Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1151,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.t (of order \(6\), degree \(2\), not 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Character | \(\chi\) | \(=\) | 1890.1151 |
Dual form | 1890.2.t.b.1601.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.17997 | + | 2.36805i | −0.445987 | + | 0.895040i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | − | 0.751037i | − | 0.226446i | −0.993570 | − | 0.113223i | \(-0.963883\pi\) | ||
0.993570 | − | 0.113223i | \(-0.0361175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.72204 | − | 1.57157i | −0.754958 | − | 0.435875i | 0.0725244 | − | 0.997367i | \(-0.476894\pi\) |
−0.827483 | + | 0.561491i | \(0.810228\pi\) | |||||||
\(14\) | 2.20591 | − | 1.46081i | 0.589554 | − | 0.390417i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.433117 | + | 0.750180i | −0.105046 | + | 0.181945i | −0.913757 | − | 0.406261i | \(-0.866832\pi\) |
0.808711 | + | 0.588206i | \(0.200166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.23551 | − | 0.713322i | 0.283446 | − | 0.163647i | −0.351537 | − | 0.936174i | \(-0.614341\pi\) |
0.634982 | + | 0.772527i | \(0.281007\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.375518 | + | 0.650417i | −0.0800608 | + | 0.138669i | ||||
\(23\) | − | 5.06153i | − | 1.05540i | −0.849430 | − | 0.527701i | \(-0.823054\pi\) | ||
0.849430 | − | 0.527701i | \(-0.176946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.57157 | + | 2.72204i | 0.308210 | + | 0.533836i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.64078 | + | 0.162142i | −0.499060 | + | 0.0306420i | ||||
\(29\) | 5.23368 | − | 3.02167i | 0.971870 | − | 0.561110i | 0.0720645 | − | 0.997400i | \(-0.477041\pi\) |
0.899806 | + | 0.436290i | \(0.143708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.38301 | − | 3.10788i | 0.966817 | − | 0.558192i | 0.0685524 | − | 0.997648i | \(-0.478162\pi\) |
0.898264 | + | 0.439456i | \(0.144829\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.750180 | − | 0.433117i | 0.128655 | − | 0.0742789i | ||||
\(35\) | −1.17997 | + | 2.36805i | −0.199451 | + | 0.400274i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.60391 | + | 6.24216i | 0.592479 | + | 1.02620i | 0.993897 | + | 0.110309i | \(0.0351842\pi\) |
−0.401418 | + | 0.915895i | \(0.631482\pi\) | |||||||
\(38\) | −1.42664 | −0.231432 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 2.08432 | − | 3.61015i | 0.325516 | − | 0.563811i | −0.656101 | − | 0.754673i | \(-0.727795\pi\) |
0.981617 | + | 0.190863i | \(0.0611286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.69510 | + | 6.40010i | 0.563497 | + | 0.976006i | 0.997188 | + | 0.0749440i | \(0.0238778\pi\) |
−0.433690 | + | 0.901062i | \(0.642789\pi\) | |||||||
\(44\) | 0.650417 | − | 0.375518i | 0.0980540 | − | 0.0566115i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.53076 | + | 4.38341i | −0.373141 | + | 0.646299i | ||||
\(47\) | 1.72922 | − | 2.99510i | 0.252233 | − | 0.436880i | −0.711907 | − | 0.702273i | \(-0.752168\pi\) |
0.964140 | + | 0.265393i | \(0.0855018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.21534 | − | 5.58846i | −0.602192 | − | 0.798352i | ||||
\(50\) | −0.866025 | − | 0.500000i | −0.122474 | − | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 3.14314i | − | 0.435875i | ||||||
\(53\) | 0.790248 | + | 0.456250i | 0.108549 | + | 0.0626707i | 0.553292 | − | 0.832988i | \(-0.313372\pi\) |
−0.444743 | + | 0.895658i | \(0.646705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.751037i | − | 0.101270i | ||||||
\(56\) | 2.36805 | + | 1.17997i | 0.316444 | + | 0.157680i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.04334 | −0.793529 | ||||||||
\(59\) | 4.21910 | + | 7.30769i | 0.549280 | + | 0.951381i | 0.998324 | + | 0.0578710i | \(0.0184312\pi\) |
−0.449044 | + | 0.893510i | \(0.648235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.30244 | + | 5.37077i | 1.19106 | + | 0.687656i | 0.958546 | − | 0.284938i | \(-0.0919729\pi\) |
0.232510 | + | 0.972594i | \(0.425306\pi\) | |||||||
\(62\) | −6.21576 | −0.789403 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.72204 | − | 1.57157i | −0.337628 | − | 0.194929i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.44637 | + | 9.43339i | 0.665380 | + | 1.15247i | 0.979182 | + | 0.202984i | \(0.0650639\pi\) |
−0.313802 | + | 0.949489i | \(0.601603\pi\) | |||||||
\(68\) | −0.866234 | −0.105046 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.20591 | − | 1.46081i | 0.263657 | − | 0.174600i | ||||
\(71\) | 5.43339i | 0.644825i | 0.946599 | + | 0.322413i | \(0.104494\pi\) | ||||
−0.946599 | + | 0.322413i | \(0.895506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.539702 | + | 0.311597i | 0.0631673 | + | 0.0364697i | 0.531251 | − | 0.847214i | \(-0.321722\pi\) |
−0.468084 | + | 0.883684i | \(0.655055\pi\) | |||||||
\(74\) | − | 7.20782i | − | 0.837892i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.23551 | + | 0.713322i | 0.141723 | + | 0.0818237i | ||||
\(77\) | 1.77849 | + | 0.886201i | 0.202678 | + | 0.100992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.00292607 | + | 0.00506811i | −0.000329209 | + | 0.000570206i | −0.866190 | − | 0.499715i | \(-0.833438\pi\) |
0.865861 | + | 0.500285i | \(0.166771\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.61015 | + | 2.08432i | −0.398674 | + | 0.230175i | ||||
\(83\) | −1.01834 | − | 1.76381i | −0.111777 | − | 0.193603i | 0.804710 | − | 0.593668i | \(-0.202321\pi\) |
−0.916487 | + | 0.400065i | \(0.868988\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.433117 | + | 0.750180i | −0.0469781 | + | 0.0813685i | ||||
\(86\) | − | 7.39020i | − | 0.796905i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.751037 | −0.0800608 | ||||||||
\(89\) | 1.22452 | + | 2.12093i | 0.129799 | + | 0.224819i | 0.923599 | − | 0.383361i | \(-0.125233\pi\) |
−0.793800 | + | 0.608179i | \(0.791900\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.93349 | − | 4.59153i | 0.726827 | − | 0.481323i | ||||
\(92\) | 4.38341 | − | 2.53076i | 0.457002 | − | 0.263850i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.99510 | + | 1.72922i | −0.308921 | + | 0.178355i | ||||
\(95\) | 1.23551 | − | 0.713322i | 0.126761 | − | 0.0731853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.23519 | − | 5.33194i | 0.937692 | − | 0.541377i | 0.0484558 | − | 0.998825i | \(-0.484570\pi\) |
0.889236 | + | 0.457449i | \(0.151237\pi\) | |||||||
\(98\) | 0.856363 | + | 6.94742i | 0.0865057 | + | 0.701795i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 5.74239 | 0.571389 | 0.285695 | − | 0.958321i | \(-0.407776\pi\) | ||||
0.285695 | + | 0.958321i | \(0.407776\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.6548i | 1.54251i | 0.636526 | + | 0.771255i | \(0.280371\pi\) | ||||
−0.636526 | + | 0.771255i | \(0.719629\pi\) | |||||||
\(104\) | −1.57157 | + | 2.72204i | −0.154105 | + | 0.266918i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.456250 | − | 0.790248i | −0.0443149 | − | 0.0767557i | ||||
\(107\) | −11.6558 | + | 6.72947i | −1.12681 | + | 0.650562i | −0.943130 | − | 0.332425i | \(-0.892133\pi\) |
−0.183677 | + | 0.982987i | \(0.558800\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.28955 | + | 10.8938i | −0.602430 | + | 1.04344i | 0.390022 | + | 0.920806i | \(0.372467\pi\) |
−0.992452 | + | 0.122634i | \(0.960866\pi\) | |||||||
\(110\) | −0.375518 | + | 0.650417i | −0.0358043 | + | 0.0620148i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.46081 | − | 2.20591i | −0.138033 | − | 0.208439i | ||||
\(113\) | 2.91695 | + | 1.68410i | 0.274404 | + | 0.158427i | 0.630887 | − | 0.775875i | \(-0.282691\pi\) |
−0.356484 | + | 0.934302i | \(0.616024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.06153i | − | 0.471990i | ||||||
\(116\) | 5.23368 | + | 3.02167i | 0.485935 | + | 0.280555i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.43820i | − | 0.776799i | ||||||
\(119\) | −1.26540 | − | 1.91083i | −0.115999 | − | 0.175166i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4359 | 0.948722 | ||||||||
\(122\) | −5.37077 | − | 9.30244i | −0.486246 | − | 0.842204i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.38301 | + | 3.10788i | 0.483408 | + | 0.279096i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.31880 | 0.560703 | 0.280352 | − | 0.959897i | \(-0.409549\pi\) | ||||
0.280352 | + | 0.959897i | \(0.409549\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.57157 | + | 2.72204i | 0.137836 | + | 0.238739i | ||||
\(131\) | −10.9728 | −0.958699 | −0.479350 | − | 0.877624i | \(-0.659127\pi\) | ||||
−0.479350 | + | 0.877624i | \(0.659127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.231319 | + | 3.76745i | 0.0200579 | + | 0.326680i | ||||
\(134\) | − | 10.8927i | − | 0.940990i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.750180 | + | 0.433117i | 0.0643274 | + | 0.0371395i | ||||
\(137\) | − | 21.2377i | − | 1.81446i | −0.420637 | − | 0.907229i | \(-0.638193\pi\) | ||
0.420637 | − | 0.907229i | \(-0.361807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.99525 | − | 5.19341i | −0.762967 | − | 0.440499i | 0.0673930 | − | 0.997727i | \(-0.478532\pi\) |
−0.830360 | + | 0.557227i | \(0.811865\pi\) | |||||||
\(140\) | −2.64078 | + | 0.162142i | −0.223187 | + | 0.0137035i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.71670 | − | 4.70546i | 0.227980 | − | 0.394873i | ||||
\(143\) | −1.18031 | + | 2.04435i | −0.0987023 | + | 0.170957i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.23368 | − | 3.02167i | 0.434634 | − | 0.250936i | ||||
\(146\) | −0.311597 | − | 0.539702i | −0.0257880 | − | 0.0446660i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.60391 | + | 6.24216i | −0.296240 | + | 0.513102i | ||||
\(149\) | − | 12.9684i | − | 1.06241i | −0.847242 | − | 0.531207i | \(-0.821739\pi\) | ||
0.847242 | − | 0.531207i | \(-0.178261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9105 | 1.86443 | 0.932217 | − | 0.361900i | \(-0.117872\pi\) | ||||
0.932217 | + | 0.361900i | \(0.117872\pi\) | |||||||
\(152\) | −0.713322 | − | 1.23551i | −0.0578581 | − | 0.100213i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.09712 | − | 1.65672i | −0.0884085 | − | 0.133502i | ||||
\(155\) | 5.38301 | − | 3.10788i | 0.432374 | − | 0.249631i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.74720 | − | 4.47285i | 0.618294 | − | 0.356972i | −0.157911 | − | 0.987453i | \(-0.550476\pi\) |
0.776204 | + | 0.630481i | \(0.217143\pi\) | |||||||
\(158\) | 0.00506811 | − | 0.00292607i | 0.000403197 | − | 0.000232786i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | − | 0.500000i | 0.0684653 | − | 0.0395285i | ||||
\(161\) | 11.9860 | + | 5.97245i | 0.944626 | + | 0.470695i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.68748 | − | 15.0472i | −0.680456 | − | 1.17858i | −0.974842 | − | 0.222898i | \(-0.928448\pi\) |
0.294386 | − | 0.955687i | \(-0.404885\pi\) | |||||||
\(164\) | 4.16864 | 0.325516 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.03667i | 0.158076i | ||||||||
\(167\) | −8.49076 | + | 14.7064i | −0.657035 | + | 1.13802i | 0.324345 | + | 0.945939i | \(0.394856\pi\) |
−0.981380 | + | 0.192079i | \(0.938477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.56033 | − | 2.70257i | −0.120025 | − | 0.207890i | ||||
\(170\) | 0.750180 | − | 0.433117i | 0.0575362 | − | 0.0332185i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.69510 | + | 6.40010i | −0.281749 | + | 0.488003i | ||||
\(173\) | 4.57540 | − | 7.92483i | 0.347861 | − | 0.602514i | −0.638008 | − | 0.770030i | \(-0.720241\pi\) |
0.985869 | + | 0.167516i | \(0.0535746\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.17997 | + | 2.36805i | −0.0891973 | + | 0.179008i | ||||
\(176\) | 0.650417 | + | 0.375518i | 0.0490270 | + | 0.0283058i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.44904i | − | 0.183564i | ||||||
\(179\) | 17.2805 | + | 9.97688i | 1.29160 | + | 0.745707i | 0.978938 | − | 0.204157i | \(-0.0654452\pi\) |
0.312664 | + | 0.949864i | \(0.398779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.6898i | − | 1.61219i | −0.591784 | − | 0.806097i | \(-0.701576\pi\) | ||
0.591784 | − | 0.806097i | \(-0.298424\pi\) | |||||||
\(182\) | −8.30034 | + | 0.509636i | −0.615262 | + | 0.0377767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.06153 | −0.373141 | ||||||||
\(185\) | 3.60391 | + | 6.24216i | 0.264965 | + | 0.458933i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.563413 | + | 0.325287i | 0.0412008 | + | 0.0237873i | ||||
\(188\) | 3.45844 | 0.252233 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.42664 | −0.103500 | ||||||||
\(191\) | 6.10266 | + | 3.52337i | 0.441573 | + | 0.254942i | 0.704265 | − | 0.709938i | \(-0.251277\pi\) |
−0.262692 | + | 0.964880i | \(0.584610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.20239 | + | 2.08260i | 0.0865498 | + | 0.149909i | 0.906051 | − | 0.423169i | \(-0.139083\pi\) |
−0.819501 | + | 0.573078i | \(0.805749\pi\) | |||||||
\(194\) | −10.6639 | −0.765622 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.73208 | − | 6.44482i | 0.195148 | − | 0.460345i | ||||
\(197\) | 1.58424i | 0.112873i | 0.998406 | + | 0.0564364i | \(0.0179738\pi\) | ||||
−0.998406 | + | 0.0564364i | \(0.982026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.71297 | + | 3.87574i | 0.475870 | + | 0.274744i | 0.718694 | − | 0.695327i | \(-0.244740\pi\) |
−0.242824 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.97305 | − | 2.87119i | −0.349903 | − | 0.202017i | ||||
\(203\) | 0.979879 | + | 15.9591i | 0.0687740 | + | 1.12011i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.08432 | − | 3.61015i | 0.145575 | − | 0.252144i | ||||
\(206\) | 7.82738 | − | 13.5574i | 0.545360 | − | 0.944591i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.72204 | − | 1.57157i | 0.188740 | − | 0.108969i | ||||
\(209\) | −0.535731 | − | 0.927914i | −0.0370573 | − | 0.0641851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.64182 | − | 11.5040i | 0.457242 | − | 0.791966i | −0.541572 | − | 0.840654i | \(-0.682171\pi\) |
0.998814 | + | 0.0486881i | \(0.0155040\pi\) | |||||||
\(212\) | 0.912500i | 0.0626707i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.4589 | 0.920034 | ||||||||
\(215\) | 3.69510 | + | 6.40010i | 0.252004 | + | 0.436483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00784 | + | 16.4144i | 0.0684164 | + | 1.11429i | ||||
\(218\) | 10.8938 | − | 6.28955i | 0.737823 | − | 0.425982i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.650417 | − | 0.375518i | 0.0438511 | − | 0.0253174i | ||||
\(221\) | 2.35792 | − | 1.36135i | 0.158611 | − | 0.0915742i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.8018 | + | 7.96848i | −0.924237 | + | 0.533609i | −0.884984 | − | 0.465621i | \(-0.845831\pi\) |
−0.0392529 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(224\) | 0.162142 | + | 2.64078i | 0.0108336 | + | 0.176444i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.68410 | − | 2.91695i | −0.112025 | − | 0.194033i | ||||
\(227\) | 13.1879 | 0.875314 | 0.437657 | − | 0.899142i | \(-0.355808\pi\) | ||||
0.437657 | + | 0.899142i | \(0.355808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.7537i | − | 1.30536i | −0.757633 | − | 0.652681i | \(-0.773644\pi\) | ||
0.757633 | − | 0.652681i | \(-0.226356\pi\) | |||||||
\(230\) | −2.53076 | + | 4.38341i | −0.166874 | + | 0.289034i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.02167 | − | 5.23368i | −0.198382 | − | 0.343608i | ||||
\(233\) | −23.8501 | + | 13.7699i | −1.56247 | + | 0.902094i | −0.565467 | + | 0.824771i | \(0.691304\pi\) |
−0.997006 | + | 0.0773231i | \(0.975363\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.72922 | − | 2.99510i | 0.112802 | − | 0.195379i | ||||
\(236\) | −4.21910 | + | 7.30769i | −0.274640 | + | 0.475690i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.140453 | + | 2.28753i | 0.00910421 | + | 0.148279i | ||||
\(239\) | −6.52234 | − | 3.76567i | −0.421895 | − | 0.243581i | 0.273993 | − | 0.961732i | \(-0.411656\pi\) |
−0.695888 | + | 0.718151i | \(0.744989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.9813i | − | 0.771785i | −0.922544 | − | 0.385892i | \(-0.873894\pi\) | ||
0.922544 | − | 0.385892i | \(-0.126106\pi\) | |||||||
\(242\) | −9.03779 | − | 5.21797i | −0.580971 | − | 0.335424i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.7415i | 0.687656i | ||||||||
\(245\) | −4.21534 | − | 5.58846i | −0.269308 | − | 0.357034i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.48415 | −0.285319 | ||||||||
\(248\) | −3.10788 | − | 5.38301i | −0.197351 | − | 0.341821i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | 30.3694 | 1.91690 | 0.958449 | − | 0.285265i | \(-0.0920816\pi\) | ||||
0.958449 | + | 0.285265i | \(0.0920816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.80139 | −0.238992 | ||||||||
\(254\) | −5.47224 | − | 3.15940i | −0.343359 | − | 0.198238i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.800054 | 0.0499060 | 0.0249530 | − | 0.999689i | \(-0.492056\pi\) | ||||
0.0249530 | + | 0.999689i | \(0.492056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.0343 | + | 1.16869i | −1.18273 | + | 0.0726190i | ||||
\(260\) | − | 3.14314i | − | 0.194929i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.50274 | + | 5.48641i | 0.587081 | + | 0.338951i | ||||
\(263\) | 20.8541i | 1.28592i | 0.765900 | + | 0.642960i | \(0.222294\pi\) | ||||
−0.765900 | + | 0.642960i | \(0.777706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.790248 | + | 0.456250i | 0.0485445 | + | 0.0280272i | ||||
\(266\) | 1.68340 | − | 3.37837i | 0.103216 | − | 0.207141i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.44637 | + | 9.43339i | −0.332690 | + | 0.576236i | ||||
\(269\) | 15.0545 | − | 26.0752i | 0.917889 | − | 1.58983i | 0.115273 | − | 0.993334i | \(-0.463226\pi\) |
0.802616 | − | 0.596497i | \(-0.203441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3296 | + | 7.11850i | −0.748970 | + | 0.432418i | −0.825322 | − | 0.564663i | \(-0.809006\pi\) |
0.0763514 | + | 0.997081i | \(0.475673\pi\) | |||||||
\(272\) | −0.433117 | − | 0.750180i | −0.0262616 | − | 0.0454864i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.6188 | + | 18.3924i | −0.641508 | + | 1.11112i | ||||
\(275\) | − | 0.751037i | − | 0.0452892i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9306 | −1.01726 | −0.508631 | − | 0.860985i | \(-0.669848\pi\) | ||||
−0.508631 | + | 0.860985i | \(0.669848\pi\) | |||||||
\(278\) | 5.19341 | + | 8.99525i | 0.311480 | + | 0.539499i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.36805 | + | 1.17997i | 0.141518 | + | 0.0705167i | ||||
\(281\) | 16.7637 | − | 9.67853i | 1.00004 | − | 0.577373i | 0.0917791 | − | 0.995779i | \(-0.470745\pi\) |
0.908260 | + | 0.418407i | \(0.137411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4542 | − | 15.2734i | 1.57254 | − | 0.907907i | 0.576685 | − | 0.816966i | \(-0.304346\pi\) |
0.995856 | − | 0.0909409i | \(-0.0289874\pi\) | |||||||
\(284\) | −4.70546 | + | 2.71670i | −0.279218 | + | 0.161206i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.04435 | − | 1.18031i | 0.120885 | − | 0.0697930i | ||||
\(287\) | 6.08958 | + | 9.19565i | 0.359457 | + | 0.542802i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.12482 | + | 14.0726i | 0.477931 | + | 0.827800i | ||||
\(290\) | −6.04334 | −0.354877 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.623194i | 0.0364697i | ||||||||
\(293\) | −0.844143 | + | 1.46210i | −0.0493154 | + | 0.0854167i | −0.889629 | − | 0.456683i | \(-0.849037\pi\) |
0.840314 | + | 0.542100i | \(0.182371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.21910 | + | 7.30769i | 0.245645 | + | 0.425470i | ||||
\(296\) | 6.24216 | − | 3.60391i | 0.362818 | − | 0.209473i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.48421 | + | 11.2310i | −0.375620 | + | 0.650593i | ||||
\(299\) | −7.95455 | + | 13.7777i | −0.460024 | + | 0.796784i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.5159 | + | 1.19826i | −1.12488 | + | 0.0690667i | ||||
\(302\) | −19.8411 | − | 11.4553i | −1.14173 | − | 0.659177i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.42664i | 0.0818237i | ||||||||
\(305\) | 9.30244 | + | 5.37077i | 0.532656 | + | 0.307529i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.15873i | − | 0.408570i | −0.978911 | − | 0.204285i | \(-0.934513\pi\) | ||
0.978911 | − | 0.204285i | \(-0.0654869\pi\) | |||||||
\(308\) | 0.121775 | + | 1.98332i | 0.00693876 | + | 0.113010i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.21576 | −0.353032 | ||||||||
\(311\) | −12.3177 | − | 21.3350i | −0.698475 | − | 1.20979i | −0.968995 | − | 0.247080i | \(-0.920529\pi\) |
0.270520 | − | 0.962714i | \(-0.412804\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0002 | − | 6.35095i | −0.621766 | − | 0.358977i | 0.155790 | − | 0.987790i | \(-0.450208\pi\) |
−0.777556 | + | 0.628813i | \(0.783541\pi\) | |||||||
\(314\) | −8.94569 | −0.504835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.00585214 | −0.000329209 | ||||||||
\(317\) | −22.1158 | − | 12.7685i | −1.24214 | − | 0.717152i | −0.272614 | − | 0.962123i | \(-0.587888\pi\) |
−0.969530 | + | 0.244971i | \(0.921222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.26938 | − | 3.93069i | −0.127061 | − | 0.220076i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.39392 | − | 11.1653i | −0.412047 | − | 0.622217i | ||||
\(323\) | 1.23581i | 0.0687622i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.72204 | − | 1.57157i | −0.150992 | − | 0.0871751i | ||||
\(326\) | 17.3750i | 0.962310i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.61015 | − | 2.08432i | −0.199337 | − | 0.115087i | ||||
\(329\) | 5.05212 | + | 7.62901i | 0.278532 | + | 0.420601i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.01463 | − | 12.1497i | 0.385559 | − | 0.667807i | −0.606288 | − | 0.795245i | \(-0.707342\pi\) |
0.991847 | + | 0.127438i | \(0.0406754\pi\) | |||||||
\(332\) | 1.01834 | − | 1.76381i | 0.0558884 | − | 0.0968016i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7064 | − | 8.49076i | 0.804700 | − | 0.464594i | ||||
\(335\) | 5.44637 | + | 9.43339i | 0.297567 | + | 0.515401i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7946 | − | 23.8930i | 0.751442 | − | 1.30154i | −0.195682 | − | 0.980667i | \(-0.562692\pi\) |
0.947124 | − | 0.320868i | \(-0.103975\pi\) | |||||||
\(338\) | 3.12066i | 0.169741i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.866234 | −0.0469781 | ||||||||
\(341\) | −2.33413 | − | 4.04284i | −0.126400 | − | 0.218932i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2077 | − | 3.38793i | 0.983126 | − | 0.182931i | ||||
\(344\) | 6.40010 | − | 3.69510i | 0.345070 | − | 0.199226i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.92483 | + | 4.57540i | −0.426041 | + | 0.245975i | ||||
\(347\) | 10.1962 | − | 5.88676i | 0.547359 | − | 0.316018i | −0.200697 | − | 0.979653i | \(-0.564321\pi\) |
0.748056 | + | 0.663635i | \(0.230987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.3085 | + | 14.6119i | −1.35473 | + | 0.782155i | −0.988908 | − | 0.148530i | \(-0.952546\pi\) |
−0.365824 | + | 0.930684i | \(0.619213\pi\) | |||||||
\(350\) | 2.20591 | − | 1.46081i | 0.117911 | − | 0.0780835i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.375518 | − | 0.650417i | −0.0200152 | − | 0.0346673i | ||||
\(353\) | −0.301856 | −0.0160662 | −0.00803309 | − | 0.999968i | \(-0.502557\pi\) | ||||
−0.00803309 | + | 0.999968i | \(0.502557\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.43339i | 0.288375i | ||||||||
\(356\) | −1.22452 | + | 2.12093i | −0.0648995 | + | 0.112409i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.97688 | − | 17.2805i | −0.527294 | − | 0.913301i | ||||
\(359\) | −22.8586 | + | 13.1974i | −1.20643 | + | 0.696534i | −0.961978 | − | 0.273126i | \(-0.911942\pi\) |
−0.244455 | + | 0.969661i | \(0.578609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.48234 | + | 14.6918i | −0.446439 | + | 0.773255i | ||||
\(362\) | −10.8449 | + | 18.7840i | −0.569996 | + | 0.987263i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.44312 | + | 3.70881i | 0.390126 | + | 0.194395i | ||||
\(365\) | 0.539702 | + | 0.311597i | 0.0282493 | + | 0.0163097i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.73338i | 0.508079i | 0.967194 | + | 0.254039i | \(0.0817592\pi\) | ||||
−0.967194 | + | 0.254039i | \(0.918241\pi\) | |||||||
\(368\) | 4.38341 | + | 2.53076i | 0.228501 | + | 0.131925i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 7.20782i | − | 0.374717i | ||||||
\(371\) | −2.01289 | + | 1.33299i | −0.104504 | + | 0.0692052i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2585 | −0.997168 | −0.498584 | − | 0.866841i | \(-0.666146\pi\) | ||||
−0.498584 | + | 0.866841i | \(0.666146\pi\) | |||||||
\(374\) | −0.325287 | − | 0.563413i | −0.0168202 | − | 0.0291334i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.99510 | − | 1.72922i | −0.154460 | − | 0.0891777i | ||||
\(377\) | −18.9951 | −0.978296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.4361 | −1.51203 | −0.756015 | − | 0.654554i | \(-0.772856\pi\) | ||||
−0.756015 | + | 0.654554i | \(0.772856\pi\) | |||||||
\(380\) | 1.23551 | + | 0.713322i | 0.0633804 | + | 0.0365927i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.52337 | − | 6.10266i | −0.180271 | − | 0.312239i | ||||
\(383\) | −17.8073 | −0.909912 | −0.454956 | − | 0.890514i | \(-0.650345\pi\) | ||||
−0.454956 | + | 0.890514i | \(0.650345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.77849 | + | 0.886201i | 0.0906405 | + | 0.0451650i | ||||
\(386\) | − | 2.40478i | − | 0.122400i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.23519 | + | 5.33194i | 0.468846 | + | 0.270688i | ||||
\(389\) | − | 12.5302i | − | 0.635306i | −0.948207 | − | 0.317653i | \(-0.897105\pi\) | ||
0.948207 | − | 0.317653i | \(-0.102895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.79706 | + | 2.19223i | 0.192026 | + | 0.110866i | ||||
\(392\) | −5.58846 | + | 4.21534i | −0.282260 | + | 0.212907i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.792122 | − | 1.37200i | 0.0399066 | − | 0.0691202i | ||||
\(395\) | −0.00292607 | + | 0.00506811i | −0.000147227 | + | 0.000255004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.6549 | + | 15.3892i | −1.33777 | + | 0.772361i | −0.986476 | − | 0.163905i | \(-0.947591\pi\) |
−0.351293 | + | 0.936266i | \(0.614258\pi\) | |||||||
\(398\) | −3.87574 | − | 6.71297i | −0.194273 | − | 0.336491i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 7.17154i | 0.358129i | 0.983837 | + | 0.179065i | \(0.0573071\pi\) | ||||
−0.983837 | + | 0.179065i | \(0.942693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5370 | −0.973208 | ||||||||
\(404\) | 2.87119 | + | 4.97305i | 0.142847 | + | 0.247419i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.13096 | − | 14.3109i | 0.353903 | − | 0.710240i | ||||
\(407\) | 4.68809 | − | 2.70667i | 0.232380 | − | 0.134165i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.0919 | − | 13.3321i | 1.14182 | − | 0.659232i | 0.194942 | − | 0.980815i | \(-0.437548\pi\) |
0.946881 | + | 0.321583i | \(0.104215\pi\) | |||||||
\(410\) | −3.61015 | + | 2.08432i | −0.178293 | + | 0.102937i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.5574 | + | 7.82738i | −0.667926 | + | 0.385627i | ||||
\(413\) | −22.2834 | + | 1.36819i | −1.09649 | + | 0.0673241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.01834 | − | 1.76381i | −0.0499881 | − | 0.0865820i | ||||
\(416\) | −3.14314 | −0.154105 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.07146i | 0.0524070i | ||||||||
\(419\) | −12.2128 | + | 21.1533i | −0.596636 | + | 1.03340i | 0.396677 | + | 0.917958i | \(0.370163\pi\) |
−0.993314 | + | 0.115446i | \(0.963170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.84702 | + | 15.3235i | 0.431177 | + | 0.746821i | 0.996975 | − | 0.0777229i | \(-0.0247649\pi\) |
−0.565798 | + | 0.824544i | \(0.691432\pi\) | |||||||
\(422\) | −11.5040 | + | 6.64182i | −0.560005 | + | 0.323319i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.456250 | − | 0.790248i | 0.0221574 | − | 0.0383778i | ||||
\(425\) | −0.433117 | + | 0.750180i | −0.0210093 | + | 0.0363891i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.6949 | + | 15.6913i | −1.14667 | + | 0.759356i | ||||
\(428\) | −11.6558 | − | 6.72947i | −0.563403 | − | 0.325281i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 7.39020i | − | 0.356387i | ||||||
\(431\) | 20.5184 | + | 11.8463i | 0.988335 | + | 0.570616i | 0.904776 | − | 0.425887i | \(-0.140038\pi\) |
0.0835591 | + | 0.996503i | \(0.473371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.1077i | − | 1.15854i | −0.815135 | − | 0.579271i | \(-0.803337\pi\) | ||
0.815135 | − | 0.579271i | \(-0.196663\pi\) | |||||||
\(434\) | 7.33441 | − | 14.7192i | 0.352063 | − | 0.706547i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.5791 | −0.602430 | ||||||||
\(437\) | −3.61050 | − | 6.25357i | −0.172714 | − | 0.299149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.925536 | − | 0.534359i | −0.0441734 | − | 0.0255035i | 0.477751 | − | 0.878495i | \(-0.341452\pi\) |
−0.521924 | + | 0.852992i | \(0.674786\pi\) | |||||||
\(440\) | −0.751037 | −0.0358043 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.72270 | −0.129505 | ||||||||
\(443\) | 26.8115 | + | 15.4796i | 1.27385 | + | 0.735459i | 0.975711 | − | 0.219062i | \(-0.0702998\pi\) |
0.298142 | + | 0.954522i | \(0.403633\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.22452 | + | 2.12093i | 0.0580479 | + | 0.100542i | ||||
\(446\) | 15.9370 | 0.754637 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.17997 | − | 2.36805i | 0.0557483 | − | 0.111880i | ||||
\(449\) | 22.4824i | 1.06101i | 0.847682 | + | 0.530505i | \(0.177998\pi\) | ||||
−0.847682 | + | 0.530505i | \(0.822002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.71135 | − | 1.56540i | −0.127673 | − | 0.0737119i | ||||
\(452\) | 3.36820i | 0.158427i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.4211 | − | 6.59397i | −0.536018 | − | 0.309470i | ||||
\(455\) | 6.93349 | − | 4.59153i | 0.325047 | − | 0.215254i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.6626 | + | 35.7886i | −0.966554 | + | 1.67412i | −0.261174 | + | 0.965292i | \(0.584110\pi\) |
−0.705380 | + | 0.708829i | \(0.749224\pi\) | |||||||
\(458\) | −9.87685 | + | 17.1072i | −0.461515 | + | 0.799367i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.38341 | − | 2.53076i | 0.204378 | − | 0.117997i | ||||
\(461\) | 13.0109 | + | 22.5356i | 0.605979 | + | 1.04959i | 0.991896 | + | 0.127052i | \(0.0405516\pi\) |
−0.385917 | + | 0.922533i | \(0.626115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.54762 | + | 9.60876i | −0.257820 | + | 0.446557i | −0.965658 | − | 0.259818i | \(-0.916337\pi\) |
0.707838 | + | 0.706375i | \(0.249671\pi\) | |||||||
\(464\) | 6.04334i | 0.280555i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.5397 | 1.27575 | ||||||||
\(467\) | −18.7366 | − | 32.4527i | −0.867025 | − | 1.50173i | −0.865022 | − | 0.501734i | \(-0.832696\pi\) |
−0.00200339 | − | 0.999998i | \(-0.500638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.7653 | + | 1.76617i | −1.32826 | + | 0.0815543i | ||||
\(470\) | −2.99510 | + | 1.72922i | −0.138154 | + | 0.0797630i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.30769 | − | 4.21910i | 0.336364 | − | 0.194200i | ||||
\(473\) | 4.80671 | − | 2.77515i | 0.221013 | − | 0.127602i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.23551 | − | 0.713322i | 0.0566891 | − | 0.0327295i | ||||
\(476\) | 1.02213 | − | 2.05129i | 0.0468492 | − | 0.0940206i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.76567 | + | 6.52234i | 0.172238 | + | 0.298325i | ||||
\(479\) | −13.9632 | −0.637996 | −0.318998 | − | 0.947755i | \(-0.603346\pi\) | ||||
−0.318998 | + | 0.947755i | \(0.603346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 22.6552i | − | 1.03299i | ||||||
\(482\) | −5.99066 | + | 10.3761i | −0.272867 | + | 0.472620i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.21797 | + | 9.03779i | 0.237181 | + | 0.410809i | ||||
\(485\) | 9.23519 | − | 5.33194i | 0.419349 | − | 0.242111i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.90704 | − | 3.30309i | 0.0864163 | − | 0.149677i | −0.819578 | − | 0.572968i | \(-0.805792\pi\) |
0.905994 | + | 0.423291i | \(0.139125\pi\) | |||||||
\(488\) | 5.37077 | − | 9.30244i | 0.243123 | − | 0.421102i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.856363 | + | 6.94742i | 0.0386865 | + | 0.313852i | ||||
\(491\) | −23.7383 | − | 13.7053i | −1.07129 | − | 0.618512i | −0.142760 | − | 0.989757i | \(-0.545598\pi\) |
−0.928535 | + | 0.371245i | \(0.878931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.23494i | 0.235770i | ||||||||
\(494\) | 3.88339 | + | 2.24207i | 0.174722 | + | 0.100876i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.21576i | 0.279096i | ||||||||
\(497\) | −12.8666 | − | 6.41124i | −0.577144 | − | 0.287584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7894 | 1.15449 | 0.577247 | − | 0.816570i | \(-0.304127\pi\) | ||||
0.577247 | + | 0.816570i | \(0.304127\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.3006 | − | 15.1847i | −1.17386 | − | 0.677726i | ||||
\(503\) | −17.3517 | −0.773675 | −0.386838 | − | 0.922148i | \(-0.626433\pi\) | ||||
−0.386838 | + | 0.922148i | \(0.626433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.74239 | 0.255533 | ||||||||
\(506\) | 3.29210 | + | 1.90070i | 0.146352 | + | 0.0844963i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.15940 | + | 5.47224i | 0.140176 | + | 0.242792i | ||||
\(509\) | −28.1334 | −1.24699 | −0.623497 | − | 0.781826i | \(-0.714288\pi\) | ||||
−0.623497 | + | 0.781826i | \(0.714288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.37471 | + | 0.910367i | −0.0608136 | + | 0.0402723i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.692867 | − | 0.400027i | −0.0305611 | − | 0.0176444i | ||||
\(515\) | 15.6548i | 0.689831i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.24943 | − | 1.29871i | −0.0989298 | − | 0.0571171i | ||||
\(518\) | 17.0685 | + | 8.50501i | 0.749947 | + | 0.373689i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.57157 | + | 2.72204i | −0.0689179 | + | 0.119369i | ||||
\(521\) | −3.97534 | + | 6.88549i | −0.174163 | + | 0.301659i | −0.939871 | − | 0.341529i | \(-0.889055\pi\) |
0.765708 | + | 0.643188i | \(0.222389\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.614490 | − | 0.354776i | 0.0268698 | − | 0.0155133i | −0.486505 | − | 0.873678i | \(-0.661728\pi\) |
0.513375 | + | 0.858165i | \(0.328395\pi\) | |||||||
\(524\) | −5.48641 | − | 9.50274i | −0.239675 | − | 0.415129i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.4271 | − | 18.0602i | 0.454641 | − | 0.787462i | ||||
\(527\) | 5.38430i | 0.234544i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.61907 | −0.113873 | ||||||||
\(530\) | −0.456250 | − | 0.790248i | −0.0198182 | − | 0.0343262i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.14705 | + | 2.08405i | −0.136442 | + | 0.0903552i | ||||
\(533\) | −11.3472 | + | 6.55131i | −0.491502 | + | 0.283769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6558 | + | 6.72947i | −0.503923 | + | 0.290940i | ||||
\(536\) | 9.43339 | − | 5.44637i | 0.407461 | − | 0.235247i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.0752 | + | 15.0545i | −1.12418 | + | 0.649046i | ||||
\(539\) | −4.19714 | + | 3.16588i | −0.180784 | + | 0.136364i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.152089 | − | 0.263426i | −0.00653882 | − | 0.0113256i | 0.862737 | − | 0.505652i | \(-0.168748\pi\) |
−0.869276 | + | 0.494327i | \(0.835415\pi\) | |||||||
\(542\) | 14.2370 | 0.611532 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.866234i | 0.0371395i | ||||||||
\(545\) | −6.28955 | + | 10.8938i | −0.269415 | + | 0.466640i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.14876 | + | 7.18586i | 0.177388 | + | 0.307245i | 0.940985 | − | 0.338448i | \(-0.109902\pi\) |
−0.763597 | + | 0.645693i | \(0.776569\pi\) | |||||||
\(548\) | 18.3924 | − | 10.6188i | 0.785684 | − | 0.453615i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.375518 | + | 0.650417i | −0.0160122 | + | 0.0277339i | ||||
\(551\) | 4.31085 | − | 7.46661i | 0.183648 | − | 0.318088i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.00854886 | − | 0.0129093i | −0.000363535 | − | 0.000548959i | ||||
\(554\) | 14.6623 | + | 8.46531i | 0.622943 | + | 0.359657i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 10.3868i | − | 0.440499i | ||||||
\(557\) | 2.70966 | + | 1.56442i | 0.114812 | + | 0.0662867i | 0.556306 | − | 0.830977i | \(-0.312218\pi\) |
−0.441494 | + | 0.897264i | \(0.645551\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.2284i | − | 0.982458i | ||||||
\(560\) | −1.46081 | − | 2.20591i | −0.0617304 | − | 0.0932167i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.3571 | −0.816528 | ||||||||
\(563\) | −10.4373 | − | 18.0780i | −0.439881 | − | 0.761897i | 0.557799 | − | 0.829976i | \(-0.311646\pi\) |
−0.997680 | + | 0.0680796i | \(0.978313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.91695 | + | 1.68410i | 0.122717 | + | 0.0708507i | ||||
\(566\) | −30.5467 | −1.28397 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.43339 | 0.227980 | ||||||||
\(569\) | −20.0446 | − | 11.5727i | −0.840313 | − | 0.485155i | 0.0170577 | − | 0.999855i | \(-0.494570\pi\) |
−0.857371 | + | 0.514700i | \(0.827903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3844 | + | 21.4504i | 0.518271 | + | 0.897671i | 0.999775 | + | 0.0212272i | \(0.00675732\pi\) |
−0.481504 | + | 0.876444i | \(0.659909\pi\) | |||||||
\(572\) | −2.36061 | −0.0987023 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.675912 | − | 11.0085i | −0.0282120 | − | 0.459484i | ||||
\(575\) | − | 5.06153i | − | 0.211080i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.6396 | + | 18.2671i | 1.31717 | + | 0.760470i | 0.983273 | − | 0.182138i | \(-0.0583019\pi\) |
0.333900 | + | 0.942609i | \(0.391635\pi\) | |||||||
\(578\) | − | 16.2496i | − | 0.675896i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.23368 | + | 3.02167i | 0.217317 | + | 0.125468i | ||||
\(581\) | 5.37840 | − | 0.330230i | 0.223134 | − | 0.0137003i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.342660 | − | 0.593505i | 0.0141915 | − | 0.0245805i | ||||
\(584\) | 0.311597 | − | 0.539702i | 0.0128940 | − | 0.0223330i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.46210 | − | 0.844143i | 0.0603987 | − | 0.0348712i | ||||
\(587\) | 12.1405 | + | 21.0280i | 0.501092 | + | 0.867918i | 0.999999 | + | 0.00126186i | \(0.000401662\pi\) |
−0.498907 | + | 0.866656i | \(0.666265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.43384 | − | 7.67964i | 0.182693 | − | 0.316434i | ||||
\(590\) | − | 8.43820i | − | 0.347395i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.20782 | −0.296240 | ||||||||
\(593\) | −19.7837 | − | 34.2664i | −0.812419 | − | 1.40715i | −0.911166 | − | 0.412039i | \(-0.864817\pi\) |
0.0987467 | − | 0.995113i | \(-0.468517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.26540 | − | 1.91083i | −0.0518764 | − | 0.0783365i | ||||
\(596\) | 11.2310 | − | 6.48421i | 0.460039 | − | 0.265604i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.7777 | − | 7.95455i | 0.563411 | − | 0.325286i | ||||
\(599\) | −35.4500 | + | 20.4671i | −1.44845 | + | 0.836263i | −0.998389 | − | 0.0567354i | \(-0.981931\pi\) |
−0.450060 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.48642 | − | 2.59023i | 0.183005 | − | 0.105658i | −0.405699 | − | 0.914007i | \(-0.632972\pi\) |
0.588704 | + | 0.808349i | \(0.299639\pi\) | |||||||
\(602\) | 17.5004 | + | 8.72021i | 0.713262 | + | 0.355409i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.4553 | + | 19.8411i | 0.466108 | + | 0.807323i | ||||
\(605\) | 10.4359 | 0.424281 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.09536i | − | 0.125637i | −0.998025 | − | 0.0628183i | \(-0.979991\pi\) | ||
0.998025 | − | 0.0628183i | \(-0.0200089\pi\) | |||||||
\(608\) | 0.713322 | − | 1.23551i | 0.0289290 | − | 0.0501066i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.37077 | − | 9.30244i | −0.217456 | − | 0.376645i | ||||
\(611\) | −9.41402 | + | 5.43519i | −0.380850 | + | 0.219884i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.39906 | + | 2.42324i | −0.0565075 | + | 0.0978739i | −0.892895 | − | 0.450264i | \(-0.851330\pi\) |
0.836388 | + | 0.548138i | \(0.184663\pi\) | |||||||
\(614\) | −3.57936 | + | 6.19964i | −0.144451 | + | 0.250197i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.886201 | − | 1.77849i | 0.0357060 | − | 0.0716576i | ||||
\(617\) | 20.0878 | + | 11.5977i | 0.808706 | + | 0.466906i | 0.846506 | − | 0.532379i | \(-0.178702\pi\) |
−0.0378006 | + | 0.999285i | \(0.512035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.82235i | − | 0.394793i | −0.980324 | − | 0.197397i | \(-0.936751\pi\) | ||
0.980324 | − | 0.197397i | \(-0.0632487\pi\) | |||||||
\(620\) | 5.38301 | + | 3.10788i | 0.216187 | + | 0.124816i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.6355i | 0.987793i | ||||||||
\(623\) | −6.46738 | + | 0.397093i | −0.259110 | + | 0.0159092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.35095 | + | 11.0002i | 0.253835 | + | 0.439655i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.74720 | + | 4.47285i | 0.309147 | + | 0.178486i | ||||
\(629\) | −6.24366 | −0.248951 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4402 | 1.05257 | 0.526285 | − | 0.850308i | \(-0.323585\pi\) | ||||
0.526285 | + | 0.850308i | \(0.323585\pi\) | |||||||
\(632\) | 0.00506811 | + | 0.00292607i | 0.000201598 | + | 0.000116393i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.7685 | + | 22.1158i | 0.507103 | + | 0.878329i | ||||
\(635\) | 6.31880 | 0.250754 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.69167 | + | 21.8367i | 0.106648 | + | 0.865203i | ||||
\(638\) | 4.53877i | 0.179692i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | 27.8267i | 1.09909i | 0.835465 | + | 0.549543i | \(0.185198\pi\) | ||||
−0.835465 | + | 0.549543i | \(0.814802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.4628 | + | 21.0518i | 1.43795 | + | 0.830203i | 0.997707 | − | 0.0676745i | \(-0.0215580\pi\) |
0.440246 | + | 0.897877i | \(0.354891\pi\) | |||||||
\(644\) | 0.820687 | + | 13.3664i | 0.0323396 | + | 0.526709i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.617904 | − | 1.07024i | 0.0243111 | − | 0.0421081i | ||||
\(647\) | 11.5301 | − | 19.9708i | 0.453296 | − | 0.785132i | −0.545292 | − | 0.838246i | \(-0.683581\pi\) |
0.998588 | + | 0.0531139i | \(0.0169146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.48835 | − | 3.16870i | 0.215436 | − | 0.124382i | ||||
\(650\) | 1.57157 | + | 2.72204i | 0.0616421 | + | 0.106767i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.68748 | − | 15.0472i | 0.340228 | − | 0.589292i | ||||
\(653\) | − | 25.7997i | − | 1.00962i | −0.863230 | − | 0.504810i | \(-0.831563\pi\) | ||
0.863230 | − | 0.504810i | \(-0.168437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9728 | −0.428743 | ||||||||
\(656\) | 2.08432 | + | 3.61015i | 0.0813790 | + | 0.140953i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.560759 | − | 9.13298i | −0.0218607 | − | 0.356040i | ||||
\(659\) | −25.3231 | + | 14.6203i | −0.986447 | + | 0.569525i | −0.904210 | − | 0.427088i | \(-0.859540\pi\) |
−0.0822364 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.4429 | − | 12.9574i | 0.872926 | − | 0.503984i | 0.00460675 | − | 0.999989i | \(-0.498534\pi\) |
0.868320 | + | 0.496005i | \(0.165200\pi\) | |||||||
\(662\) | −12.1497 | + | 7.01463i | −0.472211 | + | 0.272631i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.76381 | + | 1.01834i | −0.0684491 | + | 0.0395191i | ||||
\(665\) | 0.231319 | + | 3.76745i | 0.00897017 | + | 0.146096i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2943 | − | 26.4904i | −0.592196 | − | 1.02571i | ||||
\(668\) | −16.9815 | −0.657035 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 10.8927i | − | 0.420823i | ||||||
\(671\) | 4.03364 | − | 6.98648i | 0.155717 | − | 0.269710i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.62323 | − | 8.00767i | −0.178212 | − | 0.308673i | 0.763056 | − | 0.646332i | \(-0.223698\pi\) |
−0.941268 | + | 0.337660i | \(0.890365\pi\) | |||||||
\(674\) | −23.8930 | + | 13.7946i | −0.920325 | + | 0.531350i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.56033 | − | 2.70257i | 0.0600127 | − | 0.103945i | ||||
\(677\) | 12.3613 | − | 21.4103i | 0.475082 | − | 0.822866i | −0.524511 | − | 0.851404i | \(-0.675752\pi\) |
0.999593 | + | 0.0285376i | \(0.00908502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.72906 | + | 28.1610i | 0.0663554 | + | 1.08072i | ||||
\(680\) | 0.750180 | + | 0.433117i | 0.0287681 | + | 0.0166093i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.66827i | 0.178757i | ||||||||
\(683\) | 26.9472 | + | 15.5580i | 1.03111 | + | 0.595309i | 0.917301 | − | 0.398194i | \(-0.130363\pi\) |
0.113804 | + | 0.993503i | \(0.463696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.2377i | − | 0.811451i | ||||||
\(686\) | −17.4623 | − | 6.16984i | −0.666715 | − | 0.235565i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.39020 | −0.281749 | ||||||||
\(689\) | −1.43406 | − | 2.48386i | −0.0546333 | − | 0.0946276i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.9609 | + | 16.1432i | 1.06368 | + | 0.614118i | 0.926449 | − | 0.376421i | \(-0.122845\pi\) |
0.137235 | + | 0.990539i | \(0.456179\pi\) | |||||||
\(692\) | 9.15080 | 0.347861 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.7735 | −0.446917 | ||||||||
\(695\) | −8.99525 | − | 5.19341i | −0.341209 | − | 0.196997i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.80551 | + | 3.12723i | 0.0683885 | + | 0.118452i | ||||
\(698\) | 29.2237 | 1.10613 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.64078 | + | 0.162142i | −0.0998120 | + | 0.00612839i | ||||
\(701\) | 26.3883i | 0.996673i | 0.866984 | + | 0.498337i | \(0.166056\pi\) | ||||
−0.866984 | + | 0.498337i | \(0.833944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.90534 | + | 5.14150i | 0.335871 | + | 0.193915i | ||||
\(704\) | 0.751037i | 0.0283058i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.261415 | + | 0.150928i | 0.00983849 | + | 0.00568025i | ||||
\(707\) | −6.77585 | + | 13.5983i | −0.254832 | + | 0.511416i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.53937 | − | 7.86242i | 0.170480 | − | 0.295279i | −0.768108 | − | 0.640320i | \(-0.778802\pi\) |
0.938588 | + | 0.345041i | \(0.112135\pi\) | |||||||
\(710\) | 2.71670 | − | 4.70546i | 0.101956 | − | 0.176593i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.12093 | − | 1.22452i | 0.0794854 | − | 0.0458909i | ||||
\(713\) | −15.7306 | − | 27.2462i | −0.589117 | − | 1.02038i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.18031 | + | 2.04435i | −0.0441410 | + | 0.0764545i | ||||
\(716\) | 19.9538i | 0.745707i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.3949 | 0.985048 | ||||||||
\(719\) | −19.1759 | − | 33.2136i | −0.715140 | − | 1.23866i | −0.962906 | − | 0.269839i | \(-0.913030\pi\) |
0.247766 | − | 0.968820i | \(-0.420304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.0713 | − | 18.4722i | −1.38061 | − | 0.687939i | ||||
\(722\) | 14.6918 | − | 8.48234i | 0.546774 | − | 0.315680i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.7840 | − | 10.8449i | 0.698100 | − | 0.403048i | ||||
\(725\) | 5.23368 | − | 3.02167i | 0.194374 | − | 0.112222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.55880 | − | 4.94142i | 0.317428 | − | 0.183267i | −0.332817 | − | 0.942991i | \(-0.607999\pi\) |
0.650246 | + | 0.759724i | \(0.274666\pi\) | |||||||
\(728\) | −4.59153 | − | 6.93349i | −0.170173 | − | 0.256972i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.311597 | − | 0.539702i | −0.0115327 | − | 0.0199753i | ||||
\(731\) | −6.40164 | −0.236773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.99187i | − | 0.258251i | −0.991628 | − | 0.129125i | \(-0.958783\pi\) | ||
0.991628 | − | 0.129125i | \(-0.0412169\pi\) | |||||||
\(734\) | 4.86669 | − | 8.42936i | 0.179633 | − | 0.311133i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.53076 | − | 4.38341i | −0.0932852 | − | 0.161575i | ||||
\(737\) | 7.08483 | − | 4.09043i | 0.260973 | − | 0.150673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.75535 | − | 16.8968i | 0.358856 | − | 0.621558i | −0.628914 | − | 0.777475i | \(-0.716500\pi\) |
0.987770 | + | 0.155918i | \(0.0498334\pi\) | |||||||
\(740\) | −3.60391 | + | 6.24216i | −0.132482 | + | 0.229466i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.40971 | − | 0.147955i | 0.0884632 | − | 0.00543158i | ||||
\(743\) | −33.4098 | − | 19.2892i | −1.22569 | − | 0.707651i | −0.259563 | − | 0.965726i | \(-0.583578\pi\) |
−0.966125 | + | 0.258075i | \(0.916912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12.9684i | − | 0.475126i | ||||||
\(746\) | 16.6784 | + | 9.62926i | 0.610638 | + | 0.352552i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.650573i | 0.0237873i | ||||||||
\(749\) | −2.18226 | − | 35.5421i | −0.0797380 | − | 1.29868i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.7427 | −0.720423 | −0.360211 | − | 0.932871i | \(-0.617295\pi\) | ||||
−0.360211 | + | 0.932871i | \(0.617295\pi\) | |||||||
\(752\) | 1.72922 | + | 2.99510i | 0.0630582 | + | 0.109220i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.4502 | + | 9.49753i | 0.599081 | + | 0.345880i | ||||
\(755\) | 22.9105 | 0.833800 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2004 | −0.770540 | −0.385270 | − | 0.922804i | \(-0.625892\pi\) | ||||
−0.385270 | + | 0.922804i | \(0.625892\pi\) | |||||||
\(758\) | 25.4924 | + | 14.7180i | 0.925926 | + | 0.534584i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.713322 | − | 1.23551i | −0.0258749 | − | 0.0448167i | ||||
\(761\) | −1.39505 | −0.0505706 | −0.0252853 | − | 0.999680i | \(-0.508049\pi\) | ||||
−0.0252853 | + | 0.999680i | \(0.508049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3757 | − | 27.7484i | −0.665244 | − | 1.00456i | ||||
\(764\) | 7.04674i | 0.254942i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.4216 | + | 8.90367i | 0.557205 | + | 0.321703i | ||||
\(767\) | − | 26.5224i | − | 0.957670i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8209 | − | 6.24747i | −0.390213 | − | 0.225289i | 0.292040 | − | 0.956406i | \(-0.405666\pi\) |
−0.682252 | + | 0.731117i | \(0.738999\pi\) | |||||||
\(770\) | −1.09712 | − | 1.65672i | −0.0395375 | − | 0.0597040i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.20239 | + | 2.08260i | −0.0432749 | + | 0.0749543i | ||||
\(773\) | 19.4887 | − | 33.7554i | 0.700960 | − | 1.21410i | −0.267169 | − | 0.963650i | \(-0.586088\pi\) |
0.968130 | − | 0.250449i | \(-0.0805783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.38301 | − | 3.10788i | 0.193363 | − | 0.111638i | ||||
\(776\) | −5.33194 | − | 9.23519i | −0.191406 | − | 0.331524i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.26510 | + | 10.8515i | −0.224615 | + | 0.389044i | ||||
\(779\) | − | 5.94717i | − | 0.213079i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.08068 | 0.146018 | ||||||||
\(782\) | −2.19223 | − | 3.79706i | −0.0783941 | − | 0.135783i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.94742 | − | 0.856363i | 0.248122 | − | 0.0305844i | ||||
\(785\) | 7.74720 | − | 4.47285i | 0.276509 | − | 0.159643i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.6682 | + | 14.2422i | −0.879326 | + | 0.507679i | −0.870436 | − | 0.492281i | \(-0.836163\pi\) |
−0.00888998 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(788\) | −1.37200 | + | 0.792122i | −0.0488753 | + | 0.0282182i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.00506811 | − | 0.00292607i | 0.000180315 | − | 0.000104105i | ||||
\(791\) | −7.42996 | + | 4.92030i | −0.264179 | + | 0.174946i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8811 | − | 29.2389i | −0.599465 | − | 1.03830i | ||||
\(794\) | 30.7784 | 1.09228 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.75147i | 0.274744i | ||||||||
\(797\) | −3.94399 | + | 6.83119i | −0.139703 | + | 0.241973i | −0.927384 | − | 0.374110i | \(-0.877948\pi\) |
0.787681 | + | 0.616083i | \(0.211282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.49791 | + | 2.59445i | 0.0529922 | + | 0.0917852i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.58577 | − | 6.21073i | 0.126618 | − | 0.219309i | ||||
\(803\) | 0.234021 | − | 0.405336i | 0.00825841 | − | 0.0143040i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.9860 | + | 5.97245i | 0.422450 | + | 0.210501i | ||||
\(806\) | 16.9196 | + | 9.76851i | 0.595966 | + | 0.344081i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 5.74239i | − | 0.202017i | ||||||
\(809\) | −2.59994 | − | 1.50108i | −0.0914092 | − | 0.0527751i | 0.453599 | − | 0.891206i | \(-0.350140\pi\) |
−0.545008 | + | 0.838431i | \(0.683473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.71594i | − | 0.270943i | −0.990781 | − | 0.135472i | \(-0.956745\pi\) | ||
0.990781 | − | 0.135472i | \(-0.0432549\pi\) | |||||||
\(812\) | −13.3311 | + | 8.82816i | −0.467828 | + | 0.309808i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.41334 | −0.189737 | ||||||||
\(815\) | −8.68748 | − | 15.0472i | −0.304309 | − | 0.527079i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.13067 | + | 5.27159i | 0.319442 | + | 0.184430i | ||||
\(818\) | −26.6643 | −0.932295 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.16864 | 0.145575 | ||||||||
\(821\) | 42.1560 | + | 24.3388i | 1.47125 | + | 0.849429i | 0.999479 | − | 0.0322902i | \(-0.0102801\pi\) |
0.471775 | + | 0.881719i | \(0.343613\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3935 | + | 42.2508i | 0.850304 | + | 1.47277i | 0.880934 | + | 0.473238i | \(0.156915\pi\) |
−0.0306307 | + | 0.999531i | \(0.509752\pi\) | |||||||
\(824\) | 15.6548 | 0.545360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.9821 | + | 9.95682i | 0.695266 | + | 0.346442i | ||||
\(827\) | 28.6190i | 0.995181i | 0.867412 | + | 0.497591i | \(0.165782\pi\) | ||||
−0.867412 | + | 0.497591i | \(0.834218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2964 | − | 12.8728i | −0.774386 | − | 0.447092i | 0.0600511 | − | 0.998195i | \(-0.480874\pi\) |
−0.834437 | + | 0.551103i | \(0.814207\pi\) | |||||||
\(830\) | 2.03667i | 0.0706939i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.72204 | + | 1.57157i | 0.0943698 | + | 0.0544844i | ||||
\(833\) | 6.01809 | − | 0.741810i | 0.208514 | − | 0.0257022i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.49076 | + | 14.7064i | −0.293835 | + | 0.508937i | ||||
\(836\) | 0.535731 | − | 0.927914i | 0.0185287 | − | 0.0320926i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.1533 | − | 12.2128i | 0.730727 | − | 0.421886i | ||||
\(839\) | −16.6271 | − | 28.7990i | −0.574032 | − | 0.994252i | −0.996146 | − | 0.0877095i | \(-0.972045\pi\) |
0.422114 | − | 0.906543i | \(-0.361288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.76096 | − | 6.51417i | 0.129688 | − | 0.224626i | ||||
\(842\) | − | 17.6940i | − | 0.609777i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.2836 | 0.457242 | ||||||||
\(845\) | −1.56033 | − | 2.70257i | −0.0536770 | − | 0.0929712i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3141 | + | 24.7129i | −0.423117 | + | 0.849144i | ||||
\(848\) | −0.790248 | + | 0.456250i | −0.0271372 | + | 0.0156677i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.750180 | − | 0.433117i | 0.0257310 | − | 0.0148558i | ||||
\(851\) | 31.5949 | − | 18.2413i | 1.08306 | − | 0.625304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.801658 | − | 0.462837i | 0.0274482 | − | 0.0158473i | −0.486213 | − | 0.873840i | \(-0.661622\pi\) |
0.513661 | + | 0.857993i | \(0.328289\pi\) | |||||||
\(854\) | 28.3660 | − | 1.74165i | 0.970665 | − | 0.0595982i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.72947 | + | 11.6558i | 0.230008 | + | 0.398386i | ||||
\(857\) | 16.2250 | 0.554236 | 0.277118 | − | 0.960836i | \(-0.410621\pi\) | ||||
0.277118 | + | 0.960836i | \(0.410621\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9123i | 0.781759i | 0.920442 | + | 0.390880i | \(0.127829\pi\) | ||||
−0.920442 | + | 0.390880i | \(0.872171\pi\) | |||||||
\(860\) | −3.69510 | + | 6.40010i | −0.126002 | + | 0.218242i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.8463 | − | 20.5184i | −0.403486 | − | 0.698859i | ||||
\(863\) | 1.28485 | − | 0.741810i | 0.0437369 | − | 0.0252515i | −0.477972 | − | 0.878375i | \(-0.658628\pi\) |
0.521709 | + | 0.853123i | \(0.325295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.57540 | − | 7.92483i | 0.155568 | − | 0.269452i | ||||
\(866\) | −12.0538 | + | 20.8779i | −0.409606 | + | 0.709459i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.7114 | + | 9.08004i | −0.465396 | + | 0.308197i | ||||
\(869\) | 0.00380633 | + | 0.00219759i | 0.000129121 | + | 7.45481e-5i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 34.2374i | − | 1.16009i | ||||||
\(872\) | 10.8938 | + | 6.28955i | 0.368911 | + | 0.212991i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.22100i | 0.244254i | ||||||||
\(875\) | −1.17997 | + | 2.36805i | −0.0398903 | + | 0.0800548i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.6373 | −1.37222 | −0.686112 | − | 0.727496i | \(-0.740684\pi\) | ||||
−0.686112 | + | 0.727496i | \(0.740684\pi\) | |||||||
\(878\) | 0.534359 | + | 0.925536i | 0.0180337 | + | 0.0312353i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.650417 | + | 0.375518i | 0.0219255 | + | 0.0126587i | ||||
\(881\) | −5.36428 | −0.180727 | −0.0903636 | − | 0.995909i | \(-0.528803\pi\) | ||||
−0.0903636 | + | 0.995909i | \(0.528803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.15422 | 0.308064 | 0.154032 | − | 0.988066i | \(-0.450774\pi\) | ||||
0.154032 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(884\) | 2.35792 | + | 1.36135i | 0.0793055 | + | 0.0457871i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.4796 | − | 26.8115i | −0.520048 | − | 0.900750i | ||||
\(887\) | 36.1166 | 1.21268 | 0.606338 | − | 0.795207i | \(-0.292638\pi\) | ||||
0.606338 | + | 0.795207i | \(0.292638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.45600 | + | 14.9633i | −0.250066 | + | 0.501851i | ||||
\(890\) | − | 2.44904i | − | 0.0820921i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.8018 | − | 7.96848i | −0.462119 | − | 0.266804i | ||||
\(893\) | − | 4.93397i | − | 0.165109i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.2805 | + | 9.97688i | 0.577622 | + | 0.333490i | ||||
\(896\) | −2.20591 | + | 1.46081i | −0.0736943 | + | 0.0488022i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.2412 | − | 19.4703i | 0.375123 | − | 0.649733i | ||||
\(899\) | 18.7820 | − | 32.5313i | 0.626414 | − | 1.08498i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.684539 | + | 0.395219i | −0.0228053 | + | 0.0131667i | ||||
\(902\) | 1.56540 | + | 2.71135i | 0.0521222 | + | 0.0902782i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.68410 | − | 2.91695i | 0.0560124 | − | 0.0970163i | ||||
\(905\) | − | 21.6898i | − | 0.720995i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.0774 | 0.766272 | 0.383136 | − | 0.923692i | \(-0.374844\pi\) | ||||
0.383136 | + | 0.923692i | \(0.374844\pi\) | |||||||
\(908\) | 6.59397 | + | 11.4211i | 0.218828 | + | 0.379022i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.30034 | + | 0.509636i | −0.275154 | + | 0.0168943i | ||||
\(911\) | −30.4817 | + | 17.5986i | −1.00990 | + | 0.583068i | −0.911163 | − | 0.412045i | \(-0.864815\pi\) |
−0.0987403 | + | 0.995113i | \(0.531481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.32469 | + | 0.764808i | −0.0438407 | + | 0.0253114i | ||||
\(914\) | 35.7886 | − | 20.6626i | 1.18378 | − | 0.683457i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.1072 | − | 9.87685i | 0.565238 | − | 0.326340i | ||||
\(917\) | 12.9476 | − | 25.9842i | 0.427567 | − | 0.858074i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.86747 | + | 17.0910i | 0.325498 | + | 0.563779i | 0.981613 | − | 0.190882i | \(-0.0611348\pi\) |
−0.656115 | + | 0.754661i | \(0.727801\pi\) | |||||||
\(920\) | −5.06153 | −0.166874 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 26.0218i | − | 0.856983i | ||||||
\(923\) | 8.53897 | − | 14.7899i | 0.281063 | − | 0.486816i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.60391 | + | 6.24216i | 0.118496 | + | 0.205241i | ||||
\(926\) | 9.60876 | − | 5.54762i | 0.315763 | − | 0.182306i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.02167 | − | 5.23368i | 0.0991911 | − | 0.171804i | ||||
\(929\) | −26.1679 | + | 45.3241i | −0.858540 | + | 1.48703i | 0.0147821 | + | 0.999891i | \(0.495295\pi\) |
−0.873322 | + | 0.487144i | \(0.838039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.19447 | − | 3.89771i | −0.301337 | − | 0.127742i | ||||
\(932\) | −23.8501 | − | 13.7699i | −0.781236 | − | 0.451047i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.4732i | 1.22616i | ||||||||
\(935\) | 0.563413 | + | 0.325287i | 0.0184256 | + | 0.0106380i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.5989i | − | 1.19563i | −0.801633 | − | 0.597816i | \(-0.796035\pi\) | ||
0.801633 | − | 0.597816i | \(-0.203965\pi\) | |||||||
\(938\) | 25.7946 | + | 12.8531i | 0.842223 | + | 0.419669i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.45844 | 0.112802 | ||||||||
\(941\) | −6.92046 | − | 11.9866i | −0.225601 | − | 0.390752i | 0.730899 | − | 0.682486i | \(-0.239101\pi\) |
−0.956499 | + | 0.291734i | \(0.905768\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.2729 | − | 10.5498i | −0.595047 | − | 0.343550i | ||||
\(944\) | −8.43820 | −0.274640 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.55031 | −0.180456 | ||||||||
\(947\) | 18.8005 | + | 10.8545i | 0.610935 | + | 0.352724i | 0.773331 | − | 0.634002i | \(-0.218589\pi\) |
−0.162396 | + | 0.986726i | \(0.551922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.979394 | − | 1.69636i | −0.0317925 | − | 0.0550662i | ||||
\(950\) | −1.42664 | −0.0462865 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.91083 | + | 1.26540i | −0.0619305 | + | 0.0410119i | ||||
\(953\) | 7.37332i | 0.238845i | 0.992844 | + | 0.119423i | \(0.0381043\pi\) | ||||
−0.992844 | + | 0.119423i | \(0.961896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.10266 | + | 3.52337i | 0.197477 | + | 0.114014i | ||||
\(956\) | − | 7.53135i | − | 0.243581i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0925 | + | 6.98162i | 0.390691 | + | 0.225566i | ||||
\(959\) | 50.2920 | + | 25.0598i | 1.62401 | + | 0.809224i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.81785 | − | 6.61271i | 0.123156 | − | 0.213313i | ||||
\(962\) | −11.3276 | + | 19.6200i | −0.365217 | + | 0.632574i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.3761 | − | 5.99066i | 0.334193 | − | 0.192946i | ||||
\(965\) | 1.20239 | + | 2.08260i | 0.0387062 | + | 0.0670412i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.66184 | − | 6.34250i | 0.117757 | − | 0.203961i | −0.801122 | − | 0.598502i | \(-0.795763\pi\) |
0.918878 | + | 0.394541i | \(0.129096\pi\) | |||||||
\(968\) | − | 10.4359i | − | 0.335424i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.6639 | −0.342397 | ||||||||
\(971\) | −25.1933 | − | 43.6361i | −0.808491 | − | 1.40035i | −0.913909 | − | 0.405920i | \(-0.866951\pi\) |
0.105418 | − | 0.994428i | \(-0.466382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9124 | − | 15.1731i | 0.734537 | − | 0.486429i | ||||
\(974\) | −3.30309 | + | 1.90704i | −0.105838 | + | 0.0611055i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.30244 | + | 5.37077i | −0.297764 | + | 0.171914i | ||||
\(977\) | 51.0807 | − | 29.4915i | 1.63422 | − | 0.943515i | 0.651444 | − | 0.758697i | \(-0.274164\pi\) |
0.982773 | − | 0.184818i | \(-0.0591696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.59290 | − | 0.919661i | 0.0509093 | − | 0.0293925i | ||||
\(980\) | 2.73208 | − | 6.44482i | 0.0872730 | − | 0.205872i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.7053 | + | 23.7383i | 0.437354 | + | 0.757520i | ||||
\(983\) | 10.7629 | 0.343284 | 0.171642 | − | 0.985159i | \(-0.445093\pi\) | ||||
0.171642 | + | 0.985159i | \(0.445093\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.58424i | 0.0504782i | ||||||||
\(986\) | 2.61747 | − | 4.53359i | 0.0833572 | − | 0.144379i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.24207 | − | 3.88339i | −0.0713299 | − | 0.123547i | ||||
\(989\) | 32.3943 | − | 18.7028i | 1.03008 | − | 0.594716i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.9427 | + | 41.4700i | −0.760566 | + | 1.31734i | 0.181993 | + | 0.983300i | \(0.441745\pi\) |
−0.942559 | + | 0.334039i | \(0.891588\pi\) | |||||||
\(992\) | 3.10788 | − | 5.38301i | 0.0986753 | − | 0.170911i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.93715 | + | 11.9856i | 0.251751 | + | 0.380160i | ||||
\(995\) | 6.71297 | + | 3.87574i | 0.212816 | + | 0.122869i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.4211i | 0.868435i | 0.900808 | + | 0.434217i | \(0.142975\pi\) | ||||
−0.900808 | + | 0.434217i | \(0.857025\pi\) | |||||||
\(998\) | −22.3343 | − | 12.8947i | −0.706980 | − | 0.408175i | ||||
\(999\) | 0 | 0 |
(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 | 1890.2.t.b.1151.4 | 28 | ||
3.2 | odd | 2 | 630.2.t.b.311.12 | ✓ | 28 | ||
7.5 | odd | 6 | 1890.2.bk.b.341.10 | 28 | |||
9.2 | odd | 6 | 1890.2.bk.b.521.10 | 28 | |||
9.7 | even | 3 | 630.2.bk.b.101.13 | yes | 28 | ||
21.5 | even | 6 | 630.2.bk.b.131.6 | yes | 28 | ||
63.47 | even | 6 | inner | 1890.2.t.b.1601.4 | 28 | ||
63.61 | odd | 6 | 630.2.t.b.551.12 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.12 | ✓ | 28 | 3.2 | odd | 2 | ||
630.2.t.b.551.12 | yes | 28 | 63.61 | odd | 6 | ||
630.2.bk.b.101.13 | yes | 28 | 9.7 | even | 3 | ||
630.2.bk.b.131.6 | yes | 28 | 21.5 | even | 6 | ||
1890.2.t.b.1151.4 | 28 | 1.1 | even | 1 | trivial | ||
1890.2.t.b.1601.4 | 28 | 63.47 | even | 6 | inner | ||
1890.2.bk.b.341.10 | 28 | 7.5 | odd | 6 | |||
1890.2.bk.b.521.10 | 28 | 9.2 | odd | 6 |