Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.12 | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.g.1469.11 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.321854 | + | 1.70188i | −0.185822 | + | 0.982583i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.20838 | − | 0.350775i | −0.987619 | − | 0.156871i | ||||
\(6\) | 0.321854 | − | 1.70188i | 0.131396 | − | 0.694791i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.79282 | − | 1.09552i | −0.930940 | − | 0.365172i | ||||
\(10\) | 2.20838 | + | 0.350775i | 0.698352 | + | 0.110925i | ||||
\(11\) | 3.78464i | 1.14111i | 0.821259 | + | 0.570556i | \(0.193272\pi\) | ||||
−0.821259 | + | 0.570556i | \(0.806728\pi\) | |||||||
\(12\) | −0.321854 | + | 1.70188i | −0.0929111 | + | 0.491292i | ||||
\(13\) | 6.40306 | 1.77589 | 0.887945 | − | 0.459950i | \(-0.152132\pi\) | ||||
0.887945 | + | 0.459950i | \(0.152132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30776 | − | 3.64551i | 0.337661 | − | 0.941268i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.57902i | − | 1.35311i | −0.736391 | − | 0.676556i | \(-0.763472\pi\) | ||
0.736391 | − | 0.676556i | \(-0.236528\pi\) | |||||||
\(18\) | 2.79282 | + | 1.09552i | 0.658274 | + | 0.258215i | ||||
\(19\) | − | 2.10349i | − | 0.482575i | −0.970454 | − | 0.241287i | \(-0.922430\pi\) | ||
0.970454 | − | 0.241287i | \(-0.0775696\pi\) | |||||||
\(20\) | −2.20838 | − | 0.350775i | −0.493810 | − | 0.0784357i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.78464i | − | 0.806887i | ||||||
\(23\) | 4.70837 | 0.981763 | 0.490882 | − | 0.871226i | \(-0.336675\pi\) | ||||
0.490882 | + | 0.871226i | \(0.336675\pi\) | |||||||
\(24\) | 0.321854 | − | 1.70188i | 0.0656981 | − | 0.347396i | ||||
\(25\) | 4.75391 | + | 1.54929i | 0.950783 | + | 0.309859i | ||||
\(26\) | −6.40306 | −1.25574 | ||||||||
\(27\) | 2.76332 | − | 4.40046i | 0.531801 | − | 0.846869i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.55401i | 1.40274i | 0.712795 | + | 0.701372i | \(0.247429\pi\) | ||||
−0.712795 | + | 0.701372i | \(0.752571\pi\) | |||||||
\(30\) | −1.30776 | + | 3.64551i | −0.238762 | + | 0.665577i | ||||
\(31\) | − | 3.43184i | − | 0.616377i | −0.951325 | − | 0.308188i | \(-0.900277\pi\) | ||
0.951325 | − | 0.308188i | \(-0.0997227\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.44102 | − | 1.21810i | −1.12124 | − | 0.212044i | ||||
\(34\) | 5.57902i | 0.956794i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.79282 | − | 1.09552i | −0.465470 | − | 0.182586i | ||||
\(37\) | − | 2.75706i | − | 0.453259i | −0.973981 | − | 0.226629i | \(-0.927229\pi\) | ||
0.973981 | − | 0.226629i | \(-0.0727706\pi\) | |||||||
\(38\) | 2.10349i | 0.341232i | ||||||||
\(39\) | −2.06085 | + | 10.8973i | −0.330000 | + | 1.74496i | ||||
\(40\) | 2.20838 | + | 0.350775i | 0.349176 | + | 0.0554624i | ||||
\(41\) | −8.77986 | −1.37118 | −0.685592 | − | 0.727986i | \(-0.740457\pi\) | ||||
−0.685592 | + | 0.727986i | \(0.740457\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.04507i | 1.07436i | 0.843467 | + | 0.537181i | \(0.180511\pi\) | ||||
−0.843467 | + | 0.537181i | \(0.819489\pi\) | |||||||
\(44\) | 3.78464i | 0.570556i | ||||||||
\(45\) | 5.78334 | + | 3.39897i | 0.862129 | + | 0.506689i | ||||
\(46\) | −4.70837 | −0.694211 | ||||||||
\(47\) | 2.55610i | 0.372845i | 0.982470 | + | 0.186422i | \(0.0596893\pi\) | ||||
−0.982470 | + | 0.186422i | \(0.940311\pi\) | |||||||
\(48\) | −0.321854 | + | 1.70188i | −0.0464556 | + | 0.245646i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.75391 | − | 1.54929i | −0.672305 | − | 0.219103i | ||||
\(51\) | 9.49485 | + | 1.79563i | 1.32955 | + | 0.251438i | ||||
\(52\) | 6.40306 | 0.887945 | ||||||||
\(53\) | 3.08554 | 0.423831 | 0.211916 | − | 0.977288i | \(-0.432030\pi\) | ||||
0.211916 | + | 0.977288i | \(0.432030\pi\) | |||||||
\(54\) | −2.76332 | + | 4.40046i | −0.376040 | + | 0.598827i | ||||
\(55\) | 1.32756 | − | 8.35793i | 0.179008 | − | 1.12698i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.57990 | + | 0.677017i | 0.474170 | + | 0.0896731i | ||||
\(58\) | − | 7.55401i | − | 0.991890i | ||||||
\(59\) | 12.9727 | 1.68890 | 0.844452 | − | 0.535631i | \(-0.179926\pi\) | ||||
0.844452 | + | 0.535631i | \(0.179926\pi\) | |||||||
\(60\) | 1.30776 | − | 3.64551i | 0.168830 | − | 0.470634i | ||||
\(61\) | 10.3401i | 1.32391i | 0.749542 | + | 0.661957i | \(0.230274\pi\) | ||||
−0.749542 | + | 0.661957i | \(0.769726\pi\) | |||||||
\(62\) | 3.43184i | 0.435844i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.1404 | − | 2.24604i | −1.75390 | − | 0.278587i | ||||
\(66\) | 6.44102 | + | 1.21810i | 0.792834 | + | 0.149938i | ||||
\(67\) | 1.48871i | 0.181875i | 0.995857 | + | 0.0909373i | \(0.0289863\pi\) | ||||
−0.995857 | + | 0.0909373i | \(0.971014\pi\) | |||||||
\(68\) | − | 5.57902i | − | 0.676556i | ||||||
\(69\) | −1.51541 | + | 8.01310i | −0.182433 | + | 0.964664i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.06254i | 0.600812i | 0.953811 | + | 0.300406i | \(0.0971222\pi\) | ||||
−0.953811 | + | 0.300406i | \(0.902878\pi\) | |||||||
\(72\) | 2.79282 | + | 1.09552i | 0.329137 | + | 0.129108i | ||||
\(73\) | 3.33557 | 0.390399 | 0.195199 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195199 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(74\) | 2.75706i | 0.320502i | ||||||||
\(75\) | −4.16678 | + | 7.59197i | −0.481138 | + | 0.876645i | ||||
\(76\) | − | 2.10349i | − | 0.241287i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.06085 | − | 10.8973i | 0.233345 | − | 1.23387i | ||||
\(79\) | −7.07694 | −0.796218 | −0.398109 | − | 0.917338i | \(-0.630333\pi\) | ||||
−0.398109 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(80\) | −2.20838 | − | 0.350775i | −0.246905 | − | 0.0392179i | ||||
\(81\) | 6.59969 | + | 6.11916i | 0.733299 | + | 0.679906i | ||||
\(82\) | 8.77986 | 0.969573 | ||||||||
\(83\) | 9.49058i | 1.04173i | 0.853640 | + | 0.520863i | \(0.174390\pi\) | ||||
−0.853640 | + | 0.520863i | \(0.825610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.95698 | + | 12.3206i | −0.212265 | + | 1.33636i | ||||
\(86\) | − | 7.04507i | − | 0.759689i | ||||||
\(87\) | −12.8560 | − | 2.43129i | −1.37831 | − | 0.260661i | ||||
\(88\) | − | 3.78464i | − | 0.403444i | ||||||
\(89\) | −10.6182 | −1.12552 | −0.562761 | − | 0.826620i | \(-0.690261\pi\) | ||||
−0.562761 | + | 0.826620i | \(0.690261\pi\) | |||||||
\(90\) | −5.78334 | − | 3.39897i | −0.609617 | − | 0.358283i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.70837 | 0.490882 | ||||||||
\(93\) | 5.84059 | + | 1.10455i | 0.605641 | + | 0.114537i | ||||
\(94\) | − | 2.55610i | − | 0.263641i | ||||||
\(95\) | −0.737854 | + | 4.64532i | −0.0757022 | + | 0.476600i | ||||
\(96\) | 0.321854 | − | 1.70188i | 0.0328491 | − | 0.173698i | ||||
\(97\) | −4.90516 | −0.498044 | −0.249022 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249022 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.14613 | − | 10.5698i | 0.416702 | − | 1.06231i | ||||
\(100\) | 4.75391 | + | 1.54929i | 0.475391 | + | 0.154929i | ||||
\(101\) | 5.63646 | 0.560849 | 0.280424 | − | 0.959876i | \(-0.409525\pi\) | ||||
0.280424 | + | 0.959876i | \(0.409525\pi\) | |||||||
\(102\) | −9.49485 | − | 1.79563i | −0.940130 | − | 0.177794i | ||||
\(103\) | 6.76706 | 0.666779 | 0.333389 | − | 0.942789i | \(-0.391808\pi\) | ||||
0.333389 | + | 0.942789i | \(0.391808\pi\) | |||||||
\(104\) | −6.40306 | −0.627872 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.08554 | −0.299694 | ||||||||
\(107\) | 9.09162 | 0.878920 | 0.439460 | − | 0.898262i | \(-0.355170\pi\) | ||||
0.439460 | + | 0.898262i | \(0.355170\pi\) | |||||||
\(108\) | 2.76332 | − | 4.40046i | 0.265901 | − | 0.423435i | ||||
\(109\) | −15.3307 | −1.46842 | −0.734208 | − | 0.678925i | \(-0.762446\pi\) | ||||
−0.734208 | + | 0.678925i | \(0.762446\pi\) | |||||||
\(110\) | −1.32756 | + | 8.35793i | −0.126578 | + | 0.796897i | ||||
\(111\) | 4.69220 | + | 0.887371i | 0.445364 | + | 0.0842255i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.83057 | 0.266277 | 0.133139 | − | 0.991097i | \(-0.457494\pi\) | ||||
0.133139 | + | 0.991097i | \(0.457494\pi\) | |||||||
\(114\) | −3.57990 | − | 0.677017i | −0.335289 | − | 0.0634085i | ||||
\(115\) | −10.3979 | − | 1.65158i | −0.969608 | − | 0.154011i | ||||
\(116\) | 7.55401i | 0.701372i | ||||||||
\(117\) | −17.8826 | − | 7.01465i | −1.65325 | − | 0.648505i | ||||
\(118\) | −12.9727 | −1.19424 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.30776 | + | 3.64551i | −0.119381 | + | 0.332788i | ||||
\(121\) | −3.32348 | −0.302135 | ||||||||
\(122\) | − | 10.3401i | − | 0.936148i | ||||||
\(123\) | 2.82583 | − | 14.9423i | 0.254797 | − | 1.34730i | ||||
\(124\) | − | 3.43184i | − | 0.308188i | ||||||
\(125\) | −9.95501 | − | 5.08899i | −0.890403 | − | 0.455173i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6271i | 1.47542i | 0.675119 | + | 0.737709i | \(0.264092\pi\) | ||||
−0.675119 | + | 0.737709i | \(0.735908\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.9899 | − | 2.26748i | −1.05565 | − | 0.199640i | ||||
\(130\) | 14.1404 | + | 2.24604i | 1.24020 | + | 0.196990i | ||||
\(131\) | 0.210484 | 0.0183901 | 0.00919504 | − | 0.999958i | \(-0.497073\pi\) | ||||
0.00919504 | + | 0.999958i | \(0.497073\pi\) | |||||||
\(132\) | −6.44102 | − | 1.21810i | −0.560618 | − | 0.106022i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.48871i | − | 0.128605i | ||||||
\(135\) | −7.64604 | + | 8.74860i | −0.658067 | + | 0.752960i | ||||
\(136\) | 5.57902i | 0.478397i | ||||||||
\(137\) | −3.87172 | −0.330784 | −0.165392 | − | 0.986228i | \(-0.552889\pi\) | ||||
−0.165392 | + | 0.986228i | \(0.552889\pi\) | |||||||
\(138\) | 1.51541 | − | 8.01310i | 0.129000 | − | 0.682121i | ||||
\(139\) | 17.4338i | 1.47871i | 0.673314 | + | 0.739357i | \(0.264870\pi\) | ||||
−0.673314 | + | 0.739357i | \(0.735130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.35018 | − | 0.822689i | −0.366351 | − | 0.0692829i | ||||
\(142\) | − | 5.06254i | − | 0.424839i | ||||||
\(143\) | 24.2333i | 2.02649i | ||||||||
\(144\) | −2.79282 | − | 1.09552i | −0.232735 | − | 0.0912929i | ||||
\(145\) | 2.64976 | − | 16.6821i | 0.220051 | − | 1.38538i | ||||
\(146\) | −3.33557 | −0.276053 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.75706i | − | 0.226629i | ||||||
\(149\) | 8.65775i | 0.709270i | 0.935005 | + | 0.354635i | \(0.115395\pi\) | ||||
−0.935005 | + | 0.354635i | \(0.884605\pi\) | |||||||
\(150\) | 4.16678 | − | 7.59197i | 0.340216 | − | 0.619881i | ||||
\(151\) | 16.8301 | 1.36961 | 0.684806 | − | 0.728726i | \(-0.259887\pi\) | ||||
0.684806 | + | 0.728726i | \(0.259887\pi\) | |||||||
\(152\) | 2.10349i | 0.170616i | ||||||||
\(153\) | −6.11191 | + | 15.5812i | −0.494118 | + | 1.25967i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.20380 | + | 7.57882i | −0.0966919 | + | 0.608745i | ||||
\(156\) | −2.06085 | + | 10.8973i | −0.165000 | + | 0.872480i | ||||
\(157\) | −6.23745 | −0.497802 | −0.248901 | − | 0.968529i | \(-0.580069\pi\) | ||||
−0.248901 | + | 0.968529i | \(0.580069\pi\) | |||||||
\(158\) | 7.07694 | 0.563011 | ||||||||
\(159\) | −0.993092 | + | 5.25123i | −0.0787573 | + | 0.416450i | ||||
\(160\) | 2.20838 | + | 0.350775i | 0.174588 | + | 0.0277312i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.59969 | − | 6.11916i | −0.518521 | − | 0.480766i | ||||
\(163\) | − | 3.22815i | − | 0.252848i | −0.991976 | − | 0.126424i | \(-0.959650\pi\) | ||
0.991976 | − | 0.126424i | \(-0.0403500\pi\) | |||||||
\(164\) | −8.77986 | −0.685592 | ||||||||
\(165\) | 13.7970 | + | 4.94938i | 1.07409 | + | 0.385309i | ||||
\(166\) | − | 9.49058i | − | 0.736612i | ||||||
\(167\) | − | 10.9301i | − | 0.845797i | −0.906177 | − | 0.422899i | \(-0.861013\pi\) | ||
0.906177 | − | 0.422899i | \(-0.138987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.9992 | 2.15379 | ||||||||
\(170\) | 1.95698 | − | 12.3206i | 0.150094 | − | 0.944948i | ||||
\(171\) | −2.30441 | + | 5.87468i | −0.176223 | + | 0.449248i | ||||
\(172\) | 7.04507i | 0.537181i | ||||||||
\(173\) | 4.83283i | 0.367434i | 0.982979 | + | 0.183717i | \(0.0588129\pi\) | ||||
−0.982979 | + | 0.183717i | \(0.941187\pi\) | |||||||
\(174\) | 12.8560 | + | 2.43129i | 0.974614 | + | 0.184315i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.78464i | 0.285278i | ||||||||
\(177\) | −4.17532 | + | 22.0781i | −0.313836 | + | 1.65949i | ||||
\(178\) | 10.6182 | 0.795864 | ||||||||
\(179\) | − | 8.55562i | − | 0.639477i | −0.947506 | − | 0.319739i | \(-0.896405\pi\) | ||
0.947506 | − | 0.319739i | \(-0.103595\pi\) | |||||||
\(180\) | 5.78334 | + | 3.39897i | 0.431065 | + | 0.253344i | ||||
\(181\) | − | 11.2205i | − | 0.834013i | −0.908904 | − | 0.417006i | \(-0.863079\pi\) | ||
0.908904 | − | 0.417006i | \(-0.136921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.5976 | − | 3.32800i | −1.30086 | − | 0.246013i | ||||
\(184\) | −4.70837 | −0.347106 | ||||||||
\(185\) | −0.967110 | + | 6.08865i | −0.0711033 | + | 0.447647i | ||||
\(186\) | −5.84059 | − | 1.10455i | −0.428253 | − | 0.0809895i | ||||
\(187\) | 21.1146 | 1.54405 | ||||||||
\(188\) | 2.55610i | 0.186422i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.737854 | − | 4.64532i | 0.0535295 | − | 0.337007i | ||||
\(191\) | 2.85343i | 0.206467i | 0.994657 | + | 0.103234i | \(0.0329189\pi\) | ||||
−0.994657 | + | 0.103234i | \(0.967081\pi\) | |||||||
\(192\) | −0.321854 | + | 1.70188i | −0.0232278 | + | 0.122823i | ||||
\(193\) | 26.7793i | 1.92762i | 0.266598 | + | 0.963808i | \(0.414100\pi\) | ||||
−0.266598 | + | 0.963808i | \(0.585900\pi\) | |||||||
\(194\) | 4.90516 | 0.352170 | ||||||||
\(195\) | 8.37364 | − | 23.3425i | 0.599649 | − | 1.67159i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7242 | 1.04905 | 0.524527 | − | 0.851394i | \(-0.324242\pi\) | ||||
0.524527 | + | 0.851394i | \(0.324242\pi\) | |||||||
\(198\) | −4.14613 | + | 10.5698i | −0.294653 | + | 0.751164i | ||||
\(199\) | 16.4657i | 1.16722i | 0.812032 | + | 0.583612i | \(0.198361\pi\) | ||||
−0.812032 | + | 0.583612i | \(0.801639\pi\) | |||||||
\(200\) | −4.75391 | − | 1.54929i | −0.336152 | − | 0.109552i | ||||
\(201\) | −2.53361 | − | 0.479146i | −0.178707 | − | 0.0337964i | ||||
\(202\) | −5.63646 | −0.396580 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.49485 | + | 1.79563i | 0.664773 | + | 0.125719i | ||||
\(205\) | 19.3893 | + | 3.07976i | 1.35421 | + | 0.215100i | ||||
\(206\) | −6.76706 | −0.471484 | ||||||||
\(207\) | −13.1496 | − | 5.15809i | −0.913963 | − | 0.358512i | ||||
\(208\) | 6.40306 | 0.443973 | ||||||||
\(209\) | 7.96096 | 0.550671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8206 | −1.08913 | −0.544567 | − | 0.838717i | \(-0.683306\pi\) | ||||
−0.544567 | + | 0.838717i | \(0.683306\pi\) | |||||||
\(212\) | 3.08554 | 0.211916 | ||||||||
\(213\) | −8.61585 | − | 1.62940i | −0.590348 | − | 0.111644i | ||||
\(214\) | −9.09162 | −0.621490 | ||||||||
\(215\) | 2.47124 | − | 15.5582i | 0.168537 | − | 1.06106i | ||||
\(216\) | −2.76332 | + | 4.40046i | −0.188020 | + | 0.299413i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.3307 | 1.03833 | ||||||||
\(219\) | −1.07356 | + | 5.67675i | −0.0725447 | + | 0.383599i | ||||
\(220\) | 1.32756 | − | 8.35793i | 0.0895039 | − | 0.563492i | ||||
\(221\) | − | 35.7228i | − | 2.40298i | ||||||
\(222\) | −4.69220 | − | 0.887371i | −0.314920 | − | 0.0595565i | ||||
\(223\) | 21.9853 | 1.47224 | 0.736122 | − | 0.676849i | \(-0.236655\pi\) | ||||
0.736122 | + | 0.676849i | \(0.236655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5796 | − | 9.53488i | −0.771970 | − | 0.635659i | ||||
\(226\) | −2.83057 | −0.188286 | ||||||||
\(227\) | − | 27.5101i | − | 1.82591i | −0.408063 | − | 0.912954i | \(-0.633796\pi\) | ||
0.408063 | − | 0.912954i | \(-0.366204\pi\) | |||||||
\(228\) | 3.57990 | + | 0.677017i | 0.237085 | + | 0.0448366i | ||||
\(229\) | 16.1836i | 1.06944i | 0.845029 | + | 0.534720i | \(0.179583\pi\) | ||||
−0.845029 | + | 0.534720i | \(0.820417\pi\) | |||||||
\(230\) | 10.3979 | + | 1.65158i | 0.685616 | + | 0.108902i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 7.55401i | − | 0.495945i | ||||||
\(233\) | 17.8328 | 1.16827 | 0.584133 | − | 0.811658i | \(-0.301435\pi\) | ||||
0.584133 | + | 0.811658i | \(0.301435\pi\) | |||||||
\(234\) | 17.8826 | + | 7.01465i | 1.16902 | + | 0.458562i | ||||
\(235\) | 0.896615 | − | 5.64484i | 0.0584887 | − | 0.368229i | ||||
\(236\) | 12.9727 | 0.844452 | ||||||||
\(237\) | 2.27774 | − | 12.0441i | 0.147955 | − | 0.782351i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.4508i | − | 1.19348i | −0.802433 | − | 0.596742i | \(-0.796462\pi\) | ||
0.802433 | − | 0.596742i | \(-0.203538\pi\) | |||||||
\(240\) | 1.30776 | − | 3.64551i | 0.0844152 | − | 0.235317i | ||||
\(241\) | − | 13.4629i | − | 0.867223i | −0.901100 | − | 0.433612i | \(-0.857239\pi\) | ||
0.901100 | − | 0.433612i | \(-0.142761\pi\) | |||||||
\(242\) | 3.32348 | 0.213641 | ||||||||
\(243\) | −12.5382 | + | 9.26244i | −0.804328 | + | 0.594186i | ||||
\(244\) | 10.3401i | 0.661957i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.82583 | + | 14.9423i | −0.180168 | + | 0.952687i | ||||
\(247\) | − | 13.4688i | − | 0.857000i | ||||||
\(248\) | 3.43184i | 0.217922i | ||||||||
\(249\) | −16.1519 | − | 3.05458i | −1.02358 | − | 0.193576i | ||||
\(250\) | 9.95501 | + | 5.08899i | 0.629610 | + | 0.321856i | ||||
\(251\) | 21.5154 | 1.35804 | 0.679020 | − | 0.734120i | \(-0.262405\pi\) | ||||
0.679020 | + | 0.734120i | \(0.262405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8195i | 1.12030i | ||||||||
\(254\) | − | 16.6271i | − | 1.04328i | ||||||
\(255\) | −20.3384 | − | 7.29600i | −1.27364 | − | 0.456893i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.2419i | 0.826004i | 0.910730 | + | 0.413002i | \(0.135520\pi\) | ||||
−0.910730 | + | 0.413002i | \(0.864480\pi\) | |||||||
\(258\) | 11.9899 | + | 2.26748i | 0.746458 | + | 0.141167i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −14.1404 | − | 2.24604i | −0.876951 | − | 0.139293i | ||||
\(261\) | 8.27553 | − | 21.0970i | 0.512243 | − | 1.30587i | ||||
\(262\) | −0.210484 | −0.0130038 | ||||||||
\(263\) | −15.5680 | −0.959961 | −0.479981 | − | 0.877279i | \(-0.659356\pi\) | ||||
−0.479981 | + | 0.877279i | \(0.659356\pi\) | |||||||
\(264\) | 6.44102 | + | 1.21810i | 0.396417 | + | 0.0749688i | ||||
\(265\) | −6.81405 | − | 1.08233i | −0.418584 | − | 0.0664871i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.41749 | − | 18.0709i | 0.209147 | − | 1.10592i | ||||
\(268\) | 1.48871i | 0.0909373i | ||||||||
\(269\) | −8.37779 | −0.510803 | −0.255401 | − | 0.966835i | \(-0.582208\pi\) | ||||
−0.255401 | + | 0.966835i | \(0.582208\pi\) | |||||||
\(270\) | 7.64604 | − | 8.74860i | 0.465323 | − | 0.532423i | ||||
\(271\) | − | 0.305606i | − | 0.0185642i | −0.999957 | − | 0.00928212i | \(-0.997045\pi\) | ||
0.999957 | − | 0.00928212i | \(-0.00295463\pi\) | |||||||
\(272\) | − | 5.57902i | − | 0.338278i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.87172 | 0.233899 | ||||||||
\(275\) | −5.86351 | + | 17.9918i | −0.353583 | + | 1.08495i | ||||
\(276\) | −1.51541 | + | 8.01310i | −0.0912167 | + | 0.482332i | ||||
\(277\) | 20.9930i | 1.26135i | 0.776047 | + | 0.630675i | \(0.217222\pi\) | ||||
−0.776047 | + | 0.630675i | \(0.782778\pi\) | |||||||
\(278\) | − | 17.4338i | − | 1.04561i | ||||||
\(279\) | −3.75963 | + | 9.58451i | −0.225083 | + | 0.573810i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.67638i | − | 0.338624i | −0.985562 | − | 0.169312i | \(-0.945845\pi\) | ||
0.985562 | − | 0.169312i | \(-0.0541546\pi\) | |||||||
\(282\) | 4.35018 | + | 0.822689i | 0.259049 | + | 0.0489904i | ||||
\(283\) | −15.8411 | −0.941658 | −0.470829 | − | 0.882224i | \(-0.656045\pi\) | ||||
−0.470829 | + | 0.882224i | \(0.656045\pi\) | |||||||
\(284\) | 5.06254i | 0.300406i | ||||||||
\(285\) | −7.66832 | − | 2.75086i | −0.454232 | − | 0.162947i | ||||
\(286\) | − | 24.2333i | − | 1.43294i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.79282 | + | 1.09552i | 0.164569 | + | 0.0645539i | ||||
\(289\) | −14.1255 | −0.830911 | ||||||||
\(290\) | −2.64976 | + | 16.6821i | −0.155599 | + | 0.979609i | ||||
\(291\) | 1.57875 | − | 8.34802i | 0.0925477 | − | 0.489370i | ||||
\(292\) | 3.33557 | 0.195199 | ||||||||
\(293\) | − | 23.2810i | − | 1.36009i | −0.733170 | − | 0.680045i | \(-0.761960\pi\) | ||
0.733170 | − | 0.680045i | \(-0.238040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.6487 | − | 4.55051i | −1.66799 | − | 0.264941i | ||||
\(296\) | 2.75706i | 0.160251i | ||||||||
\(297\) | 16.6542 | + | 10.4582i | 0.966372 | + | 0.606844i | ||||
\(298\) | − | 8.65775i | − | 0.501530i | ||||||
\(299\) | 30.1480 | 1.74350 | ||||||||
\(300\) | −4.16678 | + | 7.59197i | −0.240569 | + | 0.438322i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.8301 | −0.968462 | ||||||||
\(303\) | −1.81412 | + | 9.59260i | −0.104218 | + | 0.551081i | ||||
\(304\) | − | 2.10349i | − | 0.120644i | ||||||
\(305\) | 3.62705 | − | 22.8349i | 0.207684 | − | 1.30752i | ||||
\(306\) | 6.11191 | − | 15.5812i | 0.349394 | − | 0.890718i | ||||
\(307\) | 20.2759 | 1.15721 | 0.578604 | − | 0.815608i | \(-0.303598\pi\) | ||||
0.578604 | + | 0.815608i | \(0.303598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.17800 | + | 11.5168i | −0.123902 | + | 0.655165i | ||||
\(310\) | 1.20380 | − | 7.57882i | 0.0683715 | − | 0.430448i | ||||
\(311\) | −11.8199 | −0.670244 | −0.335122 | − | 0.942175i | \(-0.608778\pi\) | ||||
−0.335122 | + | 0.942175i | \(0.608778\pi\) | |||||||
\(312\) | 2.06085 | − | 10.8973i | 0.116673 | − | 0.616937i | ||||
\(313\) | 4.00427 | 0.226335 | 0.113167 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113167 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(314\) | 6.23745 | 0.351999 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.07694 | −0.398109 | ||||||||
\(317\) | 0.211278 | 0.0118665 | 0.00593327 | − | 0.999982i | \(-0.498111\pi\) | ||||
0.00593327 | + | 0.999982i | \(0.498111\pi\) | |||||||
\(318\) | 0.993092 | − | 5.25123i | 0.0556898 | − | 0.294474i | ||||
\(319\) | −28.5892 | −1.60069 | ||||||||
\(320\) | −2.20838 | − | 0.350775i | −0.123452 | − | 0.0196089i | ||||
\(321\) | −2.92617 | + | 15.4729i | −0.163323 | + | 0.863612i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.7354 | −0.652977 | ||||||||
\(324\) | 6.59969 | + | 6.11916i | 0.366650 | + | 0.339953i | ||||
\(325\) | 30.4396 | + | 9.92022i | 1.68849 | + | 0.550275i | ||||
\(326\) | 3.22815i | 0.178790i | ||||||||
\(327\) | 4.93424 | − | 26.0911i | 0.272864 | − | 1.44284i | ||||
\(328\) | 8.77986 | 0.484787 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −13.7970 | − | 4.94938i | −0.759497 | − | 0.272454i | ||||
\(331\) | −4.13421 | −0.227237 | −0.113618 | − | 0.993524i | \(-0.536244\pi\) | ||||
−0.113618 | + | 0.993524i | \(0.536244\pi\) | |||||||
\(332\) | 9.49058i | 0.520863i | ||||||||
\(333\) | −3.02041 | + | 7.69999i | −0.165517 | + | 0.421957i | ||||
\(334\) | 10.9301i | 0.598069i | ||||||||
\(335\) | 0.522202 | − | 3.28764i | 0.0285310 | − | 0.179623i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.99207i | − | 0.108515i | −0.998527 | − | 0.0542576i | \(-0.982721\pi\) | ||
0.998527 | − | 0.0542576i | \(-0.0172792\pi\) | |||||||
\(338\) | −27.9992 | −1.52296 | ||||||||
\(339\) | −0.911028 | + | 4.81730i | −0.0494803 | + | 0.261640i | ||||
\(340\) | −1.95698 | + | 12.3206i | −0.106132 | + | 0.668179i | ||||
\(341\) | 12.9883 | 0.703354 | ||||||||
\(342\) | 2.30441 | − | 5.87468i | 0.124608 | − | 0.317666i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 7.04507i | − | 0.379844i | ||||||
\(345\) | 6.15740 | − | 17.1644i | 0.331503 | − | 0.924102i | ||||
\(346\) | − | 4.83283i | − | 0.259815i | ||||||
\(347\) | 21.4429 | 1.15111 | 0.575557 | − | 0.817761i | \(-0.304785\pi\) | ||||
0.575557 | + | 0.817761i | \(0.304785\pi\) | |||||||
\(348\) | −12.8560 | − | 2.43129i | −0.689157 | − | 0.130331i | ||||
\(349\) | 17.1982i | 0.920598i | 0.887764 | + | 0.460299i | \(0.152258\pi\) | ||||
−0.887764 | + | 0.460299i | \(0.847742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.6937 | − | 28.1764i | 0.944420 | − | 1.50395i | ||||
\(352\) | − | 3.78464i | − | 0.201722i | ||||||
\(353\) | − | 3.05545i | − | 0.162625i | −0.996689 | − | 0.0813125i | \(-0.974089\pi\) | ||
0.996689 | − | 0.0813125i | \(-0.0259112\pi\) | |||||||
\(354\) | 4.17532 | − | 22.0781i | 0.221916 | − | 1.17344i | ||||
\(355\) | 1.77581 | − | 11.1800i | 0.0942503 | − | 0.593374i | ||||
\(356\) | −10.6182 | −0.562761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.55562i | 0.452179i | ||||||||
\(359\) | − | 15.3615i | − | 0.810751i | −0.914150 | − | 0.405375i | \(-0.867141\pi\) | ||
0.914150 | − | 0.405375i | \(-0.132859\pi\) | |||||||
\(360\) | −5.78334 | − | 3.39897i | −0.304809 | − | 0.179141i | ||||
\(361\) | 14.5753 | 0.767122 | ||||||||
\(362\) | 11.2205i | 0.589736i | ||||||||
\(363\) | 1.06967 | − | 5.65618i | 0.0561433 | − | 0.296872i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.36621 | − | 1.17003i | −0.385565 | − | 0.0612424i | ||||
\(366\) | 17.5976 | + | 3.32800i | 0.919844 | + | 0.173957i | ||||
\(367\) | 4.12440 | 0.215292 | 0.107646 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107646 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(368\) | 4.70837 | 0.245441 | ||||||||
\(369\) | 24.5206 | + | 9.61847i | 1.27649 | + | 0.500718i | ||||
\(370\) | 0.967110 | − | 6.08865i | 0.0502777 | − | 0.316534i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.84059 | + | 1.10455i | 0.302821 | + | 0.0572683i | ||||
\(373\) | − | 23.8319i | − | 1.23397i | −0.786976 | − | 0.616983i | \(-0.788355\pi\) | ||
0.786976 | − | 0.616983i | \(-0.211645\pi\) | |||||||
\(374\) | −21.1146 | −1.09181 | ||||||||
\(375\) | 11.8649 | − | 15.3044i | 0.612702 | − | 0.790314i | ||||
\(376\) | − | 2.55610i | − | 0.131821i | ||||||
\(377\) | 48.3688i | 2.49112i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0694 | 1.49319 | 0.746596 | − | 0.665277i | \(-0.231687\pi\) | ||||
0.746596 | + | 0.665277i | \(0.231687\pi\) | |||||||
\(380\) | −0.737854 | + | 4.64532i | −0.0378511 | + | 0.238300i | ||||
\(381\) | −28.2974 | − | 5.35150i | −1.44972 | − | 0.274165i | ||||
\(382\) | − | 2.85343i | − | 0.145994i | ||||||
\(383\) | 19.4986i | 0.996333i | 0.867081 | + | 0.498166i | \(0.165993\pi\) | ||||
−0.867081 | + | 0.498166i | \(0.834007\pi\) | |||||||
\(384\) | 0.321854 | − | 1.70188i | 0.0164245 | − | 0.0868489i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 26.7793i | − | 1.36303i | ||||||
\(387\) | 7.71798 | − | 19.6756i | 0.392327 | − | 1.00017i | ||||
\(388\) | −4.90516 | −0.249022 | ||||||||
\(389\) | 6.51453i | 0.330300i | 0.986268 | + | 0.165150i | \(0.0528108\pi\) | ||||
−0.986268 | + | 0.165150i | \(0.947189\pi\) | |||||||
\(390\) | −8.37364 | + | 23.3425i | −0.424016 | + | 1.18199i | ||||
\(391\) | − | 26.2681i | − | 1.32844i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0677451 | + | 0.358220i | −0.00341729 | + | 0.0180698i | ||||
\(394\) | −14.7242 | −0.741793 | ||||||||
\(395\) | 15.6286 | + | 2.48242i | 0.786360 | + | 0.124904i | ||||
\(396\) | 4.14613 | − | 10.5698i | 0.208351 | − | 0.531153i | ||||
\(397\) | −33.0474 | −1.65860 | −0.829300 | − | 0.558803i | \(-0.811261\pi\) | ||||
−0.829300 | + | 0.558803i | \(0.811261\pi\) | |||||||
\(398\) | − | 16.4657i | − | 0.825352i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.75391 | + | 1.54929i | 0.237696 | + | 0.0774646i | ||||
\(401\) | 13.3058i | 0.664461i | 0.943198 | + | 0.332230i | \(0.107801\pi\) | ||||
−0.943198 | + | 0.332230i | \(0.892199\pi\) | |||||||
\(402\) | 2.53361 | + | 0.479146i | 0.126365 | + | 0.0238976i | ||||
\(403\) | − | 21.9743i | − | 1.09462i | ||||||
\(404\) | 5.63646 | 0.280424 | ||||||||
\(405\) | −12.4282 | − | 15.8284i | −0.617562 | − | 0.786522i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4345 | 0.517218 | ||||||||
\(408\) | −9.49485 | − | 1.79563i | −0.470065 | − | 0.0888969i | ||||
\(409\) | 24.4460i | 1.20877i | 0.796691 | + | 0.604387i | \(0.206582\pi\) | ||||
−0.796691 | + | 0.604387i | \(0.793418\pi\) | |||||||
\(410\) | −19.3893 | − | 3.07976i | −0.957569 | − | 0.152098i | ||||
\(411\) | 1.24613 | − | 6.58923i | 0.0614670 | − | 0.325023i | ||||
\(412\) | 6.76706 | 0.333389 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.1496 | + | 5.15809i | 0.646269 | + | 0.253506i | ||||
\(415\) | 3.32906 | − | 20.9588i | 0.163417 | − | 1.02883i | ||||
\(416\) | −6.40306 | −0.313936 | ||||||||
\(417\) | −29.6703 | − | 5.61112i | −1.45296 | − | 0.274778i | ||||
\(418\) | −7.96096 | −0.389383 | ||||||||
\(419\) | 27.0524 | 1.32160 | 0.660799 | − | 0.750563i | \(-0.270217\pi\) | ||||
0.660799 | + | 0.750563i | \(0.270217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.39064 | 0.262724 | 0.131362 | − | 0.991334i | \(-0.458065\pi\) | ||||
0.131362 | + | 0.991334i | \(0.458065\pi\) | |||||||
\(422\) | 15.8206 | 0.770134 | ||||||||
\(423\) | 2.80024 | − | 7.13872i | 0.136152 | − | 0.347096i | ||||
\(424\) | −3.08554 | −0.149847 | ||||||||
\(425\) | 8.64354 | − | 26.5222i | 0.419273 | − | 1.28652i | ||||
\(426\) | 8.61585 | + | 1.62940i | 0.417439 | + | 0.0789445i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.09162 | 0.439460 | ||||||||
\(429\) | −41.2422 | − | 7.79957i | −1.99119 | − | 0.376567i | ||||
\(430\) | −2.47124 | + | 15.5582i | −0.119174 | + | 0.750283i | ||||
\(431\) | 3.21022i | 0.154631i | 0.997007 | + | 0.0773155i | \(0.0246349\pi\) | ||||
−0.997007 | + | 0.0773155i | \(0.975365\pi\) | |||||||
\(432\) | 2.76332 | − | 4.40046i | 0.132950 | − | 0.211717i | ||||
\(433\) | −39.7769 | −1.91155 | −0.955777 | − | 0.294092i | \(-0.904983\pi\) | ||||
−0.955777 | + | 0.294092i | \(0.904983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.5382 | + | 9.87879i | 1.32036 | + | 0.473652i | ||||
\(436\) | −15.3307 | −0.734208 | ||||||||
\(437\) | − | 9.90403i | − | 0.473774i | ||||||
\(438\) | 1.07356 | − | 5.67675i | 0.0512969 | − | 0.271246i | ||||
\(439\) | − | 26.5159i | − | 1.26553i | −0.774342 | − | 0.632767i | \(-0.781919\pi\) | ||
0.774342 | − | 0.632767i | \(-0.218081\pi\) | |||||||
\(440\) | −1.32756 | + | 8.35793i | −0.0632888 | + | 0.398449i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.7228i | 1.69916i | ||||||||
\(443\) | −21.5549 | −1.02410 | −0.512052 | − | 0.858955i | \(-0.671114\pi\) | ||||
−0.512052 | + | 0.858955i | \(0.671114\pi\) | |||||||
\(444\) | 4.69220 | + | 0.887371i | 0.222682 | + | 0.0421128i | ||||
\(445\) | 23.4489 | + | 3.72459i | 1.11159 | + | 0.176562i | ||||
\(446\) | −21.9853 | −1.04103 | ||||||||
\(447\) | −14.7345 | − | 2.78653i | −0.696917 | − | 0.131798i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.27232i | − | 0.0600445i | −0.999549 | − | 0.0300222i | \(-0.990442\pi\) | ||
0.999549 | − | 0.0300222i | \(-0.00955781\pi\) | |||||||
\(450\) | 11.5796 | + | 9.53488i | 0.545865 | + | 0.449479i | ||||
\(451\) | − | 33.2286i | − | 1.56467i | ||||||
\(452\) | 2.83057 | 0.133139 | ||||||||
\(453\) | −5.41682 | + | 28.6428i | −0.254504 | + | 1.34576i | ||||
\(454\) | 27.5101i | 1.29111i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.57990 | − | 0.677017i | −0.167644 | − | 0.0317042i | ||||
\(457\) | 7.38402i | 0.345410i | 0.984974 | + | 0.172705i | \(0.0552507\pi\) | ||||
−0.984974 | + | 0.172705i | \(0.944749\pi\) | |||||||
\(458\) | − | 16.1836i | − | 0.756209i | ||||||
\(459\) | −24.5503 | − | 15.4166i | −1.14591 | − | 0.719586i | ||||
\(460\) | −10.3979 | − | 1.65158i | −0.484804 | − | 0.0770053i | ||||
\(461\) | 14.6635 | 0.682950 | 0.341475 | − | 0.939891i | \(-0.389074\pi\) | ||||
0.341475 | + | 0.939891i | \(0.389074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.8566i | − | 1.29460i | −0.762233 | − | 0.647302i | \(-0.775897\pi\) | ||
0.762233 | − | 0.647302i | \(-0.224103\pi\) | |||||||
\(464\) | 7.55401i | 0.350686i | ||||||||
\(465\) | −12.5108 | − | 4.48801i | −0.580175 | − | 0.208126i | ||||
\(466\) | −17.8328 | −0.826089 | ||||||||
\(467\) | − | 17.7307i | − | 0.820478i | −0.911978 | − | 0.410239i | \(-0.865445\pi\) | ||
0.911978 | − | 0.410239i | \(-0.134555\pi\) | |||||||
\(468\) | −17.8826 | − | 7.01465i | −0.826624 | − | 0.324252i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.896615 | + | 5.64484i | −0.0413578 | + | 0.260377i | ||||
\(471\) | 2.00754 | − | 10.6154i | 0.0925028 | − | 0.489132i | ||||
\(472\) | −12.9727 | −0.597118 | ||||||||
\(473\) | −26.6630 | −1.22597 | ||||||||
\(474\) | −2.27774 | + | 12.0441i | −0.104620 | + | 0.553205i | ||||
\(475\) | 3.25893 | − | 9.99983i | 0.149530 | − | 0.458824i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.61736 | − | 3.38026i | −0.394562 | − | 0.154771i | ||||
\(478\) | 18.4508i | 0.843920i | ||||||||
\(479\) | 4.63276 | 0.211676 | 0.105838 | − | 0.994383i | \(-0.466247\pi\) | ||||
0.105838 | + | 0.994383i | \(0.466247\pi\) | |||||||
\(480\) | −1.30776 | + | 3.64551i | −0.0596906 | + | 0.166394i | ||||
\(481\) | − | 17.6537i | − | 0.804937i | ||||||
\(482\) | 13.4629i | 0.613220i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.32348 | −0.151067 | ||||||||
\(485\) | 10.8325 | + | 1.72061i | 0.491878 | + | 0.0781289i | ||||
\(486\) | 12.5382 | − | 9.26244i | 0.568746 | − | 0.420153i | ||||
\(487\) | − | 43.6309i | − | 1.97711i | −0.150876 | − | 0.988553i | \(-0.548209\pi\) | ||
0.150876 | − | 0.988553i | \(-0.451791\pi\) | |||||||
\(488\) | − | 10.3401i | − | 0.468074i | ||||||
\(489\) | 5.49393 | + | 1.03899i | 0.248444 | + | 0.0469848i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4021i | 1.32690i | 0.748221 | + | 0.663449i | \(0.230908\pi\) | ||||
−0.748221 | + | 0.663449i | \(0.769092\pi\) | |||||||
\(492\) | 2.82583 | − | 14.9423i | 0.127398 | − | 0.673651i | ||||
\(493\) | 42.1440 | 1.89807 | ||||||||
\(494\) | 13.4688i | 0.605990i | ||||||||
\(495\) | −12.8639 | + | 21.8878i | −0.578188 | + | 0.983785i | ||||
\(496\) | − | 3.43184i | − | 0.154094i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.1519 | + | 3.05458i | 0.723782 | + | 0.136879i | ||||
\(499\) | 21.1826 | 0.948264 | 0.474132 | − | 0.880454i | \(-0.342762\pi\) | ||||
0.474132 | + | 0.880454i | \(0.342762\pi\) | |||||||
\(500\) | −9.95501 | − | 5.08899i | −0.445202 | − | 0.227586i | ||||
\(501\) | 18.6018 | + | 3.51790i | 0.831067 | + | 0.157168i | ||||
\(502\) | −21.5154 | −0.960279 | ||||||||
\(503\) | − | 9.61653i | − | 0.428780i | −0.976748 | − | 0.214390i | \(-0.931224\pi\) | ||
0.976748 | − | 0.214390i | \(-0.0687763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4475 | − | 1.97713i | −0.553905 | − | 0.0879812i | ||||
\(506\) | − | 17.8195i | − | 0.792172i | ||||||
\(507\) | −9.01165 | + | 47.6514i | −0.400221 | + | 2.11627i | ||||
\(508\) | 16.6271i | 0.737709i | ||||||||
\(509\) | −10.1694 | −0.450750 | −0.225375 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225375 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(510\) | 20.3384 | + | 7.29600i | 0.900600 | + | 0.323072i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.25635 | − | 5.81263i | −0.408678 | − | 0.256634i | ||||
\(514\) | − | 13.2419i | − | 0.584073i | ||||||
\(515\) | −14.9443 | − | 2.37372i | −0.658523 | − | 0.104599i | ||||
\(516\) | −11.9899 | − | 2.26748i | −0.527825 | − | 0.0998202i | ||||
\(517\) | −9.67389 | −0.425457 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.22492 | − | 1.55547i | −0.361034 | − | 0.0682773i | ||||
\(520\) | 14.1404 | + | 2.24604i | 0.620098 | + | 0.0984952i | ||||
\(521\) | 20.3300 | 0.890674 | 0.445337 | − | 0.895363i | \(-0.353084\pi\) | ||||
0.445337 | + | 0.895363i | \(0.353084\pi\) | |||||||
\(522\) | −8.27553 | + | 21.0970i | −0.362210 | + | 0.923390i | ||||
\(523\) | 41.0473 | 1.79487 | 0.897436 | − | 0.441144i | \(-0.145427\pi\) | ||||
0.897436 | + | 0.441144i | \(0.145427\pi\) | |||||||
\(524\) | 0.210484 | 0.00919504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.5680 | 0.678795 | ||||||||
\(527\) | −19.1463 | −0.834026 | ||||||||
\(528\) | −6.44102 | − | 1.21810i | −0.280309 | − | 0.0530110i | ||||
\(529\) | −0.831243 | −0.0361410 | ||||||||
\(530\) | 6.81405 | + | 1.08233i | 0.295984 | + | 0.0470135i | ||||
\(531\) | −36.2305 | − | 14.2118i | −1.57227 | − | 0.616740i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.2180 | −2.43507 | ||||||||
\(534\) | −3.41749 | + | 18.0709i | −0.147889 | + | 0.782003i | ||||
\(535\) | −20.0778 | − | 3.18912i | −0.868038 | − | 0.137877i | ||||
\(536\) | − | 1.48871i | − | 0.0643024i | ||||||
\(537\) | 14.5607 | + | 2.75366i | 0.628340 | + | 0.118829i | ||||
\(538\) | 8.37779 | 0.361192 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.64604 | + | 8.74860i | −0.329033 | + | 0.376480i | ||||
\(541\) | −2.37649 | −0.102173 | −0.0510866 | − | 0.998694i | \(-0.516268\pi\) | ||||
−0.0510866 | + | 0.998694i | \(0.516268\pi\) | |||||||
\(542\) | 0.305606i | 0.0131269i | ||||||||
\(543\) | 19.0960 | + | 3.61136i | 0.819487 | + | 0.154978i | ||||
\(544\) | 5.57902i | 0.239199i | ||||||||
\(545\) | 33.8561 | + | 5.37763i | 1.45024 | + | 0.230353i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.09789i | − | 0.175213i | −0.996155 | − | 0.0876066i | \(-0.972078\pi\) | ||
0.996155 | − | 0.0876066i | \(-0.0279218\pi\) | |||||||
\(548\) | −3.87172 | −0.165392 | ||||||||
\(549\) | 11.3277 | − | 28.8780i | 0.483456 | − | 1.23248i | ||||
\(550\) | 5.86351 | − | 17.9918i | 0.250021 | − | 0.767175i | ||||
\(551\) | 15.8898 | 0.676929 | ||||||||
\(552\) | 1.51541 | − | 8.01310i | 0.0645000 | − | 0.341060i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 20.9930i | − | 0.891909i | ||||||
\(555\) | −10.0509 | − | 3.60557i | −0.426638 | − | 0.153048i | ||||
\(556\) | 17.4338i | 0.739357i | ||||||||
\(557\) | 37.9488 | 1.60794 | 0.803971 | − | 0.594669i | \(-0.202717\pi\) | ||||
0.803971 | + | 0.594669i | \(0.202717\pi\) | |||||||
\(558\) | 3.75963 | − | 9.58451i | 0.159158 | − | 0.405745i | ||||
\(559\) | 45.1100i | 1.90795i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.79580 | + | 35.9346i | −0.286919 | + | 1.51716i | ||||
\(562\) | 5.67638i | 0.239443i | ||||||||
\(563\) | − | 2.75056i | − | 0.115922i | −0.998319 | − | 0.0579611i | \(-0.981540\pi\) | ||
0.998319 | − | 0.0579611i | \(-0.0184599\pi\) | |||||||
\(564\) | −4.35018 | − | 0.822689i | −0.183176 | − | 0.0346414i | ||||
\(565\) | −6.25098 | − | 0.992893i | −0.262981 | − | 0.0417713i | ||||
\(566\) | 15.8411 | 0.665853 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 5.06254i | − | 0.212419i | ||||||
\(569\) | 31.3355i | 1.31365i | 0.754043 | + | 0.656825i | \(0.228101\pi\) | ||||
−0.754043 | + | 0.656825i | \(0.771899\pi\) | |||||||
\(570\) | 7.66832 | + | 2.75086i | 0.321191 | + | 0.115221i | ||||
\(571\) | −17.2218 | −0.720709 | −0.360354 | − | 0.932816i | \(-0.617344\pi\) | ||||
−0.360354 | + | 0.932816i | \(0.617344\pi\) | |||||||
\(572\) | 24.2333i | 1.01324i | ||||||||
\(573\) | −4.85622 | − | 0.918388i | −0.202871 | − | 0.0383662i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3832 | + | 7.29464i | 0.933443 | + | 0.304208i | ||||
\(576\) | −2.79282 | − | 1.09552i | −0.116368 | − | 0.0456465i | ||||
\(577\) | 17.2429 | 0.717829 | 0.358915 | − | 0.933370i | \(-0.383147\pi\) | ||||
0.358915 | + | 0.933370i | \(0.383147\pi\) | |||||||
\(578\) | 14.1255 | 0.587543 | ||||||||
\(579\) | −45.5753 | − | 8.61901i | −1.89404 | − | 0.358194i | ||||
\(580\) | 2.64976 | − | 16.6821i | 0.110025 | − | 0.692688i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.57875 | + | 8.34802i | −0.0654411 | + | 0.346037i | ||||
\(583\) | 11.6776i | 0.483639i | ||||||||
\(584\) | −3.33557 | −0.138027 | ||||||||
\(585\) | 37.0311 | + | 21.7638i | 1.53105 | + | 0.899823i | ||||
\(586\) | 23.2810i | 0.961729i | ||||||||
\(587\) | − | 14.3325i | − | 0.591567i | −0.955255 | − | 0.295784i | \(-0.904419\pi\) | ||
0.955255 | − | 0.295784i | \(-0.0955807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.21885 | −0.297448 | ||||||||
\(590\) | 28.6487 | + | 4.55051i | 1.17945 | + | 0.187341i | ||||
\(591\) | −4.73903 | + | 25.0588i | −0.194938 | + | 1.03078i | ||||
\(592\) | − | 2.75706i | − | 0.113315i | ||||||
\(593\) | 26.7511i | 1.09854i | 0.835646 | + | 0.549268i | \(0.185093\pi\) | ||||
−0.835646 | + | 0.549268i | \(0.814907\pi\) | |||||||
\(594\) | −16.6542 | − | 10.4582i | −0.683328 | − | 0.429104i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.65775i | 0.354635i | ||||||||
\(597\) | −28.0228 | − | 5.29956i | −1.14690 | − | 0.216896i | ||||
\(598\) | −30.1480 | −1.23284 | ||||||||
\(599\) | 16.5006i | 0.674195i | 0.941470 | + | 0.337097i | \(0.109445\pi\) | ||||
−0.941470 | + | 0.337097i | \(0.890555\pi\) | |||||||
\(600\) | 4.16678 | − | 7.59197i | 0.170108 | − | 0.309941i | ||||
\(601\) | 2.77557i | 0.113218i | 0.998396 | + | 0.0566089i | \(0.0180288\pi\) | ||||
−0.998396 | + | 0.0566089i | \(0.981971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.63090 | − | 4.15770i | 0.0664155 | − | 0.169314i | ||||
\(604\) | 16.8301 | 0.684806 | ||||||||
\(605\) | 7.33952 | + | 1.16579i | 0.298394 | + | 0.0473963i | ||||
\(606\) | 1.81412 | − | 9.59260i | 0.0736934 | − | 0.389673i | ||||
\(607\) | 14.8382 | 0.602266 | 0.301133 | − | 0.953582i | \(-0.402635\pi\) | ||||
0.301133 | + | 0.953582i | \(0.402635\pi\) | |||||||
\(608\) | 2.10349i | 0.0853080i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.62705 | + | 22.8349i | −0.146855 | + | 0.924558i | ||||
\(611\) | 16.3668i | 0.662132i | ||||||||
\(612\) | −6.11191 | + | 15.5812i | −0.247059 | + | 0.629833i | ||||
\(613\) | − | 8.33176i | − | 0.336517i | −0.985743 | − | 0.168258i | \(-0.946186\pi\) | ||
0.985743 | − | 0.168258i | \(-0.0538143\pi\) | |||||||
\(614\) | −20.2759 | −0.818270 | ||||||||
\(615\) | −11.4819 | + | 32.0071i | −0.462995 | + | 1.29065i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.6210 | 0.588620 | 0.294310 | − | 0.955710i | \(-0.404910\pi\) | ||||
0.294310 | + | 0.955710i | \(0.404910\pi\) | |||||||
\(618\) | 2.17800 | − | 11.5168i | 0.0876122 | − | 0.463272i | ||||
\(619\) | − | 2.57516i | − | 0.103504i | −0.998660 | − | 0.0517522i | \(-0.983519\pi\) | ||
0.998660 | − | 0.0517522i | \(-0.0164806\pi\) | |||||||
\(620\) | −1.20380 | + | 7.57882i | −0.0483460 | + | 0.304373i | ||||
\(621\) | 13.0107 | − | 20.7190i | 0.522103 | − | 0.831425i | ||||
\(622\) | 11.8199 | 0.473934 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.06085 | + | 10.8973i | −0.0825000 | + | 0.436240i | ||||
\(625\) | 20.1994 | + | 14.7304i | 0.807975 | + | 0.589216i | ||||
\(626\) | −4.00427 | −0.160043 | ||||||||
\(627\) | −2.56226 | + | 13.5486i | −0.102327 | + | 0.541080i | ||||
\(628\) | −6.23745 | −0.248901 | ||||||||
\(629\) | −15.3817 | −0.613309 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.65345 | −0.145442 | −0.0727208 | − | 0.997352i | \(-0.523168\pi\) | ||||
−0.0727208 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(632\) | 7.07694 | 0.281506 | ||||||||
\(633\) | 5.09191 | − | 26.9248i | 0.202385 | − | 1.07017i | ||||
\(634\) | −0.211278 | −0.00839092 | ||||||||
\(635\) | 5.83238 | − | 36.7190i | 0.231451 | − | 1.45715i | ||||
\(636\) | −0.993092 | + | 5.25123i | −0.0393787 | + | 0.208225i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.5892 | 1.13186 | ||||||||
\(639\) | 5.54608 | − | 14.1388i | 0.219400 | − | 0.559320i | ||||
\(640\) | 2.20838 | + | 0.350775i | 0.0872940 | + | 0.0138656i | ||||
\(641\) | 45.2701i | 1.78806i | 0.448005 | + | 0.894031i | \(0.352135\pi\) | ||||
−0.448005 | + | 0.894031i | \(0.647865\pi\) | |||||||
\(642\) | 2.92617 | − | 15.4729i | 0.115487 | − | 0.610666i | ||||
\(643\) | −27.7814 | −1.09559 | −0.547796 | − | 0.836612i | \(-0.684533\pi\) | ||||
−0.547796 | + | 0.836612i | \(0.684533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.6829 | + | 9.21322i | 1.01126 | + | 0.362770i | ||||
\(646\) | 11.7354 | 0.461725 | ||||||||
\(647\) | − | 4.09747i | − | 0.161088i | −0.996751 | − | 0.0805441i | \(-0.974334\pi\) | ||
0.996751 | − | 0.0805441i | \(-0.0256658\pi\) | |||||||
\(648\) | −6.59969 | − | 6.11916i | −0.259260 | − | 0.240383i | ||||
\(649\) | 49.0970i | 1.92723i | ||||||||
\(650\) | −30.4396 | − | 9.92022i | −1.19394 | − | 0.389103i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3.22815i | − | 0.126424i | ||||||
\(653\) | 30.9842 | 1.21251 | 0.606253 | − | 0.795272i | \(-0.292672\pi\) | ||||
0.606253 | + | 0.795272i | \(0.292672\pi\) | |||||||
\(654\) | −4.93424 | + | 26.0911i | −0.192944 | + | 1.02024i | ||||
\(655\) | −0.464830 | − | 0.0738326i | −0.0181624 | − | 0.00288488i | ||||
\(656\) | −8.77986 | −0.342796 | ||||||||
\(657\) | −9.31564 | − | 3.65416i | −0.363438 | − | 0.142563i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.2668i | 1.37380i | 0.726752 | + | 0.686900i | \(0.241029\pi\) | ||||
−0.726752 | + | 0.686900i | \(0.758971\pi\) | |||||||
\(660\) | 13.7970 | + | 4.94938i | 0.537046 | + | 0.192654i | ||||
\(661\) | 21.8678i | 0.850560i | 0.905062 | + | 0.425280i | \(0.139824\pi\) | ||||
−0.905062 | + | 0.425280i | \(0.860176\pi\) | |||||||
\(662\) | 4.13421 | 0.160681 | ||||||||
\(663\) | 60.7961 | + | 11.4975i | 2.36113 | + | 0.446527i | ||||
\(664\) | − | 9.49058i | − | 0.368306i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.02041 | − | 7.69999i | 0.117038 | − | 0.298368i | ||||
\(667\) | 35.5671i | 1.37716i | ||||||||
\(668\) | − | 10.9301i | − | 0.422899i | ||||||
\(669\) | −7.07605 | + | 37.4164i | −0.273576 | + | 1.44660i | ||||
\(670\) | −0.522202 | + | 3.28764i | −0.0201744 | + | 0.127013i | ||||
\(671\) | −39.1335 | −1.51073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.23782i | − | 0.124809i | −0.998051 | − | 0.0624045i | \(-0.980123\pi\) | ||
0.998051 | − | 0.0624045i | \(-0.0198769\pi\) | |||||||
\(674\) | 1.99207i | 0.0767318i | ||||||||
\(675\) | 19.9542 | − | 16.6382i | 0.768037 | − | 0.640405i | ||||
\(676\) | 27.9992 | 1.07689 | ||||||||
\(677\) | 10.5188i | 0.404271i | 0.979358 | + | 0.202136i | \(0.0647881\pi\) | ||||
−0.979358 | + | 0.202136i | \(0.935212\pi\) | |||||||
\(678\) | 0.911028 | − | 4.81730i | 0.0349878 | − | 0.185007i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.95698 | − | 12.3206i | 0.0750469 | − | 0.472474i | ||||
\(681\) | 46.8190 | + | 8.85422i | 1.79411 | + | 0.339294i | ||||
\(682\) | −12.9883 | −0.497346 | ||||||||
\(683\) | −46.9660 | −1.79710 | −0.898552 | − | 0.438867i | \(-0.855380\pi\) | ||||
−0.898552 | + | 0.438867i | \(0.855380\pi\) | |||||||
\(684\) | −2.30441 | + | 5.87468i | −0.0881113 | + | 0.224624i | ||||
\(685\) | 8.55025 | + | 1.35811i | 0.326688 | + | 0.0518905i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.5426 | − | 5.20874i | −1.05081 | − | 0.198726i | ||||
\(688\) | 7.04507i | 0.268591i | ||||||||
\(689\) | 19.7569 | 0.752678 | ||||||||
\(690\) | −6.15740 | + | 17.1644i | −0.234408 | + | 0.653439i | ||||
\(691\) | 35.7893i | 1.36149i | 0.732520 | + | 0.680745i | \(0.238344\pi\) | ||||
−0.732520 | + | 0.680745i | \(0.761656\pi\) | |||||||
\(692\) | 4.83283i | 0.183717i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.4429 | −0.813961 | ||||||||
\(695\) | 6.11534 | − | 38.5005i | 0.231968 | − | 1.46041i | ||||
\(696\) | 12.8560 | + | 2.43129i | 0.487307 | + | 0.0921576i | ||||
\(697\) | 48.9830i | 1.85537i | ||||||||
\(698\) | − | 17.1982i | − | 0.650961i | ||||||
\(699\) | −5.73955 | + | 30.3494i | −0.217090 | + | 1.14792i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.5930i | − | 1.38210i | −0.722808 | − | 0.691049i | \(-0.757149\pi\) | ||
0.722808 | − | 0.691049i | \(-0.242851\pi\) | |||||||
\(702\) | −17.6937 | + | 28.1764i | −0.667806 | + | 1.06345i | ||||
\(703\) | −5.79947 | −0.218731 | ||||||||
\(704\) | 3.78464i | 0.142639i | ||||||||
\(705\) | 9.31828 | + | 3.34275i | 0.350947 | + | 0.125895i | ||||
\(706\) | 3.05545i | 0.114993i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.17532 | + | 22.0781i | −0.156918 | + | 0.829744i | ||||
\(709\) | −23.6152 | −0.886888 | −0.443444 | − | 0.896302i | \(-0.646243\pi\) | ||||
−0.443444 | + | 0.896302i | \(0.646243\pi\) | |||||||
\(710\) | −1.77581 | + | 11.1800i | −0.0666450 | + | 0.419579i | ||||
\(711\) | 19.7646 | + | 7.75290i | 0.741231 | + | 0.290756i | ||||
\(712\) | 10.6182 | 0.397932 | ||||||||
\(713\) | − | 16.1584i | − | 0.605136i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.50043 | − | 53.5164i | 0.317898 | − | 2.00140i | ||||
\(716\) | − | 8.55562i | − | 0.319739i | ||||||
\(717\) | 31.4011 | + | 5.93846i | 1.17270 | + | 0.221776i | ||||
\(718\) | 15.3615i | 0.573287i | ||||||||
\(719\) | −28.3294 | −1.05651 | −0.528255 | − | 0.849086i | \(-0.677153\pi\) | ||||
−0.528255 | + | 0.849086i | \(0.677153\pi\) | |||||||
\(720\) | 5.78334 | + | 3.39897i | 0.215532 | + | 0.126672i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.5753 | −0.542437 | ||||||||
\(723\) | 22.9123 | + | 4.33309i | 0.852119 | + | 0.161149i | ||||
\(724\) | − | 11.2205i | − | 0.417006i | ||||||
\(725\) | −11.7034 | + | 35.9111i | −0.434652 | + | 1.33370i | ||||
\(726\) | −1.06967 | + | 5.65618i | −0.0396993 | + | 0.209920i | ||||
\(727\) | −5.04231 | −0.187009 | −0.0935045 | − | 0.995619i | \(-0.529807\pi\) | ||||
−0.0935045 | + | 0.995619i | \(0.529807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7281 | − | 24.3198i | −0.434375 | − | 0.900732i | ||||
\(730\) | 7.36621 | + | 1.17003i | 0.272636 | + | 0.0433049i | ||||
\(731\) | 39.3046 | 1.45373 | ||||||||
\(732\) | −17.5976 | − | 3.32800i | −0.650428 | − | 0.123006i | ||||
\(733\) | −41.9089 | −1.54794 | −0.773969 | − | 0.633223i | \(-0.781732\pi\) | ||||
−0.773969 | + | 0.633223i | \(0.781732\pi\) | |||||||
\(734\) | −4.12440 | −0.152234 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.70837 | −0.173553 | ||||||||
\(737\) | −5.63422 | −0.207539 | ||||||||
\(738\) | −24.5206 | − | 9.61847i | −0.902615 | − | 0.354061i | ||||
\(739\) | 24.0720 | 0.885502 | 0.442751 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442751 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(740\) | −0.967110 | + | 6.08865i | −0.0355517 | + | 0.223823i | ||||
\(741\) | 22.9223 | + | 4.33498i | 0.842074 | + | 0.159250i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.7877 | 0.615880 | 0.307940 | − | 0.951406i | \(-0.400360\pi\) | ||||
0.307940 | + | 0.951406i | \(0.400360\pi\) | |||||||
\(744\) | −5.84059 | − | 1.10455i | −0.214127 | − | 0.0404948i | ||||
\(745\) | 3.03692 | − | 19.1196i | 0.111264 | − | 0.700489i | ||||
\(746\) | 23.8319i | 0.872546i | ||||||||
\(747\) | 10.3971 | − | 26.5055i | 0.380409 | − | 0.969785i | ||||
\(748\) | 21.1146 | 0.772025 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.8649 | + | 15.3044i | −0.433246 | + | 0.558836i | ||||
\(751\) | −44.2677 | −1.61535 | −0.807675 | − | 0.589627i | \(-0.799275\pi\) | ||||
−0.807675 | + | 0.589627i | \(0.799275\pi\) | |||||||
\(752\) | 2.55610i | 0.0932112i | ||||||||
\(753\) | −6.92481 | + | 36.6167i | −0.252354 | + | 1.33439i | ||||
\(754\) | − | 48.3688i | − | 1.76149i | ||||||
\(755\) | −37.1672 | − | 5.90357i | −1.35265 | − | 0.214853i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.9657i | − | 1.52527i | −0.646829 | − | 0.762635i | \(-0.723905\pi\) | ||
0.646829 | − | 0.762635i | \(-0.276095\pi\) | |||||||
\(758\) | −29.0694 | −1.05585 | ||||||||
\(759\) | −30.3267 | − | 5.73526i | −1.10079 | − | 0.208177i | ||||
\(760\) | 0.737854 | − | 4.64532i | 0.0267648 | − | 0.168504i | ||||
\(761\) | −51.0849 | −1.85183 | −0.925913 | − | 0.377736i | \(-0.876703\pi\) | ||||
−0.925913 | + | 0.377736i | \(0.876703\pi\) | |||||||
\(762\) | 28.2974 | + | 5.35150i | 1.02511 | + | 0.193864i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.85343i | 0.103234i | ||||||||
\(765\) | 18.9629 | − | 32.2654i | 0.685606 | − | 1.16656i | ||||
\(766\) | − | 19.4986i | − | 0.704514i | ||||||
\(767\) | 83.0651 | 2.99931 | ||||||||
\(768\) | −0.321854 | + | 1.70188i | −0.0116139 | + | 0.0614115i | ||||
\(769\) | − | 34.0876i | − | 1.22923i | −0.788827 | − | 0.614616i | \(-0.789311\pi\) | ||
0.788827 | − | 0.614616i | \(-0.210689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.5361 | − | 4.26194i | −0.811618 | − | 0.153490i | ||||
\(772\) | 26.7793i | 0.963808i | ||||||||
\(773\) | 3.58252i | 0.128854i | 0.997922 | + | 0.0644271i | \(0.0205220\pi\) | ||||
−0.997922 | + | 0.0644271i | \(0.979478\pi\) | |||||||
\(774\) | −7.71798 | + | 19.6756i | −0.277417 | + | 0.707225i | ||||
\(775\) | 5.31692 | − | 16.3147i | 0.190990 | − | 0.586040i | ||||
\(776\) | 4.90516 | 0.176085 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 6.51453i | − | 0.233557i | ||||||
\(779\) | 18.4684i | 0.661699i | ||||||||
\(780\) | 8.37364 | − | 23.3425i | 0.299824 | − | 0.835794i | ||||
\(781\) | −19.1599 | −0.685594 | ||||||||
\(782\) | 26.2681i | 0.939346i | ||||||||
\(783\) | 33.2411 | + | 20.8741i | 1.18794 | + | 0.745981i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7747 | + | 2.18794i | 0.491639 | + | 0.0780910i | ||||
\(786\) | 0.0677451 | − | 0.358220i | 0.00241639 | − | 0.0127773i | ||||
\(787\) | −15.5828 | −0.555466 | −0.277733 | − | 0.960658i | \(-0.589583\pi\) | ||||
−0.277733 | + | 0.960658i | \(0.589583\pi\) | |||||||
\(788\) | 14.7242 | 0.524527 | ||||||||
\(789\) | 5.01060 | − | 26.4949i | 0.178382 | − | 0.943242i | ||||
\(790\) | −15.6286 | − | 2.48242i | −0.556041 | − | 0.0883204i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.14613 | + | 10.5698i | −0.147326 | + | 0.375582i | ||||
\(793\) | 66.2083i | 2.35113i | ||||||||
\(794\) | 33.0474 | 1.17281 | ||||||||
\(795\) | 4.03513 | − | 11.2484i | 0.143111 | − | 0.398939i | ||||
\(796\) | 16.4657i | 0.583612i | ||||||||
\(797\) | 33.4891i | 1.18625i | 0.805112 | + | 0.593123i | \(0.202105\pi\) | ||||
−0.805112 | + | 0.593123i | \(0.797895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.2605 | 0.504501 | ||||||||
\(800\) | −4.75391 | − | 1.54929i | −0.168076 | − | 0.0547758i | ||||
\(801\) | 29.6546 | + | 11.6323i | 1.04779 | + | 0.411009i | ||||
\(802\) | − | 13.3058i | − | 0.469845i | ||||||
\(803\) | 12.6239i | 0.445488i | ||||||||
\(804\) | −2.53361 | − | 0.479146i | −0.0893535 | − | 0.0168982i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.9743i | 0.774011i | ||||||||
\(807\) | 2.69642 | − | 14.2580i | 0.0949185 | − | 0.501906i | ||||
\(808\) | −5.63646 | −0.198290 | ||||||||
\(809\) | − | 18.8243i | − | 0.661827i | −0.943661 | − | 0.330914i | \(-0.892643\pi\) | ||
0.943661 | − | 0.330914i | \(-0.107357\pi\) | |||||||
\(810\) | 12.4282 | + | 15.8284i | 0.436682 | + | 0.556155i | ||||
\(811\) | 9.05687i | 0.318030i | 0.987276 | + | 0.159015i | \(0.0508318\pi\) | ||||
−0.987276 | + | 0.159015i | \(0.949168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.520106 | + | 0.0983604i | 0.0182409 | + | 0.00344965i | ||||
\(814\) | −10.4345 | −0.365729 | ||||||||
\(815\) | −1.13235 | + | 7.12898i | −0.0396646 | + | 0.249717i | ||||
\(816\) | 9.49485 | + | 1.79563i | 0.332386 | + | 0.0628596i | ||||
\(817\) | 14.8193 | 0.518460 | ||||||||
\(818\) | − | 24.4460i | − | 0.854733i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.3893 | + | 3.07976i | 0.677104 | + | 0.107550i | ||||
\(821\) | − | 0.724927i | − | 0.0253001i | −0.999920 | − | 0.0126501i | \(-0.995973\pi\) | ||
0.999920 | − | 0.0126501i | \(-0.00402675\pi\) | |||||||
\(822\) | −1.24613 | + | 6.58923i | −0.0434637 | + | 0.229826i | ||||
\(823\) | − | 7.32363i | − | 0.255286i | −0.991820 | − | 0.127643i | \(-0.959259\pi\) | ||
0.991820 | − | 0.127643i | \(-0.0407411\pi\) | |||||||
\(824\) | −6.76706 | −0.235742 | ||||||||
\(825\) | −28.7328 | − | 15.7698i | −1.00035 | − | 0.549032i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.6605 | −0.857529 | −0.428764 | − | 0.903416i | \(-0.641051\pi\) | ||||
−0.428764 | + | 0.903416i | \(0.641051\pi\) | |||||||
\(828\) | −13.1496 | − | 5.15809i | −0.456981 | − | 0.179256i | ||||
\(829\) | − | 43.1620i | − | 1.49908i | −0.661961 | − | 0.749538i | \(-0.730276\pi\) | ||
0.661961 | − | 0.749538i | \(-0.269724\pi\) | |||||||
\(830\) | −3.32906 | + | 20.9588i | −0.115553 | + | 0.727492i | ||||
\(831\) | −35.7277 | − | 6.75669i | −1.23938 | − | 0.234387i | ||||
\(832\) | 6.40306 | 0.221986 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 29.6703 | + | 5.61112i | 1.02740 | + | 0.194297i | ||||
\(835\) | −3.83401 | + | 24.1379i | −0.132682 | + | 0.835326i | ||||
\(836\) | 7.96096 | 0.275336 | ||||||||
\(837\) | −15.1017 | − | 9.48327i | −0.521990 | − | 0.327790i | ||||
\(838\) | −27.0524 | −0.934511 | ||||||||
\(839\) | −14.2292 | −0.491247 | −0.245623 | − | 0.969365i | \(-0.578993\pi\) | ||||
−0.245623 | + | 0.969365i | \(0.578993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0630 | −0.967691 | ||||||||
\(842\) | −5.39064 | −0.185774 | ||||||||
\(843\) | 9.66053 | + | 1.82696i | 0.332726 | + | 0.0629239i | ||||
\(844\) | −15.8206 | −0.544567 | ||||||||
\(845\) | −61.8330 | − | 9.82143i | −2.12712 | − | 0.337868i | ||||
\(846\) | −2.80024 | + | 7.13872i | −0.0962743 | + | 0.245434i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.08554 | 0.105958 | ||||||||
\(849\) | 5.09853 | − | 26.9598i | 0.174981 | − | 0.925258i | ||||
\(850\) | −8.64354 | + | 26.5222i | −0.296471 | + | 0.909704i | ||||
\(851\) | − | 12.9813i | − | 0.444993i | ||||||
\(852\) | −8.61585 | − | 1.62940i | −0.295174 | − | 0.0558222i | ||||
\(853\) | 10.7205 | 0.367064 | 0.183532 | − | 0.983014i | \(-0.441247\pi\) | ||||
0.183532 | + | 0.983014i | \(0.441247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.14971 | − | 12.1652i | 0.244515 | − | 0.416042i | ||||
\(856\) | −9.09162 | −0.310745 | ||||||||
\(857\) | 17.2656i | 0.589781i | 0.955531 | + | 0.294890i | \(0.0952831\pi\) | ||||
−0.955531 | + | 0.294890i | \(0.904717\pi\) | |||||||
\(858\) | 41.2422 | + | 7.79957i | 1.40799 | + | 0.266273i | ||||
\(859\) | 6.33253i | 0.216063i | 0.994147 | + | 0.108032i | \(0.0344548\pi\) | ||||
−0.994147 | + | 0.108032i | \(0.965545\pi\) | |||||||
\(860\) | 2.47124 | − | 15.5582i | 0.0842684 | − | 0.530530i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 3.21022i | − | 0.109341i | ||||||
\(863\) | 4.44663 | 0.151365 | 0.0756826 | − | 0.997132i | \(-0.475886\pi\) | ||||
0.0756826 | + | 0.997132i | \(0.475886\pi\) | |||||||
\(864\) | −2.76332 | + | 4.40046i | −0.0940101 | + | 0.149707i | ||||
\(865\) | 1.69524 | − | 10.6727i | 0.0576398 | − | 0.362884i | ||||
\(866\) | 39.7769 | 1.35167 | ||||||||
\(867\) | 4.54634 | − | 24.0400i | 0.154402 | − | 0.816440i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 26.7837i | − | 0.908573i | ||||||
\(870\) | −27.5382 | − | 9.87879i | −0.933634 | − | 0.334922i | ||||
\(871\) | 9.53229i | 0.322989i | ||||||||
\(872\) | 15.3307 | 0.519163 | ||||||||
\(873\) | 13.6992 | + | 5.37368i | 0.463649 | + | 0.181872i | ||||
\(874\) | 9.90403i | 0.335009i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.07356 | + | 5.67675i | −0.0362724 | + | 0.191800i | ||||
\(877\) | − | 40.7210i | − | 1.37505i | −0.726161 | − | 0.687525i | \(-0.758697\pi\) | ||
0.726161 | − | 0.687525i | \(-0.241303\pi\) | |||||||
\(878\) | 26.5159i | 0.894868i | ||||||||
\(879\) | 39.6215 | + | 7.49307i | 1.33640 | + | 0.252735i | ||||
\(880\) | 1.32756 | − | 8.35793i | 0.0447520 | − | 0.281746i | ||||
\(881\) | −16.0602 | −0.541081 | −0.270540 | − | 0.962709i | \(-0.587202\pi\) | ||||
−0.270540 | + | 0.962709i | \(0.587202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9924i | 0.639145i | 0.947562 | + | 0.319572i | \(0.103539\pi\) | ||||
−0.947562 | + | 0.319572i | \(0.896461\pi\) | |||||||
\(884\) | − | 35.7228i | − | 1.20149i | ||||||
\(885\) | 16.9651 | − | 47.2922i | 0.570277 | − | 1.58971i | ||||
\(886\) | 21.5549 | 0.724151 | ||||||||
\(887\) | 32.7978i | 1.10124i | 0.834755 | + | 0.550621i | \(0.185609\pi\) | ||||
−0.834755 | + | 0.550621i | \(0.814391\pi\) | |||||||
\(888\) | −4.69220 | − | 0.887371i | −0.157460 | − | 0.0297782i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −23.4489 | − | 3.72459i | −0.786010 | − | 0.124848i | ||||
\(891\) | −23.1588 | + | 24.9774i | −0.775848 | + | 0.836776i | ||||
\(892\) | 21.9853 | 0.736122 | ||||||||
\(893\) | 5.37673 | 0.179925 | ||||||||
\(894\) | 14.7345 | + | 2.78653i | 0.492795 | + | 0.0931954i | ||||
\(895\) | −3.00110 | + | 18.8941i | −0.100316 | + | 0.631560i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.70324 | + | 51.3084i | −0.323982 | + | 1.71314i | ||||
\(898\) | 1.27232i | 0.0424578i | ||||||||
\(899\) | 25.9241 | 0.864619 | ||||||||
\(900\) | −11.5796 | − | 9.53488i | −0.385985 | − | 0.317829i | ||||
\(901\) | − | 17.2143i | − | 0.573491i | ||||||
\(902\) | 33.2286i | 1.10639i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.83057 | −0.0941432 | ||||||||
\(905\) | −3.93587 | + | 24.7791i | −0.130833 | + | 0.823687i | ||||
\(906\) | 5.41682 | − | 28.6428i | 0.179962 | − | 0.951594i | ||||
\(907\) | − | 57.7453i | − | 1.91740i | −0.284420 | − | 0.958700i | \(-0.591801\pi\) | ||
0.284420 | − | 0.958700i | \(-0.408199\pi\) | |||||||
\(908\) | − | 27.5101i | − | 0.912954i | ||||||
\(909\) | −15.7416 | − | 6.17483i | −0.522117 | − | 0.204806i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.3826i | 0.973490i | 0.873544 | + | 0.486745i | \(0.161816\pi\) | ||||
−0.873544 | + | 0.486745i | \(0.838184\pi\) | |||||||
\(912\) | 3.57990 | + | 0.677017i | 0.118542 | + | 0.0224183i | ||||
\(913\) | −35.9184 | −1.18873 | ||||||||
\(914\) | − | 7.38402i | − | 0.244242i | ||||||
\(915\) | 37.6950 | + | 13.5223i | 1.24616 | + | 0.447034i | ||||
\(916\) | 16.1836i | 0.534720i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.5503 | + | 15.4166i | 0.810280 | + | 0.508824i | ||||
\(919\) | 42.6061 | 1.40545 | 0.702723 | − | 0.711464i | \(-0.251967\pi\) | ||||
0.702723 | + | 0.711464i | \(0.251967\pi\) | |||||||
\(920\) | 10.3979 | + | 1.65158i | 0.342808 | + | 0.0544510i | ||||
\(921\) | −6.52588 | + | 34.5073i | −0.215035 | + | 1.13705i | ||||
\(922\) | −14.6635 | −0.482918 | ||||||||
\(923\) | 32.4157i | 1.06698i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.27150 | − | 13.1068i | 0.140446 | − | 0.430950i | ||||
\(926\) | 27.8566i | 0.915424i | ||||||||
\(927\) | −18.8992 | − | 7.41342i | −0.620731 | − | 0.243489i | ||||
\(928\) | − | 7.55401i | − | 0.247972i | ||||||
\(929\) | 26.5385 | 0.870700 | 0.435350 | − | 0.900261i | \(-0.356625\pi\) | ||||
0.435350 | + | 0.900261i | \(0.356625\pi\) | |||||||
\(930\) | 12.5108 | + | 4.48801i | 0.410246 | + | 0.147168i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.8328 | 0.584133 | ||||||||
\(933\) | 3.80427 | − | 20.1161i | 0.124546 | − | 0.658571i | ||||
\(934\) | 17.7307i | 0.580165i | ||||||||
\(935\) | −46.6291 | − | 7.40647i | −1.52493 | − | 0.242218i | ||||
\(936\) | 17.8826 | + | 7.01465i | 0.584511 | + | 0.229281i | ||||
\(937\) | −33.5524 | −1.09611 | −0.548054 | − | 0.836443i | \(-0.684631\pi\) | ||||
−0.548054 | + | 0.836443i | \(0.684631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.28879 | + | 6.81481i | −0.0420581 | + | 0.222393i | ||||
\(940\) | 0.896615 | − | 5.64484i | 0.0292444 | − | 0.184114i | ||||
\(941\) | −14.9463 | −0.487237 | −0.243618 | − | 0.969871i | \(-0.578334\pi\) | ||||
−0.243618 | + | 0.969871i | \(0.578334\pi\) | |||||||
\(942\) | −2.00754 | + | 10.6154i | −0.0654093 | + | 0.345869i | ||||
\(943\) | −41.3388 | −1.34618 | ||||||||
\(944\) | 12.9727 | 0.422226 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.6630 | 0.866890 | ||||||||
\(947\) | 21.5510 | 0.700312 | 0.350156 | − | 0.936691i | \(-0.386129\pi\) | ||||
0.350156 | + | 0.936691i | \(0.386129\pi\) | |||||||
\(948\) | 2.27774 | − | 12.0441i | 0.0739775 | − | 0.391175i | ||||
\(949\) | 21.3578 | 0.693305 | ||||||||
\(950\) | −3.25893 | + | 9.99983i | −0.105734 | + | 0.324437i | ||||
\(951\) | −0.0680006 | + | 0.359571i | −0.00220507 | + | 0.0116599i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.489212 | −0.0158471 | −0.00792356 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792356 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(954\) | 8.61736 | + | 3.38026i | 0.278997 | + | 0.109440i | ||||
\(955\) | 1.00091 | − | 6.30148i | 0.0323888 | − | 0.203911i | ||||
\(956\) | − | 18.4508i | − | 0.596742i | ||||||
\(957\) | 9.20153 | − | 48.6555i | 0.297443 | − | 1.57281i | ||||
\(958\) | −4.63276 | −0.149678 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.30776 | − | 3.64551i | 0.0422076 | − | 0.117658i | ||||
\(961\) | 19.2225 | 0.620080 | ||||||||
\(962\) | 17.6537i | 0.569177i | ||||||||
\(963\) | −25.3913 | − | 9.96001i | −0.818222 | − | 0.320957i | ||||
\(964\) | − | 13.4629i | − | 0.433612i | ||||||
\(965\) | 9.39351 | − | 59.1389i | 0.302388 | − | 1.90375i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.7126i | − | 1.43786i | −0.695083 | − | 0.718930i | \(-0.744632\pi\) | ||
0.695083 | − | 0.718930i | \(-0.255368\pi\) | |||||||
\(968\) | 3.32348 | 0.106821 | ||||||||
\(969\) | 3.77709 | − | 19.9724i | 0.121338 | − | 0.641605i | ||||
\(970\) | −10.8325 | − | 1.72061i | −0.347810 | − | 0.0552455i | ||||
\(971\) | −8.30533 | −0.266531 | −0.133265 | − | 0.991080i | \(-0.542546\pi\) | ||||
−0.133265 | + | 0.991080i | \(0.542546\pi\) | |||||||
\(972\) | −12.5382 | + | 9.26244i | −0.402164 | + | 0.297093i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.6309i | 1.39802i | ||||||||
\(975\) | −26.6802 | + | 48.6118i | −0.854449 | + | 1.55682i | ||||
\(976\) | 10.3401i | 0.330978i | ||||||||
\(977\) | 11.6472 | 0.372625 | 0.186313 | − | 0.982490i | \(-0.440346\pi\) | ||||
0.186313 | + | 0.982490i | \(0.440346\pi\) | |||||||
\(978\) | −5.49393 | − | 1.03899i | −0.175677 | − | 0.0332233i | ||||
\(979\) | − | 40.1859i | − | 1.28435i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.8159 | + | 16.7950i | 1.36701 | + | 0.536224i | ||||
\(982\) | − | 29.4021i | − | 0.938259i | ||||||
\(983\) | − | 18.4536i | − | 0.588577i | −0.955717 | − | 0.294289i | \(-0.904917\pi\) | ||
0.955717 | − | 0.294289i | \(-0.0950827\pi\) | |||||||
\(984\) | −2.82583 | + | 14.9423i | −0.0900842 | + | 0.476343i | ||||
\(985\) | −32.5166 | − | 5.16488i | −1.03607 | − | 0.164567i | ||||
\(986\) | −42.1440 | −1.34214 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 13.4688i | − | 0.428500i | ||||||
\(989\) | 33.1708i | 1.05477i | ||||||||
\(990\) | 12.8639 | − | 21.8878i | 0.408841 | − | 0.695641i | ||||
\(991\) | −51.2911 | −1.62932 | −0.814658 | − | 0.579942i | \(-0.803075\pi\) | ||||
−0.814658 | + | 0.579942i | \(0.803075\pi\) | |||||||
\(992\) | 3.43184i | 0.108961i | ||||||||
\(993\) | 1.33061 | − | 7.03594i | 0.0422256 | − | 0.223279i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.77577 | − | 36.3626i | 0.183104 | − | 1.15277i | ||||
\(996\) | −16.1519 | − | 3.05458i | −0.511791 | − | 0.0967880i | ||||
\(997\) | 17.6179 | 0.557964 | 0.278982 | − | 0.960296i | \(-0.410003\pi\) | ||||
0.278982 | + | 0.960296i | \(0.410003\pi\) | |||||||
\(998\) | −21.1826 | −0.670524 | ||||||||
\(999\) | −12.1324 | − | 7.61865i | −0.383851 | − | 0.241043i |
(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 | 1470.2.d.g.1469.12 | yes | 24 | |
3.2 | odd | 2 | 1470.2.d.h.1469.11 | yes | 24 | ||
5.4 | even | 2 | 1470.2.d.h.1469.13 | yes | 24 | ||
7.6 | odd | 2 | inner | 1470.2.d.g.1469.13 | yes | 24 | |
15.14 | odd | 2 | inner | 1470.2.d.g.1469.14 | yes | 24 | |
21.20 | even | 2 | 1470.2.d.h.1469.14 | yes | 24 | ||
35.34 | odd | 2 | 1470.2.d.h.1469.12 | yes | 24 | ||
105.104 | even | 2 | inner | 1470.2.d.g.1469.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.d.g.1469.11 | ✓ | 24 | 105.104 | even | 2 | inner | |
1470.2.d.g.1469.12 | yes | 24 | 1.1 | even | 1 | trivial | |
1470.2.d.g.1469.13 | yes | 24 | 7.6 | odd | 2 | inner | |
1470.2.d.g.1469.14 | yes | 24 | 15.14 | odd | 2 | inner | |
1470.2.d.h.1469.11 | yes | 24 | 3.2 | odd | 2 | ||
1470.2.d.h.1469.12 | yes | 24 | 35.34 | odd | 2 | ||
1470.2.d.h.1469.13 | yes | 24 | 5.4 | even | 2 | ||
1470.2.d.h.1469.14 | yes | 24 | 21.20 | even | 2 |