Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.13 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.32 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17292 | − | 1.90375i | 0.524547 | − | 0.851382i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37828i | 0.898905i | 0.893304 | + | 0.449453i | \(0.148381\pi\) | ||||
−0.893304 | + | 0.449453i | \(0.851619\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.77093 | −0.835467 | −0.417734 | − | 0.908570i | \(-0.637175\pi\) | ||||
−0.417734 | + | 0.908570i | \(0.637175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.720315i | 0.199780i | 0.994999 | + | 0.0998898i | \(0.0318490\pi\) | ||||
−0.994999 | + | 0.0998898i | \(0.968151\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.90375 | − | 1.17292i | −0.491545 | − | 0.302847i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.36647i | − | 0.816489i | −0.912873 | − | 0.408245i | \(-0.866141\pi\) | ||
0.912873 | − | 0.408245i | \(-0.133859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.08557 | −1.16671 | −0.583355 | − | 0.812217i | \(-0.698260\pi\) | ||||
−0.583355 | + | 0.812217i | \(0.698260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.37828 | 0.518983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.99724i | 1.45903i | 0.683967 | + | 0.729513i | \(0.260253\pi\) | ||||
−0.683967 | + | 0.729513i | \(0.739747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.24851 | − | 4.46590i | −0.449701 | − | 0.893179i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0764 | −1.87114 | −0.935569 | − | 0.353144i | \(-0.885113\pi\) | ||||
−0.935569 | + | 0.353144i | \(0.885113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.55706 | 1.35729 | 0.678644 | − | 0.734468i | \(-0.262568\pi\) | ||||
0.678644 | + | 0.734468i | \(0.262568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.77093i | 0.482357i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.52764 | + | 2.78954i | 0.765311 | + | 0.471518i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4627i | 1.72006i | 0.510244 | + | 0.860030i | \(0.329555\pi\) | ||||
−0.510244 | + | 0.860030i | \(0.670445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.720315 | 0.115343 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6294 | 1.66003 | 0.830016 | − | 0.557740i | \(-0.188331\pi\) | ||||
0.830016 | + | 0.557740i | \(0.188331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.57505i | 1.15518i | 0.816326 | + | 0.577592i | \(0.196007\pi\) | ||||
−0.816326 | + | 0.577592i | \(0.803993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.17292 | + | 1.90375i | −0.174849 | + | 0.283794i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.513534i | − | 0.0749066i | −0.999298 | − | 0.0374533i | \(-0.988075\pi\) | ||
0.999298 | − | 0.0374533i | \(-0.0119245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.34379 | 0.191970 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.36647 | −0.471400 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.32405i | − | 0.319233i | −0.987179 | − | 0.159617i | \(-0.948974\pi\) | ||
0.987179 | − | 0.159617i | \(-0.0510258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.25009 | + | 5.27515i | −0.438242 | + | 0.711301i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.08557i | 0.673600i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.22703 | 1.20126 | 0.600629 | − | 0.799528i | \(-0.294917\pi\) | ||||
0.600629 | + | 0.799528i | \(0.294917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6979 | 1.75384 | 0.876919 | − | 0.480638i | \(-0.159595\pi\) | ||||
0.876919 | + | 0.480638i | \(0.159595\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.37828i | − | 0.299635i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.37130 | + | 0.844874i | 0.170089 | + | 0.104794i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.99724 | 0.842369 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5610 | −1.37204 | −0.686018 | − | 0.727585i | \(-0.740643\pi\) | ||||
−0.686018 | + | 0.727585i | \(0.740643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.90896i | 0.574550i | 0.957848 | + | 0.287275i | \(0.0927494\pi\) | ||||
−0.957848 | + | 0.287275i | \(0.907251\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.46590 | + | 2.24851i | −0.515677 | + | 0.259635i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.59005i | − | 0.751006i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.46242 | −0.277044 | −0.138522 | − | 0.990359i | \(-0.544235\pi\) | ||||
−0.138522 | + | 0.990359i | \(0.544235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.91192i | 0.868446i | 0.900805 | + | 0.434223i | \(0.142977\pi\) | ||||
−0.900805 | + | 0.434223i | \(0.857023\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.40891 | − | 3.94861i | −0.695144 | − | 0.428287i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.0764i | 1.08030i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.49779 | −0.370765 | −0.185382 | − | 0.982666i | \(-0.559352\pi\) | ||||
−0.185382 | + | 0.982666i | \(0.559352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.71311 | −0.179583 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.55706i | − | 0.783630i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.96498 | + | 9.68164i | −0.611994 | + | 0.993315i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5554i | 1.27481i | 0.770531 | + | 0.637403i | \(0.219991\pi\) | ||||
−0.770531 | + | 0.637403i | \(0.780009\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.77093 | 0.278489 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.64280 | −0.760487 | −0.380243 | − | 0.924887i | \(-0.624160\pi\) | ||||
−0.380243 | + | 0.924887i | \(0.624160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2781i | 1.70246i | 0.524793 | + | 0.851230i | \(0.324143\pi\) | ||||
−0.524793 | + | 0.851230i | \(0.675857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.78954 | − | 4.52764i | 0.272231 | − | 0.441853i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.37539i | 0.519659i | 0.965655 | + | 0.259829i | \(0.0836663\pi\) | ||||
−0.965655 | + | 0.259829i | \(0.916334\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1319 | −1.25781 | −0.628906 | − | 0.777481i | \(-0.716497\pi\) | ||||
−0.628906 | + | 0.777481i | \(0.716497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4627 | 0.993077 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.0631i | − | 1.32295i | −0.749969 | − | 0.661473i | \(-0.769932\pi\) | ||
0.749969 | − | 0.661473i | \(-0.230068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.3210 | + | 8.20722i | 1.24219 | + | 0.765327i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.720315i | − | 0.0665932i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00641 | 0.733947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.32194 | −0.301995 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10.6294i | − | 0.958420i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1393 | − | 0.957565i | −0.996326 | − | 0.0856472i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.35357i | 0.829995i | 0.909822 | + | 0.414998i | \(0.136218\pi\) | ||||
−0.909822 | + | 0.414998i | \(0.863782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.57505 | 0.666946 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.05269 | −0.528826 | −0.264413 | − | 0.964409i | \(-0.585178\pi\) | ||||
−0.264413 | + | 0.964409i | \(0.585178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 12.0949i | − | 1.04876i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.90375 | + | 1.17292i | 0.163848 | + | 0.100949i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.84119i | − | 0.669918i | −0.942233 | − | 0.334959i | \(-0.891278\pi\) | ||
0.942233 | − | 0.334959i | \(-0.108722\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8995 | 1.17894 | 0.589469 | − | 0.807791i | \(-0.299337\pi\) | ||||
0.589469 | + | 0.807791i | \(0.299337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.513534 | −0.0432473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.99594i | − | 0.166909i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.8188 | + | 19.1829i | −0.981500 | + | 1.59305i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.34379i | − | 0.110834i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0593509 | 0.00486222 | 0.00243111 | − | 0.999997i | \(-0.499226\pi\) | ||||
0.00243111 | + | 0.999997i | \(0.499226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.668221 | −0.0543790 | −0.0271895 | − | 0.999630i | \(-0.508656\pi\) | ||||
−0.0271895 | + | 0.999630i | \(0.508656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.36647i | 0.272163i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.86384 | − | 14.3867i | 0.711961 | − | 1.15557i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.374589i | 0.0298954i | 0.999888 | + | 0.0149477i | \(0.00475818\pi\) | ||||
−0.999888 | + | 0.0149477i | \(0.995242\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.32405 | −0.184309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.6414 | −1.31153 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2079i | 0.956196i | 0.878307 | + | 0.478098i | \(0.158674\pi\) | ||||
−0.878307 | + | 0.478098i | \(0.841326\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.27515 | + | 3.25009i | 0.410670 | + | 0.253019i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8326i | 1.14778i | 0.818933 | + | 0.573889i | \(0.194566\pi\) | ||||
−0.818933 | + | 0.573889i | \(0.805434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4811 | 0.960088 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.08557 | 0.388903 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6634i | 1.19086i | 0.803406 | + | 0.595431i | \(0.203019\pi\) | ||||
−0.803406 | + | 0.595431i | \(0.796981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6211 | − | 5.34757i | 0.802883 | − | 0.404239i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.22703i | − | 0.693546i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1453 | 1.13201 | 0.566006 | − | 0.824401i | \(-0.308488\pi\) | ||||
0.566006 | + | 0.824401i | \(0.308488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.11499 | 0.0828767 | 0.0414384 | − | 0.999141i | \(-0.486806\pi\) | ||||
0.0414384 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 13.6979i | − | 1.01258i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.9184 | + | 12.2720i | 1.46443 | + | 0.902252i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.32826i | 0.682150i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.37828 | −0.172994 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.189407 | 0.0137050 | 0.00685250 | − | 0.999977i | \(-0.497819\pi\) | ||||
0.00685250 | + | 0.999977i | \(0.497819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.12381i | − | 0.368820i | −0.982849 | − | 0.184410i | \(-0.940963\pi\) | ||
0.982849 | − | 0.184410i | \(-0.0590374\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.844874 | − | 1.37130i | 0.0605027 | − | 0.0982007i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.44327i | − | 0.102829i | −0.998677 | − | 0.0514144i | \(-0.983627\pi\) | ||
0.998677 | − | 0.0514144i | \(-0.0163729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0443 | −1.20824 | −0.604119 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604119 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 23.9645i | − | 1.68198i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4675 | − | 20.2357i | 0.870765 | − | 1.41332i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.99724i | − | 0.486342i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0918 | 0.974748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2415 | −1.53117 | −0.765584 | − | 0.643336i | \(-0.777550\pi\) | ||||
−0.765584 | + | 0.643336i | \(0.777550\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.5610i | 0.792145i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4210 | + | 8.88494i | 0.983502 | + | 0.605948i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.9728i | 1.22007i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.90896 | 0.331717 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.42492 | 0.163118 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.9462i | − | 1.67052i | −0.549855 | − | 0.835260i | \(-0.685317\pi\) | ||
0.549855 | − | 0.835260i | \(-0.314683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.24851 | + | 4.46590i | 0.149900 | + | 0.297726i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.95027i | 0.660423i | 0.943907 | + | 0.330211i | \(0.107120\pi\) | ||||
−0.943907 | + | 0.330211i | \(0.892880\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.8825 | −1.90861 | −0.954304 | − | 0.298838i | \(-0.903401\pi\) | ||||
−0.954304 | + | 0.298838i | \(0.903401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.59005 | −0.433593 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.721388i | − | 0.0472597i | −0.999721 | − | 0.0236298i | \(-0.992478\pi\) | ||
0.999721 | − | 0.0236298i | \(-0.00752231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.977638 | − | 0.602335i | −0.0637741 | − | 0.0392920i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.46242i | 0.159951i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.356570 | 0.0230646 | 0.0115323 | − | 0.999934i | \(-0.496329\pi\) | ||||
0.0115323 | + | 0.999934i | \(0.496329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1224 | 1.81152 | 0.905762 | − | 0.423787i | \(-0.139300\pi\) | ||||
0.905762 | + | 0.423787i | \(0.139300\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.57616 | − | 2.55823i | 0.100697 | − | 0.163439i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.66321i | − | 0.233085i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.91192 | 0.501398 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.2989 | 1.65997 | 0.829986 | − | 0.557784i | \(-0.188348\pi\) | ||||
0.829986 | + | 0.557784i | \(0.188348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.3889i | − | 1.21897i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.94861 | + | 6.40891i | −0.247272 | + | 0.401342i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.4382i | − | 0.838252i | −0.907928 | − | 0.419126i | \(-0.862337\pi\) | ||
0.907928 | − | 0.419126i | \(-0.137663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.8833 | −1.54617 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0764 | 0.623713 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 25.4628i | − | 1.57010i | −0.619430 | − | 0.785052i | \(-0.712636\pi\) | ||
0.619430 | − | 0.785052i | \(-0.287364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.42441 | − | 2.72593i | −0.271789 | − | 0.167453i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.49779i | 0.214061i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.0428 | −0.795235 | −0.397617 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397617 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.15043 | 0.0698839 | 0.0349419 | − | 0.999389i | \(-0.488875\pi\) | ||||
0.0349419 | + | 0.999389i | \(0.488875\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.71311i | 0.103682i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.23045 | + | 12.3747i | 0.375710 | + | 0.746222i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0377i | 1.38420i | 0.721802 | + | 0.692100i | \(0.243314\pi\) | ||||
−0.721802 | + | 0.692100i | \(0.756686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.55706 | −0.452429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.1204 | 1.37925 | 0.689623 | − | 0.724169i | \(-0.257776\pi\) | ||||
0.689623 | + | 0.724169i | \(0.257776\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.85938i | − | 0.467192i | −0.972334 | − | 0.233596i | \(-0.924951\pi\) | ||
0.972334 | − | 0.233596i | \(-0.0750493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.68164 | + | 5.96498i | 0.573491 | + | 0.353335i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.2797i | 1.49221i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.66686 | 0.333345 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5554 | 0.736010 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.5975i | 1.78753i | 0.448539 | + | 0.893763i | \(0.351945\pi\) | ||||
−0.448539 | + | 0.893763i | \(0.648055\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8226 | − | 17.5659i | 0.630116 | − | 1.02273i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.77093i | − | 0.160786i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.04022 | −0.291483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.0156 | −1.03840 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.64280i | 0.439067i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.0666 | − | 26.0774i | 0.919970 | − | 1.49319i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.70770i | − | 0.154536i | −0.997010 | − | 0.0772682i | \(-0.975380\pi\) | ||
0.997010 | − | 0.0772682i | \(-0.0246198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2781 | 0.982916 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.2358 | 1.48770 | 0.743848 | − | 0.668349i | \(-0.232999\pi\) | ||||
0.743848 | + | 0.668349i | \(0.232999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.83735i | 0.442993i | 0.975161 | + | 0.221496i | \(0.0710941\pi\) | ||||
−0.975161 | + | 0.221496i | \(0.928906\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.52764 | − | 2.78954i | −0.255104 | − | 0.157173i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7895i | 0.662166i | 0.943602 | + | 0.331083i | \(0.107414\pi\) | ||||
−0.943602 | + | 0.331083i | \(0.892586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.9210 | 1.56327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.37539 | 0.300025 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.1204i | 0.952606i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.21685 | − | 1.61963i | 0.178439 | − | 0.0898411i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1319i | 0.726198i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.22133 | 0.0673339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3704 | 1.66931 | 0.834655 | − | 0.550774i | \(-0.185667\pi\) | ||||
0.834655 | + | 0.550774i | \(0.185667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 10.4627i | − | 0.573353i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.90375 | − | 1.17292i | −0.104013 | − | 0.0640836i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5035i | 0.735582i | 0.929909 | + | 0.367791i | \(0.119886\pi\) | ||||
−0.929909 | + | 0.367791i | \(0.880114\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0631 | −0.763803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.9401 | −1.13397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8439i | 1.07147i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.20722 | − | 13.3210i | 0.441862 | − | 0.717177i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.07645i | − | 0.111470i | −0.998446 | − | 0.0557348i | \(-0.982250\pi\) | ||
0.998446 | − | 0.0557348i | \(-0.0177501\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6334 | −1.58624 | −0.793120 | − | 0.609065i | \(-0.791545\pi\) | ||||
−0.793120 | + | 0.609065i | \(0.791545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.720315 | −0.0384476 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1611i | 1.17952i | 0.807579 | + | 0.589759i | \(0.200777\pi\) | ||||
−0.807579 | + | 0.589759i | \(0.799223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.5601 | + | 22.0092i | −0.719697 | + | 1.16813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8.00641i | − | 0.423744i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1318 | −0.693071 | −0.346535 | − | 0.938037i | \(-0.612642\pi\) | ||||
−0.346535 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.86303 | 0.361212 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.32194i | 0.174357i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.34541 | + | 5.75783i | 0.489161 | + | 0.301378i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.55491i | − | 0.185565i | −0.995686 | − | 0.0927824i | \(-0.970424\pi\) | ||
0.995686 | − | 0.0927824i | \(-0.0295761\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.6294 | −0.553344 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.52725 | 0.286960 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.3162i | − | 0.689485i | −0.938697 | − | 0.344742i | \(-0.887966\pi\) | ||
0.938697 | − | 0.344742i | \(-0.112034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.957565 | + | 11.1393i | −0.0494484 | + | 0.575229i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.25818i | − | 0.373815i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1125 | −0.981742 | −0.490871 | − | 0.871232i | \(-0.663321\pi\) | ||||
−0.490871 | + | 0.871232i | \(0.663321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.35357 | 0.479198 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7.39217i | − | 0.377722i | −0.982004 | − | 0.188861i | \(-0.939520\pi\) | ||
0.982004 | − | 0.188861i | \(-0.0604796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.5458 | − | 7.72962i | −0.639392 | − | 0.393938i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.57505i | − | 0.385061i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5282 | −0.736608 | −0.368304 | − | 0.929705i | \(-0.620061\pi\) | ||||
−0.368304 | + | 0.929705i | \(0.620061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.5560 | 1.19128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.05269i | 0.305318i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.88822 | + | 4.68782i | −0.145322 | + | 0.235870i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.89164i | − | 0.496447i | −0.968703 | − | 0.248223i | \(-0.920153\pi\) | ||
0.968703 | − | 0.248223i | \(-0.0798467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0949 | −0.605503 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50802 | −0.374933 | −0.187466 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187466 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.44346i | 0.271158i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.17292 | − | 1.90375i | 0.0582830 | − | 0.0945979i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 28.9915i | − | 1.43705i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.7809 | −0.928654 | −0.464327 | − | 0.885664i | \(-0.653704\pi\) | ||||
−0.464327 | + | 0.885664i | \(0.653704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.84119 | −0.386777 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.9445i | 1.07982i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0623 | + | 9.28007i | 0.739379 | + | 0.455541i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 13.8995i | − | 0.680661i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.1865 | −0.497643 | −0.248821 | − | 0.968549i | \(-0.580043\pi\) | ||||
−0.248821 | + | 0.968549i | \(0.580043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3680 | −0.846464 | −0.423232 | − | 0.906021i | \(-0.639104\pi\) | ||||
−0.423232 | + | 0.906021i | \(0.639104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.513534i | 0.0249689i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.0343 | + | 7.56953i | −0.729271 | + | 0.367176i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.5775i | 1.57653i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.99594 | −0.0963651 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.7039 | −0.708260 | −0.354130 | − | 0.935196i | \(-0.615223\pi\) | ||||
−0.354130 | + | 0.935196i | \(0.615223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.1141i | − | 1.25496i | −0.778632 | − | 0.627481i | \(-0.784086\pi\) | ||
0.778632 | − | 0.627481i | \(-0.215914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.1829 | + | 11.8188i | 0.919749 | + | 0.566669i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 35.5850i | − | 1.70226i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.69256 | 0.128509 | 0.0642543 | − | 0.997934i | \(-0.479533\pi\) | ||||
0.0642543 | + | 0.997934i | \(0.479533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.34379 | −0.0639899 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.0794i | 1.09654i | 0.836302 | + | 0.548268i | \(0.184713\pi\) | ||||
−0.836302 | + | 0.548268i | \(0.815287\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.10263 | + | 6.65890i | −0.194483 | + | 0.315662i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 0.0593509i | − | 0.00280720i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.3397 | −0.959888 | −0.479944 | − | 0.877299i | \(-0.659343\pi\) | ||||
−0.479944 | + | 0.877299i | \(0.659343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.4533 | −1.38690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.668221i | 0.0313957i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00935 | + | 3.26133i | −0.0941996 | + | 0.152894i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.04045i | 0.329338i | 0.986349 | + | 0.164669i | \(0.0526557\pi\) | ||||
−0.986349 | + | 0.164669i | \(0.947344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.36647 | 0.157133 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.3191 | 0.713482 | 0.356741 | − | 0.934203i | \(-0.383888\pi\) | ||||
0.356741 | + | 0.934203i | \(0.383888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 33.8371i | − | 1.57254i | −0.617882 | − | 0.786271i | \(-0.712009\pi\) | ||
0.617882 | − | 0.786271i | \(-0.287991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.3867 | − | 8.86384i | −0.667168 | − | 0.411051i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.8753i | 1.10482i | 0.833573 | + | 0.552410i | \(0.186292\pi\) | ||||
−0.833573 | + | 0.552410i | \(0.813708\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.37828 | 0.109819 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.374589 | 0.0172601 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 20.9899i | − | 0.965118i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.4349 | + | 22.7116i | 0.524671 | + | 1.04208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.32405i | 0.106411i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.1876 | 1.33362 | 0.666808 | − | 0.745230i | \(-0.267660\pi\) | ||||
0.666808 | + | 0.745230i | \(0.267660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.53645 | −0.343633 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.6414i | 0.757210i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.9023 | + | 14.7265i | 1.08535 | + | 0.668696i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.4217i | 1.28791i | 0.765064 | + | 0.643954i | \(0.222707\pi\) | ||||
−0.765064 | + | 0.643954i | \(0.777293\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2079 | 0.552060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.33763 | −0.331142 | −0.165571 | − | 0.986198i | \(-0.552947\pi\) | ||||
−0.165571 | + | 0.986198i | \(0.552947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.9219i | 1.52776i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.25009 | − | 5.27515i | 0.146081 | − | 0.237100i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 27.4952i | − | 1.23333i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4402 | −0.780728 | −0.390364 | − | 0.920661i | \(-0.627651\pi\) | ||||
−0.390364 | + | 0.920661i | \(0.627651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.8326 | 0.662670 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20.0264i | − | 0.892934i | −0.894800 | − | 0.446467i | \(-0.852682\pi\) | ||
0.894800 | − | 0.446467i | \(-0.147318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.96441 | + | 14.5499i | −0.398911 | + | 0.647464i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.4811i | − | 0.554307i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.3450 | −0.680157 | −0.340078 | − | 0.940397i | \(-0.610454\pi\) | ||||
−0.340078 | + | 0.940397i | \(0.610454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6749 | −0.516466 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 5.08557i | − | 0.224533i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.8931 | + | 20.2658i | 1.44944 | + | 0.893020i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.42297i | 0.0625820i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6634 | 0.687545 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.5178 | 1.73131 | 0.865654 | − | 0.500643i | \(-0.166903\pi\) | ||||
0.865654 | + | 0.500643i | \(0.166903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3082i | 0.888017i | 0.896023 | + | 0.444008i | \(0.146444\pi\) | ||||
−0.896023 | + | 0.444008i | \(0.853556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.34757 | − | 10.6211i | −0.233387 | − | 0.463545i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 25.4406i | − | 1.10821i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.9614 | −1.12876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.22703 | −0.400419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.65651i | 0.331640i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.2334 | + | 6.30492i | 0.442428 | + | 0.272585i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 15.1453i | − | 0.653567i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.72354 | −0.160384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.4449 | −0.921988 | −0.460994 | − | 0.887403i | \(-0.652507\pi\) | ||||
−0.460994 | + | 0.887403i | \(0.652507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.11499i | − | 0.0478489i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.4028 | + | 24.9999i | −0.659782 | + | 1.07088i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.981250i | 0.0419552i | 0.999780 | + | 0.0209776i | \(0.00667787\pi\) | ||||
−0.999780 | + | 0.0209776i | \(0.993322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.6979 | −0.584613 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.2442 | 2.18308 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.85632i | − | 0.249036i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.2720 | − | 19.9184i | 0.520915 | − | 0.845487i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 44.7526i | − | 1.89623i | −0.317927 | − | 0.948115i | \(-0.602987\pi\) | ||
0.317927 | − | 0.948115i | \(-0.397013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.45642 | −0.230782 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.32826 | 0.393840 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 28.6701i | − | 1.20830i | −0.796870 | − | 0.604151i | \(-0.793513\pi\) | ||
0.796870 | − | 0.604151i | \(-0.206487\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.7726 | − | 16.4949i | −1.12633 | − | 0.693947i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37828i | 0.0998783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.0606 | −0.840985 | −0.420492 | − | 0.907296i | \(-0.638143\pi\) | ||||
−0.420492 | + | 0.907296i | \(0.638143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.70606 | −0.238791 | −0.119396 | − | 0.992847i | \(-0.538096\pi\) | ||||
−0.119396 | + | 0.992847i | \(0.538096\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.189407i | − | 0.00791259i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.2489 | − | 15.7333i | 1.30317 | − | 0.656125i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 41.7552i | − | 1.73829i | −0.494555 | − | 0.869146i | \(-0.664669\pi\) | ||
0.494555 | − | 0.869146i | \(-0.335331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.12381 | −0.212938 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.8168 | −0.780651 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.43979i | 0.266709i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.37130 | − | 0.844874i | −0.0566962 | − | 0.0349312i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.1527i | 1.32709i | 0.748139 | + | 0.663543i | \(0.230948\pi\) | ||||
−0.748139 | + | 0.663543i | \(0.769052\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.4319 | −1.58356 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44327 | −0.0593682 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 39.5633i | − | 1.62467i | −0.583192 | − | 0.812335i | \(-0.698196\pi\) | ||
0.583192 | − | 0.812335i | \(-0.301804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.39090 | − | 15.2422i | 0.384989 | − | 0.624869i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.0443i | 0.697576i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.07245 | −0.166396 | −0.0831978 | − | 0.996533i | \(-0.526513\pi\) | ||||
−0.0831978 | + | 0.996533i | \(0.526513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.9987 | −1.10130 | −0.550651 | − | 0.834736i | \(-0.685620\pi\) | ||||
−0.550651 | + | 0.834736i | \(0.685620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.89638 | + | 6.32414i | −0.158410 | + | 0.257113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2983i | 0.864471i | 0.901761 | + | 0.432236i | \(0.142275\pi\) | ||||
−0.901761 | + | 0.432236i | \(0.857725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.9645 | −0.971089 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.369906 | 0.0149648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.31314i | 0.0530374i | 0.999648 | + | 0.0265187i | \(0.00844216\pi\) | ||||
−0.999648 | + | 0.0265187i | \(0.991558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.2357 | − | 12.4675i | −0.815981 | − | 0.502736i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.9225i | − | 0.520240i | −0.965576 | − | 0.260120i | \(-0.916238\pi\) | ||
0.965576 | − | 0.260120i | \(-0.0837622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.47314 | 0.139597 | 0.0697986 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0697986 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.99724 | −0.280790 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8.31871i | − | 0.333282i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8884 | + | 20.0832i | −0.595538 | + | 0.803327i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 14.0918i | − | 0.562771i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.2224 | 1.40441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.3398 | −0.968954 | −0.484477 | − | 0.874804i | \(-0.660990\pi\) | ||||
−0.484477 | + | 0.874804i | \(0.660990\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.2415i | 0.884020i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.8068 | + | 10.9710i | 0.706643 | + | 0.435372i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.967950i | 0.0383516i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.5610 | 0.457345 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0349 | 0.396356 | 0.198178 | − | 0.980166i | \(-0.436498\pi\) | ||||
0.198178 | + | 0.980166i | \(0.436498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.2175i | 1.66490i | 0.554103 | + | 0.832448i | \(0.313061\pi\) | ||||
−0.554103 | + | 0.832448i | \(0.686939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.88494 | − | 14.4210i | 0.349844 | − | 0.567825i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.43176i | 0.0562884i | 0.999604 | + | 0.0281442i | \(0.00895976\pi\) | ||||
−0.999604 | + | 0.0281442i | \(0.991040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.5675 | −1.00361 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.9728 | 0.704409 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.6570i | 0.456173i | 0.973641 | + | 0.228087i | \(0.0732469\pi\) | ||||
−0.973641 | + | 0.228087i | \(0.926753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.09934 | + | 11.5228i | −0.277394 | + | 0.450233i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.90896i | − | 0.191517i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.62294 | 0.102175 | 0.0510877 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510877 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.25395 | −0.243251 | −0.121625 | − | 0.992576i | \(-0.538811\pi\) | ||||
−0.121625 | + | 0.992576i | \(0.538811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.42492i | − | 0.0941762i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.0256 | − | 14.1864i | −0.892896 | − | 0.550125i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 70.5069i | − | 2.73004i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.9462 | −0.964475 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.9560 | −1.46527 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.6011i | 0.408644i | 0.978904 | + | 0.204322i | \(0.0654990\pi\) | ||||
−0.978904 | + | 0.204322i | \(0.934501\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.46590 | − | 2.24851i | 0.171892 | − | 0.0865450i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.25826i | − | 0.0483589i | −0.999708 | − | 0.0241794i | \(-0.992303\pi\) | ||
0.999708 | − | 0.0241794i | \(-0.00769731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.8602 | −1.14593 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.95027 | 0.381295 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.31165i | − | 0.164981i | −0.996592 | − | 0.0824904i | \(-0.973713\pi\) | ||
0.996592 | − | 0.0824904i | \(-0.0262874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.9276 | − | 9.19710i | −0.570356 | − | 0.351403i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.8825i | 1.10194i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.67405 | 0.0637762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.4992 | −1.73087 | −0.865436 | − | 0.501019i | \(-0.832959\pi\) | ||||
−0.865436 | + | 0.501019i | \(0.832959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.59005i | 0.250335i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.3030 | − | 26.4611i | 0.618409 | − | 1.00373i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 35.7835i | − | 1.35540i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.721388 | −0.0272854 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2773 | 0.501475 | 0.250738 | − | 0.968055i | \(-0.419327\pi\) | ||||
0.250738 | + | 0.968055i | \(0.419327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 53.2089i | − | 2.00681i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.602335 | + | 0.977638i | −0.0226853 | + | 0.0368200i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 18.1767i | − | 0.683605i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0531 | −0.490220 | −0.245110 | − | 0.969495i | \(-0.578824\pi\) | ||||
−0.245110 | + | 0.969495i | \(0.578824\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.46242 | 0.0923479 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.8785i | 1.98032i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.79977 | − | 2.34109i | −0.142103 | − | 0.0875517i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.356570i | − | 0.0133164i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.1616 | 1.31131 | 0.655653 | − | 0.755062i | \(-0.272393\pi\) | ||||
0.655653 | + | 0.755062i | \(0.272393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.0921 | −1.53035 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 28.1224i | − | 1.04588i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.6568 | + | 45.0001i | 0.841453 | + | 1.67126i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.79429i | 0.251986i | 0.992031 | + | 0.125993i | \(0.0402117\pi\) | ||||
−0.992031 | + | 0.125993i | \(0.959788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.5012 | 0.943195 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 7.30768i | − | 0.269915i | −0.990851 | − | 0.134958i | \(-0.956910\pi\) | ||
0.990851 | − | 0.134958i | \(-0.0430898\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.55823 | − | 1.57616i | −0.0943617 | − | 0.0581375i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.77093i | 0.102069i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7162 | 0.578130 | 0.289065 | − | 0.957310i | \(-0.406656\pi\) | ||||
0.289065 | + | 0.957310i | \(0.406656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.66321 | −0.134572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.72768i | − | 0.210128i | −0.994465 | − | 0.105064i | \(-0.966495\pi\) | ||
0.994465 | − | 0.105064i | \(-0.0335048\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0696140 | − | 0.112989i | 0.00255046 | − | 0.00413960i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.91192i | − | 0.289482i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.7842 | −0.467124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.2342 | 1.43167 | 0.715837 | − | 0.698267i | \(-0.246045\pi\) | ||||
0.715837 | + | 0.698267i | \(0.246045\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 26.2989i | − | 0.958385i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.783771 | + | 1.27212i | −0.0285244 | + | 0.0462973i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6988i | 1.22481i | 0.790546 | + | 0.612403i | \(0.209797\pi\) | ||||
−0.790546 | + | 0.612403i | \(0.790203\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.3889 | −0.703771 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.0023 | −1.70383 | −0.851916 | − | 0.523679i | \(-0.824559\pi\) | ||||
−0.851916 | + | 0.523679i | \(0.824559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 31.2314i | − | 1.13065i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.40891 | + | 3.94861i | 0.231715 | + | 0.142762i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.64637i | 0.239987i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.0445 | 1.66041 | 0.830203 | − | 0.557462i | \(-0.188225\pi\) | ||||
0.830203 | + | 0.557462i | \(0.188225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.4382 | −0.483965 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 52.2738i | − | 1.88016i | −0.340956 | − | 0.940079i | \(-0.610751\pi\) | ||
0.340956 | − | 0.940079i | \(-0.389249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.9921 | − | 33.7490i | −0.610373 | − | 1.21230i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.8833i | 0.892682i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −54.0565 | −1.93678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0347 | 1.14629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.0764i | − | 0.360101i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.713122 | + | 0.439364i | 0.0254524 | + | 0.0156816i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.8463i | − | 1.31343i | −0.754139 | − | 0.656715i | \(-0.771945\pi\) | ||
0.754139 | − | 0.656715i | \(-0.228055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.4628 | −0.906500 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.4460 | 1.18920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.86682i | 0.350381i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.72593 | + | 4.42441i | −0.0966789 | + | 0.156918i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 54.7014i | − | 1.93762i | −0.247802 | − | 0.968811i | \(-0.579708\pi\) | ||
0.247802 | − | 0.968811i | \(-0.420292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.72880 | −0.0611604 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.49779 | 0.123588 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 13.6024i | − | 0.480018i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.5191 | + | 31.6810i | −0.687957 | + | 1.11661i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.0428i | 0.459129i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4389 | −0.824067 | −0.412034 | − | 0.911169i | \(-0.635181\pi\) | ||||
−0.412034 | + | 0.911169i | \(0.635181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.1032 | −1.09218 | −0.546091 | − | 0.837726i | \(-0.683885\pi\) | ||||
−0.546091 | + | 0.837726i | \(0.683885\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.15043i | − | 0.0403475i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.2407 | + | 14.3189i | 0.814088 | + | 0.501570i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 38.5234i | − | 1.34776i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.71311 | 0.0598610 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.1313 | −0.702588 | −0.351294 | − | 0.936265i | \(-0.614258\pi\) | ||||
−0.351294 | + | 0.936265i | \(0.614258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.2268i | 1.22793i | 0.789334 | + | 0.613964i | \(0.210426\pi\) | ||||
−0.789334 | + | 0.613964i | \(0.789574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.3747 | − | 6.23045i | 0.430831 | − | 0.216917i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 42.3723i | − | 1.47343i | −0.676204 | − | 0.736714i | \(-0.736376\pi\) | ||
0.676204 | − | 0.736714i | \(-0.263624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.39630 | −0.152690 | −0.0763449 | − | 0.997081i | \(-0.524325\pi\) | ||||
−0.0763449 | + | 0.997081i | \(0.524325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.0377 | 0.799168 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.52382i | − | 0.156741i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.2374 | + | 17.3974i | 0.977196 | + | 0.602063i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.55706i | 0.261210i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.86188 | −0.236898 | −0.118449 | − | 0.992960i | \(-0.537792\pi\) | ||||
−0.118449 | + | 0.992960i | \(0.537792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 72.5335 | 2.50116 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 23.1204i | − | 0.796308i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.6394 | − | 23.7609i | 0.503611 | − | 0.817401i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.90051i | − | 0.271465i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.85938 | −0.269733 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −73.2101 | −2.50961 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.9115i | 1.12687i | 0.826161 | + | 0.563433i | \(0.190520\pi\) | ||||
−0.826161 | + | 0.563433i | \(0.809480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.96498 | − | 9.68164i | 0.203998 | − | 0.331105i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0105i | 0.478591i | 0.970947 | + | 0.239295i | \(0.0769164\pi\) | ||||
−0.970947 | + | 0.239295i | \(0.923084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0337 | 1.63889 | 0.819444 | − | 0.573160i | \(-0.194282\pi\) | ||||
0.819444 | + | 0.573160i | \(0.194282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.2797 | 0.861528 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.4258i | 1.30803i | 0.756482 | + | 0.654014i | \(0.226916\pi\) | ||||
−0.756482 | + | 0.654014i | \(0.773084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.8191 | + | 18.3719i | 1.01388 | + | 0.624663i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.66686i | − | 0.192457i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.82319 | 0.231461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.720315 | 0.0244070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.5554i | − | 0.424935i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.27736 | − | 26.4923i | 0.0769887 | − | 0.895602i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 5.67108i | − | 0.191499i | −0.995405 | − | 0.0957495i | \(-0.969475\pi\) | ||
0.995405 | − | 0.0957495i | \(-0.0305248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.5975 | 1.03203 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.1998 | 1.48913 | 0.744564 | − | 0.667551i | \(-0.232657\pi\) | ||||
0.744564 | + | 0.667551i | \(0.232657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.9735i | − | 1.58078i | −0.612602 | − | 0.790391i | \(-0.709877\pi\) | ||
0.612602 | − | 0.790391i | \(-0.290123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.5659 | − | 10.8226i | −0.590472 | − | 0.363797i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 57.1559i | 1.91911i | 0.281525 | + | 0.959554i | \(0.409160\pi\) | ||||
−0.281525 | + | 0.959554i | \(0.590840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2454 | −0.746087 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.77093 | −0.0928297 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.61161i | 0.0873942i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.7642 | − | 28.8328i | 0.593793 | − | 0.963774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.04022i | 0.168288i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −76.1478 | −2.53967 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.82386 | −0.260651 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.0156i | 0.599521i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.30780 | − | 2.12266i | 0.0434727 | − | 0.0705597i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.1649i | 1.26725i | 0.773642 | + | 0.633623i | \(0.218433\pi\) | ||||
−0.773642 | + | 0.633623i | \(0.781567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.64280 | 0.253496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9785 | −0.728181 | −0.364091 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364091 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 21.9234i | − | 0.725558i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.0774 | − | 16.0666i | −0.862091 | − | 0.531145i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 14.3950i | − | 0.475365i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.487617 | −0.0160850 | −0.00804250 | − | 0.999968i | \(-0.502560\pi\) | ||||
−0.00804250 | + | 0.999968i | \(0.502560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.70770 | −0.0892217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.32755i | − | 0.274105i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.7254 | − | 23.5255i | 1.53632 | − | 0.773513i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 17.2781i | − | 0.567487i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.4850 | 1.88602 | 0.943011 | − | 0.332760i | \(-0.107980\pi\) | ||||
0.943011 | + | 0.332760i | \(0.107980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.83392 | −0.223973 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 26.2358i | − | 0.858921i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.7587 | + | 10.9413i | 0.580770 | + | 0.357820i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.12013i | 0.167267i | 0.996497 | + | 0.0836337i | \(0.0266526\pi\) | ||||
−0.996497 | + | 0.0836337i | \(0.973347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.83735 | 0.255762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.6449 | 1.39018 | 0.695092 | − | 0.718921i | \(-0.255364\pi\) | ||||
0.695092 | + | 0.718921i | \(0.255364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.3764i | 2.42203i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.78954 | + | 4.52764i | −0.0907437 | + | 0.147284i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 5.18927i | − | 0.168629i | −0.996439 | − | 0.0843143i | \(-0.973130\pi\) | ||
0.996439 | − | 0.0843143i | \(-0.0268700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.53600 | −0.114783 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.7895 | 0.382302 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.05769i | − | 0.0990484i | −0.998773 | − | 0.0495242i | \(-0.984230\pi\) | ||
0.998773 | − | 0.0495242i | \(-0.0157705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.222160 | − | 0.360583i | 0.00718892 | − | 0.0116682i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 27.9210i | − | 0.902557i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.6485 | 0.602192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1091 | 0.842228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 5.37539i | − | 0.173220i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.75444 | − | 6.00984i | −0.314007 | − | 0.193463i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.2072i | − | 0.585505i | −0.956188 | − | 0.292753i | \(-0.905429\pi\) | ||
0.956188 | − | 0.292753i | \(-0.0945712\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1204 | 0.549988 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.1652 | −0.518767 | −0.259384 | − | 0.965774i | \(-0.583519\pi\) | ||||
−0.259384 | + | 0.965774i | \(0.583519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.0569i | 1.05975i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.61963 | − | 3.21685i | −0.0518698 | − | 0.103022i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.1608i | 1.31685i | 0.752647 | + | 0.658425i | \(0.228777\pi\) | ||||
−0.752647 | + | 0.658425i | \(0.771223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.69212 | 0.309762 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1319 | 0.419271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 14.0301i | − | 0.447491i | −0.974648 | − | 0.223746i | \(-0.928172\pi\) | ||
0.974648 | − | 0.223746i | \(-0.0718285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.74762 | − | 1.69284i | −0.0875465 | − | 0.0539385i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.22133i | − | 0.0388752i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.0044 | −1.68544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.351627 | −0.0111698 | −0.00558489 | − | 0.999984i | \(-0.501778\pi\) | ||||
−0.00558489 | + | 0.999984i | \(0.501778\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30.3704i | − | 0.963776i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.9916 | + | 32.4480i | −0.633777 | + | 1.02867i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.3690i | 0.771775i | 0.922546 | + | 0.385887i | \(0.126105\pi\) | ||||
−0.922546 | + | 0.385887i | \(0.873895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.4627 | −0.331026 |
(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 | 4020.2.g.c.1609.13 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.32 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.13 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.32 | yes | 38 | 5.4 | even | 2 | inner |