | 0.256242 | ||||||||
\(569\) | 152.671 | 0.268315 | 0.134158 | − | 0.990960i | \(-0.457167\pi\) | ||||
0.134158 | + | 0.990960i | \(0.457167\pi\) | |||||||
\(570\) | − | 168.721i | − | 0.296002i | ||||||
\(571\) | −348.236 | −0.609871 | −0.304936 | − | 0.952373i | \(-0.598635\pi\) | ||||
−0.304936 | + | 0.952373i | \(0.598635\pi\) | |||||||
\(572\) | 0.581715i | 0.00101698i | ||||||||
\(573\) | − | 76.0567i | − | 0.132734i | ||||||
\(574\) | 730.787 | − | 1334.61i | 1.27315 | − | 2.32510i | ||||
\(575\) | 111.383 | 0.193709 | ||||||||
\(576\) | 237.624 | 0.412541 | ||||||||
\(577\) | − | 216.610i | − | 0.375407i | −0.982226 | − | 0.187703i | \(-0.939896\pi\) | ||
0.982226 | − | 0.187703i | \(-0.0601044\pi\) | |||||||
\(578\) | 253.934 | 0.439333 | ||||||||
\(579\) | 80.8617i | 0.139657i | ||||||||
\(580\) | − | 175.731i | − | 0.302985i | ||||||
\(581\) | 376.911 | − | 688.338i | 0.648728 | − | 1.18475i | ||||
\(582\) | 555.856 | 0.955078 | ||||||||
\(583\) | 173.879 | 0.298249 | ||||||||
\(584\) | − | 173.959i | − | 0.297875i | ||||||
\(585\) | 0.334220 | 0.000571316 | ||||||||
\(586\) | 944.865i | 1.61240i | ||||||||
\(587\) | − | 549.987i | − | 0.936945i | −0.883478 | − | 0.468473i | \(-0.844805\pi\) | ||
0.883478 | − | 0.468473i | \(-0.155195\pi\) | |||||||
\(588\) | 322.649 | − | 206.285i | 0.548722 | − | 0.350824i | ||||
\(589\) | 95.0407 | 0.161359 | ||||||||
\(590\) | −28.2599 | −0.0478981 | ||||||||
\(591\) | − | 475.986i | − | 0.805392i | ||||||
\(592\) | 97.7587 | 0.165133 | ||||||||
\(593\) | − | 496.397i | − | 0.837095i | −0.908195 | − | 0.418547i | \(-0.862539\pi\) | ||
0.908195 | − | 0.418547i | \(-0.137461\pi\) | |||||||
\(594\) | − | 39.2280i | − | 0.0660403i | ||||||
\(595\) | 195.109 | + | 106.835i | 0.327914 | + | 0.179555i | ||||
\(596\) | −412.231 | −0.691663 | ||||||||
\(597\) | −468.313 | −0.784443 | ||||||||
\(598\) | 3.23814i | 0.00541495i | ||||||||
\(599\) | 837.957 | 1.39893 | 0.699463 | − | 0.714669i | \(-0.253422\pi\) | ||||
0.699463 | + | 0.714669i | \(0.253422\pi\) | |||||||
\(600\) | 12.9429i | 0.0215714i | ||||||||
\(601\) | − | 643.195i | − | 1.07021i | −0.844786 | − | 0.535104i | \(-0.820272\pi\) | ||
0.844786 | − | 0.535104i | \(-0.179728\pi\) | |||||||
\(602\) | 1420.14 | + | 777.621i | 2.35904 | + | 1.29173i | ||||
\(603\) | 147.540 | 0.244677 | ||||||||
\(604\) | 95.6755 | 0.158403 | ||||||||
\(605\) | 255.593i | 0.422467i | ||||||||
\(606\) | 488.865 | 0.806707 | ||||||||
\(607\) | − | 137.690i | − | 0.226837i | −0.993547 | − | 0.113419i | \(-0.963820\pi\) | ||
0.993547 | − | 0.113419i | \(-0.0361801\pi\) | |||||||
\(608\) | − | 685.586i | − | 1.12761i | ||||||
\(609\) | 101.420 | − | 185.219i | 0.166535 | − | 0.304137i | ||||
\(610\) | 715.476 | 1.17291 | ||||||||
\(611\) | −4.05358 | −0.00663433 | ||||||||
\(612\) | − | 192.376i | − | 0.314340i | ||||||
\(613\) | 844.662 | 1.37792 | 0.688958 | − | 0.724801i | \(-0.258068\pi\) | ||||
0.688958 | + | 0.724801i | \(0.258068\pi\) | |||||||
\(614\) | − | 1583.79i | − | 2.57946i | ||||||
\(615\) | 288.551i | 0.469188i | ||||||||
\(616\) | −23.7436 | − | 13.0012i | −0.0385448 | − | 0.0211059i | ||||
\(617\) | −601.594 | −0.975031 | −0.487515 | − | 0.873114i | \(-0.662097\pi\) | ||||
−0.487515 | + | 0.873114i | \(0.662097\pi\) | |||||||
\(618\) | −540.517 | −0.874623 | ||||||||
\(619\) | 389.067i | 0.628542i | 0.949333 | + | 0.314271i | \(0.101760\pi\) | ||||
−0.949333 | + | 0.314271i | \(0.898240\pi\) | |||||||
\(620\) | −64.2223 | −0.103584 | ||||||||
\(621\) | − | 115.752i | − | 0.186397i | ||||||
\(622\) | 1182.62i | 1.90132i | ||||||||
\(623\) | −261.426 | + | 477.433i | −0.419625 | + | 0.766345i | ||||
\(624\) | 1.18126 | 0.00189305 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 128.677i | − | 0.205554i | ||||||
\(627\) | −66.9196 | −0.106730 | ||||||||
\(628\) | 1212.66i | 1.93099i | ||||||||
\(629\) | − | 101.492i | − | 0.161355i | ||||||
\(630\) | −65.7991 | + | 120.166i | −0.104443 | + | 0.190740i | ||||
\(631\) | 394.214 | 0.624745 | 0.312372 | − | 0.949960i | \(-0.398876\pi\) | ||||
0.312372 | + | 0.949960i | \(0.398876\pi\) | |||||||
\(632\) | 147.709 | 0.233717 | ||||||||
\(633\) | − | 666.940i | − | 1.05362i | ||||||
\(634\) | −713.664 | −1.12565 | ||||||||
\(635\) | 155.261i | 0.244505i | ||||||||
\(636\) | 525.180i | 0.825755i | ||||||||
\(637\) | 2.05685 | − | 1.31504i | 0.00322896 | − | 0.00206443i | ||||
\(638\) | −131.488 | −0.206093 | ||||||||
\(639\) | −292.159 | −0.457213 | ||||||||
\(640\) | 106.062i | 0.165722i | ||||||||
\(641\) | 98.0430 | 0.152953 | 0.0764766 | − | 0.997071i | \(-0.475633\pi\) | ||||
0.0764766 | + | 0.997071i | \(0.475633\pi\) | |||||||
\(642\) | − | 167.186i | − | 0.260414i | ||||||
\(643\) | 585.514i | 0.910598i | 0.890339 | + | 0.455299i | \(0.150468\pi\) | ||||
−0.890339 | + | 0.455299i | \(0.849532\pi\) | |||||||
\(644\) | −617.156 | − | 337.934i | −0.958317 | − | 0.524743i | ||||
\(645\) | −307.043 | −0.476036 | ||||||||
\(646\) | −619.099 | −0.958358 | ||||||||
\(647\) | − | 1256.79i | − | 1.94248i | −0.238099 | − | 0.971241i | \(-0.576524\pi\) | ||
0.238099 | − | 0.971241i | \(-0.423476\pi\) | |||||||
\(648\) | 13.4506 | 0.0207571 | ||||||||
\(649\) | 11.2087i | 0.0172707i | ||||||||
\(650\) | 0.726805i | 0.00111816i | ||||||||
\(651\) | −67.6899 | − | 37.0647i | −0.103978 | − | 0.0569351i | ||||
\(652\) | −232.665 | −0.356848 | ||||||||
\(653\) | −687.810 | −1.05331 | −0.526654 | − | 0.850080i | \(-0.676554\pi\) | ||||
−0.526654 | + | 0.850080i | \(0.676554\pi\) | |||||||
\(654\) | 252.059i | 0.385411i | ||||||||
\(655\) | 88.8822 | 0.135698 | ||||||||
\(656\) | 1019.85i | 1.55465i | ||||||||
\(657\) | 349.195i | 0.531499i | ||||||||
\(658\) | 798.044 | − | 1457.44i | 1.21283 | − | 2.21495i | ||||
\(659\) | 757.250 | 1.14909 | 0.574545 | − | 0.818473i | \(-0.305179\pi\) | ||||
0.574545 | + | 0.818473i | \(0.305179\pi\) | |||||||
\(660\) | 45.2199 | 0.0685151 | ||||||||
\(661\) | 652.355i | 0.986922i | 0.869768 | + | 0.493461i | \(0.164268\pi\) | ||||
−0.869768 | + | 0.493461i | \(0.835732\pi\) | |||||||
\(662\) | −1508.05 | −2.27802 | ||||||||
\(663\) | − | 1.22637i | − | 0.00184974i | ||||||
\(664\) | − | 167.551i | − | 0.252336i | ||||||
\(665\) | 204.994 | + | 112.248i | 0.308262 | + | 0.168794i | ||||
\(666\) | 62.5085 | 0.0938566 | ||||||||
\(667\) | −387.988 | −0.581691 | ||||||||
\(668\) | 411.568i | 0.616120i | ||||||||
\(669\) | −244.835 | −0.365972 | ||||||||
\(670\) | 320.845i | 0.478873i | ||||||||
\(671\) | − | 283.779i | − | 0.422919i | ||||||
\(672\) | −267.370 | + | 488.288i | −0.397873 | + | 0.726619i | ||||
\(673\) | −798.483 | −1.18645 | −0.593227 | − | 0.805035i | \(-0.702146\pi\) | ||||
−0.593227 | + | 0.805035i | \(0.702146\pi\) | |||||||
\(674\) | −1878.13 | −2.78654 | ||||||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | 762.558 | 1.12804 | ||||||||
\(677\) | 512.802i | 0.757462i | 0.925507 | + | 0.378731i | \(0.123639\pi\) | ||||
−0.925507 | + | 0.378731i | \(0.876361\pi\) | |||||||
\(678\) | 562.063i | 0.829001i | ||||||||
\(679\) | −369.804 | + | 675.358i | −0.544630 | + | 0.994636i | ||||
\(680\) | 47.4922 | 0.0698414 | ||||||||
\(681\) | 517.301 | 0.759620 | ||||||||
\(682\) | 48.0532i | 0.0704592i | ||||||||
\(683\) | −1332.72 | −1.95127 | −0.975636 | − | 0.219394i | \(-0.929592\pi\) | ||||
−0.975636 | + | 0.219394i | \(0.929592\pi\) | |||||||
\(684\) | − | 202.123i | − | 0.295501i | ||||||
\(685\) | 201.161i | 0.293666i | ||||||||
\(686\) | 67.8743 | + | 998.424i | 0.0989422 | + | 1.45543i | ||||
\(687\) | −4.11850 | −0.00599490 | ||||||||
\(688\) | −1085.21 | −1.57734 | ||||||||
\(689\) | 3.34797i | 0.00485917i | ||||||||
\(690\) | 251.719 | 0.364810 | ||||||||
\(691\) | 1065.65i | 1.54218i | 0.636724 | + | 0.771092i | \(0.280289\pi\) | ||||
−0.636724 | + | 0.771092i | \(0.719711\pi\) | |||||||
\(692\) | − | 543.919i | − | 0.786010i | ||||||
\(693\) | 47.6615 | + | 26.0979i | 0.0687756 | + | 0.0376593i | ||||
\(694\) | −748.133 | −1.07800 | ||||||||
\(695\) | 283.053 | 0.407270 | ||||||||
\(696\) | − | 45.0849i | − | 0.0647772i | ||||||
\(697\) | 1058.80 | 1.51908 | ||||||||
\(698\) | − | 1196.78i | − | 1.71459i | ||||||
\(699\) | 637.602i | 0.912163i | ||||||||
\(700\) | −138.522 | − | 75.8498i | −0.197888 | − | 0.108357i | ||||
\(701\) | −953.569 | −1.36030 | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||||
−0.680149 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(702\) | 0.755318 | 0.00107595 | ||||||||
\(703\) | − | 106.634i | − | 0.151685i | ||||||
\(704\) | 204.956 | 0.291130 | ||||||||
\(705\) | 315.107i | 0.446961i | ||||||||
\(706\) | 753.413i | 1.06716i | ||||||||
\(707\) | −325.235 | + | 593.965i | −0.460022 | + | 0.840120i | ||||
\(708\) | −33.8545 | −0.0478171 | ||||||||
\(709\) | 68.0675 | 0.0960050 | 0.0480025 | − | 0.998847i | \(-0.484714\pi\) | ||||
0.0480025 | + | 0.998847i | \(0.484714\pi\) | |||||||
\(710\) | − | 635.339i | − | 0.894843i | ||||||
\(711\) | −296.503 | −0.417023 | ||||||||
\(712\) | 116.214i | 0.163222i | ||||||||
\(713\) | 141.793i | 0.198869i | ||||||||
\(714\) | 440.935 | + | 241.441i | 0.617556 | + | 0.338153i | ||||
\(715\) | 0.288272 | 0.000403178 | ||||||||
\(716\) | −231.085 | −0.322744 | ||||||||
\(717\) | − | 728.480i | − | 1.01601i | ||||||
\(718\) | −445.774 | −0.620855 | ||||||||
\(719\) | 137.609i | 0.191389i | 0.995411 | + | 0.0956947i | \(0.0305073\pi\) | ||||
−0.995411 | + | 0.0956947i | \(0.969493\pi\) | |||||||
\(720\) | − | 91.8261i | − | 0.127536i | ||||||
\(721\) | 359.599 | − | 656.722i | 0.498751 | − | 0.910849i | ||||
\(722\) | 402.779 | 0.557866 | ||||||||
\(723\) | 248.730 | 0.344025 | ||||||||
\(724\) | − | 243.792i | − | 0.336730i | ||||||
\(725\) | −87.0845 | −0.120117 | ||||||||
\(726\) | 577.625i | 0.795627i | ||||||||
\(727\) | − | 853.429i | − | 1.17391i | −0.809621 | − | 0.586953i | \(-0.800328\pi\) | ||
0.809621 | − | 0.586953i | \(-0.199672\pi\) | |||||||
\(728\) | 0.250333 | − | 0.457173i | 0.000343864 | − | 0.000627985i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −759.371 | −1.04023 | ||||||||
\(731\) | 1126.65i | 1.54125i | ||||||||
\(732\) | 857.120 | 1.17093 | ||||||||
\(733\) | − | 1225.71i | − | 1.67219i | −0.548586 | − | 0.836094i | \(-0.684834\pi\) | ||
0.548586 | − | 0.836094i | \(-0.315166\pi\) | |||||||
\(734\) | − | 1148.06i | − | 1.56412i | ||||||
\(735\) | −102.226 | − | 159.890i | −0.139082 | − | 0.217538i | ||||
\(736\) | 1022.84 | 1.38973 | ||||||||
\(737\) | 127.257 | 0.172668 | ||||||||
\(738\) | 652.109i | 0.883616i | ||||||||
\(739\) | −1314.44 | −1.77867 | −0.889334 | − | 0.457258i | \(-0.848832\pi\) | ||||
−0.889334 | + | 0.457258i | \(0.848832\pi\) | |||||||
\(740\) | 72.0565i | 0.0973737i | ||||||||
\(741\) | − | 1.28851i | − | 0.00173888i | ||||||
\(742\) | −1203.74 | − | 659.127i | −1.62229 | − | 0.888312i | ||||
\(743\) | 1209.47 | 1.62782 | 0.813908 | − | 0.580994i | \(-0.197336\pi\) | ||||
0.813908 | + | 0.580994i | \(0.197336\pi\) | |||||||
\(744\) | −16.4766 | −0.0221460 | ||||||||
\(745\) | 204.283i | 0.274206i | ||||||||
\(746\) | 948.101 | 1.27091 | ||||||||
\(747\) | 336.332i | 0.450243i | ||||||||
\(748\) | − | 165.929i | − | 0.221830i | ||||||
\(749\) | 203.128 | + | 111.226i | 0.271200 | + | 0.148500i | ||||
\(750\) | 56.4986 | 0.0753315 | ||||||||
\(751\) | −173.085 | −0.230473 | −0.115236 | − | 0.993338i | \(-0.536763\pi\) | ||||
−0.115236 | + | 0.993338i | \(0.536763\pi\) | |||||||
\(752\) | 1113.71i | 1.48100i | ||||||||
\(753\) | 516.736 | 0.686236 | ||||||||
\(754\) | − | 2.53174i | − | 0.00335774i | ||||||
\(755\) | − | 47.4125i | − | 0.0627981i | ||||||
\(756\) | −78.8255 | + | 143.956i | −0.104266 | + | 0.190418i | ||||
\(757\) | 723.857 | 0.956218 | 0.478109 | − | 0.878301i | \(-0.341322\pi\) | ||||
0.478109 | + | 0.878301i | \(0.341322\pi\) | |||||||
\(758\) | −428.723 | −0.565598 | ||||||||
\(759\) | − | 99.8390i | − | 0.131540i | ||||||
\(760\) | 49.8983 | 0.0656557 | ||||||||
\(761\) | − | 187.223i | − | 0.246023i | −0.992405 | − | 0.123011i | \(-0.960745\pi\) | ||
0.992405 | − | 0.123011i | \(-0.0392552\pi\) | |||||||
\(762\) | 350.881i | 0.460473i | ||||||||
\(763\) | −306.248 | − | 167.691i | −0.401374 | − | 0.219779i | ||||
\(764\) | 198.139 | 0.259344 | ||||||||
\(765\) | −95.3330 | −0.124618 | ||||||||
\(766\) | − | 1040.36i | − | 1.35817i | ||||||
\(767\) | −0.215819 | −0.000281380 | ||||||||
\(768\) | − | 309.074i | − | 0.402441i | ||||||
\(769\) | − | 94.5845i | − | 0.122997i | −0.998107 | − | 0.0614984i | \(-0.980412\pi\) | ||
0.998107 | − | 0.0614984i | \(-0.0195879\pi\) | |||||||
\(770\) | −56.7532 | + | 103.646i | −0.0737055 | + | 0.134606i | ||||
\(771\) | 328.106 | 0.425559 | ||||||||
\(772\) | −210.656 | −0.272871 | ||||||||
\(773\) | − | 561.473i | − | 0.726356i | −0.931720 | − | 0.363178i | \(-0.881692\pi\) | ||
0.931720 | − | 0.363178i | \(-0.118308\pi\) | |||||||
\(774\) | −693.901 | −0.896513 | ||||||||
\(775\) | 31.8257i | 0.0410655i | ||||||||
\(776\) | 164.391i | 0.211845i | ||||||||
\(777\) | −41.5861 | + | 75.9471i | −0.0535214 | + | 0.0977440i | ||||
\(778\) | 291.048 | 0.374098 | ||||||||
\(779\) | 1112.44 | 1.42804 | ||||||||
\(780\) | 0.870691i | 0.00111627i | ||||||||
\(781\) | −251.994 | −0.322655 | ||||||||
\(782\) | − | 923.648i | − | 1.18114i | ||||||
\(783\) | 90.5008i | 0.115582i | ||||||||
\(784\) | −361.305 | − | 565.115i | −0.460848 | − | 0.720810i | ||||
\(785\) | 600.942 | 0.765531 | ||||||||
\(786\) | 200.869 | 0.255558 | ||||||||
\(787\) | − | 1113.97i | − | 1.41547i | −0.706479 | − | 0.707734i | \(-0.749718\pi\) | ||
0.706479 | − | 0.707734i | \(-0.250282\pi\) | |||||||
\(788\) | 1240.01 | 1.57362 | ||||||||
\(789\) | − | 403.750i | − | 0.511724i | ||||||
\(790\) | − | 644.785i | − | 0.816184i | ||||||
\(791\) | −682.900 | − | 373.933i | −0.863337 | − | 0.472735i | ||||
\(792\) | 11.6015 | 0.0146483 | ||||||||
\(793\) | 5.46404 | 0.00689034 | ||||||||
\(794\) | 1885.84i | 2.37512i | ||||||||
\(795\) | 260.256 | 0.327366 | ||||||||
\(796\) | − | 1220.02i | − | 1.53269i | ||||||
\(797\) | 262.831i | 0.329776i | 0.986312 | + | 0.164888i | \(0.0527262\pi\) | ||||
−0.986312 | + | 0.164888i | \(0.947274\pi\) | |||||||
\(798\) | 463.275 | + | 253.674i | 0.580545 | + | 0.317887i | ||||
\(799\) | 1156.24 | 1.44711 | ||||||||
\(800\) | 229.578 | 0.286973 | ||||||||
\(801\) | − | 233.281i | − | 0.291237i | ||||||
\(802\) | 639.880 | 0.797855 | ||||||||
\(803\) | 301.189i | 0.375079i | ||||||||
\(804\) | 384.363i | 0.478064i | ||||||||
\(805\) | −167.465 | + | 305.835i | −0.208031 | + | 0.379920i | ||||
\(806\) | −0.925244 | −0.00114795 | ||||||||
\(807\) | −452.365 | −0.560551 | ||||||||
\(808\) | 144.579i | 0.178935i | ||||||||
\(809\) | 779.689 | 0.963769 | 0.481885 | − | 0.876235i | \(-0.339952\pi\) | ||||
0.481885 | + | 0.876235i | \(0.339952\pi\) | |||||||
\(810\) | − | 58.7151i | − | 0.0724877i | ||||||
\(811\) | − | 1414.43i | − | 1.74406i | −0.489454 | − | 0.872029i | \(-0.662804\pi\) | ||
0.489454 | − | 0.872029i | \(-0.337196\pi\) | |||||||
\(812\) | 482.523 | + | 264.214i | 0.594241 | + | 0.325386i | ||||
\(813\) | −298.357 | −0.366983 | ||||||||
\(814\) | 53.9150 | 0.0662346 | ||||||||
\(815\) | 115.298i | 0.141471i | ||||||||
\(816\) | −336.944 | −0.412921 | ||||||||
\(817\) | 1183.74i | 1.44888i | ||||||||
\(818\) | 286.530i | 0.350281i | ||||||||
\(819\) | −0.502503 | + | 0.917702i | −0.000613557 | + | 0.00112052i | ||||
\(820\) | −751.717 | −0.916728 | ||||||||
\(821\) | 301.987 | 0.367829 | 0.183914 | − | 0.982942i | \(-0.441123\pi\) | ||||
0.183914 | + | 0.982942i | \(0.441123\pi\) | |||||||
\(822\) | 454.613i | 0.553058i | ||||||||
\(823\) | 411.340 | 0.499805 | 0.249903 | − | 0.968271i | \(-0.419601\pi\) | ||||
0.249903 | + | 0.968271i | \(0.419601\pi\) | |||||||
\(824\) | − | 159.855i | − | 0.193999i | ||||||
\(825\) | − | 22.4090i | − | 0.0271624i | ||||||
\(826\) | 42.4891 | − | 77.5962i | 0.0514396 | − | 0.0939421i | ||||
\(827\) | −86.0106 | −0.104003 | −0.0520015 | − | 0.998647i | \(-0.516560\pi\) | ||||
−0.0520015 | + | 0.998647i | \(0.516560\pi\) | |||||||
\(828\) | 301.552 | 0.364193 | ||||||||
\(829\) | 810.197i | 0.977318i | 0.872475 | + | 0.488659i | \(0.162514\pi\) | ||||
−0.872475 | + | 0.488659i | \(0.837486\pi\) | |||||||
\(830\) | −731.398 | −0.881202 | ||||||||
\(831\) | − | 391.053i | − | 0.470581i | ||||||
\(832\) | 3.94634i | 0.00474319i | ||||||||
\(833\) | −586.697 | + | 375.103i | −0.704318 | + | 0.450304i | ||||
\(834\) | 639.684 | 0.767007 | ||||||||
\(835\) | 203.955 | 0.244257 | ||||||||
\(836\) | − | 174.335i | − | 0.208535i | ||||||
\(837\) | 33.0743 | 0.0395153 | ||||||||
\(838\) | 1158.79i | 1.38280i | ||||||||
\(839\) | 82.0394i | 0.0977823i | 0.998804 | + | 0.0488912i | \(0.0155687\pi\) | ||||
−0.998804 | + | 0.0488912i | \(0.984431\pi\) | |||||||
\(840\) | −35.5386 | − | 19.4598i | −0.0423079 | − | 0.0231664i | ||||
\(841\) | −537.652 | −0.639301 | ||||||||
\(842\) | −435.937 | −0.517740 | ||||||||
\(843\) | − | 270.401i | − | 0.320760i | ||||||
\(844\) | 1737.48 | 2.05862 | ||||||||
\(845\) | − | 377.890i | − | 0.447207i | ||||||
\(846\) | 712.125i | 0.841755i | ||||||||
\(847\) | −701.808 | − | 384.287i | −0.828581 | − | 0.453703i | ||||
\(848\) | 919.846 | 1.08472 | ||||||||
\(849\) | −163.941 | −0.193099 | ||||||||
\(850\) | − | 207.314i | − | 0.243899i | ||||||
\(851\) | 159.090 | 0.186945 | ||||||||
\(852\) | − | 761.117i | − | 0.893330i | ||||||
\(853\) | 970.162i | 1.13735i | 0.822561 | + | 0.568677i | \(0.192544\pi\) | ||||
−0.822561 | + | 0.568677i | \(0.807456\pi\) | |||||||
\(854\) | −1075.73 | + | 1964.56i | −1.25963 | + | 2.30042i | ||||
\(855\) | −100.163 | −0.117150 | ||||||||
\(856\) | 49.4443 | 0.0577620 | ||||||||
\(857\) | 692.118i | 0.807606i | 0.914846 | + | 0.403803i | \(0.132312\pi\) | ||||
−0.914846 | + | 0.403803i | \(0.867688\pi\) | |||||||
\(858\) | 0.651479 | 0.000759299 | ||||||||
\(859\) | 480.223i | 0.559048i | 0.960139 | + | 0.279524i | \(0.0901767\pi\) | ||||
−0.960139 | + | 0.279524i | \(0.909823\pi\) | |||||||
\(860\) | − | 799.893i | − | 0.930108i | ||||||
\(861\) | −792.305 | − | 433.840i | −0.920214 | − | 0.503879i | ||||
\(862\) | −703.463 | −0.816083 | ||||||||
\(863\) | 929.311 | 1.07684 | 0.538419 | − | 0.842677i | \(-0.319022\pi\) | ||||
0.538419 | + | 0.842677i | \(0.319022\pi\) | |||||||
\(864\) | − | 238.585i | − | 0.276140i | ||||||
\(865\) | −269.542 | −0.311609 | ||||||||
\(866\) | − | 1141.31i | − | 1.31791i | ||||||
\(867\) | − | 150.751i | − | 0.173876i | ||||||
\(868\) | 96.5590 | − | 176.342i | 0.111243 | − | 0.203159i | ||||
\(869\) | −255.741 | −0.294293 | ||||||||
\(870\) | −196.806 | −0.226214 | ||||||||
\(871\) | 2.45027i | 0.00281317i | ||||||||
\(872\) | −74.5451 | −0.0854875 | ||||||||
\(873\) | − | 329.990i | − | 0.377995i | ||||||
\(874\) | − | 970.445i | − | 1.11035i | ||||||
\(875\) | −37.5878 | + | 68.6452i | −0.0429575 | + | 0.0784516i | ||||
\(876\) | −909.704 | −1.03847 | ||||||||
\(877\) | 1730.63 | 1.97336 | 0.986678 | − | 0.162685i | \(-0.0520154\pi\) | ||||
0.986678 | + | 0.162685i | \(0.0520154\pi\) | |||||||
\(878\) | 325.217i | 0.370406i | ||||||||
\(879\) | 560.930 | 0.638145 | ||||||||
\(880\) | − | 79.2021i | − | 0.0900024i | ||||||
\(881\) | − | 461.033i | − | 0.523307i | −0.965162 | − | 0.261653i | \(-0.915732\pi\) | ||
0.965162 | − | 0.261653i | \(-0.0842677\pi\) | |||||||
\(882\) | −231.024 | − | 361.343i | −0.261932 | − | 0.409686i | ||||
\(883\) | −942.531 | −1.06742 | −0.533710 | − | 0.845668i | \(-0.679202\pi\) | ||||
−0.533710 | + | 0.845668i | \(0.679202\pi\) | |||||||
\(884\) | 3.19489 | 0.00361412 | ||||||||
\(885\) | 16.7768i | 0.0189568i | ||||||||
\(886\) | −73.8651 | −0.0833692 | ||||||||
\(887\) | − | 178.185i | − | 0.200885i | −0.994943 | − | 0.100443i | \(-0.967974\pi\) | ||
0.994943 | − | 0.100443i | \(-0.0320259\pi\) | |||||||
\(888\) | 18.4866i | 0.0208182i | ||||||||
\(889\) | −426.316 | − | 233.436i | −0.479546 | − | 0.262583i | ||||
\(890\) | 507.300 | 0.570000 | ||||||||
\(891\) | −23.2881 | −0.0261370 | ||||||||
\(892\) | − | 637.832i | − | 0.715058i | ||||||
\(893\) | 1214.83 | 1.36039 | ||||||||
\(894\) | 461.669i | 0.516408i | ||||||||
\(895\) | 114.515i | 0.127950i | ||||||||
\(896\) | −291.225 | − | 159.465i | −0.325028 | − | 0.177975i | ||||
\(897\) | 1.92236 | 0.00214310 | ||||||||
\(898\) | −1419.28 | −1.58049 | ||||||||
\(899\) | − | 110.861i | − | 0.123316i | ||||||
\(900\) | 67.6837 | 0.0752041 | ||||||||
\(901\) | − | 954.975i | − | 1.05991i | ||||||
\(902\) | 562.458i | 0.623568i | ||||||||
\(903\) | 461.643 | − | 843.081i | 0.511233 | − | 0.933645i | ||||
\(904\) | −166.227 | −0.183880 | ||||||||
\(905\) | −120.813 | −0.133495 | ||||||||
\(906\) | − | 107.150i | − | 0.118267i | ||||||
\(907\) | 617.574 | 0.680897 | 0.340449 | − | 0.940263i | \(-0.389421\pi\) | ||||
0.340449 | + | 0.940263i | \(0.389421\pi\) | |||||||
\(908\) | 1347.64i | 1.48419i | ||||||||
\(909\) | − | 290.220i | − | 0.319274i | ||||||
\(910\) | −1.99567 | − | 1.09276i | −0.00219304 | − | 0.00120083i | ||||
\(911\) | −518.521 | −0.569178 | −0.284589 | − | 0.958650i | \(-0.591857\pi\) | ||||
−0.284589 | + | 0.958650i | \(0.591857\pi\) | |||||||
\(912\) | −354.015 | −0.388174 | ||||||||
\(913\) | 290.094i | 0.317737i | ||||||||
\(914\) | 1027.05 | 1.12369 | ||||||||
\(915\) | − | 424.750i | − | 0.464208i | ||||||
\(916\) | − | 10.7293i | − | 0.0117132i | ||||||
\(917\) | −133.635 | + | 244.053i | −0.145731 | + | 0.266143i | ||||
\(918\) | −215.447 | −0.234692 | ||||||||
\(919\) | 1516.75 | 1.65044 | 0.825219 | − | 0.564813i | \(-0.191052\pi\) | ||||
0.825219 | + | 0.564813i | \(0.191052\pi\) | |||||||
\(920\) | 74.4445i | 0.0809179i | ||||||||
\(921\) | −940.234 | −1.02088 | ||||||||
\(922\) | − | 624.139i | − | 0.676940i | ||||||
\(923\) | − | 4.85203i | − | 0.00525681i | ||||||
\(924\) | −67.9887 | + | 124.165i | −0.0735809 | + | 0.134378i | ||||
\(925\) | 35.7080 | 0.0386033 | ||||||||
\(926\) | 422.102 | 0.455833 | ||||||||
\(927\) | 320.884i | 0.346153i | ||||||||
\(928\) | −799.708 | −0.861754 | ||||||||
\(929\) | 777.683i | 0.837118i | 0.908189 | + | 0.418559i | \(0.137465\pi\) | ||||
−0.908189 | + | 0.418559i | \(0.862535\pi\) | |||||||
\(930\) | 71.9244i | 0.0773380i | ||||||||
\(931\) | −616.422 | + | 394.108i | −0.662107 | + | 0.423316i | ||||
\(932\) | −1661.05 | −1.78224 | ||||||||
\(933\) | 702.078 | 0.752495 | ||||||||
\(934\) | 285.662i | 0.305848i | ||||||||
\(935\) | −82.2269 | −0.0879432 | ||||||||
\(936\) | 0.223381i | 0.000238655i | ||||||||
\(937\) | − | 1118.28i | − | 1.19347i | −0.802439 | − | 0.596734i | \(-0.796465\pi\) | ||
0.802439 | − | 0.596734i | \(-0.203535\pi\) | |||||||
\(938\) | −880.979 | − | 482.395i | −0.939210 | − | 0.514280i | ||||
\(939\) | −76.3903 | −0.0813529 | ||||||||
\(940\) | −820.900 | −0.873298 | ||||||||
\(941\) | − | 478.740i | − | 0.508757i | −0.967105 | − | 0.254378i | \(-0.918129\pi\) | ||
0.967105 | − | 0.254378i | \(-0.0818709\pi\) | |||||||
\(942\) | 1358.09 | 1.44171 | ||||||||
\(943\) | 1659.68i | 1.76000i | ||||||||
\(944\) | 59.2957i | 0.0628132i | ||||||||
\(945\) | 71.3381 | + | 39.0624i | 0.0754901 | + | 0.0413359i | ||||
\(946\) | −598.505 | −0.632669 | ||||||||
\(947\) | 93.2440 | 0.0984625 | 0.0492313 | − | 0.998787i | \(-0.484323\pi\) | ||||
0.0492313 | + | 0.998787i | \(0.484323\pi\) | |||||||
\(948\) | − | 772.434i | − | 0.814803i | ||||||
\(949\) | −5.79926 | −0.00611092 | ||||||||
\(950\) | − | 217.818i | − | 0.229282i | ||||||
\(951\) | 423.675i | 0.445504i | ||||||||
\(952\) | −71.4050 | + | 130.404i | −0.0750053 | + | 0.136979i | ||||
\(953\) | 774.591 | 0.812792 | 0.406396 | − | 0.913697i | \(-0.366785\pi\) | ||||
0.406396 | + | 0.913697i | \(0.366785\pi\) | |||||||
\(954\) | 588.164 | 0.616524 | ||||||||
\(955\) | − | 98.1887i | − | 0.102815i | ||||||
\(956\) | 1897.80 | 1.98514 | ||||||||
\(957\) | 78.0590i | 0.0815664i | ||||||||
\(958\) | 940.376i | 0.981603i | ||||||||
\(959\) | −552.350 | − | 302.448i | −0.575965 | − | 0.315379i | ||||
\(960\) | 306.771 | 0.319553 | ||||||||
\(961\) | 920.485 | 0.957841 | ||||||||
\(962\) | 1.03811i | 0.00107912i | ||||||||
\(963\) | −99.2515 | −0.103065 | ||||||||
\(964\) | 647.978i | 0.672176i | ||||||||
\(965\) | 104.392i | 0.108178i | ||||||||
\(966\) | −378.462 | + | 691.171i | −0.391783 | + | 0.715497i | ||||
\(967\) | 1070.58 | 1.10711 | 0.553555 | − | 0.832813i | \(-0.313271\pi\) | ||||
0.553555 | + | 0.832813i | \(0.313271\pi\) | |||||||
\(968\) | −170.830 | −0.176477 | ||||||||
\(969\) | 367.535i | 0.379293i | ||||||||
\(970\) | 717.606 | 0.739800 | ||||||||
\(971\) | − | 807.893i | − | 0.832022i | −0.909360 | − | 0.416011i | \(-0.863428\pi\) | ||
0.909360 | − | 0.416011i | \(-0.136572\pi\) | |||||||
\(972\) | − | 70.3389i | − | 0.0723652i | ||||||
\(973\) | −425.573 | + | 777.208i | −0.437383 | + | 0.798775i | ||||
\(974\) | −1021.05 | −1.04831 | ||||||||
\(975\) | 0.431476 | 0.000442539 | ||||||||
\(976\) | − | 1501.23i | − | 1.53815i | ||||||
\(977\) | −1653.68 | −1.69261 | −0.846306 | − | 0.532696i | \(-0.821179\pi\) | ||||
−0.846306 | + | 0.532696i | \(0.821179\pi\) | |||||||
\(978\) | 260.568i | 0.266430i | ||||||||
\(979\) | − | 201.210i | − | 0.205526i | ||||||
\(980\) | 416.538 | − | 266.312i | 0.425039 | − | 0.271747i | ||||
\(981\) | 149.637 | 0.152536 | ||||||||
\(982\) | −1421.89 | −1.44795 | ||||||||
\(983\) | − | 651.566i | − | 0.662834i | −0.943484 | − | 0.331417i | \(-0.892473\pi\) | ||
0.943484 | − | 0.331417i | \(-0.107527\pi\) | |||||||
\(984\) | −192.858 | −0.195994 | ||||||||
\(985\) | − | 614.496i | − | 0.623854i | ||||||
\(986\) | 722.154i | 0.732407i | ||||||||
\(987\) | −865.223 | − | 473.767i | −0.876619 | − | 0.480008i | ||||
\(988\) | 3.35675 | 0.00339752 | ||||||||
\(989\) | −1766.04 | −1.78569 | ||||||||
\(990\) | − | 50.6431i | − | 0.0511546i | ||||||
\(991\) | 459.963 | 0.464140 | 0.232070 | − | 0.972699i | \(-0.425450\pi\) | ||||
0.232070 | + | 0.972699i | \(0.425450\pi\) | |||||||
\(992\) | 292.260i | 0.294617i | ||||||||
\(993\) | 895.270i | 0.901581i | ||||||||
\(994\) | 1744.52 | + | 955.239i | 1.75505 | + | 0.961005i | ||||
\(995\) | −604.589 | −0.607627 | ||||||||
\(996\) | −876.193 | −0.879712 | ||||||||
\(997\) | 613.898i | 0.615745i | 0.951428 | + | 0.307872i | \(0.0996170\pi\) | ||||
−0.951428 | + | 0.307872i | \(0.900383\pi\) | |||||||
\(998\) | −43.7850 | −0.0438727 | ||||||||
\(999\) | − | 37.1089i | − | 0.0371460i |
(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 | 105.3.h.a.76.9 | ✓ | 12 | |
3.2 | odd | 2 | 315.3.h.d.181.4 | 12 | |||
4.3 | odd | 2 | 1680.3.s.c.1441.7 | 12 | |||
5.2 | odd | 4 | 525.3.e.c.349.20 | 24 | |||
5.3 | odd | 4 | 525.3.e.c.349.13 | 24 | |||
5.4 | even | 2 | 525.3.h.d.76.4 | 12 | |||
7.6 | odd | 2 | inner | 105.3.h.a.76.10 | yes | 12 | |
21.20 | even | 2 | 315.3.h.d.181.3 | 12 | |||
28.27 | even | 2 | 1680.3.s.c.1441.4 | 12 | |||
35.13 | even | 4 | 525.3.e.c.349.19 | 24 | |||
35.27 | even | 4 | 525.3.e.c.349.14 | 24 | |||
35.34 | odd | 2 | 525.3.h.d.76.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
105.3.h.a.76.10 | yes | 12 | 7.6 | odd | 2 | inner | |
315.3.h.d.181.3 | 12 | 21.20 | even | 2 | |||
315.3.h.d.181.4 | 12 | 3.2 | odd | 2 | |||
525.3.e.c.349.13 | 24 | 5.3 | odd | 4 | |||
525.3.e.c.349.14 | 24 | 35.27 | even | 4 | |||
525.3.e.c.349.19 | 24 | 35.13 | even | 4 | |||
525.3.e.c.349.20 | 24 | 5.2 | odd | 4 | |||
525.3.h.d.76.3 | 12 | 35.34 | odd | 2 | |||
525.3.h.d.76.4 | 12 | 5.4 | even | 2 | |||
1680.3.s.c.1441.4 | 12 | 28.27 | even | 2 | |||
1680.3.s.c.1441.7 | 12 | 4.3 | odd | 2 |